Difference between revisions of "Talk:Counterexamples to Relativity"
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::::: NotesTH, you list some unproven dead ends like neverobserved "Gravitation Waves," but fail to identify any verified insight. Indeed, the length of your list highlights its lack of a quality insight.[[User:AschlaflyAndy Schlafly]] 16:38, 15 August 2010 (EDT)  ::::: NotesTH, you list some unproven dead ends like neverobserved "Gravitation Waves," but fail to identify any verified insight. Indeed, the length of your list highlights its lack of a quality insight.[[User:AschlaflyAndy Schlafly]] 16:38, 15 August 2010 (EDT)  
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+  :::::: Gravitational waves have not been directly observed, no, but there is significant indirect evidence. Most commonly cited is the [http://www.conservapedia.com/PSR_B1913_16  HulseTaylor binary]. In the linked article it is claimed that a "0.2%" demonstrates the failing of relativity. On the contrary, the fact that a theoretical model for a binary star system could predict a gravitational wave emission that matches observations so extremely closely is extraordinary. The supposed correction term for "galactic acceleration" exists because the initial model is not perfect and nor was it ever meant to be. A 0.2% error is a fantastically small difference and demonstrates that GR provides an extremely accurate and verified prediction for the observed decay of a binary system due to emission of gravitational waves. The authors of the quoted paper state "Accuracy of the test for gravitational radiation damping is now dominated by the uncertainty in the galactic acceleration term. Work now underway should lead to improved accuracy of the pulsar proper motion, and the Sun’s galactocentric distance may be better known in the future. However, we see little prospect for a significant improvement in knowledge of the pulsar distance. Consequently, it seems unlikely that this test of relativistic gravity will be improved significantly in the foreseeable future"  that's simply a statement to the effect that there were some unknown parameters not included in the initial model but nowhere near enough to even remotely claim that the model is being tweaked to fit the theory, not for a 0.2% difference.  
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+  :::::: You also seem to have neglected the other points. Rather than trying to talk about everything, it would take far too long in one sitting, I'll focus on the particle side of things. I've already stated that modern particle accelerators take into account relativistic effects  e.g. particle energies (using the relativistic energy equation: <math> E^2 = m^2 c^4 + p^2 c^2 </math>, synchotron radiation [http://www.lhccloser.es/php/index.php?i=1&s=4&p=12&e=0  Synchotron at the LHC], particle lifetimes and so on. All of these require calculations from relativity that have been experimentally measured and verified. For instance all the predicted particle lifetimes and decay rates would require quantum field theories (which require relativity as a relativistic quantum theory) to predict the expected values which can then be matched to observations. We find that they are an extremely good fit to observations. Another example of such a calculation would be in predicting the [http://arxiv.org/pdf/hepph/9810512  magnetic moments] of particles  theory matches observations extraordinarily well.  
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+  :::::: As another point, just for a further example (could keep going...) we could look at neutron stars or pulsars as objects that are intrinsically relativistic. We can use observations of millisecond pulsars and, for example, compare models of synchrotron radiation (relativistic) to the observations. We find that the relativistic predictions are again in good agreement. Relativity has led to the development of many astrophysical phenomena which are intrinsically relativistic. Without the framework and foundations of relativity such insight would be impossible. The fundamental concepts introduced by relativity are absolutely essential in many, many branches of modern day science with many of the intrinsic relativistic effects being tested to a vast degree. No one claims that GR is the complete theory, it's treated as an effective field theory valid in some low energy limit, but the revolutionary concepts introduced by relativity have led to irrefutable developments in many areas of science.  15th August 2010 [User:NotesTH  NotesTH]  
== "from the muons' point of view, the Earth would have to be rushing in all directions to meet them"? ==  == "from the muons' point of view, the Earth would have to be rushing in all directions to meet them"? == 
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Contents
 1 Point 4
 2 Counterexample 4 (limiting behavior)
 3 Counterexample 9 (Jesus actionatadistance)
 4 lack of a single useful device
 5 GPS revisited
 6 Several Clarification/Corrections
 7 Curvature of Space
 8 Reversion explained
 9 Proposed page move
 10 Curl of the gravitational field
 11 Misleading Reference
 12 Ehrenfest's Paradox
 13 Momentum issues
 14 Wormholes
 15 Inability of theory to lead to other insights?
 16 "from the muons' point of view, the Earth would have to be rushing in all directions to meet them"?
 17 Number 29: the fastedframe contradiction
 18 Continuation of "Curl of the gravitational field"
 19 Reversion of my edit
 20 My Greatgrandfather
Point 4
Andy, can you clarify #4 for me? I'm not sure I understand it. JacobB 21:50, 28 November 2009 (EST)
 Sure, I welcome discussion of these important points. As I've said, I have an open mind about this and if something is true, then I accept it. But if something is false, I'll criticize it.
 The theory of relativity has taught for decades that as the velocity of a mass increases, then its (scalar) relativistic mass increases per the Lorentzian transformation. Now apply a force ORTHOGONAL to the velocity. Does that force encounter the increased mass, as relativity says, or encounter the rest mass, as logic would dictate?Andy Schlafly 22:02, 28 November 2009 (EST)
 Ah, I see what you mean. May I suggest a rewording? "The logical problem of a force which is applied at a right angle to the velocity of a relativistic mass." I think that might be a little clearer than it is currently stated. Your thoughts? JacobB 22:06, 28 November 2009 (EST)
 Please do. Your edits are always welcome, and you've suggested an improvement here. Thank you for making this change.Andy Schlafly 22:20, 28 November 2009 (EST)
 Why would logic dictate that? Mass is a scalar, and a force from any direction should encounter the same increased mass, not different masses from different directions.
 I suppose that under Newtonian mechanics, a moving object has a velocity of 0 within the plane perpendicular to its line of motion, and any forces operating in that plane will act on the object as if it is at rest. But that's not what logic dictates, that's what the previous theory dictates.
 Essentially your counterexample to relativity is that it makes a prediction that contradicts Newton's laws. This is neithe r a contradiction nor a logical problem, and it is should be edited out.NgSmith
 No, it's a logical problem. If you're suggesting that one force can affect the inertial in an entirely independent, orthogonal direction, that's illogical. One thing cannot affect something else that is entirely independent.Andy Schlafly 15:40, 12 December 2009 (EST)
 Why is that illogical? What logical principle does it violate?
 See, in relativity, orthogonal doesn't mean independent. In relativity, velocity vectors do not add. In relativity, the effect of a new force is not independent of the object's existing momentum. And there is nothing illogical about that; it's just a new theory that contradicts the intuition from the previous theory.NgSmith
 Ng, something cannot be independent (orthogonal) and yet dependent at the same time. Unfortunately, you're arguing with your own theory at this point. Even most relativity promoters have abandoned the position you take here.Andy Schlafly 21:37, 12 December 2009 (EST)
 It seems that his point is that something can be orthogonal and dependent. I agree: The crossproduct of two vectors is orthogonal to both and yet obviously dependent on both. EvanW 21:41, 12 December 2009 (EST)
 OK, good point, an orthogonal vector can be a function of other orthogonal vectors. But that's a bit different from what we're discussing. Here it's an orthogonal force that is not dependent on anything else, and yet Ng says it encounters relativistic mass due to a different orthogonal force.
 I think relativists have abandoned Ng's position, so he's really arguing with his own side at this point. As a result, I urge him to reconsider his views with an open mind once he confirms that.Andy Schlafly 21:59, 12 December 2009 (EST)
 First of all, relativity has not "abandoned" the prediction we're talking about. The velocity addition formulas for both parallel and perpendicular velocities have not changed, and they still predict that an orthogonal force will have a harder time accelerating a fastmoving object. Physicists may have changed their informal interpretation of this formula, but not the formula itself, nor its predictions.
 Note also that relativity's prediction can't be all that illogical, because this is what we actually observe happening to particles at high speeds. If you think that fastmoving particles commit some terrible offense against basic logic, take it up with God.
 There is a very simple way to settle this matter: write an encyclopedia article where the material is properly sourced. If this is indeed some counterexample or logical flaw in relativity, then one can easily find a book or paper exposing that flaw, and cite it.NgSmith Sun Dec 13 17:55:04 EST 2009
 OK, I think I see part of the problem you people are having. The word "independent" has two different meanings. Being linearly independent is a concept from pure mathematics. Being causally independent is an unrelated metaphysical concept. Whether a force pushing on something causes it to move, and by how much, is completely, umm, independent of whether the vectors involved are linearly independent (orthogonal). Please try to be very careful about the meanings of the terms. SaraT 17:00, 13 December 2009 (EST)
 I don't think that's the source of our confusion. I think the main problem is that, according to Newtonian mechanics and thus according to our mechanical intuition, orthogonal things tend to operate independently. Not only that, but a force exerted on an object is usually independent of the object's momentum.
 In relativity, none of these things are true, due to the fact that velocities no longer add like vectors (and thus acceleration no longer incurs a cumulative change in velocity in the usual way.) This is seen as some sort of logical flaw or paradox simply because it contradicts the deeply ingrained intuition that came from the previous theory.NgSmith Sun Dec 13 18:10:46 EST 2009
 Theories that don't produce anything useful are often a waste of time, or simply false. I realize that liberals tend to downplay accountability  a conservative insight, but theories should be accountable by what value they yield, particularly when taxpayer dollars are spent (wasted) on the theory.Andy Schlafly 16:55, 7 January 2010 (EST)
 I call gps a pretty darned useful invention but it doesn't work if you don't take into account relativistic effects. I think that not knowing where relativity is used speaks volumes as to how close minded those trying to disprove relativity, which is different from relativism. (a point completely overlooked by the page) Gaurdro 12:31, 24 May 2010 (EDT)
MLS 16:07, 15 August 2010 (EDT) I would argue that the nuclear bomb and atomic energy in general are pretty useful inventions. These came about once it was understood that energy and matter were manifestations of the same thing and could be interchanged. E=mc^{2} is not just a fancy mathematical equation but a new & different way of understanding the physical universe. It took scientists about 3 years (1942  1945) between concept and execution (poor word choice) to develop a weapon based on this understanding that ended WW II. MLS 15 August 2010.
Counterexample 4 (limiting behavior)
For the fourth "counterexample," the author points out that the momentum does not approach the momentum of light as and
Aside from the mathematical sloppiness of taking two independent variables to a limit at the same time, at unspecified rates, these sorts of "discontinuities" can be found in just about any scientific theory. In Newtonian mechanics, for example, take the orbit of a planet as the planet's mass goes to 0. For any nonzero mass the orbit is an ellipse; at m=0 it is suddenly a straight line. Is this a "counterexample" to Newton's laws?
Or in electronics, I=V/R. The limiting case is no voltage, no resistance, no current; but if someone foolishly took V/R as both V and R go to zero, he would get a nonsensical answer. Let them both go at the same rate and you get I=1. Is this a "counterexample" to basic electronics?
Or more to the point, momentum in Newtonian mechanics is , and this also fails to give the momentum of a photon at m=0, v=c. Again, is that a "counterexample" to ? Will we see this entry in a corresponding page of "Counterexamples to Newton's laws?"
But none of these are counterexamples or "discontinuities": they are just a misinterpretation of the formulas. You don't get the momentum of a photon by taking the momentum formula for a mass and setting m=0 and v=c. That's just not what the formula means, or what they are for. This item should also be removed.NgSmith Tue Dec 15 10:16:21 EST 2009
I agree that this point is invalid. I have personally checked that if you take a massive particle, and make its rest mass tend to zero and its speed tend to c while keeping its energy constant, its fourmomentum approaches that of a photon. No discontinuity at all. Since this point has been raised 8 months ago and no opposition has been heard, I will delete point 4 from the list. If anyone is interested to see the details of my calculations, let me know and I'll put them in my userspace. Toph 09:38, 14 August 2010 (EDT)
 The "keeping its energy constant" is a new condition that has no clear relevance to the discontinuity. Please explain further.Andy Schlafly 09:54, 14 August 2010 (EDT)
Counterexample 9 (Jesus actionatadistance)
The quoted verse doesn't strongly suggest "actionatadistance" in the relativistic sense. Light could travel the distances mentioned in the passage in a fraction of a second, which is well within the precision given in the verse (an hour). The verse and relativity are not in contradiction here. This should be removed.
