# What was Einstein's motivation for relativity theory?

I'm a high school student who never studied any relativity before, but I'm just wondering what was the question that Einstein asked himself before going into this field. I knew he has done lots of work such as Brownian motion, photoelectric effect,etc. What was the question that baffled and therefore motivated him to work on relativity?

• Are you talking about special or general relativity?
– Danu
Dec 9 '14 at 0:51
• The motivator was the mighty electrodynamics -- the mother of all in physics. Problem was that it was not invariant under Galilean transformations: en.wikipedia.org/wiki/Galilean_transformation. Turned out electrodynamics was more important than classical mechanics, that is why we have now not special electrodynamics but special mechanics, which is called special theory of relativity.
– Asphir Dom
Dec 9 '14 at 1:34
• The question is allegedly what would happen if you chased a beam of light. I say allegedly because posterity has a tendancy to tidy up the messy business that constitutes research.
– John Rennie
Dec 9 '14 at 6:45
• You can see : Arthur Miller, The Special Relativity Theory : Einstein's response to the Physics of 1905, in Gerald Holton & Yehuda Elkana (editors), Albert Einstein, Historical and Cultural Perspectives (ed or 1982, also Dover reprint). Dec 9 '14 at 11:14
• The histories that I read as a high-school kid said that the Michelson–Morley experiment was the key motivation for special relativity. I don't know enough to confirm or deny that. Dec 9 '14 at 12:02

Let's talk about special relativity (1905) first, then general relativity (1915).

The motivation for special relativity is stated clearly in the first sentence of Einstein's paper "On the Electrodynamics of Moving Bodies":

It is known that Maxwell's electrodynamics -- as usually understood at the present time -- when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena.

Let me unpack that. Maxwell's equations differ from the equations of Newtonian mechanics in one crucial aspect: Maxwell's equations seem at first glance to single out a particular reference frame. The clearest example is the speed of electromagnetic waves: this is given by the formula $c=1/\sqrt{\epsilon_0\mu_0}$, where $\epsilon_0$ and $\mu_0$ are universal physical constants. The speed of the source has nothing to do with the speed of the wave, according to this formula. If you turn on a flashlight while standing still, the light beam that comes out should have the same speed as a light beam from a flashlight on a train whizzing along as fast as you please. (The speed of both beams being measured in the same frame.)

Before special relativity, physicists invoked an invisible medium, the aether, to explain this. Sound waves have a certain speed in air, independent of the source of the wave; likewise water waves on a pond. If EM waves are waves in the so-called luminiferous ("light-carrying") aether, then the formula $c=1/\sqrt{\epsilon_0\mu_0}$ makes sense. Here, $\epsilon_0$ and $\mu_0$ are constants describing aspects of the aether. And $c$ then describes the speed of light in the rest frame of the aether.

On the other hand, Maxwell's equations also contain hints that there is no special frame of reference. Right after that first sentence, Einstein gives an example. Move a coil of wire through the field of a magnet. A current will be induced. (This is one of Faraday's most famous discoveries: electromagnetic induction. Also discovered independently by Joseph Henry.) You can calculate the current using Maxwell's equations in two ways: either pick a frame where the wire is at rest, or one in which the magnet is at rest. You get the same current either way!

Another famous example: the Michelson-Morley experiment. I won't go into details, but the upshot is that Michelson and Morley failed to detect the speed at which the earth was, supposedly, traveling through the aether. Einstein alludes to this briefly in his 1905 paper:

Examples of this sort [the wire and magnet], together with the unsuccessful attempts to discover any motion of the earth relatively to the "light medium", suggest that the phenomena of electrodynamics as well as of mechanics [i.e., Newton's laws] possess no properties corresponding to the idea of absolute rest.

I should say that historians disagree on how critical this experiment was to Einstein's thought.

And now the punchline:

They suggest rather that ... the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the "Principle of Relativity") to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely that light is always propagated in empty space with a definite velocity $c$ which is independent of the state of motion of the emitting body.

The key phrase here is "apparently irreconcilable". I hope you see the apparent contradiction right away. How can a light beam appear to travel at the same speed $c$ to all observers, regardless of how they are moving themselves?

That was Einstein's motivation for special relativity (SR).

Now let's turn to general relativity (GR). This started off as an attempt to reconcile Newton's law of gravity with special relativity. Newton's law says that two point masses $m$ and $M$ attract each other with force $F=GmM/r^2$, where $r$ is the distance between them. SR doesn't like this for several reasons. Writing in 1920, Sir Arthur Stanley Eddington described some of the difficulties:

The most serious objection against the Newtonian law as an exact law was that it had become ambiguous. The law refers to the product of the masses of the two bodies; but the mass depends on the velocity -- a fact unknown in Newton's day. Are we to take the variable mass, or the mass reduced to rest? Perhaps a learned judge, interpreting Newton's statement like a last will and testament, could give a decision; but that is scarcely the way to settle an important point in scientific theory.

Further distance, also referred to in the law, is something relative to an observer. Are we to take the observer travelling with the sun or with the other body concerned, or at rest in the aether or in some gravitational medium? [from Space, Time, and Gravitation, Eddington's pop-sci treatment]

(Eddington was one of first scientists to master GR, and played a key role in its early history, post-1915.)

But the following point probably loomed as even more problematic:

• According to Newton's law, if you move one mass to a new position, this affects the gravitational force on the other mass instantaneously, according to Newton's formula. In principle, you could use this to send signals faster than light, indeed, instantaneously.

