Evidence for preferred frames?

In summary: The Einstein postulates assert an invariance of the propagation speed of light in vacuum for any observer, and which amounts to a presumed absence of any preferred frame. The postulates appear to be directly linked to relativistic effects which emerge from Einstein's Special Theory of Relativity, which is based upon the concept of a flat spacetime ontology, and which then lead to the General Theory of Relativity with its curved spacetime model for gravity. While the relativistic effects are well established experimentally it is now known that numerous experiments, beginning with the Michelson-Morley experiment of 1887, have always shown that the postulates themselves are false, namely that there is a detectable local preferred frame of reference. This critique briefly
  • #1
ohwilleke
Gold Member
2,361
1,353
http://uk.arxiv.org/abs/physics/0412039

The Einstein Postulates: 1905-2005 A Critical Review of the Evidence
Authors: Reginald T. Cahill (Flinders University)
Comments: PDF 12 pages, 7 figures
Subj-class: General Physics

The Einstein postulates assert an invariance of the propagation speed of light in vacuum for any observer, and which amounts to a presumed absence of any preferred frame. The postulates appear to be directly linked to relativistic effects which emerge from Einstein's Special Theory of Relativity, which is based upon the concept of a flat spacetime ontology, and which then lead to the General Theory of Relativity with its curved spacetime model for gravity. While the relativistic effects are well established experimentally it is now known that numerous experiments, beginning with the Michelson-Morley experiment of 1887, have always shown that the postulates themselves are false, namely that there is a detectable local preferred frame of reference. This critique briefly reviews the experimental evidence regarding the failure of the postulates, and the implications for our understanding of fundamental physics, and in particular for our understanding of gravity. A new theory of gravity is seen to be necessary, and this results in an explanation of the `dark matter' effect entailing the discovery that the fine structure constant is a 2nd gravitational constant.

Sounds off base to me, but I'd welcome an informed critique.
 
Physics news on Phys.org
  • #2
If you look at his references, you will see the experiments cited are either unpublished (performed by others) or very old (an 1887 Michelson Morley citation if you can believe it). More recent experiments which disagree with his conclusion are completely ignored.

And that is the good part of the paper, as much of the rest is devoted to slamming the physics establishment for wasting the past 100 years.
 
Last edited:
  • #3
Cahill also mentions Dayton Miller. Compare this to the Usenet FAQ on the subject:

The Michelson-Morley experiment was repeated with greater accuracy in the years that followed. In 1925 Dayton Miller announced that he had detected a change in velocity of the speed of light and was even awarded prizes for the discovery, but a 1950s appraisal of his work indicated that the most likely origin of his results lay with diurnal and seasonal variations in the temperature of his equipment.

Modern instruments could easily detect any ether drift if it existed. The Earth moves around the sun at a speed of about 30 km/s, so if velocities added vectorially as Newtonian mechanics requires, the last 5 digits in the value of the speed of light now used in the SI definition of the metre would be meaningless. Today, high energy physicists at CERN in Geneva and Fermilab in Chicago routinely accelerate particles to within a whisper of the speed of light. Any dependence of the speed of light on reference frames would have shown up long ago, unless it is very slight indeed.
 
  • #4
Cahill claims that the Michelson-Morley data (by his analysis) indicates a non-zero velocity with respect to a preferred reference frame. According to Tom Roberts (in sci.physics.relativity) Cahill did not properly take into account the experimental uncertainties in the M-M data, which can be extracted from the data themselves. Taking the actual uncertainties into account, Cahill's analysis actually is statistically consistent with a velocity of anywhere between zero and several thousand km/sec in any direction.
 
  • #5
I'm very interested...

Reg Cahill is a senior member of the Faculty of Science and Engineering at an Australian university (http://www.flinders.edu.au" ), is the chairman of the Courses and Curricula committee for the School of Chemistry, Physics, and Earth Sciences in that faculty, but seems to be operating in the realm of fringe science...

Is this good or bad?

Check out the http://www.scieng.flinders.edu.au/cpes/people/cahill_r/processphysics.html page. Remember, this is not a run-of-the-mill crackpot site, this is a serious academic website at an accredited University.
 
Last edited by a moderator:
  • #6
He is a pottery magician.
 
  • #7
In English?
 
  • #8
This work looks professional and Reginald T. Cahill has referenced some interesting work on Dalton Miller and Roland De Witte (recently deceased), which I fully agree with - namely a sidereal variation in the speed of light.

