16.02.09 philosophers, physicists, help!
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I’ve blinded myself with science.
Every time I read about physics, I get stuck at the whole Heisenberg Uncertainty Principle thing. I actually remember straining to understand it one night as a (very nerdy) teenager, and later on in science college, I would spew back the theory without ever really understanding it. Now I’ve finally picked up A Brief History of Time, and sure enough, nothing is more certain than my getting blocked at the Uncertainty Principle.
Here’s my problem:
Some believe that because everything in the universe is governed by a set of rules, if you know the state and velocity of everything in the universe at a given point, you could infer, by applying the rules of the universe, the state of everything at every other time. Hence everything can be said to be predictable. Let’s call this Determinism, which was at a time accepted by the scientific community. That makes sense to me.
But Heisenberg says that you can never measure the position of a particle perfectly, without changing its velocity (this is because you’d have to shed light on the particle to measure its position, and the light would alter the particle’s velocity). So, you can’t ever perfectly know the position AND velocity of a particle. Either you’re uncertain about its position, or about its velocity. Fair enough.
What’s always bugged me about this is that it seems to rest on nothing but an experimental limitation. Just because an experimental limitation introduces uncertainty, it doesn’t follow that uncertainty is a fundamental property of the universe. Yet Hawking explicity says it is; that this is the case no matter what experimental method you use to measure velocity or position. Why?
Hawking even says that some supernatural being could know all (ie. not be limited by experimental limitations), but “such models of the universe are not of much interest to us ordinary mortals”. Well, why wasn’t it a problem to accept Determinism, when there are also obvious experimental limitations to knowing the state and velocity of every particle in the universe?
More importantly, why must the very way the universe works be affected by our ability to measure it? It seems ballsy to suggest that the universe itself operates uncertainly, simply because we ordinary mortals can never know it perfectly. Sure, science must measure and predict, and the introduction of this principle increases the accuracy of our predictions. But why not say that’s the best science can do to be predictive? Why does it follow that this uncertainty is a property of the universe itself?
In other words, why assert that God plays dice with the universe? Why not say, “God doesn’t play dice, it just seems to our imperfect observational abilities that he does”?
I’m not sure this incertity principle is based on our technical limitation but on the fact that subatomical particles are both particles and wavelenght (dualité onde-particule).
From Wikipedia
“In quantum physics, the Heisenberg uncertainty principle states that the values of certain pairs of conjugate variables (position and momentum, for instance) cannot both exist with arbitrary precision. That is, the more precise one property is, the less precise the distribution of the other. […] This is not a statement about the limitations of a researcher’s ability to measure particular quantities of a system, but rather about the nature of the system itself.
In quantum mechanics, the particle is described by a wave. The position is where the wave is concentrated and the momentum, a measure of the velocity, is the wavelength. The position is uncertain to the degree that the wave is spread out, and the momentum is uncertain to the degree that the wavelength is ill-defined.
The only kind of wave with a definite position is concentrated at one point, and such a wave has an indefinite wavelength. Conversely, the only kind of wave with a definite wavelength is an infinite regular periodic oscillation over all space, which has no definite position. So in quantum mechanics, there are no states which describe a particle with both a definite position and a definite momentum. The narrower the probability distribution is for the position, the wider it is in momentum.”
But isn’t this too a result of measurement: “When the position of a particle is measured, the particle’s wavefunction collapses and the momentum does not have a definite value”. I’ve never seen an explanation of the HUP that doesn’t involve measurement or observation.
I’m not 100% of what I’m saying as I’m not very knowledgeable of quantum mechanics… or newtonian for that matter.
But the theoritical way to measure the speed of a wave, regarless of technical limitations, is to measure the time it takes for the wave to pass thru a point and complete a full cycle, summit to summit, for instance. But when you do that, you’re considering your wave/particle as a wave. So that manifestation you’re studying is no longer a dot in the space, it’s information is encrypted throughout the whole wave, from summit to summit. It doesn’t have a position, the wave itself is both the beggining and the end of that cycle.
I was fact checking, and this seems to be the modern explanation of HUP.
From the Wave-Particle Duality article on Wikipedia
“In fact, the modern explanation of the uncertainty principle, extending the Copenhagen interpretation first put forward by Bohr and Heisenberg, depends even more centrally on the wave nature of a particle: Just as it is nonsensical to discuss the precise location of a wave on a string, particles do not have perfectly precise positions; likewise, just as it is nonsensical to discuss the wavelength of a “pulse” wave traveling down a string, particles do not have perfectly precise momenta (which corresponds to the inverse of wavelength). Moreover, when position is relatively well defined, the wave is pulse-like and has a very ill-defined wavelength (and thus momentum). And conversely, when momentum (and thus wavelength) is relatively well defined, the wave looks long and sinusoidal, and therefore it has a very ill-defined position.”
