Last time, I showed you that a simple quantum system, consisting of a single particle in a superposition of traveling from the left OR from the right, leads to a striking quantum interference effect. It can then produce the same kind of result as the famous double-slit experiment.
The pre-quantum version of this system, in which (like a 19th century scientist) I draw the particle as though it actually has a definite position and motion in each half of the superposition, looks like Fig. 1. The interference occurs when the particle in both halves of the superposition reaches the point at center, x=0.
Then I posed a puzzle. I put a system of two [distinguishable] particles into a superposition which, in pre-quantum language, looks like Fig. 2.
with all particles traveling at the same speed and passing each other without incident if they meet. And I pointed out three events that would happen in quick succession, shown in Figs. 2a-2c.
And I asked the Big Question: in the quantum version of Fig. 2, when will we see quantum interference?
- Will we see interference during events 1, 2a, 2b, and 3?
- Will we see interference during events 1 and 3 only?
- Will we see interference during events 2a and 2b only?
- Will we see interference from the beginning of event 1 to the end of event 3?
- Will we see interference during event 1 only?
- Will we see no interference?
- Will we see interference at some time other than events 1, 2a, 2b or 3?
- Something else altogether?
So? Well? What’s the correct answer?
The correct answer is … 6. No interference occurs — not in any of the three events in Figs. 2.1-2.3, or at any other time.
- But wait. . . how can that make sense? How can it be that particle 1 interferes with itself in the case of Fig. 1 and does not interfere with itself in the case of Fig. 2?!
How, indeed?
Perhaps thinking of the particle as interfering with itself is . . . problematic.
Perhaps imagining individual particles interfering with themselves might not be sufficient to capture the range of quantum phenomena. Perhaps we will need to focus more on systems of particles, not individual particles — or more generally, to consider physical systems as a whole, and not necessarily in parts.
Intuition From Other Examples
To start to gain some intuition, consider some other examples. Some have interference, some do not. What distinguishes one class from the other?
For example, the case of Fig. 4 looks almost like Fig. 2, except that the two particles in the bottom part of the superposition are switched. Is there interference in this case?
Yes.
How about Fig. 5. In this case, the orange particle is stationary in both parts of the superposition. Is there interference?
Yes, there is.
And Fig. 6? Again the orange particle is stationary in either part of the superposition.
No interference this time.
What about Fig. 7 and Fig. 8?
Yes, interference in both cases. And Figs. 9 and 10?
There is interference in the example of Fig. 10, but not that of Fig. 9.
To understand the twists and turns of the double-slit experiment and its many variants, one must be crystal clear about why the above examples do or do not generate interference. We’ll spend several posts exploring them.
What’s Happening (and Where)?
Let’s focus on the cases where interference does occur: Figs. 1, 4, 5, 7, 8, and 10. First, can you identify what they have in common that the cases without interference (Figs. 2, 6 and 9) lack? And second — bringing back the bonus question from last time, which now comes to the fore — in the cases that show interference, exactly when does it happen, and how can we observe it?
Next time we will start the process of going through the examples in Fig. 2 and Figs. 4-10, to see in each case
- How does the wave function actually behave?
- Why is there (or is there not) interference?
- If there is interference,
- where does it occur?
- how exactly can it be observed?
From what we learn, we will try to extract some deep lessons.
If you are truly motivated to understand our quantum world, I promise you that this tour of basic quantum phenomena will be well worth your time.
8 Responses
We find a reasonable result when we assume a continuously waving pilot wave field that is constantly correlated with the structures of the entire environment and updated according to its changes. A particle and quantum state entering the field interferes with the finished waving environment – neither with itself nor with its superposition. Symmetries and asymmetries are decisive. When the double slit considered, the interference pattern already exists – energy only makes it visible.
Those are nice words, but this is not very precise. Where precisely is the pilot wave?
Everywhere. I see that the pilot wave set by Bohm is an ad hoc rescue, but when the entire structural environment is understood as an environment of standing waves on average, the interferences are just waiting for energy and momentum pulses.
The field of unification is physically locally tense memory-structured, correlating, not only to the quantum statistics of the immediate environment, but also in the vacuum as a field continuum of matter particles, producing as the sum of its vacuum boost actions a proper accelerating continuum, in relation to which we see gravity as a coordinate system term, a virtual force.
Here described as a slightly more detailed idea. A publication of the whole is in preparation, probably getting out in the next summer.
This is still not clear. What is the “Everwhere” of which you speak. In these examples, everywhere means “everywhere on the x axis”?
Physics can only be done by being precise. Vagueness leads to mistakes.
Everywhere in and between all causal structures is the most precise hint i can give here.
Still, this is all math, Schrödinger’s equation, the “probability space”, but what is really, physically, happening?
Assumption 1: Everything is derived from “energy”.
Assumption 2: Energy is a thing, i.e. it has mass and momentum.
Assumption 3: The variables, time and position are illusionary manifestations of quantum entanglement, i.e. they are real, they are part of the math we humans use to try and characterize reality.
So, the obvious question then is: how can you create particles, fermions, which have mass and momentum from a waves, bosons with zero rest mass? Answer: impossible.
So, it means that EVERYTHING, all energy, has mass and momentum and we are still not capable of observing and measuring the “rest mass” of the fundament field that creates everything.
Could this “aether” be a micro black hole, so tiny the electromagnetic spectrum it produces cannot observe it for the obvious reason, it create it so it is impossible to get the resolution to see it, i.e. a singularity.
Does the interference have something to do with both parts of the superposition reaching a shared state? Like the example from last post, there is never a position where both particles are at the same positions in both halves of the superposition, but for the examples today there are states where the particles on both halves are all in the same positions.
That’s got to be it. It’s consistent with the ones that have interference and which ones don’t; 4, 5, 7, 8 and 10 all eventually reach a state where both parts match, but 6 and 9 don’t.
I think what this means is that, as the Prof said, it’s not that a particle or wavicle is interfering with itself: it’s that the different parts of a superposition will interfere with each other if they match up.
I’m not sure if that applies to cases where the superposition “collapses,” such as when the position is finally measured? You would expect such, naively; if the positions in each part of the superposition match, then you know the position regardless of which part we’re “true.” So, of only for a moment, you have much higher precision, as if the superposition had “collapsed.”
But, as Prof. Strassler has said in previous posts, the notion of superpositions “collapsing” is misleading in some ways. I’m just not sure how that applies here.