[ExI] Feynman's approach

[Bryan Bishop]

After looking at the recent emails about MWI, Copenhagen, etc., I just 
wanted to add my 2c and point anybody interested over to this page that 
I found a good while back:

(so-called) Kantian quantum mechanics
http://www.friesian.com/space-2.htm

> These days, many of us working on quantum gravity believe that
> causality itself is fundamental -- and is thus meaningful even at a 
> level where the notion of space has disappeared.   
- Lee Smolin, The Trouble with Physics, The Rise of String Theory, the 
Fall of a Science, and What Comes Next [Houghton Mifflin Company, 2006, 
pp.240, 241].

Quoted from the page. Kelley L. Ross, author. The HTML version (link 
above) has formatting and emphasis and so on, so go check it if you're 
able to, but the excerpt below provides a good place to start reading.

What is the most striking in Feynman's version of quantum mechanics is 
his impatience with the wave-particle duality: 
For many years after Newton, partial reflection by two surfaces was 
happily explained by a theory of waves, but when experiments were made 
with very weak light hitting photomultipliers, the wave theory 
collapsed:  as the light got dimmer and dimmer, the photomultipliers 
kept making full-sized clicks -- there were just fewer of them. Light 
behaved as particles. [pp.23-24, boldface added]

This is the key to Feynman's views:  he likes particles and is not 
interested in waves. This puts him more in the metaphysical camp of 
Einstein and the older realists and out of step with the developments 
detailed above which try and preserve the determinism of the wave 
function. He definitely doesn't like duality: 
You had to know which experiment you were analyzing in order to tell if 
light was waves or particles. This state of confusion was called 
the "wave-particle duality" of light, and it was jokingly said by 
someone that light was waves on Mondays, Wednesdays, and Fridays; it 
was particles on Tuesdays, Thursdays, and Saturdays, and on Sundays, we 
think about it! It is the purpose of these lectures to tell you how 
this puzzle was finally "resolved." [p.23, note]

The puzzle, however, was not "resolved," which may be why Feynman here 
carefully puts that word in "scare" quotes. We get a fuller statement 
here: 
...the wave theory cannot explain how the detector makes equally loud 
clicks as the light gets dimmer. Quantum electrodynamics "resolves" 
this wave-particle duality by saying that light is made of particles 
(as Newton originally thought), but the price of this great advancement 
of science is a retreat by physics to the position of being able to 
calculate only the probability that a photon will hit a detector, 
without offering a good model of how it actually happens. [p.37]

It is worse than that, since Feynman himself must say that the light 
goes everywhere at once, follows all possible paths, which is something 
a single finite particle can't do, regardless of the probability of 
where it may be found by a detector (cf. p.46, about diffraction 
gratings). So the wave-particle duality is not so easily "resolved." 
Indeed, Feynman himself later describes rather well how the 
wave-particle duality works: 
Nature has got it cooked up so we'll never be able to figure out how She 
does it:  if we put instruments in to find out which way the light 
goes, we can find out, all right, but the wonderful interference 
effects disappear. But if we don't have instruments that can tell which 
way the light goes, the interference effects come back! Very strange, 
indeed! [p.81]

With this, we don't need the "Monday, Wednesday, and Friday" rule. If we 
know where the particle is, then clearly it can't be everywhere, and 
the effects that depend on it being everywhere (interference, 
diffraction), disappear. If we don't know where the particle is, then 
all the effects explicable by wave mechanics appear. When the cat is 
away, the mice will play. 

But Feynman also retreats occasionally from his flat "light is made of 
particles" assertion: 
In fact, both objects [i.e. electrons and photons] behave somewhat like 
waves, and somewhat like particles. In order to save ourselves from 
inventing new words such as "wavicles," we have chosen to call these 
objects "particles." [p.85]

So now they aren't really particles, we have just "chosen" to call them 
that, just to avoid irritating neologisms. This is rather different 
from the "the wave theory collapsed" stage of the account. But are we 
really dealing with something like "wavicles"? No, because these things 
actually don't behave "somewhat like waves, and somewhat like 
particles" -- they behave entirely like waves in some situations, and 
entirely like particles in others. And what is the difference? As 
Feynman understands quite well himself, we get particles with 
localizing detectors, waves without. 

Given his preference for particles, what Feynman does is create a 
mathematical means of duplicating the effects of wave mechanics. His 
system is called "summing over histories." The "histories" are all the 
possible tracks that a particle can take, like a photon reflecting off 
of a surface. The Classical rule is that light follows the shortest 
path, and that the angle of incidence is equal to the angle of 
reflection. Most possible paths violate both these rules. What Feynman 
does is that each possible path is represented by a vector. The length 
of the vector can be the square root of the probability of the particle 
going that way, but for reflections (in Chapter 2), Feynman makes the 
arrows of "arbitrary standard length" (p.41). What is important is the 
direction of the arrow, and that is determined by a little "stopwatch," 
which runs, with the arrow rotating as the hand of the watch, as the 
particle travels. The direction of the arrow when the watch stops gives 
us what we need to work with. The vectors of a number of possible paths 
are then put end to end ("summed"). It turns out that vectors for 
lengthy and improbable paths point in many different directions and 
result in little net length when put end to end. When we look at the 
area representing the least distance and the least time, confirming to 
the classical rules, the vectors point in more or less the same 
direction; and when they are put end to end add up to a substantial 
vector, whose square is the overall probability of the particle taking 
that path. What we get is therefore more or less the Classical result. 

