Monday, 1 October 2018

On The Nature Of Time: How It Informs & How It Beguiles

Time is one of the most intriguing aspects of the reality we inhabit - it informs us and it beguiles us, often simultaneously. In this blog post I will explain both. I will begin with how it informs us. The first thing to say is that time is not just a concept in our head (although it is certainly that too) - it is a fundamental part of the reality we study empirically. Time informs us of the age of just about everything, from the age of the universe (about 14 billion years), to the age of the earth (about 4.6 billion years) and the age of life on earth (about 3.8 billion years). 

Whether it is radioactive analysis regarding rates of decay, the potassium-argon method of dating, geologic observation, isotopic analyses, or paleontological evidence, the age of the earth is measured using reliable multivariate evidence gathering (those same methods work equally well with other astronomical objects too - meteorites, specifically - that formed out of the same material as the earth did). The science is reliable and robust.

On top of that we have a wealth of material gathered on the unification of genetic and paleontological data for creating phylogenetic trees in biological evolution. The human genome project has provided us with accurate information about the history of evolution through analysis of DNA and the chain of events which led to our species and other primates. The dates all complement the overall picture perfectly, from studies of taxa and the many ancestral lineages (although in some cases, with cladistic ‘hierarchies’ or ‘trees’ it can be difficult to practically place species in their correct topological relations, even though the theoretics are robust), to translocation of individual genes, even knowing at which point in the tree of evolution the chromosomal fusion occurred in our ancestors for Homo-sapiens to evolve. 

The upshot is, time is a very real and epistemologically robust phenomenon. The notion of an arrow of time - time as a one way forward direction - has its root in the second law of thermodynamics. And at the Einsteinian level of physics, the more intense the gravitational field, the slower time passes. In other words, an atomic clock on top of the Eiffel tower will show a slightly faster time than an atomic clock at the bottom of the Eiffel tower due to the earth's gravitational effects on time.

To give you an idea of how absurd it is to argue against time being a real, measurable thing - the ultra-precision of atomic clocks in the present day can measure the accuracy of time to about a margin of error of 1 second every 30 million years. The gulf between people who argue for a young earth and those who accept the multitude of repeated, verifiable scientific measurements of time is about as wide as can be.

To put that into perspective; if Jack wrongly believes the universe is 6,000 years old, and Jill rightly believes it is 14 billion years old, then Jack is wrong by an astronomical 7 orders of magnitude. To understand what a whopping error this is, an order of magnitude is written as 10 to the nth power (100,000 has six digits, 1,000,000 has seven, and so on). The universe is literally 2.3 million times older than Jack thinks it is.

Time, Einstein and relativity
I said that time provides us with a reliable dating metric, but I also said that it is an utterly beguiling phenomenon - and that is what we'll turn to next. The first key thing to understand is that the nature of time is very much bound up in our perceptions of reality from a given vantage point. When asking "What is reality?" Einstein showed with his special relativity that we are as well to ask “What is reality for ‘me, and under what condition am I experiencing it?”. I do not mean to suggest that all of the things we call objective facts are to be swallowed up and swiftly replaced by some form of woolly relativism – I mean merely that reality is perspectival, because facts about reality depend on the perspective of the individual, and time is no different. 

Reality cannot be confined to a single perspective, because for a human being, reality changes when perspective changes. Here’s an example of how the mind and the universe harmonise to confound our intuition. Our intuition tells us that an object cannot be both 2 metres long and 3 metres long at the same time - it seems logically impossible, particularly as Euclidean geometry forbids it, and because we intuit ‘facts’ such as ‘a line connecting two points can only have one length’ as being concrete truths about nature. 

But Euclidean geometry is an intuitive part of our brain that does not apply at the deeper cosmological level where other geometries can be used. If every truth or fact or observation remains true relative to the mind’s frame and reference point at any given moment, then it stands to reason that there are going to be a number of lenses through which we view reality, just as there are a number of ways to describe the world using ordinary language.

Once we learn to describe reality through the lens of various perspectives, we see how an object can be both 2 meters long and 3 meters long at the same time. Much of this was thanks to Einstein, who showed that the faster an object moves, the more compressed it becomes, and that if the object was travelling at a substantial fraction of the speed of light, then someone measuring it who was moving at the same speed could measure it as 3 metres in length, whilst an outside observer would observe it as 2 metres in length. 