 I have an open mind about it. In the the healing of the centurion's servant, if the Greek is translated as same "moment" then relativity is impossible, but if translated as the same "hour" then there is no conflict with relativity.
 But the healing of the centurion's servant is probably not the only place where there is action at a distance in the Bible.Andy Schlafly 14:52, 5 January 2010 (EST)
 Any distance on the earth is less than 20,000km. A force acting with the speed of light takes less than 1/15,000 ≈ 0.0000667 seconds for this distance.
 I don't think how eyewitnesses could spot such a short time...
 So, there may probably be no other places where action at a distance is described in the Bible.
 FrankC aka ComedyFan 16:17, 5 January 2010 (EST)
 You make an interesting point, Frank. But according to this site, it takes 1/7.4 seconds for light to circle the globe, which is much longer than your figure.[1] More generally and more importantly, there is the issue of how this action in the Bible isn't light.Andy Schlafly 19:30, 5 January 2010 (EST)
 Indeed, an error in my calculation: 20,000,000m / 300,000,000 m/sec = 1/15 seconds.
 Fast enough, still.
 Whether the action in the Bible isn't light doesn't matter: it is indistinguishable from an action happening at the speed of light for the witnesses of the time, so it doesn't say anything about the validity of the theory of relativity...
 FrankC aka ComedyFan 19:46, 5 January 2010 (EST)
 Frank you make an interesting point, and I have an open mind about it. But I'm not entirely convinced. When the woman cured herself of bleeding and Jesus felt power leaving him, that sounds more like heat than light. And for heat to travel virtually instantaneously (or at the speed of light) WOULD violate the theory of relativity.Andy Schlafly 20:48, 5 January 2010 (EST)
 Yes, it would. And it would also violate classical physics, the laws of thermodynamics etc.
 But of course a miracle is going to violate the laws of physics. I don't see how this can be cited to discredit one physical theory over another.NgSmith
I have to respectfully disagree with you on that point, Andy  I'm not sure this action could comment on relativity any more than the sun stopping for Joshua could comment on the Copernican model of the solar system. If God wanted heat/light to travel at some finite speed except in certain instances, how is that different from the sun and moon moving in the sky, except in certain instances? JacobB 21:32, 5 January 2010 (EST)
 I have an open mind about this. You make good points, Jacob. But your analogy is not perfect because:
 the Joshua account might be understood as the perception of the army that they sun did not set until they completed their job, but the healing in the New Testament cannot be explained as mere perception
 if the Joshua account is taken absolutely literally, Newtonian mechanics does not say it is impossible, while relativity does say actionatadistance is impossible
I look forward to our translation work on the Joshua passage (and New Testament passages) to see if that brings forth insights.Andy Schlafly 22:30, 5 January 2010 (EST)
 Your second point is a good one, and I suppose my example wasn't very good. But on a different note, what makes you say that the Joshua account might be understood as only a perception of the army? I think I'm going to go translate that chapeter, I'll be interested to see what Hebrew words are used for that bit. JacobB 22:49, 5 January 2010 (EST)
 Shall we look at it next? Joshua 10:1114, I think.Andy Schlafly 23:18, 5 January 2010 (EST)
IMO, the discussion is a little bit bizarre: Following David Hume's definition of a miracle as a "a violation of the laws of nature", for evaluating the laws of natures, miracles can't be taken into account.
As I said earlier: we shouldn't try to restrict God with the laws of our logic  or even physics.
FrankC aka ComedyFan 07:27, 6 January 2010 (EST)
 Frank, perhaps what you mean is that you don't want the logic of the Bible to be used to evaluate claims by scientists. If so, I completely disagree. And so would Isaac Newton and most great scientists.
 As our Conservative Bible Translation project is revealing, Jesus said his works were not miracles, but signs. So any definition of miracle by Hume (who, by the way, leaned toward atheistic rather than Christianity) is not terribly helpful.Andy Schlafly 08:00, 6 January 2010 (EST)
 So, what's the definition of a sign, then? FrankC aka ComedyFan 08:06, 6 January 2010 (EST)
 The same as its name suggests: a disclosure of reality, rather than a violation of it.Andy Schlafly 08:35, 6 January 2010 (EST)
 I took Hume's definition as I found it on conservapedia's page on miracles.
 The page on signs doesn't describe Jesu works  perhaps you can fix this
 If you don't like Hume, what's about Thomas Aquinas:
 Now, there are various degrees and orders of these miracles. Indeed, the highest rank among miracles is held by those events in which something is done by God which nature never could do. For example, that two bodies should be coincident; that the sun reverse its course, or stand still; that the sea open up and offer a way through which people may pass. And even among these an order may be observed. For the greater the things that God does are, and the more they are removed from the capacity of nature, the greater the miracle is. Thus, it is more miraculous for the sun to reverse its course than for the sea to be divided.
 Then, the second degree among miracles is held by those events in which God does something which nature can do, but not in this order. It is a work of nature for an animal to live, to see, and to walk; but for it to live after death, to see after becoming blind, to walk after paralysis of the limbs, this nature cannot do—but God at times does such works miraculously. Even among this degree of miracles a gradation is evident, according as what is done is more removed from the capacity of nature.
 Now, the third degree of miracles occurs when God does what is usually done by the working of nature, but without the operation of the principles of nature. For example, a person may be cured by divine power from a fever which could be cured naturally, and it may rain independently of the working of the principles of nature.
 Acts 2:43 Everyone was filled with awe, and many wonders and miraculous signs were done by the apostles (KJB) So, we have miraculous signs and wonders
 John 2:11 This was the first of the miracles Jesus did in Cana of Galilee, and by doing showed his glory, and so his disciples believed in him. (CBP) Changing water into wine is something nature never could do: it's an outright miracle, miraculous sign, whatever...
 FrankC aka ComedyFan 09:00, 6 January 2010 (EST)
 That's great recitation, Frank, but how about simply applying logic yourself? You're a bright guy, why simply hunt and repeat quotes from others? On this site we encourage thinking in a logical way.Andy Schlafly 09:21, 6 January 2010 (EST)
 I'm trying to use the fact that I'm standing on the shoulder of giants... FrankC aka ComedyFan 09:23, 6 January 2010 (EST)
 How about using "the fact" of simple logic and the power of your own mind?Andy Schlafly 09:27, 6 January 2010 (EST)
 To make it as clear as possible in my own words:
 I won't restrict God by laws which men made or observed. Can I understand God's ways? Can I expect God to act the way I think to be logical? That would be hubris.
 Testing scientific hypotheses using God's miracles or signs seems to be odd!
 But which part of Thomas Aquinas's definition of miraculous events didn't you like? Granted, he had a slightly other view of the capacity of nature than we have today, but his line of reasoning was as valid in the 15th century as it is today! I hoped that his definition would be more helpful than that of David Hume.
 To make it as clear as possible in my own words:
 FrankC aka ComedyFan 10:41, 6 January 2010 (EST)
A miraculous healing seems to violate the Second Law of Thermodynamics  whether it happens on a distance or not. Does this mean that John 4:4654 is a counterexample to the laws of thermodynamics, too? PhilG 09:58, 2 February 2010 (EST)
 How so? Do you think eating an apple to feel better, or taking an aspirin to alleviate a headache, also violates the Second Law of Thermodynamics?Andy Schlafly 11:02, 2 February 2010 (EST)
 No. Eating an Apple helps you by giving your body some of the chemical components that constitute the apple. Components which also happen to help you fight off viruses and the like. The same is true for the aspirin. Both are well defined chemical processes that involve no increase or decrease in the amount of matter or energy in the system. Healing (such as Jesus mending the ear of the soldier), would involve the rapid solidification of matter that was not there before (ie. the new ear). This is a clear violation of the second law of thermodynamics. The point is,if you're going to use miracles or signs to disprove a physical theory, you have to apply the argument to universally. But you don't because attacking the Second Law of Thermodynamics would knock the crutch of misinterpreted Newtonian Physics you have been leaning on out from underneath you.
 LoganBertram 3:32 9 August 2010 (EST)
Following was taken from Schlafly user page and put here, where it should have been (my apologies)
(This is my first edit ever on a wiki/conseri board, so you'll have to excuse me if I did it incorrectly)
I have a concern with your post of "Counterexamples of Relativity" Your argument labeled 9:
The actionatadistance by Jesus, described in John 4:4654.
It is not a counter example of relativity. The concept that the theory is broken down because Jesus is able to break it does not apply. Jesus worked miracles. So does God. Because of this, they are able to break laws and/or theories of physics. I haven't taken the time to go over the rest of the points in your counterexamples, but that one definitely doesn't work. If you are going to argue against me, then you are arguing against the Bible. Jesus broke several laws of physics. The biggest example is when he walked on water. Physics would state that by buoyancy laws he would not be able to do this. Does this call into question the physics buoyancy? It definitely does not.mvgilpatrick 10 August 2010 (CDT)
 Relativity says that actionatadistance is impossible. That's not true of other examples. No physical law, for example, proves that rising from the dead is impossible.Andy Schlafly 13:40, 12 August 2010 (EDT)
 Wouldn't the physical law of gravity and buoyancy make walking on water "impossible"? The only way Jesus could have done it would to have either had some sort of special technology that hadn't been invented yet, or, he is God and can break the laws of gravity and therefore physics (you know, do the "impossible"). Why can he break this law, but not break the theory of relativity? Please address this specific example.
 I can add another example. What about the law of mass conservation? Mass can not be created or destroyed. This is a law, and it is taught as a matter of fact that it is impossible to do otherwise. In Matthew 14:1321, Jesus was able to feed 5,000 people with 5 loaves and 2 fish. He created mass (lots of food) out of very little (small amount of food). He broke another law of physics. He did the impossible. Again I say, is it not possible for him to break the theory of relativity, whilst still leaving it intact?
 Also please note that I am arguing for Jesus being God, not against, so please do not mistake that. mvgilpatrick 17:50, 12 August 2010 (CDT)
 No, I don't think all these examples are the same. Physics does not categorically state that it is impossible for a creature to walk on water. Physics does not say that replication is impossible. There is no reason to think the multiplication of the loaves generated mass from nothing, rather than using existing mass to replicate. But Relativity does insist that actionatadistance is impossible.
 Nothing described in the Bible violates physics. Newton used the Bible to guide him to the truth for that reason.Andy Schlafly 21:36, 12 August 2010 (EDT)
lack of a single useful device
At conservapedia's article on the Global Positioning System, one can read:
These receivers rely on precisely timing signals sent from GPS satellites, with corrections for atmospheric attenuation and relativistic effects.
GPS seems to be a useful device!
FrankC aka ComedyFan 10:53, 6 January 2010 (EST)
 Great catch of a misleading statement, Frank! I've corrected it.
 Our theory of relativity entry explains how it did not aid the development of GPS. The repeated attempt by relativists to falsely claim credit for GPS reinforces the lack of any legitimate contributions.Andy Schlafly 11:29, 6 January 2010 (EST)
 Well, you are consistent! Just another question: What's about particle accelerators? Generally, the theory of relativity is used to explain why it takes more energy to accelerate an electron from 200,000,000 m/sec to 200,002,000 m/sec than from 2,000 m/sec to 4,000 m/sec.
