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Offline glovesforfoxes

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Randomness and quantum mechanics
« on: 03/07/2009 16:04:02 »
Can somebody explain how the idea of randomness and quantum mechanics are often paired up? Why is it that quantum mechanics is random?


 

Offline JP

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« Reply #1 on: 03/07/2009 17:33:36 »
In classical mechanics, the models you use are all based around predicting the exact state of something.  For example, you could predict exactly where a ball will go when you throw it.  The only limit to how precise your predictions are is how well you can measure things.

One of the main features of quantum mechanics is that the best your models can do is to predict the probability of finding your system in a given state.  For example, instead of predicting exactly where an electron is, you would instead predict a range of places it could be, with probabilities of finding it in each place.  This seems to be an actual property of quantum mechanical objects.  No matter how accurate your theory and measurements are, you still can do no better than give probabilities of different measurements.  I think the idea that you can't predict exact outcomes of measurements is what often gets called "randomness."
 

Offline lightarrow

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« Reply #2 on: 03/07/2009 17:50:56 »
Can somebody explain how the idea of randomness and quantum mechanics are often paired up? Why is it that quantum mechanics is random?
Quantum mechanics is not random, even if this is the way some scientists thought of it. The Schrodinger equation of QM is totally deterministic: the wave equation, which describes a quantum system, evolves through that equation in a deterministic, that is totally non-random, way.

What were confused with 'random' is the fact they pretended to use classical descriptions for concepts that requires instead a totally different description.

Let's say, as a metaphor, that you want to describe the behaviour of the sea using a float which is connected to a mechanism that limits its movements because of friction. Observing the float's movements you could think that the sea's behaviour is 'random'. But you know that the sea waves, actually, are not.
« Last Edit: 03/07/2009 17:54:32 by lightarrow »
 

Offline glovesforfoxes

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Randomness and quantum mechanics
« Reply #3 on: 03/07/2009 19:59:33 »
yeah, i was thinking about randomness in general and then thought about why quantum mechanics is considered random. my main thought is that we have just not developed the tools to predict properly what happens as such a small scale, which is confirmed by the above post. however.. hard to falsify.. still.. i can't see why everything else would be so non-random if the quantum mechanical mathematics/system/tools show it is random.

i strongly believe in Einstein's quote: "God does not play dice with the Universe" - I have seen nothing that disputes this, although of course i cannot see the entire universe.
 

Offline JP

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Randomness and quantum mechanics
« Reply #4 on: 03/07/2009 22:41:20 »
There's pretty good evidence that god does play dice with the universe.  In other words, there's good reason to believe that quantum mechanics isn't just a case of us not being able to see the underlying deterministic universe.
 

lyner

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Randomness and quantum mechanics
« Reply #5 on: 04/07/2009 00:32:25 »
Surely the Heisenberg principle implies randomness - due to the uncertainty involved. I.e if the value of a body's position cannot be known exactly then is there not a randomness about that effective position?
 

lyner

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« Reply #6 on: 04/07/2009 01:33:43 »
I know Albert was credited with 'that quote' but, if you discount the existence of god, the statement is meaningless. It counts for nothing in any argument and need not be associated with the bits that he got right. He was human, after all.
 

Offline lightarrow

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« Reply #7 on: 04/07/2009 08:21:35 »
Surely the Heisenberg principle implies randomness - due to the uncertainty involved. I.e if the value of a body's position cannot be known exactly then is there not a randomness about that effective position?
Do you want to know what Heisenberg said?

"The invisible elementary particle of modern physics does not have the property of occupying space any more than it has properties like color and solidity. Fundamentally, it is not a material structure in space and time but only a symbol that allows the laws of nature to be expressed in especially simple form."

I found this citation in this book:

"Introduction to the Quantum Theory" - David Park - Third Edition -
pag.55:

<<Much has been written on what indeterminacy means, but not many words are needed here. Most people's first reaction to it is something like: "All right, you can't measure this position or this momentum accurately but the number is there, whether you can measure it or not."

Some very distinguished older physicists thought that, but the general opinion now is that they were almost certainly wrong. Now it seems like a metaphysical assumption impossible to test by experience and useless to assume.

