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# GEM (split from Thought experiment: how would physics develop without Einstein?)

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Most of them directly use GEM, like Gravity Probe B - please specify experiment and we can discuss it.

This question is not only "alternative history", but also many e.g. in SETI hypothesize existence of other civilizations - it might be worth understanding if their physics would be based on GR, or maybe on adding corrections to GEM - which might asymptotically reach GR?

Not having Einstein, which experiment could convince e.g. them that it is necessary to give up flat spacetime and introduce intrinsic curvature?

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3 minutes ago, Duda Jarek said:

Most of them directly use GEM, like Gravity Probe B

Again, your source contradicts this:

Quote

The much smaller frame-dragging effect is an example of gravitomagnetism.

There are two effects, the smaller one could be explained by GEM. The other cannot.

It is up to you provide the detailed, quantitative analysis to support your claims. Until you do that, there is nothing much to discuss.

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This article starts with below diagram with caption "Diagram regarding the confirmation of gravitomagnetism by Gravity Probe B" - which is this second set of Maxwell's equations.

https://en.wikipedia.org/wiki/Frame-dragging starts with "More generally, the subject that deals with the effects caused by mass–energy currents is known as gravitomagnetism, which is analogous to the magnetism of classical electromagnetism. "

https://en.wikipedia.org/wiki/Lense–Thirring_precession starts with "It is a gravitomagnetic frame-dragging effect."

Where do you see a disagreement?

Edited by Duda Jarek
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1 minute ago, Duda Jarek said:

This article starts with below diagram with caption "Diagram regarding the confirmation of gravitomagnetism by Gravity Probe B" - which is this second set of Maxwell's equations. Where do you see a disagreement?

You are cherry picking. And hand-waving. It is getting tedious.

I am waiting for some quantitative data from you to support your claims.

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I have just added:

https://en.wikipedia.org/wiki/Frame-dragging starts with "More generally, the subject that deals with the effects caused by mass–energy currents is known as gravitomagnetism, which is analogous to the magnetism of classical electromagnetism. "

https://en.wikipedia.org/wiki/Lense–Thirring_precession starts with "It is a gravitomagnetic frame-dragging effect."

I still don't know where do you see a disagreement?

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5 hours ago, Duda Jarek said:

Or imagine some hypothetical other civilization e.g. SETI is looking for - would it automatically get to GR? If not, how their physics would develop?

Assuming their minds, bodies, and technologies are roughly similar to our own, they would certainly get to GR sooner or later - but they might formulate the model differently.

5 hours ago, Duda Jarek said:

Beside Newton's gravity, there was also known GEM before ( https://en.wikipedia.org/wiki/Gravitoelectromagnetism ) - just take Maxwell's equations to gravity, making it Lorentz-invariant theory.

GEM is not Lorentz-invariant, unlike Maxwell's EM. It works only in the low-velocity, low energy, weak gravity domain; it's only an approximation. It gives fairly good predictions for slow-moving observers in our solar system (so it can be very useful, since the maths are much simpler than full GR), but it fails pretty spectacularly for relativistic scenarios, similar to Newtonian gravity.

5 hours ago, Duda Jarek said:

Where the problems would start - which experiments leave no doubts that we have to use GR instead of GEM? Which cannot be repaired with added terms to GEM Lagrangian?

Any observation that involves motion at relativistic speeds, and/or strong gravitational fields will quickly show discrepancies with GEM. The Wiki article you quoted mentions one such case, have a look under the "Pulsar" section. Also, the polarisation modes (and general dynamics, really) for gravitational radiation are wrong in GEM, which would have been noticed with the advent of gravitational wave observatories.

To get back to the original question, it is quite likely that without Einstein we might have used GEM for a while, but eventually people would have started to notice that some observational data deviates from the model, which would eventually have led to GR in some form.

