Einstein equations don't work at large scale?

[Ibix]

Unfortunately it's the nature of the beast. Physics isn't given to us by revelation and we can only work with the information we have. We can see that what we have is incomplete, but we haven't any solid leads on which way to proceed from here.

And, furthermore, unless we ever get to a theory that both says how the universe works and how it could not work any other way, we will always have to consider the possibility that there's something we haven't seen yet.

 

[Sagittarius A-Star]

What is ... energy?

Kinetic energy of a moving object is force integrated over distance.

With proper acceleration $\alpha=\gamma^3 \frac{dv}{dt}$ (follows from relativistic velocity addition), $m=$ invariant mass, and with force in direction of movement, the relativistic kinetic energy of a moving object is

$K=\int F \cdot ds = \int m\alpha \cdot ds= \int m \gamma^3 \frac{dv}{dt} \cdot ds$
$= m\int_0^V \gamma^3 v \cdot d v = mc^2(\gamma -1) = E-E_0$

calculation

With $(1-x)^{-\frac{1}{2}} \approx 1+\frac{1}{2}x$ for small $x$

$K=mc^2(\frac{1}{\sqrt{1-V^2/c^2 }} -1) \approx mc^2(1+\frac{1}{2}\frac{V^2}{c^2} -1)$

$K \approx \frac{1}{2}mV^2$

 

[Dale]

I don't like that every few hundreds years it turns out that our theories are not complete

There is a possibility that our theories will always be incomplete.

(polite expression of wrong)

Incomplete and wrong are different things. Newtonian mechanics is incomplete, but it is still a correct description of reality where it applies. Same with quantum mechanics and relativity.

 

[A.T.]

I would like that theories are always 100% truth just like in math.

How would you ever confirm that a physical theory is 100% correct, given that all our measurements have limited accuracy, and we also have no idea what observations will be done at some point in the future?

 

[PeterDonis]

I would like that theories are always 100% truth just like in math.

Unfortunately, that's not possible. As Bertrand Russell said, to the extent that math refers to reality, it is not certain, and to the extent it is certain, it does not refer to reality.

 

[javisot]

Below short video explain that Einstein equations don't work at large scale

I just wanted to make a note about the term "large scale". While "large scale" refers to vast distances, it also implies a lack of fine detail. For instance, in cosmology, we study the universe "on a large scale," meaning we analyze only the largest structures (to a cosmologist, neither you nor I, nor individual astrophysical objects exist).

Cosmologists study the universe at such a vast scale that everything can be averaged out homogeneously. Big Bang theory, a theory regarding the evolution of the universe "on a large scale", describes how the universe's largest structures evolve. The expansion of the universe is an effect perceptible only on a large scale; it is a cosmological phenomenon.

I wouldn't say GR fails on a large scale simply because we add something *ad hoc* to make everything fit. Everything does fit. A failure would be if it didn't fit even with that addition.

 

[SongDog]

How would you ever confirm that a physical theory is 100% correct, given that all our measurements have limited accuracy, and we also have no idea what observations will be done at some point in the future?

You can’t. A theory is simply a viable hypothesis: one for which no conclusive disproof exists. Such disproof might yet be found on any given day by some new test.

Newtonian mechanics was shown to be invalid for very small and very fast cases, but it remains a usefully close approximation to correct for slow moving macroscopic objects.

 

[javisot]

I don't like that every few hundreds years it turns out that our theories are not complete(polite expression of wrong). I would like that theories are always 100% truth just like in math.

In university we didnt even touch relativity, so I was shocked when I find that everything we learned was not 100% correct. But I understand that Newton physics is accurate enough for every day jobs.
I also understand that Newton with math, experimental devices and knoweldege from 17th century cant see everything that we can see today.

It is not just that Newton's laws provide a good approximation at low speeds and in weak gravitational fields; rather, the equations of relativity actually reduce to Newton’s equations in that limit.

One way to understand this is to imagine an object initially at rest. As long as it moves slowly compared with the speed of light and remains in a weak gravitational field, its motion can be described accurately by Newtonian mechanics. As its speed increases and relativistic effects become significant, Newtonian mechanics gradually ceases to be an adequate description, and the relativistic equations become necessary. The important point is that there is no abrupt transition between the two theories. The relativistic description contains the Newtonian one as a limiting case.

