The Nature of Time

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By Ravi Sinha

11.1Dawn broke and as light illuminated his cave, our primeval ancestor woke up to experience a déjà vu. Perhaps, in that epiphanous moment, his newfangled consciousness discerned an inherent periodicity in nature- the sun rises again. On that day, several thousand years ago, man’s eternal quest to understand time began.

In 2018 AD, today – if I want to know the time, I look at the smartwatch on my wrist. The watch synchronises with my phone which syncs to the network which syncs with an atomic clock. The value of time which I finally have is accurate enough to not be off by more than a second over the span of a million human lifetimes. Neither the rotation of earth around its axis nor its revolution around the sun is accurate enough to be used as a timekeeping standard anymore. Still, with all this progress, we must humbly admit that we do not know if what we measure as time is an entity inherent in physical laws of nature or a figment of man’s creation.

Our understanding of the flow of time started with understanding correlations between observable periodicities of nature. What could be seen and measured has shaped the theories of time proposed by contemporary thinkers, philosophers and scientists over the course of human history. The earliest farmers (over 10,000 years ago) used periodicity in constellations to predict seasons, and scheduled night-time work for full moon nights. Around 1500 BC, the quest to be more granular in modeling natural periodicity inspired us to build sundials and water clocks. The ubiquitous circular face of contemporary analog clocks is inherited from sundials.

In Vedic texts dating to the 2nd millenium BC, Indian philosophers professed that the universe goes through repeated cycles of creation, destruction and rebirth-  through “kaal-chakra”, the “wheel of time”. This was not the only reference to a cyclical idea of time in our history. Plato, who lived in 4th century BC, believed that we are part of a big time-churning machine and when planetary configurations return to its initial state (a process that takes 25,800 years), everything would start again. This idea of cyclical time, in some form, enjoys some following even today. A group of modern cosmologists hold the view that the universe has a “bouncy fate”, that it’d go through repeated cycles of expansion and contraction, and we are currently in an accelerated expansion phase.

Plato’s student Aristotle held a different view of time. He saw time as an attribute of movement, a measure of change. To him, time does not exist on its own. He called time “the numeration of continuous movement” or “the number of change in respect of before and after”. He argued, since time is essentially a measurement of change, it requires the presence of a soul capable of “numbering” the movement. He also questioned the realness of time:

If time essentially consists of two different kinds of non-existence (the past or the “no longer”, and the future or the “not yet”) separated by a nothing (the instantaneous and vanishing present or “now”), how then can we talk of time as actually existing at all?

11.2The idea that time is an illusion has been a common theme in Buddhist philosophy (since 6th century BC). In the modern scientific era, since John Wheeler and Bryce  DeWitt formulated their equation (in 1967), several physicists believe that time might not be a fundamental phenomenon of nature but an emergent one. It’s worthwhile to trace the evolution of scientific thought that led us here.

This first leap into modern science is often attributed to the Italian physicist and mathematician Galileo Galilei. It is believed that he began his work with time as a result of observing the swinging of the bronze chandelier in the cathedral of Pisa one day and comparing its periodic motion to the regular beat of his own pulse. Galileo realised that, contrary to what we might expect, the number of beats the chandelier took to complete a swing did not decrease as the lantern’s motion reduced, it remained virtually the same. This was a very important discovery which influenced the science of flow of time from that point on.

Applying Galileo’s discovery to use, Dutch inventor Christiaan Huygens invented pendulum-driven clocks (in the late 17th century) which, over time, became accurate enough that minute hands began to be added to the clock face. For a long time (until 1927), the pendulum clock reigned as the most accurate measurement of time.

As these clocks could not be used for navigation on the deck of rocking ships, marine chronometers were developed. These portable, accurate timepieces helped accelerate the Age of Discovery and Colonialism. At around the same time, Newton saw the apple fall. His view on time is best described by the scholium at the beginning of Principia. To paraphrase:

Absolute, true, and mathematical time, from its own nature, passes equably without relation to anything external, and thus without reference to any change or way of measuring of time (e.g., the hour, day, month, or year)

He believed that absolute time is measurable but imperceptible and can only be truly understood mathematically. For him, one-dimensional absolute time and three-dimensional geometry of the universe were independent and separate aspects of objective reality, and at any given point in absolute time, all events in the universe occurred simultaneously.

