Heisenberg Uncertainty vs Measurement Error

[Derek P]

I think you are missing my point, although I seriously doubt your calculation makes sense (but don't care to debate it). There won't be anything in that very small region that came from any known region at any particular point in time. You won't have a sample.

It's not a small region. The first dynode can be as big as you like.

 

[Lord Jestocost]

Nope but it works with very thin films, so I don't think you are going to recover five orders of magnitude that way.

Ok. But, maybe, I don’t get it. Now you have a point source which emits electrons and a curved snippet of a metallic thin film which acts as a dynode and is placed some distance away from the point source. The fuzziness about position is related to that of momentum in the same direction. After measurement, the uncertainties of the x-, y- and z-components of the momentum and of the position where the electron arrived at the dynode must thus to my mind be estimated on base of the source-detector solid angle.

 

[Derek P]

Ok. But, maybe, I don’t get it. Now you have a point source which emits electrons and a curved snippet of a metallic thin film which acts as a dynode and is placed some distance away from the point source. The fuzziness about position is related to that of momentum in the same direction. After measurement, the uncertainties of the x-, y- and z-components of the momentum and of the position where the electron arrived at the dynode must thus to my mind be estimated on base of the source-detector solid angle.

Sure. The HUP limit (h-bar) applies to each axis. But the question I was answering was about a specific experiment that only measures the x components. I dare say you could use a spark chamber at low pressure to measure all three at once. But that would be a different experiment. The analysis is left as an exercise for the reader

 

[DrChinese]

It's not a small region. The first dynode can be as big as you like.

If you are trying to determine both p and q simultaneously, no. Which is what I understood your initial idea to be, please correct if I misunderstood that. You will want to determine p quite accurately. That requires knowing delta x & delta t accurately, among other things. So a large source region won't work.

 

[Derek P]

If you are trying to determine both p and q simultaneously, no. Which is what I understood your initial idea to be, please correct if I misunderstood that.

Not simultaneously. That would be silly.

A. Neumaier had objected that the method proposed by Gerinski would not work because it would be impossible to make the timing shutters accurate enough. So I provided a counter example. Not to measure p & q simultaneously but to measure them the way Gerinski said - by time of flight. And obviously not using mechanical shutters.

You will want to determine p quite accurately. That requires knowing delta x & delta t accurately, among other things. So a large source region won't work.

Actually it will. For example if we have parallel plates we would be interested in just the x components regardless of which path the electron took. However I spelled out a more practical arrangement in post #10 where the emitter is a needle point and the detector curved concentrically to ensure equal time of flight.

 

[DrChinese]

1. Not simultaneously. That would be silly.

2. A. Neumaier had objected that the method proposed by Gerinski would not work because it would be impossible to make the timing shutters accurate enough. So I provided a counter example. Not to measure p & q simultaneously but to measure them the way Gerinski said - by time of flight. And obviously not using mechanical shutters.

1. OK, I didn't read it that way but stand corrected.

2. You said: "It depends on the experimental arrangement but it is not difficult to use a shutter to fix the position and time with arbitrary precision at both measurements."

I guess I don't see how your #10 post accomplishes that (to arbitrary precision). Are you thinking of a particular type of particle to observe?

 

[Derek P]

1. OK, I didn't read it that way but stand corrected.
2. You said: "It depends on the experimental arrangement but it is not difficult to use a shutter to fix the position and time with arbitrary precision at both measurements."
I guess I don't see how your #10 post accomplishes that (to arbitrary precision).

Electrons are emitted from a needle tip when its potential is raised by an electronic pulse. They drift to the concave dynode and are detected. The distance is the distance from the tip to the concave surface, the time of flight is the time between the emission pulse and the detected signal.

 

[ftr]

From my discussion with, who else, DR. Neumaier just recently I was introduced to the wonderful world of single electron beam.
https://www.google.com/search?sourc......1c..64.psy-ab..1.1.211.6...211.MGrKjZsCErE

It looks more complicated than I thought. it seems a lot of approximations are involved.

