Heisenberg Uncertainty Principle

[Chris Hamilton]

Hi all,

I am 18 years old, and am looking to go into engineering, but I have a strong interest in theoretical physics. As such I have recently written a short research paper into the Heisenberg Uncertainty Principle, and I wondered if anyone would be willing to have a quick read and give me any feedback? Any advice on any aspect would be much appreciated, be it technical, editorial etc.

I have attached the paper.

Thanks,
Chris Hamilton

 

[PeroK]

I got totally lost at the bottom of page 1. Then, at the bottom of page 2, you have $arctan(\alpha_1) = \frac{s/2}{y}$. This looks like it should be $tan$ not $arctan$ and I can't figure out how you got the relationship between $s$ and $d$. In any case, I couldn't follow what you were doing in deriving the key formula.

Who is this paper aimed at?

 

[Khashishi]

You said "only applies to particular particles, or wave packets... those following a Gaussian normal distribution".
A particle isn't a wave packet*, and it doesn't really matter that they are in a Gaussian normal distribution. You can use a Gaussian beam as an example, but nowhere do you actually use any properties of the Gaussian distribution (for momenta? for position?)

Figure 2 caption, you use E notation for the number. It's convenient, but I don't think it's acceptable in publication.

When you say "starting with the de Broglie wavelength equation..." it might help to cross reference (equation 1) in your own paper, and similarly for other equations.

You use the diffraction grating equation, but I don't see a diffraction grating here.
You say you consider only the first minimum, but why? Is the minimum where you have a standard deviation in position? What does $\Delta p_x$ mean really? (You can calculate the standard deviation in a sinc function distribution to compare.)

I can't figure out what you are trying to show with equations 8 and 9.

In your data table, it might be better to use millimeters. In your momentum column, does (E-31) mean you multiplied everything by 10^31? It isn't clearly defined.

You talk about a classical regime and a quantum regime. Clearly the grating equation only works if s >> d. It should be possible to come up with a more general equation, if you are so inclined.

In your graph of p vs x, I only see one curve. Aren't you supposed to compare two curves here? Are you plotting data or $\Delta x\Delta p=h$?

You claim a match to h to 5 significant figures, but your data table has fewer significant figures. How is that possible? Why are you only using one point of your data? Shouldn't you use all of it?

Did you assume the result you are trying to prove?

*You might be envisioning a light wave as being a sum of many short packets, but that would be wrong.

 

[bhobba]

It's good you wrote the paper because it shows clearly many of the misconceptions about the uncertainty principle.

First you need to see a correct statement of it. Suppose you have a large number of similarly prepared systems ie all are in the same quantum state. Divide them into two equal lots. In the first lot measure position to a high degree of accuracy. QM places no limit on that accuracy - its a misunderstanding of the uncertainty principle thinking it does. The result you get will have a statistical spread. In the second lot measure momentum to a high degree of accuracy - again QM places no limit on that. It will also have a statistical spread. The variances of those spreads will be as per the Heisenberg Uncertainty principle.

You correctly identify its relationship the the famous double slit - but unfortunately your treatment is a bit convoluted.

Here is a correct treatment:
http://cds.cern.ch/record/1024152/files/0703126.pdf

Note, while the above is way way better than usual pop-sci treatments its not correct either:
http://arxiv.org/abs/1009.2408

To make matters worse even that is wrong. Its a very disconcerting issue with physics that as you progress you often need to unlearn and relearn things. Its quite maddening really.

To understand the uncertainty relation you need to read an advanced book like Ballentine that carefully explains it. Discussions by the early pioneers like Heisenberg were WRONG as pointed out by Bohr. Yet get trotted out and repeated over and over again.

I know you put a lot of work into that paper and I would not be inclined to waste it. Instead learn a bit more about what it really says and use it as an example of misconceptions in physics that get corrected as you progress. Other examples you mention are wave-particle duality and complementary. They are both wrong (although complementarity is a bit too wishy washy to actually disprove, so best to use it with great care for that exact reason) but beginner texts, like micsonceptions about the uncertainty relations, promulgate it.

IMHO here is a MUCH better view of QM:
http://www.scottaaronson.com/democritus/lec9.html

Like I said see if you can make your paper about quantum misconceptions rather than scrap it. There are many of them - its actually quite insidious:
http://arxiv.org/abs/quant-ph/0609163

Also be very careful of what early QM pioneers said. With the notable exception of Dirac they were basically all wrong:
http://www.fisica.ufmg.br/~dsoares/cosmos/10/weinberg-einsteinsmistakes.pdf

The reason Dirac wasn't wrong is he basically said - shut up and calculate - although often attributed to him or Feynman it was in fact a quote from David Mermin
http://www.physicsandmore.net/resources/Shutupandcalculate.pdf

Nor do I think that is basically Copenhagen - but that is a whole new thread. Most interpretations are simply arguments about the meaning of probability:
http://math.ucr.edu/home/baez/bayes.html

Shut up and calculate doesn't worry about that either.

Thanks
Bill