Relativity of simultaneity

The relativity of simultaneity is a following from the special theory of relativity statement. After that there is no universal simultaneity of events, on which all observers agree.

Explanation

Simultaneity is a fundamental concept in physics. All statements of the schedule based on time comparisons and thus on the concept of simultaneity. But what is it? If there are two events that take place in the same place, is directly observable, whether they take place simultaneously. For events that occur farther away from one another, a comparison on synchronized clocks is possible, which are placed directly to the various event locations and are compared.

Within the framework of Newtonian physics, it seems possible to define a uniform time system that applies to our entire universe. With this assumption, it is perfectly acceptable that our subjective sense of time sometimes deceptive, such as the perception of sound events that are transmitted from different distances. We know the delay by the speed of sound - so can be estimated from the time between lightning and thunder distance of the flash. Also, the light transmission takes time - this is known to us from the observation of stars whose light is decades or centuries on the road until it reaches us. Such observations are in full accordance with the notion of Newtonian physics, that there would be a universally valid time in the universe. And thus a universal understanding of simultaneity - - Only in the special theory of relativity the existence of a universally valid time is refuted. The reason is confirmed by numerous observations fact that the speed of light in all reference systems - is constant - in whatever way they move against each other. Under this assumption, we do the following thought experiment:

A train and a train station are to have each other a relative speed of v = 0.6 c. It is centrally triggered in the train between two clocks A1 and A2 a flash of light, with the arrival of the light flashes each clock starts to run. As an observer in the rest frame of the train (ie the inertial frame in which the train rests ) due to the theory of relativity assumes that the speed of light is the same in all directions, in his opinion, A1 and A2 are reached by the flashes of light simultaneously and synchronously to begin to run.

From the standpoint of an observer in the rest frame of the station the sequence of events but it looks different. In order to determine the time of arrival of the light flashes at A1 and A2 exactly, he has secured with light signals synchronized and equipped with sensors watches on the tracks. Now the speed of light is for this observer also constant in all directions, and the train moving at high speed to the right. It follows that the flash to A2 must travel a longer path than A1 because A2 from the place from which emanated the lightning moves, whereas A1 moves toward this place. The secured to the tracks Watches View consequently that A1 has been hit by lightning before A2 and began to run sooner. A1 and A2 are from the perspective of the rest system of the station that is not synchronized.

The relativity of simultaneity implies therefore that are not the same in different places events taking place that are in an inertial system at the same time, from the perspective of a movable relative to the inertial system. It is important that the measurements were performed in all inertial systems at the site of events - it is thus clear that the relativity of simultaneity has nothing to do with purely optical effects and illusions.

For example, in an inertial frame, two events at different locations take place simultaneously. To another, relative to this moving observer from the place of an event 50,000 km, and the other place is 300,000 km away, so it the first signal is reached before the second. However, by taking into account the different distance to the two events, he can count out the light travel times and would in validity of classical physics now also notice that the two events took place simultaneously. In contrast to the validity of the theory of relativity the observer will note also taking into account the optical effects that has passed a difference in time between two events.

The four areas in the Minkowski diagram

However, this means in particular that the temporal order of two events by different observers can be assessed in different ways.

The only statements whose validity does not depend on the observer, are:

In case 1, there is a reference system in which events take place both at the same time, that differ only in the place. Therefore, we call this situation of events each spacelike. Only in this case the temporal order of events is not generally defined, but dependent on the observer.

In case 2, there is a reference system in which both events occur at the same place and at the same time. This location of the events to each other is called light-like.

In case 3, see the events in any reference frame instead of at the same time. This location of events is called each time-like.

In case 4, the space-time coordinates of the events coincide in each reference system. The events are virtually identical.

The animation demonstrates the left, how is the Minkowski space-time for an accelerated observer. The dotted line in this case represents the world line of the observer is located at the centers of the image. Curves of this line mean an acceleration of the observer. These accelerations can be observed that points of spacetime upwards, ie, contrary to the " flow of time ", run. However, they never cross it the light cone ( the diagonal lines) from below; it is crossed by the passage of time always just downward. Thus, a point never in the forward light cone occur (you can by no acceleration event in the absolute future move ) and never leave the backward light cone (you can by accelerating events not from the absolute past extract ).

One also sees that the world line of the observer always runs within the light cone. Events that will reach the observer or has reached lie only in its absolute future or the past; the order of these events can not be changed by acceleration. In particular, the observer can not make future events past events.

Causality

Since the order of space-like events from the observer (or his state of motion ) depends, would be the possibility that one of the two events can affect the other, lead to problems with causality. For if in a reference system event A occurs before event B, in another reference system, however, event B before event A, then it follows that both A cause of B, and B may be the cause of A. This paradox can be constructed in which an event itself prevents retroactively in the past. At the same time this means that travel faster than light would allow time travel. You travel from A to B. Then later event is replaced by normal acceleration in a reference system in which A is later than B. Then you travel again with superluminal velocity of B to an event before A.

Only time-like or light-like to each other located events can therefore influence each other without causality problems, and here are fixed temporal order and thus cause and effect. Therefore, it is generally assumed that superluminal velocity is not possible, especially as the theory of relativity also not allowed to accelerate a body of sub light speed faster than light.

Verbal and formulaic specification of the relativity of time

Clarification of what is said is best achieved by following verbal and formulaic representation:

It should be noted that not dt, but only this proper time for all Lorentz transformation has the same value.

Dt between time and measured in a moving system with a velocity v in accordance with the Lorentz transformation time is the relationship where V is the speed of the system and c is the speed of light. Further, the distance traveled.

For the interval and the proper time arises and with the fundamental relation

In the above example is at best of the order of magnitude the velocity of sound in air, m / s, as compared to C is very small (km / s). So you need to practice already extremely accurate clocks to measure the effects.

Opposite is dt increased ( time dilation ).

General Theory of Relativity

In the general theory of relativity, simultaneity, even for " comoving " is ( here means " free falling " ) observers hard to define because the ratio now depends not only on v, but from all gravitating masses. In addition, two different events need not always be " causally connected ". The particular consequence that statements like " something is happening now in the Andromeda Nebula " little sense.

For human everyday experience these effects do not play a role, even if you are standing on top of Mount Everest and could look out to sea, the relativity of simultaneity to a range of a few milliseconds would be for the entire visible area of ​​the earth's surface to the horizon is limited. This time interval is below the threshold at which we are ever able to resolve the sequence of events, and below the threshold at which we can perceive optical properties than non- simultaneously. For the everyday experience so the light is always infinitely fast and the simultaneity well defined.