The streaks in the cloud chamber

One of the most convincing demonstrations of the particle nature of matter is the straight-line trajectories traced out in cloud chambers. How can you explain this with any kind of wave theory of matter?

One of the early great successes of the wave theory was the explanation of radioactive decay due to George Gamow. Gamow treated the uranium atom as a simple potential well, just like the ones we analyze in second-year physics. From the hyperphysics website, here is a picture of how it works:

This is the wave-theoretic explanation of how a uranium atom emits alpha particles, and it works very well. But what happens when we place the uranium atom next to a cloud chamber? According to this picture, the cloud chamber is innundated by a steady, ultra-low intensity alpha wave field, which decays over a period of some four billion years. During that same time period, the uranium, initially in its pritstine state, is subsequently found as a superposition of uranium and lead, with the lead component increasing gradually over that same four-billion year span. That's the wave picture of decay.

Ridiculous, you say? That seems to be the general opinion of the physics world. Following the Copenhagen interpretation, we reject the notion of a superposition of uranium and lead. We say that the wave picture represents merely the probability of a transition, and when a transition actually happens, it takes place with infinite suddenness. At once the uranium is gone, the lead is in its place, and a straight-line trace appears in the cloud chamber.

It's an interesting exercise to try and say exactly why the notion of a uranium-lead hybrid is so clearly impossible. Remember for one thing that such experiments are typically not carried out with single atoms, but with samples numbering in the millions or more. (With a mere million uranium atoms we would wait four thousand years for a single click in the geiger counter, so it would be an inconveniently small sample to work with.) Furthermore, there seems to be a respected point of view, based on density matrix theory, which holds that an ensemble of uranium mixed with lead is indistinguishable in principle from a corresponding ensemble of urnaium/lead superpositions. (I refer you to this discussion on stackexchange.com for more details).

But leaving aside the problematic question of the uranium/lead superposition, we are still left with the very vexing question: how can the wave theory of matter explain the straight-line tracks in the cloud chambers? Because according the wave picture, the cloud chamber is innundated by a very slow, steady, low-intensity alpha wave field. By what possible mechanism can this extremely tenuous field leave such obvious concentrated havoc in its wake? And if it can, why is it not doing it all the time and everywhere? Why do ionization events not occur here, there, and everywhere, continuously for four billion years? Why the lone single track, so clearly identifiable as a single concentrated particle?

In 1929, Nevill Mott published a paper that claimed to show the straight line tracks were not only consistent with the wave theory, but to be expected. Mott's analysis was widely recognized in its day, but it was not considered to be evidence of the wave nature of matter, nor did Mott intend it that way. His wave function is calculated in multi-dimensional phase space, and he clearly explains his analysis in terms of probabilities, with the wave function simply being used as a calculation tool to determine the probabilities of simultaneous ionization events. Following the Copenhagen school, Mott does not ascribe physical reality to his wave function.

I don't believe that physics takes place in multi-dimensional phase space. I believe it happens in real four-dimensional space-time, and that's where we have to be able to explain things. I don't see how you can have this intricate wave mechanics going on in abstract space, and then describe the physical reality by saying an alpha particle crashes into an obstacle and knocks out an electron. If that's all that's happening, then why do you need all that wave machinery to calculate it?

I think there must be a physical, real-time wave explanation to what goes on in the cloud chamber, and over the next few days I'm going to try and lay it out.

How does a Lemon Battery work?

I have been trying to figure out how batteries work ever since Mr. White (on Breaking Bad) started his van by using ground-up bits of zinc and copper to make a primitive battery. Everyone knows you can make a battery by sticking pieces of zinc and copper in a lemon. But why does it work?

Your Grade 9 science teacher probably wrote a chemical equation something like this, combining the two half-cell reactions for zinc and copper to get:

This would be fine except there is no copper in solution. This reaction works for the fully-developed zinc-copper cell with the copper strip immersed in copper sulfate solution, and the zinc strip immersed in zinc sulfate solution, and the two solutions linked by the "salt bridge". It really doesn't explain the lemon battery. (And it doesn't explain where Mr. White got ahold of copper sulfate solution for his battery.)

A thorough search of the internet confirms that it is the hydrogen ions from the acid, not copper ions, that participate in the reaction. Hydrogen from the citric acid is reduced at the copper electrode, consuming electons and completing the circuit. The copper has nothing to do with the reaction. (Maybe Mr. White used some no-name acid to complete his battery, but the episode was a little sketchy on that point.)

There's still one thing that bothers me. Why does the hydrogen gas only form at the copper electrode? Shouldn't it form just as readily at the zinc electrode? I can't find any explanation as to why it wouldn't, except for this article by Jerry Goodisman where he refers, near the very end, to the fact that Zinc is supposedly a poor absorber of hydrogen.

But if it was hard getting to the bottom of the lemon battery, it is much harder to figure out how the original Voltaic Pile of 1799 could have worked. The story is that Volta stacked copper and zinc discs and separated them with pieces of cardboard soaked in salt water. No copper sulfate, no hydrogen ions...just salt water. I've scoured the internet looking for anyone who has ventured to write a chemical equation to show what is going on, with no success. The closest I found was this article by Franco Decker, who alludes to the difficulties people had back in the 19th century trying to explain it, and concluding that no one was successful until Nernst published his analysis of the reaction in 1890...almost a hundred years after the fact! But then, Decker goes on to analyze the pile assuming an acidic electrolyte. Well, it's easy to see what happens if you use an acid...it's the same as the lemon battery. What I still can't figure out is how it worked originally with salt water.

Any ideas?

Lamb and Scully on Stern Gerlach

About a year ago I posted some articles about how the traditional explanation of the Stern Gerlach experiment is all wrong. Everyone says you shoot a beam of silver atoms through the apparatus and it splits into two beams. So if you put a screen up and collect the atoms, you get two silver dots on the screen.

There is no such experiment. It can't be done. I explained this last year, and drew a very nice picture of exactly what the beam does. You don't get two dots on the screen; you get a donut that looks like this:

 

Actually, that's the picture for a polarized beam...one where the silver atoms are pre-selected so they're all spin-up. I even worked out the wave equation, expressed in terms of the angular dependence of phase. It looks like this:

 

At least that's what I figured out. I haven't found any source to confirm my result...until today. I was reading the Wikipedia article on the Stern Gerlach experiment and it included a link to this article by Lamb, Scully and Barut.   (It's a Springer article and I was pretty surprised when it opened up without me having to pay for it.) The article is from 1987 and the authors make pretty much the same point I was making last year, and they also come up with an equation for the wave function. Here is the equation they give:

I don't know about you, but I can't exactly figure out what it all means.The beta's which they are summing over seem to be the spinor components, so I think they are treating the case of the unpolarized beam.  It's quite possible that this formula is saying exactly the same thing as my much simpler formula, but I just can't tell. The quadratic in the argument of the exponential almost suggests to me that they're trying to actually follow the wave function of the silver atom as it passes through the lengthwise magnetic field, whereas my function is essentially the far-field outcome. But it's all just a little over my head.

So I'd be interested if anyone can tell me: based on the result from Lamb and Scully, is my formula right or wrong?