different *levels* of energy behave differently.

no contradiction.

also, Pie in the Sky!

As a physicist, I'll cheerfully admit I have no idea what you are talking about.

LoL, whom do you address YJ ?

I'll admit I have no idea what orathaic is talking about either :P

Really, i mean, apart from interactions under gravity, i can think of no energy system where dispersal is not a feature... Mass under electromagnetic interactions disperses, atoms under high enough temperatures break up, dispersing the energy until the temperature is too low to break them down and then at best they remain stable...

Photons in a laser remain coherent (not dispering) for some limited lenght and then disperse...

I was talking to OP, fiedler. ora I"m not sure i see any contradiction. Is dispersion of energy a law, or just an observation you've made in a few specific cases that happen to support your perceived contradiction?

Anyways, matter "clumps" for various different reasons at various different scales (you probably know more than me), so whatever behavior energy displays will interact with each of these behaviors in different ways (much the same as the strong nuclear force trumps EM within the nucleus, but nowhere else).

Maybe I"m way oversimplifying your concern though - I don't do much real physics anymore :P

I see clumping as a feature of gravity, and as you rigthly pointed out different forces dominate different regimes (oh and. I see gravity as a property of mass... Which may be my mistake)

I'm pretty sure that energy always disperses. Black holes evapourate. Generally you can take measure to limit the rate of dispersion, but not reverse it...

Well ok, even if we assume energy always disperses (and I really have no idea, I'm just rolling with you) I'm not sure you can say that matter = energy, at least not in the way that you are trying to. Both have extraordinarily different behaviors in most every single way, at least on the macroscopic scale.

I guess I just don't follow why your intuition would lead you to expect them to behave similarly as far as clumping/dispersion, specifically, goes.

I think a big step towards the answer is the fact that E=mc^2 is giving you the *rest* energy of a massive particle. You cannot apply this formula to massless particles (mainly photons) directly.

You can still view matter and energy on the same footing, but then you need another ingredient: the pressure. In General Relativity, this is encoded in the equation of state. Radiation (energy in the form of massless particles) does not disperse, because it has a pressure equal to 1/3 times the density. Matter has effectively no pressure.

Two answers come to mind, on different time-scales.

First, on normal time-scales, I would say that 1 is just too much of a generalization. In fact, what you've basically done is proven it wrong. There's no law of physics that says "energy disperses" (except see point two below). There are laws of physics that say that energy in different modes behave in particular ways. The dynamical features of most of these modes lead to dispersion, but the dynamical features of stable particles lead to clumping -- via GR, basically.

Gravity, incidentally, isn't a property of mass. The geometry is determined by both mass and energy, and to the same extent, once you've applied E = mc^2. However, massless energy is usually moving extremely fast and isn't going to stick around to clump (to oversimplify).

The second point -- when I say there's no law of physics that says energy disperses, that is of course a lie. There's the second law of thermodynamics. What's true is there's no DYNAMICAL law that says so, but there is a statistical law. And so on long timescales, it does, and actually, you've already given the answer to your riddle, so far as I can tell.

Matter clumps; but once it clumps too much, it starts clumping into supermassive black holes. And then those radiate away eventually, and thus spread out the energy and matter.

No?

Yeah, ok so black holes eventually evapourate, that is an example of a gravitational system getting to a high enough energy density that it starts to disperse.

I think the laws of entropy are equivalant to my intuition that energy disperses, which begs the question, does gravity break the second law of thermodynamics? To which i say, no but i don't understand why/how.

@bas, i like the direction you are taking, but i don't fully understand. Never studied GR, can you explain a bit more, as if i'm an idiot.

Matter does disperse, at 'low' temperatures where protons and atoms are stable they tend to spread out, and as matter is energy this means the energy is being more widely dispersed. (like gaseos atoms in a room released from a small container) at lower temperature those atoms will form a solid which is again stable, but even then i suspect only under gravity do such solid clump, at best they remain stable holding their energy density...

I guess the intuition that matter clumps comes from looking at examples - the solar system is a great example of clumping matter. 99.9% in the sun, then of the rest 75% in Jupiter... On a galactic scale you see similar clumping...