 Have you thought about an explanation for this phenomenon?
 Accelerators have applications beyond basic research!
 FrankC aka ComedyFan 12:02, 6 January 2010 (EST)
 Frank, I have an open mind about this, but I'm not aware of a single benefit from what you describe, nor do you identify one. Do you have an open mind about this?Andy Schlafly 14:44, 6 January 2010 (EST)
 Synchrotron radiation is used in medicine
 So, may I ask again: what your explanation for the phenomenon? I suppose you are aware of the phenomenon I described above?
 FrankC aka ComedyFan 15:47, 6 January 2010 (EST)
 Frank, inventors and doctors and engineers don't typically even bother learning relativity. Should I repeat that? Complain to engineering departments and medical schools if you think that should change. Nothing useful has even been designed or built using relativity. If you want to look and look and look for a counterexample then you'll be wasting your time. I'm not going to waste mine. This is my final reply on this topic for now. Do something logical, such as editing the Bible, and after benefiting from that experience we can revisit this issue in a month or so.Andy Schlafly 15:52, 6 January 2010 (EST)
 Why does it matter whether the users of the invention learn relativity? Most users of microwaves never learn Maxwell's equations either. That doesn't mean that the laws are irrelevant to the gadget's operation.
 Likewise, the engineers who correct the clocks of GPS satellites may not know or care that relativistic effects are behind the clock skew. But that dodges the point that relativistic effects are real, observable, and must be corrected for in several useful inventions.NgSmith
 Here's a good source:  US Navy. As for engineers not bothering to learn relativity, I think that's a mite off the mark. I'm an engineer and I had to take a class dealing with the basics of SR, and I'm just an electrical engineer. Aerospace engineers certainly deal with relativity a great deal, as do nuclear engineers. DanieleGiusto 00:26, 7 April 2010 (EDT)
 Bah... My engineering professor worked at a synchrotron at Brookhaven National Laboratory. He was in charge of a beam line for the Naval Research Laboratory. They are actually very interesting devices in that they really help with all fields of science and even fields outside of it. My one friend conducted some research with a synchrotron when doing research with fuel cells. My engineering professor studied magnetic materials with a synchrotron. Every once in a while you also find stories like this http://news.discovery.com/human/brainhumanancestorskull.html which actually wouldn't have been possible without the synchrotron. I'm only just scratching the surface of how useful they are. Would you like some more information? AdamYak 14:35, 10 August 2010 (EDT)
 Yes, I would like more support for your claim. Relativity is not even part of most engineering curricula.Andy Schlafly 09:17, 11 August 2010 (EDT)
Are not the atomic bomb and nuclear power examples of inventions based on the equivalence of matter and energy? MLS 9 Aug 10
GPS revisited
The same Tom von Flandern who is quoted in the article on the theory of relativity saying that the GPS programmers "have basically blown off Einstein", wrote in an article in 1998:
So we can state that the clock rate effect predicted by GR is confirmed to within no worse than ±200 / 45,900 or about 0.7%, and that predicted by SR is confirmed to within ±200 / 7,200 or about 3%. This is a very conservative estimate. In an actual study, most of that maximum 200 ns/day variance would almost certainly be accounted for by differences between planned and achieved orbits, and the predictions of relativity would be confirmed with much better precision.
As for how the satellites take into account the relativistic effects, here is his explanation of the socalled factory offset of the atomic clocks for the satellites:
GPS atomic clocks in orbit would run at rates quite different from ground clocks if allowed to do so, and this would complicate usage of the system. So the counter of hyperfine cesium transitions (or the corresponding phenomenon in the case of rubidium atomic clocks) is reset on the ground before launch so that, once in orbit, the clocks will tick off whole seconds at the same average rate as ground clocks. GPS clocks are therefore seen to run slow compared to ground clocks before launch, but run at the same rate as ground clocks after launch when at the correct orbital altitude.
Seems to me that relativistic effects have to be taken into account.
FrankC aka ComedyFan 13:13, 6 January 2010 (EST)
 Frank, your intuition ("seems to me") is wrong here, and the entry explains it clearly. GPS is a work of engineering and any timing discrepancies between the satellite and ground are obviously better handled directly by synchronization rather than asking a physicist what he thinks of relativity. Engineers don't even bother taking general relativity courses, let alone try to build a satellite system using them.Andy Schlafly 14:44, 6 January 2010 (EST)
 The Time Service Department – a department of the U. S. Navy  states: “The Operational Control System (OCS) of the Global Positioning System (GPS) does not include the rigorous transformations between coordinate systems that Einstein’s general theory of relativity would seem to require – transformations to and from the individual space vehicles (SVs), the Monitor Stations (MSs), and the users on the surface of the rotating earth, and the geocentric Earth Centered Inertial System (ECI) in which the SV orbits are calculated. There is a very good reason for the omission: the effects of relativity, where they are different from the effects predicted by classical mechanics and electromagnetic theory, are too small to matter – less than one centimeter, for users on or near the earth.”
 As far as I can see there is no reason to feel sorry for FrankC: Your article only covers the idea of using the Lorentz transformation instead of the Galileo transformation when calculating the position of an object: one could say that it is about the relativistic effects caused by the movement of the GPS receiver, not of the GPS satellites. That's why it's talking about fast moving airplanes and satellites.
 FrankC (and others) have shown that there are relativistic effects on the satellites which are taken account of:
 Global Positioning System Standard Positioning Service Signal Specification, 2nd edition, June 1995:
 p. 13: To compensate for relativistic effects, the output frequency of the satellite's frequency standard  as it would appear to an observer located at the satellite  is 10.23 MHz offset by a Df/f = 4.4647 x 1018 or a Df = 4.567 x 103 Hz.
 p. 39: The coefficients transmitted in subframe 1 describe the offset apparent to the control segment twofrequency receivers for the interval of time in which the parameters are transmitted. This estimated correction accounts for the deterministic satellite clock error characteristics of bias, drift and aging, as well as for the satellite implementation characteristics of group delay bias and mean differential group delay. Since these coefficients do not include corrections for relativistic effects, the user's equipment must determine the requisite relativistic correction. Accordingly, the offset given below includes a term to perform this function.
 (From Talk:Global Positioning System)
 RonLar 12:44, 3 August 2010 (EDT)
 I would like to second the points made by RonLar in that there is far too much evidence and calculations that indicate just how vital GR is to accurate calculations. The effects of gravitational and time dilation predicted by general relativity are not negligible over the course of one day. The article linked to above by RonLar is a fantastic review of some of the mathematics behind the (verifiable) predictions made by the theory of general relativity.  14th August 2010 NotesTH
Several Clarification/Corrections
I am new to Conservapedia, so I don't fully understand exactly how this site is structured; in particular who has the ability to edit protected pages. This page is apparently protected, but in need of dire work even on the formatting/punctuation/style side of things. I hope someone with the required access to protected pages can incorporate some of these changes. In any event, here are some things that need to be clarified or corrected:
1. It is unclear what #6 is referring to by "overall space". Is this a reference to the flatness problem in cosmology? If so, that should be made explicit, and the most commonly accepted solution (inflation) should be mentioned for completeness. If not, the curvature of space locally is clearly demonstrated by the observed phenomenon of gravitational lensing.
2. #7 is just a feature of the incompatibility between general relativity and quantum field theory. In this sense, general relativity is of course wrong (just as Newtonian mechanics is, for example), because it doesn't apply accurately below distance scales where quantum effects emerge.
3. #8 is not a problem because quantum nonlocality doesn't allow for information transfer. Hence special relativity is not violated.
4. #10 is not a counterexample because gravitons are not predicted by general relativity. They are expected to exist and be predicted by a successful quantum theory of gravity, but general relativity is not such a theory.
5. #11 is not a counterexample to the theory at all. It may be an argument for why the theory should not be studied, but that doesn't mean it is false, and thus is not a counterexample.
6. #13 is presumably a reference to the horizon problem of cosmology. This should be stated, and, as for the flatness problem, the theory of cosmological inflation should be mentioned. (I realize inflation has not been empirically verified, but since the majority of cosmologists believe it is the correct explanation, it deserves a mention in an encyclopedia article.)
7. #14 is again the problem of the incompatibility of general relativity and quantum field theory (namely that QFT is not backgroundinvariant). This is not a problem with general relativity, other than in the sense that it is only an approximation (like, say, Maxwellian electrodynamics are just an approximation to quantum electrodynamics).
8. #15, aside from the obvious grammatical error (violated instead of the correct violate), is again not a counterexample to general relativity. General relativity predicts wormholes only on the assumption that socalled "exotic matter" exists. This is matter that has net negative mass/energy, and so is predicted not to exist for precisely the reasons listed here (time travel and the like). But this is not a counterexample to general relativity itself, merely the observation that a mathematically possible solution does not have a physical manifestation.
9. #16 is again a quantum gravity issue. It is wrong to call black holes "highly ordered (and thus low entropy)", though. The fact is that science does not yet know how to count black hole microstates, so we don't know whether they are highly ordered or extremely disordered. But the best explanation seems to be that general relativity and the Second Law together suggest that black holes should have extremely high entropy, not low entropy. But again, this is not a counterexample to general relativity per se, since it makes no predictions about what black hole entropy should be.
::I believe a blackhole's entropy is determined by the surface area of its event horizon. In this sense, it doesn't have low entropy at all.
10. #18 appears to be a restatement of #11, and is thus both redundant, and not a counterexample for the reasons listed discussion #11.
I apologize for the length of this list of edits, but something really must be done to improve the quality of this article. I hope that someone with the appropriate access sees fit to make the necessary changes soon. Yill 17:12, 30 March 2010 (EDT)
 REPLY BELOW:
 1. It is unclear what #6 is referring to by "overall space". Is this a reference to the flatness problem in cosmology? If so, that should be made explicit, and the most commonly accepted solution (inflation) should be mentioned for completeness. If not, the curvature of space locally is clearly demonstrated by the observed phenomenon of gravitational lensing.
 I'll clarify the obvious. It's still a counterexample. Science is not done by consensus, and inflation does not explain the overall flatness of space if relativity were true.
 You needn't be so condescending. I wasn't saying that it isn't a problem with general relativity, I was just saying that since this is an encyclopedia, relevant information should be included. Since a proposed solution exists, it should be mentioned, and perhaps debunked if it is flawed. So you could mention inflation, and then say why it fails to solve the flatness problem. Yill 21:19, 30 March 2010 (EDT)
 The theory of inflation does nothing "to solve the flatness problem" with respect its role as a counterexample to relativity.Andy Schlafly 03:02, 31 March 2010 (EDT)
 Could you clarify this point? Perhaps you could state exactly what you believe the flatness problem is and how it is a counterexample to GR, just to be sure we aren't talking past each other, as I fear we may have been so far. Yill 16:55, 4 April 2010 (EDT)
 2. 7: is just a feature of the incompatibility between general relativity and quantum field theory. In this sense, general relativity is of course wrong (just as Newtonian mechanics is, for example), because it doesn't apply accurately below distance scales where quantum effects emerge.
 So at what distances do you declare general relativity to be false? Is there a discontinuity at that distance? Such an approach is absurd.
 I mean, technically it is false at all length scales, just like any classical (nonquantum) theory (Newtonian mechanics, Maxwellian electromagnetism, classical statistical mechanics, etc.). But there exists a range of length scales at which it is extremely accurate, and those are the only ones to which it makes claims having any epistemological value. There is no discontinuity, it just gets progressively worse as quantum effects become more and more apparent, which occurs at smaller and smaller length scales. Quantum effects definitely need to be taken into account around the level of a nanometer or so in most systems of interest, so I would say this is about the regime where GR needs to stop being used. But of course, it depends on the system in question. Yill 21:19, 30 March 2010 (EDT)
 Not "technically it is false," but "it is false." So teach it that way.Andy Schlafly 03:02, 31 March 2010 (EDT)
 See KrisJ's discussion below. Yill 16:49, 4 April 2010 (EDT)
 3. 8 is not a problem because quantum nonlocality doesn't allow for information transfer. Hence special relativity is not violated.
