I Who is Ballentine and why is he important in the world of quantum mechanics?

[vanhees71]

It depends on which observable you describe. E.g., if you deal with single unpolarized photons and measure the polarization, i.e., their helicity (to have a concrete "observable") you do not get the expectation value, which is of course 0 in this case, but either +1 or -1 (each with 50% probability). An expectation value represents a property of the ensemble/statistical sample not of the single member of the ensemble.

 

[A. Neumaier]

It depends on which observable you describe. E.g., if you deal with single unpolarized photons and measure the polarization,

In this thread we measure fields, not the polarization of a single particle.

The fields are the functions of E(x) and B(x) and include the polarization tensor, which is quadratic in these. Thus what we measure is a smeared 2-point function on a screen, which we get after sufficiently long exposure to the field in the beam, characterized by a thermal coherent state of the e/m field.

 

[gentzen]

In this thread we measure fields, not the polarization of a single particle.

vanhees71 does not think of photons as particles in your sense. A single particle here just means a single excitation of the photon field. I don't like the word particle in that sense either, but that is just how it is.

You also know some of those experiments were single photons or correlated pairs of photons are generated, and then measured, including correlations in their polarization.

 

[A. Neumaier]

vanhees71 does not think of photons as particles in your sense. A single particle here just means a single excitation of the photon field. I don't like the word particle in that sense either, but that is just how it is.

Photon particles are (both in the sense of vanhees71 and in my sense) very special states of the quantum field along a beam, namely sequences of 1-photon Fock states, or in the entangled case of 2-photon Fock states generated by parametric down-conversion, for use in Aspect type experiments).

You also know some of those experiments were single photons or correlated pairs of photons are generated, and then measured, including correlations in their polarization.

Nevertheless a detector event at a photosensitive screen (or a pair of them in Aspect-type experiments) is not at all a measurement of the electromagnetic field at the screen(s). What would be the measured value of E(x) or B(x) at the screen?

 

[vanhees71]

Of course it is a measurement of the electromagnetic field. What else do you think you measure with a photoplate exposed by some electromagnetic radiation? You can nowadays prepare true single-photon states and observe the "detection-probability distribution" building up repeating the single-photon experiment again and again to build your "statical sample" (aka the "ensemble" in normal physics lingo).

It's also clear that a photon detector measures "smeared" correlation functions since it necessarily has a finite position resolution (e.g., finite extensions of pixels on a silicon detector) and also theoretically realistic observables are always smeared. Distributions/generalized functions do not represent "true states", as already well-known from introductory QM.

 

[PeterDonis]

@strangerep if you want to continue the MOND subthread it should be moved to its own thread in the appropriate forum.

 

[gentzen]

Photon particles are (both in the sense of vanhees71 and in my sense) very special states of the quantum field along a beam, namely sequences of 1-photon Fock states, or in the entangled case of 2-photon Fock states generated by parametric down-conversion, for use in Aspect type experiments).

So your point is that those sequences of 1-photon Fock states or entangled 2-photon Fock states are not beables in the thermal interpretation, hence vanhees71's point does not apply? I tentatively concluded this from your answer, together with your earlier answers to vanhees71, like:

It is about measuring fields, not particles - cf. the subject of the thread.

In the thermal interpretation, particles are not beables; only their probability distributions are. For this is what objectively distinguishes particles prepared in different states; see your answer and my reply here.

Nevertheless a detector event at a photosensitive screen (or a pair of them in Aspect-type experiments) is not at all a measurement of the electromagnetic field at the screen(s). What would be the measured value of E(x) or B(x) at the screen?

Fine. But ... I can't really blame vanhees71 in this specific case for not getting your point. If you want to distinguish between fields and detector events, you have to make that clear. Or rather, you have to make it clearer what you mean when you talk of fields. Apparently some measurable effects occuring in the context of fields in the QFT sense are not included in your notion of measuring fields.

 

[A. Neumaier]

Of course it is a measurement of the electromagnetic field.

If it is, what are the values of E(x) and B(x) obtained through the measurement?

What else do you think you measure with a photoplate exposed by some electromagnetic radiation?

