What tests can falsify general relativity?

[PeterDonis]

it is not generally accepted that c is a constant in time

Yes, it is. Scientists have looked very carefully for evidence of variation in time (not of $c$ but of the fine structure constant, which is the meaningful variation to look for) and have not found any:

https://en.wikipedia.org/wiki/Fine-structure_constant#Past_rate_of_change

Wikipedia VSL-Theories

None of the proposals described in that article have gained any acceptance. Note also that some of them really mean violation of Lorentz invariance (instead of variation of the fine structure constant) when they say "variation of c with time"; scientists have also looked very carefully for evidence of violations of Lorentz invariance and have not found any:

https://en.wikipedia.org/wiki/Modern_searches_for_Lorentz_violation

 

[pervect]

Thanks for the answers but i think my point concerning velocity of light was misunderstood.
It is currently described and agreed as a constant in space, but it is not generally accepted that c is a constant in time, as well, as several VSL-approaches of the last years show.

Wikipedia VSL-Theories

Even Albert Einstein was discussing that in 1911 ...

I think it is my point that's not been understood here. At a minimum, it's not been acknowledged. Perhaps you could quote some references that suggest that the speed of light is "not generally accepted" as "constant with time", and, to get back to the point I made, describe in principle how you are measuring the speed of light. To measure the speed of light, you need two standards, one for time, one for space. And you haven't told us what these standards are even in principle. That was basically the point, and I have no idea how you think that the speed of light should be measured, and why you think the standards that you are using to measure the speeds themselves are "constant with time".

I can say that if you look at the actual language of the current version of the standards, there's no mention of the speed of light changing with time, and is defined as a constant.

See for instance (again) https://www.bipm.org/metrology/length/units.html

The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299 792 458 when expressed in the unit m s–1, where the second is defined in terms of the caesium frequency

Cs.

It's not my intent to say that you absolutely must adopt the current generally accepted and well documented standard, set by the body (the bipm) that is charged with the task of setting standards, but given that you apparently do not, in order to have a meaningful conversation you would at least have to tell us what standard(s) you are using.

For instance, you might be using the old meter prototype standard, or some variant therof that has been idealized.

 

[PeterDonis]

we have a recent study that casts a lot of trouble for the SEP

That study is not investigating the SEP directly. It's investigating a claimed "External Field Effect" in the context of MOND. So you have to be careful about taking its claims of SEP "violation" at face value. There is quite a bit of model-dependent interpretation involved.

All the paper is really claiming is "if we use our model of galaxy rotation curves, it matches the data better for these particular galaxies than the $\Lambda C D M$ model". But a model has to account for all of the data, not just data for one particular set of galaxies or data that are claimed to illustrate one particular group of theorists' ideas about one particular claimed effect.

 

[Olorin]

That study is not investigating the SEP directly. It's investigating a claimed "External Field Effect" in the context of MOND.

But if the SEP holds true, neighbouring objects should not exert any gravitational influence on the studied galaxies and thus should not have any dynamical effects on them. But the contrary is indeed claimed to be observed. The fact that this is done in the context of MONDIAN dynamics only further emphasizes the fact that such an effect is manifest. The study is definitely a test of the SEP. Furthermore, we need to bear in mind that the lead author was a proponent of LCDM and was convinced that his data would falsify MOND once and for all and ended up finding that the opposite was truth. That’s something worth noticing.

But a model has to account for all of the data, not just data for one particular set of galaxies or data that are claimed to illustrate one particular group of theorists' ideas about one particular claimed effect.

Exactly’ and that’s exactly what MOND has been doing recently. LCDM not so much. 2020 has been a pretty amazing year for MONDIAN astrophysics. See this for example: https://darkmattercrisis.wordpress.com/2020/11/10/the-crisis-in-cosmology-is-now-catastrophic/.

This review about MOND consecutive recent successes and LCDM lack off is pretty telling, wouldn't you agree? I find all those studies extremely telling and I defy agree with Pavel Kroupa statements. Has anyone specific objections on any of those arguments? They directly concern the survival of the concordance cosmology model of which GR is the theoretical pilar, its very foundation. can we agree on the idea that a falsification of GR is a falsification of the SMoC and vice versa somehow?

