Are clicks proof of single photons?

[meopemuk]

On the other hand, my claim is that no more than one pixel will "click".

Here we agree.

Ok, so possibly we are not so far apart as I thought. The difference is only in interpretation. I say that the pixel "clicks" because a photon has arrived there. You say that this was a result of a quantum field "magic".

Eugene.

 

[meopemuk]

An atom is indivisible (at the energies of the experiment)

Yes.

...and can therefore go only through one of the slits.

I am not sure about that. I would prefer not to make any statements about situations in which the atom is not observed. Anyway, such statements cannot be verified experimentally, so they are beyond scientific discourse.

The atom [...] is nonexistent (or in a state of limbo where it has no physical property at all) during a period of time corresponding to the flight of time to the screen.

Again, in order to avoid contradictions, I prefer not to say anything about the state of the atom between preparation and observation events. I can assign a wave function to such a state, but this is just a mathematical device. Using the wave function I can say something meaningful (probabilities) about possible observations. However, I cannot say anything useful about the non-observed state.

The quantum field view has none of these problems.

Please remind me what was the field theory explanation for the interference experiment with atomic deposition? In particular, how the atomic "field" collapses to a specific position on the substrate? Isn't it the same dreadful Copenhagen collapse?

I hope in this explanation you wouldn't invoke the quantum nature of the substrate as M&W did in their Chapter 9.

Eugene.

 

[A. Neumaier]

I would prefer not to make any statements about situations in which the atom is not observed. Anyway, such statements cannot be verified experimentally, so they are beyond scientific discourse.

You narrow the scientific endeavor to a very tiny realm. According to your criteria, you would consider talk about the temperature or composition of the core of the Earth or the interior of the sun, about the time of impact of one of the big meteors in the far past, or about the functioning of the inside of your computer to be beyond scientific discourse. All these are not observed.

Again, in order to avoid contradictions, I prefer not to say anything about the state of the atom between preparation and observation events. I can assign a wave function to such a state, but this is just a mathematical device. Using the wave function I can say something meaningful (probabilities) about possible observations. However, I cannot say anything useful about the non-observed state.

Saying something about possible but unperformed observations should be beyond scientific discourse according to your criteria. How then can you call it meaningful? You cannot make any definite statement without running into contradictions. This is what I meant by saying ''The atom [...] is nonexistent (or in a state of limbo where it has no physical property at all) during a period of time corresponding to the flight of time to the screen.'' If the atom had some physical properties, one would be allowed to state and use them consistently.

Please remind me what was the field theory explanation for the interference experiment with atomic deposition? In particular, how the atomic "field" collapses to a specific position on the substrate? Isn't it the same dreadful Copenhagen collapse?

I hope in this explanation you wouldn't invoke the quantum nature of the substrate as M&W did in their Chapter 9.

It would be very strange if the quantum nature of the substrate were immaterial.

I have no explicit calculations for this, but judging from what I expect a calculation would reveal, the atomic field simply ends at the substrate, with a randomly growing density at the boundary, this time (because of a mass conservation law) due to the quantum nature of both the atomic field and the substrate. No collapse is needed for this, and everything happens locally, with nonlocal correlations but no nonlocal information transfer.

 

[meopemuk]

You narrow the scientific endeavor to a very tiny realm. According to your criteria, you would consider talk about the temperature or composition of the core of the Earth or the interior of the sun, about the time of impact of one of the big meteors in the far past, or about the functioning of the inside of your computer to be beyond scientific discourse. All these are not observed.

Saying something about possible but unperformed observations should be beyond scientific discourse according to your criteria. How then can you call it meaningful? You cannot make any definite statement without running into contradictions. This is what I meant by saying ''The atom [...] is nonexistent (or in a state of limbo where it has no physical property at all) during a period of time corresponding to the flight of time to the screen.'' If the atom had some physical properties, one would be allowed to state and use them consistently.

I cannot talk about things, which I do not observe, but I am allowed to talk (predict) about results of future experiments. There is a subtle philosophical difference.

For example, in the original double-slit experiment I cannot say whether the photon (or electron, or whatever) passes through one slit or through two slits. Whichever answer I choose I will find myself in a logical contradiction. So, I decide to answer simply "I don't know". And you cannot blame for that, because you cannot find the truth experimentally without totally changing the experimental setup, so that the original question does not make sense anymore.

However, I *can* predict that if we modify the double-slit setup by adding particle detectors near each slit, then this new experiment will find that the photon is passing through one slit only. But experimental conditions have changed, so this result tells me nothing about the single-slit or double-slit passage in the original setup.

