Vacuum energy

[Alan Grayson]

Does the Casimir effect establish that the vacuum has intrinsic energy, and if so, what is its form? TIA, AG

[Alan Grayson]

On Saturday, April 18, 2020 at 9:40:45 PM UTC-6, Alan Grayson wrote:

Does the Casimir effect establish that the vacuum has intrinsic energy, and if so, what is its form? TIA, AG

A related question is this: if the vacuum energy is, in part, from the EM field, and forgetting about the wrong prediction from theory, what is the energy form if theory gives 1/2 photon for each frequency? AG 

[Lawrence Crowell]

The only thing that is measured is a difference in energy, and the modes between two parallel plates are different from those outside. So the difference in energy results in this slight pressure.

LC

[Alan Grayson]

On Sunday, April 19, 2020 at 9:11:46 AM UTC-6, Lawrence Crowell wrote:

The only thing that is measured is a difference in energy, and the modes between two parallel plates are different from those outside. So the difference in energy results in this slight pressure.

LC

From Wiki, below. Apparently there's an interpretation of the Casimir effect which doesn't depend on vacuum energy, which, as I recall, is Bruce's position on this issue. If no vacuum energy, then the claim that photons and other elementary particles arose from the vacuum in the very early universe is on dubious grounds. AG

 

Relativistic van der Waals force[edit]

Alternatively, a 2005 paper by Robert Jaffe of MIT states that "Casimir effects can be formulated and Casimir forces can be computed without reference to zero-point energies. They are relativistic, quantum forces between charges and currents. The Casimir force (per unit area) between parallel plates vanishes as alpha, the fine structure constant, goes to zero, and the standard result, which appears to be independent of alpha, corresponds to the alpha approaching infinity limit," and that "The Casimir force is simply the (relativistic, retarded) van der Waals force between the metal plates."^[17] Casimir and Polder's original paper used this method to derive the Casimir-Polder force. In 1978, Schwinger, DeRadd, and Milton published a similar derivation for the Casimir Effect between two parallel plates.^[18] In fact, the description in terms of van der Waals forces is the only correct description from the fundamental microscopic perspective,^[19][20] while other descriptions of Casimir force are merely effective macroscopic descriptions.

[Lawrence Crowell]

Sure the Casimir effect involves QED. The virtual photons are in a sense a set of gauge redundancies that can be removed, though one need the moduli from these redundancies. This still defines a form of quantum topological number. 

LC

[Alan Grayson]

On Sunday, April 19, 2020 at 2:37:28 PM UTC-6, Lawrence Crowell wrote:

Sure the Casimir effect involves QED. The virtual photons are in a sense a set of gauge redundancies that can be removed, though one need the moduli from these redundancies. This still defines a form of quantum topological number. 

LC

You refer to QED, but aren't wan der Waal forces non quantum? AG 

[Lawrence Crowell]

On Sunday, April 19, 2020 at 4:50:52 PM UTC-5, Alan Grayson wrote:

On Sunday, April 19, 2020 at 2:37:28 PM UTC-6, Lawrence Crowell wrote:

Sure the Casimir effect involves QED. The virtual photons are in a sense a set of gauge redundancies that can be removed, though one need the moduli from these redundancies. This still defines a form of quantum topological number. 

LC

You refer to QED, but aren't wan der Waal forces non quantum? AG 

Van der Waal force is just a dipole-dipole interaction, such as what happens with water on the fluid surface. This can well enough be quantized.

LC

[Alan Grayson]

On Sunday, April 19, 2020 at 7:23:00 PM UTC-6, Lawrence Crowell wrote:

On Sunday, April 19, 2020 at 4:50:52 PM UTC-5, Alan Grayson wrote:

On Sunday, April 19, 2020 at 2:37:28 PM UTC-6, Lawrence Crowell wrote:

Sure the Casimir effect involves QED. The virtual photons are in a sense a set of gauge redundancies that can be removed, though one need the moduli from these redundancies. This still defines a form of quantum topological number. 

LC

You refer to QED, but aren't wan der Waal forces non quantum? AG 

Van der Waal force is just a dipole-dipole interaction, such as what happens with water on the fluid surface. This can well enough be quantized.

LC

But if you can explain Van der Waal forces without QED, why would you invoke it? I mean, if it's not necessary, and there's no need to invoke it, doesn't that put the EM vacuum energy on a dubious basis?  AG

[Lawrence Crowell]

On Monday, April 20, 2020 at 2:30:53 AM UTC-5, Alan Grayson wrote:

On Sunday, April 19, 2020 at 7:23:00 PM UTC-6, Lawrence Crowell wrote:

On Sunday, April 19, 2020 at 4:50:52 PM UTC-5, Alan Grayson wrote:

On Sunday, April 19, 2020 at 2:37:28 PM UTC-6, Lawrence Crowell wrote:

Sure the Casimir effect involves QED. The virtual photons are in a sense a set of gauge redundancies that can be removed, though one need the moduli from these redundancies. This still defines a form of quantum topological number. 

LC

You refer to QED, but aren't wan der Waal forces non quantum? AG 

Van der Waal force is just a dipole-dipole interaction, such as what happens with water on the fluid surface. This can well enough be quantized.

LC

But if you can explain Van der Waal forces without QED, why would you invoke it? I mean, if it's not necessary, and there's no need to invoke it, doesn't that put the EM vacuum energy on a dubious basis?  AG

You are missing the big picture. The pointing to Van der Waal forces is just a way of saying this is a boundary effect. However, the VdW force is quantized to look at molecules on liquid and material surfaces. The dipole for is 1/r^3 in it property, and the dipole-dipole interaction is then 1/r^6 and is then fairly weak.

