OK I'm reading "About Time" by Paul Davies and, buried in 300+ pages, is a one-liner about how pressure causes gravity. I've never heard this before, but I am extraordinarily intrigued. The concept happens to fit a pet theory of mine, but is it really well established and/or discussed?
Pressure is caused by gravity, temperature, and volume constraints. (In short.) But pressure certainly isn't causing gravity.
Scintillating discussion AN! Please Register or Log in to view the hidden image! Your definitive response only confuses me more, because I don't believe I'm misinterpreting Paul Davies' words: Actually, what your response does is confirm that this concept is not widely discussed, whether factual or not. I'm curious is anyone else has heard of this?
OK this is pretty trippy but when I try Googling "quantum antigravity and pressure" for more info the first link is the page from the book I'm referencing, and the second link is to this thread which was just started! I know that pop-science authors frequently gloss over subjects to make them more palatable for the masses but I just don't see how there's a "truer" interpretation of Davies' suggestion (even in context if you read surrounding material in the book). Are you guys flatly saying that Davies is wrong? And, by extension, the work that Thorne did?
No, I have never heard of it before - but I *have* heard quite a bit about Paul Davies. Anything with his name attached to it should be automatically suspect. He's got a solid scientific background but frequently goes WAY beyond the bounds or reason with some of his hare-brained ideas.
I'm pretty sure that what he is referring is how the potential energy of the Earth under pressure contributes to the stress energy tensor, which in GR, is the source of the gravitational sphere.
Yes, I'm glad I refreshed before hitting "submit" because you wrote what I was about to ask. Does the stress energy momentum tensor include a parameter for pressure? I believe the answer is yes. Does that imply that if pressure is increased then space-time curvature is increased?
The stress-energy tensor (the source of gravity in GR) includes energy density, energy flux, momentum density, and momentum flux. Pressure "causes" gravity only because it involves internal momentum flux in matter. (Similarly I'd imagine temperature also "causes" gravity in the sense that higher temperature means more internal energy, which is a source of gravity.) Actually, most people who have studied GR, and in particular some examples of the interaction of matter with gravity (eg. cosmological models, gravitational collapse of a star), will have seen a contribution, associated with pressure, included in the stress-energy tensor.
In my mind's eye I equate pressure with energy density more readily than internal momentum flux, whereas I see momentum flux to be directly connected to temperature. Is this wrong? Granted, the sample size is limited, but that's not the conclusion most would draw from this thread! Please Register or Log in to view the hidden image! As an application of this newfound knowledge, doesn't this imply that the gravitational pull from a BH at a given distance from its center of mass is actually greater than that from a star of equivalent mass? This does not coincide with what I've read!
Yes. Temperature is basically a measure of average internal kinetic energy and pressure is basically a form of internal momentum flux. Though of course energy and momentum are related (eg. a single particle's energy and momentum are related by E[sup]2[/sup] = p[sup]2[/sup]c[sup]2[/sup] + m[sup]2[/sup]c[sup]4[/sup]), so you could expect pressure to generally increase for higher internal energy and temperature to generally increase for higher momentum flux, but they're not synonymous. No. Though to be clear, by "mass" we mean total energy divided by c[sup]2[/sup], or total relativistic mass if you prefer. It's a well known result that the gravitational field outside a spherically symmetric gravitational source is given by the Schwarzschild solution and is completely determined by the total mass of the source. I don't recall offhand how the details work out, but I'd imagine the resolution is that (partly owing to conservation laws which mean matter can't have just any arbitrary stress-energy tensor), any contribution the pressure would give to the gravitational field is already included in the mass. (That's outside the star. I'm sure the pressure affects the details of the gravitational field within the star itself).
It's not horribly relevant and you're rarely wrong but I still "see" temperature, or kinetic energy, as related to momentum flux because they are directly related (E = p^2/2m); whereas energy density is a function of volume which has an inversely direct relationship with pressure. Ahh, let me rephrase the question and choose my words more carefully: Doesn't this imply that the gravitational pull from a BH at a given distance from its center of mass is actually greater than the gravitational pull of that same body prior to its collapse? (Do we need to qualify this somehow by claiming that all supernova discharge has been reabsorbed?)
Pressure does indeed add to gravity. And negative pressure results in a repulsive gravity. This is the driving energy behind Inflation.
Elaborate. 1) What is causing the pressure? 2) How is it adding to gravity, or are you trying to say that the pressure applies a force with a similar vector to gravity. 3) What is causing the negative pressure, and what evidence exists for it?
That's wrong, RJ. What pryzk was right, pressure is like temperature in that it doesn't cause gravity so much as contributes to it. Search google on pressure contributes to gravity. More pressure means more energy hence more gravity. Conservation of energy means a collapsing body doesn't gain energy.
Actually, I wrote what I did because I tried to make the question compatible with what przyk wrote. But I agree with you that it seems to lead us to an incompatibility with energy conservation which is why I started the OP! And what's the difference between "causes" and "contributes to"? If there is any contributory effect whatsoever then the problem exists. If the stress-energy-momentum-tensor determines space-time curvature and essentially contains parameters for temperature and pressure, how is this contradiction avoided? The "classical" mass of a star is not reduced after gravitational collapse, but the temperature and certainly the pressure are greatly increased. Unless there is some offsetting phenomenon or parameter that keeps the curvature constant I can't see how we can deny that the gravitational pull has now been increased from a fixed distance. My point is that the following two statements contradict themselves:
Fair enough. It's a subtle distinction. If you've got a container of gas at some given temperature and pressure, this comprises some given amount of energy. To increase the temperature and pressure you have to add energy. Then you've got more energy. This will result in more gravity. It isn't the pressure itself that causes more gravity, it's the extra energy that causes that pressure. By looking at it another way. A concentration of energy "conditions" the surrounding space causing light to curve, giving what we call spacetime curvature. The stress-energy-momentum tensor is a matrix that describes this, but it's that concentration of energy that made it happen. When an object gets smaller the profile of the gravitational potential will change. It's like replacing the bowling ball on the rubber sheet with a small sphere of depleted uranium. Please Register or Log in to view the hidden image! The central portion deepens and steepens, but if you're hovering up on the shoulders you don't start finding yourself falling in. More pressure in the same volume means more energy. Halve the volume and double the pressure and there is no more energy. Energy is conserved.
By this logic, then the ONLY difference between the measured space-time curvature at a fixed distance between a star "on the brink" of gravitational collapse and that of one which has just collapsed is the extra energy supplied by the last particle, photon, etc, to join the system. Because I can make the value of this "tipping point" contribution be arbitrarily small its really the equivalent of saying that the effect doesn't exist at all, contradicting what Przyk said was a well-known effect. This is actually what you appear to be saying anyway which I continue to find contradictory if you agree with the premise of the OP. Using this rubber sheet analogy, before this thread was started I would've claimed that the rubber sheet's central portion would be bluntly "rounded off" on the bottom portion coinciding with measuring the gravity field from within the mass in question. As the radius of the mass is reduced the sheet's central portion would indeed deepen. However, making the claim that increased pressure and temperature increases space-time curvature beyond existing classical mass would then steepen the existing slope of the curve as well, wouldn't it? There isn't? If there is no more energy in the system then doesn't that imply that I can compress a sealed system to half of its volume with no energy expenditure?
That is essentially correct on a unrealitic theoretical level. In actuallity the star would collapse and and the shock wave would throw of a tremendous amount of material so the gravity at that fixed point would be much less than before the collapse. If by some miracle no material was ejected by the star upon collapse then your statement would be correct the gravity would be the same (+ the extra photon).
