My comment here is taken out of a context which is my personal vision towards a solution to several open problems in theoretical physics, here is an attempt.
meopemuk said:
I guess it would be very hard for you to explain me how one can measure the probability of an event which happens only once. I just don't get it.
To first contrast:
the frequentist view means that you can only determine the probability of an event in retrospect by simply noticing the continuum or "large-n" limit of relative frequencies. Clearly to conclude what the relative frequency was in the past is of no survival value unless you can use this also to infer the relative frequency also in the future. Also we have the problem that the continuum probability seems to also be an idealisation, since it makes no sense to actually consider the continuum limit to be physical.
To clarify what the purpose of the probability concept is to me, my view contains a reconstruction of the probability concept and information theory from a discrete scenario of counting information
Probability of a given future event is the an observers measure of the degree of expectation of something. This measure has great utility when it comes to choosing an action to prepare yourself for the future. The observers future persistence and survival depends on it. Ideally the preferred action is the one that maximises the observers benefits.
This is a conjecture I make, that I use as a constructing principle that onw can call the
"rational action conjecture". This conjecture does not mean that observers always behaves rationally - it rather means that a second observers best single bet, is that the observer acts rationally as per the construced measures of expectations.
So probability to me, is not really something you measure, it is an acquired expectation you have, that by the rational action conjecture determines your actions. So as I see it, the measures of expectations and the corresponding "probability spaces" and state spaces are coded in he observers past. And thus the probability is simply an expectation of the future. The expectation can be real and rational, even if the actual future later proves to be in contradiction to the prior expecations. Because this is the non-trivial case where we have non-trivial interactions, which revises the expectations.
To me, the case where past expecations where are in line with the actual futures is what I call equilibrium because nothing happens apart from confirmation of expectations.
This is why, in my view that observer is always active, there is no such thing as a passive observer just collecting information. The observers actions is effectively the perturbations that we call "measurement", so the CHOICE of the measurement is actually constrained. Some "choices" are simply "less likely".
The state space is my view, is then not timeless, it's spanned by a recoded truncated part of a subjective history. This acquired state eventually codes the expectations of the future (in a sense quite similar to thermodynamic arrow of time), but with the difference that evolution will favour clever datacompression, this should give rise to non-commutative state spaces, so the actual microtructure of the observer contains several sub.structures whose states are not commuting.
The ideas I have aims to find out if these relations follow from these principles, if they do there will be plenty of predictions.
But it's a completely new way of thinking of probability and information. I think it's best thought of as actual expectation of the future. In this sense, the probabilities are actually "subjectively physically real", but not objective. So in my view, the corresponding state vector, is actually subjectively real, in the sense that it's encoded in the microstates of the
observers internal structure. But this also is the key to allow for the state spaces to evolve.
Also in my view, the unitary evolution, is just an "expected evolution" that is valid in differential time - not globally. It follows from this thinking that each observer "sees" a spaces of possible differential changes, and on this space there is a measure defined. This becomes the action measure and by this one can calculate a correspondence to the feymann transition amplitudes. But this entire amplitude is really just an expectation.
The case where some of these expectations are in fact in perfect match with the actual future, is just a special case of we beeing close to equilibirum. Each observer "expects" a unitary evolution, and this is reflected in this observers action. This is the rational action conjecture. Howver, when such observers, that are not generally previously tuned, their expectations will be scattered, and they are forced to revise this expectations and action patterns. This is my view of what happens when systems interact in a way that they deform, destruct or severely change appearance.
/Fredrik
A particle of particle.