Yep, Maxwell equations do produce the same results. The fun quantum thing is that this also happens with individual photons.
Klao
Karma: 168
This left me totally confused too.
But then, I realized that there is a property of photons that can help with this confusion here: spin. So, the configuration space is not a “a photon here and a photon there...”, but a “a photon with a +1 spin here, a photon with −1 spin there...” And then this phase thing arises from the values of the amplitude distribution for the configurations with photons of opposite spins. This makes the math quite a bit easier too.
I might be completely mistaken about this, though.
This post (together with the previous one) left me in a quite a bit of a confusion. How does this model with polarization vectors correspond to the old “amplitude distribution over a configuration space of «a photon here and a photon there»”? What are the configurations here, and when are they distinct? (And it seems I am not the only one who got confused by this.)
I think, I found the solution; the photons have a distinguishing property: spin. So, if configurations are more like “a photon with a +1 spin here, a photon with a −1 spin there...”, then it all fits nicely in the same model. And the amplitude distribution corresponding to the situation described in the article would be:
|a+> |b-> - |a-> |b+>
(modulo a constant factor). Where |p+> (a photon with a +1 spin at P) corresponds to the P=(1 ; i) and |p-> to the P=(1 ; -i) in the article’s notation. Of course, the math remains the same, but now I can see a bit more clearly the amplitude distribution and what are the distinct configurations.
Hmm, it’s nice that there is this pretty compact formulation for two coupled but separately “unpolarized” photons. But, this still leaves me with a question of how does one “unpolarized” photon (a photon for which half of the squared amplitude would pass any polarized filter) looks like?
I would guess that there is no such thing. We might be ignorant about the photon’s polarization, but it does have some definite polarization even before it passes any filter. Otherwise, it has to be in a similarly tangled state with something (eg. its source).
Hmm, how would I check this?..
Motivated skepticism: it’s harder to avoid than I’d think
Yes, of course, I realize that there are all kind of subtleties why one way might be better for some people and something else for others etc.
But, the frightening realization for me was, that in the heat of the debate my brain can come up with all kind of elaborate arguments. But because the reason I came up with them was to win the debate (and not to figure out how the things really are), I am screwed, no matter how clever are my arguments. (http://lesswrong.com/lw/js/the_bottom_line/)
And yeah, it would be cool to come up with ways to figure out how the things really are and how can we test our hypotheses. But, now I think that this is really-really hard: to switch in that mode of thinking in the middle of an argument. The best I could do, was to let it go and walk away. (And write this post; maybe someone else comes up with a better idea. :))
Thanks for the link, looks very relevant!
Good advice, I will look into it!
Count me in!
I half-counted it. I counted from the time when I finally created an account at lesswrong.com.
Same here. I had to look them up to understand what they are about and answer the question meaningfully. (But, after looking the options up the choice was actually easy.)
I completed the survey. Thanks, Yvain, for doing it!
The option “Atheist but spiritual” gave me a pause. What does it actually mean?
General applicability of Bayesian inference: Judea Pearl, “Probabilistic Reasoning in Intelligent Systems”, chapter 2. (Definitely not an explanation suitable for a teenager, but for a college student interested in the topic it is very good, I think.)
So, a person who doesn’t believe in god, but still thinks that he has an “immortal soul” or something? Thanks for explaining!
I guess, this is similar to the second part of thomblake’s comment. Thank you for explaining this!
But, if it really can mean such different things, then that particular in the survey question wasn’t formulated very carefully.
Do we have it too easy?
No, it’s not too dark, it is useful to see an even stronger expression of caution. But, it misses the point a bit. It’s not very helpful to know that Eliezer is probably wrong on some things. Neither is finding a mistake here or there. It just doesn’t help.
You see, my goal is to accept and learn fully that which is accurate, and reject (and maybe fix and improve) that which is wrong. Neither one is enough by itself.
This sounds like a very good piece of advice. A slight problem is that some of the jargon is very useful for expressing things that otherwise would be hard to express. But, I’ll try to be conscious about it.
Yes, I saw it coming. :) Thanks! It does matter to me.
Two ideas I got after 5 minutes (by the clock :)) thinking.
If the tests are stressful and mentally (and possibly physically) exhausting, then even if it is still possible to prepare just for the test, it will not be as far from preparing for the “real thing”. So, something like Initiation Ceremony could be done periodically and not just for initiation.
Give the students “stories” and see if they can make heads or tails of them. (How accurately can they guess the omitted details? Can they predict how it continues? Etc.) But, where can you get real stories? An authored story is very bounded in usefulness for this.
The idea: we have court cases. A lot of them, in all kind of domains, dating back to centuries. And they are very real, even if it’s distorted (fake evidence, false testimony), it’s done by someone for some concrete reason, which can be analyzed rationally. This might require learning some Law, but even without formal training many non domain-specific cases can be understood with moderate work. And Law is one of the oldest applications of human rationality.
Both of the ideas are mostly applicable to the second use-case: measuring a bunch of students in a school, but not good for comparing schools or designing a standardized “rationality test”.