Does potential energy have mass?

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Re: Does potential energy have mass?

Postby Quizatzhaderac » Mon Mar 28, 2016 2:50 pm UTC

In a sense yes, but the "astronomical" in "astronomical amount of time" is a severe understatement, in that the time scales involved for a one cubic meter box of STP air sorting itself that way drastically dwarf the timescales astronomy happens on; we can safely make predictions based on the Sun dying before the box sorts itself and still have many, many sigmas of certainty.

This rounding down is called taking the thermodynamic limit, and this typically involves ignoring one in 2^10^23 chances. For smaller systems as part of a larger system it can make sense to not take the take the thermodynamic limit; for example the chance that a tiny area in a room filled with air and methane will spontaneously heat up and cause ignition.

For universes, not taking the thermodynamic limit basically means throwing out induction. If an astronomical survey concluded the universe as a whole* decreased in entropy last year**, it's conceivable that that's what actually happened, but it's much more likely that the best possible instruments all measured incorrectly the same way, or that all the scientists had the same hallucination, or that the Earth formed last Thursday with all of our consistent memories and history.

*
Spoiler:
The universe is not a closed box in the classic thermodynamic sense. Stuff can leave the observable universe. Space itself changes, which can create/destroy energy. If we actually got this result my first (non-scientist) guess would be that something cosmological was happening that makes the known universe even less like a closed box.
**
Spoiler:
The last year along our past light cone. Even with the Copernican principle this is as likely as any other section of the same size.
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Re: Does potential energy have mass?

Postby Frenetic Pony » Tue Mar 29, 2016 12:03 am UTC

Certainly it would take a "long time" but assuming time as some defined "quantity" is infinite and you continue going with random chance/quantum fluctuations being random, you'd still get a 100% certainty of reverse entropy.

Some "scale" type extended theories (eg, supersymmetry) even posit (well, some use them to posit) that quantum fluctuations are eventually responsible for creating a new universe out of a heat thermal equilibrium universe. AFAIK the idea is that your higher energy order universe dies its heat death, but the uncertainty principle from that heat dead universe produces quantum fluctuations of a high enough energy to produce and an entire universe of a much lower energy in comparison, but still there.

Fluctuations could, would I think under certain interpretations? Also be responsible for your max entropy universe going to "one side of the box". Though I don't see how the talk of "boxes" is relevant to a universe which also has a universal constant responsible for continued expansion and a flat spacetime curvature, which admittedly might possibly be what we're in. So the idea might be moot if you take those 2 presumptions as given.

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Re: Does potential energy have mass?

Postby ijuin » Tue Mar 29, 2016 10:34 am UTC

Oh, you could get a new universe spawned from a random fluctuation all right, but the average timespan for that to happen is thousands of orders of magnitude greater than the lifespan of an individual universe from Big Bang to heat death.

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Re: Does potential energy have mass?

Postby Quizatzhaderac » Tue Mar 29, 2016 4:01 pm UTC

Frenetic Pony wrote:Certainly it would take a "long time" but assuming time as some defined "quantity" is infinite and you continue going with random chance/quantum fluctuations being random, you'd still get a 100% certainty of reverse entropy.
Again, this breaks induction.

In those scenarios, any measurement or experience has an (approximate) 1 to 10^10^64 chance of being real versus being a mirage. Cause has essentially nothing to do with effect.

With these extreme odds we also need to go back and look at all of the experiments we've done to determine the laws of physics. What's the chance they're all wrong by statistical fluke? Really, really small, but still much more likely than entropy ticking back a tiny little bit.
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Re: Does potential energy have mass?

Postby elasto » Tue Mar 29, 2016 4:57 pm UTC

Not really sure that helps your cause: You seem to be saying that either science turns out to be wrong or entropy ticks backwards. Either way the statement 'nothing happens to a universe at maximum entropy' is incorrect (or misleading, at least).

