Are tracks in collision experiments proof of particles?

[mfb]

Why is this known in advance?

We know the detector, and the detector will still be there once the spherical wave function arrives.

Why does decoherence imply that one can replace the spherical wave by flying particles? Wouldn't this mean decoherence in a preferred momentum basis, not decoherence in position?

In a basis of detector positions (to a good approximation), which is neither a pure momentum nor a pure position basis as seen from the initial collision.
I don't have links to papers.

That's precisely the step that lacks a detailed quantum field description when applied to multiple particles. Quantum field scattering theory just defines a scattering matrix for a single particle colliding with a target, prepared at time $-\infty$, detected at time $+\infty$, and leaves the interpretation of the S-matrix to ordinary QM and its ensemble interpretation.

The target is a second particle already. I am not aware of limits for the number of participating particles - the number of outgoing particles is certainly not limited, why should the number of incoming particles be? The whole process is time-symmetric (in principle).

 

[Orodruin]

The entire program of 16th to 20th century physics has been about this: What is reality? How does some particular description of reality arises form an even more fundamental level below? That is precisely how all progress in physics occurs, and it upsets me greatly that people are effectively disparaging your question, saying "Well, there are easier was to calculate

This statement is fundamentally flawed and misguided in terms of what physics is. Physics and many other natural sciences are about finding a description which describes reality, not a quest for what it actually is, which is the domain of philosophy. Physics is an empirical science, driven by the will to do experiments to figure out how Nature behaves, create theories about it, and then test the new predictions arising from this. There is no underlying quest for reality, just the question of how it will behave when we change the input parameters and developed based on flaws in current theories, be they actual empirical flaws or more constructed theoretical ones.

If there is an easier way to describe how something works, then this is exactly the path we should take based on Occam's razor. Otherwise you are inviting wild speculation without experimental verification, which leads to a slippery slope towards crackpot land.

 

[Jilang]

It can be regarded as property of both.

There are many reasons electrons are considered particles rather than field. Going back to Millikan's measurements, oil drop was found to have only electric charge that is multiple of elementary charge $e$. If electron was a field, one would expect the electric charge of the oil drop to be distributed continuously, not in multiples of $e$.

I have been thinking about this on the drive home from work strangley enough, before I saw this post. The electrons are in oil are quantised as they are confined in atoms/molecules and so are "measured". Perhaps, just as spin is only quantised when electrons are subjected to a magnetic field, the other properties are similar?

 

[Bruno81]

Are chairs proof of particles?

 

[A. Neumaier]

If electron was a field, one would expect the electric charge of the oil drop to be distributed continuously, not in multiples of e.

This would hold for a classical field but not for a quantum field. In quantum mechanics, discreteness is not rigidly associated with decomposability into pieces.

Orbital angular momentum is also quantized, but nobody deduces from the http://espace.library.uq.edu.au/view/UQ:161172/UQ161172.pdf the existence of angular momentum particles.

 

[Haelfix]

This step is not so obvious. Why is this known in advance? Why does decoherence imply that one can replace the spherical wave by flying particles? Wouldn't this mean decoherence in a preferred momentum basis, not decoherence in position? I would like to see papers that actually support this with proper formulas and derivations, not just uncheckable allusions to collective knowledge. That it works in practice is good for the practitioner but not a sufficient explanation for the theorist.

The Mott paper gives precisely this analysis, namely that everything must collapse to a particle pointer state. Why this pointer state and not another? As I'm sure you know, that required work much later by Zurek, Jooh and Zeh who proposed Einselection (environmentally selected decoherence), which selects out the position basis b/c in this case the form of the force law (Coulombs law) depends on distance. Thus, after the partial tracing out of the environment, the interaction Hamiltonian commutes with an approximate position observable, and you get the desired 'particle' like behaviour that seems to be robust. See
Joos, E., and H. D. Zeh, 1985, Z. Phys. B 59, 223

The nice part of this analysis is that it makes definite predictions about what type of pointer state's different systems will have. So depending on how much the environment 'monitors' the system you get different results (this corresponds to which term dominates in the full Hamiltonian)

 

[atyy]

Thus, precisely because the concept of particles is incredibly useful, I want to see clearly how it arises from the underlying quantum field picture beyond the (apparently almost nonexistent) discussion in books and articles. Perhaps the discussion exists and I am only unaware of it, but there is definitely something to be understood.

