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Friday, October 30, 2009

On spacetime, theory of incompleness and the axiom of choice (and the wave-particle duality)

NOTE: No guarantee on the correctness of anything mentioned in this article. It's just impression on what I read and I might have got it wrong or haven't read enough.

"Past and future,..
relativity to the speed of light,..
light speed is constant to all observers, the difference is only in red/blue-shift."

1- Invalidity of using the terms "Past" and "Future" as dimensions because they are relativistic terms. We can say positive and negative because they are well defined in relation to zero. But past and future, by analogy is like saying positive and negative with regards to unknown variable x.

2- Assume there is a light wave moving in some direction A. And there are 2 observers. One moving in the same direction with speed I, and one moving in the other direction with speed K. Speed of light to both must have different signs. Also assume I=c, then the "relative" speed between the light wave and the first observer (let it be another light wave to justify it), would be either 0 or c). It should be 0 because otherwise this totally says that the speed of light does NOT obey the laws of algebra.

3- Red and blue shifts are confirmed by observations. But let's look closer at the cause. They say that it's blue if it's coming to you, and red if it's departing from you. If it's departing from you, then how you've got the light wave ? That means that light waves has no direction and they move in all directions at one with only difference in frequency. Imagine a light wave that consists of one photon, is that even possible !!

I don't mean to say that some of these results -which are confirmed with many experiments- are incorrect. I only mean that the explanation provided either needs a total rethinking or I need someone to explain it better to me.

The Godel's theory of incompleteness can be thought of having similarity to the liar's paradox. But however I don't think it's true. It says that given some formal axiomatic system, there is a statement that can not be proven (incomplete) or there is two contradictory statements that can be derived (inconsistency).

Well, incompleteness is relative to what is to be proven. There is no set of formal axioms that can prove everything. But the theory implies that no matter how much axioms we have we can not prove everything.

Ironically, this theory is unprovable ! However, I think that we should think of the domain of the field the axioms was set up for. The set of axioms are complete within the set of theories they prove. If you want to prove something else you changed your field and need axioms related to this field.

I discuss the axiom of choice as an example of that. Think of this result: axiom of choice is independent of ZFC ! Well, doesn't that reflect part of the insight of the previous paragraph ?

Think too that axiom of choice is needed in case your set has subsets which are actually intervals in the Real domain. I am not sure if anyone thought of this, or I am too ignorant or too lazy to read and search for it, but doesn't this signal the end of the domain of "discrete" sets into "continuous" sets ? There is a difference between infinite sets and continuous sets -in my humble/ignorant opinion. However the axiom of choice seems to me more like of a hack to get the -completely in other domain- set of ZFC axioms to work with continuous sets !

Back to the wave-particle duality of photons and waves. One experiment that make me think about it is the refraction experiment where you send a ray of light in a hole whose diameter is less than the wavelength, and you'll get refraction. They claim that if you sent photon by photon instead you'll get the same refractive pattern and the claim is that this confirms the wave-particle duality. However did anyone consider the fact that it came from incapability to orient the photon with this wavelength to be in the same position when in hits the hole ?

Back to quantum randomness theory, that everything in quantum world is random. However I do not think it's random. Seeming random doesn't mean it's random. And randomness -no matter how low- can not build such a bigger coherent system. There is rules and not being able to know the rules made some of us try to interpret it by randomness, shame on you, lazy guys. I agree with Einstein who said that "God does not play dice".

Please if anyone has any insights or corrections he is welcome to comment here for a discussion. Thank you for reading so far and I hope I could deliver my points.