How does the theory of relativity point to a block universe?

Question

Please explain in layman's terms how Einstein's theory of relativity points to a universe that is eternal and non moving, where past, present and future all coexist simultaneously.

Answer 1

To understand this point of view, you really need to have a good understanding of the relativity of simultaneity, so for instance, here on Earth: you need to have an idea of what "the Universe, right now, means".

Aside: you also need to be able to abstract. You can't go carrying on about the Earth in a gravity field, and it rotates, and revolves around the sun, and the sun move...blah blah. We're sitting here on a "stationary" earth.

Now, for what right-now means, consider Betelgeuse: a star that is supposed to go supernova "soon". Let's say it's 500 ly away, and exploded 499y 364d ago (in our frame). That means: we will see a supernova tomorrow (and many neutrino astronomers will get tenure).

So you're inclined to say, it happened, and we will see it tomorrow b/c of light delay.

But that is a frame dependent statement. There are reference frames, here on Earth, that are moving towards Betelgeuse where it has not happened yet....that's just how Lorentz transformations (LT) work. So which frame is right? Did it happened almost 500y ago, or is it still in the future?

Another good example is related to The Andromeda Paradox. When is it right now here on Earth in Andromeda? Well, it's 2024 here on Earth, and over in Andromeda, right now, it's also 2024.

Fine, so you're in Andromeda, Earth: 2024. When it is right now on Earth? OK, Andromeda is closing at 300 km/sec, or $c/1000$.

The time (t') right now on Earth, there, now at $t$, is given by the LT:

$$ t' = \gamma(t - \frac v {c^2} x)$$

Let's wing it:

Andromeda is $\pm x=2.5\,$ Mly away, closing at $v=\mp c/1000$. (The $\pm$ and $\mp$ depends on whether you think Andromeda is to the right or the left...for is personal choice. I feel it's to the right, but all that matters is $|x|$ is getting smaller so $v$ has the opposite sign).

The time dilation factor:

$$ \gamma = \frac 1 {\sqrt{1-\frac{v^2}{c^2}}} $$ $$ \gamma = \frac 1 {\sqrt{1-\frac 1 {10^6}}} \approx \frac 1 {1-\frac 1 2 10^{-6}} $$ $$ \gamma \approx 1 + \frac 1 2 10^{-6} \approx 1 $$

We can ignore time-dilation at that velocity^1, but not the relativity of simultaneity, as follows:

$$ t' \approx t + \frac{vx}{c^2} $$ $$ t' = 2024{\rm AD} + \frac c{1000} 2.5{\rm Mly}$$

$$ t' \approx t + \frac v {c^2} x = 2024{\rm AD} + \frac c{1000} 2.5{\rm Mly}$$ $$ = 2024{\rm AD} + 2500{\rm years}$$ $$ = 4525{\rm AD} $$

Well that is weird. Right now, in Andromeda, it is 2500 years in the future. fr fr. I wonder what happens?

[1] I think with the JWST, we now see galaxies where time-dilation is large. Which is really great: a directly observable macroscopic observation of a relativistic phenomenon that was once relegated to thought experiments.