Ever wish you could travel backwards in time and do things differently? Good news: the
laws of physics seem to say traveling backwards in time is the same as traveling forwards.
So why do we seem to be stuck in this inexorable flow towards the future? It's time to begin
our journey towards really understanding time.
The laws of physics describe how the universe at one instant evolves into the universe at
the next. But those laws don’t distinguish between the future and the past. Reverse the flow
of time and their equations work exactly the same to describe a universe in rewind. That’s
true from the subatomic realm of quantum mechanics to the cosmic realm of Einstein’s general
relativity. But if time doesn’t have a preferred direction in physics, why does time seem to
drag us with it, and only in one direction? Why is there an arrow of time?
There are two distinct ways in which we perceive the unidirectionality of time. One is external:
an egg might splatter when you drop it, but will never spontaneously reassemble. Our whole
universe decays in the inexorable rise in entropy as time ticks forward. The other place
we perceive the arrow of time is internal: we lay down our memories in an ordered sequence
of prior events. We remember the past, but not the future.
Today we’re going to dive into the first part of this - How does entropy break the
symmetry of time, and cause the future to differ from the past. We’ll follow with
an episode exploring why this breaking of time symmetry on the cosmic scale defines
the experience of time that we experience in our own brains.
So what exactly do we mean when we say the laws of physics don’t care about the direction
of time? Basically, if you reversed the motion of all particles in the universe - sent them
back exactly in the direction they came, and used the laws of physics to calculate what
would happen - you’d predict that those particles should perfectly retrace their steps,
all the way to the Big Bang if you calculated that far.
Let’s look at a simple example. We’re going to use our good-old block universe picture,
where we have 2-dimensions of space and one dimension of time, with time flowing upwards.
The block universe just sort of exists a-temporally. The experience of time is had by looking at
time-slices in a particular sequence, like a flip book. OK, so imagine two particles
moving towards each other - let’s say, electrons. They move up in time and towards each other
in space. When they get close they deflect due to the repulsive electrostatic force between
them.
Newton’s laws of motion combined with Coulomb’s law perfectly describe how the electrons’
positions change over time. But if we flip this diagram on its head - reverse the flow
of time, it still looks like two electrons bouncing off each other. The same equations
perfectly describe the bounce in both directions, and those equations don’t seem to prefer
one direction or the other.
So the laws of physics don’t care about the direction of time. They just describe
the relationship between time slices of our block universe. Time has a symmetry in the
sense that the past and future aren’t differentiated by the laws of physics. And those laws don’t
even require time to “flow” - it’s just another dimension like space.
There is a powerful exception to this. The second law of thermodynamics states that this
stuff called entropy must always increase or stay constant - entropy never decreases
over time. So the 2nd law does dictate a direction for time - it breaks the symmetry. To see
why, we’ll need to review entropy. We’ve talked about it before, and this is a great
episode for a refresher. There are actually several ways to think about entropy. Today
we’ll talk about it in terms of distribution of energy. Energy can take many forms, and
can be transferred between forms and between objects. For example, kinetic energy is transferred
between our electrons when they collide.
Over time, energy tends to get shared out as evenly as possible due to, say, collisions.
So if you had many ele ctrons in a box, and half of them had a lot of kinetic energy - were
moving fast, while the others had none - pretty quick energy would be shared out and it would
stay shared out. It’s very unlikely that through random collisions, half the electrons
would get all the energy and the other half end up with none.
So if you start from a situation where energy is not perfectly randomly spread out, then
over time it’ll become more spread out. Entropy measures how randomly distributed
the energy in a system is. Higher entropy means more random. The second law of thermodynamics
tells us that entropy must increase over time - which just means that a system that starts
out in a very specific, non-random state will tend to become more random. It’s a statistical
effect - it’s possible for small fluctuations to happen, local drops in entropy, but the
larger the system the less likely it is for entropy to reverse.
So how does this set the forward direction of time? Actually, it doesn’t. The 2nd law
just tells us how a system is likely to change from a position of low entropy - in either
time direction. To understand why one particular direction ends up being chosen, we need to
return to the block universe.
Let’s start with a handful of particles with low entropy. You can do low entropy by
having a weird distribution of velocities, but you can also do it by clustering the particles
in one spot in the available space. Let’s give those particles random velocities and
see what happens in the following time steps.Even though the velocities pointed in random
directions, the cluster will inevitably disperse. Entropy increases as energy spreads out to
all possible states - in this case towards all possible locations the particles could
occupy.
In this case, we defined the “up” time direction in the block universe as “towards
the future”. But what does this look like going backwards in time? Uh, exactly the same
actually. Random velocity directions will tend to spread this cluster apart in both
time directions.
Again: if you take any low-entropy system and look at steps either before or after it
in time, entropy is likely to be higher. Entropy actually doesn’t care about the direction
of time any more than the other laws of physics - it just wants to increase in adjacent time-steps,
in either direction.
But if you live on either side of the starting, low-entropy point, you perceive an asymmetry
in time - particles expanding, entropy increasing on one side, or particles converging,and entropy
decreasing on the other. Zoom in to individual particle interactions and you see perfect
reversibility of the laws of physics, but zoom out and time’s arrow emerges. The presence
of an entropy minimum dictates the arrow of time - on either side of that minimum, the universe is overwhelmingly
likely to evolve in a very particular way.
The real-world situation represented by this diagram is called an entropy fluctuation.
