Is the Uncertainty Principle Caused by a Distortion in a Field of Probability?

As you know, the Heisenberg Uncertainty Principle (HUP) is a relationship between quantum mechanical observables. I can’t be certain, and I certainly wouldn’t dare make any assumptions about what an entire group of individuals believe, but it’s my impression that most laymen in quantum mechanics believe that the quantities that appear in the HUP are the results apply to individual measurements when in fact they don’t.

Most laymen don’t know what the term uncertainty means. They confuse it with experimental error. That is incorrect. In fact they aren’t even related to each other.

The mathematical quantities that appear in the uncertainty relationship are two statistical quantities, namely the standard deviation of the observable. As such they do not apply to measurements of a single individual particle.

All too often people mistake the uncertainty of an observable with the in accuracy in the measurement process. That’s quite far from the truth. In fact they aren’t even related.

Let me give you an example; when you measure the components of the spin of an electron there are only two possible values, up or down. They correspond to two different values for the z-component of spin angular momentum. Therefore there are only two possible values that you be measured and therefore when you measure the z-component of spin angular momentum you will know that the result you measure is exact. However if the system is not in a spin eigenstate then there are two possible values that can result. Depending on the exact state the system is in you might have more spin up’s than spin down’s in a large ensemble of identically prepared experiments. In all cases your measurements yield exact values and yet the uncertainty can still be large.

 

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If all I have ever known was turd's, then a turd would look really nice about now.

No, it was more like, I have never heard an interpretation that used space and time like that with relativity in any quantum theory. You could sit an argue the finer points of relativity day and night and get nowhere, never-mind actually using it to be applied or explain something...

I do have to give wellwisher credit for using the specific example of motion blur. I think it is a very good analogy, although I don't think it would be an accurate enough analogy for this problem to be fixed simply with a high speed camera.

 

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I disagree on this point. It's an extremely poor analogy. They have nothing in common at all.

 

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My back problem has overwhelmed me today so I was unable to get to that work. I was laid up for most of day. Here's an idea. Let me ask you a question which has a definite unique answer which can be calculated based on the information provided in the question itself. Here it is

What is the uncertainty in the number on the face of a fair die?

 

Well it does leave an impression of it being experimental error like you mentioned, but I don't feel like you really read that much into it.

I would think that you would have to be able to actually know a good analogy or have a proper understanding of its mechanism in order to determine that. The last time I checked, there hasn't been one that has been accepted as science. To say that it is/isn't actually anything would be pseudoscience!

You cannot ever know or not know what something is that has never been properly explained yet. They just know that it is there!

 

I suspect answering that will lead to a red herring about probability which won't help much as far understanding the Uncertainty Principle is concerned, so for now at least, I'm going to decline to answer.

What I'm unclear about is whether you consider that the Uncertainty Principle - and indeed more generally the wave nature of matter - applies to a single wave-particle or not.

The way I see it, it does, because (a) the double slit experiment shows the wave nature of matter applies eve to single particles sent sequentially through the slits and (b) once this wave nature is given, then position and momentum can't be simultaneously determinable.

 

Sure. But I don't see where the Uncertainty Principle features in your electron spin example. Does it? And if so can you explain a bit more how?

 

It's not a red herring by any means whatsoever, I promise you. I'm confused as to why you'd think so. If I may ask, why is that? I'll send the solution to you in a PM. I think it'd be worthwile to see how people respond to the question before I post the answer here on open forum.

I already answered that explicitly above, i.e. I wrote

So no. It doesn't apply to a single measurement. It applies to an esemble of experiments done on identically perpared systems.

 

Another way to explain the uncertainty principle is with the thermodynamic variable called entropy. In thermodynamics, entropy is a measure of the number of specific ways in which a thermodynamic system may be arranged. For entropy to increase, the system needs to absorb energy. This is why entropy is often associated with waste heat, and not the heat going into work, since work does not cause a change in entropy.

What we have it is more or less a cyclic system, which in the case of the atom, is based on EM force. When the force cycles, energy is given off and absorbed some of which goes into and is taken away from internal entropy, thereby changing the specific ways in which the system can be defined; uncertainty. If there was not entropy it would remain very predictable without entropic fuzziness.

 

That's even worse than your previous analogy. Where in the world did you learn physics from?

 

OK, but I was asking about a single wave-particle, rather than a single measurement.

The principle tells you you cannot know the exact values of TWO specific things (position and momentum) SIMULTANEOUSLY. This is why I think the die example is unhelpful, by the way. Heisenberg himself illustrated it with a thought experiment involving a single particle, which suggests he thought it applied to single particles, not just ensembles.

