# Reversing Reality

“Time is out of joint.”

I’ve long puzzled over the idea that physics is reversible. That its laws, with some caveats, work the same if time runs forwards or backwards. It’s even been suggested that, except for entropy, time could run backwards just as easily as forwards.

But this seems contrary to our everyday experience. With some exceptions, we can tell if a film or video clip is shown in reverse. Objects that fall, break, or grow (such as plants or crystals), look different seen in reverse.

I think there is more going on there than just entropy.

To begin with, and for the record, I see time as fundamental and axiomatic. Nothing comprises time; it just is. And it only moves forward; its “arrow” is built in. (Also, it’s not a spatial dimension. Even Einstein’s theories, which give us that concept of spacetime, do distinguish space from time.)

I’ve written plenty about this view of time and won’t explore it here. I’ll mention two points. Firstly, if the Big Bang was an event that happened, that seems to imply a before in addition to the obvious after. Secondly, every particle’s proper time always moves at one second per second; it’s impossible to directly (objectively) experience time slowing down or speeding up.

Reversing time might seem, as with space or charge, as simple as changing a plus sign to a minus sign. Yet there are physical properties with only positive (or zero) values. For instance, physicists imagine negative mass and negative energy, but the former is exotic (like unicorns) and the latter mostly an accounting device. And note that with mass and time (and energy), some and zero are significantly different states. Massless and timeless are special states.

Negative time would be like negative weight. Possibly useful for tracking debits, but not real. (Horses and forward time are real. Unicorns and reverse time are ideas.)

More importantly, I think reverse time raises some serious questions regarding causality and locality.

§

In its math and fundamental dynamics, physics does work the same regardless of the direction of time. Particle interactions, quantum and classical, do work the same way forwards and backwards.

Both are valid interactions.

And sideways. Feynman diagrams, which describe particle interactions, are valid descriptions of interactions in all four 90° rotations Which means they’re valid forwards and backwards (180° rotations).

Our experience of quantum wavefunction collapse adds a wrinkle. As far as we can tell, collapse is random and nonlocal (the latter arguably what Einstein actually meant by “spooky action at a distance”). But a basic tenet of physics says information is never lost, so, at least in principle, any interaction can be recovered, if not rewound.

[I think our faith in the conservation of information should be reexamined, but that’s another matter.]

In many regards it does seem that, at a small enough scale and except for wavefunction collapse, we can’t tell whether the movie runs forwards or backwards.

But at only slightly higher levels there are many things are immediately obvious when viewed in reverse. The higher the level, the more obvious it is. Contrast that with another form of reversal, reality in a mirror. Without text or other clues, mirror reality is largely indistinguishable (except for baseball games).

§

A common view is that entropy accounts for our experience of time’s apparent arrow. Some see it as responsible for it; the arrow emerges from entropy.

Rather than seeing entropy as time’s “ratchet” — a one-way mechanism — I see it as a consequence, an abstract measure of the dynamics of a closed system. It’s what happens with physics, particles, and time. It’s statistics. [I’ve written plenty about entropy, too, and won’t belabor it here.]

It seems to me there is something deeper, more fundamental. Time is only rational when it goes forwards.

Consider the difference between making a tree and burning (or otherwise destroying) it. The former inescapably takes a lot of time, but the latter is accomplished quickly. Likewise making glass versus breaking glass. Or eggshells. Or making gunpowder (or gasoline) versus burning it.

Some processes, chemical usually, require time but the reverse of that process may not. One can compress a spring slowly or quickly with the same result, but what process creates an instant tree? Or egg? (The ability to make gasoline as quickly as we burn it would certainly be a boon.)

§

Oops!

A canonical example is the falling, breaking glass or egg. It’s claimed that the right application of forces — the exact reverse of forces expelled in the breaking — will reverse this, resulting in an intact glass or egg back on the table.

I don’t buy it. Not even in principle.

When a glass falls and shatters, the individual pieces go flying due to their individual momenta (their mass, directions, and speeds). As these pieces strike the floor, each other, and any objects on the floor, their momenta diffuse, eventually becoming zero relative to surrounding objects. The energy of the fall dissipates into the environment.

Supposedly, if the environment gave back that energy in just the right places at just the right times, the still pieces would move towards each other and reform the glass with the right momentum to leap back up onto the table where it lands perfectly upright.

The first objection: What combination of physical forces fuses glass pieces seamlessly into whole glass? The formation of glass requires a slow phase change from molten to solid. Pushing two solid pieces together isn’t that.

A second objection involves causality. A single cause pushed the glass off the table. That started a series of diverging events. The initial nudge may only have been enough to tip the glass over but falling converts potential energy into kinetic, providing the force to shatter the glass. The process of a large force dissipating is very different from a collection of tiny forces conspiring towards a specific result.

What causes those tiny pushes? How do they act in perfect concert towards a specific end result? Who or what conducts that symphony? There is also a question of locality. Widespread points acting in synch implies communication between those points.

