Remarks on the Passing of Time

Many philosophers and physicists deny temporal passage; they think that the experience of temporal passage is an illusion, e.g., Julian Barbour, Huw Price, Laurie Paul and Albert Einstein.

For us faithful physicists, the separation between past, present and future has only the meaning of an illusion, although a persisting one. -Einstein

Against this view, Tim Maudlin defends the view that time passes:

I want to defend the claim that the passage of time is an intrinsic asymmetry in the structure of space-time itself, an asymmetry that has no spatial counterpart and is metaphysically independent of the material contents of space-time. It is independent, for example, of the entropy gradient of the universe.

That last remark was to those that hold that time just is the direction of increasing entropy; i.e. that entropy increases in time is analytic.

In “Remarks on the Passing of Time” Tim Maudlin attempts to diffuse the negative arguments against temporal passage.  The positive arguments for temporal passage will be outside the scope of this paper.  There are three types of objections to temporal passage: logical, scientific, and epistemological.

  1. Logical: there is something conceptually incoherent about the passage of time.
  2. Scientific: temporal passage is incompatible with science.
  3. Epistemological: temporal passage is underdetermined by observation: both veridical experience of temporal passage and illusory experience have the same observational consequences. I found this section less interesting so I won’t go over the details.

Diffusing logical objections

In Huw Price’s book Time’s Arrow and Archimedes’ Point, Price lays out a logical problem.

If it made sense to say that time flows then it would make sense to ask how fast it flows, which doesn’t seem to be a sensible question. Some people reply that time flows at one second per second, but even if we could live with the lack of other possibilities, this answer misses the more basic aspect of the objection. A rate of seconds per second is not a rate at all in physical terms. It is a dimensionless quantity, rather than a rate of any sort. (We might just as well say that the ratio of the circumference of a circle to its diameter flows at pi seconds per second!)

Maudlin recognizes three objections to be diffused here.  The first has to do with the logic of rates of change, so let’s examine how we think of rates or flows.  Consider a fair rate of exchange from euros to dollars: it will be something like 1 euro per 1.29 dollars.  What about a fair rate of exchange from dollars to dollars?  Obviously, it will be 1 dollar per dollar.  Next, consider the question: How fast does the river flow?  This question asks how much the position of the river will change after a certain period of time.  So it will be something like 5 miles per hour.  Similarly, the question “How fast does time flow?” asks how much time will change after a certain period of time.  Obviously, after 1 hour time will have changed 1 hour: so time passes at 1 hour per hour, or 1 second per second etc.

The second objection is that the rate of 1 second per second seems to be a dimensionless number as if the two units cancel out.  So suppose we are exchanging floor tiles for liquorice, where the rate of exchange is square feet of tiles for feet of liquorice.  If units cancel out, the rate of exchange would incorrectly be feet instead of the correct square feet for feet.  Similarly, pi is the ratio of the length of the circumference to the length of the diameter: length per length.  The units don’t cancel out.

While I’m mostly convinced by Maudlin, I still have some reservations, because there seems to be something disanalogous in that time’s passing at 1 second per second seems like an unsubstantive tautology whereas the other cases seem substantive.

Price gives the third objection with regards to the direction of the passage of time:

If time flowed, then–as with any flow–it would only make sense to assign that flow a direction with respect to a choice as to what is to count as a positive direction of time. In saying that the sun moves from east to west or that the hands of a clock move clockwise, we take for granted that the positive time axis lies toward what we call the future. But in the absence of some objective grounding for this convention, there isn’t an objective fact as to which way the sun or the hands of the clock are ‘really’ moving. Of course, proponents of the view that there is an objective flow of time might see it as an advantage of their view that it does provide such an objective basis for the usual choice of temporal coordinate. The problem is that until we have such an objective basis we don’t have an objective sense in which time is flowing one way rather than another.

