Heisenberg Uncertainty Principle and Gaussian Distributions

[RogerPink]

Never Mind.

 

[reilly]

Now, apparently no one has understood what the OP is talking about (post #28). If there is still an issue to be resolved here, then a re-phrasing of the question would be helpful.[/QUOTE]

........
Perhaps you might explain the specifics of my lack of understanding. Thank you. Reilly Atkinson

 

[masudr]

Perhaps you might explain the specifics of my lack of understanding. Thank you. Reilly Atkinson

Eek. I'm very sorry, I meant post #27 not post #28.

 

[RogerPink]

I don't think I'm cut out for the forum format. Being in a better mood I think that rather than cut off storm off like a child I'll give you guys a play by play as I try to answer my own question (or my question evolves). Maybe if you see what I'm looking at you'll have a better idea what I'm trying to find out.

http://arxiv.org/PS_cache/quant-ph/pdf/0210/0210044.pdf

An interesting paper but contradicts what I thought kennard did. According to this paper kennard generalized the uncertainty relation for all distributions. The paper reformulates the uncertainty principle and lists possible violations.

 

[RogerPink]

Here is a great paper that has answered some of my questions.

Generalized Uncertainty Relations Phys Rev. A vol 35 pg 1486

And just so I'm clear here, I'm no longer asking a question of the forum, I'm just posting things I found helpful in my search for a clearer understanding of the limits of the uncertainty relation. If this is not an appropriate use of the forum, I won't be offended if this thread is killed.

 

[Careful]

Here is a great paper that has answered some of my questions.

Generalized Uncertainty Relations Phys Rev. A vol 35 pg 1486

And just so I'm clear here, I'm no longer asking a question of the forum, I'm just posting things I found helpful in my search for a clearer understanding of the limits of the uncertainty relation. If this is not an appropriate use of the forum, I won't be offended if this thread is killed.

Great, so why did you not simply ask about gravitational modifications of the uncertainty principle ? You have to be careful what you mean here since [x,p] = i \hbar is valid by definition. In Newtonian gravity coupled to the Schrodinger equation, you are not going to get anything new (what is done in these papers is a classical analysis of error propagation) : the momentum here is still the free Euclidean momentum m dx/dt, moreover in order to import the Planck scale, you need G,c and \hbar, that is at least a relativistic quantum theory coupled to a gravitational background. In that case, choose a particular coordinate system as well as some state, and you will see that the kinetic term (mass) receives gravitational corrections. Hence, the correct momentum deviates from ``free'' momentum - just as this occurs in gauge theories. So, it is obvious that corrections arise on the uncertainty relations for the ``free'' momentum mdx/dt which you can guess by dimensional analysis.

So, both the question as well as the answer seem to be fairly trivial (we did not need to go into the meaning of the Heisenberg inequalities for that at all, neither about why Heisenberg used a Gaussian to start with !).

Careful

 

[msohl]

data tells

The uncertainty equation is equal to h-bar over 2 and as I understand it, the 2 comes from the minimum standard deviation for a gaussian distribution. Which is to say the relation would be different if the error for position and momentum were represented by a different kind of distribution. Was there a physical reason for this choice of distribution or did this type of distribution just fit the data. Considering the precision to which Quantum Mechanics has been tested, the gaussian distribution is obviously correct, I'm just wondering if there was a physical reason he chose it.

why it is.
isnt this a physical reason to say the data tells?
every thing starts from here that:
we'll suppose we have a particle in between to walls in infinite distance we'll ask what is the momentium. then we'll bring the two walls to very near each other. then again we'll ask what is the momentium. in this between, all we know is that the particle is between the two walls, and we have the distance of the two walls measured. This will produce us with a normal distribution. which if we draw the curve will ressemble a bell, so it is called the bell curve as also.