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Tag Archives: Relativity

Relativity of time at any speed

It is not well known that the Theory of Relativity is almost misnamed. Relativity was well known in physics since Galileo Galilei. That is, the relativity of space was well known. With Albert Einstein’s derivation of the Lorentz transform, the relativity of time was introduced. But the relativity of time was not of the same order as the relativity of space since it required speeds approaching that of the speed of light.

Nicholas Copernicus wrote in his 1543 book, The Revolutions of the Heavenly Spheres: “Every observed change of place is caused by a motion of either the observed object or the observer or, of course, by an unequal displacement of each. For when things move with equal speed in the same direction, the motion is not perceived, as between the observed object and the observer.”

Galileo in his 1632 book Dialogue Concerning the Two Chief World Systems noted that a person below the deck of a uniformly moving ship has no sense of movement and so objects dropped fall directly toward the feet. He articulated a principle of relativity: “any two observers moving at constant speed and direction with respect to one another will obtain the same results for all mechanical experiments.”

That is, a Galilean inertial frame of reference is in relative uniform motion to absolute space. This leads to the notion of absolute time and relative space: although different observers on different reference frames see space differently, they observe time the same way.

Einstein derived the Lorentz transformation from this foundation, allowing measures of time and space to affect one another. This solved the problem of electromagnetism and the result of the Michelson–Morley experiment.

One could say that time in the theory of relativity is relative in a minor way, whereas space is relative in a major way. The relativity of time requires speeds approaching that of the speed of light in a vacuum. The relativity of space is true at any speed.

But note one could modify Galileo’s statement to say that any two observers moving at constant pace and direction with respect to one another will obtain the same results for all mechanical experiments. In that case, time is relative at any speed, too. The key is to measure motion with pace, rather than speed, so that the independent variable is space. That allows time to be relative and have multiple dimensions.

Kinds of relativity

A simple way to look at the world is to assume that space and time are absolute: the locations, the distances, the durations, speeds, and so forth as measured by one person are the same for everyone. That is, if my automobile speedometer shows 50 mph (80 kph), then the police with a laser gun at the side of the road will show the same speed.

For many purposes of everyday life, that works just fine. But for those who think about it more or those who perform experiments, that breaks down. Galileo Galilei was the first express a principle of relativity in his 1632 work Dialogue Concerning the Two Chief World Systems using the example of a ship travelling at constant velocity on a smooth sea: any observer doing experiments below the deck would not be able to tell whether the ship was moving or stationary. He still accepted absolute time, however.

We can call Galilean relativity “spatial relativity” since it applies only to space. Since we have seen the symmetry between space and time, we could develop a similar “temporal relativity” in which time is relative but space is not. This may seem odd at first but it is as consistent (and limited) as spatial relativity. For reference, here are the transformations for spatial and temporal relativity, given two reference frames, S and S’, with an event having space and time displacements r and t (r’ and t’) respectively, with S’ moving at constant velocity v relative to S, then:

r’ = r – vt and t’ = t for spatial (Galilean) relativity, and

r’ = r and t’ = t – r/v for temporal relativity.

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Reality and relativity

As a realist I respect what is often called “common sense.” This means that our faculties of discerning reality in everyday life are basically correct. Yes, we make some mistakes, we can get fooled by a illusionist, but we almost always agree what it is that happens when things happen to us or in front of us. These are the faculties we use to determine if a mistake has been made. Our human faculties show us reality.

The corolary to this in the sciences is twofold: (1) observation is a reliable method to gather information about the universe, and (2) the observer who is closest to an object or event is the one who is in the best position to describe the object or event. This could be called the View from Everywhere (as opposed to The View from Nowhere).

One thing this means is that an observer who is at rest with respect to some object or phenomena is in the best position to measure it properly. So the proper time, length, mass, etc. of something is the measurement at rest. What other observers measure may be different but should be related to these rest measurements. That is the origin of transformations that are made between observers, or frames of reference.

At this point there are two ways to proceed: (a) either the laws of physics are defined with respect to observers at rest, or (b) the laws of physics are independent of any particular observer. Option (b) has been chosen because option (a) does not consider how observers should relate their observations to one another. So while we might say that the real time, length, mass, etc. of something is what the observer at rest measures, nevertheless it is best to transform all observations into ones that are invariant with respect to each observer.

The result is to affirm the relativity principle (RP) that Albert Einstein articulated: “all inertial [reference] frames are totally equivalent for the performance of all physical experiments.” But it also affirms that, for example, the rest mass is the real mass of a particle (not to be confused with what is called the relativistic mass).