(Note: the length of a mass gaining object in uniform relative motion is less than that measured by an observer at rest with respect to the Lorentz-Fitzgerald contraction. That is, a material body moving through the ether with a velocity v, contracts by a factor of V(1-v2/c2) in the direction of motion, where c is the speed of light in a vacuum.)

What all this means is that Euclidean geometry is a good approximation to reality which doesn't, on first inspection, appear to be violated, but can be with further knowledge of different lenses of reality. That doesn’t alter the fact that the shortest distance between two points is a straight line, any more than the fact that a wall is made up of largely empty space alters the fact that if I kick it hard I will hurt my foot. This is the key to perspectivalism; one approximation to reality does not necessarily make it wrong if in other aspects of realty it is violated somewhere, because it all depends on the perceptual lens of reality for the beholder. 

That was an example of how the reality of space changes for a when perspective changes. Now consider how the reality of time changes for a human when their perspective changes. In physics, time is defined in terms of gravitational and electromagnetic vibrations, because vibrations have a wavelength in terms of a space metric. The term spacetime is so-named because it consists of three dimensions of space - which in simple terms one may think of as up/down, left/right, and forward/back - and a single dimension of time, represented in a four dimensional manifold (this is known as Minkowski space). 

In physics, space and time are a continuum, yet we experience them as separate, and psychologically distinct. Time is dependent on physical concepts in order to gain cogent meaning, because time is also a measurement construct, and a useful one when it has real events to bookend a discrete package of moments between one event and another. If I say "10 minutes has passed", it doesn't mean as much as saying "10 minutes has passed since I woke up at 7am this morning" - I immediately link the past to the present. 

Time itself does not seem to exist as an event, it merely helps us "locate" events and order in the universe. The same is true of space; if I say "I’m five metres away", it would also be meaningless unless I have linked it in reference to another previously established point in space with specific reference to at least one of the 3 space dimensions. If I say “I’m five metres away from the tennis court net” we now have two established points in space with which to give the five metres context. Entropy is closely linked with time (especially in its direction), because entropy increases with time. That is a statistical law which tells us that you can turn an egg into an omlette, but never an omlette into an egg.

Even though space and time are, to us, discretely package together - in physics the time component of the distance measured in spacetime is different to the space components. We are able to move freely in three dimensions in space (up-down, forward-backwards, left-right), but we can’t move freely in the linear constraints of time. 

Now things get really interesting…
To show perspective in its most potent force, let’s return to spacetime for another fascinating duality of perspective. With his special relativity, Einstein showed that if one measures time and space using electromagnetic phenomena (such as the case when light bounces between mirrors) then due to c (the constancy of the speed of light), time and space are mathematically interlocked in Minkowski space. This entails that things moving at different velocities can measure different distances, times, and states of events (called the Lorentz transformation)*

(Note: This also explains our earlier topic of how from different perspectives an object can be both 2 metres long and three metres long. It all depends on the perspective, just as the slowness of a 3 hour wait in a hospital waiting room depends on the perspective of the person waiting.)

With Minkowski space we have the interlocking of the derivative physical quantities such as energy, force, momentum, and mass, with special relativity showing that the concept of time depends on the spatial reference frame of the person making observations. I call this the inertial reference frame effect, because there is a kind of ‘frame’ impact on states of mind at different speeds. That's also why, once we plug the mathematics into the physics, we find there is no true single frame to describe physical reality. Here’s an illustration that should help:

Imagine a human observer (A) travelling in a spaceship at moderate speeds, and another observer (B) travelling in a spaceship at a speed close to the speed of light. Special relativity provides equations that respectively quantify the extent to which observer B experiences the contraction of space and slowing of time. The faster B travels the more slowly time is for him. From his own first person perspective, observer B is totally unaware of this contraction of space and slowing of time. The reason being; B’s spaceship has contracted with him, and so any attempt he makes to measure the contraction would fail because any object that he might use as a standard of length to measure the contraction has also become contracted. The same is true of his time - he would observe no peculiarity with his time, as all the standards he could use to measure time would be slowed – that would include, presumably, his brain processes and thus there would be no subjective sense of time being slowed.

