I What tests can falsify general relativity?

[Olorin]

Well, I'm never easy with "the equivalence principle", particularly the strong one. What does this precisely mean in math and for observables?

The wiki article section in the strong equivalence principle is pretty good. You can have a look.

I think GR is very well defined given the Einstein equation, and one should just apply GR as it is to make predictions for an observable fact.

That is what scientists have been doing. GR field equations works very well in some circumstances and not so well in others. There are 3 Einstein field predictions that didn’t pass the test: galactic dynamics and clusters (motion and lensing), rate of extension past and present. The first discrepancy gives rise to the Dark Matter hypothesis which is still missing a proper proof even if we have been looking for it for decades now in a lot of different ways ( not good for GR predictions and hence validity so far). The second discrepancies concern the homogeneity of the CMB which leads to the horizon problem for which there is still no agreement on how it should be solved, inflation being one proposed solution but not one which has grown in acceptance, all the contrary. The last one is about the rate of expansion of the universe and its acceleration which give rise to the dark energy problem, still unsolved. So 3 predictions that came wrong and needed add ons, all of which are still of unknown, unproven nature. Not proper falsifications but still very troubling in Occam’s razor sense up to this day for GR.

The same holds for MOND. If they give different results, then you have a testable prediction.

MOND doesn’t toy with invisible stuff at galactic scales the way GR has to. So it is much less flexible in terms of what it frameworks can and can’t predict. With GR you can always adjust the distribution of the invisible stuff in arbitrary ways so as to fit the observable. You can’t do that in MOND. Just for that reason MOND is more testable and falsifiable than the combo GR+DM. It has superior scientific merits as a conjecture (as a reminder, MOND is not a theory but a conjecture that gives an effective force law in the very weak acceleration regime).

At least it's not too convincing for me, because there's so much evidence against MOND and so little evidence against GR that I'm a bit skeptical.

There is no evidence that goes against MOND the conjecture. It is perfectly verified in its regime of validity, it has predicted a lot of a priori observables that the DM paradigm struggles with ( Baryonic Tully Fischer Relation, abundance of plane of satellites, galaxies without or lacking dark matter and so on...). MOND still lacks its proper parent theory which could very well arise from a paradigm shift clue. GR as a foundational framework of our cosmological paradigm is still lacking from a proper understanding of its key missing ingredients: DM, dark energy and solving the horizon problem for the CMB. That’s quite a lot and very demanding under the prism of Ockam’s razor.

It's somehow similar to the case of the Standard Model. Only here the majority of physicists likes to disprove it, but so far there's no observation at the 5σ level disproving it.

Well there is now one at 7 sigmas: https://academic.oup.com/mnras/article/499/2/2845/5939857.
And MOND works here pretty well, again. Other ideas to why this paper is relevant can be found in here: https://academic.oup.com/mnras/article/499/2/2845/5939857
and here: https://tritonstation.com/2020/10/23/big-trouble-in-a-deep-void/. A explanatory video made by its authors can also be found here: .

 

[Olorin]

This is all to show how dicey it is to try to falsify GR via equivalence principle when reputable GR experts don’t necessarily agree that GR itself is consistent with them.

At least we can agree on some non-dicey outcomes from equivalence principle violations and implications for GR, can’t we? Do we agree that if anti hydrogen atoms are observed to fall up with -g acceleration at CERN it would ontologically falsifies GR by falsifying weak and Einstein equivalence principles at once? For sure in this situation GR field equation would be completely powerless to describe this new found physical situation right?

 

[PAllen]

At least we can agree on some non-dicey outcomes from equivalence principle violations and implications for GR, can’t we? Do we agree that if anti hydrogen atoms are observed to fall up with -g acceleration at CERN it would ontologically falsifies GR by falsifying weak and Einstein equivalence principles at once? For sure in this situation GR field equation would be completely powerless to describe this new found physical situation right?

Yes, we can definitely agree on that. Of course, my guess of the probability of that is exceedingly near zero.

