Logical implication vs physical causality

[entropy1]

There is something I don't understand that I want to ask quantum physics experts here:

Suppose the happening of event X results logically speaking in the happening of event A. So we could for instance have the following logical implication

$X.happens \rightarrow A.happens$.

If this is logically true, does that mean there is also a physical necessity for A to happen if X happens, and is there a physical causal relationship between the happening of X and the happening of A?

I ask this because I found you could find logical inferences about physical events without having to refer to causality immediately.

Thanks!

 

[Fra]

Such causal physical relationship is the meaning of the timeless physical law. Initial conditions implies the future state, as per the immutable deterministic laws of physics. So there is no novelty.

The problem is however, how can be infer the premises, and the timeless law? These questions show the practical and conceptual weakness of the determinism. How you do infer a timeless "logical necessity" from empirical science? I would claim you can't. This is the problem. We can effectively do it for special cases, with small systems we can easily repeat enough times to make it without doubt that the implication from initial to final state holds. But on cosmological and evolutionart scales "always" is a strong word,

/Fredrik

 

[entropy1]

How you do infer a timeless "logical necessity" from empirical science? I would claim you can't. This is the problem. We can effectively do it for special cases, with small systems we can easily repeat enough times to make it without doubt that the implication from initial to final state holds.

$X.happens \rightarrow A.happens$

Yes, if this implication is true, you would probably only corroborate it by confirming it with measurement and statistics, directly and indirectly. However, it is possible to motivate logical statements by reasoning.

But I am no scientist. So I ask the experts here.

 

[entropy1]

I think I found the answer. If A is true if X is true, they don't have to have a causal relationship between them, because there for instance could be a third event C that has a causal relationship with A and X.

I think I have to rephrase my question. Suppose that the logical statement "X.happens implies A.happens", holds. Does "NOT(A.happens) then imply NOT(X.happens)"? Could it be just a statistical relation. Does causality have to be involved somewhere?

Thanks.

 

[Morbert]

I think I found the answer. If A is true if X is true, they don't have to have a causal relationship between them, because there for instance could be a third event C that has a causal relationship with A and X.

I think I have to rephrase my question. Suppose that the logical statement "X.happens implies A.happens", holds. Does "NOT(A.happens) then imply NOT(X.happens)"? Could it be just a statistical relation. Does causality have to be involved somewhere?

Thanks.

$\lnot A \rightarrow \lnot X$ is the contrapositive of $X \rightarrow A$ and so would also be true.

 

[Morbert]

Are you asking if $X\rightarrow A$ implies $\lnot X \rightarrow \lnot A$? No, but $X\leftrightarrow A$ would. Quantum mechanically, we would say that $X\rightarrow A$ if $$\frac{\mathrm{Tr}\left[\Pi_A\Pi_X\rho\Pi_X\Pi_A\right]]}{\mathrm{Tr}\left[\rho\Pi_X\right]}\approx 1$$ whereas $X\leftrightarrow A$ is only satisfied if $$\frac{\mathrm{Tr}\left[\Pi_A\Pi_X\rho\Pi_X\Pi_A\right]]}{\mathrm{Tr}\left[\rho\Pi_X\right]}\approx\frac{\mathrm{Tr}\left[\Pi_A\Pi_X\rho\Pi_X\Pi_A\right]]}{\mathrm{Tr}\left[\rho\Pi_A\right]}\approx 1$$

 

[PeterDonis]

Suppose the happening of event X results logically speaking in the happening of event A. So we could for instance have the following logical implication

$X.happens \rightarrow A.happens$.

Where would such a logical implication come from?

 

[entropy1]

Where would such a logical implication come from?

I could tell you that in nine lines, but you could deem it personal theorizing.

 

[PeterDonis]

I could tell you that in nine lines, but you could deem it personal theorizing.

In other words, you're admitting that this thread is based on your personal theory? That makes it off limits for PF discussion.

Thread closed.