8.7 The Arrow of Time

This section has some further musings on the many worlds interpretation. One question is why it matters. What is wrong with postulating a fairy-tale collapse mechanism that makes people feel unique? The alternate realities are fundamentally unobservable, so in normal terms they do truly not exist. For all practical purposes, the wave function really does collapse.

The main reason is of course because people are curious. We would also want to understand what nature is really all about, even if we may not like the answer very much.

But there is also a more practical side. An understanding of nature can help guess what is likely to happen under circumstances that are not well known. And clearly, there is a difference in thinking. The Everett model is a universe following the established equations of physics in which observers only observe a very narrow and evolving part of a much larger reality. The Copenhagen model is a single universe run by gnomes that allow microscopic deviations from a unique reality following the equations of physics, but kindly eliminate anything bigger.

One major difference is what is considered to be real. In Everett's theory, for an observer reality is not the complete wave function but a small selection of it. That becomes a philosophical point when considering vacuum energy. According to quantum field theory, even empty space still contains half a photon of electromagnetic energy at each frequency, {A.23.4}. That is much like a harmonic oscillator still has half a quantum of kinetic and potential energy left in its ground state. The electric and magnetic fields have quantum uncertainty. If you measure the electric or magnetic field in vacuum, you will get a nonzero value. The same applies to other fields of particles. Unfortunately, if you sum these energies over all frequencies, you get infinity. Even if the frequencies are assumed to be limited to scales about which there is solid knowledge, there is still an enormous amount of energy here. Its gravitational effect should be gigantic, it should dwarf anything else.

Somehow that does not happen. Now, in Everett’s interpretation a particle only becomes real for a universe when a state is established in which there is no doubt that the particle exists. That obviously greatly limits the vacuum energy that affects that universe. The existence of other particles might be firmly established in other universes, but these will then affect those other universes. In the Copenhagen interpretation, however, there are no other universes, and therefore no good reason to exclude any vacuum energy from affecting the gravity of the only universe there is.

Then there is the arrow of time. It is observed that time has directionality. So why does time only go one way, from early to late? You might argue that early” and “late are just words. But they are not. They are given meaning by the second law of thermodynamics. This law says that a measurable definition of disorder in the observed universe, called entropy, always increases with time. The law applies to macroscopic systems. However, macroscopic systems consist of particles that satisfy microscopic mechanics. And the Schrö­din­ger equation has no particular preference for the time $t$ above the backward time $\vphantom0\raisebox{1.5pt}{$-$}$$t$. So what happened to the processes that run according to $\vphantom0\raisebox{1.5pt}{$-$}$$t$, backwards to what we would consider forward in time? Why do we not observe such processes? And why are we composed of matter, not antimatter? And why does nature not look the same when viewed in the mirror? What is so different about a mirror image of the universe that we observe?

The conventional view postulates ad-hoc asymmetries that “just happened” to be that way. Why would that happen and why would it be in the same direction everywhere in an infinite space-time and an infinity of possible universes therein?

Then the conventional view adds evolution equations that magnify that asymmetry using small perturbation theory. That sounds reasonable until you examine those evolution equations more closely, chapter 11.10. The mechanism that provides the increasing asymmetry is, you guessed it, exactly that poorly defined collapse mechanism. Collapse is simply stated to apply for times greater than the measurement time. Obviously that produces asymmetry in time. But why could the collapse not apply for times less than the collapse time instead?

Now stand back from the details and take a look at the larger philosophical question. The well established equations of nature have no particular preference for either direction of time. True, the direction of time is correlated with matter versus antimatter, and with mirror symmetry. But that still does not make either direction of time any better than the other. According to the laws of physics that have been solidly established, there does not seem to be any big reason for nature to prefer one direction of time above the other.

According to Everett's theory, there is no reason to assume that it does. The many-worlds interpretation allows the wave function to describe both universes that are observed to evolve towards one direction of time and universes that are observed to evolve in the other direction.

That is not a trivial observation. The problem of the observed time asymmetry for a symmetric physics has now been removed. It has been replaced by the question why forward evolving systems appear to correlate with forward evolving systems, and backward evolving systems with backward evolving ones. While that is not a trivial question either, it is not implausible.

Perhaps, if we spend more time on listening to what nature is really telling us, rather than make up stories for what we want to believe, we would now understand those processes a lot more clearly.