Essay Sample on Einstein's Concept of Relativity of Simultaneity

Introduction

The theory of special relativity, formulated by Albert Einstein in 1905, constitutes one of the most important scientific advances in history. It altered the way of conceiving space, energy, time, and even had philosophical repercussions, eliminating the possibility of an absolute space/time in the universe. With the special theory of relativity, people understood time was not a constant but a variable.

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The theory of relativity arose from a contradiction between the laws of motion of Isaac Newton and the laws of electromagnetism of the Scottish scientist James Clerk Maxwell. Newton had described nature in terms of matter in motion, governed by forces acting between objects. Maxwell addressed the behavior of electric and magnetic fields and said that light was an oscillation that passed through those fields at a constant speed, regardless of the speed at which the light source was moving (Einstein 49). Einstein’s concept was based on two hypotheses (Einstein 36). First, the laws of physics are the same as long as the reference frame is the same and inertial. That is, they both move at a constant speed. If a law is fulfilled in one system, it must also be fulfilled in the other. Secondly, the speed of light is a universal constant, which is defined as c.

Concept of Relativity

Einstein used the “embankment & train” example to further explain the concept of relativity. The most important consisted of two men: one on a speeding train and the other on the platform (Einstein 32). In one version, Bob (an example), inside the train, turns on a flashlight, points to a mirror directly above him on the roof of the car, and measures the time it takes for light to reach the mirror and return (Einstein 33). Simultaneously, the train passes the platform at almost the speed of light. From the platform, Pat (second example), the stationary observer, sees the beam of light reaching the mirror and descending again, but the train has moved during the time it took for the light to make that journey, which means that instead of moving straight up and down, it has traveled diagonally. For Pat, on the platform, the beam of light has traveled further and, since light always travels at the same speed, more time must have passed.

Einstein's explanation of this became the basis for special relativity. Speed is a measure of units of distance per unit of time. Therefore, the constancy of the speed of light has to be explained by an inconsistency in the flow of time. Objects that move rapidly through space move more slowly in time. The train clock and the station clock advance at different rates depending on the frame of reference from which they are observed. Bob sees that the clock on the moving train is ticking normally, but for Pat that clock ticks very slowly.

The passenger of the fast train will not notice the slowdown in time. The mechanisms that measure time (the oscillation of a pendulum, the vibration of a quartz crystal, or the behavior of an atom) are physical phenomena that obey universal laws (Einstein 35). According to special relativity, these laws remain unchanged within the frame of reference, be it the moving train or any other group of objects moving at the same time.

Imaginary Experiments

Einstein developed his ideas through imaginary experiments. Another famous example is illustrated using two observers: an observer who is on the mainland, and another observer who is located in a train that moves at a constant speed in reference to the first, say to 100 km/h. If the latter, from his wagon, throws an object in the same direction as the train is moving at a speed of 10 km/h, the observer on land will see the thrown object move at 110 km/h. Up to here, the daily logic prevails. But what happens if instead of launching an object the observer from the train "shoots photons"? If the two observers, both the one on the ground and the one on the train, measure that the light is moving at 300,000 km/s, there is already something that does not fit the most basic intuition, since one would expect the same result as in the previous example, and that the speed of light measured by the observer on the mainland would be different.

In the second scenario, one would imagine that the observer on the train has a mirror on the roof of the car and a light detector on the floor of the car. The observer illuminates the mirror, and the detector can measure how long it takes for the light signal to reach him, after tracing a path that for him is rectilinear (up and down). The observer on the platform also observes the experiment. As he sees the train moving, he observes that the light travels a different and longer path than the observer inside the train.

If the speed of light measured by the two observers is the same, this can only happen (speed = space traveled/interval of time used) if the time that the two observers measure to see how long it takes for light to reach the detector is different. The observer who is in motion sees that time passes more slowly (time dilation). For the observer on the platform, more time has elapsed in the process that passes from when the light is emitted until it reaches the receiver.

The effect of time dilation does not enter into people’s daily reality because to be appreciable on a human scale, the train would need to move at a very high speed, close to that of light. Since moving observers who take measurements usually move slowly, it is impossible to take note of time dilation. These examples show that time and longitude are not relative but depend on the state of motion of the observer. In general, it is not only necessary to give the spatial coordinates of an event, but also the temporal one, associated with a specific reference system. That is why people speak of space-time, and that these coordinates and the space-time intervals depend on the reference system or observer that measures them.

