At the end of the nineteenth century John McTaggart discovered a serious problem with the idea of time and, on the basis of this, he proposed that time was unreal. He considered the way that things could be ordered in time and reasoned that the procedure that creates the temporal ordering from future to present to past was outside time. His argument is simplified below.
Consider a simple ordered list of events, if the list were read from the bottom upwards the items would occur in a different progression in time from reading them from top to bottom. McTaggart called this list the "C Series". This list of events, the "C" Series, has no definite ordering in time. As an alternative there could be a convention that the list is always read from the bottom upwards (B Series), the list itself represents events arranged from earlier to later but has within it no change, it is fixed forever. Lastly a cursor could be placed against the items as the list is read and the items below the cursor called "past" and those ahead of the cursor called "future" with the cursor being in the present (A Series). The last way of ordering events is closest to the way that we think of the passing of time.
What McTaggart spotted was that if the cursor moves up the list it is not a part of the list but creates a new list, with different relations between past, present and future, at every point that it traverses. If the lists are regarded as events distributed in time then the changes that give events the labels "past", "present" or "future" cannot be in time. McTaggart puts it thus:
"The difficulty may be put in another way, in which the fallacy will exhibit itself rather as a vicious infinite series than as a vicious circle. If we avoid the incompatibility of the three characteristics [past,present and future] by asserting that M is present, has been future, and will be past, we are constructing a second A series, within which the first falls, in the same way in which events fall within the first. It may be doubted whether any intelligible meaning can be given to the assertion that time is in time. But, in any case, the second A series will suffer from the same difficulty as the first, which can only be removed by placing it inside a third A series. The same principle will place the third inside a fourth, and so on without end. You can never get rid of the contradiction, for, by the act of removing it from what is to be explained, you produce it over again in the explanation. And so the explanation is invalid."
It is intriguing that the Buddhist philosopher Nagarjuna, in his 2nd century AD work the "Mulamadhyamikakarika", also spotted this problem of past, present and future being present in a series that is apparently about the past.
McTaggart's conclusion that time is unreal is unwarranted because there are other possibilities. One possibility is that the future does not exist as a fixed entity. If this were the case then, given that instantaneous observation is impossible, there is only "becoming", the sudden appearance of events in the immediate past. All events would then be past. The A Series would be a growing list generated by something that is indeed outside time. There are other possibilities but this possibility seems closest to our conscious experience. We have an extended present moment that includes events from the present instant back through a second or so of time and this is indeed like a growing A Series (see Notes 1 & 2).
What McTaggart does demonstrate in his paper is that the sort of time that he defines, the everyday nineteenth century idea of time, is unreal. What he calls time has a component that is like space, being a direction in which things can be arranged (time as a dimension), and another component that involves change (what might be called "becoming"). Change is different from time as a dimension.
It is interesting to compare McTaggart's time with space. A position in space can be marked by points on a scale but it is accepted that we can go forward or backwards in space. However, we can only go forward or backwards in space because there is "time", if time is unreal then space is unreal.
The analysis given above leaves the question of the nature of "becoming" wide open. Why is our conscious experience just one thing after another? In the Newtonian paradigm events occur entirely because of the previous state of the world (determinism) but in the twenty first century events are thought to occur because of both the previous state of the world and as a result of quantum mechanical uncertainty. In modern analyses qm events are held to be dominant but statistically reduce to a picture that is almost indistinguishable from the classical prediction (See Ogborn and Taylor 2005 for a simple introduction).
In the most extreme cases, such as in the double slit experiment, there are periods of time where qm uncertainty is actually the dominant factor and even the appearance of determinism takes a back seat. This is disturbing because our brains may be sensitive to occasional qm uncertainties. A synapse might be on the verge of becoming facilitated and as it is being "read out" could be in a superposed state of facilitated/not facilitated. How far would the uncertainty propagate downstream in the brain and into the world as a superposition of actions? Does the form of conscious experience, in which there is an interrelationship between time and spatial distance ensure that only one alternative is realised (See Time and Conscious Experience)? Or do both alternatives occur and is there a "me" in both?
(With thanks to the blog:True Nature: Notes on Spirit and Science for pointing out the work of Nagarjuna).
McTaggart, J. (1908). The Unreality of Time. Mind: A Quarterly Review of Psychology and Philosophy 17 (1908): 456-473. http://en.wikisource.org/wiki/The_Unreality_of_Time
Ogborn, K. and Taylor, E.F. (2005). Quantum Physics explains Newton's laws
of motion. Physics education. 40(1) 26-34. http://www.eftaylor.com/leastaction.html#qm2newton
Why you don’t want to get in the box with Schrödinger’s cat. David Papineau
A Many-Minds Interpretation Of Quantum Theory. Matthew J. Donald http://www.bss.phy.cam.ac.uk/~mjd1014/
Horwitz, L.P. (2005) On the significance of a recent experiment demonstrating quantum interference in time. http://arxiv.org/abs/quant-ph/0507044
Earman, J. (2002) Thoroughly Modern McTaggart: Or, What McTaggart Would Have Said if He Had Read the General Theory of Relativity. Ann Arbor, MI: Scholarly Publishing Office, University of Michigan, University Library vol. 2, no. 3, pp. 1-28, August 2002. http://quod.lib.umich.edu/cgi/t/text/text-idx?c=phimp;cc=phimp;rgn=main;view=text;idno=3521354.0002.003
Note 1: McTaggart dismisses what he pejoratively labels the "specious present" and I have here called the "extended present". He notes that only the present instant can be present without noticing that distant past instants are visibly and audibly present as movements and sounds that project through time to the observer's present instant. Just look at someone speaking, you hear whole words extended in time at the apparent position of their lips, now. However, I would agree with McTaggart that we cannot use our subjective experience of time as an absolute guide to the current time. This is also the case for length, I would not trust a subjective estimate of the length of a thing but this would not invalidate the concept of length.
Note 2: The "growing block" model of time was proposed by CD Broad. It differs from the purely empirical growing block idea of time presented here because the "becoming" of an individual could be a personal event.