# Interpretation of vacuum fluctuation

## Main Question or Discussion Point

to preserve commutation relations in the quantized field operators (basically simple harmonic oscillator raising/lowering operators), a vacuum mode must be introduced in the case of a usual 50-50 beam splitter.

thus, one has 4 modes:

1. vacuum
2. incident mode
3. reflected mode
4. transmited mode

how does one interpret the vacuum mode interacting with the real photon modes? does this mean that empty space always interacts with matter... so that it is inherently impossible for schrodinger's cat to stay in a superposition of states (and thus things are determinate).

there is also a multiverse view presented by Deutsch in his book The Fabric of Reality. does the vacuum state correspond to his "shadow photon"? (or rather, is it the signal-sender between shadow/real photons?)

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yosofun said:
to preserve commutation relations in the quantized field operators (basically simple harmonic oscillator raising/lowering operators), a vacuum mode must be introduced in the case of a usual 50-50 beam splitter.
Err come again ?

Besides, why do you think that quantized fields only have simple harmonic oscillator raising and lowering operators ? This is WRONG. You are using a QM-vocabularium within a QFT-context. In QFT, particles arise due to fluctuations of fields. The analogy with a QM creation abd annihilation operator is very dangerous to make.

virtual particles are an intermediate stage of an interaction between elementary particles in QFT. They are a tool to describe these interactions, yet their existence can be proven with experiments : see the Casimir-effect.

The QFT-vaccuum is not empty because the lowest possible energy cannot be zero (you know, because of Heisenberg uncertainty : zero energy implies infinite spread of position). thus via E=mc², the vaccuum is filled with these socalled virtual particles. It was Dirac who came up with the idea that the vacuum was filled with virtual positron and electron pairs (the reason that they were pairs has to do with conservation laws like that of electrical charge). You can break up such a pair and make the particles real when you have enough energy coming from some interaction between two charged particles that were placed inside the vaccuum.

Indeed, virtual particles and their fields (remember that position is not a well defined quantity in QFT ) do not exist for ever. In theory this can be proven by the fact that the socalled number-operator of such particles does NOT commute with the hamiltonian (it is not a conserved quantity). Therefore we can call these virtual particles : vacuum-fluctuations.

Problem is that if the vaccuum has a gazzillion virtual particles (suppose each such particle is represented by one LOWEST energy quantum of a harmonic oscillator), the energy of this vaccuum (the zero-point energy) becomes infinite. This will lead to difficulties with curvature of space time and this effect also predicts a very large cosmological constant. This is however against observations. A possible way out is to renormalize this positive infinity by saying that each such virtual electron and positron has a supersymmetric counterpart with opposite energy. This leads to the situation that the positive infinity is \"eliminated\" (it is not really gone , though) by a negative infinity coming from the supersymmetry.

how does one interpret the vacuum mode interacting with the real photon modes?
One word : vacuum polarization tensor !!!

This is the self energy of the photon propagator...We have debated this issue many times in the Nuclei and Particles subforum. I suggest you do a search for this tensor there.

does this mean that empty space always interacts with matter
YES, thanks to the HUP.

... so that it is inherently impossible for schrodinger's cat to stay in a superposition of states (and thus things are determinate).
Ohh no, please no, do not bring in this artificial Schrödinger Cat-bull****.
Look the interaction between the vacuum (which actually is a dielectric constited out of virtual particle/anti-particle pairs) is described in terms of the virtual dipoles aliging themselves with present electric fields. these E-fields can come from the interaction between two charged particles for example. One can also have colour electric fields when we talk about quarks that are interacting.

The biggest difference between these two situations is that the vacuum (ie the dielectric) lowers the strength of the EM-interaction when you move away from the interacting particles (bigger distance scales, thus bigger de Broglie wavelengths, thus lower energy scale), while in the case of interacting quarks, the interaction gets stronger when you use bigger distance scales or lower energy scale. that is why in the vacuum state, quarks are never single entities : they are confined : Welcome to the world of asymptotic freedom.

marlon

vanesch
Staff Emeritus
Gold Member
I found an interesting problem set related to what you write, you can find it at:

http://info.phys.unm.edu/~deutschgroup/Classes/Phys566F04/ProblemSets/Phys566F04_PS7.pdf

cheers,
Patrick.

yosofun said:
to preserve commutation relations in the quantized field operators (basically simple harmonic oscillator raising/lowering operators), a vacuum mode must be introduced in the case of a usual 50-50 beam splitter.
thus, one has 4 modes:
1. vacuum
2. incident mode
3. reflected mode
4. transmited mode
how does one interpret the vacuum mode interacting with the real photon modes? does this mean that empty space always interacts with matter... so that it is inherently impossible for schrodinger's cat to stay in a superposition of states (and thus things are determinate).
there is also a multiverse view presented by Deutsch in his book The Fabric of Reality. does the vacuum state correspond to his "shadow photon"? (or rather, is it the signal-sender between shadow/real photons?)

Why again follows a zero-point energy for the vacuum from HUP?
I see that for bound states in QM (with a particle that's confined in space) it clearly follows from HUP but for a vacuum? I know there is an easy answer, but I forgot.

thanks

edit: Hah, that's how
http://zebu.uoregon.edu/~imamura/209/apr14/virtual.html [Broken]

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