"Filming" a quantum measurement

[Demystifier]

If you mean by "macroscopic pointer" some macroscopic observable (like a pointer position), I agree, because indeed it's an average (over some macroscopic small but microscopic large space-time interval), and there are (quantum as well as thermal) fluctuations around the mean value.

But the average evolves deterministically, due to the Ehrenfest theorem. And thermal fluctuations can in principle be eliminated, by performing the experiment at zero temperature. So basically, the randomness of measurement outcomes arises from quantum fluctuations, I think you would agree with that. My problem is this: How do we know that the effect of these quantum fluctuations is smooth?

 

[vanhees71]

I agree. What's smooth are the probability distributions, whose time evolution on the fundamental level is defined by differential equations (von Neumann equation for the stat. op.).

Of course, if you go to effective descriptions of fluctuations a la Langevin you describe them by stochastic differential equations.

 

[Demystifier]

What's smooth are the probability distributions, whose time evolution on the fundamental level is defined by differential equations (von Neumann equation for the stat. op.).

Yes, but this evolution is also deterministic. I am interested in the random non-deterministic evolution.

Of course, if you go to effective descriptions of fluctuations a la Langevin you describe them by stochastic differential equations.

Fine, this effective description suggests that the random time evolution is smooth. But another effective description based on quantum jumps suggests that it isn't smooth. So it seems that effective descriptions alone cannot decide. Is there a more fundamental argument for the thesis that the random time evolution is smooth?

 

[EPR]

The state is given by the wave function, and this is evolving smoothly with time. What's "random" are the outcome of measurements, not the states!

Do those outcomes arise smoothly or instantaneously? How would they arise smoothly if measuring the position of a particle means that the particle is found at a classically impossible location, e.g. on the other side of a barrier(quantum tunneling).
Does the term smoothly as you are using it include instantaneous jumps?

 

[andrew s 1905]

But the average evolves deterministically, due to the Ehrenfest theorem. And thermal fluctuations can in principle be eliminated, by performing the experiment at zero temperature. So basically, the randomness of measurement outcomes arises from quantum fluctuations, I think you would agree with that. My problem is this: How do we know that the effect of these quantum fluctuations is smooth?

It seems to me that by definition a macroscopic pointer obeys classical physics and hence would have to respond smoothly to any fluctuations.

Regards Andrew

 

[Demystifier]

It seems to me that by definition a macroscopic pointer obeys classical physics and hence would have to respond smoothly to any fluctuations.

What do you mean by "classical"? If it responds to quantum (that is, non-classical) fluctuations, then I wouldn't call it classical.

 

[andrew s 1905]

What do you mean by "classical"? If it responds to quantum (that is, non-classical) fluctuations, then I wouldn't call it classical.

I mean classical in the sense used "in the measuring apparatus is treated classically" i.e. obeys classical mechanics. I thought that was the whole QM measurement issue. By some means the quantum state being measured is converted to a state in a classical macroscopic object, the pointer. Is that not that the only way a "permanent" record can be made?

Regards Andrew
PS My working model is a photo multiplier tube where the photons are detected statistically but thus induces a macroscopic current detected by a galvometer who's pointer moves smoothly.

I apologise if this is all a red herring by I am trying to follow the discussion as best I can.

 

[Demystifier]

I mean classical in the sense used "in the measuring apparatus is treated classically" i.e. obeys classical mechanics. I thought that was the whole QM measurement issue.

But if it's behavior is random, then it doesn't obey classical mechanics. I know that books often carelessly say "the measuring apparatus is treated classically", but strictly speaking it can't be true. If the measurement outcomes are random, then the behavior of the apparatus at least partially must be non-classical.

By some means the quantum state being measured is converted to a state in a classical macroscopic object, the pointer. Is that not that the only way a "permanent" record can be made?

The italics is the crucial issue. By what means precisely? In particular, is it by smooth or non-smooth means?

 

[andrew s 1905]

The italics is the crucial issue. By what means precisely? In particular, is it by smooth or non-smooth means?

Thanks, that takes me back to my original question in post #5.

Given the above discussions and assuming the paper did actually describe a measurement and it indeed showed it was not instantaneous does that at least allow the possibility of some dynamics beyond that modeled by a projection operator?

Clearly, there are differing views so I will study more to better understand the various points of view.

Thanks all for taking my questions seriously and giving considered responses.

Regards Andrew

 

[vanhees71]

Yes, but this evolution is also deterministic. I am interested in the random non-deterministic evolution.Fine, this effective description suggests that the random time evolution is smooth. But another effective description based on quantum jumps suggests that it isn't smooth. So it seems that effective descriptions alone cannot decide. Is there a more fundamental argument for the thesis that the random time evolution is smooth?

There are no quantum jumps, at least not in standard quantum mechanics. It is an old ad-hoc description of the emission and absorption of photons in the Bohr atom model by electrons jumping between different allowed orbits. Today we describe it dynamically, often sufficiently in first-order perturbation theory with an external classical em. field (semi-classical approximation), which describes of course only induced emission and absorption or the quanum em. field, which includes spontaneous emission too.

