Conservapedia - User contributions [en]

Talk:Second Law of Thermodynamics

2016-08-02T18:36:34Z

Bobklein:

{{unprotected|19 March 2007|Tsumetai}}
== Protection and other issues ==

The trend towards protecting articles by users in edit conflicts is worrisome. Furthermore, the protected version is simply wrong. One of the Conservapedia Commandments is that everything should be sourced. I therefore would very much like to know if there is any source for the claim that "he Second Law of Thermodynamics states that the entropy of the universe tends towards a maximum" This statement is wrong at multiple levels- the 2nd Law is about closed systems (or can be stated about open systems with a some tweaking of the consequent), it says nothing about the universe. Furthermore, tending towards a maximum doesn't even mean that the entropy levels can't decrease. For example, the sequence, 1,3,2,5,4,7,6,9,8... tends towards infinity but is not an increasing sequence. [[User:JoshuaZ|JoshuaZ]] 04:05, 4 March 2007 (EST)

:Second law also says nothing about an upper bound to the entropy of a system; the entropy of the Universe could increase without limit, in principle, making the 'maximum' part wrong too.

:To be fair to Philip, the increase of the Universe's entropy ''is'' a tendency, not an absolute. The total entropy of an isolated system can decrease; it's just hugely improbable on the scales we're used to dealing with. Quantum effects can lead to a decrease in entropy; one has to deal with a very small system over short periods of time to actually notice this, however. Arbitrarily large decreases in entropy are also possible, given sufficient time. This is true whether one is discussing the fluctuation theorems of QM, or good old-fashioned classical systems.

:But these are not, strictly speaking, parts of the second law. Second law doesn't say anything about tendency. The rest of physics just says that second law is not absolute. So I don't think using the word 'tends' in the definition is very useful.

:The main problem with the article is, of course, the part about evolution, which as Horace says is just wrong, and painfully so. It's a seductive argument to the layman; after all, entropy is all about order and disorder, and evolution clearly requires the production of order. Right?

:Wrong, of course. The second law of '''thermo'''dynamics is a statement about '''thermodynamic''' quantities; 'order' is not one. One can choose to ''define'' the term 'order' in thermodynamic terms, in which case the statement that the Universe must become, on net, more disordered over time is true, for certain definitions. But the price for that is rejecting one's intuitive understanding of what constitutes 'order' and 'disorder,' and going with the maths. By a thermodynamic definition of order, my hot chocolate is self-organizing as we speak. Therein lies the danger of describing esoteric physics in terms which carry the baggage of their lay definition. Better to stick with entropy, and check one's prejudices at the door.

:Perhaps the simplest way to illustrate this is with a different statement of the second law; the Clausius statement, which reads:

::It is impossible to construct a heat engine which, operating in a cycle, produces no effect other than the transfer of a quantity of heat from a colder to a hotter body.

:Now, precisely which part of evolution violates ''that''? This version of the second law makes it abundantly clear that we're talking about a specific, mathematically rigorous statement about heat flow, not some general philosophical statement about order and chaos. [[User:Tsumetai|Tsumetai]] 07:51, 4 March 2007 (EST)

:Oh, yes, I forgot to weigh in on the page protection issue. Tonya Harding strategy, right?

:A while ago, I [http://www.conservapedia.com/User_talk:Aschlafly#Page_protection_policy suggested to ASchlafly] that a written policy on when page protection should be used, and for how long it should last would be helpful. Anyone else agree? [[User:Tsumetai|Tsumetai]] 07:58, 4 March 2007 (EST)

== The following is incorrect ==

From the article:

"It is impossible for the total entropy of an isolated system to decrease, therefore the universe is becoming more and more disordered. In this way the Second Law of Thermodynamics disproves evolution."

The first sentence is true, but the second is false. Evolution does not cause the total entropy in the universe to decrease, only local variations. By analogy, a fridge does not cool the universe, only a small part of it at the expense of the rest. Please correct this clear error to avoid the increasing levels of criticisms being levelled at this wiki. [[User:Nematocyte|Nematocyte]] 07:45, 5 March 2007 (EST)

:To add my thoughts on this: there are two errors in this article. First, the second law ''only'' applies to ''isolated'' systems, not to systems that are merely closed, let alone open. Then it becomes clear that the "disproving" of evolution by referring to the second law is severely flawed. There is nothing against a local decrease in entropy, as long as it is balanced by at least as large an increase elsewhere. Moreover, the assumption that evolution is directly linked to a decrease in thermodynamic entropy is not immediately obvious. I agree with Nematocyte that in its present state, this article will just serve to invite more criticism. [[User:PaulB|PaulB]] 09:16, 13 March 2007 (EDT)

::Strictly speaking, second law applies to all systems; for instance, consider the Clausius statement, which I posted up the page. No mention of an isolated system there. [[User:Tsumetai|Tsumetai]] 12:01, 13 March 2007 (EDT)

:::That not what my stat.mech. text says ;-). Let's put it this way: the ''entropy'' formulation only applies to isolated systems. In fact, I think that the heat engine in the Clausius formulation should itself be taken as isolated. If we allow it to be (thermally or otherwise) coupled to anything else than a hot and a cold "temperature bath", I think we could make the heat flow up the temperature gradient, at the expense of course of something happening outside the engine. Of course, these thermal reservoirs are abstractions, etc. etc. Anyway, here as well, either we should take the system (engine) as isolated, or we should take it as the entire universe. Both cases are not going to help disprove evolution at any rate. [[User:PaulB|PaulB]] 12:24, 13 March 2007 (EDT)

::::I think even the entropy formulation will work with open systems, so long as one takes care to quantify the entropy flow through the boundary. The requirement then becomes that entropy decrease within the boundary is no greater than the net entropy flow out of the system through the boundary. [[User:Tsumetai|Tsumetai]] 12:37, 13 March 2007 (EDT)

:::::I think it's effectively the same as looking at an isolated system made out of two parts, inside and outside, and applying the second law to the total system. But what you propose should indeed work. I hadn't thought of doing it that way. [[User:PaulB|PaulB]] 13:04, 13 March 2007 (EDT)

::::::Absolutely; you can always expand the boundary of an open system to obtain an isolated one, in principle. But it's very useful to be able to work with open systems, if the boundary terms can be computed, since it allows one to ignore entropy generation in the environment. [[User:Tsumetai|Tsumetai]] 13:08, 13 March 2007 (EDT)

== Time to unprotect ==

OK, it's been over a week now, and no one has attempted to defend the inclusion of such rubbish. Might we have the article unprotected so that those of us who actually understand elementary thermodynamics can fix it? [[User:Tsumetai|Tsumetai]] 07:50, 12 March 2007 (EDT)
:Nothing doing sir, the numbskulls are the experts. Who said Sri Lanka became independent in the 1970s, none other than the owner of this site! [[User:Zaheerabbas|Zaheerabbas]] 02:12, 15 March 2007 (EDT)

== Ressurection a violation? ==

I think we should add a section about the resurrection of Jesus and that it "technically" violates the second law of thermodynamics, but that since it was a miracle, it does not need to adhere to the second law. Thoughts?
:...*blinks* Are there sources that are actually saying that? *honestly curious* --[[User:Sid 3050|Sid 3050]]

:I think the latter part is pretty obvious, and negates the need for the former. [[User:Tsumetai|Tsumetai]] 11:58, 13 March 2007 (EDT)

:: Gonna back Tsumetai up on this one. Also, it's shocking and appalling that this article is protected while containing such tripe in the content of it.--[[User:AmesG|AmesG]] 12:00, 13 March 2007 (EDT)

:::Not to mention the fact that in the ten days since criticisms were first raised, no one who supports the article in its current state has bothered to defend it.[[User:Tsumetai|Tsumetai]] 12:03, 13 March 2007 (EDT)

::::Agreed. I'll leave a message on the protecting admin's Talk page, maybe it'll help. Talking on here doesn't seem to have any impact. =/ --[[User:Sid 3050|Sid 3050]] 12:05, 13 March 2007 (EDT)

Oh, of course. Many intellectuals here! Long live the stone age numbskull army!!! [[User:Zaheerabbas|Zaheerabbas]] 02:11, 15 March 2007 (EDT)

:::::AmesG, aren't you the person who owns and wrote for the blog'' Submitted to a Candid World''. Many people would find it shocking and appalling that several of your close friends are engaging in [[polyamory]] (See: [[Atheist leaders and immoral relationships]]). "Do not be deceived: 'Bad company corrupts good morals.'" - the Apostle Paul.

:::::By the way, I noticed you stopped writing for your blog in late 2012. That saved you from writing about liberalism/progressivism/Darwinism having a very bad year in 2013.[http://questionevolution.blogspot.com/2014/01/the-pro-evolution-news-website-daily.html] I wouldn't start up your blog again in 2014. :) [[User:Conservative|Conservative]] 21:36, 8 February 2014 (EST)

==This law and evolution==

Timothy Wallace wrote:

*Evolutionist theory faces a problem in the second law, since the law is plainly understood to indicate (as does empirical observation) that things tend towards disorder, simplicity, randomness, and disorganization, while the theory insists that precisely the opposite has been taking place since the universe began (assuming it had a beginning).

*Beginning with the “Big Bang” and the self-formation and expansion of space and matter, the evolutionist scenario declares that every structure, system, and relationship—down to every atom, molecule, and beyond—is the result of a loosely-defined, spontaneous self-assembly process of increasing organization and complexity, and a direct contradiction (i.e., theorized violation) of the second law. [http://www.trueorigin.org/steiger.asp]

Comments? --[[User:Ed Poor|Ed Poor]] 16:24, 3 April 2007 (EDT)

:Its a considerable misunderstanding. Points:
::*The second law refers to the flow of heat, it is unclear how exactly that translates into "disorder" and "order" when applied to something like life.
::*The second law refers to closed systems, open systems are a much more complex processes and the "law" does not apply cleanly here. Life and Earth are open systems.
::*Evolution is essentially a favored random walk, these systems are able to produce violations of "disorder" all the time. For example any [[Monte Carlo method]] algorithm demonstrates this beautifully, you can reach local "maximum" and avoid "minimums" by using evolutionary algorithms and many other variations on the theme.
::*Complexity theory and Self-organizing systems also routinely violate the maxim that order can not be created from disorder. The sorts of things needed to produce an SOS or complex system are just the kinds of things we find in life.

:Life is not a good place to be trying to appeal a mathematical description of heat. [[User:Etaroced|Etaroced]] 16:31, 3 April 2007 (EDT)

Also, applying the second law to evolution reflects a plain misunderstanding. Beings today are not "more perfect" than those that came before. Greater "perfection" may be a violation of the idea of entropy. However, evolved organisms are not more "perfect" than earlier organisms, since Darwin's point is that there is no biological level of "perfection." Evolved organisms don't violate entropy anymore than ''older'' organisms (a 20 year old relative to a 10 year old) do!-'''AmesG'''[http://www.conservapedia.com/User_talk:AmesG yo!] 17:02, 3 April 2007 (EDT)

:Ames, you're disagreeing with one of the best Renaissance minds, [[William Shakespeare]]:
:*"What a piece of work is man! how noble in reason! how infinite in faculty! in form and moving how express and admirable! in action how like an angel! in apprehension how like a god! the beauty of the world, the paragon of animals! ". - ([[Hamlet]], Act II, Scene II).

