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In Quantum Mechanics the value of an observable results from the interaction between the "system" with the "Measuring gadget".

But when the experimenter[or the technologist concerned] is devising/constructing the gadget he has a view the "system" with its stand alone properties/attributes.It seems to be so.

But theory itself cannot ascribe the value of some observable to the system alone. How does one explain this?

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If you have some system in a superposition of states, then when your measuring gadget interacts with it it becomes entangled with the original system and it too is in a superposition of states. If you walk over to look at your measuring gadget you too become entangled and enter a superposition of states, and so on up to and including the journal you publish the results in.

In real life we don't see macroscopic objects, cats or otherwise, in a superposition of states, and the reason is generally considered to be decoherence. The describes the interaction of a system with the rest of the universe and the loss of coherence that results. The rate at which a system decoheres increases with the complexity of the system, so while a superposition of states can be maintained for an atom or molecule, it is lost almost instantaneously for something the size and complexity of lab equipment, and your experiment returns a definite value for whatever you were looking at.

The largest system that has been observed in a superposition of states contains about ten trillion atoms.

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"Decoherence can be viewed as the loss of information from a system into the environment (often modeled as a heat bath),[2] since every system is loosely coupled with the energetic state of its surroundings."...from Wikipedia[en.wikipedia.org/wiki/Quantum_decoherence]. When we talk of the "loss of information from a system" we seem to consider certain well defined stand alone properties of the system.This "leaked" information interacts with the evironment, the gadget being a part of it to produce the value of the measurement. –  Anamitra Palit Aug 3 '12 at 0:48
    
Information leaks out of the system----this information "leaked" is indicative of properties of the system $independent{\;} of{\;} the{\;} environment$ . The leaked information gets modified by interaction with the environment,the gadget being a part of it.Is it possible to eliminate the effect of the environment in the process of measurement? –  Anamitra Palit Aug 3 '12 at 0:56
    
In the last sentence of the previous comment I have tried to indicate at a mathematical/theoretical elimination of environmental effects to get to the stand alone properties of the system in a theoretical manner –  Anamitra Palit Aug 3 '12 at 1:06
    
You might want to ask this as a separate question. It is certainly possible to calculate the properties of an isolated system, and in fact that's what we normally do. The problem is that eventually a measurement is looked at by a human and we are part of the environment. –  John Rennie Aug 3 '12 at 5:41
    
The comments to the Original Posting "The Lorentz transformations in the Micro-world" may be related to the issue at hand. Link: physics.stackexchange.com/questions/18619/… –  Anamitra Palit Aug 3 '12 at 7:05

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