Warp wrote:
> Darren New <dne### [at] sanrrcom> wrote:
>> But seriously, for there to be an interference pattern, something has to 
>> interfere with something else, right?
> 
>   If the photon is a wavefront which traverses from the emitter to the
> detector, passing throug the slits splits it into two wavefronts, which
> interfere with each other. When the wavefront collides with the detector,
> it collapses back into a particle.

But it doesn't work that way. If you look to see which slit the particle 
passed through, you find out that it only went through one. You never, ever 
see it go through both slits. You basically never see a wave or measure a 
wave. You always measure a particle, even as the whatever goes through the 
slits, even *after* the whatever goes through the slits.

>   I'm not saying that is what happens. I'm just saying it's exactly as
> plausible as eg. a particle being in many places at the same time or
> affecting another particle instantly.

Plausible? Yes. Confirmed by experimental evidence? No. Contradicted by 
experimental evidence? Yes.

I'm just stating what the guys who study this say. You're trying to tell me 
it sounds absurd. Sure, maybe it does. Maybe the world *might* work a 
different way than it does. Maybe if the only experiment you did was the 
two-slit experiment, you'd think photons are sometimes waves. But they're not.

>   So why does the interference pattern appear? 

You know when you do something with macro-sized objects, you get 
one-dimensional probabilities, right?  If you say "flip a coin, twice", 
you'll have the probability of getting two heads being the probability of 
getting one head *times* the probability of getting one head, right? (I'll 
leave it as an exercise for you to decide *why* that is the case, beyond 
"common sense.")  The probability of getting heads either time is the 
probability of getting heads the first time *plus* the probability of 
getting heads the second time *minus* the probability of getting both (just 
so you don't count the same event twice).

It's the same way with quantum particles, except the probabilities are 
complex numbers, hence "amplitudes". The probability of it hitting the 
screen at a given position is the amplitude of it going from the emitter to 
the left slit to that point on the screen *plus* the probability of it going 
from the emitter to the right slit to that point on the screen. But those 
probabilities change based on the distance the particle travels, and when 
you do all the adding and multiplying, the imaginary components wind up 
canceling out some of the "real" components in a way that looks like waves.
Because the probability of a quantum particle going in any given direction 
is a function of its amplitude.  "Amplitude" is a technical term meaning 
"two-dimensional probability." You get the probability of finding a particle 
at a particular place by adding together all the amplitudes of it getting 
there, then taking the absolute value (i.e., the length of the result).

In other words, the probability of something going from A to B is the sum of 
all the amplitudes of the ways it can get from A to B, then you take the 
resulting size. Just like if you want to get a heads on the first flip or a 
heads on the second flip, you add the probabilities.

The probability of two things happening is the multiplication of the two 
*probabilities*, because you know the things happened.

If you measure the likelihood of the particle going from the emitter to the 
screen without checking which slit it went through, the probability is the 
absolute value of the sum of all the ways it could get there.

If you check which slit it went through, it's the probability that it got 
there by going through the first slit plus the probability that it got there 
by going thru the second slit. (Since it never goes through both, you don't 
have to subtract out that possibility like you do with flipping coins.) The 
probability of it going from the emitter to either one of the slits, or from 
the slit to any point on the screen, you still measure by adding up complex 
amplitudes for each possible path, and not just using probabilities.

Note that when you don't check which slit, you add up a bunch of complex 
numbers, then take the absolute value. When you check which slit, you add up 
a bunch of *real* numbers (one for each possible measurement), each of which 
is the result of adding up a bunch of complex numbers.

That's why doing things in the *future* can affect what you measure *now*, 
which isn't how waves work.

> Is nature trying to confuse
> us to make it look exactly like it was a wave, without it being so?

Not every addition of complex numbers is a wave. Just so, not every 
collection of converging lines is caused by perspective. Having converging 
lines in nature that don't converge to the horizon isn't any more 
"confusion" than complex numbers not caused by waves.  In much the same way, 
I can show you that *those* lines are *not* perspective, because if you 
shift your point of view, they don't converge at the horizon. But if you 
only look at exactly one experiment, namely the two slits with no other 
measurements made, it *look* like perspective/waves, but as soon as you do 
another experiment, it stops looking like that.

-- 
Darren New, San Diego CA, USA (PST)
   Human nature dictates that toothpaste tubes spend
   much longer being almost empty than almost full.

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