The issue is with a bundle construction

H^1(A) → H^1(A/G) ─d→ H^2(A)

which is a short exact sequence on the space of connections A. This is a form of deRham cohomology. The first map is from the connections to its moduli or moduli space. This is then mapped by the differential operator to the second cohomology ring over the fields, which in QED would be the electric and magnetic fields. The A/G means connections modulo diffeomorphisms or gauge changes. 

Now this middle cohomology ring has another map as H^0(ψ) ─d→ H^1(ψ), with the ψ a state, really I should have a state space, that connects to the gauge potential as ψ → ψe^{-i∮A∙dx} under a gauge induced phase change, such as the Aharanov-Bohm effect. The map in effect removes this phase term, just as in the diagram above we have modulo-diffeomorphisms. This is a map from a Hilbert space ℋ to a projective Hilbert space ℋ → Pℋ. which defines the Fubini-Study metric.

This can be taken to more general geometries, which in a short post such as this I do not have time to go into. These involve entanglements, and entanglements are invariant under gauge transformations or unitary transformations of states.

We can remove the whole business of virtual particles, and really Feynman diagrams in general. These are nice cartoons that have helped up think about things, but in many ways, they are just representations of redundancies that are not that necessary. The BCFW method comes close to removing some of these redundancies. We can see a part of this with Feynman diagrams, for a virtual loop is an entangled pair of particles that just happen to “exist” off-shell. We can remove the idea of virtual particles and replace this with the topology and geometry of entanglement. This is a part of why I think entanglement and gauge symmetries exist in a dualism or complementarity. 

Now let us get back to more brass-tacks physics. If you have two parallel plates and the Casimir force pushes them together, the force in a displacement FΔx = ΔW, or work. The elementary work-energy theorem of mechanics tells us that work is kinetic energy. This then clearly means there is a difference in potential energy between the plates relative to outside. So we can call this what we want, but clearly there is an energy associated with empty space or the vacuum.

LC

[Alan Grayson]

On Monday, April 20, 2020 at 5:00:50 AM UTC-6, Lawrence Crowell wrote:

On Monday, April 20, 2020 at 2:30:53 AM UTC-5, Alan Grayson wrote:

On Sunday, April 19, 2020 at 7:23:00 PM UTC-6, Lawrence Crowell wrote:

On Sunday, April 19, 2020 at 4:50:52 PM UTC-5, Alan Grayson wrote:

On Sunday, April 19, 2020 at 2:37:28 PM UTC-6, Lawrence Crowell wrote:

Sure the Casimir effect involves QED. The virtual photons are in a sense a set of gauge redundancies that can be removed, though one need the moduli from these redundancies. This still defines a form of quantum topological number. 

LC

You refer to QED, but aren't wan der Waal forces non quantum? AG 

Van der Waal force is just a dipole-dipole interaction, such as what happens with water on the fluid surface. This can well enough be quantized.

LC

But if you can explain Van der Waal forces without QED, why would you invoke it? I mean, if it's not necessary, and there's no need to invoke it, doesn't that put the EM vacuum energy on a dubious basis?  AG

You are missing the big picture. The pointing to Van der Waal forces is just a way of saying this is a boundary effect. However, the VdW force is quantized to look at molecules on liquid and material surfaces. The dipole for is 1/r^3 in it property, and the dipole-dipole interaction is then 1/r^6 and is then fairly weak.

The issue is with a bundle construction

H^1(A) → H^1(A/G) ─d→ H^2(A)

which is a short exact sequence on the space of connections A. This is a form of deRham cohomology. The first map is from the connections to its moduli or moduli space. This is then mapped by the differential operator to the second cohomology ring over the fields, which in QED would be the electric and magnetic fields. The A/G means connections modulo diffeomorphisms or gauge changes. 

Now this middle cohomology ring has another map as H^0(ψ) ─d→ H^1(ψ), with the ψ a state, really I should have a state space, that connects to the gauge potential as ψ → ψe^{-i∮A∙dx} under a gauge induced phase change, such as the Aharanov-Bohm effect. The map in effect removes this phase term, just as in the diagram above we have modulo-diffeomorphisms. This is a map from a Hilbert space ℋ to a projective Hilbert space ℋ → Pℋ. which defines the Fubini-Study metric.

This can be taken to more general geometries, which in a short post such as this I do not have time to go into. These involve entanglements, and entanglements are invariant under gauge transformations or unitary transformations of states.

We can remove the whole business of virtual particles, and really Feynman diagrams in general. These are nice cartoons that have helped up think about things, but in many ways, they are just representations of redundancies that are not that necessary. The BCFW method comes close to removing some of these redundancies. We can see a part of this with Feynman diagrams, for a virtual loop is an entangled pair of particles that just happen to “exist” off-shell. We can remove the idea of virtual particles and replace this with the topology and geometry of entanglement. This is a part of why I think entanglement and gauge symmetries exist in a dualism or complementarity. 

Now let us get back to more brass-tacks physics. If you have two parallel plates and the Casimir force pushes them together, the force in a displacement FΔx = ΔW, or work. The elementary work-energy theorem of mechanics tells us that work is kinetic energy. This then clearly means there is a difference in potential energy between the plates relative to outside. So we can call this what we want, but clearly there is an energy ,associated with empty space or the vacuum.

LC 

 

Bruce; since you still follow this message board, I'd really like to have your comment about the above, and specifically, whether IYO, the Casimir effect establishes the existence of vacuum energy. TIA, AG 

[Alan Grayson]

On Monday, April 20, 2020 at 5:00:50 AM UTC-6, Lawrence Crowell wrote:

On Monday, April 20, 2020 at 2:30:53 AM UTC-5, Alan Grayson wrote:

On Sunday, April 19, 2020 at 7:23:00 PM UTC-6, Lawrence Crowell wrote:

On Sunday, April 19, 2020 at 4:50:52 PM UTC-5, Alan Grayson wrote:

On Sunday, April 19, 2020 at 2:37:28 PM UTC-6, Lawrence Crowell wrote:

Sure the Casimir effect involves QED. The virtual photons are in a sense a set of gauge redundancies that can be removed, though one need the moduli from these redundancies. This still defines a form of quantum topological number. 