In free quantum field theory, eg. QED with only photons, the quantum particle picture is exact, because the Hilbert space is a fock space.

Of course, there is no unique photon or "quantum of the free massless EM field", rather there are many different types of photons, some more like a classical bullet than others.

 

[atyy]

But I want to understand why! QFT should be a fundamental theory, hence should allow in principle to model a train of electrons as a process happening at finite times inside its own framework, and within this model one should be able to derive the interpretation of the S-matrix dynamically instead of having to postulate it in addition to its formalism! What I am interested in is how quantum field theory can achieve that. Saying that one can simplify things to get the correct predictions doesn't answer this more fundamental quest!

Electrons are easier, because they are massive, so one can use the Mott picture (and later developments) as has been said many times. Incidentally, the LSZ formalism does have to assume wave packets, so both the position and momentum of the particle are measured which is why we do get particle tracks.

 

[vanhees71]

Often one can indeed do the latter. But both the Kadanoff-Baym equations and the Boltzmann-Vlasov equations are field theories in phase space, not particle theories.

Instead of particles one has only phase space densities. Thus talking about particles seems to be simply a left-over from the 19th century when Boltzmann derived his equation from a classical particle picture.

In classical physics you also have only phase space densities. So what? As soon as you do relativistic dynamics the point-particle idealization becomes problematic anyway (keyword: radiation reaction). A continuum-mechanical description is much more natural in relativistic dynamics.

The interaction between "particles" can only be described adequately with quantum theory (in the relativistic case as a QFT). A particle interpretation makes sense only in terms of asymptotic free states.

 

[vanhees71]

But I want to understand why! QFT should be a fundamental theory, hence should allow in principle to model a train of electrons as a process happening at finite times inside its own framework, and within this model one should be able to derive the interpretation of the S-matrix dynamically instead of having to postulate it in addition to its formalism! What I am interested in is how quantum field theory can achieve that. Saying that one can simplify things to get the correct predictions doesn't answer this more fundamental quest!

Again, for "transient states" a particle interpretation in the relativistic case is at least problematic. You can only interpret asymptotic free states in terms of a particle picture, because only then a clear Fock-space construction is possible (as far as I know). If massless particles are present even this is not fully correct either (cf. the analysis by Kulisch and Fadeev, Kibble, and many others). In the standard treatment that's "cured" by appropriate soft-photon resummations (see Weinberg QT of Fields, Vol I). That's why the observable facts for "few-body systems" are in terms of scattering experiments and S matrices. To derive the S matrix from QFT (LSZ reduction) is not as simple as it seems. Most textbooks use a pragmatic approach, using "box quantization" and then taking the appropriate "infinite-volume limit". This is mathematically most simple and leads to the correct results, but it's not very physical. Often scattering theory appears to be "weird" to many people because of that. In this case I can only recommend to read the corresponding chapter in Peskin&Schroeder, where a wave-packet treatment is used. Although this book is full of typos and sometimes very sloppy, this chapter is really worth to be studied carefully. For a very thorough discussion of the somewhat simpler case of non-relativistic QT (where you can simplify the problem by looking at potential scattering first), see the good old textbook by Messiah. This is anyway full of very careful discussions of issues often treated not very thoroughly in the modern books.

