Seeking God in Science, part 11: Time (part 1 of 2)

It's time to talk about time.

Time, like consciousness, is another one of those things that is at once intimately familiar and deeply mysterious.  What is time?  What is it made of?  Is time-travel possible?  In this installment we will start (though by no means finish) attacking these questions.

Way back in February, in the third installment of this series, I introduced the Objective Reality Hypothesis (ORH) with the slogan, "Things exist," with Things being deliberately capitalized to indicate that the word refers exclusively to physical objects.  The ORH, you will recall, says that the reason Things appear to exist is that they actually do exist, which seems absurdly obvious even though it will ultimately turn out to be false.  In this installment I am going to address another absurdly obvious hypothesis that will also turn out to be false.  I'm going to call it the Time Hypothesis, and its slogan, analogous to "Things exist" will be "things change" or "things happen", with the word "things" here deliberately starting with lower-case t.

To be more precise, the Time Hypothesis states that the reason we perceive that things change is because they actually do change in point of objective fact.  The reason I can say something like, "Back in February I published a blog post entitled "Things Exist" is that this actually happened.  Again, this seems absurdly obvious until you try to nail down what it means to say that something "actually happened".  It means something like: there is this thing (emphatically lower-case t) we call "time" which divides objective reality into two parts, "the past" and "the future", by a "moment" we call "now".  That "now" moment keeps "moving", always "into the future", turning parts of the future into the past at a seemingly steady rate.  The past and future maintain a sort of order.  There is the "recent past" and the "near future" which are in some sense closer to "now" than the "distant past" or the "distant future". But (and this is the important part) the only part of Objective Reality which is actually real is Now.  The past was real, but isn't any more.  The future will be real, but isn't yet.

A logical consequence of this is that there has to be some sense in which "now" is (more or less) the same for everyone, which indeed naively seems to be the case.  We can ask someone "what time is it now?" and expect to receive a sensible, informative answer.  We make schedules and appointments and predictions about the future and those appear to produce coherent behavior in our environments.  People and trains and planes don't always show up or depart "on time" but the phrase "on time" at least has a coherent meaning.  Likewise, we have memories and create records of the past that seem to have coherent meanings.  We can speak coherently of some events happening before or after others.  "The universe is 6000 years old" is a statement that may or may not be true, but it is a coherent claim that can be argued, as contrasted with, say, "Time wants to be green."  Time is the sort of thing that passes.  It is not the sort of thing that has color or desires.

Most importantly, time is something we can objectively measure using devices called clocks.  We can build two clocks, put them next to each other, and observe that their states are correlated (i.e. they show the "same time") despite the fact that there doesn't seem to be any direct causal connection between them.  If we have three clocks, we can destroy one of them and the other two will keep on doing their thing, indicating that their operation did not depend on the other clock.  Whatever keeps the clocks synchronized, it's not any kind of connection between the clocks, it is something outside the clocks, something that exists independent of the clocks.  It is at once objectively real (because we can measure it) and yet completely ineffable and mysterious.

One feature of time dominates the human experience: the events of the past seem to be objective facts which cannot be changed, but the events of the future are not.  There is a sense in which different things "could" happen in the future which is very different from the sense in which different things "could have happened" in the past.  The idea of traveling back in time and changing the past is a logically incoherent fantasy.  The idea of influencing future events is essential to our subjective perception of being sentient agents, of having free will.  We feel like we can make choices.  We do not feel like puppets on strings.  The winds of fate may blow, but we feel as if we nonetheless have a hand on the tiller.

This distinction between past and future, that the past is fixed, an unchangeable part of objective reality and the same for everyone, but that the future is still malleable, is an essential part of the human condition.  Almost everything we do depends on it.  We "prepare for the future" because we think there actually is such a thing as "the future" and it is the sort of thing that can be prepared for.  We have entire industries like insurance and finance based on the premise that the future is malleable but not entirely random, and we have other human institutions, like the law, based on the premise that the past is fixed and the same for everyone.

All this might seem like a tedious and unnecessary belaboring of the obvious.  I'm doing it for two reasons.  First, I want to very explicitly make the point that neither the Objective Reality Hypothesis nor the Time Hypothesis are assumptions baked into the scientific method, as religious apologists will often claim (I'm looking at you, Publius!)  They are not.  They are explanations of observations.  They are not often called out this way precisely because they are tediously obvious and everyone accepts them even if they don't think explicitly about why.  But they are explanations nonetheless.

