I have always been intensely loyal to Pluto.
I remain fairly obsessed. Alas, our love is destined to go unrequited. The problem is that if Pluto were reclassified as a planet it would mean adding not one more but hundreds of objects. Better to be King of the Kuiper Belt.
Where does stochasticity arise in relativity?
Ok I’m not a physicist. (If that wasn’t already obvious.) So I can’t give you a real answer, i.e., math. My actual interest is pretty much restricted to cosmology in this instance. Stochasticity appears to be an emergent property of Relativistic models of universe formation. It turns out that randomness is, as the cliché has it, not a bug but a feature. As writer Robert Anton Wilson so piquantly put it, the universe contains a Yes, a No, and a Maybe.
But the “Maybe” is just as determined as the “Yes” or “No”. This highlights the inadequacy of the “machine” metaphor for the universe. A machine is an instrument designed for a purpose whose parts combine to fulfill this purpose. Spontaneous, purposeless self-regulating organization is counterintuitive. We need a new metaphor but science seems to have passed beyond the point where it can be expressed in other than mathematical terms. Perhaps there exists somewhere an artist with the imagination to do so. All our current metaphors look backwards. They have become idols, objects of worship lesser than those who worship. Restricting our thought. A living metaphor allows our vision to pass through and beyond to grasp that which is beyond thought. What an awful fate! Blinded by our lack of imagination.
Stochasticity appears to be an emergent property of Relativistic models of universe formation.
Without details, I don’t know what to make of this. The equations of relativity–unlike QM–all have fixed answers.
Probability distributions is the stuff of QM: the math might give you a probability, but the actual measurement isn’t determined by the math; you have to actually measure to get a single definite value.
Fair enough Robert. I’ve tried to think this through as best I can but I’m still hampered by my own limitations so I have to take recourse in analogies as imperfect as they may be. Fools rush in, as they say. So I’ll have a go.
Let me start with this. Even in a fundamentally deterministic cosmos, in our understanding, measurements, and predictions we perceive a level of uncertainty and randomness. Even in a cosmos based on a level of fundamental uncertainness and randomness, order and pattern can be identified and described. It’s not a binary or a switch – on/off. Determinism and uncertainty are woven into the very warp and weft of the universe. This all becomes readily apparent on the quantum level. On the macro level, where we spend our time, it is less obvious but it does have a consequence. So an analogy.
The Weather. The weatherman can tell us that in the summer it will be hot but he can’t tell us what the actual weather will be five days from now. There are so many variables involved that he can only make a probabilistic determination as to what to expect. An 80% chance of rain. Yet at no point in the process is there a discontinuity between the current state of affairs and the prior state.
Take the example of a hurricane. When the initial conditions are right, a hurricane spontaneously forms, goes through its life-cycle, and then passes out of existence. But the forecaster only has a probabilistic computer model available to predict the time or the place of its formation or its course. There is a level of uncertainty and randomness in the process we call a hurricane that makes a precise prediction impossible. But at no point in the process of a hurricane is the current state of affairs not dependent on the prior state of affairs.
(Actually I’ve often thought the example of hurricane formation is a good analogy for the formation of our universe. When the initial conditions for universe formation are “right’, a universe spontaneously forms, goes through its life-cycle and then passes away. The fact that we have a pretty good awareness of how hurricanes form and we don’t have a very good idea of how universes form is neither here nor there.)
Does this make any sense?
ps: There are certainly some who want to distinguish between determinism and probability. Fine. These folks tend to regard determinism as strictly “hard” in the way I described earlier. Newtonian clockwork. Ok. But that doesn’t seem to me to be the cosmos we inhabit. And to state the obvious, sometimes all we can do, none of this seems to leave room for a coherent concept of free-will.
Stephen, it seems to me you are describing chaotic systems. A system is chaotic if it demonstrates an extreme sensitivity to its initial state, such that even a minuscule change in the starting state will yield a completely different outcome. So it isn’t random–a chaotic system is totally mechanistic and deterministic–, but it *looks* random because our measurement of the initial state is nowhere near accurate enough to let us make a prediction of the end state.
The double pendulum is a classic example of this. We know the math that describes perfectly how a double-pendulum will swing. The problem is even a minuscule difference is the starting position of the pendulum quickly evolves into a completely different motion. ** you do not have permission to see this link ** All 1000 double pendula start in what appears to be the same position. Initially, for about 15 seconds, they seem to be perfectly in sync–you can’t even tell from the video that there is more than one pendulum. From 15 to about 30 seconds, they begin to diverge, but in a way that is still pretty coherent, they are all basically doing the same thing and following the same pattern of motion; even if they aren’t in exactly the same position, they are close. But after 30 seconds, they begin to significantly diverge and follow totally different paths. By 50 seconds, you have pure chaos. There is no pattern.
