Quantum Fluctuations questions
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 Ixtellor
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Quantum Fluctuations questions
As a complete neophyte:
1) Why do empty spaces have more energy than spaces filled with matter.
2) Why do particles 'pop' into existence near zero point energy?
3) What are those particles and can they form more complex matter?
Basically... trying to brush up theories of how the universe began.
(I understand that many postulate time doesn't exist so there doesn't have to a 'before the big bang')
Last question:
1) "The cat that jumps is not the cat that lands." The argument that time is an illusion and there are just an endless series of nows.... how does that explain memory? Why can I recall everything before NOW if I am not the same me that exist 1 second ago?
1) Why do empty spaces have more energy than spaces filled with matter.
2) Why do particles 'pop' into existence near zero point energy?
3) What are those particles and can they form more complex matter?
Basically... trying to brush up theories of how the universe began.
(I understand that many postulate time doesn't exist so there doesn't have to a 'before the big bang')
Last question:
1) "The cat that jumps is not the cat that lands." The argument that time is an illusion and there are just an endless series of nows.... how does that explain memory? Why can I recall everything before NOW if I am not the same me that exist 1 second ago?
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 thoughtfully
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Re: Quantum Fluctuations questions
Sean Carroll at Caltech posted recently on his blog on this.
http://www.preposterousuniverse.com/blo ... ctuations/
1) Empty is not special. Virtual particles happen everywhere.
2) The basic idea behind fluctuations is the Uncertainty Principle. You can't have a unit of space with precisely zero energy; there is an intrinsic uncertainty. The "conjugate variable" of energy is time, so they have complementary (im)precisions/(un)certainties.
3) They can be any particle, although more massive particles have greater uncertainty in energy and have a more precisely zero existence in time (they disappear faster). Virtual particles do not stick around long enough to form complex structure.
Your last question is more philosophical. I'll leave it for another time/person.
http://www.preposterousuniverse.com/blo ... ctuations/
1) Empty is not special. Virtual particles happen everywhere.
2) The basic idea behind fluctuations is the Uncertainty Principle. You can't have a unit of space with precisely zero energy; there is an intrinsic uncertainty. The "conjugate variable" of energy is time, so they have complementary (im)precisions/(un)certainties.
3) They can be any particle, although more massive particles have greater uncertainty in energy and have a more precisely zero existence in time (they disappear faster). Virtual particles do not stick around long enough to form complex structure.
Your last question is more philosophical. I'll leave it for another time/person.
Last edited by thoughtfully on Sat Feb 27, 2016 11:38 am UTC, edited 1 time in total.
 Xanthir
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Re: Quantum Fluctuations questions
thoughtfully wrote:2) The basic idea behind fluctuations is the Uncertainty Principle. You can't have a unit of space with precisely zero energy; there is an intrinsic uncertainty. The "conjugate variable" of energy is time, so they have complementary (im)precisions/(un)certainties.
To be slightly more specific  per the Uncertainty Principle, (uncertainty in energy)*(uncertainty in time ) must be greater than hbar. If you say "this field is exactly zero", you've reduced one of those values to 0, so there's no way to satisfy the inequality  0 times any value is less than hbar. Thus, the field must never have *exactly* zero energy  it's got a slightly uncertain amount of energy which *averages* to zero.
The only way for a field to be exactly zero is for it to not exist at all. All fields that exist will produce virtual particles.
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Re: Quantum Fluctuations questions
The only real difference between empty space and occupied space is that if a real particle is present, then any virtual particle will be under the effects of the real particle's field (electromagnetic, etc.). There is nothing preventing virtual particles from existing arbitrarily close to a real particle other than the possibility of them literally overlapping (taking up the same space and energy level at the same timePauli Exclusions prohibits this unless you have neutronstarlevel pressure forcing them together).
First of all virtual particles exist in particleantiparticle pairse.g. an electron and a positron are born together in the same time and place. This ensures that all quantum measurements other than energy are conserved (charge, parity, spin, quark number, etc.). The energy constraint is what keeps them "virtual"they can only exist within the boundaries of Heisenberg Uncertainty unless they can be granted enough energy to become a Real Boy, er, a Real Particle.
A virtual particle's energy also has an inverse relationship to its halflife. More massive/energetic particles thus live for a shorter timespanindeed, virtual Top and Bottom quarks are constrained to decay in less than the minimum amount of time required for the Strong Interaction, which means that they can not form multiquark particles. If a virtual particle within its brief lifetime absorbs enough energy to exceed its restmassenergy, then it can become a Real Particlethis is usually accomplished either by absorbing enough highenergy photons, or by being forcefully ripped from its partner (pulling the pair from their mutual energy well is a sufficiently energetic event, and this is the source of Hawking Radiation in the region immediately outside of the event horizon of a black hole).
