= 27d567bc2d48d9f40e9ccc20ea370b15)
This post is tagged "signaling". :-)
In response to
Decoherence
Nick and Recovering,
Off the top of my head (I Am Not A Physicist), if you tried this in real life:
Imagine the light thingy starting out in many different positions. Now imagine the track is frictionless. The light thingy will swing back and forth over the heavy thingy, its exact position and orbit depending on its starting position.
Does the light thingy roll to a halt? There must be friction. Friction generates heat. Heat is entropy. One subspace may go from light gray to dark gray, but another subspace goes from dark gray to light gray, and the total amplitude density is conserved.
Also, the heavy thingy itself will move as the light thingy moves toward it; pulling forces are symmetrical, by conservation of momentum. If the heavy thingy is made up of lots of little particles, they all end up in slightly different places, depending on where the light thingy was originally.
I think you're confusing classical probabilities with quantum amplitudes.
The classical case is what you describe. We start with a probability distribution in which the two particles are know to be stationary but they have uniform distributions for their starting positions. Then as the system evolves they get drawn closer together and so our uncertainty about their position goes down. But their momentum depends on their initial positions and so we gain uncertainty about their momentum. Thus the total entropy is conserved. (If we wish we can then use friction to shift the entropy into the heat degrees of freedom.)
But in the quantum case the amplitudes are assigned only to the configuration space of the particles i.e. to their positions. There is no momentum space into which we can put our spare entropy. In fact it is possible for quantum amplitudes to become tighter as time passes, even without any outside interference (this doesn't contradict the Second Law because the Second Law is about our uncertainty about the wavefunction, not the spread-out-ness of the wavefunction itself). For example there are solutions of the Schrodinger equation for a free particle where a Gaussian wavepacket evolves into one with a smaller variance (of its associated "probability distribution").
So I think you're literally wrong when you say:
If instead we'd started out with a big light-gray square—meaning that both particles had amplitude-factors widely spread—then the second law of thermodynamics would prohibit the combined system from developing into a tight dark-gray diagonal line.
A system has to start in a low-entropy state to develop into a state of quantum entanglement, as opposed to just a diffuse cloud of amplitude.
Because in the quantum case the light gray square isn't representing a spread out probability distribution. We know exactly what the wavefunction is. The light gray square and the dark gray line both represent cases of total certainty! The time when entropy would come in would be if we had some Bayesian uncertainty about what the wavefunction actually was - a probability distribution on the space of amplitude assignments.
In response to
Feynman Paths
(PS: I'm given to understand that the Feynman path integral may be more fundamental than the Schrödinger equation: that is, you can derive Schrödinger from Feynman. But as far as I can tell from examining the equations, Feynman is still differentiating the amplitude distribution, and so reality doesn't yet break down into point amplitude flows between point configurations. Some physicist please correct me if I'm wrong about this, because it is a matter on which I am quite curious.)
Feynman really does give you the amplitude for going from one point distribution to another point distribution. The formula for the path integral doesn't involve any derivatives of the amplitude distribution. But your fundamental point is still correct. Nature can't be viewed as classical just by thinking only in terms of point distributions. This is because the point distribution evolves into a non-point distribution. So even if you start out thinking in terms of point distributions you are immediately forced to consider other distributions.
(You might be worried that the point distribution has infinite second derivative, and so can't be evolved using the Schrodinger equation. But if you turn down your rigour dial you can find the solution:
phi = exp[i x^2 / (4t) ]/sqrt[4 pi i t]
(This is the solution for a free particle in one dimension where I've picked the mass hbar/2 for convenience.) One can sort of see how this becomes a point distribution as t tends to zero. The amplitude becomes very oscillatory everywhere except zero, and at zero all those oscillations cancel out. Meanwhile the magnitude increases like 1/sqrt(t) as t tends to zero, so at zero it has the correct value of sqrt(infintiy).)
In response to
Classical Configuration Spaces
My understanding is that classical configuration space as you mentioned is usually thought of as including dimensions for velocities, or even better, momenta, in addition to positions. For even two particles in a one dimensional space, that is already four dimensions and you can't graph it, so I can understand why you showed it the way you did. However you can show one particle, perhaps in a force field, which can be useful.
The advantage of including momentum is that a single point in configuration space has all the information needed to calculate its evolution forward (or backward) in time. A single point determines an entire trajectory (a line, or curve) in configuration space. That means that two nearby points determine two different trajectories, and in fact all of configuration space can be divided into non-intersecting trajectory lines. Only in this formulation is the Liouville Theorem true, about conservation of configuration space volumes. If you start with a certain volume in configuration space, and evolve it forward (or again, backward) in time, the volume doesn't change. However, in most classical configurations, physics tends to be chaotic and the shape does change as you describe, developing "fingers" and "folds" and becoming very complex in structure, which leads on a crude scale to an apparent increase in the volume.