 

[Sagittarius A-Star]

and I have no idea how you think that the speed of light should be measured, and why you think the standards that you are using to measure the speeds themselves are "constant with time".
...
For instance, you might be using the old meter prototype standard, or some variant therof that has been idealized.

The length of the old meter prototype $L_1$ is a multiple (factor := $k$) of the Bohr radius $a_0$:
$L_1 = k * a_0 = k * \frac {\hbar}{m_ec\alpha}$.

Source:
https://en.wikipedia.org/wiki/Bohr_radius

=> $\ \ \ c = k * \frac {\hbar}{m_e L_1 \alpha}$

So, if $L_1$ is assumed to be "constant with time", then you will measure a constant $c$.

 

[PeterDonis]

if the SEP holds true, neighbouring objects should not exert any gravitational influence on the studied galaxies and thus should not have any dynamical effects on them. But the contrary is indeed claimed to be observed.

Yes, I know that's what the paper claims, but, as I said, that claim is based on quite a bit of model-dependent theoretical interpretation. It's not the same as if we could run a controlled experiment in which we could directly test the SEP.

that’s exactly what MOND has been doing recently

Yes, but the whole question is still open; there is not general agreement among cosmologists about how these issues (and many others) are going to be resolved. If you are asking if it is possible that "we have to modify GR" will be part of the final resolution, yes, of course that is possible. But "modification" is not the same as "falsification". See below.

can we agree on the idea that a falsification of GR is a falsification of the SMoC

No. The implication doesn't work in either direction.

First, as far as GR is concerned, "falsification" is not the right term, any more than it was for Newtonian physics when GR was discovered. Newtonian physics still works just fine for many applications. So will GR even if we someday find that we have to modify it in order to account for certain observations in cosmology. (These remarks would apply to the OP of the thread as well.)

That said, we could end up finding issues with GR in areas that do not have any implications for the SMoC--for example, issues to do with black holes. We could also end up finding issues with the SMoC that require it to be modified in ways that don't involve GR. ("Modify our assumptions for the equation of state and density of dark matter" is one obvious way that could happen.)

 

[PeterDonis]

This review about MOND consecutive recent successes and LCDM lack off is pretty telling, wouldn't you agree?

If you only read what the prosecution says, of course you're going to think the case is open and shut.

As I said in my previous post, this whole area is still open. I would be careful putting too much credence in what partisans on any side say, particularly in informal contexts like blog posts.

 

[vanhees71]

I think the usual strategy to test GR is to use some model or fit functions for measured quantities with some parameters to fit. The fit functions are chosen such that GR predicts certain values for parameters included in these fit functions and measure with which significance/confidence the values of these constants agree with or deviate from GR. An example is to use pulsar-timing measurements and post-Newtonian approximations with the various coefficients of the corresponding expansion, which have well-determined values within GR. These high-precision observations (via radio astronomy) so far haven't shown any deviations.

I think the case is not so clear concerning the question, whether there's dark matter or deviations from GR (alternative models like MOND) to explain the findings from cosmology (CMBR fluctuations, structure formation) and astronomy (velocity curves for stars in galaxies, dynamics "galaxy collisions").

For me among the most convincing observations in favor of GR and against alternative theories of gravity is the finding of galaxies which seem to have only a small amount of dark matter, i.e., where the velocity curves of stars follow the mass distribution of the visible matter, which thus makes up the galaxy with no or only a negligible amount of dark-matter content. If MOND were right, there should be the same deviations of the velocity curves from the predictions of GR (or Newton for that matter) as in the galaxies, where the "Standard Model" assumes the presence of dark matter.

 

[Olorin]

Yes, I know that's what the paper claims, but, as I said, that claim is based on quite a bit of model-dependent theoretical interpretation. It's not the same as if we could run a controlled experiment in which we could directly test the SEP.