Finally, QFT is (in its present status) an effective theory with limited energy-momentum range of validity anyway. So far there is no more comprehensive theory in sight. As long as there is no such more comprehensive theory we shall have to live with QFT, and it's amazingly successful. There's not even a clear hint of where the Standard Model breaks down (although maybe there's a new hint recently with the new findings on anti-neutrinos by the Daya Baye collaboratin; so there may be some hope to find hints how to go "beyond the Standard Model").

 

[A. Neumaier]

The Mott paper gives precisely this analysis, namely that everything must collapse to a particle pointer state.

Did you read the paper?? Mott nowhere mentions collapse. Instead he shows (quote from p.80) that [in the absence of a deflecting magnetic field]

the atoms cannot both be ionized unless they lie in a straight line with the radioactive nucleus.

This fully explains the tracks, without making any claims about collapse or a particle pointer state, or position measurement. The spherical wave is nowhere replaced by flying particles, as @mfb wants us make believe.

you get the desired 'particle' like behaviour that seems to be robust. See
Joos, E., and H. D. Zeh, 1985, Z. Phys. B 59, 223

They refer to Mott on p.225 (top left) but don't take it up later. The present thread is about microscopic particles, but they consider (already visible from the title and the abstract) instead the problem of localization of macroscopic objects. Or did I miss something? Where do they discuss how a particle in a spherical state decoheres into a flying particle with well-defined momentum and reasonably well-defined position?
You say,

The nice part of this analysis is that it makes definite predictions about what type of pointer state's different systems will have. So depending on how much the environment 'monitors' the system you get different results

but I don't see how their analysis applies to the case under discussion here.

 

[A. Neumaier]

In classical physics you also have only phase space densities. So what? As soon as you do relativistic dynamics the point-particle idealization becomes problematic anyway (keyword: radiation reaction). A continuum-mechanical description is much more natural in relativistic dynamics.

So you seem to agree with me that the particle picture is limited and approximate, and the correct language and formal treatment needs field theory everywhere, both in the classical and in the quantum case. The particle view is just there to aid intuition and for historical reasons, while in fact fields concentrated in fairly narrow regions move along flow lines determined by the field equations.

 

[A. Neumaier]

the LSZ formalism does have to assume wave packets, so both the position and momentum of the particle are measured

The LSZ formalism is derived in Weinberg, Vol. I, Sections 12.2-3 without any mentioning of wave packets.

But even in the wave packet treatment of Peskin & Schroeder (Section 7.2), nothing is assumed related to measurement. To evaluate the S-matrix and justify the LSZ formula one can use an arbitrary complete or overcomplete set of test functions - this is enough to prove correctness for arbitrary matrix elements. P&S use wave functions with a fairly narrow width in momentum space overlapping in a region around $x=0$ and separating in the far past and future. For example one can use (for scalar fields, the case treated by P&S) coherent states with a narrow momentum spread and a large position spread, corresponding to a beam of scalar particles. This is indeed the form appropriate for analyzing collision experiments. But by taking linear combinations, the formula is valid for arbitrary in and out states.

 

[vanhees71]

The LSZ formalism is derived in Weinberg, Vol. I, Sections 12.2-3 without any mentioning of wave packets.

But even in the wave packet treatment of Peskin & Schroeder (Section 7.2), nothing is assumed related to measurement. To evaluate the S-matrix and justify the LSZ formula one can use an arbitrary complete or overcomplete set of test functions - this is enough to prove correctness for arbitrary matrix elements. P&S use wave functions with a fairly narrow width in momentum space overlapping in a region around $x=0$ and separating in the far past and future. For example one can use (for scalar fields, the case treated by P&S) coherent states with a narrow momentum spread and a large position spread, corresponding to a beam of scalar particles. This is indeed the form appropriate for analyzing collision experiments. But by taking linear combinations, the formula is valid for arbitrary in and out states.

Well, Weinberg is well aware that wave packets are the better treatment, but he uses the "box-quantization approach" (QTF 1, Sect. 3.4].