In contrast, in the forward direction, there is no need or expectation of synchronization. Each moving piece is on its own interacting with the local environment, all driven by the single cause of the falling glass. The process after the cause is asynchronous. The reverse process is necessarily perfectly synchronized.

§

Let’s consider something that, at least on the large scale, we can deliberately reverse: a rocket taking off. In fact, reversing rocket takeoff is all the rage these days.

Because of its ballistic nature, as far as its flight profile is concerned, a rocket taking off looks the same as a rocket landing. Both go slow at the bottom and fast at the top, both have an orbit on one end of things and standing still on the ground at the other. And in both cases, a large amount of force from the business end is responsible for it all.

The normal version of a rocket landing involves firing the engine to generate the necessary force. As with takeoff, the force comes from the engine exhaust leaving the engine. Newton’s third law pushes the rocket in the other direction. On takeoff, that accelerates; on landing, it decelerates. In terms of forces, these look identical.

But in the time-reversed version, once again, causality is weirdly intentional and nonlocal. Somehow, certain cold particles drifting in a very large region of space, must begin moving towards a common location. Along the way they collide with other particles, gaining their momentum. These collectively get faster and hotter until they combine to a jet of fire where the forces align just right to slam it backwards into the oncoming rocket.

Inside the rocket engine, this hot exhaust undergoes a chemical reaction that robs it of its heat and converts it to very cold fuel which the rocket pumps suck into large tanks. This process slows the rocket, which has been in stable orbit, such that it descends and lands. It turns out the timing of this allows it to land in a desired spot (given some reverse aerodynamics to trim the flight).

Once it lands, the energy of its orbit is stored in the cryogenic fuel. Presumably it could be used to launch the same rocket back into the same orbit.

Which, in suggesting perpetual motion, shows something must be wrong with this picture (or with thermodynamics). Obviously, entropy has to play a role in preventing time from running both ways. But it’s not entirely clear to me it plays a role in which way that is. Issues of causality and locality seem more significant in disallowing reverse time.

§ §

A key difference between forward and reverse time, with regard to causality, involves light cones and the difference between our past and future ones.

We all have one light cone extending into our past and another extending into our future. The former contains all the events that could affect our present moment, the latter all the future events our present actions might affect (or effect). Events outside these two cones can neither affect us nor can we affect them.

They’re called “cones” but that’s due to the simplified views of spacetime (the 1D and 2D views). In reality we’re each at the center of two sets of nested expanding spheres. One set is the past, the other the future. The closer the sphere surface, the closer in time. (The scale is one nanosecond per foot.)

In terms of causality, our past light cone converges on us while our future light cone diverges from us as our effects dissipate into the environment. (“For want of a nail…”)

These are significant differences when it comes to time reversal. As illustrated with the breaking glass and rocket, reversing time requires turning divergence into convergence. But the causal rules of those aren’t the same. A backwards movie is obvious.

§

One could rightfully chalk this up to entropy. In both cases it’s the massive unlikeliness of moving from diffuse random states to highly organized states.

What I think is missing is the roles played by causality and locality. Given some random state, it’s highly unlikely to move spontaneously to any ordered state, but especially unlikely to move to a desired ordered state.

Why would a collection of widely dispersed cold molecules begin to move towards the specific end goal of coalescing into exactly the right sort of fireball to slow down a rocket — an event many days in their future?

Keep in mind that some fraction of the energy is in the form of photons that are a long distance away. Once in the atmosphere, sound waves are part of the picture as well. A lot has to come together to reverse divergence, and the necessary cause seems to be in the future.

§ §

So, bottom line:

Forward time; divergent; from one to many; from a known state to a random state. Calculation is serial and parallel. Each state begets the next based on local conditions.

Backward time: convergent; from many to one; from a random state to a known state. All calculation must be done in advance. Each part acts in synchronization. Each requires specific inputs at specific times.

Because I believe time is fundamental, there is no question about time’s arrow emerging. It’s axiomatic. And therefore, no question about reversing time. But beyond that, I think the issues with causality and locality, and that some chemical processes are time-dependent, suggest that reverse time is a unicorn.

Stay divergent, my friends! Go forth and spread beauty and light.

The canonical fool on the hill watching the sunset and the rotation of the planet and thinking what he imagines are large thoughts. View all posts by Wyrd Smythe

#### 29 responses to “Reversing Reality”

• Wyrd Smythe

A version of this has been sitting in my Drafts folder for quite a few months. I wanted to explore the ideas of divergence and convergence in more detail, but the post got long. Topic for another time, perhaps.