To clarify (seven years later), "configuration space" is the name physicists use for the space recording just the particle's positions, and "phase space" is the name for the space recording their positions and momentums.
In response to
Babies and Bunnies: A Caution About Evo-Psych
An article with a possible explanation of this:
http://www.wsj.com/articles/why-we-melt-at-puppy-pictures-1428504897
In response to
Harry Potter and the Methods of Rationality discussion thread, March 2015, chapter 119
I can't remember, what was respectively in the Phoenix's Price and Phoenix's Fate rooms. I though both were passwords for the broken wands and similar things, but the narration implies otherwise. I also wonder what will be in the Phoenix's Egg room. It can't be prophecies (which could otherwise be the obvious choice), and I don't think Dumbledore had the foresight to store frozen brains of wizards who died so that Harry could resurrect them.
In response to
comment
by
on
Harry Potter and the Methods of Rationality discussion thread, March 2015, chapter 119
Narcissa
In response to
Open thread, July 21-27, 2014
Sometime in the near future, I will be running an iterated prisoner's dilemma tournament in which bots can access their opponents' source code, similar to the IPD tournament that was held last year. This tournament will be open to the Internet at large (i.e. not just LW) and will probably include some Hacker News folks and some folks from my real-life social network, who are primarily programmers and people in the finance world. Once everything is officially announced, there will be a large window (a month?) in which users can submit entries before the tournament is run. Also, to help out non-programmer participants, I will be translating some participants' pseudocode/descriptions of algorithms into code. More details on this later.
The (work in progress) code that will be used to run the tournament is here.
Right now everything is still in the preliminary stages, so I would appreciate:
- comments about what made last year's tournament good/bad/etc.
- suggestions for the rules and payoff matrix/feature requests to make the tournament more interesting
- code review
- general comments (i.e., yell at me)
IIRC last time the winners were programs that had some random element in their code and "got lucky" (in the sense that if the tournament had been run multiple times and the results averaged, they would not have won). So maybe you should guard against this by performing sufficiently many copies of the tournament.
In response to
Open thread, July 29-August 4, 2013
After a short discussion on irc regarding basilisks I declared that if anyone has any basilisks that they consider dangerous or potentially real in anyway to please private message me about them. I am extending this invitation here as well. Furthermore, I will be completely at fault for any harm caused to me by learning about it. Please don't let my potential harm discourage you.
Did anything come of this in the end? Were any of the basilisks harmful or otherwise interesting?
I see no justification whatsoever for concluding that gravity must therefore be detectable in the weak-field limit.
Suppose we perform an experiment where, based on the measured spin value, we move some macroscopic object with detectable gravity in opposite directions. In the Newtonian background spacetime approach there is no issue with MWI, as both branches live on the same spacetime. In a full GR case, however, the spacetime itself must decohere into different branches, or else we could detect the interaction between different branches gravitationally (I don't know if this has been tested, but it would be extremely surprising if detected). I am not sure what would the mechanism which splits the spacetime itself be, since all current QM/QFT models are done on a fixed background (ignoring ST and LQG). So presumably this requires Quantum Gravity. Yet the whole thing happens at very low energies, slow speeds and weak spacetime curvatures, so that's why I said that this would have to be a QG effect in the weak-field limit. Of course it would only be "detectable" in a sense that if there is no gravitational interaction between branches, then the spacetime itself must decohere by some QG mechanism.
Suppose we perform an experiment where, based on the measured spin value, we move some macroscopic object with detectable gravity in opposite directions. In the Newtonian background spacetime approach there is no issue with MWI, as both branches live on the same spacetime. In a full GR case, however, the spacetime itself must decohere into different branches, or else we could detect the interaction between different branches gravitationally (I don't know if this has been tested, but it would be extremely surprising if detected).
I can't get past the paywall, but I think this is what Page and Geilker do in "Indirect Evidence for Quantum Gravity".
View more: Next
= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
= f037147d6e6c911a85753b9abdedda8d){kind=logo}
What about treating the collapse as the Bayesian probabilities update in light of the measurement (new evidence)?
There are lots of thought experiments and actual experiments that suggest this view doesn't work. "PBR" is the one that springs to mind. Some people still support this view, but I've never seen any of them straightforwardly state what they think the underly reallity (that the amplitudes are supposed to represent beliefs about) actually is.