Introduction
The fundamental laws of physics appear to have little concern for the direction of time. They seem, mathematically, to happily go about their business irrespective of the direction that time runs. However we in the macroscopic, so-called, real world are very conscious that time’s arrow points from past to future, that cause precedes effect and that broken eggs do not spontaneously reassemble. Volumes have been written by philosophers, physicist, poets and peasants about time with no clear consensus regarding the conundrum it presents. Conventionally what science requires of time is discussed at the following location
http://www.iep.utm.edu/requires/
and a thorough discussion of the subject of time is available at
Perhaps we should ask ourselves seriously whether the problem time poses in physics stems from our historical view of it. Should we be asking if time, as conventionally thought of, really is one of nature’s givens, a brute fact of the universe, or is it, rather like the property of liquidity in fluids, an emergent property? That time (and indeed space) may be emergent phenomena is a recent development in physics and can be placed on a firm mathematical footing as in
http://scitation.aip.org/content/aip/journal/jmp/55/11/10.1063/1.4899081
To give some direction to this enquiry perhaps the question we need to answer is:
Did time exist alongside the dinosaurs?
This question may seem frivolous but the way we conceptualize time arises from habit – the habit of convention and authority. John Locke once said something along the lines that we should not accept authority simply because it is authoritative unless, through our own endeavours, we reach the same authoritative conclusion. That gives us leave to seriously consider an alternative approach to time which moves us away from the accepted scientific view.
In our discussion we shall refer to time in several different ways as follows:
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time (plain typeface) – meaning the ordinary everyday notion of time which seems to flow from past to present to future. It seems to pass quickly in old age or when we are having fun and passes more slowly when we are bored or watching pots! This time is one of the fundamental givens in most physical theories; we are questioning its fundamental nature.
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duration (plain typeface) – conventionally a length of time measured by a clock.
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“time” (in quotes) – meaning Newton’s concept of absolute time.
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“duration” (in quotes) – meaning Newton’s concept of a length or portion of “time” which if extended without limit would include the whole of “time” (absolute time).
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time (in italics) – symbol τ – that which is measured by a clock usually in units called seconds. It has a value equal to the product of the clock reading n and the clock period tp. ie τ = ntp assuming that n = 0 when τ = 0.
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duration (in italics)-symbol Δτ – a length or portion of time given by Δτ = (nf -ni)tp where nf and ni are final and initial clock readings for the portion of time measured.
The meaning of time may also be used as a generic term in the sense that two separate durations are part of the extended temporal concept called time.
The philosophical background
Rather then inexpertly reproduce here what has been expertly written elsewhere it will suffice to direct anyone with an interest in the philosophy of time (and space) to the appropriate entries in the on-line Stanford Encyclopaedia of Philosophy available at:
http://plato.stanford.edu/entries/time/
Here different philosophical interpretations are available of the possible meanings of the word ‘time’ which of course is a rich field of study in its own right.
For our simple purposes here we may consider the following:
“An operational definition of time, wherein one says that observing a certain number of repetitions of one or another standard cyclical event (such as the passage of a free-swinging pendulum) constitutes one standard unit such as the second, is highly useful in the conduct of both advanced experiments and everyday affairs of life. The operational definition leaves aside the question whether there is something called time, apart from the counting activity just mentioned, that flows and that can be measured.”
http://www.andersoninstitute.com/
It is precisely time as a ‘counting activity’ which we are considering here rather than the concept of a time ‘that flows’. This counting activity is performed by a clock where the position of the hands indicate, in effect, the number of counts (ticks) which have occurred. How far can we get in physics with this simple concept?
Comparison of space and time
Philosophers of space and time, for example Reichenbach, point to a distinction between the two in that space is (at least) 3-dimensional whereas time possesses only one dimension. A further distinction arises when we compare points in space with points of time; there is an ordering relationship about temporal points absent from the relationship between spatial points. Points of time possess the property of a before-after relationship which is absent from their spatial counterparts – and so on. If we count our clock ticks with the cardinal numbers (1, 2, 3…) we get a measure of the quantity or length of the time interval measured. If we also associate the ordinal numbers (1st, 2nd, 3rd…) respectively with these cardinal numbers we recover the ordering relationship of ‘before’ and ‘after’ traditionally and uniquely associated with points of time because that relationship is implicit in the ordinal numbers.