The general opinion is that concepts like position and momentum are formed in our minds out of daily experience with things we can see and touch and that it is a mistake to assume that particles can be discussed as if they were scaled-down versions of those things.

Consider, for example, the two-slit experiment....The size of the pattern depends on the separation between the slits. If a particle is a thing, one would like to say that it goes through one slit or the other, but if it goes through one slit, how does it know the slit separation? And if it goes through both, what is the number that tell where it is? On the whole, physics makes more sense if we do not regard photons and electrons as things.

As Heisenberg wrote (1959, p.80):
"The invisible elementary particle of modern physics does not have the property of occupying space any more than it has properties like color and solidity. Fundamentally, it is not a material structure in space and time but only a symbol that allows the laws of nature to be expressed in especially simple form."

In this view, the indeterminacy relations are a tax we pay for using classical terminology where it is not really applicable>>
« Last Edit: 04/07/2009 08:24:34 by lightarrow »
 

lyner

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Randomness and quantum mechanics
« Reply #8 on: 04/07/2009 13:27:55 »
Interesting but does it specifically rule out the random element if the outcome is measured in a conventional way? Or are you implying that what goes on at a level we don't understand and can't measure may, in fact be non-random and capable of being determined exactly?
Is it the reduction to a "simple form" that introduces the random experience?
 

Offline lightarrow

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« Reply #9 on: 04/07/2009 16:02:07 »
Interesting but does it specifically rule out the random element if the outcome is measured in a conventional way?
No, certainly. I just wanted to point out something like this: what is the 'exact' position of a finite-lenght light pulse, for example? It doesn't have an exact 'beginning' or 'end' or 'centre' so our conventional ways of measuring things are not adequate any longer in these cases, isnt'it?

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Or are you implying that what goes on at a level we don't understand and can't measure may, in fact be non-random and capable of being determined exactly?
If you mean 'classical determinism' or hidden variable-like theories, no, I'm not saying that.

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Is it the reduction to a "simple form" that introduces the random experience?
Yes, it is our demand to 'measure eggs with squares', if you pass me the expression  :)
 

Offline wolfekeeper

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« Reply #10 on: 04/07/2009 17:02:44 »
Can somebody explain how the idea of randomness and quantum mechanics are often paired up?
When you do the twin slit experiment with a photodetector the photon arrives at a random place each time you run it; if you collect a lot of data, the shape of the probability curve of getting a hit on the photodetector if you move the photodetector around is statistically the same as the wavefunction intensity squared at the detector.
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Why is it that quantum mechanics is random?
Nobody knows.

What we do know is that when you do an experiment that displays the type of physics known as quantum mechanics, the results are somewhat different every time you perform the experiment, but the results are consistent with the passage of a quantum mechanical wavefunction.

Why the universe picks one point of the wavefunctions to decide to put an interaction, rather than another- I'm pretty sure that that is something nobody knows.

It's an assumption that this is random, but there's no way to prove it. Ockham's razor makes you pick it, because it's the simplest explanation for the results you get.
« Last Edit: 04/07/2009 17:08:37 by wolfekeeper »
 

Offline glovesforfoxes

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Randomness and quantum mechanics
« Reply #11 on: 05/07/2009 16:02:23 »
ok, so let's say i believe that quantum mechanics is truly random. how is it, then, the the classical world seems so deterministic? is that just a psychological bias? also, if the quantum mechanical scale is so small, does/could it have an impact on free will?

i know these are very big questions, but they're ones that i find interesting, even if they are very hard to answer!

by the way sophiecentaur, Einstein meant God in a different way -

"I believe in Spinoza's God who reveals himself in the orderly harmony of what exists, not in a God who concerns himself with the fates and actions of human beings." in other words, Einstein believed that God & nature were exactly the same - God isn't a being, he is everything materialistic.
 

Offline wolfekeeper

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« Reply #12 on: 05/07/2009 16:29:22 »
ok, so let's say i believe that quantum mechanics is truly random. how is it, then, the the classical world seems so deterministic?
Again, nobody really knows the answer to this.