• Wyrd Smythe

I skipped the math, but I did have myself some fun exploring what happens with a few basic equations. Average velocity is defined as distance ÷ time (as in MPH or m/s):

$\displaystyle{v}_\textrm{average}=\frac{{d}_\textrm{total}}{{t}_\textrm{total}}=\frac{{d}_\textrm{end}-{d}_\textrm{start}}{{t}_\textrm{end}-{t}_\textrm{start}}$

To reverse time, there are two options. Firstly, reverse the equation:

$\displaystyle{v}_\textrm{average}=\frac{{d}_\textrm{total}}{{t}_\textrm{total}}=\frac{{d}_\textrm{start}-{d}_\textrm{end}}{{t}_\textrm{start}-{t}_\textrm{end}}$

Secondly, reverse the sign of the time variable:

$\displaystyle{v}_\textrm{average}=\frac{{d}_\textrm{total}}{{t}_\textrm{total}}=\frac{{d}_\textrm{end}-{d}_\textrm{start}}{{-t}_\textrm{end}-{-t}_\textrm{start}}$

Let’s try a simple example: Going from the 20-yard line to the 40-yard line while a watch second hand goes from 17 to 21 seconds. In forward time:

$\displaystyle\frac{(40-20)\,\textsf{yards}}{(21-17)\,\textsf{secs}}=\frac{20\,\textsf{yards}}{4\,\textsf{secs}}=5\,\textsf{yards/sec}$

Reversing the equation gives us:

$\displaystyle\frac{(20-40)\,\textsf{yards}}{(17-21)\,\textsf{secs}}=\frac{-20\,\textsf{yards}}{-4\,\textsf{secs}}=5\,\textsf{yards/sec}$

The same answer, which is a big part of why it’s said physics is reversable. Do things in reverse order, and the physics is the same. Making time negative gives us:

$\displaystyle\frac{(40-20)\,\textsf{yards}}{((-21)-(-17))\,\textsf{secs}}=\frac{20\,\textsf{yards}}{-4\,\textsf{secs}}=-5\,\textsf{yards/sec}$

Which gives us a negative answer. Which makes sense. Reverse time and the outcome is reversed.

• Wyrd Smythe

It gets interesting with acceleration, because time gets squared, which removes any sign of its sign:

$\displaystyle{a}=\frac{v}{t}=\frac{d}{t}\times\frac{1}{t}=\frac{d}{t^2}$

Or, for instantaneous acceleration:

$\displaystyle{a}=\frac{d}{dt}{v}=\frac{d}{dt}\frac{d}{dt}{x}=\frac{d^2}{dt^2}{x}$

Which seems to imply that, with negative time, acceleration works the same way regardless.

• Lee Roetcisoender

Enjoy your musings on these type of topics Wyrd, they always get me thinking…..

In contrast to your perspective; I see change as fundamental and time is merely a useful invention of the mind. As an invention, time is a unit by which a mind can measure a duration of that underlying fundamental (change).

Furthermore, even the atomic clock which is an instrument used to measure a “duration of change” is itself a “duration of change”, a duration of change that is not fixed but changes with the influence of the mysterious force we call gravity.

It’s a chicken or the egg sort of thing I guess. What comes first, change or the measurement of a “duration of change”?

Maybe we are saying the same thing but how we choose to express that idea is different. But then again, maybe not…

• Wyrd Smythe

Hey, Lee, thanks!

The idea that change is fundamental isn’t an uncommon one. What I struggle with is understanding how one defines change without something along the lines of: First, that state, then, this state. But the words “first” and “then” imply that time is the underlying basis for change. I don’t see how change can happen without time existing first to provide the background. Without time, isn’t everything fixed and static?

As an aside, relativistic time effects are always from the perspective of observers in other frames of reference. The atomic clock, in its own frame of reference, always runs at one-second-per-second. Observers in other frames of motion see it differently, but everyone’s proper time is constant. What twists the mind a bit is that, if two people are in motion relative to each other, they both (correctly!) see the other person’s clock as running slow but, of course, their own appears to run normally.

• Lee Roetcisoender

“I don’t see how change can happen without time existing first to provide the background.”

If I grok your meaning; as a background, time would be equivalent to or defined as infinity. Whereas relativistic time is a discrete unit of that infinite continuum where durations of change take place that are relative to the perspectives of observers in other frames of reference.

Am I getting warm?????

• Wyrd Smythe

In terms of terminology, I wouldn’t equate time and infinity, but, as background, time would extend infinitely into the past and infinitely into the future. It and some underlying laws of physics would be axiomatic and eternal. Spinoza’s god, in many regards.

A common term in relativity is “slicing”. Different frames of motion (or gravity) “slice” the 4D spacetime “loaf” at different angles, which gives those frames different perspectives on distant events. Note that all frames see causality the same; they all agree A causes B (when, in fact, that is the case). That’s because all observers perceive the same light cone for any given event, local or remote.

Duration appears to change because the speed of light is constant to all observers. If you zip past me with a light clock that bounces light up and down, from your frame the light only covers the distance between up and down. But since I see you in motion, the light moves at an angle, so its path appears longer to me. Since your light clock is what determines time in your frame, and since the speed of light is fixed, I can only conclude things must run slower in your frame.

But I think we’ve wandered off the question here. How do you define change without time? How does one state lead to another without a concept of before and after?

(If you’re curious about the details of (Special) Relativity, I wrote a long series of posts getting into it.)

• Lee Roetcisoender

“How do you define change without time? How does one state lead to another without a concept of before and after?”

