James Thurber wrote in 1945 at the dawn of a fascinating or potentially terrible
age, the atomic age: "It is better to know some of the questions than all of the
answers."
I don't pretend full understanding (x-rays & electrons <<diffraction>> &
<<Diffraction & Compton Effect, e.g., x-rays or gamma rays>> curious Gamma
functions), but I too, have wondered how two fundamentally different concepts as
waves and particles can be reconciled one and the same, or why one must be
forced to choose. I have read a little on the subject of the wave-particle
duality, some had suggested one point-of-view, some the other, and many just
accept the evidence from experiments and say each are in part both.
Seems like lack of commitment to me, being a creature where I am either here or
not here, in my box or on my travels to
and from my assigned box, leaving me to wonder on average where am I? This is
one question, which I have not given complete information, one answer is: that
depends. Depends on how long I am here or not here, how long a time am I talking
about? On average I am probably somewhere in-between.
Time and energy appears key, but not one or the other, the fuzzy product of
both, taken at once and as inseparable.
The chemists where I work have complicated models of molecules adorning their
office walls. I am still stuck on the hydrogen atom not being a chemist. My work
is with water; water is more than complication enough. Where are those two
hydrogen atoms? On average near to oxygen, and on average the hydrogen atoms fan
out like butterfly wings about 105 degrees apart.
Without Heisenberg's Indeterminacy principle the quantum theory falls apart.
Wanting to know more I consulted Richard Feynman, Max Born, Edward Teller, David
Bohm, Alan Lightman, Brian Greene, and Cristoph Schiller to see what I could
discover for myself.
I have been for sometime kicking about gamma, beta, and error functions in Boas.
Having a poor memory I keep many books.
For a very good discussion, Schiller has his book on-line:
(http://motionmountain.dse.nl/welcome.html) his book is very well written and is
thought provoking, also a slow read when read well.
Max Born's Atomic Physics, Dover Pub. ISBN 0-486-65984-4 on page 471 (as does
Feynman, in the Feynman
Lectures) compares the classical and quantum oscillator to explain the zero
point energy. This to me is a most compelling argument that supports the quantum
theory but does not, like all models, exclude deeper interpretation, one nobody
has found yet.
From Edward Teller, "Conversation on the Dark Secrets of Physics", and D'Abro,
"The Rise of the New Physics, Vol.1&2"
'The symbol d = delta
Given: A plane wave propagating in an arbitrary direction relative to cartesian
coordinates. Draw equiphase planes with perpendicular planes, put this wave
packet in a direction inclined at an arbitrary angle, this wave drawn as a
vector, in unit of distance, the number of crests can be counted each of
wavelength distance.
Let k be a number called "wave number" In this example, wave number as a vector
with projections (k_x, k_y, k_z) components, representing the number of wave
crests intersecting the three axes over length of unit distance.
The projected distance along each axis can vary slightly with a slight change in
direction of each wave packet, or, if the wave packets are of different
frequency.
k_x can spread by dk_x, etc
The volume of a wave packet is dx*dy*dz and dt is the time it takes to pass a
fixed point on the line of advance.
Wave number = k = 1/wavelength
With dx>=1/dk_x
This give 4 relations: dx*dk_x>=1, dy*dk_y>=, dz*dk_z>=1, dt*dfreq.>=1
Momentum
p=k*h
Therefore: dx*dp_x>=h, etc.
E=freq.*h, dt*dE>=h (approximately)
A better derivation from the error-function is in Born's book, page 472 show ½*h
bar = ½ * h/2*pi for the above relationships - shows in more subtly detail.
Basic Assumptions of QT
From Richard Feynman's Summary 37-7 in vol.1
"(1) The probability of an ideal experiment is given by the square of the
absolute value of a complex number "phi"
called the probability amplitude. (Discovered by Max Born)
P = probability
Phi=probability amplitude
P= |phi1+phi2|^2
(2) When an event can occur in several alternate ways, the probability amplitude
for the event is the sum of the probability amplitudes for each way considered
separately. There is interference.
(3) If an experiment is performed which is capable of determining whether one or
another alternative is actually taken, the probability of an event is the sum of
the probabilities for each alternative. The interference is lost.
P=P1+P2"
The connection between energy and probability, Euler.