The second reason I am taking pains to belabor this is that both the Objective Reality Hypothesis and the Time Hypothesis (as I've pointed out before) actually turn out to be wrong!  The Objective Reality Hypothesis is falsified by quantum mechanics, and the Time Hypothesis is falsified by relativity.  But I'm getting ahead of myself.  Let's forget both quantum mechanics and relativity for a moment and pretend that the world is purely Newtonian, that is, it really is just as it naively appears to be (at least to a modern eye): a world populated by Things, physical objects which behave according to strict laws that can be written with mathematical precision.  Furthermore, these laws have the property that they are deterministic: given a state of the world, the future motions of all of the Things in the world are fixed and cannot be changed.  Indeed, some parts of the universe seem to behave exactly like this, which is why can can predict some phenomena, like the movements of celestial bodies, with extreme precision.

This seems to lead to a Problem: if the universe really does behave according to deterministic laws, then the future can't be malleable.  And yet it manifestly is (or at least seems to be) especially when humans are involved.  This is what leads some people to conclude that our behavior cannot possibly be explained by deterministic mathematical laws, and so we humans must have some extra ingredient that allows us to somehow transcend determinism.

There are two problems with this argument.  First, it turns out that Newtonian mechanics is not 100% deterministic.  There is one known edge case (and possibly others) where the behavior predicted by Newton's laws is mathematically non-deterministic.  But these edge cases only arise, well, at the edges.  The tiniest deviation from the mathematical conditions they require gets you back to determinism, so it is not at clear whether this can plausibly account for non-deterministic behavior in humans.  The second problem, of course, is that nature is not actually Newtonian, but that is for another day.

A much more plausible explanation for apparent non-determinism is that past a certain point, the predictability of Newtonian systems falls to the limits of our ability to carry out the math.  It turns out that the reason we can predict the motions of celestial bodies as well as we can is not because we can actually make these predictions in general but because the  movements of celestial bodies just happen to fall within the bounds of a few special cases where we can carry out the math.  In general, if you have even just three objects with arbitrary masses and initial conditions, it is not possible, even in principle, to accurately predict how they will move.  This is the famous "three-body problem".  It turns out that these systems do admit partial solutions, so we can make some general predictions about their behavior even though we can't know exactly what they are going to do.  This is "chaos theory".  So it's possible that all of the apparent non-determinism in the universe is due to this effect.  The future really is fixed.  We can't possibly know what it is in every last detail, but God can.

Quantum mechanics offers a similar escape hatch from classical determinism.  Quantum randomness can be shown to be truly random, that is, not predictable from anything that exists in our universe, not even in principle.  But it's far from clear that this helps us recover agency from the stark mathematical facts.  Having your strings pulled by the flip of a coin isn't much better than having them pulled by deterministic laws.  Your strings are still being pulled by something that isn't you.

But there is something else we need to contend with: relativity.  I'm not going to try to give a full primer on relativity here.  I tried that in my first draft of this post and it spun wildly out of control (that's the reason it has taken me so long to post this).  Explaining relativity properly, accessibly, and completely turns out to be Really Hard (tm).  If you really want to understand it, I recommend this book by Tim Maudlin.

What I'm going to do here is to aim for two out of three: properness and accessibility at the expense of completeness.  I'm going to focus specifically on something that young-earth creationists tend to fixate on, and that is the fact (and it is a fact) that it is not possible to measure the one-way speed of light.  The reason YECs have a bee in their bonnet about this is that the fact that we can (apparently) see things that are further away than 6000 light years seems to indicate that the universe must be more than 6000 years old, and they can't have that.

Discussions of relativity usually start by stating as a bare fact that "the speed of light is constant in all inertial reference frames" and concluding from this that, among other things, "Moving clocks run slow."  There is also some common rhetoric, which I have employed myself, that "Everything is always moving at the speed of light through space-time, so the faster you move through space, the slower you move through time."  These things are not wrong per se, but they are misleading, and I feel like it's a disservice to people struggling to understand what is really going on to use this rhetoric.  (The real truth, of course, is that space-time is a curved four-dimensional manifold, but that's not much help either.)

The real struggle with understanding relativity is that the whole idea of "the speed of light" is misleading in two ways.  The first is that it has nothing to do with light.  It's really about the propagation of electromagnetic waves, of which light is but one example.   And it's not really that either, because gravitational waves also "propagate at the speed of light", and gravitational waves are not electromagnetic waves.

The second problem is that the "speed of light" is not a speed.  (Note that the video I've linked to here is AI-generated and not actually Leonard Susskind speaking.)

Wait, what?  Of course the speed of light is a speed!  It's 186,000 miles per second.  (Wikipedia says so, so it must be true!)  How is that not a speed?  Well, it's not a speed because the whole concept of "speed" depends on some assumptions about time that turn out not to be true.  Those assumptions start to creak around the edges when things start moving fast.  At "the speed of light" they break down completely.