:Now, how does Evolution explain man evolving through an unguided process from one-celled organisms? --[[User:Ed Poor|Ed Poor]] 17:56, 3 April 2007 (EDT)

Shakespeare is not a scientist. Science and art are different. I realize they may not be for creationists, which is shocking and kind of funny. But they are different in the real world.-'''AmesG'''[http://www.conservapedia.com/User_talk:AmesG yo!] 18:15, 3 April 2007 (EDT)

== Discuss here before deleting information ==

OK. I deleted the "three types of systems the Second Law can apply to," because it only applies to closed systems. I also deleted the claim that it disproves evolution and relativity, because it doesn't. Evolution is nonsense, but isn't disproved by the Second Law because EARTH IS NOT A CLOSED SYSTEM. As for relativity, the Second Law has no connection to it at all. This article is about one of the key laws of science, and if it's blatant nonsense the credibility of the whole site suffers. --[[User:DonauKind|DonauKind]] 23:47, 16 February 2012 (EST)

:There is no such thing as a perfectly closed system, so your attempt to limit the important Second Law to closed systems is misplaced. The Second Law is far more meaningful than that.--[[User:Aschlafly|Andy Schlafly]] 23:49, 16 February 2012 (EST)
::Irrelevant. The Second Law only applies to closed systems. If a system isn't closed then energy can be added, thus reducing entropy. That is the MEANING of the Second Law. --[[User:DonauKind|DonauKind]] 23:52, 16 February 2012 (EST)
:::OK, give me a statement of the Second Law that works in an open system. --[[User:DonauKind|DonauKind]] 23:53, 16 February 2012 (EST)

::::Your approach would appear to limit the Second Law to something that doesn't exist. It's more meaningful than that. Its entry here explains its insight.--[[User:Aschlafly|Andy Schlafly]] 23:58, 16 February 2012 (EST)
:::::No ''ideal gas'' exists either, yet the Ideal Gas Law only applies to this non-existent hypothetical gas. --[[User:JoshuaB|JoshuaB]] 00:00, 17 February 2012 (EST)
::::::The Second Law isn't an ''insight''. It's a description of energy available for work in a closed system. It doesn't have some deep ''meaning'' that can be applied to whatever you like. The Second Law is an accurate description of entropy (note: ''entropy'', not ''disorder'') in a closed system, and if ever a closed system is found then rest assured that overall entropy will not decrease inside it. But to say it disproves evolution is nonsense, especially when you yourself admit that Earth is NOT a closed system! --[[User:DonauKind|DonauKind]] 00:05, 17 February 2012 (EST)
:::::::And your point is ....? Attempts to limit the Ideal Gas Law to perfectly ideal gases would be misguided also.--[[User:Aschlafly|Andy Schlafly]] 00:02, 17 February 2012 (EST)
::::::::Uh what? How can the Ideal Gas law be applied to something that isn't an ideal gas? --[[User:DonauKind|DonauKind]] 00:06, 17 February 2012 (EST)

:::::::::The Ideal Gas Law has insights that extend beyond ideal gases. Ditto for the Second Law with respect to closed systems.--[[User:Aschlafly|Andy Schlafly]] 00:10, 17 February 2012 (EST)
::::::::::OK then, tell me an "insight" that the Second Law can bring to a system that is ''not'' closed. --[[User:DonauKind|DonauKind]] 00:14, 17 February 2012 (EST)
:::::::::::The entry explains this well.--[[User:Aschlafly|Andy Schlafly]] 00:25, 17 February 2012 (EST)
After going back and re-reading the article a few times, I think I know where the confusion lies with some editors. It appears that the article is conflating the thermal definition of entropy with the information theory definition of entropy. This conflation allows the topic of "disorder" to arise. Which has absolutely nothing to do with thermaldynamics. The basic definition of thermal entropy is simply a measure of energy that is unusable to perform work in a system. How a law that breaks down in layman's terms to: "heat won't travel from a cooler body to a hotter body without an additional input of energy" or "no process is possible in which the sole result is the transfer of energy from a cooler to a hotter body" can be used to "disprove" evolution or relativity escapes me. --[[User:JoshuaB|JoshuaB]] 02:19, 17 February 2012 (EST)

:Perhaps [[Talk:Counterexamples_to_an_Old_Earth#Major earthquakes are doubling every 40 years? |this discussion]] sheds some light on Aschlafly's misconception of the 2nd law. [[User:AugustO|AugustO]] 08:27, 17 February 2012 (EST)

The thing is, is that there is a link between thermodynamics and disorder. This is the tour de force result of statistical thermodynamics vs classical thermodynamics - i.e. that the macroscopic quantity which we can measure called "entropy" is related to the number of possible microstates the system can explore. As has been correctly pointed out, the problems start when we directly equate this with "information", or entropy as defined in information theory i.e. "Shannon entropy". This is an analogous concept, based on the fundamental information content of a system. But there isn't an equivalence between information-theoretic entropy and thermodynamic entropy. In the actual physical world, there is no need to directly connect the quantities of "disorder" and "information". This, in part, along with the more important facts that all these things apply to closed systems and the Earth is not a closed system, means that any argument based on how "entropy" disproves evolution due to some information argument is bogus. [[User:DanPW]]

== Second Law and Evolution ==

I have removed the statement about the Second Law disproving evolution. It is pretty obvious that Mr. Schlafly does not have a correct understanding of the Second Law of Thermodynamics, and with all due respect, his inaccurate contributions to this article must be removed. From what I understand, Mr. Schlafly's reasoning is based on his belief that evolution is "disorder changing by itself into a more ordered state," which is not true. This has been explained in most of the above sections on this talk page, so I will not rehash arguments. I just expect a better explanation if the article is to be changed back to saying that the Second Law does disprove evolution.

I suspect that the Second Law does not disprove the theory of relativity either, but I have not looked into the arguments for or against this claim so I am leaving this in the article.

--[[User:Randall7|Randall7]] 01:31, 9 June 2012 (EDT)

:Your edit was reverted because the Second Law does ban disorder becoming more orderly, just as it bans heat spontaneously flowing to hotter locations. The theory of evolution is based on the contrary claim that random (disordered) mutations create greater order.--[[User:Aschlafly|Andy Schlafly]] 01:35, 9 June 2012 (EDT)

::In thermodynamic terms, the concept of "order" is not usually applied to the Second Law except in rigorous terms of "molecular ordering," which you have not made a clear connection to the theory of evolution. Also, you are ignoring the fact that the Second Law only applies to a closed system (and the Earth is not a closed system), which has been explained many times above. --[[User:Randall7|Randall7]] 02:02, 9 June 2012 (EDT)
:::And just what is this "closed system" that the 2nd Law here has to be restricted to? [[User:Karajou|Karajou]] 02:16, 9 June 2012 (EDT)
::::The standard thermodynamic definition of a closed system is one that cannot exchange mass with its surroundings. But in the context of Mr. Schlafly's assertions about the Second Law and evolution, his misunderstanding about the thermodynamic concept of order is even more significant. --[[User:Randall7|Randall7]] 02:38, 9 June 2012 (EDT)
:::::And why can't that happen on earth? [[User:Karajou|Karajou]] 02:42, 9 June 2012 (EDT)
::::::The Earth is actually pretty close to being a closed system, but obviously it is possible for matter to leave or enter the Earth's atmosphere. But the main problem with the Second Law being used as an argument against evolution is the claim that evolution requires "disorder changing by itself into a more ordered state" (this was most recently stated on [[Talk:Main_Page]]) and the idea that "disorder" (however that is defined) is always increasing. Mr. Schlafly has not provided any substantial evidence or explanation for this, and that is why I removed the claim about evolution from the article. --[[User:Randall7|Randall7]] 03:05, 9 June 2012 (EDT)
:::::::You and everyone else above kept right on saying that earth is a closed system; now you're changing it to "''pretty close'' to being a closed system"? Have you ever put together logs in a fireplace and watched them burn? Which was more complex: the logs assembled, or the ashes several hours later? [[User:Karajou|Karajou]] 03:10, 9 June 2012 (EDT)
::::::::As I stated in my most recent 2 comments, the fact that the Earth is not a closed system is not as relevant to Mr. Schlafly's Second Law vs. evolution argument as is his concept of order. (And I do believe much of the discussion above on this talk page is not well focused.) I am not seeing the connection between your burning log example and evolution. Please elaborate. --[[User:Randall7|Randall7]] 03:27, 9 June 2012 (EDT)
:::::::::Now it's back to being a closed system? Did "pretty close" just disappear? Answer the question about the logs. [[User:Karajou|Karajou]] 03:45, 9 June 2012 (EDT)
::::::::::The logs are more complex; in the act of burning them, matter goes from an ordered state to a more disordered one, and energy is given off. Are you going to elaborate on how this relates to evolution as Randall asked? [[User:CWest|CWest]] 08:28, 9 June 2012 (EDT)
:::::::::::That is correct. Now explain why the 2nd Law only applies to a closed system. Those are your words, Randall7, and I expect you to answer it...not CWest. [[User:Karajou|Karajou]] 12:41, 9 June 2012 (EDT)

::::::::::::The two statements that make up the foundation of the Second Law of Thermodynamics - the Kelvin-Planck statement and the Clausius statement - both describe systems that exchange heat and/or work with their surroundings, but not mass. But as I said before, my concern is less about the closed system argument and more about the abuse of the concept of "order" to claim that the Second Law disproves evolution. --[[User:Randall7|Randall7]] 20:37, 9 June 2012 (EDT)

Several more questions, Mr. Randal7, because now you're drifting away from the "closed" system here.
:1. Is iron more complex than rust? And when iron does rust, does it constitute an improvement, or a breakdown?
:2. What happens to boiling water when you turn off the stove? Does it stay the same, or does it get cooler?
:3. Is CWest's statement above correct, in that ''"matter goes from an ordered state to a more disordered one"''? Does that statement apply only to the fireplace? Could it also apply to a freshly-cleaned living room, just prior to adding three eight-year-old spoiled brats with pop guns and a baby sitter unable to control the outcome? [[User:Karajou|Karajou]] 03:25, 10 June 2012 (EDT)

::I feel like this discussion is becoming less productive and more of a waste of time, but I'll answer the questions because I want to see how you relate them to the Second Law of Thermodynamics disproving evolution. (I so far have failed to see the connection.)
::#Iron is generally less complex than rust. (Although "complex" is not a very precise term.) Iron is a single element, whereas rust can be a number of iron oxide or iron hydroxide compounds. Iron is usually much more homogeneous than rust. When iron rusts it is a chemical and thermodynamic improvement - it would not happen spontaneously if it were not energetically favorable. In practical terms, rusting is not an improvement because pure iron is more useful for structural or electrical applications, but pure iron does not usually stay pure for long because of its propensity to oxidate. This is why iron alloys are much more common.
::#When the stove is turned off, boiling water cools as heat is transferred from the water to its cooler surroundings. Entropy is generated from this heat transfer.
::#In the burning log example, it is true that "matter goes from an ordered state to a more disordered one," and there are plenty of other examples where this statement is true. There are also many instances where matter goes from a disordered state to a more ordered one, such as water freezing or magnetization. But in theses cases of matter becoming more ordered, net entropy of the matter and its surroundings will still never decrease. The statement could also apply to a room of spoiled brats, but in this case the term "order" is no longer being used in a thermodynamic or chemical sense.
::--[[User:Randall7|Randall7]] 15:27, 10 June 2012 (EDT)

===My answers to Randall7===
With regards to the iron, you are wrong. Rust is a breakdown; it is a disintegration of the iron itself. The rust can be stopped; the iron can be prevented from rusting further, but rust in and of itself can never be restored into iron. It goes one-way only. Likewise the water on the stove; take away the heat which makes the water boil, and the water temperature will drop to the lowest level possible, which one can call "room temperature". Likewise the fireplace logs, likewise the living room. One-way only. Complex to simple, order to disorder. It never, ever happens in reverse.

The 2nd Law of thermodynamics is the same way. You can restrict the 2nd Law to heating and/or energy concepts all you want, but the very core of this law is the same thing cited above: order ''always'' goes to disorder; complex ''always'' goes to simple. The 2nd Law may be about heat, but turn off the fire and what do you get? Water cooling down, heat cooling and dissipating, complex to simple, order to disorder. The fireplace scene has the heat, but the logs always end up as ashes. The ashes ''never'' turn back into logs.