LC

You refer to QED, but aren't wan der Waal forces non quantum? AG 

Van der Waal force is just a dipole-dipole interaction, such as what happens with water on the fluid surface. This can well enough be quantized.

LC

But if you can explain Van der Waal forces without QED, why would you invoke it? I mean, if it's not necessary, and there's no need to invoke it, doesn't that put the EM vacuum energy on a dubious basis?  AG

You are missing the big picture. The pointing to Van der Waal forces is just a way of saying this is a boundary effect. However, the VdW force is quantized to look at molecules on liquid and material surfaces. The dipole for is 1/r^3 in it property, and the dipole-dipole interaction is then 1/r^6 and is then fairly weak.

The issue is with a bundle construction

H^1(A) → H^1(A/G) ─d→ H^2(A)

which is a short exact sequence on the space of connections A. This is a form of deRham cohomology. The first map is from the connections to its moduli or moduli space. This is then mapped by the differential operator to the second cohomology ring over the fields, which in QED would be the electric and magnetic fields. The A/G means connections modulo diffeomorphisms or gauge changes. 

Now this middle cohomology ring has another map as H^0(ψ) ─d→ H^1(ψ), with the ψ a state, really I should have a state space, that connects to the gauge potential as ψ → ψe^{-i∮A∙dx} under a gauge induced phase change, such as the Aharanov-Bohm effect. The map in effect removes this phase term, just as in the diagram above we have modulo-diffeomorphisms. This is a map from a Hilbert space ℋ to a projective Hilbert space ℋ → Pℋ. which defines the Fubini-Study metric.

This can be taken to more general geometries, which in a short post such as this I do not have time to go into. These involve entanglements, and entanglements are invariant under gauge transformations or unitary transformations of states.

We can remove the whole business of virtual particles, and really Feynman diagrams in general. These are nice cartoons that have helped up think about things, but in many ways, they are just representations of redundancies that are not that necessary. The BCFW method comes close to removing some of these redundancies. We can see a part of this with Feynman diagrams, for a virtual loop is an entangled pair of particles that just happen to “exist” off-shell. We can remove the idea of virtual particles and replace this with the topology and geometry of entanglement. This is a part of why I think entanglement and gauge symmetries exist in a dualism or complementarity. 

Now let us get back to more brass-tacks physics. If you have two parallel plates and the Casimir force pushes them together, the force in a displacement FΔx = ΔW, or work. The elementary work-energy theorem of mechanics tells us that work is kinetic energy. This then clearly means there is a difference in potential energy between the plates relative to outside. So we can call this what we want, but clearly there is an energy associated with empty space or the vacuu

LC

As I understand it, the vacuum energy is a residue of various fields we're familiar with, such as the EM field. But how can the EM field contribute anything to the vacuum energy in a region of empty space far away from charged particles? Same for the nuclear and weak forces which are effective over very short distances. AG

[John Clark]

On Tue, Apr 21, 2020 at 4:42 AM Alan Grayson <agrays...@gmail.com> wrote:

> how can the EM field contribute anything to the vacuum energy in a region of empty space far away from charged particles? 

Because Quantum Mechanics tells us that some things can happen for no reason, and because it tells us that the law of conservation of energy can be violated, if only for a very short amount of time. So 2 particles with opposite charges can briefly pop into existence, and so can electromagnetic waves. And we know what Quantum Mechanics is telling us is true because it has been experimentally verified to very high precision.

John K Clark

[Lawrence Crowell]

On Tuesday, April 21, 2020 at 3:42:16 AM UTC-5, Alan Grayson wrote:

On Monday, April 20, 2020 at 5:00:50 AM UTC-6, Lawrence Crowell wrote:

On Monday, April 20, 2020 at 2:30:53 AM UTC-5, Alan Grayson wrote:

On Sunday, April 19, 2020 at 7:23:00 PM UTC-6, Lawrence Crowell wrote:

On Sunday, April 19, 2020 at 4:50:52 PM UTC-5, Alan Grayson wrote:

On Sunday, April 19, 2020 at 2:37:28 PM UTC-6, Lawrence Crowell wrote:

Sure the Casimir effect involves QED. The virtual photons are in a sense a set of gauge redundancies that can be removed, though one need the moduli from these redundancies. This still defines a form of quantum topological number. 

LC

You refer to QED, but aren't wan der Waal forces non quantum? AG 

Van der Waal force is just a dipole-dipole interaction, such as what happens with water on the fluid surface. This can well enough be quantized.

LC

But if you can explain Van der Waal forces without QED, why would you invoke it? I mean, if it's not necessary, and there's no need to invoke it, doesn't that put the EM vacuum energy on a dubious basis?  AG

You are missing the big picture. The pointing to Van der Waal forces is just a way of saying this is a boundary effect. However, the VdW force is quantized to look at molecules on liquid and material surfaces. The dipole for is 1/r^3 in it property, and the dipole-dipole interaction is then 1/r^6 and is then fairly weak.

The issue is with a bundle construction

H^1(A) → H^1(A/G) ─d→ H^2(A)

which is a short exact sequence on the space of connections A. This is a form of deRham cohomology. The first map is from the connections to its moduli or moduli space. This is then mapped by the differential operator to the second cohomology ring over the fields, which in QED would be the electric and magnetic fields. The A/G means connections modulo diffeomorphisms or gauge changes. 