P.S. Thanks for the message, but this seems just to refer me to the same site you referenced in an earlier public post, which I had looked at.

 

I answered that the uncertainty relation does not apply to a single particle.

The thing that people get tripped up on is what it means when it is said that “one cannot know”.

Just to be clear on what the HUP says I’ll say it in words rather than in equations - Quantum mechanics says that the x-component of position R = (x, y, z) (which is x) with the the x-component of momentum are not simultaneously determined.

The purpose of me asking you the question using the die example was to see if you know what the word uncertainty means. It’s now clear to me that you don’t know what it means. That implies that you don’t have a solid understanding of the HUP.

When I’m 100% certain that you know what uncertainty is, how it is calculated and how it is measured then we can move on. Until then I don’t see that we can move on.

That’s not quite accurate. I’ll explain later

Yes. They are the exact same thing. I sent it to show what uncertainty is.

I’m going to my doctors office today to see if he can help me with my back. If so we can move forward much faster. Wish me luck my friend.

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OK good luck with the back. Meanwhile I have a suggestion for you. If you make a series of repeated measurements of p and x on the same, single, QM particle, you will get the probability distribution you evidently have in mind. This illustrates how it is that the UP does apply to a single wave-particle. One wave-particle, but multiple measurements on it.

That's why I was keen to clarify whether your meant one wave-particle or one measurement.

 

Quantum Uncertainty does apply to a single particle. It is as if the quantum world has a statistical nature in of itself.

Another analogy could be that God Himself does not like scientist, because they are atheist. So then HE starts screwing around with particles to prevent them from understanding them better.

It isn't a measurement problem. It is a problem with reality itself.

 

pmb, I don't think you're giving exchemist enough credit. At least for the most widely accepted interpretations of quantum mechanics, the uncertainty principle does apply to single particles. Maybe not to the measurement statistics of single particles, but certainly to the states of single particles. If you know that your particle's wavefunction is some spread-out superposition in the position basis, the uncertainty principle puts a lower bound on how spread-out it must be in the momentum basis. This way of thinking about it is admittedly more theoretical than what most people think of, but it's perfectly valid to frame the uncertainty principle as a constraint on the representations of states in conjugate bases.

That said, exchemist, you are operating under at least one assumption that is incorrect:

It's important to realize that after taking a measurement, the state does not "spring back" into the distribution it was in before the measurement. As soon as you measure a particle to be in a certain position, it is in that position, and its wavefunction changes accordingly. This effect is called "measurement backaction", and it implies that one cannot reconstruct a wavefunction by sampling from it repeatedly; one needs to take many copies of the wavefunction and sample each copy once. I think this is what pmb is getting at when he says the uncertainty principle only applies to ensembles. In fact, there are "hidden variable" interpretations of quantum mechanics in which the uncertainty principle really is just a statistical property of ensembles, and each particle is secretly deterministic. Most physicists don't put stock in such interpretations for other reasons, but measurement backaction guarantees that they can't be experimentally distinguished from more conventional interpretations.

 

It’s not my place to judge. I try never to judge anybody. I’m doing my best to determine what his understanding of uncertainty is. When I finish that page on uncertainty I’ll post it and them leave it at that.

I the mean time please tell me what textbooks you’ve used in your QM courses so I can take a look at where you’re coming from. Thanks.

 

Many thanks for the intervention Fednis48, and for the correction about the effect of measurement - of course you are quite right. Thanks too for raising the hidden variable point. My own feeling is that idea seems rather like like an optimist wanting to get rid of quantum indeterminacy, without really being able to justify it (yet), but I concede I may be wrong. A chemist after all is happy to use probability waves without enquiring too deeply, since it's the orbitals that really interest him or her.

 

I'm curious about something. Since every single post thing I’ve posted in this thread has been backed up I have to ask you what makes you think that by just making a statement to the opposite of what I’ve said will make me change my mind? Did you attempt to prove your assertion? No, you didn't. What I've said can be found in any QM text. In fact I posted a reference to my QM text I used in graduate school and the page numer of where the derivation can be found. ''

 

And for my part, I didn't mean to imply that you were being judgmental or condescending, just that exchemist's arguments have more merit than you seem to think they do.

As far as textbooks go, I'm really bad at them; most of what I know can be traced back to lectures and conversations rather than reading. When I do need to look something up, though, Cohen-Tannoudji is my standby.

 

Every pop physics book will tell you the same thing along with what I just said. All of the biggest names of physics hold to this interpretation. If you want to be a douche-bag that believes something else, that is your own problem.