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.