Now this middle cohomology ring has another map as H^0(ψ) ─d→ H^1(ψ), with the ψ a state, really I should have a state space, that connects to the gauge potential as ψ → ψe^{-i∮A∙dx} under a gauge induced phase change, such as the Aharanov-Bohm effect. The map in effect removes this phase term, just as in the diagram above we have modulo-diffeomorphisms. This is a map from a Hilbert space ℋ to a projective Hilbert space ℋ → Pℋ. which defines the Fubini-Study metric.

This can be taken to more general geometries, which in a short post such as this I do not have time to go into. These involve entanglements, and entanglements are invariant under gauge transformations or unitary transformations of states.

We can remove the whole business of virtual particles, and really Feynman diagrams in general. These are nice cartoons that have helped up think about things, but in many ways, they are just representations of redundancies that are not that necessary. The BCFW method comes close to removing some of these redundancies. We can see a part of this with Feynman diagrams, for a virtual loop is an entangled pair of particles that just happen to “exist” off-shell. We can remove the idea of virtual particles and replace this with the topology and geometry of entanglement. This is a part of why I think entanglement and gauge symmetries exist in a dualism or complementarity. 

Now let us get back to more brass-tacks physics. If you have two parallel plates and the Casimir force pushes them together, the force in a displacement FΔx = ΔW, or work. The elementary work-energy theorem of mechanics tells us that work is kinetic energy. This then clearly means there is a difference in potential energy between the plates relative to outside. So we can call this what we want, but clearly there is an energy associated with empty space or the vacuu

LC

As I understand it, the vacuum energy is a residue of various fields we're familiar with, such as the EM field. But how can the EM field contribute anything to the vacuum energy in a region of empty space far away from charged particles? Same for the nuclear and weak forces which are effective over very short distances. AG'

There is energy in the vacuum for the same reason an EM wave far removed from charges have energy. 

A harmonic oscillator that is not vibrating classically will by the Heisenberg uncertainty principle have an uncertainty in position, think of a mass on a spring or a pendulum, which means by the potential V = ½kx^2 where with the Heisenberg uncertainty principle ΔxΔp ≥ ħ/2 there is an energy of uncertainty V(Δx) = ΔV = ½k(Δx)^2. There is a kinetic energy part K = p^2/2 and we have a spread in that as well with momentum uncertainty. This gives a complete energy uncertainty ΔE. 

Now suppose you have to such oscillators with different spring coefficients k, or pendula with different lengths. We then couple these together with some means, say another spring, a single mass connected to two springs or as a pendulum suspected under another. There will then be some complicated motion. This interaction of two harmonic oscillator this way is analogous to the existence of different Fourier modes of the vacuum inside and outside the Casimir plates.

LC

[Alan Grayson]

The latest research by planetary scientists shows that planets formed due to, at first, electrostatic forces of attraction, not gravity. (Gravity became dominant only when bodies became fairly large.)  Could it be the case that Casimir plates attract each other due to electrostatic forces and not vacuum energy? Maybe this is what Bruce had in mind when he, IIRC, rejected the apparently usual interpretation for the existence of vacuum energy. But he doesn't seem interested in offering his opinion. Moreover, and less important, is the fact that when assuming a vacuum, a true vacuum, we are denying the existence of far away charges (which is my response to your first paragraph above). TIA, AG 

[John Clark]

On Wed, Apr 22, 2020 at 1:39 AM Alan Grayson <agrays...@gmail.com> wrote:

> Could it be the case that Casimir plates attract each other due to electrostatic forces and not vacuum energy? 

Of course not! Don't you thing getting rid of electrostatic forces would be the very first thing any even halfway competent experimental scientists would think of before he even dreamed of performing such a super delicate experiment?

 John K Clark 

[Alan Grayson]

Experiments done on the space shuttle and in Germany (where free fall is simulated) have shown that dust particles accumulate due to electrostatic forces, thus changing the model for how planets formed. And if you read the excerpt from the Wiki article I posted, MIT physicists, in 1997 IIRC, were able to explain the Casimir effect without appealing to vacuum energy. AG

[Alan Grayson]

It was in 2005. If the Casimir effect can be explained without appeal to vacuum energy, wouldn't it be a violation of Occam's Razor to invoke its existence as the cause? AG 

[Lawrence Crowell]

If the two Casimir plates are grounded there will be no electrostatic potential between them.  Elementary electricity.

LC

[Alan Grayson]

I'm not sure how the MIT physicist did the experiment. I just know the claim; that he accounted for the forces on the plates without need of appealing to vacuum energy. I'll see if I can find the paper and post it. AG 

[Alan Grayson]

Try this, by another physicist:    

Proof that Casimir force does not originate from vacuum energy    https://arxiv.org/abs/1605.04143  AG

[Alan Grayson]

Here's his bio; a heavy dude!    https://www.fetzer-franklin-fund.org/media/hrvoje-nikolic/   AG

[Lawrence Crowell]

There has to be something wrong. For one he says the EM Hamiltonian commutes with the matter Hamiltonian, and so there is no interaction between the EM field and matter. This would be the case if the matter possesses no charges. There can be two Hamiltonians that commute with each other, and it is the case the two sectors are independent. However, there is the interaction H_i = ∫d^4x j*A that the two operators separately do not have involution with. This is where the interaction happens. So I have suspicions about this claim.

LC 

[Alan Grayson]

Then try this:   The Casimir Effect and the Quantum Vacuum   https://arxiv.org/abs/hep-th/0503158  AG

[Alan Grayson]

The above is authored by Robert L. Jaffe, another heavy dude!  https://web.mit.edu/physics/people/faculty/jaffe_robert.html   AG

[Lawrence Crowell]

Jaffe is more in line. He is just demonstrating how one gets the Casimir effect even if one removes the vacuum with procedures such as normal ordering.

