How flexible is the principle of causality?

[Mudhammam]

Question: If a specific effect is the consequence of a specific cause, will that same cause or causes always produce the same effect(s)? It seems like the presumption that science is largely conducted on. But if A causes B, can it also cause C or D or E? Or if AB = CD, is it due to necessity? Or can AB also = EF or GH? What degree of flexibility lies in the apparent regularities of causes and effects?

[Alex K]

Question: If a specific effect is the consequence of a specific cause, will that same cause or causes always produce the same effect(s)? It seems like the presumption that science is largely conducted on. But if A causes B, can it also cause C or D or E? Or if AB = CD, is it due to necessity? Or can AB also = EF or GH? What degree of flexibility lies in the apparent regularities of causes and effects?

As I like to do so often, I'll ask a question back: when do you say that B is caused by A, i.e. what is your definition, notion of causation?

But concerning your (and my) question:
Famously, in quantum systems there are many processes without deterministic outcome. Likewise, in classical chaotic systems, tiny perturbations get blown up macroscopically such that asking for e.g. the cause of a storm does not seem to be a well-defined question.

Finally, the notion of an arrow of time we have is largely based on entropy: processes without entropy increase are called "reversible" for a reason: if you watch them played back backwards, you will not be able to tell. Your notion what is earlier and what is later therefore relies on statistics, the second law etc, and the second law is not strictly true, but only on average. If you wait long enough for a given number of particles in a system, you will see a violation.

http://en.wikipedia.org/wiki/Poincar%C3%...ce_theorem

The time you have to wait however goes exponentially with the number of particles, and so for any macroscopic system never comes for all practical purposes. Still, I think it's an important point to remember.

[Mudhammam]

Question: If a specific effect is the consequence of a specific cause, will that same cause or causes always produce the same effect(s)? It seems like the presumption that science is largely conducted on. But if A causes B, can it also cause C or D or E? Or if AB = CD, is it due to necessity? Or can AB also = EF or GH? What degree of flexibility lies in the apparent regularities of causes and effects?

As I like to do so often, I'll ask a question back: when do you say that B is caused by A, i.e. what is your definition, notion of causation?

But concerning your (and my) question:
Famously, in quantum systems there are many processes without deterministic outcome. Likewise, in classical chaotic systems, tiny perturbations get blown up macroscopically such that asking for e.g. the cause of a storm does not seem to be a well-defined question.

Finally, the notion of an arrow of time we have is largely based on entropy: processes without entropy increase are called "reversible" for a reason: if you watch them played back backwards, you will not be able to tell. Your notion what is earlier and what is later therefore relies on statistics, the second law etc, and the second law is not strictly true, but only on average. If you wait long enough for a given number of particles in a system, you will see a violation.

http://en.wikipedia.org/wiki/Poincar%C3%...ce_theorem

The time you have to wait however goes exponentially with the number of particles, and so for any macroscopic system never comes for all practical purposes. Still, I think it's an important point to remember.

Generally, I think of causality in these terms: the present variables are the summation of all past variables. If any of those past variables were to be slightly altered, the present summation would also be slightly altered. So everything is interconnected by the specific causal mechanisms of Newtonian physics that precede, at least on the macroscopic level. I don't even want to begin to speculate at what level quantum indeterminacy ceases to be relevant.

Anyway, would that be a correct overview? In other words, all chemical reactions are limited to a set reproducible outcomes if the specific conditions in which the atoms "exchange greetings" are met? Or is this where indeterminacy comes into play?

[Alex K]

Generally, I think of causality in these terms: the present variables are the summation of all past variables. If any of those past variables were to be slightly altered, the present summation would also be slightly altered. So everything is interconnected by the specific causal mechanisms of Newtonian physics that precede, at least on the macroscopic level. I don't even want to begin to speculate at what level quantum indeterminacy ceases to be relevant.

Anyway, would that be a correct overview? In other words, all chemical reactions are limited to a set reproducible outcomes if the specific conditions in which the atoms "exchange greetings" are met? Or is this where indeterminacy comes into play?

Hmm, hard to tell. In some instances, you will get near deterministic outcomes, in others, they remain a chance event, it depends on the situation, on the system you study. Whether and when a chemical reaction between two particular atoms or molecules happens is probably probabilistic akin to a tunneling process. Which ones can occur, and how likely each is, seems to be fixed.

The problem I have about neglecting tiny quantum uncertainties is that in combination with chaos, the quantum effects get blown up to macroscopic proportions rather quickly, this killing off determinism at macroscopic scales in such systems.

[MindForgedManacle]

@Alex I thought quantum mechanics was deterministic? After all, like other areas of physics it's rooted in differential equations over time. I thought that the apparent indeterminism was due to the fact that in order to measure the system, we have to interact with and force it to a particular result by doing so, hence the uncertainty?

[Alex K]

@Alex I thought quantum mechanics was deterministic? After all, like other areas of physics it's rooted in differential equations over time. I thought that the apparent indeterminism was due to the fact that in order to measure the system, we have to interact with and force it to a particular result by doing so, hence the uncertainty?

Hey,
You're certainly correct that the time evolution of a system isolated from the observer is simply described by the Schrödinger equation, and thus completely deterministic. I think where you may have a misunderstanding is in your assumption that in the measurement process, the result is uniquely determined by the quantum state of the observer and the system. It is not.

