Kind of an arcane philosophical point, here, so I'll be a little surprised if anybody responds, but this occurred to me while writing the previous post, and I thought I'd throw it out there. In the previous post, I quoted Feynman's one sentence for the future:
Everything is made of atoms.
and suggested as an alternative:
Light is both a particle and a wave.
Part of the idea behind these is that the sentences would allow people who had received that bit of information as Revealed Truth to reconstruct much of modern physics. If you take seriously the idea that material objects are made of atoms, and set out to prove it, you can end up rediscovering most of modern physics.
But is this really true for both of these?
Obviously, we have reason to believe that the atomic hypothesis alone can lead to modern science because, in a sense, it did. The idea that matter is made of atoms dates back to the ancient Greeks, and investigations into the atomic structure of matter were crucial for the development of quantum theory in the early 20th century. (Though many people will say that the atomic hypothesis wasn't really nailed until Einstein's Brownian motion paper of 1905, if not later.)
It seems plausible to say that people who had been told that matter was made of atoms would be able to rediscover the rest of our modern theory of the world through experiments to look at the properties of atoms. What about the other way around, though? If you knew about the quantum nature of light, but not atoms, would you end up with modern physics?
The really arcane physics inspiration for this question is that there are well-known semi-classical theories of most of the experiments that are usually said to demonstrate the existence of photons. You can get nearly all of the classic results from considering atoms with quantized levels, but treating light as a classical electromagnetic wave. So, the ultra-nerdy version of this question is: Could you do the same thing in reverse? That is, could you construct a theory of the world in which you quantized the EM field, but treated atoms classically?
It would be really bizarre, sure, and I doubt it would be good for anything (other than making physicists' heads hurt) but that's not the question. The question is, could you do it?
Do you mean "treated atoms classically" or "treated matter as a continuum"? Big difference.
It's hard to imagine holding as sophisticated a notiion as the quantization of the EM field in the absence of a modern notion of atoms and electrons. But I don't see the causal chain working so well in reverse. Does a quantized EM field suggest the existence of corpuscles of charge? Is it compatible with the existence of caloric? Phlogiston?!
I have papers to grade, I really shouldn't be thinking these thoughts!!
Just to clarify... the power of the Feynman proposal is not so much the fact that it points you in the direction of modern physics, but that it settles so many questions of basic chemistry and thermodynamics. It's a small leap from "everything is made of atoms" to recognizing that chemical reactions are the reshuffling of said atoms and that heat is the motion of said atoms. This takes care of most of the physics and chemistry done from 1700 - 1850 or so. I have a hard time seeing how the insight about light will lead you backwards into those questions without a lot of difficult work.
Do you mean "treated atoms classically" or "treated matter as a continuum"? Big difference.
I'm not sure you could really do matter-as-a-continuum in any sensible way, as you would need to account for things like electrons. That's why I said "treated atoms classically," even though "treated matter as a continuum" would be a better parallel.
When I was thinking about my answer to the original question (while walking the dog), I had this weird flash of a world in which scientists were in general agreement about the existence of light quanta, but the existence of single atoms was not a well established fact, and I thought that would be kind of cool.
It's a small leap from "everything is made of atoms" to recognizing that chemical reactions are the reshuffling of said atoms and that heat is the motion of said atoms. This takes care of most of the physics and chemistry done from 1700 - 1850 or so. I have a hard time seeing how the insight about light will lead you backwards into those questions without a lot of difficult work.
Well, if you know that light is quantized, then the minute you start looking at absorption and emission you end up with the notion of quantized energy bands in material objects, which has to go somewhere. But yeah, I agree that it would be difficult.
Even more fun is trying to imagine an alternate history of discovery that would have led to a belief in a quantized EM field BEFORE the nature of matter was fully worked out. Can we imagine an apparatus that would allow you to demonstrate the photoelectric effect using 18th century technology alone?
I smell a SF work in the making here.
well Dr. Dave, Planck in 1900 was before Bohr so.....Also much of the photoelectric effect (except for the possiblility the electron comes out instantly) can be explained by semiclassical theory.
As I understand it, even the instantaneous emission of electrons can be explained semi-classically. You do a Fermi Golden Rule sort of thing, and find that the emission rate is constant in time, which means some electrons will be emitted even at very short times.
Also, the photo-electric effect was discovered using 19th century technology-- it was one of the things that came out of Hertz's experiments in the 1880's.
perry - i was talking about much earlier than Bohr, though... I mean back when Franklin was talking about positive and negative "electrical fluids" and Carnot was deriving the laws of heat engines based on caloric theory.
Dr. Dave - gotcha. That would be a very different version of the way things evolved!
Chad - I don't think you can get the instantaneous emission from perturbation theory, the derivation of Fermi's golden rule involves dealing with a square of a delta function, and you sort of take a long time limit. Physically the idea is that the energy of the field (E^2 *Area*ct basically) is insufficient for some times t, that is its is less than the work function, so with a classical field it would take some time to get to the level of the work function. For a quantized field, the energy is (at least can be) in lumps, and that lump can then cause instantaneous emission at least some of the time (using very loose language there....)
Chad - I don't think you can get the instantaneous emission from perturbation theory, the derivation of Fermi's golden rule involves dealing with a square of a delta function, and you sort of take a long time limit. Physically the idea is that the energy of the field (E^2 *Area*ct basically) is insufficient for some times t, that is its is less than the work function, so with a classical field it would take some time to get to the level of the work function.
The trick is that you're going from a single bound state to one of a nearly infinite number of degenerate free-electron states. When you do the integral over all those states, you find an overall transition probability that's proportional to time, which means the transition rate is constant, which means there must be some instantaneous emission.
Lamb and Scully worked this out in the 60's, (in Polarisation, Matiere et Rayonnement, Presses University de France (1969)), and Jaynes has a more readily accessible derivation in Phys. Rev. 179, 1253-1261 (1969).
I'm not so sure. The Jaynes-Crisp paper talks about spontaneous emission. Also Jaynes did some "additions" to standard semiclassical theory, sort of put in a half photons worth of noise to take into account the vaccum fluctuations. That actually gets you a real long way! BUT then that vaccum noise thats been put in "by hand" has real energy in it and can make detectors click, so it gets something fundamentally wrong. So I wonder if I can trick things to make photoelectrons instantaneous, but gets something else really screwy.
I'm remembering that the transition probability amplitude for a two-level transition looks like [sinc (Delta omega*t)]t. If I square that, and integrate over a wide range of frequencies, I get a transition probability that goes as t, for a constant rate, and thats true. But if there is a finite bandwidth in any sense, there is then an early time where the transition rate is not constant, I need to go back and look at Marlon's paper, I wish I had his Laser Physics book here at home. I wonder if this makes things not be instantaaneous, that is the rate is NOT constant early on.
I know that the constant transition rate comes about after a time integral, where T->infinity, to derive Fermi's golden rule. Now the time blurring can also be accomplished by a frequency blurring, which is why Doppler broadening will allow rate equations to be used for treatments of lasers. If there is no frequency broadening, then the rate is not constant.
One things for sure, it is much more subtle than is let on in a typical sophomore modern physics book, then in the senior level books on perturbation theory, they don't take the care to point out "look we kind of lied to you two years earlier!"
I think its not instantaneous, as in zero delay time. The integral over frequencies from zero to infinity would give a constant rate. But the lower limit of the integral is not zero but something like the work function/hbar. So that means the rate is a constant minus a piece (small albeit) that depends on time. I don't know unless I do the danged integral if it starts at zero at t=0. Some rough numbers give me a time that is pretty short, but the time delay till you get to the constant rate is intensity dependent so......