Those are great questions Wyrd, the kind of questions that makes one’s mind a little squishy. Unfortunately, our current paradigm of subject/object metaphysics is unable to effectively respond to those questions without invoking some form of dualism.

The answers to tough questions always reduce back to a metaphysics that is capable of transcending the limitations of our current model. So the short answer to your questions is that I look to and rely upon reality/appearance metaphysics (RAM).

• paultorek

First off, I WANT THAT CLOCK!

Second, I’ve been away too long.

I think entropy (or technically, the physics underlying it – like the evolution of quantum states from simpler to more complex, perhaps) really does explain the arrow of time. And it explains causality, too. (Assuming you define “causality” as inherently one-way, which I think is a better choice for ease of communication. The alternative is to leave it an open question, to be settled by physics, whether causality is one-way or mutual-way, and then the answer is going to be the latter.)

You *can* assemble metals into a whole by throwing parts at each other – it’s called explosion welding. But for glass, this is impossible in practice. And even “in principle”, if we note that we can never know all the micro-details we would need to know, and the reason we can’t know them is – wait for it – entropy. Maxwell’s Demon is thermodynamically impossible.

• Wyrd Smythe

You can order that clock from Amazon!

My first question is: How would perfect knowledge of the micro-details enable seamless fusing of glass through the application of forces?

My second question is: When you refer to causality as one-way, do you mean in time?

[FWIW, based on previous conversations, I believe we see entropy quite differently. To me it’s just a consequence of physics+time. A measure we apply to a system’s behavior. I can’t see time’s arrow as emerging from entropy because we don’t see any effect on time when we reduce entropy by applying external energy (time doesn’t slow or reverse in a freezer), nor does time “jitter” like entropy does (as a statistical process, entropy constantly reverses on the micro-scale, but time does not; to the contrary time continues to run forward even when entropy temporarily reverses).]

• paultorek

Perfect knowledge is just the beginning – and the easy part! (Even though impossible for all practical purposes!) You’d also need perfect skills and perfect control, to launch all the particles, phonons, and photons, back along the CPT-reversed paths toward the (soon to be) wine glass.

Yes, causality one-way in time. Actually in both space and time, spacetime. This asymmetry requirement (one-way-ness) implies that causality applies only in sufficiently large systems – mitochondria, crystals within a metal, and of course trees and people, for examples.

Time is one thing, arrow-of-time another. In very simple systems, jitter happens and the “arrow of time” is like an honorary title that we could bestow on such systems. We treat them as having the same arrow that their macroscopic surrounding have, just because it makes thought and talk easier that way.

• Wyrd Smythe

I’m not sure I understand. Are you saying time jitter happens in simple systems? (Entropy jitter happens because particles occasionally enter a lower-entropy macrostate, but time is considered to still move forward in such cases.)

I’m also not clear on how or why the asymmetry of causality only applies in large systems. How do you define causality? What makes it one-way in time?

(And just to clarify with regard to spacetime: A cause can move any direction in space (albeit not simultaneously) but only one direction in time. It’s the time axis that’s strictly one-way?)

It might help to decouple the notions: [1] perfect knowledge of a system’s state at a given time allows knowledge of its state at any other time; [2] restrictions may exist on movement from some states to other states; [3] the ability to manipulate states.

Classical mechanics assumes #1 is reasonable in principle. If we could know the positions and momenta of every particle in a system (along with any forces acting on that system), then we can use Newton, Lagrange, or Hamilton, to predict its trajectory into the past and future. Quantum mechanics plays along, at least partway, using position, energy, and either Schrödinger or Dirac, but explicitly denies full knowledge, even in principle, and introduces the one-way probabilistic nature of wavefunction collapse. CPT is a quantum thing, so we lose the in principle deterministic behavior.

Even if the final state of the broken glass allowed knowledge of its past trajectory to its initial state, it’s item #2 that I’m pondering here. Even if #3 is somehow implied, and we have a system moving from «broken glass fully at rest» to «intact glass standing on table», my question is whether the molecular reactions involved are allowed at that timescale. I agree metals can be fused rapidly (there is also vacuum welding). Metals and glasses have different structures, though, so I’m not confident manipulation of particles and forces can fuse pieces of broken glass seamlessly. (Or unexplode a firecracker back into gunpowder wrapped in a paper cylinder.)

Item #3 is an interesting proposition. The glass becomes broken due to a single cause — knocking it over. Everything diverges from that point. I’m not sure how to take the notion of widespread synchronized micro-causes acting in concert to converge on a future event. It seems to be getting into fantasy physics and I’m just not sure how seriously to take the idea.

(FWIW, I would argue that taking time (with its built-in arrow), and the laws of physics, as axiomatic simplifies the picture. Causality, entropy, thermodynamics, and spacetime, all follow naturally as consequences. They all derive from physics+time.)

• paultorek

Entropy jitter happens in simple systems. Because it does, time (still exists but) does not have a definitive arrow in simple systems except an honorary one borrowed from the larger world around it.

