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In Nitzens & Bichlers Capital as Power, they quote from Weinbergs Dreams of a Final Theory:

I pointed out [to Einstein] that we cannot, in fact, observe such a path [of an electron in an atom]; what we actually record are frequencies of the light radiated by the atom, intensities and transition probabilities, but no actual path. And since it is but rational to introduce into a theory only such quantities as can be directly observed, the concept of electron paths ought not, in fact, to figure in the theory.

To my astonishment, Einstein was not at all satisfied with this argument. He thought that every theory in fact contains unobservable quantities. The principle of employing only observable quantities simply cannot be consistently carried out. And when I objected that in this I had merely been applying the type of philosophy that he, too, had made the basis of his special theory of relativity, he answered simply: ‘Perhaps I did use such philosophy earlier, and also wrote it, but it is nonsense all the same’.

Contra Einstein is there a theory that has only observable quantities?

It may be that Einstein is thinking of only fundamental theories - in which case the answer must be a no. Of course numbers are unobservable, so we can't allow any mathematical theories. Nitzen & Bichler also rule out classical & marxist economics.

  • Why are numbers unobservable? I see 2 bottles of water in front of me...+1 still an interesting question. – draks ... Dec 19 '13 at 22:57
  • thats two bottles, not the number two; and a piece of card with the number two written on it isn't it either - its a representation – Mozibur Ullah Dec 20 '13 at 0:01
  • So what's a number then? Can you give a example for a observable variable without using numbers? – draks ... Dec 20 '13 at 7:32
  • @draks: Speed is an observable quantitity; in physics recall we don't use pure numbers - well only occasionally, like pi - but affix physical quantities, so we say a car has a speed of 2 metres per second. So like 2 bottles, not like 2. – Mozibur Ullah Dec 20 '13 at 13:39
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The problem with Einstein's argument is not the insistence that the theory needs unobservable quantities, but the insistence that the theory in question needs the particular unobservable quantities he had in mind, such electron paths. Quantum mechanic of course has introduced other unobservable quantities, just not the ones classical physicists used to deal with at that time.

Historically there were many physical theories, such as the original formulation of Classical Mechanics by Newton, that would consider only observable quantities. It has become handy to use unobservable quantities, hence Lagrange introduced the expressions we now call "lagrangians" into Classical Mechanics. Nobody can observe or measure lagrangians (they are not physical quantities), but many problems of Newtonian Mechanics are easier to solve with their aid.

So if the question is about any fundamental theory that deals only with observable quantities then the answer is yes: Newtonian formulation of Classical Mechanics.

If, on the other hand, the question is about a theory compatible with Quantum Mechanics, then I'm not certain about the answer, but seriously doubt the existence of such theory because unobservable quantum states seem to be essential to both Heisenberg-Schroedinger formulation (as elements of Hilbert space) and Feynmann formulation (as possible paths). QM insists, in the form of Heisenberg inequalities, on some ambiguity of observable quantities, and the introduction of unobservable ones is the way to build a theory despite those ambiguities, as far as I know.

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    +1 Maybe it's worth noting "Hidden Variable Theories". A recent development was done by Colbeck and Renner. They write: "In the present work, we have ... excluded the possibility that any extension of quantum theory (not necessarily in the form of local hidden variables) can help predict the outcomes of any measurement on any quantum state. In this sense, we show the following: under the assumption that measurement settings can be chosen freely, quantum theory really is complete". – draks ... Dec 19 '13 at 23:03

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