Uncertain on Uncertainty

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Background_Noise
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Uncertain on Uncertainty

Postby Background_Noise » Mon Feb 28, 2011 10:40 am UTC

I have a missunderstanding about the uncertainty principle and wonder if any light can be shed on it. I'm a chemistry undergrad and have done some of the maths/derivation behind some quantum theory, but by no means a comprehensive amount.

So my problem is basically thus:

Take 2 identical electrons at rest, accelerate them both by 1 eV. Take the momentum of one, and the position of the other. By inference you can work out the momentum of the position electron. Provided the measurements are syncronised; one one presumably know both components of the electron, despite the operators not producing an eigenstate (or something of that nature, I get hazy over that bit; but the thrust is you can't know both iirc).

I'm going wrong here somewhere, anyone know where?
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Re: Uncertain on Uncertainty

Postby Qaanol » Mon Feb 28, 2011 1:20 pm UTC

Background_Noise wrote:Take 2 identical electrons at rest,

You now have no idea where either of your electrons are.

Background_Noise wrote:accelerate them both by 1 eV.

You now have no idea how much time it took to do so.

Does that clear things up?
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Re: Uncertain on Uncertainty

Postby doogly » Mon Feb 28, 2011 1:22 pm UTC

You don't even need two electrons for this, you just imagine, "I have an electron. I apply a known force. I can calculate <x> and <p> for it."
Sure, you can! But expectation values are not measurement results. <x^2>-<x>^2 != 0, that sort of thing.
Identical electrons are only identical in the sense that you should get the same expectation values for both. They could easily have different observed values.


Qaanol wrote:
Background_Noise wrote:accelerate them both by 1 eV.

You now have no idea how much time it took to do so.

Just a word of caution: t is not an operator the way that x, p and E are, so the (delta t)(delta E) uncertainty relationship needs to be interpreted with more care.
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Re: Uncertain on Uncertainty

Postby xepher » Mon Feb 28, 2011 2:24 pm UTC

The momentum of the position electron would change as soon as you look at it, because to see it you'd have to see a photon that bounced off of it. Wouldn't that make it move in a different direction?

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Re: Uncertain on Uncertainty

Postby KingXimana » Mon Feb 28, 2011 6:36 pm UTC

The photon coming off it is the entire basis for the uncertainty princable. If the photon has a high wave length (ultra violet or whatever) you are seeing its location more accurately that a lower wave length (microwave). The issue here is a microwave would effect the partial relatively little (you know the position not well but the velocity pretty good) if you use a uv your getting the position very accurately, but the high energy would change the particles momentum a lot.

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Re: Uncertain on Uncertainty

Postby doogly » Mon Feb 28, 2011 7:59 pm UTC

KingXimana wrote:The photon coming off it is the entire basis for the uncertainty princable.

not quiiiiiiiite. You want to avoid the temptation to say "The electron actually has a definite momentum and position at a given time, but the process of measurement disturbs it in some way so it can't ever be measured to arbitrary accuracy in both position and momentum." This is not so. Statements about the properties of a thing made before measurement sound like they are just philosophy anyway, but the Bell stuff is to point out that there is a real difference between "The properties are fuzzed up by measurement" and "reality is inherently fuzzy," and observations favor the latter.
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Re: Uncertain on Uncertainty

Postby KingXimana » Mon Feb 28, 2011 8:55 pm UTC

Hmm, I guess I still don't want to believe there might be a limiting factor to our knowledge. In all practicality is there really a difference? If reality is inherently fuzzy or our observations make iy fuzzy, seems to me its just how you view it. (I have only a high school science background, so saying Im wrong is more helpful then agreeing, I get to learn then)

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Re: Uncertain on Uncertainty

Postby Moose Hole » Mon Feb 28, 2011 9:17 pm UTC

KingXimana wrote:Hmm, I guess I still don't want to believe there might be a limiting factor to our knowledge. In all practicality is there really a difference? If reality is inherently fuzzy or our observations make iy fuzzy, seems to me its just how you view it. (I have only a high school science background, so saying Im wrong is more helpful then agreeing, I get to learn then)
No, it's not about our inferior observation technology, it's about reality actually being fuzzy. Here's a cool little story that will either help you wrap your mind around the concept or confuse the hell out of you, or both. http://lesswrong.com/lw/ps/where_physic ... xperience/

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Re: Uncertain on Uncertainty

Postby KingXimana » Mon Feb 28, 2011 10:06 pm UTC

Hmm, I feel as if I almost understand something after reading that. I'm sadly left feeling how they do at the end "what?"