However, the rest of his work is quite advanced and I can't say whether it's good or bad, without spending more time on it.
 
  • #9
"pottery magician"
...and a search through the archives reveals all.

It's certainly an easy label to apply, but don't you think he's not your run-of-the-mill crackpot? Do you think you might be applying that label a little hastily in this case?

How does he measure up on the crackpot index?
 
  • #10
wisp said:
This work looks professional and Reginald T. Cahill has referenced some interesting work on Dalton Miller and Roland De Witte (recently deceased), which I fully agree with - namely a sidereal variation in the speed of light.

What makes you agree with those but not these:

1. "Tests of Relativity Using a Cryogenic Optical Resonator", C. Braxmaier et al., PRL v.88, p.010401 (2002).

2. "Tests of Lorentz Invariance using a Microwave Resonator", P. Wolf et al., PRL v.90, p.060403 (2003).

3. "New Limit on Signals of Lorentz Violation in Electrodynamics", J.A. Lipa et al., v.90, p.060403 (2003).

4. Muller et al., PRL v.91, p.020401 (2003).

5. http://arxiv.org/abs/astro-ph/0410742

Zz.
 
  • #11
PeteSF said:
Check out the http://www.scieng.flinders.edu.au/cpes/people/cahill_r/processphysics.html page. Remember, this is not a run-of-the-mill crackpot site, this is a serious academic website at an accredited University.

...And it is run by Cahill himself.

Face it, Cahill is trying to tell us that one of the most fundamental concepts of relativity is wrong without himself performing a single experiment to support the charge; and he ignores or rejects all modern published experiments (i.e. in the last 50+ years) which contradict him.

There is no peer acceptance of this work and I don't expect any in the near future for obvious reasons.
 
Last edited by a moderator:
  • #12
ZapperZ said:
What makes you agree with those but not these:

1. "Tests of Relativity Using a Cryogenic Optical Resonator", C. Braxmaier et al., PRL v.88, p.010401 (2002).

2. "Tests of Lorentz Invariance using a Microwave Resonator", P. Wolf et al., PRL v.90, p.060403 (2003).

3. "New Limit on Signals of Lorentz Violation in Electrodynamics", J.A. Lipa et al., v.90, p.060403 (2003).

4. Muller et al., PRL v.91, p.020401 (2003).

5. http://arxiv.org/abs/astro-ph/0410742

Zz.

ZapperZ

It is possible to for Lorentz Symmetry to be upheld 100%, even when the one-way speed of light is only constant relative to a preferred reference fame.
The above experiments seem to imply that Lorentz Violation is a test of the constancy of the speed of light, which it is not. However, there link is strong to the two-way speed of light measurements, but not for the one-way.
 
  • #13
wisp said:
ZapperZ

It is possible to for Lorentz Symmetry to be upheld 100%, even when the one-way speed of light is only constant relative to a preferred reference fame.
The above experiments seem to imply that Lorentz Violation is a test of the constancy of the speed of light, which it is not. However, there link is strong to the two-way speed of light measurements, but not for the one-way.

Yet, when the SAME type of experiments (Dalton Miller and Roland De Witte) showed hints of such violation, how come you didn't question why it would show up IF what you said is true? I didn't ask why you buy or don't buy the experiments I listed. I asked why you believe in one set, but NOT the other, especially when the latter are testing the SAME thing, with BETTER and more accurate measurements? If you wish to throw out the latter as being "two-way speed of light measurements" and not show any lorentz invariant, then you should also not buy into the experiments that you prefer to believe in.

Zz.
 
  • #14
Hey wisp,

I remember seeing a discussion on your idea somewhere (may have even been here on PF, a year or more ago) where you described a relatively simple experiment that would (in your view) settle this matter (for you) in a straight-forward way.

IIRC, it wouldn't involve a lot of expensive equipment; with accurate clocks and good lasers being now available at quite reasonable prices, less than a mortgage on an average family home (and maybe not much more than the cost of new Toyota sedan).

It sounded like an interesting experiment, in its own right, so perhaps with the right kind of marketing, and wrapping it up in a nice package, you might be able to find a way to get it done?

Seems to me that spending lots of time discussing how many teeth a horse has is inferior to going out and actually counting them!

