trafficanalyst
01-28-05, 11:14 AM
Any of you want to discuss Schrödinger's Cat?
Which is about the experiment (research the "Uncertainty Principle") by which the observer "interferes" with the outcome merely through an attempt to observe something (a useful overarching concept is Godel's undecidabililty theorem). We want to know whether the cat (Schrödinger's Cat) is dead or alive. So we open the box. The cat is dead. However, we do know enough to know that the very act of opening the box will kill the cat if not dead already (nice bit of omniscent break-out here!), yet we cannot know with certainty the state of the cat prior to the need to observe it.
Which leads me to my idea: we can determine that the cat was dead (or alive) not via direct experiment, but by proxy -> We don't worry about observing the cat, nor the box, but firstly observe, or measure, our matrix of influence, our system of change-effects that occur, and are directly measuarable and independent from the cat. The other 2 parts, that we cannot observe, because we cannot observe the cat, the cat system's change, is the cat system's independent variation, and the covariance between us and the cat (the influence variation, or what I call below the "interaction matrix"). This latter variation is the crux of the problem, and the core issue surrounding this issue in Quantum Physics. We cannot measure these last 2, as any attempts to do so sets up an infinite sequence of "if it is false then it is true, then it is false" recursive loops. If quantum physicists want a solution, then the following properties have to be present:
1. The cat "system" (the cat, the box, and whatever else is part of that which we are trying to observe) is known to be able to be made causally independent from us, the observer, ie it exists outside of our observation of it, influential or otherwise; likewise, we are, excepting our will to know the state of the cat, able to be causally independent from the cat "system".
2. Both our system (the observer) and the cat system, can be shown to be both continuous at the limit O, where O is the observation point, and differentiable at O.
3. There is a neighbourhood subsystem joint set AB of the cat system and observer system, such that the covariance or "interaction matrix" is zero.
If 2. above is able to be satisfied, then the covariance between the 2 systems, the "interaction matrix" will still be a non-zero matrix at O, but can be estimated given that there can be a state, or position of the observer, and a state, or postition of the cat system, such that the interaction between the 2 can be made zero, and yet still have a proxy, or known measurement of the cat system. That is what I tried (perhaps confusingly) to say with requirement 3.
What all this means, intuitively, is that if the functions are both continuous (the fact that in opening the box we know that this kills the cat, implies a discontinuity, given that we operate on the assumption that the cat might be alive, and we need to be continuous, the observer, as we need to be able to reduce our influence by reducing the extent to which we observe, so as to be able to infer, when the covariance matrix, if possible, is zero, that joint system's state, when at O) and differentiable, then we can determine precisely the state of that which we are trying to observe, not by observing it, but by observing that which does not influence it, yet can tell us it's state. However, the mathematical requirements, and consequential real-world needs, are not necessarily going to be easy, perhaps not possible!
Anyways, all in good fun!
Justin
Which is about the experiment (research the "Uncertainty Principle") by which the observer "interferes" with the outcome merely through an attempt to observe something (a useful overarching concept is Godel's undecidabililty theorem). We want to know whether the cat (Schrödinger's Cat) is dead or alive. So we open the box. The cat is dead. However, we do know enough to know that the very act of opening the box will kill the cat if not dead already (nice bit of omniscent break-out here!), yet we cannot know with certainty the state of the cat prior to the need to observe it.
Which leads me to my idea: we can determine that the cat was dead (or alive) not via direct experiment, but by proxy -> We don't worry about observing the cat, nor the box, but firstly observe, or measure, our matrix of influence, our system of change-effects that occur, and are directly measuarable and independent from the cat. The other 2 parts, that we cannot observe, because we cannot observe the cat, the cat system's change, is the cat system's independent variation, and the covariance between us and the cat (the influence variation, or what I call below the "interaction matrix"). This latter variation is the crux of the problem, and the core issue surrounding this issue in Quantum Physics. We cannot measure these last 2, as any attempts to do so sets up an infinite sequence of "if it is false then it is true, then it is false" recursive loops. If quantum physicists want a solution, then the following properties have to be present:
1. The cat "system" (the cat, the box, and whatever else is part of that which we are trying to observe) is known to be able to be made causally independent from us, the observer, ie it exists outside of our observation of it, influential or otherwise; likewise, we are, excepting our will to know the state of the cat, able to be causally independent from the cat "system".
2. Both our system (the observer) and the cat system, can be shown to be both continuous at the limit O, where O is the observation point, and differentiable at O.
3. There is a neighbourhood subsystem joint set AB of the cat system and observer system, such that the covariance or "interaction matrix" is zero.
If 2. above is able to be satisfied, then the covariance between the 2 systems, the "interaction matrix" will still be a non-zero matrix at O, but can be estimated given that there can be a state, or position of the observer, and a state, or postition of the cat system, such that the interaction between the 2 can be made zero, and yet still have a proxy, or known measurement of the cat system. That is what I tried (perhaps confusingly) to say with requirement 3.
What all this means, intuitively, is that if the functions are both continuous (the fact that in opening the box we know that this kills the cat, implies a discontinuity, given that we operate on the assumption that the cat might be alive, and we need to be continuous, the observer, as we need to be able to reduce our influence by reducing the extent to which we observe, so as to be able to infer, when the covariance matrix, if possible, is zero, that joint system's state, when at O) and differentiable, then we can determine precisely the state of that which we are trying to observe, not by observing it, but by observing that which does not influence it, yet can tell us it's state. However, the mathematical requirements, and consequential real-world needs, are not necessarily going to be easy, perhaps not possible!
Anyways, all in good fun!
Justin