©Fernando Caracena, 2014
Preliminaries—Existential vs. Temporal Causality as Time's two Aspects
Part 1 of this series introduced the dual nature of time in relation to causality in physics. First, there is the existential aspect of time associated with being, which is part of the stationary states associated with the internal motions (usually sub-quantum scale) that form a background, against which change is made perceptible. This is the time that constitutes the fourth component of the time-space manifold of Einstein's Theory of Relativity. It is a time that runs forward and backward in causality relative to the direction from present into the future. Second, there is evolutionary time that we associate with temporal causality, which we also find important in every day living. In this kind of causal time, we experience a cause's acting, before it produces an effect. Both aspects of time are important in physics; but which of them is more fundamental? And so what does time mean?
Existential time in Electrodynamics through the Sacrifice of Temporal Causality
An example of the role of existential time is how it is used in advanced and retarded potentials to compute the effects of electromagnetic radiation (Wheeler and Feynman, 1945). The issues are: (1) any time a charge is accelerated, it radiates an electromagnetic wave; and (2), the fundamental equations of physics work as well if the t-component is replaced by -t, i.e. they are time reversal invariant. This issue deals with accurately accounting for the radiation reaction on a radiating charge and how energy and momentum are later communicated to an absorbing charge, both of which accelerate at the beginning and end of the energy-momentum transfer. The problem can be simplified into a two electron interaction through electro-magnetic radiation.
An accelerated charge is subject to a force of radiation damping that acts simultaneously with its acceleration. Later after its emission, the electromagnetic radiation is absorbed by another charge, which results in that absorbing charge' s acquiring the energy and momentum lost by the first charge. To properly handle that exchange, physicists learned that they had to add together half the advanced and retarded, electromagnetic potentials. Both of signals travel at the speed of light, the advanced potential into the past and the retarded one into the future. This solution is able to solve the problem of radiative transfer, but at the cost of giving up on the idea of temporal causality.The reason for this runs as follows:
At a time t1, the first charge accelerating radiates a retarded wave from past into the future travelling at the speed of light, c. At a later time t2 , that wave is absorbed by a second charge, in the process of which it is also accelerated, but now it radiates a wave travelling at c into the past. That second wave arrives in the past, just as the first charge is beginning to be accelerated.
This is truly a remarkable result, because it destroys the notion of temporally sequenced causality. Let us stretch this way out so that you can see how remarkable this result is. Suppose that an antenna absorbs some cosmic background radiation that originated about 13.7 billion years ago during the Big Bang. The electrons that radiated these electromagnetic waves, way back then immediately felt the reaction to to those waves being absorbed by our detection of them now. This kind of temporal connection of being means that at the moment of the Big Bang, there would be advanced potentials arriving from the indefinite future of the universe, which could form part of the initial conditions of the universe.
Advanced and retarded potentials are discussed in technical terms in more detail than in the Wheeler and Feynman article (cited above) in an article on Retarded and Advanced Potential at mathpages.com. The concluding comment at the end of the article indicates that the author is here thinking in terms of temporal causality:
“...[I]f we postulate that the charge configuration in the future can be freely established by the exercise of free will, independent of the charge distribution of the past, we encounter the same conflict with causality, so it isn’t surprising that a classical theory of electrodynamics of arbitrarily moving charges leads to acausal results. ”
IT is interesting that the above cited article refers to free will as introducing an element of acausality into the problem of radiating charges. At the time of the Big Bang, there would be the effects of the exercise of free will on the initial action of charge distributions. This idea puts an entirely different spin on the question of free will, which I should discuss in a future blog.
Another interesting aspect of advanced and retarded electromagnetic potentials is that it is a mechanism for entangling a particle in the past with one in the future. Further, it is a way of entangling free will with the quantum behavior of nature itself.