@ora: Let me apologize in advance, because I'm going to reply with something that isn't quite the answer to the question you asked, but I think is the answer to the question you meant to ask. I'm also going to slightly lie to you, again in ways I'm happy to discuss but that would mainly get in the way of seeing what's going on.

When you say "energy disperses", what you really mean is that entropy increases. One way of thinking about what it means for entropy to increase: you should be able to keep describing the system you are looking at using less and less information.

In the case of radiation, this means spreads out until it's at a constant energy density (temperature). It is easier to describe a box as "the box is at 50 degrees" than "the left side is 40 degrees and the right side 60 degrees"; the box will move from the latter to the former.

In the case of matter, it turns out that very compact things are easier to describe. For example, consider galaxies. A spiral galaxy, like our own, is a complicated thing. You have to tell me where the spiral arms are, how big the bulge is in the center, etc., and all of that structure has a lot of detail. An elliptical galaxy (basically, a big round/oval blob) is more compact, but easier to describe "it's a big ball of stuff, a little longer in this direction than in that one". So, even though the elliptical galaxy is less spread out, it actually has higher entropy, and spiral galaxies will eventually become elliptical, not the other way around.

I realize it's a bit counterintuitive, but I hope that helps.

Which bit was the lie? And if all matter were to find itself in one bosonic state with a low enough temp, in on position... That would be very easy to deacribe, but i somehow assume that it would not be low entropy...

Also, i'd have thought a spiral galaxy was more concentrated, basically the stars are confined to a 2-Dimensional ( 2 ) plane; it seems like spreading in a 3 sphere/ellipse would be lower density (assuming the little i know about galaxy formations, which iirc says elliptical galaxies are the result of the merger of two spiral galaxies - on different planes - that gives a redistribution of matter within a sphere... And that ignores any lose of mass as stars are spun out during the galactic collision.

@Csteinhardt: I think you've got the example backwards: high entropy systems have many residual degrees of freedom, low entropy systems are essentially fixed by their thermodynamic variables. And black holes have a *huge* entropy.

@Ora: The difference between matter and energy (more specifically, energy in the form of radiation) is that matter can stand still. Light is always moving with the speed of light (duh), and that's where it gets its energy from.

Now to the pressure bit: Suppose you have a volume with lots of radiation in it (we don't care at this point what produces the radiation, for all we care it's been there forever), and you hold a plate next to it. This plate is going to experience a force due to all the light particles hitting it. In other words, the radiation exerts a pressure. (http://en.wikipedia.org/wiki/Radiation_pressure). One can calculate (this is remarkably easy) that the pressure is 1/3 of the energy (in c=1 units).

This answers the question why radiation doesn't clump. Once you get enough of it in a fixed volume to assign it an appreciable mass (and you need a lot of it!), it has a very large outward pressure ripping it apart. The difference with matter is that you can have high concentrations of mass with negligible pressure.

Oh, and I would like to point out that the second law of thermodynamics is not in contradiction with General relativity.

I know that the second law of thermodynamics isn't in contradiction with general rel, but i don't intuit this...

Ok, i imagine mass - as a form of energy - as dispersing (under certain conditions), so this brings us back to gravity.

For massless energy, you are saying that the radiation pressure accounts for the lack of clumping under gravity, and that matter - being a special way of binding energy together - doesn't disperse. Now ignoring the special relativity for a moment; what is going on with the energy is a gravitational system? Lets assume that the is a large amount of gravitational potential energy to begin with - some unstable random system interacting under gravity, with many hydrogen atoms for simplicity, or many neutrons if you like... - no lets assume after some time the gravitational potential energy of the system is reduced, that energy has to go somewhere. Fine kinetic energy of the atoms.

Is that a complete description of the simplified system?

And is the energy density now, like the particle density, much higher (with the componets of kinetic and potential energy taken into account)

From an entropy perspective, have we just increased the number of accessible states? I can't intuit counting those states...

Hmm, in general, energy tends to move from a high energy state to a lower one, so in a u-shaped potential well, ( u-shaped valley, say ) particles will gather around the bottom of the well ( water gathering in the middle of the valley ) and if energy is given out the total energy density in the area is lower, but the particles can concentrate at the very center (so if you look just at that central point you will see a much higher energy density - counting the mass of the particles in your densit total)

Ok i think i see, different ways of averaging...

