My catch on the role of
Simultaneity in Relativity


Newtonian physics incorporates the notion of absolute position (in a Cartesian grid) and absolute time (on a time-line). The idea is that every point in space and moment in time is assigned a numerical coordinate, and everybody refers to events in space and time using those coordinates. Altogether, I’ll call this an absolute coordinate system.

The notion of an absolute coordinate system has been very successfully used in discussions of all sorts of physical questions, from mundane mechanics to the motions of planets about the sun. But every system has its limitations, and so does this one.

Relativity dispenses with the absolute coordinate system, along with the absolute time. It’s often said that these concepts were done in by relativity, and that may be, but here I’ll argue that they were weak to begin with.

Some people say that relativity is counter-intuitive, or basically wrong, because it dispenses with our innate knowledge or daily experience of this absolute coordinate system. But I deny that the absolute coordinate system is identical to our daily experience.

I’ll argue that the absolute coordinate system

People did not always talk in terms of an absolute coordinate system. When called upon to describe the position and time of remote events, people would refer to perhaps a well-known city nearby the event, and the reign of a famous king.

The absolute coordinate system is an invention of the 12th century. It captures some part of our experience, but amounts to an extrapolation from our experience. It was always an artifice. It has turned out that this extrapolation is more trouble than it is worth for many physical considerations.

The naturalness of an absolute coordinate system

An absolute coordinate system requires that a special point in space (an “origin”) should be specified, where the space coordinates are all zero. Furthermore, it needs directions for the three space coordinates. Next it needs a time to refer to as “time zero”.

Well, Greenwich, England is damned special. And surely everybody will agree that North-South, East-West, and up-down are very obvious directions. We might identify time zero with the supposed birth date of a savior, and the time of day with that at Greenwich (this is called Greenwich Mean Time or GMT.)

If the particular town and the particular time in the life of the particular savior are quite important to you, this will seem quite natural.

Normally when we report a position, we do not report its position with respect to Greenwich. We report it relative to some other well-known place in the proximity. Likewise, for daily times, we refer to time relative to some other occurrence.

However, a simple arithmetic conversion can take us from these “local coordinates” to Greenwich and GMT coordinates.

Nowadays, it is an almost daily concern that the world is round, and the directions we picked at Greenwich aren’t quite as obvious on the other side of the world. But this can be accounted for.

In the case when two observers are in motion relative to one another, the conversion to Greenwich coordinates is more complicated, but assuming the observers know where they are in the absolute coordinates, they can still report everything with respect to Greenwich and GMT.

It is rather ridiculous, for an astronaut orbiting the moon, to report their position relative to an English village (which is moving about relative to the astronaut's position in space), and and their time relative to a poorly-known birthday. However, an astronaut with access to this absolute coordinate system, could in principle report coordinates in terms of Greenwich and the savior’s birth.

Of course, one can argue that the origin and directions of an absolute coordinate system are arbitrary, and can be picked to be convenient to any given observer. But the point remains, a coordinate system that is convenient for one observer, can be quite inconvenient for another observer.

But inconvenience and arbitrariness aren’t the worst of the absolute coordinate system’s problems.

Absolute coordinates succumb to a practicality

The worst problem of an absolute coordinate system is a practicality: How does a moving observer (say in space) determine their position relative to an absolute coordinate system?

The only actual way we have to measure position at great distance, is by means of light. Although it is a practical statement, but it is a profound one.

Since (so far as anybody knows) we are confined to measurement using light, let us consider, how does one know a position relative to this absolute grid.

Some consideration is required, but it isn’t very hard to show that in the ideal situation of a coordinate grid, using just a wave that travels in the grid, an observer cannot determine their motion relative to the grid. The concrete version of this statement is that in space, an observer has no way of measuring their absolute motion, but only their motion relative to other things in space.

Such ideas were a big shock at the beginning of the 20th century, but maybe aren’t so surprising nowadays, as people have become accustomed to the idea of space flight, where there are no preferred directions…

So now to the philosophical watershed: if there is no way to make measurements relative to the supposed absolute coordinate system, should we refer to it at all? In the light of its artificiality even from a non-relativistic standpoint, was it such a good idea to bother with it in the first place?


In real life, we talk about some of our extended events as being simultaneous. We are referring to things that are rather nearby, and we mean this in a sort of approximate way, and it has mostly sufficed.

