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 independant of quantum theory?
I think what the OP is asking is can you make independant 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.

 

[shaun_o_kane]

Umm. IMHO there is no such thing as a direct measurement. Bohr used to say measuring device are essentially classical (no reference to prove that). It is our knowledge of classical mechanics that allows us to understand what is being measured. I guess there is some sort of unstated principle here: If measuring device A and measuring device B return "measurements" which are consistent with one another, then A and B measure the same thing, and the underlying is assumed to be something real - however that is not always the case (e.g. pressure)

What about thermal expansion etc. IMHO the commutator relations can be used to determine whether an measuring device is drifting from true (or is just way out). Suppose [A,B] = C, then if A -> f(l) A, then Commutator relations vary. I.e. [f(l) A,B] = f(l) C. The commutator relations can be extracted experimentally.

I think (i) your original post is the type of deep question that physicists don't always seem to ask themselves anymore, (ii) these types of issues can get bogged down in battles over interpretations.

I've also asked myself this question on-and-off for many years.

 

[RandallB]

I think (i) your original post is the type of deep question that physicists don't always seem to ask themselves anymore, (ii) these types of issues can get bogged down in battles over interpretations.

I don’t think it is a case of physicists not asking the question anymore, it is that most feel the answer given by Bohr (in QM/HUP & its equivalents) is a complete solution to the problem. Which from a practical application view (Transistors to Chemistry) as worked out rather well, but from a science philosophy view maybe not so much.

Anyone new and just learning physics can not possibly understand that till they actually learn what HUP and QM interpretations are.

And science does get “bogged down with interpretations” where thy all agree on the HUP or an interpretation equivalent to it, but still desire a science philosophy that better describes the “Non-Local and/or Unrealistic” nature of it (BM, MWI, Strings, etc.).

Again, most new it the science will see these as different things when in fact they all support the same HUP like solution, just hoping somehow to establish a scientific philosophy that seems more sensible even understandable. Learning that distinction in the debate over various interpretations is part of learning where current science is.

And then there are a few (like myself) that spend their time looking for something actually “more complete” i.e. Local & Realistic. Most might call that “waste their time” like Einstein did for his last twenty years or so. After all the last serious progress supporting Local Realism was about 1935, so it is not a popular area of study.

So for those new to physics they need to learn enough about what is currently known to not use personal terms like “direct measurement” and translate their thinking into a more widely accepted current science vocabulary.
Only by understanding what is current can the OP see that HUP does answer the question asked in the OP, at least as completely as science current expects it is possible to answer it.

 

[newbee]

RandallB

Despite my chosen moniker, newbee, I am not new to physics. I have been in the field for 20 years
but have been away from hard core physics for about ten years. I presently work in medical physics. I just thought this would help yourself and others to know this.

My QFT is rusty but my CM, EM, QM and Statistical Thermo is still solid. When learning QM as an under graduate and grad student I easily adapted to the axioms of QM and the manner in which they differ from QM. I understood and embraced the Copenhagen interpretation... and still do. It wasn't until my introduction to QFT that I started having questions about what this thing we call space is. My OP was an expression of my dissatisfaction with or notion/s of space. My OP was also couched as what psychologists call an "open question" which is a question that doesn't really expect an "answer" but is designed in the spirit of probing what others think.

I want to know what others are thinking. I am really enjoying this discussion.

 

[RandallB]

My OP was an expression of my dissatisfaction with or notion/s of space. My OP was also couched as what psychologists call an "open question" which is a question that doesn't really expect an "answer" but is designed in the spirit of probing what others think.

That approach can be interpreted as being a Troll
I’ll just unsubscribe from this thread.

 

[newbee]

That approach can be interpreted as being a Troll

Psychologists and masters of communication ask "open questions" for very good reasons. I'm sorry that you don't see the value in doing so.

 

[newbee]

The mathematical definition of a coordinate system is more or less the same in all of those theories,

As far as I can tell they are not more or less the same but simply the same.

but we're not talking about points in the mathematical model of space. We're talking about measurements,

I think we are or I am talking about both.

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.

I would not disagree with that statement.

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,

I disagree with this line of reasoning. You have already "you're going to have to use two physical objects to define two positions". If you can do that much then you need no more. The theory about the objects behavior adds nothing. You have already presumed that the objects "define" two positions.

 

[newbee]

Umm. IMHO there is no such thing as a direct measurement. Bohr used to say measuring device are essentially classical (no reference to prove that). It is our knowledge of classical mechanics that allows us to understand what is being measured.

That has been my conclusion as well.

 

[Fredrik]

I disagree with this line of reasoning. You have already "you're going to have to use two physical objects to define two positions". If you can do that much then you need no more. The theory about the objects behavior adds nothing. You have already presumed that the objects "define" two positions.

That's not what I meant. I was just trying to say that the best thing we can do is to use two physical objects when we're attempting to define the two positions, but quantum theory tells us that objects don't really have well-defined positions, so the definition will fail. We need the theory that describes the behavior of these objects to tell us how serious the failure is.

