In response to:

After Einstein: The Dark Mysteries from the June 9, 2016 issue

To the Editors:

Priyamvada Natarajan’s essay [“After Einstein: The Dark Mysteries,” NYR, June 9] is largely devoted to general relativity and its implications. Unfortunately, Professor Natarajan’s brief exposition of special relativity suffers from a serious defect.

Natarajan states Einstein’s conclusion concerning the measurement of lengths and times as follows: “The same object will appear shorter to a fast-moving observer than it will to a slow-moving or stationary observer. Likewise time will appear to move more slowly to a fast-moving observer than to a slower one.” This statement is highly misleading because it identifies observers as being stationary or in slow or rapid motion, a notion directly contrary to Einstein’s postulate.

A central feature of special relativity is that we cannot speak of a stationary observer or of a slow- or fast-moving one; if two observers are moving uniformly with respect to one another, only their relative velocity is a valid concept. The correct statement of Einstein’s conclusion is that if observers measure the length of an object that according to them is moving, they find it to be less than the value found by observers who see the object as being at rest. When observers measure the rate of a moving clock, they find it to be running slow compared to an identical stationary clock. The speed of the observers never enters into consideration.

Leo Sartori
Professor Emeritus of Physics, Astronomy
University of Nebraska–Lincoln
Lincoln, Nebraska

Priyamvada Natarajan replies:

I thank Professor Sartori for his note and would like to clarify the use of the term “observer” in my review. As a physicist, Mr. Sartori knows that in special relativity the word “observer” is used in a sense that is somewhat different from standard English usage. I have used it as physicists do, and I believe it was clear in the following discussion that we were not talking of sentient beings making measurements.

The term “observer” is used in physics and special relativity to denote a specific frame of reference in which events and properties of objects are measured. Therefore, in special relativity, when we talk about an observer, we are not specifically hypothesizing the presence of an individual person who is experiencing events or making measurements, but rather referring to a mathematical context or frame in which objects and events are to be evaluated. The effects of special relativity occur whether or not there is a sentient being within the inertial frame of reference to witness them. In fact, I find Mr. Sartori’s suggested re-statement misleading, since it somehow suggests that we can talk of observers in the plural but not in the singular.