# Decay and scattering: What happens between the final and the initial state?

• Demystifier
In summary, QFT predicts well the probabilities of various final states for given initial states. Technically, this is described by the S-matrix, which is the unitary-evolution matrix describing the transitions from t=-infinity to t=infinity. However, what happens in between at intermediate times is still unknown. It is possible that it is a continuous process or an instantaneous jump. If it is a jump, when and where exactly does it happen? In the detector? Or much before, during the collision itself? Can QFT answer these questions at all? Are these questions really physically relevant? Are they physical questions, or purely philosophical ones? I would say that yes, these are physical questions, but that they are

## What happens between the final and the initial state?

• Total voters
10
Demystifier
Gold Member
For processes of particle decay and inelastic scattering, quantum field theory (QFT) predicts well the probabilities of various final states for given initial states. Technically, this is described by the S-matrix, which is the unitary-evolution matrix describing the transitions from t=-infinity to t=infinity.
But what happens in between at intermediate times?
How exactly the initial particle(s) get transformed to the final particles?
Is that a continuous process or an instantaneous jump?
If it is a jump, when and where exactly does it happen?
In the detector? Or much before, during the collision itself?
Can QFT answer these questions at all?
Are these questions really physically relevant? Are they physical questions, or purely philosophical ones?

Here, I do not ask you to give, with a confidence, the final answer, but merely to express your opinion and intuition about it.

Demystifier said:
Are these questions really physically relevant? Are they physical questions, or purely philosophical ones?

Here, I do not ask you to give, with a confidence, the final answer, but merely to express your opinion and intuition about it.
Purely philosophical. There is no scientific way to talk about that, since it is not measurable by definition.

If string theory is correct, we could imagine things going continuously from one particle to another. It LQG is, we can on the contrary imagine things go in discrete steps... Well, my two cents.

Demystifier said:
For processes of particle decay and inelastic scattering, quantum field theory (QFT) predicts well the probabilities of various final states for given initial states. Technically, this is described by the S-matrix, which is the unitary-evolution matrix describing the transitions from t=-infinity to t=infinity.
But what happens in between at intermediate times?

My preference tends to go to option 3 here. However, probably for the
opposite reason as you might expect. Of course, One adds the amplitudes
and not the probabilities of the different diagrams. Thus: all of the diagrams
must be existing simultaneously.

So yes, subdividing a complex process in separate things we artificially label
"virtual particles" should be done always with this in mind.

Now, for me personally, this is ALWAYS the case when one artificially groups
an extended object together by giving it a single label. For real particles
just as well as for virtual particles!

Does the wave-function of a "real" particle at some space-time point
have a notion that is part of a "real" photon or a "real" electron? That is,
is each point in space-time effectively labeled as such, or is it just we
who put these labels there? Let me use a (rather different) metaphor:

Does a moving air-molecule have a notion that it is part of a spoken lie
or a spoken truth? We humans have absolutely no problem of grouping a
bunch of moving air molecules together and label them in such a way!
We do this on a daily basis!

Now for me there is always this artificiality in labeling extended objects
as a whole, and it is wrong to somehow assume that each individual part,
or point of the extended objects individually also bears this label physically.

In ths sense one could say that "virtual"particles are not so much more
artificial as "real" particles are.

This point of view has as a consequence that one can not take Unitarity as
something which is automatically implied. Rather, one has to find a physical
explanation of the effect.
Demystifier said:
How exactly the initial particle(s) get transformed to the final particles?
Is that a continuous process or an instantaneous jump?
If it is a jump, when and where exactly does it happen?
In the detector? Or much before, during the collision itself?

Yes, these are all the central questions.

The final state particles are typically monochromatic, with a momentum in
a given direction. This implies that one can define a rest frame where the
phase is synchronized: the same everywhere.

So, one might suspect that such a phase synchronization mechanism is
at the base of the projection process which selects one of the many
outcomes.

A photon in an interference experiment has multiple momenta (in different
directions) at each space-time point. Furthermore, it doesn't have a rest-
frame. Projecting out a monochromatic, single momenta state can only
take place during an interaction where the speed is less then c.

Demystifier said:
Can QFT answer these questions at all?
Are these questions really physically relevant? Are they physical questions, or purely philosophical ones?

I would give a non-pertubative QFT treatment a better chance.

QFT often uses a lot of simplifications. For instance the use transversal
photons which is a non Lorentz invariant treatment. (A transversal photon
has a longitudinal component in other rest frames.)

