Comments on Markosian s How Fast Does Time Pass?

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1 Comments on Markosian s How Fast Does Time Pass? In 2 of his paper Markosian tries to spell out what he means to say when he says that time passes. Most of his discussion has to do with temporal language (his preference for tensed rather than eternal propositions and the ineliminability of tensed in favour of tenseless language). I will set these discussions of temporal language aside. Even if correct, they do not concern the nature of time, as opposed to temporal language. He does eventually state a view about the metaphysics of time itself. He calls it the thesis of the pure passage of time: the process by which times and events successively posses different A-properties. (835) The existence of A-properties is dubious. I think it best to note that the process to which Markosian alludes events becoming ever less future, then present, then ever more past is what Broad called the transitory aspect of time. Markosian calls it the pure passage of time. (835) Markosian adds the claim that there is no spatial analog to the pure passage of time. [I note that one can admit the existence of the pure passage of time without committing oneself to the doubtful existence of McTaggart s A-properties. One can argue (as Broad in fact did

2 argue) that even though the sentence The death of Queen Anne is past looks as if it predicates a property of a subject, it need not in fact do so. It may be of some other logical form than subject-predicate. I find it surprising that Markosian does not even consider this possibility, much less offer some reason(s) that one should not take it seriously.] But if this process, the pure passage of time, exists, it should be possible to say at what rate it occurs. But is it possible? Following J. J. C. Smart s paper The River of Time, Markosian introduces two arguments that it is not possible: The First Rate of Passage Argument (1) If time flows or passes, then there is some second timedimension with respect to which the passage of normal time is to be measured. (2) If there is some second time-dimension with respect to which the passage of normal time is to be measured, then the second time dimension must flow or pass. (3) If the second time-dimension flows or passes, then there must be some third time-dimension with respect to which the passage of the second time-dimension is to be measured, and 2

3 hence some fourth time-dimension with respect to which the passage of the third time-dimension is to be measured, and so on ad infinitum. (4) It s not the case that there is some third time-dimension with respect to which the passage of the second timedimension is to be measured, and hence some fourth time dimension with respect to which the passage of the third timedimension is to be measured, and so on ad infinitum. (5) It s not the case that time flows or passes. Markosian rejects the conclusion, (5), of this valid argument, so he must reject one of the four premises. In fact, he says on page 838 that he rejects premise (1) and also the principle on which it is based: P1: For any time-dimension T, if T flows or passes, then there is some time-dimension T' such that T' is distinct from T and the flow or passage of events in T is to be measured with respect to T'. What are the alternatives to P1? 3

4 A rate is a ratio. Generally (but perhaps not invariably) a rate is a ratio of the change or difference in some quantity to the number of units of time in which the change takes place. What are the quantities in the ratio when we try to specify the rate of time s passing or lapsing or flow? One might suppose that the numerator is the elapsed amount of time in the time dimension T. Then the denominator will, if the general rule is observed, also be the amount of elapsed time in which the change takes place. So the rate might look like 1 hour / hour. Here is one well-known argument that this way of construing the rate of time s passing is incoherent: [P]erhaps the strongest reason for denying the objectivity of the present is that it is so difficult to make sense of the notion of the objective flow or passage of time. Why? Well, the stock objection is that 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 [that is, with there seeming to be no other possible rates at which time could flow ], this answer misses the more basic aspect of the objection. A rate of seconds per 4

5 second is not a rate at all in physical terms. It is a dimensionless quantity, rather than a rate of any sort. (We might as well say that the ratio of the circumference of a circle to its diameter flows at π seconds per second!) from Time s Arrow and Archimedes Point by Huw Price (Oxford University Press, 1996). page 13. If this argument is correct, then the one clear alternative to (P1), that the same time dimension is invoked in the both the numerator and denominator of the ratio expressing the rate of time s passing, collapses. The apparent rate is a pure number that expresses no rate at all! [Here is one contemporary response to this apparent collapse of rate to pure number. Typically, one thinks of a rate as the ratio of some change in a quantity to some number of time units. But the second quantity need not always be time. We speak, for instance, of the rate of exchange of currencies say the exchange rate of Canadian dollars for US dollars. But can we then not, asks Tim Maudlin, also speak of the exchange rate of Canadian dollars with respect to itself one dollar per dollar? If so, then why not 1 second per second as well? Let us put this question aside for now and get back to Markosian s argument.] 5

