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/sci/ - Science & Math

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4491809 No.4491809 [Reply] [Original]

So I was trying to explain the uncertainty principle to my dad and he asked a good question:

What value would knowing both position and momentum have? What would you gain or be able to do with the knowledge of both at the same time?

>> No.4491820

>>4491809
You can't know both values. That is the entire point of the formulation. It is not possible. If you want both, take a classical limit <span class="math">\hbar \to 0[/spoiler], but then you loose quantum mechanical effects/accuracy.

See
http://www.falstad.com/qm1d/

>> No.4491835

>>4491809
lol Op you're trying to explain it to your dad and you don't even know the answer to that.

the thing is that there is a DUALITY that says we CANNOT know both.

(it also turns out we can't even know either one completely), so Ops equation is only the surface of the crazy world of quantum.

>> No.4491838

>>4491820\
>>4491835

Way to not answer OP's question

>> No.4491842

>>4491820
>>4491835
The OP obviously knows it isn't possible. His father asked the question (implying that his son told him you can't know both).

>> No.4491844

Like most questions in science OP, their answers really don't have a purpose other than knowledge. If it had any other purpose, it would be engineering.

>> No.4491848

>>4491809

You'd be able to get exact predictions of atomic interaction rather than probability clouds.

>> No.4491850

>>4491838
his question has no answer. dude. take even the angular momentum of a very simple hydrogenic atom. you cannot even know more than the total angular momentum L and one component (either Lx,Ly, or Lz)

We can't even know all 3 components of the angular momentum of a simple hydrogen atom due to further dualities.

You have no idea how crazy shit gets.

>> No.4491851

>>4491809
If you know both then there is no uncertainty in your predictions. Given the starting conditions you could predict the behavior of a quantum system at any point in time from there. Since we can't know both, we can't say with certainty, we can just make predictions of how likely something is at the quantum level.

>> No.4491856

>>4491838
>>4491842
I'm >>4491820
What are you talking about? If you knew both, you can do anything you can do in classical physics with momentum/position values. There isn't much more. We could imply a completely deterministic universe as it would eliminate uncertainty, and phenomena like entanglement would not be possible.

>> No.4491860

>>4491850
i should also elaborate, you really cannot even know 1 component, say Lz, and the total angular momentum L......

We can only know probabilities of finding certain eigenvalues.

>> No.4491861

The whole idea is that, given the momentum (a vector, mind you--it tells you which direction the particle is going) and position of every particle in a system, you could in principle work out exactly how that system would evolve. Each future state is precisely determined by any given past state. The uncertainty principle illustrates that this deterministic outlook is untrue.

>> No.4491863

>>4491842
Correct.

I used a macroscopic example of a hypothetical rocket ship in the outer solar system. In order to land it on Earth, you need to know its position and momentum at the same time in order to fire the rocket boosters correctly to send it home.

What could you do quantumly IF you COULD know both? For example, would there be quantum computing application, etc?

>> No.4491864

>>4491809
To answer OPs question you could answer a lot if you knew both position and momentum. FOr example in denisty functional theory (essentially quantum mechanics for a many electron system) we make a bunch of approximates based upon the motion. If we could know exact position and momentum we would have no need for these approximations, and would be able to calculate values closer to expected values.

>> No.4491868

>>4491861
>implying the Klein-Gordon/Kemmer equations do not time evolve

>> No.4491869

>>4491864
So you would be able to solve exactly all molecules.

>> No.4491873

>>4491861

Not at all. The uncertainty principles implies that you could never have knowledge of the position and state of every particle. If a wizard came down from the heavens and told you what they were, then nothing would prevent you from deterministically predicting every future state.

>> No.4491880
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4491880

>>4491856
>implying quantum mechanics isn't deterministic

>> No.4491889

>>4491880
HURRRR DURRRRRR
http://en.wikipedia.org/wiki/Bell's_theorem

>> No.4491922

>>4491809
Get a sufficient answer yet OP?

>> No.4491936

>>4491922

Umm.. I believe so.

Question: Does a particle have a defined position and momentum at any and all times but it is simply not possible to transmit this information with absolute clarity?

>> No.4491941

OP, ask a physics prof or something. /sci/ hasn't even figured out whether QM implies determinism or not.

>> No.4491943 [DELETED] 

>>4491936
Yes. The uncertainty is in our measurement.

>> No.4491953

The uncertainty principle means that the position and momentum operator don't commute. If there was no uncertainty principle I could get the momentum and position regardless in the order of which I made a measurement, without collapsing the wave function into one set of eigenstates of that particular operator. This would ruin wave/particle duality and the de Broglie relation. It would fuck with A LOT of shit beyond obscure stuff like entanglement and probability distributions. Namely, how light behaves and propagates, how all modern electronics works (quantum tunneling) and countless other stuff.

>> No.4491954

>>4491936
No. And it's not good to think of it as a particle. The statistical interpretation is fucking retarded.

In quantum field theory, a QHO is assigned to every point in space for a field. Particles are normal modes of this field as energy eigenstates. The best interpretation is to imagine a particle as a fluctuation on a field/manifold.

