Creation and annihilation as measuring processes?

[itssilva]

From a purely theoretical standpoint, I'm quite comfortable with the concept of particle creation/annihilation, but, as a chemist, I cannot but feel that there's something missing in the way of interpretation, so I came up with the following 'explanation' of the phenomenon based on the measured property=eigenvalue postulate of QM:
Consider the reaction e^-e⁺→μ^-μ⁺; suppose that the 'in' states are prepared at past infinity such that they are indeed one-particle Fock states of the electron field, but then they evolve, through the exponential of the free Hamiltonian plus the interaction Hamiltonian, into a superposition of Fock states of all kinds of particles (muons inclusive); when e^- and e⁺ interact (in a local sense), this situation then becomes akin to a measurement process in QM: as a result of this "measurement", the Fock superpositions collapse into well-defined one-particle muon eigenstates, which then proceed to future infinity. Is this the correct viewpoint, from a field-theoretical perspective? Is there an alternative, simpler way to visualize this process?

 

[Simon Bridge]

What do you think is being measured?

 

[itssilva]

What do you think is being measured?

In a loose sense, the number eigenstate; the analogy goes as, in a QM problem, you have a 'system' and a 'measuring apparatus' which are both quantized subsystems, but whose interaction makes the system's wavefunction collapse into a definite state (e.g., if I'm measuring momentum, the system wavefunction collapses into a momentum eigenstate); if you will, then you may reimagine the scattering process in these terms: say, the electron is the 'system', the positron the 'measuring apparatus'. Point is, interacting quantum subsystems collapse into definite eigenstates, in both cases.

 

[Jilang]

I see where you are coming from I think. All possible outcomes of the interaction are in a superposition until one is detected?

 

[itssilva]

I see where you are coming from I think. All possible outcomes of the interaction are in a superposition until one is detected?

Yes; at least, it's how I see it. There doesn't appear to be much discussion of stuff like this in a field context, though.

 

[vanhees71]

First of all, in relativistic quantum theory the particle interpretation of field operators only works for (asymptotically) free states. It's not easy (if not impossible) to make sense of interacting fields in terms of a clear particle interpretation in "transient states". For some of the difficulties in a quite simple but still not so easy case, see this:

F. Michler, H. van Hees, D. D. Dietrich, S. Leupold, C. Greiner, Non-equilibrium photon production arising from the chiral mass shift
Ann. Phys. 336, 331 (2013)
http://arxiv.org/abs/1208.6565

Then, I don't think that such an elementary process like the dielectron annihilation to dimuons, mentioned in #1, qualifies as a "measurement". For a measurement you need, by definition, a detector which admits the identification of the muons, and for that you need the interaction of these with some macroscopic apparatus.

 

[Jilang]

Isn't it the detection of the muon though that causes the collapse rather than the interaction with the positron?

 

[vanhees71]

Yes, exactly! I only don't like to call this "collapse", but that's another story about the interpretation of QT, and we already had too many discussions on this here in the forum!

 

[Jilang]

These transient states, would they be described as virtual particles?

 

[naima]

Then, I don't think that such an elementary process like the dielectron annihilation to dimuons, mentioned in #1, qualifies as a "measurement". For a measurement you need, by definition, a detector which admits the identification of the muons, and for that you need the interaction of these with some macroscopic apparatus.

I am not sure that such apparatus is needed. Look at the excited atoms thru the Young slits. when atoms decay behind the slits, photons carry information about which way path but they have not to be seen by an apparatus. The fringes on the screen are modified by the fact that the atoms can decay not by the measuring of the photons. I think that this does not also require that the atom decay at a given moment.

 

[vanhees71]

These transient states, would they be described as virtual particles?

Although I work with relativistic quantum field theory for quite a while now, I never could make sense of the expression "virtual particles" except as a name for a mathematical object in the perturbative evaluation of S-matrix elements, the free propagator of particles, symbolized by a line in Feynman diagrams (which are not more and not less than a very clever notation for these matrix elements) connected two inner points of this diagram. If there's an intuitive meaning to this at all, it's more like a field, describing the interaction between particles than a "particle" hitting other particles.

 

[vanhees71]

I am not sure that such apparatus is needed. Look at the excited atoms thru the Young slits. when atoms decay behind the slits, photons carry information about which way path but they have not to be seen by an apparatus. The fringes on the screen are modified by the fact that the atoms can decay not by the measuring of the photons. I think that this does not also require that the atom decay at a given moment.

I don't know which experiment you are referring to. In many cases, you don't need to make use of the possibility to gain the which-way information. It's sufficient that this information is realized in the sense that there is some observable you could measure telling you through which way a quantum goes to destroy the interference pattern. If you can know only with some uncertainty about the path the quantum has taken, you destroy the interference pattern only partially, i.e., its contrast becomes weaker. If you point me to the experiment you have in mind, I can try to figure it out in more detail for this particular case.

 

[naima]

In the first thread Itssilva describes a pair of electron e+ e- coming from past infinity he says "when they interact..." they have the choice between several decay channels and this look like measurement.

I think that there is the implicit idea that at a given moment something happen that will be measured later (the choice of the decay channel).
Can we say without looking at the products that they collide? If at t = + infinity we still have still them?
My question is about things "happening" If an electron passes in a Stern Gerlach its spin is not measured if the two ways are merged again.
So I wrote that in the Young experiment the photon had not to be seen by an apparatus but i am not comfortable with these things.

 

[itssilva]

One underlying aspect of this discussion is the following: forget about the interaction, just look at past and future infinity, and put yourselves on layman's shoes: I start with electrons, something happens and I end up with muons. So, I annihilated stuff and created new stuff to replace it; is this magic? Can I build a machine to create me a sandwich out of nothing? (layman's question)
Of course, you can look at the formalism as purely that, and that's it, but I think it's worthwhile remembering that perturbation theory of scattering processes is done using free-theory quantities, like the vacuum (|0>), and not the true interaction quantities, like the interaction vacuum (|Ω>); you do transition amplitude calculations this way, plus incorporating boundary conditions such as <Ω|0>|_t=-∞ = <Ω|0>|_t=+∞ = 1, and you get excellent agreement with experiment, although, from the free-theory perspective we're adopting, it seems that we've actually created and annihilated particles. But, if we could swap to the interaction quantities (which we can't), the measuring mechanism I described at posts #1 and #3 seems plausible, at the least, and you wouldn't see electrons turning into muons, but 'interaction eigenstates' (mixes of free electrons and free muons) deterministically evolving from past to future through exp(-iH_{free+interaction}t), just like a stationary state does in nonrelativistic QM.
Bear in mind QFT is much more general than perturbation theory, which is only an approximation of the former, so what I'm trying here is to have a better grasp on my concepts ;) , so thanks for sharing your thoughts on the matter!

 

[itssilva]

If you point me to the experiment you have in mind, I can try to figure it out in more detail for this particular case.

naima's talking about the Young interference experiment, where the source of light are excited atoms behind the screen.

 

[vanhees71]

I don't know of such an experiment. Can you point to a reference?

 

[naima]

Read http://www.atomwave.org/rmparticle/ao%20refs/aifm%20pdfs%20by%20group%20leaders/pfau%20pdfs/PSK94.pdf