6 The Second Rate of Passage Argument (1) If it makes sense to say that time passes, then it makes sense to ask How fast does time pass?. (2) If it makes sense to ask How fast does time pass?, then it s possible for there to be a coherent answer to this question. (3) It s not possible for there to be a coherent answer to this question. (4) It doesn t make sense to say that time passes. Since the forgoing argument supports premise (3) and the first two premises seem quite reasonable, this second argument seems to support the negative conclusion (4). Nevertheless, Markosian thinks that this argument fails too. He begins by noting that when we measure an ordinary (average) rate, like an average velocity, what we actually do is compare the amount of the measured quantity (for instance, a distance) to the change in some other standard reference quantity, like the position of the sun. 6

7 [Even ancient astronomers knew that the length of the day as measured by the sun varied quite a bit, so they constructed an average solar motion, or mean sun. The standard reference process should be thought of as the motion of this mean sun. Nowadays, the reference process is a complex process in an atomic clock. 1 Bear in mind that Poincaré, who was quite in touch with the basic processes of standards setting, argued that the reference process is chosen to maximize the simplicity of the laws of nature. We choose a standard, he says, for our convenience, not because it is more correct.] Markosian says that if the thesis of the pure passage of time is false, then all we can ever do is compare one process to another, as above. But if the thesis of the pure passage of time is true, he thinks we have more options. For one, we can compare the change in some ordinary quantity (like position) to the change of the pure process of time. Then, if we invert this ratio, we have an expression for the rate at which the pure process of time passes. In this case, he claims, we can deny premise 3 of the second negative argument. 1 In fact, here is the official (English translation from French though) definition of the second: The second is the duration of periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. (See page 66 of Splitting the Second: The Story of Atomic Time by Tony Jones.) 7

8 Consider, however, this interesting passage from The Science of Mechanics by Ernst Mach: If a thing A changes with time, then this only means that the circumstances of A depend on the circumstances of another thing B.... We are entirely incapable of measuring the changes of things against time itself. Time is an abstraction that we arrive at through the changes of things.... One motion can be uniform relative to another. The question of whether a motion in itself is uniform has no sense at all. Nor can we speak of absolute time (independently of any change). The more I think about actual time measurement, the more convincing I find this passage. 2 So while one can claim or one can say that certain ratios are the ratios of changes in certain quantities to the change of time itself, it does not seem as if any of these claims or sayings can be true. But if one is only comparing processes to processes, what is one asking when one asks: How fast does time pass?] Markosian also feels that he can take the line (843) that it really is OK to compare the rate of the passage of time itself to 2 I don t endorse the initial claim about meaning, since Mach is clearly thinking here of empirical meaning, a term that has never been clearly explicated. 8

9 the rate of the passage of time itself, but he does not discuss the objection that the rate of one second per second collapsed into a pure number and is no rate at all. Finally, he rejects the question itself as a category mistake. (This kind of argument used to be more popular than it is now, but I still have certain fondness for it. 3 ) Since (one might claim) all rates are and must be comparisons to the change of the pure passage of time, the pure passage of time itself is the one process that (as a matter of logic) cannot have a rate. Asking for this rate, then, is the category mistake. This tactic undermines premise 1 of the Second Rate of Passage argument. 3 Shortly after the 9/11 attack on the World Trade Centre buildings and the announcement of the US response, the Economist magazine said that a war on terror was a category mistake. 9