LC 

[Alan Grayson]

Which suggests the vacuum energy has nothing to do with the Casimir effect (if you get the same result by removing the vacuum!) AG

[Lawrence Crowell]

There is this procedure called normal ordering where raising operators a^† are pushed to the left and lowering a operators are pushed to the right. This by hand removes the [a,a^†] commutator responsible for the zero point energy. The harmonic oscillator Hamiltonian is H = ½(a^†a + aa^†} and to add and substract ½a^†a gives H = a^†a +½ [a,a^†]. Normal ordering removes that commutator term, which eliminates the zero point energy. This is alright because the ZPE does not interact with anything in this free field theory.

The thing is this commutator by itself does not produce the Casimir effect anyway. It is the term H_i = ℘∙A or in a relativistic setting ∫d^4x j∙A where we can start to see this physics. With the first term the ℘ is the dipole moment of an atom ℘ = p(σ_+ + σ_-), which in this reduce theory is two states toggled by the σ operators, and A = A_0(a^†e^{kx} - ae^{-kx}), Thus if there is a vacuum state, no photons, the interaction Hamiltonian has the operator terms from σ_-a^†e^{kx}, the rotating term, and σ_+a^†e^{kx} the counter rotating term apply. It is from here that we can get the interaction of the zero point modes with matter states. This does not though directly give Casimir effect. We have to go to a higher order quadupole interaction term A∙Q∙A. This will  appear as aQa^†, for the quadrupole moment operator Q ~ σ_+σ_-. With a vacuum the raising operator a^† makes |0> for photons into |1> an upper atomic state is lowered, but then raised again and the lowering photon operator a recovers the |0> state again. 

This term can be thought of as the virtual generation of a photon that winks in and out of existence with the atomic state lowering and raising back up. There are also counter rotating terms as well. The evaluation of this term <0| aQa^† |0> is not zero. In a perturbation series there can be a product of  j∙A terms which give rise to much the same physics. From a Feynman diagram perspective a single vertex, an electron transition with a photon, is built up to make the interaction of two electrons with a photon, and from there higher order terms are built up. 

LC

[John Clark]

On Wed, Apr 22, 2020 at 12:19 PM Lawrence Crowell <goldenfield...@gmail.com> wrote:

> If the two Casimir plates are grounded there will be no electrostatic potential between them.  Elementary electricity.

Yes, and even if the plates were electrically charged they'd have the same charge, so they'd repel each other, but the Casimir effect attracts so if anything electrostatics would tend to cause an experimenter to underestimate the strength of the casimir effect not produce it.

John K Clark

[Alan Grayson]

I assume the charged particles in the plates somehow excite the quantized EM field, to produce real photons, which produce the forces on the plates. Where, in the math above, is this interaction taken into account? AG 

[Alan Grayson]

More specifically, in your model, is the excitation of the quantized EM field dependent on the use of virtual particles? AG  

 

[Alan Grayson]

How does QM tell us that conservation of energy can be violated for brief durations? If you apply the time-energy form of the UP for your proof, please state the context of your proof, that is, exactly what do E and t stand for in your proof. TIA, AG 

[Alan Grayson]

Also, IMO, QM doesn't tell us that events are uncaused. All it tells us is the probability of some event being measured. Big difference! HOWEVER, you might want to argue that if a cause of a quantum event can be identified, it implies a local hidden variable, which has been shown not to exist. Is this what you claim to be able to show? AG 

[John Clark]

On Sat, Apr 25, 2020 at 12:49 PM Alan Grayson <agrays...@gmail.com> wrote:

> How does QM tell us that conservation of energy can be violated for brief durations? If you apply the time-energy form of the UP for your proof, please state the context of your proof, that is, exactly what do E and t stand for.

The shorter the time (t) a system is under observation the larger the amount of energy (E) could pop into existence from nothing without direct detection, enough energy to create virtual particles. And you can calculate how large the indirect effects these virtual particles would have on the system.

> in your proof.

This is physics not mathematic so there is no proof. However if you take the above as a working assumption and you use it to calculate the magnetic moment of an electron you get a value of 0.001,159,652,181. When you make no assumptions or theoretical calculations at all and just determine the value experimentally you get a value of 0.001,159,652,182. And you just don't get agreement between theory and experiment that is much better than that in science. So I'd say it's a pretty damn good assumption!

John K Clark

[Alan Grayson]

On Sunday, April 26, 2020 at 9:48:45 AM UTC-6, John Clark wrote:

On Sat, Apr 25, 2020 at 12:49 PM Alan Grayson <agrays...@gmail.com> wrote:

> How does QM tell us that conservation of energy can be violated for brief durations? If you apply the time-energy form of the UP for your proof, please state the context of your proof, that is, exactly what do E and t stand for.

The shorter the time (t) a system is under observation the larger the amount of energy (E) could pop into existence from nothing without direct detection, enough energy to create virtual particles. And you can calculate how large the indirect effects these virtual particles would have on the system.

As I understand the UP, it's a statistical statement about an ensemble of observations, say for position and momentum of identical particles. It says nothing about the result of events, say for the position and momentum of a single particle or event. Doing some arithmetic to get the time-energy form of the UP does not change this reality. As a result, your description of what happens to a single particle, virtual or not, is not intelligible. Please try again. AG 

> in your proof.

This is physics not mathematic so there is no proof.

The UP follows from the postulates of QM. So if one assume these postulates, there is indeed a proof of the UP.  AG

[John Clark]

On Sun, Apr 26, 2020 at 12:24 PM Alan Grayson <agrays...@gmail.com> wrote:

> As I understand the UP, it's a statistical statement 

No. It says the more exactly you specify the position of a particle the less exactly you can specify the velocity of the particle; or stated in a alternativ form, the shorter the time duration the more energy a particle (or even empty space) can have without detecting any violation of the law of conservation of energy.

> The UP follows from the postulates of QM. So if one assume these postulates, there is indeed a proof of the UP.