If a human could get to c (light speed), he would have converted all available motion through time into motion through space; he can't go any faster. Naturally in real life terms, this is impossible for a human, but obviously it is not for a photon. In theory, if you could shrink your consciousness into a photon you would be timeless. Point of note on this: when observer B looks back at observer A he sees an exactly similar situation: observer A’s spaceship appears to have shrunk to nothing in the direction of motion with all processes in observer A’s spaceship appearing to come to a standstill.

(Note: For a photon it exists at all points along its trajectory at the same time, and only for literally an instant, a subjective duration of zero seconds.)

The only way we could record how time passes from the frame of reference of a photon is to be in that reference frame - but technically, of course, it is impossible for consciousness to reach c. Given that, as far as we can tell, consciousness is time-dependent, we require necessary awareness of the passage of time from moment to moment in order to experience the feeling of being conscious. And yet time is just another direction of motion, so when you hit c you stop moving in the time 'direction' (so to speak). 

I’ve already said that to approach c every conceivable standard in one’s frame shrinks so that one has no way of detecting a change, because the shrinkage of the moving frame is relative – relative to the standards of the “stationary” frame. The stationary aspect is important because, of course, from your reference frame there is no way to tell if it's you that is moving near c, or whether you are stationary and something else is moving past you at c.

Given the foregoing observations, as you approach c, an observer at rest relative to you will see your time slow down, but you will also see their time slow down (it’s what they call the 'twin paradox'). But it is not so much of a paradox really, because theoretically the time dilation doesn't happen to you, it happens to you as seen from another reference frame. But it is still very real, because with relativity all observations from all reference frames are seemingly equally real for the person doing the observing, yet each is different from the other when seen in overarching terms.

This is the peculiar truth attached to human perceptions of reality; if you plug the speed of light into the equation for time dilation you end up dividing by zero, which doesn't really result in infinity – it just leaves us with a hypothetical nonsense. The outcome in relativity is the same - either the time dilation is infinite at c, or time doesn't apply to motion at c. There have been lots of tests that confirm this (using two atomic clocks), as well as confirming that time does have a real status when twinned with space. The atomic clocks are quite incredible; they tick at around 7 or 8 billion times per second, and the time differential is always to the exact degree predicted by Einstein.

Another test that proves this is with the many satellites we use – they wouldn’t function properly without the allowances for relativity, because they rely on an exact timed signal being sent. This is delicate and precise because the satellites are moving very fast, and they have been tested many times, and again they match Einstein’s predictions. In the four-dimensional manifold of Minkowski space, time is motion, so at c the direction of time ceases. 

Time as a psychological force
Einstein once said - “Put your hand on a hot stove for a minute, and it seems like an hour. Sit with a pretty girl for an hour, and it seems like a minute. That's relativity!". We know from our own everyday experiences that this is true. Observing a kettle boil for three minutes will seem like longer than having a three minute chat with a fascinating person. When watching an exciting 90 minute film at the cinema, time will go much quicker than when watching a dull 90 minute film. Time is perspectival at a psychological level. 

Have you ever noticed that when you turn to look at a clock the first second seems to take a bit longer to arrive? You are actually genuinely experiencing the delay, due to the brain editing your own perception of time. This is because when you turn your head to look at the clock, the brain extends what you see backwards in time by about 50 milliseconds, back to the moment before you turned your head, which is why the first second appears fractionally longer.

The mental representation of time is contingent upon the person observing it, and it seems to me that this is because time is a fundamental concept that cannot be broken down to smaller pieces, or constructed by use of other concepts, or turned on itself for analysis. Of course one can create concepts to practically engage with time, like seconds, minutes, hours, days months and years - but they are only fictional constructs that help us order our world.

Time, like personality itself, cannot be turned on itself and be separated from the context of the mind that hosts it. This is because trying to define temporal things with anything other than the concepts related to temporality is impossible, just as trying to define mental things with anything other than the concepts related to mentality is impossible. Once we hit that discrete barrier of personal conception, we know that time out there (like say the decay of a carbon atom) isn’t time like the clinical experience of watching a kettle boil – it is a definition of a concept based on quantitative measurements and/or personal experience. 

