What tests can falsify general relativity?

[meopemuk]

I think one interesting experiment that can falsify GR is to measure acceleration of photons near the Earth surface.

The usual story is that this acceleration must be equal to g, just as for any other body (the principle of equivalence), but this (Newtonian) prediction underestimates the observed gravitational deflection of the starlight by the Sun. The other half of the observed deflection angle should come from the global spacetime curvature around the Sun.

However, a closer inspection of GR equations shows that things are not that straightforward. It was even shown by Hilbert in 1916 that light acceleration vector can be directed away(!) from the massive body. For details I refer to you to the excellent article by Kirk McDonald "Gravitational Acceleration of a Moving Object at the Earth’s Surface"

The measurements of the light acceleration in terrestrial conditions looks like a difficult task, but it turns out that one can confine a light beam within a Fabry-Perot resonator for a time long enough to see how it falls Gravitational light deflection in Earth-based laser cavity experiments

Eugene.

 

[PeterDonis]

It was even shown by Hilbert in 1916 that light acceleration vector can be directed away(!) from the massive body. For details I refer to you to the excellent article by Kirk McDonald "Gravitational Acceleration of a Moving Object at the Earth’s Surface"

On an initial read, I do not think this article is correct. It appears to be mistaking coordinate-dependent effects for actual physical effects. For example, the analysis in Appendix A appears to be claiming that the "antigravity" effect should be observed in an accelerating rocket in flat spacetime, which is clearly wrong.

 

[pervect]

I tend to assume that when people ask if a theory can be falsified, a yes answer is a good thing, as a theory that can't be falsified is of no use at all.

I also tend to assume (perhaps incorrectly) that when people use that language, they are referring to the concept as presented by writers such as Popper about the philosophy of science.

 

[vanhees71]

As a general statement, I agree with you; what counts as the SEP depends on who you ask.

In the specific case discussed in this thread, however, "SEP" is given a specific meaning: that the internal behavior of a system held together by its own self-gravity, such as the rotation curves of a galaxy as a function of its mass distribution, should not depend on the external gravitational field in which it is embedded. More precisely, it should only depend on the tidal gravity due to external objects, not on the "gravitational potential" or any other such property. This is indeed what GR predicts.

The paper referenced claims to find galaxies whose rotation curves cannot be explained without violating the above constraint, i.e., without adding an effect of the external "gravitational field" (not tidal gravity, but something like the "gravitational potential" due to other galaxies--though I have not dug in any detail into exactly how the "external gravitational field" is being defined or estimated) to the equations used to predict the rotation curves, an effect that is not predicted by GR.

I couldn't agree more. So "SEP" is just GR, i.e., a gauge theory with well defined gauge independent quantities describing the observables.

I think what's necessary heuristics to physically motivate the idea of "gauging" Lorentz invariance is the weak equivalence principle based on an idealization, the "test particle" and the conclusion that "test particles" follow geodesics in 4D spacetime (leading to a Lorentzian manifold when restricted to classical descriptions of matter and (classical or quantized) electromagnetism with the pseudo-metric as generic dynamical object and the then unique torsion-free connection or to a Einstein-Cartan manifold with a connection and a pseudo-metric as generic dynamical objects). From this gauge principle and the assumption of a theory with an action that is derived from the usual assumption of the interaction terms with a minimal order of derivatives (leading unique to $R$ as the building block for the Lagrangian, which is equivalent to a Lagrangian with only first-order derivatives).

This clearly defines what has an objective meaning, namely gauge-invariant objects, i.e., local gauge-independent/generally covariant tensor fields. Since this is quite a restriction it's a strong prediction and, of course, in principle falsifiable.

In other words: It's much simpler to just define what's meant by GR by establishing this clear mathematical structure than to rely on pretty vague heuristics like the various EPs. That the EPs are vague heuristics is indeed underlined by the fact that there are as many versions of them as there are textbook writers on GR!

Whether or not the above cited paper really falsifies GR, is another question. As I said before, I doubt it that one can draw such a strong conclusion from one observation, apparently in favor of MOND, given the fact that there are many observations in disfavor of MOND.

 

[vanhees71]

The SMoP does not make a positive claim that the particles it models are the only ones that exist, only the much weaker negative claim that no other particles have been observed so there's no need to try to include them in the model. Particle physicists don't really have any good criterion for predicting which particles, of all the ones that are mathematically possible, actually exist. But as you note, experimentally it seems to be the case to a very good approximation that the particles contained in the SMoP are the only ones that exist.

