What Determines Critical Boson Exchange Rates in Sub-Atomic Interactions?

[questionpost]

According to the mathematics of sub-atomic particles, unless your force parameters on them, their wave function extends indefinitely through space, so why is it that interactions only happen at certain distances? Is there some kind of critical boson exchange rate?

 

[Simon Bridge]

You have mixed up two models.
In wave-mechanics, we often use approximations in which wavefunctions have infinite tails on them because the math is easier and the inaccuracies are very small compared with our ability to measure stuff.

We "force" limits on our calculations because IRL there are imits on our measurements. eg. we may have a particle in a trap with a particular geometry but the particle is also certain to be found someplace inside the lab - thus, it's wavefunction cannot extend to infinity. Rather than compute the actual confining potential represented by the lab with all its atomic fields we can approximate it as an infinite square well.

However, you can have very long range interactions and results - look up "quantum entanglement" and "Bell's inequality". Interactions do not always happen "at certain distances".

But some do - so the question can be refined to: how come the short-range interactions are so short-range? In wave-mechanics this is because their operator is short-range.

In the standard model, which is a different model, interactions are governed by virtual particles. The range of the interaction is determined by the lifetime of the particle. Thus the range for an EM interaction is, potentially, infinite as photons do not decay.

The lifetime for massive virtual particles is well predicted by the uncertainty relation ΔEΔt≥h/2π ...

Thus the virtual boson life-times pop out as a kind of "property of space-time".

Why these times/energies and not some other times?
Well we don't know - that's just the universe we live in.
Maybe there are other Universes with people asking why they see their particular sets of physical properties?

You will notice that science is really crap at answering the "why" questions - we focus on the "how" and "where" and "when" type of questions and leave the "why" to philosophers.

 

[questionpost]

You have mixed up two models.
In wave-mechanics, we often use approximations in which wavefunctions have infinite tails on them because the math is easier and the inaccuracies are very small compared with our ability to measure stuff.

We "force" limits on our calculations because IRL there are imits on our measurements. eg. we may have a particle in a trap with a particular geometry but the particle is also certain to be found someplace inside the lab - thus, it's wavefunction cannot extend to infinity. Rather than compute the actual confining potential represented by the lab with all its atomic fields we can approximate it as an infinite square well.

This notion that a particle is not likely to appear outside of a lab would make sense, but what is actually stopping there form being a "probability" of it being outside the lab if there is uncertainty in it's position when it is not being directly measured? The notion that "if it's mostly likely to be found in a lab means it has a 100% probability of not being found in a lab" doesn't make sense to me. It would make more sense if you actually meant "it's a lot less likely to be found outside of the lab" due to how the wave-mechanics dies out over distance. But in those wave mechanics equations, isn't there a horizontal asymtote at y=0 and thus the probability never actually fades to 0 no matter how far away you are? Unless that is what you mean to go on to say with "infinite square well".

Or are you perhaps trying to say that because the probability get's so close to 0 at large distances that even though computer models predict it's probability at that range, that scientists generally throw it out because it's like considering the gravity of Pluto here on Earth?

However, you can have very long range interactions and results - look up "quantum entanglement" and "Bell's inequality". Interactions do not always happen "at certain distances".

But some do - so the question can be refined to: how come the short-range interactions are so short-range? In wave-mechanics this is because their operator is short-range.

In the standard model, which is a different model, interactions are governed by virtual particles. The range of the interaction is determined by the lifetime of the particle. Thus the range for an EM interaction is, potentially, infinite as photons do not decay.

The lifetime for massive virtual particles is well predicted by the uncertainty relation ΔEΔt≥h/2π ...

Thus the virtual boson life-times pop out as a kind of "property of space-time".

Why these times/energies and not some other times?
Well we don't know - that's just the universe we live in.
Maybe there are other Universes with people asking why they see their particular sets of physical properties?

You will notice that science is really crap at answering the "why" questions - we focus on the "how" and "where" and "when" type of questions and leave the "why" to philosophers.

