So now is as good a time as any to ask the obvious question: what has Richard Feynman’s thought about a single electron jumping all through time, creating the illusion that many electrons exist, got to do with a Square in a fiction book about Victorian Britain? And if you think you know the answer I am very impressed.
Richard Feynman’s thought is essentially a hypothesis. Confirmation of that hypothesis would overthrow two intuitively obvious things we can figure out from what we see. Firstly, since we ‘see’ many electrons, the single time-travelling electron would overthrow the idea that seeing many electrons means there are many electrons. Secondly, it would overthrow the idea that when you see two electrons and a positron there are actually two electrons and a positron*. In both these situations what you would actually be looking at is a single electron. It would be the same as seeing all the Dr Whos in your living room: you know they are all one person from different times in their life, but it looks like many people.
* this is what we suspect happens in atoms when energy is absorbed in atoms.
The thing with a hypothesis is that it needs a way to be tested. The graphs from part one of this series start to give us an answer as to how we could test Feynman’s thought (I hesitate to really call it ‘Feynman’s Hypothesis’ because he was only really having fun with some ideas and I seriously doubt that he took the idea seriously himself).
The first graph is created by seeing three independent points and tracing their movements with lines. If you were to take a straight horizontal line, put it at the bottom of the graph and move it up the graph slowly, that line moving line would represent you, the observer, moving forwards through time. The place where that moving line intersects the coloured lines would create individual points: each observed particle. It is the movement of those points that we observe and use to draw the lines on the graph.
Imagine, then, an analogy to Flatland. We observe moving points, and we use those points to create lines. This is what the Square experiences as it moves through Lineland; in the one-dimensional Lineland the Square sees each line as a point because he sees them end on. But once he moves out of the one-dimensional world into a two-dimensional world he sees the lines as lines. Similarly, by taking points (particles) and using them to create meaningful lines we have created a model of what our universe looks like from a dimension higher than ourselves.
Is that dimension a real thing? Well, I ended part two with the Sphere telling the Square that a dimension higher than the third-dimension is ridiculous. But the point I hoped to get across is that that is an arrogant claim given the context of the book. In String Theory there are numerous dimensions. A majority of theoretical physicists seem to settle on 11 dimensions, but depending on the model the number can be much higher. There is a difference between a space dimension and a time dimension, but most theoretical physicists settle on there only being one time dimension. But some do propose that there are two time dimensions. I can’t follow the conversation, personally, but I can take away this: there is a dimension from which we would look at our dimension and not see points moving through time, but instead would see a line carved out showing everywhere each thing had been through all time. This is what my two graphs are: attempts to model what our dimension would look like from ‘above’.
And that is where the experiment to test Feynman’s thought must take place. From one dimension up we could see all the moments of time at once: each object would be a line, in length, that represents the amount of time that thing exists for. And from that perspective we could see if all electrons are actually a series of lines (like in graph 1) or one giant scribbled line (graph 2).