And the final answer to the question "what does this have to do with evolution?". It was evolutionists who stated we should ''accept'' their scenario as to how life came to be: ''simple'' organisms ''evolved'' into more and more ''complex'' ones over time. ''Simple'' to ''complex''; ''disorder'' to ''order''. When making scientific investigations the very first step of the [[scientific method]] that must be followed is ''observation''; a scientist has to ''observe'' what is going on, and every single minute of every day scientists and layman alike are observing the 2nd Law in action; no one can get away from it. ''Observation'' proves complex always goes to simple; ''observation'' proves order always goes to disorder. ''Observation'', scientific or not, ''confirms'' the validity of the 2nd Law. The examples I posted above - the fireplace, the iron, the living room, the stove top - are perfect examples of the 2nd Law in action, closed system or not. It's impossible to go into reverse.

That is why we're going to post the impossibility of evolution on this website, ''vis-a-vis'' the 2nd Law. Case closed. [[User:Karajou|Karajou]] 01:14, 12 June 2012 (EDT)

:You make a good point that irreversibility is an unavoidable consequence of the Second Law. There is no such thing as a truly reversible process and all processes generate entropy. But your claim that "order ''always'' goes to disorder; complex ''always'' goes to simple" is absurd. More ordered/"complex" materials can be formed through [[work]]. ("Simple" and "complex" do not have rigorous thermodynamic definitions, by the way.) Otherwise every single ordered object would have to have existed existed exactly as it is since the beginning of time, or have existed in a larger or more ordered form. Organisms gain energy - the capacity do do work - by eating, respiring, photosynthesizing, or otherwise absorbing energy from their surroundings. This allows them to become more ordered or more "complex," but this is not in violation of the the Second Law because during their processes of converting energy and exerting work, net entropy is generated. --[[User:Randall7|Randall7]] 23:57, 12 June 2012 (EDT)
::Randall7, these organisms do take in food, use it as energy, and continue on with their lives, but their status as organisms remains unchanged until they ''cease the work''; when that happens they wither away and die; they decompose, they turn to dust. Complex to simple, order to disorder. [[User:Karajou|Karajou]] 00:03, 13 June 2012 (EDT)
:::I suppose that is true, but you did not refute anything I just said. --[[User:Randall7|Randall7]] 00:11, 13 June 2012 (EDT)
::::If you can sit there and "suppose it is true", then I did refute everything you just said. [[User:Karajou|Karajou]] 02:00, 13 June 2012 (EDT)
:::::You seem to focus very much on the "withering away" part of the cycle. What about the observations of growing crystals, growing plants, growing children? Those processes do go from simple to complex - whether the complex states can exist forever (they can't) is not relevant, what's important is that these processes occur naturally. And they're not in contradiction to the second law either; e.g. in the case of crystal growth the evaporating water occupies a larger volume afterwards and hence has increased entropy. --[[User:FrederickT3|FrederickT3]] 02:35, 13 June 2012 (EDT)
::::::Frederick, "growing" crystals do not constitute life. Grown humans and plants are still the same species; I don't see children take on a totally different form when growing up into completely-normal adult human beings, and I don't see an acorn grow into anything other than an oak. You don't have a valid argument. [[User:Karajou|Karajou]] 22:50, 13 June 2012 (EDT)

::::::Oh, Frederick, don't forget to tell the viewing audience here that your "crystal" things are actually water-soluable; they dissolve in water, and reappear back into crystals when the water evaporates. Nothing to do with entropy, the 2nd Law, or the antics of trolling via China. [[User:Karajou|Karajou]] 23:08, 13 June 2012 (EDT)

:::::::The physical processes that I mentioned are exactly the processes to which the Second Law applies. Growth of crystals is a very simple process that can be described quantitatively in much detail; it's a toy model for the growth of living beings (not evolution!). I used it to clarify the relationship between entropy and order: A crystal is an ordered state that arises naturally from the unordered state of a solution. This process is compatible with the Second Law, because if you take the entropy of the evaporated water into account, the entropy of the full system increases. Of course the crystal is water-soluble, and the dissolution is even the simpler process, because the increased entropy of the crystal's particles alone is sufficient to fulfil the Second Law. What it shows is that order can arise from disorder in full compliance with the Second Law. Which is just as well, because otherwise we wouldn't be here. God created the Second Law, and it allows His creation to grow and prosper. Now, evolution is not a thermodynamical process, the Second Law has no relevance to it and it is not a good argument against it. My point is that if we argue against evolution, we need the right arguments - forwarding wrong or irrelevant arguments, making up or arbitrarily changing the meaning of words will not help the cause. --[[User:FrederickT3|FrederickT3]] 02:45, 14 June 2012 (EDT)
::::::::Now, I can concede your argument about the crystals, but only to a certain extent. It cannot be a model for living organisms because the crystals are lifeless. Evolution is not a thermodynamic process, but as I said above, the core point of the 2nd Law - and this is confirmed every day by direct observation - is that complex always goes to simple. Period. The explanations by scientists - and I stress the fact that they are nothing more than explanations - concerning evolution is that life came from ''simple'' cells which evolved into more and more complex life forms. It is on that context which violates the 2nd Law. [[User:Karajou|Karajou]] 02:56, 14 June 2012 (EDT)

===Discussion about order/disorder===

:Andy, how do you explain the growth of a crystal (an ordered arrangement of ions) from a solution (a disordered arrangement), if "the Second Law does ban disorder becoming more orderly", as you say? --[[User:FrederickT3|FrederickT3]] 03:39, 9 June 2012 (EDT)

::Order is not really increasing when a crystal grows in a solution, or when water changes its phase and becomes ice. If the crystal or ice is melted again, then one back to where it started. This is no increase in order.--[[User:Aschlafly|Andy Schlafly]] 19:53, 9 June 2012 (EDT)

:::Mr. Schlafly, it is clear that your concept of order differs from the thermodynamic concept of order. When water freezes, its entropy decreases and when ice melts, its entropy increases, but during these processes the entropy of the water's surroundings also increase/decrease (such that total net change in entropy is never negative, and in reality is net positive). I would like to hear an explanation of how changes in "order" during evolution relate to the actual Second Law of Thermodynamics. --[[User:Randall7|Randall7]] 20:37, 9 June 2012 (EDT)

::::: Mr. Schlafly, are you honestly suggesting there is no change in entropy when water melts? --[[User:MatthewQ|MatthewQ]] 01:57, 10 June 2012 (EDT)

:::::: That's a question about semantics - the answer depends entirely on how one decides to define "entropy".--[[User:Aschlafly|Andy Schlafly]] 01:01, 13 June 2012 (EDT)
:::::::Entropy has a very clear definition which you can look up in any textbook on thermodynamics. According to that definition, the entropy changes (increases) when water/ice melts. And of course a clear definition is prerequisite to being able to formulate and understand the second law properly in the first place. --[[User:FrederickT3|FrederickT3]] 02:35, 13 June 2012 (EDT)

:::::::: I'm aware of two definitions of entropy in the context of thermodynamics. The statistical entropy, S, of a system is defined as <math>S = -k_{B}\sum_{j}P_{j}\log\left(P_{j}\right)</math> where <math>k_{B}</math> is Boltzmann's constant and <math>P_j</math> is the probability of the system to be in the ''i''th microstate (this reduces to <math>S = k_{B} \log \Omega</math> where <math>\Omega</math> when all the microstates are equiprobable and <math>\Omega</math> is the number of microstates). Alternatively, one has the thermodynamic definition of entropy <math>dS = \frac{\delta Q}{T} \!</math> where <math>\delta Q</math> in an infinitesimal change in heat and <math>T</math> is the temperature of the system. However, Boltzmann showed this was equivalent to the statistical entropy, so these two definitions are really just two different descriptions of the same thing. In any case, the second law of thermodynamics is talking about the statistical/thermodynamic entropy. It clearly changes when ice melts. If you have your own definition of entropy Mr. Schlafly that's fine, although it's confusing to use a word that already has a clear meaning and then use your particular definition in the talk page of the second law of thermodynamics. However, people here are using 'entropy' as its understood by actual scientists. What is your definition? --[[User:MatthewQ|MatthewQ]] 22:00, 13 June 2012 (EDT)

::::::::: I don't have any reason to doubt your formulas for entropy, and thanks for posting them. But for the purposes of the Second Law the dictionary definition for entropy works fine: a measure of disorder in a system. It's always increasing unless there is some kind of intelligent intervention, like [[God]] creating the world. Perhaps [[faith]] can operate to reduce entropy. Otherwise, without intervention or faith, disorder is always increasing, and the Second Law is an expressing of that logical truth. Otherwise a [[perpetual motion machine]] would be possible, and it is isn't.

:::::::::: Considering we're talking about physics the definition used by physicists should take precedent. But fine, often "a measure of disorder in a system" is used to define entropy for the layman. However, under this definition the entropy ''still'' increases when ice melts since the structure becomes less ordered. --[[User:MatthewQ|MatthewQ]] 23:15, 13 June 2012 (EDT)

::::::::::: The melting of ice is simply a phase change to reflect the temperature. Refreeze the water and it's back to where it started. Observing water rather than ice is logically the same as observing the temperature on a nearby thermometer. This doesn't illustrate the basic truth that a [[perpetual motion machine]] is impossible. Do you think a perpetual motion machine -- one that that moves forever in a consistent manner without intelligent intervention -- may be possible?--[[User:Aschlafly|Andy Schlafly]] 23:34, 13 June 2012 (EDT)

While this isn't really my area a scientific expertise, there are a few things I'd like to say.

1. Perhaps a "layman's dictionary" definition of entropy could get away with just saying it's a measure of disorder, but that really isn't good enough for a web site that prides itself on its articles on science and math. Look at the [[Banach-Tarski Paradox]] for an example of the sophistication we have. By the way, my Webster's New Twentieth Century (yeah, it's out of date) Dictionary is a layman's dictionary, albeit unabridged. It gives its first definition as "a thermodynamic measure of the amount of energy unavailable for work in a system undergoing change." In any case, if you use the hand-wavy "disorder" definition, you can't then talk about thermodynamics and the fact that entropy increases. You'd have to explain how the act of cleaning one's room, or sorting a deck of cards, doesn't violate the second law. Of course we know why it doesn't, but we can't explain that without at least some thermodynamic terms. One needs to understand the connection between decks of cards naturally becoming ordered when we shuffle them, and heat spontaneously flowing from a colder object to a warmer one. It's not simple.

2. The connection between iron and rust, and the connection between wood and ashes, is not one of "disintegration". Iron does not disintegrate when it rusts. (In fact, because of its place on the nuclear binding energy graph, iron is the most indestructible element that there is.) Iron combines with oxygen. That is a chemical reaction, and it can be reversed, though, unfortunately, it doesn't naturally reverse itself when rusty objects are left outside. An understanding of how chemical reactions work, and how they can be reversed, is the result of the hundreds of years of research, first by the alchemists, followed by the more careful research of people like Priestley, Lavoisier, Dalton, Scheele, Gay-Lussac, and many others.

3. The oxidation of wood to make ash (it's more complicated than that, actually) is another chemical reaction, and it is also reversible. Trees burn down all the time. The ash goes into the ground, and, eventually, the forest grows back. The cycle repeats again and again, all over the world. The change in entropy between water and ice also goes in cycles, every year. When water freezes in winter, the entropy goes down. When the ice thaws, it goes up. Repeatedly. The heat budget of the Sun-Earth system (warm in summer, cold in winter) is easily enough to drive the entropy of all of these reactions. The same thing is true of salts going between solution (disorder, and high entropy) and crystals (order, and low entropy.) The energy needed to make these reactions go back and forth is easily available, from, say, a Bunsen burner. Or just leaving something out to dry.

4. The same sort of thing happens in the field of biology. The transition from a bunch of amino acids (disordered system) into, say, a kidney (ordered system) can take place easily, because the necessary energy is available. By the way, the force involved in turning amino acids into kidneys is related to the force turning a salt solution into a crystal. The ribosomes that put an amino acid into place are acting under electrostatic forces, albeit in a much more complex pattern than a positive Sodium ion falling into place next to a negative Chlorine ion.