 

[vanhees71]

Do those outcomes arise smoothly or instantaneously? How would they arise smoothly if measuring the position of a particle means that the particle is found at a classically impossible location, e.g. on the other side of a barrier(quantum tunneling).
Does the term smoothly as you are using it include instantaneous jumps?

Also tunneling takes of course some time. It's not easy to define the "tunneling time" in a consistent way, and I'm not sure, whether there's a definition to which all quantum physicists agree.

An instantaneous jump is of course the opposite of smooth transitions, and according to standard quantum (field) theory there are no instantaneous jumps.

 

[EPR]

Also tunneling takes of course some time. It's not easy to define the "tunneling time" in a consistent way, and I'm not sure, whether there's a definition to which all quantum physicists agree.

An instantaneous jump is of course the opposite of smooth transitions, and according to standard quantum (field) theory there are no instantaneous jumps.

Even on the double slit detection screen? The collapse happens smoothly and takes some time?
I haven't read about that. Has this time been measured?

Edit: there was this Bulgarian guy who worked on this field. It seems you are right. https://www.quantamagazine.org/quantum-leaps-long-assumed-to-be-instantaneous-take-time-20190605/

 

[Demystifier]

It's not easy to define the "tunneling time" in a consistent way, and I'm not sure, whether there's a definition to which all quantum physicists agree.

There isn't. Anyway, my definition (which I think is consistent) is in https://arxiv.org/abs/2010.07575

 

[Demystifier]

Given the above discussions and assuming the paper did actually describe a measurement and it indeed showed it was not instantaneous does that at least allow the possibility of some dynamics beyond that modeled by a projection operator?

The paper analyses how the probability distribution changes with time. Probability distribution is measured on a large ensemble of events. It says nothing about time evolution of individual events. Theoretically, the time evolution of probability distribution is described by a deterministic equation, so there is nothing surprising in the fact that it is smooth. But randomnes is a property of single events. The experiment says nothing about the question whether the individual random events are smooth or involve instantaneous jumps.

 

[PeterDonis]

The 422 nm laser pulse is a measurement.

No, it isn't. As I've already said, the actual measurement is the detection of the fluorescence photons. The paper even says so. I know the paper calls the 422 nm laser pulse a "measurement", but that makes no sense because it goes on to say that this "measurement" happens by measuring the fluorescence photons.

You even acknowledge that yourself:

If you want to verify that you really have prepared a certain quantum state you have to measure something (here the fluorescence photons)

Yes, exactly: the measurement is of the fluorescence photons.

 

[vanhees71]

This is again a semantics discussion. You can also call the 422 nm laser pulse a preparation procedure and only the detection of the fluroescence photons a measurement. It doesn't change the fact that the laser pulse realizes (with larger intensitities of the laser) a projection, which is often called a von Neumann filter measurement in the literature.

 

[PeterDonis]

assuming the paper did actually describe a measurement

The question, as I have been saying, is what measurement the paper describes. The actual measurement in the experiment is the detection of fluorescence photons, and the paper does not describe that at all--it just says it happens and statistics on the detections are collected and then math is done to reconstruct the state that was prepared by the experimental process. Nowhere does the paper describe or explain the detection of fluorescence photons in terms of any continous, non-random process.

 

[PeterDonis]

the laser pulse realizes (with larger intensitities of the laser) a projection

What projection? Please point out the specific equation in the paper that you are referring to.

 

[andrew s 1905]

The question, as I have been saying, is what measurement the paper describes. The actual measurement in the experiment is the detection of fluorescence photons, and the paper does not describe that at all--it just says it happens and statistics on the detections are collected and then math is done to reconstruct the state that was prepared by the experimental process. Nowhere does the paper describe or explain the detection of fluorescence photons in terms of any continous, non-random process.

I realize and appreciate what you are saying. You have a definite use of the term measurement but in the paper they define what they mean by an "Ideal Quantum Measurement" which seems acceptable to the referees and Physical Review Letters but is not to you.

I am in no position the judge the issue I was just reflecting the disagreement and trying to be fair to you in acknowledging your doubt.

Regards Andrew

 

[vanhees71]

Well, do you describe mathematically, how you read with your ey

What projection? Please point out the specific equation in the paper that you are referring to.

In the paragraph right at the page break between pp 2-3. A bit later in the paper Eq. (7) shows that for $t \rightarrow \infty$ you realize the projection (in the usual literature it's called a measurement; I'm also not happy with that formulation, and I'd rather call it a preparation procedure).

 

[EPR]

What is a measurement? Is every interaction a measurement?

No one can tell.

 

[PeterDonis]

In the paragraph right at the page break between pp 2-3.

And in that paragraph, it says "if at least one photon is scattered into the environment, then...the coupling to the photon corresponds to the measurement of the qutrit projection..."