Talking about non-observable things can be OK if we are dealing with purely classical effects, where Z follows from Y and Y follows from X without any quantum probabilities involved. Most of observations in physics belong to this class. For example, from temperature X in the middle of the sun follows temperature Y on the surface of the sun. And from temperature Y on the surface of the sun follows photon spectrum Z observed on earth. So, by measuring the photon spectrum on Earth I can follow this cause-effect relationship backwards and recreate the value of the parameter X. Of course, this is a gross simplification and many other parameters are involved. However, the important thing is that all these parameters are in unambiguous (non-quantum) cause-effect relationships with each other.

The same with the meteorite. By looking at the crater I can roll back the classical cause-effect relationship chain and say what was the meteorite's mass, velocity, when the impact has occurred, etc.

In the quantum case this roll back is not possible. If I see that a photon landed at the point Z on the screen I cannot recreate the cause-effect chain and say whether the photon passed through the left slit or through the right slit. Quantum processes have inherent unexplainable probability, which does not allow me to make definite statements about things that have not been observed.

It would be very strange if the quantum nature of the substrate were immaterial.

Do you then expect that the shape of the interference picture would depend on the chemical composition of the sustrate? Of course, I assume that the substrate is chemically neutral, that atoms cannot migrate on the surface, etc. As far as I know, all interference patterns (with photons, electrons, atoms, etc.) have the same form, which depend only on the geometry of the two slits and the momentum of projectiles. There is absolutely no dependence on the chemical composition of the diaphragm and the screen/substrate. If your model predicts such dependence, then it can be verified experimentally.

I have no explicit calculations for this, but judging from what I expect a calculation would reveal, the atomic field simply ends at the substrate, with a randomly growing density at the boundary, this time (because of a mass conservation law) due to the quantum nature of both the atomic field and the substrate. No collapse is needed for this, and everything happens locally, with nonlocal correlations but no nonlocal information transfer.

I don't really get it. We've fired just one atom. According to you, the situation is described by a continuous field, which is spread over the entire substrate surface. Nevertheless, the atom lands at one fixed location. How exactly this location is chosen? Which physical mechanism has chosen this particular location?

Eugene.

 

[PhilDSP]

No. I see the sufficiency of standard quantum mechanics. Bohmian mechanics adds nothing to understand the photoelectric effect:

There is no Bohmian mechanics version of photon absorption consistent with Maxwell's equation, though models for Bohmian photons with a Maxwell pilot wave exist: http://arxiv.org/pdf/0907.2667

But even if this were improved, I don't see any reason for postulating unobservable Bohmian ghost particles with nonlocal instantaneous influences over galactic spacetime regions, just in order to explain seeing the light of stars.

Fair enough. I'm hoping that the next couple of years will start to rectify the lack of usable mechanics, though what emerges may not be at all Bohmian. Thanks for the references, I'll read them as soon as time permits.

 

[Zarqon]

No. Even according to a hypothetical Hamiltonian multiparticle theory accounting for photodetection, one could ''find'' a photon in this way only when it no longer exists! The very act of attempting to observe a photon kills it!

Therefore, one cannot use observations to prove the existence of photons! They are ghosts conjured by Einstein and Dirac! Whereas in quantum field theory, one just has states of the electromagnetic field, and the number of photons in a given region is a
non-observable.

One CAN in fact measure single photons without destroying them, as is done in the experiments in the group of Serge Haroche.

See e.g. http://www.nature.com/nature/journal/v455/n7212/abs/nature07288.html"

In their experiments they detect photons in a QND type way, where repeated measurement of the same photon is possible. With this they can detect the differences between photons in coherent states and in pure Fock states.

 

[A. Neumaier]

I cannot talk about things, which I do not observe, but I am allowed to talk (predict) about results of future experiments. There is a subtle philosophical difference.

We are talking most of the time about things we do not observe. We trust that all the transistors in the VLSI chips of our computers behave in a particular way predicted by quantum mechanics, although we hardly ever check it. We _could_ check it (thereby destroying the chip = changing the experimental setup), but we never do it. Even at the manufacturer, one only checks the consistency of some peripheral test results with the predictions.

For example, in the original double-slit experiment I cannot say whether the photon (or electron, or whatever) passes through one slit or through two slits. Whichever answer I choose I will find myself in a logical contradiction.

That's the problem with the particle picture. You buy it at the cost of a very strange picture of reality that takes years of brain washing to get used to. The field picture doesn't have these difficulties.

So, I decide to answer simply "I don't know". And you cannot blame for that, because you cannot find the truth experimentally without totally changing the experimental setup, so that the original question does not make sense anymore.

