# The Heisenberg Uncertainty Principle

The HUP says (I think), among other things, that if you know exactly one of a pair of conjugate variables then the other variable doesn’t exist, (delta x)*(delta p) > hbar.

But if a photon impinges on a screen couldn’t you know exactly both its position and its momentum?

no, because the postion displayed on the screen itslef would have the uncertainity compare to the photons postion greater than or equal to h bar.

Well, no, it says that you cannot measure both conjugate variables to a precision that is less than the uncertainly associated with h bar. The more precision you use on one half of the paired measurement, the more imprecise the other paired measurement must become.

So you can’t know both the position and momentum of the photon. By measuring one to an arbitrary precision, you disturb the other so that it is imprecise.

You can do better than the screen. Experiments have been done that on the face of it would seem to allow you to know both the position and momentum of a particle with a high degree of accuracy.

The item is called a Bose-Einstein Condensate (BEC). Basically you cool a particle down to near absolute zero. Reaching absolute zero is impossible but scientists have come close and have gotten particles to within a few billionths of a degree above absolute zero.

Absolute zero is the place where all motion ceases so a particle at absolute zero would have zero momentum. At a few billionths of a degree above absolute zero there is still some momentum but not much at all.

One would suppose you could now look at the particle and see it sitting placidly thus defeating the HUP (you know its momentum with a high degree of accuracy and since it isn’t moving it should just be lying there so you’d know the position very accurately as well). However, nature conspired to keep the HUP together. At that exceedingly low momentum the particle spread-out (I’m sure there is a better term but hopefully that conveys the idea…like a dot that grows in size and gets fuzzy) such that its position could not be known and the degree of uncertainty was in keeping with the HUP.

Back to the drawing boards…

Yes but. When the photon impinges on the screen you know its position exactly (say the screen a photo sensitive plate) and by measuring the momentum imparted to the screen you’d know its momentum exactly. How can this not be true?

No measurement in physics is exact, there is always a degree of uncertainty. What HUP says is that this is a fundamental property of nature, not a short coming of our methods of measuring.

Because you don’t know exactly where the photon hit. You only have an estimate of where it hit, based upon what you observed when it interacted with some other particles.

And you don’t know exactly what its momentum is, either. The momentum of a photon is h/[symbol]λ[/symbol]. Maybe its wavelength is 700nm, but how certain are you that its wavelength isn’t 700.000001nm? Well, you get that by, again, having it interact with other particles which will, again, only give you an estimate.

That’s very true, but it would be true whether the HUP existed or not.

**

I agree the HUP is an inherent fact of nature. But I gaurantee that the position and momentum of a photon incident on a screen could be measured to an accuracy that would violate the HUP.

Really? So you have experimental evidence of this? I await with bated breath your cites.

Well, if that were true then there would be no HUP and we wouldn’t be talking about it.

These two sentences contradict each other, so they can’t both be right. Fortunately, it’s very easy to see that the second one is incorrect.

Hey, don’t discourage him. He might come back and prove that .9999999… is not equal to 1.

That’s not funny.

I left off his first sentence.

Strangely enough, my copy of The Feynman Lectures on Physics contains an extra line which clears everything up:

You must have got the discount version.
:rolleyes:

Feynman says we can determine “what its momentum would have had to have been to have gotten there”. This is not the same as its momentum upon reaching that position. You can calculate what the average momentum of a particle between time t and time t + [symbol]Δ[/symbol]t, but if you try to measure the position and momentum of a particle at time t, there will be an inherent inaccuracy in your measurements.

The “measurement after the fact” is referring to the fact that you got the exact position at both points in time, and can then calculate the momentum it “would have taken”, but that is not the same as finding the momentum at any given point in time.

If anyone else is curious the quoted paragraph is in Volume III section 2-3. Sorry, meant to put that in my post.

Thanks for the rolleyes donut. Does using them make you feel superior?

Your added sentence doesn’t clear anything up, read the whole article again. After the particle has reacted with the screen both the position and momentum are known to arbitrary accuracy. That is all I have been saying.

The uncertainty principle hasn’t been violated because it doesn’t say you can’t know both values of the conjugate variables after a destruction measurement has been made. The photon doesn’t exist anymore.

I also found this post by Peter Brown. I don’t know a lot about this guy but I do know he was involved in writing Wheeler’s elementary GR textbook Exploring Black Holes.