k98sven's Journal: More cold fusion nonsense

This is basically an addendum to my previous journal entry.
(So read it first, if you want to know where I'm coming from here..)

In the latest "Cold fusion for real!" story on Slashdot, several commenters pointed out (without any justification) that they think the Coulomb barrier (that's the like-charges-repel force) stopping two nuclei from getting close enough to fuse can be overcome by tunneling.

Ok.. well I guessed someone would say that. The simple answer is: NO.

Ok. But if you're not satisfied with that. Let's think about this. The first, big issue is that tunneling is not a novel idea when it comes to nuclear physics. So if someone thinks this is a 'new approach', they've only proven they don't know the first thing about this subject. (Again, I'm not a nuclear or plasma physicist, yet I know these things. That should tell you something.)

The first person to apply tunneling theory to nuclear physics (alpha-decay to be precise) was Gamow in 1928, Gurney and Condon in 1929.
(Quantum phyics itself was only formulated in 1925, so this counts as an early application)

And their models worked. Tunneling is the explanation to how alpha-decay occurs. Think about it: The Strong nuclear force holding the nucleus together is, well, STRONG.

How could any part of the nucleus break away and get out of there? Well, the answer is: The strong force (as I mentioned in my other entry) is extremely short-range. This means that the fragment only has to tunnel a very small bit, (and we're talking about ~1E-15 m here) until the coulomb forces overtakes the Strong force.

And this actually defines what the half-life of an isotope really is: A measure of the tunneling probablity!
(Google found this nice explanation. I didn't steal their material though, note they have the wrong year for Gurney-Condon's paper)

Now, here comes the kicker: If a particle can tunnel into the nucleus. It may just as well tunnel out of it. It's the same barrier.

So.. can a hydrogen nucleus, a proton, tunnel out? (proton emission) Yes it can. But only in very particular circumstances. It only occurs in some elements during the chain of radioactive decay, when there's lots of energy flying around, enough to give the protons in the nucleus enough 'height' to be able to tunnel through the barrier.

Proton emission does not occur in Helium-3 or Helium-4, which would be the products of our fusion. Protons can't tunnel out. Therefore, it does not seem reasonable to assume they can tunnel in, either. That would mean the only way in is the traditional way: get enough energy and run up and over the Coulomb barrier. This is of course what is done in 'hot' fusion. (the only kind we actually know of)

Resonance
Some commenters suggested that resonance phenomena would somehow change the tunneling probability. I have yet to understand how they intend this to occur, and that of course makes it difficult to respond to.

But, after thinking about it for a while, I realized that this is actually something which is appears completely silly. You cannot get two hydrogen nuclei close to each other with help from interference.

To begin with: they do not normally interefere with eachother. Waves can only resonate when they are identical. This applies to both quantum and classical mechanics. In quantum mechanics two wavefunctions are identical only if they have the same quantum numbers. (quantum numbers are basically the parameters of the wavefunction)

One of these parameters is spin. In normal conditions (e.g. in the absence of a large, and I mean really large magnetic field), at room temperature a group of protons will have randomly oriented nuclear spins. If two protons have different spin, they are not identical. So there is no chance of resonance for those ones.

But what if we did apply a magnetic field and gave them all the same spin? Couldn't they resonate onto eachother. Yes they could. But two nuclei cannot be in the same place at the same time. This is the "Pauli exclusion principle", which dictates that two particles with the same quantum numbers can't be in the same place at the same time. It is a fundemental postulate of quantum physics. Being a postulate means that we have assumed it's true, but we can't prove it other than by experiment. However, this also means it's one of the most verified things in physics.

Nothing has ever been shown to violate it. And if it wasn't true, Quantum physics itself, which is built on this assumption, would also be false. And we don't know of anything which violates quantum physics.

Ok.. so what if they can't resonate exactly onto eachother, but sufficiently close? Not a chance. The closest two waves can interfere with each other constructively (resonance), barring zero distance, is one wave length. The wavelength can easily be calculated. It's de Broglie's formula lambda = h/p, where h = Planck's constant, and p = momentum. At room temperature the speed of a proton is on the order of 1000 m/s (fast, but they collide a lot), it's mass is about 1.66E-27 kg.

This means a wavelength of about 1E-10 meters. That very far from the 1E-15 meters they need to get within for fusion. In fact, it's the distance between two hydrogen atoms in an ordinary hydrogen-gas molecule.
(e.g. it's not even within the electron shell)

So my conclusion, again, is: Cold fusion is unrealistic pseudoscience.