5. In discussing the second law, one must keep in mind that there are two kinds of hypothetical "perpetual motion machines." A "perpetual motion machine of the first kind" violates the first law of thermodynamics, that is, conservation of energy. It is what people usually think of when they talk about perpetual motion machines. A "perpetual motion machine of the second kind" violates the second law of thermodynamics. It makes a cold thing colder and a hot thing hotter, while conserving energy. That is, it moves heat "uphill" without any external energy source.

6. Biological evolution is, of course, more complicated than all that. Whether the second law makes biological evolution impossible is a complicated question, and I have to defer to scientists who have studied this in much more detail than I.

[[User:JudyJ|JudyJ]] 00:51, 14 June 2012 (EDT)

:Thank you, JudyJ, for your context and your perspective. One thing I was a little confused about was the heat budget of the Sun-Earth system "driving" the entropy of the reactions you discussed. But I think your point about materials going back and forth between high- and low-entropy states is a good one. This is absolutely possible as long as the total entropy of the materials and their surroundings always increases (so this is not true reversibility in a thermodynamic sense). Even ashes can go back to logs, but this requires substantial work, changes at the atomic level, and usually many processes, all generating net entropy.

:Mr. Schlafly, no one here is seriously arguing that perpetual motion machines are possible, so please stop bringing them up as a distraction. Instead, please address the substantial criticism of your position: Entropy/disorder is not always increasing everywhere all the time. Local decreases in entropy can occur without violating the Second Law. Simply saying that entropy or disorder is always increasing cannot be used as an argument against evolution because it is not always true - it is true for the universe as a whole, but not for every single thing in the universe. --[[User:Randall7|Randall7]] 21:02, 14 June 2012 (EDT)

::Nearly all processes, with a few exceptions that are easily explained (such as phase changes), are thermodynamically irreversible and thus generate an increase in disorder or entropy. Only intelligent intervention can preserve order. Do you agree with that? If so, theories that defy this Law are no more plausible than suggesting that heat can flow spontaneously to a warmer location.

::The impossibility of a [[perpetual motion machine]] that keeps going with constant energy illustrates this. But notice how some deny, or won't admit, its impossibility. If you agree this type of [[perpetual motion machine]] is impossible, then why do you think it is impossible, if not due to the Second Law?--[[User:Aschlafly|Andy Schlafly]] 00:33, 15 June 2012 (EDT)

:::Why do you ignore half of what I'm trying to say? I do agree with almost everything you just wrote (although even phase changes are thermodynamically irreversible because they require heat transfer or some other irreversible factor). But that doesn't change the fact that individual objects/materials/subsystems can have decreases in entropy (increases in "order") even though overall net entropy increases. That is why you can't use the argument "everything becomes more disordered" as an argument against evolution. --[[User:Randall7|Randall7]] 20:37, 15 June 2012 (EDT)

::::I repeatedly addressed the arguments, yet I don't recall any response anyone explaining '''''why''''' a [[perpetual motion machine]] is impossible. The reason is this: disorder is always increasing, except when there is intelligent intervention. This is the essence of the Second Law, and explains the many formulations, such as heat always flowing spontaneously to colder locations.--[[User:Aschlafly|Andy Schlafly]] 00:23, 12 July 2012 (EDT)

:::::Even if we ignore the unfalsifiable assertion about intelligent intervention, that is not the essence of the Second Law. Order can and does increase all the time without violating the Second Law. You know this, but you choose to ignore it for the purpose of making an ideological argument about another scientific theory that you have a history of misrepresenting.

:::::I can see you've made up your mind about what Conservapedia's version of the Second Law is, so I will not argue further. --[[User:Randall7|Randall7]] 19:20, 13 July 2012 (EDT)

===This discussion has been dormant for a while. If no refutation of evolution is presented in the next few days based on a proper application of the Second Law of Thermodynamics, I will remove the part of the article in question.===

--[[User:Randall7|Randall7]] 13:56, 4 July 2012 (EDT)
:Since it's been a while since any new argument has been presented, I removed the claim that the Second Law disproves evolution from the article. The above discussion makes it clear that this claim was being based on an incorrect understanding of the Second Law. Please do not re-add this claim unless you make a supporting argument on this talk page based on what the law actually says. --[[User:Randall7|Randall7]] 19:03, 11 July 2012 (EDT)

::Attempts to limit the insight of the Second Law are misplaced. A correct understanding of it does not try to limit its implications.--[[User:Aschlafly|Andy Schlafly]] 00:24, 12 July 2012 (EDT)

== Zero sum game ==Liberal abuse of the second law of thermodynamics== ==

A zero sum game is a mathematical game whereby the gains of one player is directly matched by the losses of another. This section mentions 'zero sum game' and then goes on to state something about increasing the gains of everyone.

What is discussed might be more accurately considered a type of Pareto effiency. A pareto improvement is one which causes no loss to other people. It has nothing to do with zero sum games. None of this has much to do with the 2nd law of thermodynamics, as far as I can infer. [[User:LucoDaw|LucoDaw]] 00:22, 6 July 2012 (EDT)

:The section is correct in stating that free-market economics is ''not'' a zero-sum game, and that the Second Law of Thermodynamics is not a great analogy for natural resource economics. However, that does not necessarily mean that there are no limits to economic growth. Also, there is no evidence given that "it has become common in recent years for environmentalists to claim that the second law of thermodynamics implies limits to economic growth." (There is no indication that this is a widespread belief.) --[[User:Randall7|Randall7]] 21:33, 6 July 2012 (EDT)

== Perpetual Motion Machine ==

Mr. Schlafly recently reverted a change I made explaining the impossibility of a perpetual motion machine. I believe saying that "entropy will inevitably reduce the amount of energy available to keep the machine in motion" is a more precise explanation than saying that "entropy will inevitably derail the machine." The reason given for the reversion is "energy issues are not the only reason a perpetual motion machine is impossible." So I am wondering, what are the other issues? --[[User:Randall7|Randall7]] 11:06, 29 September 2012 (EDT)
:Mr. Schlafly, for many days I got no response from you here or on your talk page, so I decided to make some further improvements to the explanation of the impossibility of a perpetual motion machine. Now I see that these changes have been overwritten within hours. Setting aside the other changes you have made to the article, I fail to see how the current sentence about a perpetual motion machine is an improvement. It is so vague and imprecisely worded that it is almost useless in an encyclopedia article.
:*Why do you insist on using the word "derail" instead of describing what actually happens from a thermodynamic standpoint? (Increasing entropy decreases energy available to keep the machine in motion.)
:*The phrase "even if energy remains constant" is too vague. What energy? I believe you are referring to the total energy of the machine's system, implying that the system is isolated and the First Law of Thermodynamics holds true, but this is not very clear. Keep in mind that true hypothetical perpetual motion machines are isolated systems by definition.
:--[[User:Randall7|Randall7]] 16:52, 11 October 2012 (EDT)

== 100 billion ==

It is mentioned in the article that some estimate that the Earth can harbor 100 billion people. This seems like the kind of thing that should have an external link attached to it for those who want to know who "some" are. I don't know if the person who originally added that still has the relevant information handy.
:I suspect the estimate comes from [http://fatknowledge.blogspot.tw/2008/11/how-many-people-can-earth-support.html here]. I fail to see how this issue relates to the second law, tho. [[User:PeterKa|PeterKa]] 05:01, 8 February 2014 (EST)
::So is it something that should be trimmed from the article to keep it concise? The article does look like it meanders a bit (compared to, say, [[refrigerator]]). [[User:JamesWS|JamesWS]] 19:57, 8 February 2014 (EST)
:::IMO, the entire "liberal abuse" section is tangental at best and should be removed. Entropy doesn't directly relate to the issues of overpopulation or how many people the world can feed. [[User:PeterKa|PeterKa]] 01:25, 9 February 2014 (EST)

::::It does seem tangential, but it is placed lower in the entry. There is an appropriate reluctance to delete educational information that some may find to be enlightening.--[[User:Aschlafly|Andy Schlafly]] 03:37, 9 February 2014 (EST)

== Statistical Nature of the law ==

I just want to point out that the second law is statistical in nature, which has not really been discussed. Suppose you have a container with a partition separating two gases A and B. When the partition is removed, the entropy increases as the number of different microstates for this state is greater. It is possible that, just by chance, all the particles of gas A end up on one side and those of gas B on the other, so that it is the same state as when we started. Now there is only one microstate corresponding to this state, so the entropy has decreased. However, we never see this happen because the number of microstates for a more disordered system is vastly greater. My point is that it is wrong to say things like "heat always flows from hot to cold" or that "it is impossible for order to come from disorder". (Note that I'm not intentionally trying to quote anyone or say anything about evolution, I'm just talking about the physics)--[[User:bobklein|bobklein]] 14:34, 2 August 2016 (EST)

Theory of relativity

2016-08-01T16:46:57Z

Bobklein:

''See also [[Counterexamples to Relativity]].''

In physics, the '''theory of relativity''' is a scientific theory describing the effects due to the invariance of the speed of light. In particular, the meaning of space and time are altered by the motion of the observer. Relativity predicts phenomena such as time dilation and length contraction for observers moving relative to one another at very high ("relativistic") speed.

'''Relativity''' refers to two closely-related mathematical theories in [[physics]]:
[[Image:600px-Albert Einstein Head.jpg|thumbnail|right|200px|
*"I do not share the crusading spirit of the professional [[Atheism|atheist]] whose fervor is mostly due to a painful act of liberation from the fetters of religious indoctrination received in youth. I prefer an attitude of humility corresponding to the weakness of our intellectual understanding of nature and of our own being." - [[Albert Einstein]]<ref name="Isaacson390">Isaacson, Walter (2008). [http://books.google.com/books?id=cdxWNE7NY6QC&pg=PT390 ''Einstein: His Life and Universe''] (New York: Simon and Schuster), p. 390. Retrieved from GoogleBooks archive on February 19, 2015.</ref>]]
*'''[[Special theory of relativity|Special relativity]]''' (SR) is a theory which describes the laws of motion for non-accelerating bodies traveling at a significant fraction of the [[speed of light]]. As speeds approach zero, Special Relativity tends towards equivalence with [[Newton's Laws of Motion]]. Special Relativity was developed by [[Hendrik Lorentz]], [[Henri Poincaré]], and Hermann Minkowski,<ref>"German mathematician who developed the geometrical theory of numbers and who made numerous contributions to number theory, mathematical physics, and the theory of relativity." [http://www.britannica.com/eb/article-9052860/Hermann-Minkowski Hermann Minkowski -- Britannica Online Encyclopedia]</ref><ref>[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Minkowski.html Hermann Minkowski, Biography]</ref> and [[Albert Einstein]].

*'''[[General theory of relativity|General Relativity]]''' (GR) is a theory which explains the laws of motion as viewed from accelerating reference frames and includes a geometric explanation for gravity. This theory was developed by [[David Hilbert]] and [[Albert Einstein]] as a generalization of the postulates of Special Relativity.<ref>"[T]he German mathematician David Hilbert submitted an article containing the correct field equations for general relativity five days before Einstein."[http://nobelprize.org/educational_games/physics/relativity/history-1.html Nobel Prize historical account]</ref> A dramatic but later discredited claim by Sir [[Arthur Eddington]] of experimental proof of General Relativity in 1919 made Einstein a household name.

These theories have augmented earlier approaches, such as [[Galilean Relativity]].

