All pressure is differential pressure. What we call "absolute" is when the reference is zero. So your objection is exactly like pointing out that you can't extract energy from a reservoir at 100C if your sink is also at 100C. True, but it doesn't change the fact that it has energy.
Gravitational collapse
- Thread starter arfa brane
- Start date
Not true at all. Indeed, engineers are careful to refer to gauge (differential) or absolute pressure when discussing pressures.
I'm a mechanical engineer and quite aware of that specificity. But you are missing the point: the point is that you specify the reference to avoid ambiguity if it isn't clear in the context. For "absolute" the reference is zero. It is the same as with temperature, except we created a different unit to label the absolute.
Look at the functioning of a pressure gauge sometime. You will NEVER find one without a reference.
By the way, the wiki on pressure measurement has a big section devoted to this.
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It sounds weird to say pressure is a form of energy when you really mean energy density. The units don't match. And of course it's implicit that there is a volume present when you talk about a tank or the ambient, so I get your meaning, and you are correct in saying it, as long as you clarify that the pressure in a given volume is a form of energy. Or just: pressure is a form of energy density. That's somewhat more obscure since it leaves it a pure property without any matter to hang its hat on. (Or like on the other side of the ideal gas equation, removing n and talking abut RT without any substance for it to apply to.)
No, as per my examples last post, dimensional consistency need have no relation to functionality - they can be chalk and cheese. Which is the case when comparing pressure on it's own, to elastic/hydraulic/pneumatic energy densities. Latter, over at least a limited range, are parametric functions of pressure. There is stress - there is necessarily also strain if energy change occurs!
Agreed - as I said there are various versions and formulations of BE. As listed in the cited Wiki article.
I am not agreeing. I made it clear one must distinguish the use of 'dynamic pressure' = KE density in BE, with static pressure, latter which is what I'm on about. There is this claim that you among others endorse that static - read static - pressure 'is a form of energy'. And it's nonsense.
Energy density, even for a compressed gas, is never given just by or even simply proportional to the pressure - never. And as soon as one looks at the situation with solids or even liquids, the notion energy equates to pressure is ludicrous. Check out any good article on elastic energy density. Like I said, a parametric relationship exists, mediated via material dependent elastic constants that vary enormously. Chalk is not cheese.
Well of course I agree there, but I figured you were going to argue the pressure of the compressed air feeding the motor 'was the energy'. Which it is not. It works together with displacement to constitute pneumatic energy. Fundamental difference. And so basic why are we even arguing this elementary stuff?
Fair enough - it may have been slightly sloppy wording, but I think that in context should be pretty clear.
In the same equation, as separate terms added together, they must be the same. One apple plus one apple does not equal two pears. Bernoulli's equation says:
Kinetic Energy + Static Pressure Energy + Potential Energy = Constant
If dynamic (velocity) pressure is a form of energy then static pressure has to be as well, otherwise you can't add them together in the equation and you can't use it to turn a turbine and extract mechanical work.
Pressure energy is not the only form of energy in a compressed gas, and its use alone is subject to complexities dependent on the precision needed, yes. So what? It still exists! Ie, Bernoulli's equation can be used with or without the assumption that the fluid is incompressible, with a term added for compressibility if desired.
It would seem we're arguing about it because you saw a statement that may not have been perfectly precise and jumped on a hairsplitting tangent, down an unintended rabbit hole, chasing and arguing against a meaning of my initial statement that was never intended. Heck, even arfa brane seems to have recognized it and he appears to be trolling!
I'm not sure though because:
1. The clarification of pressure being energy per unit volume (and not just pressure = energy) was given and you disagreed with it.
2. That clarification was given before you made your initial reply.
3. You claim to disagree with multiple academic sources about the issue.
The point is GR includes energy associated with pressure as a component of the stress energy tensor of the Einstein equations. If pressure wasn't a form of energy then Einstein wouldn't have to include it as a form of energy. Like Walter said the Bernoulli equation sums the energy associated with pressure to kinetic energy and potential energy.
