6 ms·

If space is expanding, does that also mean that gravitational potential energy is always increasing, too? I'd never thought of that before

oopsemist 3y ago
Yes, it should increase on paper, but no source of energy to power that expansion is found yet. Big Shrink can power itself, so I'm voting in favor of https://en.wikipedia.org/wiki/Shapley_Attractor https://en.wikipedia.org/wiki/Shapley_Attractor
pdonis 3y ago
No, it doesn't, because the concept of "gravitational potential energy" is not meaningful for an expanding universe considered as a whole. It's only meaningful for isolated systems within the universe.
- thx-2718 3y ago
  Wouldn't there be meaning in saying it would take this much energy to push all the matter in the universe to one place? Which that amount should be increasing as space-time expands. Thought experiment, if you could place a mass of an arbitrary amount at any one point in space, how much mass would you need such that all the mass of the universe is now falling towards it. Or could you bend space-time to a point that all mass falls into it.
  - pdonis 3y ago
    > Wouldn't there be meaning in saying it would take this much energy to push all the matter in the universe to one place? No. The universe is not an isolated system that we can operate on from the outside. You can't treat it as though it is. So your thought experiments aren't meaningful.
    - thx-2718 3y ago
      Obviously the thought experiment requires energy that doesn't 'exist' or doesn't have meaning in the sense that it could happen literally. It's a what-if and that does have a number and that does have meaning. So there is meaning to the previous persons question which is what the thought experiments were meant to show but obviously that's something you can't imagine.
      - pdonis 3y ago
        > Obviously the thought experiment requires energy that doesn't 'exist' No, it requires energy to be added to the system from outside the system. Which is precisely what you cannot do with the universe as a whole. That's what makes such thought experiments meaningless for the universe as a whole.
        thx-2718 3y ago
        > it requires energy to be added to the system from outside the system. Yes that is exactly what energy that doesn't 'exist' means.
        pdonis 3y ago
        But you can't do that for the universe as a whole. Asking what would be the case if you could is meaningless; it's like asking what would be the case if 2 + 2 were 5. No consistent model exists of such a situation, so the question is meaningless.
        thx-2718 3y ago
        > you can't do that for the universe as a whole. Yes correct, that's why that energy doesn't 'exist' because it's outside of the universe.
        pdonis 3y ago
        There is no such thing as "outside of the universe". If you disagree, please show me the consistent model on which your scenario is based.
- wyager 3y ago
  Why is it not meaningful? "Isolated systems" seems meaningless - there is no objective cutoff where a gravitational system becomes "isolated", except perhaps in the sense of "non-intersecting light cones".
  - pdonis 3y ago
    See my response to thx-2718 downthread, about having to add energy from outside the system.
    - wyager 3y ago
      I have read all of your comments and not one of them actually says anything concrete. It's the exact same vague objection repeated over and over again. Please explain exactly why you think calculating the total gravitational potential energy of the entire universe or a well-defined sub-volume of it is intractable. Feel free to use arbitrarily technical mathematical or physics language, just please stop being vague.
      - pdonis 3y ago
        I responded to this in the other subthread where we are having this discussion.
- deleted 3y ago
  [deleted]
cyberax 3y ago
It's not. Moreover, the total energy is actually being lost, as particles "lose" kinetic energy due to expansion (and the light is red-shifted). If this seems to violate the law of energy conservation, you're spot on. It is indeed being violated. This is not fundamentally problematic by itself, because the law of conservation of energy depends on time invariance. Which doesn't hold in the case of an expanding universe. But it is an unsatisfying copout, and we hope that it can be resolved by the quantum gravity.
- titzer 3y ago
  Space in our universe has a vacuum energy and our expanding (actually, accelerating) universe is in fact gaining "dark" energy. https://en.wikipedia.org/wiki/Dark_energy https://en.wikipedia.org/wiki/Dark_energy
  - cyberax 3y ago
    There is no known mechanism by which the lost energy can drive the expansion. Moreover, expansion without dark energy would still cause the kinetic energy loss. There are attempts to define the total energy of the universe in GR in such a way that it is preserved, but so far none are really successful.
- mnky9800n 3y ago
  https://ptolemy.berkeley.edu/eecs20/week9/timeinvariance.html#:~:text=A%20time%2Dinvariant%20system%20is,invariance%20is%20a%20mathematical%20fiction https://ptolemy.berkeley.edu/eecs20/week9/timeinvariance.htm.... Time invariance is mathematical fiction. Haha. What a wonderful quote.