Ill read it again when Im not in chemistry class. Thank you for this :)

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Re: Uncertain on Uncertainty

Postby p1t1o » Wed Mar 02, 2011 2:43 pm UTC

If it helps to visualise: when you say "take an electron at rest" what you are saying, in practice, is "prepare an electron so that the volume containing its most probable locations is as small as I can make it" - there will be a non-zero probability that your electron is not where you think it is.

**EDIT**
You will/may already have, come across these concepts with reference to electron orbitals, probability curves, wavefunctions etc.
Apologies if I'm a bit too vague :)

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Re: Uncertain on Uncertainty

Postby BlackSails » Wed Mar 02, 2011 3:23 pm UTC

Its impossible to even be sure you have 2 electrons!

There is a possibility that you have less or more, from things tunneling into or out of your apparatus.

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Re: Uncertain on Uncertainty

Postby Yakk » Wed Mar 02, 2011 3:29 pm UTC

KingXimana wrote:Hmm, I guess I still don't want to believe there might be a limiting factor to our knowledge. In all practicality is there really a difference?

Yes.

Bell's Inequality experiments are examples of people probing the difference between "your measurements disturb what you look at by hitting them" and "measured things don't have a value outside of the measurement itself" in concrete tests. The "QM is due to hitting things" comes out poorly (in order for it to be true, the it isn't the hitting that disturbs them, but rather the fact that the particle knew it was going to be hit at a point in the future (by communicating through time, or by being able to observe the past state of the universe and determine a complete description of everything that will ever happen to it in the future and work out what it needs to act like in order to mess with our heads) that caused the particle to behave differently in the past, or a weird Everett-style model in which your interacting with the particle causes all of the possible interactions to actually take place, most of which in ways that split the results of the interaction from re-interacting again.)

The scale on which we experience the universe in our day-to-day lives is weird, so our intuition is all messed up and we find it hard to fit our heads around how the universe works.
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Re: Uncertain on Uncertainty

Postby p1t1o » Wed Mar 02, 2011 3:48 pm UTC

Found this quantum weirdness on another thread aaaages ago, blew my mind:

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Re: Uncertain on Uncertainty

Postby thoughtfully » Wed Mar 02, 2011 5:40 pm UTC

<affects Crocodile Dundee voice>
That's not quantum weirdness! This is quantum wierdness!
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Re: Uncertain on Uncertainty

Postby p1t1o » Wed Mar 02, 2011 8:02 pm UTC

I see you've played sigmaknifeysigmaspooney > hbar/2 before!

*chortle*

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Re: Uncertain on Uncertainty

Postby EdgarJPublius » Thu Mar 03, 2011 4:58 am UTC

thoughtfully wrote:<affects Crocodile Dundee voice>
That's not quantum weirdness! This is quantum wierdness!


I wanted to read that article, but I got a message from myself that said if I did there would be dire consequences, so I didn't, but then I never learned how to send messages back to myself, so I read it...
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Re: Uncertain on Uncertainty

Postby KingXimana » Thu Mar 03, 2011 5:55 am UTC

If the universe is inherently "random" what the hell is going on? Before when i just thought it was the photons hitting things i could except it but if thats not right then I am left wondering if maybe we are just missing a variable? I cant bring myself to believe that the universe has a degree of randomness to it.... Yet maybe one day (i'm probably greatly misunderstanding things thus my confusion)

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Re: Uncertain on Uncertainty

Postby thoughtfully » Thu Mar 03, 2011 6:27 am UTC

You're in good company. Einstein, Schrodinger, and deBroglie all made important contributions to the early development of QM, and they couldn't bring themselves to accept it, either.
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Re: Uncertain on Uncertainty

Postby BlackSails » Thu Mar 03, 2011 6:31 am UTC

KingXimana wrote:If the universe is inherently "random" what the hell is going on? Before when i just thought it was the photons hitting things i could except it but if thats not right then I am left wondering if maybe we are just missing a variable? I cant bring myself to believe that the universe has a degree of randomness to it.... Yet maybe one day (i'm probably greatly misunderstanding things thus my confusion)


Nope, no hidden variables either.

