Times Two

The concept of a process is important when trying to understand what time is. A process is any sequence of actions or events that lead to a consistent outcome. A food recipe is a typical process. Do this then do that then cook it then there is the cake. The petrol engine combustion cycle is another process: intake - compression - combustion - exhaust. Most processes exhibit two important concepts that relate to time: duration and order. A cake needs to be in the oven for a particular duration to be cooked properly. An engine that has compression before intake will not run. Most physical processes, including natural phenomena, have stages that are in a particular order and take a minimum duration for each stage to get from start to finish. There is a third concept of time that we can usually ignore when running a process, which is the particular moment at which we start it. A cake will come out the same whether made in the morning or the afternoon. An engine will run as well on a Wednesday as a Saturday. Let's now think more about these three important concepts of time: Time as duration; Time as order and Time as specific moments.

Time as Duration

Duration is represented in physics as Δt (change in t) or τ (time period). For example, if a clock reads 45.6 seconds at the start of a process and 51.3 seconds at the end of the process, the process took a duration of Δt = 51.3 - 45.6 = 5.7 seconds to complete. Duration is measured with a timing device so we might call it clock-time.

For any real physical process, clock-time is very useful because it will be the same providing that the clock accompanies the measuring process. For example, imagine an ideal process that takes a perfectly precise time to complete. Imagine also an ideal clock that records duration perfectly precisely. If we run this process at the top of a mountain, then in a valley, the clock-time recorded at each location will be precisely the same.

Einstein's Relativity shows that the situation is different for a clock that does not travel with the process. Suppose that we first synchronise two of these perfect clocks when they are located together in the valley. Next, one clock goes up to the mountain top to record our process as it is run there. The other stays in the valley where it records the process as it is run separately down below. Next, the clock in the mountain is brought down to sit alongside the clock in the valley again. The two clocks, which were left running, now indicate a slightly different number. Even though each clock gave exactly the same amount for the process durations, they now indicate different "times". This is a fact proven by experiment, not just a theoretical prediction. Clocks up a mountain run faster than clocks in a valley below. However, the recorded durations of the process are still the same. This is because ALL physical processes run faster up the mountain than they do in the valley below. A clock is just one example of a physical process, so the clock up the mountain and the process that it was recording are both sped up by precisely the same amount. Put another way, a clock that travels with a process shares the same concept of duration and therefore records the same duration.

The thing that speeds up the clock and the process in the mountains is the reduced gravity due to being slightly further from the bulk of the Earth's mass. It is perhaps easier to think of the clock and the process in the valley as being slowed down by the "drag" of the increased gravity. Gravity and, equivalently, acceleration cause a slowing of all physical processes. Even if the difference were large enough to detect with an ordinary clock, people running the process would not notice because they too are each a physical process. They also would be slowed by precisely the same amount as their accompanying clocks. They would perceive everything around them as happening at the same speed as normal.

We can therefore conclude that clocks indicate the duration of whatever is travelling with them. But clocks do not count the number of moments that have occurred over any duration.

Time as Order

Looking into the distant universe with modern telescopes, all processes appear to proceed just as they do according to the laws of physics we find here on earth. The rates of processes, the durations of each stage, can vary but only in the ways that we expect. The order of the stages of each process remain unchanged. We never see a non-reversible process running backwards. We never see one of the stages of a process appearing out of sequence. Cause always precedes effect. Thus order appears to be as consistent a universal feature at the largest scales of size and distance as it is at our everyday scales and locally.

Einstein's Relativity shows that space and clock-time are related and the relationship can be viewed as a single concept: spacetime. A neat way of picturing spacetime is with a light cone drawn in Minkowski space. Care is needed when using light cones to demonstrate some of the effects of Relativity. This is because Minkowski space is a hyperbolic geometry and, unlike common trigonometric geometry, tilting the axes is not a valid operation. To picture the view that observer A has of the events of an observer B travelling at a different velocity to A, one must transpose the events of observer B using the hyperbolic geometry of Minkowski space. These transpositions leave the light cone boundaries in their original positions; space-like events remain in the space-like domain; time-like events remain in the time-like domain; observer B's events become "squashed up" clockwise or anticlockwise. When transposed correctly (and contrary to some common misrepresentations) future events remain in observer A's future and past events remain in observer A's past. Also, observer A will always see (allowing for light to reach A) observer B's events occurring in the same order as observer B sees them. Relativity does NOT provide a means for an observer to see future events or to access their own past. When gravity and acceleration are taken into account, the picture becomes even more complicated and requires yet more care to interpret. The apparent durations of all processes are reduced by gravity but, and this is a critical point, the order of events are not changed. Our most reliable physics for describing large-scale processes up to extremes of gravity and acceleration show that order is universally consistent.