We experience entropy decrease very occasionally and, typically, on very small scales due to
random alignments of particle trajectories or however else energy is moving around. Entropy
can decrease, reach a minimum, and then will be seen to increase - now on both sides of
the point in time of that minimum.
OK, what does all of this mean for our universe and the universal arrow of time? Well it’s
no accident I chose “expanding particles” to illustrate evolving entropy. When we measure
the velocities of particles across our universe - in the form of galaxies
- we don’t see random motion. We see galaxies racing away from each other, which means they
were once more closely clustered. This is the expansion of the universe, and it’s
the manifestation of the 2nd law on the largest of scales. We know that entropy was lower
in the past because we can trace the positions of galaxies and the particles that comprise
them back and calculate a much denser, more “special” arrangement - in fact an incredibly
low entropy arrangement. That would be the Big Bang. Given that knowledge, it’s not
surprising that entropy is increasing in what we now think of as the forward direction of
time in our universe.
So this is one argument for the direction of the arrow of time. If we think of time
as just a series of instances - slices of the block universe connected by the laws of
physics, then we can break the symmetry in the direction of time if one of those slices
has a very unusual arrangement. The universe must get less special in either direction,
so someone looking at the universe from either side would see a directionality to time. OK,
so in our universe, what caused this initial special arrangement, this extreme density of
the Big Bang and its corresponding ridiculously low entropy? This is actually an open question
in physics, and we’re not going to address it right now. But one possible consequence
is that if you trace all particles backwards in time to this original “special” slice,
at which velocities are all random, and keep tracing out the other side then you should
see entropy increasing again, but now backwards in time. It’s not crazy to imagine a symmetric
universe in which those particles fan out again like a reverse Big Bang. This might
be the case if the Big Bang resulted from an insanely improbable, universe-sized entropy
fluctuation.
There’s no evidence that this is true - but if it was true we’re presented with a fun
scenario. If entropy increases backwards in time before the big bang, does that mean time
runs in reverse back then? Would that reverse Big Bang lead to a time-reversed universe?
It’s not entirely crazy to think so - but first you need to explain one thing. How is
the thermodynamic arrow of time - the flow of time defined by increasing entropy -connected
to our sense of the flow of time? Why do we experience time sequences passes in the same order
as increasing entropy? To understand why we only remember the past, not the future, we
need to delve deeper. In fact it involves information theory and quantum entanglement,
so we need another episode. Or more than one. Because on Space Time we’ve always given
plenty of time to space, but it’s timely to spend time on that fascinating dimension
that deserves more space: time.
Hey Guys. So we're going to be taking a short release break for Thanksgiving here in in the US,
for right now we’re looking at comments from the last two episodes - electroweak theory
and our discussion on free will in physics.
On electroweak theory Marik Zilberman has a really good comment. If the current fundamental
forces that were once combined, could they be broken further? Honestly, I think the answer
has to be yes, at least to some degree. The Higgs field sits at a non-zero vacuum energy
so could potentially decay to zero, or even to a lower non-zero state non-zero state.
IF the universe went thorugh another phase transition - a vacuum decay - then the weak
interaction would fundamentally change - to become a different force with different bosons.
given we hgaven't actually done a vacuum decay eposide yet I'll save my deep dive into this
for then.
Vacuum Diagrams dropped a lot of wisdom as always. I’m going to try to restate one
point to see if I understood. Dr. Diagrams can correct me if I mess it up. So the idea
is that that new information doesn’t need to arise in the decision-making patch of the
universe - AKA our brain - in order for us to consider that region the origin of a choice
AKA grant it some version of free will. In a deterministic universe, we imagine all information
as being generated at the beginning and then just rearranged as the universe evolves. But
we can think of that initial event as a random number generator whose gigantic store of random
numbers are then used by, like, physics and stuff for the rest of time. And our brains
use those random numbers as part of their choice-making mechanics. They become informational
fuel for our choices.. Now if those random numbers are not even in principle learnable
by some snooping entity, then it doesn’t matter whether they were generated in our
brains or in the big bang. The effect is the same: effective free will, in the sense that
our choices have fundamental unpredictability. Dr Diagrams also points us to Scott Aaronson’s
essay "The Ghost in the Quantum Turing Machine”, which I’m going to go and read now.
Dave Jacob asks why the terms "compatibilistism" and "incompatibilistism" weren’t mentioned,
given that they define the the philosophical positions we discussed. Well I wanted to make
sure it was more of a physics episode than a philosophy episode. But I also may have
a personal distaste for overuse of philosophical-isms. I find that neat labels encompassing
entire philosophical positions are helpful in verbal shortcuts in highly academic discussions,
but can also generate an illusion of understanding. They’ are very static entities by nature of
being a handful of syllables - but are meant to represent a whole family positions whose
subtle variations are important. Are these terms essential to discussion the question?
No - they’re useful for discussing it efficiently if we’re confident that everyone understands
all the content and nuance embedded in a term. Anyway, they’ve been mentioned now, and
wikipedia awaits those keen to expand their philosophy vocab.
And back to matters quantum. Zahaquiel reminded us of the best proof regarding quantum electrodynamics,
which comes from ontology: 1. A physics theory with a cool abbreviation
is inherently better than a physics theory without a cool abbreviation.
2. Quantum electrodynamics has a pretty cool abbreviation.
therefore Quantum electrodynamics is better than other physics theories.
Q.E.D.