Viewing a single comment thread. View all comments

Any-Broccoli-3911 t1_jajtiak wrote

The expansion of the universe is kinetic energy. The matter is going farther from you (the observer) at a given observed speed and you can compute an energy for that, that's an accurate measure of the kinetic energy. Father things go faster, so they have more energy. Also, the observed speed is always less than the speed of light, so everything has a finite energy.

All the mass between you and a far object cause a gravitational pull towards you which slows down objects. The mass distribution is approximately spherical, so all the mass that is farther than a object gets its gravitational pull on that object canceled.

Things get more complicated when you consider général relativity, and a constant energy that doesn't get diluted by the expansion (cosmological constant, dark energy or vacuum energy) accelerate the expansion of the universe rather than slowing down.

However, for the effect of ordinary matter, Newtonian gravity works fine to explain why it makes the expansion decelerate. General relativity agrees with it.

All observers see themselves in the center, and agree that galaxies decelerate (if only ordinary matter is involved) which correspond to the deceleration of the expansion. It doesn't need a center in the comoving coordinates (the coordinates in which there's no center and no specific observer) to get the same result.

2

crazunggoy47 OP t1_jajwm2d wrote

>The expansion of the universe is kinetic energy. [...] Also, the observed speed is always less than the speed of light, so everything has a finite energy.

Is that true? I thought that for distant galaxies, the recessional speed was often greater than c, since c is only a local speed limit, and does not apply to space time inflation.

Consider the rapid inflation of the universe, which went from electron-sized to golf-ball sized in 10–35 seconds; applying a naïve speed calculation would yield speed = distance / time = 43 mm / 10^(–35) seconds >>>>>> 3 x 10^(–8) m/s.

This is all to say, I'm mostly questioning whether the perceived recessional velocity can really correspond to kinetic energy.

3

Aseyhe t1_jakbf7x wrote

Relative velocities of distant objects aren't well defined in curved spacetimes. It's often said that distant objects are receding faster than light, and there are standard ways of writing down their distance such that the distance grows faster than the speed of light. However, there is no relativistically meaningful sense in which these objects are moving faster than light in relation to us. Also, the distance isn't uniquely defined either.

In intuitive terms, the relative velocity is the angle between two vectors in spacetime. Imagine drawing two arrows on a sheet. If those arrows are in the same place, you can measure the angle between them. If they are in different places, but the sheet is flat, you can also define the angle between them uniquely. However, if they are in different places and the sheet is not flat, the angle between the arrows is not uniquely defined.

5

Any-Broccoli-3911 t1_jajx0tj wrote

The observed speed is always less than c.

The comoving speed is not limited. If you consider ont special relativity, it's equal to gamma*v so as v goes towards c, the comoving speed goes to infinity. Even with general relativity, it's still true that the comoving speed goes to infinity as the observed speed goes to c.

gamma is the Lorentz factor 1/sqrt(1-v2/c2)

2

crazunggoy47 OP t1_jajyba4 wrote

Hmm. So if I understand you correctly, you're saying that an object that's moving away from us due to cosmic expansion has a finite kinetic energy (relative to us). So, from our perspective we should "expect" that kinetic energy to be falling, as our own gravity pulls them back in.

And then that galaxy, will also see the exact same thing. From its perspective every other galaxy is fleeing *it*. And if every galaxy sees this, and it just so happens that every trajectory has too little KE, then every galaxy would see the other galaxies crashing down on them.

Is that right?

3

Any-Broccoli-3911 t1_jajymds wrote

Yes, though the galaxies that are outside the local group have enough energy not to crash into us even if we don't consider dark energy which will push them away even faster. Without dark energy, they would decelerate relative to us, but still always going away.

3

Inside_Olive5504 t1_japjy77 wrote

This is a nice Newtonian explanation, but I've always felt that there is more subtly than it acknowledges. It relies on Gauss' law applied to a frame centered on us, but why is that the correct frame? An argument can be made that gravity exerts no net force, just using Newton's law and symmetry.

1

Any-Broccoli-3911 t1_japkex4 wrote

All inertial frames are correct in special relativity. Special relativity works well in this case.

Though we aren't perfectly inertial due to the acceleration of the sun and the galaxy, it's still close enough. Those accelerations are relatively small.

1

Inside_Olive5504 t1_japr7ao wrote

You make an interesting point. I believe (possibly wrongly) that you are saying that one should only consider mass that is within the local Hubble volume to compute the force on test galaxies, in which case we are at the gravitational center of the frame (because it truly is a finite sphere centered on us). One should not compute the force from the test galaxy's frame, since it is non-inertial to us. I think I can buy that argument. To me, it hinges on the finiteness of the Hubble volume and the speed of gravity. If the universe is infinite and if Newtonian gravity acted instantly, I think one could still argue that the test galaxy would feel no gravitational force, even in our inertial frame.

1

Aseyhe t1_jaqbsge wrote

> An argument can be made that gravity exerts no net force, just using Newton's law and symmetry.

That's what Newton believed, but a more careful look reveals that the integral over all space that determines the gravitational force does not converge to a well defined value. See for example the dynamics of Newtonian cosmology.

1

Inside_Olive5504 t1_jaqjuco wrote

Thanks, I appreciate the response. I like the discussion of convergence and the care to consider the shape of the volume in the limit of infinite size.

2