What makes measurement possible in the physical world?

[ZapperZ]

Huh? It's simple HUP. When particles have a defined location, they don't have a defined momentum... all that good stuff. I suppose I should clarify spin in a certain direction rather than just spin in general, but that's beside the point. Unless you are arguing that particles always have a defined spin in every direction, I don't see how you could disagree with the statement that some particles have undefined spin (in a given direction).

See http://arxiv.org/abs/quant-ph/0110102 for some published rigor on complementarity. Also http://arxiv.org/abs/quant-ph/9905042. As for particles in QFT: http://arxiv.org/abs/quant-ph/0103041. I don't claim to be a QFT expert, but I thought we were pretty set on HUP when it comes to particle properties, no? If it's about "essential properties," fine, that's a philosophical concept that my claim relies on. Hence the "so the argument goes" above.

I'd be happy to follow to the QM forum if you'd care to explain where I'm wrong here.

This is a common misunderstanding of the HUP.

If I have ONE particle, and I measure it's position to the precision that's allowed by my instrument, I can then determine its momentum with arbitrary precision, again, that's allowed by my instrument. The accuracy of each of those measurement, one after the other, has nothing to do with the HUP. This is NOT the HUP.

I've described an example of this using the single-slit example a few times. The HUP says nothing about the accuracy of one measurement of position and one measurement of momentum. The uncertainty in each of those measurement is the instrumentation uncertainty, not the HUP. So to say that "... particles have a defined location, they don't have a defined momentum... " is incorrect. Each of those particle can have well defined position and well-defined momentum. It is the spread in the values of the positions and the values of the momentum, measured under identical conditions, that is governed by the HUP. If the spread in the values of the position is small, then the spread in the values of the momentum will be big. This means that your ability to predict what the next value of the momentum is is not very accurate.

One needs to carefully look at the mathematical expression for the HUP. This is not some handwaving argument. It is deeply rooted (as is with the rest of physics) in some underlying mathematical description. And if one does that, one can see the statistical nature of the HUP.

Zz.

 

[ZapperZ]

Why does every post in this thread address theory instead of empirical methodology? Why can't people just explain how their observables are empirically observed and measured?

My avatar shows where electrons hit a CCD screen. Due to the nature of the instrument (a hemispherical electron analyzer), the vertical axis corresponds to the energy that that electron has (very much like a mass spectrometer), while the horizontal axis is the momentum along a particular direction of the analyzer corresponding to the direction of the slit.

The justification for being able to designate those position are covered in any text on angle-resolved photoemission spectroscopy. In other words, these are extensively covered and well-established to allow us to deduce those "spots" on the screen to correspond to a particular set of observables, in this case, E and k.

It is strange that this is in the Philosophy forum.

Zz.

 

[brainstorm]

If I have ONE particle, and I measure it's position to the precision that's allowed by my instrument, I can then determine its momentum with arbitrary precision, again, that's allowed by my instrument.

How does the instrument measure position and momentum exactly?

 

[brainstorm]

The justification for being able to designate those position are covered in any text on angle-resolved photoemission spectroscopy. In other words, these are extensively covered and well-established to allow us to deduce those "spots" on the screen to correspond to a particular set of observables, in this case, E and k.

Why do you cite a text instead of just saying how it works?

 

[humanino]

How does the instrument measure position and momentum exactly?

I have already said how one can measure the momentum of a charged particle, using magnetic fields and trackers.

Take a photon now. An optical lens will select for a given deviation a given momentum. The position can simply be registered by a photographic plate. The slit or simply a punched hole will select a position without destroying the photon.

Alternatively, one could measure energy and position for an electron or a photon using a calorimeter. A calorimeter is simply a segmented stack of individual cells, each of which absorbing a certain amount of energy in the electromagnetic shower, usually recorded by collecting the amount of light out of the material. Typically for instance, one could use crystals. Alternatively one could use a stack of heavy material, such a lead, and scintillators, such as plastic. Then we call it a sandwich calorimeter.

Your question is very vague.

 

[brainstorm]

This seems to be getting closer, but it's still not at the level of the instrument's methodology and how one observation is linked to another to relate the unit to what is measured.

I have already said how one can measure the momentum of a charged particle, using magnetic fields and trackers.

You did? When?

Take a photon now. An optical lens will select for a given deviation a given momentum.

How? Because momentum determines the angle/path the light takes through the lens? Many things are being left implicit.

The position can simply be registered by a photographic plate. The slit or simply a punched hole will select a position without destroying the photon.

For what purpose? What is being measured exactly this way?

Alternatively, one could measure energy and position for an electron or a photon using a calorimeter. A calorimeter is simply a segmented stack of individual cells, each of which absorbing a certain amount of energy in the electromagnetic shower, usually recorded by collecting the amount of light out of the material.

