Are Feynman Diagrams in MWI Just Mathematical Tools or Realities of Existence?

[tzimie]

Please check my logic.

1. Feynman diagram is a tool to calculate 'final state' from an 'original state'. It is mostly used for simple processes, like scattering.
2. 'Final state' usually have a precise meaning due to observation of particles trajectories.
3. However, in MWI there is nothing special about measurement and evolution is unitary, so time of the 'final state' can be chosen arbitrary.
4. Also, (having an infinite computation power) we can shift time of the final state to, say, 1 day after the initial state.
5. So (again having infinite computation power) we take an isolated spaceship today and calculate its final state one day later in terms of MWI, which of course, contain different decoherenced 'branches'. However, as evolution is unitary, we can do it.
6. Traditional view of what is inside Feynman diagram between initial and final states is 'virtual particles' which are 'just math', just mathematical tool to calculate a final state.
7. However, an astronaut, lived that day on that spaceship, would definitely not agree with the claim that his whole day was 'virtual' and 'just math'

 

[Demystifier]

All correct, except 2: In the final state one observes the final position/momentum, not the whole trajectory.

Note also that "final" state in scattering really means "after a time much longer than duration of the scattering interaction". This is really a very short time, only a tiny fraction of a second.

 

[tzimie]

Thank you. Yes, trajectory in fuzzy camera is just a sequence of position measurements.
But #6 and #7 are still valid?

Personally I don't find it strange and I don't see any problems viewing unitary evolution in MWI as some sort of "unbounded" F.D.
But it contradicts the traditional view "Stop thinking about virtual particles as something real! It is a myth created by popular books! They are just math! Go and learn math!"

 

[nikkkom]

7. However, an astronaut, lived that day on that spaceship, would definitely not agree with the claim that his whole day was 'virtual' and 'just math'

Why not? If someone believes that there exists a mathematical model which describes Nature perfectly, then the model and Nature itself are isomorphic. Then *everything* is 'just math'.

 

[tzimie]

Why not? If someone believes that there exists a mathematical model which describes Nature perfectly, then the model and Nature itself are isomorphic. Then *everything* is 'just math'.

Sure - I like Mathematical Universe Hypothesis.
But I am trying to understand the meaning (in the context) of the claim that "virtual particles are just math" (... which usually means "contrary to "real" particles).
What is a definition of virtual particles in MWI+MUH then?

 

[Demystifier]

Personally I don't find it strange and I don't see any problems viewing unitary evolution in MWI as some sort of "unbounded" F.D.
But it contradicts the traditional view "Stop thinking about virtual particles as something real! It is a myth created by popular books! They are just math! Go and learn math!"

I think you misunderstood virtual particles. Yes, they are just math and nothing real, but not for the reason you think. The reason they are not real is not because they appear at intermediate times. There are real states at intermediate times, and they are solutions of the Schrödinger equation. Virtual particles, on the other hand, are not themselves solutions of the Schrödinger equation, but only an auxiliary tool in a calculation of those physical solutions.

I often use the following metaphor. Suppose that at some intermediate times you have 1 apple. That apple is real. But you can write
1 apple = -1 apple + 2 apples
In this case neither -1 apple nor 2 apples are real. Only 1 apple is real, while -1 apple and 2 apples are virtual.

 

[tzimie]

I think you misunderstood virtual particles. Yes, they are just math and nothing real, but not for the reason you think. The reason they are not real is not because they appear at intermediate times. There are real states at intermediate times, and they are solutions of the Schrödinger equation. Virtual particles, on the other hand, are not themselves solutions of the Schrödinger equation, but only an auxiliary tool in a calculation of those physical solutions.

I am afraid you are reading my mind. Yes, thank you for the explanation.
However, I still have few questions:

1. It appears quite mysterious that the whole bestiary of virtual particles mimics the bestiary of the Standard Model. Even more, these beasts use the same set of interactions and conservation laws. I understand that it is just a mathematical fact, but it makes people believe into the reality of the Interpretation, given by Mr. Feynman. So my next question is:

2. Can the viewpoint, given by Mr. Feynman in his popular book be accepted as some kind of Interpretation, in the same sense we have different interpretations of QM? Are there any issues with that Interpretation?

 

[Vanadium 50]

It appears quite mysterious that the whole bestiary of virtual particles mimics the bestiary of the Standard Model.

It's also not true. Show me a box of pomerons, and we'll talk.

(And, as an aside, the method of learning by posting a stream of incorrect statements, in the hope they will be corrected has been tried here before, never with great success.)

 

[Demystifier]

2. Can the viewpoint, given by Mr. Feynman in his popular book be accepted as some kind of Interpretation, in the same sense we have different interpretations of QM? Are there any issues with that Interpretation?

If by "Feynman interpretation" you mean interpretation in which virtual particles are "real", I don't think that any serious physicist takes such an interpretation seriously. One good reason for this is that virtual particles appear only in the perturbative method of calculation, while other methods of calculation do not lead to virtual particles. See also
http://lanl.arxiv.org/abs/quant-ph/0609163
Sec. 9.3.

 

[tzimie]

If by "Feynman interpretation" you mean interpretation in which virtual particles are "real", I don't think that any serious physicist takes such an interpretation seriously. One good reason for this is that virtual particles appear only in the perturbative method of calculation, while other methods of calculation do not lead to virtual particles. See also
http://lanl.arxiv.org/abs/quant-ph/0609163
Sec. 9.3.

I understand, but for, say, hardcore Macroscopic Objectivist everything in QM (including "real" particles) is just a method of calculation of probability and correlation between macroscopic events. What is a difference? Macroscopic Objectivist can say that everything in QM appears only in the calculation, so even particles can't be taken seriously at all. (let me play devil's advocate)

Also, "other methods of calculation" (unitary evolution of universal wavefunction + decoherence) do not lead to real particles ))) so talking about particles should be banned )))

 

[Demystifier]

I understand, but for, say, hardcore Macroscopic Objectivist everything in QM (including "real" particles) is just a method of calculation of probability and correlation between macroscopic events. What is a difference?

For such a hardcore macroscopic objectivist, there is probably no difference. But such people are quite rare.