Through his theory of special relativity (in the early 20th century), Einstein deposed the concept of simultaneity from its Newtonian pedestal. According to theory of relativity, simultaneity is not an absolute relation between events; what is simultaneous in one frame of reference will not necessarily be simultaneous in another. According to Einstein, there is no single timekeeper for the Universe; precisely when something is occurring depends on one’s precise location relative to what one is observing.

To highlight how simultaneity is relative, we have to consider an example: imagine an observer seated midway inside a speeding traincar and another observer standing on a platform as the train moves past. A flash of light is given off at the center of the traincar just as the two observers pass each other. For the observer on the train, the front and back of the traincar are at fixed distances from the light source and according to him, the light will reach the front and back of the traincar at the same time. For the observer standing on the platform, on the other hand, the rear of the traincar is moving (catching up) toward the point at which the flash was given off, and the front of the traincar is moving away from it. As the speed of light is finite and the same in all directions for all observers, the light headed for the back of the train will have less distance to cover than the light headed for the front. Thus, the flashes of light will strike the ends of the traincar at different times. What was a simultaneous flash for the observer inside the traincar is not a simultaneous event for the observer outside.

11.3This difference in observed time for observers moving at different speeds is referred to as time dilation. Although it sounds counter-intuitive, time dilation has been verified experimentally by precise measurements of atomic clocks flown in aircraft and satellites. This theory, conceptually and practically, allows time-travel into the future. By going really fast one can travel to the future at a rate faster than 1 hour per hour. For this time-travel to be significantly observable by us, the speed needs to be very high, near light-speed. A cosmic ray muon is an unstable subatomic particle that has a mean lifetime of 2.2 microseconds. They get created in the upper atmosphere and though we expect them to travel just 660 meters before decaying (considering light speed = 300,000 km/s), the effects of time dilation allows cosmic ray muons to survive the over 100 km long flight to Earth’s surface and beyond. In the Earth’s reference frame, the muons have a longer half life due to their high velocity. As a consequence, approximately one muon passes through the palm of each human’s hand every second.

In 1907, Einstein’s former professor, Hermann Minkowski conceived of space and time in a single formulation: a four dimensional continuum called spacetime. Spacetime behaves like a stage for particles to move through the universe relative to one another. When particles occupy the same spacetime location, they can interact with one another. This version of spacetime was incomplete, however. It didn’t include gravity, until Einstein’s theory of general relativity in 1916.

The fabric of spacetime is continuous, smooth, and gets curved and deformed by the presence of matter and energy. The theory suggests that what we experience as gravity is the warping of space and time. Gravity is the curvature of the universe, caused by massive bodies and other forms of energy, which determines the path along which objects travel. That curvature is dynamical, moving as those objects move. In physicist Wheeler’s words:

Spacetime grips mass, telling it how to move. Mass grips spacetime, telling it how to curve.

The theory also provides an explanation of how gravitational fields can slow the passage of time for an object as seen by an observer outside the field. The GPS satellites that help us navigate use both special and general relativity to keep their clocks synchronised with the ones on Earth. The satellite transmits a time signal to a GPS receiver which can then determine its distance from the satellite by measuring the time that the signal took to reach the receiver. Even small misalignments would add up over time to cause major errors in on-ground navigation. Both the speed of the satellite in orbit around Earth and the difference in the spacetime curvature between the satellite in orbit and the receiver on Earth’s surface must be accounted for to obtain an accurate positioning system.

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If we extrapolate and imagine places of extreme gravity, such as a black hole, an object falling into a black hole appears, to an external observer to slow as it approaches the event horizon, taking an infinite time to reach it. For an observer outside the event horizon, the object seems to be immortally stuck at the event horizon. For the observer who falls in, however, time would seem to pass as normal. From his perspective, it’d only take him seconds before he hits the singularity at the centre of even the most massive black holes.

There could also be potential distortions in spacetime that’d allow time-machines to work. Some scientists like the idea of “wormholes,” which can be shortcuts through spacetime. When you connect two causally disconnected regions, it holds the possibility of not only linking two different locations in the Universe, but two different locations in time. If such a wormhole were traversable, travel back to the past could be possible in reality. Although it’s theoretically sound, we haven’t seen any evidence of a wormhole in our universe yet.

We’ve always deployed the best of contemporary technology for measuring the flow of time and defining its universal standards. The international standard unit of time is the second and its definition has evolved from being a fraction of solar day to a fraction of an ephemeris year to the “atomic” second in the modern, quantum era. Since 1967, the second has been defined as exactly 9,192,631,770 times the period of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. Our tools complement our flights of imagination in understanding time. Over the past century, we have increasingly looked at time through the quantum lens.

