Is the Uncertainty Principle Caused by a Distortion in a Field of Probability?

Ok, so what you're saying is that one measurement on N particles is the same as N measurements on one particle, somewhere in the statistical landscape?

So if we fire a beam of N electrons at the same double slit, this is the same as firing "one electron" N times at the same double slit, since each single electron can be considered "identical", like the faces of a die?

 

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This may not have anything to do with the current subject, but something struck me about an experiment about harmonics in wave functions.
I recently saw a program about M theory and the proposition of 11 dimensions (branes) of different frequencies which may bump into each other under certain circumstances. This reminded me of our 11 half-tone scale in music, from which all harmonics may be created.
Anyway, as layman I cannot offer any conclusions or mathematical proofs, but perhaps someone knowledgeable in physics (probability wave function and uncertainty theory) under discussion might see a fundamental connection.

In any case the demonstration is fascinating as is appears to evolve into several well known functions (including double helix) and synchronicities. In any case it is a fascinating demonstration by Harvard students.

http://sciencedemonstrations.fas.ha...ram_name=indepth.html#a_icb_pagecontent341734

Unfortunately this experiment has 15 elements. I would love to see this performed with 11 elements (or 12 half-tones for a full octave) tuned relative to our western musical scale and watch the change in synchronicity and behaviors.

 

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Yes. Feynman touches on this in his Lectures.

Yes. Or it’s like having N identical double slit experiments and one photon is fired.

(sniff… sniff …) sorry. I get emotional at times like this. Just tears of joy mind you!

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I have to slow down right now and I won’t be able to talk too much. People kept posting questions and I felt like I should respond to them. That’s got to stop for a while due to the amount of damage I caused to my back this week from all this work of posting. It may seem like nothing to you here but it caused so much pain that I collapsed on the floor yesterday in so much pain that it took me a few seconds before I could stand up again.

To everyone - Please take some advice from me – Stop thinking about the uncertainty principle. Before this discussion goes anywhere everyone must have a solid agreement on the value of uncertainty in a given situation. I’ve said this from the beginning but everyone was too impatient and assumed that it didn’t matter what order we look at it in. Please take my advice this time and think about how to calculate the uncertainty of the z-component of the spin of an electron which is initially in a mixed state of spin up and spin down. Please take this advice? Pretty please?

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I have to take a break for now – Doctors orders. Then we’ll get back to this later.

 

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In general terms can the spin of an electron be called a "frequency" (a wave form)?

 

No.

 

I called one of the physics professors are the college I got my BA from and spoke to him about this. He agreed with me regarding my interpretation of the UP. He noted that there is a dichotomy on the UP in physics, perhaps due to historical reasons. The one I adhere to and have been talking about is the one you'd learn in upper classman and graduate quantum mechanics courses. The other seems to be used more in the layman literatue as well as in modern physics texts and basic physics. After that conversation I brought the subject up with another friend of mine and he thought the UP meant the otherone but changed his mind when I explained the situation. He then sent me an article which clears up this dochotomu. See http://statintquant.net/siq/siqse2.html

 

"The position and momentum of a particle cannot be simultaneously measured with arbitrarily high precision."

We could if we could see it. Then we could work out the position and momentum just like we do for planets and things on the comic scale. Limited by technology?

A combination of spin, temperature, density (mass to volume ratio), momentum, induced external fields, etc... Would all effect the emitted frequency of the object, I would assume.

 

I just realized I never posted the answer. I worked out the answer in this page

http://home.comcast.net/~peter.m.brown/qm/probability.htm

Warning – Although the essence of the solution is correct there are a few mistakes I want to point out. I’ll get around to fixing them soon

The expansion coefficients in Eq. (2) should not be 1/6 but 1/sqrt(6). This is because the expansion coefficients c is related to the probability P by c^2 = P = probability. Therefore c = sqrt(P) = sqrt(6).

Another error in that page is incorrect. Eq. (6) reads

ΔA = sqrt [<(A - <A>^2)>]

when it should read (from Eq C-23 in Quantum Mechanics by Cohen-Tannoudji et al page 230)

ΔA = sqrt [<(A - <A>)^2>]

Although the expression I ended up with in Eq. (8)

ΔA = sqrt [<A^2> - <A>^2]

is correct. I'll fix this and let you know what I get. It's a good thing I brought all of this up, otherwise I'd have missed this for God only knows how long.In retrospect I came to learn that there are two versions of the uncertainty principle floating around. Although a friend of mine told me this a long time ago I didn't take him seriously. That was my mistake because he's extremely knowledgeable in all other areas of physics that I know of. Although the one I brought up seems to be the one more commonly accepted in advanced treatments of quantum mechanics.

 

That's only according to the older version of the uncertainty principle. Not the one taught in more advanced moden quantum mechanics courses and textbooks.

 

Now it gets interesting. I don't know anything about modern text on QM. LOL. What you just said is interesting for me because I want to know how the 'new' predictive model works. Read these three posts by Mr_Homm. These posts are my favorite in all the years reading posts. The thing that captured my attention was the discussion on the Hilbert space with respect to physicists and mathematicians. Choice of coordinates in a coordinate dependent Hilbert space or a frame invariant Hilbert space. BTW Mr_Homm is Stuart Anderson who teaches physics and mathematics at UW.

This was the first installment: Mr_Homm, Jan. 23, 2008 05:41 AM

http://www.physforum.com/index.php?showtopic=19663&st=0

This was the second installment: Mr_Homm, Jan. 26, 2008 06:22 AM

http://www.physforum.com/index.php?showtopic=19663&st=15

Final installment: Mr_Homm Jan. 30, 2008 06:15 AM

http://www.physforum.com/index.php?showtopic=19663&st=30

 

Do you want to?

I'm on doctors orders to take it easy for a while so I can't sit in from of the monitor too long and when Im reading off line I spend all that time preping for gradschool. However I'll take some sorrof look. See http://statintquant.net/siq/siqse2.html

and I'll try to look at those links when the pain subsides in my back.