I What tests can falsify general relativity?

[PeterDonis]

Inferring something based on an assumption is different from a measurement or hard evidence.

True, but irrelevant, since we have plenty of measurements and hard evidence regarding the speed of light. It seems as though you do not understand what this evidence means, physically.

Since a speed is a length divided by a time duration at all times, I cannot avoid different speeds if I divide the same length by different durations.

Which is not what is going on with the relativistic Doppler shift. @Ibix has already explained what is going on and why it is perfectly consistent with an invariant speed of light.

 

[Speady]

Light is not easy to measure. Is there a measurement of the speed of light where the light source and observer move with respect to each other at high speed? If not, how can you be sure?

 

[Ibix]

Is there a measurement of the speed of light where the light source and observer move with respect to each other at high speed?

Synchrotron radiation. Black hole jets. See also section 3.3 of the experimental basis of special relativity FAQ, linked from a pinned post at the top of this forum.

Note that you are shifting your goalposts here. Your initial claim was that a constant speed of light was inconsistent with Doppler effects. I showed that this was false. You are now asking a different question about the experimental basis of relativity, which seems to me to be rather off topic for this thread.

 

[Vanadium 50]

Is there a measurement of the speed of light where the light source and observer move with respect to each other at high speed?

Alväger, T.; Nilsson, A.; Kjellman, J. (1963), "A Direct Terrestrial Test of the Second Postulate of Special Relativity", Nature 197 (4873): 1191.

Note the year.

 

[Sagittarius A-Star]

Is it enough if c is not constant ?! When I approach a light source, the frequency increases, but the duration of the pulse that passes also becomes shorter. Conversely, the frequency decreases when removed, but the duration of the pulse also becomes longer. The same pulse passes me in a shorter and longer time. This is only possible if the speed of light (the pulse) (relative to me) becomes higher and lower.

No. The observation of far away spectroscopic double-stars proved, that the light arrives with the same speed relative to a telescope on earth, when one star is moving away from the Earth and appears red-shifted, and later is moving back towards the Earth and appears blue-shifted.

Sources:
https://en.wikipedia.org/wiki/De_Sitter_double_star_experiment
https://en.wikisource.org/wiki/A_proof_of_the_constancy_of_the_velocity_of_light

If the speed of light would depend on the speed of the light source, then multiple optical copies of each star in a far enough double-star system would be measured in a spectroscopic analysis as moving slowly in only one direction - apparently violating Keplers law. But that is not measured. See animations for one of the two stars, for different observation distances:
http://www.physik.li/beispiele/Doppelstern/Doppelstern.htm

 

[PAllen]

It seems the basic absurdity with @Speady 's argument has not been raised. The statement

Is it enough if c is not constant ?! When I approach a light source, the frequency increases, but the duration of the pulse that passes also becomes shorter. Conversely, the frequency decreases when removed, but the duration of the pulse also becomes longer. The same pulse passes me in a shorter and longer time. This is only possible if the speed of light (the pulse) (relative to me) becomes higher and lower.

The italicized part of this argument would apply exactly as stated for blue light versus red light for flash bulbs, stationary with respect to some detector. Does @Speady believe different colors of light travel at different speeds? I hope not, and the resolution is that the wavelength of a pulse is different. Doppler changes the wavelength of a pulse exactly inversely to frequency change. A shorter wavelength divided by a shorter duration, then produces exactly same speed. The key point is simply that red light doppler shifted to blue has all the same properties as blue light directly emitted as blue, including shorter wavelength. Quite frankly, the misunderstanding here is one that would be surprising even for someone with no background beyond a typical high school physics discussion of waves.

 

[Grasshopper]

It seems the basic absurdity with @Speady 's argument has not been raised. The statementThe italicized part of this argument would apply exactly as stated for blue light versus red light for flash bulbs, stationary with respect to some detector. Does @Speady believe different colors of light travel at different speeds? I hope not, and the resolution is that the wavelength of a pulse is different. Doppler changes the wavelength of a pulse exactly inversely to frequency change. A shorter wavelength divided by a shorter duration, then produces exactly same speed. The key point is simply that red light doppler shifted to blue has all the same properties as blue light directly emitted as blue, including shorter wavelength. Quite frankly, the misunderstanding here is one that would be surprising even for someone with no background beyond a typical high school physics discussion of waves.

