Does Space Expansion Add Potential Energy?

[Daniel Bolstad]

Space is expanding, which separates objects from each other in space. Won't this add potential energy? Doesn't this violate the law of conservation of energy? But if it does not, how can space be added without adding potential energy?

 

[phinds]

From what I've understood, no energy is being added to the universe.
Yet space is expanding, which separates objects from each other in space. Doesn't this add potential energy? How can this be?

If anything, I would expect the potential energy to be decreasing since galactic clusters are moving apart and thus have less gravitational attraction towards each other but in any case it's moot because expansion is just Metric Expansion (see https://en.wikipedia.org/wiki/Metric_expansion_of_space)

 

[A.T.]

If anything, I would expect the potential energy to be decreasing since galactic clusters are moving apart and thus have less gravitational attraction towards each other

You confuse the potential with the gradient of the potential.

 

[Daniel Bolstad]

I don't entirely understand. I should disclose that I have no formal education in science or physics. I'm just quite interested in the universe and how it works, and I'm attempting to wrap my head around these things without a good educational background on the topic. So perhaps you can help me clear up a few points?:

1) I thought it took energy to separate objects, and the more separation, the more potential energy you add which gravity can convert to kinetic energy?

2) why does the metric expansion of space make it moot? I just finished reading the Wikipedia article - and I'm sure I missed something, but I could not find an explanation as to why metric expansion did not add that potential energy. Perhaps answering my first question above will answer this second question as well.

 

[phinds]

1) I thought it took energy to separate objects, and the more separation, the more potential energy you add which gravity can convert to kinetic energy?

Yes, that is true, when the things are in the same frame of reference, but on cosmological scales you can't define a single frame of reference in which both objects are "local". This is totally non-intuitive, so you are hardly alone in being confused by it when you first encounter it.

2) why does the metric expansion of space make it moot? I just finished reading the Wikipedia article - and I'm sure I missed something, but I could not find an explanation as to why metric expansion did not add that potential energy. Perhaps answering my first question above will answer this second question as well.

See above (yes, answering the first answers the second)EDIT: to further confuse the issue, but I hope eventually make it more clear, thing in a single frame cannot have one moving faster than c relative to the other, but on cosmological scales, things can and do recede (which is not proper motion) from each other at WAY more than c. For example, the things at the edge of our observable universe are receding from us at about 3c. No speeding tickets are issued because this is not proper motion.

 

[Daniel Bolstad]

Yes, that is true, when the things are in the same frame of reference, but on cosmological scales you can't define a single frame of reference in which both objects are "local". This is totally non-intuitive, so you are hardly alone in being confused by it when you first encounter it.

Thanks for the quick and good answers! I'm not entirely there yet, though. Perhaps if you could explain this hypotetical to me I would understand:
Say we are in a universe with properties just like the properties of our own universe, but there are only two planetary bodies in it, and no other matter. The bodies are far enough apart so that the expansion of space takes them faster apart than gravity can bring them together.

If the expansion of said universe were to stop, the bodies would be pulled towards each other to a common centre in one single frame of reference experienced by both bodies. The energy with which they collide would depend on how far apart they are when the expansion stopped. Early in this universe that energy would be less than later in this universe.

Is this statement false? If so, why?

EDIT: to further confuse the issue, but I hope eventually make it more clear, thing in a single frame cannot have one moving faster than c relative to the other, but on cosmological scales, things can and do recede (which is not proper motion) from each other at WAY more than c. For example, the things at the edge of our observable universe are receding from us at about 3c. No speeding tickets are issued because this is not proper motion.

Is what you are saying that separation in expanding space does not affect proper motion, only relative motion? How can this be if there is a measure and increasing distance between two bodies from both their frames of reference?

 

[Markus Hanke]

How do you even define gravitational potential in the case of FRW space-time ? All Killing vectors here are space-like - I always thought that the very notion of "gravitational potential" intrinsically relies on the space-time admitting a time-like Killing field. Am I wrong ?

 

[phinds]

Thanks for the quick and good answers! I'm not entirely there yet, though. Perhaps if you could explain this hypotetical to me I would understand:
Say we are in a universe with properties just like the properties of our own universe, but there are only two planetary bodies in it, and no other matter. The bodies are far enough apart so that the expansion of space takes them faster apart than gravity can bring them together.

If the expansion of said universe were to stop, the bodies would be pulled towards each other to a common centre in one single frame of reference experienced by both bodies. The energy with which they collide would depend on how far apart they are when the expansion stopped. Early in this universe that energy would be less than later in this universe.

Is this statement false? If so, why?

Yes, since they would be farther apart later in the age of that universe, they would be moving much faster when they eventually reached other and so would collide with greater force.

