Re: Why field theories are deterministic, but QM isn't?

[I had sent this before, but apparently it never appeared
in the newsgroup.]


Gerard Westendorp schrieb:
dudajar@xxxxxxxxx wrote:

So why its predecessor which we commonly use - quantum mechanics is
completely undeterministic - we can usually talk only about
probabilities????

The indeterminism only shows up in connection with observation.
The dynamic equations of quantum (field) theory do not have any probability element in them.

For example, the Schrodinger equation is a deterministic wave equation. Only when we set up an experiment to measure either position or momentum, do we get a probability.


How can QM be stochastic while the Schroedinger equation is not?


The Schroedinger equation is a deterministic wave equation.
But when we set up an experiment to measure either position or
momentum, we get uncertain, stochastic outcomes.

So - is quantum mechanics deterministic or stochastic?


One has to be careful in the interpretation of the foundations...


Fortunately, the same apparent paradox already occurs in classical
physics; hence the paradox cannot have anything to do with the
peculiarities of quantum mechanics.

Indeed, a Focker-Planck equation is a deterministic partial
differential equation. But when measuring a process modelled by it
- such as the position of a grain of pollen in Brownian motion -,
we get only probabilistic results. Now Focker-Planck equations are
essentially equivalent to classical stochstic differential equations.

So - do they describe a deterministic or a stochastic process?


The point resolving the issue is that, both in stochstic differential
equations and in quantum mechanics, probabilities satisfy deterministic
equations, while the quantities observed to deduce the probabilities
do not.

Thus, in both cases, probabilities are deterministic ''observables''
while the position of a grain of pollen in classical mechanics, or
position and momentum in quantum mechanics, ar not.



Arnld Neumaier


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Relevant Pages

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