What are Virtual Photons

[Johnny5]

I'm not talking about specific experiments' date=' I'm talking about [i']undeterminism[/i]. It basically says that there exist random physical states, not that there are multiple parallel futures. Your argument is not even against undeterminism. It is against one possible interpretation of it, and it's not even clear to me that that argument is sound.

 

 

 

That conclusion is perfectly compatible with undeterminism. In this interpretation, at any given moment, an electron has precisely one randomly decided location.

 

Well I wasn't talking about undeterminism, but since you bring it up...

 

the term 'random' is highly suspect. What does it mean to say something is random?

 

Suppose you drop an apple in earth's gravitational field, and you track the center of mass of the apple in some frame. What does undeterminism say about the path of the CM?

[Johnny5]

"Any statement is either true or false' date=' and no statement is true and false simultaneously." and "Not all sentences are statements" are asserted without proof.

 

The contradiction can also be that one or both of those two statements are false.

 

Basically, you've defined a statement to be something that must be either true or false, which is a subset of sentences. Your proof is a tautalogy.[/quote']

 

Yes, they are asserted without proof, because you can't prove them, you can offer numerous reasons for stipulating that they are true though. For what it's worth, I actually tried to prove that the basis of binary logic was true, using reductio ad absurdum, and learned I couldn't deductively prove the statement which is the basis of the logic I use, is true. All I could show clearly, was that there are at least two truth values. I couldn't show that there are at most two truth values.

 

They are what Aristotle would have called axioms, true statements which you don't prove.

 

I am just trying to express the basis of binary logic:

 

For any statement S: |S|=0 XOR |S|=1

For any sentence S: if |S|=0 XOR |S|=1 then S is a statement.

 

Nowhere does the basis of binary logic forbid statements from having a truth value which can vary in time.

 

 

 

In practice, we judge something to be a statement rather quickly, it is then the determination of its truth value which we spend most of our time on. As for how you determine whether or not some sentence is a statement, I will go with Tom on this, and say it's a highly random process in nature.

[Tom Mattson]

Severian, I'm with you except on a couple of points.

 

In a way it is completely the other way round. Since the propogation of a particle is inversely proportional to the square of [math]E^2-p^2-m^2[/math] an on-shell particle has an infinite life-time (since [math]E^2-p^2-m^2=0[/math]).

 

Gotcha.

 

Therefore it is actually impossible to observe a 'real' on-shell particle because in observing it you end its life. Any particle which we observe has a finite lifetime and is therefore 'virtual'.

 

Hold on: When you say "infinite lifetime"' date=' I take that as "perfectly stable against [i']decay[/i]", not "indestructible". That is, the particle that is detected would have an infinite lifetime if it were not interfered with. So say a real photon (on mass shell) is scattered off a proton, and then the outgoing (real) photon is detected. Do you say that the detected photon goes from being real to being virtual, just by being detected?

 

If you are unwilling to accept this, you still must accept that we have indirectly observed virtual particles in processes such as [math]e^+e^- \to Z^* \to \mu^+ \mu^-[/math]. This evidence is as direct as the evidence for quarks...

 

Yes, I accept the evidence for the massive vector bosons. Actually, I accept the predictions of QED as evidence of virtual photons, too. I'm just saying that the squiggly internal lines (that which we normally call "virtual photons") in the Feynman diagrams are actually components of a perturbation expansion.

[Tom Mattson]

Well I wasn't talking about undeterminism' date=' but since you bring it up...

[/quote']

 

Yes, you were talking about undeterminism. When you say that determinism is deducible, you are simultaneously saying that ~(undeterminism) is deducible.

 

the term 'random' is highly suspect. What does it mean to say something is random?

 

A random system is one whose time evolution is not predictable.

 

Suppose you drop an apple in earth's gravitational field, and you track the center of mass of the apple in some frame. What does undeterminism say about the path of the CM?

 

"Undeterminism" isn't a theory of mechanics. It's a feature of a particular theory of mechanics, namely the quantum theory of mechanics.

[Tom Mattson]

The correct conclusion is that S isn't a statement' date=' therefore it does not provide a counterexample, as JC suggested.

[/quote']

 

You could have saved yourself a lot of typing by just saying, "I don't accept that self-referential statements are statements at all."

[Johnny5]

Yes' date=' you were talking about undeterminism. When you say that determinism is deducible, you are simultaneously saying that ~(undeterminism) is deducible.

 

[/quote']

 

Well no, that's not what I proved. I proved that there is at most one possible next moment in time. I was interested in whether or not the Born interpretation of the quantum mechanical wavefunction led to any contradiction.

 

As I understood the interpretation, there were multiple possible locations an electron could be at the next moment in time, instead of only one. By proving that there is only one possible next moment in time, I succeeded in finding a problem with the Born interpretation.

 

As for whether or not where that electron will be obeys undeterminism, you are now focusing more on whether or not the motion of the electron follows some precise mathematical formula in some frame of reference. I didn't address that issue at all, and that's not what I meant by determinism.

 

You say that if I prove determinism then I can also prove not (undeterminism).

 

I don't see your reasoning, but then again I don't fully understand what you are referring to as undeterminism... but I have a pretty good idea. I just want to see if I am right.

[Tom Mattson]

Well no' date=' that's not what I proved.

[/quote']

 

LOL, I know that. I even said as much. But you said you could prove that determinism is deducible, and when I asked you "How?" you posted your argument.

 

You say that if I prove determinism then I can also prove not (undeterminism). I don't see your reasoning, but then again I don't fully understand what you are referring to as undeterminism... but I have a pretty good idea. I just want to see if I am right.