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While quantum mechanics regards the flow of time as universal and absolute in a selected rest-frame, general relativity regards the flow of time as malleable and relative. In the 1960s, a successful attempt to combine previously incompatible ideas – quantum mechanics and general relativity – gave birth to what is known as the Wheeler-DeWitt equation. This equation solved one problem but created another. In this equation, time has no role. This led to a big conundrum among physicists which is referred to as the “problem of time”. Does this mean time is of no significance in the fundamental laws of nature? Carlo Rovelli, an Italian theoretical physicist and the author of The Order of Time, has a strong opinion on this:

We never really see time. We see only clocks. If you say this object moves, what you really mean is that this object is here when the hand of your clock is here, and so on. We say we measure time with clocks, but we see only the hands of the clocks, not time itself. And the hands of a clock are a physical variable like any other. So in a sense we cheat because what we really observe are physical variables as a function of other physical variables, but we represent that as if everything is evolving in time.

11.6What happens with the Wheeler-DeWitt equation is that we have to stop playing this game. Instead of introducing this fictitious variable—time, which itself is not observable—we should just describe how the variables are related to one another. The question is, is time a fundamental property of reality or just the macroscopic appearance of things? I would say it’s only a macroscopic effect. It’s something that
es only for big things.

Sean Carroll, cosmologist at CalTech, believes the questions about whether time is real or not are unproductive. A worthwhile question for scientific exploration is whether time is emergent or fundamental. Temperature and pressure didn’t stop being real once we understood them as emergent properties of an underlying atomic description. While this may be the biggest open question about time, it is far from the only temporal conundrum.

A close second is the strange fact that has confused philosophers and physicists since the 19th century: the laws of physics don’t explain why time always points to the future. All the fundamental laws—whether Newton’s, Einstein’s, or the quantum rules—would work equally well if time ran backwards. On the other hand, our most common experience of the world is that time has a certain direction. We are born, grow old, and die; eggs break; liquids mix; and our offices tend to get more disordered – not the other way around. As far as we can tell, though, time is a one-way street; it never reverses, even though no laws restrict it from doing so. This one-way behavior is inherent in only one law in science, the second law of thermodynamics, which says – the entropy of isolated systems usually increases and never decrease with time. Entropy can be thought of as a measure of disorder or of information contained by the system; thus the Second Law implies that time is asymmetrical with respect to the amount of order in an isolated system: as a system advances through time, it becomes more statistically disordered. An ice cube dropped into a hot cup of coffee cools the coffee and heats the ice cube simultaneously. But the process is not reversible: it is a one-way street. The law says nothing about why it happens this way.

11.7Reversing time’s arrow would be equivalent to lowering entropy. In a thought experiment from 19th century, a powerful imp called Maxwell’s demon is able to perform such a separation for a gas by knowing the position and speed of every gas molecule in a box with a partition. Using a shutter over a hole in the partition, the demon restricts high-energy molecules to one side and allows the low-energy molecules to collect on the other side. It turns out that the demon would have to expend energy and raise its own entropy, so the Universe’s total entropy would still rise. A recent experiment claims to replicated Maxwell’s demon for about 60 atoms, lowering entropy of the system by 2.44. This could have immense potential in the world of quantum computing. If Maxwell’s demon were replicable at classical scale, one could then argue that time-reversal would be thermodynamically feasible, but this still might not lead to us experiencing yesterday again. That relates to a different notion of time; the perceptive arrow of time which corresponds to the human’s psychological perception of time.

Things we remember are in the past. We know we have moved forward in time if we can remember more things “now” than we did in a “previous” moment. We seem to be capable of remembering whether we knew something “in the past.” We seem to be able to predict, with some degree of accuracy, events which happen in the future, yet we also lack complete knowledge of the future. The psychological flow of time is deeply entwined with human memory and our perception of cause and effect. It is heavily influenced by dopamine levels in our brains. In subjects with impairments which affect dopamine levels, like Parkinson’s disease, schizophrenia, and attention deficit hyperactivity disorder (ADHD), time perception impairment has been observed. The relationship between thermodynamic arrow and perceptive arrow of time is not well-established in physics by experimental evidence, but there are several theories that could offer a solution.