Meaning and Significance of Einstein's "Chest"

The Principle of Relativity can be successfully applied to all those reference systems with rectilinear, uniform, and irrotational relative motion. However, what happens to the rest of the reference systems with different relative motion? Unlike the electromagnetic field, bodies that move under the action of a gravitational field experience an acceleration that does not depend on the material of the body or its state of motion. This is equivalent to stating that the inertial mass of a body is equal to the gravitational mass. A body manifests one or another mass depending on the situation.

The consideration of a force, the gravitational force, allows to unify all the reference systems and to unify the uniform movement with the accelerated movement. It is a new hidden symmetry of nature that emerges when considering a new force. Gravity exists so that symmetry between the reference frames is preserved. From the theoretical analysis of the principle of general relativity, some conclusions can be drawn about the characteristics that the gravitational field must-have. A body maintains a state of uniform rectilinear motion of rest unless forces act on it and force it to change state (the law of inertia) (Einstein 12). This is the tendency or an inclination of a body to resist any variation in its state of motion. An object tends to remain at rest if it is at rest and to remain in motion at a constant speed if it is in motion. If an object experiences a variation in speed (or acceleration), it is necessary because a net force is affecting it.

Einstein uses an example of a spacious chest that resembles a room. There is an observer in the chest and he has an (Einstein 78). Since there is no gravity, the person has to use strings to fasten himself to the floor. If he does not do so, any slight impact against the floor will result in him rising steadily towards the room’s ceiling. The chest has a lid that is centrally placed and a hook is attached to the lid (Einstein 78). When the hook starts being pulled with a constant force, the person inside the chest (and the chest itself) starts moving upwards at a uniformly accelerated motion. Soon afterward, their velocity will increase very fast and since the chest’s acceleration will be transmitted to the observer in the chest through the reaction of the chest’s floor, the observer must use his legs to take up the pressure (Einstein 79). The person will conclude that the gravitational force that he (and the chest) are experiencing is constant regarding time.

This example is similar to that of the rotating disk. The centrifugal force in the example of a rotating disk can be interpreted as the action of a gravitational field. If one places a clock in the center and another at one end, this second clock will have a speed with respect to the first, so according to the Theory of Special Relativity they will not mark the same time (Einstein 95). Specifically, the clock at the end will slow down. Therefore, one can think that in general the clocks within a gravitational field will not mark the same time depending on where they are.

Conclusion

Similarly, if an observer at the end of the disk tangentially places a ruler of length 1 at rest relative to it, this ruler will measure less than 1 for the observer at the center of the disk. If you place it radially, then the ruler is not shortened. If the observer in the center of the disk calculates then the relation between the perimeter and the diameter will not obtain the value π, with which the Euclidean geometry is no longer valid. Therefore, to generalize the principle of relativity one cannot continue to base ourselves, unlike Special Relativity, on Euclidean geometry and we must abandon Cartesian coordinates, as they are exclusive to this geometry. And as long as the coordinates and times of events are not defined, the laws of nature in which those coordinates appear have no exact meaning.

For an observer rotating at a certain distance from the center, space is no longer Euclidean. Considering that the distances vary in the direction of movement (tangential) but not perpendicular to the movement (radial), an observer at the end of the disk will measure a greater perimeter but the same radius. This will give one a value greater than π for the quotient between the length of the circumference and the diameter of the disk.

If instead of a rotating disk one had a disk that does not rotate but which expands and contracts cyclically, then space would appear. This space is not isotropic because, when the disk rotates, there is a privileged direction, that of the direction of the axis of rotation. A uniformly accelerated straight-line movement is present when the speed of a body changes to the same extent at the same time (when the amount of acceleration is constant). In the case of a uniformly accelerated linear movement, both the amount of acceleration and the direction of acceleration is always the same. Evenly accelerated movements can also take place on any other path.

Works Cited

Einstein, Albert. Relativity: The Special and the General Theory. Henry Holt and Company Press, 2019. https://www.ibiblio.org/ebooks/Einstein/Einstein_Relativity.pdf