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Author Topic: How can I know a particle's velocity without knowing it's position?  (Read 7066 times)

Offline Eric A. Taylor

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According to Quantum Physics I can't know a particle's position AND it's velocity at the same time. The more accurately I measure one the less accurately I'll know the other.

However velocity is a function of distance over time. If I want to know how fast something is moving I measure it's position once, then later I measure it's position again then divide the difference by the amount of time elapsed between measurements and I get it's speed. So if I can't know WHERE a particle is without destroying the data of it's speed how can I measure it's speed at all?


 

Offline jartza

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You just have to be careful to measure the positions inaccurately.

Then the accuracy of speed measurement depends on how much time and effort you
are willing to invest into making the position measurements at two distant positions.
 

Offline CD13

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Is it the method of measurement that causes the problem, or merely the act of measuring? By that, I mean if you could measure the position of an electron without disturbing it, would that give both seed and position accurately?
 

Offline Soul Surfer

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It is quite easy to measure an object's radial velocity accurately without knowing anything much about its position.  You just bounce light or radio waves off it and measure the doppler frequency shift.  also if the object happens to emit light containing spectrum lines (like a star) the doppler shift of these will give it's radial velocity.

An objects angular velocity can be measured using a locally generated information via an imaging device (i.e. a camera)  the distance to an object can be measured using a second camera and its true velocity found by using all these measurements without specifically measuring the object's precise position.

I agree that bouncing a signal off an object and the ambient illumination needed to perform these functions may affect the motion of a body slightly (precisely the amount defined by the uncertainty principle) but there is very little effect unless you are trying to measure the position and velocity of something extremely small and light like a single electron.
 

Offline syhprum

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I had an identical post prepared but you beat me to it, any particle or object that emits electromagnetic radiation of a predictable frequency such as a cold molecular hydrogen cloud gives away its velocity by its Doppler shift.
 

Offline jartza

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When you use doppler radar to measure speed, the distance that the moving object moved during the reflection process is measured, by measuring how much the radar wave shortened.

 
 

Offline Eric A. Taylor

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some great answers but that wasn't quite what I was asking. I'm not speaking of macroscopic objects who's quantum uncertainties average out to the point that the errors are very small, I'm speaking of single particles like electrons.

First, if I understand correctly (which is questionable) electrons don't interact with light in the same way macroscopic things do. I don't know about free electrons but when a photon with just the right energy hits an atom it will absorb it's energy and it's electrons go into a higher "orbit". very quickly the electrons will drop back down to lower orbits again re-emitting the photon, but not necessarily the same energy photon.

For an atom to become excited by a photon it needs to have just the right amount of energy. Think of the game of Sorry (don't know what it's called outside the states) where, to reach the goal you need to roll the right number on the dice. If you're 4 spaces away from the goal and you roll a 5 or 6 you can't move the piece. However if you roll two 2's you can move in.

The atom, which has just become excited by an x-ray with just the right energy might re emit that energy in several blue photons, or any variety of photons that equal the total of the absorbed photon. It's from this that we get the spectrum. Each atom will emit different photons depending on what it is.
 

Offline jartza

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Accurate speed measurement procedure must involve a position fuzzyfying procedure,
here is one:

1. We measure position accurately, speed becomes inaccurate.
2. We wait, position becomes constantly more inaccurate.

After this we may measure position accurately, which will tell us what the speed was, but not what the speed is now.

Or we can measure the position inaccurately, which will tell us what the speed was, and still is.
 

Offline JP

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I'm not sure there's a nice interpretation in terms of particles.  This is a weird quantum effect that requires a bit of waviness of the particles.  Sometimes it's stated that to measure a particle's position, you have to hit it with another measurement particle (such as a photon) which changes it's momentum.  That's a nice hand-waving explanation, but it's not perfectly correct. 

Your question also raises the point of measuring velocity by taking two position measurements in time.  This is true if it's a particle and if you care about velocity, but the uncertainty principle is about momentum, not velocity, and the particle is a wave.   You can quantum mechanically cause a collision, and by conservation of momentum, you can figure out the momentum from a single collision. 

If you deal with waves instead of particles and look at what it means to have perfectly localized position or a given momentum, it becomes much clearer that the waves will have unknown momentum and position, respectively.
 

Offline Soul Surfer

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The uncertainty principle is not just hand waving.  If you use electromagnetic radiation (light) to measure the position or velocity of a particle the change in position of momentum coincides with the errors introduced by the interaction with the light quantum.  The energy in light quanta can be proved and measured using completely classical physics and requires no weird quantum effects.
 

Offline imatfaal

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Uncertainty is definitely not handwaving.  I think JP was saying (and apologies if I am wrong) that the simple particle being hit by an energetic particle to determine position - The Heisenberg Microscope - description of uncertainty is handwaving.   

The reduction of a quantum mechanical effect to a classical simile is a great way of understanding it, and an extremely good approximation but is incomplete.  Uncertainty arises due to the non-commutative nature of important matrices in quantum mechanics (originally the infinite matrices describing momentum and position) - Newtonian/Classical observables commute, but in general the matrices/observables in qm do not commute.   
 

Offline JP

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Uncertainty is definitely not handwaving.  I think JP was saying (and apologies if I am wrong) that the simple particle being hit by an energetic particle to determine position - The Heisenberg Microscope - description of uncertainty is handwaving.   

Exactly. 

The uncertainty principle itself is rigorous.
 

Offline Geezer

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The uncertainty principle itself is rigorous.

He said, while doing a rather poor impersonation of Magnus Pyke.

 

Offline Eric A. Taylor

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The uncertainty principle is not just hand waving.  If you use electromagnetic radiation (light) to measure the position or velocity of a particle the change in position of momentum coincides with the errors introduced by the interaction with the light quantum.  The energy in light quanta can be proved and measured using completely classical physics and requires no weird quantum effects.

I understand that it's not "hand waving" In fact a particle doesn't even posses definite position or velocity before it's measured. (The experimental proof is too complicated to explain here but this has point has been examined and found to be in standing with the theory)

I'll give a real life example. The other day I lost my car keys. I spent quite a while looking for them. First I looked in the most likely places they might be, on the hook, in my pocket ect... I finally found them under the news paper on the table. Of course they were there the entire time, but in particle physics the particle is smeared out so it's everywhere at once. It would be like saying my keys were everywhere before I found them. Not just everywhere in the house but EVERYWHERE. In the fridge, in England, on the moon and in the Andromeda Galaxy.
 

Offline yor_on

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Uncertainty is definitely not handwaving.  I think JP was saying (and apologies if I am wrong) that the simple particle being hit by an energetic particle to determine position - The Heisenberg Microscope - description of uncertainty is handwaving.   

The reduction of a quantum mechanical effect to a classical simile is a great way of understanding it, and an extremely good approximation but is incomplete.  Uncertainty arises due to the non-commutative nature of important matrices in quantum mechanics (originally the infinite matrices describing momentum and position) - Newtonian/Classical observables commute, but in general the matrices/observables in qm do not commute.   

Very sweetly formulated imatfaal. That's my understanding too, that even though all measurements somehow need to involve 'interactions' by what you're measuring with, even though 'passive', we still even without measuring will have this HUP alive and well. Meaning that you can't really trick it.

=
An awful lot of 'even' in that one :)
« Last Edit: 12/02/2011 20:35:47 by yor_on »
 

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