Of course, every test of every theory is based on model-dependent interpretation: You build a theory and compute a numerical prediction that is derived from your model and test it against the experimentally obtained data. That’s just how science works. In this case, you take MOND equation for rotation curves and you apply it to galaxies. Furthermore your model predicts that in some cases the neighboring galaxies should be able to change the acceleration scale under which the MOND regime manifests itself, the so called External Field Effect (EFE). You can compute it very precisely for each galaxy. Now the idea is, where the EFE is computed to be negligible, the rotation curves are readily fitted by the MOND equation and where EFE is computed to be significant, the fit is not that good without taking it into account, and when you take into account, the fit is spot on. Hence, this demonstrates that there is a correlation between the neighbooring astronomical objects and the stellar dynamics within the studied galaxies with a 5 sigma confidence interval. This correlation between neighboring object and stellar dynamics should not exist if the Strong Equivalence Principle holds true, hence the conclusion that this experimentally evidenced correlation falsifies it and puts General Relativity on the edge of falsification as it is the only metric theory that needs the SEP to be valid.

 

[Olorin]

First, as far as GR is concerned, "falsification" is not the right term, any more than it was for Newtonian physics when GR was discovered. Newtonian physics still works just fine for many applications. So will GR even if we someday find that we have to modify it in order to account for certain observations in cosmology. (These remarks would apply to the OP of the thread as well.)

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.

 

[Olorin]

If you only read what the prosecution says, of course you're going to think the case is open and shut.

As I said in my previous post, this whole area is still open. I would be careful putting too much credence in what partisans on any side say, particularly in informal contexts like blog posts.

The evidence pieces have been mounting in an unprecedented way during recent times in favor of the prosecution though. I‘m not saying that the case is open and shut as I think it never really is in science (regarding the discovery of processes at least because for the ingredients is a bit different imo). But I'll be all ears about everything the defense has to say in opposition to each and every prosecution piece of evidence that is presented in the blog article ( maybe not here as it might be off topic).
As for the partisanship, I think it can’t be avoided in science as there will always be better roads at solving persistent problems than others. In other words, all the paths are not equivalent as a physical problem doesn’t realistically have multiple final solutions. Thus commitment to what seems the most plausible solution or enlightening paths will always be preferable.
As for the blog form, this is not your usual amateur blog, it is Pavel Kroupa’s blog, one of the leading astronomers and cosmologist of our time and listening to his insights in a different communicating format is always relevant and very instructive, especially since it is so well sourced and documented with all the references to peer to peer reviewed articles.

 

[Olorin]

I think the usual strategy to test GR is to use some model or fit functions for measured quantities with some parameters to fit. The fit functions are chosen such that GR predicts certain values for parameters included in these fit functions and measure with which significance/confidence the values of these constants agree with or deviate from GR. An example is to use pulsar-timing measurements and post-Newtonian approximations with the various coefficients of the corresponding expansion, which have well-determined values within GR. These high-precision observations (via radio astronomy) so far haven't shown any deviations.

Well that’s exactly what has been done in the SEP test studies I quoted but using the prediction of the MOND conjecture and in this case it has shown correlations between the dynamics of studied galaxies and neighboring objects just as predicted by the conjecture and excluded by GR. It is a perfectly well designed test and SEP/GR didn’t pass this one. In other words, if SEP/GR were correct, it shouldn’t be possible to correlate 2 independent observables ( rotation curves and neighboring galaxies physical properties) under an a priori theoretical framework with a 5 sigma confidence interval on the correlations.

I think the case is not so clear concerning the question, whether there's dark matter or deviations from GR (alternative models like MOND) to explain the findings from cosmology (CMBR fluctuations, structure formation) and astronomy (velocity curves for stars in galaxies, dynamics "galaxy collisions").

The mounting pieces of evidence are trending towards the MOND conjecture and a profound overall crisis in current cosmological paradigm that will most likely need a great amount of revision ( see Pavel Kroupa blog post « the crisis in cosmology is now catastrophic » linked above). Still unclear what will bring and push the consensus in that direction. My bet is on gravitational tests of antimatter at CERN and an ontological falsification of GR ( as explained in a post above).