First of all virtual particles exist in particleantiparticle pairse.g. an electron and a positron are born together in the same time and place. This ensures that all quantum measurements other than energy are conserved (charge, parity, spin, quark number, etc.). The energy constraint is what keeps them "virtual"they can only exist within the boundaries of Heisenberg Uncertainty unless they can be granted enough energy to become a Real Boy, er, a Real Particle.
A virtual particle's energy also has an inverse relationship to its halflife. More massive/energetic particles thus live for a shorter timespanindeed, virtual Top and Bottom quarks are constrained to decay in less than the minimum amount of time required for the Strong Interaction, which means that they can not form multiquark particles. If a virtual particle within its brief lifetime absorbs enough energy to exceed its restmassenergy, then it can become a Real Particlethis is usually accomplished either by absorbing enough highenergy photons, or by being forcefully ripped from its partner (pulling the pair from their mutual energy well is a sufficiently energetic event, and this is the source of Hawking Radiation in the region immediately outside of the event horizon of a black hole).
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Re: Quantum Fluctuations questions
This may be a weird notion but could the virtual particles be (a part of) dark matter? The density is extremely low but space is extremely big.
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 thoughtfully
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Re: Quantum Fluctuations questions
Neil_Boekend wrote:This may be a weird notion but could the virtual particles be (a part of) dark matter? The density is extremely low but space is extremely big.
Not Dark Matter, but Dark Energy, yes (could be). The predicted energy density and what's observed is off by some hundred orders of magnitude, however.
http://science.nasa.gov/astrophysics/fo ... rkenergy/
http://profmattstrassler.com/articlesa ... arethey/

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Re: Quantum Fluctuations questions
Neil_Boekend wrote:This may be a weird notion but could the virtual particles be (a part of) dark matter? The density is extremely low but space is extremely big.
Right now, theoretically, vacuum doesn't have the energy to account for dark matter, though I've certainly thought about how that might work personally, as it's at least a slightly interesting idea.
To refute thoughtfully's (first) link though, A. the counter argument presented rests on many worlds, which is unlikely and cannot account for the, still highly theoretical but potentially useful, "soft particles" which are among other things proposed as a possible solution to the black hole information paradox. I've found the "truly static" vacuum argument to be presenting ideas because you don't want evidence to be true rather than trying something more useful, EG thinking of a physically useful test to show it is so one way or another. But then that's a lot of theoretical quantum mechanics, ideas with some sketchy math and not of lot of ways to test practically, so it's not like it's a unique problem.
Re: Quantum Fluctuations questions
thoughtfully wrote:2) The basic idea behind fluctuations is the Uncertainty Principle. You can't have a unit of space with precisely zero energy; there is an intrinsic uncertainty. The "conjugate variable" of energy is time, so they have complementary (im)precisions/(un)certainties.
Xanthir wrote:To be slightly more specific  per the Uncertainty Principle, (uncertainty in energy)*(uncertainty in time ) must be greater than hbar. If you say "this field is exactly zero", you've reduced one of those values to 0, so there's no way to satisfy the inequality  0 times any value is less than hbar. Thus, the field must never have *exactly* zero energy  it's got a slightly uncertain amount of energy which *averages* to zero.
But, vacuum bubbles have zero energy. One of the particles has positive energy, and the other one has negative. They exist offshell, so they can individually have any energy at all, but their sum must be exactly zero. It must also have a total of zero in every other quantum number like electron number, color charge, etc.
The Uncertainty Principle is not the cause of the phenomenon, but a characterization of the limits of the effect that causes it.
That effect is:
1) every transformation on the universe that preserves total quantum numbers (energy, momentum, etc) is dynamically available and actually occurs. Before you go 'what', see point 3.
2) These transformations are suppressed to different degrees depending on how closely they hew to individual particles having the right energies for their mass and momentum (closer is better, but not so much that you can't deviate a little).
3) Because this has been happening all along, everything has adapted to it and it hardly matters except in special cases  most of the transformations are feeding into each other in a way that produces no net effect. Like vacuum bubbles  they are created and collapse perfectly continuously and smoothly, so there is no fluctuation in the fluctuation, just a flat, continuous availability of background objects.
ijuin wrote:Pauli Exclusions prohibits this unless you have neutronstarlevel pressure forcing them together).