Anyhow, the laws of thermodynamics are only statistical, not absolute: There's no reason we know of that entropy can't decrease - it's just overwhelmingly likely not to do so. But, as stated, given enough time, it's arbitrarily likely to do so.

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Re: Does potential energy have mass?

Postby Quizatzhaderac » Tue Mar 29, 2016 6:35 pm UTC

I'm saying that "entropy ticks backwards" implies "science is impossible, not just wrong"; you can fix wrong science, but if your metaphysics allows this to be a Boltzmann universe, you can't even start doing science.

I'm saying we take the thermodynamic limit and round down and ignore a probability so extreme it breaks our metaphysics.
There's no reason we know of that entropy can't decrease - it's just overwhelmingly likely not to do so. But, as stated, given enough time, it's arbitrarily likely to do so.
It's not that they can't in the sense that the mathematical model doesn't allow it, it does.

It's that there can't be an empirically meaningful measurement of it happening. We can describe what we'd expect to see if the universe spontaneously decreased in entropy last year, but even seeing exactly that isn't significant evidence of it, because literally every other explanation is more likely. Example in spoiler.
Spoiler:
Seriously, think of the stupidest explanation you can for "observing the universe ticking backward" apart from entropy actually decreasing universally, now add in a monkey dressed as Hitler.

Now let's apply Occam's razor: let's see the world conspiracy and all those coincidences make quite a few entities, and the mere existence of magic itself subtly implies entities all over the place...

On the other side the mathematical model of entropy combined with standard physics model, ... imputing our observations gives.... literally all the entities. All of the entities in the directly observable universe are doing odd things; all the entities in the indirectly observable universe are aggregating to do odd things.

Your idea skateboarding wizard lizard people using invisible pink unicorns to replace all the scientists with straw golems is much more likely than the universe actually ticking backward; by orders of magnitude of orders of magnitude. Although I think we can do better. Why was that monkey dressed as Hitler anyway?

Tell you what: first well focus on ways our conceptions of the less understood areas of science might be wrong and ways the mathematical model of entropy might not apply to physical reality. We'll put the magic and lizard people and Hitler-monkeys on the back burner.
We'll have to ignore the possibility of entropy just happening to tick backward, it would be silly to let that distract us when there are Hitler-monkeys to consider.
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Re: Does potential energy have mass?

Postby tomandlu » Wed Mar 30, 2016 6:18 am UTC

ijuin wrote:Oh, you could get a new universe spawned from a random fluctuation all right, but the average timespan for that to happen is thousands of orders of magnitude greater than the lifespan of an individual universe from Big Bang to heat death.


Isn't that a reasonable mechanism for the creation of a new universe after the heat-death of the previous one? As long as the necessary random fluctuation can happen, it will happen, given that the there is no time-constraint?
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Re: Does potential energy have mass?

Postby Frenetic Pony » Wed Mar 30, 2016 10:46 pm UTC

Quizatzhaderac wrote:
Frenetic Pony wrote:Certainly it would take a "long time" but assuming time as some defined "quantity" is infinite and you continue going with random chance/quantum fluctuations being random, you'd still get a 100% certainty of reverse entropy.
Again, this breaks induction.

In those scenarios, any measurement or experience has an (approximate) 1 to 10^10^64 chance of being real versus being a mirage. Cause has essentially nothing to do with effect.

With these extreme odds we also need to go back and look at all of the experiments we've done to determine the laws of physics. What's the chance they're all wrong by statistical fluke? Really, really small, but still much more likely than entropy ticking back a tiny little bit.


Again, the statistics don't matter. You are saying, essentially, over an infinite set, that a non impossible part of that set can't be in that set because it's too unlikely.

Which... it doesn't matter how likely it is, the set (t) in this thought experiment is infinite. If you want to assume a reverse of entropy is totally impossible as a condition then you can say it's not going to happen. But if you assume it's possible, then it's part of (t). Now whether it will happen or not is undecidable until such time as it "does" happen, but that's not what you seem to be arguing. Instead you're argue that it "can't happen" just because it's highly improbable. Something that can't happen and something that's unlikely to happen are to distinct things.

