Hans de Vries
Sep9-04, 03:03 PM
<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>(re-submission with improved formatting)\n\n=================================== ==============\nTalbot Lau interferometry of carbon-70 fullerenes\n====================================== ===========\n\nI\'ve looked at most of the documents published on these\nmacroscopic quantum interference experiments of fundamental\nimportance. These experiments seems to shift the border between\nthe quantum mechanical and the classical world further and further.\nThe (clickable) references can be found at the end of this post.\n\nI did a number of simulations and also did some analysis of the\nexperiment with the help of the path-integral formalism of QED.\nIt allows us to say considerably more about the experiment than\nwith Schroedinger\'s equation or let alone Heisenberg\'s principle\nof uncertainty.\n\nI hope we can have something like a technical discussion on the\nsubject here:\n\n\n==============================\nBasic Setup of the Experiment:\n==============================\nThree identical gratings exactly lined up behind each other on\nequal distances. line spacing: ~1000 nanometer, line width: ~500\nnanometer, grating distance: 22cm in early, and 38 cm in later\nexperiments.\n\n\n==============\nTest Particle:\n==============\nCarbon-70 fullerene (840 atomic masses (420 protons + 420 neutrons)\nmass: 1.406 10-24 kg is equal to ~1.55 million times the mass of an\nelectron. De Broglie wavelength in the 1.406 10-24 kg, experiment:\n2 to 6 picometer.\n\n\n=====================\nInterferenc e Pattern:\n=====================\nThe interference pattern is exactly equal as the grating pattern\n(line spacing ~ 1 micrometer) and measured at the location of the\nthird grating. (The third grating is used to measure the pattern\nby shifting it sideways to let more or less of the pattern pass\nthrough to the detector)\n\n\n===================\nSignal Noise ratio:\n===================\nAmazingly good: Up to 66% and more of the fullerenes take part in\nthe Interference Process, That is: Each of these molecules passes\nthrough 2 or more splits simultaneously and diffract away from the\nstraight-line path in order produce the interference pattern.\nThis even though the split spacing is ~1000 nm.\n\n\n========================================\ nAverage distance between Test particles:\n====================================== ==\nThe fullerenes are on average 0.3 meter to 1.5 meter apart in the\nexperiment so it is typically an experiment were one-particle-a-time\nbuilds up the pattern.\n\n\n==================================== =============\nEquivalent experiment with visible light photons:\n======================================== =========\nVisible light wavelengths are circa 100,000 larger then the de Broglie\nwave-length tested in the experiment. The equivalent experiment for\nvisible light would scale up to gratings with a split width of 5 cm\nand a split spacing of 10 cm. What is amazing is that most of the\nphotons would not diffract here (only at the edges of the splits),\nmost of them would pass straight through resulting in a very low\nsignal/noise ratio for the interference patterns. This contrasts with\nthe extremely good signal/noise ratio for the non-scaled experiment.\n\n\n===========================\nPart icle "shadow" patterns.\n===========================\nThe interference pattern is exactly the same as the grating pattern\nin front of it. The experiment must thus make sure that we are not\nlooking to a shadow pattern of particles which behavior is dominantly\nparticle-like rather than wavelike.\n\n\n=================================== ==============\nExact cancellation of particle "shadow" patterns.\n======================================= ==========\nThe experiment setup arguments for this can be found in [8] on page\n26. It is argued that the shadow patterns exactly cancel at the\nlocation of the 3rd grating because of the beams unique radial density\ndistribution.\n\nThe particle beams overlap with their left and right neighbors and\nthe split width / spacing ratio (50%) in both the 1st and 2nd grating\nshould provide the exact radial density distribution of the narrow\nbeam and the right fan-out angle (circa 3 micro radians)\n\nThe simulation I did shows that the pattern will reappear again\nfurther away and disappear and reappear repetitively at equal\ndistances. The image of a simulation I did can be found here:\nhttp://www.chip-architect.com/physics/talbot_lau_01.jpg\n\n\n=========================== ======================================\nParticle speed dependent aberrations / van der Waals interactions\n==================================== =============================\nThe first experiments use a 22 cm distance between the gratings\nand show a large discrepancy with theory. The maximum found in the\nexperiment almost correspond with the minimum of the theoretical\nprediction. See the image in [1] , page 3. It is argued that this\ndiscrepancy is caused by van der Waals interactions with the walls\nof the gratings. A nice image can be found in [8] on page 25 which\nshows the experimenters theoretical model for interference and\ntheir theoretical model which combines interference with a van der\nWaals effect.