Essentially what we are saying is that most of the philosophical reasoning associated with time can also be applied to time. This leads to the simple statement that the difference between time and time is that time is not fundamental; similarly for duration and duration.
So where do we start?
As with much of our everyday physics we could do worse than begin with Newton because his concept of “time”, as “duration”, perhaps unwittingly offers us a clue to a different view. He firmly believed that “time” rolled along uniformly and universally in its own sweet way, one moment following another in a regular procession. Although Einstein cast doubt on this idea with his concept of the relativity of simultaneity this should not deter us from investiagting the clue Newton left by his insistence that “time” and “duration” are pretty much the same thing.
Newton’s “duration” is a portion, ‘length’ or piece of his absolute “time” which if extended without limit would comprise the whole of it. However what we mean by duration is that which marks the start and finish of a particular aspect of the behaviour of matter. It is what our clock, in counting a “certain number of repetitions of one or another standard cyclical event,” conventionally measures.
Now duration (and even “duration”) is a metrical concept – a measure of an amount of time between two happenings, in whatever units we choose. Similarly distance is a measure of the amount of space between two given spatial points again in arbitrary units. We are quite happy to accept that something we call distance implies the existence of something we call space; after all we experience space quite directly in our everyday lives as that which exists between (and within) material objects. We also experience durations – the journey to work, a period of our lives or the ticking of clocks – but should we then necessarily infer that something called time exists as an independent fundamental entity akin to space? Newton drew our attention to his concept of “duration” but have we allowed ourselves to be lured into accepting that time also exists? Are we emulating Koerstler’s Sleepwalkers?
If distance implies space does duration necessarily imply time?
If we answer no to this question what then could replace the concept of time? Assuming, for now, that we are happy to accept space as fundamental it would seem logical to enquire whether space alone provides a sufficiently rich environment to accommodate time as a secondary concept – an emergent property. Minkowski introduced us to the 4-dimensional continuum of spacetime encouraging us to represent this idea in purely spatial terms by introducing a fourth dimension of space as a representation of time. Let us modify this idea and adopt a 4-dimensional space to see how we can recover from it our notion of time. In other words we are starting our construction of a model of physical reality taking as our primary construct a 4-dimensional space as distinct from a 4-dimensional spacetime. On the Space page we argue that the existence of space is contingent upon the prior existence of matter but that has no direct bearing on our present discussion.
We have already talked about distance as a measure of space but we readily accept that distance only has meaning when measured with respect to material points ie matter. Mathematicians happily point out that space bears no landmarks and in physics such landmarks are provided by material points. Thus distance is a concept associated with space and given meaning through the presence of matter. We have now arrived at two fundamental requirements – the existence of matter and space – which allow us to talk about distance (or length) in the absence any notion of time or duration. This may seem rather trivial but it runs counter to Reichenbach who establishes, to his satisfaction, that time is more fundamental than space because spatial distances can be obtained by measuring the flight time of light. Reichenbach’s result rests on the pre-existence of time; if we are replacing time with time then his carefully rendered argument is invalid.
We have already made a rudimentary definition of a clock as an instrument which counts and records some repetitive behaviour of matter and can therefore give us a measure of duration based on, for example, the number of recorded pendulum swings. By choosing a particular example we have decided on a metric for measuring duration and by calling the duration of one complete pendulum swing a ‘second’ we have named our unit of time. We can now measure any duration in units of ‘seconds’ without ever considering the existence of time. Now we can measure durations – by counting material processes – we may suppose that any particular duration could be extended by millions upon millions of ‘seconds’ into something we recognise as the future and projected backwards into something we recognise as the past.
Past and future are readily encompassed within the broader concept of time analogous to our previous concept of time.