I blame you for that because you cannot find the truth experimentally about the trnsistors in your computer without totally changing the experimental setup, but the original question still makes sense, and we know!

Why should one quantum system be different than the other? How many particles does a quantum system need to have to be able to be blamed for pretending not to be knowable?

by measuring the photon spectrum on Earth I can follow this cause-effect relationship backwards[...]
In the quantum case this roll back is not possible. [...] Quantum processes have inherent unexplainable probability, which does not allow me to make definite statements about things that have not been observed.

So you sacrifice the cause-effect relationship on the level at a single quantum particle, but you claim that such a relationship exists on the level of N quantum particles where N is the number of particles in the sun? At which value of N do you switch between the two modes?

Moreover, what you say is restricted to the quantum particle view. In a quantum field view, the causal uncertainty is not bigger than classically, involving the inherent unexplainable probability of predicting or retrodicting a chaotic system.

Do you then expect that the shape of the interference picture would depend on the chemical composition of the sustrate? Of course, I assume that the substrate is chemically neutral, that atoms cannot migrate on the surface, etc. As far as I know, all interference patterns (with photons, electrons, atoms, etc.) have the same form, which depend only on the geometry of the two slits and the momentum of projectiles. There is absolutely no dependence on the chemical composition of the diaphragm and the screen/substrate.

Under the conditions you stated, QFT probably predicts absolutely no dependence on the chemical composition of the diaphragm and the screen/substrate - just as it doesn't predict any such dependence on the nature of a photodetection device, where M&W did the calculations.

I don't really get it. We've fired just one atom. According to you, the situation is described by a continuous field, which is spread over the entire substrate surface. Nevertheless, the atom lands at one fixed location. How exactly this location is chosen? Which physical mechanism has chosen this particular location?

Considered as a microscopic system, the detector is a highly chaotic dynamical system. Therefore, the individual binding sites for the atomic field behave like random qubits responding to the intensity of the incident atom field, just as the outer electrons in a photodetector behave like random qubits responding to the intensity of the incident electromagnetic field. The response rate is proportional to the incident energy. Once one of the qubits fires, it uses up the whole energy and matter of the atom field, and the choice has been made. No other qubit can fire, by a most likely existing analogue of M&W's formula (14.8-16).

In quantum field theory, causality is therefore as well-behaved as in any classical stochastic process.

 

[meopemuk]

So you sacrifice the cause-effect relationship on the level at a single quantum particle, but you claim that such a relationship exists on the level of N quantum particles where N is the number of particles in the sun? At which value of N do you switch between the two modes?

Yes, the transition between the random quantum regime and the predictable classical regime occurs gradually as N grows. There is no unique threshold value. Some systems show quantum behavior even for very large N. The usual examples are superconductors and superfluid helium.

Considered as a microscopic system, the detector is a highly chaotic dynamical system. Therefore, the individual binding sites for the atomic field behave like random qubits responding to the intensity of the incident atom field, just as the outer electrons in a photodetector behave like random qubits responding to the intensity of the incident electromagnetic field. The response rate is proportional to the incident energy. Once one of the qubits fires, it uses up the whole energy and matter of the atom field, and the choice has been made. No other qubit can fire, by a most likely existing analogue of M&W's formula (14.8-16).

In quantum field theory, causality is therefore as well-behaved as in any classical stochastic process.

I see. So, you are a follower of Einstein's "God does not play dice" camp. So, you are saying that quantum uncertainties result from classical "hidden variables"? So, if we could entangle all these stochastic chaotic classical processes, we would be able to predict the exact location of the atom deposition or pixel firing in each case. Is it right?

On the other hand, your position is not pure as you mix classical fields and quantum mechanics in your version of quantum field theory. I find it inconsistent. I think you should either deny quantum uncertainty and go all the way with classical hidden variables or accept fundamental unpredictability of nature and then work with Hilbert spaces, wave functions, and all that machinery of quantum mechanics.

Eugene.

 

[harrylin]

[..]
On the other hand, your position is not pure as you mix classical fields and quantum mechanics in your version of quantum field theory. I find it inconsistent. I think you should either deny quantum uncertainty and go all the way with classical hidden variables or accept fundamental unpredictability of nature and then work with Hilbert spaces, wave functions, and all that machinery of quantum mechanics.
Eugene.

Isn't QM a theory that predicts output observables based on input observables? If so, it can make no claim about unmeasurable things like "fundamental unpredictability of nature". It cannot make such philosophical claims. Instead, it can make claims about our limits of prediction of observables, and the machinery of QM serves for quantifying such claims.

