Uncertainity Principle: possible to know the momentum and position?

[Praveen Vijayan]

The principle states it is impossible to 'simultaneously' know the position and momentum(velocity)of an object. Position is something that can be noted at a particular instant, as from a photograph whereas velocity is something that can only be measured over a period of time,as from a movie. The principle doesn't prevent us from knowing the exact position of an object. Thus isn't it possible to take "photographs" of the particle for a long enough period and to know the trajectory it traces? So is it that, it is possible to know the momentum and position of a particle at any instant in the past and impossible to know at the present moment?

 

[bhobba]

No.

The reason is once you measure the position exactly its momentum becomes unknown. So every time you measure its position to trace out the path that path changes.

Thanks
Bill

 

[ddd123]

Would it essentially induce Brownian motion?

 

[ZapperZ]

The principle states it is impossible to 'simultaneously' know the position and momentum(velocity)of an object. Position is something that can be noted at a particular instant, as from a photograph whereas velocity is something that can only be measured over a period of time,as from a movie. The principle doesn't prevent us from knowing the exact position of an object. Thus isn't it possible to take "photographs" of the particle for a long enough period and to know the trajectory it traces? So is it that, it is possible to know the momentum and position of a particle at any instant in the past and impossible to know at the present moment?

I think you are having the same https://www.physicsforums.com/threads/misconception-of-the-heisenberg-uncertainty-principle.765720/ that a lot of people have.

Please note that the uncertainty in each of the value involves the "statistical average" of that value. What is the statistical average of ONE single measurement of a quantity?

Zz.

 

[bhobba]

Would it essentially induce Brownian motion?

Not really. Because with Brownian motion it has specific values of position and momentum that changes when it collides with other objects.

There is an interesting connection however. The path integral approach to QM is essentially a Weiner process (that's a Brownian motion process) in imaginary time. Why that is, is a deep foundational principle of QM first sorted out by Feynman. In QM complex numbers equals 'mystery':
http://arxiv.org/pdf/1204.0653.pdf

Well when I mystery I mean 'surface' mystery. Its equally deep answer is that its required for continuous transformations of so called pure states:
http://www.scottaaronson.com/democritus/lec9.html

Thanks
Bill

 

[Vinay080]

Position is something that can be noted at a particular instant

But, do instants (duration-less time intervals) exist? I have heard about Zeno's arrow paradox, which seems to conclude non-existence of instants. But, I am not sure.

Sorry, if this is confusing more for the OP. But, I wish if this could also be solved here in short words. Thank you.

 

[Nugatory]

But, do instants (duration-less time intervals) exist? I have heard about Zeno's arrow paradox, which seems to conclude non-existence of instants. But, I am not sure.

Sorry, if this is confusing more for the OP. But, I wish if this could also be solved here in short words. Thank you.

In short words: Yes, instants exist and Zeno's paradox is wrong.

If you want a longer and more satisfying answer (which would be reasonable, as the answer I just gave is not especially satisfying) it would be best to start a new thread... but if you do, take a moment to find some of the other threads here that discuss Zeno's paradox. You may find that the answer is already out there.

 

[mac_alleb]

There present h/mc value,
but if we consider h/mv
where v is nonrelativistic
then it seems all right.

 

[bhobba]

In short words: Yes, instants exist and Zeno's paradox is wrong.

Just as a heads up on background material examining that, either to sort it out yourself or prior to a new thread, real analysis is the area that explains it eg:
http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_REAL_ANALYSIS.PDF

It was one of the great achievements of 19th century mathematics sorting this out.

Thanks
Bill

 

[Praveen Vijayan]

No.

The reason is once you measure the position exactly its momentum becomes unknown. So every time you measure its position to trace out the path that path changes.

But knowing the change in momentum caused by the measurement isn't it possible to calculate the original momentum? In that way I could trace the path that the particle would have taken if there were no measuring process. I think it is somewhat like measuring the strength of a rod by breaking it.

 

[Nugatory]

But knowing the change in momentum caused by the measurement isn't it possible to calculate the original momentum?

We do not know the change in momentum; we know that the position measurement has changed the momentum, but we do not know by how much.