Not only Einstein, but several other physicists saw these problems, and set about trying to find the correct law of gravity for SR. In 1921, looking back, Einstein described his motivation this way:

When, in 1907, I was working on a comprehensive paper on the special theory of relativity for the Jahrbuch der Radioaktivität und Electronik, I had also to attempt to modify the Newtonian theory of gravitation in such a way that its laws would fit in the [special relativity] theory. Attempts in this direction did show that this could be done, but did not satisfy me because they were based on physically unfounded hypotheses. [quoted in Pais, Subtle is the Lord, p.178]

Einstein then described how there occurred to him "the happiest thought of my life":

The gravitational field has only a relative existence in a way similar to the electric field generated by magnetoelectric induction. Because for an observer falling freely from the roof of a house there exists -- at least in his immediate surroundings -- no gravitational field [his italics; op cit.]

This led to the famous Principle of Equivalence. Roughly speaking, a free-falling frame of reference in a gravitational field, is equivalent to a non-accelerating frame of reference in a gravity-free field. Also, an accelerating frame of reference in a gravity-free field is equivalent to a non-accelerating frame of reference in a gravitational field (again, roughly speaking).

You can see why Einstein regarded this as an essential clue. To study what gravity should look like according to SR, we can study accelerating frames of reference without gravity. It turns out that there are useful ways to approach the latter question.

One of the early successes of the Principle of Equivalence was an explanation of why so-called gravitational mass is equal to inertial mass. In Newtonian mechanics, this equality explains why all things fall with the same acceleration (ignoring air resistance). The Principle of Equivalence takes a different tack on this: it replaces the two falling objects in a gravitational field, with freely floating objects viewed from an accelerating frame of reference. So they appear to accelerate at the same rate. You can then argue from that result back to the equality of gravitational and inertial mass. This discovery must have reassured Einstein that he was on the right track.

Einstein wrote his first paper on this new approach in 1907. He did not arrive at the equations of GR until 1915. The "happiest thought of his life" provided his initial motivation (plus the need to reconcile gravity with SR), but the full tale is much longer, with many twists and turns.

I suppose you are asking about Special relativity, which Einstein proposed in 1905. (Special relativity is about light and kinematics, while General relativity is about gravity).

There was an apparent contradiction concerning the speed of light. On the one hand there was Maxwell theory which predicted that the speed of light must be the same in all frames of reference. Maxwell's theory was well established and experimentally tested (by Hertz and others. Wireless communication was based on Maxwell theory). On the other hand, this contradicted classical mechanics, which was even better established and tested.

Some of the most striking consequences of Maxwell theory (obtained by Lorenz and Poincare) were that such things as length of a rod and time interval between two events depends on the frame of reference. This is why it is called "relativity".

Einstein's theory of special relativity was essentially a new kinematics which removed all these apparent contradictions. The famous formula $$E=mc^2$$ is a consequence of the special relativity.

Later general relativity was a different theory which was not motivated by any experiment. There, the main motivation was the strange fact (well known since Galileo) that the "gravitational mass" (or "gravitational charge", the thing which stands in the gravity law) is identical to the "inertial mass", the thing which stands in the Newton second law. (For example, electric charge has nothing to do with mass. Why gravitational charge equals mass?) This strange coincidence is responsible for the well-known fact that all bodies fall with the same acceleration (in vacuum). General relativity was designed to explain this strange fact. As far as I know, nobody before Einstein even tried. The fact was considered as "evident". Unlike special relativity, the effects of general relativity are small, and difficult to measure. But there were two consequences of the new theory which could be measured: the gravitational lensing, and shift of Mercury perihelion. Gravitational lensing was measured and found to conform to general relativity by Eddington in 1918, and this immediately made Einstein famous. (Newton's mechanics also predicts gravitational lensing, if light has a mass, but the effect is smaller by a factor of 2).

References. E. Whittaker, A history of the theories of aether and electricity. This is not for a high school student. When I was a high school student I read Martin Gardner, Relativity for the million, but there are many other good popular books.

I suggest to see these sources:

as well as :

From this one, page 2 :

A fi rst indication of the primary context of the early theory of relativity is found in the very title of Einstein's founding paper: On the electrodynamics of moving bodies. This title choice may seem bizarre to the modern reader, who defi nes relativity theory as a theory of space and time. In conformity with the latter view, the first section of Einstein's paper deals with a new kinematics meant to apply to any kind of physical phenomenon.

Much of the paper nonetheless deals with the application of this kinematics to the electrodynamics and optics of moving bodies. Clearly, Einstein wanted to solve difficulties he had encountered in this domain of physics.

The main question puzzling scientists at the time was:

Why does the speed of light seem constant in all observational frames?

The main question puzzling Einstein at the time was:

How can I make the train station clocks more accurate?

• No. The main question puzzling Einstein wasn't about making train station clocks accurate. Can you provide any reference for your (kind of insulting) statement? Jun 15 '17 at 16:27
• @Dvij: There is a link in my answer, in the very first sentence. Here is another. Also, many of the Einstein biographies mention this fact. It is as well-known an anecdote as Newton hating Cook or Archimedes sitting in the bathtub. Jun 16 '17 at 6:07
• I did see the link in your answer. It doesn't claim in any way that the "main question puzzling Einstein was how to make the train station clocks more accurate". Neither does your new (otherwise interesting) link in the comment. Rather they all clearly state that Einstein was interested in the fundamental questions related to "how time works and what does light have to do with this". Jun 16 '17 at 11:15