[ExI] QT and SR

[The Avantguardian]

--- On Tue, 9/16/08, Mike Dougherty <msd001 at gmail.com> wrote:
> On Mon, Sep 15, 2008 at 10:15 PM, The Avantguardian
> <avantguardian2020 at yahoo.com> wrote:
> >
> > Now imagine that that binary string of ones is written
> in the tiniest font imaginable -- merely one Planck length
> wide. Written on space-time, the big binary integer would
> stretch the distance between Earth and the Sun. So now when
> I add a 1 to it, an additional 1 bit gets added to the end
> of the string near the sun and the rest of the bits from the
> earth to the sun become zeroes. . . instaneously! Even
> though if Superman used his supervision to watch that
> distant bit change, he would have to wait 8 long minutes for
> the information to arrive.
> 
> This reminds me of the topological deformation question I
> think I
> asked in this thread.  What you are describing sounds like
> a state
> change without a propagation from one state to another. 

Yes, I was decribing a state change without propagation. What I was alluding to was that there was no reason that a given quantum system could not itself change state in no time, provided that any information, regarding the state change does not propagate faster than light. As my example shows, a large integer could be considered non-local.

In other words, even though the binary string changed from all ones to almost all zeros in abstract non-time, Superman, were he watching, would see the zeroes start at Earth and propagate toward the Sun at the speed of light. However if he was hovering in outer space halfway between the Earth and the Sun, looking down perpendicularly on the bit string, he would see it start to change to zeroes in the middle and spread outward toward the ends.

I guess the best way to describe what I what I was trying to show by my example is that there really isn't a reason why an abstract waveequation could not could not switch between states instaneously, even if the information took a while to catch up. Just like if Superman *knew* that I was simply adding one to my large integer, he could have done math and known exactly what would happen, without having to *wait* for the information to actually get to him. Keep in mind this is a very loose analogy for collapse/decoherence because a wavefunction is more complex than an integer. 

In this regard, the wavefunction is the mathematical decription of our *a priori ignorance* about the state of a quantum system much like a prior distribution is in Bayesian inference. I consider it axiomatic that ignorance is necessarily subjective and a recurrent theme in QM seems to be that the universe enforces a minimal degree of ignorance in all observers, even if the system under consideration has to act highly counter-intuitively to do so.

I believe this may be a side-effect of our conscious perception of time in the sense that if we were certain about the future it would cease to be the future as distinguishable from the past. But then again, the deep past is just as unknowable as the future.

> I
> was
> thinking about photon being related to electron shells in
> discrete
> units - it either exists in one state or another, but there
> is no 'in
> between' - or is that a probability of indeterminate
> states?

That is an excellent question, Mike. Quantum mechanics traditionally ascribes these photons to be in a superposition of both states until you attempt to observe them, whereupon they snap to one state or another. It is not so much the probability of the indeterminate state as a vector addition of *all* the possible states which can be used to find the probability of each state individually.

If you are a maverick who believes that the particle is *a priori* in one state or the other, that is called a "hidden variable theory". None of the prevailing interpretations is a hidden variable theory, but in the early days Bohm did some interesting work with what he called pilot waves that you may want to read up on.

The reason for this is that there are some quantum phenomena that can't be explained by hidden variables. People like to talk about the Bell Theorem in regards to this but there other problems with hidden variables as well. Quantum tunneling is an example. You can put a particle inside a box, and if the wavefunction of the particle extends outside of the box, there is a *chance* the particle will escape the box even if you designed the box to be impervious to the particle. Obviously the particle cannot be *a priori* outside of the box, because you put the particle in the box to begin with. If that isn't the universe messing with your mind, what is? BTW how does MWI explain quantum tunneling?

>  If a
> probability, then does the probability move toward a state,
> or does
> the eventual state reflect the outcome of a wave collapse?

That depends on the situation. For example if a physicist generates a slow moving low momentum particle in freespace, the large wavelength of the wavefunction would be interpreted by him to mean that particle was smeared out over huge area at a fairly low probability density. 

If our physicist were to sample a small section of that space for the particle by enclosing that area in an inpenetrable box, for example and not find it, that new information would change the particle's wavefunction and therefore its probability density and its momentum.

So in effect, repeated observations would not so much "collapse" the wave function as to cause it to evolve in increments toward the final state. So the more boxes he uses to sample the space, the fewer places the particle could be. And when he eventually found it, it would be going a lot faster than it was when he generated it, because it would be confined to the space within the box, removing uncertainty about its position but increasing its momentum.

> To reference Lee's response to this post, is there any
> difference in
> Platonia from our observation of moment t1 to moment t2? 
> is there a
> way to distinguish the moment t'2.

Well the rest of your post is something I would hand off to Lee. He is more familar with other universes than I am. I for one don't believe in Platonia any more than I believe in the Langoliers. For me the realm of abstraction is the mind. And in the mind, t1 to t2 can take as long or as short as you want. Don't believe me? Then close your eyes and imagine yourself flying a few laps around Jupiter. I bet it takes you less than a minute even if you pose for pictures over the red spot. How's that for FTL? ;-)


Stuart LaForge

"See them clamber, these nimble apes!  They clamber over one another, and thus scuffle into the mud and the abyss."- Friedrich Nietzsche