The Dog School of Mathematics Presents:

An Aside Concerning Language

Albert Einstein once characterized intuition as the sum total of prejudices acquired by age 18. Those "prejudices" are the result of our experiences. Since we all spend the first 18 years of our lives on the earth moving at speeds very much below c (relative to the earth) many of our concepts about space, time and movement are formed with prejudices that reflect this upbringing. Our language also reflects this set of prejudices as well.

The traffic laws that limit speeds to 55 miles per hour do not specifically mention that that speed must be measured in the earth's frame of reference. Deeds to real estate do not specifically mention that the points and boundaries of the property are to be in the earth frame of reference.

When speaking of relativistic effects, however, our normal language can easily lead to confusion.

For example, when saying that moving meter sticks shorten in the direction of the motion we mean:

When a meter stick is measured in a frame in which it is
moving in the direction of its length then it will be measured
as shorter than it would be measured in a frame in which it is
at rest.
That's a mouthful but it is necessary to cover all the points. The points are that velocity, length, simultaneity and (as we will find out) the duration between ticks of a clock are different when measured in different inertial frames. Thus, to be meaningful, all results of such measurements must be tied to a frame.

Any discussion about the length of a moving meter stick must be carefully tied to a reference frame in which the measurement is made either explicitly or by common understanding. Thus when we say

"moving clocks run slower"
We mean
"The time between ticks of a clock moving past us with velocity
v will be measured in our frame as taking longer than the time
between ticks of a clock which is at rest with respect to us."

The fact that all these measurements, of velocity, simultaneity, length and elapsed time between events are "frame dependent" means that the quantities themselves are frame dependent. This must be since the quantities are defined via operational definitions as the result of a measurement procedure.

For an object such as a meter stick there is one frame that gets special treatment: The frame in which the object is at rest. The length of the object as measured in the frame in which it is at rest is referred to as the object's "proper" length.  Similarly the time duration between events measured by a clock which is at rest in the frame of measurement is referred to as the "proper" time of the clock. There is nothing "improper" about other measurements made in other frames. "proper" is simply a much shorter phrase than "as measured in a frame in which the object is at rest"

Many messages to the usenet sci.physics group claiming to have found flaws in relativity theory are nothing other than attempts to apply good old earth language to relativistic situations.  Usually the culprit is loose usage of the concept of simultaneity.  A close second is treating velocity as if it were absolute.

If it is not clear which frames all measurements are made in then things can quickly become befuddled into meaninglessness. It is a good exercise to mentally translate all statements into the full detailed version in which all objects and measurements are assigned to an inertial frame.

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© 1999, 2000 by Arfur Dogfrey