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Still, all these experimental falsifications of GEM would not have taken place until the middle of the last century, Markus.
That would have made GEM the ruling gravitational theory for about 40 years before people noticed enough of a problem to search for different formulations.
Whereas SR was just waiting to be pulled together and published ( probably by H Poincare ) when A Einstein beat him to it in 1905, GR might have taken up to a century without A Einstein.
We might just be at the stage now, where A S Eddington was in 1920; one of three people in the world who understood GR.

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12 hours ago, Markus Hanke said:

GEM is not Lorentz-invariant, unlike Maxwell's EM.

But mathematically GEM is also Maxwell, can be analogously realized with Lorentz invariant F_munu F^munu in Lagrangian ... why do you think it cannot be Lorentz-invariant?

7 hours ago, Danijel Gorupec said:

Thinking out loud... At the time, Einstein did not have to feel embarrassed because he didn't know how to reconcile his theory with QM. If one would be developing GR some 40 years later, he would be under some pressure to provide a theory that includes QM. Some guys/girls might abandon their work out of frustration... So maybe, we won't ever have GR as it is now, but we would directly have (eventually) a version given with QM in mind.

Exactly!

GR has renormalization problem as e.g. Feynman ensemble of all shapes of specetime leads to "larger infinities than usual" ...

In contrast, flat spacetime GEM is just second F_munu F^munu in Lagrangian - is trivial to unify with the rest of physics, renormalize.

Without Einstein, a few decades later a non-renormalizable concept would be nearly impossible to accept (needed extremely strong evidence), definitely more difficult than adding new terms/corrections to GEM to repair experimental disagreements, like in the "Standard Model way".

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14 minutes ago, Duda Jarek said:

But mathematically GEM is also Maxwell[...] ... why do you think it cannot be Lorentz-invariant?

They are almost Maxwell, but not quite - they are invariant under hyperbolic rotations and translations, but not under boosts, because two of the quantities in the equations don't transform in the necessary way.

Quote

can be analogously realized with Lorentz invariant F_munu F^munu in Lagrangian

Actually no, they can't. The GEM field is a rank-3 tensor, which arises from a rank-2 potential, giving the Lagrangian density

$\mathcal{L} =-\frac{1}{16\pi } F_{\mu \nu \alpha } F^{\mu \nu \alpha } -\frac{G}{c} J^{\nu \alpha } A_{\nu \alpha }$

This is different than would be the case for electromagnetism (which arises from a vector potential, and has a rank-2 field tensor). The above is a good approximation for the linear part of the Einstein equations, so it is a weak field approximation to GR.

36 minutes ago, Duda Jarek said:

is trivial to unify with the rest of physics, renormalize

Hm, I don't think this is obvious at all. For one thing, since it is not Lorentz invariant, it's also not CPT invariant, so adding this into the Standard Model is not trivial. Renormalizability also cannot just be assumed, this will have to be specifically checked; I don't know if anyone has done these (pretty complex) maths for the case of GEM.

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1 hour ago, Markus Hanke said:

It would certainly be non-trivial. However, what I was trying to point out is that, if someone develops QFT first, then they would very quickly realise that a standard QFT for spin-2 bosons that couple to energy-momentum (a reasonable ansatz if one wants to find a model for gravity) yields something that is physically meaningless. So they would begin to wonder if perhaps gravity can't be described via a QFT at all. This would eventually bring them to consider metric theories instead - and GR is the simplest example of that.

Having GEM in analogy to EM, which was known 20 years before GR, gravity in QFT can be made analogously to EM - through photon/graviton exchange, e.g. with additional summation over alpha=0,1,2,3 as you have written ... so after Higgs they might be confident of having (renormalizable) theory unifying all the forces.

While I don't see how the above could lead to acceptance of non-renormalizable theory, the strong field regime might (?)

Using GEM instead of GR, such hypothetical civilization wouldn't be aware of black holes, probably expecting heavy neutron stars instead ... what might convince them that it just wrong?

Edited by Duda Jarek

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