Examples of using Hidden variables in English and their translations into Danish
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Bell thus supported realism in the form of hidden variables.
There are hidden variables, so it's difficult to predict the outcome.
There might be other quantities giving extra information-- hidden variables.
There are hidden variables, so the results of the experiments are pre-ordained; or.
In Einstein 's terms, quantum theory was not complete butneeded to be supplemented by hidden variables.
The other property of hidden variables that Bell demonstrated was that they must be contextual.
Nevertheless it would appear natural that the possibility of supplementing the Schrödinger equation with hidden variables would have been taken seriously.
Thus hidden variables cannot be thought of as saying what value a quantity'has', only what value we will get if we measure it.
Once this mistake was realised,it was clear that hidden variables theories of quantum theory were possible.
He found that, even when hidden variables are allowed, in some cases the result obtained in one wing must depend on which component of spin is measured in the other; this violates locality.
He was delighted by the creation in 1952 by David Bohm of a version of quantum theory which included hidden variables, seemingly in defiance of von Neumann 's result.
Faster than light;(2) There are hidden variables, so the results of the experiments are pre-ordained; or(3) Quantum theory is not exactly true in these rather special experiments.
They were therefore pleased when John von Neumann proved a theorem claiming to show rigorously that it is impossible to add hidden variables to the structure of quantum theory.
A complete theory of hidden variables must actually be more complicated than this-- we must remember that we wish to predict the results of measuring not just s z, but also s x and s y, and any other component of s.
In EPR-type experiments,this inequality is obeyed by local hidden variables, but may be violated by other theories, including quantum theory.
A complete theory of hidden variables must actually be more complicated than this-- we must remember that we wish to predict the results of measuring not just sz, but also sx and sy, and any other component of s. Nevertheless it would appear natural that the possibility of supplementing the Schrödinger equation with hidden variables would have been taken seriously.
The result of this argument is that at least one of three statements must be true:(1) The particles must be exchanginginformation instantaneously i.e. faster than light;(2) There are hidden variables, so the results of the experiments are pre-ordained; or(3) Quantum theory is not exactly true in these rather special experiments.
Von Neumann had illegitimately extended to his putative hidden variables a result from the variables of quantum theory that the expectation value of A+ B is equal to the sum of the expectation values of A and of B. The expectation value of a variable is the mean of the possible experimental results weighted by their probability of occurrence.
Von Neumann had illegitimately extended to his putative hidden variables a result from the variables of quantum theory that the expectation value of A+ B is equal to the sum of the expectation values of A and of B.
However Bell then demonstrated certain unwelcome properties that hidden variable theories must have.
First he constructed his own hidden variable account of a measurement of any component of spin.
This turned out to be the result of a hidden variable- the orientation of the switch.
Realism and determinism would both be restored; sz would have a value at all times, and, with full knowledge of the state of the system,including the value of the hidden variable, we can predict the result of the measurement of sz.
Sz would have a value at all times, and, with full knowledge of the state of the system,including the value of the hidden variable, we can predict the result of the measurement of sz.
As a simple example, the state-vector above might apply to an ensemble of many systems, but in addition a hidden variable for each system might say what the actual value of sz might be. Realism and determinism would both be restored; sz would have a value at all times, and, with full knowledge of the state of the system,including the value of the hidden variable, we can predict the result of the measurement of sz.