Uncertainty Principle and a photon

[backward]

Let a photon of a definite wavelength (hence a definite momentum ) start it's journey at time 0. After 8.3 minutes it hits a detector on earth. So it's position is exactly known (in fact it can be predicted for any time less than 8.3 minutes). So we have particle with definitely known momentum and position at t=8.3 minutes in violation of the UP. Where have I committed a mistake.

 

[PeterDonis]

Where have I committed a mistake.

By not doing the actual math. If you do, you will find that your ordinary language description is not correct, for, at a minimum, the following reasons:

a photon of a definite wavelength (hence a definite momentum )

...is not what you think it is. There actually is no such thing--there is no quantum state of the electromagnetic field that actually has this property.

it's position is exactly known

This is not possible; there is no quantum state of the electromagnetic field that has this property either. (Strictly speaking, this is true for any particle, even one with nonzero rest mass; but the dodge that is used to get around that with massive particles, called Newton-Wigner localization, doesn't work with massless particles, so thinking of a "photon" as having a definite position is even more problematic than thinking that way about a massive particle.)

(in fact it can be predicted for any time less than 8.3 minutes)

As should be obvious from the above, this is not correct.

So we have particle with definitely known momentum and position at t=8.3 minutes in violation of the UP.

And here, even if we disregard all of the above criticisms, you still have a problem: measuring a particle's position changes its state, so even if it was in a state of definitely known momentum before measurement, it will not be after measurement. So your scenario does not violate the HUP even if you formulate it for a quantum object that doesn't have all the issues that a "photon" has.

 

[Simon Bridge]

The initial conditions violate HUP so of course the conclusion does also.
Consider - the only way you know that the photon takes 8.3 minutes to reach the detector from it's initial position is if you know it is 8.3 light minutes away from the detector at t=0 to some precision ... but any precision to the position measurement at t=0, with "definite wavelength" at t=0, violated HUP at t=0.
So even if it were possible to get those eigenstates IRL, which it isn't, the logic of the thought experiment fails.

Then there is the phenomenon that the subsequent measurement will disturb the photon ... so even if you had a very precise momentum to begin with, that precision changes with the position measurement. Strictly, by detecting the photon, you have destroyed it. So what is the momentum after detection?

 

[backward]

Thanks.
I understand that the best way to describe QP is mathematical; but I was trying to get as much coceptual clarity as possible.
Does it imply that a traveling electromagnetic wave cannot be represented by a particle traveling with velocity c subject to HUP?
Of course I realize that as one measures a particles position accurately, it's momentum would become uncertain.

 

[houlahound]

Strictly, by detecting the photon, you have destroyed it. So what is the momentum after detection?

I swear this is not a joke question but wouldn't the destroyed photon have a precise momentum of zero?

 

[PeroK]

Thanks.
I understand that the best way to describe QP is mathematical; but I was trying to get as much coceptual clarity as possible.
Does it imply that a traveling electromagnetic wave cannot be represented by a particle traveling with velocity c subject to HUP?
Of course I realize that as one measures a particles position accurately, it's momentum would become uncertain.

One thing your are missing is that a measurement of a quantum object changes its state. Strictly speaking, this is not the HUP, but it is an equally important aspect of QM. In terms of a particle

1) You measure its momentum to a high degree of accuracy.

2) You measure its position to a high degree of accuracy.

3) If you now remeasure its momentum, then will get probabilistically a large range of values. Measurement 2 has effectively destroyed the state of "known" momentum. After measurement 2 you have uncertain momentum and no longer a known value.

If you repeat this experiment many times you will find that measurements 2 & 3 obey the HUP, which actually deals with the expected values of momentum and position over many identical cases. The HUP does not in fact say anything about any two specific measurements of position and momentum.

 

[backward]

I swear this is not a joke question but wouldn't the destroyed photon have a precise momentum of zero?

After destruction, the particle doesn't exist. So it's momentum has no value, which is different from having a value equal to 0.

 

[backward]

One thing your are missing is that a measurement of a quantum object changes its state. Strictly speaking, this is not the HUP, but it is an equally important aspect of QM. In terms of a particle

1) You measure its momentum to a high degree of accuracy.

2) You measure its position to a high degree of accuracy.

3) If you now remeasure its momentum, then will get probabilistically a large range of values. Measurement 2 has effectively destroyed the state of "known" momentum. After measurement 2 you have uncertain momentum and no longer a known value.

If you repeat this experiment many times you will find that measurements 2 & 3 obey the HUP, which actually deals with the expected values of momentum and position over many identical cases. The HUP does not in fact say anything about any two specific measurements of position and momentum.

Thanks a lot PeroK

 

[backward]

Let a photon of a definite wavelength (hence a definite momentum ) start it's journey at time 0. After 8.3 minutes it hits a detector on earth. So it's position is exactly known (in fact it can be predicted for any time less than 8.3 minutes). So we have particle with definitely known momentum and position at t=8.3 minutes in violation of the UP. Where have I committed a mistake.