 

[PAllen]

It occurs to me that the particular issue of galactic curves being affected by apparent gravitational potential, rather than tidal gravity may relate to the precise debate around Ohannian's questioning of the equivalence principle in GR. In particular, he showed that the dynamics of a bound system ( a water droplet in his example) are can be affected in significant ways by arbitrarily small tidal gravity "force" over the scale of the system. The counter argument is that looking at spatial scales alone is incorrect - the EP is local in time as well as space. The effects described by Ohannian take long time scales to accumulate and manifest. Now I wonder whether modeling of the effects of an "external gravitational field" supposedly with insignificant tidal effects properly accounts for the fact that over long time scales, even the tiniest tidal gravity can produce substantial effects on galactic curves and overall shape. That is, I am quite suspicious that claimed violated predictions of GR in this regime are, in fact, incorrect predictions dues to incorrect simplifications.

 

[Olorin]

Yes, we can definitely agree on that. Of course, my guess of the probability of that is exceedingly near zero.

Amazing! We reached the goal of OP. We have a clear experimental situation that if realized would falsify GR in a very profound way. I guess we would also agree that in this case there is no way we could say: GR needs modifications or extensions, it is incomplete etc... as this would be of the order of magnitude of the copernician revolution, right? Let’s now wait for the outcome and see what nature has to say. The experimental results may be around the corner. We could have almost had them if it were not for the LHC shutdown and following Covid shenanigans as Jeff Hangst team was supposedly ready to tackle the up or down issue.

 

[PAllen]

Well there is now one at 7 sigmas: https://academic.oup.com/mnras/article/499/2/2845/5939857.
And MOND works here pretty well, again. Other ideas to why this paper is relevant can be found in here: https://academic.oup.com/mnras/article/499/2/2845/5939857
and here: https://tritonstation.com/2020/10/23/big-trouble-in-a-deep-void/. A explanatory video made by its authors can also be found here: .

Here I think you misunderstood @vanhees71. He was referring to Standard Model of particle physics. Your links are about standard model of cosmology, a completely different beast with much less a-priori confidence.

 

[Olorin]

It occurs to me that the particular issue of galactic curves being affected by apparent gravitational potential, rather than tidal gravity may relate to the precise debate around Ohannian's questioning of the equivalence principle in GR. In particular, he showed that the dynamics of a bound system ( a water droplet in his example) are can be affected in significant ways by arbitrarily small tidal gravity "force" over the scale of the system. The counter argument is that looking at spatial scales alone is incorrect - the EP is local in time as well as space. The effects described by Ohannian take long time scales to accumulate and manifest. Now I wonder whether modeling of the effects of an "external gravitational field" supposedly with insignificant tidal effects properly accounts for the fact that over long time scales, even the tiniest tidal gravity can produce substantial effects on galactic curves and overall shape. That is, I am quite suspicious that claimed violated predictions of GR in this regime are, in fact, incorrect predictions dues to incorrect simplifications.

This might very well be the core of a proper rebuttal to the SEP violations claims. It still remains to be seen how these tidal forces are formally computed and applied to galactic systems in a proper peer review paper. On the other hand it seems that the authors have taken great precautions in evaluating the gravitational tidal forces as they were very well aware that those where out of SEP requirements.

 

[Olorin]

Here I think you misunderstood @vanhees71. He was referring to Standard Model of particle physics. Your links are about standard model of cosmology, a completely different beast with much less a-priori confidence.

Even worse then since in order for the SMoC ( Standard Model of Cosmology ) to be valid we need to falsify SMoP ( Standard Model of Particle) as SMoC needs exotic matter not predicted by the SMoP. So in all logic non SMoC is compatible with SMoP ( with massive neutrinos), but SMoC is only compatible with non SMoP which is still very well verified ( no non SMoP predicted particles detected as of yet).

 

[PeterDonis]

It still remains to be seen how these tidal forces are formally computed and applied to galactic systems in a proper peer review paper.

It's not so much computing the magnitude of the tidal gravity at some particular time; it's a matter of integrating its effects over time and seeing if they accumulate into something that could significantly change the predictions of the standard GR model. My understanding is that the current GR predictions assume that there would not be any such accumulation of tidal effects over time.

 

[PeterDonis]

we need to falsify SMoP

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.

 

[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.