Science

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Swaminathan Venkataraman <nachiketas

 

>I have read " Shadows of the mind " by Roger Penrose, only a part of it

>actually. He lost me in the part where he delved into the proof of Godell's

>theorem. Can you direct me to some source where this theorem is proved in a

>slightly less rigorous manner i.e. a more " popular " version of the proof?

 

Kurt Godel's incompleteness theorem is quite dramatic - it denies us the

possibility of constructing a complete consistent mathematical description

of reality. The proof is not that difficult to explain it uses infinite sets

and one-to-one correspondence.

 

The conclusions are:- Mathematics proves that mathematics is not adequate

enough as a tool to explain 'REALITY' in total. (The system will be either

consistent or complete - cannot be both).

 

>can I paraphrase the theorem to mean that no system of logic can be both

> " sufficient " and " complete " at the same time? If so, dosent this have

>drastic implications for how much science can understand of nature?

 

 

Yes - the implications are that mathematics itself can never be enough to

get a complete picture. (This proof pops out of mathematics itself! This is

the greatness of mathematics - it shows its own limitations)

 

>Also, I thought that chaos theory was a very respected field even within

the

> " establishment " . However all that I understand of chaos is the very famous

>example about a butterfly flapping its wings in the Amazon forest causing a

>storm in Asia.

 

 

Chaos theory is respectable to the extent that it talks about everything

connected to everything else in a non-linear fashion. (The classical

physics had a habit of connecting things in a linear manner). The result of

non-linear relationship allows for dramatic things to happen which defies

linear physics - hence the use of the word Chaos. When the Chaos theory

talks of some 'underlying unity which connects everything to everything

else in the universe instantaneously -- then the 'Science establishment' is

not too keen.

 

>Has the scientific establishment pronounced the last word on Aspect's

>experiment? i.e. have they come up with a " causal " explanation for the

>observation?

 

>thanks and regards

>Swami

>

 

EPR thought experiment was set up by Einstein to get away from the

uncertainty theorem of quantum mechanics. He was sure that at a deeper level

there is no uncertainty in the universe - just hidden variables which we

have yet to be discovered. He thought that once we find these we can have

complete picture of the universe (this is normal reductionist approach of

classical physics). The Thought experiment became a real possibility in

1981. The idea behind this experiment was that if uncertainty principle

holds then it may be possible to send information at speeds faster than

light. This would throw a spanner in the works because in science we do not

mess about with the law of causality. If information can travel at speeds

faster than light 'the law of causality would be the victim'. Quite

dramatic.

 

The Aspect experiment uses pairs of entangled photons emitted in opposite

directions to a distance of 12 meter separation. The direction in which to

make the measurements of polarisation of the photons at each end is done

while the photons are in flight -hence the photons do not have that

information - yet the results at both ends " seem to show a spontaneous

exchange " of information between the two photons! How did this information

travel? - and it seems to have travelled at speeds faster than light!

 

These result excited lot of interest from the 'new-age type scientists'. But

the more established scientists say -- the key word is " seem to show

spontaneous exchange " -- nothing more. You cannot use this experiment to do

anything more than say devise a system of passing coded information between

two people (the code that no one can ever break -- that is the best

possible use, - there is nothing more - it cannot do anything to violate

law of causality!). Hence we are back to square one.

 

regards

jay