Neutron stars do not override the Pauli Exclusion principle.
 Ixtellor
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Re: Quantum Fluctuations questions
ijuin wrote:The only real difference between empty space and occupied space is that if a real particle is present, then any virtual particle will be under the effects of the real particle's field (electromagnetic, etc.). There is nothing preventing virtual particles from existing arbitrarily close to a real particle other than the possibility of them literally overlapping (taking up the same space and energy level at the same timePauli Exclusions prohibits this unless you have neutronstarlevel pressure forcing them together).
First of all virtual particles exist in particleantiparticle pairse.g. an electron and a positron are born together in the same time and place. This ensures that all quantum measurements other than energy are conserved (charge, parity, spin, quark number, etc.). The energy constraint is what keeps them "virtual"they can only exist within the boundaries of Heisenberg Uncertainty unless they can be granted enough energy to become a Real Boy, er, a Real Particle.
A virtual particle's energy also has an inverse relationship to its halflife. More massive/energetic particles thus live for a shorter timespanindeed, virtual Top and Bottom quarks are constrained to decay in less than the minimum amount of time required for the Strong Interaction, which means that they can not form multiquark particles. If a virtual particle within its brief lifetime absorbs enough energy to exceed its restmassenergy, then it can become a Real Particlethis is usually accomplished either by absorbing enough highenergy photons, or by being forcefully ripped from its partner (pulling the pair from their mutual energy well is a sufficiently energetic event, and this is the source of Hawking Radiation in the region immediately outside of the event horizon of a black hole).
It took me a long time and reading some books, but I finally understood this answer.
I don't want to start a new thread, but here is my new question:
Can you understand Quantum Mechanics without understanding the math.
I think I understand the above equation, but I have no idea what the symbols mean or how to use them.
Also, I finally get this quote. "If quantum mechanics hasn't profoundly shocked you, you haven't understood it yet." Neil Bohr
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 doogly
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Re: Quantum Fluctuations questions
Ixtellor wrote:Can you understand Quantum Mechanics without understanding the math.
Not really. You can do your best to follow along with explanations that use analogies, but there will always be some gap. In fact, people who can turn the crank on the math but have not achieved fluency in the math will also likewise have a gap in their fluency of the physics.
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 Ixtellor
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Re: Quantum Fluctuations questions
doogly wrote:Ixtellor wrote:Can you understand Quantum Mechanics without understanding the math.
Not really. You can do your best to follow along with explanations that use analogies, but there will always be some gap. In fact, people who can turn the crank on the math but have not achieved fluency in the math will also likewise have a gap in their fluency of the physics.
Thanks for the frank response.
Question:
Using Beyesian probability/statistics how likely is the many worlds theory? Is it more likely than other theories of time or theoretical physics predictions of reality?
My main goal is understand the reality of our universe. Since this isn't possible with modern science, I am trying to understand the various theories and which ones have the most 'evidence' or in lack of evidence, Beyesian probablities of true.
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 doogly
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Re: Quantum Fluctuations questions
Many worlds is not something which can be true or not, because it is an interpretation. You may or may not find it compelling storytelling. But if it makes no distinct predictions from, say, decoherent histories, then it can have no distinct truth value or evidence.
And I don't mean that in a pessimistic way though  you can totally understand the math! It's available.
And I don't mean that in a pessimistic way though  you can totally understand the math! It's available.
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Re: Quantum Fluctuations questions
What is the difference between many worlds and "decoherent histories"? I thought the idea of MWI was that the "branching events" were physically just decoherence. In other words, there is no collapse (no particular history is ever selected), but decoherent histories are noninteracting, so they are effectively separate worlds.
Re: Quantum Fluctuations questions
doogly wrote:↶Ixtellor wrote:Can you understand Quantum Mechanics without understanding the math.
Not really. You can do your best to follow along with explanations that use analogies, but there will always be some gap. In fact, people who can turn the crank on the math but have not achieved fluency in the math will also likewise have a gap in their fluency of the physics.
Pretty much. Even classical quantum mechanics is tough to understand without a decent understanding of concepts like Hilbert spaces, and this gets worse and worse the further you get into more modern physics like quantum field theory. Whenever you hear physicists talking about QM on popular science programmes, you can be sure they've had to tack on copious amounts of bullshit to make up for the mathematics they removed from the explanation. In the end, it's easier to learn the mathematics than it is to try to understand the physics without it.
