What would it take to prove Albert Einstein Wrong?

Firstly, I am not rejecting GR.
I am wondering why it hasn't been rejected in this case, due to the missing mass issue.
You and others have addressed that concern. Thanks again.
Secondly, I am sure there are a few other issues that are still being dealt with, but that is not the issue of Dark Matter per see.
And now finally with amazing clarity:
"GR is agnostic about the form that mass takes." so as long as matter is present, it is irrelevant to GR what from it is.
If Dark matter or other is not found to be present then GR fails...
Which is what you guys have been saying all along...

so again thank you all for clearing up this misconception I have been dealing with.

 

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No, cold dark matter is a falsifiable theory. (And some even claim it is already falsified.) This is because CDM is a very special very particular model of imaginable dark matter. Namely, it is simply a massive particle, with some mass. Which is the only unknown parameter of the theory. Everything else follows from the equations. Of course, as for usual matter, observations have to be used to find the distribution of the dark matter. This has been done, by using their gravitational field.

Note: The gravitational field has ten components. The cold dark matter is dust, thus, is defined by the distribution of density and velocity.

No. GR does not predict anything about matter, neither of dark matter nor of visible matter. It describes the gravitational field, and how it interacts with matter. The theory of matter is separate.

Without adding a theory of matter, GR is not really complete. The full Lagrangian - which is what you need to get the full equations - consists of the GR Lagrangian (Hilbert Lagrangian) and a matter Lagrangian which depends on the theory of matter. If you find a new particle in the particle accelerator or so, you have to add a new term to the Lagrangian of the Standard Model of particle physics, and this new term changes the equations of GR too because the energy-momentum tensor of the energy of these new particles appears in the equations too.

So, you can have equations for GR + standard model without dark matter, and GR + standard model + some dark matter model. The equations and the solutions will be different.

This suggests nothing about GR. Except that one needs some theory about matter too, if one wants to have the complete equations, and, moreover, assumptions about its distribution, if one wants to make some nontrivial predictions. (Which is essentially a triviality. Say, Newtonian gravity does also not tell us anything about the Solar System without assumptions about the masses and locations of the Sun and the planets.)

Given that for the complete equations we need as a theory of gravity, as a theory about the masses (say, the SM), a failure of the resulting predictions cannot be simply attributed to one of them. Both may be the cause of the failure.

This is a quite general problem of experimental physics. In any real prediction, a lot of different theories are involved. Starting from the theories about what the particular measurement devices really measure, with which accuracy. If a single experiment fails, there are always many candidates. The way to solve this problem is to use many different experiments. So, say, measurement devices will many times measure what they are assumed to measure, compared with other measurement devices (of the same as well as of different construction), and other runs of the same to identify the measurement errors independently, so that their errors can (at least in principle) be excluded easily.

 

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Yep, well put!
Some more interesting points. When GR was first formulated, we didn't even know about other galaxies and thought the MW was all there was.
And when data started being received and researched with regards to the other galaxies, the rotational curves anomaly was discovered. Some of that missing mass was BHs which GR predicted to the annoyance of Albert.
So unseen DM was used as a fudge to explain the missing mass.
The rotational curves are calculated using both GR and Newtonian, but of course we need GR to explain gravitational lensing.
This is similar in many ways that lead to the discovery of Neptune via Newtonian maths, and perturbations in the orbit of Uranus.

 

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I think there's a small misconception here about what James R was referring to. General Relativity can, in principle, handle any form of matter or energy, including forms with exotic properties which have yet to be observed in the lab. The only requirement is that you're able to describe those properties within a mathematical object known as the stress-energy tensor, which determines the corresponding spacetime geometry. Different forms of matter and energy, such as gas, dust, electromagnetic radiation and dark energy, will all result in different effects on the spacetime geometry; for instance, not only is the general mass-energy equivalence of the gravitational source important, but the internal pressure of the source also has an effect, among other quantities.

 

The Cosmological Constant
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The Path Integral Formulation of Quantum Mechanics
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Gravitational Waves
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was he wrong ?

how much of the value of the third person speculation is defined by the need to attribute a sense of polar delineation to gain a sense of personal gain ?

what can be taken ?
thus it must be there to be taken
it can not be gone once taken, only converted
thus "moved"
what can be moved to prove Albert Einstein wrong ...