>> No.4491957

>>4491936
>>4491943
No, it is not just because of our measurement. THe math shows that position and momentum are not commutators, so that means they cannot be determined at the same time. It has to deal with everything being casted in terms of probabiltiy density.

>> No.4491960

>>4491954
To add, uncertainty is in the definition. It's not a result of the way information is organized

>> No.4491965

>>4491873
Wow, really?
Please leave this thread (or at least stop posting in it), you have absolutely no idea what you are saying. Quantum uncertainty is a fundamental aspect of the behavior of particles. They do not have a "hidden" momentum and position floating around somewhere. How would QM ever arise if they did?

>> No.4491968

>>4491953
>>4491957

Please go into more detail about the concept of "commuting."

>> No.4491975

>>4491968
http://en.wikipedia.org/wiki/Commutative_property
Go to the Examples section.

>> No.4491979

>>4491943
No. No. No. No. No.
No.
No.
Have you even seen how the uncertainty principle is derived? It is a purely mathematical process based on known facts about matter, with no link whatsoever to any "observation." That is the absolute worst word to ever be introduced into quantum mechanics.

>> No.4491981

>>4491968

AB=/=BA

or AB-BA =/= 0

where A and B are position and momentum. Specifically the commutator of position and momentum is i*hbar. I can show it but it would require knowledge of the quantum mechanical momentum operator (-i*h*d/dx) which can be sort of hard to understand without an explicit proof the involves several steps including and integration by parts and some substitutions which I'm too lazy to write out right now.

>> No.4491990

>>4491965

That's the same chain of reasoning that leads to a cat in a superstate.

>> No.4491994
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4491994

>>4491990
>superstate

>> No.4492001

>>4491990
Your point? That's how it is. Deal with it.

>> No.4492004

Heisenberg got pulled over for speeding. The cop says "Do you know how fast you were going?" And Heisenberg sayd "No, but I know exactly where I am."

AMIRIGHT /SCI/?

>> No.4492018

mfw i come back to this thread 45 minutes later after posting 3 comments and im one of the only people unattacked because i actually knew what i was talking about

>> No.4492030

>>4491990
Every particle within everything is always, ALWAYS, in a quantum "superposition." Particles interact with each other probabilistically in a way precisely determined by their wave function. The reason you don't see this on the macro scale is because things average out over many particles and you might as well treat it as one object with a very tiny deBroglie wavelength.
You have a wavefunction, and so does the cat, but it allows such tiny variation that it functionally doesn't exist.

>> No.4492034

>>4492004
technically he should also say "where am i" and the cop should say "theres a 50% chance youre in california" "a 5% chance you're in new york" and a "45% chance you're in texas"

and then heisenberg jumps out of the car and attacks the cop, gets thrown in the cop car, and realizes he no longer has a finite probability of being found infinitely far away.

>> No.4492042

>>4492030
> Particles interact with each other probabilistically in a way precisely determined by their wave function.
>probabilistically
>precisely determined
Pick one.
It is not probabilistic, it is intrinsic uncertainty.

>Every particle within everything is always, ALWAYS, in a quantum "superposition."
No, decoherence removes all possibilities for superposition between states. You need a very tight environment/experimental setup to get particles into this condition.

>The reason you don't see this on the macro scale is because things average out over many particles
No, it is due to decoherence, which is a result of wave function interference and interaction via exchange of quanta.

>> No.4492050

>>4492042
>intrinsic uncertainty
you know technically its not even uncertainty. the position of an electron IS the bell curve. space doesn't exist.

>> No.4492057

>>4492004
I like it!

>>4491861
This guy is right.


Also I want to point out that in the argument over determinism and non-determinism, it is interesting to note how the math of QM works.
All the actual math of QM is completely deterministic. If we know the state at one time and any potentials or whatnot then we know the state of the system for ANY future time as long as it is not disturbed.

The non-deterministic part comes from observations. What we do is simply erase the original state and just replace it with the state that is actually observed.
(very mathematical right?)

So the act of observation in QM is the only non-deterministic thing, and it's sort of just a mathematical hack job.
Without any information about what the outcome is after the observation we simply look at the state before it was observed and we can at best give the probability for it to be in another state.

>> No.4492065

>>4491954
Are you somehow under the mistaken impression that a statistical interpretation cannot be given to the state vector in quantum field theory?

>> No.4492094

>>4492042
>No, decoherence removes all possibilities for superposition between states.
That doesn't even mean anything. Whether something is a "superposition" depends on the basis you're using.

>> No.4492118

>>4492065
I think what he is saying is for example if I have a state describing position:
|x> = A|1> + B|2>

Then it's stupid to say that |x> has |A|^2 probability of being at |1>, and |B|^2 probability of being at |2>

It can be given a statistical interpretation, but it requires sensitive wording which is usually done wrong.
It would be accurate, however, to say:
|x> has |A|^2 probability of being found at |1> after a measurement is made.
But this says nothing about the current state (before measurement).

So I think what he means is that the statistical interpretations only apply to what you can expect to get after making an observation in the future, but that the statistical interpretation is somewhat meaningless to apply to the state as it is before a measurement.