Looking into the smallest-scale processes, the same is true. Here is where quantum effects are most evident. At this scale, most processes are reversible. Nevertheless, the order of the stages of a process (whether running forwards or backwards) remains consistent. Indeed, at the quantum scale, there is the special case of non-commutating variables. This is where two measurable properties are what is called conjugate or complementary: interacting with one affects the other. Suppose there are two related quantum events in close succession. The first event depends on one of a conjugate pair of properties; the second event depends on the other property of the same conjugate pair. The order is crucial. The precision with which the first property is accessed affects the precision with which the second property is available. Larger scale processes that depend on access to both properties of conjugate pairs are likely to have different outcomes depending on the order in which the paired properties are accessed. The fact that many macroscopic processes are consistent indicates that the underlying quantum processes on which they depend must remain consistent in their order of events.

So it seems that order is a universal feature at all scales. Unlike clock-time (the rate of physical processes) which is different almost everywhere, the order of physical processes is fixed at all scales.

Time as specific moments

Now, for me, is the moments when I am typing these very words that you are reading. There is another Now which is the moments, for you, when you are reading these words. Everything that happens; every subjective experience that we undergo; every physical process that occurs, happens at a particular moment or over a particular range of moments. I am not typing these words in the eighteenth century or the twenty-third century. I cannot step into yesterday or tomorrow at will. Now is here at this moment that I am typing.

We have our memories of the past so we are aware that those moments did exist. There appears to be a flow of time or sequence of moments. But the past is not still here; it has had its moments. The future has not arrived; it is yet to have its moments. Out of the whole history of the universe and the whole potential future of the universe, events only actually happen in the present moment which we call "Now".

Time as duration, which I discussed a few paragraphs ago, says nothing about when Now is. The variable "t" that occurs in many theories of physics and certainly in the theories of Relativity, does not refer to the concept of Now at all. Clock-time refers to the rate of physical processes but it does not refer to when they happen. The Spacetime of Einstein's Relativity incorporates this same "time as duration", the passage of clock-time, the rate of physical processes, and completely avoids any reference to moments and Now. It always surprises me when books about time discuss the concepts of Now and moments as if they can be deduced from the theories of Relativity. Even Einstein himself makes it clear, to my understanding, that this is a mistake. While one can use mathematical tools such as light cones to refer to past and future from an observer's perspective, the origin of the light cone (which is where Now is for the observer) is an arbitrary point in spacetime. The flow of moments is artificially frozen. The observer's clock is not running. Also, while one can place distant future events and event sequences onto the diagram, the observer remains at the origin and sees none of these at that moment. Any projection onto the diagram, indicating what the observer might see at a later moment, uses clock-time to make the calculations, the same clock-time that avoids any reference to moments and Now. For those that know about "proper time" and "coordinate time", please note that they are both derived from and relate to clock-time. They provide a means to envisage what two observers might perceive the other's clock to be showing but not whether they are both experiencing Now simultaneously.

The difficulty of referring to Now and moments is that they cannot be measured. There is no objective entity in the universe that tells us what today's date is. The scientific method eschews things that cannot be measured or observed, quite rightly. Physics, in particular, tends to rely exclusively on what can be measured. But can we observe anything that would indicate the reality of moments and Now?

