# The Wave Equation IS the electron

1. Feb 7, 2005

### saltydog

"The Wave Equation IS the electron"

Hello everyone,
I've heard it said that well, "the Wave Equation IS the electron". Can anyone explain this to me? I know what the Wave Equation is (even solved a few of them) and have a degree in Chemistry but I probably would not be able to follow advanced QM dialog.

Thanks,
Salty

2. Feb 7, 2005

### dextercioby

You needn't know too much to tell that
1.The wave equation is an equation,a mathematical object,if u want to,an abstraction.It exists only on paper,in a computer,or in your mind.

2.The electron is a pointlike particle which experinces wave character as well.It has PHYSICAL RELEVANCE,it's not a mathematical abstraction.

Daniel.

3. Feb 7, 2005

### saltydog

Well, this was my rational for the statement:

The wave equation describes the dynamics of the electron. Would QM say that the wave equation "totally describes" the electron? I think so, and tell me if not. But if it does, then the wave equation describes a "dynamics" which exhibits itself in the substrate of "electron". I suggest that the essential property of the electron IS that dynamics independently of what the electron is made up of. My analogy: anything that acts like an electron (exhibiting the same behavior), IS an electron. The dynamics is all that matters and that dynamics is described by the wave equation. Ergo: the wave equation is the electron.

Salty

4. Feb 7, 2005

### dextercioby

Let's be specific:the time evolution of the quantum state of a SYSTEM is described by the wave equation.The time evolution of the quantum state of an ELECTRON is described by the wave equation FOR THE ELECTRON.

The state vector describes the quantum state of the electron.

I wouldn't make that assertion.

I would contradict you by telling you that an internal structure would affect the dynamics...

Yes.

Yes.

Nope.The wave equation for the electron is an equation,a mathematical abstraction.The electron is a particle...

Daniel.

5. Feb 7, 2005

### saltydog

Thanks Daniel, I don't remember where I read the statement and will try to track it down for further discussion. My summary was my own effort to explain it. I like your suggestion of how an internal structure might "affect" that idea.

Salty

6. Feb 7, 2005

### ZapperZ

Staff Emeritus
That doesn't make any sense. Next door to my office is a facility called the Intense Pulsed Neutron Source. Physicists describe beams of neutrons using a "wave equation". There are no electrons here!

The same can be said about the proton-antiproton beams in the tevatron at Fermilab.

In each of these, the wave equation can fully describe those two systems. Simply by these examples, I've already proven why what you heard is wrong.

Zz.

7. Feb 7, 2005

### dextercioby

For a second i really thought you were really assuming that the experimentalists would accelerate wave equations up to speeds close to "c" and then crash them and observe the fraction lines,the derivatives,the operators and the bra/kets coming out of the crashes by using sophisticated detectors... :tongue2: :tongue2:

Daniel.

8. Feb 7, 2005

### saltydog

That's pretty convincing . . .

Thanks,
Salty

9. Feb 8, 2005

### honestrosewater

What do you mean by "internal structure"? Can you give an example? Is internal structure something physics cannot model, even in principle?

10. Feb 8, 2005

### dextercioby

I didn't say it cannot model.It can model compound particles,but not in an elementary way.
Think of the proton as it was conceived b4 the '60's.Fundamental massive,spin 1/2,electrically charged particle.In principle,its dynamics & properties could be accounted for by the Dirac equation.Was i was simply saying was that,once the proton was discovered to have an internal structure,the Dirac equation and hence the initial dynamics could not account for the physics behind the proton.

Daniel.

11. Feb 8, 2005

### honestrosewater

I didn't say you did; I was asking.

12. Feb 8, 2005

### Tom Mattson

Staff Emeritus
Heh. This thread reminds me of the epic battles I used to have with Alexander, except he'd say that the wavefunction is the electron.

Another argument against this in addition to the ones that have already been presented is that it leaves no room for advances in our knowledge. You say that the wavefunction is the electron? But what about quantum field theory? Now is the electron the quantized field? But a wavefunction and a quantized field are not the same thing, so how can the electron be both?

The obvious answer is that neither the wavefunction nor the quantized field are identical to the electron. They are precise, quantitative conceptual tools that we used to describe electrons. And protons, and neutrons, and pions, Oh My!