The theory of relativity is defended with religious-like zeal, such that no college faculty tenure, Ph.D degree, or Nobel Prize is ever awarded to anyone who dares criticize the theory, as the example of denying a Nobel Prize to the most accomplished physicist of the 20th century, [[Robert Dicke]], illustrates. Another critic of the theory was Louis Essen [1908-1997], the man credited with determining the speed of light. He wrote many fiery papers against it such as ''Relativity and Time Signals''<ref>http://gsjournal.net/Science-Journals/Journal%20Reprints-Relativity%20Theory/Download/3297</ref> and ''Relativity - Joke or Swindle?''.<ref>http://www.ekkehard-friebe.de/Essen-L.htm</ref> Perhaps the most famous website opposing relativity is this one, with its [[Counterexamples to Relativity]] page. The cornerstone item in that page involves the experimental measurements of the advance of the perihelion of Mercury that show a shift greater than predicted by Relativity, well beyond the margin of error.

Unlike most of physics, the theories of relativity have discontinuities whereby the limit of a physical quantity as a variable (such as mass or velocity) approaches a fixed value is not the same as the physical quantity at the fixed value. For example, the limit of momentum as mass approaches 0 and velocity approaches the speed of light is not equal to the momentum of (massless) light.<ref>Discontinuities in General Relativity are also well-recognized. See, e.g., [http://www.springerlink.com/content/u47l341u2q555455/]</ref>

More generally, the theories of relativity consist of complex mathematical equations relying on several hypotheses. For example, at Hofstra University general relativity is taught as part of an upperclass math course on differential geometry, based on three stated assumptions.<ref>http://people.hofstra.edu/Stefan_Waner/diff_geom/tc.html</ref> The equations for special relativity assume that it is forever impossible to attain a velocity faster than the speed of light and that all inertial frames of reference are equivalent, hypotheses that can never be fully tested. Relativity rejects Newton's [[action at a distance]], which is basic to Newtonian gravity and [[quantum mechanics]]. The mathematics of relativity assume no exceptions, yet in the time period immediately following the origin of the universe the relativity equations could not possibly have been valid.

The "continuous" nature of space and time postulated by relativity is in conflict with the "discrete" nature in [[quantum mechanics]],<ref>For example, Relativity claims that space and time are smooth and continuous, while [[quantum mechanics]] suggests otherwise. [http://www.csmonitor.com/Science/Cool-Astronomy/2010/1025/Is-the-universe-a-big-hologram-This-device-could-find-out.] Relativity also denies [[action-at-a-distance]], while quantum mechanics suggests otherwise. Relativity denies any role for chance, while quantum mechanics is heavily dependent on it.</ref> and although theories like [[string theory]] and [[quantum field theory]] have attempted to unify relativity and quantum mechanics, neither has been entirely successful or proven.

Unlike [[Classical mechanics|Newtonian physics]], in which space and time intervals are each invariant as seen by all observers, in SR the only invariant quantity is a quadratic combination of space and time intervals (x2 - c2 t2). The (assumed) instantaneous transmission of Newtonian gravitational effects also contradicts special relativity.

In quantum mechanics, the [[uncertainty principle]] suggests that virtual particles can sometimes travel faster than the speed of light which would violate causality, but "[t]he only known way to resolve this tension involves introducing the idea of antiparticles."<ref>http://nobelprize.org/nobel_prizes/physics/laureates/2004/wilczek-lecture.pdf (p. 102)</ref> Consequently, in 1928 Paul Dirac derived the Dirac equation, one of the first quantum mechanical equations compatible with special relativity, by which Dirac predicted the existence of antimatter. Four years later, antimatter (the positron) was discovered by Carl Anderson, as successfully predicted by relativistic quantum mechanics. [[Quantum field theory]], a generalization of quantum mechanics, is fully compatible with special relativity but not with general relativity, and still lacks a vital piece: evidence of the [[graviton]].

A famous critic of Theory of relativity is [[Nikola Tesla]], who called it a "...magnificent mathematical garb which fascinates, dazzles and makes people blind to the underlying errors. The theory is like a beggar clothed in purple whom ignorant people take for a king ... its exponents are brilliant men but they are metaphysicists, not scientists...".<ref>[http://www.plasmacosmology.net/tesla.html New York Times, July 11, 1935, p23, c8]</ref>

== Special Relativity ==
Lorentz and Poincaré developed Special Relativity as way of understanding how Maxwell's equations for electromagnetism could be valid in different frames of reference. Einstein famously published an explanation of Poincaré's theory in terms of two assumptions (postulates):

# ''The [[speed of light]] is constant for all (inertial) observers, regardless of their velocities relative to each other.''
# ''The laws of physics are identical in all inertial reference frames.''

In layman's terms, these two assumptions can be restated as:
# It is impossible ever to transmit information faster than the speed of light.<ref>This assumption is commonly restated in this manner. For example, a discussion of hypothetical [[tachyons]] talks "about using tachyons to transmit information faster than the speed of light, '''in violation of Special Relativity'''."[http://www.math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html] However, there is some question whether the Theory of Special Relativity really restricts faster-than-light communication of information.</ref>
# The laws of physics are identical, without any variation, in every location throughout the universe.
# The laws of physics are identical, without any variation, no matter how fast something is traveling (in the absence of acceleration).

Or, in more concise, clearer terms, these assumptions are this:

#there is no [[action at a distance]] (because that would make observations dependent on the frame of reference)
#space and time are completely symmetric throughout the universe (because otherwise frames of reference would not be interchangeable)

When the assumptions are stated clearly as above, the weaknesses in the theory are more apparent. There “is” action at a distance in [[quantum entanglement]] and apparently also in gravity, as no gravitons can be found. However, no information has yet been transmitted via quantum entanglement, so while non-locality violates the spirit of relativity it is consistent with it if relativity is limited to the transmission of information. [[Quantum field theory]], an attempt to partially reconcile [[quantum mechanics]] with relativity, is incomplete at best. As to the second assumption, it is contrary to the [[arrow of time]], which illustrates the lack of symmetry in time. Logical defects include the incoherence of relativistic mass (see discussion below) and the lack of relativistic constraints near the beginning the universe (see above).

Special Relativity (SR) was initially developed by [[Henri Poincaré]] and [[Hendrik Lorentz]], working on problems in electrodynamics and the [[Michelson-Morley experiment]], which had not found any sign of Earth's orbital motion through the [[aether (science)|luminiferous aether]], which was believed to be the substance which carried electromagnetic waves. Special relativity alters [[Isaac Newton]]'s laws of motion by assuming that the speed of light will be the same for all observers, despite their relative velocities and the source of the light. (Therefore, if A sends a beam of light to B, and both measure the speed, it will be the same for both, no matter what the relative velocity of A and B. In Newtonian/Galilean mechanics, If A sends a physical object at a particular velocity towards B, and nothing slows it, the velocity of the object relative to B depends on the velocities of the object and of B relative to A.)

At low speeds (relative to light-speed), the Lorentz-Poincaré relativity equations are equivalent to Newton's equations. The media-promoted equation ''[[E=mc²]]'', implausibly suggests a relationship between typically unrelated concepts of energy, the rest mass of a body and the speed of light.

Under relativity, particles at low mass and low speed can be accurately approximated by [[classical mechanics]] (such as [[Isaac Newton]]'s laws of motion). At the two extremes, modeling the behavior of electrons requires that relativistic effects be taken into account (the chemically significant phenomenon of electron spin arises from relativity), and the course of light passing through a region containing many massive bodies such as galaxies will be distorted ([[classical mechanics]], in which light travels in straight lines, does not predict this). These are both experimentally confirmed (electron spin was known before relativity arose, and telescopic observations confirm that galactic clusters distort the paths of the light passing through them).

Many scientists have indicated problems with the postulates of special relativity. Paul Davies, formerly of Macquarie University and now at the University of Arizona believes that the speed of light has changed over time. Since the speed of light is a constant speed 'c' this indicates problems with the theory [http://news.bbc.co.uk/2/hi/science/nature/2181455.stm light speed]. Other engineers and scientists have written about problems in the basic set of special relativity equations. Based on the ideas of not Einstein but of the scientist Fitzgerald as well as others, a length contraction effect was predicted as an explanation of the failure of the Michelson-Morley experiment to detect Earth's orbital motion. This idea was taken up by Hendrik Lorentz and shown by others to be a useful mechanism by which theory could be forced into conformance with experimental results. However, in 2005, Michael Strauss a computer engineer invalidated much of Special Relativity theory by showing clear contradictions in the theory. [http://www.relativitycollapse.com relativity]

== General Relativity ==

::::''See the [[General theory of relativity]] page for more in-depth coverage of this topic.''

General Relativity is a theory of gravity that is compatible with Special Relativity. Einstein explains a thought experiment involving two elevators. The first elevator is stationary on the Earth, while the other is being pulled through space at a constant acceleration of g. Einstein realized that any physical experiment carried out in the elevators would give the same result. This realization is known as the equivalence principle and it states that accelerating frames of reference and gravitational fields are indistinguishable. General Relativity is the theory of gravity that incorporates Special Relativity and the equivalence principle.

General Relativity is a mathematical extension of Special Relativity. GR views space-time as a 4-dimensional [[manifold]], which looks locally like [[Minkowski space]], and which acquires [[curvature]] due to the presence of massive bodies. Thus, near massive bodies, the geometry of space-time differs to a large degree from [[Euclidean geometry]]: for example, the sum of the angles in a triangle is not exactly 180 degrees. Just as in classical physics, objects travel along [[geodesic]]s in the absence of external forces. Importantly though, near a massive body, geodesics are no longer straight lines. It is this phenomenon of objects traveling along geodesics in a curved spacetime that accounts for gravity.

The anomalous precession of Mercury's [[perihelion]] seems to support the Theory of General Relativity, though that is disputed on the[[Counterexamples to Relativity]] page. Keep in mind that the precession in question is the ''"anomalous"''
precession after the effects of other planets' gravitation action has been compensated for. Those other effects are much larger, and are purely Newtonian in nature. There was another explanation based on Newtonian gravity, involving a slight alteration to the precise inverse-square relation of Newtonian gravity to distance, but it was discarded when it gave very bad results for the Moon's orbit.

British Historian Paul Johnson declares the turning point in 20th century to have been when fellow Briton Sir [[Arthur Eddington]], an esteemed English astronomer, ventured out on a boat off Africa in 1919 with a local Army unit to observe the bending of starlight around the sun during a total eclipse. Upon his return to England declared that his observations proven the theory of relativity. In fact recent analysis of Eddington's work revealed that he was biased in selecting his data, and that overall his data were inconclusive about the theory of relativity. The prediction was later confirmed by more rigorous experiments, such as those performed by the [[Hubble Space Telescope]].<ref>[http://www.spaceimages.com/gravlen.html Hubble Gravitational Lens Photo]</ref><ref>[[Gravitational lensing]]</ref><ref>[http://www.iam.ubc.ca/~newbury/lenses/glgallery.html]</ref> Lorentz has this to say on the discrepancies between the empirical eclipse data and Einstein's predictions.

::''It indeed seems that the discrepancies may be ascribed to faults in observations, which supposition is supported by the fact that the observations at Prince's Island, which, it is true, did not turn out quite as well as those mentioned above, gave the result, of 1.64, somewhat lower than Einstein's figure.''<ref>Lorentz, H.A. [http://ia331314.us.archive.org/2/items/theeinsteintheor11335gut/11335-h/11335-h.htm The Einstein Theory of Relativity]</ref>

The prediction that light is bent by gravity is predicted both by Newtonian physics and relativity, but relativity predicts a larger deflection.

Special relativity is the limiting case of general relativity where all gravitational fields are weak. Alternatively, special relativity is the limiting case of general relativity when all reference frames are inertial (non-accelerating and without gravity).

==Lack of evidence for Relativity==
The Theory of relativity assumes that time is symmetric just as space is, but the biggest early promoter of relativity, Arthur Eddington, coined the term "[[arrow of time]]" admitting how time is ''not'' symmetric but is directional. The passage of time is tied to an increase in disorder, or [[entropy]]. The Theory of relativity cannot explain this, and implicitly denies it, specifically allowing for theoretical time travel (e.g., [[wormholes]]) and different rates of passage of time based on velocity and acceleration.

