Essay:Rebuttal to Counterexamples to Relativity

This is intended as an article rebutting the points in the Counterexamples to Relativity article. That article's talk page has proven to be less than satisfactory for this purpose, because it gets archived, and much of its material has degenerated into personal disputes. We believe that the two sides of the issue are better handled in two articles—this one and Counterexamples to Relativity, rather than a talk page.

Unlike most essay pages, anyone is welcome to contribute. We ask that you abide by the usual guidelines—do not remove non-vandal, non-parody, non-libelous material without discussing it first on the talk page, or explaining after-the-fact for serious problems.

1: Despite wasting millions of taxpayer dollars searching for gravity waves predicted by the theory, none has ever been found. Sound like global warming?

This is because the experimental capability to do so doesn't exist.

It has nothing to do with global warming.

2: The eccentricity of the Moon's orbit is increasing contrary to the theory of relativity

This could be a counterexample to both GR and Newtonian gravity--in both, the eccentricity is defined in terms of conserved quantities.

3: Subatomic particles have a speed observed to be faster than the speed of light, which contradicts a fundamental assumption of Relativity.[4] The Italian lab that "shocked the scientific world" has announced more precise results, confirming their previous announcement

Saying this a bit prematurely, aren't you?

4: The Pioneer anomaly.

Wasn't this shown to be due to heat engines?

5: Anomalies in the locations of spacecraft that have flown by Earth ("flybys").

See above

6: Spiral galaxies confound Relativity, and unseen "dark matter" has been invented to try to retrofit observations to the theory.

Correct me if I'm wrong, but wasn't it due to the acceleration of various parts of galaxies that accelerated funny that led to dark matter (based on simple Newtonian dynamics)?

7: The acceleration in the expansion of the universe confounds Relativity, and unseen "dark energy" has been invented to try to retrofit observations to the theory.

Uh-oh....the dark energy/cosmological constant argument....That term was added by Einstein after he discovered that his field equations (<math>\mathbf{G}=8\pi \mathbf{T}</math>) predicted that the universe was expanding, contradicting his firm philosophical belief in a static universe. So he inserted <math>\Lambda \mathbf{g}</math> to the LHS so that it would predict a static universe. A few years later, Hubble showed the universe to be expanding, and Einstein called the cosmological constant the worst mistake of his career. So, it sort of had a bad reputation, and people didn't want to seriously consider it, until recent observations have shown the universe's expansion to be accelerating forced them to do so. It could have had a very different history. Einstein could have had that term in the EFE's from the start, and pointed out that it would determine if the universe's expansion was accelerating (or not expanding at all!) and it would take further observation to determine its value.

8: Increasingly precise measurements of the advance of the perihelion of Mercury show a shift greater than predicted by Relativity, well beyond the margin of error.

A footnote goes on to say that "In a complicated or contrived series of calculations that most physics majors cannot duplicate even after learning them, the theory of general relativity's fundamental formula, <math>G_{\mu\nu} = 8 \pi K T_{\mu\nu}\,</math>, was conformed to match Mercury's then-observed precession of 5600.0 arc-seconds per century. Subsequently, however, more sophisticated technology has measured a different value of this precession (5599.7 arc-seconds per century, with a margin of error of only 0.01) ..."

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, general relativity predicts 42.98 ±0.04 arcseconds per century. Some observed values 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: Pijper 2008]

These error bars, and that of the relativity formula, all overlap.

The formula for mechanics under general relativity is complicated, but it is not contrived or conformed. "Conformed" suggests that it was somehow adjusted or "tweaked" to match the 42.98 figure. The formula is

<math>G_{\mu\nu} = 8 \pi K T_{\mu\nu}\,</math>

To begin to explain the formula, Newton's law of gravity, combining F = ma and <math>F = \frac{KMm}{r^2}\,</math>, is

<math>a = \frac{KM}{r^2}\,</math>

In Einstein's equation, <math>T_{\mu\nu}\,</math> is the "stress-energy tensor", and <math>8 \pi T_{\mu\nu}\,</math> gives the density of the Sun, taking the place of <math>\frac{M}{r^2}\,</math>. <math>G_{\mu\nu}\,</math> is the "Einstein curvature tensor", and says how spacetime curves to create an apparent gravitational acceleration.