I think the above just demonstrates how you should be careful when using terms that have an exact physical meaning.
Pressure and energy density have the same units (perhaps not coincidentally). Pressure is not a form of energy, the units are different.
Einstein doesn't include it as a form of energy, otherwise there would be a big problem with units not matching up either side of the equation.
Ultimately it doesn't matter what you call it, it does however need to have the correct physical 'meaning' in units.
Setting c to 1 is unphysical (obviously it isn't equal to 1; 1 what?). Likewise any other constant; doing this is an heuristic, you need to recover the proper units so you need to plug the constants back in.
Pressure and energy density have the same units (perhaps not coincidentally). Pressure is not a form of energy, the units are different.
Einstein doesn't include it as a form of energy, otherwise there would be a big problem with units not matching up either side of the equation.
Ultimately it doesn't matter what you call it, it does however need to have the correct physical 'meaning' in units.
Setting c to 1 is unphysical (obviously it isn't equal to 1; 1 what?). Likewise any other constant; doing this is an heuristic, you need to recover the proper units so you need to plug the constants back in.
Too bad that Misner, Thorne , Wheeler (and many other mainstream physicists) didn't get your above memo. They have been doing the "mistake" since, at least, 1973. You should write to them and correct their "error" .
What units you use is irrelevant. Look at the three components of the Bernoulli energy conservation equation expressed dimensionally in SI and Geometricized units. The Geometricized units for pressure and energy density are L^-2. They're summed together as energy per unit volume. Common. The energy associated with pressure is a component of the stress energy momentum tensor. It should be obvious. ?.
http://en.wikipedia.org/wiki/Geometrized_unit_system
As long as you use the same ones either side of an equation?
Do you think it's obvious that, since pressure is included in the stress-energy tensor, then it will contribute to gravitational collapse?
You can label pressure as 'pressure energy' but it's still just pressure = force/area. In fluid flow dynamics pressure just acts the way it does as per BE.
No. You are conflating 'just pressure' with either pneumatic energy (gas-compression-via-piston-motion) or hydraulic head ρgh depending on what fluid you have in mind.
Apart from the pneumatic energy of compression, the only other appreciable form of sensible energy in a static body of inert compressed gas is thermal. Period. Your mysterious extra 'pressure energy' is just not there. If you think otherwise then precisely and quantitatively define this 'pressure energy'.
That energy has been tacked on to 'static' pressure in some author's use of BE is unfortunate and confusing imo. Others avoid such inference altogether, e.g.
http://www.princeton.edu/~asmits/Bicycle_web/Bernoulli.html
What?! Where? This is a red herring. Occasionally both of us may have been loose in terminology but the meaning was always understood. The argument is not and never was over densities vs absolutes, but pressure/stress as 'energy density' ('energy' occasionally used and understood in context) in it's own right.
See above.
You hang onto Bernoulli equation here I notice, and one author's use in particular. Bernoulli equation has engendered some peculiarities such as 'dynamic pressure' which is actually not a pressure, but fits into the conceptual framework of BE, as does 'pressure energy' in one author's mind. I can't help the historic occurrence of those peculiarities. See my response to brucep for further on this matter, that escapes your narrow focus on Bernoulli equation.
You should well remember I clearly made the point elsewhere that ALL energy densities associated with pressure appear in the first diagonal - in the Too term only. Pressure, or more generally the principal stress terms appear as the remaining three diagonal terms Tii. Pressure/stress has the same dimensional units as energy density but is not energy density. Pressure is pressure. Stress is stress.
And did Einstein himself ever specifically declare pressure to be just of itself a form of energy? Can someone furnish a quote to that end?
Let's step away from the peculiarities of the BE nomenclature shall we. Here's a simple test I propose. You and Russ Watters and some others claim static pressure/stress is a form of energy in it's own right. OK then, try this one out.