Our day-to-day experience has two features that make it really hard to get away from our naive intuitions about speed.  The first is that we live on the surface of a planet, and that makes a natural reference frame that we tend to treat as absolute.  When we say, for example, that a car is moving at 60 miles per hour what we mean is that it's moving at 60 miles per hour relative to the surface of the earth.  And what we mean by that is that after an hour the car will have traveled 60 miles.  The phrase "after an hour" seem innocuous, but that is only because of the second feature of our day-to-day experience, which is that everything we're familiar with moves much, much slower than light.  The fastest man-made object ever was the Parker solar probe, which reached a top speed of 435,000 miles per hour at its closest approach to the sun.  That is less than 1% of the speed of light.  Closer to earth the fastest objects are satellites in low-earth orbit, which move at about 17,000 miles per hour, less than 0.003% of the speed of light.  Inside earth's atmosphere the fastest objects travel at a few times the speed of sound, which is pretty much indistinguishable from zero compared to light.

At those slow speeds, all clocks tick along at pretty much the same rate.  You can detect relativistic effects on the surface of the earth, but it takes extraordinary precision because the effects are so tiny.  For the most part you can say things like, "the distance traveled in an hour" without worrying about how you measure that hour.  But when things speed up that is no longer the case.  When things speed up, clocks start to behave very strangely.  When things speed up, phrases like "the distance traveled after an hour" start to become ambiguous.

I think the best place to anchor an intuitive understanding of relativity is to observe that mundane objects can travel at different speeds.  What this means in a world where we can't trust our intuitions about clocks is that it is possible for two objects to start moving from the same place at the same time, trace out the same trajectory (in space), and up up arriving in the same place but at different times.  Note that we don't need a clock to ascertain this.  To know that the speeds were different we don't need to know how much time has elapsed, only that one object arrived before the other.

With light, this is not possible.  If you take two beams of light and they travel along the same trajectory (in space) they will always arrive at their destination, wherever that may be, simultaneously.  You can throw a baseball faster or slower.  You can't do that with light.  You can change the power, you can change the frequency, you can change the speed of the source, but no matter what you do the light will always arrive at the same time as any other beam of light that started it journey at the same time and followed the same path.  This is both an experimentally observed fact and a theoretical prediction from the laws of electrodynamics.

A brief detour: the laws of electrodynamics are like Newton's laws but for electrically charged particles.  They were worked out in the 19th century and codified by James Clerk Maxwell into four concise equations that today bear his name.  If you take those equations and crunch the math in a certain way, what pops out is a description of something that looks like a wave traveling through space.  Moreover, the speed of that wave depends on some properties of the space it's traveling through — and nothing else.  We can measure those properties, and when you crunch the numbers the resulting speed turns out to be the measured value of the (round-trip) speed of light.  This is one of the ways we know that light is an electromagnetic wave, and why this speed is called "the speed of light" rather than "the speed of electromagnetism".

It is worth emphasizing that although we can't measure the one-way speed of light, we can measure its round-trip speed, that is to say, we can measure the time it takes for light to reach a distant object and return to its original location after being reflected back.  The reason we can do that is that this only requires one clock, whereas measuring the one-way speed would require two.  They would have to be far apart, and they would have to be synchronized, and that turns out to be impossible.  And, as previously noted, we can also demonstrate that, whatever the one-way speed might be, it's always the same for any two beams of light that follow the same trajectory.

Now, it is very, very tempting to say that because 1) all light that departs a location at the same time and moves along the same trajectory arrives at the same time and 2) the round-trip speed of light can be measured and it always comes out to be the same value, that the one-way speed of light must be this same value.  How could it be otherwise?  It is tempting, but it is wrong.  The reason it is wrong is because it considers the situation only from one point of view, from one frame of reference.  Again, it is very tempting to consider things from only one frame of reference because we have a natural frame of reference in the planet we all live on.  And it is possible that there is a privileged frame of reference, and it is even possible that earth is stationary with respect to that privileged frame of reference.  But here is the problem: if there is a privileged frame of reference, then there has to be an experiment we can do that tells us whether or not we are moving with respect to that frame.  The laws of physics would be different to a moving observer compared to a stationary one.  And we have tried many times to find such differences, but with no success.  In particular, we have failed to find any differences in the laws of electrodynamics resulting from the earth's movement around the sun.  Earth moves around the sun at about 30 meters per second, or 0.01% of the speed of light.  That's pretty slow, but plenty fast enough to be detectable using modern technology or clever experimental techniques.  (The first such experiment was done in 1887.)