Claims that relativity was used to develop the [[Global Positioning System]] ([[GPS]]) are false. A 1996 article explains:

:"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."<ref>http://tycho.usno.navy.mil/ptti/1996/Vol%2028_16.pdf</ref><ref>Some do claim that relativity is "vital" to GPS even though GPS developed independently of theoretical predictions and theoreticians disagree about how the relativistic effects for GPS should be calculated. ''See id. See also'' [http://www.rand.org/pubs/monograph_reports/MR614/MR614.appb.pdf]</ref>

This article, which was published in 1996, goes on to propose relativistic corrections that might be used to design more accurate GPS systems. Clocks on board GPS satellites require adjustments to their clock frequencies if they are to be synchronized with those on the surface of the Earth.

Tom Van Flandern, an astronomer hired to work on GPS in the late 1990s, concluded that "[t]he GPS programmers don't need relativity." He was quoted as saying that the GPS programmers "have basically blown off Einstein."<ref>http://archive.salon.com/people/feature/2000/07/06/einstein/index.html See also [http://www.metaresearch.org/solar%20system/gps/absolute-gps-1meter-3.ASP], where Van Flandern discusses how relativistic corrections might improve GPS accuracy.</ref> Asynchronization can be easily addressed through communications between the satellites and ground stations, so it is unclear why any theory would be needed for GPS. While Van Flandern believed that relativity is unnecessary for GPS, he also asserted that observations of GPS satellites supported both general and special relativity, writing that "we can assert with confidence that the predictions of relativity are confirmed to high accuracy over time periods of many days," with unrelated factors interfering with longer-term observations.<ref>http://www.metaresearch.org/cosmology/gps-relativity.asp</ref>

Some internet articles claim that GPS timing differences ''confirm'' the Theory of Relativity or its Lorentzian counterpart (which uses a preferred frame of reference). GPS clocks run slower in the weaker gravitation field of the satellites than on ground stations on Earth, with the effects predicted by general relativity far outweighing the effects predicted by special relativity. However, the articles claiming that the slower GPS satellite clocks confirm relativity do not address the effect, if any, of the weaker gravitational force under Newton's theory on the GPS satellite clocks, likely because in Newtonian Mechanics every clock in the universe keeps time at the same rate regardless of velocity, acceleration, or the presence or absence of force.

Currently, GPS satellites are synchronized to Coordinated Universal Time by radio signals from the ground; therefore, they cannot currently be used to test general relativity.<ref>[http://www.phys.lsu.edu/mog/mog9/node9.html "General Relativity in the Global Positioning System."] Neil Ashby, U. of Colorado</ref>

There are claims that the effects of relativity have been observed with the frequency shift of the signal being sent back to [[Earth]] several times as various spacecraft have dipped into the gravity wells around massive objects such as the [[sun]] (see image at right)<ref>[http://saturn.jpl.nasa.gov/news/press-releases-03/20031002-pr-a.cfm Saturn-Bound Spacecraft Tests Einstein's Theory]</ref> or Saturn.<ref>[http://www.newscientist.com/article/mg12517102.600-science-encounter-with-saturn-confirms-relativity-theory.html Encounter with Saturn confirms relativity theory]</ref> A satellite called [[Gravity Probe B]] was put in orbit about the Earth to examine the effects of frame dragging and geodetic warping of space,<ref>[http://www.nasa.gov/mission_pages/gpb/index.html NASA Gravity Probe B mission page]</ref><ref>[http://einstein.stanford.edu/ Gravity Probe B project page]</ref> but the results were inconclusive. Note, however, that Newtonian mechanics also predicts deflection of light by gravity, and in the initial theory of relativity it predicted the same amount of deflection, but only if we treat light as capable of being accelerated and decelerated like ordinary matter, which is contrary to all measurements and observations to date.<ref>http://www.mathpages.com/rr/s6-03/6-03.htm</ref> Adjustments to the theory of relativity resulted in a prediction of a greater deflection of light than that predicated by Newtonian mechanics, though it is debatable how much deflection Newtonian mechanics should predict.

None of the NASA spacecraft incorporates predictions of relativity into their own timing mechanisms, as Newtonian mechanics is adequate even for probes sent deep into space so long as they do not undergo accelerations near the speed of light or enter any massive gravity wells.<ref>There is no reported reliance on relativity by any space probe.</ref>

A decade of observation of the [[pulsar]] pair [[PSR 1913 16|PSR B1913+16]] detected a decline in its orbital period, which was attributed to a loss in energy by the system. It is impossible to measure the masses of the pulsars, their accelerations relative to the observers, or other fundamental parameters. Professors Joseph Taylor and Russell Hulse, who discovered the binary pulsar, found that physical values could be assigned to the pulsars to make the observed decline in orbital period consistent with the Theory of General Relativity, and for this they were awarded the 1993 [[Nobel Prize]] for Physics, which is the only award ever given by the Nobel committee for the Theory of Relativity.<ref>http://nobelprize.org/nobel_prizes/physics/laureates/1993/press.html</ref> In 2004, Professor Taylor utilized a correction to the derivative of the orbital period to fit subsequent data better to the theory. At most, assumptions can be made and altered to fit the data to the theory, rather than the data confirming the theory.

The [[perihelion]] of Mercury's [[orbit]] [[precession|precesses]] at a measurable rate, but even after accounting for gravitational perturbations caused all other planets in the [[solar system]], Newton's theory (assuming a precise inverse-square relationship for distance) predicts a rate of precession that differs from the measured rate by approximately 43 [[arcsecond]]s per century. General relativity was developed in part to provide an estimate for this rate of precession that better matches observations.<ref>http://physics.ucr.edu/~wudka/Physics7/Notes_www/node98.html#SECTION032121000000000000000</ref><ref>http://www.alberteinstein.info/gallery/pdf/CP6Doc30_English_pp146-200.pdf</ref><ref>http://farside.ph.utexas.edu/teaching/336k/lectures/node117.html</ref> Newton's theory can also explain this perihelion by making tiny adjustments to parameters in the gravitational equation.

General relativity predicts twice as much bending in light as it passes near massive objects than Newton's theory might predict.<ref>http://www.mathpages.com/rr/s6-03/6-03.htm</ref> This phenomenon is known as [[gravitational lensing]]. A large number of instances of gravitational lensing have been observed, and it is now a standard astronomical tool.<ref>http://imagine.gsfc.nasa.gov/docs/features/news/grav_lens.html</ref><ref>http://astro.berkeley.edu/~jcohn/lens.html</ref><ref>http://www.iam.ubc.ca/~newbury/lenses/glgallery.html</ref> Note, however, that the extent of bending of light predicted by Newton's theory is open to debate, and depends on assumptions about the nature of light for gravitational purposes.<ref>http://cosmictimes.gsfc.nasa.gov/1919/guide/gravity_bends_starlight.html</ref>

In 1972, scientists flew extremely accurate clocks ("atomic clocks") around the world in both directions on commercial airlines, and claimed to observe relativistic time dilation; the eastbound clock gained 273 ns and the westbound clock lost 59 ns, matching the predictions of general relativity to within experimental accuracy.<ref>[http://www.answers.com/topic/hafele-keating-experiment Hafele-Keating Experiment]</ref> However, the inventor of the atomic clock, Louis Essen, declared that the experiment was inaccurate.<ref>Louis Essen, Electron. Wireless World 94 (1988) 238.</ref> Dr A. G. Kelly examined the raw data from the experiment and declared it inconclusive.<ref>A. G. Kelly,Reliability of Relativistic Effect Tests on Airborne Clocks, Monograph No.3 Feb.1996, The Institution of Engineers of Ireland, ISBN 1-898012-22-9</ref> The Nobel Committee chose not to honor this experiment for the significance that was claimed.

Despite [[censorship]] of dissent about relativity, evidence contrary to the theory is discussed outside of [[liberal]] universities.<ref>http://scitizen.com/screens/blogPage/viewBlog/sw_viewBlog.php?idTheme=8&idContribution=922</ref>

==Experiments that Fail to Prove Relativity==

Predictions of general relativity turn out to be obscure and difficult to test. The two most famous predictions were the bending of light in a gravitational field and the precession of the perihelia of orbiting planets.

*The first of these was famously tested during a total eclipse in 1919. That test was somewhat muddled by an incorrect initial calculation, by several people including Einstein himself, of what the effect would be, and some "cherry picking" of the data to be used.<ref>''Einstein's Luck'', John Waller, Oxford University Press, ISBN 0-19-860719-9</ref> The data selection could be considered "manipulation" or "fudging", by a person (Arthur Eddington) who had a personal stake in the outcome. His analysis techniques would not pass muster today.

:It should be noted that pre-relativistic (Newtonian) physics may also predict a bending, of half the observed value, depending on whether one uses the 17th century "corpuscular" formulation or the 19th century "wave" formulation.

:Nevertheless, it has been verified with ever-increasing precision in subsequent eclipses, and in the observations of quasar 3C273.

*The second "classical" test of general relativity was the advance of the perihelion of the orbit of Mercury. There are many complex effects contributing to this, including gravitational perturbations from other planets and the effect of the oblateness of the Sun. These are hard to calculate accurately, but, by 1900 it was known quite accurately that there was an "anomalous" precession, that is, a precession beyond all other known effects, of 43 arc seconds per century. This is a very tiny effect, but astronomical measurements were sufficiently accurate by that time to show it clearly.

:Increasingly precise measurements of the precession demonstrate that it conflicts with General Relativity, despite claims of relativists for decades that it predicted the precession accurately in the amount of <math>3{}v^2/c^2</math> revolutions per planet's "year", where <math>v</math> is the planet's average orbital speed.<ref>That is a simple approximation, designed to relate the precession to the planet's speed relative to the speed of light. A more accurate approximation is <math>\frac{3GM}{c^2 a(1-e^2)}</math>, where a is the semi-major axis and e is the eccentricity.</ref> The conflict is greater than the margin of error, and many relativists avoid the discrepancy rather than address it.

==Experimental and Observational Evidence Confirming Relativity==

The different effects predicted by special relativity, compared to classical formulations, are extremely tiny. Most relativistic effects are negligible at the speeds of ordinary phenomena observed by humans. The effects only become significant when the speeds involved are a significant fraction of the speed of light, which is <math>3 \times 10^8</math> meters per second—such speeds are called ''relativistic''. (However, it's worth noting that ordinary magnetism can be considered an effect of relativity, dictated by the need for electrostatic theory to be correct under relativity. The speed of light in fact appears in the formulas ([[Maxwell's Equations]]) governing electricity and magnetism, though these equations were developed long before relativity was proposed.)

Because the effects of relativity are so tiny, scientists have been devising sophisticated and sensitive tests ever since the theory was formulated in 1905.

The most famous experiment, and the one that is commonly cited in textbooks as the experiment that established the case for relativity,<ref>Though relativity did not actually originate from this experiment</ref> was the [[Michelson-Morley experiment]]. This showed that all observers will obtain the same measured value for the speed of light (3x108 meters per second) no matter what their state of motion. This is the first of the two fundamental principles:
#''The [[speed of light]] is constant for all observers, regardless of their velocities relative to each other.''
#''The laws of physics are identical in all reference frames.''
(The second is just a restatement of Galilean relativity, that is, the "common sense" that had been accepted for centuries.)
A naive "common sense" interpretation of Galilean relativity would require that measurements of the speed of light (or anything else) by different observers would get results that differ by the observers' relative speeds, and hence that principle #1 can't be true. Special relativity fixes this apparent paradox.

All of special relativity derives for these two principles, plus assumptions of exact conservation of momentum and energy in all cases.