 Your statement is a non sequitur, and may not be true. Special relativity does deny nonlocality.
 It's not a non sequitur; the problem as I thought it was stated on the page is that special relativity does not allow information transfer faster than the speed of light. Since quantum entanglement cannot actually transfer information, this does not violate that provision of special relativity. Yill 21:19, 30 March 2010 (EDT)
 Special relativity does not define "information" nor was it developed in that context.Andy Schlafly 03:02, 31 March 2010 (EDT)
 It is true that SR does not define information, but it does define causality (only events within each other's lightcones can be causally connected). Physical transfer of information (as defined by Shannon, and encoded in physical systems in Minkowski spacetime) between points in spacetime can only occur if those points are causally connected. (This SR fact is what the horizon problem, which is cited as another GR counterexample, relies on.) Yill 16:49, 4 April 2010 (EDT)
 Will respond to your other points later.Andy Schlafly 18:11, 30 March 2010 (EDT)
 I appreciate your attention to my concerns, and I hope I have adequately outlined them. Also, I hope I would not be asking too much to request formatting consistency (like adding periods at the ends of nos. 7, 8, and 9). It would make it look more professional, like other articles I've seen on Conservapedia. Yill 21:19, 30 March 2010 (EDT)
 Yill, your grand total of contributions to this site has been 3 edits to this page, all easily refutable. Frankly, I don't think greater efforts at "formatting consistency" are justified.Andy Schlafly 03:01, 31 March 2010 (EDT)
 Your not going to be able to attract many users if you disparage newcomers with respect to how few edits they've made. I would like to be a positive contributor to this site, but I have to start somewhere. I would appreciate encouragement and constructive criticism, not condescension and personal attacks. Yill 16:49, 4 April 2010 (EDT)
 Yill, good grammar requires "you're", not "your", in your statement above. All your edits have been 100% talk, in violation of our 90/10 rule, and honestly I see no insights in your talk. I suggest you try contributing substantively to Epistle to the Hebrews (Translated); it is on a much higher educational level and you'll benefit enormously from it.Andy Schlafly 00:15, 5 April 2010 (EDT)
 You're right, I had a typo there; I apologize for the error. And I am well aware of the 90/10 rule, but seeing as the page I'm working on is protected, I'm not actually able to make any edits. If it were unblocked or I were given the ability to edit it, I would be more than happy to stop posting on this talk page and instead edit the article itself. And frankly I don't particularly see how it's relevant whether you personally happen to see any insights in my talk; my understanding is that Conservapedia is shaped and edited by its users, with appropriate oversight from administrators to ensure accuracy and prevent the chaos of Wikipedia. If need be, I'll appeal to those administrators to get the article fixed, since none seem to have come forward to help. I would love it if you would be willing to work with me to improve this article, but as it stands you seem to have little interest in doing so, having made no further contributions to the substance of the discussion. If you change your mind, I would be happy to work with you on this endeavor.
 As for your suggested article for me to work on, I don't really understand what you mean by it being on a "much higher educational level." However, as I have no expertise in Biblical Greek, I don't think I'd be able to make any meaningful contributions to the translation. I'll let the experts in that subject deal with that article. Yill 16:37, 5 April 2010 (EDT)
 Yill, I recommended the Bible because, as Isaac Newton pointed out, working on translating the Bible increases the quality of one's work in other areas, including science. Sure, I could drop everything else I'm doing and spend all day correcting you about this entry, but if you just picked up a Bible and improved your own work, then I could learn from you instead. I'll correct your misunderstandings below but doubt I will spend much more time responding to you if you're not willing to put in openminded effort on your own.Andy Schlafly 23:58, 6 April 2010 (EDT)
Yill, you raise excellent points, most of which have not been raised before. We should sharpen those points, here on this page, and then address them on the actual article page. This will take a fair amount of discussion. I could start by bringing up the discussion of point 7, inaccuracy of relativity at the quantum mechanical scale. One question that was raised was "Is there a discontinuity at that [microscopic boundary] distance? Such an approach is absurd.". No. The way quantum mechanics and classical theories interact at the (microscopic) scales where this happens is well known. It is, of course, generally known as the Bohr correspondence principle, described in any textbook on quantum mechanics, and known in more detail as Ehrenfest's theorem, described in more advanced textbooks. (Very briefly, the quantum mechanical realm eases into the classical realm according to the Ehrenfest theorem.) We should make some citations to those, and put in a careful explanation that, under QM, all classical theories are incorrect, and QM is the correct theory for everything, from atoms to planets. Classical theories are just extremely good approximations outside of the quantummechanical realm. And, of course, we do not know how that quantummechanical realm operated immediately after the big bang (that's what inflation theory is about), but that doesn't affect what we do know about general relativity in the macroscopic realm.
The item about point 10 is excellent. Gravitons arose after GR, from attempts to unify the theories. They have nothing to do with the macroscopic aspects of GR, which is what GR is actually all about.
KrisJ 10:04, 31 March 2010 (EDT)
 Teach that relativity is incorrect, if you concede the point. There are relativists who claim their theory is the most precisely verified theory of all.
 Those relativists claim that with respect to the macroscopic realm, as KrisJ referred to above. We are discussing how it breaks down at the microscopic level, when QM starts to play a role. Yill 16:49, 4 April 2010 (EDT)
 Gravitons are based on GR, and they are nonexistent. Enough said.Andy Schlafly 11:37, 31 March 2010 (EDT)
 No, for gravitons to be a counterexample to GR, they must be predicted by it. But they are not, just as photons are not predicted by Maxwellian electrodynamics. They are the "quantum" of the gravitational field, as photons are for the electromagnetic field, and are quantum by definition. GR is not a quantum theory; it manifestly does not predict them. Yill 16:49, 4 April 2010 (EDT)
 KrisJ, I appreciate your assistance with this project. I absolutely agree with your suggestions about 7 and 10, and hopefully we can find an editor with the ability to edit protected pages to help us implement them. If you know of any that could help us, you should ask if they would be willing. Yill 16:49, 4 April 2010 (EDT)
I guess I was wrong about not being able to edit this article. I'm going to delete #10, as per above, and make some formatting changes. I may also make some other clarifying edits. Yill 17:45, 5 April 2010 (EDT)
I also deleted the references to relativity being useful, since those have nothing to do with its epistemological validity. Yill 17:52, 5 April 2010 (EDT)
Curvature of Space
Re this edit: I don't disagree, but the example is a bad one. Based on local observations, one would assume that the Earth itself is flat, but it clearly isn't. My own point of view is that since the Universe can never be proved to be one thing or another, it is part of God's own ineffable being  it is almost folly to inquire further. RobertE 18:24, 30 March 2010 (EDT)
 No, one would not assume the Earth is flat based on local observations, as a ship can be observed to "rise" over the horizon. I don't agree with the "nature is God" view either.Andy Schlafly 11:34, 31 March 2010 (EDT)
 Funny coincidence(?) that a defender of relativity invokes pantheism, since it was Einstein's (and Spinoza's) "god." DouglasA 13:50, 31 March 2010 (EDT)
 I actually think the edit has merit, as long as the word "initial" is inserted before curvature, since the problem is that any initial curvature should be vastly amplified over time as the universe undergoes its usual expansion. And it is in fact the global curvature that is the issue here; any manifold we use to model the universe is by definition locally flat (since this is a fundamental property of manifolds). The ship and horizon observation is not a local observation, since it is fundamentally predicated on the global curvature of the Earth. "Local" means that it can be done at arbitrarily small distance scales, which that observation cannot. Yill 17:06, 4 April 2010 (EDT)
General relativity predicts that spacetime should be curved and not just spatial sections of the 4D spacetime manifold. And spacetime is indeed observed to be curved (because the universe is expanding and is hence described by a curved FRW metric). This is true even if space alone is flat, as it is observed to be. That space is observed to be flat doesn't contradict relativity  it is a question of initial conditions of the universe and has a neat solution in inflationary cosmology. So Point no. 6 is absolutely unnecessary. Of course, most of the other points are too. But I just want to see how Andy will respond to this and edit the article so that it indeed can be said to belong to a "trustworthy encyclopedia".
Saywhat 08:19, 13 August 2010 (EDT)
 Your "of course" convinces no one. Why would you start with point 6 if you "of course" had answers for points 15?
 Relativity does imply that space as well as spacetime are curved. The observation of a flat universe does contradict what would be expected if Relativity were true.Andy Schlafly 10:03, 13 August 2010 (EDT)
 A trivial solution to Einsteins field equations for a vacuum can result in Minkowski spacetime. This is a 4D metric describing a pseudoRiemannian manifold with no spatial curvature (i.e. flat). A requirement of GR is that in locally inertial frames (i.e. small enough regions of spacetime) we recover Minkowski spacetime. It's just that in GR the requirement of a locally Minkwoski spacetime does not always extend to a global case with curvature effects breaking down the notion of inertial frames for all observers. This means that a flat spacetime is a valid prediction arising from General Relativity. The presence of matter will, generically, curve spacetime but certain models such as the FLRW models used in cosmology permit solutions that predict a spatially flat Universe under a given condition. It should also be noted that the FLRW models are not static and do change with time.
 The observation of a flat Universe (spatial curvature parameter, K = 0 in the FLRW metric) is not in violation of GR and is a valid solution to Einsteins field equations (see e.g. Friedmanns Equations) and a generic prediction of models for inflationary cosmology whereby a rapid expansion in the early Universe drives the Universe towards a spatially flat solution, certainly within the observable Universe. Predictions from GR are still obeyed contrary to the comment "flat universe does contradict what would be expected if Relativity were true".
 I do not feel that the point in discussion is in any way a counterpoint to relativity. If other objections arise then perhaps this point would need to be further clarified so that any issues may be appropriately discussed? 15th August 2010
Reversion explained
Reversion was necessary for two reasons: first, to restore material that was improperly censored, and second, to revert an imprecise label put on one of the counterexamples.Andy Schlafly 17:53, 5 April 2010 (EDT)
 I don't want to get into an edit war here, so I won't undo your reversion for now. But I fail to understand your reasoning, so perhaps you could clarify a bit instead of making the one sentence assertions that have made up your discourse so far. There is no censorship here, merely deletion of objectively incorrect statements. Perhaps you could actually bother to respond to my points above, rather than just reverting my edits without justification. In the meantime, I will replace the periods I added at the end of several of the counterexamples for formatting consistency; hopefully you don't consider that to be "censorship" as well. Yill 20:48, 5 April 2010 (EDT)
 You deleted valid information. Gravitons are predicted by an attempt to reconcile GR with quantum mechanics. Without GR gravitons would not be expected; with GR people do expect to find them. The wholesale deletion of reference to this is unwarranted, and simply conceals a real flaw in GR.