I do not mean that to be a comprehensive explanation, just enough to 
give us a picture here. Anyone wanting more detail should consult QED 
itself. The key element is the "stopwatch," which gives us the 
direction of the vector, which makes it possible that the vectors are 
going to add up to something or cancel each other out. But this is a 
very unusual stopwatch. It does not measure time. Feynman says, "the 
stopwatch hand turns around faster when it times a blue photon compared 
to a red photon" [p.47]. What is it that is "faster" about blue light 
than red light? Not the velocity, not the rate of time itself (no 
Relativistic effect here), just the frequency. The rate of 
the "stopwatch" is determined by the frequency of the photon. But 
particles do not have frequencies. Waves do. Feynman's stopwatch 
corresponds, not to time, like ordinary watches, but to the phase of a 
wave function. The summing of the vectors reproduces the interference 
effects of waves. 

Thus Feynman is able to smuggle characteristics of waves into a theory 
that is supposed to be about particles. There seems little pretence 
here that the "stopwatch" represents anything the particle is actualy 
doing, as a particle. It is simply a mathematical device that gets us 
good results, and its very abstraction and dissociation obscures its 
correspondence to the natural characteristics and behavior of waves. 
Feynman, again, seems to rather enjoy the peculiarity of it. As he says 
elsewhere: 
...adding arrows for all the ways an event can happen -- there is no 
need for an uncertainty principle! [p.56]

But the uncertainty principle is not eliminated by the little arrows. 
Not only does it remain uncertain where particles are when they are 
behaving like waves, but it remains impossible that they should be any 
one place in particular to do what they do. Feynman's enthusiasm 
mistakes a mathematical abstraction for a substantive conclusion -- a 
precise and excellent example of the Sin of Galileo. But Feynman knows 
better than this. He knows that successful mathematics in a successful 
theory does not mean that we understand what is going on. But he gets 
carried away, and it is always a temptation to explain what is not 
understood as something that cannot and need not be understood. We see 
that in the following passage: 
I am not going to explain how the photons actually "decide" whether to 
bounce back to go through; that is not known. (Probably the question 
has no meaning.) [p.24]

Not only does it have meaning but there is even an answer:  the photons 
both bounce back and go through, just as Schrödinger's Cat is both dead 
and alive. They can do that as waves. They can't do that as particles 
(unless we use an indefinite number of particles, even in single 
particle experiments, as Feynman does). Which is the problem. What the 
photon must "decide" is where it is going to be when the wave function 
collapses. This is the crux of quantum indeterminacy, and Feynman 
simply doesn't want to deal with it. 

But it is a problem larger than quantum mechanics. It is a problem of 
the metaphysics of possibility and probability, which no physicist or 
metaphysician (or physician) has done a very good job of dealing with. 
When we have just rolled three or four "boxcars" in a row (i.e. 12 on 
the dice), how do the dice then "know" that it is time to even out the 
statistical average by avoiding boxcars for a while in the future? Of 
course, the dice can't "know" because the earlier rolls of the dice 
have no physical effect on the later ones. But we have similar 
situations with sub-atomic particles. How do atoms of Uranium "know" 
that enough other atoms have decayed to account for the statistical 
half-life of the isotope, and that they need to wait, perhaps for 
millennia, to decay? Again, it looks like they can't "know," but the 
individual events just happen to conform to the statistical average. 
The standard response of the mathematician to give up at that point (or 
say that it is a question that "has no meaning") is now troubled by the 
results of the Einstein-Podolsky-Rosen (EPR) Paradox, discussed above. 
Distant particles, whose properties have some indeterminate quantum 
correlation, "know" instantaneously what happens to the other 
particles, if this implies determinate states. This happens 
without "hidden variables," i.e. without determinate but unknown 
properties of the particles. What it means is that the wave function is 
a physical connection and that its collapse is instantaneous, violating 
Special Relativity. If we apply this to dice throwing, it could mean 
that the dice do "know," without any Classical physical connection, 
what has happened in the past. 

Richard Feynman, of course, has no intention, and really no interest, in 
getting into such territory. His statement that the question of how 
particles "decide" where to go probably "has no meaning" is an 
afterthought in which fragments of philosophical theory bob like 
flotsam in the flood. What it would get Feynman, as a theory, is that 
Nature is incomprehensible because it cannot be understood, i.e. there 
is no meaning for understanding to get. If true, this would certainly 
justify his phlegmatic disinterest -- "theoretical physics has given up 
on that." But Feynman really expresses it more as a wishful thought, or 
as a decision, than as a real conclusion. It is a limit that he is 
willing to accept, because what interests him is the mathematical 
technique that is productive of the predictive results. That is the 
real stuff, and the philosophical questions, the metaphysics, are less 
important -- as, in physics, they actually are less important. 

Feynman's quantum mechanics in the end benefits from the abstraction 
that is possible in scientific theories. Not all questions need to be 
answered, understood, or even addressed to have a successful theory 
with dramatic results. It is therefore no disqualification to Feynman's 
greatness that he didn't resolve the basic philosophical problems of 
quantum mechanics. Certainly nobody else has. What is of interest is 
his theory as an example of one direction in which we can go with 
particles alone, avoiding wave mechanics, even though, in the end, 
characteristics of wave mechanics (the "stopwatch") must be attached, 
rather extraneously, to the particles. This is revealing -- namely that 
the physical waves in fact cannot be dispensed with, as Feynman himself 
occasionally seems aware, as when he says that his "particles," 
hitherto the vindication of Newton, are actually "somewhat" like waves.

________________________________________
Bryan Bishop
http://heybryan.org/