\n\n\n=================================\nVa rying the de Broglie wavelength\n=================================\nA key assumption in the experiments to differentiate between\nmacroscopic quantum interference and particle beam shadow effects:\nBy varying the speed of the fullerene molecules one can vary the\nde Broglie wave-length of the center of mass of the molecule.\n\nThe repetition distance of the interference pattern changes with\nthe varying de Broglie wave-length. Such a variation is said to\nbe impossible with particle beam shadow patterns and thus proves\nmacroscopic quantum interference.\n\n\n\n============================= ================\nMore particle beam shadow pattern simulations\n===================================== ========\nI presumed that slower beams would be more deflected by the van\nder Waals interaction with the walls of the gratings than faster\nbeams. A result for three different speeds can be seen in this image.\nhttp://www.chip-architect.com/physics/talbot_lau_02.jpg\nIt shows a pattern very similar to that of what the experimenters\nexpect from macroscopic quantum interference. (It should be noted\nthat the fan-out angles in the experiment are in the order of 3 micro\nradians. the image above should be stretched by a factor of 10,000\nin the x-direction to scale to the ratio of the experiment)\n\n\n================================\ nQED Path Integral considerations\n================================\n The path integral formalism allows us to determine the probabilities\nfor the paths taken by the fullerenes. The probability is given as\nthe square of the amplitude. The total amplitude is the sum of the\namplitudes of all possible paths. The amplitude of a single path is\nthe product of the amplitudes of all the sub-paths. This product\nrule is important: If a part of a path has a very low amplitude then\nit follows that the entire path has a very low amplitude.\n\nThe product rule excludes paths for instance that include a turn\nsomewhere in "mid-vacuum" Only paths that pass very close to aborder\n(within a wavelength) do diffract. paths further away from borders\nare straight lines.\n\n\n====================================== ==================\nThe split width compared with the de Broglie wave-length\n========================================== ==============\nWhen we scaled the experiment to visible wave-lengths we saw that\nthe gratings sized up to a split period of 10 cm with a split width\nof 5 cm. Very large compared to the wavelength. Nevertheless.\nThe experimenters presume that the fullerenes do diffract even if\nthey are passing at a distance from the wall tens of thousands\ntimes larger then the de Broglie wave-length.\n\nThe high ratio of the fullerenes (>50%) that passes through two or\nmore splits simultaneously and diffracts in order to get the very\nhigh signal to noise ratio requires such a diffraction which seems\nto be at odds with the path-integral formalism. A schematic drawing\nof the diffraction can be found in [8] at page 18.\n\n\nRegards, Hans\n\n\n[1] Matter-wave interferometer for large molecules\nhttp://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:quant-ph/0202158\n\n[2] Collisional decoherence observed in matter wave interferometry\nhttp://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:quant-ph/0303093\n\n[3] Collisional decoherence reexamined\nhttp://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:quant-ph/0303094\n\n[4] Decoherence in a Talbot Lau interferometer: the influence of\nmolecular scattering\nhttp://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:quant-ph/0307238\n\n[5] The wave nature of biomolecules and fluorofullerenes\nhttp://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:quant-ph/0309016\n\n[6] Decoherence of matter waves by thermal emission of radiation\nhttp://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:quant-ph/0402146\n\n[7] Exploring the classical limits of quantum interferometry with\nclusters and molecules\nhttp://latsis2004.epfl.ch/Jahia/engineName/filemanager/site/latsis2004/pid/40719/Ardnt_U.pdf?actionreq=actionFileDownload&fid=118993\n\n[8] Matter wave interferometry with large molecules\nhttp://www-lab15.kuee.kyoto-u.ac.jp/~lc/proceedings/2-3.pdf\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>(re-submission with improved formatting)
=================================================
Talbot Lau interferometry of carbon-70 fullerenes
=================================================
I've looked at most of the documents published on these
macroscopic quantum interference experiments of fundamental
importance. These experiments seems to shift the border between
the quantum mechanical and the classical world further and further.
The (clickable) references can be found at the end of this post.
I did a number of simulations and also did some analysis of the
experiment with the help of the path-integral formalism of QED.
It allows us to say considerably more about the experiment than
with Schroedinger's equation or let alone Heisenberg's principle
of uncertainty.
I hope we can have something like a technical discussion on the
subject here:
==============================
Basic Setup of the Experiment:
==============================
Three identical gratings exactly lined up behind each other on
equal distances. line spacing: ~1000 nanometer, line width: ~500
nanometer, grating distance: 22cm in early, and 38 cm in later
experiments.