One measures the response of the detector to the field. One needs to use theory of the detector to know how to translate this into a statement about the electric field. The theory tells you the relation after a sufficiently long exposure to a stationary field, but not the relation about the exposure to a single 1-photon state.

It's also clear that a photon detector measures "smeared" correlation functions

What is the value of the smeared correlation function known once the photon has left its mark? How to get a whole function from a single mark???

 

[vanhees71]

The electromagnetic field is operationally defined by its actions on charged matter already in classical electrodynamics.

The photoplate after repeating a single-photon detection experiment many times depicts the energy density of the em. field (of course, as you stress yourself all the time, "coarse grained" due to finite resolution).

A correlation function is a statistical quantity and cannot be empirically studied with just a single experiment. One photon leaves one dot at a random spot, not a distribution.

 

[A. Neumaier]

So your point is that those sequences of 1-photon Fock states or entangled 2-photon Fock states

States of the field are beables, but not the traveling photons.

If you want to distinguish between fields and detector events, you have to make that clear.

I had clearly emphasized it in my answer.

Or rather, you have to make it clearer what you mean when you talk of fields.

In our case, the fields are the electric field E(x) and the magnetic field B(x).
They are spread out over the lab where the experiment is performed and E(x) has a nonnegligble intensity in the beam where the alleged photons are supposed to travel.

Apparently some measurable effects occuring in the context of fields in the QFT sense are not included in your notion of measuring fields.

Yes. Not every measurable effect is a measurement of its cause. If rain caused your trousers to be wet, did you measure the rain?

Measuring the electromagnetic field in some region means getting approximate values for E(x) and B(x) in that region. Just like measuring the trajectory of a classical particle in some time interval means getting approximate values for x(t) during that time.

 

[A. Neumaier]

The photoplate after repeating a single-photon detection experiment many times depicts the energy density of the em. field (of course, as you stress yourself all the time, "coarse grained" due to finite resolution).

Yes. Thus scanning the plate after long exposure is indeed a measurement of the coarse-grained field intensity.

A correlation function is a statistical quantity and cannot be empirically studied with just a single experiment. One photon leaves one dot at a random spot, not a distribution.

So the observation of the dot is not a measurement of the field or its correlation function.

 

[vanhees71]

I think, we are splitting hairs here. Of course is the detection of a single photon a measurement. How else would you call it?

 

[A. Neumaier]

I think, we are splitting hairs here.

No, we are at the very basis of our eternal differences!

Of course is the detection of a single photon a measurement. How else would you call it?

It might be called a random position measurement of the photon.

But it is certainly not a measurement of a field. The latter would produce approximate values for the field.

 

[PeterDonis]

Of course is the detection of a single photon a measurement

But it's not a measurement of the field, since, as you have said, such a measurement requires a large number of dots so you can compute statistics from them.

A "detection of a single photon" is a measurement of where on the detector the single photon hit. (Even that requires theoretical interpretation based on knowledge of the detector, as @A. Neumaier has pointed out.)

 

[Peter Morgan]

No, we are at the very basis of our eternal differences!

It might be called a random position measurement of the photon.

But it is certainly not a measurement of a field. The latter would produce approximate values for the field.

I've thought of this in terms of the moment when an analog signal out of some device is converted to a digital form that we then record. The output current from an Avalanche PhotoDiode or similar device is noisy but near zero, then it is noisy but near some value that is distinctly different from zero, which we commonly say is because of an "avalanche" within the device. Discriminating hardware typically monitors the current and decides what time to record as the time at which the output current became non-zero, an event. Either such hardware is from a trusted manufacturer, off a slightly less trusted storeroom shelf, or else an experimenter has designed and built it. In any case, the experimenter will have to verify that the hardware responds appropriately to the signal it receives, and perhaps debug its operation, presumably as shown on a good oscilloscope that can also measure the current from the device at GHz rates.

