Scrodinger's cat experiment
Article Published in Ganita Chandrika (ISSN 0973-3493), [Special Issue International Physics year] 6, 19 (2005).
Dr N. V. Prasad
Lecturer, Department of Physics, Postgraduate Centre
P.B. Siddhartha College of Arts and Science
Siddhartha nagar, Vijayawada-10
Imagine a chamber, which houses a cat together with a machine, a bottle of cyanide and a radioactive substance. The machine has triggering mechanism which, when activated
by the decay of an atom of the radioactive substance, will trip a hammer and break the bottle of cyanide. The quantity of the radioactive substance in the chamber is such that
there is equal probability for one atom to decay in a hour and for nun to decay during the time. At the end of one hour will the cat is alive or not?
Untying The Scrodinger's Cat
"It is typical in such a case that an uncertainty initially restricted to an atomic domain has become transformed in to a macroscopic uncertainty which can be resolved through direct observation" - Schrodinger
By looking into the above Scrodinger's puzzle it seems to be very interesting. If one opted the same puzzle to quantum mechanical theory then at the end of one hour, the
wave function of the system can be treated as a liner combination of equal parts of functions corresponding to a 'live cat' and 'dead cat'. Bohr defined that dead cat means the reduction of wave function. This example was quoted according to Copenhagen (N.Bohr head quarters place) point of view that the wave function provides a complete
description of an individual system. Thus Schrodinger wave equation is defined as thefundamental equation of quantum mechanics, determining the type of functions required
for various cases of motion and interaction of micro particles.
However, Einstein interrupted the same event in terms of the following ensemble reference, where the ensemble means the collection of large particles (large number of
Schrodinger cats). Based on this assumption the wave function can be assumed as a liner combination of wave packets of functions corresponding to 'half live cats and half dead cats.
Einstein ensemble interpretation: Based on the above paradox, Einstein concluded and quoted in the article entitled 'Physics and relativity' that the system at initial state of lower energy ε1 should have corresponding function ψ1. Then the wave function of the system can be expressed as:
ψ = Σr Cr ψr
Where the coefficient Cr satisfies the condition that Σr ⏐Cr ⏐2 = 1 and give the probability for the system state ψr. In other words the probability ⏐Cr ⏐2 is
proportional to the number of individual systems in the ensemble, which have energy εr.
Finally, the Einstein picture of quantum mechanics is as follows:
"The laws of quantum physics are of statistical character. This means they concern not on one single system but an aggregation of identical systems and they cannot be verified by measurement of one individual bur only by a series of repeated measurements".
[Einstein and Infled "The evolution of Physics, NY (1938)]
In this connection, the following debate conversation is more adequate.
Einstein wrote a letter to Schrodinger in 1928 that:
'The Heisenberg and Bohr tranquilizing philosophy is so delicately contrived that, for the time being it provides a gentle pillow for the true believer from which he can not very easily be aroused'.
In his 'reply to criticism', presented on his 70th birth day [Einstein Philosopher-Scientist,(ed) P.A. Schilpp, Illinois (1949)]:
"One arrives at very implausible theoretical conceptions, if one attempts to maintain the thesis that the statistical quantum theory is in principle capable of producing a complete description of individual physical system. On the other hand, those difficulties of theoretical interpretation disappear, if one views the quantum mechanical description as the description of the ensemble of systems".
Reference: Quantum Mechanics, V.K. Thankappan, New age International (P) Ltd.,
Acknowledgements: Author thanks Siddhartha Academy of General and Technical Education for their constant encouragement.
