Achernar is right as far as Special Relativity goes, but also right that in GR things are different. It’s simply not correct to say that “nothing can go faster than light with respect to anything else”. Things that go faster than light with respect to us are outside our horizon. As time goes on, tho, more and more galaxies become visible to us. If you like, you can consider them as springing into existence at the moment they enter our visible universe. If you go there and ask the inhabitants, tho, they might disagree.
A couple of thoughts:
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If you’re going to talk about the universe, you really have to include everything in the way JasonFin specified. If you’re defining our universe as everywhere within our cosmic horizon, you’re really talking about a universe. People in different galaxies are then in different universes if their cosmic horizon doesn’t match ours (even if most of their and our universes overlap). I believe this is counter to most people’s expectation of what the term means.
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When conservation of energy is applied to a finite volume, it’s never been “The energy in the volume must be constant, even if things are coming and going through the boundary surface”. It’s that the only change in energy in a volume is through energy entering or leaving the volume.
I’ll be the first to admit I was mistaken, but this doesn’t make sense to me. If they’re receding from us at greater than c, then how do they enter our horizon? That is, how does our horizon (which is expanding at c) overtake them?
There are two different horizons we’re talking about here. First what JasonFin called the cosmic horizon – the boundry outside of which space is receeding at speeds greater than c. As the universe expands, objects cross the cosmic horizon and we can never see those objects after they cross. And secondly the observable universe – that portion of the universe contained within our past light cone. As time goes forward, our past light cone expands to allow us to see events that had been outside our past light cone. The observable universe is contained within the cosmic horizon.
Nitpick: Objects do not go faster than light in GR (or SR for that matter). Things can go faster than c in GR (but not in SR). But light is still the fastest any signal or object can travel.
Okay, I don’t understand how anything can cross the cosmic horizon. That means that an object that is inside the cosmic horizon (v < c) would have to move outside it (v > c). How can that happen?
You are trying to apply SR where you need to apply GR. SR only applies to (local) inertial reference frames. In SR, light travels at a constant velocity, c, and no signal can travel faster than that particular speed. When you have expanding space you cannot use SR; you need to use GR. In GR, there is no upper limit on the velocity of light or any other signal, but you still cannot have any object or signal traveling faster than light can travel locally. Note the nitpick in my previous post.
There is nothing special that happens to an object when it crosses our cosmic horizon from its point of reference, except that we also cross its cosmic horizon. It’s not like the object jumps to warp speed. Remember it is space itself that is expanding and objects are dragged along with it.
In order for the observable horizon to expand the universe must be closed and the rate of expansion must be decelerating. Based on the latest data this does not seem to be what is happening, and in fact if the expansion is accelerating the horizon will actually contract.
But if contrary to the latest data the expansion is decelerating then the universe will obviously expand slower and slower with time, and light from progressively more distant galaxies will be able to reach us. Its like running down an upward moving escalator where the escalator’s speed is decreasing – eventually you’ll get to the bottom.
Okay then, if light can travel faster than c, why is an object outside our cosmic horizon (that is, in a region of space in which v > c) necessarily impossible for us to detect? Why couldn’t we get light signals from it that were initally moving faster than c?
Light can never locally travel faster (or slower) than c. So if space is expanding superluminally it will forever, inexorably, drag light along with it……unless the expansion is decelerating.
Put another way: Special Relativity can only be used when you’ve got an inertial reference frame. But there is no single inertial reference frame which can cover a region of space comparable to the Hubble Scale. If we take a frame which is inertial here, and extend that frame to another galaxy ten billion lightyears away, it will not be an inertial frame there.
Another thing to remember is that a point in space does not have a well-defined cosmic horizon. An event in spacetime does. So, Earth yesterday had a cosmic horizon, but it’s not the same horizon that Earth today has. This is what folks mean when they say that our horizon is expanding or contracting: They’re actually looking at different horizons corresponding to different events.
So do things moving out of the “Hubble’s Horizon” cause the mass of our observable universe to decrease ? What about entropy ?
I suppose that when an object with mass moves outside the observable universe it necessarily must cause the total mass of the observable universe to decrease. The same applies to entropy; the total entropy of the observable universe will be reduced if a system with positive entropy crosses the cosmic horizon.
This is not a violation of the law of conservation of mass/energy because the observable universe is not a closed system. The net change of mass/energy for the observable universe in any frame of reference over any time period should be equal to inputs - outputs, just as for any open system. Analogous reasoning should apply to entropy.
Thanks Jason. So this discussion would seem to question the conventional wisdom that the entropy of the universe is increasing because it is expanding. I mean yes, expansion causes entropy to increase but the universe may also lose entropy when the mass moves out of the boundary because it is not a closed system.
Any research into this or even rough estimates into net entropy change ?