Spin polarization is generally handled in a purely statistical way:
An electron with a spin A has an X% chance to have a spin B. There's no
deeper physical explanation of these effects in QFT. Regards, Hans.

Hans de Vries said:
In ths sense one could say that "virtual"particles are not so much more artificial as "real" particles are.
I strongly disagree. A real particle can be measured. An air molecule can be trapped in a box. On the contrary, virtual particles are mere mathematical objects which can not, by definition, be measured.

humanino said:
I strongly disagree. A real particle can be measured. An air molecule can be trapped in a box. On the contrary, virtual particles are mere mathematical objects which can not, by definition, be measured.

Likewise, many physicists, (not me) will claim that the wave function of a
real particle is a mere mathematical object.

In many QFT textbook you'll find the claim, at one place or another, that:
"Most so-called real photons are, strictly speaking, virtual, in the sense that
they are emitted at one place and absorbed at another."

There is no way to distinguish, by measurement, that this process of
emission and absorption is different for real particles and virtual particles.

It is not impossible, "by definition", as you say. We don't "define" nature,
we just try to describe it.

Regards, Hans.

Hans de Vries said:
Likewise, many physicists, (not me) will claim that the wave function of a real particle is a mere mathematical object.
The unobservability of an absolute phase is at the heart of the so successful gauge principle. I am aware of the Aharonov-Bohm effect, but want to point out that this corresponds only to a phase shift. Actually, mere intereferences are already sufficient to understand that phase shifts are observable.
In many QFT textbook you'll find the claim, at one place or another, that:
"Most so-called real photons are, strictly speaking, virtual, in the sense that
they are emitted at one place and absorbed at another."

There is no way to distinguish, by measurement, that this process of
emission and absorption is different for real particles and virtual particles.
I have never considered this a serious difficulty. This is a rethorical argument. If you want me to accept that "real" photons have billionth of eV mass, I'm fine with that

Let me describe a fairly recent event in electron scattering. One photon exchange has been for decades taken for granted. I myself describe my data everyday by using a single virtual photon exchange. It so occurs that for some polarisation observables (that is, non averaging over spins) it has been shown that two photons eschange can produce a few percent deviations at 1 GeV scale. Older theoretician did not expect this to happen at all.

The way I picture it, truncating the infinite sum over Feynman diagrams is most of the time a very good approximation to what is actually happening, but interpreting single Feynman diagrams as real processes might be misleading. To me, the virtual particles are mere convenient tools.
It is not impossible, "by definition", as you say. We don't "define" nature, we just try to describe it.
Sure. But we define mathematical objects. As you pointed out, one can not, strictly speaking, measure a really real photon. But on the other hand, they are at first defined as massless, with regards to the Poincare group.

This is a very old debate, and as usually, most probably just a matter of taste

humanino said:
The unobservability of an absolute phase is at the heart of the so successful gauge principle. I am aware of the Aharonov-Bohm effect, but want to point out that this corresponds only to a phase shift. Actually, mere intereferences are already sufficient to understand that phase shifts are observable.
I have never considered this a serious difficulty. This is a rethorical argument. If you want me to accept that "real" photons have billionth of eV mass, I'm fine with that

Let me describe a fairly recent event in electron scattering. One photon exchange has been for decades taken for granted. I myself describe my data everyday by using a single virtual photon exchange. It so occurs that for some polarisation observables (that is, non averaging over spins) it has been shown that two photons eschange can produce a few percent deviations at 1 GeV scale. Older theoretician did not expect this to happen at all.

The way I picture it, truncating the infinite sum over Feynman diagrams is most of the time a very good approximation to what is actually happening, but interpreting single Feynman diagrams as real processes might be misleading. To me, the virtual particles are mere convenient tools.

I agree with this point of view. The way I see the whole Feynman diagram expansion is as a mere convenient trick to remember the mathematical expressions obtained from a perturbation expansion. Nothing more. I don't see virtual particles as being more "physical" than, say, the ghost particles generated by gauge fixing non-abelian gauge theories. Those are clearly unphysical but it's convenient to see their contributions as coming from loops containing particles obeying the "wrong" statistics.

Hans de Vries said:
There is no way to distinguish, by measurement, that this process of emission and absorption is different for real particles and virtual particles.

This is the heart of the issue. I agree.

humanino said:
If string theory is correct, we could imagine things going continuously from one particle to another.
I like this. See
http://arxiv.org/abs/hep-th/0702060
especially Fig. 1 that summarizes various possible answers to the main question of this thread.