 First of all, I want to thank you for actually explaining your claims. Now we can actually have the real discussion KrisJ suggested above. You are perfectly correct in stating the gravitons are predicted by an attempt to reconcile GR with QM; that is precisely the point I was trying to make. But by your logic we could rightly conclude that the flaw is with QM rather than GRwithout QM gravitons would not be expected either. On what basis do you claim that the nonobservance of gravitons is a counterexample to GR rather than a counterexample to QM? (Also, I should note that just because gravitons have not yet been observed, that doesn't mean they won't be. For example, the nonobservation of the Z boson did not constitute a counterexample to the electroweak theory between 1979 and 1983.) Yill 22:55, 5 April 2010 (EDT)
 Gravitons were historically proposed in trying to reconcile GR with QM. Other theories of gravity may not require gravitons at all. Does string theory? Gravitons are thereby attributable to GR, not to the more developed and better verified QM. Simply look at the name "gravitons" itself.Andy Schlafly 00:23, 6 April 2010 (EDT)
 Actually, any quantum theory of gravity, whether it reduces to GR at large scales or not, requires gravitons by definition. Do you even understand what a graviton is? The quantum of a gravitational field. Just as any quantum theory of electromagnetism must include the photon in its particle spectrum, any quantum theory of gravity must include the graviton in its particle spectrum. And yes, string theory requires them; the entire reason string theory started being developed as a theory of everything is that gravitons (i.e. massless spin2 bosons) naturally appear as part of its particle spectrum! Yill 14:57, 6 April 2010 (EDT)
 Yill, do you know what actionatadistance is? It doesn't require the fictional gravitons. Newtonian mechanics doesn't require such imaginary particles.Andy Schlafly 00:00, 7 April 2010 (EDT)
 Do you know what quantum means? Please acknowledge that you do, and that you know Newtonian mechanics is not a quantum theory, and therefore that your response does not address my concern. Yill 00:19, 9 April 2010 (EDT)
 The "flatness problem" refers primarily to curvature expected from inflation, not GR itself. It is misleading to call the counterexample the "flatness problem," and then pretend it has a solution. The counterexample described is not resolved.Andy Schlafly 21:12, 5 April 2010 (EDT)
 The flatness problem refers to the fact that, in an inflationfree universe, the FRW metric with matter and radiation equationofstate parameters predicts that any initial nonzero curvature will increase vastly in magnitude, leaving a highly curved universe at present. Inflation is proposed as a solution to the flatness problem; it is not the cause of it. The process of inflation drastically flattens any initial curvature in the universe so dramatically that even after the curvature increase undergone under normal evolution, the universe still appears nearly perfectly flat. Yill 22:55, 5 April 2010 (EDT)
 Wait, I just realized that I think we may be talking past one another here. I interpreted the counterexample listed on the page to be the flatness problem, but based on your response I guess that it is not. (Obviously the flatness problem is not a counterexample to GR itself, just to the use of the FRW metric for modeling the universe.) This counterexample seems to be more fundamental, namely the claim that space is nowhere curved, as GR says it must be by matter and energy. Is that correct? Yill 23:25, 5 April 2010 (EDT)
 A type of inflation is proposed to try to explain the unexpected flatness. But there's no way around the basic problem: GR says that space is curved by matter, and an overall flatness is impossible under such a model. Yet an overall flatness is what is observed.Andy Schlafly 00:23, 6 April 2010 (EDT)
 I still don't understand what you're saying. The overall visible universe is flat, at scales large enough that it can accurately be modeled as homogeneous and isotropic. (These scales are beyond the sizes of galactic clusters.) But on much smaller scales, where these assumptions obviously break down, matter does indeed curve spacetime; the phenomenon of gravitational lensing is precisely such an example. If you are at all confused by these different notions, I would recommend taking a look at a modern textbook on the subject; Barbara Ryden's Introduction to Cosmology is a good place to start. Yill 14:57, 6 April 2010 (EDT)
 Dark matter supposedly permeates the universe, and there's no way it would be flat if GR were true.Andy Schlafly 00:48, 7 April 2010 (EDT)
 Okay, now that is a total non sequitur. Again, instead of making blanket assertions, perhaps you should learn why, given that they believe dark matter permeates the universe and that it is flat on large scales, cosmologists still think GR works. Let me enlighten you. If the universe were evenly filled with a uniformly dense substance, the curvature would be flat. Yet there were would be matter in it! And that's it. On large enough scales, that's how the universe appears. Hence there is no contradiction. Yill 00:19, 9 April 2010 (EDT)
 An additional clarification to the previous discussions: According to Einsteins equations (neglecting the cosmological constant for now):
in which: is representative of the curvature of spacetime (Ricci tensor) and is representative of the matter/energy content of the given model (StressEnergy tensor). So Einsteins equations state that the presence of matter gives rise to curvature effects in spacetime. In FLRW cosmology the existence of a spatially flat solution is possible if the total density ~ critical density required for a flat Universe. The fact that the Universe is nonstatic and we currently include a dark energy component does not mean that a Universe that is currently observed to be spatially flat is in conflict with predictions of General Relativity. The flatness problem is more of an initial value problem/fine tuning problem than that of a breakdown in GR.
Proposed page move
Can someone rename the article so the R is lowercase in the title? Thanks, GregoryZ 22:21, 29 July 2010 (EDT)
 Why? The term refers to a specific theory, and the many counterexamples to it.Andy Schlafly 22:31, 29 July 2010 (EDT)
 My simple rationale is "relativity" is not a proper noun. Wikipedia uses the lowecase and so does Wester's, so why not here? GregoryZ 22:36, 29 July 2010 (EDT)
 It's not a traditional proper noun, you're right, but it does satisfy all the conditions underlying why proper nouns are capitalized. It is a unique termofart, having a specific meaning other than the general meaning of the word. As used in physics, "Relativity" is different from the generic "relativity".Andy Schlafly 23:01, 29 July 2010 (EDT)
 However, it is my belief, "relativity" in this case should not be treated differently. Look at the Wikipedia article, it uses "relativity" in that sense. Also, the CP article on the subject uses the lowercase as well, so I still see no point in capitalizing it here. GregoryZ 23:07, 29 July 2010 (EDT)
 The word "relativity" dates from the early 1800s. That's not what is being discussed here. If preceded with "theory of" then there is no need to capitalize; if standalone, however, it does add clarification to capitalize as is done for other specific concepts that differ from the generic names.Andy Schlafly 23:52, 29 July 2010 (EDT)
Curl of the gravitational field
Sorry to get overtechnical, but the fundamental law of "fictitious forces" (including gravity) is that the force field (divided by the mass of the test object) is
Its curl is
where the semicolon indicates the covariant gradient.
When you work this out, it involves derivatives of the quantities. In general relativity, the results are zero by symmetries of Riemann's tensor.
Simeon 21:33, 30 July 2010 (EDT)
 Perhaps so, but the "twin paradox" in Relativity states that the age of each twin is dependent on his path of travel. For a conservative field, all physical parameters are path independent.Andy Schlafly 23:07, 30 July 2010 (EDT)
 Simeon, your mathematical work is rigorous and correct. However, the twin paradox example is interesting to study here. I am aware that the twin paradox is solved by the noninertial turnaround of the ship when it is going back home. However, in this solution, it is still noted that there is an age difference between the twins. Wikipedia affirms this and so do other sites. Such an age difference in twins shows that there is some sort of path dependence. I understand that traveling at nearc speeds in space is not the same thing as moving from point A to B in a gravitational field, but the concept does seem to be a bit similar. Could you maybe explain this for us a bit? Thanks. PhyllisS 00:52, 31 July 2010 (EDT)
OK, I think I understand. I assumed that the "conservative field" / "curl is zero" stuff referred to the gravitational force field. If it refers to the passage of time, that's different. It isn't true that "all physical parameters are path independent". An extremely important one that isn't path independent is the arc length of the path or arc. You can draw a short straight line from A to B, or a long loopy line that starts at A, wanders around, and eventually gets to B. Why is this relevant to the twin paradox? Because, in relativity, an observer's own elapsed time ("local time") is really just the arc length of his "world line" in Minkowski space. Minkowski was an extremely smart guy, by the way. The twin that stays home takes a direct route from point A (their birth) to point B (the moment they compare ages and see that one has gray hair and wrinkled skin.) The other twin takes a very roundabout route, getting in a rocket and going to Alpha Centauri and back. Their path lengths are their local times, which are different. (Why is the length of the roundabout path actually shorter, so that that twin ages less? Because, in Minkowski space, using the "timelike convention" that all the best people use :), motion in space subtracts from the elapsed time. That's just the way it works.)
Now I assume that there is no dispute about the facts of relativistic time dilation. In addition to being predicted exactly by the Lorentz transform, it has been observed in practice in cosmic ray muon decays, as well as countless observations in particle accelerators. The "twin paradox" is just an extreme consequence of this. It has of course never been observed in that form, just as we don't know whether Schrodinger's cat is alive.
The "twin paradox" is a consequence of special relativity, not general, and hence does not relate to gravity. I hate to be the umpteenth person to tell you that general relativity is too hard to explain, but it's kind of true. I barely understand the most rudimentary basics. (When Eddington made his comment about only 3 people in the world who understand gen. rel., I wasn't the third! :) But I can say that you don't need to worry about general relativity to understand the "twin paradox". You can finesse the Minkowskispace curvature of the path during the turnaround at Alpha Centauri, and just say that the twin went there and came back. So was something physically different, that the twins could observe? You bet. The "younger" twin will remember having experienced 6 months of horrendous acceleration in the ionicdrive rocket, followed by a year of horrendous turnaround, and another 6 months of horrendous deceleration at the end. She will have soft, smooth skin, but at a great cost. :)
Sorry to be so longwinded. In quick summary, the thing that's different about the paths is their length, and that is exactly the local elapsed time. Simeon 00:07, 1 August 2010 (EDT)
 Simeon, time dilation occurs under the Theory of General Relativity also, so your analysis above is not persuasive in resolving this example of a nonconservative effect. Moreover, your repeated claims about how supposedly only geniuses can understand this are getting tiresome. That approach is a recipe for mistaken reliance on unjustified authority.
 If you don't feel this is understandable, then simply say so and stop there; please do not imply that people should just accept what someone of undisclosed political views claims.Andy Schlafly 10:58, 1 August 2010 (EDT)
I give up.
 The only scientists I mentioned were Minkowski and Eddington, and the latter just as a joke. I never said anything about their, or anyone else's, politics.
 Time dilation does indeed occur under both general and special relativity. The point I was trying to make is that general relativity is simply not needed to understand the twin paradox. It only takes special relativity, which is much better understood. I'm sorry to hear that, by not analyzing the twin paradox in terms of general relativity, my persuasiveness suffered.
 I apologize if I "talked down" to you and Phyllis with my comments about GR being too complicated. I assume that both of you have heard, many times, that GR is exceedingly complicated. I was simply trying to soften the blow by pointing out that you don't need GR. And cracking that joke about how Eddington could not have been referring to me.
 In fact, I know a fair amount about GR. I could analyze the twin paradox in terms of the gravitation of Earth and Alpha Centauri. But there is simply no need to.
 This "nonconservative effect" business simply makes no sense. If the integration of a vector field along different paths gets different final results, then that field is nonconservative. You seem to be saying that the passage of time is some kind of vector field, and that the final results of "integrations" (the two different values of local time at the end of the experiment) are supposed to be the same, and that the difference shows that this "vector field" is not conservative, and that that is a counterexample to relativity. The passage of time is not a vector field. The different values of time, as seen by different observers, is not a counterexample to relativity, it is one of the principal effects of relativity. It's really what the word "relativity" means when discussing the scientific Theory of Relativity.
 If you really think that the nonglobality and nonabsoluteness of time is a counterexample to relativity, then so be it.
Simeon 23:13, 1 August 2010 (EDT)
 Simeon, if you "give up," then that is your own choice. You have not disproved the counterexample. Instead, you first described the twin paradox as being only about special relativity, and when I pointed out that it exists under general relativity too, you then agree yet do not fully address the substantive issue presented by the paradox. For example, the amount of acceleration undertaken by the twin in his journey will affect his age independent of his time spent away. His subsequent age is not path independent even in timespace coordinates.