So clumping represents a increase in the local average density, but still requires a decrease in the global average... Or that feels awkward and perhaps wrong.

Plus i don't see where the energy is lost to in the gravitational potential to kinetic energy example above :(

Look at it this way...

Energy (photons) disperse because they are mass-less and so *must* travel at lightspeed.

Matter clumps because it has mass and so *may not* travel at lightspeed.

Gravity may be thought of (in this simplified example) as a field that attracts everything (matter and energy) near it. It is generated by things that have mass and/or energy.

Therefore, the slower something is travelling the longer it spends in the gravitational field and the more it is influenced by that field. Slow moving things are pulled towards a centre of gravity more than faster moving things, so matter "clumps" together.

Two additional points:
Photons have a gravitational field equivalent to the mass the energy of the photon [e=mc^2, m=e/(c^2)]. Throw mass into a black hole and the black hole gets heavier. Fire a laser into a black hole and the black hole gets heavier.

Protons and neutrons (may) have a half-life (10^36 years). They (might) eventually breakdown releasing sub-atomic particles and gamma-ray photons.

I still say you want to consider stuff like this:

http://www.astronomy.com/en/News-Observing/News/2010/04/Connecting%20black%20holes%20and%20galaxy%20death.aspx

So you have a galaxy... but then eventually a lot of it falls into the black hole at the center, and the rest gets blown apart by the violence. So you start off with

(a) A bunch (M) of matter in a galaxy;

and you end up with

(b) Less matter (m < M) that will maybe form another galaxy, and
(c) A black hole.

The black hole will disperse, but not as matter. It will emit radiation, which, as STA points out, will move too fast to get caught up.

So the process is, in fact, turning mass back into energy and dispersing it, over time.

> Plus i don't see where the energy is lost to in the gravitational potential to kinetic energy example above.
Imagine a sealed bicycle pump with a ratchet to hold it down once compressed. A lead weight drops onto it pushing the plunger down, then falls off. The ratchet holds the plunger down. The gas inside the cylinder is compressed by the kinetic energy of the falling lead weight. This increases the pressure and temperature of the gas. You can use the pressure of the gas to do work (turning a wheel say). The gravitational potential energy becomes kinetic energy becomes a the energy available in a hot, compressed gas.

'Energy (photons) disperse because they are mass-less and so *must* travel at lightspeed. '

No, that is entirely unsatisfying. First, i don't think of energy as just photons - heat is a form of energy - it tends to difuse, radiate, and generally escape from and concetration of heat (clump of heat?)

However it does lead me to blackholes, just because light happen to travel at 300 million m/s doesn't mean it disperses (in a black hole it will remain inside) but i guess this is a feature of the shape of space (a black hole is essentially a closed self-contained space) and obviously if the space you are in is closed there is a maximum possible dispersal.

On the other hand a laser pulse also doesn't disperse (for as long as it remains coherent) even though it is travelling at the speed of light.

I find almost everything about 'fast requires dispersal' to be difficult... However the question of the shape of space ultimately does open a nice avenue of inspection. I'm not entirely sure how to explore it...

@smeck: thanks for that, i think it is equivalent to the U-shaped potential which gives off energy but 'finishes' with a higher local energy density at the center of the well...

The point where you have an m mass blackhole is like this end point...

No, orathaic, m is the mass of the new universe, not the black hole. The point is that the whole process tends to convert mass into other forms of energy, which then disperse.

"First, i don't think of energy as just photons - heat is a form of energy - it tends to difuse, radiate, and generally escape from and concetration of heat (clump of heat?)"

Again, I think you need to more carefully analyze dynamics versus statistics in this process. Heat does that for statistical reasons. If you go down to the QFT level, there isn't some form of energy called heat. There are just individual particles/fields in different energy states interacting.

'magine a sealed bicycle pump...' - no i don't think that will help at all.

I understand your system, but i don't see how it addresses what i was trying to ask.

Oh and lastl about photons - if you get a high enough photon density you should be able to create a black hole!

Actually if you get enough bosons in one place by forming a bose-einstien condensate i guess you'd also form a black hole... I wonder how expensive/hard that would be.

