Direct Position Measurement on a Microscopic Scale with Twin Photons

[newbee]

Can anybody provide an example of a device capable of "directly" measuring position relative to some
origin on a microscopic scale? By microscopic I mean on the scale that QM is important.

 

[Naty1]

What is a "direct" measure? Scattering? electron microscope?

 

[newbee]

By direct I mean that the result of the measurement should be independent of any physical theory.

 

[Fredrik]

By direct I mean that the result of the measurement should be independent of any physical theory.

... on the scale that QM is important.

That requirement means that you have to use your knowledge of QM to design the device, so I'm not sure it makes sense to also require "independent of any physical theory".

 

[Vanadium 50]

By direct I mean that the result of the measurement should be independent of any physical theory.

I don't think this is possible even with everyday measurements. How do you know a ruler doesn't undergo thermal expansion by a factor of 2? Physical theory.

 

[Naty1]

If it's independent of any physical theory, how will you know what units to measure? what units you used? what the units size is? I don't get it.

 

[Naty1]

Wikipedia doesn't have anything useful in the first twenty listings under DIRECT MEASUREMENT.
At http://en.wikipedia.org/wiki/Quantum_measurement

you won't like the implication of "observables" which is perhaps what you had in mind...lots of theory dependence...

 

[mgb_phys]

Can you make direct measuremnts of somethigns position on the order of an atom - yes atomic force microscopes and laser interferometers can measure on that scale.

Are these measurements independent of quantum theory?
I think what the OP is asking is can you make independent measurements of quantum effects without having to first use the same effect in the measurement - leading to a circular argument.

But can you make lots of direct measuremnts of the properties of a particle and show that they are random because of QM - no because QM says that when you make the measuremnt you effect that randomness.
There is no way to 'step outside' QM and make a measurement of a quantum effect without affecting that effect - being 'an observer' in quantum terminology.

 

[newbee]

To make my OP a bit clearer and remove any reference to theory let me state it as:

Can anybody provide an example of a device capable of "directly" measuring position relative to some origin on a nanometer scale? By "directly" I mean that the result of the measurement should be independent of any physical theory.

 

[newbee]

I don't think this is possible even with everyday measurements. How do you know a ruler doesn't undergo thermal expansion by a factor of 2? Physical theory.

So are you saying that one can never measure anything because something about the measuring device might change? I think you will get some resistance to that notion.

 

[Vanadium 50]

To make my OP a bit clearer and remove any reference to theory let me state it as:

Can anybody provide an example of a device capable of "directly" measuring position relative to some origin on a nanometer scale? By "directly" I mean that the result of the measurement should be independent of any physical theory.

I'm confused. It doesn't look like you are removing this reference at all.

So are you saying that one can never measure anything because something about the measuring device might change? I think you will get some resistance to that notion.

What I am saying is that this requirement that you are imposing on quantum mechanical measurements is so severe that classical measurements will fail as well.

 

[newbee]

I'm confused. It doesn't look like you are removing this reference at all.

I removed the reference to QM.

What I am saying is that this requirement that you are imposing on quantum mechanical measurements is so severe that classical measurements will fail as well.

Note that what I am talking about here isn't the measurement of a particles position but the notion of an underlying field of position variables. Both QM and CM assume such an underlying field.

 

[Fredrik]

I removed the reference to QM.

You removed a reference that no one had a problem with and kept the one that everyone was objecting to.

Note that what I am talking about here isn't the measurement of a particles position but the notion of an underlying field of position variables. Both QM and CM assume such an underlying field.

CM: six numbers, QM: a wavefunction. Is that what you mean by "underlying field"? The wavefunction isn't a measurable quantity.

 

[newbee]

You removed a reference that no one had a problem with and kept the one that everyone was objecting to.

I removed the one that makes the question that I am asking more clear. What did I keep that you object to?

CM: six numbers, QM: a wavefunction. Is that what you mean by "underlying field"? The wavefunction isn't a measurable quantity.

No. Both assume that there is an underlying coordinate system of spatial variables. This underlying coordinate system does not change when going from CM to QM to QFT.

 

[Fredrik]

I removed the one that makes the question that I am asking more clear. What did I keep that you object to?

"independent of any physical theory". Three different people objected to that in #4, #5 and #6. No one objected to "on the scale that QM is important".