Is what you are saying that separation in expanding space does not affect proper motion, only relative motion? How can this be if there is a measure and increasing distance between two bodies from both their frames of reference?

You misunderstand, I think, the meaning of "frame of reference" as it is used in physics. There IS no common inertial frame for objects on cosmological scales so "relative motion" is ill defined for the recession part of their motion relative to each other. There is a small component of their motions that is proper motion and can be correctly described as motion relative to each other in the same inertial frame that that is utterly trivial compared to the recession velocity but the recession velocity just can't be thought of the same way.[/quote]

 

[phinds]

How do you even define gravitational potential in the case of FRW space-time ? All Killing vectors here are space-like - I always thought that the very notion of "gravitational potential" intrinsically relies on the space-time admitting a time-like Killing field. Am I wrong ?

Markus I suspect that this is getting way too far over the OP's head for this discussion even though it is relevant to what he asked.

 

[Daniel Bolstad]

You misunderstand, I think, the meaning of "frame of reference" as it is used in physics. There IS no common inertial frame for objects on cosmological scales so "relative motion" is ill defined for the recession part of their motion relative to each other. There is a small component of their motions that is proper motion and can be correctly described as motion relative to each other in the same inertial frame that that is utterly trivial compared to the recession velocity but the recession velocity just can't be thought of the same way.

[/QUOTE]

You're right, I'm not understanding this thoughly. Is there some recommend reading or perhaps a book or two I should read that will help me get my head around this and lay the groundwork for a proper understanding before I come back and read your answer again?

 

[phinds]

You're right, I'm not understanding this thoughly. Is there some recommend reading or perhaps a book or two I should read that will help me get my head around this and lay the groundwork for a proper understanding before I come back and read your answer again?

Good question and a good approach. Asking questions on an internet forum about basics is a terrible way to learn them because you have to try to go off in too many directions at once just to understand the terms being used. A systematic approach is WAY more informative and as you do it you'll find this forum to be invaluable in clearing up any confusions you have from the reading.

That said, I don't have any recommendation for you but I'm sure some of our members will.

 

[Daniel Bolstad]

Yeah, I suppose asking on the Internet is not the best approach. As mentioned before, I'm no physics student. In fact I'm nothing more than a photographer, but I think understanding how the universe we inhabit works and why it exists is an important and incredibly interesting part of the human experience.

That being said, my approach to understanding the universe so far has been to think about what I don't know and Google it / watch a few lectures. Then to think about what won't make sense in the universe based on my current knowledge and google that or ask a physicist-friend. In the absence of him I ask here. But obviously this approach leaves some gaping holes in what I know and understand, but a more organized approach to learning physics is a very time-consuming procedure so I haven't quite decided what route to take in learning yet. It tends to come in conflict with many other interests and hobbies.

So in addition to my request to reading about this threads topic, are there any recommendations in the form of layman's understanding of the universe, similar to for instance dr. Hawking books.

 

[Nugatory]

Space is expanding, which separates objects from each other in space. Won't this add potential energy? Doesn't this violate the law of conservation of energy? But if it does not, how can space be added without adding potential energy?

Conservation of energy is tricky in General Relativity. Baez does a whirlwind tour of the problem here http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html, and closes with a good list of references.

 

[phinds]

Yeah, I can appreciate that point of view. There are a lot of pop-science books out and they are very informative and entertaining but they DO mislead you on some stuff. I DO suggest you seek them out, as they tend to make for an easy read and will at least get you familiar with many concepts (sadly, misleading you on some, but you'll get straighten out here quickly enough ). I don't have specific recommendations but again, I'm sure some of our members will.

 

[Markus Hanke]

Markus I suspect that this is getting way too far over the OP's head for this discussion even though it is relevant to what he asked.

Ok, no problem

 

[bcrowell]

We have a FAQ entry on this: https://www.physicsforums.com/threads/what-is-the-total-mass-energy-of-the-universe.506985/ .

For someone without the mathematical training, the basic idea to take away is that there is no conservation of energy in general relativity, except in special cases. Cosmology isn't one of those special cases. In addition to the Baez article linked by Nugatory, there is also this: http://physics.stackexchange.com/questions/2838/total-energy-of-the-universe

 

[Daniel Bolstad]

First of all, thanks for the excellent resources and good answers. I'll be spending a bit of time chewing through them and discussing what I don't understand with my friend when he's back. From what I can tell so far, though, it seems digestible :)

Secondly, I apologise for asking a question that's answered in the FAQ. I looked through the FAQ, but the question was phrased differently there so I didn't think to look in that thread.

EDIT: also, not wishing to stray too far off-topic, but what are some common things pop-sci tends to mislead you.