 

[nfelddav]

RandallB

Despite my chosen moniker, newbee, I am not new to physics. I have been in the field for 20 years but have been away from hard core physics for about ten years.
...
My OP was also couched as what psychologists call an "open question" which is a question that doesn't really expect an "answer" but is designed in the spirit of probing what others think.

I want to know what others are thinking. I am really enjoying this discussion.

I thought that was readily apparent...
Your OP could have been a simple question looking for an "answer" but it became quickly clear that you already knew quite a bit about - and had put much thought into - the subject.
I also find this discussion very interesting.

I disagree with this line of reasoning. You have already "you're going to have to use two physical objects to define two positions". If you can do that much then you need no more. The theory about the objects behavior adds nothing. You have already presumed that the objects "define" two positions.

The assumptions are not made in order that there be a distance between them. They must be made to measure that distance, that is, we must assume how they interact with the measuring device.

IMHO there is no such thing as a direct measurement. Bohr used to say measuring device are essentially classical (no reference to prove that). It is our knowledge of classical mechanics that allows us to understand what is being measured.

That has been my conclusion as well.

I agree as well (this seems almost unfortunate).
This statement seems to tie a lot together. It is also the point I was trying to make before: this issue of measurement assuming theory is not peculiar to QM.

 

[newbee]

nfelddav

Here's another direction from which one might enter such a discussion as this which will also expose the motivation for my OP. (I have tried using Latex here yet so I hope I don't screw this up.)

Suppose we wanted to do a QM calculation of the time evolution of the expectation value of a particles position in 3D. We would, using Ehrenfest's Theorem, need to calculate the commutator of the Hamiltonian with the position operator and take the expectation value of the resulting operator. So we would need to calculate

[{\hat H},{\bf r}] = [{\hat H},{\hat x} {\bf x} + {\hat y} {\bf y} + {\hat z} {\bf z}]

where {\bf x}, {\bf y} and {\bf z} are unit vectors. Continuing according to QM we write

[{\hat H},{\bf r}] = [{\hat H},{\hat x}] {\bf x} + [{\hat H},{\hat y}]{\bf y} + [{\hat H},{\hat z}] {\bf z}]

and then we take the expectation value

<[{\hat H},{\bf r}]> = <[{\hat H},{\hat x}]> {\bf x} + <[{\hat H},{\hat y}]>{\bf y} + < [{\hat H},{\hat z}]> {\bf z}].

Notice that the commutators nor the calculation of the expectation values acted upon the unit position vectors. That is, nothing about quantumy happened to these unit vectors. So what are these unit position vectors and why aren't they subject to QM? The way I have come to grips with this is to conclude that the unit vectors, which define or unit measure and direction, are classical objects.

So the motivation for my OP was to see if anybody could attach a meaning to these unit vectors other than that which I presently attach to them. If one could directly measure position on a microscopic scale I think that would challenge my present notion of what these unit vectors - what this space that QM is embedded in is. Notice also that since the commutators and expectations did not operate on the unit vectors in any way that is quantumy no theory was invoked to give meaning to the unit vectors - ie the space. Whats more CM isn't even really invoked for we had operation definitions of position before we had CM.

 

[newbee]

OK so my first attempt at using Latex didn't work. Should have used the previewer.

nfelddav

Here's another direction from which one might enter such a discussion as this which will also expose the motivation for my OP.

Suppose we wanted to do a QM calculation of the time evolution of the expectation value of a particles position in 3D. We would, using Ehrenfest's Theorem, need to calculate the commutator of the Hamiltonian with the position operator and take the expectation value of the resulting operator. So we would need to calculate

[{\hat H},{\mathbf r}] = [{\hat H},{\hat x} {\mathbf x} + {\hat y} {\mathbf y} + {\hat z} {\mathbf z}]

where {\mathbf x}, {\mathbf y} and {\mathbf z} are unit vectors and the carats denote operators. Continuing according to QM we write

[{\hat H},{\mathbf r}] = [{\hat H},{\hat x}] {\mathbf x} + [{\hat H},{\hat y}]{\mathbf y} + [{\hat H},{\hat z}] {\mathbf z}]<br />
and then we take the expectation value
&lt;[{\hat H},{\mathbf r}]&gt; = &lt;[{\hat H},{\hat x}]&gt; {\mathbf x} + &lt;[{\hat H},{\hat y}]&gt;{\mathbf y} + &lt; [{\hat H},{\hat z}]&gt; {\mathbf z}].

Notice that the commutators nor the calculation of the expectation values acted upon the unit position vectors. That is, nothing quantumy happened to these unit vectors. So what are these unit position vectors and why aren't they subject to QM? The way I have come to grips with this is to conclude that the unit vectors, which define our unit measure and direction, are akin to classical observables.

So the motivation for my OP was to see if anybody could attach a meaning to these unit vectors other than that which I presently attach to them. If one could directly measure position on a microscopic scale I think that would challenge my present notion of what these unit vectors are - what this space that QM is embedded in is. Notice also that since the commutators and expectations did not operate on the unit vectors in any way that is quantumy then no theory was invoked to give meaning to the unit vectors - ie the space. Whats more CM isn't even really invoked for we had operational definitions of position before we had CM.

