1

We saw last time how the pendulum clock revolutionized our means

of keeping track of time, but today we’ll see how the analysis of its

movements by Galileo and others eventually did far more than that.

Galileo’s work involved

taking the motion of the

pendulum out of time, and

describing its movement

mathematically. Rene

Descartes – he of “I think,

therefore I am” fame – was a

contemporary of Galileo, and

developed a system for

recording the position and

movement of objects in time

which we still call the

Cartesian coordinate system.

2

This was another great

revolution in our thinking

about time and space – it

suggested a uniform,

measurable space around us

that could be contained

within this coordinate

system, and the flow of time

could then be represented by

timeless mathematical

curves within that space.

Further, time itself could be assigned to a coordinate – giving us

our first mathematical view of time as a space-like dimension.

A basic “spacetime” diagram

showing the orbit of the

Earth around the Sun.

3

These mathematical tools, invented in the 1600’s, were

critical to the work of Newton in the formulation of his laws

of motion, and fundamentally shaped his views on space and

time. Space itself was absolute and infinite, and the objects

in it moved in perfectly predictable ways as time passed.

Time itself, according to

Newton, was “absolute,

true and mathematical

time, [which] of itself, and

from its own nature, flows

equably without relation to

anything external.”

Any object at any point in

space experiences that

same universal and

absolute time – including a

shared ‘present moment’.

4

This notion of a constant and universal time allowed Newton’s

laws to be extended into the infinite future and past – given a

set of initial conditions, the laws of motion seemed able to

describe all future (and past!) behaviors of objects in space.

This so-called “clockwork universe” was a key development in

the philosophy of determinism, an idea we’ll return to later.

However, our issue at the

present is Newton’s view on

the universal nature of time.

By the late 19th century, this

view had begun to be

seriously questioned by

scientists like Hendrik

Lorentz and our old friend

Henri Poincaré. Henri Poincaré,

1854-1912

Hendrik

Lorentz,

1853-1928

5

Poincaré was working for the French government on ways to

synchronize clocks across the newly developed time zones by using

beams of light. In the process, he and Lorentz had begun

developing the mathematics necessary to describe how light would

appear to move through the universe if its speed were constant to

all observers in some particular state of motion, or reference frame.

But their work was soon

deeply extended by a

young German physicist,

Albert Einstein, who

argued that the speed of

light really was constant –

to all observers, regardless

of their state of motion.

6

Einstein had long been troubled by a simple idea – imagine

riding a bicycle with a headlight shining out of its front. Is the

light from your bike moving faster because of the speed at

which you are riding? If you could ride your bicycle at the

speed of light, would you ‘catch up’ to the light in some way?

Light arrives at v+c?

Einstein postulated that the answer was “no” – that all observers

would see light moving at the same speed regardless of their own

relative motion. That demanded that observers in relative motion

must measure space and time intervals (the components of speed)

differently – space and time were not absolute, but relative!

No!

7

This difference in the rate

at which time ‘runs’ is an

effect often referred to as

“relativistic time dilation”,

and is one of the most

fundamental – and best-

tested! – outcomes of what

Einstein would call his

theory of special relativity.

In particular, special

relativity demands that

clocks in motion measure

time moving ‘more slowly’

than clocks at rest.

Einstein’s bicycle rider can never catch up

to the light from the flashlight, because his

‘clock’ runs slower and slower as he

approaches the speed of light!

One way to visualize how this might work is to imagine a laser

reflecting off of a mirror in a moving spaceship. The astronaut

only sees the beam go back and forth – but the observer on Earth

sees the beam take a much longer path. The only way that the

beam can be moving at the speed of light for both observers is if

time is running slower on the spaceship than on the Earth!

8

This is a profound effect –

and one that we’ll explore

in some more detail next

time when we discuss the

role of time in space travel.

But the impact of special

relativity on our notions of

time runs far deeper, and

ultimately reveal a central

flaw in our notion of the

present moment.

An insightful illustration of this deeper issue is Einstein’s

famous “moving train” thought experiment. Imagine you are

observing a train car as it passes directly in front of you.

9

Now suppose at precisely the moment that the car is front of you,

lightning strikes just in front of and just behind the train car. You

observe the two lightning strikes to take place simultaneously.

However, an observer on the moving train car will experience

something very different. Because of her motion, light from the

strike at the front of the car – along with all other possible

physical effects caused by that strike – will reach her before

light from the back of the car will.

10

So the two observers here report something very different

about how the events occurred in time – the ‘stationary’

observer says both strikes occurred at the same time, while the

‘moving’ observer says that one occurred before the other!

Two lightning strikes

at once – cool!

Back-to-back lightning strikes – cool!

And what if there are

two cars, moving in

opposite directions?

In that case the situation

really gets strange

indeed!

11

The strikes are

simultaneous.

The strike on

the left

happened first,

then the one

the right.

12

The strike on the

right happened

first, then the

one on the left.

The two observers on the train, despite being in almost exactly

the same place, experience a completely reversed sense of the

past, present, and future! This neatly illustrates the “Relativity

of Simultaneity” – the simple fact that observers in motion

relative to each other experience a completely (and potentially

radically) different version of “now” unfolding. Holy Crap!

13

Think about what this does to the traditional vision of 4-dimensional

spacetime. Newton had thought that time was a universal absolute,

and that all observers experienced the same “now” as time passed.

The present was like a wave passing through time – and as such had

a meaningful physical reality, even if it wasn’t clear from the laws of

motion which way the future or past lay.

Special relativity does away with even this aspect of time – not

only is there no clear distinction between the past and future, there

is no meaningful definition of the present either. Observers in

motion (as we all are!) experience different versions of “now”,

along with different versions of the past and future!

14

This way of thinking about the universe is often referred to as

“block time” or the “block universe”. Because there is no

distinction between past, present, and future in the block universe,

there is arguably no passage of time at all – just a collection of

configurations in space-time, whose relationships depend entirely

on the changing positions of objects within the universe.

Is our universe really like

this? Does time not really

exist? Many modern

physicists believe so, and

Einstein himself would have

agreed in some ways. But

what about those ‘arrows of

time”? What about our

conscious awareness of

time, or concepts like free

will? Is the relativistic

universe as deterministic as

the Newtonian universe?

If all moments are equally real, why

do I only experience “now”?

15

We’ll pick up on those topics again in a couple of weeks –

first we’ll need to explore the universe a bit more

carefully, and we’ll start next week with a trip to the stars!