And you seem to assume that reverse of entryopy somehow breaks logic, which it simply doesn't. Entropic time reversal is not physical action and reaction time reversal. Under a perfectly logical system entropic time reversal can still be required to come from some previous state that leads to its new state. I totally understand the objection to a hypothesis that rejects action and reaction as a system, in fact I rather suspect most time travel as such is provably undecidable from a mathematical standpoint, but that doesn't necessitate that entropic time is the exact same fundamental thing.

And remember, quantum randomness, which is the exact sort of statistical fluke you reject out of hand, doesn't "make sense" to us in an extremely similar fashion. To whit "god does not play dice". But, at least as of our understanding of Bell's Theorem right now, that's how the universe works anyway. You could very well say that on planet X all (insert intelligent organism pronoun here) with blue eyes always quantum tunnel through concrete whenever they try it, every time without fail, and you'd still not "break" the universe as we understand it. Oh sure the probability might be ten to the power of asymptotically approaching infinity against for this to happen, but that it could still happen is just a consequence of how randomness works.

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Re: Does potential energy have mass?

Postby Quizatzhaderac » Thu Mar 31, 2016 4:04 pm UTC

Frenetic Pony wrote:Again, the statistics don't matter. You are saying, essentially, over an infinite set, that a non impossible part of that set can't be in that set because it's too unlikely.
No, I'm not saying the math is wrong. Your conclusions are the perfectly correct output of the mathematical model you're using. I'm saying the math doesn't apply, somewhat like how one can't apply addition to adding one liter of water to one liter of vodka (less than two liters), except the point where the math doesn't stick is because of the assumptions we do science under.
Instead you're argue that it "can't happen" just because it's highly improbable.
I'm saying it can't happen because it's unmeasurable; or rather that unmeasurable things aren't worthy of consideration.
And you seem to assume that reverse of entryopy somehow breaks logic, which it simply doesn't.
It breaks induction, not deduction. From outside of a spontaneously entropy reversing universe we can still consider the odds of it happening and the implications of it doing so. We cannot do so from within because all of our mental processes are compromised.

If we were a mind not subject to this reverse entropy, but only observing this reverse entropy universe, we still couldn't determine the laws of nature accurately because every measurement is an extreme statistical artifact.
And remember, quantum randomness, which is the exact sort of statistical fluke you reject out of hand, doesn't "make sense" to us in an extremely similar fashion.

Statistics is collection multiple sample data points to make predictions about a larger population.

We are very large compared to quantum randomness. There's more than one electron and each one can be observed multiple times. We can meaningfully say tunneling happens as a statistical fluke because we've collected statistics on electrons. Statistics apply to the population of electrons.

We only get one universe (by definition). If we observe the universe as X, it's X. If we observe it as Y it's Y. Mathematically, we can say we observe it as X but it's probably Y under some a priori model of physics, but if we're being empirical, we have to take the universe as it's presented to us.
You could very well say that on planet X all (insert intelligent organism pronoun here) with blue eyes always quantum tunnel through concrete whenever they try it, every time without fail, and you'd still not "break" the universe as we understand it.
That would not break the universe, but it would break our understanding of the universe. Science is the process of changing our understanding of the universe based on what we observe. Once an empiricist observes this regular tunneling process, they can no longer keep the standard model of physics.

The exact best new model is complicated, but there is now an inordinate amount of evidence a new model is needed. From outside the hypothetical we might be tempted to say "But that's not how the physics really works in this hypothetical universe, and a rational person should approach an understanding of their universe, not move away from it." But this scenario isn't really fair to our hypothetical scientist.

Let's stop and really think about how this hypothetical universe works. In general it's physics is like ours except for the blue-eyed-tunnelers. The blue eyed tunnelers are an inherent part of the hypothetical and therefore an inherent part of the hypothetical universe. The list of physical laws of that universe is our list of physical laws plus some special conditions for blue eyed tunnelers.