Of course, in the derivation of the cross section you don't use a detailed analysis of the detection mechanism. There's anyway no discussion about concrete detector physics in QFT books, because it's off-topic there. The usual S-matrix elements are idealized quantities to be measured with appropriate accuracy by the practical detectors (and this accuracy is amazing nowadays!).

There's one example, where you really need the wave-packet approach in HEP, and that's the case of neutrino oscillations. I don't know of any topic of high importance that's taught in a so confusing way as this ;-)). There are tons of paper wasted to get rid of the problems with the sloppy handwaving "mixing formula", which turns out to be roughly right.

First of all one has to note that a particle interpretation is possible only for asymptotic free mass eigenstates. So neutrinos are hard to define as such, because they are never produced in mass eigenstates but in flavor eigenstates, which are not the same, and this is the very point of the neutrino oscillations. To get a satisfactory definition of what oscillating neutrinos are, you simply have to think about how the neutrino oscillations are measured: You have some source at a (pretty unsharply) defined place (e.g., an accelerator, where pions or muons are produced that subsequently decay to neutrinos + X) and another (also pretty unsharply) defined place, where they are detected. This detection process is via reactions with the detector material and the detection of the charged leptons involved in these reactions (e.g., in Kamiokande/SNO via Cherenkov radiation (RICH) detectors). Nowhere do you need asymptotic free neutrinos in this picture! So you have wavepackets localized at the source of the particles producing the neutrinos and other wavepackets for the particles detected at the far-away detector. From this you get the detection rate in dependence of the distance between source and target, the energy and squared masses of the neutrinos and their mixing-matrix. The naive formula can be found as an approximation.

 

[A. Neumaier]

So you have wavepackets localized at the source of the particles producing the neutrinos and other wavepackets for the particles detected at the far-away detector. From this you get the detection rate in dependence of the distance between source and target, the energy and squared masses of the neutrinos and their mixing-matrix.

I'd be interested in a reference where details about this can be found.

 

[vanhees71]

One is here

http://arxiv.org/abs/hep-ph/0205014

 

[A. Neumaier]

there are many different types of photons, some more like a classical bullet than others.

How collisions of classical bullets with plexiglas produce random radial tracks in the observing medium is discussed in
M. Schirber, Focus: Windshield Cracks Hold Secrets of Impact, Physics 6 (2013), 48.

A projectile traveling at 22.2 meters per second generates four cracks in a 1-millimeter-thick sheet of Plexiglas.

Believers in the theory that observed tracks in a high energy collision energy experiment are conclusive evidence for the existence of elementary particles should perhaps conclude that the projectile produced four elementary ''crack particles'', according to the nuclear reaction $[projectile] \leftrightharpoons 4[crack particle]$ (in the presence of a plexiglas catalyzer).

Or is it eight?

A 56.7 meter-per-second projectile generates eight radial cracks in the same thickness Plexiglas sheet as above.

Obviously, the number of alleged crack particles produced by the projectile is a function of the energy of the projectile. Thus crack particle number is not conserved.

Just as the number of alleged photons produced by a laser beam (treated as a classical electromagnetic field) impacting a photodetector is a function of its brightness. And photon number is not conserved.

Moral: Don't treat the number of discrete detection events as obvious evidence for the existence of the same number of associated invisible objects. They are at best evidence of the impact of something.

 

[vanhees71]

Well this only shows that not all setups are good "particle detectors" :-).

 

[A. Neumaier]

Well this only shows that not all setups are good "particle detectors" :-).

Yes, but it is fun that Mott's analysis has a classical analogue, although

It is a little difficult to picture how it is that an outgoing spherical wave can produce a straight track.

The projectile also creates an outgoing spherical stress wave in the plexiglas and produces straight cracks. In fact, once initiated, the growth of a crack in a solid is not very different from the growth of a track in a bubble chamber, except that the energies and time scales are quite different. Only the initiation is random.

 

[atyy]

The LSZ formalism is derived in Weinberg, Vol. I, Sections 12.2-3 without any mentioning of wave packets.