No. Both assume that there is an underlying coordinate system of spatial variables. This underlying coordinate system does not change when going from CM to QM to QFT.

OK, that's true.

 

[newbee]

OK, that's true.

Good. So what do you think of the OP then (or the restated version)?

 

[RandallB]

assume that there is an underlying coordinate system of spatial variables. This underlying coordinate system does not change when going from CM to QM to QFT.

The coordinate system is not the problem.
To make the measurement you want in the OP, you need to define what you wish to measure (A buckyball, an individual atom) and what you want to measure it with say electrons (electron microscope) or gamma particles or something “quantum small” that can cast a shadow you can measure with detectors. With a few tricks you can make the measures even more accurate.
BUT the very first thing you will need to do is defining clearly what these things are in some detail (the thing you are measuring and what you are measuring it with).

Off the top I’m betting you do not have any special knowledge to tell us exactly what these things are, accept by using details to describe them fundamentally based on some theory of physics.
And at the scale you are addressing I’m confident you cannot describe these things without a theory that includes some form of HUP equivalent included.

So, to what I believe the intent of your OP is; the simple answer is:
NO

 

[newbee]

Well I think the answer is no as well. So doesn't that bother anybody?

 

[Fredrik]

Good. So what do you think of the OP then (or the restated version)?

What Randall said. I can't really improve on that.

Well I think the answer is no as well. So doesn't that bother anybody?

It's annoying, but a lot of things in physics are. The most annoying thing is that experiments can't really reveal "the truth about reality". The only thing they can tell us is how accurately a theory predicts the results of experiments.

 

[newbee]

The coordinate system is not the problem.
NO

Well it's not the coordinate system per se that troubles me but rather the inability
to directly measure position at the nanometer scale. All of our physical theories presume
an underlying space and some metric associated with position in that space. Well if that
metric can not be operationally defined in a "direct" manner at microscopic spatial scales, and
therefore measured, then what does that say about our theories that are intended to describe
physics at those scales? Are macroscopic measurements the only direct measurements we have
access to? Is it that all predictions based on our physical theories only pertain to that which
we can measure on a macroscopic scale despite the fact that some are meant to describe
the microscopic?.

 

[montoyas7940]

How about a foucault test. It can pretty easily show variations in a surface as small 1/4 to 1/10 wave of visible light. Not the scale of an atom but into the nanometer scale.

 

[nfelddav]

You seem to have a problem that you cannot define some kind of measurement independent of anything. But to change the original question slightly:

Can anybody provide an example of a device capable of "directly" measuring position relative to some origin? By "directly" I mean that the result of the measurement should be independent of any physical theory.

 

[Fredrik]

You can't define that origin in a way that's independent of any physical theory.

 

[newbee]

You can't define that origin in a way that's independent of any physical theory.

But we do just that in CM, EM, QM, and QFT don't we? And it appears to me that
it is not changing as the theory changes. Am I wrong?

 

[DrChinese]

You seem to have a problem that you cannot define some kind of measurement independent of anything. But to change the original question slightly:

Can anybody provide an example of a device capable of "directly" measuring position relative to some origin? By "directly" I mean that the result of the measurement should be independent of any physical theory.

Welcome to PhysicsForums!

If the implication is that you must assume quantum theory to arrive at the evidence in favor of quantum theory, that would not really be a fair assessment. You can design experiments that hold some variables constant, and observe the results. Position measurements can be made with any hypothesis, and then the results compared to validate or invalidate it. In other words, you really propose a working theory and then test it. Quantum theory has been subjected to a lot of such tests, and has survived them all pretty well. That is why it is used today.

A recent experiment tracks the path of an electron (i.e. acting as series of position measurements) to attosecond accuracy. That's 10^-18 of a second, or a billionth of a billionth of a second. Those position measurements are essentially classical, and I would consider them pretty "direct". I guess there is always a degree of subjectivity in that term though.

 

[atyy]

But we do just that in CM, EM, QM, and QFT don't we? And it appears to me that
it is not changing as the theory changes. Am I wrong?