Kind Regards
Nereid
 
  • #15
Last edited:
  • #16
The experiment didn't appear to reveal the anomalous effect of the eclipse on the Pendulum as reported in other eclipse events - but as they pointed out - it may be because of the geometric relationship involved in this particular eclipse. What does the principle of mutual interaction say about the periodic effects?
 
  • #17
Are you referring to the principle of mutual interation of self creation cosmology?

The experiment needs to be replicated under stricter conditions. In particular it needs to be in a high vacuum isolated from any other field effects and vibrations. It is an interesting concept as it is claiming a higher order Foucault's pendulum effect.

As far as the PMI is concerned the interesting question is to see whether any confirmed results are correlated with the Earth's motion relative to the surface of last scattering of the CMB. They mention a possible correlation with the direction of the centre of the galaxy.

Garth
 
  • #18
Garth said:
The experiment needs to be replicated under stricter conditions. In particular it needs to be in a high vacuum isolated from any other field effects and vibrations.

May I ask WHERE exactly do you propose to find such conditions?

Zz.
 
  • #19
Zz - In a carefully constructed laboratory experiment?

Garth
 
  • #20
Garth said:
Zz - In a carefully constructed laboratory experiment?

Garth

How do you propose to achieve isolation from "other field effects" such as gravity, and how high of a vacuum would suffice?

Zz.
 
  • #21
Garth said:
The experiment needs to be replicated under stricter conditions. In particular it needs to be in a high vacuum isolated from any other field effects and vibrations.
ZapperZ said:
How do you propose to achieve isolation from "other field effects" such as gravity, and how high of a vacuum would suffice?

Zz.

Come on! The significant word is "other"!
The pendulum has to be in a gravitational field to be a pendulum!

However local fluctuations in the gravitational field have to be guarded against, i.e. no nearby observers; therefore observations would have to be remote.
I would put the pendulum in a vacuum dewar jar, which internally would be cooled to be isothermal to a high degree and possibly near absolute zero.

The vacuum need not be too high, just sufficient that any Brownian motion type perturbation could not possibly influence the result.

The whole apparatus would be made of all non-magnetic materials and cleansed from any contamination by ferrous particles. Furthermore it could be placed, if necessary, in a Faraday cage and earthed to remove any electrostatic forces.

The whole apparatus might be mounted on a bedrock-anchored platform, which was stable to a sufficient degree, or floating in a mercury bath to absorb vibration.

The experiment will also need to be repeated at different longitudes.

I will leave any other details up to the experimenters. But it is important that all spurious noise in the signal is eliminated before periodic pendulum effects can be accepted as a real phenomenon.

Nevertheless, There are these three separate experiments, which were set up to detect a total eclipse effect and recorded a null result, and yet all recorded some periodic pendulum anomaly that might be correlated with matter distribution in the universe. It is worth pursuing the matter further.

Garth
 
Last edited:
  • #22
The experiment involving pendulums necessarily involves gravity - I think Garth has in mind the elimination of all other fields. Oops - Just noticed Garth already posted his answer while I was typing the first sentence.
 
  • #23
Interestingly, Einstein's original paper of 1905 (The most widely known and least cited paper) does not mention the Michelson Morely expt. Einstein sometimes used the constancy of light as a starting point simply because was, to him, "the thing we knew most about". (The Meaning of Relativity AE).

Later in life, AE always spoke of the MM experiment as fundamental to his thoughts. When AE was asked if the MM expt. was fundamental to his original construction of Relativity, AE replied he wasn't certain at that time if he'd heard of it!
 
  • #24
That is something Einstein's biographers have had difficulty with - i suspect that he felt the beauty of the symmetry would be destroyed if it were based soley or primarily upon explaining a particular experiment. SR had greater applicability than disproving light anisotropy and confirming MMx - for example, SR works whether or not there is an ether - it works even though the two arms of the interferometer are of unequal length, and it appears to work for one way isotrophy (MMx only confimed over and back isotrophy - the second postulate of SR went way beyond what is required to explain Mmx) In summary, the theory was much more important than the experiment.

Recall, Einstein had worked on the theory since he was 16 years old - he had began to suspect time as the culpret - and he reached that conclusion before Lorentz's publication. So over and back isotrophy as confirmed by MMx would be of interest, but would not add anything to the path he was already on - I guess what I am saying, Einstien would not be surprised at any experimental result that was consistent with what he already determined theoretically.
 