How is an amount of light collected out of a material? Is this a measurement of units of a particular chemical change that represents a given amount of light energy? What is light affecting exactly in these "cells?"

Typically for instance, one could use crystals. Alternatively one could use a stack of heavy material, such a lead, and scintillators, such as plastic. Then we call it a sandwich calorimeter.

What would change in each or any of these materials that could be measured in terms of units?

Your question is very vague.

My question? Have you been reading how all the posts in this thread avoid actually describing the logic behind measurement by spouting off about the complexities?

 

[apeiron]

So to answer why is anything measurable? I would refer to discussions of why is there something rather than nothing? I really think they reduce to the same question of why observables exist, or rather, why anything is observable. There is a technical difference on the matter of unobservable properties, but unobservable properties aren't what anyone is asking about when they ask why there's something rather than nothing. That technicality isn't a concern for any of the arguments.

Unless, of course, your issue is with the holism of scientific theories and properties. Then see above .

The issue at the heart of this is the difference between treating reality as a system and reality as a construction.

Yes, we can model reality as a construction - a bunch of small localised stuff (events, substance, atoms, information) glued together to create additive effects. That works. Although it then introduces paradoxes, such as how did that local stuff get created in the first place? And oh, we also seem to need a global spacetime, a void, a vacuum, a dimensionality, for the stuff to do its constructing in.

So the success of mechanical modelling - gluing together particles, or masses, or energies, or force vectors, or even microstates - is undeniable. But it leaves unanswered some basic metaphysical questions. Which is why it can be such a puzzle over, well, how can we have the measured without also having a measurer?

You will say, I want to be a good mechanist, a good reductionist, and do away with everything but the measured local stuff. Yet I cannot get away from the nagging realisation that a measurer, a global context that makes a measurement meaningful, is also always required.

The best recent philosopher on these issues I believe is CS Peirce. And his theory of semiosis is exactly about this issue. What gives meaning to a sign?

The radical step he made (or was trying to make) was to frame things so that he was talking simultaneously about epistemology and ontology.

Semiosis is how we (as reality modelling creatures) dichotomise the world into our formal models and the measurements they entail.

And then pan-semiosis would be saying well, the world has that logic itself. The world self-organises into a model (the classical, decohered, prevailing state of the universe) and its measurements (the acts of decoherence that create the events, or particles, or bits, or however you chose to think about the local stuff, out of which the whole is being created).

So if Conrad's question is why is anything measurable? The answer would be that systems are measuring devices. The local stuff out of which they are constructed is also the local stuff which they are creating (via the causality of downward "observational" constraint).

It is all about reality modeled as a self-organising system. And to do that properly, you require Peirce's firstness, secondness and thirdness. Or what I normally talk about as vagueness, dichotomies and hierarchies (as Peircean terminology is even more opaque, and I also prefer to connect to the larger bodies of thought on these matters).

 

[apeiron]

Real particles always have a well-defined mass.

Do you mean a well-defined average mass? That would seem to be the more accurate statement in a QM context.

There would also be the GR view of "well-defined". We would be talking there about rest-mass? And so the local definite status flows from the fixed global measurement frame.

 

[brainstorm]

Interesting post, but I'm bracketing it in favor of getting to the empirical specifics of specific measurement instruments/techniques to see if people actually understand the basic logical principles their tools are based on.

So if Conrad's question is why is anything measurable? The answer would be that systems are measuring devices. The local stuff out of which they are constructed is also the local stuff which they are creating (via the causality of downward "observational" constraint).

Is this not vague to you? How can any or every "system" be a measuring device? Is such a "system" knowable according to you, or does that transcend the dichotomy of the system/construction approach where only in the mindset of constructionism can a system actually be dissected to its mechanics - and presumably you have some reason that you should not engage in such constructionist mechanical dissections. It's a clever cop out, but still a cop out, imo.

It is all about reality modeled as a self-organising system. And to do that properly, you require Peirce's firstness, secondness and thirdness. Or what I normally talk about as vagueness, dichotomies and hierarchies (as Peircean terminology is even more opaque, and I also prefer to connect to the larger bodies of thought on these matters).

Is "reality as a self-organizing system" the reason why any measurement instrument generates valid measurements without having any logic for how it measures what it is supposedly measuring?

 

[apeiron]

If there are basic properties essential to the existence of particles, we haven't found them yet.

The best candidate could be local gauge symmetries. In general, like me, you would seem to be taking a constraints-based soliton approach to concieving of particles. Well, what the wider observing system cannot constrain, is then by definition able to exist locally as a degree of freedom.

This is how intrinsic spin and inertial motion would have to arise - as properties that the system cannot see directly. They can only be measured intermittently as events - collisions or polarisations and other kinds of systems measurement.