Now let us consider the famous "light clock" experiment.  This is usually set up as one experimenter on a moving train (the "moving experimenter") and another standing nearby on the ground (the "stationary experimenter") but this again is misleading.  All motion is relative, so there is nothing about the train that allows it to be designated as "moving" while the person standing on the ground is "stationary".  Instead let's make the situation perfectly symmetric by putting both experimenters on trains traveling in opposite directions.  I'm going to call them Linda and Ralph.  Linda is on a train moving left, and Ralph is on a train moving right.  The instant they pass each other they each turn on a light located on the floor of their respective trains.  Next to each light source is a clock, and on the ceiling of the train is a mirror.  The clock is going to measure the time it takes for the light to bounce off the mirror and return to the clock.  Because the setup is symmetric, both clocks are going to register the same result.  It doesn't matter what the actual number is.  What matters is that both clocks will give the same result, and both Linda and Ralph will agree on what that result was.

What Linda and Ralph will not agree on (and this is the key!) is how far the light traveled!  Each one will look at the light in the other train and insist that it traveled farther than it did in their train because the clock in the other train moved in between when the light was turned on and when it returned to the clock.  So for both Linda and Ralph, the path traced out by the light in the other train is longer than the path traced by the light in their own train.  And yet, they will both agree that the clock readings were the same.

How is this possible?  If we were talking about baseballs the answer would be simple: the speed of the ball depended on who was watching it.  Linda would see Ralph's ball moving faster than her own, and Ralph would see Linda's ball moving faster than his.

But for light, as we noted above, this is not possible.  All light moves at the same speed.

So the only conclusion that Linda can reach is that Ralph's clock is wrong, and likewise the only conclusion that Ralph can reach is that Linda's clock is wrong.  But note that this disagreement originated as a disagreement over the distance that the light traveled.  Linda and Ralph each sees the other's light travel a longer distance than their own.  So this ultimately boils down to a seemingly mundane disagreement over where "here" is.  Linda's "here" is not the same as Ralph's -- except at the instant that they pass each other.  That part is easy to understand.  But put that together with the observed (and theoretically predicted) fact that light can only move at one speed and the logical consequence is that not only do they disagree about where "here" is (except at the instant that they pass each other) they will also disagree about when now is (again, except at the instant that they pass each other).  At the instant that they pass each other, Linda and Ralph share a single "here" and "now".  But as soon as they start to move apart both their "here" and their "now" begin to diverge.

This has profound philosophical implications.  Linda sees Ralph's clocks running slow, and Ralph sees Linda's clocks running slow.  This means that Linda sees herself moving into the future faster than Ralph, and Ralph sees himself moving into the future faster than Linda.  And this in turn means that Linda's "now" is Ralph's future, and Ralph's "now" is Linda's future.  But this is true in general, not just for this specific setup.  And that means that there are potential observers in our universe for which our future is in their past, and that is only possible if our future already exists.

I'm going to stop there for now and leave you with three exercises as homework.

First, think about what happens if Linda and Ralph are moving fast enough so that they each see other's light moving at a 45-degree angle relative to their direction of motion, i.e. each one see's the other's train moving the same distance sideways as the light moves vertically.  How fast is that?  The intuitive answer is that it would have to be the speed of light.  In order to move the same distance sideways in the same amount of time as it takes for the light moves vertically you have to be traveling at the same speed, right?  But no, that is wrong.  Remember, light travels at the same speed for all observers, but different observers will disagree about where the same light starts and ends, and so they will disagree about the distance that it travels, and hence the time it takes to get there.  I'm going to leave it as an exercise to figure out how fast you need to move to turn vertical light into 45-degree-angle light.  Hint: it's less than the speed of light.

Second question: what would actually happen if the trains could move past each other at the speed of light?  What would happen to Linda and Ralph's here's and now's?

Question 3: you may have heard of the twin paradox.  If Linda and Ralph are twins and Linda takes a trip into outer space and returns, she will be younger than Ralph.  This is (the story goes) a consequence of her clocks running slower.  But this is not possible because all motion is relative, so there is no sense in which you can say that Linda "went into space and came back".  From Linda's point of view, it is Ralph who went into space and came back, and so Ralph should be younger.  But that's obviously not possible.  How do we reconcile this apparent contradiction?  Hint: the usual answer is that it has something to do with acceleration, but this is wrong.  We can set up the experiment in such a way that nothing is accelerated.  To do this we use three clocks.  One is stationary, one is moving to the right, and the third is moving to the left.  Let's call them S, R and L.  We start with clocks S and R at the same location and we synchronize them.  Clock L is initially to the right of the other two.  Because L and R and moving towards each other, they will meet.  When they do, we synchronize them.  Clock L will then return to S.  The total time registered by L will be less than the time registered by S despite the fact that nothing has accelerated.

If you manage to answer that last puzzle you will have a true understanding of how time actually works.

The bottom line here is that relativity shows that the naive Time Hypothesis cannot be true.  Not even God can know what time it is.  The question "What time is it?" simply does not have an objectively correct answer.  Just as there can be legitimate disagreement among observers of where "here" is, there is legitimate disagreement over when "now" is.