The Arrow of Time from an Overlooked Physical Law


In this post, I’m going to disagree with the following statement by physicist Sean Carroll concerning the nature of time:

“The weird thing about the arrow of time is that it’s not to be found in the underlying laws of physics. It’s not there. So it’s a feature of the universe we see, but not a feature of the laws of the individual particles. So the arrow of time is built on top of whatever local laws of physics apply.”–Sean Carroll,

That is a common position, but it could very well be wrong. Specifically, what could be wrong with it is the claim that the arrow of time is “not to be found in the underlying laws of physics.” That claim comes from ignoring the possibility that there could be real, dynamical, irreversible collapse in quantum theory. If there is such collapse, that provides the missing link between physical theory and the phenomena we see that reflect the arrow of time.

First, it should be noted that collapse has been a formal part of standard quantum mechanics since the brilliant mathematician/physicist John von Neumann formalized the theory back in the 1920s. Von Neumann referred explicitly to collapse as a discontinuous, indeterministic process, and noted that it was irreversible. However, in recent decades, it has become fashionable to ignore collapse, which means to (explicitly or implicity) use an Everettian or “Many-Worlds” approach to quantum theory. The Everettian approach denies that collapse ever occurs, so in that interpretation, all the laws are time-reversible. This assumption underlies the usual negative conclusion (exemplified above by Carroll’s statement) about the existence of any physical law that could account for the irreversibility we see around us.

This evolution toward Everettianism has occurred for several reasons, probably chief among them the ad hoc nature of many of the specific models of collapse, which make changes to quantum theory. Alternatively, many physicists assume that collapse is just something that happens in our minds–that it corresponds to updating our own subjective information about the world as we advance through spacetime. But in that case, it is assumed that we somehow ‘move through’ the world, following an unexplained arrow of time. Clearly, if we are going to just help ourselves to an arrow of time in our ‘movement through the world,’ we are not explaining it.

Carroll’s assumption that the arrow of time has to be ‘built on top’ of laws that lack such an arrow involves appealing to notions of entropy increase– roughly, the idea that in a closed system, disorder always increases over time. But entropy increase, which is a time-asymmetric law, cannot itself be obtained from the allegedly underlying time-symmetric laws; that’s part of the ‘mystery’ of time’s arrow.  Moreover, trying to get time’s arrow from entropy considerations alone involves identifying the future solely with the direction of decreasing order in systems. This identification rules out identifying a future direction with processes of increasing order, which are commonplace (e.g., plant growth). Allowing exceptions for ordering process associated with living things on the basis that they are open systems doesn’t take into account that the universe as a whole is a closed system, and that such order-increasing processes take place, alongside other order-decreasing processes, within that closed system. Since entropy both increases and decreases all around us, and yet our experience is always future-directed, appealing to entropy increase is inadequate to the task of explaining time’s arrow.

Thus, the problem will not be properly solved unless physical laws really do have some irreversible component. But maybe they do: maybe we should not be neglecting collapse. And there is a model of collapse that does not involve changing the basic theory–it’s the Transactional Interpretation (TI). The transactional process corresponds precisely to Von Neumann’s intrinsically irreversible ‘measurement’ process. According to TI, ‘measurement’ is not about the consciousness of an observer (a very common misconception)–rather, it’s a real, physical process. That process is defined non-arbitrarily here,  here  and here.

Thus, we gain an irreversible step at a fundamental level of physical systems. For example, take a closed box of gas. With only time-symmetric (reversible) laws, it’s actually impossible to explain why entropy does not decrease in that box of gas. Appealing to ‘random thermal interactions’ doesn’t help, because the sort of ‘randomness’ one needs is time-asymmetric (this is explained very nicely by Price).

With collapse included, as in the transactional process, the thermal interactions between the gas molecules give rise to true randomness. Each such interaction consists of one or more photons being delivered from one gas molecule to another, in an irreversible process (the technical term is ‘non-unitary’). One molecule is the emitter and the other is the absorber, and the process of delivery of the photon(s) establishes the future direction. (For details on this account of spacetime emergence, see this paper.)

Interestingly, this picture also disagrees with the common assumption that ‘even in empty space, time and space still exist.’ (S. Carroll, same reference) However, Einstein himself also disagreed with that common assumption: he stated that ‘There is no such thing as an empty space, i.e. a space without field. Space-time does not claim existence on its own, but only as a structural quality of the field.’  (Einstein, Relativity and the Problem of Space.) The transactional account of spacetime emergence is completely consistent with Einstein’s observation. In that account, transactions establish, through exchanges of mass/energy,  the structure that we call ‘spacetime.’ Without those transfers of mass/energy, there is no spacetime, and therefore no arrow of time.