 

[Dale]

the equations of relativity actually reduce to Newton’s equations in that limit.

This is worth emphasizing. This means that Newtonian mechanics is part of relativity. Relativity cannot really disprove Newtonian physics because it contains it.

This is similar to Maxwells equations and circuit theory. Maxwell’s equations contain circuit theory. And when we build devices where the simplifying assumptions are not valid, then we use Maxwell’s equations without claiming that circuit theory is wrong. (Except for Walter Lewin). You cannot have Maxwell’s equations without implying circuit theory, nor can you have relativity without implying Newtonian mechanics.

 

[javisot]

This is worth emphasizing. This means that Newtonian mechanics is part of relativity. Relativity cannot really disprove Newtonian physics because it contains it.

This is similar to Maxwells equations and circuit theory. Maxwell’s equations contain circuit theory. And when we build devices where the simplifying assumptions are not valid, then we use Maxwell’s equations without claiming that circuit theory is wrong. (Except for Walter Lewin). You cannot have Maxwell’s equations without implying circuit theory, nor can you have relativity without implying Newtonian mechanics.

Exact.

It is incorrect to say "Newton = wrong and Einstein = right". If Newton = wrong, then Einstein = wrong, since they state the same thing in the appropriate limit.

 

[gen x]

I don't think we should rule out any of these three possibilities with respect to the dark sector. It could be evidence of GR failing (as MOND advocates would say)

Can you explain why we need to modify Newton dynamics, didn't we already said that Newton physics is wrong and we must use GR for objects in universe with large distances etc?
So Newton and Einstein physics are both deliver wrong results for rotating galaxies?

 

[Matterwave]

This is worth emphasizing. This means that Newtonian mechanics is part of relativity.

I think this phrasing is going too far. The equations of motion of Newtonian mechanics is the low velocity limit of the equations of motions of relativity, but saying straight up Newtonian mechanics is "part of" relativity is too far.

Relativity has an inherent light cone structure which is simply not present in Newtonian mechanics. Newtonian mechanics has an absolute time which simply is not present in relativity.

Relativity cannot really disprove Newtonian physics because it contains it.

Only in the sense that a theory doesn't disprove another. It is experiments which disprove theories.

 

[Ibix]

Can you explain why we need to modify Newton dynamics, didn't we already said that Newton physics is wrong and we must use GR for objects in universe with large distances etc?

MOND is used at intermediate scales such as galaxies. Large scales, in this sense, means when you consider distances of millions of light years, not thousands.

As to why you modify Newtonian gravity, it turns out to be easier to do than modifying GR. People have attempted to create modified GR theories that produce MOND on the intermediate scale where it differs from Newtonian gravity, but without success.

So Newton and Einstein physics are both deliver wrong results for rotating galaxies?

Whether they give wrong results is up for debate.

They give wrong results if you only plug in the visible matter (although some researchers dispute this and say GR gives correct results and has been incorrectly applied - very much a minority view, I think). They give correct results if you plug in dark matter.

So if you believe dark matter is a real kind of stuff (and note that LUX-ZEPLIN announced a possible direct detection yesterday, although it remains to be seen whether it pans out) then Newtonian gravity/GR is fine. If you don't believe dark matter is a real kind of stuff you need a modified theory of gravity. MOND is one such, and it works well for describing galaxy dynamics but has the same problems Newtonian gravity has at solar system scales and very large scales.

There is no current consensus on the correct approach.

 

[javisot]

I think this phrasing is going too far. The equations of motion of Newtonian mechanics is the low velocity limit of the equations of motions of relativity, but saying straight up Newtonian mechanics is "part of" relativity is too far.

Relativity has an inherent light cone structure which is simply not present in Newtonian mechanics. Newtonian mechanics has an absolute time which simply is not present in relativity.


Only in the sense that a theory doesn't disprove another. It is experiments which disprove theories.

You mean that even if the equations of one theory reduce to those of another in a certain limit, they remain distinct theories.

What we mean is that the most complete theory we can construct must explain why Newton's theory was effective in a certain limit, why Einstein's was effective in another range, and so on. From a mathematical standpoint, we interpret this to mean that we can transform the equations of theory A into the equations of theory B.

In this context, no new theory discards the experimental successes of previous theories; rather, it explains those results from a different perspective.

