Laplace's Demon?

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Radium
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Laplace's Demon?

Postby Radium » Thu Aug 18, 2011 3:46 am UTC

First, a quick explanation for those of you who don't know what Laplace's demon actually IS. It's the concept that if you know the position and momentum of every particle in the entirety of the universe, the entirety of future of the universe can be predicted through the laws of classical physics.
Now, this idea is discredited due to thermodynamics, chaos theory and quantum mechanics, because mainly of increasing entropy and the Heisenberg Uncertainty principle.

However, my question is, WHY?
First of all, the Heisenberg Uncertainty principle states that the uncertainty in a measurement of position multiplied by the uncertainty in a measurement of momentum is greater than or equal to 5.272859×10^-35. However, it will still have a position and it will still have a momentum, just that they can't be measured without affecting each other.
Secondly, when your quantum wave-functions collapse a new universe with the different possibilities is created, right?

But still, shouldn't Laplace's Demon still be valid, given that all these facts could still be taken into consideration, and 'predict the future' as all the possible timelines of all the possible universes? Still not as 'useful' as the idea of Laplace's demon, as instead of predicting one definite outcome you predict EVERYTHING, but shouldn't it still be, in theory, possible?

Also, first-post-long-time-lurker hi.

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Re: Laplace's Demon?

Postby gmalivuk » Thu Aug 18, 2011 5:39 am UTC

Radium wrote:However, it will still have a position and it will still have a momentum, just that they can't be measured without affecting each other.
No. The uncertainty is actually a part of it, and not merely an artifact of our measuring of it.
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Re: Laplace's Demon?

Postby Tass » Thu Aug 18, 2011 6:19 am UTC

Radium wrote:But still, shouldn't Laplace's Demon still be valid, given that all these facts could still be taken into consideration, and 'predict the future' as all the possible timelines of all the possible universes? Still not as 'useful' as the idea of Laplace's demon, as instead of predicting one definite outcome you predict EVERYTHING, but shouldn't it still be, in theory, possible?


Yeah, if you knew the precise wavefunction of the entire universe and had infinite computing power, then you could predict the amplitudes for all future worlds.

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Re: Laplace's Demon?

Postby Technical Ben » Thu Aug 18, 2011 7:25 am UTC

Would you be able to compute all possible worlds but not which ones are probable?
IE you would know the state of the universe, what it could do, but no necessarily which bounds it falls between. If something like atomic/particle decay is truly random, could the "infinite computer" not simulate all possible results from it decaying at each possible moment in time?

This seems to give a nice combination of what we know about predictability and also what (at least so far) is random. We cannot model the universe entirely deterministic or entirely randomly at the moment. So you need something with a bit of both.
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Re: Laplace's Demon?

Postby Jakell » Thu Aug 18, 2011 7:44 am UTC

First of all, the Heisenberg Uncertainty principle states that the uncertainty in a measurement of position multiplied by the uncertainty in a measurement of momentum is greater than or equal to 5.272859×10^-35. However, it will still have a position and it will still have a momentum, just that they can't be measured without affecting each other.


It is important to note that the concept of uncertainty which we use here is not something that we get to deal with on a day-by-day basis, and so it can be tough to try to wrap your head around. When I say I throw a ball North at 5 m/s, you can pretty much plug those numbers into any sort of equation and get a reasonable answer; since the ball has such a very small deBroglie wavelength, the amount of uncertainty in it's position and velocity is pretty much negligible. If you start trying to talk about smaller things, like slow moving electrons for example, you can't just say they're moving to the left with some velocity at this point in space because our universe is inherently fuzzy in this respect. We instead have to rely on this wavefunction which is by it's nature smeared out in space and time to some degree. If you start out with a particle that is extremely localized (you know it's position very well), the moment you kick it out of it's box, it's wave function will start to spread out over a larger area, making it much harder to know it's velocity (momentum, essentially). If start with the particle in a larger area, so that it can begin spread out, then kick it out of the area, it's wavefunction will spread out a little more, but not nearly as much as the first particle; by sacrificing some certainty in position measurements, you gain some accuracy in momentum.

