uncertainty principle is untenable !!!

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UNCERTAINTY  PRINCIPLE

IS

UNTENABLE



By reanalysing the experiment of Heisenberg Gamma-Ray Microscope and 
one of ideal experiment from which uncertainty principle is derived , 
it is found that actually uncertainty principle can not be obtained 
from these two ideal experiments . And it is found that uncertainty 
principle is untenable.



Key words :

uncertainty principle; experiment of Heisenberg Gamma-Ray Microscope; 
ideal experiment





Ideal  Experiment  1

Experiment  of  Heisenberg Gamma-Ray  Microscope



A free electron sits directly beneath the center of the microscope's 
lens (see the picture below or AIP page: 
http://www.aip.org/history/heisenberg/p08b.htm). 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 in the x direction 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 never lost (it 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

     .

Reanalysis

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)

It is the resolving limit of the microscope, and it is the uncertain 
quantity of the object's position.

Microscope can not see the object which the size is smaller than its 
resolving limit dx.

Therefore, to be seen by the microscope, the size of the electron 
must be larger than the resolving limit dx or equal to the resolving 
limit dx.

But if the size of the electron is larger than or equal to the 
resolving limit dx, electron will not be in the range dx. dx can not 
be deemed to be the uncertain quantity of the electron's position 
which can be seen by microscope, dx can be deemed to be the uncertain 
quantity of the electron's position which can not be seen by 
microscope only.

dx is the position's uncertain quantity of the electron which can not

be seen by 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 momentum's uncertain quantity of the electron which can be 
seen by microscope.

What relates to dx is the electron which the size is smaller than the

resolving limit .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 which the size is larger than or 
equal to the resolving limit .The electron is not in the range dx, it 
can be seen by the microscope, so its position is certain.

Therefore, the electron which relate to dx and dPx respectively is 
not the same.

What we can see is the electron which the size is larger than or 
equal to the resolving limit dx and has certain position, dx = 0..

Quantum mechanics does not relate to the size of the object. but on 
the Experiment Of Heisenberg Gamma-Ray Microscope, the using 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 it does not 
exist alleged the uncertain quantity of the electron's position dx.

To be seen by the microscope, none but the size of the electron is 
larger than or equal to the resolving limit dx, the gamma ray which 
diffracted by the electron can be scattered into any angle within the 
cone of angle 2A, we can measure the momentum of the electron.

What we can see is the electron which has certain position, dx = 0, 
so that none but dx = 0£¨we can 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 can gained dPx = 0.

Therefore ,

dPx dx =0.                                     (6)





Ideal experiment 2

Experiment of single slit diffraction



Supposing a particle moves in Y direction originally and then passes 
a slit with width dx . So the uncertain quantity of the particle 
position in X direction is dx (see the picture below) , 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°Øs constant.       (2)

So uncertainty principle can be obtained

dPx dx ~ h                                    (5)



Reanalysis

According to Newton first law , if the external force at the X 
direction does not affect particle ,the particle will keep the 
uniform straight line Motion State or Static State , and the motion 
at the Y direction unchangeable .Therefore , we can lead its position 
in the slit form its starting point .

The particle can have the certain position in the slit, and the 
uncertain quantity of the position dx =0 .

According to Newton first law , if the external force at the X 
direction does not affect particle,and the original motion at the Y 
direction is unchangeable , the momentum of the particle at the X 
direction will be Px=0 , and the uncertain quantity of the momentum 
will be dPx =0.

Get:

dPx dx =0.                                     (6)

It has not any experiment to negate NEWTON FIRST LAW, in spite of 
quantum mechanics or classical mechanics, NEWTON FIRST LAW can be the 
same with the microcosmic world.

Under the above ideal experiment , it considered that slit°Øs width 
is the uncertain quantity of the particle°Øs position. But there is 
no reason for us to consider that the particle in the above 
experiment have position°Øs uncertain quantity certainly, and no 
reason for us to consider that the slit°Øs width is the uncertain 
quantity of the particle°Øs position.

Therefore,  uncertainty principle

dPx dx ~ h                                      (5)

which is derived from the above experiment is unreasonable .



Concluson

>From the above reanalysis , it is realized that the ideal experiment 
>demonstration for uncertainty principle is untenable .

uncertainty principle is untenable.                      .



Reference book :

1.   Max Jammer. (1974)  The philosophy of quantum mechanics  (John 
wiley & sons , Inc New York )   Page 65

2.  Max Jammer. (1974)  The philosophy of quantum mechanics  (John 
wiley & sons , Inc New York )   Page 67

http://www.aip.org/history/heisenberg/p08b.htm



Author  :   Gong BingXin

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