But in general, properties would arise contextually in a systems (as in condensed matter approaches to particles) rather than being intrinsically existing. And so in existence even in the absence of a measuring context.

 

[kote]

The HUP says nothing about the accuracy of one measurement of position and one measurement of momentum. The uncertainty in each of those measurement is the instrumentation uncertainty, not the HUP.

Agreed.

So to say that "... particles have a defined location, they don't have a defined momentum... " is incorrect. Each of those particle can have well defined position and well-defined momentum.

Each particle can have a well defined position or a well defined momentum. Not both at the same time. You left out a critical "when" at the beginning of quoting me here.

It is the spread in the values of the positions and the values of the momentum, measured under identical conditions, that is governed by the HUP. If the spread in the values of the position is small, then the spread in the values of the momentum will be big. This means that your ability to predict what the next value of the momentum is is not very accurate.

It's not just about accuracy of predictions though. There are metaphysical implications. As you know, it's not just about our knowledge of position and momentum, it's about their existence as well defined properties. A particle with a well defined momentum does not exist at any specific location. I think it's misleading to talk about small vs larger spreads in this context. There is no reason to assume that during measurement properties have anything but sharp values ontologically. In practice, of course, you'll always have uncertainty. But as you mentioned, it doesn't need to be the HUP variety of uncertainty when just considering a single property by itself.

See http://arxiv.org/abs/quant-ph/0003074 for the math on properties having sharp values. From the abstract: "I shall show that the same subtle issues arise with respect to continuous quantities in classical and quantum mechanics; and that it is, after all, possible to describe a particle as possessing a sharp position value without altering the standard formalism of quantum mechanics." Notice that it was written by a philosopher (with tenure at Princeton) - these are the details philosophers care about.

I'll concede that mentioning mass didn't help my case any. It is clear, though, that (defined) location is a property that particles may lack. Per http://plato.stanford.edu/entries/essential-accidental/, if something can lack a property and still be the same thing, that property is said to be accidental and not essential. You could make a case against this distinction. As it's currently understood however, existing at a defined location is not an essential property of a particle.

 

[apeiron]

Each of those particle can have well defined position and well-defined momentum. It is the spread in the values of the positions and the values of the momentum, measured under identical conditions, that is governed by the HUP. If the spread in the values of the position is small, then the spread in the values of the momentum will be big. This means that your ability to predict what the next value of the momentum is is not very accurate.

What Kote said was:

Huh? It's simple HUP. When particles have a defined location, they don't have a defined momentum... all that good stuff.

And I can't see any real difference to what Kote meant.

Both Zapper and Humanino seem to be saying that well-defined uncertainty is the same, philosophically, as well-defined existence. Plainly it is not, otherwise QM would not be a challenge to classical conceptions of reality.

 

[ZapperZ]

Why do you cite a text instead of just saying how it works?

Because I will have to teach you the physics of photoemission spectroscopy, and I'm not good enough (nor do I have the patience) to do that on a public forum, when it took me 2 years to learn it myself. Furthermore, I believe that I HAD given you ample example of how the quantity is measured. What I said what the exact details of how the location on the detector corresponds to these quantities will require further digging into the physics.

I don't know why this is so difficult. When you look at the interference pattern on a screen, and then arrive at the frequency based on the location of the peaks, it is the same thing. So why is this that mysterious?

And why do you want everyone to spoodfeed you?

Zz.

 

[ZapperZ]

What Kote said was:


And I can't see any real difference to what Kote meant.

Both Zapper and Humanino seem to be saying that well-defined uncertainty is the same, philosophically, as well-defined existence. Plainly it is not, otherwise QM would not be a challenge to classical conceptions of reality.

Er.. this is what I said? I have no clue what you just said here.

Zz.

 

[ZapperZ]

Agreed.



Each particle can have a well defined position or a well defined momentum. Not both at the same time. You left out a critical "when" at the beginning of quoting me here.

I construct a single slit with width $\Delta(x)$ So any particle that passes through that slit has an uncertainty in position equal to the width of that slit. Now, after the slit, the particle hits a detector at a position x1 measured from the centerline of the slit. The uncertainty of this measurement depends on the resolution of the detector. This is not the HUP. Knowing the distance from the slit to the detector, I can use the x1 position to arrive at the value of momentum along the x direction, i.e. p_x1. The uncertainty of this corresponds to the resolution of the detector. I can make the width as small as I want, it would not affect the uncertainty of the momentum.

Each of the measurement of the position (at the location of the slit) and the measurement of the momentum, has been made with arbitrary accuracy independent of each other. How are they not well defined "at the same time"? Besides, what is this "at the same time" business? In QM, there is an order of the operation of the operator. That's the whole point of non-commutativity. You operate first on one, and then the other. You never operate them "at the same time", so this issue here is non-existent. In this case, I operate my position operator first (by imposing the slit) and then I do the momentum measurement when it hits the screen. How soon or how late I do that doesn't matter, as long as I do one after the other.

