Exotic Matter

[tomBitonti]

In a quantum mechanical sense, that's what the double-slit experiment already does.

Ok, but the objection was that a mirror would cause problems. If it is unnecessary, then remove it from the setup. The goal was to create places where particles from either slit had a probability of reaching with the same travel time.

I think what is throwing me off is that having an amplitude to reach a coordinate along two paths is not to say that the particle traverses both paths simultaneously, at least not in an everyday sense.

Thx!
TomB

Thx!
TomB

 

[freyar]

Ok, but the objection was that a mirror would cause problems. If it is unnecessary, then remove it from the setup. The goal was to create places where particles from either slit had a probability of reaching with the same travel time.

That also happens in the regular double-slit experiment. As Umbran says, the interference pattern is a type of basic quantum mechanical "interaction" but not the type of scattering that I was talking about above.

I think what is throwing me off is that having an amplitude to reach a coordinate along two paths is not to say that the particle traverses both paths simultaneously, at least not in an everyday sense.

Right, the "everyday sense" is the issue. There's a mathematical formulation due to Feynman that looks like the particle takes every possible path simultaneously, but that's far from the whole picture.

 

[Umbran]

I think what is throwing me off is that having an amplitude to reach a coordinate along two paths is not to say that the particle traverses both paths simultaneously, at least not in an everyday sense.

Yes, but as soon as you start talking about quantum mechanics, you have to remember that "the everyday sense" probably does not apply. Your intuition is formed and trained using your observation of the slow-moving, macro-world - the world of baseballs and pool tables. And quantum objects just *don't* follow the same behaviors.

For example, you say above: "having an amplitude to reach a coordinate along two paths is not to say that the particle traverses both paths simultaneously".

But, the double-slit experiment exists to demonstrate and maximize the *WAVE* nature of light or matter. In this setup, discussing the *particle* traversing anything is going to confuse you, because it isn't behaving at all like a particle.

 

[tomBitonti]

Yes, but as soon as you start talking about quantum mechanics, you have to remember that "the everyday sense" probably does not apply. Your intuition is formed and trained using your observation of the slow-moving, macro-world - the world of baseballs and pool tables. And quantum objects just *don't* follow the same behaviors.

For example, you say above: "having an amplitude to reach a coordinate along two paths is not to say that the particle traverses both paths simultaneously".

But, the double-slit experiment exists to demonstrate and maximize the *WAVE* nature of light or matter. In this setup, discussing the *particle* traversing anything is going to confuse you, because it isn't behaving at all like a particle.

Yeah.

What kindof still throws me is that if we put two double slits facing each other, and sent different particles through each at the same time, there is a probability that the particles will scatter, at locations as determined by the diffraction pattern across the line of intersection of the streams. And if you split a stream of particles and sent through through the slits, if there were many particles at once, there would be scattering, but for just one particle at a time there won't. Then, there is a bit of care needed when representing what is happening, in that an approximate description of what is happening, which works for multiple particles, doesn't work for sending one particle at a time. I think this ends up being a matter of how to interpret an amplitude and what that means for just one particle vs. how it is used for multiple particles.

Thx!
TomB

 

[freyar]

What kindof still throws me is that if we put two double slits facing each other, and sent different particles through each at the same time, there is a probability that the particles will scatter, at locations as determined by the diffraction pattern across the line of intersection of the streams. And if you split a stream of particles and sent through through the slits, if there were many particles at once, there would be scattering, but for just one particle at a time there won't. Then, there is a bit of care needed when representing what is happening, in that an approximate description of what is happening, which works for multiple particles, doesn't work for sending one particle at a time. I think this ends up being a matter of how to interpret an amplitude and what that means for just one particle vs. how it is used for multiple particles.