For me among the most convincing observations in favor of GR and against alternative theories of gravity is the finding of galaxies which seem to have only a small amount of dark matter, i.e., where the velocity curves of stars follow the mass distribution of the visible matter, which thus makes up the galaxy with no or only a negligible amount of dark-matter content. If MOND were right, there should be the same deviations of the velocity curves from the predictions of GR (or Newton for that matter) as in the galaxies, where the "Standard Model" assumes the presence of dark matter.

Well this is defy not convincing at all since the authors of the studies ( van dokkum and al. If my memory serves ) have forgotten about the External Field Effect that exist in MOND ( see: http://astroweb.case.edu/ssm/papers/MNRASv480p473.pdf ). It is now clear that they got their conclusions wrong regarding MOND not only for ignoring the external field effect but also for a lot of other reasons.

 

[PeterDonis]

I disagree with your take on falsification.

My objection was to the word "falsification". If you're willing to say that Newtonian mechanics has been "falsified" because GR says gravity is not a force any more, for example, even though people all over the world use Newtonian mechanics every day to make predictions that are accurate enough for their purposes, then that's your preference for choice of words; it doesn't mean we disagree about what Newtonian physics can and can't do in terms of predictions.

A drawback of using the word "falsification" this way is that, by this criterion, every theory we have is potentially false and we can never say a theory is "true" because we could discover something in the future that makes us have to modify or replace it. But again, that's a matter of choice of words; it doesn't change what any given theory is capable of in terms of predictions. And predictions are what we actually use theories for.

The evidence pieces have been mounting in an unprecedented way during recent times in favor of the prosecution though.

Sure, if you only read what the prosecution says.

As for the blog form, this is not your usual amateur blog, it is Pavel Kroupa’s blog

That doesn't make it a valid reference for PF discussion. Physicists can get away with saying things in informal contexts--not just blogs but even published books, if they aren't textbooks (check out all the PF threads we've had triggered by some overstatement in one of Brian Greene's books)--that they would never get away with in a textbook or peer-reviewed paper. That's why we don't treat physicists' blogs and other informal sources as valid references, no matter who the author is or how knowledgeable they are about the field in question.

What you personally want to put credence in is, of course, up to you. I'm just explaining why you shouldn't expect others here to agree with you if all you have is an informal source, especially if it's only presenting one side of the argument.

 

[Olorin]

A drawback of using the word "falsification" this way is that, by this criterion, every theory we have is potentially false and we can never say a theory is "true" because we could discover something in the future that makes us have to modify or replace it. But again, that's a matter of choice of words; it doesn't change what any given theory is capable of in terms of predictions.

That’s the exact definition of «falsification» you can find in Popper’s books and whom coined the very term we are discussing here.

And predictions are what we actually use theories for.

Science is not only about making predictions and being usable, it is all about finding and understanding the inner workings of nature and of the physical, material world. A lot of wrong theories in the ontological sense can be used to make valid predictions. It doesn’t make them valid or true at explaining our universe, which is the very essence of fundamental science.

That doesn't make it a valid reference for PF discussion. Physicists can get away with saying things in informal contexts--not just blogs but even published books, if they aren't textbooks (check out all the PF threads we've had triggered by some overstatement in one of Brian Greene's books)--that they would never get away with in a textbook or peer-reviewed paper. That's why we don't treat physicists' blogs and other informal sources as valid references, no matter who the author is or how knowledgeable they are about the field in question.

Except Kroupa’s blog post is a formal-informal context as each of its arguments is sourced with links to several peer-reviewed article. It is not like if he was making up the arguments out of thin air, he is literally quoting peer reviewed scientific literature. So I guess you could make an exception here due to very well documented and sourced content of Pavel Kroupa’s blog as it is easier for everyone to go and look for themselves instead of me having to copy paste each article link with each corresponding argument.