It's not just about accuracy of predictions though. There are metaphysical implications. As you know, it's not just about our knowledge of position and momentum, it's about their existence as well defined properties. A particle with a well defined momentum does not exist at any specific location. I think it's misleading to talk about small vs larger spreads in this context. There is no reason to assume that during measurement properties have anything but sharp values ontologically. In practice, of course, you'll always have uncertainty. But as you mentioned, it doesn't need to be the HUP variety of uncertainty when just considering a single property by itself.

You need to be careful here. AFTER the particle passes through the slit, BEFORE it hits the detector that determines its momentum, it is fine to say that it has no specific momentum. This is because it can acquire a range of momentum, depending on how small the width is. The smaller the width of the slit, the larger the range of momentum it can have, and thus, you are not able to say with greater certainty of what momentum it will be WHEN you measure! However, if you look at my example, AFTER it hits the screen, it has a definite momentum!

But here's the next thing. If I do this only ONCE, i.e. one particle passes through the slit, and that one particle then hits the detector, where is the HUP here? I have, in my possession, a definite position and definite momentum values of that particle. Where, in all of this, is the HUP? Can you use the values that I've just obtained to find $\Delta(x)$ and $\Delta(p_x)$?

Zz.

 

[kote]

AFTER the particle passes through the slit, BEFORE it hits the detector that determines its momentum, it is fine to say that it has no specific momentum.

All I'm saying is that it's possible for a particle to not have a defined momentum while still being a particle. Similarly, it's possible for a particle to not have a defined location while still being a particle. Therefore, location and momentum are not essential properties of particles.

I agree with you on everything else you said.

 

[ZapperZ]

All I'm saying is that it's possible for a particle to not have a defined momentum while still being a particle. Similarly, it's possible for a particle to not have a defined location while still being a particle. Therefore, location and momentum are not essential properties of particles.

Show me the exact phenomenon where this is occurring. You'd notice that I gave you a specific illustration on what I was trying to emphasize.

Zz.

 

[brainstorm]

Because I will have to teach you the physics of photoemission spectroscopy, and I'm not good enough (nor do I have the patience) to do that on a public forum, when it took me 2 years to learn it myself. Furthermore, I believe that I HAD given you ample example of how the quantity is measured. What I said what the exact details of how the location on the detector corresponds to these quantities will require further digging into the physics.

I don't know why this is so difficult. When you look at the interference pattern on a screen, and then arrive at the frequency based on the location of the peaks, it is the same thing. So why is this that mysterious?

And why do you want everyone to spoodfeed you?

Zz.

This post wasn't about spoonfeeding or learning photoemission spectroscopy. It was about why things are measurable. I have been trying to get people to provide clear reasoning about how their instrumentation measures at the level of direct empirical data.

When you look at the interference pattern on a screen, and then arrive at the frequency based on the location of the peaks

Take this sentence, for example. What generates the interference pattern you speak of? What is interfering with what and how do you know that it is?

I'm trying to get at the precise comparison taking place in measurement and what the medium/media are linking the different empirical observations. For example, when volume is measured by displacement of fluid, the fluid is the medium and the level of the fluid in the container is measured in increments of length. So when one object submerged causes the water-level to rise 1cm, its volume is half that of an object that causes the water-level to rise 2cm. The comparison is made between the two volumes of water displaced by the different objects, not by comparison of the objects themselves directly. It is reasoned that the water will not dissolve into the water, and as such all displaced water will correspond to the volume of the submerged object. Likewise it is assumed that no more water will be displaced than the volume of the object. As such, comparing the volumes of displaced water is regarded as analogous to comparing the volumes of the objects themselves.

 

[kote]

Show me the exact phenomenon where this is occurring. You'd notice that I gave you a specific illustration on what I was trying to emphasize.

Zz.

Apologies - I thought you agreed that particles don't always have defined momentum. We know that when a particle has a sharp momentum, its position isn't just hidden by uncertainty, it's undefined... right? I'd feel a little silly walking through Bell to show that there is no defined momentum when you define location.

Can I show you a positive situation which demonstrates that this is the case? No, I'm not sure that's possible. We have indirect mathematical proof from Bell though. This is all assuming, of course, that QM is valid.

http://arxiv.org/abs/quant-ph/0603277 (Foundations of Physics) is another more recent and concise version of the same argument:

A very simple illustration of the Bell-Kochen-Specker contradiction is presented using continuous observables in infinite dimensional Hilbert space. It is shown that the assumption of the existence of putative values for position and momentum observables for one single particle is incompatible with quantum mechanics.

