# The first postulate in special relativity

In Einstein's special relativity, there are two postulates:
1. the laws of physics are invariant in all inertial frames of references; and
2. the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source or observer.

What did Einstein mean by the first postulate?

My confusion mainly comes from the terminology "the laws of physics". I know there is a similar question recently and anna v gave an excellent answer there. But my question is a little bit different. I am asking about what Einstein had in mind when he proposed the postulate for the first time in history. By "the laws of physics", did he mean the differential equations governing the motions of moving objects?

• Btw the second postulate is not independent. From the first you may get Lorentz transformations without physical meaning of limiting speed. Combining this with Maxwell-Clerk equations you get speed of light as the limit of speed. Only historical reasons is behind such postulate formulation. Logical structure is much more direct Dec 22, 2019 at 10:08
• I just want to note that the first postulate existed before Einstein. It's the first postulate of Galilean Relativity Dec 22, 2019 at 11:48
• @kakaz How does one get speed of light as the limit of speed from Maxwell's equations? Do you have a reference on the derivations? Dec 23, 2019 at 15:16
• @YuhangChen Take a look for Andrzej Szymacha works. Here's a short explanation, but written in polish. But mathematics is straightforward: jakubw.pl/faq/fizyka/node31.html Dec 24, 2019 at 23:43

AFAIK Einstein was motivated for special relativity from the framework of electromagnetism. It is in Maxwell's theory of electromagnetism that the Lorenz transformations appear naturally.

If you look at Maxwell's equations, for example in this form here, it is based on four "laws" , there are four "laws" . These are an example of the laws that Einstein must be talking about, to start with . These laws are a distillate of experimental observations. By using them as axioms Maxwell picks those solutions of his differential equations which fit the experimental observations by intent. His theory has to fit the "axioms" he is using to pick up the valid solutions. Since his theory is well validated, i.e. is predictive of data, the domain where the laws hold is the inertial frame domain, as defined by " an inertial frame of reference is a reference frame in which a body at rest remains at rest and a body in motion moves at a constant speed in a straight line unless acted on by an outside force."

So what Einstein did with his special relativity is to extend the electromagnetic behavior to the behavior of massive particles. He chose such postulates, so that the electromagnetic theory would remain intact, and there would be new predictions for the behavior of matter. These predictions have been validated and the special theory of relativity holds.

Inertial frames are necessary in the definition because special relativity deals with the concept of energy. Momentum , energy, angular momentum are conserved in inertial systems, there are conservation laws. BUT these laws hold only within inertial systems. When accelerated systems are introduced these laws do not hold without corrections.

• This is a truly awesome answer. But I don't follow what you mean by "Maxwell picks those solutions of his differential equations which fit the experimental observations by intent". Once the differential equations are set up, the solutions are determined. Did you mean Maxwell designed four differential equations such that their solutions match the experimental results? Dec 23, 2019 at 15:10
• Yes, as the experimental results are embedded in the laws of Ampere , Gaus .. The dfferential equations themselves, without the axiomatic limits placed by the laws accepted by Maxwell have a much larger phase space of definition. Dec 23, 2019 at 15:33
• So the combination of special relativity and Maxwell's equations leads to quantum electrodynamics, right? Dec 23, 2019 at 15:42
• The four laws, and maxwell's brilliant guesses lead to classical electrodynamics which contain Lorenz transformtions. . Quantum electrodynamics is a different story, one has to quantize the Maxwell's equations, i.e. turn the differentials into operators on the wavefunction of a photon. A different story. cds.cern.ch/record/944002?ln=en Dec 23, 2019 at 18:33

He means that there is no test you can do, in your inertial frame, that will show whether you are moving in relationship to the Universe, or whether you are sitting still and the Universe is moving past you. All physical laws are the same in either case, therefore there is no absolute frame of reference.

• You haven’t really answered the question, which is about what is meant by “physical law”, not its invariance. Dec 22, 2019 at 3:59
• I think “no test you can do” pretty much provided a nice operational definition of physical law: no matter what you do, in the two frames, the universe does the same thing. Dec 22, 2019 at 7:03

In the context of classical mechanics there is no difference if a body is "at rest" or have constant velocity. Any passenger inside an airplane at constant 900 km/h can move and move things as in the airport.

It was well established at least for more than a century in the dawn of 20 century, even while the examples involved ships or trains and not airplanes, with its more dramatic speed.

The problem is that the notion of fields was at the heart of the electromagnetism, and that is more naturally linked to the idea of an absolute reference frame. A static field in the airport frame, would change with time to someone at 900 km/h, leading to different measurements results. Maxwell equations give different outcomes for static or time changing fields. It is not easy to deal with it.

Einstein managed to fit the EM theory in the framework of the principle of relativity, already used for mechanics. Of course it was necessary to change it to use Lorentz transformations.

The effects on mechanics, even for airplane velocities is negligible. But it solved the fields conundrum joining the magnetic and electric field in a way that can explain why different frames can measure the same EM force, and see the same movement of charged bodies.