Velocity of the Earth

Main Question or Discussion Point

What's the velocity of earth relative to that of the centre of the universe or to a reference frame that gives maximum speed.

What about the Lorentz factor? V signifies relative speed there?

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Integral
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Just consider the surface of a balloon, now where is the center? It could be argued that any, and every point is the center. Likewise for the universe, so it can be argued that our velocity wrt to the center of the universe is zero.

The v in the Lorentz transform is the velocity of the observed wrt to the observer.

How do we know it's comparable with the surface of a balloon?

I'm curious about at what fraction of the speed of light earth is moving. We have this self rotation, then orbit around the sun, galaxy and the galaxy around the local group. But after that? Does the local group move too?

And how do we know that we are moving and not someone who has 0 velocity compared to our reference frame? Won't time go faster for the one that moves? But how can we determine who's moving and who's not?

A.T.
But how can we determine who's moving and who's not?
Well, we can't. That's the whole point of relativity.

There is no "center of the universe" to refer velocities to. There is no frame that results in a "maximum speed," but you can choose a frame in which the speed of the Earth is as close to c as you like.

As A.T. says, you can't determine who is moving and who is not. That's why it's called "Relativity."

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The best you can ask is what is the velocity of the Earth relative to the reference frame where cosmic relic radiation is (almost) isotropic.

If you have these movements away from a centre, can't we set that centre as a reference frame? Aren't the galaxies moving away from the location of the big bang? And if we interpolate we find that place?

What about space travellers whose local time passes slower than that of earth? Why isn't it the other way around? Is it just because they accelerated? But say we all forgot that, how do we then know whose time is going faster etc? Or let's say that it really was everything apart from the space travellers that accelerated. In that case why is time going slower for the people remaining on earth?

There is no movement away from the centre because there is no centre =) there was an "explosion" of space itself, not like a big bomb. Imagine like we are on the surface of a balloon that is being inflated. Where is the centre of the surface? it is not in any point on the surface.

If you have these movements away from a centre, can't we set that centre as a reference frame? Aren't the galaxies moving away from the location of the big bang? And if we interpolate we find that place?
No, you are suffering from a misconception. The galaxies are certainly NOT moving away from a center. There is no center, and no void into which they stream. The universe is uniformly filled with them everywhere and the distances between them are increasing.

What about space travellers whose local time passes slower than that of earth? Why isn't it the other way around?
Also a misconception. There is no absolute sense in which the space traveler's time is slower than that of the Earth. It is observed to be so from the Earth, but there are frames that disagree. In particular, the space traveler observes his clock to run normally and the Earth's to run slow. So it is also the other way around.

If the space traveler turns around, then when he returns to Earth, everyone agrees he is younger. In the Earth's reference frame, this is because the traveler's clock has run slow the entire time. To the space traveler, it is because when he turns around he switches inertial frames and in doing so shifts his slice of spacetime that he observes to be simultaneous. The solution to every "paradox" is that you have ignored relativity of simultaneity.