Direct Position Measurement on a Microscopic Scale with Twin Photons

[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

[{$$\hat H},{\mathbf r}] = [{\hat H},{\hat x}] {\mathbf x} + [{\hat H},{\hat y}]{\mathbf y} + [{\hat H},{\hat z}] {\mathbf z}]$$
and then we take the expectation value
$$<[{\hat H},{\mathbf r}]> = <[{\hat H},{\hat x}]> {\mathbf x} + <[{\hat H},{\hat y}]>{\mathbf y} + < [{\hat H},{\hat z}]> {\mathbf z}].$$

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