Light can exhibit a tendency known as loss of simultaneity, according to Einstein’s theory of special relativity. Consider the following situation: there are two sources of pulsed light. Both of these sources are placed in the middle of the craft. One is pointed towards the front and the other towards the back. They are pointed towards targets placed equal distances from their source.
Both emit pulses at the same time. Do the pulses arrive at their targets at the same time? From the perspectives of the astronauts on board, yes, but not for the controller. While both controller and astronaut see the light being emitted from their sources at the same time, the controller sees the pulse pointed towards the back as reaching its target first. The one towards the front still has some ways to go before it reaches its target.
This is because from his perspective, the pulse reaching towards the back has less distance to travel, since the target at the back of the craft is moving forward to meet its pulse. In the case of the pulse moving to the front of the craft, it is having to chase the light. Even though both pulses are traveling at the speed of light, the pulse moving to the back reaches its target in a shorter amount of time, from the perspective of the controller. Although both observers are agreed in the simultaneity of the beginning of the events, there is perspectival disagreement about when the light pulses reach their source.
Keep in mind that there can only be such disagreement when it comes to observing two events that are causally distinct from one another. For example, there can never be an instance in which a rock is thrown at a window and the window breaks before the rock even reaches it. This paradox, therefore, has nothing to do with causation. But the question still remains: Who is right? Is it the case that the two light pulses actually hit their respective targets at the same time, or does the front hit its target first, or does the back hit its target first?
From a relativistic perspective, the question is meaningless. Indeed, it is as meaningless as asking what the “actual” time was from the journey from the earth to another body or the actual length of the craft. “The concepts of time, space, and simultaneity take on meaning only in the context of a specific observer – one whose motion relative to what is being observed has been defined.”
Perhaps you have heard special relativity being summarized in terms of everything being relative. In other words, someone who has misunderstood relativity might think space and time is a free for all and anyone can believe anything they want. This is not true at all. While different observers can have different perspectives on space and time, all observers agree on how the respective values are related to one another (specifically, the relations between spatial distances and time intervals). These relations are determined with a great deal of mathematical rigor, and there is nothing “relative” when it comes to the correctness of these formulas.
Suppose you hold up a pencil in front of a group of people. Is it a short or a long pencil? That depends upon one’s viewpoint. That is, it depends upon if you are looking at it end-on or broadside-on. This is commonsense to us because we are familiar with the idea that what we see is simply a two-dimensional projection of the pencil at right angles to our line of sight. What one observers can be photographed at the same location and these photographs are merely two-representations of objects that actually exist in three dimensions, rather than two. When one changes the line of sight, one gets a different projected length of the pencil.
This is commonsense to us because we live in three dimensions. We know that when one takes into account the pencil’s extension, in the third dimension (along the line of sight) then all of the observers in the room agree on the value of the actual length of the pencil. This is the length of the pencil in three dimensions. Those who view the pencil end-on and see a “short” pencil must add a great deal for the component of “length” along the line of sight. For those who view the pencil broadside-on with a long projected length, they do not have to add much when it comes to the component along their line of sight. In either case, there is agreement concerning the length of the pencil in three dimensions.
Hermann Minkowski, a former teacher of Einstein, suggested that time be viewed in a similar manner. He believed that space and time were very much alike. Instead of thinking of reality in terms o a three-dimensional space and a separate one-dimensional time, reality was to be seen as a four-dimensional spacetime. This involved joining space and time together. The three-dimensional distance we measure is simply a three-dimensional projection of a four-dimensional reality. When we measure one dimension (that of time) with a clock, this is simply a one-dimensional projection of a four-dimensional reality. The ruler and the clock measurements are mere appearances. They do not, however, represent reality.
These appearances change depending upon one’s viewpoint. In the case of the pencil being held up, a change of viewpoint means changing one’s position in the room relative to this pencil. In spacetime, however, changing one’s viewpoint involves changing one’s speed (which, keep in mind, is simply spatial distance divided by time). Thus, observers in relative motion will have distinct viewpoints and will observe distinct projections of a four-dimensional reality.