We should be careful by what we mean by the word "interacting." When I, as a physicist, talk about interference in a double-slit experiment, which as Umbran says is a manifestation of the wave nature of particles, I do not mean an interaction. The idea is that a wave passing through the slits naturally has some points where it will be zero. On the other hand, an "interaction" is what it sounds like --- two different things interacting with each other (ie, doing things together). Mathematically, the universe can tell the difference between one and two particles.

 

[Umbran]

What kindof still throws me is that if we put two double slits facing each other, and sent different particles through each at the same time, there is a probability that the particles will scatter, at locations as determined by the diffraction pattern across the line of intersection of the streams.

And if you split a stream of particles and sent through through the slits, if there were many particles at once, there would be scattering, but for just one particle at a time there won't.

I think I may now have a more clear picture of what you mean... but that leaves me going, wha? I'm not sure why this is a question.

If you send a bazillion particles through the slits, you have roughly a bazillion chances for scattering. If you reduce it down to one particle at a time, you reduce your chances of interaction to nigh zero, simply because the number of particles to interact with is near zero.

The classical model may help us here:

Take two nerf guns, and point them at each other. Nerf guns aren't terribly accurate, so there's a lot of scatter from shot to shot. Turn them on full-automatic fire, and let them run. You'll see some darts bouncing off each other, because there's darts all over the place. Compare this to having each gun shoot only one dart. What's the chance that those two darts will just happen to hit each other? Very small.

Now, for your reflective surface case -

Take one of the guns, and fire it at a wall. Darts will bounce back from the wall. If you have this on full-auto, some bouncing darts may collide with new incoming darts, again, because there's a bazillion darts flying around to run into. But, if you go to single shot, a dart that bounces *has no incoming dart to collide with*. It *can't* scatter off itself in that sense. If you have it on slow-auto, the chance of the bouncing dart colliding with a new incoming dart is still extremely small, simply because the chance that those two will be in the right place is very small.

 

[tomBitonti]

I think I may now have a more clear picture of what you mean... but that leaves me going, wha? I'm not sure why this is a question.

If you send a bazillion particles through the slits, you have roughly a bazillion chances for scattering. If you reduce it down to one particle at a time, you reduce your chances of interaction to nigh zero, simply because the number of particles to interact with is near zero.

The classical model may help us here:

Take two nerf guns, and point them at each other. Nerf guns aren't terribly accurate, so there's a lot of scatter from shot to shot. Turn them on full-automatic fire, and let them run. You'll see some darts bouncing off each other, because there's darts all over the place. Compare this to having each gun shoot only one dart. What's the chance that those two darts will just happen to hit each other? Very small.

Now, for your reflective surface case -

Take one of the guns, and fire it at a wall. Darts will bounce back from the wall. If you have this on full-auto, some bouncing darts may collide with new incoming darts, again, because there's a bazillion darts flying around to run into. But, if you go to single shot, a dart that bounces *has no incoming dart to collide with*. It *can't* scatter off itself in that sense. If you have it on slow-auto, the chance of the bouncing dart colliding with a new incoming dart is still extremely small, simply because the chance that those two will be in the right place is very small.

The issue is how to reason about the motion of the particle after it passes through the double slits. One chooses a mode of reasoning, then uses it to determine expected outcomes, then compares those outcomes with experimental results as a test of the mode of reasoning.

Then, there is an equation which describes the probability of a particle being at a particular location (for a certain class of measurements), and an amplitude (for a different class).

For a self intersection, how do we decide to use probabilities instead of amplitudes? We use amplitudes for the particle arriving at a detector. We use simple probabilities for the particle interacting with itself. Why? What is different about these two types of events?

Edit1: Let me ask in this way: When a particle moves through a double slit, can we describe the motion as the particle moving simultaneously through both slits? Or, must we say that a field describing the probable location of the particle moves through the slits simultaneously?

Edit2: The line of reasoning that led to the question of self-interaction was the possible interaction of two photons in free space, where the two EM fields have a chance to interact with a virtual electron. The local description of that interaction: Two EM fields meeting in free space, seems exactly the same -- locally -- as the interaction of two segments of the EM fields of a single photon.