The output current at the input to the hardware discriminator is a proxy for the electromagnetic field in a small region of the wire where it connects to the discriminating hardware. Loosely, that's a smeared measurement of E(x), not in the original device but at the connection to the discriminating hardware. That's a proxy for what is happening within the APD. The precise timing of recorded events depends on the noisy EM field environment that surrounds the APD, which is in turn determined by whatever other apparatus has been assembled around it. If we change the apparatus around the APD in any way, the statistics of events in the APD will change, although the response to a given modulation might be small enough that it would take months of data collection to be sure any change at all was made.

From a noisy EM perspective such as this, we don't suppose that every event in an APD is caused by one particle. Instead, the statistics of the recorded events allow us to infer properties of the whole apparatus. We have effectively replaced the "'particle and its properties' metaphysics" by a "'prepared noisy EM field and the events it causes in devices that we designed so that events would happen' metaphysics". I like to say that we don't use rocks as measurement devices in physics experiments, we use materials and supporting hardware that two centuries or more of experience have found to be fit for the purpose of providing us with events that we can record. Photographic plates were a good beginning, but we've come a long way since.

I've seen something like this all too many times, but the example I always use as an illustration is Gregor Weihs's Bell-violating experiment from the 1990s because I'm most familiar with it and because his schematic is significantly simpler and clearer than one usually sees for more modern experiments:

Obviously the output from an APD doesn't look much like the purely notional plot at the bottom left, which is directly below what I have called the discriminating hardware that is attached to the "Silicon Avalanche Diode" by a signal line, but certainly there has to be some feature of the signal on the signal line that the discriminating hardware can identify so that it decides to put a time into the "Time-Tag List".
With apologies that I'm no kind of experimentalist and not much of a theorist to be saying all this. This kind of thinking works for me, for what it's worth.

 

[Fra]

I interpret these questions, and the "construction" of complex observables from elementary inputs in a context, where the observer/agent/physicists just processes and categorizis inputs, where the representation can also be changed, for example by creating higher phase spaces and embedding dimensions. All this is all internal to the observer, postprocessing that per see has nothing todo with "exernal reality". So in a way I think all "measurements" may well be hiearchial, and it's what I would expect from a unification approach anyway.

It's tempting to ask: Can we from a sequence of "one-type-clicks" (say quanta of a "unificatonfield") find patterns, create another "layers" with the illusion of more "complex/composite clicks", time and space? to the point where in the other hand, we have the standard model phenomenology? Where other fields are defind in terms of postprocessing the clicks from our uberfield counter?

I liked this old but suggestive mind-challenge of how to create dimensions from almost nothing iterating processing in layers https://math.ucr.edu/home/baez/nth_quantization.html. i think this is even key to grasp what a quantum field is, or can be at least.

This is I think the perspective linking registering a click event to thinking "we measured the field".

How to get a whole function from a single mark???

The same way you get (or don't get) a whole function from n marks?

/Fredrik

 

[A. Neumaier]

The output current at the input to the hardware discriminator is a proxy for the electromagnetic field in a small region of the wire where it connects to the discriminating hardware. Loosely, that's a smeared measurement of E(x), not in the original device but at the connection to the discriminating hardware.

It is a measurement of the current in thewire, not of the electromagnetic field that caused the ejection of an electron. That's quite different!

The same way you get (or don't get) a whole function from n marks?

But for n=1 (as in the case under discussion) you don't get a function but only a point.

 

[Fra]

But for n=1 (as in the case under discussion) you don't get a function but only a point.

Yes, would you get a "function" for n=100? so the find the "best match" of a function from that one point, perhaps it in practice is some dirc or gaussian, sharply peaking around that point, with a width corresponding to the "size" of the point. The size of a "real point", would be like the size of hte pixel or whatever the sensor element is like.

Indeed such an approximation is terribly bad. But it's still an approximation, and one can argue, the best one possible, given only one sample? What I am getting at is that I think the distinction is not a conceptually distinct one, but a scale when the uncertainty is "small enough".

/Fredrik

 

[Peter Morgan]

It is a measurement of the current in thewire, not of the electromagnetic field that caused the ejection of an electron. That's quite different!