What you personally want to put credence in is, of course, up to you. I'm just explaining why you shouldn't expect others here to agree with you if all you have is an informal source, especially if it's only presenting one side of the argument.

Again, Kroupa’s blog is not your usual informal source of information due to that many sourced peer reviewed articles linked to his insights. As for the other side of the argument, I haven’t heard any convincing rebuttal as of yet. So still waiting to learn about serious counter claims. But this is proby not the place to discuss those.

 

[PeterDonis]

Science is not only about making predictions and being usable, it is all about finding and understanding the inner workings of nature and of the physical, material world.

Not all scientists agree with this. Particularly those who work on quantum mechanics.

I guess you could make an exception here

Nope. If he provides links to peer-reviewed papers, great--then give references to one of those papers to back up a particular claim, not what he says about it in the blog.

it is easier for everyone to go and look for themselves

No, it's easier for everyone to go to the particular place in the particular peer-reviewed paper that is relevant, as pointed to by you (or whoever is making the claim). If you're not willing to do that work to back up a claim that you are making, why should anyone else do it for you?

As for the other side of the argument, I haven’t heard any convincing rebuttal as of yet.

Where have you looked?

 

[Olorin]

Not all scientists agree with this. Particularly those who work on quantum mechanics.

Let’s agree to disagree on this one then...

Nope. If he provides links to peer-reviewed papers, great--then give references to one of those papers to back up a particular claim, not what he says about it in the blog.

Let’s forget about Kroupa’s blog then, the only piece of argument that concerns this topic is the one that implies observational SEP violations and the peer reviewed article link was already posted somewhere here.

Where have you looked?

Since the SEP violations claim that concerns us is very recent, I didn’t find any of the peer reviewed kind. All the rebutals are the kind of ones you give yourself like : « it is not a proper test », « it is model dependendent » etc... which I have already adressed here as not convincing nor correct. If you have any links to peer to peer reviewed rebutals, I’ll be happy to have a look at them.

 

[PeterDonis]

Since the SEP violations claim that concerns us is very recent, I didn’t find any of the peer reviewed kind.

Which indicates, as I said before, that this is an open area of research, and it's too soon to make any definite pronouncements about how it will come out. It takes time for scientists to respond to a new publication.

All the rebutals are the kind of ones you give yourself like : « it is not a proper test », « it is model dependendent » etc... which I have already adressed here as not convincing nor correct.

Not convincing to you. That does not mean those concerns are not valid. It means, once more, that this is an open area of research and so of course people have different opinions about how they think it will come out--but those are opinions. We'll have to wait and see how things develop.

 

[Olorin]

Not convincing to you. That does not mean those concerns are not valid. It means, once more, that this is an open area of research and so of course people have different opinions about how they think it will come out--but those are opinions. We'll have to wait and see how things develop.

Your arguments are defy not valid. As long as the 5 sigma confidence observational correlations between galaxy dynamics and neighboring objects properties remains valid there is a SEP violation. There are not a lots of ways out here:
- The data is wrong ( experimental errors)
- The analysis is wrong ( correct numbers and figures are not correctly extracted from a valid data set)
- If data and analysis is correct, then for SEP and GR not to be falsified it would be needed to invoke the existence of non-gravitational forces that somehow are influencing the galaxy dynamics and imparted from the neighboring objects as SEP is only required for pure, non tidal gravitational forces. This hypothesis would be very awkward and would add a new and particularly awful epyciclic to our physics.

 

[PeterDonis]

Your arguments are defy not valid.

I guess we'll have to agree to disagree about this. In any case, it's really off topic for this thread, since this thread is only about what tests can falsify GR (or force it to be modified), not whether any tests actually have. I have already agreed that one possible outcome of the research that you refer to is that GR will need to be modified. So it counts as an example of what the OP of the thread was asking about.

 

[Olorin]

In any case, it's really off topic for this thread, since this thread is only about what tests can falsify GR (or force it to be modified), not whether any tests actually have.