The photon being "scattered into the environment" means a fluorescence photon is detected. So what they are saying, though they are saying it in rather roundabout language, is that the detection of the fluorescence photon is the actual measurement. Or, more precisely, if such a photon is detected, then we can deduce that the atom is in the state $|0\rangle$. If such a photon was not detected, we cannot deduce anything about the state of the atom.

None of this is saying that the previous application of the 422 nm laser pulse is the actual measurement. It's not even a preparation procedure because applying the pulse does not guarantee that the atom is in a particular state. So I still think that the paper's description of the 422 nm laser pulse as a "measurement process" is misleading.

 

[PeterDonis]

A bit later in the paper Eq. (7) shows that for $t \rightarrow \infty$ you realize the projection

There is no $t \rightarrow \infty$. $t$ in that equation is a constant, the length of the 422 nm laser pulse, fixed by the experimental procedure; its value, as noted in the text right after that equation, is 1 microsecond.

 

[vanhees71]

OK, it's a fight about words and slang in different scientific communities. I'd also say the actual measurement is indeed the detection of the fluorescence photon.

Yes, it's not $t \rightarrow \infty$, and indeed with fixed $t$ you don't get an exact projection, but that's the point: It takes time to "measure", and increasing $\Omega$ (via the intensity of the laser) you get closer and closer to the ideal projection. That's what they want to demonstrate, and in my opinion they have done so. They use the fact that what has to get large is $\mathrm{Re} [\Omega^2/(\Gamma+4 \mathrm{i} \Delta)] t$ to get close to the ideal projective preparation.

It's not surprising after 95 years of modern quantum mechanics being successul but nice to have been measured and demonstrated.

 

[PeterDonis]

It takes time to "measure"

But varying the power of the 422 nm laser pulse does not vary the "time to measure". It varies the probability that a fluorescence photon will be detected, i.e., that a "measurement" will be made at all. The actual "time to measure" is determined by the length and power of the fluorescence detection step, which, as far as I can tell from the paper, is not varied at all from run to run.

increasing $\Omega$ (via the intensity of the laser) you get closer and closer to the ideal projection. That's what they want to demonstrate, and in my opinion they have done so.

I have no issue with saying that they have shown that varying the intensity of the laser varies the probability that a fluorescence photon will be detected ("closer and closer to the ideal projection" means that probability gets closer and closer to 1), which in turn varies the probability that the quantum coherence between the $|0\rangle$ state and the other atom states $|1\rangle$ and $|2\rangle$ is destroyed.

I just don't think that corresponds to "filming a quantum measurement in progress". If the actual measurement is the detection of the fluorescence photon (and you say you agree with that), that process is not being "filmed" at all.

 

[vanhees71]

No. They say clearly what was filmed in the paper.

It's not about how fluorescence works or is mathematically described. You are also not interested in the specific mathematical description of the inner workings of your digital voltmeter when measuring a voltage.

 

[Demystifier]

There are no quantum jumps, at least not in standard quantum mechanics. It is an old ad-hoc description of the emission and absorption of photons in the Bohr atom model by electrons jumping between different allowed orbits. Today we describe it dynamically, often sufficiently in first-order perturbation theory with an external classical em. field (semi-classical approximation), which describes of course only induced emission and absorption or the quanum em. field, which includes spontaneous emission too.

As @samalkhaiat recently said in another thread, it's a mess so let me clarify this once and for all.

In QM it's essential to distinguish the ensemble level from the individual level.

In a nutshell, the situation in standard QM can be concisely summarized as follows:

Time evolution at the ensemble level:
- Is it deterministic or random? Deterministic.
- Is it continuous or jumping? Continuous.

Time evolution at the individual level:
- Is it deterministic or random? Random.
- Is it continuous or jumping? Agnostic (minimal standard QM does not specify).

What about other (non-standard) interpretations of QM?
- On the ensemble level, they all agree with the above.
- On the individual level, many of them disagree with the above.

 

[Demystifier]

Is every interaction a measurement?

No one can tell.

I can, no it isn't.

 

[PeterDonis]

They say clearly what was filmed in the paper.

I know what they say in the paper. I am simply saying that I think what they say in the paper is misleading, because when you look at what is actually being done, what is being "filmed", which, as you say, they describe in the paper, quite apart from just using the word "measurement", is not the actual measurement (the detection of the fluorescence photons); it is something else, that they call a "measurement process" in the paper, but I've already explained why I think that's misleading as well.

 

[PeterDonis]

You are also not interested in the specific mathematical description of the inner workings of your digital voltmeter when measuring a voltage.

Measuring a voltage is a classical process so it is a bad example.

If I am doing a double slit experiment with a photon, I don't call the effect of the slits on the photon a "measurement". The measurement is when the photon hits the detector screen and makes a dot. Nobody has a specific mathematical description of this either, the mathematical description is all about the effect of the slits, but that doesn't mean the effect of the slits on the photon is the measurement.