  • #25
ZapperZ said:
What makes you agree with those but not these:

1. "Tests of Relativity Using a Cryogenic Optical Resonator", C. Braxmaier et al., PRL v.88, p.010401 (2002).

2. "Tests of Lorentz Invariance using a Microwave Resonator", P. Wolf et al., PRL v.90, p.060403 (2003).

3. "New Limit on Signals of Lorentz Violation in Electrodynamics", J.A. Lipa et al., v.90, p.060403 (2003).

4. Muller et al., PRL v.91, p.020401 (2003).

5. http://arxiv.org/abs/astro-ph/0410742

Zz.
DrChinese said:
Face it, Cahill is trying to tell us that one of the most fundamental concepts of relativity is wrong without himself performing a single experiment to support the charge; and he ignores or rejects all modern published experiments (i.e. in the last 50+ years) which contradict him.
Cahill hasn't ignored or rejected the results of any modern published experiment including those listed here by Zz; neither has he contradicted any of them. What he has reported (which you guys have failed to notice much less even begin to refute) is that all published (valid) experimental data (both the modern and the not-so-modern) are consistent with one particular locally preferred frame (first identified by Miller) with anisotropies that are proportional to (n-1) where n is the refractive index of the interferometric medium. Virtually all of the modern experiments, including those listed here by Zz, were performed in a high-vacuum where n=1.
 
Last edited:
  • #26
Relativity predicts that there will be anisotropies in the measured velocity of EM radiation when EM radiation interacts with matter, because the matter will absorb the EM radiation, drift for a bit with some velocity, then re-emit the EM radiation. The result is a different average propagation velocity than 'c'. The less matter, the less effect.

This does not impact in any way shape or form the fact that the velocity of EM radiation when it has not been absorbed is equal to 'c'.

So the results above are consistent with relativity, and since the relativistic behavior in the limit as the media approaches a vacuum will be different than the Newtonian limit, the results should not be consistent with Newtonian physics.

In short, yet another proof of relativity is apparently being miscontrued as an objection to it.
 
  • #27
pervect said:
Relativity predicts that there will be anisotropies in the measured velocity of EM radiation when EM radiation interacts with matter, because the matter will absorb the EM radiation, drift for a bit with some velocity, then re-emit the EM radiation. The result is a different average propagation velocity than 'c'. The less matter, the less effect.

This does not impact in any way shape or form the fact that the velocity of EM radiation when it has not been absorbed is equal to 'c'.
I see...so all of these experiments that purport to test for Lorentz invariance can't possibly be valid if the EM radiation measured is absorbed by matter at any time during the measurement process?

pervect said:
So the results above are consistent with relativity, and since the relativistic behavior in the limit as the media approaches a vacuum will be different than the Newtonian limit, the results should not be consistent with Newtonian physics.

In short, yet another proof of relativity is apparently being miscontrued as an objection to it.
What has Newton got to do with any of this?
 
  • #28
Aether said:
I see...so all of these experiments that purport to test for Lorentz invariance can't possibly be valid if the EM radiation measured is absorbed by matter at any time during the measurement process?

The basic issues is: how long it takes light to go from point A to point B when nothing (like having a wall in the way, for instance) interferes with the progress of the light. More specifically, one is interested in whether this time (the time it takes light to go from A to B) depends in any way on any absolute "state of motion" of the emitter and receiver.

Because the interest is in how long it takes light to go from point A to point B in the absence of other disturbing effects, other disturbing effects (like matter, which can absorb the light and re-emit it after a time delay) are routinely eliminated.

This is just good science.

Objecting that "But if you put a wall in the way, the light will never get there", and "your theory didn't cover what happens when you build walls between the emitter and source" is silly, though I suppose it might momentarily impress people who either didn't know anything about the topic, or had some sort of personal axe to grind.
 
  • #29
pervect said:
The basic issues is: how long it takes light to go from point A to point B when nothing (like having a wall in the way, for instance) interferes with the progress of the light. More specifically, one is interested in whether this time (the time it takes light to go from A to B) depends in any way on any absolute "state of motion" of the emitter and receiver.
That's right, but the issue is complicated by the fact that the absolute state of motion of the emitter and receiver may affect our measurements of time as well as of the distance between the two.

pervect said:
Because the interest is in how long it takes light to go from point A to point B in the absence of other disturbing effects, other disturbing effects (like matter, which can absorb the light and re-emit it after a time delay) are routinely eliminated.