 

[meopemuk]

Isn't QM a theory that predicts output observables based on input observables?

No, QM is not that kind of theory. Even if you know your input observables as well as possible QM allows you to predict the output observables only probabilistically.

It is impossible to prepare the initial states of your particles, so that after passing the double-slit setup all of them will land at the same point on the screen. QM cannot tell you where each individual particle will land. QM can only tell you the probability distribution. The exact landing points is a matter of chance. QM does not explain this random behavior of nature. No other theory can explain this.

Eugene.

 

[harrylin]

No, QM is not that kind of theory. Even if you know your input observables as well as possible QM allows you to predict the output observables only probabilistically.

That is what I would call a yes, although you said "no". Or do you claim that probability theory makes no predictions about the results of throwing dice?

[..] QM does not explain this random behavior of nature. [..]

Exactly.

No other theory can explain this.

That claim is not a postulate of QM, or is it?

 

[meopemuk]

Or do you claim that probability theory makes no predictions about the results of throwing dice?

The probability theory predicts that in 50% of cases you'll see head up and in 50% of cases you'll see tail up. Similarly, QM predicts that a polarized photon will pass through the filter in 50% of cases and not pass in other 50% of cases. If you call this "prediction of output observables based on input observables", then yes, we agree.

The important thing is that both theories cannot tell you what will be the outcome in each individual case. So, there are some aspects of nature, which are totally unpredictable. That was my point.

Eugene.

 

[strangerep]

Please remind me what was the field theory explanation for the interference experiment
with atomic deposition? In particular, how the atomic "field" collapses to a specific position
on the substrate? Isn't it the same dreadful Copenhagen collapse?

I hope in this explanation you [Arnold] wouldn't invoke the quantum nature of the
substrate as M&W did in their Chapter 9.

I don't see anything fundamentally wrong with a similar calculation as in M&W ch9.

For the benefit of other readers, I'll quickly review sections 9.2 and 9.3 of Mandel & Wolf:

M&W work in the interaction picture, with the Schroedinger equation

<br /> \partial_t \; |\psi(t)\rangle<br /> ~=~ \frac{1}{i\hbar} \, \hat{H}_I(t) \, |\psi(t)\rangle<br /> ~~~~~~~~(9.2-1)<br />

where |\psi(t)\rangle is the state of an electron in the detector,
and \hat{H}_I(t) is the interaction part of the Hamiltonian.
For such a quantized detector interacting with a classical EM field, the latter is

<br /> \hat{H}_I(t) ~=~ - \frac{e}{m}\, \hat{p}_i(t) \hat{A}^i(r,t) ~.<br /> ~~~~~~~~(9.2-3)<br />

where \hat{p}_i(t) is the electron momentum,
\hat{A}_i(r,t) is the (classical, c-number) EM vector potential,
and the electron is initially in a tightly bound state at position r.

By standard techniques, equation (9.2-1) is formally integrated
iteratively (as usual for Volterra-type integral equations) to obtain:

<br /> |\psi(t)\rangle ~=~ |\psi(t_0)\rangle<br /> ~+~ \frac{1}{i\hbar} \int_{t_0}^t dt_1 \hat{H}_I(t_1) \, |\psi(t_0)\rangle<br /> ~+~ \mbox{(higher order terms in } \hat{H}_I) \dots<br /> ~~~~~~~~(9.2-8)<br />

In the situation being considered, truncation of the higher order terms
is acceptable. The transition probability from an initial state
|\psi(t_0)\rangle to some new state \Phi at time t
which is orthogonal to |\psi(t_0)\rangle is then approximately:

<br /> \left| \mbox{Transition probability} \right|<br /> ~=~ \left| \langle \Phi | \psi(t)\rangle \right|^2<br /> ~=~ \frac{1}{\hbar^2} \left| \int_{t_0}^t dt_1<br /> \langle \Phi | \hat{H}_I(t_1) |\psi(t_0)\rangle \right|^2<br /> ~~~~~~~~(9.2-9)<br />

Since we're working in the interaction picture, and the EM field is
a c-number here, the interaction part of the Hamiltonian at t_1
can be expressed in terms of an arbitrary initial time t_0 as

<br /> \hat{H}_I(t) ~=~ - \frac{e}{m} ~<br /> e^{i H_0 \Delta t/\hbar} \, \hat{p}_i(t_0) \,<br /> e^{-i H_0 \Delta t/\hbar} ~ \hat{A}^i(r,t) <br />

where \Delta t := t_1 - t_0.