>> No.4492163

>>4492118
Interpretations that posit the way things are before a measurement aren't meaningless; they're just making statements that can't be supported by evidence. That said, I agree we should remember the standard interpretation is about measurement outcomes.

And none of this changes between particle and field theories, as that guy seemed to imply.

>> No.4492165

>>4492042
>1
Don't be an ass; I mean the probabilities are precisely determined
>2
*MASSIVE OVEREXAGGERATED SIGH*
Decoherence explains the macro scale, but to say even one particle ever has its wavefunction completely collapsed violates Heisenberg's Uncertainty. And any particle that isn't stuck to a single point (which is impossible) is in a superposition.
>3
That's what exactly what I just said in less precise language...

tl;dr stop being a dick

>> No.4492210
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4492210

>>4491889
Schrodinger's equations explicitly and exactly determines the time development of a wavefunction. That's a deterministic theory if I've ever seen one.

>> No.4492229

>>4492210

Yes and no. In a theoretical sense, the SE is showing the time evolution of the system but still only probabilistic. Higher energy levels for the system, and then plotting gives you several peaks where the particle is actually at.

Once you measure that, then the the wave function collapses into a state. So its not deterministic.

Further explanation, set up 100 identical experiments with 100 identical particles. If you measure position at the exact same time for all 100 experiments, you will NOT get 100 identical answers.

Im fucking tired, not sure if that made sense

>> No.4492241

>>4492229
>he thinks wave functions collapse
Ishiggity wiggity whoo hoo

>> No.4492254

>>4492241
I am seriously starting to hate all of you retarded MWI/pilot wave fags.
>HURR INFINITE UNIVERSES
>DERP THE WAVE FUNCTION IS REAL ITS A RIPPLE IN SPACE TIME
>MATH IS REALITY
No. Fuck off.

>> No.4492265

>>4492254
ok faggot then what is the wave function and why does the double slit experiment produce waves if its a point particle

what is wrong about thinking about a particle as a oscilating wave

and why does the math describe reality so well

>> No.4492266

>>4492229
You are looking at it as a point particle whose position just so happens to be governed by a wavefunction.

That's the problem with asking "where is the particle now"? Before the collapse, and you think that the probabilities tell you the probability that the particle IS at some location.


This is all false by the copenhagen interpretation. In this case, we don't think of it as a point particle before collapse, there is no meaning to asking where is the particle now before collapse, and the probabilities tell us where the collapsed wavefunction will BE localized AFTER the collapse, not where a particle is at the current moment.

>> No.4492268

>>4492265

If I put a measuring device in one of the slits I no longer get interference though.

>he thinks wave functions don't collapse

>> No.4492288

>>4492268
Nope. You just so happen to be in a universe where the photon deterministically took that path. There's another universe where the photon doesn't even exist.

>> No.4492295

>>4492288
>herpaderp infinite parallel universes because mathematically elegant

>> No.4492300 [DELETED] 

>>4492241
There's no arguing that epistemic wavefunctions collapse. I personally find ontological wavefunctions distasteful because to posit such a thing needlessly treats time on a different footing from space, but that isn't science.

>> No.4492307

>>4492241
There's no arguing with the fact that epistemic wavefunctions collapse. I personally find ontological wavefunctions distasteful because to posit such a thing needlessly treats time on a different footing from space, but that isn't science.

>> No.4492310

>>4492295
Buttmad experimentalist with no imagination who thinks the Higgs boson doesn't exist because too low of sigma detected

>> No.4492322

>>4492268
The wavefunction cannot collapse without violating Heisenburg's uncertainty principle.
The measuring device doesn't collapse the wavefuction because it allows us to "see" the particle, it just forces some amount of decoherence into the system by interacting with it.

>> No.4492338

Seems like you guys might have different ideas of what it means for it to "collapse".

>> No.4492335

>>4492322
"Collapse" is a colloquialism for applying projection operators to the state vector / density operator and renormalizing; nobody thinks the wavefunction ever collapses to a point. Unless you had different reasoning behind your claim of uncertainty principle violation?

>> No.4492340

Is the "wave function" a real thing?

>> No.4492343

>>4492340
As "real" as particles are.

>> No.4492344

>>4492340
Epistemic wavefunctions are not real things except insofar as they exist in your mind. Ontological wavefunctions (wavefunctions which are real objective things) may or may not exist.

>> No.4492351

>>4492340
The wavefunction gives the probability of finding a particle. It is not real.

>> No.4492360

>>4492351
What you are describing would be a "hidden variable" theory.

It is pretty much unanimously accepted that this is very unlikely to be true.

>> No.4492370

>>4492360
As stupid and meaningless as the phrase is, I don't think most scientists would consider the Copenhagen interpretation to be a "hidden variable theory."

>> No.4492373

>>4492360
So you are saying there is a wave instead of a particle?

>> No.4492388

>what value
LaPlacian Determinism maybe, for starters.

>> No.4492391

More information, and accurate information, would always lead to better theories... and maybe even contribute to the GUT.

>> No.4492398

>>4492373
No, it seems that they are neither waves nor particles, but something that has properties of both in certain conditions.

That is the wave-particle duality.