Bose-einstien to neutron star densities should allow you explore what happens when fermi repulsion is overcome.. If ou add some fermions to the system of course.

Obviously I meant galaxy, not universe, lol.

Yikes.

It's 3:45 AM, in my defense.

"Plus i don't see where the energy is lost to in the gravitational potential to kinetic energy example above :( "

Exactly which example was this referring to?

By the way, thanks smeck.

Ok yes, it is for statistical reasons for heat, and diffusion of matter in a non gravitational regime; but it is also the case for light (photons) and sound (phonons) - though that may be a feature of the geometry (shape) of the space, ie if it is locally flat things can move out and when you locally look at the energy density is seems to decrease... You could argue that there are good statistical reasons for this (there being more empty states available - and if they were filled you'd get something more like a standing wave...)

I appear to have been talking about this example: 'in a u-shaped potential well, ( u-shaped valley, say ) particles will gather around the bottom of the well ( water gathering in the middle of the valley ) and if energy is given out the total energy density in the area is lower, but the particles can concentrate at the very center (so if you look just at that central point you will see a much higher energy density'

But i confused by what i said...

As for your black hole m < M, the galaxy m and the blackhole (M-m) sorry i misread, but m>0 so both the possible new galaxy and the black hole hage a mass < M...

Ok, cool quality of central force systems i just noticed : if you have some escape velocity v < c and some random (chaotic) collisions with this potential well, some particles with gain enough energy to reach escape velocity and then (having higher than average energy) reducing the average (and thus the 'heat') - this lower of energ is a self-organised system which naturally takes the energy density down to a critical point where no more particles can escape until energy enters the system from somewhere; (lacking from this, at least in the case of gravity, is the effect of losing energy on the gravitational field reducing the amount of energy needed to escape... Or reducing the steepness of the well)

Orathaic,

Yes, sorry I was unclear -- I do agree that _photons_ appear to disperse for reasons that are much more directly dynamical/geometrical. They're travelling super fast and there isn't enough matter to trap most of them, etc. As you say, one could view this in terms of state counting, but it's not clearly necessary at this level (though certainly if one wanted to be rigorous). I was just saying that in the heat case, it's more statistical.

OK, I agree, the black hole has mass M - m. The point is that by the end of all this, there is LESS mass than there used to be -- only m now. M - m is being converted into radiation, and the process will repeat itself, yielding a galaxy of mass m' < m and (m - m') in radiation, etc., so mass is getting dispersed this way, or so it seems to me.

As to your example of the U-shaped potential -- if the particles are not in the center initially, then they will NOT focus at the center -- they will oscillate; unless, of course (which is what really happens) they colide and convert kinetic energy (which came from the potential energy) into heat (and/or mutual interaction energy) -- i.e., they clump at the bottom but still have all the kinetic energy in some of their degrees of freedom. If they're massive objects like stars or planets, the degrees of freedom will probably be internal -- higher kinetic energy (temperature) of the constituent particles, so that there's a lot of disorganized low-amplitude oscillation around the center, instead of a a single high-amplitude oscillation.

This U-shaped potential / entropy problem comes up in a really interesting way in Landauer's principle, which says that erasing memory always increases entropy. If you model a bit of memory as a twin-well potential with (say) a ball that can roll back and forth, then there is no single force / potential that can be applied to deterministically set the ball back to (say) well/state 1, unless the ball is dispersing energy / increasing entropy at some point in the process. Or in brief, erasing requires an entropy increase of at least k log 2 on average. But I digress quite badly.

Launder's principle is indeed tangential at best, but awesome when i saw this:
'At 25 °C (room temperature, or 298.15 kelvins), the Landauer limit represents an energy of approximately 0.0178 electron volt. Theoretically, room‑temperature computer memory operating at the Landauer limit could be changed at a rate of one billion bits per second with only 2.85 trillionths of a watt of power being expended in the memory media.'

But back on topic, for U shaped potential the internal energy and degrees of freedom (makes me think of molecules exchanging translational motion for rotational or vibrational energy, i think that's equivalent) - this does seem problematic (for my inital assertions) you are also explaining a more complicated system so at least it highligts the simpleness of the systems i've been imagining.