Don’t misunderstand. The quantitative measurements in quantum theory enable us to define time in terms of vibrations of the caesium standard, but that is only because we compromise external reality in order to have a clear and linear notion. It’s not just the caesium standard - you can add to that virtually every model or metaphor we use to decipher reality – our entire set of descriptions of reality are partial and compromised, because they are implicitly human, and as a consequence, explicitly analogical and metaphorical (as are most of the rest of our descriptions).

Just as the limit of realistic perspective occurs in quantum theory where the more thinly spread the wavelength the less precise the specifics, with time one only gets a precise but narrow perspective by focusing on one single moment, where the wider one frames the context to get a clearer overall picture the less one zooms in on the detail.

The next oddity of time
This is where we reach a hugely significantly truth about the mind in relation to the time-dependent nature of consciousness itself. That is to say, the flow of time is essential for consciousness to sustain self-awareness. Given that consciousness (or brains) cannot achieve infinite energy, travelling at c is impossible - but what is clear is that the dialectic between the physical and the theoretical is also hugely prohibitive to clear cut communicable facts, and that leaves us with a brute mystery of reality that we'll probably wholly solve. This is because from whatever inertial reference frame one measures, there is a true result relative to the reference point of the one doing the measuring - so we have a simultaneity that defies our intuitive thinking. 

In other words, something has got to give here, because the theoretical equations lead to a physical conclusion that cannot be realised in real life. Theoretically time ceases at c, which means you’d stop aging, but yet consciousness is needed for time to be perceived, and consciousness cannot get to c without the body’s mass increasing to infinite amount of energy to speed.

So which is real, the practical limit on the physics of the body, or the infinite equations that embed the reality? I think the best way to answer is to say that the physical truths are accurate through the physical lens, and the theoretical parts (zeros, infinities, and difficult to interpret negative numbers) will, when pursued, tap us into the more complex reality of mathematics that exists over and above the physical universe. This is problem I attempted to solve here (and I did so, at least to my satisfaction - although it is only a snippet of a whole book I have written on the subject). 

To keep it as simple as possible, here’s another example of something theoretical that does not cross over into the practical or physical. Think of Hooke's’ law of spring compression, which states that the force needed to extend or compress a spring is proportional to that distance. In theory one can use a variation of it to predict zero or even negative lengths under certain compressive forces. But even a child knows that, in practice, it is obvious that in the physical world a spring cannot be compressed to zero or to negative lengths.

We define things in human terms by using human constructs, so length is defined in relation to other objects and sizes. What the above shows is that we are forced to use hypothetical inferences, because in nature consciousness cannot reach c and springs cannot compress to zero, and if they could, very weird things happen that run counter to our intuition. To theoretically approach c where every conceivable standard in my frame shrinks, it is still only true to say that any such contraction occurring would be contraction with respect to one's relationally defined frame at a stationary position - so the contraction is relative to every other reference frame. 

Here’s another one to consider; take the example of gravitational singularities in black holes. Say an object was approaching the black hole; the object would be torn apart by tidal forces. As the debris settled into the event horizon, time would pass much more slowly for the stuff than it passes for an outside observer of the stuff. But then the debris would be trapped in a 'forever falling around the hole' situation, never making it into the hole, because time becomes distorted at the event horizon and approaches infinity as a limit (for anything to happen in the event horizon).

This shows another clear problem between the theoretical and the actual; terms like ‘event horizon’ and ‘infinity’ or even 'time coming to a stand still at c' cannot really be literally true in a finite spatio-temporal cosmos. They are only useful as theoretical approximations, not as actual facts about reality. Although current physics does come up with two infinities in the form of gravitational singularities and in re-normalisation in quantum field theory, this involves the hypothetical subtraction of one infinity from another, so it is only applicable as a concept of ideals rather than as practically comprehensive in dealing with nature. 

Imagination is a way of leaving reality behind - but there are some interesting overlaps between reality and imagination, as the imagined is part of reality at a different conceptual level. Infinities may be thought to be a place where the real and the imagined lock horns, but a proper understanding of the real nature of mathematics helps square this circle.