B Measuring momentum and position in particle colliders

[Sophrosyne]

When we look at those pictures of colliding particles in particle colliders, we see a large collection of curves and lines radiating out from the point of collision, representing the new particles which have been created.

So two questions about this:

1) Why are these acting like particles in the detector, and not waves? They look like very distinct paths marked out by these particles. In other words, why does the wave function for these particles, no matter how small their mass, even as small as neutrinos, stay collapsed as distinct particles during the detection process?

2) It seems these lines are tracing both the velocities and positions of these resultant particles at any given point in time. But this would seem to violate the Heisenberg Uncertainty Principle regarding position and momentum, doesn't it?

 

[PeterDonis]

Why are these acting like particles in the detector, and not waves?

Because that's what the detector is measuring--it's measuring the particle aspects of these objects, not wave aspects. (A more detailed answer can't really be given at the "B" level.)

They look like very distinct paths marked out by these particles.

Distinct in a macroscopic sense, yes. But these particles are not macroscopic; there's plenty of room for position uncertainty in the observed tracks without violating the Heisenberg uncertainty principle.

why does the wave function for these particles, no matter how small their mass, even as small as neutrinos, stay collapsed as distinct particles during the detection process?

Collapse is an interpretation, which is not needed to analyze these experiments. The basic math of QM plus the properties of the detector are enough to explain why distinct particle-like tracks are observed.

Note also that neutrinos don't appear directly as tracks in the detectors; only their decay products do.

It seems these lines are tracing both the velocities and positions of these resultant particles at any given point in time.

No, they're not. You don't seem to appreciate how tiny these particles are, and how narrow a track can be in a macroscopic sense and still satisfy the Heisenberg uncertainty principle. I suggest trying to run some numbers.

 

[atyy]

1) Why are these acting like particles in the detector, and not waves? They look like very distinct paths marked out by these particles. In other words, why does the wave function for these particles, no matter how small their mass, even as small as neutrinos, stay collapsed as distinct particles during the detection process?

Each observation collapses the wave function. In order to get an observed trajectory or path, one must make multiple observations - one observation for each point in the path. Each observation collapses the wave function.

2) It seems these lines are tracing both the velocities and positions of these resultant particles at any given point in time. But this would seem to violate the Heisenberg Uncertainty Principle regarding position and momentum, doesn't it?

These path do not violate any of the uncertainty principles of quantum mechanics. Roughly speaking, position is not very accurately measured in these paths.

 

[Nugatory]

They look like very distinct paths marked out by these particles.

You might want to try googling for "Mott problem".

 

[Vanadium 50]

It seems these lines are tracing both the velocities and positions of these resultant particles at any given point in time. But this would seem to violate the Heisenberg Uncertainty Principle regarding position and momentum, doesn't it?

Doesn't violate it for baseballs, right? Why not?

 

[Sophrosyne]

Doesn't violate it for baseballs, right? Why not?

Because baseballs are supposedly not quantum-sized subatomic particles, whereas things like electrons apparently are. Why would an electron act like a wave when it's around an atomic nucleus, but not when it's in a particle collider?

The Mott problem, mentioned above, seems interesting. It seems this was initially a question even for the early pioneers of quantum mechanics, like Heisenberg. I am thinking the answer lies somewhere in the complex equations of quantum field theory, which were developed later. I guess I'm going to have to study those a little more for this to make sense on a more rigorous mathematical basis.

 

[Sophrosyne]

Each observation collapses the wave function. In order to get an observed trajectory or path, one must make multiple observations - one observation for each point in the path. Each observation collapses the wave function.
These path do not violate any of the uncertainty principles of quantum mechanics. Roughly speaking, position is not very accurately measured in these paths.

This makes some sense. Thank you.

 

[Vanadium 50]

Because baseballs are supposedly not quantum-sized subatomic particles, whereas things like electrons apparently are.

OK, let's take a step back. Why do electrons have a well-defined trajectory in your (old-style) television tube?

 

[Nugatory]

Why would an electron act like a wave when it's around an atomic nucleus, but not when it's in a particle collider?

That's not a very good description of the situation; the "wave-particle duality" it's based on was abandoned decades ago and you you won't find it any serious modern textbook. In the modern (meaning after 1930 or thereabouts) formulation of quantum mechanics, the electron follows the exact same quantum mechanical laws in both situations, and in neither does it behave "like a wave" or "like a particle". It behaves like an electron.

The Mott problem, mentioned above, seems interesting. It seems this was initially a question even for the early pioneers of quantum mechanics, like Heisenberg. I am thinking the answer lies somewhere in the complex equations of quantum field theory, which were developed later.

The Mott problem was indeed a problem in the early days of quantum mechanics. It's called the "Mott problem" because Mott solved it, and no quantum field theory is required.

 

[Sophrosyne]

OK, let's take a step back. Why do electrons have a well-defined trajectory in your (old-style) television tube?

To be honest, now I am not sure. But I am thinking of something like what happens in a camera as the light gets focused on the film. As the light is traveling from the lens to the fim, they are superposed probability waves. But when they hit the film, they are acting as discreet photon particles. You seem to be suggesting, from what I understand, that they follow discrete paths that we might theoretically be able to trace from the lens to the film, in the same way that the paths of the electrons are traced in the particle collider.

I guess I am too used to hearing about this idea of wave-particle duality. I have to read up on how this duality is now an obsolete way of thinking about these things. After all, this is how they still present things to the public in popular science articles. Do you have any recommendations for some reading on this?

 

[Sophrosyne]

That's not a very good description of the situation; the "wave-particle duality" it's based on was abandoned decades ago and you you won't find it any serious modern textbook. In the modern (meaning after 1930 or thereabouts) formulation of quantum mechanics, the electron follows the exact same quantum mechanical laws in both situations, and in neither does it behave "like a wave" or "like a particle". It behaves like an electron.

The Mott problem was indeed a problem in the early days of quantum mechanics. It's called the "Mott problem" because Mott solved it, and no quantum field theory is required.

I see. Looking up "the Mott Problem", this is something I found:

"Mott demonstrated that by considering the interaction in configuration space, where all of the atoms of the cloud chamber play a role, it is overwhelmingly probable that all of the condensed droplets in the cloud chamber will lie close to the same straight line. What is uncertain is which straight line the wave packet will reduce to; the probability distribution of straight tracks is spherically symmetric."
https://en.m.wikipedia.org/wiki/Mott_problem

This is fine. But as each individual atom in the cloud chamber is tracing out the path of the electron, it is revealing both its momentum and position simultaneously to a fairly high degree of certainty. The best answer for this I have seen here yet is that despite this, there is enough uncertainty in both to satisfy Heisenberg's uncertainty Principle.

 

[Vanadium 50]

it is revealing both its momentum and position simultaneously to a fairly high degree of certainty

Be quantitative. How high? Compare that with hbar.

 

[Sophrosyne]

Yeah, I see your point. Thanks.