But even in the wave packet treatment of Peskin & Schroeder (Section 7.2), nothing is assumed related to measurement. To evaluate the S-matrix and justify the LSZ formula one can use an arbitrary complete or overcomplete set of test functions - this is enough to prove correctness for arbitrary matrix elements. P&S use wave functions with a fairly narrow width in momentum space overlapping in a region around $x=0$ and separating in the far past and future. For example one can use (for scalar fields, the case treated by P&S) coherent states with a narrow momentum spread and a large position spread, corresponding to a beam of scalar particles. This is indeed the form appropriate for analyzing collision experiments. But by taking linear combinations, the formula is valid for arbitrary in and out states.

Yes, the LSZ does not treat the decoherence. I only mentioned LSZ wave packets since that means that at the end of LSZ we have a fixed number of quantum particles. For massless particles, I am not so sure whether the Mott picture goes through straightforwardly, but at least for massive partcles, one should now be back at relativistic quantum mechanics (we can use the non-problematic part of it). I do agree that decoherence has not been worked out for relativistic cases, but this is close enough to non-relativistic quantum mechanics, that I think we can leave it as an exercise :P

I do think a proper derivation of LSZ needs wave packets, eg. http://isites.harvard.edu/fs/docs/icb.topic474176.files/LSZ.pdf.

 

[vanhees71]

Yes, you either need wave packets or you can use a finite volume (cube) and impose periodic boundary conditions. Then your momentum eigenstates are welldefined (since the momentum operator is self-adjoint contrary to the case with rigid boundary conditions) square-integrable functions. At the end after (!) squaring the so regularized S-matrix elements, and dividing by the four-volume to get transition rates, you can take the infinite-volume limit getting a single energy-momentum conserving $\delta$ distribution as it should be.

 

[A. Neumaier]

I do think a proper derivation of LSZ needs wave packets

But this is unrelated to measurement/decoherence issues. It is just a choice of test functions.

 

[vanhees71]

True, but what is it then what you are after concerning "measurement issues"? I always leave the measurements to the experimentalists, because they are much better in that as any theorist can be ;-)).

 

[atyy]

But this is unrelated to measurement/decoherence issues. It is just a choice of test functions.

But if one has a wave packet, then we get to the point where we can use some variant of Mott's analysis, and decoherence etc. (In the Copenhagen view, a wave packet does not imply a particle with a trajectory, which is why one still needs additional argument to say why the wave packet leaves a track similar to a classical particle.)

Are you thinking that we cannot use Mott's analysis, or that we can, but he doesn't give enough detail of the decoherence process?

 

[atyy]

There are two approaches to why a quantum particle which has no trajectory can leave a track.

1) Decoherence style arguments, eg. Mott and later work: http://arxiv.org/abs/1209.2665

2) Repeated measurement, eg. http://arxiv.org/abs/quant-ph/0512192

 

[A. Neumaier]

what is it then what you are after concerning "measurement issues"?

It was not me who tried to answer my quest with informal references to decoherence and measurement; so I pointed out that the information provided by a reference to LSZ does not give support to the idea that decoherence or measurement resolve the problem.

From my point of view it is a purely formal question how to reduce trains of particles in a beam (a prepared ensemble of single particles in a quantum mechanical textbook setting) to something interpretable in many-particle quantum field theory. Thus there should be a purely formal answer to my quest. Or at least an outline that looks like being formalizable.

The S-matrix from QFT doesn't do it, as it describes what happens to a single 2-particle system (1 beam particle plus 1 target particle) prepared at infinite distance upon collision, producing an additional outgoing spherical wave that extends to infinity.

But QFT is a description that gives correlation functions at all space-time positions, hence a complete history of everything.
In particular, QFT should be able to model the train of particles in a beam as a temporally resolved something in the QFT description, without having to resort to the interpretation of the single temporal train of $N\gg 1$ particles as an ensemble of 1-particle systems.

