Lecture 32: Time’s Arrow

Astronomy 1143 Spring 2014

Key IdeasWhy is there a past, present & future in time?

Time moves forward in the direction of increasing entropy

Entropy is a measure of• Disorder in a system• Number of arrangements that give same appearance

Entropy increases because easier to end up in a state that has lots of ways to be

Entropy is always increasing = 2nd Law of Thermodynamics

Our Universe must have been born with very low entropy

Could our Universe be

• Born of another Universe

• A low-entropy patch of an infinite Universe?

Time is different than space in our Universe

Although space and time are joined in relativity, there remains a fundamental difference.

We can move both ways in each spatial direction, but not in time.

We all agree that there is a past, present and future.

Why does time only flow in one direction?

Moving from order to disorderImportant work on this subject was done in the

nineteenth century by• Nicolas Carnot – wanted to know what the most

efficient engine was• Rudolf Clausius – saw that Carnot’s engine was

the same phenomenon as why things tended to reach equilibrium (such as the same temperature)

• Ludwig Boltzmann – our current understanding of microstates

Need to discuss work, energy and entropy

1st Law of Thermodynamics

Energy is conserved.

Total amount of energy does not change, it is only transformed.

Examples:

Expanding gases cool down energy is transformed into work

Ice melting in a glass total energy in particles is the same before & after

But why do ice cubes always melt instead of sometimes getting colder in hotter water?

2nd Law of ThermodynamicsDisorder (or “entropy”) increases.

This happens in ‘closed’ systems.

In open systems, entropy can be decreased through application of outside energy

Example: Earth is not a closed system

Orderly (low entropy) state:

hot cold

Disordered (high entropy) state:

lukewarm lukewarm

fast particles on one side

slow particles on other side

Energy flows from regions of high thermal energy density to regions of low thermal energy density.

(The hot get colder and the cold get hotter.)

The flow of energy from hot regions to cold can do work.

Once a system is of uniform energy density, it can’t do any more work. It has reached maximum entropy.

We obviously haven’t reached that state yet

End of the Line

Entropy Increases with Time

Unlike space, it seems as if the Universe has an arrow of time.

Time passes in the direction in which entropy increases

Later times = higher entropy everywhere in the Universe

Why this is the case is the subject of much thought and musing, but no definite answers (yet)

Measuring “Disorder”Only one way to arrange all particles on the left

Measuring “Disorder”

Six ways to arrange 5 particles on left, 1 on right

Measuring “Disorder”

Maximum number of ways is to have 3 particles on right, 3 on left

EntropyEntropy is a count of the number of

macroscopically indistinguishable states that are possible for a certain set up

Another example

Very few ways to have all billiard balls in center

Many ways for them to be spread out on the table

Not surprising: watching the cue ball break the rack and send the balls flying

Surprising: Having the cue ball round up all the balls into the rack

Explanation of the 2nd Law

So why does entropy increase?

There are more ways to have high entropy than low entropy so a system is more likely to end up in a high entropy state

But the 2nd Law can be violated

It is very, very unlikely, but possible for a system to randomly fall into a low entropy state (for example, to have all the air in this room end up on one side)

Entropy & Gravity

Gravity increases entropy (more difficult to think about than number of states)

Black Holes have very high entropy• A single supermassive black hole has more

entropy than the entire Universe did at early times.

Having gravity steadily pull matter into stars and galaxies has been increasing the entropy in the Universe

One Past, Uncertain Future

A definition of entropy – number of ways that stuff can be arranged to give the same overall appearance

If there is only one way to arrange something to have low entropy, then we can figure out what something looked like in the past.

But if we see a system with high entropy, it is unclear what it is going to do next.

We can reconstruct the past, not the future

All the King’s horses & all the King’s men….

The Beginning of our Universe

Universe must have started out in a state of very low entropy

Is this an unlikely event or a likely one?

Thermodynamics suggests unlikely, but it depends on how our Universe was born

Maybe born as a low-entropy bubble as part of a larger Universe

Leads into the idea of the multiverse

Interesting speculation, not a scientific theory

Our Universe – Low Entropy at Start

Our observed Universe is creating disorder from order

Can life be defined as something which creates order in itself by creating disorder elsewhere?

So, we need our Universe to start out at low entropy

It is extremely unlikely for this to be the case.

Evolution of our Universe“End” state of our Universe will be dark, cold

and disordered

This state will last for an infinitely long period of time

So if we transport ourselves to some random point in the history of the Universe, we will almost certainly been in the dark, disordered phase.

We are here

Most Likely State of the Universe

Most entropy in the Universe would likely be a de Sitter Universe

Empty space with a positive vacuum energy (or cosmological constant or dark energy)

Such a Universe would have everything at equilibrium and could not support life

Our Universe is headed in that direction

Is our Universe a baby Universe?

To avoid having to appeal to an extremely unlikely event to explain the low entropy of the early Universe, we maybe can appeal to the (unknown) theory of quantum gravity

Quantum mechanics allows for fluctuations in energy, etc

Maybe a quantum theory of gravity will allow for fluctuations in spacetime in de Sitter universe, creating something very interesting

Making Babies• In a Universe ….

•Quantum fluctuation in spacetime creates a bubble connected by a wormhole.

• Wormhole is pinched off, leaving a baby Universe that can’t communicate with any other Universes

• Creation of a baby Universe increases entropy, even if it is born in a low-entropy state

Eternal Inflation?

A related possibility is that many observable Universes have sprouted from patches undergoing inflation

Under inflation, entropy increases a lot less than it otherwise would

Could one of these Universes be our Universe?

Problem Solved?

In this scenario, no beginning of time, etc. Baby universes are continually being born and breaking off or new patches inflating

The whole of these multiverses is an infinite number of possibilities, including a Universe with the properties that ours has

Back to our (possibly one of many) Universe. Is it infinite?

Possible Curvatures of Space

Is our Universe Infinite?

We don’t know. Measurement of geometry can give us a clue

How can we measure the geometry of the Universe?

If the Universe has positive curvature (> 1), then volume of Universe is finite. A light ray would eventually come back to you

If the Universe is flat or has negative curvature – not clear – I don’t like this option!

The Observable Universe is Finite. What about the Unobservable One?

Multiverse in our Universe & others

Is our observable Universe the only one?At the heart of many of these explorations of

particle physics lies the question “Why does the Universe have the properties that it has”

If there is only one Universe, how likely is it that it would make a rich, full Universe like we see today.

Philosophical appeal of “baby Universe” idea

These different “universes” may have very different physical laws