 

[dabi]

That's nonsense.
http://www.shareapic.net/content.php?id=12668640&owner=dabi

 

[nfelddav]

Notice that the commutators nor the calculation of the expectation values acted upon the unit position vectors. That is, nothing quantumy happened to these unit vectors. So what are these unit position vectors and why aren't they subject to QM? The way I have come to grips with this is to conclude that the unit vectors, which define our unit measure and direction, are akin to classical observables.

So the motivation for my OP was to see if anybody could attach a meaning to these unit vectors other than that which I presently attach to them. If one could directly measure position on a microscopic scale I think that would challenge my present notion of what these unit vectors are - what this space that QM is embedded in is. Notice also that since the commutators and expectations did not operate on the unit vectors in any way that is quantumy then no theory was invoked to give meaning to the unit vectors - ie the space. Whats more CM isn't even really invoked for we had operational definitions of position before we had CM.

I think we have to conclude that "space" and "position" exist without theory and without measurement. I would find it more disturbing if the unit vector were somehow changed by QM.
How exactly do you mean they are akin to classical observables?
By direct measurement you mean some hypothetical method which would allow us to know the position without any experiment, correct?
How would such direct measurement impact your notion of space?

That's nonsense.
http://www.shareapic.net/content.php?id=12668640&owner=dabi

I think we'd appreciate a little more clarity, dabi.

 

[newbee]

I think we have to conclude that "space" and "position" exist without theory and without measurement.

I think that is what is usually assumed and is at the core of what bothers me.

How exactly do you mean they are akin to classical observables?

They are assumed to be measured in such a manner that is not complicated by the HUP.

By direct measurement you mean some hypothetical method which would allow us to know the position without any experiment, correct?

No. I think measurement and experiment are to close in meaning to admit such a statement.

How would such direct measurement impact your notion of space?

It woud give physical meaning to the unit vectors on a microscopic scale.

More later.

 

[nfelddav]

I think that is what is usually assumed and is at the core of what bothers me.

Interesting... if we do not assume the consistency of space... the implications are fascinating.

They are assumed to be measured in such a manner that is not complicated by the HUP.

Alright, I thought you had additional implications here.

No. I think measurement and experiment are to close in meaning to admit such a statement.

But a direct measurement relies on nothing external to be made, correct?

It woud give physical meaning to the unit vectors on a microscopic scale.

Which you consider a problem, because if they have physical meaning that means they do have some inherent meaning?

More later.

I look forward to it.

 

[newbee]

Interesting... if we do not assume the consistency of space... the implications are fascinating.

Well I don't know of a single implication so I can't say there is anything fascinating about it. I am simply bothered by extrapolating our notion of space as fundamental
(or space time) to the microscopic realm. As I remarked on another thread if I were a hypothetical microscopic being, mini-me, subject to the laws of QM I don't think I would be assuming space to be fundamental. How would mini-me measure position in this fundamental space given the HUP?

But a direct measurement relies on nothing external to be made, correct?

I have no idea what you mean by this statement. Perhaps you would clarify it.

 

[nfelddav]

Well I don't know of a single implication so I can't say there is anything fascinating about it. I am simply bothered by extrapolating our notion of space as fundamental (or space time) to the microscopic realm.

Yet as you say, there are no implications: as you've shown above, the position vectors are not affect by anything "quantumy", so whether or not they are fundamentally constant, they appear to be at least practically constant.

As I remarked on another thread if I were a hypothetical microscopic being, mini-me, subject to the laws of QM I don't think I would be assuming space to be fundamental. How would mini-me measure position in this fundamental space given the HUP?

I would guess mini-you would measure position in this space in much the same way we do (measure "quantum-sized" things, that is). I don't see how being of a size with the objects being measured is significant.

I have no idea what you mean by this statement. Perhaps you would clarify it.

A "direct measurement" is one that requires no theory and could somehow be made certain, not changing with any assumptions.

 

[mn4j]

I think if the opening post would define what he means by "position", his question will be answered. If position does not have a meaning in the microscopic realm then the opening question is meaningless as well. In fact, the very statement "microscopic realm" will be meaningless as well.

 

[DaTario]

I would propose the following procedure:

Consider a source of twin photons. Put one detector in a angle of , for instance, 30 degrees. You will sometimes detect photons on this channel. At each detection it implies that another photon is traveling with the same angle, in the opposite side relatively to the input source line which irradiates the non linear cristal.

This second photon (traveller) has its origin in time marked by the detection of the first photon (detected). Now put on the way of the second photon a filter to make sure that in this second channel we are only interested in photons with the same spectral content of the first.

Put now a slit and an ecran a given distance after the slit.
When a photon reaches the ecran you will have completed a measurement of position of photon 2 at the plane of the slit.

It may work as well for tiny particles as electrons.

Best wishes

DaTario