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.