Indeed, but for me MOND is pretty much falsified by the observation of galaxies where the velocity curves follow the "visible-matter content", i.e., (interpreted within in the standard DM hypotehsis) the absense of a significant amount of DM. If MOND were right the velocity curves should deviate from the GR predictions in any case, because within MOND it's not caused by presence of some DM but by a generally valid modification of the fundamental laws of the gravitational interaction. There are also the observations related to collisions of galaxies.

 

[Olorin]

As I said before, I doubt it that one can draw such a strong conclusion from one observation, apparently in favor of MOND, given the fact that there are many observations in disfavor of MOND.

Please source your claim of facts and observations in disfavor of MOND. Actually there are none, the MOND conjecture is as alive as ever and getting all of his predictions right. Most recent and serious studies are clearly disfavoring GR+DM. See https://darkmattercrisis.wordpress.com/2020/11/10/the-crisis-in-cosmology-is-now-catastrophic/ for a comprehensible review of all studies that are strongly disfavouring GR+DM and favouring a modified gravity conjecture.

Indeed, but for me MOND is pretty much falsified by the observation of galaxies where the velocity curves follow the "visible-matter content", i.e., (interpreted within in the standard DM hypotehsis) the absense of a significant amount of DM. If MOND were right the velocity curves should deviate from the GR predictions in any case, because within MOND it's not caused by presence of some DM but by a generally valid modification of the fundamental laws of the gravitational interaction. There are also the observations related to collisions of galaxies.

Your opinion is very wrong and doesn’t correspond to the current status of research. And again you must quote a peer reviewed paper to support your claims. If you are talking about Peter Van Dokkum et al. paper, I’ve already pointed to you the debunking of his claims by not accounting for the External Field Effect. So please again always quote the scientific literature that sustains your claims in order not to bring confusion to the discussion and to be more precise about what you’re talking about. Thanking you in advance.

 

[Demystifier]

Not if the singularities are part of nature, then the theory makes good predictions.

If a singularity (not hidden behind a horizon) existed in nature, how would it manifest in observations?

 

[Olorin]

If a singularity (not hidden behind a horizon) existed in nature, how would it manifest in observations?

Whenever you compute a physical quantity and find infinity, you’re wrong. Energy density can’t be infinite, it doesn’t make any sense. The prediction of singularities in GR points towards the theory not being quite right. But it is not the kind of not right that destroys its relevance completely, just the kind that gives clues of its incompleteness.

 

[martinbn]

If a singularity (not hidden behind a horizon) existed in nature, how would it manifest in observations?

The initial(big bang) singularity is not behind a horizon.

 

[martinbn]

Whenever you compute a physical quantity and find infinity, you’re wrong. Energy density can’t be infinite, it doesn’t make any sense. The prediction of singularities in GR points towards the theory not being quite right. But it is not the kind of not right that destroys its relevance completely, just the kind that gives clues of its incompleteness.

Do you know what a singularity in this context is?

 

[vanhees71]

Your opinion is very wrong and doesn’t correspond to the current status of research. And again you must quote a peer reviewed paper to support your claims. If you are talking about Peter Van Dokkum et al. paper, I’ve already pointed to you the debunking of his claims by not accounting for the External Field Effect. So please again always quote the scientific literature that sustains your claims in order not to bring confusion to the discussion and to be more precise about what you’re talking about. Thanking you in advance.

Just a few I found in google scholar easily (restricting to papers newer than 2015)

https://academic.oup.com/mnras/article-abstract/485/2/1886/5364560
https://academic.oup.com/mnras/article-abstract/482/1/1248/5132879
https://www.worldscientific.com/doi/abs/10.1142/S0218271818470272
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.96.124016

 

[Demystifier]

The initial(big bang) singularity is not behind a horizon.

Yes, but this singularity cannot be seen in observations.

 

[martinbn]

Yes, but this singularity cannot be seen in observations.

Only naked singularities could be seen, but those shouldn't exist.

 

[PeterDonis]

Your opinion is very wrong

Please stop making such dogmatic claims. You have been repeatedly reminded that this is an open area of research. In an open area of research you do not say things like this about the opinions of people who disagree with you. If you are unable to abide by this rule, you will be banned from further posting in this thread.

 

[PeterDonis]

this singularity cannot be seen in observations.

