Re: How to make measurements of a particle

From: Alex Green (dralexgreen_at_yahoo.co.uk)
Date: 08/05/04 

Date: Thu, 5 Aug 2004 08:24:01 +0000 (UTC)

mhelland@techmocracy.net (Mike Helland) wrote in message news:<ad157aec.0408031215.7d67303@posting.google.com>...
> The HUP states that when you measure the position of a particle with
> some degree of certainty your ability to measure the momentum of that
> particle will be limited to another degree of certainty.
>
> The particle being measured can be an electron and the measuring tool
> can be some photons. Right? It thats not right, please correct me.
>
> Ok, so, can anyone point me to an accessible text on how exactly how
> the measurements are made, all the way through setting up the
> experiment, describing what happens, and then ending up with the
> numbers?
>
> If you could point me to web page or maybe explain it here, that would
> be great.
>

I can sketch the outline for measuring electron parameters with
photons using a hypothetical light microsope to observe the electron:

Einstein's empirical equation for photon energy: E=hf
Momentum of photon p=E/c
Therefore p=h/W where W is wavelength

The lens on the microsope subtends an angle '2A' radians at the
electron

Compton effect shows that momentum of photon in x direction
(perpendicular to microscope optical axis) varies from -p(sinA ) to
+p(sin A), as does momentum of electron.

Uncertainty in momentum, Dp approx= 2p(sin A) = 2(h/W) sin A

>From optics the resolution available in a microscope is:
 Minimum resolveable separation, Dx = W/(sin A)

Therefore Dp * Dx = (2(h/W)(sin A))*(W/(sin A))

So the product of uncertainties is Dp * Dx = 2h in this case,
demonstrating that the product of uncertainties is always greater than
or equal to h/(4pi).

The minimum product of uncertainties can be derived from fourier
analysis of a particle as a superposition of pure sine waves. To get a
spread of Dx the wavelengths must have a spread of DW and, according
to fourier analysis:
 Dx*D(1/W) must be greater than or equal to 1/(4pi). W=h/p for a
photon so
Dx*Dp is greater than or equal to h/(4pi).

I hope this makes sense.

The derivations are all quite questionable (looking at a stationary
electron (!), assuming fourier analysis, the assumption that photons
just flash on and off in their own frame of reference etc....). But
they work! They are also consistent with Schrodinger's equation and
this is highly predictive with a suite of tested predictions.

Best Wishes

Alex Green

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