SEP tests can falsify GR. We have a new and novel kind of SEP test that if confirmed might end up falsifying GR, even if we could consider that in the absence of a proper rebuttal and discussion about what we should make out of the outcome of the test it is preferable to be cautious and not say SEP/GR are already falsified. I really don’t see how any of this is off topic.

 

[PeterDonis]

SEP tests can falsify GR.

Yes. We have already agreed on this.

I really don’t see how any of this is off topic.

Saying that this test could end up falsifying GR (or requiring it to be modified) is not off topic. But I've already agreed to that, so there's no need to belabor it.

What is off topic is to continue arguing about whether this test already has falsified GR, when that's (a) still an open research question, and (b) irrelevant to the thread anyway, since the thread was only about what tests can falsify GR, not what tests already have.

 

[Olorin]

To pursue on the topic of GR falsifiability, I have already emphasized the prime importance of the experimental validity of the 3 equivalence principle which serve as the foundational pillars of General Relativity: any breach, rupture or proper collapse of these principles would effectively falsify GR but not necessarily with the same consequences. I think that the 3 anti matter gravitational properties experiments being built and soon run at CERN are of great significance with respect to the potential falsifiability of GR as they will provide a direct test of the weak and Einstein equivalence principle for anti matter. There are two possible outcomes:

-1/ anti hydrogen atoms fall with the same acceleration g as ordinary matter: this is the expected result and GR prediction.
- 2/ anti hydrogen atoms doesn’t fall with the same acceleration as ordinary matter: this will demonstrate a WEP and EEP violation which can bear different implications for GR depending on the amplitude of the discrepancy.

Let‘s further discuss the implications of 2: if the discrepancy is 200% as it will be if anti hydrogen falls up with a -g acceleration ( as some anti- gravity theories suggest), then it is what I would call a collapse of the two pillars that the WEP and EEP are to GR. Here we will have a falsification of the ontological kind with unbearable consequences for GR because its worldview as gravity as a geometrical effect of space time curvature would fail in the most dramatic sense: this could not in any means account for two test objects having such a different behavior in the local Earth space time curvature. Now there are obviously a lot of possible outcomes in between, like slight variations in the rate of fall which could allow for modifications or extension without necessarily demanding a revision of GR proposed worldview for gravity as they could be accounted for by considering the addition of subtle effects.

 

[vanhees71]

Well, I'm never easy with "the equivalence principle", particularly the strong one. What does this precisely mean in math and for observables? 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. The same holds for MOND. If they give different results, then you have a testable prediction.

The other question is, how well you can really calculate the predictions of the measured observables in both models. Usually you need approximations for these calculations or rely on solving approximate equations numerically. So it's not so easy to say from the measurement alone, whether the one or the other theory is falsified, even when the measurement is accurate enough and correct.

Whether or not the above cited paper really "falsifies" GR, I cannot judge, because I'm not an expert of the topic. At least it's a peer-reviewed paper, and if it's taken seriously enough, further investigations shall be made.

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.

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 $5 \sigma$ level disproving it. There's some issue with $g_{\mu}-2$ (but there it's also a theoretical problem with the QCD contributions, which provide the largest theoretical uncertainty in the prediction). Also here one has to wait, what further experimental and theoretical research will result in (I hope there's soon a new measurement from Fermilab with the former BNL experiment).

 

[PAllen]

Left me just add that J.L. Synge, author of one of the more famous texts on GR, held the view that the various equivalence principles were heuristics important to history of science, understanding the path to GR, but they are not part of GR at all. Further, that they cannot be precisely formulated. This is a minority view that I don’t hold, but a key point is that Synge and e.g. Clifford Will, would never disagree on a prediction of GR, even though the former holds that the EP is wholly irrelevant to GR, while latter holds that it is central. What they agree on, as alluded to by @vanhees71, is the predictions of GR are based on the field equations of GR plus definitions of the correspondence between mathematical objects and measurements.

Oh, another example is that Ohannian argues that GR actually falsifies the equivalence principle. I completely agree on on the predictions on which he bases his argument, but disagree on his interpretation of those predictions.

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.

 

[PeterDonis]

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

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.

 

[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.