I would define causality as an asymmetric relation between events, based on natural law, such that C makes E probable (or even guarantees it) while E does not do the same for C. The “E does not do the same” is the asymmetry part. I admit that you can reasonably drop that part of the definition, but I just think more confusion results if you do. Some confusion will result either way, because nature stubbornly refuses to indulge our expectations.

Of [1] perfect knowledge, [2] allowed transitions, and [3] manipulability, I’m most interested in [2] as well. I think everything about [3] follows from the other two (I have no intention of trying to explain why, here).

CPT is quantum / standard-model stuff, but whether we lose determinism depends on your interpretation of QM. On the explication of Everett that I like – by David Wallace (and I think also Sean Carroll) – QM is still deterministic at the level of the multiverse. Of course, this puts [3], practical manipulability of the glass shards to reconstruct a wine glass, even further out of reach. That’s because some of the information that may represent what the original glass looked like may lie in “other worlds”. Then again, (a) this division of the quantum state of the multiverse into “worlds” is arbitrary at its edges, and (b) we couldn’t actually know the full state of our world anyway. The most we ever could have hoped for was a fantastically, mind-bogglingly lucky guess. More later.

• paultorek

Back again. (I wish the real world would just stop hassling me.)

So, on allowed transitions from states to other states: I think you put your finger on it with this bit, concerning the rocket example:

Why would a collection of widely dispersed cold molecules begin to move towards the specific end goal of coalescing into exactly the right sort of fireball to slow down a rocket — an event many days in their future?

Indeed, the past that led to the present is wildly improbable, if we just consider the macroscopic facts about the present, and what probability distribution we have about the microscopic facts that might underlie our macroscopic present. Only an absurdly tiny proportion of those microscopic facts would lead back to the actual macroscopic events of the past.

Which is just to say that our past is very low-entropy. Which leads me to think that a cosmology that could explain that fact would have an enormous evidential advantage over one that could not.

Oh, and I forgot to clarify about spacetime and one-way-ness. I just meant that when A causes B, there is a one-way arrow in spacetime from A to B. That’s true by definition, given the asymmetry requirement I stuck into my definition. What’s not true by definition, but is an empirical fact, is that all the arrows go the same way in time – at least, within our observable universe. And that fact can be explained by the ridiculously low entropy of the Big Bang.

• Wyrd Smythe

Entropy jitter happens constantly in all systems. A system can always move to a macrostate with a lower entropy value. It’s just unlikely. And hugely unlikely to do it repeatedly over time. That said, simpler systems have fewer micro- and macrostates, so the odds of entropy jitter do increase. It’s like how a 7:3 result in 10 flips of a fair coin don’t raise eyebrows but 7168:2832 in 10,000 calls for questioning the fairness of the flip. The degree of change is also greater (8 and 9 compared to 7168 and 7169).

I’m afraid we may have to just disagree about time’s arrow emerging from entropy. For me the notion is a speculation. GPS depends on our understanding of SR and GR, and we define the second in terms of cesium atom vibrations (a simple system). Our technology is fine-scale-dependent enough these days that, if time ever did lose its arrow, even on the small scale, it seems we should have noticed. (Such an effect might be small, but it would be ubiquitous.)

If “natural law” is how/why C causes E, does it include time? Both classical and quantum physics assume a background of (forward) time. In spacetime, the arrow comes from the time axis itself. Lateral, let alone backward, motion on that axis is forbidden. (In fact, in the usual units, motion in time is confined to the 45° forward light cone.) FWIW, I’ve found that change and causality are very hard to define without implicitly (or explicitly) assuming a background of forward-running time!

Maybe a question I should have asked earlier is: Why do you find an emergent arrow dependent on entropy a better explanation than that it’s axiomatic? Do I understand correctly you may accept time as axiomatic (but as potentially two-way)? Do you think time jitter accompanies entropy jitter? (Does time reverse momentarily when entropy does?)

I don’t think we want to get into the MWI. 🤐 What matters is that, regardless, our experience is of a world with probabilistic quantum mechanics. And, of course, even in the context of the MWI, Heisenberg Uncertainty applies, so perfect knowledge is forbidden under QM and merely practically impossible under CM.

I think it’s easy to overlook the implications of [3]. When we talk about marshalling the forces to move the pieces on a reverse trajectory, we typically frame it in forward time. We think about first moving the smallest most distant pieces, and then moving closer larger pieces, followed by more pieces, etc. We’re evolving the system forward in time but backwards along the path it took to get there.

It requires careful management and forward-thinking because it’s a converging process. It requires myriad synchronized causes for a desired final effect in the future (forward time again). It’s a process that requires intelligence, planning, control. The diverging process we’re backtracking did not.

The alternative is to frame it as time literally running backwards (CPT reversal), but this leads to a universe with causes coming before effects. What the rocket and glass show isn’t just the improbability of the final state — there are an infinite number of equally improbable final states; entropy doesn’t care — but the apparent reverse cause and effect of supposedly random motions resulting in the specific desired state (allowing the rocket to land on target).

