My manuscript offers a somewhat sacrilegious but intuitive explanation of (special) relativity theory (The Emperor Has No Clothes: the force law and relativity, p. 24-27). It is one of my lighter and more easily accessible pieces of writing. The argument is based on the idea that we may define infinity or infinite velocities as some kind of limit (or some kind of limiting idea), but that we cannot really imagine it: it leads to all kinds of logical inconsistencies.
Let me give you a very simple example here to illustrate these inconsistencies: if something is traveling at an infinite velocity, then it is everywhere and nowhere at the same time, and no theory of physics can deal with that.
Now, if I would have to rewrite that brief introduction to relativity theory, I would probably add another logical argument. One that is based on our definition or notion of time itself. What is the definition of time, indeed? When you think long and hard about this, you will have to agree we can only measure time with reference to some fundamental cycle in Nature, right? It used to be the seasons, or the days or nights. Later, we subdivided a day into hours, and now we have atomic clocks. Whatever you can count and meaningfully communicate to some other intelligent being who happens to observe the same cyclical phenomenon works just fine, right?
Hence, if we would be able to communicate to some other intelligent being in outer space, whose position we may or may not know but both he/she/it (let us think of a male Martian for ease of reference) and we/me/us are broadcasting our frequency- or amplitude-modulated signals wide enough so as to ensure ongoing communication, then we would probably be able to converge on a definition of time in terms of the fundamental frequency of an elementary particle – let us say an electron to keep things simple. We could, therefore, agree on an experiment where he – after receiving a pre-agreed start signal from us – would starting counting and send us a stop signal back after, say, three billion electron cycles (not approximately, of course, but three billion exactly). In the meanwhile, we would be capable, of course, to verify that, inbetween sending and receiving the start and stop signal respectively (and taking into account the time that start and stop signal needs to travel between him and us), his clock seems to run somewhat differently than ours.
So that is the amazing thing, really. Our Martian uses the same electron clock, but our/his motion relative to his/ours leads us to the conclusion his clock works somewhat differently, and Einstein’s (special) relativity theory tells us how, exactly: time dilation, as given by the Lorentz factor.
Does this explanation make it any easier to truly understand relativity theory? Maybe. Maybe not. For me, it does, because what I am describing here is nothing but the results of the Michelson-Morley experiment in a slightly more amusing context which, for some reason I do not quite understand, seems to make them more comprehensible. At the very least, it shows Galilean relativity is as incomprehensible – or as illogical or non-intuitive, I should say – as the modern-day concept of relativity as pioneered by Albert Einstein.
You may now think (or not): OK, but what about relativistic mass? That concept is, and will probably forever remain, non-intuitive. Right? Time dilation and length contraction are fine, because we can now somehow imagine the what and why of this, but how do you explain relativistic mass, really?
The only answer I can give you here it to think some more about Newton’s law: mass is a measure of inertia, so that is a resistance to a change in the state of motion of an object. Motion and, therefore, your measurement of any acceleration or deceleration (i.e. a change in the state of motion) will depend on how you measure time and distance too. Therefore, mass has to be relativistic too.
QED: quod erat demonstrandum. In fact, it is not a proof, so I should not say it’s QED. It’s SE: a satisfactory explanation. Why is an explanation and not a proof? Because I take the constant speed of light for granted, and so I kinda derive the relativity of time, distance and mass from my point of departure (both figuratively and literally speaking, I’d say).
Post scriptum: For the mentioned calculation, we do need to know the (relative) position of the Martian, of course. Any event in physics is defined by both its position as well as its timing. That is what (also) makes it all very consistent, in fact. I should also note this short story here (I mean my post) is very well aligned with Einstein’s original 1905 article, so you can (also) go there to check the math. The main difference between his article and my explanation here is that I take the constant speed of light for granted, and then all that’s relative derives its relativity from that. Einstein looked at it the other way around, because things were not so obvious then. 🙂
Reading Feynman 