Warp wrote:
> When I accuse you of making straw men, that never is the case.
> How convenient.

Well, to be a straw man, it has to be something I'm arguing against. 
Maybe it's some other fallacy, but it isn't a straw man.

> "In the path integral formulation, a particle such as a photon takes
> every possible path through space-time to get from point A to point B. In
> the double-slit experiment, point A might be the emitter, and point B the
> screen upon which the interference pattern appears, and a particle takes
> every possible path, including paths ***through both slits at once***, to
> get from A to B."

Yes. It also take paths that go in circles, thru both slits, backwards 
in time so it goes thru both slits multiple times at once, etc. It can 
also split into multiple virtual particles that go thru both slits and 
recombine into a single photon when it's done.

The "path integral formulation" is an infinite series of different ways 
something can happen. The different paths each have a complex number 
representing the likelihood of it happening. This number is based on 
surprisingly few parameters (six, two of which are universal constants, 
if I remember right). You get the probability of an event happening by 
doing the normal probability math (multiplication is "and" and addition 
is "or") on the complex numbers.

The math doesn't work (i.e., doesn't match experimental evidence) if you 
assume photons can go thru both slits but can't go back in time.

I'm not saying you're making it up. I'm saying electrons aren't waves. 
They don't go through both slits the same way a "wave" does. If they go 
through both slits, it's by either going around in a circle, or by going 
back in time (equivalent, turn into two virtual particles and then 
happen to run into each other and recombine on the other side) so they 
go thru each slit separately and then interact again. At no point are 
they waves in the "water" sense of the word.

> "When a detector is placed at one of the slits, ***the situation changes***,
> and we now have a different point B. Point B is now at the detector, and a
> new path proceeds from the detector to the screen. In this eventuality
> there is only empty space between (B =) A' and the new terminus B', no
> double slit in the way, and so an interference pattern no longer appears."

Right. You integrate the paths up to the detection event, and the 
probability is the magnitude of the square of the complex number. From 
then on, it's normal real-valued probability calculations. In other 
words, if you have event A is "electron leaves generator at time T1", 
event C is "electron hits wall at time T3", then you take all the 
possible ways that could happen, including the electron that is created 
at T1 actually going to T5 (after T3) turning into two particles that 
fly apart, bump into other particles, and smash back together again to 
turn back into an electron, then back to T0 (before T1) and then to T3, 
and add them together using complex addition. (That's the "path 
integral". You can see why the math is hard.) Then you take the 
magnitude of the square of the result, and that's the likelyhood that 
"Electron leaves generator at T1 and hits wall at T3."

If you stick a detector in there and say "Electron leaves generator at 
T1, is detected by the detector at T2, and hits wall at T3", then you 
build the path integral for generator->detector, then for 
detector->wall, and then you add up the magnitudes of the squares of the 
path integrals. I.e., you use normal probability when you're talking 
about "normal" events, rather than probability based on complex numbers.

Note that the retroactive quantum eraser has things like
   leaves generator at T0
   hits wall at T1
   decides which slits to go thru at T2

-- 
   Darren New / San Diego, CA, USA (PST)
     "That's pretty. Where's that?"
          "It's the Age of Channelwood."
     "We should go there on vacation some time."

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