Monday, July 16, 2007

Feynman diagrams

Grasping the many strange and often counter intuitive phenomena that comprise “normal” quantum phenomena is a daunting task for many non-physicists. It takes time, persistence, and careful consideration to visualize these fascinating concepts-but when you do the rewards are worth the effort.

So it is that when an exceptional description or concise, easy to understand representation of quantum theory comes along it is immensely appreciated. Among the more difficult quantum level events to grasp are the various force/particle interactions, their relationship to virtual particles, and the unconventional use of space time that allows for the unfolding of a beautiful interplay of interactions.

If many quantum features such as granular matter, uncertainty, and the constant annihilation/creation of particles can be visualized, a much clearer understanding of larger physical concepts can be attained. Learning about the nature of how these subatomic particles interact and understanding that these are events of the very small can help one avoid the pitfalls of confusing these phenomena with more mundane esoteric beliefs (i.e.; quantum consciousness as alternative medicine describes it). The Feynman diagrams attain just this kind of connection to natural events.

As Kenneth Ford (The Quantum World) notes “Richard Feynman invented a method for diagramming events in the subatomic world that is a great aid to visualizing what is going on there. In particular, these ‘Feynman diagrams’ reveal what we think is ‘really’ happening when a force carrier gets exchanged between two other particles, accounting for an interaction between them.” He adds “A Feynman diagram is a miniature space time map.” They could be considered shorthand outlining the calculations depicting electromagnetic and weak interactions between particles.

In essence, these diagrams provide a visual glimpse into this strange world while combining a variety of ideas into one dynamic representation. Ford clarifies “In relativity theory, an ‘event’ is something that happens at a particular space time point- that is, at a point in space and at an instant of time….In the particle world, events seem to occur at exact space time points, not spread over space and not spread over time. Indeed, experiments indicate that everything that happens in the subatomic world happens ultimately because of little explosive events at space time points-events, moreover, in which nothing survives. What comes into this point is different from what leaves it.”


The hyperphysics web site details the diagrams as follows “The time axis points upward and the space axis move to the right. Particles are represented by lines with arrows to denote the direction of their travel, with antiparticles having their arrows reversed. Virtual particles are represented by wavy or broken lines and have no arrows. All electromagnetic interactions can be described with combinations of primitive diagrams like this one.”


These diagrams reveal two central and critical qualities that define quantum interactions. The first is the fact that where the lines meet describe an interaction in space time called a vertex. Ford notes “Here is the stunning generality that physicists now believe to be true. Every interaction in the world results ultimately from the emission and absorption of bosons (the force carriers) by leptons and quarks at space time points. Three-prong vertices's lie at the heart of every interaction.”

The second quality involves a fascinating reality. Ford elucidates “…the interaction event is a truly catastrophic event in which every particle is either annihilated or created…The electron flying upward to the left in the figure [above] cannot be said to be the same as the electron that entered from the lower left. They are identical, because they are both electrons, but saying that the one leaving is the same as the one that arrived has no meaning.”

Another rather amazing fact about this quantum world is how particles essentially move independent of time- anti-particles could be looked at as a particle moving backward through time. Again Ford explains “To think of this process proceeding forward in time, you could again imagine a horizontal ruler moved slowly upward [see first two illustrations below]...the arrows are labels…Their purpose is to tell whether the line is that of a particle or an anti-particle. So the line on the right with a downward-pointing arrow represents a positron moving forward in time- that is, upward in the diagram. But…the forward in time positron is equivalent to a backward in time electron…An electron comes along from the left, moving forward in time, emits photons…and then reverses its course through time. Strange but true. Wheeler and Feynman showed that the descriptions in terms of a forward in time and a backward in time electron are both ‘correct’ because they are mathematically equivalent and indistinguishable.”

The Feynman diagrams shed light on these peculiar subatomic interactions and help reduce some of the confusion in other areas of quantum phenomena .They provide the basis for an improved view of a profoundly mysterious realm. In addition, the foundational concepts that gave rise to these diagrams provide the basis for formulating a complementary- yet alternate description (Feynman’s sum over histories description of quantum phenomena) of particle/wavelength behavior that diminishes, to some degree, the confusion caused by the wavelength description of events at this level of reality.

Ref: Ford, Kenneth. The quantum world. Harvard univ press. Mass. 2004

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