What does this have to do with DERIVE? Derive is a learning tool, helps with
some of my mathematical difficulties and best of all helps with visualization. I
get confused by words, what thinking I can do; I mostly do in pictures, pictures
of ideas. What is the use . thought Alice in quantum land, "without pictures or
conversations?" - Lewis Carrol, Alice in Wonderland.
I liked your suggestion, made for a wonderful conversation.
A couple of other links from physicists with a passion for their subject,
sharing with us their best work, proving that life is more than just our next
meal.
http://www.lightandmatter.com/
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
Regards,
Mike Law
**************************************************
On flâne sur l'avenue de Jean-Jaurès,
et comme Paul Langevin, on essaie
de se poser des questions.
--- Mike Law
----- Original Message -----
From: "guest" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Monday, June 16, 2003 9:53 PM
Subject: The Uncertainty Principle Is Untenable
please reply to [log in to unmask]
thank you.
THE UNCERTAINTY PRINCIPLE IS UNTENABLE
By re-analysing Heisenberg's Gamma-Ray Microscope experiment and the ideal
experiment from which the uncertainty principle is derived, it is actually found
that the uncertainty principle can not be obtained from them. It is therefore
found to be untenable.
Key words:
uncertainty principle; Heisenberg's Gamma-Ray Microscope Experiment; ideal
experiment
Ideal Experiment 1
Heisenberg's Gamma-Ray Microscope Experiment
A free electron sits directly beneath the center of the microscope's lens
(please see AIP page http://www.aip.org/history/heisenberg/p08b.htm or diagram
below) . The circular lens forms a cone of angle 2A from the electron. The
electron is then illuminated from the left by gamma rays--high energy light
which has the shortest wavelength. These yield the highest resolution, for
according to a principle of wave optics, the microscope can resolve (that is,
"see" or distinguish) objects to a size of dx, which is related to and to the
wavelength L of the gamma ray, by the expression:
dx = L/(2sinA) (1)
However, in quantum mechanics, where a light wave can act like a particle, a
gamma ray striking an electron gives it a kick. At the moment the light is
diffracted by the electron into the microscope lens, the electron is thrust to
the right. To be observed by the microscope, the gamma ray must be scattered
into any angle within the cone of angle 2A. In quantum mechanics, the gamma ray
carries momentum as if it were a particle. The total momentum p is related to
the wavelength by the formula,
p = h / L, where h is Planck's constant. (2)
In the extreme case of diffraction of the gamma ray to the right edge of the
lens, the total momentum would be the sum of the electron's momentum P'x in the
x direction and the gamma ray's momentum in the x direction:
P' x + (h sinA) / L', where L' is the wavelength of the deflected gamma ray.
In the other extreme, the observed gamma ray recoils backward, just hitting the
left edge of the lens. In this case, the total momentum in the x direction is:
P''x - (h sinA) / L''.
The final x momentum in each case must equal the initial x momentum, since
momentum is conserved. Therefore, the final x momenta are equal to each other:
P'x + (h sinA) / L' = P''x - (h sinA) / L'' (3)
If A is small, then the wavelengths are approximately the same,
L' ~ L" ~ L. So we have
P''x - P'x = dPx ~ 2h sinA / L (4)
Since dx = L/(2 sinA), we obtain a reciprocal relationship between the minimum
uncertainty in the measured position, dx, of the electron along the x axis and
the uncertainty in its momentum, dPx, in the x direction:
dPx ~ h / dx or dPx dx ~ h. (5)
For more than minimum uncertainty, the "greater than" sign may added.
Except for the factor of 4pi and an equal sign, this is Heisenberg's uncertainty
relation for the simultaneous measurement of the position and momentum of an
object.
Re-analysis
To be seen by the microscope, the gamma ray must be scattered into any angle
within the cone of angle 2A.
The microscope can resolve (that is, "see" or distinguish) objects to a size of
dx, which is related to and to the wavelength L of the gamma ray, by the
expression:
dx = L/(2sinA) (1)
This is the resolving limit of the microscope and it is the uncertain quantity
of the object's position.
The microscope can not see the object whose size is smaller than its resolving
limit, dx. Therefore, to be seen by the microscope, the size of the electron
must be larger than or equal to the resolving limit.