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(can you please delete the first duplicate of this comment, I forgot to proof-read, tnx).
I’m not 100% sure of what I’m saying as I’m not very knowledgeable of quantum mechanics… or newtonian for that matter.
But the theoritical way to measure the speed of a wave, regarless of technical limitations, is to measure the time it takes for the wave to pass thru a point and complete a full cycle, summit to summit, for instance. But when you do that, you’re considering your wave/particle as a wave. So that manifestation you’re studying is no longer a dot in the space, it’s information is encrypted throughout the whole wave, from summit to summit. It doesn’t have a position, the wave itself is both the beggining and the end of that cycle.
Ok.. i paused to do a bit of fact checking, as I was starting to doubt myself even more, but this seems to be the modern explanation of HUP.
From the Wave-Particle Duality article on Wikipedia
“In fact, the modern explanation of the uncertainty principle, extending the Copenhagen interpretation first put forward by Bohr and Heisenberg, depends even more centrally on the wave nature of a particle: Just as it is nonsensical to discuss the precise location of a wave on a string, particles do not have perfectly precise positions; likewise, just as it is nonsensical to discuss the wavelength of a “pulse” wave traveling down a string, particles do not have perfectly precise momenta (which corresponds to the inverse of wavelength). Moreover, when position is relatively well defined, the wave is pulse-like and has a very ill-defined wavelength (and thus momentum). And conversely, when momentum (and thus wavelength) is relatively well defined, the wave looks long and sinusoidal, and therefore it has a very ill-defined position.”
Still sounds like just math to me, but it looks like you’re right. Someone on the Wikipedia Reference Desk asked the same question and got the following: http://en.wikipedia.org/wiki/Wikipedia:Reference_desk/Archives/Science/2008_October_14#Is_Heisenburg.27s_Uncertainty_Principle_really_universal.3F
Cheers!
Je pense que je t’ai perdue quelque part au deuxième paragraphe.
Okay, je vais relire ton texte et repenser à tout ça.
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Ok we’ll take out the math factor, let’s use an exemple that might not be totally in sync with quantum mechanics but that still illustrates the phenomenon pretty well.
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Suppose you’re at the beach and want to measure the speed of waves.
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You’ll stand in the water and measure the time it takes for two consecutives summit of the wave to hit you. But the wave itself is not the summit that hit you, it’s included all allong the two summits. You can’t pinpoint it’s position. By the way, the summit is a totally arbitrary point of reference, you could choose the bottom of the swell as well since they’re just as part of the wave.
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The only time this wave has a position is when it is concentrated at a point. For exemple, when the wave hits a concrete wall and all its energy is transfered from the x axis along wich it runs (the horizon line basically) to the y axis (the vertical of the wall it hits). So at this very moment, your wave is all concentrated at a definite x position (the only axis we’re interested in for this measurement). It’s not just the summit that hits the wall, it’s the whole wave, that’s why it’ll reach higher on that wall then the original summit (twice the horizon to summit distance (amplitude) if I remember well, or base to summit (2*amplitude). When we see an actual wave smashing into a well, it does indeed reach much higher than the tip of the wave itself.
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But as it does this, the wavelengt collapses into this definite point which makes it impossible to discuss speed, since speed is defined as the time in takes for the wave to complete a full cycle. There are no cycles anymore, the wave became a point.
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In quantum mechanics, instead of speed, they discuss moment, which is the inverse of the wavelenght (1/wavelenght). So when the wavelenght collapses and approaches zero we get 1/0 which is a mathematical impossibility. Sorry, math popped again.
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Is that any clearer?
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We got to keep in mind that quantum mechanics is not meant to be understood with our newtonian experience of life and frame of reference. Like for instance, when you approach the speed of light, your mass diminuishes. This makes no sense at all to me and I can’t wrap my head around it. All I can do is say … well, Ok then. I’ll take your word for it
So in my example, the concrete wall our wave hit is the beam of light you shed on it, or whatever measurement you’re doing. Trying to determine the position of a wave is basically like making it hit that concrete wall. It now has a definite position, but it no longer has a wavelength.
Sorry, maybe I’m getting a little too much into this, it’s just that explaining it to you was a way for me to understand the process better. I’m tutoring kids in secondaire and even sometimes Cegep, and it’s good to be able to answer such questions without too much hesitation. I now understand the HUP and the WPD much better, or at least, what were intuitions became known facts.
Holy shit, it actually is pretty clear that way. Mais faut que j’y pense un ti peu plus. Bear with me.
“This is not a statement about the limitations of a researcher’s ability to measure particular quantities of a system, but rather about the nature of the system itself.”
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but then again
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http://www.scienceblog.com/cms/quantum-paradox-directly-observed-milestone-quantum-mechanics-19156.html
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please note that I don’t understand anything about that article
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