Mistakes in Applying Special Relativity

(The github repository for these notes is here.)

When speaking about physical situations in which the theory of special relativity applies, physicists who know relativity inside out often spontaneously revert back to Newtonian ways of thinking. They then make fundamental mistakes, and fail to apply the ideas of special relativity correctly. (See the examples listed below.) It's as if there are two parts of their brain that just don't talk to each other. You could say that this is an example of cognitive dissonance.

This happens with surprising frequency. Something curious is going on here. Why is this happening? Why do these intelligent people make these kinds of simple mistakes so often?

I assert that these errors are caused mostly by bad jargon. The jargon we use when talking about physical quantities related to space and time are obsolete, inappropriate, and incompatible with the concepts of relativity. Bad jargon is leading us down the path of error and confusion. In the context of special relativity, the old Newtonian jargon is insidious.

I also assert that a reasonable way of improving the jargon is to use a rel- prefix for all items that are relative to an inertial frame of reference.

For example:

While invariant quantities (which are the same in all inertial frames of reference) are given no special prefix:

In a context in which relativistic effects are present, it would be necessary to insist on such jargon. The rel prefix reminds us gently, again and again, that the Newtonian ideas are no longer valid, and that there's a new game in town. And we need to be reminded of that.

Over the years, I have come across such errors repeatedly. Here, I have started to collect them as I find them:

Contradicting the Principle of Relativity

Sean Carroll - lecture at the Royal Institution (15:50):

The minus sign [in the formula for the space-time interval] means the more you travel in space, the less time you are going to feel elapsing.

This ambiguity of this statement is deeply misleading, especially for a popular audience. The person travelling quickly doesn't feel anything different at all. That's just the content of the principle of relativity.

Neglecting Time Dilation

Alternatively, neglecting time dilation can be viewed instead as neglecting the pancake effect (the Lorentz-Fitzgerald contraction).

George F. R. Ellis - The Unique Nature of Cosmology:

If we were to move away from this spatial position [the solar system] at almost the speed of light for say 10,000 years, we would not succeed in leaving our own galaxy, much less in reaching another one...

Neil deGrasse-Tyson - public talk (4:33):

At the speed of light, [it takes] two million years [to reach the Andromeda Galaxy]. So, we're not going anywhere, because the distances of space are incommensurate with the longevity of our biological form. So either we find a new understanding of the fabric of space-time, or you give up this dream [of travelling to another galaxy].

Neil deGrasse-Tyson - public talk (3:22):

The diameter of the galaxy is 100,000 light-years. If you travelled as fast as light, it would take you 100,000 years to cross the galaxy. Okay? At least everyone on Earth would wait that long for you to get there.

He adds the qualification at the end, but he fails to make the complete point about time dilation, which in this context is deeply pertinent.

Les Johnson - Lecture at the Royal Institution (09:56):

To cover distances like to the nearest galaxy, in a reasonable amount of time, right now, according to what we know about physics, is impossible.

Referring to Distances and Times Without Specifying a Frame of Reference

Various authors:

The age of the universe is 13.8 billion years.

The distance from the solar system to Proxima Centauri is 4.23 light-years.

Such statements are very common. But in unqualified form, without mentioning any frame of reference, such statements about durations and distances are completely Newtonian. This makes them objectionable. The age of the universe is not an absolute duration, because all durations are relative to a frame of reference.

You might object, saying, "Well, of course the frame of reference is assumed to be attached to the barycenter of the solar system. You're just being pedantic." And you're right, it is pedantic. But that feeling of pedantry comes directly from our inadequate jargon. If instead one said that "The rel-age of the universe is 13.8 billion years", then the problem would go away, because that statement is both unobjectionable and not overbearingly pedantic.

Relevant Quotes

Words promote insight.

- John Wheeler, A Journey Into Gravity and Spacetime (1990)

But marching along with truth is error.

- Max Jammer, Concepts of Space (1969)

...misunderstanding is continually generated by commonplace, incorrect notions that are often implicit in the very language we use (a pre-relativistic structure) and are therefore particularly difficult to recognize.

- N. David Mermin, Space and Time in Special Relativity (1968)

Language can be enormously confusing when it is used to discuss relativity, because words and even grammar often introduce physical assumptions into what we say with such subtlety that we fail to realize that the assumptions are present.

- N. David Mermin, Space and Time in Special Relativity (1968)

In teaching physics, I sometimes feel, with only slight exaggeration, that students are confused by bad notation almost as much as by the concepts.

- Anthony Zee, Einstein Gravity in a Nutshell (2013)

In Newtonian mechanics it was possible to make statements such as: 'the length of the rod is 30 cm.' Since, in the theory of special relativity, the length of a body is not absolute, such a statement has no meaning unless the length is specified relative to some standard of rest.

- W. G. V. Rosser, Introductory Relativity (1967)

Let us then frankly admit that thinking about relativity puts one in a state of mental tension. It is so easy for some Newtonian idea to leak out from the subconscious and vitiate an otherwise (relativistically) impeccable discussion. Only under two conditions do I find myself secure against that leak: when I make a space-time diagram... and secondly when immersed in a mathematical argument in which the various symbols are natural to relativity. In the domain of mere words, I feel insecure and liable to slip into Newtonian ways of thinking unless I exercise great care.

- J. L. Synge, Talking About Relativity (1970)