Tuesday, March 01, 2005

Great Blunders of the Great Bohr-Einstein Debate

The Bohr Einstein debate of the light box gedanken experiment was probably one of the best well known scientific debates. But rarely any one noticed that both of these two great men made fatal mistakes in the logoc of their argument.

Bohr's detailed recount of the debate can be read here:
http://www.marxists.org/reference/subject/philosophy/works/dk/bohr.htm

In summary, Einstein proposed a light box in which a fast acting shuttle releases a photon at a very precise moment. Before and after the release of the photon, the total weight of the light box can be weighed arbitrarily accurately to deduce the exactly mass-energy of the photon release. Therefore, both the photon's emitting time and mass-energy can be known to arbitrary precision, hence break the Heisenberg uncertainty principle which says the time and energy can not both be known precisely.

Bohr could not dispute Einstein's arguments. He could not sleep and spent the whole night desperately trying to find an argument to disprove Einstein. Next morning he did figure out a way to rescue the uncertainty principle, using time dilation of Einstein's own General Relativity. Einstein never thought his own theory will be used against his arguments. So Einstein was defeated.

But what Einstein never realized was that Bohr's logic was frauded. Intentionally or un-intentionally, he confused two completely different logical concept. One is the uncertainty of time measurement, Delta T, which should be the time internal during which the shuttle is open. Another concept, also expressed using the same symbol Delta T, is the time difference caused by time dilation due to general relativity.

See equation (7). The Delta T there was general relativity time dilation. It is definite, know, precisely calculable quantity. It is the difference between two clocks and has absolutely nothing to do with uncertainty of time measurement.

Bohr successfully confused Einstein by using the same symbol to represent both the time dilation and time uncertainty, two different quantities, and treat them as if they are the same thing. A confused Einstein got lost and could not see that Logic Fraud.

But certainly, Einstein's argument was also frauded, but for a totally different reason that Bohr also failed to see. That is, a photon of certain energy has a certain frequency and wavelength. If you open the shuttle for too short a time, shorter than one period of oscillation of the photon's frequency, then you would not be able to release a full photon. You would have choped a whole wavelength of the photon in halfs. Therefore, you either have not release a photon of the expected frequency, or you have released a photon who has a shorted wavelength and higher frequency.

In any case, the emitted photon would have a wavelength shorted than the distance light can travel within the short time interval that the shuttle is opened. So the uncertainty principle is still exactly true.

Quantoken

3 Comments:

Blogger Zelah said...

Hi quantoken.

Your analysis of this experiment is
SPOT ON.

However, this is actually know to cognoscente. I will later post an analysis of this experiment exploring this case in more detail.

By the way, I have looked into quantum entropy, and cannot find any consistent definitions!!! Now, you say that the quantum information is conserved in the universe due to unitary action! I have investigated this idea of yours and found out this very disturbing fact.

The UNITARY action of quantum mechanics can only be proved for BOUND states. What this means is that operators like exp(-iHrep) are not to be used!

(In Elementary Quantum Mechanics - Ele QM, this is quietly pushed to the side... This is possible as the basic example in Ele QM is the Hydrogen atom which has the bounded operator exp(-iH^2rep) !!!)

Yet again I ask you to explain what is the entropy of matter and how do I calulate it? Remember that quantum entropy is conserved so exp(-iHrep) and the like is forbibben!

An Amateur Mathematician

11:45 AM

 
Blogger Quantoken said...

Zelah:

You have raised very good and legitimate points. I am glad you are thinking about the same things.

My theory is still not complete. I have some very reasonable and legitimate ideas. But the mathematics is still lacking. So no I do not know how to calculate entropy of regular matters.

What I can say is you can not calculate entropy of matter as isolated objects. You have to calculate it as a none-separatable part of the universe. i.e., the matter exists within a specific region of space for a specific amount of time.

As I discussed previously the total mass-energy of the universe is N^2, but the total entropy is N^3. The two are not linearly proportional to each other. Therefore, consider an electron in our universe, or an electron in a different and smaller universe. Their entropies would be different even though they are the same electron!

My speculation is the entropy of a spacetime region is simply proportional to the surface (which is 3-D) that encloses the 4-D spacetime region. Note that's contrary to Hawking's 2-D surface of the 3-D space (space only, no time). Note my definition is Lorentzian invariant, and Hawking's is NOT Lorentzian invariant.

As for bound state. Since the universe is limited and enclosed. All states can be considered bounded. You can not extend exp(-iHrep) to infinity!!! If you can, then the universe is infinite, and then quantum entropy conservation of the universe no longer holds. So you see there is no inconsistency.

A limited universe has to be closed, and therefore there has to be spacetime curvature. And that naturally leads to gravity, which we know is just another way of saying spacetime curvature. Limitness and conservation of quantum entropy then leads to QM and uncertainty principles. That makes it so attractive that GUITAR leads to both GR and QM naturally.

What is especially encouraging is the fact that
G = 1/2N.
and
N = PI* exp(2/(3*alpha)).

So the same alpha leads to both the scale of gravity and the scale of the universe. Or in another word: both alpha and gravity arises from the size of the observable universe.

Please ignore the psycho who repeatedly posted the same vulgar harrasments again and again. He is obviously very sick.

Quantoken

1:56 PM

 
Blogger Cartoon Nazi said...

You know this is all fine and good, the uncertainty principle is indeed intact but, I can’t help but feel that Einstein’s “Hidden Variables” argument has, over time, been proven true. What else could you call the extra dimensions of string theory? I, for one, believe that in the end, Bohr will be proven wrong and Einstein right. If “Many Worlds”, “Many Histories” and Branes are not “Hidden Variables” then I don’t know what is.

4:25 AM

 

Post a Comment

<< Home