Hydrinos - a skeptical look

Hydrinos: A State below the ground state this page found at http://www.freeenergies.org/bl/bwt/z/hydrino/hydrino.htm
this page is provided by Eric Krieg in order to show the skeptical response to hydrino claims by Randall Mills of BLP - Black Light Power
The Hydrogen Ground State

The central claim of Mills theory is that there exists a state of the hydrogen atom that is "below the ground state". Before immersing ourselves in Mills theory, lets ask ourselves the following question: What is the ground state and why do scientists believe it exists? In this short paper, we will briefly examine some basic theoretical reasons why there is a ground state. We will do so for the most part without referencing quantum mechanics, with the exception of using Heisenberg’s uncertainty principle. Beyond that, we will rely on standard, basic physics that is well-established, both theoretically and experimentally.

In the simplest terms, the ground state is the state of lowest energy a system can have. In the case of the hydrogen atom, this is the lowest energy that the electron will have when bound to the nucleus. It may have been awhile since you’ve had basic chemistry, so let’s recall that the run of the mill hydrogen atom is simply a proton (the nucleus) with a single electron. This electron is "bound" to the nucleus, like the earth is bound to the sun. In a certain basic sense, you can view the electron as being in orbit about the central proton.

We can gain some insight into the ground state of hydrogen by considering some very basic physics¹. What we will do is find out what the energy of the electron is and consider the minimum orbit that electron can have about the proton. Next, we will use the uncertainty principle to see what kind of constraints such an orbit will have on the momentum of the electron. Finally we will use the minimum orbit to determine what the ground state energy of the hydrogen atom is. These values can all be looked up in a book, but we won’t color our efforts by saying ahead of time what they are. Instead we will just see if a basic and reasonable approach will lead us to the known answers, and rule out the possibility that there is a lower energy, the "fractional" hydrino state that Mills promotes.

First, I am sure that the reader will agree that the following is true of a bound system:

Total energy = kinetic energy + potential

We can write the kinetic energy as:

Now, using the basic relation p = mv this is just:

To find the total energy of the electron, we need to know what the potential is. The potential can be found using the basic ideas of electricity and magnetism. This is something that can be easily determined since the electron is simply in the potential of the proton, which we can just consider as a point charge. Recalling that the electron and proton both have the same charge (in magnitude) and calling this charge q, the electric potential energy of a two charge system is²:

(the negative sign reflects the fact that the electron is bound to the nucleus). To simplify writing, we make the following definition:

So the potential is just:

Now, recalling the expression for the total energy:

Total Energy = kinetic energy + potential

Calling the total energy E and using the values obtained for the kinetic and potential energies, we have:

We can obtain some useful information from this expression without getting involved with any complicated physics. For example, readers who have had calculus will recall that you can obtain the location of the minimum of a function of x (call that location x_o)

by taking its derivative and setting it equal to zero:

df/dx = 0 at x = x_o

We will apply this simple procedure, which is just straightforward mathematics, to the energy of the hydrogen atom we just derived. To do so we will consider the energy to be a function of position, E = E(r). But first we need to consider the uncertainty principle to see if there are any constraints on momentum given a particular position of the electron.

The uncertainty principle of quantum mechanics states that:

where is plank’s constant ³, is the uncertainty in position and is the uncertainty in momentum. For the situation at hand, the position is the size of the orbit of the electron. Let’s say it is at some value, say r. Using the uncertainty principle, the momentum is:

Plugging this value into our expression for the energy, we have:

Now, using basic calculus, lets find the minimum value of r:

Moving the first term to the left hand side:

Now we can solve for the minimum value of r, which we will call r_o:

This result turns out to be the Bohr radius. This is a pretty amazing result, considering that up to this point we have not done anything spectacular or appealed to any breakthrough or revolutionary physics. Basic, ordinary calculus, that is beyond dispute, tells us this is the value of r at the minimum of the energy. It cannot be any smaller, so there is no way a "fractional state" can exist. Let’s briefly review the steps we took:

We started with the energy of the electron and used the fundamental fact that total energy = kinetic energy + potential energy
We used the well established laws of electricity and magnetism to state what the potential of the electron-proton system is.
Next we took the uncertainty principle to get an order of magnitude estimate of what the momentum of the electron would be for a given orbit. We did not specify what that orbit was, we simply called it r, so it could be anything.
Finally, we used ordinary calculus to find the minimum value of r by taking the derivative of E and setting it equal to zero.

I would challenge Mills or any of his supporters to argue against any of these points. Will hydrino advocates dispute that total energy = kinetic + potential? There may be some free energy gurus that might, but most of us would probably agree that this is a true statement. Mills and his supporters would also probably agree with step 2, the potential of the electron can be correctly arrived at from simple E & M theory (in fact Mills makes it clear he supports the theory of electrodynamics, as promoted in Jackson). Arguing against step 4 to find the minimum value of r would also be foolish, finding the minimum of a function using such a method is a well-established cornerstone of calculus.

That leaves only the uncertainty principle. My suspicion is that Mills would dismiss using the uncertainty principle to arrive at our value for the momentum of an electron at radius r. This is a fallacious argument, however. The uncertainty principle is well established experimentally and is well grounded in basic mathematics. Nearly a hundred years of experiment and observation have confirmed that the uncertainty principle is in fact a cornerstone of physical law.

At this point we have used ordinary calculus to find the smallest value of r that is possible. We can plug this value back into our equation for E to get the minimum energy:

This is in fact the ground state energy of hydrogen, with quantum number n = 1. Mills claims smaller values of energy can be obtained from fractional states, say with n = ½. But in fact, smaller values cannot be obtained, because this would violate all we have done up to this point.

One could of course argue that this is all theoretical and it is experiment that determines what is true and what isn’t. And that is certainly the case, and experiment clearly shows that hydrogen does have a ground state, and that the energy of this ground state is in fact equal to the theoretically predicted value. Any further argument by Mills amounts to the same types of arguments held by supporters of perpetual motion machines and their ilk.

References

1. The basic derivation here follows that outlined in Claude Cohen-Tannoudji, Bernard Diu, and Franck Laloe, Quantum Mechanics: Volume One. Hermann and John Wiley & Sons, Paris (1977).

2. Halliday and Resnick, Fundamentals of Physics, Third Edition (New York: John Wiley & Sons, Inc.), see pages 603-604 "Electric Potential Energy".

3. For an explanation of the uncertainty principle, see Richard L. Liboff, Introductory Quantum Mechanics, Third Edition. Addison-Wesley, New York (1997). We assume for the purposes of this argument that the uncertainty principle is valid, as has been determined by a century of experiment and observation.

Links
Black Light Power, Inc. -the official page
go back to the main hydrino page-the main skeptical page

Other links of interest:

Tom Bearden’s MEG device A rational review of meg claims and Randi’s info and my info

. free energy scams Tback to Eric's main Dennis Lee page what about Joe Newman? Also, Amin, Mills (who may be legit?) Tilley, Perendev, Bearden Lutec and Tewari Xogen and GWE Adams Hamel