Quantum Mechanics and Mind

[abashed]

@Half_Man_Half_Wit

It’s the other way around: experiments realize situations that occur in nature all the time within controlled circumstances, so that we can learn about what happens in nature. This learning is all that we do; what happens would have happened in just the same way if no early hominid (or wherever you want to draw the line) had ever had that first spark of consciousness.

Or at least, all that we know about the world, and quantum mechanics, is completely consistent with that picture. It’s true that other interpretations are possible; but they all suffer from extravagance. Furthermore, quantum theory has nothing to do with this: all that you’re saying can be said about classical mechanics just as well (and has, in fact, been said).

I know that it’s comforting to put consciousness, and by extension, humanity, back into the center of the universe, from where the Copernican and Darwinian revolutions have so thoroughly removed us, but nature is under no obligation to comfort us.
What you don’t understand is that nobody needs to do the calculations in order for the world to behave the way it does. Yes, there is no description of the world without somebody describing it; but the world does not depend on being described. Interference patterns vanished long before anybody came up with the math describing how they do so; they’ll continue to, long after the sun has burned this world to cinder.

As John Bell mockingly put it:

To the contrary, that’s exactly what follows from the math I presented above. If the detector is present, but does not make a detection, it simply falls out of the equation, and we’re left with what we had before.

In such a case, the evolution equations of a system going through either ‘slit’ are

          |D>|1> ---> |D>|1> (= |D,1>),
          |D>|2> ---> |D>|2> (= |D,2>).

This just means that the detector doesn’t change its state—it remains in the same state before and after having interacted with the particle (or, as the case may be, having not interacted with the particle). In other words, no ‘which-path information’ has been gathered.

And it’s important that you realize here that that’s all that which-path information (as scientists use the term) is: if a state-change has been induced in the detector (say, a light has come on, indicating ‘slit 1’, or ‘slit 2’), then which-path information has been collected; if nothing happens, we have no such ‘information’.

This means in particular that the general state of our particle-detector system afterwards is factorizable—i.e. you can write it as a product of two states of the two subsystems. This is the formal definition of not being entangled, i.e. separable.

So, whereas in the case where we did collect which-path information, we had the entangled state

          |D,s> = a|D[sub]1[/sub],1> + b|D[sub]2[/sub],2>,

after the particle has passed the slit, we now have the separable state

         |D',s'> = a|D,1> + b|D,2>
                 = |D>(a|1> + b|2>).

This makes all the difference: since there is no correlation between the detector and the particle, the quantum coherence does not get ‘smeared out’ over the whole system, and consequently, the particle system itself stays coherent; hence, we will recover an interference pattern.

We now have:

            P(o) = P(o,D)
                 = |(a[sup]*[/sup]<D,1| + b[sup]*[/sup]<D,2|)*|o,D>|[sup]2[/sup]
                 = |a[sup]*[/sup]<D,1|o,D> + b[sup]*[/sup]<D,2|o,D>|[sup]2[/sup]
                 = |a[sup]*[/sup]<1|o> + b[sup]*[/sup]<2|o>|[sup]2[/sup]
                 = |a[sup]*[/sup]<1|(c|1> + d|2>) + b[sup]*[/sup]<2|(c|1> + d|2>)|[sup]2[/sup]
                 = |a[sup]*[/sup]c<1|1> + a[sup]*[/sup]d<1|2> + b[sup]*[/sup]c<2|1> + b[sup]*[/sup]d<2|2>|[sup]2[/sup]
                 = |a[sup]*[/sup]c + b[sup]*[/sup]d|[sup]2[/sup]
                 = (a[sup]*[/sup]c + b[sup]*[/sup]d)(ac[sup]*[/sup] + bd[sup]*[/sup])
                 = |a[sup]*[/sup]c|[sup]2[/sup] + |b[sup]*[/sup]d|[sup]2[/sup] + a[sup]*[/sup]cbd[sup]*[/sup] + b[sup]*[/sup]dac[sup]*[/sup]

Here, in the third line, I used that <D|D> = 1, in the fourth line, I’ve introduced the general form of |o>, the fifth line is just a rearrangement, in the sixth line, I’ve used that <1|1> = <2|2> = 1 and <1|2> = <2|1> = 0, and then I just repeated the steps from our original calculation to once again arrive at a result showing prominent interference terms.

So, you see: it’s not whether anybody reads the information, or interprets it, or holds it somehow in conscious experience; rather, the vanishing of interference solely depends on whether the detector makes a detection, indicated by changing its state, or not, standing just idly by.

To be honest, I have no clue about the calculations you give here, but that does not change anything.

You say nature is ‘there’, regardless of whether we look at it or not, but what you keep overlooking is the fact that the models human beings create can never exist without human beings! Regardless of what is* really * there (although this doesn’t make much sense), all one can do is invent representations of nature which are really very subjective and never existed before we evolved. Language and mathematics never existed before they were invented so how can something that never existed exist and not exist at the same time, which is effectively what you are saying when you assert nature is always there even if we aren’t? Now, something *did * exist before we did, undoubtedly, but whatever that was only existed as a probability which combined with our consciousness to appear to us as what we call ‘reality’. Your mathematical calculations are mere models that your mind has constructed in order to ‘prove’ something or other but what does it all really prove? It proves mathematics is creative imagination that tries to ‘mimic’ reality and does this successfully up to a point but sooner or later fails to give accurate predictions.