I don't actually understand your question, but maybe these things are relevant. In Newtonian physics, an inertial frame is defined by the Newtonian laws themselves. In QFT, unlike QM, a position measurement is related to the Newton-Wigner operator, which is a bit un-position-like. Also position cannot be measured more precisely than the "compton wavelength", because you end up creating more particles, and you won't know which particle it was you were trying to localize.

 

[Fredrik]

You can't define that origin in a way that's independent of any physical theory.

But we do just that in CM, EM, QM, and QFT don't we? And it appears to me that
it is not changing as the theory changes. Am I wrong?

The mathematical definition of a coordinate system is more or less the same in all of those theories, but we're not talking about points in the mathematical model of space. We're talking about measurements, so you're going to have to use two physical objects to define two positions in space before you even try to measure the distance between them. The behavior of those physical objects is independent of all theories (in the sense that they are going to behave in a certain way no matter what theories humans are able to come up with), but if you're going to measure the distance between them, you're going to have to make assumptions about how they behave, and it doesn't make much sense to just guess. So you assume that they behave in accordance with the best theory you know before you even begin to design the measuring device. That's why measurements aren't independent of theories.

 

[atyy]

The mathematical definition of a coordinate system is more or less the same in all of those theories, but we're not talking about points in the mathematical model of space. We're talking about measurements, so you're going to have to use two physical objects to define two positions in space before you even try to measure the distance between them. The behavior of those physical objects is independent of all theories (in the sense that they are going to behave in a certain way no matter what theories humans are able to come up with), but if you're going to measure the distance between them, you're going to have to make assumptions about how they behave, and it doesn't make much sense to just guess. So you assume that they behave in accordance with the best theory you know before you even begin to design the measuring device. That's why measurements aren't independent of theories.

I wish someone had told me this long ago!

I think even MTW says something strange like we assume there are events everywhere in space, given by light rays crisscrossing each other. Then a little later they say actually we can't do that, because the gravity caused by those rays would cause space to collapse!

The most lucid explanation I've come across was in a book by Stephen Parrott (which I unfortunately cannot state off the top of my head without butchering), but I think similar to what you've written.

 

[nfelddav]

Thank you, Fredrik; That was the point I was trying to make. ALL measurements require theory to be assumed.

If the implication is that you must assume quantum theory to arrive at the evidence in favor of quantum theory, that would not really be a fair assessment. You can design experiments that hold some variables constant, and observe the results. Position measurements can be made with any hypothesis, and then the results compared to validate or invalidate it. In other words, you really propose a working theory and then test it. Quantum theory has been subjected to a lot of such tests, and has survived them all pretty well. That is why it is used today.

And I think this is the other critical point: The measurements using any method we have validate quantum theory. This means it is for all intents and purposes true. Anything that does not change the outcome of an experiment we can perform is beyond the realm of physics. (I've seen this called Dirac's Razor)

 

[RandallB]

Well it's not the coordinate system per se that troubles me but rather the inability to directly measure position at the nanometer scale.

All of our physical theories presume an underlying space and some metric associated with position in that space.

Well if that metric can not be operationally defined in a "direct" manner at microscopic spatial scales, ……. and therefore measured, then what does that say about our theories ……

You are being inconsistent here and taking your argument off track.

First: you say you are not troubled by the “coordinate system per se”

And you agree that:
physical theories presume an underlying metric

Then you contradict it by saying:
“Well if that metric can not be operationally defined …. what does that say about our theories ….”

It says nothing about any theory because all theories define a precise and completely detailed metric for the coordinate system, able to allow any “direct” detail you wish to define in a measurement.

What you still are not addressing is WHAT thing are you measuring and WHAT things do you intend to measure it with.
You cannot make any measurement (including a “direct” one, whatever that may mean) until you provide a detailed description of exactly what those things are.

All currently useful theories include what amounts to the equivalent of the HUP in the description of those two things.
If you have a more complete in detail description of those two things then you will have a more complete theory. (Including a more complete explanation of how WHAT is being measured reacts to What is doing the measuring so we can define a "direct" with complete detail original position, not a repositioning caused by affects of the measurement itself)

With that enhanced theory your “direct measures” can be as “direct" as you like.
But it is a more complete theory you need, not a correction to some problem with coordinate system metrics of current theories.

Note: Niels Bohr made his opinion clear in the 1920’s that no theory could be “more complete” than QM with HUP. That opinion still holds.