Those who agree with the Copenhagen interpretation of quantum mechanics believe that quantum evolution is governed by the Schrödinger equation, which is time-symmetric and the irreversibility in the quantum arrow of time emanates from wave function collapse. In the quantum mechanical version of entropy, it isn’t heat that flows when entropy changes, it’s information. Some quantum physicists claim to have found the fundamental source of the arrow of time. Energy disperses, and objects equilibrate, they say, because of the way elementary particles become intertwined when they interact — a strange effect called “quantum entanglement.” “Quantum entanglement” first emerged on the scientific horizon as a mental experiment by Einstein and his colleagues. They discovered quantum entanglement lurking in the equations of quantum mechanics and realized its utter strangeness. It described particles that are mysteriously linked regardless of how far away from each other they are. Einstein along with his colleagues Boris Podolsky and Nathan Rosen published a paper on the paradox that arises when one considers the implications of quantum entanglement. He considered such behavior to be impossible, as it violated the local realist view of causality – how can particles that are located far away influence each other, instantly. They argued that the accepted formulation of quantum mechanics must therefore be incomplete.

In 1964, an Irish physicist, John Stewart Bell, devised an experimental test that debunked the theory that there could be preset understanding between the particles, as believed by Einstein. Consequently, the prevalent understanding is that information indeed travels between entangled particles, potentially at speeds faster than light can travel. Entangled particles, hypothetically, if taken light years apart, would be able to share information instantly. Not only can two events be correlated, linking the earlier one to the later one, but two events can become correlated such that it becomes impossible to say which is earlier and which is later. It seems, to the best of our knowledge, that time does not exist for entangled particles. “If you have spacetime, you have a well-defined causal order,” said Caslav Brukner, a physicist at the University of Vienna who studies quantum information. But “if you don’t have a well-defined causal order,” he explained, then “you don’t have spacetime.” Some physicists take this as evidence for a profoundly non-intuitive worldview, in which quantum correlations are more fundamental than spacetime, and spacetime itself is somehow built up from correlations among events.

11.8Seth Lloyd, Professor of Physics at MIT, puts it into perspective:

The present can be defined by the process of becoming correlated, being entangled with our surroundings. The arrow of time, then, is an arrow of increasing correlations.

Throughout our time on Earth, we have aspired for increased correlation between our theories and experiments with Nature. The greater the correlation, the better our understanding of the universe and the higher were our chances of survival. The core essence of science is to propose theories and make predictions that, if tested

over time, yields observations which stay true to the predictions. Time is central to the scientific process. Understanding periodicity in nature helped us with agriculture, helped us survive in harsh conditions, also led to the industrial revolution and evidently prolonged our time on Earth. No other creature has been able to increase its average lifespan the way humans did. Understanding the limit to an individual’s lifetime made us preserve our learnings, our knowledge and methods, so the generations following our own do not start from a blank slate. Within the span of last 400 years, we have gone from observing pendulums to exploring the fate of our universe and our place in it. We are moving towards the future, intellectually, at a faster pace than ever. It is also true that during this time span, we have proposed, accepted, deposed and reinstated contradicting theories of time. In hindsight, it’s fascinating to see how the prevalent theories have been also periodic in some level of abstraction. We do not know what the future holds, but we’ll surely become more entangled with the universe, and more aware of each other. Until then, we continue our endeavour to develop a theory of time that can stand for all eternity.

References:

  1. https://cds.cern.ch/record/381232/files/9903010.pdf
  2. http://classics.mit.edu/Plato/timaeus.html
  3. http://faculty.arts.ubc.ca/ssavitt/Courses/Phil462A/Aristotle%20(Time).pdf
  4. http://www.buddhistinformation.com/buddhism_and_the_illusion_of_time.htm
  5. http://muse.tau.ac.il/museum/galileo/pendulum.html
  6. https://plato.stanford.edu/entries/newton-stm/scholium.html
  7. https://www.worldscientific.com/doi/abs/10.1142/9789812386540_0010
  8. http://www.drchinese.com/David/EPR.pdf
  9. https://www.quantamagazine.org/time-entanglement-raises-quantum-mysteries-20160119/
  10. http://www.preposterousuniverse.com/blog/2013/10/18/is-time-real/
  11. https://www.wired.com/2014/04/quantum-theory-flow-time/
  12. http://pi.math.cornell.edu/~numb3rs/luthy3/thearrowoftime.html
  13. http://www.w41k.com/28027
  14. https://arxiv.org/pdf/1302.2603.pdf
  15. https://www.nature.com/articles/s41586-018-0458-7
  16. https://www.quantamagazine.org/quantum-entanglement-drives-the-arrow-of-time-scientists-say-20140416/