With an extra (analytic signal representation) assumption about the
incident EM field, this is sufficient information to evaluate formula
(9.2-9) above, giving the probability that a transition occurs (i.e., a
photoelectron is produced) within a small time interval \Delta t.

In summary, one calculates the probability from an initial product state
consisting of quantized bound electron and incident EM field to a final
state in which the electron has been excited into the conduction band
under the interaction \hat{H}_I(t).

The important point from the above is that similar computations
could be done for other kinds of interactions, involving some field
incident on a many-body plate, with other possibilities for the final
state(s). For atom deposition, we could consider an field of atom type
"I" incident upon a lattice of atoms of type "L", where the final state
consists of a new bound state between a "L" atom and an "I" atom.
All that matters for the purposes of this thread is that a different final
state be possible, resulting from an interaction. Though the numbers
may differ, we still get the result that there's a certain finite transition
probability for an atom deposition at any particular point in a finite time.

The only difference from the photodetection case is that we must
think of the incident atom beam as a field, not a collection of
particles.

In any case, more accurate results are given by also quantizing the incident
field (c.f. M&W ch14) -- we still get atoms being deposited at random
places according to a transition probability per unit time.

Minimal QM (without the extra baggage of a "collapse" interpretation)
thus seems quite adequate.

 

[meopemuk]

Minimal QM (without the extra baggage of a "collapse" interpretation)
thus seems quite adequate.

strangerep,

what do you mean by "Minimal QM (without the extra baggage of a "collapse" interpretation)"? QM cannot be formulated without a collapse in some form. Once you started talking about Hilbert spaces and superpositions of states you have tacitly assumed the presence of a collapse.

The weirdness of the M&W model is that it places the collapse in an unusual place. Namely, in their model the collapse occurs when the photoelectron jumps to a continuous spectrum state. The probability of this jump is described by a square of a certain time-dependent wave function. This is exactly what is called "collapse" in quantum mechanics.

In the usual treatment of the double-slit experiment (see Feynman) the projectile is treated with a QM wave function. This treatment gives a full explanation of the shape of the interference picture and of the collapse effect. There is no need to build a quantum-mechanical model of the screen.

Eugene.

 

[strangerep]

what do you mean by "Minimal QM (without the extra baggage of a "collapse" interpretation)"?

I mean QM with an absolutely minimal amount of interpretation layered on top.
In particular, I have in mind the statistical interpretation as described by
Ballentine in his textbook and papers.

QM cannot be formulated without a collapse in some form. Once you started talking
about Hilbert spaces and superpositions of states you have tacitly assumed the
presence of a collapse.

Ballentine's statistical interpretation shows that this is not correct.

The weirdness of the M&W model is that it places the collapse in an unusual place. Namely, in their model the collapse occurs when the photoelectron jumps to a continuous spectrum state. The probability of this jump is described by a square of a certain time-dependent wave function. This is exactly what is called "collapse" in quantum mechanics.

I no longer see a need to talk about collapse at all, but only probability distributions.

Although the notion of collapse makes some semi-heuristic treatments of
certain situations easier to "explain", it comes at the cost of undesirable
features/paradoxes such as Schroedinger's cat.

In the usual treatment of the double-slit experiment (see Feynman) the projectile is
treated with a QM wave function. This treatment gives a full explanation of
the shape of the interference picture and of the collapse effect. There is no
need to build a quantum-mechanical model of the screen.

If one does utilize a simple quantum-mechanical model of the screen,
one no longer needs to postulate a collapse effect in order to account
for the observed phenomena.

 

[meopemuk]

I no longer see a need to talk about collapse at all, but only probability distributions.

Perhaps I am using a non-standard terminology, but for me "probability distribution" and "collapse" is the same thing. When you are talking about an ensemble you can say "probability distribution". When you are talking about individual event there is a "collapse". I didn't read Ballentine lately, but, as far as I remember, he didn't contradict this view.

Although the notion of collapse makes some semi-heuristic treatments of
certain situations easier to "explain", it comes at the cost of undesirable
features/paradoxes such as Schroedinger's cat.

If you follow my advice not to make statements about non-observable quantum things, then Schroedinger's cat will not pose any paradox.

If one does utilize a simple quantum-mechanical model of the screen,
one no longer needs to postulate a collapse effect in order to account
for the observed phenomena.

When M&W considered the quantum mechanical model of the screen they simply shifted the boundary between the quantum system and the measuring apparatus. Previously (e.g., in Feynman's approach), the screen played the role of the measuring apparatus. Now this role is played by the detector, which counts emitted photo-electrons. So, the collapse is still there, though not mentioned by name. The collapse occurs when the electron detector clicks.