The last attempted answer I read was something along the lines that in most large scale situations all the myriad different quantum mechanical things that could happen at the microscopic level all do more or less the same thing in aggregate, so the universe diverges a lot less than you would expect, the universe you're in is sort of riding the cusp of a whole bunch of universes that are busy splitting and remerging. So quantum mechanics may be largely normative in practice.

However, some quantum events can cause large scale changes to the universe, for example Schroedingers cat, once you open the box (or don't close it) the effect of a single quantum decay can change large scale things like whether you're burying the cat or not.

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is that just a psychological bias?
Dunno. Probably not.
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also, if the quantum mechanical scale is so small, does/could it have an impact on free will?
It doesn't seem likely to me.
 

Offline DoctorBeaver

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« Reply #13 on: 05/07/2009 23:41:32 »
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The last attempted answer I read was something along the lines that in most large scale situations all the myriad different quantum mechanical things that could happen at the microscopic level all do more or less the same thing in aggregate, so the universe diverges a lot less than you would expect

That's how I view it. Take the simple example of flipping a coin. We know the chance of it landing 1 way up is exactly the same as the chance of it landing the other way up; 50/50. However, if you flip the coin just 4 times, you could well end up with 4-0 or 3-1 in favour of 1 side or the other. But if you flip the coin 100 million times the divergence from 50/50 would be negligible. When you consider how many quantum events aggregate to form the material world we see around us it is not really surprising that it appears deterministic when all the "most probable" outcomes are summed.
 

Offline wolfekeeper

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« Reply #14 on: 06/07/2009 00:46:15 »
Yes, but it can't always average out, otherwise we wouldn't have quantum mechanics.

We don't really know what happens to the universes we never see; for example if you throw a bunch of photons slowly through twin slits you'll get a pattern of hits on the detector, but there was a very high chance that there could have been a different pattern. The many worlds theory says that the all the different patterns actually happen, but you're in the wrong subpart of the universe to see that. In some cases these different choices join back up again, and you can tell that happened (for example in the twin slit the photon has gone through *both* slits- it must have done so to give that interference pattern).
« Last Edit: 06/07/2009 00:53:53 by wolfekeeper »
 

lyner

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Randomness and quantum mechanics
« Reply #15 on: 06/07/2009 10:18:20 »
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(for example in the twin slit the photon has gone through *both* slits- it must have done so to give that interference pattern).
But, of course, it doesn't "give a pattern", does it? It is observed to arrive in just one place - it has only enough energy to interact with one atom when it arrives. You cannot assert that it has "gone through both holes"; all you can say is that the energy has probably gone through both holes because, after a lot of photons have been detected, a diffraction pattern is seen, which implies that a wave has been involved.
What 'really happened'? As you can never actually look at that level, you can only say that it behaved 'as if' blah blah.
 

Offline lightarrow

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« Reply #16 on: 06/07/2009 11:38:05 »
(for example in the twin slit the photon has gone through *both* slits- it must have done so to give that interference pattern).
To be more precise: it is *the wave* that has gone through both slits, not the particle. You cannot say that the particle went through one of the slits or through both, because in this way you had enough informations to destroy the interference pattern (yes, even if you know that the particle went through *both* slits).
 

Offline wolfekeeper

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« Reply #17 on: 06/07/2009 11:54:07 »
Well, in the quantum electrodynamics formulation of QM the particle has gone every route to get from the emitter to the receiver, so, yes you can say that it has gone through both.
« Last Edit: 06/07/2009 11:58:38 by wolfekeeper »
 

lyner

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« Reply #18 on: 06/07/2009 12:29:53 »
If it doesn't actually need to exist whilst the energy is on the way, I say that you needn't actually claim that it is anywhere in particular.
Which is the bigger problem to deal with - "it's in two places at once" or "it's nowhere"? It could hurt your brain to reconcile either of those with normal everyday experiences. No need to try.

wolfekeeper
Your reference to "every route" is more accurate. The two slits idea is too simple, really, because the slits need to be of finite width - hence a multitude of possible paths.
« Last Edit: 06/07/2009 12:32:23 by sophiecentaur »
 

