Conservation of kinetic energy in expanding space

[rocknrollkieran]

TL;DR

Kinetic energy is not conserved in expanding space; what happens in contracting space?

Classically an object moving at a constant velocity in a straight line will continue to move at the same velocity until it encounters an external force.
It has been shown that this does not hold true in our universe because of the expansion of space: the object will slow down, losing kinetic energy, and eventually stop.
If our universe was closed so that space was contracting, what effect (if any) would this have on an object moving at constant velocity in a straight line?

 

[PeroK]

TL;DR Summary: Kinetic energy is not conserved in expanding space; what happens in contracting space?

Classically an object moving at a constant velocity in a straight line will continue to move at the same velocity until it encounters an external force.

That's Newton's first law. It only applies in a local inertial reference frame. It's not generally true, in any case. There are no global inertial reference frames, so Newton's first law does not apply cosmologically.

It has been shown that this does not hold true in our universe because of the expansion of space: the object will slow down, losing kinetic energy, and eventually stop.

An object won't stop. It will follow a path determined locally be gravity (if nothing else). If it's far enough away, then it will also have a recession velocity associated with expansion.

If our universe was closed so that space was contracting, what effect (if any) would this have on an object moving at constant velocity in a straight line?

Again, the object would locally follow a path determined by gravity and globally would have an additional "contraction" velocity associated with the contraction of space.

 

[Bandersnatch]

As I see it, the poster is asking about an effect opposite to objects in expanding space asymptotically joining the Hubble flow over time. I.e. would, in contracting space, small peculiar motions be amplified?
My intuition I'd that it should be symmetrical, but I'd have to think about it some more. Somebody else has a firm idea, go ahead.

 

[phinds]

It has been shown that this does not hold true in our universe because of the expansion of space: the object will slow down, losing kinetic energy, and eventually stop.

Uh ... huh? Why do you think that?

 

[weirdoguy]

It has been shown that this does not hold true in our universe because of the expansion of space: the object will slow down, losing kinetic energy, and eventually stop.

"Movement" of expansion is not like proper movement. I don't think there is kinetic energy associated with it.

 

[jbriggs444]

"Movement" of expansion is not like proper movement. I don't think there is kinetic energy associated with it.

One can define the kinetic energy associated with peculiar movement relative to a co-moving coordinate system. In an expanding universe, the expansion reduces this kinetic energy over time.

I agree with the intuition expressed by @Bandersnatch. Since a contracting universe is the time reversal of an expanding universe, we should expect to see the kinetic energy associated with peculiar movement increase over time.

 

[rocknrollkieran]

I agree with the intuition expressed by @Bandersnatch. Since a contracting universe is the time reversal of an expanding universe, we should expect to see the kinetic energy associated with peculiar movement increase over time.

In a contracting universe would we expect to see the cosmic microwave background radiation become more blue-shifted - eventually moving into the visible spectrum?

 

[Bandersnatch]

Yes, we would. The shift is proportional to the scale factor.

But going back to the OP, you did not confirm whether the effect talked about in the thread so far is what you had in mind. Because while it does exist, it's something of an artefact of the comoving coordinates. It can be analysed using newtonian mechanics, and it doesn't break them - unlike what your post suggested.

 

[rocknrollkieran]

So if we conclude that in an expanding universe objects moving at a fixed velocity and not interacting with other objects will lose kinetic energy over time, and conversely in a contracting universe those same objects will gain kinetic energy over time, then what does this mean for the law of conservation of energy?

In our expanding universe is space itself soaking up kinetic energy and storing it somewhere as potential energy?

 

[jbriggs444]

So if we conclude that in an expanding universe objects moving at a fixed velocity and not interacting with other objects will lose kinetic energy over time, and conversely in a contracting universe those same objects will gain kinetic energy over time, then what does this mean for the law of conservation of energy?

The easy answer is that energy is not conserved in an expanding universe. The law of conservation of energy follows (via Noether's theorem) from time translation symmetry. An expanding universe is not symmetric in the required sense.

There are more complicated answers available if one asks the question over in the relativity sub-forum.

 

[phinds]

In our expanding universe is space itself soaking up kinetic energy and storing it somewhere as potential energy?

No, since energy is not conserved on cosmological scales, is just isn't there anymore.

 

[rocknrollkieran]

If our expanding universe consisted of just a single atom, would it's energy just leak away over time until eventually it entered the lowest possible energy state and could no longer lose any more energy?

 

[jbriggs444]

If our expanding universe consisted of just a single atom, would it's energy just leak away over time until eventually it entered the lowest possible energy state and could no longer lose any more energy?

An atom is not expanding.

 

[rocknrollkieran]

An atom is not expanding.

No, I mean the space around the atom

 

[PeroK]

If our expanding universe consisted of just a single atom, would it's energy just leak away over time until eventually it entered the lowest possible energy state and could no longer lose any more energy?

Energy is frame dependent. There is no such thing as "the energy of an atom" in any absolute sense. There is the ground state, which is measured relative to the atom's rest frame.

