Could Two Things Happen at the Same Time… or Is That Just a Label?
Einstein’s Clock Trick
Imagine it is 1905, and you are Albert Einstein (1879–1955), a young physicist working in a patent office. A friend in another city asks a simple question: “How do I know my clock shows the same time as yours?”
You cannot just look at both clocks at once. Light takes time to travel. If you see your friend’s clock reading noon, that light left their clock a tiny fraction of a second ago. What they are doing right now is something you have not yet seen.
Einstein realized that to compare the times of two distant events, you must make a choice—a rule. He proposed one. Imagine two clocks, one at point A and one at point B. A light beam leaves A when the clock there reads t₁. It travels to B, bounces off a mirror, and returns to A when that clock reads t₂. Einstein’s rule says: the light reached B exactly halfway between t₁ and t₂. The moment of arrival at B is simultaneous with the moment at A that was exactly in the middle. This rule became known as standard synchrony.
St. Augustine (354–430 CE) used a similar idea over 1,500 years earlier. He imagined two messengers leaving two births at the same instant, traveling at equal speeds, and meeting at the midpoint. If they met there, the births were simultaneous.
Both Augustine and Einstein used a simple idea: the signals going out and coming back must travel at the same speed.
The Big Question: Is the Rule Forced or Chosen?
Einstein’s rule works. But is it the only rule? Or is it just one convenient choice—a convention—among many possible ones?
This is the conventionality thesis: the claim that picking a rule for simultaneity is a matter of choice, not a fact forced on us by the universe. Two philosophers argued strongly for this: Hans Reichenbach (1891–1953) and Adolf Grünbaum (1923–2018).
Their reasoning starts with a hard limit in Einstein’s universe: no cause, no signal, no information can travel faster than light in a vacuum. Before Einstein, people imagined you could send an infinitely fast signal to instantly check a distant clock. In that old picture, absolute simultaneity made sense—there was a single correct answer to “what is happening over there right now?”
But with a speed limit, that certainty vanishes. Look again at the light beam traveling from A to B and back. The light leaves at t₁ and returns at t₂. You know for sure the light hit B sometime between those two moments—that is guaranteed by cause and effect. But exactly when in that interval? Einstein’s rule picks the midpoint. Reichenbach said you could pick any moment in that open interval. He used a symbol, ε (epsilon), where ε can be any number between 0 and 1. Einstein’s standard choice is ε = ½. A different ε means the one-way speed of light is different in each direction, even though the round-trip speed stays the same.
If someone picks ε = ⅔, the light takes longer to go out and comes back faster. The math still works. No experiment measuring round-trip light can tell the difference.
Can a Physics Experiment Settle It?
You might think a clever experiment could break the tie. Many have tried.
One famous attempt uses the law of conservation of momentum. Picture two particles of equal mass, sitting halfway between A and B, then pushed apart by a tiny explosion. If momentum is conserved equally, they should hit A and B at the same time. Can we use that arrival to declare the events simultaneous without ever choosing a clock rule?
Wesley Salmon (1925–2001) spotted the catch. The law of conservation of momentum, as written in physics, already uses the concept of one-way velocities. To measure a particle’s velocity going one way, you need synchronized clocks at both ends. But that is exactly the problem we are trying to solve. Using momentum to define simultaneity is arguing in a circle—it assumes the very thing it sets out to prove.
A more general argument, from John Norton and others, says this circle is unavoidable. Take any proposed synchronization scheme. Write it down using standard synchrony. Now rewrite the same sequence of events using a nonstandard clock rule. The scheme still describes a consistent sequence of events—the laws of physics just look different (sometimes very strange). The scheme itself can be described in terms of the nonstandard rule, which means it cannot rule that rule out. Every such attempt hides a choice equivalent to assuming standard synchrony somewhere inside it.
Malament’s Theorem: A Way Out?
In 1977, David Malament offered a new kind of argument. He did not propose an experiment. Instead, he asked a mathematical question: suppose you are given only the facts of what events can causally connect to what other events, plus the path of one observer. Can you define a simultaneity relation from those ingredients alone?
A causal connectibility relation just tells you whether a signal at the speed of light or slower could travel from one event to another—whether one event could possibly influence the other. Malament proved that, with a few natural requirements, only one simultaneity relation can be defined from that data: standard synchrony with ε = ½.
Some philosophers took this as the end of the debate. If the causal structure of the universe singles out one rule, then simultaneity is not a convention—it is a discovered fact.
Grünbaum disagreed sharply. He pointed out that Malament had to assume, from the start, that simultaneity is an equivalence relation—meaning it behaves like a well-mannered “same time as” should (if A is simultaneous with B, then B is simultaneous with A, and so on). Grünbaum argued that requiring this already builds in a preference for standard synchrony. If you allow simultaneity to work in a slightly looser way, the uniqueness disappears.
Other critics, following an argument by Allen Janis, claimed that Malament’s theorem gives a unique simultaneity relation for each inertial observer—but different observers still get different ε values relative to one another. The freedom to choose, they argue, is just the same freedom Reichenbach described, only expressed in a different mathematical language.
The Tachyon Dream (and Why It Matters)
What would kill the conventionality thesis for good? A signal faster than light.
Physicists call hypothetical faster-than-light particles tachyons. If they existed and could carry a message, you could bounce a signal between two moving observers and get an answer before you sent the question—a causal anomaly, which is a polite way of saying a time-travel paradox. Such a signal would pick out an absolute simultaneity and the convention debate would collapse.
The math of special relativity does not forbid tachyons outright, but they create deep trouble for causality. Most physicists believe they do not exist as signal-carriers. But the mere logical possibility keeps the philosophical question alive: if the speed limit is a physical fact about our world, and not a logical necessity, then the conventionality thesis is tied to that fact.
Why You Should Care About Distant Clocks
You probably do not spend your day worrying about synchronizing clocks light-years apart. So why does this debate matter?
Because it forces a deeper question: which parts of our scientific picture of the world are discovered—forced on us by nature—and which parts are chosen by us to make the picture simpler or more elegant?
Physicists could rewrite all of special relativity using a bizarre ε, as John Winnie showed in 1970. The universe would still be described correctly. It would just look uglier. Newton’s second law (force equals mass times acceleration) would need extra correction terms—pseudoforces that no one wants. We pick ε = ½ because it makes the laws look clean and symmetrical, not because nature screams that light must travel at the same speed in every direction.
This is like choosing a coordinate system for a map. Latitude and longitude lines are not carved into the earth; we lay them down to make navigation easy. The choice is a convention—but a convention so useful that arguing about it feels pointless. Yet noticing that a choice exists at all changes how you see the map. You stop mistaking a tool for a raw fact.
The debate over simultaneity is not settled. Smart, careful philosophers continue to publish papers on both sides. But the fight itself teaches something: physics gives us powerful tools to describe the world, and the line between the world’s own structure and our descriptive choices is thinner—and more interesting—than it first looks.
Think about it
- If every way of comparing distant clocks that follows cause and effect works equally well, should we say one is “true” or just “most convenient”?
- Is there a difference between a rule that nature forces on us and a rule we choose because it makes our equations simplest—if we can never, even in principle, tell them apart by experiment?
- You pick “unfair” video-game lag when your character stutters because a signal took too long. Could the universe have a built-in lag in what counts as “right now” for far-apart places, and we just never notice?
