The laws of physics don’t specify an arrow of time - they don’t distinguish the past from the future.

The equations we use to describe how things evolve forward in time also perfectly describe their evolution backwards in time.

So the brain is a thing and its ruled by the laws of physics - why does the brain and the conscious experience that emerges from it, see the arrow of time so clearly?

In other words why do we remember the past and not the future?

INTRO In our last episode we gave one explanation for why the universe as a whole sees an arrow of time.

The 2nd law of thermodynamics dictates that entropy must rise over time.

Disorder tends to increase from one time step to the next.

As long as we have a single timestamp in a highly ordered state, there’ll be a gradient of increasing entropy on either side of it.

But that’s a little unsatisfying.

How does this cosmic-level arrow of time get translated into our mental sense of time?

To understand this, let’s think about where our sense of the passage of time arises in our brains.

It comes down to memory.

At any one instant in time, our mental experience holds an awareness of the previous instant, and the instant before that, fading into the past.

We hold an awareness of, say, the task we’re doing and what steps we’ve completed.

On longer timescales when we think back we remember the events of the day, of the last month, or of our lives.

Time is encoded in our mental experience in the form of memories that are time-stamped, or at least time-ordered, past to present.

Brains also have internal clocks that give a sense of time elapsed, but to understand why the thermodynamic arrow of time corresponds to our own sense of temporal ordering, it may be enough to understand why memories are formed in the same direction as increasing entropy.

Now the neuroscience of memory is an incredibly deep and sophisticated field, and in the style of any good physicist, we’re going to ignore all of the subtlety and assume the brain is a perfect sphere.

Well, not quite that simple.

We’re going to model the brain as a rock.

Actually I’m an astrophysicist, so we’ll think of the brain as a very small asteroid.

I’m actually not kidding.

Just bare with me for a minute.

Let’s say that a thing - be it a brain or a rock - a thing has memory if the past has left a mark on it that can somehow be used to reconstruct the events that left that mark.

So what does an asteroid remember?

Well, it formed billions of years ago, before even Earth formed, when tiny particles of dust from a past supernova found each other in the forming solar system and built up into grains then tiny rocks then a ball of different mineral structures clumped together.

It holds a “memory” of past collisions in the chips and dents on its surface, it recalls being hit by cosmic rays in the melt-tracks through its embedded glassy grains, and those grains recall ancient heat in their crystal structures.

Any good geologist could read the asteroid’s memory and deduce a rough formation history.

And any good physicist - well, any omniscient supergenius physicist could measure the exact positions and velocities of every particle comprising the asteroid and calculate their paths backwards to recover its exact formation history.

Actually, not really - perfect measurement isn’t really possible, even assuming all the necessary information was still inside the rock.

But the point remains - there is a record of the past in the object, and to some degree that past can be reconstructed.

The state of the rock is correlated with its past.

But it doesn’t appear correlated with the future.

What is the future of that rock?

Well, more collisions building it up or breaking it down, more cosmic ray hits, that sort of thing.

NONE of that appears to be recorded in the asteroid of the present day.

Assuming it isn’t destroyed by future violence, then fast forward many, many times the current age of the universe and the asteroid will decay into a mist of subatomic particles.

None of this seems too mysterious, but let’s look at this from the point of view of the timeless laws of physics and see if we can identify where the arrow of time enters the picture.

Forget forming rocks for just a second, let’s go as simple as possible - in the crazy energy of the early universe, a positron and a neutral pion particle combine to form a proton.

We’re showing this in the style of a Feynman diagram.

Time increases upwards, while the horizontal axis is separation in space.

Let’s say this process is reversible - the particle physics jury is still out on whether protons can decay - but for this episode they can.

In 10^30+ years, the proton separates again into a pion and positron.

Does the proton have a memory of its formation?

In a perfectly deterministic universe, knowing the exact state of all parts of a system lets you perfectly retrace its past.a In that idealized scenario, could in principle trace the jiggling of its internal quarks backwards to learn when the proton formed.

We’re totally ignoring quantum indeterminacy, or that any information might be lost from the internal structure of the proton.

But the point still holds - internal information can be used to reconstruct the past, and that’s a type of memory.

The weird thing here is that the same proton has as much “memory” of its future as it does of its past.

If the laws of physics can exactly reconstruct the formation of the proton, those same laws can be used to project when the proton will decay.

We can see that when we flip the Feynman diagram on its head - it's symmetric.

For this lone proton, its formation and decay are identical events and it's fair to say this whole sequence has no arrow of time.

The “Feynman diagram” of our asteroid looks like countless particles coming together in many different ways - first subatomic particles joining, then molecules forming, then grains growing and merging.

Over time the rock changes - new clumps might hit the rock and become embedded, cosmic rays leave their mark, etc.

And then in the far, far future the rock decays.

First its heavier nuclei fall apart, and finally, maybe, its protons disintegrate.

The time-reversed view of the asteroid looks nothing like the time-forward view.

The asteroid just assembles from subatomic particles with all of its detailed structure mysteriously in place - cosmic ray tracks, embedded clumps, bumps and scratches, etc.

n those features get erased one by one - cosmic rays happen to pass through in exactly the right way to erase their tracks, seemingly random quantum jiggling ejects these embedded clumps, and so on, until we’re left with a smooth rock that falls apart into grains then molecules then a subatomic mist.

The reverse time direction seems unnatural, but what’s different in terms of the asteroid’s record, or memory of its formation?

