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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)
Every physical principle is based on an Ideal Experiment, not based on
MATHEMATICS, including heisenberg uncertainty principle.
For example, the Law of Conservation of Momentum is based on the collision
of two stretch ball in the vacuum; the Principle of equivalence(general
relativity) is besed on the Einstein's laboratory in the lift.
Heisenberg's Gamma-Ray Microscope experiment is an ideal experiment.
Einstein said, One Experiment is enough to negate a physical principle.
Heisenberg's Gamma-Ray Microscope experiment has negated the uncertainty
principle.
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
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