This is just good science.
Not necessarily. It can be an effective way to sterilize one's experiment and eliminate all traces of a locally preferred frame, but one must take care not to "throw the baby out with the bathwater". Are you familiar with the story of how the CMB was discovered? At first it was assumed to be noise, and steps were taken to try and eliminate it; Penzias & Wilson would have been so happy to have found an easy way to quench that pesky hiss: "Arno Penzias and Bob Wilson were trying to find the source of excess noise in their antenna, where pigeons were roosting. They spent hours searching for and removing the pigeon dung. Still the noise remained, and was later identified with the Big Bang."

pervect said:
Objecting that "But if you put a wall in the way, the light will never get there", and "your theory didn't cover what happens when you build walls between the emitter and source" is silly, though I suppose it might momentarily impress people who either didn't know anything about the topic, or had some sort of personal axe to grind.
Clocks and rods are typically made from atoms which are fastened together by EM forces. If a locally preferred frame were to simply affect clocks and rods in identical proportion to the way it affects EM radiation propagating through a vacuum, then local Lorentz invariance would be the result. This is a different interpretation for local Lorentz invariance than is offered by SR.

Assuming two perfectly offsetting effects (speed of light in vacuum anisotropy vs. the aberration of clocks/rods), modifying either one of these effects without modifying the other creates an imbalance that is detectable. Suppose that varying the refractive index n of the interferometric medium modifies the speed of light anisotropy in proportion to n without modifying clock/rod aberration, (n-1). Now, that's my conjecture; but it is backed-up by all of the experimental evidence gathered and reported by Cahill.
 
Last edited:
  • #30
Aether said:
Clocks and rods are typically made from atoms which are fastened together by EM forces. If a locally preferred frame were to simply affect clocks and rods in identical proportion to the way it affects EM radiation propagating through a vacuum, then local Lorentz invariance would be the result. This is a different interpretation for local Lorentz invariance than is offered by SR.

Assuming two perfectly offsetting effects (speed of light in vacuum anisotropy vs. the aberration of clocks/rods), modifying either one of these effects without modifying the other creates an imbalance that is detectable. Suppose that varying the refractive index n of the interferometric medium modifies the speed of light anisotropy in proportion to n without modifying clock/rod aberration, (n-1). Now, that's my conjecture; but it is backed-up by all of the experimental evidence gathered and reported by Cahill.
Cahill's locally preferred frame has a magnitude of 417±40km/s in the direction of (α, δ)=(17.5h, 65˚). In terms of the test theory of Mansouri & Sexl (R. Mansouri & R. Sexl, Gen. Rel. and Grav., Vol. 8, No. 7, (1997), pp. 497-513; Vol. 8, No. 7, (1997), pp. 515-524; and Vol. 8, No. 10, (1997), pp. 809-81) my conjecture finds concise expression as a dependence on n of the parameters, α(n), β(n), and δ(n) of the test theory. For example: [tex]\alpha(n)=-\frac{1}{2}n[/tex], [tex]\beta(n)=-\frac{3}{2}n[/tex], and [tex]\delta(n)=2n[/tex].

Any deviation of the test theory parameters α, β, & δ from the values predicted by special relativity (e.g. [tex]\alpha=-\frac{1}{2}[/tex], [tex]\beta=-\frac{3}{2}[/tex], and [tex]\delta=2[/tex].) can be interpreted as an anisotropy of optical path lengths.
 
  • #31
I contacted Reginald Cahill today. This is what he had to say regarding the posts in this thread:

Reginald T. Cahill said:
I had a quick look at some of the criticisms directed at my work. As usual they are based on a lack of understanding of the situation.


First, all experiments are being taken into account. The detection of absolute motion requires a clearer understanding of how each experiment works than has been given. Various kinds of experiments have been performed, and most bizarrely the theory for the operation of each of these is actually Newtonian physics, even though we all know that it failed over 100 years ago! The argument appears to run along the lines that if an experiment, whose analysis of operation is based upon Newtonian physics fails to detect absolute motion, then the Einstein theory must be correct. That is not logic. Unfortunately most of the recent resonant cavity experiments (essentially Michelson interferometers) use vacuum. Then several effects, each caused by absolute motion effects, actually cancel. But if one uses a gas in the device then that cancellation does not happen, and a residual effect occurs. Neither the Newtonian theory nor the Einstein theory has this situation arising. In fact ALL the experiments taken together are consistent, and they are implying that it is Lorentzian relativity which is being confirmed by all the experiments.