Still, we're talking about interal energy (of some system) now and that's great.

Ok, lets simplify again, a planet with this greater internal energy (heat, vibration, rotation etc) will give off more blackbody radiation, thus dispersing the energy of photons... This gives us some equivalence with the blackhole example where there is hawking radiation in place of the blackbody (though in infinitely long time scales this may not disperes all the energy in the planet, i'll disregard that as i've got a problem somewhere sooner)

So in general a collection of massive particles can clump together (around a central point) gaining internal energy and losing kinetic/potential energy.

Be it a planet or a blackhole. In both examples we have an increase in energy density (in the short term perhaps) and some clumping has occured, you may have system which start with sufficient kinetic energy (photons have a lot) that clumping is overcome (except on sufficiently small/local scales - subsystems without such energy)

But eventually all of this clumped energy will be turned into kinetic energy and escape (hawking radiation/blackbody radiation) not all planets will neccesarily fall into blackholes... Which will leaves clumps over...

The total/global energy density will then depend on the geometry of the universe itself... And i've no idea what that would contend. Help?

I'm not sure I understand your final question. But I do think that a lot of physics depends on the geometry/topology of the universe, not all of which (obviously) is known. For example, we've been ignoring dark energy, which pushes matter apart.

But anyway, I do think some clumpiness is to be expected for any finite time out. Of course, even that, over very large scales and if dark energy didn't interfere already, might eventually clump into new galaxies, so it could be a forever continuing process, but I don't think there would ever, in finite time, be a completely homogenous universe. Of course, on large enough scales, cosmologists already view the universe as homogenous. I guess one could think of it as the scales on which that was true getting smaller and smaller without ever getting to zero. (?)

Incidentally, I guess a point that IS worth making is that even in the short term, entropy does have to increase in this whole clumping process. It's not totally clear to me how that happens, but I imagine it's got a good deal to do with the heating process we're discussing. Certainly the change from gravitational PE into heat represents an increase in entropy.

Ok, i glossed over special relativity a while back, but everything seems to point to the geometry of space-time and photon kinetic energy, so i'm going to have to come back to it.

From the perspective of a massive particle approaching the speed of light the lenght of the universe (in the direction of travel) reduces. (paradoxically the universe sees the lenght of the traveller decrease by the same factor)

For a massless particle already travelling at c the lenght of the universe would be measured as 0 (leaving only two spatial dimensions) meanwhile the universe should measure the photon as having 0 length (does this is fine for a transverse wave, though the uncertainty principle should impose some limits on our knowledge of it's position)

Now this seems important because from the prespective of the photon the geometry of the universe appears very different. (similarily the time dimension is affected though it's expansion to infinity is not something i can intuit how to deal with) i feel the photons perspective is a valid as anyone elses (and at least so the laws of physics should still hold...)

Well, if we're dealing with spacetime geometry, it would be better to deal with GR than SR, probably. In this case, one would have the photon travelling along a null geodesic; so it would still remain true that it would go infinitely far in zero proper time, IF its null geodesic was complete (didn't end in a singularity somewhere).

But anyway, apart from that, I think I agree with everything, but am not completely sure I see where you're going with it?

"Now this seems important because from the prespective of the photon the geometry of the universe appears very different."

But again, you'd want to use GR and speak of a global spacetime structure. It's true that, from the perspective of the photon, objects nearby to it along its path will appear to have zero length (as will its entire path).

Ok, far too much digression. What we've come to is fairly simple, energetic systems (ie those not at some zero-point) tend to 'clump' often giving off excess energy in the process - they tend to approach a point where the reach some maximal internal energy (be is protons formed out of a quark-gluon soup, nucleus formed out of a proton-neutron-electron plamsa, molecules formed out of chemically reactive elements, planets formed out of star dust, blackholes formed out of collapsing stars...)

Usually this i volves throwing off some energy into the rest of the universe (dispersing it) which is to say clumping requires dispersing of excess energy. However a closed system can increase it's entropy without reducing it's total energy (no dispersion occuring) Though it is not clear how this can lead to an increase in energy density?

