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Quantum mechanics

This is a discussion on Quantum mechanics within the General Discussions forums, part of the Community Boards category; Not the science, the personnel. I was watching "Forbidden Planet" and heard this: "I'll bet any quantum mechanic in the ...

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    Quantum mechanics

    Not the science, the personnel.

    I was watching "Forbidden Planet" and heard this:

    "I'll bet any quantum mechanic in the service would give the rest of his life for a chance to fool around with this gadget."
    (one of my my favorite movies nonetheless)

    There is also a couple space movies out there where the ship was bombarded by meteorites

    And there is Captain Kirk saying that the "circuits are shortening", when Khan was reawakened.

    Technical accuracy never stood in the way of entertainment

    -
    Last edited by megafiddle; 08-04-2014 at 12:37 AM.

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    Quote Originally Posted by megafiddle View Post
    There is also a couple space movies out there where the ship was bombarded by meteorites
    Maybe those fragments had bounced off a planet or two before reaching the ship ....
    Right 98% of the time, and don't care about the other 3%.

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    Ironically enough, I was recently reading the wiki and the most elegant explanation for the uncertainty principle was that when you make a position observation, it's reflected as a combination of momentum states of that particle, hence the "uncertainty" because the position measurement is reflected by multiple momentum states. The opposite is true as well, a momentum observation is represented as multiple position states.

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    Quote Originally Posted by megafiddle
    Not the science, the personnel.

    I was watching "Forbidden Planet" and heard this:

    "I'll bet any quantum mechanic in the service would give the rest of his life for a chance to fool around with this gadget."
    (one of my my favorite movies nonetheless)

    There is also a couple space movies out there where the ship was bombarded by meteorites

    And there is Captain Kirk saying that the "circuits are shortening", when Khan was reawakened.

    Technical accuracy never stood in the way of entertainment

    -
    That is pretty funny. Personally, I prefer my sci-fi to be a little more on the credulous side. Star Trek always seemed to me to be more "sci-fantasy" than anything else (I mean, really, like teleporting a person's quantum state - pray tell, what the hell do you do with the *original* "copy" anyway?!).

    Quote Originally Posted by megafiddle
    Ironically enough, I was recently reading the wiki and the most elegant explanation for the uncertainty principle was that when you make a position observation, it's reflected as a combination of momentum states of that particle, hence the "uncertainty" because the position measurement is reflected by multiple momentum states. The opposite is true as well, a momentum observation is represented as multiple position states.
    Except that Heisenberg's Uncertainty Principle is not precisely true, because sometimes (albeit not usually) we *can* measure both the momentum and position of a given particle/wave-state.

    Even so, there *will* always be an uncertainty in measurement for one reason or another. For one thing, every particle and every packet of energy in the universe contributes to the overall "field" of forces streaming through a given point in space-time. How can we possibly know all of the initial states of these contributors? We can't! Another interesting force at work in the universe for which we have not only no way of precisely predicting, but no way to even identify exactly...and that is consciousness. If I we're to try to predict the exact interaction of a given particle with your body, for instance, there would be no way I could predict with 100% accuracy the end result simply because YOU, your mind, may have played a part in some aspect of that interaction. How can one possibly quantify that?!

    So yes, uncertainty *is* a certainty. Not due to limitations in our implements of measurement, but to the limitations of our own understanding of both the initial conditions and the unpredictable (or random) nature of the influence consciousness exerts on (at least) some systems...

    Besides that, there may be other external forces as well for which we may never be made aware of, operating in some other dimension perhaps.

    In other words, uncertainty nonetheless reigns in the universe.
    Last edited by Sebastiani; 08-04-2014 at 03:20 PM.

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    I'm not sure what you mean by measuring the position and momentum at the same time. From a purely mathematical perspective, I don't think it's possible to applying the position and momentum operators simultaneously and even then, I don't think that px is equal to xp, considering that x and p are position and momentum operators respectively.

    I read up on the Born rule a little bit and the gist is, the only true way to interpret the wave function is probabilistically. Because you have a distribution, you can calculate the standard deviation of the wave or wave packet. Because the momentum space is a reflection of the position space, you have these relationships between the position's standard deviation and the momentum's as well.

    This has nothing to do with our own instruments at all. The Born rule is the crux of this and it says that we HAVE to interpret the wave equation as a probability function. Because the Born rule has not yet been disproved (I think he got the Nobel prize for this too), we assume that uncertainty is inherent in the universe itself.

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    Quote Originally Posted by MutantJohn View Post
    Ironically enough, I was recently reading the wiki and the most elegant explanation for the uncertainty principle was that when you make a position observation, it's reflected as a combination of momentum states of that particle, hence the "uncertainty" because the position measurement is reflected by multiple momentum states. The opposite is true as well, a momentum observation is represented as multiple position states.
    It's not only an elegant explanation but the only one that really matters.