Reg
 
  • #32
Pervect - a side note - the explanation of the lower measured velocity of light in a medium as an absorption and re-emission is only one theory - which requires a great deal of faith in the fact that the new photon will be emitted in exactly the right direction in each an every encounter - a perfect laser effect by every atom - much more likely that the electric field of the photon interacts with the electrons in the atoms slowing down the propagation.
 
  • #33
Ever since the observation of the photoelectric effect, it hasn't taken much "faith" to see that atoms do in fact absorb light, and that the classical notions of electrons interacting with waves don't really describe well how light interacts with matter. But I suppose we are getting off on another tangent.
 
  • #34
Aether said:
I contacted Reginald Cahill today. This is what he had to say regarding the posts in this thread:
I had a quick look at some of the criticisms directed at my work. As usual they are based on a lack of understanding of the situation.


First, all experiments are being taken into account. The detection of absolute motion requires a clearer understanding of how each experiment works than has been given. Various kinds of experiments have been performed, and most bizarrely the theory for the operation of each of these is actually Newtonian physics, even though we all know that it failed over 100 years ago! The argument appears to run along the lines that if an experiment, whose analysis of operation is based upon Newtonian physics fails to detect absolute motion, then the Einstein theory must be correct. That is not logic. Unfortunately most of the recent resonant cavity experiments (essentially Michelson interferometers) use vacuum. Then several effects, each caused by absolute motion effects, actually cancel. But if one uses a gas in the device then that cancellation does not happen, and a residual effect occurs. Neither the Newtonian theory nor the Einstein theory has this situation arising. In fact ALL the experiments taken together are consistent, and they are implying that it is Lorentzian relativity which is being confirmed by all the experiments.


Reg
But isn't the trick to find a preferred frame in a vacuum??
Once you put gas into the apparatus you have introduced a 'preferred frame', that of the average centre of momentum of the gas.

Garth
 
  • #35
Garth said:
But isn't the trick to find a preferred frame in a vacuum??
That would be some trick!

Garth said:
Once you put gas into the apparatus you have introduced a 'preferred frame', that of the average centre of momentum of the gas.
Apparatus?? Now we're no longer simply in a vacuum, but also on a platform assembled from atoms fastened together by EM forces where apparently "...you have introduced a 'preferred frame', that of the average centre of momentum of the ..." apparatus (which completely determines the centroid of momentum for any gas contained within it?); at least that's my conjecture. If the effect of a preferred frame on the dimensions of a rigid apparatus are precisely the same as on the dimensions of EM radiation in vacuum, then what we have here is Lorentzian relativity. The gas merely serves to unbalance this equation so that the preferred frame can be measured using the rigid apparatus.

Cahill asserts:
Reginald T. Cahill said:
In fact ALL the experiments taken together are consistent, and they are implying that it is Lorentzian relativity which is being confirmed by all the experiments.
In terms of the test theory of Mansouri & Sexl my conjecture finds concise expression (for gas-mode interferometry) as a dependence on n of the parameters, α(n), β(n), and δ(n) of the test theory. For example:[tex]\alpha(n)=-\frac{1}{2}n,\ \beta(n)=-\frac{3}{2}n,\ and\ \delta(n)=2n[/tex] and using Cahill's locally preferred frame having a magnitude of 417±40km/s in the direction of (α, δ)=(17.5h, 65˚).

In contrast, according to Cahill, all experiments taken together are NOT consistent with SR which in terms of the test theory of Mansouri & Sexl finds concise expression as precisely: [tex]\alpha=-\frac{1}{2},\ \beta=-\frac{3}{2},\ and\ \delta=2[/tex] with no locally preferred frame.
 
Last edited:

Similar threads

  • Special and General Relativity
Replies
1
Views
1K
  • Special and General Relativity
Replies
15
Views
2K
  • Special and General Relativity
Replies
14
Views
2K
  • Special and General Relativity
Replies
2
Views
1K
  • Special and General Relativity
Replies
5
Views
2K
  • Special and General Relativity
Replies
27
Views
3K
  • Special and General Relativity
Replies
2
Views
1K
  • Special and General Relativity
Replies
13
Views
1K
  • Special and General Relativity
Replies
17
Views
1K
  • Special and General Relativity
Replies
19
Views
2K
Back
Top