Only because there are obstacles in the way. In principle, if there was an initial singularity at the beginning of our universe (which, btw, we don't know for sure is the case), we could observe the density and spacetime curvature increasing without bound as we looked further into the past and closer to that initial singularity. There is no event horizon in between, so there's nothing in principle to prevent that. The only reason we can't do that in our actual universe is that the universe's opacity to EM radiation prevents us from seeing EM radiation further back than recombination, and we don't have any other good ways of getting direct observations from earlier times (e.g., we don't have the technical capability at present to detect primordial neutrinos or gravitational waves). But that is just a technical limitation, not a limitation imposed by physics.

 

[PeterDonis]

Only naked singularities could be seen

The term "naked singularity" is usually used to refer to a timelike singularity that is not hidden behind an event horizon (e.g., the $r = 0$ singularity in super-extremal Kerr spacetime). However, an initial spacelike singularity, such as the one at $t = 0$ in FRW cosmology, could in principle be seen as well, even though the term "naked singularity" is not usually used to describe this case.

 

[Grasshopper]

I disagree with your take on falsification. You are being confused between the ontological validity of a theory, that is if in its essence it makes an acceptable and valid explanation of natural phenomena, and its effectiveness at describing the results of experimental observations and hence its utility for technology. Ontology and effectiveness are 2 very different aspects of our theories. Take Newtonian gravity: we know and Newton knew that this approach was ontolligically wrong, he knew that an instataneous action at a distance as a propriety of a force law was wrong, but it didn’t prey on the effectiveness of the model and we still use it to compute orbits etc...same can be said for Newtonian mechanics, now superseeded by quantum mechanics etc...So in this sense Newtonian mechanics is wrong, it doesn’t makes a valid and acceptable explanation of natural phenomena in the general and ontological sense, but it is nevertheless still effective for modeling a large array of physical situations.

In the same fashion, GR can one day be falsified, that is proven wrong in the ontological sense, that is if we demonstrate that its very essence as a metric theory of gravity doesn’t make sense anymore as a correct and valid explanation of the nature of gravity. One of the straightforward ways to do it is to test for the validity of its postulates that is its foundational pillars. The 3 equivalence principles are those pillars: the weak, the strong and the Einstein. For example and to add to the initial topic, there are 3 experiments being set up at CERN ( Aegis, Alpha g and g bar) that will test for the weak and indirectly the Einstein equivalence principles validity for antimatter, by testing anti hydrogen atoms interaction with the Earth gravitational field. If for exemple the outcome of these experiments is anti hydrogen falls up with an acceleration of -g then that’s a 200% violation of both the weak and the Einstein equivalence principles and GR is falsified in its essence because it wouldn’t make any sense to describe gravitational phenomena as resulting from the space time curvature of the Earth anymore as different test objects would now behave differently in the presence of one specific curvature. This still wouldn’t remove the effectiveness of GR formalism to agree with some observables but it will render its overall physical framework nonsensical. So this was my take on ontoligical validity, falsification and effectiveness of a scientific theory. Hope things are clearer for all.

I was under the impression that the entire point of physics was to make models that make correct predictions, NOT to know what’s “really” going on.

 

[martinbn]

The term "naked singularity" is usually used to refer to a timelike singularity that is not hidden behind an event horizon (e.g., the $r = 0$ singularity in super-extremal Kerr spacetime). However, an initial spacelike singularity, such as the one at $t = 0$ in FRW cosmology, could in principle be seen as well, even though the term "naked singularity" is not usually used to describe this case.

I agrer, but my impression was that Demystifier wants a singularity that is in you past and future. At least that is how i understood his reply to the big bang singularity example.

 

[Demystifier]

I was under the impression that the entire point of physics was to make models that make correct predictions, NOT to know what’s “really” going on.

The overall success of medicine is often measured by how long people live, but it doesn't mean that the entire point of medicine is to make people live longer. Similarly, the overall success of physics is often measured by how well it makes predictions, but it doesn't mean that the entire point of physics is to make good predictions. We want to have better health (which is what the purpose of medicine is) and we want to understand nature (which is what the purpose of physics is), but "health" and "understanding" are somewhat vague terms which cannot be precisely defined, which is why some people like to deal with more precise notions that can be defined quantitatively. But objective measure of something that we need is not the same as the thing what we need. Yet another example is a vague concept of wealth (which is what we need and what the point of economy is) and its objective measure - the amount of money. The entire point of economy is not to produce more money.