There is nothing to tweak to get a value of 42.98 arcseconds. 8 is 8. <math>\pi\,</math> is <math>\pi\,</math>. K is Newton's constant of gravitation in both formulas.

9: The discontinuity in momentum as velocity approaches "c" for infinitesimal mass, compared to the momentum of light.

You have to take them going to 0 at the same time! It's nonsense for a massive particle to travel at c!

10: The logical problem of a force which is applied at a right angle to the velocity of a relativistic mass - does this act on the rest mass or the relativistic mass?

The simple answer is, unequivocally, that it acts on the 'relativistic' mass. The question seems to relate to a simple misunterstanding of Special Relativity. Einstein's theories lead to the conclusion that observers in different inertial frames of reference (i.e. observers with differing, but constant velocities relative to the thing being observed) will observe different inertial masses in the body being observed. However, there is no variance in the body's mass with regard to the direction of the force. Thus to a given observer, a force in any direction will operate on the same mass. However, to a different observer, this mass may be different, although still the constant with regard to the direction of the force.

11:The observed lack of curvature in overall space.

What? Is has been observed

12: The universe shortly after its creation, when quantum effects dominated and contradicted Relativity.

We're still working on a quantum theory of gravity; this isn't so much a counter-example as saying that (classical)GR isn't valid in that domain.

13: The action-at-a-distance of quantum entanglement.

Special Relativity only forbids the transmission of matter, energy or information at a speed faster than light. There are plenty of other things that can move faster than light. Consider a laser on Earth which is rotating on a pivot, whose light shines onto the hull of a satellite 200,000Km away (2e8 metres). If the laser rotates at a sedentary one revolution ever four seconds, the speed of the laser beam's tip crossing the satellite's hull is 3.14e8 metres per second - faster than the speed of light. However, this is not a transfer of information. Any information is travelling from Earth to the satellite, obeying the universal speed limit. Similarly, the only information that can be transmitted by the quantum entanglement of two particles is from the originator of the particles to the two observers, not from one observer to another. Faster than light transmission of information using quantum entanglement has never been observed, nor has even conceived how such a mechanism might work.

14: The action-at-a-distance by Jesus, described in John 4:46-54, Matthew 15:28, and Matthew 27:51.

As an argument against relativity, there are two reasons that this is invalid (beyond simply questioning the evidential validity of the Bible):

a) These passages clearly refer to a miracle. A miracle, being an act of God, is not subject to the laws of physics.

b) It is highly debatable as to whether the verses do describe action-at-a-distance in the sense of an action whose influence travels instantaneously (and therefore faster than the speed of light). This itself may be argued from two viewpoints:

i) When reading these passages, as with consideration of many apparent relativistic anomalies, the true picture of causality must be considered. In each case there are two apparent events. Event A - Jesus does something (says 'thy son liveth', says 'be it unto thee even as thou wilt', or Christ's spirit leaving His body). Event B - the apparent result (the son lives, her daughter is made whole, or the earth quakes). However, it is not the case in any of these examples that A causes B. Both A and B are caused by a third event. In the first two cases it is Christ's thought that causes the miracle and that causes His lips to announce the miracle. This thought would have occurred fractions of a second before either event, and is the non-instantaneous cause of both. In the last case it is Christ's death that is the precursor and cause of both events.

ii) It must be considered that at the time when the Gospels were written, neither their authors nor their intended readers were aware of any concept of the speed of light and were unable to measure the billionths of a second difference between the events being considered here. Thus just as in modern parlance the phrase 'at the same moment' has a tolerance of milliseconds (unless specifically couched to mean otherwise) so do the various terms used by the Evangelists. They would never have considered it an important issue, and would therefore not have worried about the degree of precision.

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27: Relativity requires different values for the inertia of a moving object: in its direction of motion, and perpendicular to that direction. This contradicts the logical principle that the laws of physics are the same in all directions.

This is merely a restatement of item 10, (see above).

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35: Minkowski space is predicated on the idea of four-dimensional vectors of which one component is time. However, one of the properties of a vector space is that every vector have an inverse. Time cannot be a vector because it has no inverse.

Time isn't a vector. It is a component of the vector space known as "spacetime".