So our hypothetical scientist starts off thinking their universe follows a set of physical laws equivalent to our universe's. Then they see the blue eyed tunnelers and adjust their model of physics to compensate for the special case in the hypothetical universe's workings. We can't fault our scientist for moving away from using a model of physics the fits our universe towards one that better fits their universe.
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Re: Does potential energy have mass?

Postby PsiCubed » Thu Mar 31, 2016 4:06 pm UTC

doogly wrote:The potential energy due to gravity does not have mass, that's where you get off the chain. GR is all about gravity being "different" from other forces.


Huh?

A basic fact of cosmology is that in a "flat" universe, the total net energy is exactly zero because the negative gravitational energy cancels the mass of everything in it.

By the way, this statement of "potential energy = mass" only has meaning when we look at the entire system. Here is a brain-bender for you:

Say I put a stationary electron in an electric potential of 511000 volts. This electron has a rest-mass of 511000 eV/c2 and a potential energy of -511000 eV. Add these two numbers up and you get zero. So what does this mean? Does it mean that electron suddenly became massless?
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Re: Does potential energy have mass?

Postby doogly » Thu Mar 31, 2016 4:15 pm UTC

There's not really "energy" in curvature, that's some sleight of hand in the Friedmann equations.
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Re: Does potential energy have mass?

Postby PsiCubed » Thu Mar 31, 2016 4:28 pm UTC

Sorry, but what you're saying doesn't make any sense.

When an apple falls, its kinetic energy increases. Where did this additional energy come from?
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Re: Does potential energy have mass?

Postby doogly » Thu Mar 31, 2016 4:52 pm UTC

Gravity did work on it.

These are very different contexts. Like, another thing, is energy conserved globally? In GR, this is very false. We are used to reasonings in which it is true.
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Re: Does potential energy have mass?

Postby PsiCubed » Thu Mar 31, 2016 5:27 pm UTC

That's an exaggeration.

Conservation of energy holds in any system which has time translational symmetry. This may not be true in certain situations in GR, but it is true for any system which has a finite distribution of mass (because such a system will be "flat" at infinity).

So as long as we are talking about a local situation (like an apple falling on earth), we can speak of conservation of energy. And that's a good thing too, because otherwise GR would have been completely useless for almost anything other than cosmology.
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Re: Does potential energy have mass?

Postby doogly » Thu Mar 31, 2016 6:06 pm UTC

You can if you want, but, you shouldn't.
And if you did, you should realize it's a slight of hand. You take something from the gravity side of an equation, put it onto the energy side, say "this is an energy too!"
You can get away with that, but then, this doesn't also gravitate. That was my original point, that ascribing "mass" to "gravitational potential energy" is a kind of double counting.
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Re: Does potential energy have mass?

Postby tomandlu » Fri Apr 01, 2016 9:07 am UTC

tomandlu wrote:
ijuin wrote:Oh, you could get a new universe spawned from a random fluctuation all right, but the average timespan for that to happen is thousands of orders of magnitude greater than the lifespan of an individual universe from Big Bang to heat death.


Isn't that a reasonable mechanism for the creation of a new universe after the heat-death of the previous one? As long as the necessary random fluctuation can happen, it will happen, given that the there is no time-constraint?


Bump - can someone give me some info on this?
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Re: Does potential energy have mass?

Postby Wolfkeeper » Fri Apr 01, 2016 7:48 pm UTC

doogly wrote:You can if you want, but, you shouldn't.
That was my original point, that ascribing "mass" to "gravitational potential energy" is a kind of double counting.

Agreed. If potential energy has mass, at the very least, in the case of gravity, it's a negative mass; you would be losing potential energy mass as two things move towards each other.

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Re: Does potential energy have mass?

