How to make measurements of a particle [Archive]

Mike Helland

Aug4-04, 01:23 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>The HUP states that when you measure the position of a particle with\nsome degree of certainty your ability to measure the momentum of that\nparticle will be limited to another degree of certainty.\n\nThe particle being measured can be an electron and the measuring tool\ncan be some photons. Right? It thats not right, please correct me.\n\nOk, so, can anyone point me to an accessible text on how exactly how\nthe measurements are made, all the way through setting up the\nexperiment, describing what happens, and then ending up with the\nnumbers?\n\nIf you could point me to web page or maybe explain it here, that would\nbe great.\n\nThanks.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>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.

Thanks.

Alex Green

Aug5-04, 03:24 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>mhelland@techmocracy.net (Mike Helland) wrote in message news:<ad157aec.0408031215.7d67303@posting.google.c om>...\n> The HUP states that when you measure the position of a particle with\n> some degree of certainty your ability to measure the momentum of that\n> particle will be limited to another degree of certainty.\n>\n> The particle being measured can be an electron and the measuring tool\n> can be some photons. Right? It thats not right, please correct me.\n>\n> Ok, so, can anyone point me to an accessible text on how exactly how\n> the measurements are made, all the way through setting up the\n> experiment, describing what happens, and then ending up with the\n> numbers?\n>\n> If you could point me to web page or maybe explain it here, that would\n> be great.\n>\n\nI can sketch the outline for measuring electron parameters with\nphotons using a hypothetical light microsope to observe the electron:\n\nEinstein\'s empirical equation for photon energy: E=hf\nMomentum of photon p=E/c\nTherefore p=h/W where W is wavelength\n\nThe lens on the microsope subtends an angle \'2A\' radians at the\nelectron\n\nCompton effect shows that momentum of photon in x direction\n(perpendicular to microscope optical axis) varies from -p(sinA ) to\n+p(sin A), as does momentum of electron.\n\nUncertainty in momentum, Dp approx= 2p(sin A) = 2(h/W) sin A\n\nFrom optics the resolution available in a microscope is:\nMinimum resolveable separation, Dx = W/(sin A)\n\nTherefore Dp * Dx = (2(h/W)(sin A))*(W/(sin A))\n\nSo the product of uncertainties is Dp * Dx = 2h in this case,\ndemonstrating that the product of uncertainties is always greater than\nor equal to h/(4pi).\n\nThe minimum product of uncertainties can be derived from fourier\nanalysis of a particle as a superposition of pure sine waves. To get a\nspread of Dx the wavelengths must have a spread of DW and, according\nto fourier analysis:\nDx*D(1/W) must be greater than or equal to 1/(4pi). W=h/p for a\nphoton so\nDx*Dp is greater than or equal to h/(4pi).\n\nI hope this makes sense.\n\nThe derivations are all quite questionable (looking at a stationary\nelectron (!), assuming fourier analysis, the assumption that photons\njust flash on and off in their own frame of reference etc....). But\nthey work! They are also consistent with Schrodinger\'s equation and\nthis is highly predictive with a suite of tested predictions.\n\nBest Wishes\n\nAlex Green\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>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

Alex Green

Aug6-04, 03:03 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>dralexgreen@yahoo.co.uk (Alex Green) wrote in message news:<42c8441.0408040726.215b2a83@posting.google.c om>...\n> mhelland@techmocracy.net (Mike Helland) wrote in message news:<ad157aec.0408031215.7d67303@posting.google.c om>...\n[snip]\n> > Ok, so, can anyone point me to an accessible text on how exactly how\n> > the measurements are made, all the way through setting up the\n> > experiment, describing what happens, and then ending up with the\n> > numbers?\n> >\n> > If you could point me to web page or maybe explain it here, that would\n> > be great.\n\nTo my knowledge no-one has done the overall experiment but Compton\nscattering confirms the uncertainty in the momentum determination on\nthe x-axis:\n\nhttp://hyperphysics.phy-astr.gsu.edu/hbase/quantum/compeq.html#c1\n\nAnd experiments on diffraction and resolving power give us the\nuncertainty in the position measurement (used daily in electron\nmicroscope work).\n\nBut has anyone put both together? The reason they haven\'t is that it\nis the wrong approach to QM. Yu Shi considers these types of\nexperiments in: "Early Gedanken Experiments of Quantum Mechanics\nRevisited":\n\n"However, it is clearly wrong to attribute the uncertainty to the\ninteraction with a measuring agency. It is also wrong to regard the\nuncertainty as a bound for the accuracy of the measuring instrument,\ngiven by classical physics, as done in Bohr\'s analyses of gamma ray\nmicroscope and recoiling double-slit."\n\nhttp://arxiv.org/PS_cache/quant-ph/pdf/9811/9811050.pdf\n\nBest Wishes\n\nAlex Green\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>dralexgreen@yahoo.co.uk (Alex Green) wrote in message news:<42c8441.0408040726.215b2a83@posting.google.com>...
> mhelland@techmocracy.net (Mike Helland) wrote in message news:<ad157aec.0408031215.7d67303@posting.google.com>...
[snip]
> > 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.

To my knowledge no-one has done the overall experiment but Compton
scattering confirms the uncertainty in the momentum determination on
the x-axis:

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/compeq.html#c1

And experiments on diffraction and resolving power give us the
uncertainty in the position measurement (used daily in electron
microscope work).

But has anyone put both together? The reason they haven't is that it
is the wrong approach to QM. Yu Shi considers these types of
experiments in: "Early Gedanken Experiments of Quantum Mechanics
Revisited":

"However, it is clearly wrong to attribute the uncertainty to the
interaction with a measuring agency. It is also wrong to regard the
uncertainty as a bound for the accuracy of the measuring instrument,
given by classical physics, as done in Bohr's analyses of \gamma ray
microscope and recoiling double-slit."

http://arxiv.org/PS_cache/quant-ph/pdf/9811/9811050.pdf

Best Wishes

Alex Green