Measuring Electron Position with Photon: The Uncertainty Principle

[swaroopkml]

I know only basic QM, and i haven't come to grips entirely with the uncertainty principle.
I know that you can't know an electron's position and velocity simultaneously because the act of measuring itself leads to uncertainity.

Here's the question: If we isolate a single electron and we fire individual photons (one by one) at where we think we may find the elctron in the probability wave (like groping for the switch in a dark room), and we know the photon's energy. Now, we try to measure the electron's position. We then spoil the elctron's velocity, but since we know the photon's energy and hence the effect it would have on the electron, can't we, in theory, know the position and velocity (taking the photon's effect into account) at the same time?

Possible misconceptions: 1) When the photon misses an electron, i have assumed that the electron is not effected. But the act of measuring the electron's position causes it to assume a definite position, right?

2) Light can also be a wave, but i don't know how that affects our experiment.

PS: I'm only a high school kid, so please avoid complex mathematics :)

 

[DrewD]

According to the standard interpretation of QM, the uncertainty relations are fundamental limits that are not related to measurements. So it is deeper than saying that you change the momentum or position by measuring a particle. To answer your question a little bit, the light will also have an uncertainty in its energy, so the uncertainty will just be passed along. Also, I think that it would be nearly impossible to actually carry out such an experiment, but I assume you are wondering whether it would be theoretically possible and not worrying about the actual construction of an experiment.

It is important to separate fundamental uncertainty from lack of knowledge. Our current technology does not allow measurements that come anywhere near the fundamental level of uncertainty, so any real measurement will have a lot of errors from other sources. As technology gets better, we will find ways around those barriers. However, if the HUP is correct, which the vast majority of physicists believe it is, there is a limit. There is a point where it is impossible to have a value for two variables at the same time.

 

[Drakkith]

Try reading this article. If you really want to understand you will have to learn a little bit of what the math means, but not how to do it.
http://en.wikipedia.org/wiki/Introduction_to_quantum_mechanics

 

[swaroopkml]

Thank you, DrewD for your wonderful insight. QM is truly mind-blowing. I'll do some further reading as Drakkith suggested and try to understand what it really means to be uncertain :) Thanks

 

[DrChinese]

First, a welcome to PhysicsForums for swaroopkml!

However, if the HUP is correct, which the vast majority of physicists believe it is, there is a limit. There is a point where it is impossible to have a value for two variables at the same time.

It is possible to go all the way to the experimental limit with current technology. This can be easily seen with tests of spin or polarization. For example: a photon polarized at 0 degrees cannot be said to also have a definite (but unknown) polarization at 45 degrees, as the HUP forbids that. This can be readily tested with pairs of entangled photons that have the same polarization.

So I would say we are well past the "IF THE HUP IS CORRECT" statement above. This was more or less settled by EPR/Bell/Aspect.

 

[Naty1]

QM is really subtle...sometimes I think I have a vague feel for it, sometimes I know darn well that I do not!

Blokhintsev (1968) : “If the wave function were a characteristic of a single particle it would be of interest to perform such a measurement which would allow us to determine its own individual wave function. No such measurement is possible.”

Victor Stenger in "The Fallacy of Fine-Tuning: Why the Universe is Not Designed for Us". In the section 15.6 The Statistical Interpretation. It is mentioned:

"This empircal result supports that conventional interpretation of the wave function as associated not with individual particles but rather with the probability for finding a particle at a particular position. In this interpretation, the object always is a particle, not a wave, and the wave aspect is a mathematical abstraction used in the model to make probability calculations"

[It IS possible to measure position and momentum simultaneously…a single measurement of a particle. What we can't do is to prepare an identical set of states of multiple particles, an ensemble of particles with identical states.]

from Zapper's blog: [a mentor in these forums]

The HUP isn't about a single measurement and what can be obtained out of that single measurement. It is about how well we can predict subsequent measurements given the identical conditions...Where the HUP comes into play is that if you then repeat the same sequence of arbitrarily precise measurements on a large numbers of identically prepared particles (i.e. particles with the same wave function, or equivalently particles sampled from the same probability distribution), you will find that your momentum measurements are not all identical, but rather form a probability distribution of possible values for the momentum.

It IS possible to measure position and momentum simultaneously…a single measurement of a particle. What we can't do is to prepare an identical set of states of multiple particles, an ensemble of particles with identical states. Bouncing a photon off an atom tells us nothing about any [Heisenberg] uncertainties. We must bounce many ‘identically’ prepared photons off like atoms in order to get the statistical distributions of atomic position measurements and atomic momentum measurements. What we call "uncertainty" is a property of a statistical distribution.

Repeated, multiple measurements, always seem to follow a statistical distribution beyond that of the arbitrarily precise measuring equipment.

A lousy analogy would be repeated measurements of the pressure of a basketball...sometimes its sunny, sometimes partly cloudy, the external temperature changes, the atmospheric pressure changes...there is always something happening that 'disturbs' our repeated measurements. In this poor analogy, one could theoretically correct for the 'ambient' effects; in QM it appears one can never get around them.

 

[AJ Bentley]

The Heisenberg uncertainty relation is the QM effect that almost every High-School teacher picks on to introduce QM ideas of uncertainty. But it's not a good one.

Because it's an old standard, it suffers from a presentation where the lecturer concentrates on the act of measurement and how difficult it is to measure tiny values. That gives the impression that somehow it's a problem with the technique and if we were clever enough we could think of a better way to measure.

A much 'cleaner' example is electron spin. An electron can only have it's spin measured and known along one axis, unlike large objects where you can measure angular momentum along 3 axes simultaneously. Not only that, it can only take one of two values along that axis (we label them up and down).
It's too early to study stuff like that really - but keep it in mind.