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General Science => General Science => Topic started by: Devans99 on 20/05/2019 19:46:02

Title: Heisenberg's uncertainty principle and two measuring devices?
Post by: Devans99 on 20/05/2019 19:46:02
I know very little about quantum mechanics so please forgive me if this is a stupid question.

The physical explanation given for the uncertainty principle is that an attempt to measure precisely the position of a particle, will perturb it in an unpredictable way, so that a simultaneous measurement of its velocity is inaccurate.

I was wondering if you had two measuring devices. The particle hits the first measuring device and say accurate information on position is collected. Then the deflected particle hits the second measuring device. The second measuring device also collects accurate position information. In addition, we would know the velocity of the particle between the two measuring devices and the angle of deflection from the first measuring device.

I would have though this additional information could be used to work out the original velocity of the particle? To a degree greater than the uncertainty principle allows?

Title: Re: Heisenberg's uncertainty principle and two measuring devices?
Post by: evan_au on 20/05/2019 23:33:20
The problem is that the first measurement disturbs the velocity of the particle, so the second detector can't accurately measure the initial velocity (the second detector can only measure the velocity when the particle reached the second detector).

The above example applies to measuring physical states like position and velocity.

Scientists who are interested in one particular quantum parameter can make test equipment that optimizes precision in measuring that one parameter, while ignoring another parameter. This is called "squeezed coherent states". This was done with recent LIGO enhancements, where they optimized phase measurement, while increasing uncertainty in amplitude.
See: https://en.wikipedia.org/wiki/Squeezed_coherent_state#Examples
Title: Re: Heisenberg's uncertainty principle and two measuring devices?
Post by: Devans99 on 21/05/2019 05:36:45
The problem is that the first measurement disturbs the velocity of the particle, so the second detector can't accurately measure the initial velocity (the second detector can only measure the velocity when the particle reached the second detector).

You would know, however:

(a) the angle at which the particle deflected from the first detector
(b) the velocity of the particle at the second detector

I would have thought that the velocity of the particle at the first detector was a function of (a) and (b)?
Title: Re: Heisenberg's uncertainty principle and two measuring devices?
Post by: Halc on 21/05/2019 12:07:04
I don't see how an angle of deflection would be known by a measurement of its position by the first detector.
With no information on the velocity of the thing, I have no idea how one might position the second measuring device in order to take the 2nd measurement, or to know that it was the same particle being measured.
Title: Re: Heisenberg's uncertainty principle and two measuring devices?
Post by: Devans99 on 21/05/2019 14:52:48
I don't see how an angle of deflection would be known by a measurement of its position by the first detector.
With no information on the velocity of the thing, I have no idea how one might position the second measuring device in order to take the 2nd measurement, or to know that it was the same particle being measured.

I'm imagining the detectors as some sort of sensitive screen that gives the exact position the particle impacted. I'm imagining that the detector screens are big enough so there is no problem positioning the 2nd one so it detects the particle after the initial deflection (so you have to know approximately where the particle will be deflected to but not exactly). I'm also imagining firing one particle at a time so there is no confusion over which particle is which.

If you have exact position of impact on the first and second screen, then you know the angle of deflection from the first screen. The speed of the particle between the first and second screen is also known. I would of thought the original velocity (before it hit detector 1) could be derived from these two?

Title: Re: Heisenberg's uncertainty principle and two measuring devices?
Post by: alancalverd on 21/05/2019 18:44:12
The indeterminacy principle states that you can't simultaneously know the position and momentum of a particle. Having two detectors in series negates simultaneity.
Title: Re: Heisenberg's uncertainty principle and two measuring devices?
Post by: Devans99 on 22/05/2019 07:50:11
The indeterminacy principle states that you can't simultaneously know the position and momentum of a particle. Having two detectors in series negates simultaneity.

But the second detector allows us to know the exact velocity of the particle at the first detector. So we would simultaneously know the exact position and exact velocity at the first detector.

Both detectors accurately measure position of the particle. We know the distance between the two detectors and how long the particle took to travel that distance. So we know the velocity of the particle between the two detectors.