I have voted option three, because I feel that QFT already does a fairly good job, although it is far from perfect. Some tweaking and new phenomenology is necessary to create a much more precise and accurate QFT that WILL consistently and accurately describe the workings of every interaction in between the initial and final states (with very minimal errors, of course). The sum of all applicable Feynman diagrams is a nice place to start, but I sometimes feel that the quark flavor transitions are a bit hairy in QFT, and I have often wondered if the idea of composite quarks and leptons is viable and/or valid. Recent evidence against the null result for D0 - Dbar0 mixing is fairly ominous, and makes me think there is new physics phenomenology necessary here.

So, to sum it all up, I say yes to option three because I believe a more advanced and edited QFT will be able to describe the unseen inner actions between initial and final states...

mormonator_rm said:
I have voted option three, because I feel that QFT already does a fairly good job, although it is far from perfect. Some tweaking and new phenomenology is necessary to create a much more precise and accurate QFT that WILL consistently and accurately describe the workings of every interaction in between the initial and final states (with very minimal errors, of course). The sum of all applicable Feynman diagrams is a nice place to start, but I sometimes feel that the quark flavor transitions are a bit hairy in QFT, and I have often wondered if the idea of composite quarks and leptons is viable and/or valid. Recent evidence against the null result for D0 - Dbar0 mixing is fairly ominous, and makes me think there is new physics phenomenology necessary here.

So, to sum it all up, I say yes to option three because I believe a more advanced and edited QFT will be able to describe the unseen inner actions between initial and final states...

You have always posted exteremly interesting posts in the past so I can't help from using the opportunity to ask you what the situation is concerning D_0 Dbar 0 mixing?! What is going on there?

Patrick

I'm equally in favor of 3 and 4-that is, QFT may well do a good job, but who knows for sure?. Now there is, here I go again, a large literature on this subject, going back to the early days of scattering theory, when the Weiskopf-Wigner resonance structure was developed. When non-relativistic QM is included there is close to an infinite amount of work, particulary in quantum optics which deals with transitions taking place over finite times, and for which perturbation theory does not work well. The topic is huge.

See Cohen-Tannoudji --Atom-Photon Interactions, great on resolvants;Mandel and Wolf's book on Quantum Op
tics, great on non-perturbative problems. Regards,
Reilly Atkinson

.

nrqed said:
You have always posted exteremly interesting posts in the past so I can't help from using the opportunity to ask you what the situation is concerning D_0 Dbar 0 mixing?! What is going on there?

Patrick

Take a look at this URL; http://arxiv.org/PS_cache/arxiv/pdf/0704/0704.0120v2.pdf

BES-III has found evidence for D_0 - Dbar_0 mixing that is inconsistent with the null result by almost 4 standard deviations! This just came out on ArXiv on April 3rd.

You should also take a look at;
http://arxiv.org/PS_cache/arxiv/pdf/0704/0704.1000v1.pdf

The Belle Collaboration just posted this on ArXiv on April 7th. Looks like their figures for the mixing parameters "x" and "y" also show that the null result no longer appears valid.

Last edited by a moderator:

## 1. What is decay and scattering?

Decay and scattering are two fundamental processes that occur in particle physics. Decay is the spontaneous transformation of one particle into two or more different particles, while scattering is the interaction between particles that can result in changes to their direction, energy, or momentum.

## 2. How does decay and scattering affect the final and initial state of particles?

In both decay and scattering, the final state of particles is different from the initial state. In decay, the initial particle is transformed into other particles, while in scattering, the particles involved can change direction, energy, or momentum. These changes are governed by fundamental interactions such as the strong, weak, and electromagnetic forces.

## 3. What are the factors that influence decay and scattering processes?

Several factors can influence decay and scattering processes, including the type of particles involved, their energy, and the strength of the fundamental interactions. The masses and charges of the particles can also play a role in determining the outcome of these processes.

## 4. How do scientists study decay and scattering?

Scientists study decay and scattering using particle accelerators, which accelerate particles to high energies and collide them to observe the resulting interactions. They also use detectors to measure the properties of the particles produced in these processes and analyze the data to understand the underlying physics.

## 5. Why is understanding decay and scattering important?

Understanding decay and scattering processes is crucial for understanding the fundamental building blocks of matter and the interactions that govern the universe. This knowledge can also have practical applications, such as in medical imaging and cancer treatment, where the use of radioactive decay can help diagnose and treat diseases.

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