However, in modern times, we notice a short delay in the conversation of news correspondents, partly due to the time it takes for light to circumnavigate the globe. When astronauts were on the moon, the delay was much more noticeable (about two seconds). In such contexts, the exact meaning of events being simultaneous becomes practically questionable.

In the absolute coordinate system, two instantaneous events being simultaneous means that their time-coordinate is the same, regardless of where they occur in space.

Once we accept that we don’t have access to the supposed absolute coordinate system, and that we effectively do all measurements using light, a problem arises with the notion of simultaneity of events at two different places.

Imagine two lightning flashes at different points. How would an observer conclude that they were simultaneous? If the observer is closer to one flash, then the light from that flash has a head start on the other lightning flash.

For two flashes, we can always imagine an observer midway between the two, and say the two flashes are simultaneous if that observer sees the flashes at the same time. An observer anywhere else can calculate from their observation of the flashes, whether this auxiliary observer at the midpoint sees the flashes occur at the same time. So far so good (but much more complicated than the notion of absolute simultaneity).

Typically, for a different two points, a different auxiliary observer is required for each two flashes. If there are multiple flashes at different places, there is no one observer who actually sees all of them occur at the same time.

This brings us to to the question: In the situation of very widely separated events, what practical significance does simultaneity have?

The old idea of simultaneity was of practical significance. If at the same time your spouse left you, and the stock market crashed, and there was a solar eclipse, the combined effect might kill you. But in this new system, there might be no victim to whom all three happen at the same time, although they might be simultaneous, in the strange and complicated sense described above.

While one can assign a meaning for two events happening simultaneously, as before with absolute coordinates, the notion of an absolute time for all observers is unhelpful and impractical.

Finally, in the presence of a gravitational field, where things aren't just moving with regard to one another, but accelerating, the notion of a point halfway between two given points loses its meaning as well.

Just where would you put that auxiliary observer? Why, directly between the two flashers! But the flashers are accelerating with respect to one another. There isn’t a particular point. Well, you could make both flasher flash, and put an observer where they are seen to happen at the same time—but, oh oh, that’s circular…

In the presence of gravitation, even our contrived sense of simultaneity loses its meaning.

But who needed it anyway?


Relativity begins with each observer being allotted their own system of coordinates. In order to be useful as a measuring system, these individual coordinates have to be calibrated somehow. They are calibrated so that mutual observations using light among different observers are consistent.

This can be viewed as a democratization of measurement. In a practical sense, it is a better representation of how measurement actually proceeds.

Note that a common misconception holds that relativity implies that there is no absolute coordinate system. The coordinate system of any particular observer would do as a absolute, Newtonian coordinate system, if the observer is persuasive enough to get other observers to agree to blessing it with that distinction.

But it isn’t very useful for other observers to do that, generally. They are still limited by the practical problem that they can only measure their motions relative to this blessed system using light, and then they still have to transform their local coordinates to the blessed ones. Overall, it makes the best sense for each observer to attend to their own coordinates, and convert between their coordinates and the coordinates of other observers when the occasion calls for it.

Another common misconception is that relativity implies that there is no medium of propagation of light. Relativity is logically independent of the existence of such a medium (as Einstein said in his original paper.)

It is generally considered better in science not to bring in quantities that you can’t measure. So long as nobody knows how to measure, or even detect, any medium that light moves in, it must remain a matter of speculation, but not science.

(Some people will disagree with this, making some identification of existence with knowability, but in my view this is an unnecessary stretch of logic that only weakens the argument for relativity.)

D’Invierno p. 23
The example of the train car is very confused.

He talks about two firing devices placed on the tracks, a distance apart equal to the length of the car. But…the length of the car (as well as the distance between the two firing devices) depends on the observer. Then by a complicated argument, he concludes that simultaneity can’t be maintained. But we already know that the examples involves other statements that can’t be maintained.

Because of the dependence of the light velocity and the rate of the clock on the gravitational potential, the definition of simultaneity in $4 is no longer applicable. and the Lorentz transform loses its meaning. [but he’s really going on to say that SR itself isn’t valid here.]

This simultaneity is Einstein’s thought experiment 1911 Phys Z p 509

P. 9 talks about the relativity of simultaneity

points out, that it is easy to understand that there is no absolute being at the same place at different times (because that would mean all observers see an object as being stationary), but somehow the analogous statement, exchanging space and time, is not. That would be, what happens at the same time at different places, e.g. simultaneity. He thinks it is a psychological barrier.

15th century with Descartes? There were earlier writers, Omar Khayyam...