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Re: Uncertain on Uncertainty

Postby Qaanol » Thu Mar 03, 2011 7:45 am UTC

BlackSails wrote:
KingXimana wrote:If the universe is inherently "random" what the hell is going on? Before when i just thought it was the photons hitting things i could except it but if thats not right then I am left wondering if maybe we are just missing a variable? I cant bring myself to believe that the universe has a degree of randomness to it.... Yet maybe one day (i'm probably greatly misunderstanding things thus my confusion)


Nope, no hidden variables either.

Rather, you can’t have both hidden variables and causality, meaning essentially that if you accept hidden variables you also must accept non-locality.
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Re: Uncertain on Uncertainty

Postby doogly » Thu Mar 03, 2011 3:19 pm UTC

I <3 randomness. It is beautiful. Boltzmann made friends with inherently random universe even before quantum mechanics. He is clearly cooler than those other schmucks.
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Re: Uncertain on Uncertainty

Postby Moose Hole » Thu Mar 03, 2011 3:53 pm UTC

The thing is, the randomness doesn't noticeably affect us on a day to day level. My hand doesn't just randomly turn into peanut butter for no reason, I have to chop off my hand and form a new one out of Skippy for that to happen. The randomness is at the subatomic level, but it all follows enough general patterns for us not to have to really worry about it at our scale.

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Re: Uncertain on Uncertainty

Postby p1t1o » Thu Mar 03, 2011 4:03 pm UTC

Interestingly, it is starting to appear in some aspects - as CPUs become more advanced, their "wires" get thinner and thinner so we can get more on a chip and make them faster, this much is obvious.
It is approaching the point now where the lithography cannot simply be made smaller because the electrons in one "wire" are close enough to the one next to it that the chancess of them appearing over there in the other wire are becoming non-insignificant.

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Re: Uncertain on Uncertainty

Postby Antimony-120 » Thu Mar 03, 2011 4:49 pm UTC

Moose Hole wrote:The thing is, the randomness doesn't noticeably affect us on a day to day level. My hand doesn't just randomly turn into peanut butter for no reason, I have to chop off my hand and form a new one out of Skippy for that to happen. The randomness is at the subatomic level, but it all follows enough general patterns for us not to have to really worry about it at our scale.


My initial thought was that you should probably form the new hand BEFORE you chop off your old one. Skippy scuplture is a two-handed job.

p1t1o wrote:Interestingly, it is starting to appear in some aspects - as CPUs become more advanced, their "wires" get thinner and thinner so we can get more on a chip and make them faster, this much is obvious.
It is approaching the point now where the lithography cannot simply be made smaller because the electrons in one "wire" are close enough to the one next to it that the chancess of them appearing over there in the other wire are becoming non-insignificant.


That's actually not inconsistent with the "our measurements are off" hypothosis. Making experiments that show Bell inequalities is actually rather difficult, but doable. For most simple applications of QM though it won't show up that hidden variables are impossible.
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Re: Uncertain on Uncertainty

Postby Moose Hole » Thu Mar 03, 2011 4:52 pm UTC

Antimony-120 wrote:
Moose Hole wrote:The thing is, the randomness doesn't noticeably affect us on a day to day level. My hand doesn't just randomly turn into peanut butter for no reason, I have to chop off my hand and form a new one out of Skippy for that to happen. The randomness is at the subatomic level, but it all follows enough general patterns for us not to have to really worry about it at our scale.


My initial thought was that you should probably form the new hand BEFORE you chop off your old one. Skippy scuplture is a two-handed job.
I've become quite adept at doing things with one hand ever since I got married.

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Re: Uncertain on Uncertainty

Postby Joepat » Sat Mar 05, 2011 10:57 pm UTC

My, We've gotten off topic. Anyways, Here's the semi-classical explanation, of which I'm very fond.

You know the velocity of an electron. To see the electron, light must be bounced off of it. Photons carry momentum, and so when it hits the electron, the electron's velocity changes. Now you know more about it's position than it's velocity. You try to measure it's velocity, but in the process, you lose track of it's position.
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Re: Uncertain on Uncertainty

Postby BlackSails » Sat Mar 05, 2011 11:15 pm UTC

Joepat wrote:My, We've gotten off topic. Anyways, Here's the semi-classical explanation, of which I'm very fond.

You know the velocity of an electron. To see the electron, light must be bounced off of it. Photons carry momentum, and so when it hits the electron, the electron's velocity changes. Now you know more about it's position than it's velocity. You try to measure it's velocity, but in the process, you lose track of it's position.


This is however, wrong.