Treating the train as an ensemble of N-particle systems will not work since it will give the wrong statistics - at any time only one of the particles will collide with a target particle - so the cross section is that of a 2-particle collision and not one of $N+1$ particles!

All this is simply swept under the carpet if one says that for all practical purposes one may regard the system as decohered immediately after the collision (when exactly?? how??) into flying particles (where do they get their fairly well-determined momentum from if, as claimed, only a position measurement was made??) and that the measurement process (in its ill-defined quantum version!) takes care of it.

I know that this works in practice, but I am not satisfied with shut-up-and-calculate but want to look under the carpet!

 

[atyy]

The S-matrix from QFT doesn't do it, as it describes what happens to a single 2-particle system (1 beam particle plus 1 target particle) prepared at infinite distance upon collision, producing an additional outgoing spherical wave that extends to infinity.

But QFT is a description that gives correlation functions at all space-time positions, hence a complete history of everything.
In particular, QFT should be able to model the train of particles in a beam as a temporally resolved something in the QFT description, without having to resort to the interpretation of the single temporal train of $N\gg 1$ particles as an ensemble of 1-particle systems.

Well, if that's your objection, I don't believe I have ever seen a treatment of this problem. Everyone treats the particles in a train as an independent preparation.

It's only when we try to apply quantum theory to the whole universe, eg. quantum fluctuations during inflation seeding structure formation that we try to do something like this, because we don't have multiple preparations of the universe.

 

[A. Neumaier]

Are you thinking that we cannot use Mott's analysis, or that we can, but he doesn't give enough detail of the decoherence process?

''not enough detail'' is a strong exaggeration - he is completely silent about decoherence or measurement!

He just needs Born's rule for interpreting the final outcome. This makes it an exemplary contribution to the foundations. He explains without reference to anything outside the quantum formalism.

Moreover, there is no reference to the $\alpha$ particle! This makes his analysis very close to a field theoretical treatment. It is consistent with the possibility (implicitly indicated in the formulation of the thread title) that particles do not exist but are just a way of visualizing invisible happenings in the microscopic domain.

But we cannot use Mott's analysis directly in a QFT treatment since there is a mismatch between the statistical view of a train of many temporally separated particles in a beam (as an ensemble in the QM1 sense) and the temporally resolved view of many-particle QFT, where everything happening in space and time is described by correlation functions only.

 

[A. Neumaier]

Who the is secretly deleting comments in this thread, without even having the common courtesy to tell the original poster? That is rude behavior. Especially since I haven't been informed of even a single complaint or criticism.
No college or university science course I have been in has ever had an instructor act this way.

What do you mean? Your post https://www.physicsforums.com/posts/5379333/ is still here!

 

[atyy]

''not enough detail'' is a strong exaggeration - he is completely silent about decoherence or measurement!

He just needs Born's rule for interpreting the final outcome. This makes it an exemplary contribution to the foundations. He explains without reference to anything outside the quantum formalism.

Moreover, there is no reference to the $\alpha$ particle! This makes his analysis very close to a field theoretical treatment. It is consistent with the possibility (implicitly indicated in the formulation of the thread title) that particles do not exist but are just a way of visualizing invisible happenings in the microscopic domain.

I don't think anyone uses the word particle the way you use it. A particle and a field are the same in QFT, because of the Fock space. I think everyone would agree with you if they used your terminology. (And yes, Mott's analysis is severely lacking in detail, but he does enough that one can believe it ok to leave as a homework problem)

But we cannot use Mott's analysis directly in a QFT treatment since there is a mismatch between the statistical view of a train of many temporally separated particles in a beam (as an ensemble in the QM1 sense) and the temporally resolved view of many-particle QFT, where everything happening in space and time is described by correlation functions only.

Yeah, you are the only person who's ever asked this. Usually we only bother about such things if we really believe there is only one history, and not many independent preparations.