Our universe is not just a single atom. There is no way to measure expansion if all you have is a single atom. Also, you would need some explanation of how you came to have a single atom as a universe in the first place.

 

[Ibix]

No, I mean the space around the atom

To get a spacetime that you can describe as "expanding space" or "contracting space" you need it to be filled more or less uniformly with matter (or radiation or something). A single atom in an otherwise empty universe isn't such a spacetime, so your question doesn't make sense.

More generally, kinetic energy isn't a property of an object. It's a property of an object compared to something else you call "at rest". For example a cup of coffee on a table has zero kinetic energy measured by someone sitting at the table, but if the table is on a train an observer standing on a bridge over the railway will say the cup is doing 60mph and has quite a lot of kinetic energy. It's the same cup. So, when you say an object in an expanding spacetime loses kinetic energy you are implicitly taking the matter filling the universe as "at rest" and comparing the object to the matter around it. Again, your empty universe has no other matter, so there's nothing to hang an implicit "at rest" state off.

Note that GR can't actually model a single atom as a source of gravity because it can't model sources where quantum effects are significant. In my answer I've been replacing your single atom with a small spherical dust particle.

 

[rocknrollkieran]

Energy is frame dependent. There is no such thing as "the energy of an atom" in any absolute sense. There is the ground state, which is measured relative to the atom's rest frame.

Our universe is not just a single atom. There is no way to measure expansion if all you have is a single atom. Also, you would need some explanation of how you came to have a single atom as a universe in the first place.

Sorry I'm not making myself very clear.
Let's assume that a universe (not ours, but subject to the same laws of physics) consists of a single hydrogen atom in an initially energetic state surrounded by expanding space. The atom's electron gradually emits photons over time as it loses energy to the expanding space around it until it eventually reaches the ground state.

 

[rocknrollkieran]

To get a spacetime that you can describe as "expanding space" or "contracting space" you need it to be filled more or less uniformly with matter (or radiation or something). A single atom in an otherwise empty universe isn't such a spacetime, so your question doesn't make sense.

But a single hydrogen atom is 'matter', so if that is surrounded by expanding space, why does that not qualify as a universe?

 

[Ibix]

But a single hydrogen atom is 'matter', so if that is surrounded by expanding space, why does that not qualify as a universe?

It does. Just not an expanding or contracting one. To get one like that you need matter everywhere.

 

[PeroK]

Sorry I'm not making myself very clear.
Let's assume that a universe (not ours, but subject to the same laws of physics) consists of a single hydrogen atom in an initially energetic state surrounded by expanding space. The atom's electron gradually emits photons over time as it loses energy to the expanding space around it until it eventually reaches the ground state.

That's not cosmology. That's the quantum physics of a single atom, reaching its ground state.

 

[rocknrollkieran]

It does. Just not an expanding or contracting one. To get one like that you need matter everywhere.

But at the inception of this single atom universe, matter is everywhere - it occupies the entire space, until space starts expanding. As the space expands, the atom loses energy and emits photons.
Eventually it will run out of photons and reach ground state as the universe continues expanding around it forever. But the uncertainty principle means it can borrow energy from somewhere for a short period of time. Can it still borrow this energy in an expanding universe?

 

[PeroK]

But at the inception of this single atom universe, matter is everywhere - it occupies the entire space, until space starts expanding. As the space expands, the atom loses energy and emits photons.
Eventually it will run out of photons and reach ground state as the universe continues expanding around it forever. But the uncertainty principle means it can borrow energy from somewhere for a short period of time. Can it still borrow this energy in an expanding universe?

Your posts no longer have any content that is recognisable as physics. This is a forum for the discussion of serious physics.

 

[Ibix]

Can it still borrow this energy in an expanding universe?

You aren't describing a real physical model here, just throwing words onto the page.

 

[Ibix]

But at the inception of this single atom universe, matter is everywhere - it occupies the entire space, until space starts expanding. As the space expands, the atom loses energy and emits photons.

Expanding universe models require the universe to be everywhere isotropic and homogeneous, which I see I didn't make clear earlier. An object emitting radiation is not homogeneous and is only isotropic about one point, so it would not be expected to look at all like an "expanding space" model.

A body emitting radiation is better described by the outgoing version of the Vaidya metric. Again, this is not an "expanding space" model.

 

[weirdoguy]

Expanding universe models require the universe to be everywhere isotropic and homogeneous

Which in practice means that we see expansion only at a very large scales. Expansion means that distance between non-gravitationally bound objects increases. Lone atom is not that kind of situation.

But at the inception of this single atom universe, matter is everywhere - it occupies the entire space

How can single atom occupy entire space?

But the uncertainty principle means it can borrow energy from somewhere for a short period of time.

That is not necessarily true, although you can find that statement in a lot of pop-sci sources. Time-energy uncertainty relation does not work that way.

 

[jbriggs444]

But at the inception of this single atom universe, matter is everywhere - it occupies the entire space, until space starts expanding.

In models with an initial singularity, there is no inception event. The singularity is not part of the manifold.