uncertainty principle is untenable !!! (new)

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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¡¯s 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¡¯s width is the 
uncertain quantity of the particle¡¯s position. But there is no reason for us 
to consider that the particle in the above experiment have position¡¯s 
uncertain quantity certainly, and no reason for us to consider that the slit¡¯s 
width is the uncertain quantity of the particle¡¯s 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

Address :   P.O.Box A111 YongFa XiaoQu XinHua HuaDu

         GuangZhou 510800 P.R.China

E-mail  :   address@hidden

Tel:        86¡ª20---86856616


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