    The position and momentum wavefunctions are related by the Fourier transform. What's the Fourier transform of a perfectly localized peak? Why, it is a wave that extends throughout all of space. This isn't just a physical truth, it's a mathematical truth.
    Code:
    //try
    //{
    	if (a) do { f( b); } while(1);
    	else   do { f(!b); } while(1);
    //}

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    Quote Originally Posted by MutantJohn
    I'm not sure what you mean by measuring the position and momentum at the same time. From a purely mathematical perspective, I don't think it's possible to applying the position and momentum operators simultaneously and even then, I don't think that px is equal to xp, considering that x and p are position and momentum operators respectively.

    Yes, the non-commutativity of the operators is a proven mathematical certainty, but that still does NOT necessarily mean that simultaneous measurement isn't possible. Anyway, as I already pointed out, there are other sources of uncertainty.

    Quote Originally Posted by MutantJohn
    I read up on the Born rule a little bit and the gist is, the only true way to interpret the wave function is probabilistically. Because you have a distribution, you can calculate the standard deviation of the wave or wave packet. Because the momentum space is a reflection of the position space, you have these relationships between the position's standard deviation and the momentum's as well.

    This has nothing to do with our own instruments at all. The Born rule is the crux of this and it says that we HAVE to interpret the wave equation as a probability function. Because the Born rule has not yet been disproved (I think he got the Nobel prize for this too), we assume that uncertainty is inherent in the universe itself.
    Well right, and in fact every formulation of quantum mechanics, be it matrix mechanics, wave-function-based methods, Feynman's "path integral" technique, or whatever, they all rely on probability density functions.
    Last edited by Sebastiani; 08-04-2014 at 07:36 PM.

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    Quote Originally Posted by megafiddle View Post
    Technical accuracy never stood in the way of entertainment.
    Jodie Foster in Contact,

    “If there are 400 billion stars in the galaxy, and just one in a million had planets, and just one in a million of those had life, and just one in a million of those had intelligent life, that still leaves millions of planets to explore.”

    Oops!
    Matticus and Epy like this.
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    Originally Posted by brewbuck:
    Reimplementing a large system in another language to get a 25% performance boost is nonsense. It would be cheaper to just get a computer which is 25% faster.

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    Registered User MutantJohn's Avatar
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    Quote Originally Posted by Sebastiani View Post
    Yes, the non-commutativity of the operators is a proven mathematical certainty, but that still does NOT necessarily mean that simultaneous measurement isn't possible. Anyway, as I already pointed out, there are other sources of uncertainty.



    Well right, and in fact every formulation of quantum mechanics, be it matrix mechanics, wave-function-based methods, Feynman's "path integral" technique, or whatever, they all rely on probability density functions.
    Can you please elaborate on what you mean about simultaneous measurement? I know the position and momentum operators but is there a third one specifically for an instance of both? I imagine that instead of a 1-to-n mapping between states, there would be a m-to-n mapping, where m and n are some number of states corresponding to position and momentum.

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    Quote Originally Posted by MutantJohn View Post
    Can you please elaborate on what you mean about simultaneous measurement? I know the position and momentum operators but is there a third one specifically for an instance of both? I imagine that instead of a 1-to-n mapping between states, there would be a m-to-n mapping, where m and n are some number of states corresponding to position and momentum.
    It can be expressed in its simplest form as follows: One can never know with perfect accuracy both of those two important factors which determine the movement of one of the smallest particles—its position and its velocity. It is impossible to determine accurately both the position and the direction and speed of a particle at the same instant.

    Those are the words of Werner Heisenberg, of course. He eventually refines the idea with the non-commutativity of conjugates argument. Problem is, it's irrelevant. Remember, we're supposedly talking about the physical act of measurement, yet somehow Heisenberg comes up with this idea that the uncertainty is *solely* due to inherent mathematical limitations of Fourier analysis! What on Earth do analytical techniques have to do with the intrinsic nature of physical systems anyway?

    Einstein was more on target. He too realized that uncertainty was inevitable, but rather than provide some ad-hoc quasi-metaphysical explanation that "it's just in the math" (which he did recognize as a procedural source of uncertainty, nonetheless) he instead proposed a no-nonsense "hidden variables" argument, which could then be addressed by simply applying some heuristic error bound.

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    Quote Originally Posted by Sebastiani View Post
    Those are the words of Werner Heisenberg, of course. He eventually refines the idea with the non-commutativity of conjugates argument. Problem is, it's irrelevant. Remember, we're supposedly talking about the physical act of measurement, yet somehow Heisenberg comes up with this idea that the uncertainty is *solely* due to inherent mathematical limitations of Fourier analysis!
    Heisenberg never referred to the act of measurement as being somehow intrinsically limited. Instead he correctly stated that the act of observation disturbs the system. The Heisenberg Uncertainty Principle was never a statement about observation methods, techniques or technology. Instead, it was about a now well known and understood attribute of quantum systems. It's not his fault that his principle has been (purposely or not) misread by some.
    The programmer’s wife tells him: “Run to the store and pick up a loaf of bread. If they have eggs, get a dozen.”
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    Originally Posted by brewbuck:
    Reimplementing a large system in another language to get a 25% performance boost is nonsense. It would be cheaper to just get a computer which is 25% faster.