;)

As someone who has not really delved into upper division physics yet, would this be of relevance?

c = λ f

(The very first thing anyone learns in high school about light wavelength and frequency)No mention of transforming between reference frames in that lecture everyone has, and I’m pretty sure that is taught in the context of an inertial observer at rest with respect to the source.

 

[PeterDonis]

As someone who has not really delved into upper division physics yet, would this be of relevance?

c = λ f

(The very first thing anyone learns in high school about light wavelength and frequency)No mention of transforming between reference frames in that lecture everyone has

No, but that equation turns out to be valid in any frame. The wavelength and frequency are transformed when changing frames in such a way that their product is invariant.

 

[Ibix]

c = λ f

(The very first thing anyone learns in high school about light wavelength and frequency)No mention of transforming between reference frames in that lecture everyone has

The formula is true in every frame (which is why no mention of the frame needs to be made). Both $f$ and $\lambda$ are frame variant such that $c$ is invariant. That is, the Doppler shift factor for $f$ is the reciprocal of the factor for $\lambda$.

 

[vanhees71]

The Doppler effect follows simply from the Lorentz transformation properties of the electromagnetic field as a tensor, and since it is a massless field its propagation speed is $c$ in any reference frames and independent of the speed of the source emitting the waves. The (quite simple) calculation can be found in my FAQ

https://itp.uni-frankfurt.de/~hees/pf-faq/srt.pdf

sect. 3.2.1.

 

[binis]

Tests that special relativity holds locally also test GR - for instance, the Michelson Morely experiment. Wills describes this as "tests of local Lorentz invariance". So if any of the standard SR tests of the speed of light failed, GR would also be falsified.

Α simple test could be to measure the speed of light derived from a surernova.
As the universe is expanding,a supernova at the edge is apparently moving with a speed of 3c or even 4c.They could measure the speed of its light and if they find it as c,then we could say that really the speed of light is independent of the frame.
Did they measure the speed of light derived from an airplane as it lands?

 

[Ibix]

Did they measure the speed of light derived from an airplane as it lands?

I'm not sure that this particular experiment has been done. Measuring the speed of light from moving sources has certainly been done, both from astronomical sources like binary stars and lab sources. See posts #103-#105.

 

[pervect]

Α simple test could be to measure the speed of light derived from a surernova.
As the universe is expanding,a supernova at the edge is apparently moving with a speed of 3c or even 4c.They could measure the speed of its light and if they find it as c,then we could say that really the speed of light is independent of the frame.
Did they measure the speed of light derived from an airplane as it lands?

There's a problem though - space isn't a vacuum, and the light from the supernova would probably interact with atoms along the way. The usual theoretical framework is that the light is absorbed and re-emitted, so the effective source of any scattered light would be from particles it encountered along the way in many theoretical frameworks.

Lab experiments of the speed of light from the decay of various rapidly moving particles have been done however to get around this issue. No effect on the speed of light has been observed.

Wiki mentions that there were some tests measuring the constancy of the fine structure constant from quasars, though, which found a variation with time. These results were not confirmed by other tests, though. More sensitive later tests did not find such a variation. The speed of light is one of the constants that determine the fine structure constant - I've talked at some length about how the speed of light is related to the fine structure constant and why it's better to measure the fine structure constant and not c directly. The short answer to this is units, the fine structure constant is dimensionless, so it has a direct physical meaning independent of any framework based on units and measurment standards. This avoids the whole issue of needing to think about the basis of such standards, and whether the standards could themselves be varying.

See http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html#moving-source_tests for discussion about measuring the speed of light from moving sources, and https://en.wikipedia.org/w/index.php?title=Time-variation_of_fundamental_constants&oldid=994755304 for a discussion of variation of fundamental constants.

