themadchemist
Nov 20, 2004, 02:28 PM
I received this piece of spam last night:
Please reply to hdgbyi@public.guangzhou.gd.cn.
Thank you!
The limitation of the Photon Hypothesis
According to the electromagnetic theory of light, its energy is related to the amplitude of the electric field of the electromagnetic wave, W=eE^2(where E is the amplitude). It apparently has nothing to do with the light's circular frequency v.
To explain the photoelectric effect, Einstein put forward the photon hypothesis. His paper hypothesized light was made of quantum packets of energy called photons. Each photon carried a specific energy related to its circular frequency v, E=hv. This has nothing to do with the amplitude of the electromagnetic wave.
For the electromagnetic wave that the amplitude E has nothing to do with the light's frequency v, if the light's frequency v is high enough, the energy of the photon in light is greater than the light's energy, hv>eE^2. Apparently, this is incompatible with the electromagnetic theory of light.
THE UNCERTAINTY PRINCIPLE IS UNTENABLE
By re-analysing Heisenberg's Gamma-Ray Microscope experiment and one of the thought experiment from which the uncertainty principle is demonstrated, it is actually found that the uncertainty principle cannot be demonstrated by them. It is therefore found to be untenable.
Key words:
uncertainty principle; Heisenberg's Gamma-Ray Microscope Experiment; thought experiment
The History Of The Uncertainty Principle
If one wants to be clear about what is meant by "position of an object," for example of an electron., then one has to specify definite experiments by which the "position of an electron" can be measured; otherwise this term has no meaning at all. --Heisenberg, in uncertainty paper, 1927
Are the uncertainty relations that Heisenberg discovered in 1927 just the result of the equations used, or are they really built into every measurement? Heisenberg turned to a thought experiment, since he believed that all concepts in science require a definition based on actual, or possible, experimental observations.
Heisenberg pictured a microscope that obtains very high resolution by using high-energy gamma rays for illumination. No such microscope exists at present, but it could be constructed in principle. Heisenberg imagined using this microscope to see an electron and to measure its position. He found that the electron's position and momentum did indeed obey the uncertainty relation he had derived mathematically. Bohr pointed out some flaws in the experiment, but once these were corrected the demonstration was fully convincing.
Thought Experiment 1
The corrected version of the thought experiment
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 moment 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
The original analysis of Heisenberg's Gamma-Ray Microscope Experiment overlooked that the microscope cannot see the object whose size is smaller than its resolving limit, dx, thereby overlooking that the electron which relates to dx and dPx respectively is not the same.
According to the truth that the microscope can not see the object whose size is smaller than its resolving limit, dx, we can obtain that 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.
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 cannot 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 cannot 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 cannot 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. But if the size of the electron is smaller than the resolving limit dx, the electron cannot be seen by the microscope, we cannot measure the momentum of the electron. Only the size of the electron is larger than or equal to the resolving limit dx, the electron can be seen by the microscope, we can measure the momentum of the electron. According to Heisenberg's Gamma-Ray Microscope Experiment, the electron¡¯s momentum is uncertain, the uncertainty in its momentum is dPx.
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 cannot be seen by the microscope, so its position is uncertain, and its momentum is not measurable, because 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. If the electron cannot be seen by the microscope, we cannot measure the momentum of the electron.
What relates to dPx is the electron where the size is larger than or equal to the resolving limit dx .The electron is not in the range dx, so it can be seen by the microscope and its position is certain, its momentum is measurable.
Apparently, 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)
Please reply to hdgbyi@public.guangzhou.gd.cn.
Thank you!
The limitation of the Photon Hypothesis
According to the electromagnetic theory of light, its energy is related to the amplitude of the electric field of the electromagnetic wave, W=eE^2(where E is the amplitude). It apparently has nothing to do with the light's circular frequency v.
To explain the photoelectric effect, Einstein put forward the photon hypothesis. His paper hypothesized light was made of quantum packets of energy called photons. Each photon carried a specific energy related to its circular frequency v, E=hv. This has nothing to do with the amplitude of the electromagnetic wave.
For the electromagnetic wave that the amplitude E has nothing to do with the light's frequency v, if the light's frequency v is high enough, the energy of the photon in light is greater than the light's energy, hv>eE^2. Apparently, this is incompatible with the electromagnetic theory of light.
THE UNCERTAINTY PRINCIPLE IS UNTENABLE
By re-analysing Heisenberg's Gamma-Ray Microscope experiment and one of the thought experiment from which the uncertainty principle is demonstrated, it is actually found that the uncertainty principle cannot be demonstrated by them. It is therefore found to be untenable.
Key words:
uncertainty principle; Heisenberg's Gamma-Ray Microscope Experiment; thought experiment
The History Of The Uncertainty Principle
If one wants to be clear about what is meant by "position of an object," for example of an electron., then one has to specify definite experiments by which the "position of an electron" can be measured; otherwise this term has no meaning at all. --Heisenberg, in uncertainty paper, 1927
Are the uncertainty relations that Heisenberg discovered in 1927 just the result of the equations used, or are they really built into every measurement? Heisenberg turned to a thought experiment, since he believed that all concepts in science require a definition based on actual, or possible, experimental observations.
Heisenberg pictured a microscope that obtains very high resolution by using high-energy gamma rays for illumination. No such microscope exists at present, but it could be constructed in principle. Heisenberg imagined using this microscope to see an electron and to measure its position. He found that the electron's position and momentum did indeed obey the uncertainty relation he had derived mathematically. Bohr pointed out some flaws in the experiment, but once these were corrected the demonstration was fully convincing.
Thought Experiment 1
The corrected version of the thought experiment
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 moment 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
The original analysis of Heisenberg's Gamma-Ray Microscope Experiment overlooked that the microscope cannot see the object whose size is smaller than its resolving limit, dx, thereby overlooking that the electron which relates to dx and dPx respectively is not the same.
According to the truth that the microscope can not see the object whose size is smaller than its resolving limit, dx, we can obtain that 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.
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 cannot 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 cannot 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 cannot 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. But if the size of the electron is smaller than the resolving limit dx, the electron cannot be seen by the microscope, we cannot measure the momentum of the electron. Only the size of the electron is larger than or equal to the resolving limit dx, the electron can be seen by the microscope, we can measure the momentum of the electron. According to Heisenberg's Gamma-Ray Microscope Experiment, the electron¡¯s momentum is uncertain, the uncertainty in its momentum is dPx.
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 cannot be seen by the microscope, so its position is uncertain, and its momentum is not measurable, because 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. If the electron cannot be seen by the microscope, we cannot measure the momentum of the electron.
What relates to dPx is the electron where the size is larger than or equal to the resolving limit dx .The electron is not in the range dx, so it can be seen by the microscope and its position is certain, its momentum is measurable.
Apparently, 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)