Somewhere along the way M&W forgot that the incident photon should also have a quantum description. They've substituted photon's wave function with a classical field, which mimics quantum interference properties. This is OK as a rough approximation for the full quantum mechanical description of this experiment.

Eugene.

 

[A. Neumaier]

The weirdness of the M&W model is that it places the collapse in an unusual place. Namely, in their model the collapse occurs when the photoelectron jumps to a continuous spectrum state.

There is nothing weird about the M&W setting. It is the _standard_ view in quantum optics. They place the collapse precisely where it belongs: Since it only happens in a measurement, it must be due to the interaction with the measurement device.

The probability of this jump is described by a square of a certain time-dependent wave function. This is exactly what is called "collapse" in quantum mechanics.

M&W assume that an electron is actually ejected according to the probabilities computed by the QM formulas. This is assumed in any interpretation of quantum mechanics, including the most weird ones. In particular also by no-collapse interpretations such as MWI or consistent histories.

In the usual treatment of the double-slit experiment (see Feynman) the projectile is treated with a QM wave function. This treatment gives a full explanation of the shape of the interference picture and of the collapse effect. There is no need to build a quantum-mechanical model of the screen.

The quantum mechanical model is needed to explain the photoelectric effect. It explains why a photographic plate acts as a measurement device while a candle light doesn't.

While the usual treatment explains nothing but simply _postulates_ that hitting the screen produces an event.

 

[A. Neumaier]

\hat{p}_i(t) is the electron momentum,
\hat{A}_i(r,t) is the (classical, c-number) EM vector potential,

and the case of an incident quantum field would be very similar, having here the vector potential operator. To a first approximation, this can be replaced by its expectation value, which is why the treatment as a classical field is often adequate. For a nonclassical incident field, one gets minor corrections; qualitatively nothing changes but quantitatively one has the usual O(hbar) differences.

In summary, one calculates the probability from an initial product state
consisting of quantized bound electron and incident EM field to a final
state in which the electron has been excited into the conduction band
under the interaction \hat{H}_I(t).

The important point from the above is that similar computations
could be done for other kinds of interactions, involving some field
incident on a many-body plate, with other possibilities for the final
state(s). For atom deposition, we could consider an field of atom type
"I" incident upon a lattice of atoms of type "L", where the final state
consists of a new bound state between a "L" atom and an "I" atom.
All that matters for the purposes of this thread is that a different final
state be possible, resulting from an interaction. Though the numbers
may differ, we still get the result that there's a certain finite transition
probability for an atom deposition at any particular point in a finite time.

The only difference from the photodetection case is that we must
think of the incident atom beam as a field, not a collection of
particles.

In any case, more accurate results are given by also quantizing the incident
field (c.f. M&W ch14) -- we still get atoms being deposited at random
places according to a transition probability per unit time.

Minimal QM (without the extra baggage of a "collapse" interpretation)
thus seems quite adequate.

Yes. Thanks for the labor of writing out things explicitly!

 

[A. Neumaier]

The probability theory predicts that in 50% of cases you'll see head up and in 50% of cases you'll see tail up. Similarly, QM predicts that a polarized photon will pass through the filter in 50% of cases and not pass in other 50% of cases. If you call this "prediction of output observables based on input observables", then yes, we agree.

The important thing is that both theories cannot tell you what will be the outcome in each individual case. So, there are some aspects of nature, which are totally unpredictable. That was my point.

And you call both collapse. You are the first person I heard about who postulates the collapse of coins upon throwing them.

 

[A. Neumaier]

Yes, the transition between the random quantum regime and the predictable classical regime occurs gradually as N grows.

How should this come about in your interpretation? For N=1 you can say nothing without measuring it. But N times nothing is still nothing. How do you explain that you can gradually say more and more, until when N reached the size of the pointer of a measuring apparatus you can say definitely which position it has?

There is no unique threshold value. Some systems show quantum behavior even for very large N. The usual examples are superconductors and superfluid helium.

Ah. So you want to say we can't predict anything about superconductors and superfluid helium unless we have measured it? But these are used in industrial practice, where people have to rely on things working very predictably even without constantly measuring them!

Considered as a microscopic system, the detector is a highly chaotic dynamical system. Therefore, the individual binding sites for the atomic field behave like random qubits responding to the intensity of the incident atom field, just as the outer electrons in a photodetector behave like random qubits responding to the intensity of the incident electromagnetic field. The response rate is proportional to the incident energy. Once one of the qubits fires, it uses up the whole energy and matter of the atom field, and the choice has been made. No other qubit can fire, by a most likely existing analogue of M&W's formula (14.8-16).