 It's easy to search for "general relativity" and "conservative field" on the internet and see how little has been written about this. That is telling in itself. I'm happy to continue to discuss this here with you or anyone else.Andy Schlafly 23:56, 1 August 2010 (EDT)
 Could you clarify what the ages (and path dependence thereof) in the twin paradox have to do with conservative fields? KyleT 14:04, 2 August 2010 (EDT)
 Age is scalar physical attribute. It should not be path dependent in a conservative field.Andy Schlafly 14:31, 2 August 2010 (EDT)
 Yes, but which conservative field in particular are you talking about here (that implies age is not path dependent)? KyleT 14:37, 2 August 2010 (EDT)
 Gravity.Andy Schlafly 14:53, 2 August 2010 (EDT)
 Well, in Newtonian mechanics, the gravitational field is indeed conservative  it's the negative gradient of the gravitational potential! But what this means is that gravitational potential energy is pathindependent: it doesn't say anything about pathindependence any other quantities, and in particular it's not the reason for the pathindependence of age. KyleT 15:00, 2 August 2010 (EDT)
 You take a narrow view of the significance of a "conservative field." Independent physical attributes should remain pathindependent as well for the field to be conservative. In Newtonian mechanics and most other physical force fields, they do.Andy Schlafly 15:41, 2 August 2010 (EDT)
 By a conservative field, I mean a vector field on space for which there exists a scalar function V with the gradient of V given by that vector field. This doesn't imply the pathindependence of any physical quantities other than V itself. If you this view as too narrow, can you tell me what you take to be the definition of a conservative field? KyleT 15:57, 2 August 2010 (EDT)
 Your definition is too narrow when discussing the theory of relativity, which describes the framework in which the force operates. To be meaningful, the definition must be broader. It must ensure the path independence of the scalar, as well as other scalars independent of that scalar.Andy Schlafly 18:12, 2 August 2010 (EDT)
 Can you tell me what the correct definition is, then? I have pretty good background in this stuff, no need to dumb it down, just be precise. Certainly no field at all is going to conserve every scalar function, so I'd like to know which ones you want. KyleT 18:20, 2 August 2010 (EDT)
 Kyle, I have an open mind about this, and don't see a precise definition anywhere that would be meaningful with respect to the theory of relativity. It's striking how relativists avoid this issue, and even stop discussing it when it is brought up.
 I can propose a definition that you may be able to improve. How about: a conservative theory of motion is one whereby scalar values of a particle are independent of its path of motion.Andy Schlafly 18:36, 2 August 2010 (EDT)
That's an interesting proposal, and I too have an open mind about this. Can you give an example of such a conservative theory of motion? One such would greatly help in devising the correct definition. KyleT 19:29, 2 August 2010 (EDT)
 Newtonian mechanics would be an obvious example. By the way, how do you explain the general lack of discussion and papers about whether the theory of relativity is conservative, including the abrupt departure of User:Simeon from this discussion?Andy Schlafly 21:58, 2 August 2010 (EDT)
 Some scalar values in Newtonian mechanics are conserved because there exist associated conservative fields (or more generally symmetries of the Lagrangian). What is an example of a scalar value in the Newtonian mechanics that is not of this type, which makes this a conservative theory of motion while relativity is not?
 I don't know why relativity's defenders won't confront this. Maybe that could be the topic of the debate page  I'm interested using this discussion to sharpen counterexample 21. KyleT 23:55, 2 August 2010 (EDT)
 This is a really interesting discussion. I think I made a gross mistake in my first post. The theory of relativity urges us to think of the three space coordinates (x, y, and z) and the time coordinate (t) as four coordinates of spacetime  that is, that space and time are pretty much the same. I extrapolated from this that since there can be a (conservative) gravitational field in space coordinates, there can also be some sort of conservative field depending on the time coordinate. I then extrapolated this notion to special relativity, and the twin paradox; I postulated that maybe time dilation effects were the work of a nonconservative field that was dependent on the tcoordinate. Now I see that this was all somewhat foolish. However, I wanted to ask you all: can you have a conservative or nonconservative field with respect to time? If not, I think time should not be considered as almost the same thing as x, y, z space. I feel that the ability for a dimension to have a field (conservative or not) is integral to its being considered a spacelike dimension.
 Aschlafly, the fact that the twin paradox exists in general relativity is irrelevant. Yes, sure, the twin paradox occurs within space where general relativity is working, but there are no effects acting on the twins that influences the twin paradox in any way. Likewise, User:Simeon 's departure is also irrelevant.
 What about black holes, though? Surely their gravitational fields aren't conservative, since once an object passes the event horizon, you can't retrieve it. PhyllisS 01:24, 3 August 2010 (EDT)
Phyllis:
You seem to be very curious about this topic. I'm going to try to give an intuitive, but nevertheless scientifically correct, explanation of what is going on with relativity, the "twin paradox", and vector fields, potential functions, and path integrals. This explanation will probably seem long and tedious, for which I apologize in advance. I also apologize if it seems that I am being too "folksy", or talking down to you. Please bear with me, and please pay close attention.
We have a parking lot, and two twins, who are fitness enthusiasts and always wear pedometers wherever they go. There are two spots, "X" and "Y", painted on the parking lot. Both people stand on spot "X", set their pedometers to zero, and start walking. Twin A simply walks directly to spot Y. Twin B, being more into fitness, walks all over the place, eventually arriving at B.
Now there are quite a number of things we can say. First, the temperatures vary all over the place. They are a scalar field. That means that they are associated with location on the parking lot, not with any particular observer. They are objective measurements that everyone agrees on, because they are aspects of space itself. Our fitness enthusiasts are also amateur meteorologists, and carry thermometers around with them.
 Twin A: "When I was at the green Toyota, I noticed that the temperature was 67 degrees Fahrenheit."
 Twin B: "By coincidence, I also wandered past the green Toyota, and got the same reading."
By the way, since temperature is a scalar field, it has a gradient, which is a vector field. That field is conservative, according to the theorem of mathematical physics that says that curl grad Φ = 0 always. This gradient is a vector field. Like the scalar of temperature, it is a property of the space (parking lot) itself. If the twins had been measuring this gradient (perhaps they carry around fancy "differential thermometers"), they would have gotten the same vector at the green Toyota.
There is also a theorem of mathematical physics, sort of the opposite of the theorem above, that says that, if a vector field V has a curl of zero:
 You can make a scalar field (a property of the space itself, not tied to any particular observer) that it is the gradient of. That scalar field is called the "potential" for the (conservative) vector field. (By the way, this is very closely related to "exact differential equations" that you wrote about! Do you see the connection?)
 If you integrate that vector field along any path between two points A and B (that is, you calculate
for that path, where "dl" is the "line element" along the path), you will get .
 Since is a property of the scalar field itself (and the points A and B), it follows that that path integral is the same for all paths. And if the path ends on the same point it started on, the integral is zero.
 Twin A: "I was measuring the gradient of the temperature as I walked, and calculating its path integral as I went. I got an answer of 4 degrees."
 Twin B: "I was doing the same. My integral was much harder to calculate, because I was going all over the place. But I also got 4 degrees. Hey, wait a minute! The temperature at the start point was 68 degrees, and at the end point it was 72 degrees. That explains it."
Now someone at the edge of the parking lot was running a Van deGraff generator, so there were electric fields all over the place. The twins are also physics students, and carry electroscopes wherever they go. They measured the electric field, and calculated its path integrals. The electric field is conservative (in the absence of varying magnetic fields), so they got the same integral. That integral was 600 volts (it's only static electricity, so it isn't dangerous). Since the electric field is conservative, there is, by the previous theorem, a potential function. That function was 600 volts higher at point B than at point A.
Now here's the kicker:
 Twin A: "I walked directly from A to B. My pedometer says 150 feet."
 Twin B: "I took a long route all over the place. I walked half a mile."
The pedometer readings are not a scalar field. They are not a property of the space itself. They are properties of the observers. Even though they, in some sense, measure an aspect of the parking lot (how many molecules of asphalt one passes), they are artifacts of the twins' actions.
The twins could have been integrating their motion vectors; that's sort of what pedometers do. But those vectors are not a vector field on the space itself. It makes no sense to ask whether that "vector field" is conservative, because it isn't a vector field. A vector (or scalar, or tensor) field has to be a property of the space itself. These "pedometer vectors" are just things that the twins make up as they walk.
Now for the "twin paradox". The parking lot is replaced by "Minkowski space", also called "4dimensional spacetime". "Points" in this space are now "events", complete with a time. Events A and B are now the act of the twins saying goodbye as one of them got into the rocket, and the act of them reuniting after B returns. Twin A took a direct route (called her "world line") from A to B. She used a coordinate system in which the spatial coordinates of A and B were the same (Cape Canaveral, latitude yada yada, etc.) and the time coordinate differed by 30 years (2010 to 2040.) B went to Alpha Centauri and back. When she returned, they were both using the same coordinate system (location is Cape Canaveral, latitude yada yada, time is 2040.) But she looks at her watch, and only 5 years have elapsed! What the watch shows is not a scalar field on spacetime. It was not the path integral of a vector field on spacetime. What she integrated was the ticking of her watch, nothing more.
The path that A took is called a geodesic. It is the Minkowskispace equivalent of a "straight line". But, because of the peculiarities of relativity, it shows the longest elapsed time (30 years) of all paths, rather than the shortest. By going to Alpha Centauri, twin B took a shorter path, in terms of the way path length is measured in Minkowski space.
Very interesting fact: The path length in Minkowski space, that is, the sum of the tiny distances as measured by the Lorentz/Minkowski metric, is the same as the local time. That is (assuming you are using the "spacelike convention"), everyone's wristwatch measures path length along their own world line. The twins simply followed paths of different lengths. That's all there is to the "twin paradox". (That is, that's all there is to it, if you analyze it correctly, as I have described above. Most introductory treatments of relativity don't do it this way. They just throw the Lorentz transform at you.)
Now there are a few points about the "twin paradox" that people find confusing.
First, aren't the laws of physics supposed to be the same for everyone? What made twin B's watch run slower? Well, she knew she was traveling at high speed. She brought an accelerometer with her in the rocket. Just as twin B in the parking lot knew she was walking all over the place, turning around and such, twin B in space knew that her worldline was turning, and therefore wasn't a straight line (geodesic). How did she know? It takes force to make you deviate from a geodesic (this is really pretty much the same as Newton's laws of motion), and she felt the force.
Second, how can we analyze the curvature of B's world line? Here's where general relativity has to come in. As soon as world lines start to curve, you have to measure their curvature, that is "geodesic curvature". You get into complicated issues of curved coordinate systems (you're in one now; it's what you perceive as "gravity"!), and curved spacetime, and so on. And you get into the symbols, which measure the deviation from a geodesic, and hence the "fictitious forces" that you feel. This is why general relativity is related to the "twin paradox", in that the space ship followed a curved trajectory and experienced acceleration. But, to analyze the plain facts of the "twin paradox", all you really need to know is that twin B followed a crooked line. Place your ruler on a diagonal on the graph of Minkowski space, draw the line out to Alpha Centauri. Turn the ruler, draw the returning line. Ignore the impossibly sharp corners. Use special relativity to analyze the Lorentz transform for each section of B's world line.
Oh, and to try to answer some of your specific questions, the gravitational field, under either Newtonian or relativistic mechanics, is a conservative field. Its curl is zero. If it weren't, conservation of energy would be violated, and we could make a perpetual motion machine by having a planet run around in circles picking up energy. The "curl=0" aspect of gravity under general relativity is more complicated, because true vector fields have to be on Minkowski space, but it still conserves energy. When Mercury orbits the Sun, its perihelion precesses because of relativistic effects, but its energy is conserved.
I'll try to think some more about your black hole question and get back to you.