 

[PeterDonis]

As the universe is expanding,a supernova at the edge is apparently moving with a speed of 3c or even 4c.

These "speeds" are not relative velocities in the SR sense (those must always be less than $c$). So you can't use these speeds to define a "frame".

They could measure the speed of its light

You can't directly measure the speed of light going from place to place inside a very distant object.

 

[PeterDonis]

Is there an exact solution to the Einstein field equations for "n" gravitating masses?

No. This case can only be solved numerically.

 

[brotherbobby]

So no, your premise is not true, at least not in a way that would lead to the your later concerns and conclusions.

I confess I do not understand it, but it is true, as given in the quote by Einstein below.

" Here is how Einstein formulated the idea in his major, 1916 review article, written just after the completion of the general theory of relativity. Einstein points out that his considerations lead coordinates to lose their direct metrical significance. " (my emphasis)

More of it here : http://www.pitt.edu/~jdnorton/teach...nce_GR_relative/significance_GR_relative.html

The way I used to understand it is that, since all manner of transformations are possible, "length" does not have to go into "length" also, if you know what I mean. Likewise, time can go into $\text{time}^{\text{squared}}$. Or some product of space and time. Either way, the spatial significance is gone, and since no coordinate system is preferred, all observers have to admit that space and time measurements become meaningless. Or am I mistaken?

A cautionary note: You should not be trying to learn relativity from that book, for about the same reasons that we don't teach classical mechanics from Newton's Principiae.

Very different things. Newton's Principia is a scholarly presentation where he uses Euclidean geometry to show, among other things, why the gravitational force has to be central. Einstein's book is an expository one. Of course no one should learn classical mechanics from there. Likewise, no one can learn general relativity from Einstein's exposition, but can develop an idea about it. Either way, it does not answer the philisophical questions I raised - namely, do space and time become mere illusions and matter and fields the really fundamental entities that give space and time their extstance. I understand these are very subtle matters.

 

[vanhees71]

I think, Einstein's book is still a good starting point to learn general relativity, but of course today the subject is much more advanced.

It's also true that coordinates are just labels of space-time points. They usually do not refer directly to observable quantities. What's observable in GR is given by coordinate and frame-independent tensors, particularly space-time "metrics" like lengths and times.

Concerning your philosophical questions I'd say today everything is on the fundamental level described by (quantized) fields.

 

[PeterDonis]

I confess I do not understand it, but it is true, as given in the quote by Einstein below.

The quote does not say that "space and time" lose their physical meaning. It says that "coordinates" lose their physical meaning. Big difference.

since no coordinate system is preferred, all observers have to admit that space and time measurements become meaningless. Or am I mistaken?

You are most definitely mistaken. Does the lack of a preferred coordinate system mean you can't use a ruler to measure how long an object is, or a clock to tell you how much time has passed? Of course not.

 

[jbriggs444]

Einstein points out that his considerations lead coordinates to lose their direct metrical significance.

he spatial significance is gone, and since no coordinate system is preferred, all observers have to admit that space and time measurements become meaningless. Or am I mistaken?

You can measure a space-like interval with rulers. You can measure a time-like interval with clocks. No need to bring coordinates into it. Measurements that you make remain objective and invariant. In that sense, time and space remain firmly physical.

If you choose to apply coordinates to the endpoints that you are measuring, you are not required to choose coordinates in which varying the fourth coordinate value while holding the other three fixed always results in describing a time-like path. Nor are you required to choose coordinates in which varying the first coordinate value while holding the other three fixed always results in describing a space-like path.

You can use coordinate systems that are quite strange. You can even use null coordinates. The formula for the metric (when cast in terms of the coordinates you choose) will change depending on the coordinates you choose. The inability to pick out a particular element of your coordinate tuples as being "the time coordinate" does not stop you from using the coordinate system to calculate the elapsed proper time from event A to event B along a prescribed path.