Another way of posing the question which was in my mind is:
According to QP, a particle with precisely known momentum will have infinite uncertainty in its position. A monochromatic photon would then be impossible to locate anywhere. I do not know in what sense this could be true.
I know I am awfully vague.

 

[PeroK]

Another way of posing the question which was in my mind is:
According to QP, a particle with precisely known momentum will have infinite uncertainty in its position. A monochromatic photon would then be impossible to locate anywhere. I do not know in what sense this could be true.
I know I am awfully vague.

It's not true at all, because you can never know the momentum precisely. The HUP, in fact, forbids you from ever knowing precisely the momentum or position of a particle. There is always a degree of uncertainty in both.

 

[backward]

Thanks again.

 

[PeterDonis]

Does it imply that a traveling electromagnetic wave cannot be represented by a particle traveling with velocity c subject to HUP?

In general, yes. A general traveling EM wave has too many degrees of freedom. In some special cases, we can use the "particle traveling at velocity c" description as a useful approximation.

 

[bhobba]

It's not true at all, because you can never know the momentum precisely. The HUP, in fact, forbids you from ever knowing precisely the momentum or position of a particle. There is always a degree of uncertainty in both.

There is nothing in the HUP that forbids knowing precicely either the position or momentum exactly.

Thee principle says suppose you have a large number of systems in the same state. Divide them into two large lots. Measure the position in one lot. You can measure exactly as you like - only practical considerations prevent exact values ie it would require a Dirac Delta function as a wave-function and such in practice is impossible. Do the same for momentum in the other lot. Again you can measure exactly as you like. Now compare the statistical spread of each set of measurements - it will be as per the HUP.

There is a bit of confusion around the HUP but Ballentine explains it precisely.

Thanks
Bill

 

[houlahound]

I interpret (probably wrongly) that the HUP refers to making a successive measurement ie you measure the position accurately and only THEN you no longer know where the target thing is heading straight AFTER you just measured it's position?

 

[OCR]

Let a photon of a definite wavelength (hence a definite momentum ) start it's journey at time 0. After 8.3 minutes it hits a detector on earth.

I'm not sure, but it would seem that an attempt to measure the one-way speed of light is also occurring ?

The "one-way" speed of light from a source to a detector, cannot be measured independently of a convention as to how to synchronize the clocks at the source and the detector.

 

[Simon Bridge]

I'm not sure, but it would seem that an attempt to measure the one-way speed of light is also occurring ?

The thought experiment can be set up within some convention for synchronising clocks that is independent of the experiment.
Some of this thought experiment is a little bogged down by the special status of light ... pick another particle.

I interpret (probably wrongly) that the HUP refers to making a successive measurement ie you measure the position accurately and only THEN you no longer know where the target thing is heading straight AFTER you just measured it's position?

That would be relevant to the thought experiment, but Bhobba has it strictly correct in post #13. The "measurement disturbs the system" idea is broadly correct, very commonly attributed to HUP, but not quite what HUP says.

Perhaps we should rephrase things so that we have a particle, other than a photon, produced with a well defined momentum, and then measure position with a detector that has a very small aperture.

The uncertainty in momentum has been determined by the apparatus of the source, while the uncertainty in position is determined by the detector ... these two devices will be functionally independent (technically they are linked by the particle - which is probably a clue right?) so how does HUP work in this case?

@backward : that about it? Intuitively the source and detector characteristics can have whatever relationship we like right?

 

[houlahound]

The uncertainty in momentum has been determined by the apparatus of the source, while the uncertainty in position is determined by the detector ..

could not the momentum and position be simultaneously defined with a set up with an infinitely small aperture at the detector as you mentioned to narrow down position but also a very long collimating tube/"lens"/physical channel because only the particles with the slightest deviation in the velocity will be going in the correct direction to make it to the detector.

might be hard to visualise without a diagram but I think my description is clear eg only a projectile perfectly aligned with say the axis of a barrel of a gun will be selected for the velocity that is in the precise direction of the axis of the barrel.

 

[PeroK]

There is nothing in the HUP that forbids knowing precicely either the position or momentum exactly.

Thee principle says suppose you have a large number of systems in the same state. Divide them into two large lots. Measure the position in one lot. You can measure exactly as you like - only practical considerations prevent exact values ie it would require a Dirac Delta function as a wave-function and such in practice is impossible. Do the same for momentum in the other lot. Again you can measure exactly as you like. Now compare the statistical spread of each set of measurements - it will be as per the HUP.

There is a bit of confusion around the HUP but Ballentine explains it precisely.

Thanks
Bill

It depends on your definition of "know the position of a particle". Given the statistical nature of QM I would say that to know precisely the position of a particle in a given state, you would need to obtain precisely the same result on an ensemble of particles in that state. The variance of these measurements would be 0, violating the HUP.

If you do one measurement of position and declare the particle to be precisely at that position, then that is a different matter. I agree that does not violate the HUP.

I did already say in post #6 that the HUP has nothing to say about any specific measurement of position.

PS looking back, the purpose of my subsequent post #10 was to tackle the idea that the 0 uncertainty of position can be offset by an infinite uncertainty in momentum. Or, vice versa.