The entropy of the early universe is a topic in itself. Roger Penrose has a good explanation of why what seems a high-entropy state (the initial even distribution of quark plasma) evolving to the apparently low-entropy structured universe is actually a low-entropy initial state with our current state being the (increasingly) high-entropy one. Part of it is the enormous (and growing) amount of entropy in black holes. Part of it is that equating the early low-entropy universe with a room of high-entropy gas is the wrong picture because gravity. With gravity, the diffuse state is low entropy; there’s only one non-structured state completely unaffected by gravity. Quantum fluctuations cause clumping, and that causes gravity, and a positive feedback cycle leads to a structured universe. It’s high entropy because there are many equally likely configurations of collapsed gases. And because black holes.

[My own idle speculation: we don’t have a physics for the first Planck time instants of the Big Bang, so what if the first appearance of the universe was infinitely dense matter in some crystal with perfect form, a zero-entropy structure. In the first Planck time, it explodes into the quark-gluon-lepton fireball we project as existing after that first instant. This would account for the regularity of the CMB, early low entropy, and obviate the need for Inflation, which is an invention to account for the smoothness of the CMB.]

• paultorek

I beg to differ with the claim that special relativity singles out the forward light-cone for special treatment. It picks out both light-cones as possible avenues for causality; the rest is either convention or smuggling. Convention, because we call the earlier events “causes” and the later ones “effects”. However, you can certainly use other branches of physics (notably, thermodynamics!) to reason that there is a lot of substance that goes along with this convention. It’s not like drive on the left in the UK, drive on the right in the US, doesn’t matter which as long as you pick one. It’s not like that at all; the difference is more profound: but that profound difference doesn’t come from relativity.

We may have different meanings for the phrase “time’s arrow”. In my usage, the arrow is not settled by the facts that time B is between times A and C and thus that the time interval between A and C is longer than between either and B. It’s also not settled by the equality or inequality of the time intervals C-to-B, B-to-A. So time’s arrow has nothing to do with the fact that cesium atoms keep on vibrating at their characteristic frequency despite any local entropy fluctuations.

For all I know, cesium atoms were producing and absorbing radiation at 9192631770 Hz in some ur-universe in an epoch during which entropy was stagnant and thus, by my lights, there was no arrow of time. Or perhaps another universe and ours are both daughter universes in which entropy increases from a Big Bang, but in opposite temporal directions: https://arxiv.org/abs/hep-th/0410270

In my terms, time has an “arrow” iff certain patterns of causality and memory hold (at least). If it’s generally only possible to cause arbitrarily selected macroscopic events in one time-direction, and to have reliable records of events located in the other time-direction, then we can call the first direction “the future” and the second “the past”. I say, at least those two asymmetries, but we might want to throw in others, like your convergence/divergence contrast. I don’t think including or excluding more such observed contrasts into the very definition of time’s arrow will change the fact that entropy (and intimately related physical phenomena) explains time’s arrow.

The Aymara people of the Andes think of the future as being behind you and the past in front of you. You can probably guess their reason, before you look at https://www.theguardian.com/science/2005/feb/24/4

That’s not time’s arrow as I’m labelling it, but it might be instructive to imagine a “dispute” between an Aymaran and an American over how to visualize past and future. Now imagine a “dispute” between you and another philosopher who believes that time’s flow is basic, but that you have it backwards. Time actually flows, this philosopher claims, from what everyone calls “the future” to what everyone calls “the past”.

Would that “debate” be intelligible? What if anything would be at stake?

• Wyrd Smythe

Well, my first question for that philosopher would be to ask for a definition of terms to insure we’re using the same concepts. My second would be to ask why they believe time flows in the opposite direction of apparent causality and then how they account for causality. The rest would depend on their answers.

[As an aside, I find the Aymara view of time interesting sociologically. There is a logic to equating the past with what one can see in front of them while the unknown future is out of sight. I can’t help but wonder about a culture that backs into the future, though. There is good reason, I think, most cultures equate it with causality and perceive it as forward movement.]

Speaking of questions, I’m not clear on some points:

When you say “entropy […] explains time’s arrow”, what exactly do you mean by “explains” — ‘describes’ or ‘accounts for’? Does time’s arrow supervene on entropy?

For instance, when the entropy of a system runs “backwards” (moves from a macrostate with higher entropy to one with a lower one) merely due to statistical variation (not incoming energy) does the arrow of time point backwards during this? If the highly improbably sequence of, say, 1/2 second of “backwards” entropy occurs, does time’s arrow point backwards for 1/2 second in that system?

There are some points I think I can clarify:

“So time’s arrow has nothing to do with the fact that cesium atoms keep on vibrating at their characteristic frequency despite any local entropy fluctuations.”

As stated, I agree. What I said was that we define the second in terms of the vibration of a simple quantum system because time moves so regularly. The point being that time marches at a consistent and irresistible rate. I believe we agree on this, that time is fundamental?

I likewise agree that time’s arrow has no connection with the length of time intervals. I think we’d agree that the observed fact that B follows A, and C follows B (and therefore C transitively follows A), reflect time’s arrow. The question might be whether the arrow comes first and constrains events or whether it somehow derives from events.