Thx!
TomB

 

[Umbran]

For a self intersection, how do we decide to use probabilities instead of amplitudes? We use amplitudes for the particle arriving at a detector. We use simple probilities for the particle interacting with itself. Why? What is different about these two types of events?

Well, note something - the amplitude is a *probability* amplitude. Square the modulus of the amplitude, and you get a probability (well, probability density, at least).

In fact, if we are going to talk about actual measurements, we eventually have to talk about probabilities - the probability of a thing arriving in and being seen by a detector. The amplitude is a non-physical thing, and outright imaginary number. In the basic double-slit, we eventually talk about the *probability* that the particle will strike a particular point on the screen. In a scattering interaction, we discuss the "cross section" (basically, again, the probability) for the scattering to occur. And, in both cases, before we can arrive at the probability, we work with the amplitude that we will have to square.

 

[tomBitonti]

Well, note something - the amplitude is a *probability* amplitude. Square the modulus of the amplitude, and you get a probability (well, probability density, at least).

In fact, if we are going to talk about actual measurements, we eventually have to talk about probabilities - the probability of a thing arriving in and being seen by a detector. The amplitude is a non-physical thing, and outright imaginary number. In the basic double-slit, we eventually talk about the *probability* that the particle will strike a particular point on the screen. In a scattering interaction, we discuss the "cross section" (basically, again, the probability) for the scattering to occur. And, in both cases, before we can arrive at the probability, we work with the amplitude that we will have to square.

Yes. There is a careful consideration, though, of whether to add the amplitudes then square (interference) or if to square the amplitudes then add (no-interference). For indistinguishable contributions, we add the amplitudes first. For distinguishable contributions, we square first. I'm fitting this to the virtual particle photon-photon interaction, and am using the double slit case to test my understanding.

Thx!

 

[freyar]

The issue is how to reason about the motion of the particle after it passes through the double slits. One chooses a mode of reasoning, then uses it to determine expected outcomes, then compares those outcomes with experimental results as a test of the mode of reasoning.

Then, there is an equation which describes the probability of a particle being at a particular location (for a certain class of measurements), and an amplitude (for a different class).

For a self intersection, how do we decide to use probabilities instead of amplitudes? We use amplitudes for the particle arriving at a detector. We use simple probabilities for the particle interacting with itself. Why? What is different about these two types of events?

Actually, no, we also use amplitudes to describe the interactions of particles. It's all quantum mechanics, and the calculation always proceeds by finding the amplitude and then squaring for the probability. If you're familiar with Feynman diagrams, those are all amplitudes. In fact, not all the calculations would be self-consistent if it weren't for specific cancellations and additions between the diagrams.

Edit1: Let me ask in this way: When a particle moves through a double slit, can we describe the motion as the particle moving simultaneously through both slits? Or, must we say that a field describing the probable location of the particle moves through the slits simultaneously?

Both, if I understand what you mean. There are two equivalent mathematical ways to describe a particle in a double slit experiment. One is to solve the Schrodinger equation (or appropriate relativistic generalization) describing the wavefunction in the experiment. That automatically shows you the constructive and destructive interference. The other method is to consider every possible path through the experiment (including weird discontinuous paths) with an amplitude assigned to each path, which you add up to find the interference patterns. In a usual double slit experiment, the straight-line paths through the slits are the main contributions.

Edit2: The line of reasoning that led to the question of self-interaction was the possible interaction of two photons in free space, where the two EM fields have a chance to interact with a virtual electron. The local description of that interaction: Two EM fields meeting in free space, seems exactly the same -- locally -- as the interaction of two segments of the EM fields of a single photon.

I think the reason it seems that way is that you don't have the full mathematical description. The wavefunction of two photons is not mathematically the same as the wavefunction of a single photon. In fact, they don't even depend on the same number of variables. Locally, it's still different