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Added 2025-04-15 11:19:35 +0000 UTCWhy does energy disappear in General Relativity? - Noether's Theorem
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Thanks Edwin! The first thing to mention is that technically the rock never slows down all the way to zero (we were a little imprecise about that), but it will always be getting slower and slower. We did some calculations assuming a constant rate of expansion, and after about 80 billion years the rock will be at 1% of its original speed, and after 210 billion years it will be at 0.0001%. In terms of what it means for the rock to decelerate - what we technically mean is that the rock will come to rest relative to its surroundings. We say that it becomes "comoving" with the universe. In cosmology we have two kinds of velocity - let's call them peculiar and comoving. A distant galaxy, for example, gets further away from us, not because it's moving, but because the space between us is expanding. It has a comoving velocity (how far away it's getting from us because of the expansion of space), but no peculiar velocity (the galaxy isn't itself moving). Think about a stick floating on the surface of a river. The river's flow is like the comoving velocity, the stick itself isn't moving relative to the flow of the river, it's carried along by it. For our rock, the rock begins with both a peculiar and comoving velocity (peculiar because it's moving relative to its environment, and comoving because everything feels the expansion of space to some extent). Then over time, the rock's peculiar velocity is reduced further and further by the expansion until eventually it only has comoving velocity. Like if you threw the stick in the river, at first the stick will be both carried by the flow and also moving faster than the flow (force from your throw caused this). But eventually the stick ends up being carried along. -Matt D. Writer for this video
Veritasium
2025-04-17 13:41:03 +0000 UTCHi Terry, thanks for the question! I hope this might clear some things up for you. In the situation you describe the probes see microwaves due to the Doppler effect. Since the probes are moving relative to the source, the gamma rays emitted by the source are redshifted from the perspective of the probes who see them as microwaves. But an important thing to note here is that energy isn't lost so long as you describe everything relative to the same reference frame. From the reference frame of the source, the source emits two gamma rays and (assuming a static spacetime) these are gamma rays for all of their lifetime. But from the perspective of the probes, the light was a microwave when it was emitted and is still a microwave when it reaches the probe. In each frame, no energy is lost or gained, but if you switch between frames the inherent energy of the photon is different. The same thing happens when you shift frames and consider the energy of any object. If you have a rock on a table, and you're in the reference frame of the rock, then the rock is stationary and has no kinetic energy. But if you move relative to the table, from your frame of reference, the rock (and table) will be moving and you'll say they have a kinetic energy. That doesn't mean kinetic energy has been created - it's just always the case that the amount of energy you assign to different objects will change if you change reference frames. The key is to keep track of all the energy changes relative to a single frame of reference. So in your example (assuming we're not in an expanding spacetime) energy conservation is not broken because the total energy in any particular frame does not change. But in an expanding universe the situation is different! Now, even if you consider everything from a single reference frame, a photon travelling through the universe will redshift over time and lose energy. So the redshift isn't a consequence of changing reference frames now - any single observer will see the photon lose energy. That energy is gone. Cosmological redshift does break conservation of energy. - Matt D. Writer for this video
Veritasium
2025-04-17 08:00:30 +0000 UTCI'm skeptical. How long does it take for the rock to slow down to 0? How is the deceleration of the rock related to the expansion of the universe? Is the perceived deceleration merely an artifact of there being more "space" being created between you and the rock?
Edwin Pole II
2025-04-16 19:38:02 +0000 UTCDerek Muller, your video reminded me why the assertion that cosmic redshifts break energy conservation has always baffled me. Launch two probes at close to light speed by having them push off each other really, really hard. (Do not volunteer to ride in these probes!) A while after launch, a third that stayed at the launch point sent blasts of gamma rays toward both launch satellites. The moving probes look back and detect not gamma rays but microwaves. Both conclude that the gamma bursts’ energy was lost and energy conservation has failed. Three questions: (1) Was energy conservation broken? (2) If not, why not? (3) If not, does the explanation for why energy is conserved (it is) for acceleration in flat Euclidean space apply to the expansion of space in General Relativity or not?
Terry Bollinger
2025-04-16 01:59:25 +0000 UTC