Let’s zoom in to see.

Let’s look at the asteroid after its very last interaction with the outside universe.

It’s fully formed but hasn’t started to decay yet.

It’s fair to say it holds a record of its past.

Even if we can’t perfectly retrace its formation down to the subatomic particle, it has many crude features that recall that past.

But what about the future?

If the rock never interacts with any external influence and just decays over time, then in principle we could calculate that decay.

Its precise future would be recorded in its present - it would “remember” that future in the same sense that it remembers its past, just like the proton did.

But in the case of the asteroid, time symmetry is much more easily broken.

Just rewind the clock to the moment before the asteroid’s very last interaction with the outside universe.

Let’s say it’s a final cosmic ray strike.

Now we can definitely say that the rock does NOT remember its entire future, because there’s no way you could predict that future cosmic ray strike with the internal structure of the asteroid alone.

Before the cosmic ray strikes, the asteroid has no knowledge of the incoming impact.

We would say that the rock and the cosmic ray are not correlated in any way.

After the impact they ARE correlated.

Even without access to the cosmic ray, the rock now holds information about the ray, and the ray holds information about the rock.

In the time-reversed case we have an asteroid formed from an incredibly improbable coalescence of particles - but the most improbable things are yet to come.

It has this inexplicable scar running through it that is now perfectly removed by a passingly cosmic ray.

That means that before the cosmic ray hit, the asteroid was correlated with its environment.

It had a streak that freakishly already matched a particle buzzing towards it but hadn’t hit yet.

And it is already correlated with everything else in its environment that will happen to interact with it in the future.

And then the asteroid will loses those correlations one by one.

This reversed time scenario doesn't actually break any laws of physics.

It's just insanely unlikely.

As unlikely as decreasing entropy.

So the key to understanding how our brains inherit the arrow of time lies in understanding the connection between entropy and correlation.

Another way to define increasing entropy is as increasing correlation between elements in a system.

In a low-entropy state, elements are uncorrelated, but become more and more correlated over time as they interact with each other - for example, by sharing energy - which is another way to think about the rise in entropy.

Our universe started in a state of extremely low entropy - spatially separated regions were definitely uncorrelated with each other, and even within small regions correlations were low.

Over time, connections and correlations were made as entropy grew.

So you have a direction in which correlations tend to increase - the same direction as entropy.

Entropy is increasing universe-wide, but the smallest chunks of the universe - asteroids, brains for example - also tend to build correlations with their environments in a particular time direction.

It’s not that physics prefers one time direction over the other - it’s just that a low entropy allows correlations and memories - to build in one direction and not the other.

Now, obviously our brains aren’t rocks - despite the similarity in some cases.

But memory formation results from interactions with our environments - the generation of correlations.

The reason our brains can form memories in one direction and not the other is because the early universe started out with this incredibly rich resource of correlation-lite states, which our brains inherit, and then use up in the generation of memories.

Just as our bodies expend entropy by using and redistributing energy.

To talk about this properly we’d really want to talk about how entropy is also connected to the spreading of quantum entanglement.

If you have a universe of only pure quantum states they’ll become more and more entangled in adjacent time steps, the arrow of time for a patch of the universe is defined by the order in which it acquires correlations - is increasingly entangled with its environment.

In us that’s partly manifested as an ordering of memories - but that’s just one way the arrows of time plays out, tracing the gradient of increasing entropy and correlation and memory away from the inexplicably low entropy beginning of space time.

In our recent episode we explored how our universe gains its directionality to time from entropy and the 2nd law of thermodynamics - or as Ryan Gallagher always hears it - the sycamore of thermodynamics.

Let’s see what you had to say.

Chucky Dickens asks a somewhat involved question, but I’m going to extract part of it.

If the universe were reversed - time ran backwards to the big bang, wouldn’t entropy appear to increase as all structure disassembled and formed the homogeneous sea of hydrogen that preceded the formation of structure?

This highlights a real mystery with the big bang theory The distribution of matter and energy in the early universe does appear to have been random - which we normally associate with high entropy.

How, then, was it low entropy?

The answer is that the low entropy came from how compact the universe was compared to how spread out it could be.

Particle locations were restricted to being very close to each other - a state which represents a tiny fraction of the possible states those particles could be in - most of which are much further apart.

Roger Penrose puts it this way - in the early universe the low entropy was not in the degrees of freedom of the matter - that stuff was high entropy when taken separately, but rather in the degrees of freedom of the gravitational field.

Probably we need to explore this more fully in its own episode, but you’re right to think this is mysterious.

Ryan Christopherson asks whether the random nature of quantum mechanics isn’t a larger hurdle to the reversibility of time than entropy.

Yossi Sirote asks essentially the same question - doesn't the collapse of the wave function break time symmetry.

The answer is that yes, IF quantum mechanics is fundamentally random, and IF the wavefunction collapse is a random rather than deterministic event, then time-reversal symmetry is broken the arrow if time is established by quantum mechanics.

I personally don’t hold with random collapse interpretations, and at any rate invoking random collapse doesn’t tell you why the wavefunction collapses in one direction and not the other.

And to finish here’s the time joke that a surprising number of people shared in the comments.

Which is the observation that Time flies like an arrow, fruit flies like a banana.

Toughen up Fluffy came in with something a bit different: a classic Kermit the Frog quote: "Time's fun when you're having flies."