==============
Test Particle:
==============
Carbon-70 fullerene (840 atomic masses (420 protons + 420 neutrons)
mass: 1.406 10-24 kg is equal to ~1.55 million times the mass of an
electron. De Broglie wavelength in the 1.406 10-24 kg, experiment:
2 to 6 picometer.
=====================
Interference Pattern:
=====================
The interference pattern is exactly equal as the grating pattern
(line spacing ~ 1 micrometer) and measured at the location of the
third grating. (The third grating is used to measure the pattern
by shifting it sideways to let more or less of the pattern pass
through to the detector)
===================
Signal Noise ratio:
===================
Amazingly good: Up to 66% and more of the fullerenes take part in
the Interference Process, That is: Each of these molecules passes
through 2 or more splits simultaneously and diffract away from the
straight-line path in order produce the interference pattern.
This even though the split spacing is ~1000 nm.
========================================
Average distance between Test particles:
========================================
The fullerenes are on average .3 meter to 1.5 meter apart in the
experiment so it is typically an experiment were one-particle-a-time
builds up the pattern.
=================================================
Equivalent experiment with visible light photons:
=================================================
Visible light wavelengths are circa 100,000 larger then the de Broglie
wave-length tested in the experiment. The equivalent experiment for
visible light would scale up to gratings with a split width of 5 cm
and a split spacing of 10 cm. What is amazing is that most of the
photons would not diffract here (only at the edges of the splits),
most of them would pass straight through resulting in a very low
signal/noise ratio for the interference patterns. This contrasts with
the extremely good signal/noise ratio for the non-scaled experiment.
===========================
Particle "shadow" patterns.
===========================
The interference pattern is exactly the same as the grating pattern
in front of it. The experiment must thus make sure that we are not
looking to a shadow pattern of particles which behavior is dominantly
particle-like rather than wavelike.
=================================================
Exact cancellation of particle "shadow" patterns.
=================================================
The experiment setup arguments for this can be found in [8] on page
26. It is argued that the shadow patterns exactly cancel at the
location of the 3rd grating because of the beams unique radial density
distribution.
The particle beams overlap with their left and right neighbors and
the split width / spacing ratio (50%) in both the 1st and 2nd grating
should provide the exact radial density distribution of the narrow
beam and the right fan-out angle (circa 3 micro radians)
The simulation I did shows that the pattern will reappear again
further away and disappear and reappear repetitively at equal
distances. The image of a simulation I did can be found here:
http://www.chip-architect.com/physics/talbot_lau_01.jpg
================================================== ===============
Particle speed dependent aberrations / van der Waals interactions
================================================== ===============
The first experiments use a 22 cm distance between the gratings
and show a large discrepancy with theory. The maximum found in the
experiment almost correspond with the minimum of the theoretical
prediction. See the image in [1] , page 3. It is argued that this
discrepancy is caused by van der Waals interactions with the walls
of the gratings. A nice image can be found in [8] on page 25 which
shows the experimenters theoretical model for interference and
their theoretical model which combines interference with a van der
Waals effect.
=================================
Varying the de Broglie wavelength
=================================
A key assumption in the experiments to differentiate between
macroscopic quantum interference and particle beam shadow effects:
By varying the speed of the fullerene molecules one can vary the
de Broglie wave-length of the center of mass of the molecule.
The repetition distance of the interference pattern changes with
the varying de Broglie wave-length. Such a variation is said to
be impossible with particle beam shadow patterns and thus proves
macroscopic quantum interference.
=============================================
More particle beam shadow pattern simulations
=============================================
I presumed that slower beams would be more deflected by the van
der Waals interaction with the walls of the gratings than faster
beams. A result for three different speeds can be seen in this image.
http://www.chip-architect.com/physics/talbot_lau_02.jpg
It shows a pattern very similar to that of what the experimenters
expect from macroscopic quantum interference. (It should be noted
that the fan-out angles in the experiment are in the order of 3 micro
radians. the image above should be stretched by a factor of 10,000
in the x-direction to scale to the ratio of the experiment)
================================
QED Path Integral considerations
================================
The path integral formalism allows us to determine the probabilities
for the paths taken by the fullerenes. The probability is given as
the square of the amplitude. The total amplitude is the sum of the
amplitudes of all possible paths. The amplitude of a single path is
the product of the amplitudes of all the sub-paths. This product
rule is important: If a part of a path has a very low amplitude then
it follows that the entire path has a very low amplitude.
The product rule excludes paths for instance that include a turn
somewhere in "mid-vacuum" Only paths that pass very close to aborder
(within a wavelength) do diffract. paths further away from borders
are straight lines.