This rather laboured argument showing how the behaviour of matter provides us with a means of measuring duration leads eventually to a concept of time as an emergent property. A property which requires:
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the pre-existence of matter and the space in which it can perform its cyclical events
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creatures with the faculty of observing this behaviour …
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… and the ability to recall events of the recent past
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beings such as ourselves with the intellectual capacity to create and use a number system.
If these really are the minimum requirements for recognising the concept of time then it certainly is not the fundamental property we conventionally accept time to be.
With the help of the conventional balloon model of the expanding universe we can now picture the universe as a hypersphere embedded in a 4-dimensional Euclidean space and expanding at a constant rate. Material processes in its 3-dimensional surface – for example pendulum swings producing clock ticks – now occur at slightly different locations on the radius of the hypersphere marking out units of time. In this way every point on the 3-dimensional surface is equidistant from that which the universe appears to start its expansion and so are simultaneous in terms of our emergent time. The meaning of time here is very close to the conventional concept of cosmic time which is the time coordinate used in big bang models of cosmology.
This view is fully supported by arguments presented in the relativity pages.
To answer the dinosaur question posed earlier we can say that if time exists then it certainly existed in the epoch of the dinosaurs but time did not. We can of course extrapolate our concept of time to hypothetically cover any past or future epoch including the life of dinosaurs. Time may be all that is required in physics; an emergent temporal concept requiring the prior existence of all four of the above conditions.
The meaning of time has clearly developed as philosophy and science have progressed and provided us with what we hope is a clearer understanding of our world. The concept of time as anything other than a fundamental construct has very deep roots. It’s existence brings to mind the technique that some theoreticians use for imagining a 4th spacial dimension. Because we cannot picture things moving in 4 dimensions they urge us to use colour to simulate a 4-D location. Thus if a given object, apparently stationary in 3-dimensional space, is seen to be undergoing a colour change, it means it is changing its 4-D location. If the object is limited to one direction of 4-D movement we might see it changing from red to blue but never from blue to red.
Is it possible that we use time instead of colour in our representation of unidirectional 4-D movement?
We cannot picture movement through a fourth spatial dimension but we can certainly conceive of and remember earlier events in our lives. As author Janet Fitch remarks:
“Memory is the fourth dimension to any landscape.”
So are we predisposed to think in temporal terms, such as earlier and later rather than in any other modality, for coping with our unidirectional progress through a 4-dimensional space? Is that partly what memory is for?
There is at least one good reason why this may be so – simplicity.
It is far easier to arrange a meeting at The Slug and Lettuce in an hour’s time then to say we will meet at the pub when our 4th-dimensional spatial co-ordinate has increased in value by 1.08 x 109 kilometres – about 6.7 x 108 miles. We could easily miss out on that much needed pint!
Comment
Perhaps we should have gone back further than Newton during this discussion, to that wise old owl Aristotle. In Part 14, Book IV, Physics, he writes:
“Whether if soul did not exist time would exist or not, is a question
that may fairly be asked; for if there cannot be some one to count
there cannot be anything that can be counted, so that evidently there
cannot be number; for number is either what has been, or what can
be, counted. But if nothing but soul, or in soul reason, is qualified
to count, there would not be time unless there were soul, but only
that of which time is an attribute, i.e. if movement can exist without
soul, and the before and after are attributes of movement, and time
is these qua numerable.”
http://classics.mit.edu/Aristotle/physics.mb.txt
Requirement (iv) above is certainly consistent with “if there cannot be someone to count there cannot be anything that can be counted” as well as “…if nothing but soul…is qualified to count, there would not be time unless there were soul…”.
So perhaps Aristotle said all there was to say and Newton just made things more complicated!
The discussion in this section obviously presents no new ideas about ‘time’ in any of its aspects. It simply serves as an introduction to the concept of time used in the relativity pages. There we start with a 4-dimensional model of space from which time emerges as described above.
Usually in SR we start with Minkowski’s 4-dimensional spacetime but that isn’t at all off-piste.