If we assume an elastic collision, then the velocity between the two detectors is the same as the particle's initial velocity when hitting the first detector. So we know the exact position and exact velocity at the first detector.

Even for a non-elastic collision, the velocity at the first detector will be a function of the velocity between the two detectors (known) and the deflection angle at the first detector (known).
Title: Re: Heisenberg's uncertainty principle and two measuring devices?
Post by: evan_au on 22/05/2019 11:16:58
Quote from: Devans99
Both detectors accurately measure position of the particle. We know ..how long the particle took to travel that distance.
It depends what you are measuring, and how.

If the detectors emit a flash of light when the particle passes through it, the energy for the flash must come from somewhere - and it probably comes from the kinetic energy of the particle.

If it is a low-mass particle (like an electron), hitting the detector may lose much of the energy of the particle, so the time it takes to pass between the detectors is not  very indicative of the initial velocity.

Such techniques may work better with heavier particles (eg protons or mesons), which can give up more energy without affecting their kinetic energy so much.

But this all comes back to Heisenberg's uncertainty principle: Quantum uncertainty is not so significant when you are dealing with more massive objects; but it can totally dominate your results with very small objects.

Title: Re: Heisenberg's uncertainty principle and two measuring devices?
Post by: Devans99 on 22/05/2019 16:31:39
If it is a low-mass particle (like an electron), hitting the detector may lose much of the energy of the particle, so the time it takes to pass between the detectors is not  very indicative of the initial velocity.

I imagine the amount of energy lost by the low mass particle relates to the deflection angle on the first detector (narrow angle hardly any, perpendicular, a lot). So the initial velocity appears to be a function of the deflection angle and the post deflection velocity?

Title: Re: Heisenberg's uncertainty principle and two measuring devices?
Post by: evan_au on 22/05/2019 22:50:10
Quote from: Devans99
energy lost by the low mass particle relates to the deflection angle on the first detector
If there are multiple interactions in passing through the first detector, the outgoing angle is unrelated to the total energy lost in the interactions.
Title: Re: Heisenberg's uncertainty principle and two measuring devices?
Post by: Devans99 on 23/05/2019 21:48:39
Quote from: Devans99
energy lost by the low mass particle relates to the deflection angle on the first detector
If there are multiple interactions in passing through the first detector, the outgoing angle is unrelated to the total energy lost in the interactions.

Yes it could get quite complicated when you factor in the design of the detectors. So here is a simple experimental setup:

Imagine a particle for which we wish to collect the exact position and velocity. We have a detector d1 at which the particle is fired. The detector is at an acute angle to the path of the particle so little velocity is lost in the collision. Detector d1 collects the exact position of the particle (but not velocity).

After the particle has collided with detector d1, it is deflected and hits detector d2. Detector d2 collects the exact velocity of the particle (but not position).

As the angle between detector d1 and the particle’s initial course is acute, we therefore have an approximate velocity for the particle at detector d1 - the velocity measured at detector d2. Further, we can make the angle between detector d1 and the particle’s initial course as acute as we wish leading to a corresponding increase in the accuracy of the velocity estimate.

So in summary, by making the deflection angle arbitrarily small, the velocity of the particle can be determined to arbitrarily precision. The particle’s position is known to arbitrary precision, so it seems the uncertainty principle does not always hold?

Title: Re: Heisenberg's uncertainty principle and two measuring devices?
Post by: alancalverd on 24/05/2019 19:05:27
After

No simultaneity.
Title: Re: Heisenberg's uncertainty principle and two measuring devices?
Post by: yor_on on 30/07/2019 16:09:57
There are two variations of HUP. One is called MDR ( measurement-disturbance relationship ) and seems to have been the original idea of Heisenberg in where the disturbances of your measurement made it impossible to define all parameters simultaneously. The other is what we nowadays refer to as HUP, proved through wave mechanics and stuff like single photons/electrons being able to produce fringes in double slit experiments. It then becomes a probability distribution, and not as a ball 'bouncing'. Should add that this also implies that there is no such thing as measuring all parameters simultaneously. And that this is the very reason the idea of 'weak experiments' came to be. Experiments presumed not to be 'noticed' by what you really wanted to measure on. Highly questionable to me.


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