There is a "deterministic" formulation of QM, but it doesn't really give you what you would like to have in terms of determinism: Bohmian mechanics. You start with a statistical ensemble of point masses riding on the wave function, and the randomness comes from the fact that you don't know the initial distribution of these guys. It is then in principle deterministic, but the outcome is not determined by the quantum state, but by auxiliary knowledge about this funny ensemble of point masses. It would still be non-deterministic for all practical purposes since there is no known way to measure this distribution, and it may be impossible in principle. I find this formulation very artificial and it is not nicely suited to exted to field theory, and I only mention it for completeness because it is a "deterministic" formulation of QM.

In the relative state interpretation ("many worlds"), you get a split into a superposition of two system final states entangled with two observer final states. It is deterministic in the global sense that the Schrödinger equation governs everything all the time without exception, including the observer, and all possibilities are always realized in parallel. In the Copenhagen interpretation you make a probability statement at that point and discard the part of the superposition which is apparently not realized for the observer ("wave function collapse"), and in this truly random choice it is where you lose the determinism.

Even if you don't "believe" in the relative state picture as what is really going on in the world, it is useful in order to gain an intuition about what measurements do: they produce correlations (entanglement) between you and the measured system, and depending on what quantity you attempt measure, this entanglement is such that the combined observer-system state ends up as a superposition of individual states in which this quantity you have measured is without uncertainty, but then both superimposed. This interaction of observer and system which produces this entanglement is what you probably mean by forcing the system into a certain state. However, it is not the detailed process of this interaction which tells you in which state you end up, you always end up in both, and which one you actually measure is truly random. How to properly define the probability of outcomes here is one of the main theoretical problems of "many worlds" quantum mechanics. Copenhagen doesn't exactly do better in this respect, it simply supplies a prescription to calculate the probabilities.

[Mudhammam]

Generally, I think of causality in these terms: the present variables are the summation of all past variables. If any of those past variables were to be slightly altered, the present summation would also be slightly altered. So everything is interconnected by the specific causal mechanisms of Newtonian physics that precede, at least on the macroscopic level. I don't even want to begin to speculate at what level quantum indeterminacy ceases to be relevant.

Anyway, would that be a correct overview? In other words, all chemical reactions are limited to a set reproducible outcomes if the specific conditions in which the atoms "exchange greetings" are met? Or is this where indeterminacy comes into play?

Hmm, hard to tell. In some instances, you will get near deterministic outcomes, in others, they remain a chance event, it depends on the situation, on the system you study. Whether and when a chemical reaction between two particular atoms or molecules happens is probably probabilistic akin to a tunneling process. Which ones can occur, and how likely each is, seems to be fixed.

The problem I have about neglecting tiny quantum uncertainties is that in combination with chaos, the quantum effects get blown up to macroscopic proportions rather quickly, this killing off determinism at macroscopic scales in such systems.

So my broader question is then, if we were to "rewind the tape," and pause it at some exact point between now and the Big Bang, at the point we paused it, granting nothing is different from the actual past, would the present roll out precisely the way it has? Where is the space for variant outcomes?

[Alex K]

So my broader question is then, if we were to "rewind the tape," and pause it at some exact point between now and the Big Bang, at the point we paused it, granting nothing is different from the actual past, would the present roll out precisely the way it has? Where is the space for variant outcomes?

An obvious example is the time at which individual nuclear decays happen. This is not something that is even in principle determined in the context of ordinary quantum theory. Two particles scattering off each other will emerge at random directions distributed according to their outgoing wave functions (think double slit experiment)

http://en.wikipedia.org/wiki/Scattering_theory

this will almost immediately lead to completely different outcome if you rewind the clock and start over with the same quantum state.

[bennyboy]

So my broader question is then, if we were to "rewind the tape," and pause it at some exact point between now and the Big Bang, at the point we paused it, granting nothing is different from the actual past, would the present roll out precisely the way it has? Where is the space for variant outcomes?

An obvious example is the time at which individual nuclear decays happen. This is not something that is even in principle determined in the context of ordinary quantum theory. Two particles scattering off each other will emerge at random directions distributed according to their outgoing wave functions (think double slit experiment)

http://en.wikipedia.org/wiki/Scattering_theory

this will almost immediately lead to completely different outcome if you rewind the clock and start over with the same quantum state.

Will it? Are you sure that randomness isn't really a manifestation of hidden variables? How do you know that unpredictability is true temporal randomness?

[Mudhammam]

An obvious example is the time at which individual nuclear decays happen. This is not something that is even in principle determined in the context of ordinary quantum theory. Two particles scattering off each other will emerge at random directions distributed according to their outgoing wave functions (think double slit experiment)

http://en.wikipedia.org/wiki/Scattering_theory

this will almost immediately lead to completely different outcome if you rewind the clock and start over with the same quantum state.

Will it? Are you sure that randomness isn't really a manifestation of hidden variables? How do you know that unpredictability is true temporal randomness?

What do you think bennyboy?

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A big part of me thinks it must be random...yet this notion, while apparently true in many regards, is so counter-intuitive to my everyday experience in many ways as well.

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I wonder if a portion I am omitting, which may or may not be true, is that the randomness largely occurs outside of developing systems...but once systems emerge from the chaos (Universes, solar systems, ecosystems, biological systems, etc.), then other (Newtonian) laws ensure that a much more orderly fashion follows. Not sure if that is the case, though it still wouldn't really seem to undercut the demand for a system that exists at bottom to produce anything like other sub-systems at all...