If you can allow for a reality in which cesium atoms vibrate at their characteristic frequency but in which entropy doesn’t change, then it would seem we do agree on the fundamental nature of time. But how can we count the vibrations without a starting and stopping point? And, hence, an innate arrow of time?

And I would agree there is some symmetry to light cones, but I suggest that the coordinate system on the time axis, and that one cone converges (many-to-one) while the other diverges (one-to-many), do make them decidedly asymmetric within the SR framework. We call them “light cones”, but they’re more properly called causality cones. It’s just that light moves at the speed of causality, so they amount to the same thing. In any event, my point in bringing up GR and SR was just to point out that the arrow of time is built in per the definition of the time axis being a coordinate system. GR and SR assume time’s arrow is part of spacetime.

• paultorek

Time’s arrow is weakly emergent from the large-scale consistent entropy gradient over time, yes. Since that’s a common meaning for “supervenes”, the arrow supervenes, in that sense.

Entropy (and quantum underpinnings) explains the arrows of memory and macroscopic causality in the following sense. If you consider a region of spacetime with a strong consistent entropy gradient over time, you can predict that (a) records of the low-entropy time can easily exist at the higher-entropy time, but not vice versa, and (b) macroscopic manipulations at the lower entropy times may often reliably achieve specific changes at the higher entropy times, but not vice versa.

For a small system fluctuating backwards for a half-second, it seems counterproductive to communication to describe that as a brief local flipping of time’s arrow. Why bother? On the other hand, if you posited a large enough system and enough time so that intelligent beings could and did live and die there, then we *would* want to talk about a local time’s-arrow which differed from ours. Though I suspect we can only talk hypothetically, and that if it ever happened we’d never know it.

You can count cesium atom vibrations from either end of a time-period: you will get the same result. So this does not define an arrow; it defines the endpoints of the interval.

For my hypothetical philosopher (HP), he agrees with everyone else that, for example, Oswald’s shot caused JFK’s death, and so on. As for why point the “flow” of time the opposite way you do, perhaps he feels that certainty and simplicity should be considered the destination, not the origin. QM gives us uncertainty toward the future, but not so much toward the past. The Big Bang was very simple; the future not so much. HP finds it perfectly natural that causality should flow the opposite way from time. Why is he wrong?

• Wyrd Smythe

[time+physics] ⇒ [entropy] ⇒ [arrow]

Would it be fair to say your arrow is a description that points in the direction of higher entropy? A signpost, as it were.

I’m struck by the weakness of the arrow here. It’s not relevant at 1/2 second but becomes relevant in some greater scope. The question it raises for me regards time’s “ratchet” — Why does time move (so regularly) in only one direction? A weakly emergent arrow doesn’t seem sufficient to account for that. Entropy doesn’t quite fit the bill, either, since its rate can vary, and it can be locally reversed without affecting the flow of time.

The thing about the cesium atoms, part of why I brought them up, is that having a vibration of 9,192,631,770 cps requires a start time followed by a progression in time counting cycles. If you mean this works in both directions, true, but it still requires a smooth consistent progression of time in one direction. The central question, again, is why it runs in only one direction (so regularly).

I think your HP is just being contrary and offering a weak argument — there is no obvious association between simplicity and certainty as destination; it’s easy to argue the opposite. When you come down to it, causality is how we define time. First this cause, then that effect. The past recedes, the future approaches. Convergence and divergence.

• paultorek

Yes, in some sense the arrow is weak – exactly because it’s emergent and its turtles don’t go all the way down. (To mix my metaphors.) Entropy’s rate varying is not a problem, though, as long as it gives a reliable monotonicity. Which it might not in a small system over a half second, but the reliability becomes staggering at the scale of a human being. Or of an atomic clock. Once we accept the very low entropy boundary condition of the Big Bang – or your hypothesis of a zero entropy state for that matter – the extremely reliable pattern of divergence follows from physical laws. (Whether the divergence happens in only one time direction, or in both directions away from the ultra low entropy state, would depend on whether there *was* time on both sides of that state.)

The fact that time’s arrow doesn’t go all the way down is a virtue in my book. It gives the interpreted physics a simplicity advantage over one that posits an additional “flow of time”.

HP is a foil to get you to commit to identifying the “flow of time” with the direction of divergence of light rays and pond ripples etc. Or with causality. And then I say, entropy’s got ya covered.

• Wyrd Smythe

Okay, I think I understand your view, but it doesn’t work for me (sorry!). The statistical nature of entropy forces me to give it a secondary (emergent) ontological status. That’s why I see it as a somewhat arbitrary measure of a physical process (like temperature or pressure). And to the contrary, in my view assuming time flows one way is the simplifying assumption. It’s kind of already baked into the physics math.

A question I still have is: If we agree time is fundamental, why wouldn’t it come with a natural direction? Perhaps it depends on whether one sees time as flowing (giving it a natural direction) or as a static space-like dimension we could, at least in theory, traverse in either direction. (My problem with the latter is that it requires an explanation of why we’re traversing in the one direction.)