Simeon 00:00, 4 August 2010 (EDT)
 Simeon, thanks so much for your long explanation! All of that made sense to me, and cleared up the issue of field as property of space vs. path specific to person vs. curved spacetime. Also, yes, I noticed the similarity between exact differential equations and deriving potential functions from vector fields  the former I studied in Differential Equations and the latter I studied in Multivariable Calculus.
 So, if I understand you properly, gravity both (a) curves spacetime and (b) creates a conservative field. (I derived (a) from your point: "You get into complicated issues of curved coordinate systems (you're in one now; it's what you perceive as "gravity"!)", and (b) from your point: "the gravitational field, under either Newtonian or relativistic mechanics, is a conservative field. Its curl is zero.") However, you're saying that if you are in an accelerating reference frame (such as a quicklyspinning merrygoround) only (a) occurs; there is no field. Is this correct? If so, why is there this discrepancy between the two? PhyllisS 22:54, 4 August 2010 (EDT)
Yes, gravity curves spacetime. It looks as though you're ready to go to the next level. It has to do with curved coordinate systems vs. curved spacetime. This is why GR is so complicated. But here goes.
First, we have to recognize that, at some level, we could say that energy is *not* conserved. Spacecraft use "slingshot maneuvers" around one planet to gain extra energy on their way to another planet. I assume you've heard of this. Cassini used three such maneuvers, twice around Venus and once around Earth. So what was going on? If you look at a coordinate system centered on Venus, you would see Cassini come in and go out again, with complete conservation of energy. But, in a coordinate system fixed around the solar system, Venus was moving, so Cassini came in at low speed and went out at high speed. We "stole" some energy out of Venus's orbit. So, to be really correct, we have to say that gravity is a conservative field in the absence of moving gravitating bodies.
But, in the larger sense, energy is conserved. Always. Newtonian or relativistic. (But in relativity, the mass figures into the equation. Let's not worry about that just now.)
Now we get to the really cool stuff. Your comment above suggests that you are ready for it.
You will feel a "fictitious force" whenever you are in a "curved spacetime coordinate system". A curved coordinate system would include things like polar coordinates on the plane, or spherical coordinates in 3 dimensions. But this is 4dimensional spacetime. So I'd like you to take my word for this. On a rotating merrygoround, your 4dimensional spacetime coordinate system is curved. (This doesn't require relativity, special or general, to formulate this.) The 3dimensional slice of it is flat, but, when you bring in time, and the spatial coordinates are accelerating, the overall coordinate system is curved. This creates fictitious forces. In the case of the merrygoround, the forces are the centrifugal force and the Coriolis force. There are also the fictitious "acceleration G forces" in a rocket. But the spacetime itself isn't curved. It's like polar coordinates on the plane. Yes, the coordinate system is curved, but the plane isn't. There are Cartesian coordinates on the plane also. Similarly, an observer on the ground is in a flat coordinate system, and doesn't see any fictitious forces. He just sees the mechanism of the ride pushing you inward as you go around. Your recoil against that acceleration is what you perceive as the centrifugal force.
So the moral of the story would seem to be: you can choose a flat coordinate system that exposes the fictitious force for what it is. It's a perception from the curved spacetime coordinate system that the observer is operating in.
But how about gravity? In the case of gravity, spacetime itself is curved. If spacetime (properly called a "manifold") is curved, every coordinate system is curved, and the fictitious force which is gravity is inescapable.
So your statement "gravity curves spacetime", is exactly correct, but you have to distinguish "curving spacetime" and "curving some particular coordinate system". The actual curvature involves things called "Riemann's tensor" and "Ricci's tensor".
The number of people that understand this is way more than the 3 that Arthur Eddington claimed (it was more than 3 but probably less than 10 at the time), but it's still a pretty complicated subject.
Simeon 00:03, 5 August 2010 (EDT)
 Simeon: Ah, that does make a lot of sense now. Thanks so much for explaining this to me. Hmm, that really is an elegant concept  wow. Cool! PhyllisS 13:50, 5 August 2010 (EDT)
Misleading Reference
The counterexample #18 has as an reference:
Contrary to the claims of Relativists, the GPS system has never been based on Relativity. The Time Service Department, U.S. Navy, observed that "the Global Positioning System (GPS) does not include the rigorous transformations between coordinate systems that Einstein’s general theory of relativity would seem to require" in part because "the effects of relativity, where they are different from the effects predicted by classical mechanics and electromagnetic theory, are too small to matter – less than one centimeter, for users on or near the earth.”
That's wrong: From the very beginning of the program, some relativistic effects were taken into account. As Conservapedia states at its article on GPS the Naval Research Lab in Washington published its report on the Initial Results of the NAVSTAR GPS NTS2 Satellite in 1978 and listed the following GPS objectives that have been achieved to date:
 launch insertion into GPS constellation position
 demonstrated orbit stability and controllability
 first cesium frequency standard in space
 verification of relativity theory
But not only did the initial experiments bolster the theory, some relativistic effects have to addressed in general use  in the official specification for the GPS project , i.e., the Global Positioning System Standard Positioning Service Signal Specification, 2nd edition, June 1995, you find the following:
p. 13: To compensate for relativistic effects, the output frequency of the satellite's frequency standard  as it would appear to an observer located at the satellite  is 10.23 MHz offset by a Df/f = 4.4647 x 1018 or a Df = 4.567 x 103 Hz.
p. 39: The coefficients transmitted in subframe 1 describe the offset apparent to the control segment twofrequency receivers for the interval of time in which the parameters are transmitted. This estimated correction accounts for the deterministic satellite clock error characteristics of bias, drift and aging, as well as for the satellite implementation characteristics of group delay bias and mean differential group delay. Since these coefficients do not include corrections for relativistic effects, the user's equipment must determine the requisite relativistic correction. Accordingly, the offset given below includes a term to perform this function.
It's true that not all effects are covered yet: as I stated above, the quoted article of the The Time Service Department, U.S. Navy addresses effects caused by the fast movement of some of the GPSreceivers  something which will doubtless be included as the number of fast receivers grows.
RonLar 15:03, 9 August 2010 (EDT)
Ehrenfest's Paradox
This has been resolved and should be considered an apparent paradox. See here. Meatstick 11:07, 10 August 2010 (EDT)
Momentum issues
It should be explained why numbers 4 and 20 are counterexamples. It isn't adequately explained why these would even present issues with the theory. Actually they look like explanations of part of the theory. Meatstick 11:12, 10 August 2010 (EDT)
 Number 4: for mass that is infinitesimally small, its momentum goes to infinity under Relativity as its speed approaches the speed of light. But this is absurd because if the mass is precisely zero rather than infinitesimally close to zero, its momentum is finite at the speed of light.Andy Schlafly 12:05, 10 August 2010 (EDT)
 Are you sure that this is true? What are you fixing? One formula for relativistic momentum is . This remains a differential quantity in as velocity becomes infinite: . Fixing energy gives the correct momentum result in the limit as velocity becomes infinite. Maybe the misunderstanding results from taking two limits at once  the prefactor that depends on velocity becomes infinite while the restmass dependence remains linear. TylerGD 13:28, 10 August 2010 (EDT)
 Energy does not remain fixed as velocity increases to the speed of light. You seem to be avoiding the central point.Andy Schlafly 11:11, 11 August 2010 (EDT)
Wormholes
There seems to be some confusion on the difference between predicting and allowing. General relativity allows wormholes under some conditions. But a lack of observed wormholes or even a lack of wormholes would not be inconsistent with the theory. TylerGD 16:27, 10 August 2010 (EDT)
Inability of theory to lead to other insights?
Although this can hardly be considered true, would it be a counterexample to relativity if it were? Couldn't this be a failure of scientists or a testament to the finality of a theory? TylerGD 16:28, 10 August 2010 (EDT)
 No, because the theory has been around for more than a century.Andy Schlafly 09:18, 11 August 2010 (EDT)
 Why could this not be a failure of scientists? Anyway, what about the Dirac description of the electron? You can only claim that the theory failed to lead to other insights if you ignore the other insights. TylerGD 10:24, 11 August 2010 (EDT)
 Relativity has been better funded than most theories, so it is a defect in the theory that it has yielded so little for the effort expended.Andy Schlafly 11:12, 11 August 2010 (EDT)
 The theory of GR has led to many insights regarding astrophysical phenomena. In particular GR plays an important role in discussing: Neutron Stars, Black Holes, LargeScale structure, Cosmological Perturbation Theory, Stellar Evolution, Gravitation Waves, Gravitational Lensing, etc. Many concepts in modern astrophysics have been motivated using insight from GR. Additionally many developments in Quantum Field Theory (as used in Condensed Matter and Particle Physics  e.g. predictions of verifiable decay rates, crosssections and so on), Relativistic Quantum Mechanics and Particle Physics take special relativity as an absolutely fundamental starting point. Many modern day particle accelerators require special relativistic corrections in order to work properly.  15th August 2010 NotesTH
 NotesTH, you list some unproven dead ends like neverobserved "Gravitation Waves," but fail to identify any verified insight. Indeed, the length of your list highlights its lack of a quality insight.Andy Schlafly 16:38, 15 August 2010 (EDT)
 Gravitational waves have not been directly observed, no, but there is significant indirect evidence. Most commonly cited is the  HulseTaylor binary. In the linked article it is claimed that a "0.2%" demonstrates the failing of relativity. On the contrary, the fact that a theoretical model for a binary star system could predict a gravitational wave emission that matches observations so extremely closely is extraordinary. The supposed correction term for "galactic acceleration" exists because the initial model is not perfect and nor was it ever meant to be. A 0.2% error is a fantastically small difference and demonstrates that GR provides an extremely accurate and verified prediction for the observed decay of a binary system due to emission of gravitational waves. The authors of the quoted paper state "Accuracy of the test for gravitational radiation damping is now dominated by the uncertainty in the galactic acceleration term. Work now underway should lead to improved accuracy of the pulsar proper motion, and the Sun’s galactocentric distance may be better known in the future. However, we see little prospect for a significant improvement in knowledge of the pulsar distance. Consequently, it seems unlikely that this test of relativistic gravity will be improved significantly in the foreseeable future"  that's simply a statement to the effect that there were some unknown parameters not included in the initial model but nowhere near enough to even remotely claim that the model is being tweaked to fit the theory, not for a 0.2% difference.
 You also seem to have neglected the other points. Rather than trying to talk about everything, it would take far too long in one sitting, I'll focus on the particle side of things. I've already stated that modern particle accelerators take into account relativistic effects  e.g. particle energies (using the relativistic energy equation: , synchotron radiation  Synchotron at the LHC, particle lifetimes and so on. All of these require calculations from relativity that have been experimentally measured and verified. For instance all the predicted particle lifetimes and decay rates would require quantum field theories (which require relativity as a relativistic quantum theory) to predict the expected values which can then be matched to observations. We find that they are an extremely good fit to observations. Another example of such a calculation would be in predicting the  magnetic moments of particles  theory matches observations extraordinarily well.
 As another point, just for a further example (could keep going...) we could look at neutron stars or pulsars as objects that are intrinsically relativistic. We can use observations of millisecond pulsars and, for example, compare models of synchrotron radiation (relativistic) to the observations. We find that the relativistic predictions are again in good agreement. Relativity has led to the development of many astrophysical phenomena which are intrinsically relativistic. Without the framework and foundations of relativity such insight would be impossible. The fundamental concepts introduced by relativity are absolutely essential in many, many branches of modern day science with many of the intrinsic relativistic effects being tested to a vast degree. No one claims that GR is the complete theory, it's treated as an effective field theory valid in some low energy limit, but the revolutionary concepts introduced by relativity have led to irrefutable developments in many areas of science.  15th August 2010 [User:NotesTH  NotesTH]
"from the muons' point of view, the Earth would have to be rushing in all directions to meet them"?