In quantum field theory, causality is therefore as well-behaved as in any classical stochastic process.

I see. So, you are a follower of Einstein's "God does not play dice" camp. So, you are saying that quantum uncertainties result from classical "hidden variables"?

If you read again what you quoted, you'll see no reference to hidden variables.
The quantum dynamics of the detector becomes, in the approximation of a system of qubits coupled to a semiclassical background formed by the remainder of the photographic plate, a quantum-classical system where the classical part is described by a chaotic
dynamics or - with less resolution - by a stochastic process. (Already few-particle quantum systems become chaotic in such a semiclassical description.)

So, if we could entangle all these stochastic chaotic classical processes, we would be able to predict the exact location of the atom deposition or pixel firing in each case. Is it right?

No, since already the classical model involves approximations, and even tiny errors in the model preclude deterministic predictions for a chaotic process.

On the other hand, your position is not pure as you mix classical fields and quantum mechanics in your version of quantum field theory. I find it inconsistent.

Classical fields are only for convenience, since they let one see better what is going on.
As mentioned in a previous post, quantum corrections are small and do not change the classical picture drastically. As long as the field expectation dominates the field fluctuations, one can safely ignore the quantum aspects.

 

[meopemuk]

The quantum mechanical model is needed to explain the photoelectric effect. It explains why a photographic plate acts as a measurement device while a candle light doesn't.

While the usual treatment explains nothing but simply _postulates_ that hitting the screen produces an event.

Yes, the usual (Feynman) treatment is interested in demonstrating quantum properties of the photon. So, the boundary between the quantum system and the measuring apparatus is drawn in such a way that the photon is on the quantum side and is represented by a wave function. The photographic plate is on the "apparatus" side of the boundary. We are basically assuming that the photographic plate serves as an ideal measuring device for position. So, in our quantum 1-photon theory we represent this ideal measuring device by the position *operator*. (Let us not argue now about the absence of a rigorous photon position operator. I could use electron projectiles in my example to avoid your criticism.) Please note that I am not saying (as many other authors do) that the measuring apparatus is a classical object. In this theory the measuring apparatus has a quantum description, but not in terms of a wave function, but in terms of an Hermitian operator of observable -- in this case the observable of position.

This treatment coupled with the collapse postulate allows us to reproduce all significant features of the single-photon interference: the randomness of photon hits and the accumulation of these hits along the constructive interference spots.


Now, you can say that you are not satisfied with the above idealized treatment of the photographic plate, and you want to include the plate in the quantum-mechanical part of the description. Fine, you are definitely allowed to do that. But this doesn't save you from the necessity to use the collapse postulate. You've simply defined the quantum part of the world differently and thus moved the boundary between the quantum system and the measuring apparatus to a different place. Now, your quantum system includes both the incident photon and the photographic plate with all its atoms. This part of the world is described by a wave function. The measuring apparatus in this case could be a detector catching emitted photo-electrons or your eye's retina that registers sunlight reflected from the photographic plate. Just as before, the collapse occurs at the "boundary" between the physical system and the measuring apparatus. This new measuring apparatus is described by a Hermitian operator.

My point is that no matter how exact you want your quantum description to be, you must always have a boundary between the quantum physical system and the measuring apparatus. There is always a collapse happening at this boundary. This separation of the world in two distinct parts is reflected in the formalism of quantum mechanics quite naturally: the quantum system is described by a state vector or a wave function; the measuring apparatus is described by a Hermitian operator of some observable. You need both these mathematical components in order to have a complete quantum-mechanical theory. It it not possible to describe the whole world by one wave function.

Eugene.

 

[meopemuk]

And you call both collapse. You are the first person I heard about who postulates the collapse of coins upon throwing them.

You've probably misunderstood. harrylin said that QM predict output observables based on input observables. I disagreed by saying that QM prediction is only probabilistic. In this sense, QM is not doing a better job at predictions than classical probability theory with coins. There is one important difference, though. When we through a coin, we can in principle predict the result (head or tail) with 100% certainty. This is very difficult, but possible within classical mechanics. On the other hand, when we let a photon to pass through a polarizer filter, there is absolutely no way to predict the outcome. This is one important difference between quantum and classical probabilities.

I've never said that classical coin experiences any kind of collapse.

Eugene.

 

[meopemuk]

No, since already the classical model involves approximations, and even tiny errors in the model preclude deterministic predictions for a chaotic process.

