Lecture

Lecture Notes

• What is time? Linear time is wrong. As you go further, time loses its structure. Quantum gravity is at the bottom of what we know and things get complicated! Time is a sequence of moments that is ordered. We intuitively assume it has a direction. The past is known as we can remember it – history. There are traces to evidence it happened. We have memories. The future has nothing, we can measure it with clocks, we have no concrete evidence it will happen. Time is a good concept for our daily lives but it stops working when we look ahead. When we look ahead, the properties don’t work. Time is layered.
• How do we measure time? Clocks measure time, but they don’t all measure the same. If one goes higher, it measures different. Atomic clocks with precision can measure this error. Your head is older than your feet!
• General Relativity Einstein predicted and showed that mass slows down time. This means closer to masses like the Earth, time is slower. Hence why our feet age slower than our heads. In our experience, the difference is not noticeable but we can measure it and on an astronomical scale it becomes more important. There is no single time in the universe.
• What does now mean? We always see things in the past, there is no meaning of now outside small distances because of the speed of light. It takes light time to travel so when we look at an object we are seeing how it looked in the past. Again, significant for astronomical distances. There is no meaning of now outside of the bubble. We are told what is real is now, but how can it be?
• Thermodynamics and Entropy The past is different from the future. Only one equation in the whole of physics shows this. The 2nd law of thermodynamics with the concept of Entropy (S). Entropy fundamentally is a statistical measure of disorder. Entropy always flows from ordered to less ordered. So it distinguishes past from future. The order is in the eye of who is looking; the order depends on what you are categorising e.g. colour, size. The past looks ordered only because of how we observe it. So, why was the universe ordered in the past? It looks ordered to us as we are the ones categorising it. To someone else with a different set of organised criteria, it may not look it. So, does it really relate to time?
• Models of Time On the quantum level, it is probability only. Time is the counting of change. We can see this back in Aristotle. Newton introduced the idea of time passing but we now go back to a more Aristotelian model.
• The brain and time The brain works by anticipating the future and remembering the past. It is a time machine. Does this make time a truly human construct? St Augustine wrote on this back in his Confessions. For example, we only ever hear one musical note at a time but our brain acts as a memory store for the ones we have just heard to piece it together in a phrase. We cannot think without time. In Search of Lost Time – Proust covers some of these themes. Time is always emotionally charged. The Buddhists describe this as the sense of suffering due to impermanence. Time is the root of our suffering as we never beat it.

Book Notes

Perhaps Time is the Greatest Mystery

Perhaps Time is the Greatest Mystery. The universe unfolds into the future, dragged by time, and exists according to the order of time.

In those same books, I also discovered that we still don’t know how time actually works. The nature of time is perhaps the greatest remaining mystery.

Why do we remember the past and not the future? Do we exist in time, or does time exist in us? What does it really mean to say that time ‘ passes ’? What ties time to our nature as persons, to our subjectivity? What am I listening to when I listen to the passing of time?

What we call ‘ time ’ is a complex collection of structures, of two layers

Because the mystery of time is ultimately, perhaps, more about ourselves than about the cosmos.

I believe our knowledge of time has reached: up to the brink of that vast nocturnal and star-studded ocean of all that we still don’t know.

Let’s begin with a simple fact: time passes faster in the mountains than it does at sea level.

Time passes more slowly in some places, more rapidly in others

This modification of the structure of time influences, in turn, the movement of bodies, causing them to ‘ fall ’ towards each other

The Earth is a large mass and slows downtime in its vicinity

If things fall, it is due to this slowing down of time. Where time passes uniformly, in interplanetary space, things do not fall. They float, without falling

time passes more slowly for your feet than it does for your head.

Things are transformed one into another according to necessity and render justice to one another according to the order of time

the whole of our physics, and science in general, is about how things develop ‘ according to the order of time ’.

The equations tell us how things change as the time measured by a clock passes.

times that change relative to each other. Neither is truer than the other.

Times are legion: a different one for every point in space.

Einstein has given us the equations that describe how proper times develop relative to each other.

Time has lost its first aspect or layer: its unity.

If the world is upheld by the dancing Shiva, there must be ten thousand such dancing Shivas, like the dancing figures painted by Matisse …H

Past and future are different from each other. Cause precedes effect. Pain comes after a wound, not before it.

We cannot change the past; we can have regrets, remorse, memories. The future instead is uncertainty, desire, anxiety, open space, destiny

Time is not a line with two equal directions: it is an arrow with different extremities.

Rebellion is perhaps among the deepest roots of science: the refusal to accept the present order of things.

All of the sons of Adam are part of one single body, They are of the same essence. When time afflicts us with pain In one part of that body All the other parts feel it too. If you fail to feel the pain of others You do not deserve the name of man.

poetry is another of science’s deepest roots: the capacity to see beyond the visible.

Rudolf Clausius. It is he who grasps the fundamental issue at stake, formulating a law that was destined to become famous: if nothing else around it changes

heat cannot pass from a cold body to a hot one.

This is the only basic law of physics that distinguishes the past from the future.

one of these equations distinguishes the past from the future.

In the elementary equations of the world, 5 the arrow of time appears only where there is heat.fn1 The link between time and heat is therefore fundamental: every time a difference is manifested between the past and the future, heat is involved. In every sequence of events that becomes absurd if projected backwards, there is something that is heating up

Only where there is heat is there a distinction between past and future.

‘ the second principle of thermodynamics ’

heat passes only from hot bodies to cold, never the other way round.

heat passes from hot to cold, and not vice versa: by shuffling, by the natural disordering of everything. The growth of entropy is nothing other than the ubiquitous and familiar natural increase of disorder.