Postby Goemon » Tue Apr 05, 2016 1:58 am UTC

doogly wrote:"Gravity" lives on the left side. You don't count Newtonian style gravitational potential energy on the right side, because that sort of thing is already on the left side.


Then puzzle me this (from farther up this thread):

Quizatzhaderac wrote:Let's take a spherical volume of space 1 light second across. Our observer is at a constant distance from the sphere's center. We'll start with an Earth's mass of perfectly inelastic rocks evenly distributed about this space and not moving with respect to the center/observer.

The rocks would start to fall, their kinetic energy would go up and their potential energy would drop. The mass in the sphere as a whole would remain the same.

The rocks would hit each other in the center. Being perfectly inelastic, they would stick, their kinetic energy would drop and their temperature would increase. The mass in the sphere as a whole would remain the same.

The hot thing in the center would emit black-body radiation. The mass in the sphere as a whole would drop, because now something is leaving it.

The number and type of atoms in the rock wouldn't have changed, but the mass of the only group would have decreased.


if (rocks clumped at center of sphere) emit radiation and eventually cool down to return to the original temperature of (rocks scattered throughout the volume), what was the source of the radiated energy leaving the sphere, if not "gravitational potential"?

(I agree with you by the way, just find this a nice puzzle...)
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Re: Does potential energy have mass?

Postby speising » Tue Apr 05, 2016 7:37 pm UTC

The magic that created the sphere in situ?

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Re: Does potential energy have mass?

Postby SAI Peregrinus » Wed Apr 13, 2016 9:01 pm UTC

Color confinement is an example of potential energy having mass. It's not gravitational potential energy, it's strong potential energy, but you do get physical quarks out of it.

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Re: Does potential energy have mass?

Postby Himself » Sun May 01, 2016 2:34 am UTC

The scenario of the rocks falling inward is still relevant to reality, though, right? The radiation from quasars ultimately comes from gravitational potential energy, doesn't it?
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Re: Does potential energy have mass?

Postby elasto » Sun May 01, 2016 12:32 pm UTC

I think it can be stated quite simply, can't it?

Two rocks accelerate towards each other through mutual gravitational attraction. But energy isn't being created from nowhere: Energy is conserved: They gain kinetic energy but lose gravitational potential energy.

Likewise, because the energy in this self-contained system is conserved, the mass must be conserved: The 'mass' they gain from moving faster is counteracted by the 'mass' they lose by losing potential.

(Hmm. Now I've written it down like that, it seems wrong; Because stuff moving faster should get heavier else what limits the speed? Wouldn't that imply that gravity would cause things to move faster than the speed of light simply because that 'infinite' energy was already implicit in the initial setup? Now I've confused myself lol...)

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Re: Does potential energy have mass?

Postby gmalivuk » Sun May 01, 2016 7:19 pm UTC

elasto wrote:Wouldn't that imply that gravity would cause things to move faster than the speed of light simply because that 'infinite' energy was already implicit in the initial setup?
Kinetic energy approaches infinity as velocity approaches the speed of light. How do you propose gravity could use that fact to ever exceed it?
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Re: Does potential energy have mass?

Postby elasto » Mon May 02, 2016 1:21 pm UTC

gmalivuk wrote:Kinetic energy approaches infinity as velocity approaches the speed of light. How do you propose gravity could use that fact to ever exceed it?

It follows from my assumption that the energy of the system remains constant despite an increase in velocity, which means the mass remains constant despite an increase in velocity, which means that kinetic energy (mv^2) does not approach infinity as the speed of light is approached.

Obviously I'm wrong, which means my assumption is wrong. I'm asking for help understanding why, rather than simply pointing out what I already know :)

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Re: Does potential energy have mass?

Postby gmalivuk » Mon May 02, 2016 2:36 pm UTC

Your incorrect assumption is that the Newtonian kinetic energy equation applies to relativistic scenarios.

Relativistic "mass" just is the asymptotically increasing kinetic energy with increased velocity.
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Re: Does potential energy have mass?