Offline wolfekeeper

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« Reply #19 on: 06/07/2009 12:45:28 »
If it doesn't actually need to exist whilst the energy is on the way, I say that you needn't actually claim that it is anywhere in particular.
Which is the bigger problem to deal with - "it's in two places at once" or "it's nowhere"? It could hurt your brain to reconcile either of those with normal everyday experiences. No need to try.
If QM doesn't hurt your brain, you're not doing it right!
 

lyner

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Randomness and quantum mechanics
« Reply #20 on: 06/07/2009 14:51:50 »
I think that it will only stop stop hurting brains, when we accept and don't fight against certain ideas. We must stop triumphantly quoting 'paradoxes' and open up to the possibility that paradoxes can always be resolved by altering the way of looking at things. When we can achieve that, QM and the rest will no longer appear to resist us.
It's an Eastern mystic / Talkien thing, if you like. (You must believe I have not just gone loopy by saying that. I will not have wind chimes in my garden or rearrange the furniture in my room going "OMMM".)

Why did the particle have to go through any slits at all? Do the actors in a play 'go through' the wires when we see them on TV? Sometimes I wish!
 

Offline lightarrow

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« Reply #21 on: 06/07/2009 23:30:43 »
Well, in the quantum electrodynamics formulation of QM the particle has gone every route to get from the emitter to the receiver, so, yes you can say that it has gone through both.
No, you can't. If you write the wavefunction of the particle and you impose that it goes through both slits, you'll find that it's square modulus is the probability distribution of classical particles going through the slits, that is two 'lumps' located behind the slits - no interference pattern.
What goes through both slits cannot be "the particle", unless you call "particle" the quantum system we are describing (which can act as "particle" or as "wave" according to the circumstances).
« Last Edit: 06/07/2009 23:35:21 by lightarrow »
 

Offline wolfekeeper

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« Reply #22 on: 07/07/2009 02:03:58 »
Careful here, in QED the particle has a vector that rotates as the particle travels. Dyson showed that if you do that correctly then the sum of the vectors is just the wavefunction, so it's equivalent to the normal Schroedinger equation.
 

Offline wolfekeeper

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« Reply #23 on: 07/07/2009 02:07:46 »
I think that it will only stop stop hurting brains, when we accept and don't fight against certain ideas. We must stop triumphantly quoting 'paradoxes' and open up to the possibility that paradoxes can always be resolved by altering the way of looking at things. When we can achieve that, QM and the rest will no longer appear to resist us.
Well something like that. QM has lacked somebody like Einstein- even Einstein couldn't tame the QM equations like he did with the Lorentz equations. Either there's a piece missing or it's staring us in the face and nobody can put it together.
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Why did the particle have to go through any slits at all?
Because when you set up the experiment you made them?
 

Offline wanhafizi

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« Reply #24 on: 07/07/2009 09:28:45 »
I don't think I can accept randomness.

Not even a single computer in this world can create a pure random number. It simply doesn't exists.

The randomness of radioactive decay can be made as an example. They say, although we know the exact rate of decay, we don't have any idea which one will decay first. For me, the notion of half life itself shows us that there are actually some system governing it. It wasn't random, it just we don't understand it yet. Otherwise, there won't be any notion of half-lives...

The facts is, we cannot measure any small stuff without 'touching' it. We used electron, photon, magnetic waves to measure by 'touching' what we are measuring. This causes the system being measured to be literally effected. Measuring the angular momentum of electron presents this problem. Yes, if the electron was spinning around, we would never know where it is at a certain time. Because, if we 'inject' an observer into the system (such as photon/light) the particle itself bounced with the electron and causes the angular momentum to change. That's why it became uncertain. Yet, some new age scientists take this notion as some esoteric findings in nature. Crazy...

To measure really small stuff in the real world is a very very tough job. Consider this, it have to be in absolute zero temperature, no light, not a single photon, not on earth because of the gravity and magnetic distortion, not to mention the absolute necessary to protect from electromagnetic waves... Just impossible...

I hope Albert Einstein is still alive today to unscrew quantum mechanic's mess...

Just a thought.
« Last Edit: 07/07/2009 09:46:35 by wanhafizi »
 

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