There are a number of myths surrounding the theory of relativity. Some are simply factual errors, like the idea that Einstein originated the concept of relativity, spacetime, the Lorentz transformation and tensor calculus. All these pre-existed Einstein's use of them.
Some myths may be due to the fact that special relativity is now a special case of general relativity. As such, it has a different conceptual framework from that expressed in Einstein's 1905 paper. Whatever the causes may be, the myths that we look at are:
The idea that Newtonian mechanics requires an absolute space.
The relationships between points of view under Special Relativity.
The idea that time in spacetime is equivalent to a spatial dimension.
The relataionship between clocks and proper time.
Then there are specific examples:
The Twin Paradox deals with differences in the passage of time.
The Einstein's Train scenario deals with differences in simultaneity.
The Andromeda Paradox, which deals with planes of simultaneity.
The Two Towers thought experiment illustrates the dificulties in interpreting differences in simultaneity.
Lastly we consider the idea that the velocity of light is the same in all frames of reference.
It is widely held that Albert Einstein's Special Theory of Relativity did away with the need for an absolute space, which was required by Newtonian mechanics. There are two reasons why this myth may have arisen:
However, it does not follow from these that Newtonian mechanics actually required an absolute space. It was the ether theory, not Newtonian mechanics, that said that there was an absolute space. Furthermore, Galileo originated the concept of relativity a few hundred years before Einstein. At that time it was known as Galilean Invariance. Newtonian mechanics is, and always was, wholly compatible with Galilean Invariance, and the combination of them is known as Newtonian Relativity.
Following on from the absolute space myth, there is a myth that because Einstein showed that there is no absolute space, then it is not possible to relate where and when events occur between "points of view". I.e. Each point of view is unique, and unrelated to any other point of view.
There are two flaws in this myth. In Einstein's relativity:
There is a myth that time in spacetime is just another dimension, i.e. it is equivalent to a spatial dimension. This has a very significant impact on the philosophic interpretation of spacetime.
However, it is very easily shown to be false, because time has a distinctly different impact on "distances" in spacetime from the spatial dimensions. Spatial distances in spacetime add according to the Pythagorean theorem, just as in Euclidean space. So:
d2 = x2 + y2 + z2
Where x, y and z are distances, in metres, measured against the 3 dimensional axes. However, the resulting distance (d) is subtracted from the time interval. So:
s2 = (ct)2 - d2
Where s is the spacetime interval. Note: In this case, we are measuring the spacetime interval in metres, so t (the time interval), is multiplied by c (the velocity of light) to convert seconds to the distance in metres that light travels in that number of seconds (so that all the units match).
Hence the time interval has the opposite effect on the spacetime interval from the spatial distance. This is explained in more detail under the heading of Spacetime Mechanics in the section on Spacetime.
It is said that clocks tell proper time, but what is proper time?
Proper time is the name given to the interval between two events that is recorded by a clock that is co-located with the events. As we note here, under special relativity, the proper time interval between the events is unique. Under general relativity the proper time interval depends upon the path taken by the clock between the two events. There are many paths that can taken between the events, therefore the proper time interval is not unique. However, the proper time that a clock would display in taking a specific path is also the coordinate time that an observer would experience in following that path between the events.
Also, a clock at rest in any given frame of reference will tell the coordinate time interval that elapses between the same events, irrespective of whether the events are co-located when viewed from that rest frame. Hence proper time is a subset of coordinate time. So it is more accurate to say that "a clock tells coordinate time, which matches the proper time for co-located events". Furthermore, as coordinate time is what is displayed by clocks, it follows that coordinate time is real in the sense that it correlates to the actual passage of time that an observer would experience in a given rest frame, or in following a given path between two events.
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