It is different, but it can at least be thought of as the most direct record we have of a measurement of the electromagnetic field. In particular, such measurements are —I think by construction— the only recorded measurement results. From the totality of all such actually recorded measurement results, we infer what we expect we would have recorded as the results of other measurements.
For some physicists, and certainly for some philosophers, this is too empiricist, but I don't claim that those inferences are empty, only that they are of a somewhat different kind than the actually recorded measurement results that are stored on hard drives contemporaneously with the experiment. To be sure, there is a computational and hardware path (for which the finest details are hopefully well-documented) to be considered when trying to understand those actually recorded measurement results as a foundation for inferences about what happened in the rest of the experiment, so that we can think of all measurement results as inferred if we think in a wide enough sense, but it feels as if there are different levels of directness that are substantive enough for it to be worthwhile to keep them in mind.

 

[A. Neumaier]

It is different, but it can at least be thought of as the most direct record we have of a measurement of the electromagnetic field. In particular, such measurements are —I think by construction— the only recorded measurement results.

But here what is measured is inside the measurement apparatus. However, a measurement apparatus is designed to measure something outside it, otherwise
its purpose

From the totality of all such actually recorded measurement results, we infer what we expect we would have recorded as the results of other measurements.

vanhees71 claimed that the apparatus measures the electic field intensity impinging from a source to the screen. Thus we should be able to infer approximate values of the electic field intensity. But this is not the case. So whatever is measured in (inferred from) a single detector event, it is not a measurement of the electric field intensity in the beam.

 

[A. Neumaier]

Indeed such an approximation is terribly bad.

Yes. I am approximately the richest man in the world! And at the same time the poorest!

 

[Fra]

Yes. I am approximately the richest man in the world! And at the same time the poorest!

Makes perfect sense!

/Fredrik

 

[A. Neumaier]

I'm ok with basic Lie algebra.

You might be interesting in looking at my online book

• Arnold Neumaier and Dennis Westra, Classical and Quantum Mechanics via Lie algebras, 2008, 2011.

 

[PeterDonis]

@strangerep if you want to continue the MOND subthread it should be moved to its own thread in the appropriate forum.

Moderator's note: The MOND subthread has now been spun off to a new thread in the BTSM forum:

https://www.physicsforums.com/threads/mond-and-the-data.1057558/

 

[vanhees71]

No, we are at the very basis of our eternal differences!

It might be called a random position measurement of the photon.

But it is certainly not a measurement of a field. The latter would produce approximate values for the field.

A photon has no position to begin with. A photon is a one-quantum Fock state of the electromagnetic field. There is a probability distribution for detecting it at a given place and a given time (with finite resolution of both of course). The probability is given by the (normalized) energy density of the electromagnetic field, which results from the analysis of the photoelectric effect on the detector material in the standard dipole approximation. I thought that's your view: the observables are given by correlators of local observable-operators, and indeed the energy density of the em. field is such an observable.

What else should be a measurement of "a field" than that? Also in classical electrodynamics, what's observable of the field are precisely such things as the "intensity", which also classically is given by the energy density.

That's also how the electromagnetic field is operationally defined, i.e., by its actions on charged matter.

 

[A. Neumaier]

A photon has no position to begin with. A photon is a one-quantum Fock state of the electromagnetic field. There is a probability distribution for detecting it at a given place and a given time (with finite resolution of both of course).

This is commonly called an (approximate) position measurement. It measures the transverse position orthogonal to the beam direction. This is represented by a well-defined operator with two commuting components.

The probability is given by the (normalized) energy density of the electromagnetic field,

Measuring the probability would therefore be a measurement of the field intensity. But from a single photon one cannot get a probablilty, hence no measurement of the field.

I thought that's your view: the observables are given by correlators of local observable-operators, and indeed the energy density of the em. field is such an observable.

Yes, the observables are the correlation functions but:

A correlation function is a statistical quantity and cannot be empirically studied with just a single experiment. One photon leaves one dot at a random spot, not a distribution.

Thus the observation of a single photon (which is what we were discussing) impact does not measure these observables.

What else should be a measurement of "a field" than that?

Anything that results in an approximate value of the smeared field at some point.