While moments and Now cannot be measured, their effects can certainly be observed. We can identify how things would be different if there were no sequence of moments and no Now. We would then live in what is known as the block universe. All of time from the furthest in the past to the furthest in the future would exist simultaneously. We would need no memory because we would be consciously aware of all of history. Some would say that there is a block universe but we somehow travel along it so that we are located at what seems like the only moment and our brains only hold information about what we can sense at and around that moment. If this were so, there would still be a Now: the position we are at on the timeline of the universe. There would still be moments: the succession of these Now locations that we occupy. The only difference is that the block universe is usually pictured as having all of the future already fixed. Yet Quantum Theory suggests the opposite, that there is an almost infinite range of potential futures at each moment.

If there were no present, distinct from the rest of time, there would be no reason for the events of any process to be in a consistent order. All events would exist simultaneously. Of course, we picture the block universe as having the variable "t" as one of the axes but why should it be so? This is just our arbitrary way of looking at it. And I stress again that clock-time is about duration, not moments. Clocks in different places will disagree about where they are in the block universe. How then is it possible to think of the block universe, with its clock-time axis, as having any relevance to moments and Now?

One suggestion is that observers in different places, with their different clocks, really are experiencing Now at a different place in the block universe. But this cannot be so as demonstrated by the case of the perfect synchronised clocks, having experienced different gravity then brought together at the same place and the same shared moment yet showing different times.

If there were no real thing called Now, I could not be typing these words now rather than yesterday or a hundred years time. It might not be possible to measure what date it is with an instrument but I know for sure what today's date is. Of course, the actual name of the date is arbitrary but the fact that it is today's date and not tomorrow's or yesterday's means that there is such a thing as Now, this moment.

Conclusions

We have a conundrum. There is an aspect of time, duration, that we can measure and therefore use in our theories of physics. There is another aspect of time, order, that cannot be measured but its existence is evidenced by observing physical processes as they occur. Processes and phenomena have stages, separate events, that cannot all occur or exist at once. There must be the first event before the second and so on. There is a third aspect of time that also cannot be measured: the flow or sequence of moments. There is only one present moment and we call it Now. The fact that there is only one present moment, one Now, is evidenced by the fact that processes retain consistent order across all scales. Thus time as order and time as the existence of a present and flowing Now, while not measurable numerically, are nevertheless observationally evident.

If we only use the time variable that we can measure, the "t" of physics, surely we are restricting ourselves to one aspect of time and neglecting others. Many tomes on physics do restrict themselves in this way yet still talk about "when" events occur as if this can be reliably deduced from equations derived from clock-time. There are also many who argue that Now is an illusion or a misunderstanding. For example, it is not unusual to find it suggested that the scientist running an experiment at the mountain top is not sharing the same moments as the one running the experiment in the valley. This argument appears convincing at first because their clocks, previously synchronised, are now indicating different times. But when the scientists and their clocks get back together, their clocks still read different times, yet here they are undeniably in the same place and at the same moment. So clearly their clocks cannot be referring to when Now is. They can only be referring to time as duration, which varies almost everywhere.

We cannot know in any direct way that an alien in another galaxy is experiencing Now simultaneously with our experience of it. But, indirectly, we can observe that the order of processes in far galaxies matches the order of our processes. And we can detect that processes in the furthest galaxies and therefore furthest back in time, are consistent with an earlier stage in the process that is the evolving universe. This could only be so if Now in those distant galaxies occurred long before the Now that we are currently experiencing and observing. Many branches of science use observations as evidence in situations where measurement is not possible or not helpful. For me, the observational evidence for time as an ordered sequence of moments is clear enough.

I conclude that there are two quite distinct features of the universe that come under the heading of TIME. One is the rate of physical processes. It is what science refers to with the variable "t". It varies just as Einstein's Relativity (or its successors) indicate. It is clock-time. It is the time aspect of spacetime. The other feature of time is the ordered sequence of moments. It is always Now, the present moment, for all observers. The universe is a process in which each stage is a host of new events. The next host of events have not come into existence yet. The previous host of events has already gone out of existence though their evolving consequences persist within the universe in a way that is not manifest (but can be deduced). There is only ever one host of events in existence. Clock-time is simply the number of moments per clock tick. The clock at the mountain-top has fewer moments per clock tick than the clock in the valley below. Time is not one thing but two: Clock-time and moment-time.