Could you please be more clear? Are you saying that there exists a distinct classical trajectory behind each (seemingly random) quantum event? So, you are saying that this trajectory involves many degrees of freedom, is chaotic, stochastic, etc. and for this reason we cannot make deterministic predictions. However, if we (humans) had unlimited power to control the errors, to observe and calculate things, then we would be able, in principle, to disentangle this seemingly chaotic process and to predict with 100% certainty the place of photon's landing in the double-slit experiment. Is this what you're actually saying, or I am misinterpreting your words?

Eugene.

 

[meopemuk]

...no-collapse interpretations such as MWI or consistent histories.

We disagree about the meaning of "collapse" in quantum mechanics. I would say that MWI and consistent histories need the same collapse as Copenhagen. These models simply hide the fact that they use the collapse. For example, in MWI the collapse occurs when we choose the "right" universe randomly.

In general, every time we use word "probability" we mean "collapse". The collapse does not happen in classical mechanics, because everything is predictable there and probabilities reduce to either 1 (yes) or 0 (no). If sometimes we use classical probabilities, like in coin tossing, we are simply lazy and don't want to bother to specify all necessary conditions exactly.

So, there can be only two legitimate interpretations of quantum mechanics. One is the "hidden variable" interpretation, which basically says that QM is just a branch of classical mechanics, where everything is deterministic and predictable. No probabilities involved and no collapse. The other interpretation is that quantum events are truly random. Then the collapse is needed. There is no third way.

Eugene.

 

[lightarrow]

Just a question. Let's say that I radiate some form of energy into a group of many people. Sometimes, casually, one of those persons feels "excited" because of that energy and jumps for some seconds. Where is the "collapse"?

 

[QuantumClue]

Just a question. Let's say that I radiate some form of energy into a group of many people. Sometimes, casually, one of those persons feels "excited" because of that energy and jumps for some seconds. Where is the "collapse"?

Lightarrow... do we meet again? Are you the man I knew from the Naked Scientists?

To answer your question, if it was possible for some quantity of energy to be tranferred, rather than simply radiated into the body of another person, then collapses may occur if there are decoherences in the stucture of the other person. These simple decoherences are collapse-like state systems.

It's a bit of an odd question, but if you are the man I remember, then it's not a great surprise :)

 

[A. Neumaier]

Now, your quantum system includes both the incident photon and the photographic plate with all its atoms. This part of the world is described by a wave function. The measuring apparatus in this case

is the photomultiplier or the chemical reaction. Both are dissipative processes that proceed locally, and essentially classically, and need because of the large number of particles involved no special treatment beyond the statistical interpretation (without the explicit collapse).

Of course, you could call any statistical element ''collapse'', but this is not the standard way of using the term. If you use your personal terminology, the only result is that nobody understand you anymore.

 

[A. Neumaier]

When we through a coin, we can in principle predict the result (head or tail) with 100% certainty.

No, we cannot, since throwing a coin is a chaotic process, especially when it first lands on the edge. You need an accuracy for the intial data that one is never able to collect.
Not even in principle can a (classical or quantum) object collect enough information about a coin to exactly determine its state. And already tiny uncertainties magnify immensely.

 

[A. Neumaier]

Could you please be more clear? Are you saying that there exists a distinct classical trajectory behind each (seemingly random) quantum event?

No, but that there is an approximate classical description behind each quantum system, and the latter is chaotic, and sufficient to describe the behavior of a photomultiplier or the approach to chemical equilibrium. Nobody models these in a full quantum mechnaical model, since it is a huge waste of effort.

However, if we (humans) had unlimited power to control the errors, to observe and calculate things

I am interested in explaining the world as it is, not a magic version of it.

 

[A. Neumaier]

We disagree about the meaning of "collapse" in quantum mechanics.

I know. I am using the standard meaning, while you mix it up with the simpler version of Born's rule, which makes no statement about what happens to the state in a measurement.

I would say that MWI and consistent histories need the same collapse as Copenhagen. These models simply hide the fact that they use the collapse.

They claim they don't. That's all I meant when citing them. I agree that they don't succeed in that, but this is a different matter.

In any case, you can't redefine the meaning of the word collapse. It means no more and no less than that one pretends to know after a measurement that the system is in an eigenstate corresponding to the measured eigenvalue.

But this is completely irrelevant for being able to read a pointer on an instrument telling that there was a nonzero current produced by the photomultiplier. This process is so macroscopic that it is universally described in terms of thermodynamics - one gets an expectation value rather than an eigenvalue!

Moreover, the collapse is provably wrong in case a single photon is measured by a photodetector. It is after the measurement not in a position eigenstate but it has no state anymore!