Surprise for Allan

The story that surprised Allan goes like this:

On a planet called 1 lived a man Allan the Absolutist. Being of deep mind Allan often thought about the universe and watched the stars nightly. One night he noticed strange behavior of certain four stars: he named the stars 2', 3', 2", and 3". Those were strange names but it was because behavior of those stars was strange. It seemed certain that star 2' is going to collide soon with star 3' in an event he named A and star 2" is going to collide with star 3" in another event that he named B.

Collisions of stars were already strange events but it was even stranger that from all the measurement it followed that collisions A and B are going to happen simultaneously (according to the time as perceived on planet 1) and at the same distance from planet 1. Allan named O the point in time when events A and B were supposed to happen.

Another strange thing was that star 2' had accidentally the same velocity as star 2", and star 3' the same velocity as star 3". The situation was as on the diagram below:

The diagram presents "wordlines" of planet 1 and stars 2', 2", 3', 3;": their distances to planet 1 along horizontal axis as function of time that is shown along the vertical axis, running up. Distances AO and OB are equal each other. Because of identical velocities, stars 2' and 2" have their wordlines parallel on this diagram, and so have stars 3' and 3". Horizontal line on the diagram represents time of the simultaneous collisions. Allan could easily predict the time of the collisions knowing all the parameters of the movement of the stars. He expected to observe those collisions simultaneously, at some time C (point on the wordline of planet 1 on the diagram below) after light from events A and B (moving with speed of light of course, along wordlines AC and BC) reaches planet 1 (at event C):

This strange behavior of those four stars was a great thing for believers in absolute time since it could finally prove that word "simultaneous" has absolute meaning i.e. means the same thing to everybody in the universe regardless of his or her condition. To prove that it is true, exactly at the time of expected collisions (at time O) two spaceships were sent from the planet in two opposite directions. One was sent toward A (the place where stars 2' and 3' were supposed to have already collided according to calculations) and it was flying with the same velocity as velocity of stars 2' and 2". This spaceship was named spaceship 2. Another spaceship was sent towards B, with the same velocity as velocity of stars 3' and 3". This spaceship was named spaceship 3.

The theory was that flying with the same speed as stars 2' and 2", and starting at a point at the same distance from those stars (point O on the diagram), spaceship 2 would be always at the same distance form stars 2' and 2" and so when these stars collide simultaneously with something (in this case with stars 3' and 3" respectively) the light from the explosion that would mark the time of collisions would come from both collisions simultaneously to the spaceship 2 (the same distance to both stars, the same speed of light, therefore the same time of arrival of the light from both collisions).

The same theory was supposed to work for spaceship 3 and so the guys on spaceship 3 were supposed to see the both collisions simultaneously as well, the same as Allan who was sitting on planet 1 observing the soon to collide stars.

According to Allan who had known that speed of light is the same for any observer because of experiments with light made over a century earlier by famous couple Mich and Moe the Astronomers the situation must have looked for each spaceship as the one shown for spaceship 2 on the diagram below.

And so if collisions A and B happen simultaneously for everybody the spaceship crews should report simultaneous collisions. According to absolutist doctrine "simultaneous for 1 is simultaneous for all".

Almost exactly at the time when Allan saw the both collisions (simultaneously), reports (through the radio) came from spaceships 2 and 3: guys in spaceship 2 reported observing collision A, and guys on spaceship 3 reported observing collision B. This was it. Only after a long while spaceship 2 reported observing collision B, and after even longer while spaceship 3 reported observing collision A. Look at the diagram below to see why:

The guys in spaceship 2 reported collision A happening at time A', before collision B that they observed at time B'. The guys from spaceship 3 reported collision A (that they observed at time A") as observed after collision B (observed at time B").

Since Allan thought about the physics not in the terms of this diagram but in terms of the previous one (where everybody is supposed to perceive simultaneous collisions simultaneously, through some not too well defined mathematical magic and in agreement with the absolutist doctrine), he thought, that the guys drank too much during their very long and boring journey. When the instruments (quite sober) on the spaceships confirmed the reports of the spaceship crews, he got surprised.

