The discussion centers around the Heisenberg Uncertainty Principle (HUP) and its implications for the conservation of momentum at the quantum level. Participants explore the relationship between the inability to simultaneously know a particle's position and momentum and the validity of conservation laws in quantum mechanics.
Participants exhibit disagreement regarding the implications of the HUP on the conservation of momentum. While some believe conservation can be established through theoretical frameworks and historical data, others challenge the sufficiency of these arguments given the uncertainties involved in quantum measurements.
Limitations in the discussion include varying interpretations of the HUP, the dependence on definitions of measurement precision, and unresolved questions about the applicability of conservation laws at quantum scales.
As far as I know, that isn't how the HUP works. You can measure the position and measure the momentum and do each measurement to an arbitrary degree of precision. What you cannot do is prepare a state where all of the particles in that state have a well defined position and a well defined momentum.g.lemaitre said:The HUP says that I can not know the position and the momentum of a particle simultaneously,
That's it exactly. For a good discussion of this point, consult Ballentine's text: Quantum Mechanics, A Modern Development.DaleSpam said:As far as I know, that isn't how the HUP works. You can measure the position and measure the momentum and do each measurement to an arbitrary degree of precision. What you cannot do is prepare a state where all of the particles in that state have a well defined position and a well defined momentum.
g.lemaitre said:The HUP says that I can not know the position and the momentum of a particle simultaneously, therefore, from time T1 to time T2 I cannot predict its position. How does this not violate the law of conservation of momentum? If you cannot know its position and momentum exactly that how do we know the law of conservation of momentum is true at the quantum level?
DaleSpam said:We do know that conservation of momentum is "true" at the quantum level by Noether's theorem. The Lagrangians are all invariant under translations, therefore momentum is conserved. The HUP doesn't change that.
Again, you are misunderstanding how the HUP works. You can measure both P and M to arbitrary precision at the same time.g.lemaitre said:I find it very hard to believe that we know momentum is conserved at the quantum level. Let P = position and M = momentum.
10am: P = (7,4) M = ?
11am: P = ? M = 4
(7,4) is an x,y coordinate.
The form of the Lagrangian guarantees it.g.lemaitre said:How am I supposed to be able to conclude that momentum of the particle above was conserved from 10 am to 11 am if I don't even know what it was to begin with?
DaleSpam said:Again, you are misunderstanding how the HUP works. You can measure both P and M to arbitrary precision at the same time.
My point exactly. If physicists can't know what x then how do they know x is conserved?If you don't know what it was to begin with then what would make you think it wasn't conserved?
That's all we have. We can only bound our uncertainty. It's very likely momentum is conserved because the bound on it is very low.g.lemaitre said:Arbitrary precision isn't good enough. Say that momentum is between 3 and 5 at time t1, then between 3 and 5 at time t2 - how do you know it's conserved? It could be 3 at time t1 and 5 at time t2?
This is silly. Arbitrary precision means there is not a limit to the precision. That isn't good enough? How could arbitrary precision possibly not be good enough? If you want infinite precision then you have come to the wrong universe.g.lemaitre said:Arbitrary precision isn't good enough
No, it is the opposite of your point.g.lemaitre said:My point exactly. If physicists can't know what x then how do they know x is conserved?
DaleSpam said:This is silly. Arbitrary precision means there is not a limit to the precision. That isn't good enough? How could arbitrary precision possibly not be good enough? If you want infinite precision then you have come to the wrong universe.
I'm talking about experiments on the quantum level.We have a theory, that theory predicts many things, including that momentum is conserved. We have more than 100 years worth of historical measurements. Those measurements all agree with the theory, including experiments on the conservation of momentum.
atyy said:Let's talk about conservation of energy. In general, it is the average value of energy that is conserved, ie. does not change with time. So at t=0. we prepare an infinite number of systems identically in a particular state.
At t=1, we measure the energy of half of them. In general we will get a bunch of different results, but if we average across all measurements, there will be some average value <E1>.
At t=2, we measure the energy of the other half of them. Again, we get a bunch of different results, but if we average across all measurements, there will be some average value <E2>.
We will find that <E1>=<E2>, ie. the average energy does not change with time. This is what we mean by conservation of energy.
kurdt said:It is possible to break the energy conservation law but if you look yourself at the equation you will see that this can only be achieved for very small periods of time. For example try working out how long a stationary electron can exist by plugging its rest mass in the equation and finding delta t.
You don't seem to get what 'to know' means in science. That's the problem.g.lemaitre said:I'm still not satisfied with the explanations for conservation of momentum.
If a particle is at 0,0 at time t1 with uncertainty of a radius of 2*10^-18. Then we find it at time t2 at 1,0 where the units are 10^-18 m and its uncertainty is still the same radius, and we know that it's momentum is east between 30 degrees and 330 degrees, then I don't see how we know that it went on a straight line from 0,0 to 1,0
Jorriss said:You don't seem to get what 'to know' means in science. That's the problem.
g.lemaitre said:Actually I got this quote from Kurdt posted 7 years ago in this forum at this thread
atyy said:Let's talk about conservation of energy. In general, it is the average value of energy that is conserved, ie. does not change with time. So at t=0. we prepare an infinite number of systems identically in a particular state.
At t=1, we measure the energy of half of them. In general we will get a bunch of different results, but if we average across all measurements, there will be some average value <E1>.
At t=2, we measure the energy of the other half of them. Again, we get a bunch of different results, but if we average across all measurements, there will be some average value <E2>.
We will find that <E1>=<E2>, ie. the average energy does not change with time. This is what we mean by conservation of energy.
g.lemaitre said:Your analogy is flawed. You're committing the fallacy of division.
You're just begging the question. You need to prove that I've committed a fallacy.DennisN said:There's also a fallacy called Argument from fallacy; examples of such.
The HUP says that I can not know the position and the momentum of a particle simultaneously, therefore, from time T1 to time T2 I cannot predict its position. How does this not violate the law of conservation of momentum? If you cannot know its position and momentum exactly that how do we know the law of conservation of momentum is true at the quantum level?
Then arbitrary precision must be good enough.g.lemaitre said:I'm not talking about infinite precision.
You recall incorrectly. The HUP does not prevent that, as I explained in post 2.g.lemaitre said:as I recall a proton's position and momentum can be known simultaneously but an electron cannot
By Noether's theorem, as I said in post 5.g.lemaitre said:so particles smaller than 10^-15 m how do you know that momentum is conserved?