## A Different Way Out: Einstein's Relativity Paper

Einstein had been committed to Maxwell's (and Faraday's) notion of a field from his earliest days and chose to take it seriously, every bit of it. Maxwell found that electromagnetic waves propagate at $c$ and nowhere mentioned (nor did his equations support) any other speed for light. Einstein took it as a postulate – where a mathematician starts without the need to defend – that Maxwell's $c$ was the case regardless of a frame of reference. That wasn't necessarily what Maxwell meant – he meant that light moved at that special value in the ether. Einstein took Maxwell's lack of concern about another reference frame as license to declare it constant regardless.

```{admonition}    Speed of Light is Special
:class: important

In his fourth revolutionary paper of 1905, Einstein proposed that the speed of light is special: it's a constant for all observers, regardless of their relative motion.
```

> In his fourth revolutionary paper of 1905, Einstein proposed that the speed of light is special: it's a constant for all observers, regardless of their relative motion.

The fancy phrase is that *the speed of light is an invariant*. That's quite a promotion for just a number and completely different from Maxwell and Lorentz's models.

But he was only just beginning. He was also offended by the realization from Lesson \@ref(maxwell) that Maxwell's Equations and Newton's laws of motion behave differently depending on an observer's state of motion. The way out of that was to make another declaration: a big expansion of Galileo's Relativity:

> Einstein proposed that not only mechanical experiments are incapable of distinguishing relative states of motion, but that <em>all phenomena should be identically described by relatively moving observers</em>.

These two ideas were declared by the young less-than-unknown Einstein to be the Postulates of Special Relativity:

1. The "**First Postulate**," what Einstein called the "Principle of Relativity." All laws of physics – mechanical and electromagnetic – are identical in co-moving, inertial frames of reference. That's taking Galileo seriously, and adding Maxwell.

2. The "**Second Postulate**." The speed of light, $c$ is the same for all inertial observers. That's taking Maxwell more seriously than even Maxwell took Maxwell seriously!

A couple of caveats:

* Einstein did not call his theory Special Relativity. That name came from Max Planck and Einstein didn't particularly like it. He preferred to call it the Invariant Theory since it hinged on the invariance of the speed of light. Can't always get what you want. So he and we always have to fight off the inclination to believe that "everything is relative." Nope.
* Can you see that the First Postulate is not consistent with the conclusions in Lesson \@ref(relativity1) We can't have it both ways–Newton and Maxwell both working the same between inertial frames – so something has to give. He took Maxwell seriously, and then had to worry about what that meant for the 200 years' worth of reliance on Newton's laws of motion. Stay tuned.

The title of this revolutionary work from this less-than-unknown scientist with only an undergraduate physics teaching degree is:

> On the Electrodynamics of Moving Bodies

### Let's Read Some of Einstein's Paper

You can take in Einstein on this subject. He's precise and even pedantic and he asks questions that nobody else thought qualified as questions. Let's read exactly what Einstein wrote. Here's his first paragraph:

> "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. Take, for example, the reciprocal electrodynamic action of a magnet and a conductor. The observable phenomenon here depends only on the relative motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two cases in which either the one or the other of these bodies is in motion."

```{note}
He's talking about our magnet-coil demonstration. Here's what he says happens:
```

> "For if the magnet is in motion and the conductor at rest, there arises in the neighbourhood of the magnet an electric field with a certain definite energy, producing a current at the places where parts of the conductor are situated. But if the magnet is stationary and the conductor in motion, no electric field arises in the neighbourhood of the magnet. In the conductor, however, we find an electromotive force, to which in itself there is no corresponding energy, but which gives rise—assuming equality of relative motion in the two cases discussed—to electric currents of the same path and intensity as those produced by the electric forces in the former case."

```{note}
This is exaclty what we discussed in the last lesson: the results of moving the magnet and moving the coil come about for entirely different reasons.
```

The second paragraph is no less clear and he throws down the gauntlet in a battle that nobody else was willing to take on:

> "Examples of this sort, together with the unsuccessful attempts to discover any motion of the earth relatively to the 'light medium,'... "

```{note}
He's implying that he knew of the Michelson Morley experiment, although later he confused the issue by saying that he didnt' and then that he did. He did.
```

> "...suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good."

```{note}
Here he's suggesting going beyond Galilean Relativity.
```

> "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."

```{note}
Here he's introduced his two postulates.
```

> "These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell's theory for stationary bodies."

```{note}
Maxwell, not Newton, is primary for this exercise.
```

> "The introduction of a “luminiferous ether” will prove to be superfluous inasmuch as the view here to be developed will not require an “absolutely stationary space” provided with special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place."

```{note}
He just got rid of the ether because it’s “superfluous"...it's not necessary. It cannot be measured.
```

> "The theory to be developed is based—like all electrodynamics—on the kinematics of the rigid body, since the assertions of any such theory have to do with the relationships between rigid bodies (systems of co-ordinates), clocks, and electromagnetic processes. Insufficient consideration of this circumstance lies at the root of the difficulties which the electrodynamics of moving bodies at present encounters."

```{note}
Here, the less-than-unknown Einstein has just said, “Hey. None of you – for centuries – have thought hard enough about this stuff.
```

Now he's going to insult the entire physics community by patiently trying to describe what it means to measure something.

> "If we wish to describe the motion of a material point, we give the values of its co-ordinates as functions of the time. Now we must bear carefully in mind that a mathematical description of this kind has no physical meaning unless we are quite clear as to what we understand by “time.”

```{note}
Seriously. He feels the need to tell everyone what we mean by the time of event.
```

> "We have to take into account that all our judgments in which time plays a part are always judgments of simultaneous events. If, for instance, I say, 'That train arrives here at 7 o'clock,' I mean something like this: 'The pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events.'"

```{note}
Still insulting:
```

> "It might appear possible to overcome all the difficulties attending the definition of 'time' by substituting “the position of the small hand of my watch” for “time.” And in fact such a definition is satisfactory when we are concerned with defining a time exclusively for the place where the watch is located; but it is no longer satisfactory when we have to connect in time series of events occurring at different places, or—what comes to the same thing—to evaluate the times of events occurring at places remote from the watch."

```{note}
This is precisely what I described in the previous lesson. Remember, I worried about having one measurement of space being in the Away frame and the measurement of time in the Home frame.
```

> "We might, of course, content ourselves with time values determined by an observer stationed together with the watch at the origin of the co-ordinates, and co-ordinating the corresponding positions of the hands with light signals, given out by every event to be timed, and reaching him through empty space. But this co-ordination has the disadvantage that it is not independent of the standpoint of the observer with the watch or clock, as we know from experience. We arrive at a much more practical determination along the following line of thought."

```{note}
His line of thought is to use light just exactly like I introduced the little train that connected two clocks on the road.
```

The rest of this paper was to work out the consequences with special attention to one aspect of his realization, which he later characterized as:

> "A storm broke loose in my mind."