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Re: Uncertain on Uncertainty

Postby Yakk » Sun Mar 06, 2011 12:48 am UTC

So, we where off topic, so you repeated nearly verbatim posts 3 and 4 in the thread, which the majority of the thread was pointing out the errors in?

I'm just checking to see if I understood what was going on.
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Re: Uncertain on Uncertainty

Postby Glass Fractal » Sun Mar 06, 2011 4:27 am UTC

I think the best explanation I've seen about this came from HowStuffWorks. Let's see if it was right (or I remember it correctly).

Photons are both waves and particles. When treated simply as particles they can have a specific position but they don't have momentum because they are massless, zero times anything is zero. When treated as waves their momentum can be calculated but they lack a definite position. Thus you can't measure both at the same time because if you can measure its momentum with certainty then it's certainly acting like a wave and doesn't have a position, the opposite is also true.

Although now that I'm done I realize this can't possibly be right since electrons do have a mass but the Uncertainty Principle still applies.

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Re: Uncertain on Uncertainty

Postby doogly » Sun Mar 06, 2011 4:31 am UTC

Yeah, that's the wrongest yet.
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Re: Uncertain on Uncertainty

Postby EdgarJPublius » Sun Mar 06, 2011 6:33 am UTC

EDIT3:wait, no, now I'm really confused.

I can say this with a relative degree of certainty though: Electrons are not photons.
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Re: Uncertain on Uncertainty

Postby Tass » Sun Mar 06, 2011 4:41 pm UTC

EdgarJPublius wrote:Electrons are not photons.


THAT, is correct.

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Re: Uncertain on Uncertainty

Postby Glass Fractal » Sun Mar 06, 2011 8:43 pm UTC

doogly wrote:Yeah, that's the wrongest yet.


I'd like to view this as progress on my part. Didn't Edison say something about trying all the wrong answers until you get the right one? But in this case I think I'm just going to have to accept "reality is weird" and that I don't know the math well enough to understand it.

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Re: Uncertain on Uncertainty

Postby p1t1o » Sun Mar 06, 2011 9:22 pm UTC

A piece of pocket wisdom I once heard was:

"If you claim to understand quantum physics, then you have missed something."

Or something like that...

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Re: Uncertain on Uncertainty

Postby doogly » Sun Mar 06, 2011 9:23 pm UTC

It also bears pointing out that Edison was a shit poor scientist. Had a handful of inventions and was great at business management and siezing the work of others for profit and enduring misattribution.
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Re: Uncertain on Uncertainty

Postby Moose Hole » Mon Mar 07, 2011 2:37 pm UTC

Glass Fractal wrote:
doogly wrote:Yeah, that's the wrongest yet.


I'd like to view this as progress on my part. Didn't Edison say something about trying all the wrong answers until you get the right one?
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Re: Uncertain on Uncertainty

Postby Algrokoz » Wed Mar 09, 2011 12:04 am UTC

doogly wrote:
KingXimana wrote:The photon coming off it is the entire basis for the uncertainty princable.

not quiiiiiiiite. You want to avoid the temptation to say "The electron actually has a definite momentum and position at a given time, but the process of measurement disturbs it in some way so it can't ever be measured to arbitrary accuracy in both position and momentum." This is not so. Statements about the properties of a thing made before measurement sound like they are just philosophy anyway, but the Bell stuff is to point out that there is a real difference between "The properties are fuzzed up by measurement" and "reality is inherently fuzzy," and observations favor the latter.

There exist a few interpretations of QM that say that the electron does indeed have both a velocity and a position even if we don't observe either. The de Broglie wave and the Faraday wave are the results of such an interpretation, as far as i understand things.

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Re: Uncertain on Uncertainty

Postby doogly » Wed Mar 09, 2011 3:06 am UTC

Well yes, but those are silly, nonlocal and Lorentz violating.
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Re: Uncertain on Uncertainty

Postby Yakk » Wed Mar 09, 2011 3:51 am UTC

doogly wrote:Well yes, but those are silly, nonlocal and Lorentz violating.

Yes, but, tell us how you really feel?
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Re: Uncertain on Uncertainty

Postby BlackSails » Wed Mar 09, 2011 5:30 am UTC

Yakk wrote:
doogly wrote:Well yes, but those are silly, nonlocal and Lorentz violating.

Yes, but, tell us how you really feel?


Other than 2nd-law-violating, I dont think anything is worse than lorentz-violating.


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