On Maudlin’s view, time passes rather than flows.  Things flow because time passes; and time has an inherent direction.  (Maudlin uses the term ‘passes’ to distinguish the special feature that time has where all other ‘flowing’ is judged by.)  Maudlin turns Price’s modus tollens into a modus ponens: since it’s true that the sun moves east to west, it’s true that time passes in a direction.  At this point, both sides are only begging the question against each other.

Diffusing Scientific Objections

There are two types of scientific objections: the first to do with incompatibilities with relativity, and the second to do with time-reversal invariance of the fundamental laws of physics.

Kurt Godel gives a scientific objection of the first type:

The existence of an objective lapse of time, however, means (or at least is equivalent to the fact) that reality consists of an infinity of layers of ‘now’ which come into existence successively. But, if simultaneity is something relative in the sense just explained, reality cannot be split up into such layers in an objectively determined way. Each observer has his own set of ‘nows’, and none of these various systems of layers can claim the prerogative of representing the objective lapse of time.

I take it Godel pictures something like this:


Maudlin thinks that the passage of time does not require that four-dimensional spacetime be split into stacks of three-dimensional slices of nows.  All that is required is an objective distinction between the direction from past to future and from future to past. We can do this by identifying future and past light cones in relativity.


But it seems the fundamental physics can do without the labeling of future and past light cones due to the second scientific objection: the time reversal invariance of fundamental physical laws.  Newtonian physics, for example, is time reversal invariant.  If we videotaped Newtonian billiard balls and played it in reverse, we couldn’t tell whether it was in forward or reverse.

If the fundamental physical laws are time reversal invariant, then there is no direction in time, no future and past light cone, in fundamental physics.  This leads us to the puzzle of why we always see ice melting on a hot pavement and never forming, and why we remember the past and not the future.  In short, why do we see direction at the macro level?  One explanation is because of the initial condition in what David Albert calls the Past Hypothesis and not because of fundamental laws.  If we had a future boundary condition, people would remember the future and not the past.  (Because the future for them would go in the opposite direction in time compared to us.  From their point of view we would be remembering the future.)

The problem with time reversal invariance is that according to the CPT theorem, there is a case (e.g. neutral kaon decay) where the laws are not time reversal invariant.  The objector could rightly reply, as Sean Carroll points out, that these cases are very rare and it seems disconnected to the reason why we have ice melting.

But suppose, for the sake of argument, that the fundamental physical laws are time reversal invariant.  According to Maudlin, this still does not show that there is not an intrinsic direction in time.  For when we reverse the time order of states, we also need to perform a transformation of states (e.g. switching antiparticles with particles).  Suppose we have the states T0, T1, …, Tn and its reverse T*n, …, T*1, T*0.  We need to transform T to T* for this reversal to work.  Maudlin takes the necessity of this transformation to show that the states are oriented in a certain direction in time.

One might worry that you could take any made-up physical laws and perform some transformation to preserve time symmetry, making time reversal invariance trivial.  This is not true: only in some cases can information be conserved.  In other words, if information is conserved a Laplacian demon that knew any single state would be able to derive all other states at all other times.  If information is conserved, there is a broader sense (a sense which Carroll uses) in which the physical laws are time reversible.

It’s an open question if our universe is like this.  It would depend on things like the correct quantum mechanics interpretation, whether the space of states grows as the universe expands, and whether there is information loss in black holes.  See Sean Carroll’s From Eternity to Here for a good summary of this.

To conclude, I think Maudlin gives a good defense for the passage of time.

To explain why so many philosophers and physicists deny temporal passage, Maudlin thinks that people have been seduced by the particular mathematical tools they use.  If they had used different but functionally identical mathematical tools–Maudlin proposes an alternate topology–they might see time differently.

Carroll, Sean.  From Eternity to Here.

Muadlin, Tim.  Remarks on the Passing of Time.

Price, Huw. Time’s Arrow and Archimedes’ Point.

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