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    Quote Originally Posted by Mario F. View Post
    Heisenberg never referred to the act of measurement as being somehow intrinsically limited. Instead he correctly stated that the act of observation disturbs the system. The Heisenberg Uncertainty Principle was never a statement about observation methods, techniques or technology. Instead, it was about a now well known and understood attribute of quantum systems. It's not his fault that his principle has been (purposely or not) misread by some.
    That's not what I said; I said that he claimed that it was an inherent limitation of mathematics. Anyway, what you're referring to is actually an earlier formulation of the Uncertainty Principle: the Measurement-Disturbance Relationship, which itself has become a subject of debate in recent times.

    And please don't be so foolish to think that Heisenberg's principle is a settled matter, it isn't - because many do oppose the idea prima facie (Einstein included).

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    Quote Originally Posted by Sebastiani View Post
    Anyway, what you're referring to is actually an earlier formulation of the Uncertainty Principle: the Measurement-Disturbance Relationship, which itself has become a subject of debate in recent times.
    The only debate in the scientific community I'm aware of is about the depth of this disturbance. Not of its total absence. It is true it was never formally proven, but that link you provide requires peer review before I'm ready to accept it disproves the uncertainty principle. Do you have any link to the debate or conclusions of this 2012 publication?

    Quote Originally Posted by Sebastiani View Post
    And please don't be so foolish to think that Heisenberg's principle is a settled matter, it isn't - because many do oppose the idea prima facie (Einstein included).
    I said nothing like that. The uncertainty Principle hasn't been proven. Einstein, on the other hand, always opposed Quantum Physics in general. It clashed with his classic view of a perfect and deterministic universe. The Uncertainty Principle is just one example of Einstein's resistance. And is best reviewed in the Einsten-Bohr debates (which were published) where he consistently loses argument after argument. I think that there may be better -- and more modern -- opponents to the uncertainty principle than Einstein.
    Last edited by Mario F.; 08-06-2014 at 11:03 AM.
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    The programmer comes home with 12 loaves of bread.


    Originally Posted by brewbuck:
    Reimplementing a large system in another language to get a 25% performance boost is nonsense. It would be cheaper to just get a computer which is 25% faster.

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    I'm not sure if there are any mathematical uncertainties in Fourier analysis considering you can integrate it over a continuous domain of any range. I would like to hear more about this.

    I would also like to say that, Sebastiani, I'm not sure your post explains measuring position and momentum simultaneously. I'm talking about operators, not people in a lab.

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    Quote Originally Posted by Mario F.
    The only debate in the scientific community I'm aware of is about the depth of this disturbance. Not of its total absence. It is true it was never formally proven, but that link you provide requires peer review before I'm ready to accept it disproves the uncertainty principle. Do you have any link to the debate or conclusions of this 2012 publication?
    I think we're getting side-tracked here. All I'm saying is that Heisenberg's Uncertainty Principle (HUP) theories are too presumptuous and too broadly stated to deserve the designation of being true "laws of physics". Can the observer disturb the system being measured? Of course! Will we ever be able to mitigate these effects, whether by improved instrumentation or by more sophisticated analytical techniques? Open question!

    Einstein too believed in uncertainty of measurement, he just didn't feel the need to explain it's source. I mean, just how *can* we know every possible influence on a particle and then measure it with arbitrary accuracy? We can't, and we never will be! So you see, Einstein's treatment of the issue is pragmatic, practical, and 100% consistent.

    Heisenberg's, on the other hand, are based on assumptions that the laws of physics must somehow be constrained by the limitations of the tools of human understanding. Heisenberg even went on to say that the mere act of observation affects measurement. Okay, but if we accept that we then have to ask - what exactly does it *mean* to observe something anyway? In other words, by "answering" one question, we've created a hundred more because we now have a bunch of metaphysical issues to address! Such questions and answers are antithetical to the scientific approach because in science we are only concerned with models and approximations.

    Quote Originally Posted by Mario F.
    I said nothing like that. The uncertainty Principle hasn't been proven. Einstein, on the other hand, always opposed Quantum Physics in general. It clashed with his classic view of a perfect and deterministic universe. The Uncertainty Principle is just one example of Einstein's resistance. And is best reviewed in the Einsten-Bohr debates (which were published) where he consistently loses argument after argument. I think that there may be better -- and more modern -- opponents to the uncertainty principle than Einstein.
    Wrong. Einstein embraced (and indeed, helped found) QM. His argument was really just against assigning reality to intangibles. Uncertainty is everywhere, but it's usefulness as a construct in physics is both limited and dangerous. Limited because it's scope is really just a metaphysical statement, and dangerous because it only serves to stimulate speculative debate. In fact, that is precisely what has happened - these days, science has taken on a rather "mystic" appeal, where just about anything goes. Want to go back in time? - Try a wormhole! Did I really just stub my toe? - Don't worry, in another multiverse you missed the rock! Need to travel faster than the speed of light? - No problemo, we've got an equation for that too!

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