Expert: Philip A. Stahl - 3/5/2009

Question
I understand some basic physics, and I understand the math behind it, but one question puzzles me conceptually.

Say two objects are moving at, say, 3/4 the speed of light moving towards each other. How can I conceptually reconcile what is really going on there? That is to say, the two object will really only be going at max the speed of light relative to the other, but this seemingly makes no sense conceptually, whereas it does make sense mathematically.

Answer
Hello,

Actually, the two objects of which you speak would not even achieve c as their maximum, but only 0.96 c.

According to the appropriate relative velocities equation.

Conceptually, it is extremely difficult to understand how this can be because our brains are conditioned to think in terms of normal relative velocities. Say like two cars approaching each other at 50 mph for which the relative velocity of either wrt the other is then the simple addition of speeds, or 100 mph.

The trick in terms of relativity is the fact that c represents a fundamental limit on cosmic speeds, not just another everyday quantity.

I would not say that making this concept of relativistic relative speeds clear is in any way easy. However, there are two books which can help immensely, vastly more than I can convey in the space of a relatively short answer - especially without an easy capability of using diagrams to enhance any explanation.

The books are:

1- Einstein's Theory of Relativity  - by Max Born (Dover Books)

2- Relativity and Common Sense - by Hermann Bondi


The last is probably more to your liking focusing more on the conceptual bases in relation to "common sense" in two chapters, 6 ('The Uniqueness of Light') and 7 ('On Common Sense').

The great thing is that neither Bondi nor Born stint on the use of diagrams which I am certainly at a basic limit to use in any reply here. Indeed, I would not even attempt it since I'd not be able to do justice.

And the use of the diagrams is key to reconciling relativistic relative speeds with common sense.

Hope these sources help. A google search ought to quickly lead you to them!