He couldn't understand how it could happen. He even thought that maybe time doesn't exist at all. However it wasn't a viable proposition since his clock was measuring something (and what it could be if not the time?) and so were clocks of the guys in the spaceships.

Neither was viable a suspicion that at the time of collisions or later the spaceships were not at the same distance from both places where the collisions happened. Distances AO and OB were exactly equal each other, and besides he saw the collisions simultaneously, which confirmed that those distances were equal. Yet for spaceship 2 the collisions happened in some different time than for Allan. The whole story seemed utterly illogical if one assumes that the time can be only absolute, the same for everyone in the whole universe.

Who knows what would happen to Allan's trust in scientific truth if he didn't meet Jim the Skeptic who not only explained to Allan why most of the time logic alone can't be used to learn the truth (see a piece on science and magic by the same author) but also explained the physics of this strange event as it was almost a century ago explained already by Albert the Relativist, which Allan somehow missed before, remembering only the constancy of speed of light.

The physics was that each of the spaceships, because of their movements with respect to Allan, had its private time that run slightly differently than Allan's time. It couldn't be even said whether those private times run slower or faster since from point of view of Allan's they all run slower but from point of view of the spaceship's crew they run faster in their own spaceships but slower in all the other including Allan's planet, that could be consider a kind of spaceship equivalent to spaceships 2 and 3. Another thing that couldn't be "logically" explained.

Anyway, in those private times of those two spaceships, events A and B were not simultaneous as they were in Allan's time. The simultaneous events for spaceship 2 (e.g.) which Allan imagined on horizontal line on diagram above, would be above event A and below event B and so along a tilted line through O on the diagram below.

As it may be noticed, the light signals from pairs of events on this tilted line, when equally spaced around the wordline of spaceship 2 are going to be received simultaneously by the spaceship 2. So event A happened truly before event B for spaceship 2, and the opposite for the spaceship 3. "Truly" means that it is not the matter of failed observations but the matter of objective reality of those spaceships. Event A being located below the "line of simultaneity" (as happening earlier) and event B above it (happening later). This "line of simultaneity" is of course horizontal on the diagrams of spacetime of spaceship 2 and then points A and B should be placed below and above this line respectively. And the opposite for spaceship 3 (A below, B above).

Since, as far as we know, there is no physical possibility to tell whether we, as the inhabitants of the universe are in situation of Allan, or in the situation of a crew of some other spaceship (our earth being one of them), our objective reality is what we can see and what we can measure, and not the reality of some abstract "absolute reference frame" that we don't know anything about and that could "know" about all events instantly and not after a signal propagated with speed of light could inform it about them (which would be irrelevant anyway if no physical interaction can't reach any event in the universe faster than with the speed of light). So we have to conclude that "simultaneous" in our universe is not an absolute thing but something valid only for one particular reference frame.

An additional remark for more curious readers: It may be seen from the diagrams that "intervals" between events (straight lines that connect one event with another on our diagrams) of the "line of simultaneity" may be only of "spacelike" type (when their angle with time axis is greater then the angle of "light cone"), preventing them from possibility of influencing each other (possibility that is open to "timelike" connections between events, intervals within the light cone). So from physical point of view it doesn't matter which of such events happens earlier. The physical reality stays the same and only the observations of certain phenomena that don't influence each other are affected by the sequence. In other words, the nature doesn't care which event out of two or more such events has happened "first". It is purely human classification of events not having any physical sense. By the same token the idea of "simultaneous" has no physical sense neither unless it refers to events at the same point in space (which then becomes actually a single event).

All of it is only because of a single phenomenon discovered over a century ago that the local speed of light in the universe is the same for all observers ("local" meaning one measured by the observer at the place where he actually is; for certain reasons it is different from this universal local speed of light when measured, somewhere else, far form the observer). This absolute constancy of local speed of light makes impossible to construct something that would represent "absolute time". Which as a byproduct invalidates the idea of "cosmic (absolute) time" used in certain variation of cosmology known as "big bang cosmology", and whose adherents maintain that the universe has been created about 14 billion years ago (years of this absolute time that we know doesn't exist but it makes no diff to those adherents).