Quotes about Physics
"Nature is the realization of the simplest conceivable
mathematical ideas. ... I am convinced that we can discover
by means of purely mathematical constructions the concepts
and the laws connecting them with each other." - Einstein - From his Oxford lecture, 1933
Quantum mechanics just serves to describe some particular behavior of macroscopic instruments which cannot be explained classically.
Hilbert space is a big place.
The beginner should not be discouraged if he finds that he does not have the prerequisites for reading the prerequisites.
"The word 'classical' in physics means only one thing: it's wrong!" - J.R. Oppenheimer
Quantum mechanics asks: Is FALSE the SAME as NOT TRUE?
The gravitational field has only a relative existence because for an observer freely falling from the roof of a house, at least in her immediate surrounding, there exists no gravitational field.
"Your highness, I have no need of this hypothesis" - Pierre-Simon de Laplace (1749-1827) in a reply made to Napolean when asked why his celestial mechanics has no mention of God.
The word ENSEMBLE is NOT meant to imply that physical quantities HAVE values that are distributed in an unknown way among the elements of the ensemble. It only relates to the SPREAD of results for repeated measurements.
In 18th century Newtonian mechanics, the 3-body problem was insoluble. With the birth of general relativity around 1910 and quantum electrodynamics in 1930, the 2-body and 1-body problems became insoluble. Now, within moderen quantum field theory, the 0-body (vacuum) problem is insoluble. So if we are after exact solutions, no bodies at all is already too many.
My idea, paradoxically, and a little provocatively, but nonetheless genuinely, is simply this: QUANTM STATES DO NOT EXIST. The abandonment of superstitious beliefs about the existence of Phlogiston, the Cosmic Ether, Absolute Space and Time, .... or Fairies and Witches, was an essential step along the road to scientific thinking. The quantum state, too, if regarded as something endowed with some kind of objective existence, is no less a misleading conception, an illusory attempt to exteriorize or materialize our true probabilistic beliefs.
How does one justify a probability assignment in a physical theory? It is important to understand that you cannot deduce probability from certainty. No matter how profound your mathematics, to come out eventually with a probability distribution, then you have to put in a probability distribution. Nothing in the equations of motion (deterministic equations = certainty) tells you what distribution to put in. They can only give you relations between probabilities at different times. This all says that any appeal to the laws of physics (deterministic equations = certainty) will not suffice to justify a probability distribution.
The statement "there is a 70% chance that the proposition - if A is measured, then the result will bi a - is true" is quite different from "if A is measured, then there is a 70% chance that the result will be a". It is the latter that is intended in quantum mechanics by the statement: Prob(A=a|Wave function) =0.7
What is electrodynamics trying to tell us? "Fields in empty space have physical reality, the medium that supports them does not".
What is quantum mechanics trying to tell us? "Correlations have physical reality, that which they correlate does not"
When a physicist makes vague remarks about a measurement of an observable producing an "uncontrollable disturbance" in its value, whatever can that mean? The central position of quantum mechanics is NOT that a quantity like A has a value which we happen not to know, but rather that, in a typical quantum state, it is NOT meaningful to say that A possesses any value at all and that, which does not exist, cannot be disturbed, uncontrollably or otherwise.
Let H={|1>,|2>} = 2-dim Hilbert space; H1={|1>} = 1-dim Hilbert space; H2={|2>} = 1-dim Hilbert space; and |p>=a|1> +b|2> (implies Hilbert space HP). Then Hp (UNION) H1 = (empty set), Hp (UNION) H2 = (empty set) and Hp (UNION) (H1+H2) = Hp. Now if the distributive property of classical propositional logic is true, then we must have Hp (UNION) (H1+H2) = Hp (UNION) H1 + Hp (UNION) H2 = (empty set), which implies that Hp = (empty set), which is false. Most of the strange features of quantum mechanics can be traced back to the non-distributive property of the logical structure of quantum mechanics.
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