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- Thread starter chrisphd
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They will have uncertain positions, too.

However, I would expect thermal energy to introduce more error into this experiment than uncertainty.

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If you assume something to be true, then it is true.

The uncertainty principle is a restriction on what can be measured, not what can be assumed.

The uncertainty principle is a restriction on what can be measured, not what can be assumed.

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Not so. Certain things can be assumed to be true in a thought experiment, but if such assumptions contradict the laws of nature then the thought experiment achieves nothing. It is like assuming speed of light is greater than c to deduce a fact. The fact will be irrelevant to physics, as in physics the speed of light is c. The uncertainty principle is more generally that one cannot know exact position and momentum rather than one cannot measure exact position and momentum. This is because in order to know something about an observable, you need to measure it.

Basically, for the conclusion to be correct, the premises of the argument must also be correct. I am wondering if the assumption is an incorrect premise.

Basically, for the conclusion to be correct, the premises of the argument must also be correct. I am wondering if the assumption is an incorrect premise.

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Fredrik

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I don't see why not. It can have these properties, but good luck measuring both at once.

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Well, one reason why not is because relative to the observer, he would observe a momentum of 0, and therefore he would know the exact momentum of the object. Uncertainty principle is error in position times error in momentum is greater than hbar/2. However if he knows exact momentum, the left hand side of the equation will be 0 violating the law

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If you had asked "Can an object be **measured** at rest relative to an observer and not violate the uncertainty principle?" so the answer is still yes.

Now, if you asked, "Would an electron ever be**measured** at rest relative to an observer?" then the answer is no. You'd get an electron cloud if you measured an electron that's part of an atom. If you confined an electron with a very focused laser beam, you could get it to stay within a very tiny area. With good enough equipment, you could still notice it move when it's position is measured optically.

Now, if you asked, "Would an electron ever be

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That is good news. But i still don't see how it is possible looking at the mathematics.

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That is good news. But i still don't see how it is possible looking at the mathematics.

Holy mother of..., you've never seen anything stay still before??

All sorts of objects stay still relative to an observer when measured.

I'm looking around my apartment, and most of the objects I see appear still.

Sure, there is large error in my measuring tool (bad eyesight).

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The bottom line is, as Fredrik said, we're not talking about a

We're talking about a wave function.

I think that's what was initially misleading.

Say we capture an electron with an electric field.

We measure the position of the electron a bunch of times.

The probability to find the electron at any location is the square of the wave function.

The wave function has a maximum, and that maximum may be stationary.

This is not to say that the electron is stationary.

Hope this is helpful.

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That question is not unique.

If the object is small enough so that uncertainty is significant, then uncertainty effects the results of experiment.

If the object is large, then you can measure it to within the accuracy of your instruments.

You could measure an electron in the same exact place twice, but it would be a coincidence. The next time it may be somewhere else, because the photon you used to measure it last time sent it off on on a new trajectory.

Furthermore, the more accurate you want your measurements to be, the shorter wavelength of light you need to use. Shorter wavelength means higher energy, means higher momentum delivered to the poor electron being so cruelly observed.

If the object is small enough so that uncertainty is significant, then uncertainty effects the results of experiment.

If the object is large, then you can measure it to within the accuracy of your instruments.

You could measure an electron in the same exact place twice, but it would be a coincidence. The next time it may be somewhere else, because the photon you used to measure it last time sent it off on on a new trajectory.

Furthermore, the more accurate you want your measurements to be, the shorter wavelength of light you need to use. Shorter wavelength means higher energy, means higher momentum delivered to the poor electron being so cruelly observed.

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Fredrik

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It isn't possible to measure something to be stationary, period. This would make the wave function zero everywhere (and turn the uncertainty principle into [itex]\infty\cdot 0\geq\frac\hbar 2[/itex])

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Why would the wavefuntion be 0?

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What about my bookshelf? It's stationary, in a classical sense.It isn't possible to measure something to be stationary, period...

I think what chrisphd is struggling with is that our classical concept of stationary is as unreal in quantum mechanics as absolute space is in general relativity.

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Why would the wavefuntion be 0?

Actually the wave function would be zero everywhere but one point, where it would be 1.

You don't see particles behave like this in nature, though.

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The wave function is a mathematical function which, when squared, produces the probability distribution for finding a particle over all space.

Integrating the probability distribution from negative infinity to infinity must result in one, meaning the probability of finding the particle somewhere in all of space is one.

Therefore, if the particle is "still", it is described by a wave function that has the value one at some point, and zero elsewhere.

Like I said, this does not describe any particles of nature.

Integrating the probability distribution from negative infinity to infinity must result in one, meaning the probability of finding the particle somewhere in all of space is one.

Therefore, if the particle is "still", it is described by a wave function that has the value one at some point, and zero elsewhere.

Like I said, this does not describe any particles of nature.

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Fredrik

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The wave function (at a fixed time) can be written asWhy would the wavefuntion be 0?

[tex]\psi(x)=K\int_{-\infty}^\infty g(p)e^{-ipx/\hbar}dp=[/tex]

where K is a normalization factor. (This is the most general solution of the time-independent Shrödinger equation). To measure the momentum to be between a and b is to change the state so that g is 0 everywhere except in the interval (a,b). To measure the momentum to be exactly 0 is to change g so that it's 0 everywhere except at 0. So the integral is definitely 0 unless g is infinite at 0. g

[tex]\psi(x)=K\int_{-\infty}^\infty\delta(p)e^{-ipx/\hbar}dp=K[/tex]

Now try to normalize this:

[tex]1=\int_{-\infty}^\infty|\psi(x)|^2dx=K^2\int_{-\infty}^\infty dx=K^2\cdot\infty \implies K=0[/itex]

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Fredrik

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The wave function would be 0 everywhere, but its Fourier transform (i.e. the momentum-space wave function) would be 0 everywhere except at one point where it would beActually the wave function would be zero everywhere but one point, where it would be 1.

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Fredrik

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Yeah, I know. We've all been there.What about my bookshelf? It's stationary, in a classical sense.

I think what chrisphd is struggling with is that our classical concept of stationary is as unreal in quantum mechanics as absolute space is in general relativity.

In quantum mechanics, the answer to the question "where is the particle

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