...

If the predictions of quantum mechanics are correct, then we have proved that position and momentum observables can not be assigned any context independent value. The proof presented here involves elementary observables of one single particle and provides a very simple illustration of the Bell-Kochen-Specker contradiction.

Context dependent putative values are not prohibited and all attempts to replace standard quantum mechanics by some form of hidden variables theories must necessarily include the context dependence in the deterministic assignment of values to the observables. This necessity makes such deterministic theories less appealing. One of the main reasons for developing hidden variables theories was to bring the quantum world closer to the classical expectations but the necessary contextuality goes in the other direction.

So the specific situation in which a particle doesn't have a location, is any time context isn't being created for it. Any time position isn't being measured, it doesn't exist in a well defined way.

This is even a much stronger claim than is required to show that location (or momentum) isn't essential. All that is required for location to be accidental is that it is possible that at one point in time, anywhere in the universe, there might exist a particle without a well defined location.

 

[kote]

The above uses http://arxiv.org/abs/quant-ph/9912108.

However, we shall show here how direct Kochen-Specker arguments for complementarity between position and momentum can be given that are entirely independent of the uncertainty relation and its interpretation.

 

[apeiron]

Each of the measurement of the position (at the location of the slit) and the measurement of the momentum, has been made with arbitrary accuracy independent of each other. How are they not well defined "at the same time"? Besides, what is this "at the same time" business? In QM, there is an order of the operation of the operator. That's the whole point of non-commutativity. You operate first on one, and then the other. You never operate them "at the same time", so this issue here is non-existent.

It is the impossibility of measuring both aspects of a particle at a single point of spacetime which does make a particle not well-defined in this argument about measurement. It is what puts a theoretical limit on measurement itself.

I'm not sure what you motivation can be here, but you are trying to dodge behind semantics.

Just focus on answering the question for a point in spacetime, not a point in space, or a point in time. Or does the difference need further explaining?

You need to be careful here. AFTER the particle passes through the slit, BEFORE it hits the detector that determines its momentum, it is fine to say that it has no specific momentum. This is because it can acquire a range of momentum, depending on how small the width is. The smaller the width of the slit, the larger the range of momentum it can have, and thus, you are not able to say with greater certainty of what momentum it will be WHEN you measure! However, if you look at my example, AFTER it hits the screen, it has a definite momentum!

And quite clearly the discussion was about a single measurement at a single point in spacetime, not a measurement at one time, then a second measurement at another.

After it hits the screen, you could retrospectively impute that the particle had a definite momentum. And using a single slit apparatus, you would know what it managed to squeeze through (and so that it did not get deflected before passing the screen).

It seems strangely evasive of you that you are even using the single slit story here rather than the twin slit one. Although it does help to conceal the QM issues that were being discussed of course.

 

[GeorgCantor]

I construct a single slit with width $\Delta(x)$ So any particle that passes through that slit has an uncertainty in position equal to the width of that slit. Now, after the slit, the particle hits a detector at a position x1 measured from the centerline of the slit. The uncertainty of this measurement depends on the resolution of the detector. This is not the HUP. Knowing the distance from the slit to the detector, I can use the x1 position to arrive at the value of momentum along the x direction, i.e. p_x1. The uncertainty of this corresponds to the resolution of the detector. I can make the width as small as I want, it would not affect the uncertainty of the momentum.

Wouldn't this cause an interference pattern(i.e. uncertainty about position, essentially what kote was implying)?

Each of the measurement of the position (at the location of the slit) and the measurement of the momentum, has been made with arbitrary accuracy independent of each other. How are they not well defined "at the same time"?

It's not at the same time. The particle didn't pass the slit and hit the detector at the same time.

Besides, what is this "at the same time" business? In QM, there is an order of the operation of the operator. That's the whole point of non-commutativity. You operate first on one, and then the other. You never operate them "at the same time", so this issue here is non-existent.

You don't operate them at the same time, because it's impossible, as per HUP.

In this case, I operate my position operator first (by imposing the slit) and then I do the momentum measurement when it hits the screen. How soon or how late I do that doesn't matter, as long as I do one after the other.

I am sure kote agrees with this but he was talking about a particle having a definite position and momentum at the same time(not measuring them one after another).

But here's the next thing. If I do this only ONCE, i.e. one particle passes through the slit, and that one particle then hits the detector, where is the HUP here? I have, in my possession, a definite position and definite momentum values of that particle. Where, in all of this, is the HUP? Can you use the values that I've just obtained to find $\Delta(x)$ and $\Delta(p_x)$?

Zz.

Make the slit opening small enough and you'll start seeing interference(the electron/photon will start interferening with itself, even though you'd need more particles to be sent one after another to make it visible). That's where the HUP is shown experimentally, but you know this stuff better than myself.