I repeat, this is physics not mathematics, if an experiment violates somebody's postulates then that's just too bad for the postulates because experiment and observation is the ultimate authority in science. And, given that it can make predictions to 12 significant digits, experiment and observation tells us that virtual particles exist as unequivocally as science can tell us anything.

 John K Clark

[Brent Meeker]

On 4/26/2020 9:24 AM, Alan Grayson wrote:

On Sunday, April 26, 2020 at 9:48:45 AM UTC-6, John Clark wrote:

On Sat, Apr 25, 2020 at 12:49 PM Alan Grayson <agrays...@gmail.com> wrote:

> How does QM tell us that conservation of energy can be violated for brief durations? If you apply the time-energy form of the UP for your proof, please state the context of your proof, that is, exactly what do E and t stand for.

The shorter the time (t) a system is under observation the larger the amount of energy (E) could pop into existence from nothing without direct detection, enough energy to create virtual particles. And you can calculate how large the indirect effects these virtual particles would have on the system.

As I understand the UP, it's a statistical statement about an ensemble of observations, say for position and momentum of identical particles. It says nothing about the result of events, say for the position and momentum of a single particle or event. Doing some arithmetic to get the time-energy form of the UP does not change this reality. As a result, your description of what happens to a single particle, virtual or not, is not intelligible. Please try again. AG

The UP doesn't apply to virtual particles because it refers to the result of conjugate measurement (projection) operators.  You can't measure virtual particles.

Brent

[Brent Meeker]

I think you are to readily reifying the mathematics.  Virtual particles are just Feynman's invention to keep track of consistent expansions of the Green's function.  There are other mathematical techniques for calculating the same number.  So what it means for virtual particles to exist not really so unequivocal.

Brent

[Philip Thrift]

The Green's function is merely a mathematical expression. It has no physical status except as a model.

Virtual particles are at least hypothetical physical entities. Green's function don't even have that status.

@philipthrift

[Alan Grayson]

On Sunday, April 26, 2020 at 1:04:45 PM UTC-6, John Clark wrote:

On Sun, Apr 26, 2020 at 12:24 PM Alan Grayson <agrays...@gmail.com> wrote:

> As I understand the UP, it's a statistical statement 

No. It says the more exactly you specify the position of a particle the less exactly you can specify the velocity of the particle; or stated in a alternativ form, the shorter the time duration the more energy a particle (or even empty space) can have without detecting any violation of the law of conservation of energy.

Then you don't understand the meaning of deltaP and deltaX in the statement that the product must be > or = to hbar/2.  Trust me; this isn't a debatable point. AG 

> The UP follows from the postulates of QM. So if one assume these postulates, there is indeed a proof of the UP.

I repeat, this is physics not mathematics, if an experiment violates somebody's postulates then that's just too bad for the postulates because experiment and observation is the ultimate authority in science.

QM is based on specific postulates, and the UP is NOT one of them! Then, using those postulates you can actually derive, or prove, the UP. Yes, experiment and observation is the ultimate authority for any physical theory, and in this case, they validate the postulates as useful in predictions. AG

 

And, given that it can make predictions to 12 significant digits, experiment and observation tells us that virtual particles exist as unequivocally as science can tell us anything.

You need to show that the correctness of some prediction establishes the existence of virtual particles. Since virtual particles don't obey the energy equation of SR, aka "off shell", their existence as physical particles is on very shaky ground. You need to go back to the UP, derive its energy form, and make sure you really know what that form is telling us in a statistical sense. After all, the concept of "uncertainty" has a well-defined statistical meaning. AG 

 John K Clark

[Alan Grayson]

In its usual form, does the UP allow us to measure position and momentum simultaneously, or must we measure each variable independently (for an ensemble of identical particles, of course)? What is proper interpretation of the time/energy form of the principle in statistical terms? TIA, AG 

[Alan Grayson]

Since they're names for terms in a perturbation expansion, and don't obey the energy relations of SR (aka "off shell"), they have no physical status, unless you can prove they can exist in violation of the principle of energy conservation. Can you do that? AG 

[Philip Thrift]

Virtual partcle (Wikipedia):

"The term is somewhat loose and vaguely defined, in that it refers to the view that the world is made up of 'real particles'. It is not. 'Real particles' are better understood to be excitations of the underlying quantum fields. Virtual particles are also excitations of the underlying fields, but are 'temporary' in the sense that they appear in calculations of interactions, but never as asymptotic states or indices to the scattering matrix. The accuracy and use of virtual particles in calculations is firmly established, but as they cannot be detected in experiments, deciding how to precisely describe them is a topic of debate."

They are just as 'real' in Ruth Kastner's Transactional QM.

https://www.informationphilosopher.com/solutions/scientists/kastner/

Physics = Math + Witchcraft

@philipthrift

[Brent Meeker]

You can measure them simultaneously; but when you repeat the pair of measurements on many identically prepared particles you find that there is a scatter in the position  and a scatter in the momentum such that the HUP is satisfied.

Brent

[Alan Grayson]

Can you give an example of the ensembles used in applying the time-energy form of the UP? TIA, AG 

[John Clark]

On Sun, Apr 26, 2020 at 5:18 PM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

> I think you are to readily reifying the mathematics.  Virtual particles are just Feynman's invention to keep track of consistent expansions of the Green's function.  There are other mathematical techniques for calculating the same number. 

But they all involve violating the law of conservation of energy for short amounts of time, and the shorter the time the larger the violation.