 

It's pretty simple, really. "Un" is a negation. So "undeterminism" means "not determinism". By the law of double negation, "not undeterminism" is determinism.

[Johnny5]

LOL' date=' I know that. I even said as much. But you [b']said[/b] you could prove that determinism is deducible, and when I asked you "How?" you posted your argument.

 

 

 

It's pretty simple, really. "Un" is a negation. So "undeterminism" means "not determinism". By the law of double negation, "not undeterminism" is determinism.

 

I am not reasoning on single words. Really, I try to figure out someone's model, in order to understand that individual.

 

I am pretty sure you mean to imply that according to undeterminism, there can be at most one possible location for the electron to be, but that where it will be is totally random. That's what I think you mean. You might as well just come out and say there are no laws of physics, so we should all stop doing physics.

 

Ok so the motion of an electron is random, if its time evolution is not predictable. Hmmm.

 

I assert that the motion of an electron obeys an ordinary differential equation, in the right reference frame.

[Tom Mattson]

I am pretty sure you mean to imply that according to undeterminism' date=' there can be at most one possible location for the electron to be, but that where it will be is totally random. That's what I think you mean. You might as well just come out and say there are no laws of physics, so we should all stop doing physics.

[/quote']

 

LOL, no. I thought you said somewhere that you studied quantum mechanics!

 

In QM we can predict the time evolution of the quantum mechanical state vector. We can not predict the outcome of a specific measurement of a system that is not in a pure eigenstate of the operator corresponding to that observable. Determinism does not at all appear to be sacred, and yet you claim that it is "deducible".

 

I assert that the motion of an electron obeys an ordinary differential equation, in the right reference frame.

 

I really couldn't care less about your assertion.

[Johnny5]

LOL' date=' no. I thought you said somewhere that you studied quantum mechanics!

 

[/quote']

 

I certainly did study it, enough to find the generating functions for the spherical harmonics of a hydrogen atom.

 

Separation of variables.

 

The text I used was a thick blue book, I think Resnick was one of the authors. The whole solution was contained in either chapter 7 or chapter 8, and the appendix.

 

They used the reduced mass mu.

 

And, for whatever it is worth, I didn't imitate their solution entirely, they used the Legendre polynomials at some point, and I had an alternate method, so on that part I did it my way.

[Tom Mattson]

The text I used was a thick blue book' date=' I think Resnick was one of the authors. The whole solution was contained in either chapter 7 or chapter 8, and the appendix.

[/quote']

 

That would be Quantum Physisc of Atoms, Molecules, Solids, Nuclei and Particles by Eisberg and Resnick. It's only a 3rd year undergraduate text, but just the same after having studied it one should know that this:

 

I am pretty sure you mean to imply that according to undeterminism' date=' there can be at most one possible location for the electron to be, but that where it will be is totally random. That's what I think you mean. You might as well just come out and say there are no laws of physics, so we should all stop doing physics.

[/quote']

 

...is absurd. The randomness exhibited in nature is not mutually exclusive to laws of physics, and QM is the proof. Now that really is a "QED".

[Johnny5]

That would be Quantum Physisc of Atoms, Molecules, Solids, Nuclei and Particles[/i'] by Eisberg and Resnick.

 

Yes that is the exact text. I still have it.

[Johnny5]

 

The randomness exhibited in nature is not mutually exclusive to laws of physics' date=' and QM is the proof. [/quote']

 

What about the quantum measurement problem?

[Severian]

Hold on: When you say "infinite lifetime"' date=' I take that as "perfectly stable against [i']decay[/i]", not "indestructible". That is, the particle that is detected would have an infinite lifetime if it were not interfered with. So say a real photon (on mass shell) is scattered off a proton, and then the outgoing (real) photon is detected. Do you say that the detected photon goes from being real to being virtual, just by being detected?

 

It doesn't make any difference. QED has something called crossing symmetry, which means that I can move a particle from the initial state into the final state (as an anti-particle) without changing the matrix elements. So probabilities associated with two electrons exchanging a photon are the same as those associated with an electron-positron annihilation to a photon together with the subsequent decay to electron-positron again. In other words a photon exchanged between two electrons [math]e^- e^- \to (e^- \gamma) e^- \to e^- (\gamma e^-) \to e^- e^-[/math] (if you see what I mean) need not be on-shell, and in exactly the same way as the decay processes it will generally pick a momentum-squared in line with how long it lived.

 

This is slightly confusing because its off-shellness is the same for the entire flight but how does it know the other electron is going to be there to absorb it? This is the same non-locallity phenomenon as collapsing the wavefunction in QM. With the decay it is not a conceptual problem because one simply imagines that the photon 'picks' a virtuality and then when its time is up (with Heisenberg knocking on the door) it must decay and so (being a well behaved photon) does. This nice conceptual picture is really not right though. In QFT what actually happens is that the photon picks all possible virtualities and only the one which works survives (in fact there is an integration over the virtuality in the equations).

 

Of course, they can be very nearly on-shell. The most on-shell photons we can observe are those coming from the 'surface of last scattering' which is the point just after the big bang when the universe first became transparent to photons. So the photons have been travelling for 14 billion years. Since that is a pretty long life-time they will be very very close to on-shell, but still not exactly....

[Tom Mattson]

What about the quantum measurement problem?

 

That's where the randomness shows up.

[Johnny5]

That's where the randomness shows up.

 

Alright, let me ask you this. What interpretation of QM do you use?

 

I want to hear what you have to say about wavefunction collapse.