 

[GeorgCantor]

Now can you describe a situation where a particle has a undefined mass ? I suppose you are going to invoke the HUP again. That would not be a measurable particle then, but a virtual particle. Real particles always have a well-defined mass.

This is misleading. You should have said "Real particles always have a well-defined mass"... from a particular frame of reference. Otherwise, mass is not a defined property and since we are discussing the philosophical implications, this is not a minor point.

 

[apeiron]

This seems a pretty unambiguous statement...

Heisenberg Uncertainty Relation

The term Heisenberg uncertainty relation is a name for not one but
three distinct trade-off relations which are all formulated in a more or
less intuitive and vague way in Heisenberg’s seminal paper of 1927 [1].
These relations are expressions and quantifications of three fundamental
limitations of the operational possibilities of preparing and measuring
quantum mechanical systems which are stated here informally
with reference to position and momentum as a paradigmatic example
of canonically conjugate pairs of quantities:

(A) It is impossible to prepare states in which position and momentum
are simultaneously arbitrarily well localized. In every state,
the probability distributions of these observables have widths that
obey an uncertainty relation.

(B) It is impossible to make joint measurements of position and momentum.
But it is possible to make approximate joint measurements
of these observables, with inaccuracies that obey an uncertainty
relation.

(C) It is impossible to measure position without disturbing momentum,
and vice versa. The inaccuracy of the position measurement
and the disturbance of the momentum distribution obey
an uncertainty relation.

http://philsci-archive.pitt.edu/archive/00004112/01/HUR_Busch_Falkenburg_philsci.pdf

 

[apeiron]

Experimental verification of HUP with fullerene molecules and single slit diffraction...

The Heisenberg uncertainty principle for material objects is an essential corner stone of quantum mechanics and clearly visualizes the wave nature of matter. Here, we report a demonstration of the Heisenberg uncertainty principle for the fullerene molecule C70 at a temperature of 900 K. We do this by showing the increase in molecular momentum spread after passage through a narrow slit with a variable width down to 70 nm. We find good quantitative agreement with the theoretical expectation.

http://agnes.dida.physik.uni-essen.de/~backhaus/Quanten/Arndt/PRAHeisenberg.pdf

 

[ZapperZ]

This post wasn't about spoonfeeding or learning photoemission spectroscopy. It was about why things are measurable. I have been trying to get people to provide clear reasoning about how their instrumentation measures at the level of direct empirical data.

And I thought I did. My avatar was taken exactly from the raw output of an instrument.

Take this sentence, for example. What generates the interference pattern you speak of? What is interfering with what and how do you know that it is?

This is why we have to know the physics of not only the phenomenon (interference), but also the physics of the instrumentation. I've described the physics of the instrumentation (i.e. the spectrometer). The physics of the phenomenon (photoemission) is covered in books.

As far as I can tell, I've given you exactly what you wanted. Short of you actually doing the experiment yourself (which frankly I think everyone should), I'm not sure what else you would want.

Zz.

 

[ZapperZ]

Apologies - I thought you agreed that particles don't always have defined momentum. We know that when a particle has a sharp momentum, its position isn't just hidden by uncertainty, it's undefined... right? I'd feel a little silly walking through Bell to show that there is no defined momentum when you define location.

Can I show you a positive situation which demonstrates that this is the case? No, I'm not sure that's possible. We have indirect mathematical proof from Bell though. This is all assuming, of course, that QM is valid.

http://arxiv.org/abs/quant-ph/0603277 (Foundations of Physics) is another more recent and concise version of the same argument:



So the specific situation in which a particle doesn't have a location, is any time context isn't being created for it. Any time position isn't being measured, it doesn't exist in a well defined way.

This is even a much stronger claim than is required to show that location (or momentum) isn't essential. All that is required for location to be accidental is that it is possible that at one point in time, anywhere in the universe, there might exist a particle without a well defined location.

Let's go back to the basics, shall we? This is covered in standard intro QM that everyone has to take as a physics major.

The definition of the HUP of an observable is (drum roll):

$$\Delta(A) = \sqrt{<A>^2 - <A^2>}$$

I claim that, for the HUP, a single measurement of ANY observable has an uncertainty of ... ZERO!

Can you tell me where this is wrong?

Now, after you consider that, you might want to start considering that you are missing the key aspect of what I've said, which is the quantity one gets IN A MEASUREMENT. From what I've been reading, it appears that you are think of the superposition of all possible outcome before a measurement that has the effect of contradicting classical realism. This isn't the issue and this isn't what I'm arguing against (heaven knows I've been trying so hard to describe all the Schrodinger Cat states experiment that clearly shows such violation of realism).

