Time and time again

Well, this will be my third post in a row about time. I think I’ll discuss something else next week!

As I’ve said before, the path of a particle as it travels through space in the usual way can be represented as a line in a four-dimensional space-time system. There will be one and one line only that represents the history of the particle from the time it is created until the moment that it is annihilated. If we decide to plot only this particle’s location over time there will be no others lines in this space.

Diagram showing phase space plot of particle u...

Diagram showing phase space plot of particle undergoing betatron motion (Photo credit: Wikipedia)

The path will twist and turn as the particle is affected by fields and other particles. It may take a sudden turn when our particle collides with another particle. This interaction can be visualised by adding the data about the other particle to the same space-time graphs. However, since the particle is constantly jostled by other particles the diagram would quickly become crowded so to keep it simple let’s drop out the lines of all the other particles.

So we are back to the original single line we started out with. If we assume that it can’t time travel, there will be no loops and gaps in the line. In other words, for every time between its creation and destruction there will be one and only one set of three space coordinates. Of course the line will have curves and kinks as the particle interacts with other particles and fields.

English: The Markov chain for the drunkard's w...

English: The Markov chain for the drunkard’s walk (a type of random walk) on the real line starting at 0 with a range of two in both directions. (Photo credit: Wikipedia)

Suppose we allow choice into our system. Suppose we have two choices A and B. At the point that the choice is made (at a macro level), there are two possibilities for the space-time position of the particle. From that point on the particles history could be represented by an A line and a B line, which at first glance appears to contravene the single point rule. However by making a choice we are saying that either A will occur, OR B will occur, but not both, so we really have only one line.

A choice is not the same as travelling in time though, so let’s plot A AND B, and we will get a multiply branching tree of lines as the time line splits on every point where a choice is made.

English: Tree of choice for creative commons l...

English: Tree of choice for creative commons licenses. (Photo credit: Wikipedia)

The question arises as to which of these lines is the “real” life line of the particle. This we don’t know in advance because we don’t know what the choice will be, which leaves us in the uncomfortable situation of having something unpredictable happening and physics deals in things that can be predicted.

When a choice is made by someone, it is highly likely that one option is much more likely than the other. Maybe the probability is 0.8 to 0.2 (80:20 in percentage terms). Another way of looking at it is to say that, all other things being equal, if the choice were to come up 100 times, A would be chosen 80 times and B would be chosen 20 times. Of course in a 100 tests, it could be that the actual figures might be 79 and 21.

Brooklyn Museum - The Life Line - Winslow Homer

Brooklyn Museum – The Life Line – Winslow Homer (Photo credit: Wikipedia)

It would be highly unlikely that A would be chosen once and B chosen 99 times in 100 trials of course, but it remains possible. (We have to remember that the circumstances of the choice must be identical, that is, all other things being equal)

We could incorporate this into our system by adding a “probability” axis (running from 0 to 1, or equivalently to 0 to 100). A point on this axis would represent the probability of the choice that was made and the whole sheet represents the life of the particle.

It appears that two points on the line are axis, the ones at 0.8 and 0.2 are “special”. In the stated situation those at two probabilities of the outcomes A and B. The probability of any other outcome say Z are zero and effectively outcome Z does not exist.

All things being equal there appears to be no physical reason why someone would choose one option over another. It may be that, all things being equal, that one option gets chosen more often than the other, but the sum of all the probabilities is one – in other words it is absolutely certain that one of the options is chosen. I find this totally mysterious. A choice is an event where the outcome is not dictated by the prior history of the event and is decided by the person making the choice.

English: Figure 1. Demonstration of the decisi...

English: Figure 1. Demonstration of the decision space (Photo credit: Wikipedia)

However the person’s mind is making the decision, and the person’s mind is equivalent to the state of his/her brain and the state of his/her brain is determined by physics, chemistry and biology. I see no “wriggle room” to allow for a person to make a choice.

Can we solve this dilemma by introspection? Descartes looked within himself and concluded that “I think therefore I am“. I don’t know if Descartes intended or realised it, but the implication is that thinking, which happens in the mind/brain, occurs before consciousness. In other words, consciousness is an epiphenomenon of the mind, just as the mind is an epiphenomenon of the brain.

Why then do we think that we make choices and decide things? Well, by introspection I can look at any decision that I have made and I can always point at reasons why I made the choice. Well, of course this may be simple rationalisation. We look at the decision that we made we look at the reasons that might explain why we chose that course and we pick and choose the ones that we like.

While that may be the reasons that we give, and some of them may be true, I do believe that we have reasons for what we do, but those reasons are physical – the configuration of our brains, as a result of past events and happenings, results in a foregone conclusion – we perform an action which looks to the outside world like a decision.

Magnetic Resonance Imaging - Human brain side ...

Magnetic Resonance Imaging – Human brain side view. emphasizing corpus callosum. (Photo credit: Wikipedia)

For instance, if we are filling in a form and we are required to check a box, we “choose” the box depending completely on what has gone before. If the boxes are “Male” or “Female” we know what sex we are so naturally we would choose the correct box. No real decision is made. If we are annoyed at the form or we are in a joking mood we might tick the wrong box. It depends on our state of mind before making the decision what we do, and it depends only on that.

English: checkbox, check box, tickbox, tick bo...

English: checkbox, check box, tickbox, tick box Italiano: checkbox, check box, tickbox, tick box (Photo credit: Wikipedia)

 

 

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