I had a lot of nervousness about returning to this discussion because I expected to have my illustration ripped to shreds. But you’ve both made some interesting and useful points. Hopefully everyone understands I am more of a student in these matters than a teacher. So…
I am not speaking of free-will here, but only whether a hard, mechanistic determinism has some affinity to astrology. Are the positions of the stars and planets at the time of one’s birth perhaps distantly but nonetheless inextricably related to all other matter in a completely deterministic universe?
Well classical astrology is rigidly impersonally deterministic. Clockwork. The ancients had no trouble with this because they had no concept of the strictly personal. Its modern “new age” purveyors treat it like a personal self-help mechanism. Ok if I understand your question, in our current scientific understanding, for two particles to have an effect on each other they first must come into contact. This applies on either a micro or macro level. The position of Jupiter in the sky at the moment of your birth has no discernable impact on your personality. However there is at least a modicum of measurable gravitational effect. To posit some overarching relationship between you and the entire cosmos you must demonstrate some mechanism at work. On a micro level quantum entanglement is super weird but the particles have to have once been in contact. Did this come anywhere near to answering your question?
…it seems to me you are describing chaotic systems. A system is chaotic if it demonstrates an extreme sensitivity to its initial state, such that even a minuscule change in the starting state will yield a completely different outcome. So it isn’t random–a chaotic system is totally mechanistic and deterministic–, but it *looks* random because our measurement of the initial state is nowhere near accurate enough to let us make a prediction of the end state.
Yes that seems like a useful distinction to make. It would be the difference between not being able to make a prediction because of some existing limitation and it not being possible to make a prediction at all. Cool vid.
Not to change the subject but I’ve often wondered if some future self-programming AI, in complete control of it’s own, what would be the word? it’s own “nature”, could be described in any sense as having free-will? The meta-programmer? That what a God must do right? To really be a God. This is another problem with Craig’s DCT view. If you say that God’s “nature” is love then how is he free? No matter what you do you wind up right back at Euthyphro’s Dilemma and an infinite regress.
…a more fundamental deterministic relationship of all matter, energy, and space in the universe, from the very beginning of time. In this case, we are not only talking about momentary gravitational forces, but of an overall determinist and mechanistic model of the entire universe.
This is where my image of ‘building a bridge while crossing it’ applies. Even if such a state of affairs exists, we are incapable of describing it. I’m afraid at this point we enter the purview not of the physicist but of the mystic.
If by “hard determinist” you mean Newtonian Clockwork then, no. I just don’t define randomness and determinism as mutually and inherently exclusive categories. But the problem of definitions is a bottomless pit. Whatever you call it, I don’t believe in free-will. Randomness is the opposite of free-will. Determinism precludes it.
Right, but I wouldn’t call the position that Bohr and Heisenberg were defending “deterministic” (unless I’m talking about free will). Their whole thing is that the merely probabilistic–not deterministic– models that QM gives are complete. The world really is probabilistic, not deterministic. Some values really aren’t fixed.
Einstein certainly was defending determinism at the quantum level. He thought the probabilistic descriptions that QM gives were probabilistic only because of epistemic uncertainty, not real uncertainty. That is why Einstein insisted that QM must be incomplete and there must be hidden variables.
Einstein (along with Podolsky and Rosen) were, by the way, the first to draw attention to the fact that the math of QM predicts entanglement and what Einstein later called “spooky action at a distance.” Because that prediction violated the extremely intuitive principle of local realism, they thought it was proof that QM was incomplete and there must be further local hidden variables that QM didn’t include.
BTW, Schrodinger was similarly skeptical; he is the one who actually coined the term “entanglement” and his famous cat thought experiment was meant to illustrate how ridiculous it is to take QM models as a complete description of quantum reality.
But once we got around to experimentally testing Bell’s inequalities, it turned out that Bohr was right. There are no local hidden variables.
I wonder if there are there any legitimate scientists still pursuing this kind of hard determinism?
Yes, there are. This motivates ** you do not have permission to see this link ** (The whole article is really quite good, by the way.)
Here is a ** you do not have permission to see this link ** that goes over a lot of these ideas and makes many-worlds seem surprisingly not-crazy.
BDEhrman
FreedomBen
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Robert
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