 

[Derek P]

From my discussion with, who else, DR. Neumaier just recently I was introduced to the wonderful world of single electron beam.
https://www.google.com/search?sourc......1c..64.psy-ab..1.1.211.6...211.MGrKjZsCErE

It looks more complicated than I thought. it seems a lot of approximations are involved.

Fortunately we do not need to worry about single electrons. The errors result in a spread in the received pulse. You could probably get rid of the dynode altogether.

 

[Boing3000]

A. Neumaier had objected that the method proposed by Gerinski would not work because it would be impossible to make the timing shutters accurate enough. So I provided a counter example.

Not really. The setup you propose is quite basic.

Not to measure p & q simultaneously but to measure them the way Gerinski said - by time of flight.

Them ? Sorry, but all I see here is two positions detection, and a momentum computation. Who ever said this what not possible to do ?

Here is another setup: You film a cloud chamber with high speed cameras. Whatever the speed of the camera, you multiply them (by N) to the point where you have enough delta time precision.You "just" have to synchronize those N cameras so they handle the nth frame of the group. You then "just" have to assume that each of those camera have "near zero" delta in their in between frame time. Ho, and those camera have "just" to have a resolution akin to those things.

You see, there is a lot's of "just" that are going to fail miserably. In your example the cathode look like a mountain range (the timing also)
But even if we could obtain some sort of arbitrary precision, how does it relate to HUP ?

 

[Derek P]

Not really. The setup you propose is quite basic.

Them ? Sorry, but all I see here is two positions detection, and a momentum computation. Who ever said this what not possible to do ?

Here is another setup: You film a cloud chamber with high speed cameras. Whatever the speed of the camera, you multiply them (by N) to the point where you have enough delta time precision.You "just" have to synchronize those N cameras so they handle the nth frame of the group. You then "just" have to assume that each of those camera have "near zero" delta in their in between frame time. Ho, and those camera have "just" to have a resolution akin to those things.

You see, there is a lot's of "just" that are going to fail miserably. In your example the cathode look like a mountain range (the timing also)

Then correct my figures, don't just assert that they are wrong, prove it.

But even if we could obtain some sort of arbitrary precision, how does it relate to HUP ?

Find someone who says it does and ask them.

 

[Boing3000]

Then correct my figures, don't just assert that they are wrong, prove it.

Well, first you'll need to prove where I said your figures are "wrong"

Find someone who says it does and ask them.

You did (although, many have pointed out to you that your terminology is confusing)

Absolute accuracy is not relevant, it is repeatability that matters here. I'll use the term "error" here for the uncontrollable random variations.

None of the above is about some precision about a single (or a couple) of events. But a series of them (this hint at HUP). Beside you yourself said you were countering an objection based on the HUP. So from the point a view of many people here, you need to clarify things enough so it can be applied some asserting logic.

For example:
"Call the time error 100 ps". Your units are all over the place. Is it pico second ?
"Drift velocity is v = 600,000 m/s". Where does this number come from ? Where is the error margin ?
"Effective shutter width is thus .06 mm which is far worse than the limitations of the metal surfaces, which will therefore be ignored." This is so vague (and wrong given HUP) that you had to find another setup (about which none of the post#1 numbers apply)
"The actual momentum of the electron is 600,000 * 10^-30." . Again how do you know that ?
"The momentum measurement error is therefore 6 * 10^-30.". "Therefore" ... really ? What is the unit, and where does this incredible precision come from ?
"The actual positional measurement is defined by the metal surfaces to a few atomic dimensions, say 10^-9 m" This one is somewhat realistic.
"The error product is thus 6 * 10^-39". This one I have no idea how you get it. You are multiplying momentum error by position error ? Beside, errors add, they don't multiply (or worse divide).

I don't understand what point you are trying to make. First thing first: are you talking about a series of measures or a unique one ?

 

[Derek P]

I don't understand what point you are trying to make.

And I don't understand why you don't.

First thing first: are you talking about a series of measures or a unique one ?

No I'm not.

 

[DrClaude]

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