If we think about it carefully, every configuration is particular, every configuration is singular, if we look at all of its details, since every configuration always has something about it that characterizes it uniquely. Just as, for its mother, every child is particular and unique

Yes. If I observe the microscopic state of things, then the difference between past and future vanishes.

In a microscopic description, there can be no sense in which the past is different from the future.

the difference between the past and the future refers only to our own blurred vision of the world.

there is nothing intrinsic about the flowing of time. That it is only the blurred reflection of a mysterious improbability of the universe at a point in the past.

The consequence of this discovery for our basic intuitive perception of time is the most devastating of all.

Time passes more slowly for the one who keeps moving

For everything that moves, time passes more slowly.

Nobody had imagined previously that time could be different for a stationary watch and one that was being moved.

Not only is there no single time for different places – there is not even a single time for any particular place

‘ Now ’ Means Nothing

The light takes time to reach you, let’s say a few nanoseconds – a tiny fraction of a second – therefore, you are not quite seeing what she is doing now but what she was doing a few nanoseconds ago.

The truth of the matter is that we need to give up asking the question

The notion of ‘ the present ’ refers to things that are close to us, not to anything that is far away

Our ‘ present ’ does not extend throughout the universe. It is like a bubble around us

As humans, we distinguish tenths of a second only with great difficulty; we can easily consider our entire planet to be like a single bubble where we can speak of the present as if it were an instant shared by us all.

The idea that a well-defined now exists throughout the universe is an illusion, an illegitimate extrapolation of our own experience

there is no such thing as “ the same moment ” definable in the universe

A partial order establishes a relation of before and after between certain elements, but not between any two of them.

The temporal structure of the universe is very similar to this one. It is also made of cones.

defines an order between the events of the universe that is partial, not complete.

The expanded present is the set of events that are neither past nor future

Every event has its past, its future and a part of the universe that is neither past nor future, just as every person has forebears, descendants and others who are neither forebears nor descendants.

Light travels along the oblique lines that delimit these cones. This is why we call them ‘ light cones

This is the structure of spacetime that Einstein understood when he was twenty-five years old

When a gravitational wave passes, for example, the small light cones oscillate together from right to left, like ears of wheat blown by the wind.

In this way, a continuous trajectory towards the future returns to the originating event, to where it began.

This is because the mass of the black hole slows time to such a degree that, at its border ( called the ‘ horizon ’ ), time stands still

So, to exit from a black hole, you would need to move ( like the trajectory marked in black in the following diagram ) towards the present rather than towards the future!

More than a hundred years have passed since we learned that the ‘ present of the universe ’ does not exist. And yet this continues to confound us and still seems difficult to conceptualize

If the present has no meaning, then what ‘ exists ’ in the universe? Is not what ‘ exists ’ precisely what is here ‘ in the present ’?

‘ How long is forever ? ’ asks Alice. ‘ Sometimes, just one second, ’ replies the White Rabbit.

Time is elastic in our personal experience of it.

On the one hand, time is structured by the liturgical calendar

For centuries, we have divided time into days. The word ‘ time ’ derives from an Indo – European root – di or dai – meaning ‘ to divide ’.

Sundials, hourglasses and water clocks already existed in the ancient world

It is only in the fourteenth century in Europe that people’s lives start to be regulated by mechanical clocks.

Gradually, time slips from the hands of the angels and into those of the mathematicians

For centuries, as long as travel was on horseback, on foot or in carriages, there was no reason to synchronize clocks between one place and another.

It is in the United States that the first attempt is made to standardize time.

In 1883 a compromise is reached with the idea of dividing the world into time zones

Einstein worked in the Swiss Patent Office, dealing specifically with patents relating to the synchronization of clocks at railway stations.

The rhythm of the day followed by night also regulates the lives of plants and animals.

Diurnal rhythms are ubiquitous in the natural world. They are essential to life,

Living organisms are full of clocks of various kinds – molecular, neuronal, chemical, hormonal – each of them more or less in tune with the others

The diurnal rhythm is an elementary source of our idea of time

In the ancient consciousness of humanity, time is, above all, this counting of days.

counting how things change.

Aristotle is the first we are aware of to have asked himself the question ‘ What is time? ’

time is the measurement of change.

Time is the measure of change: 8 if nothing changes, there is no time.

the existence of a time that is uniform, independent of things and of their movement which today seems so natural to us is not an ancient intuition that is natural to humanity itself. It’s an idea of Newton’s.

Legend has it that Leibniz, whose name is still occasionally spelt with a ‘ t ’ ( Leibnitz ), had deliberately dropped the letter from his name following his belief in the nonexistence of the absolute Newtonian time t.

Don’t take your intuitions and ideas to be ‘ natural ’: they are often the products of the ideas of audacious thinkers who came before us.

That which seems intuitive to us now is the result of scientific and philosophical elaborations in the past.

Remember the clocks in Chapter 1 that slow down in the vicinity of a mass? They slow down because there is, in a precise sense, ‘ less ’ gravitational field there. There is less time there.

Time thus becomes part of a complicated geometry woven together with the geometry of space.

the residual temporal scaffolding of general relativity, illustrated in the previous chapter, also falls away if we take quanta into account.

The time measured by a clock is ‘ quantified ’, that is to say, it acquires only certain values and not others. It is as if time were granular rather than continuous.

A minimum interval of time exists. Below this, the notion of time does not exist – even in its most basic meaning.