Parenthetically, I should mention that the subject of advanced and retarded potentials harkens back to the ideas expressed in a previous blog entitled, “Holistic vs Reductionist Ideas in Physics”. In this case the use of advanced and retarded signals are a mechanistic way of enforcing holistic existentialism, even if you insist that everything must act according to signals that propagate no faster than the speed of light in a vacuum. The price you pay for the mechanistic maintenance of existentialism is giving up the notion of temporal causality in all interactions.
Richard Feynman in his Nobel Prize lecture on his theory of quantum electrodynamics (QED) describes some of the causality effects of his use of time in advanced and retarded potentials
“I would also like to emphasize that by this time I was becoming used to a physical point of view different from the more customary point of view...[, in which] things are discussed as a function of time in very great detail. For example, you have the field at this moment, a differential equation gives you the field at the next moment and so on; a method, which I shall call the Hamilton method, the time differential method... If you wish to use as variables only the coordinates of particles, then you can talk about the property of the paths - but the path of one particle at a given time is affected by the path of another at a different time. ”
Incidentally, toward the end of his Nobel lecture, Feynman made a statement that adds weight to my idea of the importance of grokking the equations of physics:
“...[T]he best way to proceed [, in developing physical theory,]is to try to guess equations, and disregard physical models or descriptions. For example, McCullough guessed the correct equations for light propagation in a crystal long before his colleagues using elastic models could make head or tail of the phenomena, or again, Dirac obtained his equation for the description of the electron by an almost purely mathematical proposition. A simple physical view by which all the contents of this equation can be seen is still lacking.
Therefore, I think equation guessing might be the best method to proceed to obtain the laws for the part of physics which is presently unknown. ”
The Origin of Evolutionary Time
Thermodynamics is the underlying mechanism for evolutionary time, because it orders processes in before-after sequences; hence, it is the origin of the temporal asymmetry that is known as temporal causality. Specifically, the concepts of entropy and the dynamics of entropy (the 2nd Law of Thermodynamics) drive that asymmetry. No process in the universe can decrease the total entropy of the universe, but must result in either no change in entropy, or its increase. The observational basis for this property of entropy is the simple observation about the flow of heat between two objects, one cold, and the other hot. Heat always flows from the object with the higher temperature toward the one with the lower temperature. (see “Grokking Thermodynamics”). The concept of the monotonic increase in entropy with time has been a subject of many physics discussions for several generations.
The increase of entropy has been ascribed microscopically to the probabilistic approach of the phase state of a system to a region of phase space that has the greatest distribution of micro-states, in which case the monotonic increase in entropy is not absolute, but simply the most probable outcome. Physicists who favor the probability interpretation, say that the reverse process of the Humpty-Dumpty effect can happen; however, it is very rare, so rare, that it probably would not have happened in the entire estimated lifetime of the universe. The statistical kind of arguments used by those who favor the probabilistic origin of entropy growth, and therefore, the arrow of time, are based on the idea of the universe in a fixed box, which given enough time passes through a succession of states that eventually brings it back very close to any starting conditions. However, let me point out that there is a much bigger asymmetry driving the arrow of time than thermodynamics by itself.
The Hubble expansion
The Hubble expansion of the universe is the big, obvious asymmetry in time that gives it an underlying theme of causally temporal direction. Looking at two snap shots of the universe, taken at two different cosmically significant times, you should be able to see which time slice preceded the other, because the outward expansion of the galaxy field in time would identify the earlier over the later time-slice. The Hubble expansion also orchestrates all thermodynamic systems by creating a cold thermal background in space that maintains a constant direction for the flow of heat energy from the various heated cosmic components into the darkness of cold space. In this case, space cannot approach the temperature of the radiating cosmic components because it is being cooled by the Hubble expansion. Causal time is therefore an emergent phenomenon that has its origin in the asymmetry imposed by Hubble expansion.
Causal time is very real in our limited little lives on this planet, although it is an emergent property. The chances of the reversal of the Humpty Dumpty effect are even smaller than would be possible in a static universe. However, I have much more to write on this subject that should continue in a part 3 of this series.