A unit cube of stiff elastic solid matter, Youngs modulus E, is subject to a uniform uniaxial stress σ, well within the elastic range of said solid. In order to obtain such stress, said cube had to endure an axial strain ε = σ/E, and one obtains the simple and well known formula for elastic stored energy density
W = 1/2σ^2/E -(1)
Notice how σ enters properly here as energy participant, rightfully placed as elastic energy density part of Too term, and not some mysterious 'energy' all by itself.
But evidently I must be wrong. Evidently you, or Russ, or anyone else here, can now readily derive and furnish, in this very simple case, an exact value for the additional 'pressure energy' that exists and that I have neglected. This should be instructive, if not highly amusing.
Markus Hanke
Registered Senior Member
...which in turn is equivalent to energy per unit volume :
http://hyperphysics.phy-astr.gsu.edu/hbase/press.html
Come on now people, this is basic mechanics, and just as valid in a relativistic scenario as it is in a classical one ! The SEM tensor in GR is simply a covariant generalization of the stress tensor from classical mechanics, not more and not less. As such, pressure is the momentum flux across a unit surface element ( see also the Wiki article on the SEM tensor ), since force/area is the same as momentum/area/time due to F=dp/dt. In GR we deal with 4-vectors...so if we combine all components of the 4-momentum flux with all components of the position 4-vector we get a rank-2 tensor. This is just precisely the definition of the SEM tensor. Simple as ! Both pressure and stress are all just flows of energy across surface elements, since momentum is precisely energy; disputing this is like saying that apples are not a fruit.
To which article I already remarked on in #35, #38. The supposition in the last bit there is that an unvarying pressure *somehow* magically sweeps through the entire length d as a piston so as to generate an 'energy' which in actuality is nonexistent. There is never a physical situation where this applies. It's nonsense. Always pressure builds up progressively through a process involving displacement. That is indisputable. Thus the real energy density - that corresponds to actual input - is typically, as per my elastic block example in #54, a parametric or near parametric function of stress/pressure. And in solids such genuine energy density is only the tiniest fraction of the fictitious 'energy density' given in that hyperphysics 'derivation'.
The problem with that definition is rather obvious - there is precisely zero net momentum flux anywhere in a fluid in static equilibrium, yet the pressure can be arbitrarily high. I prefer to use the notion of rate-of-change of momentum density at a boundary - in, then out again, or just force/area which is simpler and doesn't lend itself so easily to notions of fictitious 'energy densities'.
Well I sure dispute that. There is zero net flow of energy across any surface for static fluid! And since when exactly has momentum become energy? In low energy regime we used to know at school that
p = mv
KE = 1/2mv^2 = 1/2p.v
Hmm... they look different somehow. Now if you are saying that no longer holds, excuse my reluctance to participation in reeducation camp please. On the other hand if you just mean energy density and stress and momentum density are all components of the same tensor, well that's a different story. As you know, I dispute the physical justification for some of those components. But regardless, don't try telling me momentum is energy or stress is energy (density). Please. And I'm still waiting for someone to quote AE as saying just that.
Now, Markus, since you have weighed in on this, want to take up my invite in #54 and identify and quantify this 'stress energy density' that apparently must needs be there somewhere, additional to the usual elastic energy density I showed?
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I think Black-Hole is a prediction of GR. Why Einstein should object to Black-Hole creation? Do you have any reference for this?
I think Black-Hole as well as 'expansion of universe' are prediction of GR. We know that our universe is expanding at a speed higher than c. So, Gravitational-Collapse being physically opposite of 'expansion of universe' can also happen at a speed higher than c.
How you are so sure about these?
Isnt spacetime contracting (being opposite of expansion of spacetime as universe expands) in Gravitational-Collapse?
Are you viewing this as SR violation?(I think expansion of universe also can be considered as SR violation).
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Nope. You can stop posting nonsense.