I’m happy to identify the flow of time with causality since, to me, causality emerges from [time+physics]. To me it’s a little like identifying the mind with the brain.

• paultorek

I also identify the “flow” of time with causality. Or more fully, time “flows toward” what you can cause and “away from” what you can remember.

I agree that entropy is emergent. But that doesn’t mean that we could traverse time in either direction; we are emergent too, especially our minds. The same thermodynamic laws that make Maxwell’s Demon physically impossible also prevent us from remembering high-entropy times. So, psychologically, we can only “travel” away from the Big Bang.

That doesn’t prevent other beings that may “have lived” (from our perspective) “before” the Big Bang from traveling the opposite way. They would be just as stuck in their orientation as we are in ours. Call these people “PreBangers”. Then

Americans : Australians : up/down :: us : PreBangers : before/after

Time is fundamental (FWIW, I take fundamentality to be epistemic, not ontological), and conceivably could come with a natural direction. I just don’t see how the latter buys any additional explanatory power.

• Wyrd Smythe

It explains the “arrow of time” (as axiomatic along with time) and suggests that various speculative notions about reversed time are probably non-starters.

I think in the final analysis, it’s the speculative nature of the idea, and the lack of physical evidence, that I resist. I’ve sworn off speculations not well-grounded in physical reality. I want my metaphysics based as much as possible on what we (think we) know from experiment and rigorous analysis.

• paultorek

I don’t count building-in something into your axioms as “explaining” it.

The idea that time extends before the Big Bang is speculative, but the emergence of time’s arrow doesn’t depend on it. The point of considering the speculation was just to show that even in that scenario, no one can “traverse in another direction” than the only one they’ve ever seen.

• Wyrd Smythe

Well, why I asked you earlier about how you mean “explain” is due to the many ways it can be used. Identifying its axioms would seem to help “explain” reality, but if you don’t agree, that’s cool. Perhaps you associate “explain” only with a system’s theorems derived from its axioms?

Positing time (and its arrow) as axiomatic is speculative, but all the available evidence fits, and I think there’s a strong argument. The regularity of time and that we never ever see it going backwards, even with very sensitive instruments. My argument about the Big Bang is that for it to happen, there had to be a “meta-physics” that allowed it. Some physical law produced the BB (unless you want to ascribe it to God). Which suggests a time when that law existed, but the BB hadn’t happened, yet (unless there was nothing and suddenly there was law and the BB). Which suggests time may have existed before the BB.

(Alternately, there are scenarios like Rogar Penrose’s Conformal Cyclic Cosmology, where there is a chain of universes, each starting with their own BB. Big Crunch and rebound scenarios seem to be ruled out by dark energy. In both cases, though, time is more fundamental than space.)

• paultorek

Ah, I get it now. Yes you can locate the “explanation” in different places and it becomes a harmless terminological difference in many cases.

I guess both the extension or non-extension of time before the Big Bang count as speculative in my book. But FWIW I prefer the Carroll-Chen model where there are prior times, because it offers a way to explain the freakishly low entropy of the BB without positing nearly so low-entropy a condition at earlier times.

• Wyrd Smythe

Yeah, “explain” one of those words with many applications. And as far as terminology goes, I’d likely not say axioms explain so much as that they are the explanation of a system. The last turtle.

Not only is what happened pre-BB speculative, but the BB itself is unknown. What meta-law provided the context? Even the first Plank time forward is opaque to us. For that matter, inflation, although widely accepted, is a speculation designed to address the regularity of the CMB. But the “inflaton field” is a speculation. OTOH, if the BB had the innate property of extreme regularity, inflation isn’t necessary. (Inflation springs from the observation that the CMB didn’t have time for different parts to come to equilibrium, but what if there were no different parts? Would an infinitely dense mote be all one thing or differentiated?)

Getting back to speculations about time, it appears we’re at opposite poles. (Which is fine. We don’t have to agree!) It occurs to me that science fiction hardness offers an analogue here. There’s a spectrum. Some SF is grounded in reality except for one thing. Some takes place in entirely different realities where many things are different. At the far end, fantasy and magic (there be dragons there). Speculative theories, likewise, a spectrum from one new thing to many new things (or all new things). I’ve long favored the harder SF and apparently am the same with physics theories. Which is a long way to say that the Carroll-Chen model doesn’t grab me. Too many changes; too speculative.

Asserting that the appearance of time is the fact of time is indeed speculative, but it fits snuggly with reality as we know it. I see it as a low suspension of disbelief story compared to those that require a lot of imagination.

As an aside, I think Penrose has it right about entropy. One need not posit a zero-entropy BB if inflation accounts for the regularity. When gravity is a factor, an even distribution is the low entropy state. Arguably zero, because it’s the only state like it. Once gravity perturbs it, there are multiple similar states, so entropy rises. Given an initial even distribution, and the nonlinearity of massively N-body dynamics, the number of outcomes grows enormously, and entropy is even greater. Black holes are also massively entropic and only grow more so. The point being that the low entropy state of the universe doesn’t need anything but the BB itself. (The regularity of either the BB or inflation does need explaining, though.)