Regarding "the reality of our universe", I'm going to have to say that's unworkably vague. There are statements you can make about the physicality of things: Hermiticity of operators corresponding to physical observables, unitarity of time evolution, Lorentz invariance, energy conditions, etcetera  but those have almost no relation to the philosophical concept of reality. Ultimately I think the closest you can get is to discuss the space of all possible universes and the size of the subset of universes consistent with observations about our universe within that space, but that's impossible to discuss without focussing on one particular model defining the space of all possible universes. Even things like the finetuning problems in cosmology could just as well vanish in a "better" model than the ones currently used.
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Re: Quantum Fluctuations questions
drachefly wrote:But, vacuum bubbles have zero energy. One of the particles has positive energy, and the other one has negative. They exist offshell, so they can individually have any energy at all, but their sum must be exactly zero. It must also have a total of zero in every other quantum number like electron number, color charge, etc.
"Negative energy" doesn't exist, at least in any sense other than some hypothesis about wormholes and time travel. Rather, at least in current theory, virtual particles have a net of zero energy versus the surrounding vacuum. They pop into existence, then decay back into "non existence", unless you ram into them with a spaceship or something. But they still have a net total energy above zero, no negative signs required.
In fact this would make Hawking radiation ineffective if it was "negative" energy. The simplest explanation, that "virtual" particles appear on the event horizon and one is inside, going down to the singularity and the other getting shot out, thus losing the black hole net energy, does not appear to be correct. But the exact explanation is up for debate anyway, since it seems to involve information transfer out of a singularity somehow. Regardless, its agreed that somehow the net total energy of the black hole goes down because its making these virtual particles, which would otherwise disappear, into real particles by imparting enough energy into them. It does this by imparting enough energy to make both particles "real" but then losing half of them. If one was somehow "negative" energy, and assuming there was no mechanism to decide which particle was lost, then total energy would, on average, be conserved by the black hole (50/50 chance of losing or gaining energy each time) instead of losing energy overall.
doogly wrote:Many worlds is not something which can be true or not, because it is an interpretation. You may or may not find it compelling storytelling. But if it makes no distinct predictions from, say, decoherent histories, then it can have no distinct truth value or evidence.
And I don't mean that in a pessimistic way though  you can totally understand the math! It's available.
Which is always something I'm disappointed in whenever people bring it up. It seems like it wants to make definitive predictions, there's a lot written on it. But then whenever the question is asked of whether it does actually predict some differing result the answer is "well, I mean, no, the maths the same as far as results go..." Well what's the point then!
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Re: Quantum Fluctuations questions
Negative energy is totally a thing, see Casimir effect. But yeah in black holes that is not the thing which is going on.
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Re: Quantum Fluctuations questions
Another potentially relevant point is that there are two alternative pictures of what goes on internally to a Feynman diagram both of which are valid but one of which is vastly more useful. Confusing those two pictures can lead to confusions along these lines.
So, the usual (and more useful) picture is that momentum is conserved at vertices but virtual particles are offshell and don't have the mass they 'should' have and can potentially be massless or even tachyonic.
The other picture holds that virtual particles do have their correct masses but instead violate momentum conservation at vertices subject to the uncertainty principle and must 'pay it back' by the end of the diagram.
In the first picture, the propagator in your scattering amplitude suppresses scattering by how far you are offshell whilst in the second, it suppresses you by how much you don't conserve momentum (and for how long). These both turn out to be the same factor of course because these pictures are equivalent.
This nonlocal paying back looks pretty dodgy which is a big reason for not using that picture but it still seems to beloved of popsci educators everywhere for some reason (probably because it's more obviously "quantum weirdness" than offshell particles are).
So, in the first picture, one particle in the vacuum bubble (for simplicity I'm only considering two particle vacuum bubbles) has negative energy (and a tachyonic mass) whilst the other has a positive energy (and sensible nonnegative, real mass) such that their energies (and their momenta) sum to zero.
In the second picture, both have positive energies and sensible masses and so they've "borrowed" energy from the vacuum and have to pay it back at the end of the bubble.
Both of these pictures are valid but the first is vastly more useful and in it, genuinely negative energies have to be taken as a real thing.
Re: the casimir effect, I'm not sure the usual characterisation of that as negative energy is actually that justified. By my understanding, you've already subtracted off any contribution from the vacuum by declaring it to have 0 energy and, when you move the plates, all that happens is you change the energy of the vacuum so that, with respect to your previous 0, it is at negative energy but that, if we saw the system in isolation now, we'd declare it to be at 0 energy and, if we had a way of predicting finite vacuum energies, we'd consider to be positive (just a smaller one than before we moved the plates). So in my mind, this negative energy isn't really genuine.