oopsemist 3y ago

Yes, it should increase on paper, but no source of energy to power that expansion is found yet. Big Shrink can power itself, so I'm voting in favor of https://en.wikipedia.org/wiki/Shapley_Attractor https://en.wikipedia.org/wiki/Shapley_Attractor

pdonis 3y ago

No, it doesn't, because the concept of "gravitational potential energy" is not meaningful for an expanding universe considered as a whole. It's only meaningful for isolated systems within the universe.

thx-2718 3y ago
Wouldn't there be meaning in saying it would take this much energy to push all the matter in the universe to one place? Which that amount should be increasing as space-time expands. Thought experiment, if you could place a mass of an arbitrary amount at any one point in space, how much mass would you need such that all the mass of the universe is now falling towards it. Or could you bend space-time to a point that all mass falls into it.
- pdonis 3y ago
  > Wouldn't there be meaning in saying it would take this much energy to push all the matter in the universe to one place? No. The universe is not an isolated system that we can operate on from the outside. You can't treat it as though it is. So your thought experiments aren't meaningful.
  - thx-2718 3y ago
    Obviously the thought experiment requires energy that doesn't 'exist' or doesn't have meaning in the sense that it could happen literally. It's a what-if and that does have a number and that does have meaning. So there is meaning to the previous persons question which is what the thought experiments were meant to show but obviously that's something you can't imagine.
    - pdonis 3y ago
      > Obviously the thought experiment requires energy that doesn't 'exist' No, it requires energy to be added to the system from outside the system. Which is precisely what you cannot do with the universe as a whole. That's what makes such thought experiments meaningless for the universe as a whole.
      - thx-2718 3y ago
        > it requires energy to be added to the system from outside the system. Yes that is exactly what energy that doesn't 'exist' means.
        pdonis 3y ago
        But you can't do that for the universe as a whole. Asking what would be the case if you could is meaningless; it's like asking what would be the case if 2 + 2 were 5. No consistent model exists of such a situation, so the question is meaningless.
        thx-2718 3y ago
        > you can't do that for the universe as a whole. Yes correct, that's why that energy doesn't 'exist' because it's outside of the universe.
        pdonis 3y ago
        There is no such thing as "outside of the universe". If you disagree, please show me the consistent model on which your scenario is based.
wyager 3y ago
Why is it not meaningful? "Isolated systems" seems meaningless - there is no objective cutoff where a gravitational system becomes "isolated", except perhaps in the sense of "non-intersecting light cones".
- pdonis 3y ago
  See my response to thx-2718 downthread, about having to add energy from outside the system.
  - wyager 3y ago
    I have read all of your comments and not one of them actually says anything concrete. It's the exact same vague objection repeated over and over again. Please explain exactly why you think calculating the total gravitational potential energy of the entire universe or a well-defined sub-volume of it is intractable. Feel free to use arbitrarily technical mathematical or physics language, just please stop being vague.
    - pdonis 3y ago
      I responded to this in the other subthread where we are having this discussion.
deleted 3y ago
[deleted]

cyberax 3y ago

It's not. Moreover, the total energy is actually being lost, as particles "lose" kinetic energy due to expansion (and the light is red-shifted). If this seems to violate the law of energy conservation, you're spot on. It is indeed being violated. This is not fundamentally problematic by itself, because the law of conservation of energy depends on time invariance. Which doesn't hold in the case of an expanding universe. But it is an unsatisfying copout, and we hope that it can be resolved by the quantum gravity.

titzer 3y ago
Space in our universe has a vacuum energy and our expanding (actually, accelerating) universe is in fact gaining "dark" energy. https://en.wikipedia.org/wiki/Dark_energy https://en.wikipedia.org/wiki/Dark_energy
- cyberax 3y ago
  There is no known mechanism by which the lost energy can drive the expansion. Moreover, expansion without dark energy would still cause the kinetic energy loss. There are attempts to define the total energy of the universe in GR in such a way that it is preserved, but so far none are really successful.
mnky9800n 3y ago
https://ptolemy.berkeley.edu/eecs20/week9/timeinvariance.html#:~:text=A%20time%2Dinvariant%20system%20is,invariance%20is%20a%20mathematical%20fiction https://ptolemy.berkeley.edu/eecs20/week9/timeinvariance.htm.... Time invariance is mathematical fiction. Haha. What a wonderful quote.