================================================== ======
The split width compared with the de Broglie wave-length
================================================== ======
When we scaled the experiment to visible wave-lengths we saw that
the gratings sized up to a split period of 10 cm with a split width
of 5 cm. Very large compared to the wavelength. Nevertheless.
The experimenters presume that the fullerenes do diffract even if
they are passing at a distance from the wall tens of thousands
times larger then the de Broglie wave-length.
The high ratio of the fullerenes (>50%) that passes through two or
more splits simultaneously and diffracts in order to get the very
high signal to noise ratio requires such a diffraction which seems
to be at odds with the path-integral formalism. A schematic drawing
of the diffraction can be found in [8] at page 18.
Regards, Hans
[1] Matter-wave interferometer for large molecules
http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:http://www.arxiv.org/abs/quant-ph/0202158
[2] Collisional decoherence observed in matter wave interferometry
http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:http://www.arxiv.org/abs/quant-ph/0303093
[3] Collisional decoherence reexamined
http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:http://www.arxiv.org/abs/quant-ph/0303094
[4] Decoherence in a Talbot Lau interferometer: the influence of
molecular scattering
http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:http://www.arxiv.org/abs/quant-ph/0307238
[5] The wave nature of biomolecules and fluorofullerenes
http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:http://www.arxiv.org/abs/quant-ph/0309016
[6] Decoherence of matter waves by thermal emission of radiation
http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:http://www.arxiv.org/abs/quant-ph/0402146
[7] Exploring the classical limits of quantum interferometry with
clusters and molecules
http://latsis2004.epfl.ch/Jahia/engineName/filemanager/site/latsis2004/pid/40719/Ardnt_U.pdf?actionreq=actionFileDownload&fid=118993
[8] Matter wave interferometry with large molecules
http://www-lab15.kuee.kyoto-u.ac.jp/~lc/proceedings/2-3.pdf
=================================================
Talbot Lau interferometry of carbon-70 fullerenes
=================================================
I've looked at most of the documents published on these
macroscopic quantum interference experiments of fundamental
importance. These experiments seems to shift the border between
the quantum mechanical and the classical world further and further.
The (clickable) references can be found at the end of this post.
I did a number of simulations and also did some analysis of the
experiment with the help of the path-integral formalism of QED.
It allows us to say considerably more about the experiment than
with Schroedinger's equation or let alone Heisenberg's principle
of uncertainty.
I hope we can have something like a technical discussion on the
subject here:
==============================
Basic Setup of the Experiment:
==============================
Three identical gratings exactly lined up behind each other on
equal distances. line spacing: ~1000 nanometer, line width: ~500
nanometer, grating distance: 22cm in early, and 38 cm in later
experiments.
==============
Test Particle:
==============
Carbon-70 fullerene (840 atomic masses (420 protons + 420 neutrons)
mass: 1.406 10-24 kg is equal to ~1.55 million times the mass of an
electron. De Broglie wavelength in the 1.406 10-24 kg, experiment:
2 to 6 picometer.
=====================
Interference Pattern:
=====================
The interference pattern is exactly equal as the grating pattern
(line spacing ~ 1 micrometer) and measured at the location of the
third grating. (The third grating is used to measure the pattern
by shifting it sideways to let more or less of the pattern pass
through to the detector)
===================
Signal Noise ratio:
===================
Amazingly good: Up to 66% and more of the fullerenes take part in
the Interference Process, That is: Each of these molecules passes
through 2 or more splits simultaneously and diffract away from the
straight-line path in order produce the interference pattern.
This even though the split spacing is ~1000 nm.
========================================
Average distance between Test particles:
========================================
The fullerenes are on average .3 meter to 1.5 meter apart in the
experiment so it is typically an experiment were one-particle-a-time
builds up the pattern.
=================================================
Equivalent experiment with visible light photons:
=================================================
Visible light wavelengths are circa 100,000 larger then the de Broglie
wave-length tested in the experiment. The equivalent experiment for
visible light would scale up to gratings with a split width of 5 cm
and a split spacing of 10 cm. What is amazing is that most of the
photons would not diffract here (only at the edges of the splits),
most of them would pass straight through resulting in a very low
signal/noise ratio for the interference patterns. This contrasts with
the extremely good signal/noise ratio for the non-scaled experiment.
===========================
Particle "shadow" patterns.
===========================
The interference pattern is exactly the same as the grating pattern
in front of it. The experiment must thus make sure that we are not
looking to a shadow pattern of particles which behavior is dominantly
particle-like rather than wavelike.
=================================================
Exact cancellation of particle "shadow" patterns.