So, the usual (and more useful) picture is that momentum is conserved at vertices but virtual particles are offshell and don't have the mass they 'should' have and can potentially be massless or even tachyonic.
The other picture holds that virtual particles do have their correct masses but instead violate momentum conservation at vertices subject to the uncertainty principle and must 'pay it back' by the end of the diagram.
In the first picture, the propagator in your scattering amplitude suppresses scattering by how far you are offshell whilst in the second, it suppresses you by how much you don't conserve momentum (and for how long). These both turn out to be the same factor of course because these pictures are equivalent.
This nonlocal paying back looks pretty dodgy which is a big reason for not using that picture but it still seems to beloved of popsci educators everywhere for some reason (probably because it's more obviously "quantum weirdness" than offshell particles are).
So, in the first picture, one particle in the vacuum bubble (for simplicity I'm only considering two particle vacuum bubbles) has negative energy (and a tachyonic mass) whilst the other has a positive energy (and sensible nonnegative, real mass) such that their energies (and their momenta) sum to zero.
In the second picture, both have positive energies and sensible masses and so they've "borrowed" energy from the vacuum and have to pay it back at the end of the bubble.
Both of these pictures are valid but the first is vastly more useful and in it, genuinely negative energies have to be taken as a real thing.
Re: the casimir effect, I'm not sure the usual characterisation of that as negative energy is actually that justified. By my understanding, you've already subtracted off any contribution from the vacuum by declaring it to have 0 energy and, when you move the plates, all that happens is you change the energy of the vacuum so that, with respect to your previous 0, it is at negative energy but that, if we saw the system in isolation now, we'd declare it to be at 0 energy and, if we had a way of predicting finite vacuum energies, we'd consider to be positive (just a smaller one than before we moved the plates). So in my mind, this negative energy isn't really genuine.
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Re: Quantum Fluctuations questions
But it pulls on the plates.
Also it can be done rigorously by subtracting the Hadamard form from the two point function, rather than by subtracting the vacuum expectation value for the vacuum from the stress tensor. This is super helpful in curved space, where there is no unique vacuum! Curved space is the best.
Also it can be done rigorously by subtracting the Hadamard form from the two point function, rather than by subtracting the vacuum expectation value for the vacuum from the stress tensor. This is super helpful in curved space, where there is no unique vacuum! Curved space is the best.
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Re: Quantum Fluctuations questions
Thanks for partially clearing up my confusions about the casimir effect; I was just about to ask. So it's safe to say that the energy between the plates is less than the energy outside the plates, but it's not safe to say that it's negative. Unless you define the vacuum energy outside the plates to be 0, in which case you now have negative energy, but there's nothing physically significant about the negative sign when your scale was chosen somewhat arbitrarily. Did I get that right?
From largescale observations of the cosmological constant, I've read that we expect a slightly positive amount of vacuum energy, though we're unable to determine the exact amount (and the theory gives slightly different values). Is that the same vacuum energy that pushes on the casimir plates, or am I confusing two similar sounding issues?
And do the theories of wormholes etc. actually require negative energy, or just a place with "less energy than a regular vacuum"^{[1]}? For some reason, it's difficult to find credible information on those, and I wouldn't understand the original papers.
You mentioned negative energies in the context of shortlived vacuum bubbles. I found this page giving other negativeenergy situations. They claim that there are restrictions on magnitude and duration of negative energy, and that it must always be offset by positive energy. If true, then any sufficiently large system must still have a positive amount of total energy  placing upper bounds on the size of wormholes and warp bubbles: 10^{32} meters, close to the planck length. Can either of you tell me if that site is credible?
We know that the formulas of relativity aren't accurate in situations with high energies and small scales, but I couldn't find any information about the boundaries for the accuracy of relativity. Are predictions for smallscale wormholes and warp bubbles even meaningful?
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From largescale observations of the cosmological constant, I've read that we expect a slightly positive amount of vacuum energy, though we're unable to determine the exact amount (and the theory gives slightly different values). Is that the same vacuum energy that pushes on the casimir plates, or am I confusing two similar sounding issues?
And do the theories of wormholes etc. actually require negative energy, or just a place with "less energy than a regular vacuum"^{[1]}? For some reason, it's difficult to find credible information on those, and I wouldn't understand the original papers.
eSOANEM wrote:Both of these pictures are valid but the first is vastly more useful and in it, genuinely negative energies have to be taken as a real thing.