I was thinking more of chemical reactions, cause I know virtual particle's exist, and the virtual particle for the electro-magnetic force does not have mass and therefore goes on indefinitely, so why wouldn't I be able to have a chemical reaction from really far away?

 

[Simon Bridge]

You can have a chemical reaction from really far away - it is just very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very unlikely. (And I don't think I used enough "very"'s).

The probability is so small that it has no impact on your chemical equations.
My strip of Al is more likely to react with the HCl in the test-tube with it that the H2SO4 in the bottle on the shelf. In fact "more likely" does not go far enough in describing how much more likely it is.

But do you understand the difference between a chemical reaction and an EM interaction?

Did you see the bit where I said these are approximations?

Some approximations are better than others - and some things are approximately zero to such a high degree that we call them zero and have done with it. If fact, when we say this and make these approximations we have to justify them. You'll see this all through the literature.

So what is your point?

So far most of your questions in these forums have involved basic misconceptions about how QM and physics in general works.
Eg. here you started out asking "Is there some kind of critical boson exchange rate?" pretty much in the same paragraph as you used a wavefunction description. I explain that these two description apply to different models, and then boson lifetimes, you reveal that actually you know about boson lifetimes and why this affects the range of interactions ... so why did you ask the question then? [that's a rhetorical question]

You are asking awfully fast and not waiting for one discussion before starting another ... even a related one.
Slow down - start from the more basic questions and let the answers you get inform your next questions.
You'll learn more and faster that way.

It will also really help to have some idea of where you are in your science education - it will help pitch replies to your level of understanding.

 

[questionpost]

You can have a chemical reaction from really far away - it is just very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very unlikely. (And I don't think I used enough "very"'s).

The probability is so small that it has no impact on your chemical equations.
My strip of Al is more likely to react with the HCl in the test-tube with it that the H2SO4 in the bottle on the shelf. In fact "more likely" does not go far enough in describing how much more likely it is.

Did you read the bit where I said these are approximations?
Some approximations are better than others - and some things are approximately zero to such a high degree that we call them zero and have done with it. If fact, when we say this and make these approximations we have to justify them. You'll see this all through the literature.

So what is your point?

Oh, I didn't have a point, I just thought that I would have to all of a sudden change my views again if it was actually true that a particle it'self literally had absolutely no probability outside of a lab.

But there's still the question that if the virtual particles for the EM force themselves travel indefinitely, why is this distance thing still the case? Why is it so unlikely for chemical reactions to take place with that in mind?

 

[Simon Bridge]

Why should it not be the case - just because it is long range does not mean the probability cannot fall off with distance.
Presumably you are quite happy with the idea that the Earth can be affected by the gravity of a distant galaxy but so weakly there is no need to account for it in computing orbits?

Do you know what a chemical reaction is? What it means to form a chemical bond?
You need to understand the relationship between the EM interaction and chemistry.
(Curiously, wave mechanics helps a lot here - hint: look at the potentials.)

You also should look at the wave-mechanics of quantum tunneling and reflection at a potential barrier.

 

[questionpost]

Why should it not be the case - just because it is long range does not mean the probability cannot fall off with distance.
Presumably you are quite happy with the idea that the Earth can be affected by the gravity of a distant galaxy but so weakly there is no need to account for it in computing orbits?

Do you know what a chemical reaction is? What it means to form a chemical bond?
You need to understand the relationship between the EM interaction and chemistry.
(Curiously, wave mechanics helps a lot here - hint: look at the potentials.)

You also should look at the wave-mechanics of quantum tunneling and reflection at a potential barrier.

Chemical reactions should occur if atoms are in some way "unhappy" with their current relationship or there is room for some orbital to take an electron with opposite spin, and the EM force of the protons along with room of the electron would allow an atom to give, take, or share an electron. I suppose covenlent bonds wouldn't really be possible at large distances, but theoretically if the EM force virtual particles go on indefinitely, why does it even die out by the square of the distance? Is it just literally how it spreads out over 3D space?