Postby elasto » Mon May 02, 2016 3:06 pm UTC

Gotcha.

So my summary was right, I think?

- The objects fall towards each other - each gaining kinetic energy and hence mass.
- As they do so, the pairing loses potential energy, and hence mass.

The total energy and total mass of the system remains constant.

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Re: Does potential energy have mass?

Postby Himself » Mon May 02, 2016 10:08 pm UTC

So here's where I'm confused. I have read in a few places that the energy radiated by a quasar is equivalent to a significant portion of the mass of the infalling material. All of that must have originally been gravitational potential energy. But that material would still have gravitational potential energy with respect to other black holes. Wouldn't that mean that nearly all the mass in the universe is gravitational potential energy? That doesn't seem to make sense.
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Re: Does potential energy have mass?

Postby Toffo » Tue May 03, 2016 4:25 pm UTC

What's the problem Himself? Exploding nuclear bomb releases some of its nuclear gravitational potential energy as all kinds of gravitational potential energies. Sound gravitational potential energy, light gravitational potential energy, and so on.

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Re: Does potential energy have mass?

Postby doogly » Tue May 03, 2016 5:21 pm UTC

"Sound gravitational potential energy" ?
Look, you can persist in your nonsense, but don't drag poor Himself down with you.

Himself, your potential energy relative to a black hole you are not falling into is probably going to be really negligible. ~1/r^2, knocks it right down.
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Re: Does potential energy have mass?

Postby Toffo » Tue May 03, 2016 6:13 pm UTC

doogly wrote:"Sound gravitational potential energy" ?
Look, you can persist in your nonsense, but don't drag poor Himself down with you.

Himself, your potential energy relative to a black hole you are not falling into is probably going to be really negligible. ~1/r^2, knocks it right down.


Matter falling into a quasar is falling into a black hole, so that matter has non-neglible potential energy. So it makes sense, in my mind, that quasars emit lot of potential energy.

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Re: Does potential energy have mass?

Postby doogly » Tue May 03, 2016 11:39 pm UTC

Himself wrote:But that material would still have gravitational potential energy with respect to other black holes.

That's the negligible bit. The one you're falling into, sure.
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Re: Does potential energy have mass?

Postby Himself » Wed May 04, 2016 12:29 am UTC

I was under the impression that the potential energy increased with distance with U=-GMm/r simply giving negative values. I understand, for example, that the majority of the ~25k light years between us and Sagittarius A* accounts for a very small portion of our potential energy relative to it, but we still have quite a bit because of the first few hundred AU of our distance.
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Re: Does potential energy have mass?

Postby Toffo » Wed May 04, 2016 3:33 am UTC

Toffo wrote:What's the problem Himself? Exploding nuclear bomb releases some of its nuclear gravitational potential energy as all kinds of gravitational potential energies. Sound gravitational potential energy, light gravitational potential energy, and so on.


Above I created a theory, I did it by appending "gravitational potential energy" to the name of every type of energy.

Now I will create a second theory, by taking the first theory and removing every occurrence of "gravitational potential energy". So now we have these kind of statements: "Lifting an atom bomb increases its nuclear energy"

(The first theory included a term "nuclear gravitational potential energy". It makes sense that "nuclear gravitational potential energy" increases when a nuclear bomb is lifted, so the first theory had a statement "lifting an atom bomb increases its nuclear gravitational potential energy". In my second theory that becomes "lifting an atom bomb increases its nuclear". Oh it seems that I need to correct my theory: word "energy" needs to be appended.)

Doogly thank you very much, my second theory was born because of your criticism of my first theory.

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Re: Does potential energy have mass?

Postby Goemon » Wed May 04, 2016 3:57 am UTC

elasto wrote:- The objects fall towards each other - each gaining kinetic energy and hence mass.
- As they do so, the pairing loses potential energy, and hence mass.


