Agreeing with Feynman's Rules.

Contents

Clocks going Backward?

Don't Worry!

Where does the INwave come from?

 

Introduction

Richard Feynman was a mathematical physicist at Cal-Tech in Pasadena, California who wrote several books on the interactions of charged particles. He invented a clever way of simply drawing all the different possible ways that photons and particles, especially electrons, can interact. He made rules to interpret "Feynman diagrams"  See Figure 1. The diagrams were purely theoretical since at the time Feynman had no physical model of the electron. But they agreed with lab measurements and calculations of the interactions. So we knew that they were correct even though we didn't know "why".  Now the wave structure of the electron, a physical model, shows us what actually happens to the electrons. It agrees with Feynman's rules.

Feynman diagrams FEYN1.gif HERE

FIGURE 1. Feynman Diagrams.  (UNDER CONSTRUCTION)   The upward coordinate is time. Left and right is the position of an electron or positron. The wiggly lines are photon (energy) transfers between the particles.  The upper diagram shows two electrons colliding and recoiling from each other. The center diagram is a collision between an electron and a positron. The bottom diagram shows a photon of large energy being converted into a 'pair'  that is, into one electron and one positron.

Clocks going Backward?

On of Feynman's more picturesque rules was his assertion that, " An electron is a positron moving backward in time ". What did this really mean?  On his diagram it meant that if you made an electron go back in time by drawing it  downward on his diagram, then it would have the same status and reactions as a positron moving upward on the diagram. Did this mean that electrons could really go back in time?  The question was unanswered but many students puzzled over it!

Don't Worry!

Using the wave structure of an electron, it can be seen that you need never worry about time travel.  We can see this by reversing the time variable in the equations of the positron and seeing what happens.

To change the time in the equations you need to understand the equations. So, more has to be said about the  equations of the wave structure of the electron and positron. I will make it as simple as possible. Both consist of an inward wave and an outward wave. The waves are written:

                          Electron   =     Outward wave    +     Inward wave   [with  + rotation at center]

                                         =     Amplitude{expo(iwt  -  kr)   +  expo(-iwt  +  kr)}

                          Positron   =     Outward wave    +     Inward wave  [with  - rotation at center]

                                         =     Amplitude{expo(iwt  -  kr)   +  expo(-iwt  +  kr)}

The symbols mean:  t=time, r=radius, w = frequency, k= wavelength constant, expo = exponential function

These equations are plotted in Figure 2 and you can also see them, in motion, on the page Seeing the Electron. To aid clarity, I have left out the radial factor which makes the waves smaller as they go away from the center.

    

Feynman diagrams FEYN2.gif HERE

FIGURE  2. Electron Waves.  (UNDER CONSTRUCTION)  An inward wave (top), an outward wave (middle)      and the sum of the two  waves (bottom)

Notice what happens if you put a minus (-) sign in front of the time in the equations of an electron. This is equivalent, mathematically speaking, to making the electron move 'backward' in time (Feynman was a mathematician). But notice what it does physically (Some algebra is needed here. If you don't know it, ask a friend). You have merely changed the electron equation into the positron equation.  Nothing has happened to the laboratory clock!

You can also see this, without algebra, in Figure 2 by picturing the change in each wave as the time reverses. The INwave of the electron changes to an OUTwave,  the OUTwave changes to an INwave, and the rotation direction at the center changes from clockwise to counter-clockwise.  Voila! You have made the electron into a positron, just as Feynman said.  Time did not run backwards!  (That's a relief.)

There is another way to see this. Go to the page on the Spin of the Electron. There the changes of time can be done using a Dirac matrix (for time reversal) operating on the waves (a Dirac spinor) of either the positron or electron. This is neat but fancy mathematics invented by Paul Dirac. The result is the same: The electron becomes a positron and vice versa.

Where does the INwave come from?

 

 

FIGURE 3. Rodin's Thinker.
If you like to think about science ( You do or you wouldn't be reading this.) you will have asked yourself, "Where does the INwave come from and how does it know where it is going?"  You are puzzled like Rodin's Thinker in Figure 3.

The answer to this question is one of the most beautiful characteristics of the universe!  The property of communication between particles by means of their waves leads to a symmetry among all the particles of the universe.  It turns out that there is ...