=================================================
The experiment setup arguments for this can be found in [8] on page
26. It is argued that the shadow patterns exactly cancel at the
location of the 3rd grating because of the beams unique radial density
distribution.
The particle beams overlap with their left and right neighbors and
the split width / spacing ratio (50%) in both the 1st and 2nd grating
should provide the exact radial density distribution of the narrow
beam and the right fan-out angle (circa 3 micro radians)
The simulation I did shows that the pattern will reappear again
further away and disappear and reappear repetitively at equal
distances. The image of a simulation I did can be found here:
http://www.chip-architect.com/physics/talbot_lau_01.jpg
================================================== ===============
Particle speed dependent aberrations / van der Waals interactions
================================================== ===============
The first experiments use a 22 cm distance between the gratings
and show a large discrepancy with theory. The maximum found in the
experiment almost correspond with the minimum of the theoretical
prediction. See the image in [1] , page 3. It is argued that this
discrepancy is caused by van der Waals interactions with the walls
of the gratings. A nice image can be found in [8] on page 25 which
shows the experimenters theoretical model for interference and
their theoretical model which combines interference with a van der
Waals effect.
=================================
Varying the de Broglie wavelength
=================================
A key assumption in the experiments to differentiate between
macroscopic quantum interference and particle beam shadow effects:
By varying the speed of the fullerene molecules one can vary the
de Broglie wave-length of the center of mass of the molecule.
The repetition distance of the interference pattern changes with
the varying de Broglie wave-length. Such a variation is said to
be impossible with particle beam shadow patterns and thus proves
macroscopic quantum interference.
=============================================
More particle beam shadow pattern simulations
=============================================
I presumed that slower beams would be more deflected by the van
der Waals interaction with the walls of the gratings than faster
beams. A result for three different speeds can be seen in this image.
http://www.chip-architect.com/physics/talbot_lau_02.jpg
It shows a pattern very similar to that of what the experimenters
expect from macroscopic quantum interference. (It should be noted
that the fan-out angles in the experiment are in the order of 3 micro
radians. the image above should be stretched by a factor of 10,000
in the x-direction to scale to the ratio of the experiment)
================================
QED Path Integral considerations
================================
The path integral formalism allows us to determine the probabilities
for the paths taken by the fullerenes. The probability is given as
the square of the amplitude. The total amplitude is the sum of the
amplitudes of all possible paths. The amplitude of a single path is
the product of the amplitudes of all the sub-paths. This product
rule is important: If a part of a path has a very low amplitude then
it follows that the entire path has a very low amplitude.
The product rule excludes paths for instance that include a turn
somewhere in "mid-vacuum" Only paths that pass very close to aborder
(within a wavelength) do diffract. paths further away from borders
are straight lines.
================================================== ======
The split width compared with the de Broglie wave-length
================================================== ======
When we scaled the experiment to visible wave-lengths we saw that
the gratings sized up to a split period of 10 cm with a split width
of 5 cm. Very large compared to the wavelength. Nevertheless.
The experimenters presume that the fullerenes do diffract even if
they are passing at a distance from the wall tens of thousands
times larger then the de Broglie wave-length.
The high ratio of the fullerenes (>50%) that passes through two or
more splits simultaneously and diffracts in order to get the very
high signal to noise ratio requires such a diffraction which seems
to be at odds with the path-integral formalism. A schematic drawing
of the diffraction can be found in [8] at page 18.
Regards, Hans
[1] Matter-wave interferometer for large molecules
http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:http://www.arxiv.org/abs/quant-ph/0202158
[2] Collisional decoherence observed in matter wave interferometry
http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:http://www.arxiv.org/abs/quant-ph/0303093
[3] Collisional decoherence reexamined
http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:http://www.arxiv.org/abs/quant-ph/0303094
[4] Decoherence in a Talbot Lau interferometer: the influence of
molecular scattering
http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:http://www.arxiv.org/abs/quant-ph/0307238
[5] The wave nature of biomolecules and fluorofullerenes
http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:http://www.arxiv.org/abs/quant-ph/0309016
[6] Decoherence of matter waves by thermal emission of radiation
http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:http://www.arxiv.org/abs/quant-ph/0402146
[7] Exploring the classical limits of quantum interferometry with
clusters and molecules
http://latsis2004.epfl.ch/Jahia/engineName/filemanager/site/latsis2004/pid/40719/Ardnt_U.pdf?actionreq=actionFileDownload&fid=118993
[8] Matter wave interferometry with large molecules
http://www-lab15.kuee.kyoto-u.ac.jp/~lc/proceedings/2-3.pdf