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Posts tagged with quantum mechanics

  • M. You live in a society where lovers choose whom to marry based on romance. So you don’t want to give up your right to choose a partner (or no partner at all). But if you actually lived under rules of arranged marriage, you would not want to be forever-bitter about something you can’t change. So you would accept your fate, go with the flow, and learn to love whom you had to.
  • She didn’t want to be pregnant. She couldn’t afford it. She was too young. There was so much else she wanted to do with her life. But once the baby was born, s/he became the joy of her life—and the mother wouldn’t change a thing about her past choices. (P.)
  • You need a vacation. You’ve focussed on work for too long. You plan a grand adventure. You negotiate a year off with your employer. On the plane ride to the coast, somebody asks, “What do you do?” and, without thinking, you give your normal response: “I’m a lawyer.” Unsettled, you arrive at the mooring where you’re scheduled to pick up the rented boat. A week into your trip down the coast, you find that you’ve succeeded in running away from nothing. You’re still alone with your thoughts, and they still have exactly the same consistency. It’s going to be a long voyage, achieving nothing, cleansing nothing, a propos of nothing. At least you’ve got work to look forward to when you return. [[[V.]]]

There is an algebra that describes this. Something like a von Neumann algebra (the logic of quantum measurements).

In the vNA, “measuring” X changes the information that X reports. You measure the Z-spin of an atom, you get the Z-spin information but you’ve affected the atom in measuring.

Similarly, instantiating myself in a different context (a society with different social norms, being somewhere else other than where I am) would change the answers to questions M, V, P (marry, vacation, pregnant).

Self-as-function, with input parameters.

My answer to M(me, where-I-in-fact-grew-up) is that, no, I don’t want arranged marriage. My answer to M′( me, where-I-in-fact-grew-up) is that, no, I wouldn’t want arranged marriage. But different-my′ answer to M′(me′, where-I-might-have-grown-up′)M(me, where-i-in-fact-grew-up). Real-me doesn’t think like different-me, and doesn’t correctly predict different-me′’s feelings. 




Tim Maudlin reformulates topology using open lines as the basis rather than open sets.

He thinks this sheds some light on the “arrow of time” question (why does time only move forward, when physical equations can be used to postdict [forensically a bullet, for instance] motion just as easily as to predict [planning a rocket, for instance] motion?).

Notes:

  • If you don’t like some mathematics, just go make your own.
  • It’s nice to pay homage to the accepted standards, if’n you’re trying to impress people.
  • Yet another use of directed arrows (see noncommutativity and quasimetrics).
  • A “topological line” is just a total (linear) order. If you want to join two topological-lines and get another line, you have to make sure you don’t form a circle (two endpoints equate) or a loop-dee-loop. But segments can overlap if they share the same linear order.
  • A nifty slide on standard topology (as well as Maudlin’s new idea):
  • His “open lines” basis leads to an interesting conception of neighbourhood on a discrete lattice (shown on a square lattice):
     

(Source: supervenes)




Is there really such a thing as a point? Well, not really….

  • Ask any of our undergraduates, why the real numbers? Can you say there’s something √π centimetres away from here?
    —Well, not really, it’s an approximation….
    —An approximation to what?
  • “We’re not really doing science. We don’t have any data, so we’re just indulging our own mathematical and philosophical prejudices. :)”
  • “If a pile of papers appeared on your desk and claimed to be the correct theory of quantum gravity, how would you know?”
  • “All of the standard formulations of quantum theory, whether it’s whatever you want — all of them more or less presuppose the use of standard real numbers. That’s one issue I find very problematic. … That seems to me very dubious.” 
  • Heidegger asked, What is a thing? And answered, on page ~60, A thing is the bearer of properties.
  • From Heidegger’s perspective, there is no ”way that things are”. (due to the Kochen-Specker theorem)

Slides here.




The central message that Bohr and von Neumann taught us about the Standard Quantum Logic is that it can be viewed as a manifold of interlocking perspectives that cannot be embedded into a single perspective. Hence, the perspectives cannot be viewed as perspectives on one real world.

So, even considering one world as a methodological principle breaks down in the quantum micro-domain.




The act of writing is like the collapse of a quantum waveform. So many things are in your mind, interacting with each other, unsaid. Many truths — some at odds with others — could be spun into a thread. But whatever you write crystallizes as the story. The other ephemera die.

Since speech is serial, it’s hard to portray the composite quality of real-time motivations, perceptions, emotions, impulses, sentiments, choices, …. I’ve heard that Chinese poetry can multi-track — and perhaps many great writers can — but not me. 

Quantum Quacks

Even Roger Penrose was roundly mocked for suggesting that quantum interactions in the brain relate to free will. Going the other direction, What the bleep do we know? draws several intellectually limp conclusions from quantum mechanics, e.g. that QM implies the possibility of telekinesis. (I would say that the authors must have leapt to conclusions from blurbs & pamphlets, except that Niels Bohr and Wolfgang Pauli also took spiritualistic and parapsychological views on QM.)

So it would seem that connections between QM and psychology are limited to quackery.

Metaphor

However, QM is just an abstract mathematical theory. You don’t have to plug physical parameters into the formalism. In that sense you can abscond the superposition-and-collapse metaphor out of the subatomic realm where it was invented and apply it to other things — like thought.

In other words, you don’t have to talk about quantum superposition. You can talk about emotional superposition, opinion superposition, mood superposition, colour superposition (like, are these images green? red? blue? 1 2 3 4 5), personality superposition, guilt superposition, … and more.

If I say: “I had a superposition of thoughts during the bear attack which collapsed into a 1-D sequence when I told the story,” that is valid.

It’s neither what-the-bleep nor relying on quantum effects on my brain. I just appropriated the mathematical metaphor of superposition and the mathematical metaphor of collapse, to express how I can’t really tell you the whole story of the bear attack, and how the telling perverts the story itself.




Today we’re going to ask—-and hopefully answer—-this question of whether there’s free will or not. If you want to know where I stand, I’ll tell you: I believe in free will. Why? Well, the neurons in my brain just fire in such a way that my mouth opens and I say I have free will. What choice do I have?
Scott Aaronson

(Source: scottaaronson.com)




The universe is a song, singing itself.

hi-res