You mentioned negative energies in the context of shortlived vacuum bubbles. I found this page giving other negativeenergy situations. They claim that there are restrictions on magnitude and duration of negative energy, and that it must always be offset by positive energy. If true, then any sufficiently large system must still have a positive amount of total energy  placing upper bounds on the size of wormholes and warp bubbles: 10^{32} meters, close to the planck length. Can either of you tell me if that site is credible?
We know that the formulas of relativity aren't accurate in situations with high energies and small scales, but I couldn't find any information about the boundaries for the accuracy of relativity. Are predictions for smallscale wormholes and warp bubbles even meaningful?
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Re: Quantum Fluctuations questions
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Re: Quantum Fluctuations questions
In the Casimir system it's not important whether the energy is negative or just less than the outside. You can define a new zero anywhere you like, because in almost all of physics, it is only differences in energy that matters.
But it makes very good sense to do subtraction based on the Hadamard form, or, equivalently for the Casimir system, to use the farfromplates state as the notion of "vacuum" which you use to renormalize. This is a really reasonable thing and it is unambiguous. Hadamard is a hero.
Now, the one place in physics where the absolute value of energy is physically meaningful is general relativity. And wormholes and time machines are general relativistic effects, so when we say they require negative energy (or, even more extravagantly, *net* negative energy, or int T_ab t^a t^b dl < 0, t a tangent to a null curve), we mean "real" negative. And this requires us to settle on our notion of negative, positive and zero for stress tensors unambiguously. And so then we *really* need to be doing Hadamard renormalization.
Regarding the cosmological constant, this could be worked with as if it were a an expectation value of the stress tensor, like a <T^a_a>, but nothing really behaves that way and it's sort of awkward. I think really the smoothest way to think of the CC is to modify the left hand side rather than the right hand side of Einstein's equation. So instead of thinking of some weird source that behaves in this weird way, the curvature tensor you construct has, instead of Rg_ab, (RL)g_ab. (I think there's a factor of 1/2 and a sign error in that, but I am not looking them up right now.) Now it's not so weird! Pretty convincing, eh?
Oh and the Ford and Roman site is totally legit (if not as fresh as it was.) But yes, you do have to pay back, and it looks like even with curved space backreaction you can't get these netnegative energy states. That area of work was my PhD.
But it makes very good sense to do subtraction based on the Hadamard form, or, equivalently for the Casimir system, to use the farfromplates state as the notion of "vacuum" which you use to renormalize. This is a really reasonable thing and it is unambiguous. Hadamard is a hero.
Now, the one place in physics where the absolute value of energy is physically meaningful is general relativity. And wormholes and time machines are general relativistic effects, so when we say they require negative energy (or, even more extravagantly, *net* negative energy, or int T_ab t^a t^b dl < 0, t a tangent to a null curve), we mean "real" negative. And this requires us to settle on our notion of negative, positive and zero for stress tensors unambiguously. And so then we *really* need to be doing Hadamard renormalization.
Regarding the cosmological constant, this could be worked with as if it were a an expectation value of the stress tensor, like a <T^a_a>, but nothing really behaves that way and it's sort of awkward. I think really the smoothest way to think of the CC is to modify the left hand side rather than the right hand side of Einstein's equation. So instead of thinking of some weird source that behaves in this weird way, the curvature tensor you construct has, instead of Rg_ab, (RL)g_ab. (I think there's a factor of 1/2 and a sign error in that, but I am not looking them up right now.) Now it's not so weird! Pretty convincing, eh?
Oh and the Ford and Roman site is totally legit (if not as fresh as it was.) But yes, you do have to pay back, and it looks like even with curved space backreaction you can't get these netnegative energy states. That area of work was my PhD.
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Re: Quantum Fluctuations questions
doogly wrote:↶
Also it can be done rigorously by subtracting the Hadamard form from the two point function, rather than by subtracting the vacuum expectation value for the vacuum from the stress tensor. This is super helpful in curved space, where there is no unique vacuum! Curved space is the best.
Ah fair enough, I'm not familiar with the Hadamard form (because of weirdness with how I've done my degree the last year and a bit I'm about halfway through my qftwecandowithoutrenormalisation course (which I sort of did once already kinda) so some of the finer points haven't really been elaborated on too much).
From the content of this course, we only covered the Casimir effect as an example of vacuum subtraction and why it's not always best to take it too literally but if there's more theoretical justification then that is good to know and I will try to look into that more.
my pronouns are they
Magnanimous wrote:(fuck the macrons)
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