This video isn't perfect, but it kind of shows off what I am trying to say. The position of our particle is very well known to begin with then it spreads out considerably as it travels, making a good measurement of it's velocity impossible. Once the wave function has spread out a bit, though, it doesn't spread out much more, and so though you are not quite sure where the particle is, you can track the average position a bit better.

Ultimately, things simply do not have a very well defined momentum and position. They can be defined pretty darn well, since Plank's constant is so small, but there is always that minimum level of uncertainty that we get to deal with.

On a side note, it is pretty fun to thought-experiment letting plank's constant be much, much larger. If you set h to 2000 J.s, then if you were pretty sure you saw a 200 kg tiger running at you at about 10 m/s, you would only be able to measure it's position to roughly within a meter or two; which would make hunting or running in a quantum jungle fairly exciting.
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Re: Laplace's Demon?

Postby tomandlu » Thu Aug 18, 2011 10:23 am UTC

Radium wrote:Now, this idea is discredited due to thermodynamics, chaos theory and quantum mechanics, because mainly of increasing entropy and the Heisenberg Uncertainty principle.


BTW, and I could be wrong, but I think chaos theory is a red-herring in this case. It makes the problem worse, but the problem still exists without it. To put it another way, IF you could know the position and momentum of every particle with 100% accuracy, then chaos theory would not apply.
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Re: Laplace's Demon?

Postby Technical Ben » Thu Aug 18, 2011 11:37 am UTC

Jakell wrote:
Spoiler:
First of all, the Heisenberg Uncertainty principle states that the uncertainty in a measurement of position multiplied by the uncertainty in a measurement of momentum is greater than or equal to 5.272859×10^-35. However, it will still have a position and it will still have a momentum, just that they can't be measured without affecting each other.


It is important to note that the concept of uncertainty which we use here is not something that we get to deal with on a day-by-day basis, and so it can be tough to try to wrap your head around. When I say I throw a ball North at 5 m/s, you can pretty much plug those numbers into any sort of equation and get a reasonable answer; since the ball has such a very small deBroglie wavelength, the amount of uncertainty in it's position and velocity is pretty much negligible. If you start trying to talk about smaller things, like slow moving electrons for example, you can't just say they're moving to the left with some velocity at this point in space because our universe is inherently fuzzy in this respect. We instead have to rely on this wavefunction which is by it's nature smeared out in space and time to some degree. If you start out with a particle that is extremely localized (you know it's position very well), the moment you kick it out of it's box, it's wave function will start to spread out over a larger area, making it much harder to know it's velocity (momentum, essentially). If start with the particle in a larger area, so that it can begin spread out, then kick it out of the area, it's wavefunction will spread out a little more, but not nearly as much as the first particle; by sacrificing some certainty in position measurements, you gain some accuracy in momentum.

This video isn't perfect, but it kind of shows off what I am trying to say. The position of our particle is very well known to begin with then it spreads out considerably as it travels, making a good measurement of it's velocity impossible. Once the wave function has spread out a bit, though, it doesn't spread out much more, and so though you are not quite sure where the particle is, you can track the average position a bit better.

Ultimately, things simply do not have a very well defined momentum and position. They can be defined pretty darn well, since Plank's constant is so small, but there is always that minimum level of uncertainty that we get to deal with.

On a side note, it is pretty fun to thought-experiment letting plank's constant be much, much larger. If you set h to 2000 J.s,
then if you were pretty sure you saw a 200 kg tiger running at you at about 10 m/s, you would only be able to measure it's position to roughly within a meter or two; which would make hunting or running in a quantum jungle fairly exciting.

Forgetting that to even make out a tiger in such a quantum fuzzy image would be difficult at best. His poor head could end up two meters from his body! :shock:
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