I think entropy is the more fundamental factor here rather than energy density (other than being the cause of energy moving from higher densities to lower ones)

And space-time geometry is also required to change it think, taking the quark-gluon soup TO proton&electron plasma example, i suspect the if space was constant there would never be much time to be far away from anything else, so continued interations with quarks and gluons would prevent this 'clumping', however if space expands there will be an ever inceasing time between collisions, more space to be the place where you disperse excess energy to, and eventually a phase change.

So both entropy AND geometry are required...

'But anyway, apart from that, I think I agree with everything, but am not completely sure I see where you're going with it?'

Nor i, but i'm glad you understood it and have a better grasp of GR than me to explain it in those terms... It seems like it was begging to be explored.

'It's true that, from the perspective of the photon, objects nearby to it along its path will appear to have zero length (as will its entire path).'

Ok, so from this perspective,is the photon dispering energy? I'd say no, it's not moving at all.... Though i'm nowhere near convinced this demonstartes the dispersion doesn't happen, it merely highlights a context in which it doesn't appear to be dispersive...

Thanks, orathaic, it's been interesting. I definitely need to work out some of these details in GR better to understand more clearly the relationship with SR, though. Actually, I've been meaning to do this for awhile. Hopefully I'll have time in a week or two.

"Ok, so from this perspective,is the photon dispering energy? I'd say no, it's not moving at all.... Though i'm nowhere near convinced this demonstartes the dispersion doesn't happen, it merely highlights a context in which it doesn't appear to be dispersive... "

Well, no, I wouldn't say so. I mean, in the photon's own frame, it's not moving, as you say, and everything else is infinitely short. In the frame of anything else, the photon is moving at the speed of light, but has a well-defined (and fixed) energy.

So actually, maybe I misunderstood. The photon is dispering energy in the sense that it's carrying it off to infinity, and will keep doing so unless it runs into something. So, for example, if you consider any compact set in spacetime, the photon will leave that set in finite "time" (affine parameter, to be technical), so it's dispering energy in that sense.

This is all assuming, to state the obvious, that we're not in some pathalogical spacetime with closed null geodesics or some nonsense.

Thanks a huge amount semck, i don't think i'd understand half of this half aswell without this conversation...

I've enjoyed it, orathaic, thanks. Just take what I say with a grain of salt, what between my tired state and my lack of expertise. :)

'The photon is dispering energy in the sense that it's carrying it off to infinity, and will keep doing so unless it runs into something. So, for example, if you consider any compact set in spacetime, the photon will leave that set in finite "time" (affine parameter, to be technical), so it's dispering energy in that sense'

Well, ok, i admit some of time i was assume the wave nature of light would 'disperse' the energy as the wavefront expands the energy density necessarily decreases... The quantum treatment allowing for a probability wavefront with ever decreasing probability of finding the photon but constant energy density where-ever the photon actually is doesn't really fit with some definition of dispersion and from the photons persepctive in GR it's not moving thus not leaving it's own finite space...

Orathaic, yeah it depends what you mean by dispersion, but say we stick with the particle picture for now. Then in any fixed, compact region of space with initially high energy density, the density is getting lower, because the photon leaves it. This, I assumed, was the kind of dispersion you were initially interested in talking about. I mean, if you're going to follow a photon in its frame, then right enough, energy never disperses, on any timescale, so the question doesn't seem interesting.

Anyway I'm off to bed. It's been fun. : )

(I should mention I'm being informal in this discussion, talking about compact sets, though. I mean some spacelike compact set, but with time going infinitely far forward, that could be well defined in any non-pathalogical spacetime, but which I don't feel like bothering with. It matches intuition well though. Something involving the center of mass of the initial galaxy or what have you).

That's a fair definition of dispersion to stick with, and i don't think there is a valid alternative to the particle interpretation.'

The only thing missing seems to be flux of photons into said compact finite space, possibly keeping constant the energy density. Until we taking changes in space-time geometry into account...

Hmm. This might be a useful place to start thinking about that, but I will have to think about it tomorrow. You, on the other hand, have all evening.

http://en.wikipedia.org/wiki/Electromagnetic_stress%E2%80%93energy_tensor

See then this:

http://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor#Identifying_the_components_of_the_tensor