Sorry for these offtopic analogies, but I felt a strong urge to say this. Many people fail to understand the difference between purpose of something and objective measure of how well this purpose is achieved, which causes a lot of nonsense in what people do, be it in physics, medicine, economy, or anything else.

 

[Demystifier]

I agrer, but my impression was that Demystifier wants a singularity that is in you past and future. At least that is how i understood his reply to the big bang singularity example.

Just the opposite, since I can measure only the present, I want a singularity in my present.

 

[martinbn]

Just the opposite, since I can measure only the present, I want a singularity in my present.

I mean a singularity that was in your past, now is in your present, and will be in yiur future. This phasing is very non-relativistic, but i hope it is clear.

 

[PAllen]

Just the opposite, since I can measure only the present, I want a singularity in my present.

For anything not near you, you only measure information from your causal past. By definition of horizon, any singularity behind a horizon is never in your causal past (but it does change from being in your causal future to “possible present” - spacelike separation, at a specific event on your external world line). You never get information from it because it is never in your causal past.

Big bang singularity, if it really exists, would would always be in your causal past and, in principle, you get information from it.

A naked singularity from a collapse has all three causal relationships with an external observer. Causal future, whence you can send something to reach the singularity at formation. “Possible now”, whence you can no longer influence its formation or detect it yet. Causal past, whence you can get information from its formation.

 

[romsofia]

Although I can't really add to the discussion at hand, I would like to add a paper for those interested in an experiment that did deal with the SEP (Strong equivalence principle) that be found here:
https://www.nature.com/articles/347261a0

A interesting thing you may notice in the paper is the bring up speculation of a "5th force", so when I read it, I asked my advisor why they even did that. Apparently during the (80s?), there was a some work done on a potential "fifth force of nature", so in some older papers you may seem them addressing those claims. Not sure if there are many "fifth forcers" around anymore though...

Enjoy!

 

[Speady]

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.

 

[Ibix]

This is only possible if the speed of light (the pulse) (relative to me) becomes higher and lower.

No it isn't. It's trivial to Lorentz transform the leading and trailing edges of a light pulse and show that the lengths and frequencies change, qualitatively in the way you describe, but that the speed is invariant.

Say the trailing edge of a pulse of light moving in the $+x$ direction is at $x=0$ at $t=0$. Then you can write down the position of the $n$th wave crest infront of that as $x=n\lambda+ct$. Then you use the inverse Lorentz transforms, $x=\gamma(x'+vt')$ and $t=\gamma(t'+vx'/c^2)$, to eliminate $x$ and $t$ and rearrange. The result is $$x'=n\sqrt{\frac{c+v}{c-v}}\lambda+ct'$$which shows the Doppler shift factor multiplying $\lambda$ and that the wave speed is still $c$.

 

[Speady]

Ibix, your rebuttal is invalid, because this (Lorentz transforms) is derived directly from the assumption that c is constant.

 

[PeterDonis]

your rebuttal is invalid, because this (Lorentz transforms) is derived directly from the assumption that c is constant.

No, his rebuttal is valid, because he is showing you that there is a perfectly self-consistent solution to the scenario you proposed that has $c$ constant--and since $c$ being constant is an experimental fact, we should use the solution that is consistent with that fact, not some other solution that you or anyone else dreams up that isn't.

 

[Ibix]

Ibix, your rebuttal is invalid, because this (Lorentz transforms) is derived directly from the assumption that c is constant.

Your claim seemed to me to be that Doppler shifts and pulse length variation were inconsistent with an invariant speed of light (apparently Peter thought the same). I showed that they are consistent by deriving those effects with, as you say, an assumption of invariant light speed. That would not have been possible if your claim were true.

Did I not understand what you were claiming?

 

[Speady]

Inferring something based on an assumption is different from a measurement or hard evidence. It is an elaboration of an assumption and therefore remains an assumption. 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. This is evidence without assumptions, purely scientific.

 

[Ibix]

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

Of course. But we have plenty of evidence that $c$ is frame invariant. So my argument is based on an assumption with a lot of experimental justification.

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.

You continue to fail to understand how different frames measure light beams, as you did in your last two threads on the topic.

This is evidence without assumptions, purely scientific.

Rubbish. You are making assumptions, such as (incorrectly) assuming that different frames see a light beam as having the same length. This is not the case in a relativistic universe.

 

[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