 

[StevieTNZ]

Just for clarify (for my own learning) - when describing an experiment in a lab with regards to a particle's position, because we're mainly concerned with a certain area of the universe - is it possible in principle that the particle is found outside the lab? When we're describing the area we're concerned with, in an approximation do we have probabilities that add to 1 that only include the lab area? And not using an approximation, we would factor in areas outside the lab?

 

[questionpost]

Just for clarify (for my own learning) - when describing an experiment in a lab with regards to a particle's position, because we're mainly concerned with a certain area of the universe - is it possible in principle that the particle is found outside the lab? When we're describing the area we're concerned with, in an approximation do we have probabilities that add to 1 that only include the lab area? And not using an approximation, we would factor in areas outside the lab?

I think what he's saying is that outside of a lab the probability of the experimental particle appearing is so close to 0 that scientists don't even consider it, or approximate that it is 0.

 

[Simon Bridge]

I think I need to be clear about this because there are several different descriptions and I have kind-of said both.

As Questionpost says, the probability of finding the particle(s) of interest is so small outside the lab we can treat it as zero to a very high degree of accuracy.

However - it is also possible to rig up an experiment so that the probability of finding the particle outside our equipment, at least for a time, is zero. For instance, a photon created inside a laser cavity has zero chance of being created, by the experimental setup, anywhere else.

Chemical reactions should occur if atoms are in some way "unhappy" with their current relationship or there is room for some orbital to take an electron with opposite spin, and the EM force of the protons along with room of the electron would allow an atom to give, take, or share an electron.

Nice one - now try for a scientific description in terms of quantum mechanics ... you want to express your answer in terms of wavefunctions, energy levels, and potential wells. Let's keep it simple and go for a reaction like: $\text{H}+\text{H}\rightarrow\text{H}_2$ ... how does that happen?

I suppose covenlent bonds wouldn't really be possible at large distances,

Why not? This reason is central to your understanding.

but theoretically if the EM force virtual particles go on indefinitely, why does it even die out by the square of the distance? Is it just literally how it spreads out over 3D space?

You are confusing two different things - in the standard model the EM force does not exist ... except as an interaction between a photon and an electron. The classical force with it's famous inverse square law is a macroscopic phenomenon which is only obeyed on average.

The probability that a particular charge feels a force from another particular charge is the sum over all paths of the amplitudes of all the possible ways a photon could find it.
This sum produces the inverse square relationship where there is spherical symmetry in the system. You can understand it by imagining the source sending out photons equally in all directions. The probability of an interaction will be proportional to the number of photons that are detected by the target particle - which is proportional to the number of photons passing through each unit area at that distance ... the photon flux density. You should be able to see that the flux density decreases with increasing area. Which is inverse-square.

It is more complicated than that but that gives you a mental picture of how the geometric symmetry of space produces an inverse-square law. It's also a pretty standard picture - I'm surprised you have not come across it before.

 

[StevieTNZ]

As Questionpost says, the probability of finding the particle(s) of interest is so small outside the lab we can treat it as zero to a very high degree of accuracy.

So we can in principle find it outside the lab. When we calculate the probabilities for the various positions in the lab, do the positions inside the lab add up to probability 1?

 

[Simon Bridge]

Depends on the experimental setup.
Generally the walls of the lab would represent a very large potential barrier in most experiments. Not always - certain neutrino experiments spring to mind for eg. Doesn't have to be that exotic - shoot a laser-beam at the Moon and the photons have a substantial chance of being found outside the lab.

Also realize that the kinds of potentials we use, especially the ones we give to students to study, are not intended to be exact models of every nuance of a system. They don't even take account of relativity.

Remember those v-t diagrams with the sharp corners (implying infinite forces) you learned to draw when you studied kinematics? What about the equation for charging a capacitor that implies the capacitor-voltage will never be exactly the supply voltage? Does anyone take any of these literally?

The wavefunction of a free particle says it has an equal chance of being found anywhere in the Universe. Is that reasonable of real particles or has the model left something out?

So you see there are two sides to this answer.
There's the theoretical framework and the experimental one.