*At the end of Einstein's original 1905 paper [http://www.fourmilab.ch/etexts/einstein/E_mc2/www/ "Does the Inertia of a Body Depend its Energy Content?"], he speculates on the possibility that the equation <math>E = m c^2</math>, which would normally be very hard to verify, could be verified with the extremely high energies of the newly discovered phenomenon of radioactivity.<ref>This equation is not related to [[quantum mechanics]].</ref> In the 1910s, with the invention of the mass spectrometer, it became possible to measure masses of nuclei accurately. This led to the clearing up of the mystery of atomic masses not being exact integers,and strongly suggested the existence of a "mass defect" (or "packing fraction") consistent with the mass-energy equivalence. In the 1930s, experiments with known nuclear reactions showed a very accurate correlation between the masses of the nuclei involved and the energy released. See [[Quantitative Analysis of Alpha Decay]].

*Another prediction of special relativity was time dilation in rapidly moving objects. This effect was most famously verified in the anomalously slow decay of relativistic cosmic muons.<ref>Some have suggested that other explanations are possible for this effect. We are trying to track this down.</ref> Time dilation has since been verified many times, and is routinely taken into account in all high-energy nuclear physics experiments, as in Hadron collision experiments.<ref>Experiments specifically designed to check dilation are rarely conducted any more.</ref>

[[Image:Cassini-science-289.jpg|right|thumb|The Shapiro effect: A spacecraft signal dipping into a gravity well around the [[Sun]] is delayed slightly.]]
As the 20th century progressed, tests of general relativity were proposed.

*One important "classical" test of general relativity was the advance of the perihelion of the orbit of Mercury. There are many complex effects contributing to this, including gravitational perturbations from other planets and the effect of the oblateness of the Sun. These are hard to calculate accurately, but, by 1900 it was known quite accurately that there was an "anomalous" precession, that is, a precession beyond all other known effects, of 43 arc seconds per century. This is a very tiny effect, but astronomical measurements were sufficiently accurate by that time to show it clearly.

:This created quite a problem—physicists by then were accustomed to having their theories check out very accurately. One proposal that was made, by Simon Newcomb and Asaph Hall, was that the exponent of the radius in the gravitational formula wasn't exactly 2. He showed that, by choosing an exponent of <math>2+\delta</math>, the precession, as a fraction of a full orbit per planet's year, is <math>\delta/2</math>. By setting <math>\delta</math> to .000000157, that is, an exponent of 2.000000157, Newcomb was able to get a precession of .000000078 revolutions per Mercury year, or 43 arcseconds per Earth year. Whatever value is chosen for <math>\delta\,</math>, it gives the same precession, per revolution, for all orbiting bodies, but gravitational effects from other planets diminish that effect the further the planet is from the sun.

:A good approximation for the precession under general relativity is <math>\frac{3GM}{c^2 a(1-e^2)}</math> revolutions per planet's "year", where a is the semi-major axis and e is the eccentricity. A simpler but less accurate one is <math>3{}v^2/c^2</math>, where <math>v</math> is the planet's average orbital speed.

:While Newcomb's theory, and general relativity, don't lead to closed-form solutions, both theories can be solved numerically to as much precision as one desires.

:The following table shows some approximate parameters for the planets. Note that Mercury has the smallest orbit, and the fastest speed. Precession of planets other than Mercury is extremely hard to measure, but measurements of the actual anomalous precessions are in good agreement.<ref>http://www.mathpages.com/rr/s6-02/6-02.htm</ref>

{| class="wikitable"
|-
!Planet
!Period, seconds x 106
!Semimajor axis, meters x 109
!Speed, meters/second x 103
!Gravitational force, Newtons per kilogram
!Anomalous precession, arcseconds per (Earth) century, pure Newtonian mechanics
!Anomalous precession, Newtonian with exponent of 2.000000157
!Anomalous precession, general relativity
!Measured anomalous precession (estimated uncertainty)<ref>http://www.mathpages.com/rr/s6-02/6-02.htm</ref>
|-
|Mercury
|7.57
|58.9
|48
|.039
|0
|43
|43
|43.5(5)
|-
|Venus
|19.6
|108
|35
|.011
|0
|16.6
|9
|8(5)
|-
|Earth
|31.6
|150
|30
|.006
|0
|10.3
|4
|5(1)
|-
|Mars
|59.3
|227.9
|24
|.0025
|0
|5.5
|1.4
|
|-
|Jupiter
|374
|778.4
|13
|.0002
|0
|0.87
|0.07
|
|-
|Saturn
|929
|1426
|9.7
|.00006
|0
|0.35
|0.014
|
|-
|Uranus
|2651
|2870
|6.8
|.000016
|0
|0.12
|0.002
|
|-
|Neptune
|5200
|4498
|5.5
|.000007
|0
|0.063
|0.0008
|
|}

:Considering only the ''anomalous'' precession, that is, the precession that remains after all known other factors (other planets and asteroids, solar oblateness) have been accounted for, and using very accurate calculations rather than the approximations given above, general relativity predicts 42.98 ±0.04 arcseconds per century. Some observed values, as of 2008, are:
::: 43.11 ± 0.21 (Shapiro et al., 1976)
::: 42.92 ± 0.20 (Anderson et al., 1987)
::: 42.94 ± 0.20 (Anderson et al., 1991)
::: 43.13 ± 0.14 (Anderson et al., 1992)
::: [Source: [http://arxiv.org/PS_cache/astro-ph/pdf/9804/9804258v1.pdf Pijpers 2008]]
:These error bars, and that of the general relativity prediction, all overlap.

*Another is the ''Shapiro effect'', involving time delay in radio signals passing through the gravity well of the Sun or a planet. Various spacecraft have confirmed this.

*Another is ''gravitational time dilation''. This is an effect separate from the time dilation of special relativity. It was tested by the Pound-Rebka experiment in 1959.

*Later in the 20th century, even more subtle phenomena were tested. One was the phenomenon of ''gravitational radiation'', or "gravitational waves". These waves are incredibly difficult to observe, and had never been observed until 2015. But extremely dense binary pulsars radiate gravitational waves with sufficient energy loss that, even though we can't detect the waves from Earth, we can see the effect of the energy loss from the radiation. The extreme precision of the timing of pulses from pulsars makes it possible to observe their energy loss with great accuracy. Observations by Hulse and Taylor of the pulsar pair known as B1913+16, if assumptions are made,<ref>Similar to the way Kepler chose orbital parameters to fit observed planetary motion to his theory</ref> could make the energy loss appear consistent with the predicted radiation. The rotating pulsars have moved such that Earth is now out of the beams, so those observations have been discontinued.

*In late 2015 (and announced in 2016), the LIGO instruments directly detected gravitational waves. See [[Gravitational waves]].

*An additional test of general relativity was performed with radio signals to the Cassini spacecraft.<ref>http://www.nature.com/nature/journal/v425/n6956/full/nature01997.html</ref>

*Two other effects, ''geodetic precession'' (also known as "de Sitter precession"), and ''frame dragging'' (also known as the "Lense-Thirring effect") were tested by the "Gravity Probe B" satellite early in the 21st century.<ref>http://prl.aps.org/accepted/L/ea070Y8dQ491d22a28828c95f660a57ac82e7d8c0</ref><ref>http://www.digitaljournal.com/article/306430</ref><ref>http://www.nap.edu/html/gpb/summary.html</ref><ref>http://www.sciencenews.org/view/generic/id/73870/title/Gravity_Probe_B_finally_pays_off_</ref><ref>http://www.nasa.gov/mission_pages/gpb/</ref><ref>http://einstein.stanford.edu/</ref><ref>http://spectrum.ieee.org/aerospace/space-flight/the-gravity-probe-b-bailout</ref><ref>http://www.engadget.com/2011/05/06/nasa-concludes-gravity-probe-b-space-time-experiment-proves-e/</ref> The precision required to observe this was phenomenal. The results were announced on May 4, 2011.

{{clear}}

==Predicted consequences of the Theories==
===Time dilation===

[[Image:Light cone.png|right|thumb|Light-cone diagram]]
One important consequence of SR's postulates is that an observer in one reference frame will observe a clock in another frame to be "ticking" more slowly than in the observer's own frame. This can be proven mathematically using basic geometry, if the postulates are physically true without exception.

The length of an event <math>t</math>, as seen by a (relative) stationary observer observing an event is given by:

<math> t = \frac{t_{0}} {\sqrt{1 - \frac{v^{2}}{c^{2}}}}</math>

Where
:<math>t_0</math> is the "proper time" or the length of the event in the observed frame of reference.
:<math>v</math> is the relative velocity between the reference frames.
:<math>c</math> is the speed of light (3x108 ms-1).

Evidence for time dilation was discovered by studying [[muon decay]]. [[Muons]] are [[subatomic]] [[particles]] with a very short [[halflife]] (1.53 microseconds at rest) and a very fast speed (0.994c). By putting muon detectors at the top (D1) and bottom (D2) of a mountain with a separation of 1900m, scientists could measure accurately the proportion of muons reaching the second detector in comparison to the first. The proportion found was different to the proportion that was calculated without taking into account relativistic effects.

Using the equation for [[exponential decay]], they could use this proportion to calculate the time taken for the muons to decay, relative to the muon. Then, using the time dilation equation they could then work out the dilated time. The dilated time showed a good correlation with the time it took the muons to reach the second sensor, thereby supporting the existence of time dilation.

The time taken for a muon to travel from D1 to D2 as measured by a stationary observer is:

<math> t = \frac{s}{v} = \frac{1900}{0.994\times(3\times10^{8})} = 6.37\mu\textrm{s} </math>

The fraction of muons arriving at D2 in comparison to D1 was 0.732. (Given by <math> \frac{N}{N_0} = 0.732 </math>)

Since (from the equation for exponential decay) <math> \frac{N}{N_{0}} = e^{-\lambda t_{0}} </math> then

<math> t_{0} = \frac {ln(0.732)}{ln (0.2)} \times 1.53\times 10^{-6} = 0.689\mu\textrm{s}</math>

This gives the time for the proportion of decay to occur for an observer who is stationary, relative to the muon.

Putting this into the time dilation equation gives:

<math> t = \frac{t_{0}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} = \frac{0.689 \times{10^{-6}}}{\sqrt{1 - \frac{0.994^{2}}{1^{2}}}} = 6.3\times 10^{-6}\textrm{s}</math>

This is in good agreement with the value calculated above, thereby providing evidence to support time dilation.

====Time Dilation and Creation Science====

{{main|Starlight problem#Humphreys.27_model}}

Creation scientists such as physicists Dr. [[Russell Humphreys]] and Dr. [[John Hartnett]] have used relativistic time dilation to explain how the earth can be only 6,000 years old even though cosmological data (background radiation, supernovae, etc.) set a much older age for the universe.

===Length contraction===
When two inertial reference frames move past each other in a straight line with constant relative velocity, an observer in one reference frame would observe a metre rule in the other frame to be shorter along the direction parallel to the relative motion.

The length, <math>l</math>, of an object as seen by a (relative) stationary observer is given by:

<math> l = l_{0} \sqrt{1- \frac{v^{2}}{c^{2}}}</math>

Where
:<math>l_0</math> is the "proper length" or the length of the object in the observed frame of reference.
:<math>v</math> is the relative velocity between the reference frames.
:<math>c</math> is the speed of light (3x108 ms-1).

===Mass increase===

For decades the theory of relativity taught that as a body moves with increasing velocity its [[mass]] also increases.<ref>For example, this was taught as recently as in the 1991 edition of the Encyclopedia Britannica.</ref>

Under this view, the mass, <math>m</math>, of an object as detected by a (relative) stationary observer is given by:

:<math> m = \frac{m_{0}} {\sqrt{1 - \frac{v^{2}}{c^{2}}}}</math>

Where
:<math>m_0</math> is the "rest mass" or the mass of the object measured by an observer in the same reference frame as the object.
:<math>v</math> is the relative velocity of the object.
:<math>c</math> is the speed of light (3x108 ms-1).

Since speed is relative, it follows that two observers in different inertial reference frames may disagree on the mass and kinetic energy of a body. Since all inertial reference frames are treated on an equal footing, it follows that mass and energy are interchangeable.