Now, as far as having some observables simultaneously, can you please tell me, when I find the commutator of two non-commuting observables, such as [A,B], what exactly does that tell you about the sequence of measurement of those observable? Are you able to show me an example of two non-commuting observables that are measured simultaneously in a single measurement?

Zz.

 

[ZapperZ]

Make the slit opening small enough and you'll start seeing interference(the electron/photon will start interferening with itself, even though you'd need more particles to be sent one after another to make it visible). That's where the HUP is shown experimentally, but you know this stuff better than myself.

I'm not sure how this answered my question. The "interference" is part of the description of QM. The SPREAD in the available values of the momentum increase according to the HUP. The HUP itself doesn't contain all the details of the pattern that one can see if one does this with many photons. All the HUP does is give a rough idea of how well one can predict the next one, or how much of a spread in values one will get. This is why the HUP has been elevated by some people to a stature that it doesn't deserve. It isn't a "principle" at all, but rather a consequence of the wavefunction and the observable.

Zz.

 

[ZapperZ]

It seems strangely evasive of you that you are even using the single slit story here rather than the twin slit one. Although it does help to conceal the QM issues that were being discussed of course.

But we're talking about the HUP at the SIMPLEST level. I can talk about the 2-slit as well, but it is no longer as easy because now, you have two locations of x, and each of them has its own slit width, etc. It confuses those who are trying to follow the HUP applied to it, but if you notice, the envelop of the interference pattern remains identical to that of the single slit (this is a popular undergraduate optics question). So I lose no generalities by tackling the single slit as an example.

And quite clearly the discussion was about a single measurement at a single point in spacetime, not a measurement at one time, then a second measurement at another.

After it hits the screen, you could retrospectively impute that the particle had a definite momentum. And using a single slit apparatus, you would know what it managed to squeeze through (and so that it did not get deflected before passing the screen).

Then show how you are able to perform [A,B] operation if A and B are non-commuting.

Zz.

 

[apeiron]

But we're talking about the HUP at the SIMPLEST level. I can talk about the 2-slit as well, but it is no longer as easy...

The simplest example for demonstrating the essential weirdness of QM is the twin slit experiment (or so Feynman said). That is where you are compelled to adopt a non-classical model such as the path integral.

You can reason from twin slits that the path integral also applies to the single slit case. But I have never seen anyone try to demonstrate that the path integral approach arises in single slit experiments, then derive the more "complicated" twin slit case from it.

Perhaps you can provide cites to support your argument here?

 

[ZapperZ]

The simplest example for demonstrating the essential weirdness of QM is the twin slit experiment (or so Feynman said). That is where you are compelled to adopt a non-classical model such as the path integral.

You can reason from twin slits that the path integral also applies to the single slit case. But I have never seen anyone try to demonstrate that the path integral approach arises in single slit experiments, then derive the more "complicated" twin slit case from it.

Perhaps you can provide cites to support your argument here?

The simplest demonstration of the SUPERPOSITION concept is the 2-slit experiment. The simplest demonstration of the HUP is the single-slit experiment. You can't use the same phenomenon to demonstrate ALL of the weirdness of QM. Try using the 2-slit experiment to demonstrate a bipartite quantum entanglement, for example.

I've described how the single-slit shows the HUP clearly in this thread, i.e. in how the lateral momentum RANGE increases as the slit becomes smaller. I thought this is a clear example already? If you wish for a QM derivation of the single-slit phenomenon, the Marcella paper that I've cited several times (I'll find the exact reference again if you haven't heard about it) in the QM forum has it in painful detail. You can apply the HUP using the wavefunction used in that formulation.

Zz.

 

[ConradDJ]

Thanks for all your comments!... I had no idea this thread would go to four pages before I could get back to my computer a mere 24 hours later.

First, this was posted in the philosophy forum because the argument is independent of the specifics of physical measurement processes. If the argument has merit, then I think it is important to look at how actual measurements are made. But as a starting-point, I only want to emphasize the obvious fact that the measurement of any parameter depends on the measurement of others.

I will say that it all reminds me of arguments concerning language. How can we precisely define any word when we must use other undefined words to do so? Are we doomed to circular references and ambiguity? Is precision even possible?

There is a parallel with language, as an inter-referential system, but with an important difference. In human language words refer not only to other words but also to all the stuff we talk about, out there in the world. When I say “tree” I can point to a tree. In physics there is no “outside world” – the observational meaning of any physical parameter has only the observation of other physical parameters to refer to. So there is a closed / complete inter-referential system here in a much stronger sense.

My purpose in emphasizing this is not to cast any doubt on what we can measure. It’s that we know something very remarkable about the structure of the physical world – namely that it provides measurement-contexts for all its own parameters. So, we should take this into account in trying to work out a fundamental physical theory. We should figure out how to construct a model whose parameters can all be defined in terms of each other.