An accurate description from a Newtonian point of view. But as Doogly noted earlier, from a General Relativity point of view, there's no such thing as gravitational potential energy. Thus a bit of a puzzle. Interestingly enough, this comment is much closer to the mark:

elasto wrote:It follows from my assumption that the energy of the system remains constant despite an increase in velocity, which means the mass remains constant despite an increase in velocity, which means that kinetic energy (mv^2) does not approach infinity as the speed of light is approached.


Spoiler:
Drop a purple marble high above the Earth. As it falls, Newton would say that it's gaining kinetic energy. Just before it collides with the surface, convert the marble into a spray of photons headed back upward. When the pile of photons reaches the original height of the marble, convert them into an orange marble. Does the orange marble have more energy than the purple marble had? No, of course not. (If it did, we'd have a marvelous free energy source.) What happened to the extra kinetic energy the falling marble gained? The photons that were climbing back up out of the "gravitational well" were red shifted as they did so; the result was that the final energy was exactly the same as the initial energy.

A (stationary) observer high above the Earth can't reliably measure things that are happening far below because the curvature of spacetime distorts lengths and clock ticks as they travel hither and yon. This is one of the caveats of General Relativity: to measure the properties of something that's far away from you across a gravitational field, you have to very carefully transfer the information (velocity vectors etc.) along a specific path in a certain way ("parallel transport") from the point of interest to the observer's location. Any changes in the marble's property can only be measured after the information has all been gathered a single point using the correct method of transport to ensure the distortions caused by curvature are accounted for.

Assuming the marble is simply freefalling, then from the GR point of view, its energy never changes. At any point along the (free fall) path, if we take a snapshot of the marble's velocity vector in four dimensional spacetime and carefully transport it back up to the observer, all the snapshots match. From a GR point of view, the marble's energy isn't changing (why would it? there are no forces acting on it); what the distant observer sees as an "increase in kinetic energy" is nothing more than their view of the distant marble's condition being distorted by the curvature of intervening spacetime. But when the distortion is removed by the proper transport of the information, we find there's no change at all.
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Re: Does potential energy have mass?

Postby doogly » Wed May 04, 2016 11:32 am UTC

Himself wrote:I was under the impression that the potential energy increased with distance with U=-GMm/r simply giving negative values. I understand, for example, that the majority of the ~25k light years between us and Sagittarius A* accounts for a very small portion of our potential energy relative to it, but we still have quite a bit because of the first few hundred AU of our distance.

You are doing extra integrals when you don't have to. The potential energy is just the 1/r, which drops as you go away. It's not ln r, which grows slowly but by a smaller and smaller amount as you go away. (And again this is still just Newton.)
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Re: Does potential energy have mass?

Postby Himself » Wed May 04, 2016 10:04 pm UTC

I was using the formula U=-gMm/r, directly, not any logarithm. Using a 1 kg mass and a 4 million solar mass black hole I get:
~-2*10^6 J at 25 k light years
~-6*10^10 J at 1 light year
~-4*10^15 J at 1 AU

So the potential energy diminishes rapidly with increasing distance at close proximity and more slowly at larger distances.
On another note, with comments that gravitational potential energy does not exist in general relativity, wouldn't quasars violate the conservation of mass/energy?
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Re: Does potential energy have mass?

Postby doogly » Wed May 04, 2016 10:50 pm UTC

Right: so if you are far away from things, you have negligible potential energy with respect to them.

So, you have options. If you want to talk about conservation of global energy, you can do Newtonian mechanics, where it all makes sense. In GR, this isn't a global thing. Closest you get is dT=0. Which it does.
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Re: Does potential energy have mass?

Postby Himself » Wed May 04, 2016 10:55 pm UTC

Sorry, I had meant to say increases, not diminishes.
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Re: Does potential energy have mass?

Postby doogly » Wed May 04, 2016 11:23 pm UTC

It goes to zero at higher distance. If you're counting that as an increase because it's negative, sure, but you won't get to 'most of the energy in the universe is gravitational potential' this way.
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