In recent years most physicists have shifted away from Einstein's original reliance on relativistic mass and his suggestion that mass increases{{Citation needed|date=January 2012}}. Instead, most physicists today teach that

:<math>F=\frac{d}{d\tau} p</math>

where <math>p</math> is the momentum defined by <math>\gamma m v</math>, <math>\gamma</math> is the standard Lorentz factor, and <math>\tau</math> is the proper time. Force F defined this way is a vector and thus can handle the directional aspect of the relativistic effects better than the concept of relativistic mass can.

The abandonment by physicists of the concept of relativistic mass, however, has the consequence of undermining the traditional claim under relativity that

:<math>m - m_0 = \frac{E}{c^2}</math>

also popularly known as

:<math>E = m c^2</math>

Now a concept of the 4-momentum <math>p</math> of a particle is taught, such that the square of the magnitude of <math>p</math> satisfies:

<math>||p||^2 = -p_x^2-p_y^2-p_z^2+E^2 = m_0^2c^4</math>

in any inertial reference frame. The magnitude of the 4-momentum, in any inertial frame, equals the rest mass <math>m_0</math> of the particle (in units where <math>c=1</math>).

== Paradoxes ==

The predictions of the theory of relativity throw up a number of apparent paradoxes and anomalies relating to the effects of time dilatation and length contraction. Whilst these paradoxes are consistent with the theory, they are contrary to everyday human experience and therefore can seem like impossibilities.

=== The Twin Paradox ===

The twin paradox is usually stated as a thought experiment involving two twins, one of whom is sent on a long journey in a spacecraft travelling at close to the speed of light, whilst the other remains on Earth. Time dilatation means that the travelling twin, on his return to Earth, is younger that the twin who has remained at home. However, because neither twin is in a special position - each being in an inertial frame of reference - the reverse must also be true, and so the twin remaining on Earth must be younger. Hence each twin is younger than the other - a paradox.

The problem can be resolved in two ways. One is to examine the effects of General Relativity: to come back to Earth, the travelling twin must undergo acceleration in order to reverse his course, causing temporal effects which make him permanently the younger. Alternatively, it can be explained entirely using Special Relativity and noting that the twins are not in symmetrical situations: the one on earth has remained in a single inertial frame of reference, whilst the travelling twin has travelled in two.<ref>http://mentock.home.mindspring.com/twins.htm</ref>

=== The Ehrenfest Paradox ===

The Ehrenfest Paradox considers a rigid wheel or disc rotating a bout its axis at high speed (somewhat like a bicycle wheel spinning freely on its axle). The rim of the wheel travels at close to the speed of light and therefore undergoes length contraction, whereas the radius (the spokes, for the bicycle wheel) does not. Hence the circumference is no longer equal to 2<big><math>\pi</math></big>r, which is paradoxical.

The apparent paradox was finally resolved in 1975 by the Norwegian scientist [[Øyvind Grøn]].<ref>http://www.physicsforums.com/showthread.php?t=224955</ref>

== Variable Speed of Light ==

The Theory of Relativity implies that physical constants like c, the speed of light in a vacuum, have remained constant. But at least one study suggests that physical constants, and possibly even the speed of light, have changed as the universe has aged.<ref>James Glanz and Dennis Overbye, "Cosmic Laws Like Speed of Light Might Be Changing, a Study Finds," August 15, 2001.[http://www.nytimes.com/2001/08/15/science/15PHYS.html?ex=1185076800&en=d6467b6e3e346796&ei=5070]</ref>

"For the first time, scientists have experimentally demonstrated that sound pulses can travel at velocities faster than the speed of light, c. William Robertson's team from Middle Tennessee State University also showed that the group velocity of sound waves can become infinite, and even negative. ... Although such results may at first appear to violate special relativity (Einstein's law that no material object can exceed the speed of light), the actual significance of these experiments is a little different. These types of superluminal phenomena, Robertson et al. explain, violate neither causality nor special relativity, nor do they enable information to travel faster than c. In fact, theoretical work had predicted that the superluminal speed of the group velocity of sound waves should exist. 'The key to understanding this seeming paradox is that no wave energy exceeded the speed of light,' said Robertson."<ref>http://www.physorg.com/news88249076.html</ref>

"A team of researchers from the Ecole Polytechnique Fédérale de Lausanne (EPFL) has successfully demonstrated, for the first time, that it is possible to control the speed of light – both slowing it down and speeding it up – in an optical fiber, using off-the-shelf instrumentation in normal environmental conditions. Their results, to be published in the August 22 issue of Applied Physics Letters, could have implications that range from optical [[computing]] to the fiber-optic telecommunications industry."<ref>http://www.scienceblog.com/light.html</ref> Both slowing down and speeding up of light within a substance other than a vacuum is made possible, because the light travels through the material, and that material affects the speed of light, i.e. a photon hits an electron, which then exits and emits a slightly lower energy photon out in the direction that the original photon was traveling, thus maintaining conservation of momentum. No matter how transparent an object may appear, it radically impacts the speed of the light traveling through it, as demonstrated by the refractive production of a rainbow by a crystal, which Newton himself discovered.

This apparent change in speed can be explained, however, by noting that the constant c refers to the speed of light in a vacuum, i.e., when it is unimpeded. The speed of light when traveling through physical media is, in fact, variable.

"A pair of German physicists claim to have broken the speed of light - an achievement that would undermine our entire understanding of space and time. ... Dr Nimtz told New Scientist magazine: 'For the time being, this is the only violation of special relativity that I know of.'"<ref>http://www.telegraph.co.uk/earth/main.jhtml?xml=/earth/2007/08/16/scispeed116.xml</ref>

==Pending research==

Today some physicists are working on hypothesizing how general relativity might have related to the other three forces of nature during the first fraction of a second of the [[Big Bang]]. Two of the more commonly studied attempts are [[string theory]] and [[loop quantum gravity]], but they have failed to produce any evidence that science mandates a science must have, and both typically take large amounts of work to even conform to what scientists believe. Critics increasingly point out that string theory and loop quantum gravity are largely untestable and unfalsifiable, and thus potentially unscientific under the principles of science advanced by [[Karl Popper]].<ref>See, for example, ''Not Even Wrong'', by Peter Woit</ref>

Relativity continues to be tested and some physics professors remain skeptical of the theory, such as University of Maryland physics professor Carroll Alley, who served as the principle physicist on the Apollo lunar project.<ref>http://science.nasa.gov/headlines/y2004/21jul_llr.htm</ref>

== Political aspects of relativity ==

Some [[liberal]] politicians have extrapolated the theory of relativity to metaphorically justify their own political agendas. For example, [[Democratic]] [[President of the United States of America|President]] [[Barack Obama]] helped publish an article by liberal law professor [[Laurence Tribe]] to apply the relativistic concept of "curvature of space" to promote a broad legal right to [[abortion]].<ref>Tribe, acknowledging help by Obama, argued that the [[Constitution]] should be interpreted to establish a right to federally funded [[abortion]] and that, more generally, ''[[Roe v. Wade]]'' does not go far enough. They insisted that a relativistic "curvature of space" could achieve this result by expanding application of the [[Constitution]] based on its impact on personal choice. "The ''[[Roe v. Wade]]'' opinion ignored the way in which laws regulating pregnant women may shape the entire pattern of relationships among men, women, and children. It conceptualized abortion not in terms of the intensely public question of the subordination of women to men through the exploitation of pregnancy, but in terms of the purportedly private question of how women might make intimately personal decisions about their bodies and their lives. That vision described a part of the truth, but only what might be called the Newtonian part. ... [A] change in the surrounding legal setting can constitute state action that most threatens the sphere of personal choice. And it is a 'curved space' perspective on how law operates that leads one to focus less on the visible lines of legal force and more on how those lines are bent and directed by the law's geometry." Laurence H. Tribe, The Curvature of Constitutional Space: What Lawyers Can Learn from Modern Physics, 103 Harv. L. Rev. 1, 16-17 (1989).</ref> As of June 2008, over 170 law review articles have cited this [[liberal]] application of the theory of relativity to legal arguments.<ref>Search conducted by [[User:Aschlafly]] in the LEXIS database "US Law Reviews and Journals, Combined," conducted June 1, 2008.</ref> Applications of the theory of relativity to change morality have also been common.<ref>"Mistakenly, in the minds of many, the theory of relativity became relativism."[http://www.worldnetdaily.com/news/article.asp?ARTICLE_ID=38081]</ref> Moreover, there is an unmistakable effort to censor or ostracize criticism of relativity.<ref>Although the [[Examples of Bias in Wikipedia|liberally biased Wikipedia]] contains lengthy criticisms of the subjects of many entries, and even though publications like ''The Economist'' recognize the lack of scientific satisfaction in the theory (see, e.g., "Weighing the Universe," The Economist (Jan. 25, 2007)), Wikipedia's entry on [http://en.wikipedia.org/wiki/Theory_of_Relativity Theory of Relativity] omits one word of criticism.</ref>

Physicist [[Robert Dicke]] of Princeton University was a prominent critic<ref>http://www.time.com/time/magazine/article/0,9171,943324,00.html</ref> of general relativity, and Dicke's alternative "has enjoyed a renaissance in connection with theories of higher dimensional space-time."<ref>"Initially a popular alternative to General Relativity, the Brans-Dicke theory lost favor as it became clear that omega must be very large-an artificial requirement in some views. Nevertheless, the theory has remained a paradigm for the introduction of scalar fields into gravitational theory, and as such has enjoyed a renaissance in connection with theories of higher dimensional space-time."[http://nedwww.ipac.caltech.edu/level5/Glossary/Essay_bekenstein.html]</ref> Despite being one of the most accomplished physicists in the 20th century, Dicke was repeatedly passed over for a [[Nobel Prize]], and in at least one case Dicke was insulted by the award being granted to others for contributions more properly credited to Dicke.

There has been little recognition by the Nobel Prize committee of either theory of relativity, and particularly scant recognition of the Theory of General Relativity. A dubious 1993 Nobel prize in physics was awarded Hulse and Taylor for supposedly finding the first evidence of gravitational waves in the orbital decay of the binary pulsar PSR1913+16.<ref>Weisberg, Joel M.; Taylor, Joseph H. (2003), "The Relativistic Binary Pulsar B1913+16"", in Bailes, M.; Nice, D. J.; Thorsett, S. E., Proceedings of "Radio Pulsars," Chania, Crete, August, 2002, ASP Conference Series</ref> A close reading of the paper reveals that that is based heavily on assumptions in trying to retrofit the data to the theory.

===Government Support for Relativistic research===
The Federal Government has funded the building of two gravity wave detectors: The first to test the principle, and the second (upgrade) to actually perform measurements. As a result of this work, on February 11, 2016, the LIGO team reported successful detection of gravitational waves caused by the merging of two black holes.<ref>https://www.ligo.caltech.edu/news/ligo20160211</ref>

{{Relativity}}

==See also==
*[[Attempts to prove E=mc²]]
*[[Counterexamples to Relativity]]
*[[Essay:Rebuttal to Counterexamples to Relativity]]
*[[Logical Flaws in E=mc²]]
*[[Essay:Rebuttal to Logical Flaws in E=mc²]]
*[[Quantitative Analysis of Alpha Decay]]
*[[Gravitational waves]]

== References ==
{{reflist|2}}

[[Category:Physics]]
[[Category:Science]]

==External links ==
*[http://ia331314.us.archive.org/2/items/theeinsteintheor11335gut/11335-h/11335-h.htm The Einstein Theory of Relativity, by H.A. Lorentz.]
*[http://www.relativitycalculator.com Relativity Science Calculator - Learn Special Relativity Mathematics ] The mathematics of special relativity presented in as simple and comprehensive manner possible within philosophical and historical contexts.
*[http://www.relativitycalculator.com/history_of_time_clocks.shtml Relativity Science Calculator - Philosophic Question: are clocks and time separable?]
*[http://www.relativityscience.com/twin_clock_paradox.shtml Relativity Science Calculator - Twin Clock Paradox]