HUP and Conservation of momentum

In summary: We can only bound our uncertainty. It's very likely momentum is conserved because the bound on it is very low.
  • #1
g.lemaitre
267
2
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?
 
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  • #2
g.lemaitre said:
The HUP says that I can not know the position and the momentum of a particle simultaneously,
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.

I am sure one of the real experts here will correct me if I am wrong on this.
 
  • #3
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.
That's it exactly. For a good discussion of this point, consult Ballentine's text: Quantum Mechanics, A Modern Development.
 
  • #4
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?

You don't know because to paraphrase Socrates the only thing we know about indeterminacy is that we don't know. Accepting this brings enlightenment, rejecting it misery.
 
  • #5
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.
 
  • #6
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.

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.

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?
 
  • #7
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.
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:
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?
The form of the Lagrangian guarantees it.

If you don't know what it was to begin with then what would make you think it wasn't conserved?
 
  • #8
DaleSpam said:
Again, you are misunderstanding how the HUP works. You can measure both P and M to arbitrary precision at the same time.

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?



If you don't know what it was to begin with then what would make you think it wasn't conserved?
My point exactly. If physicists can't know what x then how do they know x is conserved?
 
  • #9
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?
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.

There are also many indirect ways to check conservation laws. For example conservation of angular momentum can be checked by looking at particle decay patterns, spectroscopic transitions, etc.

No one experiment shows conservation of momentum but there is plenty to suggest it and nothing that has violated it.
 
  • #10
g.lemaitre said:
Arbitrary precision isn't good enough
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:
My point exactly. If physicists can't know what x then how do they know x is conserved?
No, it is the opposite of your point.

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.

You have a new piece of data which does not contradict the theory. So what would make you think momentum wasn't conserved?
 
  • #11
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 not talking about infinite precision. The Planck Length is 10^-35 m. I'm pretty sure quantum effects occur between 10^-15 and 10^-35 m since as I recall a proton's position and momentum can be known simultaneously but an electron cannot and a proton is 10^-15 m if I have my numbers correct. So particles smaller than 10^-15 m how do you know that momentum is conserved?

To use the analogy of fireflies: we see fireflies when they light up but we do not know where they are between light-ups. How do you prove that their momentum is conserved between light-ups, imagining that the fireflies lengths is smaller than 10^-15 m?

I don't even see how you can input the values into Noether's theorem.



No, it is the opposite of your point.

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.
I'm talking about experiments on the quantum level.
 
  • #12
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.
 
  • #13
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.

Actually I got this quote from Kurdt posted 7 years ago in this forum at this thread:

https://www.physicsforums.com/showthread.php?t=120224

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.

I remember the analogy that you can borrow a loan from a bank on Friday so long as you return it on Monday when no one is looking.

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
 
  • #14
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
You don't seem to get what 'to know' means in science. That's the problem.
 
  • #15
Jorriss said:
You don't seem to get what 'to know' means in science. That's the problem.

+1

g.lemaitre said:
Actually I got this quote from Kurdt posted 7 years ago in this forum at this thread

And you should read some of the responses he got in that thread, rather than implicitly asking us to type them in again special just for you.
 
  • #16
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.

Your analogy is flawed. You're committing the fallacy of division

http://en.wikipedia.org/wiki/Fallacy_of_division

You're assuming that because a group obeys a law that its parts obeys a law. Imagine that you only had the ability to measure the strength of 3 billion humans. Given the crudity of your measurements you would assume that there is a conservation of strength among humans. When you're measuring devices finally reach the level where they can measure the strength of individual humans you'll find that not all humans have equal strength, nor is it conserved.
 
  • #17
  • #18
  • #19
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?

If you accept HUP as you stated it, it refers to knowledge of some human. But the conservation laws refer to the actual state of the particles. There is thus no direct contradiction.

Why do we think that the law of conservation of momentum is valid for particles in situations when we can't measure their momentum? Because it worked very well so far, and thus it became one of the cornerstones of the theory. There is no reason to abandon it. So we assume that conservation of momentum holds always, even if we do not check.
 
  • #20
g.lemaitre said:
I'm not talking about infinite precision.
Then arbitrary precision must be good enough.

g.lemaitre said:
as I recall a proton's position and momentum can be known simultaneously but an electron cannot
You recall incorrectly. The HUP does not prevent that, as I explained in post 2.

g.lemaitre said:
so particles smaller than 10^-15 m how do you know that momentum is conserved?
By Noether's theorem, as I said in post 5.

g.lemaitre, this is going around in circles. You are posting the same wrong statements. Please try actually responding to the substance of my post. You mention that you don't know how to plug numbers into Noether's theorem. What do you know about Noether's theorem?
 
Last edited:

1. What is the HUP?

The HUP, or Heisenberg's Uncertainty Principle, is a fundamental principle in quantum mechanics that states that it is impossible to know the exact position and momentum of a particle at the same time. This is because the act of measuring one variable will inevitably disturb the other, resulting in uncertainty.

2. How does the HUP relate to conservation of momentum?

The HUP is related to the conservation of momentum through the concept of wave-particle duality. According to quantum mechanics, particles also exhibit wave-like behavior, and the uncertainty in their position and momentum is due to the wave nature of particles. This means that the HUP applies to all particles, including those involved in momentum conservation.

3. Can the HUP be violated?

No, the HUP is a fundamental principle in quantum mechanics and has been verified through countless experiments. It is considered a law of nature and cannot be violated.

4. How does the HUP impact our understanding of the conservation of momentum?

The HUP adds an element of uncertainty to our understanding of the conservation of momentum. While the total momentum of a system is always conserved, the individual momenta of particles may have some uncertainty due to the HUP. This means that the exact behavior of particles in a system cannot be predicted with certainty, but only with a certain degree of probability.

5. Is the HUP relevant in macroscopic systems?

Yes, the HUP applies to all systems, regardless of size. However, the effects of the HUP are only significant in the microscopic world. In macroscopic systems, the uncertainty is too small to have a noticeable impact on the behavior of particles. As a result, the HUP is more relevant in understanding the behavior of subatomic particles.

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