This would only be true if the muons shared a reference frame. Which they don't. TylerGD 10:25, 11 August 2010 (EDT)
 Good point, so that edit was removed.Andy Schlafly 21:59, 12 August 2010 (EDT)
Number 29: the fastedframe contradiction
Clocks tick fastest in their rest frame. This is unique to the particular clock, but not among all clocks. No contradiction exists here. TylerGD 10:29, 11 August 2010 (EDT)
 OK, so that edit was also removed.Andy Schlafly 21:59, 12 August 2010 (EDT)
Continuation of "Curl of the gravitational field"
Phyllis (and any other interested parties, of course): You might want to take a look at the General theory of relativity page. I think you will be able to follow much of it. In particular, the "Coordinate Systems and Spacetime Diagrams" section is along the lines of what I discussed above. A better name for it might be "how the curvature of spacetime creates gravity". The "Quantitative Introduction to General Relativity" is a link to a separate page, that might be better named "how matter makes spacetime curve. The second of those is pretty daunting. The first was clearly never finished. A finished version seems to be on Wikiversity.
Good luck. Simeon 23:54, 11 August 2010 (EDT)
Reversion of my edit
I changed
Contrary to the claims of Relativists, the GPS system has never been based on Relativity. The Time Service Department, U.S. Navy, observed that "the Global Positioning System (GPS) does not include the rigorous transformations between coordinate systems that Einstein’s general theory of relativity would seem to require" in part because "the effects of relativity, where they are different from the effects predicted by classical mechanics and electromagnetic theory, are too small to matter – less than one centimeter, for users on or near the earth.”
to
Only some, but not all effects of relativity are addressed by the Global Positioning System: not yet incorporated are the effects for fast moving receivers of the signal (e.g., satellites), therefore the Time Service Department, U.S. Navy, observed that "the Global Positioning System (GPS) does not include the rigorous transformations between coordinate systems that Einstein’s general theory of relativity would seem to require" in part because "the effects of relativity, where they are different from the effects predicted by classical mechanics and electromagnetic theory, are too small to matter – less than one centimeter, for users on or near the earth.”
Andrew Schlafly changed it back, ignoring my edit comment: (changing misleading reference  as explained here and here)
The current statement of Andrew Schlafly is wrong in at least two ways, as explained several times:
 the GPS addresses effects of Relativity: From the very beginning, its builders had the Theory of Relativity in mind. [2] and [3]
 the paper quoted above addresses yet another effect.
Perpetuating a wrong statement doesn't seem to be very insightful.
RonLar 11:13, 13 August 2010 (EDT)
 You don't have to beat us over the head with it, Ron. We already knows that perpetuating wrong statements isn't insightful. We agree with that part of your remarks.
 The question is whether relativistic effects are (A) big enough to matter or (B) actually being calculated and compensated for by any major GPS.
 Now, it's interesting that the first builders considered relativity, but what our readers want to know is whether they decided that it made a big enough difference. Ed Poor ^{Talk} 11:52, 13 August 2010 (EDT)
 don't be rude sorry, but please don't mistake my exasperation for rudeness!
 The question is whether relativistic effects are (A) big enough to matter or (B) actually being calculated and compensated for by any major GPS. The answer to (A) as well to (B) is a very emphatic yes. It was given repeatedly and can be found in the source linked above  or in the section of this very talk page to which I linked in my editcomment (conveniently repeated a couple of lines above, too). But to spare you the work of actually scrolling backwards, here it is again:
 Global Positioning System Standard Positioning Service Signal Specification, 2nd edition, June 1995:
 p. 13: To compensate for relativistic effects, the output frequency of the satellite's frequency standard  as it would appear to an observer located at the satellite  is 10.23 MHz offset by a Df/f = 4.4647 x 10^{18} or a Df = 4.567 x 10^{3} Hz.
 p. 39: The coefficients transmitted in subframe 1 describe the offset apparent to the control segment twofrequency receivers for the interval of time in which the parameters are transmitted. This estimated correction accounts for the deterministic satellite clock error characteristics of bias, drift and aging, as well as for the satellite implementation characteristics of group delay bias and mean differential group delay. Since these coefficients do not include corrections for relativistic effects, the user's equipment must determine the requisite relativistic correction. Accordingly, the offset given below includes a term to perform this function.
 This Global Positioning System Standard Positioning Service Signal Specification is quoted on the talkpage of the article for the GPS, too. It is the relevant document for everyone  engineer of physicist  who wants to work with the signals of the GPS.
 This quote alone shows that the statement Contrary to the claims of Relativists, the GPS system has never been based on Relativity. is wrong. Plain and simple.
 Effects on the GPS became a textbook example for relativity, see e.g., Neil Ashby, who writes in Relativity in the Global Positioning System:
 There is an interesting story about this frequency offset. At the time of launch of the NTS2 satellite (23 June 1977), which contained the first Cesium atomic clock to be placed in orbit, it was recognized that orbiting clocks would require a relativistic correction, but there was uncertainty as to its magnitude as well as its sign. Indeed, there were some who doubted that relativistic effects were truths that would need to be incorporated! A frequency synthesizer was built into the satellite clock system so that after launch, if in fact the rate of the clock in its final orbit was that predicted by general relativity, then the synthesizer could be turned on, bringing the clock to the coordinate rate necessary for operation. After the Cesium clock was turned on in NTS2, it was operated for about 20 days to measure its clock rate before turning on the synthesizer. The frequency measured during that interval was +442.5 parts in 10^{12} compared to clocks on the ground, while general relativity predicted +446.5 parts in 10^{12}. The difference was well within the accuracy capabilities of the orbiting clock. This then gave about a 1% verification of the combined secondorder Doppler and gravitational frequency shift effects for a clock at 4.2 earth radii.
 But you don't have to take this secondary source at face value, you can go to the primary source: Initial Results of the NAVSTAR GPS NTS2 Satellite, Naval Research Lab Washington, D.C., 25 May 1978 (Full text: pdf). Ever since 1978, relativistic effects are observed and compensated in various ways. Or as the abstract states it:
 NTS2 was successfully launched on 23 June 1977 into a near 12hour circular orbit. Precise frequency and timing signals are derived from the two cesium frequency standards. This paper discusses the launch and preliminary results which include verification of the relativistic clock effect.
 PhyllisS introduced the following quote above:
 The Time Service Department – a department of the U. S. Navy  states: “The Operational Control System (OCS) of the Global Positioning System (GPS) does not include the rigorous transformations between coordinate systems that Einstein’s general theory of relativity would seem to require – transformations to and from the individual space vehicles (SVs), the Monitor Stations (MSs), and the users on the surface of the rotating earth, and the geocentric Earth Centered Inertial System (ECI) in which the SV orbits are calculated. There is a very good reason for the omission: the effects of relativity, where they are different from the effects predicted by classical mechanics and electromagnetic theory, are too small to matter – less than one centimeter, for users on or near the earth.”
 This is taken from a text of Henry F. Fliegel and Raymond S. DiEspostifrom December 1996 who are talking about another relativistic effect than the ones already implemented. Please keep in mind that the Specification above is from June 1995! Only someone who didn't read the text  or didn't understand it  could abuse this quote to invoke the impression that no effects of relativity were implemented in the GPS.
 Of course, the information above may be ignored  as it was previously: tl;dr. But actively ignoring facts which contravene a statement just to repeat the statement is a behavior which can only be described in a rude way.
RonLar 09:34, 14 August 2010 (EDT)
 Ron, the collection of statements above could be construed as easily as disproving relativity rather than proving it. Decades after GPS was launched, observers still struggle to match the data to the theoretical predictions. If some relativistic calculations are included in the synchronization but others are not, then the theory is disproved, not proved by the data.
 As the Theory of Relativity page itself explains, the engineers ignored the complex predictions of relativity. And for obvious reasons: it's easier to synchronize the clocks directly based on communications!
 Note the complete absence of any identification of a particular physicist or mathematician who supposedly provided the theoretical predictions of Relativity for the engineers. That is because there were no such theoretical predictions of Relativity used in the design!
 You might as well claim that clocks in a sporting game are synchronized based on relativity. That would lack credibility for the same reason.Andy Schlafly 10:28, 14 August 2010 (EDT)
 Ron, the collection of statements above could be construed as easily as disproving relativity rather than proving it. Decades after GPS was launched, observers still struggle to match the data to the theoretical predictions. If some relativistic calculations are included in the synchronization but others are not, then the theory is disproved, not proved by the data. Effects come in various sizes. When calculating the trajectory of the projectile of a handgun, you don't include the Coriolis effect. When the bullets get faster and the range gets bigger, you have to. Does this mean that because only some classical effects are included in the first case, it has disproved classical mechanics? Frankly, that's just absurd.
 As the Theory of Relativity page itself explains, the engineers ignored the complex predictions of relativity. And for obvious reasons: it's easier to synchronize the clocks directly based on communications! At the article of the Theory of Relativity, a quote is used to bolster this claim: the same quote I've shown to be inappropriate as it is talking about other effects. From Ashby's Relativity in the Global Positioning System : It has become common practice not to apply such offsets to Rubidium clocks as these are subject to unpredictable frequency jumps during launch. Instead, after such clocks are placed in orbit their frequencies are measured and the actual frequency corrections needed are incorporated in the clock correction polynomial that accompanies the navigation message. So, yes, the clocks aren't tempered with any longer  but the relativistic correction are incorporated nontheless.
 Note the complete absence of any identification of a particular physicist or mathematician who supposedly provided the theoretical predictions of Relativity for the engineers. That is because there were no such theoretical predictions of Relativity used in the design! No, that's because the any decent physicists can answer the questions what's the expected relative and gravitationl time dilation at the satellite. Einstein, Poincare and some others get the credit for coming up with the necessary formulas, but those who merely apply these formulas aren't mentioned...
 You might as well claim that clocks in a sporting game are synchronized based on relativity. That would lack credibility for the same reason. The clocks of a sporting game aren't accurate enough to be influenced by nonclassical effects. The clocks of the GPS are  and the effects are much greater in the height and at that velocity of a satellite.
 Sorry to keep you waiting for this answer: my ISP at home (109.90.0.0/16) is still rangeblocked (block ID is #63109), so I can contribute to Conservapedia only irregularly. But I don't think that this bothers you, as you may not like my comments anyhow.
 RonLar 09:26, 15 August 2010 (EDT)
 Ron, your edits are mostly talk, and the talk is superficial. I pointed out that no individual has ever been credited, identified or even alluded to for providing the Relativity work that was supposedly included in the GPS design. Obviously that was because there was no such inclusion of Relativity work. But you just duck that compelling point and fail to address it in a meaningful way.
 The argument that GPS includes some (but not all) relativistic adjustments is even weaker, because that implies that GPS disproves rather than proves Relativity.Andy Schlafly 16:36, 15 August 2010 (EDT)
My Greatgrandfather
This is where I came in ... Charles Lane Poor was my greatgrandfather, and he protested the media lovefest celebrating the theory of relativity on the grounds that it was premature. Based on the accuracy of observations at the time (early 20th century), there just wasn't enough proof that Einstein's idea was correct.
I'd like this article to take the scientific path of (1) explaining the theory in layman's terms, (2) describing predictions that the theory makes, e.g., observed star positions during a solar eclipse, and (3) comparing predicted to actual values. Ed Poor ^{Talk} 11:45, 13 August 2010 (EDT)
 That's very interesting about your greatgrandfather, Ed. As to explaining the theory and discussing claims supporting it, other entries like Theory of Relativity do that but can always be improved.Andy Schlafly 10:30, 14 August 2010 (EDT)