[Acausality in Discrete Reality?] - A New Kind of Science: The NKS ForumA New Kind of Science: The NKS Forum
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Acausality in Discrete Reality?
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Posted by: John Newman
Hi, I'm John Newman (not to be confused with John von Neumann :D). Thank you Stephen Wolfram and everyone else involved in the research for making all this somewhat understandable for the layman. Ever since I read NKS my mind has been brooding with philosophical questions. I've been waiting for this forum to open up and I'm happy I bumped into on google.
Now on to my question. I'm a layman by all respects, so it could be because of my ignorance, but I've never been able to reconcile the acausality endorsed by QM with any conceivable logic I can think of. I've intuitively thought that acausality is just a temporary fix for a temporary problem, conceiving the world statistically because that is the only way we can perceive it. After reading NKS, I feel even more strongly about this. However, as I said, I could be missing something. Does the NKS paradigm lean one way or the other on the issue of acausality?
And I understand "acuasality" to mean an effect without any cause. Thank you.
John
Posted by: Georges terryn
As Immanuel Kant stated long ago: causality is an a priori of thought. These are the prerequisites to be able to think : Time (memory), Depth, Height, Width, Cause and Effect, they are properties of the mind not of the perceived.
As such all effects have no cause, any cause has no effect. Just the fact that the one precedes the other makes us think there exists a causal link.
The apple falls near the tree. What is the cause ? Gravity. Gravity is not a cause, it is an explanation. It is a condition. In order for the apple to be attracted by the earth, "gravity" must exist. As there must be an apple, a tree, and earth. They are conditions necessary for the apple to be able to fall near the tree. (Some would include a witness as a condition, for otherwise we would never know if the apple has fallen and if it was near the tree on earth. ) Gravity is a construct, chaining the events.
But if we have a series of conditions - in stead of causal links- to make some events a possibility, we have a deterministic trajectory with a probability.
But modern man does not believe in deterministic trajectories - he is a an avid defender of "everything free". So our psyche hides this fact from us and changes a deterministic probability trajectory into a (simplistic) causal chain. We name the first event "cause" and the second "effect". BASTA.
We see an event and conclude it must have been preceded by a cause, which in turn is an effect of a previous cause. And so we can go back into history counting the links. At the same time we reverse the chain of events, creating newer and newer causes further in the past and effects pointing to an unknown future.
While in reality it is a chain of conditions on a deterministic probability trajectory that started in the past. The events/chain of conditions are a property of a particular CA.
No sense, no direction, no cause, no effect, just CA creating them on its way through time. (Time as changes over a nodal network)
Perhaps. For it can not be measured in a laboratory, recreated under the same circumstances and it can never be considered a science. It may be true, but speculative at best. A philosophy, for once closer to reality than all sciences lumped together.
Again as KANT said: we cannot know the "DING AN SICH".
Posted by: Jason Cawley
The question whether one can get QM results from underlying states that just aren't known before an observation is made is called the "hidden variables" issue in QM. A hidden variables model of QM is one in which one has determinism from prior states, perhaps of observables perhaps of unobservables. But there are theoretical results that show one cannot combine hidden variable determinism, the same predictions as QM, and an additional condition called "locality". (Which is in a way the opposite of "action at a distance"). These results are called Bell's inequalities.
They show that if you keep our common sense notions of space and time, and of prior states at each space-time location, limit all signals transmission to the speed of light as called for by relativity, and want the same predicted outputs as standard QM - then one must include probabilistic terms. Essentially, the outcome of an experiment at x1 and t1 can depend on a physically separated experiment at x2 and t2, without it being possible for any signal to have passed from one to the other. We say the two observations are "entangled".
They both depend on an event in a common past. For example, two electrons are emitted from x0 and t0, which must have opposite spins. At some time later at x1 the first is measured for spin up or spin down in the z direction. Over at x2 where the other one went, it will be up if the other is down and vice versa. Each of these observations depends on the angle you measure along (z direction or y direction e.g.) in a probabilistic way as you rotate the plane of measurement. But they remain (anti) correlated. The measurement at the second location can depend on a hidden state variable, only if that state variable cannot be "confined" into a tight ball around x2.
This can be handled easily by just allowing a real underlying chanciness to the spins. If instead you want to get rid of that underlying chanciness, you have to let something else go - like locality, at least measured in our usual space-time sense. That is, the event at x1 and the event at x2 might be in some sense "close" in a casual graph. But they aren't "close" in space-time.
The NKS book suggests that some discrete deterministic system is giving rise to the observations we see. By Bell's inequalities, if that is the case then the sense of space and time locality in that underlying deterministic system must differ from our ordinary sense of space and time locality. It must be possible for events we perceive as physically separated, to be connected, or the hidden variables on which the observation at x1 t1 depends cannot all be "kept" tightly around x1 t1. There must be allowed "long range" connections.
Philosophically then, determinism is not "disproven" by QM experiments. An underlying probabilistic reality can account for those experiments, and can combine the observations with a continuous mathematical model and locality. We say there are real "probability waves" (which can interfer with one another) in that case, or that the state at any given place and time is a "probability amplitude" rather than one definite thing. This can be thought of as the default or standard picture presented by QM.
But it involves several "premises" rather than just one, non-determinism. We can consider denying the other premises instead of the deteminism premise, in effect. The phenomena might be "saved" (i.e. matched or accounted for) by alternative models that are non-continuous, non-local, and deterministic. Or we might deny the other premises and determinism as well (some discrete non-local model, but with probabilitistic behavior). We can't keep all the premises of previous, classical physical theory, or we will fail to match what experiment reports.
See the section of the NKS book on "Quantum phenomena", starting on page 537 and running to the end of the chapter on page 545. In the notes, from 1056 to 1065. Bell's inequalities are discussed in particular in the last note in the chapter, starting on page 1064. I hope this helps.
http://www.wolframscience.com/nksonline/page-537
http://www.wolframscience.com/nksonline/page-1056
http://www.wolframscience.com/nksonline/page-1064
Posted by: Ray Girvan
As Immanuel Kant stated long ago ...
Well, Kant is only one view. It may be very clean philosophically to dispense with causality, but it leaves you with a model with no predictive value and no means to investigate the phenomena of which the universe we exist in (or perceive ourselves to exist in - but since it's the only one we have to work with, we might as well make do). Besides, a CA model would itself involve a causality: the state at time t and the underlying rules 'cause' the state at time t+1. It would however, be a different level of causality; our surface view might be akin to saying gliders in a CA 'collide' and 'bounce off' each other, when that's really only an appearance.
I agree, however, that human perception of causality is to be mistrusted. We're strongly wired to say "after this, therefore because of this", because it mostly works and leads to sensible practical conclusions. The downside is a by-product of all kinds of superstition when there is no causal connection.
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