John K Clark

[Alan Grayson]

I might be convinced, IF you understood the standard UP, involving position and momentum. But you don't. Do you know the definition of "standard deviation", aka "uncertainty"?  Look it up; a well defined concept in statistics; always involving ensembles! AG 

[Alan Grayson]

I trust you can see the problem with your interpretation of virtual particles. In effect you're putting the cart before the horse! Once you see that the usual form of the UP is a statistical statement involving standard deviations, the time-energy form must have the same property. And no one here, apparently, can state what the ensembles are for that form of the UP! If you don't know what ensembles you're talking about, it is egregiously premature, and prone to error, to make an interpretation of the inequality. AG

[Brent Meeker]

https://arxiv.org/pdf/quant-ph/0511245.pdf

There's also an interesting discussion of how to measure time in QM.  Since time is not an operator you have to construct a clock which defines the physical meaning of time.  http://www.god-does-not-play-dice.net/clock_peres.pdf

Brent

[Alan Grayson]

This article seems to establish a lower bound on time, but nothing related to ensembles. I have no idea about the meaning of the terms in the time-energy form of the UP. AG

[Alan Grayson]

Since the "uncertainty" in the UP is a statistical entity with a well-defined definition, aka "the standard deviation", how large must the sample size be, to calculate it? TIA, AG 

[Brent Meeker]

You mean to experimentally estimate it from the scatter of results?  That depends on how accurately you want to estimate.  The error scales as 1/sqrt(N).  In most experiments with photons or electrons, it's easy to make N big.  But it's also hard to eliminate other sources of scatter that have nothing to do with the UP.  So only experiments deliberately designed for maximum precision are going to push the UP bounds for simultaneous measurements.

Brent

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[Alan Grayson]

Clark; have you confirmed that the standard form of the UP is a statistical statement implying an ensemble, and that the UP can be mathematically proven from the postulates of QM?  Once we get past these elementary FACTS, we can discuss the meaning of the time-energy form of the UP. AG

[Alan Grayson]

What I want to know is your justification for your prior statement about virtual particles and borrowing of energy. You can't just pull it out of a hat as call it Gospel. There must have some justification. What is it? AG 

[Alan Grayson]

Here's Baez's take on the time-energy form of the UP.  https://static1.squarespace.com/static/535ddd66e4b0e268e3eae4cf/t/5695883740667a7eb9f5eb8b/1452640311781/Time-Energy_Uncertainty_Relation.pdf .

Clearly T isn't an operator in QM. Rather, it's a parameter. Instead of deltaT, he replaces it with a form I don't understand, at bottom of page 2. AG

[Alan Grayson]

Correction; bottom of page 3.  AG 

[John Clark]

On Wed, Apr 29, 2020 at 8:18 PM Alan Grayson <agrays...@gmail.com> wrote:

> What I want to know is your justification for your prior statement about virtual particles and borrowing of energy. You can't just pull it out of a hat as call it Gospel. 

I sure as hell can pull it out of a hat if it has been EXPERIMENTALLY CONFIRMED TO A HIGHER DEGREE OF PRECISION than any other idea in, not just physics, but in all of Science! And if that offends your Gospel or your delicate physical "postulates" (whatever the hell that's suposed to mean) then it's time for you to find a new Gospel.

> there must have some justification. 

There is. It works.

 John K Clark

[Alan Grayson]

Firstly, concerning the postulates of QM and the UP, you don't understand my point, which is on solid ground. There's an axiomatic approach to QM which does NOT include the UP. This is what's presented in texts on QM. Those postulates include, for example, the operators for position and momentum, and so forth. The UP is definitely NOT one of these postulates, and the UP can be derived from them. It's done in any decent course in QM. Do you agree or not? AG

Secondly, you don't seem to understand the difference between a mathematical technique which gives excellent predictions and the interpretation of variables in some equation. Once you acknowledge that the position-momentum form of the UP is a statistical statement involving ensembles (since, without doubt, deltaX and deltaP are the standard deviations of the X and P, and defined explicitly in any text on statistics), the question arises of how to interpret deltaT and deltaE in the time-energy form of the UP.  Since T is a parameter and not an operator in QM (T doesn't operate on any domain and it doesn't have eigenvalues and eigenfunctions in its range), it seems that you have a burden to explain what deltaT and deltaE means in the context of the time-energy form of the UP. I don't think this form is used in the excellent predictions of QED, so your comment that QED "works" is without substance in answering my basic question. And FWIW, your virtual particles are just terms in a perturbation expansion which helps in a calculation. This doesn't mean they actually exist in violation of energy conservation.  AG

[John Clark]

On Fri, May 1, 2020 at 8:00 AM Alan Grayson <agrays...@gmail.com> wrote:

> Firstly, concerning the postulates of QM and the UP,

Mathematics has postulates. Science doesn't. The nearest equivalent for Science is experimental results. So it doesn't matter where you originally got an idea, if the idea allows you to make better predictions than anybody else (astronomically better in the case of virtual particles) then scientists will take your idea very very seriously indeed.

> There's an axiomatic approach to QM

No there is not, like every other branch of science there is only an experimental approach.

 

> which does NOT include the UP. This is what's presented in texts on QM. Those postulates include, for example, the operators for position and momentum, and so forth. The UP is definitely NOT one of these postulates, and the UP can be derived from them. It's done in any decent course in QM. Do you agree or not? AG

I neither agree nor disagree because I don't know what the hell you're talking about.  All I know is if Virtual Particles or the Uncertainty Principle or even Quantum Mechanics itself couldn't make predictions that could be confirmed experimentally no scientist would pay them any attention. And the Virtual Particle idea can make better predictions than anything else in all of Science. Full stop.

> your virtual particles are just terms in a perturbation expansion which helps in a calculation. This doesn't mean they actually exist in violation of energy conservation. 

Hmmm...I wonder if that's why they're called VIRTUAL particles and not just particles.