 

[Matterwave]

You mean that even if the equations of one theory reduce to those of another in a certain limit, they remain distinct theories.

And why shouldn't they be? Surely you agree GR and Newtonian Gravitation are distinct theories?

What we mean is that the most complete theory we can construct must explain why Newton's theory was effective in a certain limit, why Einstein's was effective in another range, and so on.

Sure.

From a mathematical standpoint, we interpret this to mean that we can transform the equations of theory A into the equations of theory B.

"Transform" is too loose here. Some equations in GR have an appropriate limit in Newtonian gravity. But, for example, how do you "transform" the equations in GR for gravitational waves into Newtonian theory?

In this context, no new theory discards the experimental successes of previous theories;

Sure.

rather, it explains those results from a different perspective.

But this does not mean the old theory is "part of" the new theory. Why not just say the new theory has to explain the known experimental results? What does claiming the old theory is "part of" the new theory buy you?

 

[gen x]

So if you believe dark matter is a real kind of stuff (and note that LUX-ZEPLIN announced a possible direct detection yesterday, although it remains to be seen whether it pans out) then Newtonian gravity/GR is fine. If you don't believe dark matter is a real kind of stuff you need a modified theory of gravity. MOND is one such, and it works well for describing galaxy dynamics but has the same problems Newtonian gravity has at solar system scales and very large scales.

How we know that we measure mass of these stars,planets in this galaxies correctly? maybe our method for measure mass is wrong?
Tweaking theory is not solution, it is just cheating, equation will work for galaxies but not any more for solar system!

 

[Matterwave]

How we know that we measure mass of these stars,planets in this galaxies correctly?

Stars have a well understood and well studied mass-luminosity relation. https://en.wikipedia.org/wiki/Mass–luminosity_relation

Based on the brightness of stars in a galaxy and their distribution, we can estimate the mass of the luminous matter.

maybe our method for measure mass is wrong?

That's the point. We only measure the mass of the luminous matter and this mass doesn't match the mass required to give rise to the observed rotation curves of galaxies. Hence "dark" matter.

Tweaking theory is not solution, it is just cheating, equation will work for galaxies but not any more for solar system!

False. MOND theorists certainly wouldn't propose a modification that broke how gravity works inside the solar system.

also if dark matter exist, than exist inside and outside galaxy, so cancel out?

What? I don't see how any of the implications follow from "if dark matter exist(s)".

 

[gen x]

False. MOND theorists certainly wouldn't propose a modification that broke how gravity works inside the solar system.

Ok than just tweak MOND that works at all scales.
Is it possible that gravity Gm1xm2/r^2 works differently on large scales? If yes where to put limit?

 

[Ibix]

Tweaking theory is not solution, it is just cheating,

Sort of. It's called an empirical model. I don't think anybody really likes them, but if they work they can lead to a real theory. For example, Lorentz-Fitzgerald contraction was purely an "if we do this we can explain Michelson-Morley" kludge, but eventually turned out to emerge from relativity.

equation will work for galaxies but not any more for solar system!

Please don't assume the people doing this are stupid. MOND works just as well in the solar system as Newton does (but not as well as relativity).

Is it possible that gravity Gm1xm2/r^2 works differently on large scales? If yes where to put limit?

That is exactly what MOND is. Where the threshold should be is a matter of debate. Further out than the edge of our solar system, certainly, but whether there's evidence for MOND-like behaviour in slightly larger structures like the orbits of wide binaries is hotly contested.

Ok than just tweak MOND that works at all scales.

There's nothing like the redshift and CMB that we see in the real universe in any Newton-like theory. And "tweaking" Newtonian gravity to be consistent with special relativity was tried extensively between the development of SR and GR, and it didn't work. This is not a simple problem.

 

[Dale]

I think this phrasing is going too far. The equations of motion of Newtonian mechanics is the low velocity limit of the equations of motions of relativity, but saying straight up Newtonian mechanics is "part of" relativity is too far.

I don’t think it is too far. In the same sense I would say that circuit theory is part of Maxwell’s equations.

I tend to think of what is in a theory as being defined by its experimental predictions. So if you had two different sets of math that produced the same experimental predictions then I would call those the same theory.

In the same vein, if you have something that produces a subset of a theory’s predictions, then that would be a part of the overall theory.

Every correct prediction of Newtonian physics is a prediction of GR. So in that sense it is part of GR.

