wolram said:
By Marcus
you drive the measuremtn to be more and more precise by using a wave that is shorter and shorter wavelength, you keep jacking up the frequency or the photon energy of the wave to get higher precision. What is the limit?
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I agree our measuring methods must have a limit, but it is interesting to
speculate about the finness of time and if it has a reality in sub micro
states and if plank time is a meaningful measure.
limitations on what and how fine one can measure are at the heart of quantum theory
as I guess you know this----that one of the famous interpretations of QM is that if you cannot measure something (even in principle) because of some quantum mechanical limitation then it is meaningless to ask about it
something like that. probably I am saying it wrong
for instance, if you can't tell which slit the electron went thru, if the experiment is set up so that even in principle there is no way of knowing, then you cannot say it went thru one or the other
we really need someone else to tell us about this, it is about the Interpretation of QM------the Born Interp., the "Hidden Variables" interp, etc.
without getting into complicated issues, the core feature of any quantum theory is there are two separate entities the Observer and the Other thing, and a quantum theory tells you what the Observer can and cannot observe, what he can know and not know, if he measures one feature of the thing then whether he can go and measure some other feature (like position and momentum), how one measurment affects another, possible outcomes of measurment (spectra),
probabilities, uncertainty.
the reason every quantum theory has a hilbertspace is that it is a convenience for representing uncertainty inherent in what one system can know about another.
when you "quantize" a classical theory you introduce some mathematical paraphernalia like a hilbertspace that can represent essential LIMITATIONS ON KNOWLEDGE and especially limitations of a fundamental kind on how precisely things can be measured.
the curious thing is, nature seems to want us to do this, because when you introduce the gear representing uncertainty the theory calculates better numbers. singularities are removed. everything works better
the hydrogen atom can exist because nature insists on a certain leeway of uncertainty. you'd think that the electron would spiral right down and stick to the proton. but she doesn't like that because then you'd be too certain about where the damn thing is. it is only nature's insistence on vagueness that keeps us all alive.
(this is what they realized IIRC in 1925 or so: quantizing explains the stability of the hydrogen atom, a famous moment in history. it had worried people)
adding an intrinsic indefiniteness to the picture makes it more realistic (better numbers, fewer paradoxes)
a major philosophical issue, ever since 1925, has been this: if you can't measure something for some fundamental reason, then does it make any sense to ask which way it is? if you can't tell, should you ask?
if you can't measure finer than Planck, then does it make sense to ask whether something is 1.1 Planck units long or 1.2 Planck units long.
Maybe it is "both and neither" the way the electron goes thru "both and neither" slit(s).