 John K Clark

[Alan Grayson]

On Friday, May 1, 2020 at 6:37:16 AM UTC-6, John Clark wrote:

On Fri, May 1, 2020 at 8:00 AM Alan Grayson <agrays...@gmail.com> wrote:

> Firstly, concerning the postulates of QM and the UP,

Mathematics has postulates. Science doesn't. The nearest equivalent for Science is experimental results. So it doesn't matter where you originally got an idea, if the idea allows you to make better predictions than anybody else (astronomically better in the case of virtual particles) then scientists will take your idea very very seriously indeed.

> There's an axiomatic approach to QM

No there is not, like every other branch of science there is only an experimental approach.

Haven't you ever taken a course in QM? Since QM "works", we accept the postulates, but you can't have a theory without postulates. Or take GR; one of its postulates is that space-time can be modeled as a smooth pseudo-Riemannian manifold. AG

 

> which does NOT include the UP. This is what's presented in texts on QM. Those postulates include, for example, the operators for position and momentum, and so forth. The UP is definitely NOT one of these postulates, and the UP can be derived from them. It's done in any decent course in QM. Do you agree or not? AG

I neither agree nor disagree because I don't know what the hell you're talking about. 

Really? QM associates an Hermitian operator with every observable, such as X and P. That's a POSTULATE! You never heard of that!? AG

 

All I know is if Virtual Particles or the Uncertainty Principle or even Quantum Mechanics itself couldn't make predictions that could be confirmed experimentally no scientist would pay them any attention. And the Virtual Particle idea can make better predictions than anything else in all of Science. Full stop.

Of course; we accept the postulates because of excellent experimental predictions, but to deny the existence of postulates is a total non-understanding of QM and physics in general. AG 

> your virtual particles are just terms in a perturbation expansion which helps in a calculation. This doesn't mean they actually exist in violation of energy conservation. 

Hmmm...I wonder if that's why they're called VIRTUAL particles and not just particles.

They're called virtual because they violate conservation of energy, aka "off shell". but you think they're actually real and can borrow (and return) energy. That's why you can't explain the justification for the time-energy form of the UP. AG 

 John K Clark

[Alan Grayson]

There are a host of deep problems you've swept under the rug. E.g., since the UP is a statistical statement (which you have yet to acknowledge), how do you transform it into a time-energy form for a single particle, a so-called virtual particle, that pops in and out of existence, and borrows and disposes of energy while violating conservation of energy? Since QED gives excellent predictions, it must be because the mathematical perturbation techniques are excellent; not because virtual particles are physical and have the properties you assert. AG

[Alan Grayson]

If the experiment is designed for max precision, how large does N have to be to satisfy the UP? TIA, AG 

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[Brent Meeker]

On 5/2/2020 10:50 PM, Alan Grayson wrote:

You mean to experimentally estimate it from the scatter of results?  That depends on how accurately you want to estimate.  The error scales as 1/sqrt(N).  In most experiments with photons or electrons, it's easy to make N big.  But it's also hard to eliminate other sources of scatter that have nothing to do with the UP.  So only experiments deliberately designed for maximum precision are going to push the UP bounds for simultaneous measurements.

Brent

If the experiment is designed for max precision, how large does N have to be to satisfy the UP? TIA, AG 

That doesn't quite make sense.  It takes two to get an estimate of the variance and the first two you measure may satisfy the UP or they may violate the NP.  The variance, and the std deviation estimators are random variables, obey a certain distribution.  The bigger N the tighter the estimate.  In almost all experiments there will be other sources of randomness and the estimate will converge around some uncertainty bigger than h, which is satisfying the UP.

Brent

[Alan Grayson]

What is NP? If sample size doesn't satisfy the UP, how large must N be? AG 

[Alan Grayson]

On Sunday, May 3, 2020 at 12:19:52 AM UTC-6, Brent wrote:

Why doesn't my question make sense? You say that with an ensemble of 2, the product of the standard deviations might violate the UP. So how large must the ensemble be to guarantee satisfying the UP? AG 

[Brent Meeker]

There's no such guarantee.  You're not measuring the standard deviations directly, you're measuring estimators of them.  The estimators are random variables.   Suppose I said the average height of a human being is greater than 175cm.  How many people would you have to measure to guarantee that was true?

Brent

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[Alan Grayson]

On Thursday, May 7, 2020 at 7:09:04 PM UTC-6, Brent wrote:

On 5/7/2020 4:28 PM, Alan Grayson wrote:

On Sunday, May 3, 2020 at 12:19:52 AM UTC-6, Brent wrote:

On 5/2/2020 10:50 PM, Alan Grayson wrote:

You mean to experimentally estimate it from the scatter of results?  That depends on how accurately you want to estimate.  The error scales as 1/sqrt(N).  In most experiments with photons or electrons, it's easy to make N big.  But it's also hard to eliminate other sources of scatter that have nothing to do with the UP.  So only experiments deliberately designed for maximum precision are going to push the UP bounds for simultaneous measurements.

Brent

If the experiment is designed for max precision, how large does N have to be to satisfy the UP? TIA, AG 

That doesn't quite make sense.  It takes two to get an estimate of the variance and the first two you measure may satisfy the UP or they may violate the NP.  The variance, and the std deviation estimators are random variables, obey a certain distribution.  The bigger N the tighter the estimate.  In almost all experiments there will be other sources of randomness and the estimate will converge around some uncertainty bigger than h, which is satisfying the UP.

Brent

Why doesn't my question make sense? You say that with an ensemble of 2, the product of the standard deviations might violate the UP. So how large must the ensemble be to guarantee satisfying the UP? AG

There's no such guarantee.  You're not measuring the standard deviations directly, you're measuring estimators of them.  The estimators are random variables.   Suppose I said the average height of a human being is greater than 175cm.  How many people would you have to measure to guarantee that was true?

Brent

Suppose I wanted to measure the length of a rod. Couldn't I use high frequency photons to measure its endpoints with as much precision as desired (short of inducing a black hole), and its length calculated from the length differences of its endpoints? Would this procedure violate the UP? AG 

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