Relativity has an inherent light cone structure which is simply not present in Newtonian mechanics. Newtonian mechanics has an absolute time which simply is not present in relativity.

And there are many scenarios where that doesn’t matter, the light cone structure doesn’t affect the experimental predictions or results. The same is true of circuit theory. It also lacks a light cone structure that is present in Maxwell’s equations. I would still call circuit theory a part of Maxwell’s equations. And similarly for Newtonian gravity.

Only in the sense that a theory doesn't disprove another. It is experiments which disprove theories

Which is why I focus on the experimental predictions and results to determine what defines a theory and what is part of it. In my view, science is the scientific method and its results, so I place experiments at the center. I prefer experimental definitions.

I recognize that not everyone thinks about theories that way. So I don’t object to your objection. But this is how I think about the topic, what I mean by the claim, and why I feel my statement is justified.

 

[gen x]

That is exactly what MOND is. Where the threshold should be is a matter of debate. Further out than the edge of our solar system, certainly, but whether there's evidence for MOND-like behaviour in slightly larger structures like the orbits of wide binaries is hotly contested.

Does massive gravity, theory where graviton have mass produce correct results?

 

[Ibix]

Does massive gravity, theory where graviton have mass produce correct results?

If the answer to this was an uncontested yes, why wouldn't we have switched to that theory?

At best the answer is "maybe". I'm not familiar enough with it to comment beyond that.

 

[gen x]

Time will show the truth
The truth is out there

 

[Sagittarius A-Star]

Does massive gravity, theory where graviton have mass produce correct results?

I don't know. However, here is a link to a related paper
"Fitting rotation curves of galaxies by de Rham-Gabadadze-Tolley massive gravity":

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.98.064008

Arxiv-link:
https://arxiv.org/abs/1806.06271

 

[Matterwave]

In the same vein, if you have something that produces a subset of a theory’s predictions, then that would be a part of the overall theory.

Just curious, not trying to be argumentative. But would you consider Ptolemeic epicycle theory to be part of General Relativity? It did predict the orbits of planets correctly to within every-day human eye accuracy. In fact, in some respects better than the original Copernican theory.

I recognize that not everyone thinks about theories that way. So I don’t object to your objection. But this is how I think about the topic, what I mean by the claim, and why I feel my statement is justified.

Ok. Fair enough.

 

[Dale]

Does massive gravity, theory where graviton have mass produce correct results?

I am not much of an expert on massive graviton theories. They have some theoretical issues, meaning that several versions actually have internal inconsistencies that prevent them from making predictions at all, and others don't have GR as their low-mass limit. The former are excluded because they don't predict any experimental results, and the latter are excluded because they contradict existing experimental results. I am not sure what flavors of massive graviton theories might still survive. I suspect there is still some active development in this area trying to address those problems. But I am not sure how far they have gone towards resolving those issues.

 

[gen x]

I am not much of an expert on massive graviton theories. They have some theoretical issues, meaning that several versions actually have internal inconsistencies that prevent them from making predictions at all, and others don't have GR as their low-mass limit. The former are excluded because they don't predict any experimental results, and the latter are excluded because they contradict existing experimental results. I am not sure what flavors of massive graviton theories might still survive. I suspect there is still some active development in this area trying to address those problems. But I am not sure how far they have gone towards resolving those issues.

here Claudia de Rham talk about some problems:

 

[Dale]

But would you consider Ptolemeic epicycle theory to be part of General Relativity? It did predict the orbits of planets correctly to within every-day human eye accuracy.

That is a good question. Personally, I wouldn't even consider it a scientific theory because it doesn't make any predictions. There is no possible observation that it could not accommodate through some combination of epicycles. And since it cannot be contradicted experimentally, it also cannot be confirmed experimentally.

 

[PeterDonis]

Does massive gravity, theory where graviton have mass produce correct results?

What theory are you referring to? Can you give a reference?

Bear in mind that there is no way with our current technology to even test predictions about gravitons.

 

[SongDog]

If you define space as the uniform CMB rest frame then the universe is the same age at all places and this is tautologically true. If you define space a different way then the universe is a different age at different places and again this is tautologically true.

As Bill Clinton once testified, “That depends what your definition of ‘is’, is.” Other than “exists at my point in spacetime” the other definitions seem fungible.