Also in classical electrodynamics, what's observable of the field are precisely such things as the "intensity", which also classically is given by the energy density.

The classical intensity is a field, and observing it at x gives the value of the field averaged near x. The same holds in the quantum case with my definition of measurement, but not with your contrived one.

 

[Fra]

Thus the observation of a single photon (which is what we were discussing) impact does not measure these observables.

What if we view see the general pattern here as similar to a "deep learning" methods with layers of abstractions, where we are here talking about "determining/mesure one abstraction" in a higher layer based on data flowing from the lower levels. Indeed the higher abstractions are driven by data, and single samples will not drive the process. And while it is true that the confidence in higher level constructs, depends on, and requires a certain "amount" of data from lower levels, the detection of lower level "events" are still the building blocks of the "measurement process"?

The association I can't help making is that from the "quantization step", we can see define "field" as a higher layer constructs, defined in terms of processing lower layers (in it's simplest form it can be average formation, but it can also be less trivial transformations) and while it is true that the confidence in higher level constructs, depends on, and requires a certain "amount" of data from lower levels. It seems that the "mesaurement" of ANYTHING, must necessarily start with detection of some elementary events. The question is, how many data points do we need to motivate an given construct? This would also make such higher constructed contextual as expected, as they are supported by the available observations.

It seems to me this can be made a deep question, what is a field, what is an observable...how are they defined conceptaully and operationally, rather than merely mathematically (which as discussed is in part fiction)?

/Fredrik

 

[vanhees71]

This is commonly called an (approximate) position measurement. It measures the transverse position orthogonal to the beam direction. This is represented by a well-defined operator with two commuting components.

The position is the position of the detector. There's no position operator for the photon. In relativistic QFT time and position (four-vector) components are parameters with precisely this meaning.

Measuring the probability would therefore be a measurement of the field intensity. But from a single photon one cannot get a probablilty, hence no measurement of the field.

As in any QT the state refers to probabilistic properties of ensembles, of course.

Yes, the observables are the correlation functions but:

Thus the observation of a single photon (which is what we were discussing) impact does not measure these observables.

A photodetector registers a single photon at a given space-time point (within a finite resolution). That's a measurement par excellance as it is defined in standard QT.

Anything that results in an approximate value of the smeared field at some point.

This can of course only be achieved by measuring an ensemble (or rather a "statistical sample") of equally prepared systems.

The classical intensity is a field, and observing it at x gives the value of the field averaged near x. The same holds in the quantum case with my definition of measurement, but not with your contrived one.

I don't see, where we differ in this respect: the expecation value of a local observable like the electromagnetic field $(\vec{E}(x),\vec{B}(x)$ can of course again only be measured on an ensemble not a single system, and the expectation value as only one of the moments of the corresponding probability distribution only describes a small aspect of the state.

 

[Fra]

I don't see, where we differ in this respect: the expecation value of a local observable like the electromagnetic field $(\vec{E}(x),\vec{B}(x)$ can of course again only be measured on an ensemble not a single system, and the expectation value as only one of the moments of the corresponding probability distribution only describes a small aspect of the state.

In your view the "statistical samples" approximate the "ensemble". But the ensemble is a fiction in the sense of requiring infinite repeats etc. This is what is the "problem".

If I understand Neumaier, he thinks the "statistical sample" approximates not some fictional ensemble but the value of an actual "real" field (that is defined by accounting for ALL the actual varialbes the in universe, even those the local observer isn't informed about).

So I think the disagreemen it more, WHAT does our "statistical sample" approximates?

/Fredrik

 

[vanhees71]

There is no problem or if there is a problem it's a problem of all kinds of measurement also within classical physics. You can always only prepare a finite number of systems and measure them. In general also both the preparation and the measurement are only approximate etc. etc. All this is covered by the standard procedures of the experimentalists, i.e., you have to do a careful analysis of the statistical and systematic errors in an experiment.

A statistical sample approximates an ensemble. Since $\vec{E}$ and $\vec{B}$ don't commute and since there possible values are continuous, they never can be precisely determined. It's as with position and momentum in non-relativistic physics.