But if the size of the electron is larger than or equal to the resolving limit
dx, the electron will not be in the range dx. Therefore, dx can not be deemed to
be the uncertain quantity of the electron's position which can be seen by the
microscope, but deemed to be the uncertain quantity of the electron's position
which can not be seen by the microscope. To repeat, dx is uncertainty in the
electron's position which can not be seen by the microscope.
To be seen by the microscope, the gamma ray must be scattered into any angle
within the cone of angle 2A, so we can measure the momentum of the electron.
dPx is the uncertainty in the electron's momentum which can be seen by
microscope.
What relates to dx is the electron where the size is smaller than the resolving
limit. When the electron is in the range dx, it can not be seen by the
microscope, so its position is uncertain.
What relates to dPx is the electron where the size is larger than or equal to
the resolving limit .The electron is not in the range dx, so it can be seen by
the microscope and its position is certain.
Therefore, the electron which relates to dx and dPx respectively is not the
same. What we can see is the electron where the size is larger than or equal to
the resolving limit dx and has a certain position, dx = 0.
Quantum mechanics does not rely on the size of the object, but on Heisenberg's
Gamma-Ray Microscope experiment. The use of the microscope must relate to the
size of the object. The size of the object which can be seen by the microscope
must be larger than or equal to the resolving limit dx of the microscope, thus
the uncertain quantity of the electron's position does not exist. The gamma ray
which is diffracted by the electron can be scattered into any angle within the
cone of angle 2A, where we can measure the momentum of the electron.
What we can see is the electron which has a certain position, dx = 0, so that in
no other position can we measure the momentum of the electron. In Quantum
mechanics, the momentum of the electron can be measured accurately when we
measure the momentum of the electron only, therefore, we have gained dPx = 0.
And,
dPx dx =0. (6)
Ideal experiment 2
Single Slit Diffraction Experiment
Suppose a particle moves in the Y direction originally and then passes a slit
with width dx(Please see diagram below) . The uncertain quantity of the
particle's position in the X direction is dx, and interference occurs at the
back slit . According to Wave Optics , the angle where No.1 min of interference
pattern is can be calculated by following formula:
sinA=L/2dx (1)
and L=h/p where h is Planck's constant. (2)
So the uncertainty principle can be obtained
dPx dx ~ h (5)
Re-analysis
According to Newton first law , if an external force in the X direction does not
affect the particle, it will move in a uniform straight line, ( Motion State or
Static State) , and the motion in the Y direction is unchanged .Therefore , we
can learn its position in the slit from its starting point.
The particle can have a certain position in the slit and the uncertain quantity
of the position is dx =0. According to Newton first law , if the external force
at the X direction does not affect particle, and the original motion in the Y
direction is not changed , the momentum of the particle int the X direction will
be Px=0 and the uncertain quantity of the momentum will be dPx =0.
This gives:
dPx dx =0. (6)
No experiment negates NEWTON FIRST LAW. Whether in quantum mechanics or
classical mechanics, it applies to the microcosmic world and is of the form of
the Energy-Momentum conservation laws. If an external force does not affect the
particle and it does not remain static or in uniform motion, it has disobeyed
the Energy-Momentum conservation laws. Under the above ideal experiment , it is
considered that the width of the slit is the uncertain quantity of the
particle's position. But there is certainly no reason for us to consider that
the particle in the above experiment has an uncertain position, and no reason
for us to consider that the slit's width is the uncertain quantity of the
particle. Therefore, the uncertainty principle,
dPx dx ~ h (5)
which is derived from the above experiment is unreasonable.
Conclusion
From the above re-analysis , it is realized that the ideal experiment
demonstration for the uncertainty principle is untenable. Therefore, the
uncertainty principle is untenable.
Reference:
1. Max Jammer. (1974) The philosophy of quantum mechanics (John wiley & sons ,
Inc New York ) Page 65
2. Ibid, Page 67
3. http://www.aip.org/history/heisenberg/p08b.htm
Author : BingXin Gong
Postal address : P.O.Box A111 YongFa XiaoQu XinHua HuaDu
GuangZhou 510800 P.R.China
E-mail: [log in to unmask]
Tel: 86---20---86856616
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