I don’t think this will be easy, and to begin with it’s not very clear what it involves. The good news is that we have a working example of a self-defining system right in front of us, and we know an incredible amount about how it works. In other words, if we can clarify the question – which I take to be a philosophical issue – we have a whole lot of very detailed information about the physics of measurement to help us get to the answer.

Right now, the purpose of physics is to construct an elegant mathematical model that duplicates the structure of what we observe – that gives us all the right particles with their masses and charges and spin, etc. That's completely right. My point is that the model should also eventually duplicate the aspect of physical structure that makes every one of these things observable.

 

[ConradDJ]

In your minimal universe, if the only force is gravity, then that is what must be used for measurement. Introduce a third low-mass particle and see how it behaves. You can see the mass and location of the first two particles by observing what happens to your measuring device, the third particle.

... barring discussions of subjective knowledge, measurement just is interaction. Any system that undergoes an effect can be said to have measured whatever system it was that caused that effect.

But since we have no electromagnetic field in this model, we can not “see” the location of our particles. From the standpoint of any particle in this system, the most that can be observed is an acceleration in some direction. Even if we were to assume the particle has memory and an internal clock and inertial reference-frame, and so can track how this acceleration-vector changes over time, there’s no way that information could be used to determine the locations and masses of any other particles. That was the point of his illustration -- even though we can "stand outside" it and define the locations of the particles from an absolute standpoint, from inside the system itself, nothing is observable.

So I agree with you that “measurement just is interaction.” In the right context, any physical interaction constitutes a measurement. But we know from QM that interactions occur all the time (in entangled superpositions) without “measuring” anything – just because the “right context” of other interactions is missing.

So the question I'm raising is -- what makes our universe different from the minimal one? How is it that in our universe adequate information is in fact physically available to determine so much about what's in the world?

I think in the big old Misner/Thorne/Wheeler book on Gravitation there’s a construction that shows how to define spacetime intervals observationally using only gravity and light. Of course, you also need something that can detect gravity and light, but leaving that aside – the point is that if you have only gravity or only light, it’s impossible in principle to measure a spacetime interval.

If so, then space and time are only measurable in our universe, because we have these two essentially different kinds of long-distance interaction. We can use light to observe the motions of the planets, and we can measure gravity locally and use that information to interpret our visual information on how the planets move.

The traditional way physics is done, ideally we want a “unified” model in which gravity and electromagnetism turn out to be the same thing. But if measurement is actually a basic feature of our world, then the difference between gravity and light is important. Instead of eliminating this difference in our fundamental theory, we would want to explain exactly what role this difference plays in the referential structure of physics.

 

[ZapperZ]

Thanks for all your comments!... I had no idea this thread would go to four pages before I could get back to my computer a mere 24 hours later.

First, this was posted in the philosophy forum because the argument is independent of the specifics of physical measurement processes. If the argument has merit, then I think it is important to look at how actual measurements are made. But as a starting-point, I only want to emphasize the obvious fact that the measurement of any parameter depends on the measurement of others.

But with all due respect to philosophers, have they measured anything as a standard practice?

I'm a firm believer that you can't simply read about things to know what it is. You actually have to DO and practice it. I'm an experimentalist, so knowing what I'm measuring, and how I'm able to deduce that it is what it is, is extremely important. In a previous part of my career, a central issue of what I measure (related to my avatar) is whether an 'electron' that we measure in a solid is truly a well-defined particle, or weather such a concept (i.e. quasiparticle) is valid when there is a huge electron-electron interaction the that solid. So knowing what we measure and what that quantity represents is, and has always been, a central issue in physics, especially experimental physics. So that's why I am very puzzled that this is asked in the philosophy forum.

Zz.

 

[rewebster]

But with all due respect to philosophers, have they measured anything as a standard practice?

I'm a firm believer that you can't simply read about things to know what it is. You actually have to DO and practice it. I'm an experimentalist, so knowing what I'm measuring, and how I'm able to deduce that it is what it is, is extremely important. In a previous part of my career, a central issue of what I measure (related to my avatar) is whether an 'electron' that we measure in a solid is truly a well-defined particle, or weather such a concept (i.e. quasiparticle) is valid when there is a huge electron-electron interaction the that solid. So knowing what we measure and what that quantity represents is, and has always been, a central issue in physics, especially experimental physics. So that's why I am very puzzled that this is asked in the philosophy forum.

Zz.

you do lean toward the idea that just THINKING about things can be unproductive.


So, from that perspective, Einstein didn't know what he was doing and shouldn't have any attention paid to his ideas because HE didn't measure anything.

From your perspective, as an applied/experimental physicist, can you see that IDEA of anything most often comes first, rather than the experiment?----a lot of people HAVE ideas and CAN'T do experiments. Are they to be discounted for that reason?