# How did Einstein do it?

1. Feb 13, 2004

### aychamo

Ok. I have a question on SR/GR with regards to Einstein. How did he come up with this? That's what I don't understand about physics and physicists. How do they derive a formula that represents what they are trying to express?

And especially with regards to Einstein. His relativity formulas are amazing, and that they can calculate time dilation, something that I don't even know if he could prove or not.

From what I understand physics majors in college do an experiment with detecting muons from the atmosphere that verify Einstein's relativity theory, but did Einstein have access to the same type of thing in his time?

So basically what I'm asking is how was he able to come up with a formula that told him that at .865c time slows down by half or whatever.

Thanks
AYCHAMO

2. Feb 13, 2004

### Staff: Mentor

No, he could not directly prove time dilation at the time - clocks were not accurate enough.

As I understand it, Einstein was a daydreamer. That's whats so compelling about him to so many people. He knew about a problem that existed in physics: the Michelson/Morely experiment produced a result people didn't expect. The answer to the question is simple, but difficult to accept if you've never seen it before. Einstein was able to accept the logical implication of the MM experiment and had the mathematical skills to derive the models for it.
I'm not sure he was the first to come up with them (Lorenz transformations), but they are actually relatively simple geometric relationships. The big leap is accepting that time is a variable, not a constant. Basically, you think of several cases and compare them. The starting assumption is that C is constant, and the implications (time must vary) follow directly. You think: 'for a person traveling at .866C, what must happen for him to still measure C as C and not .133C?'

3. Feb 13, 2004

Staff Emeritus
Lorentz came up with the Lorentz transformations. He did it by maathematically manipulating Maxwell's equations for electromagnetism. The problem was to find the relations of space and time between two electrodynamic systems in constant motion relative to one another. The simple, or naive, transformations t -> t' and x -> x + vt when substituted into Maxwell's equations destroyed the nature of the equations and so were impossible. Lorentz found that you had to do linear transformations involving both time and space. He considered this just an electrodynamic feature.

Einstein gave a constructive proof of Lorentz's transformations by considering observers trying to measure times and lengths and communicating their findings at the speed of light. It is entirely possible that Einstein got his idea by thinking of people on a train and on the ground in the manner of his famous example. The consequence of Einstein's approach was that there was no need for an ether, and that simultenaity was also relativised.

4. Feb 14, 2004

### Integral

Staff Emeritus
Einstein was able to derive the Lorentz transforms based on his 2 postulates, the constancy of c, and universal laws of physics. He used the model of a moving mirror to create a differential equation, the solution to this equation is the Lorentz transforms. He did not use the entire frame work of Maxwell for this derivation, only the constancy of c, which by the way is a result of Maxwell's equations.

5. Feb 17, 2004

### David

Einstein didn’t come up with it. H.A. Lorentz did. Lorentz was the one who introduced “time dilation”, “length contraction”, “mass increase”, a “limiting speed of c”, and many other ideas that are now attributed to Einstein. Einstein copied much of his 1905 SR theory from H.A. Lorentz’s 1895 book. I finally obtained a copy of that rare book, and here is a page from it where Lorentz introduced length contraction and the famous Lorentz Transformation.

6. Feb 17, 2004

### pmb_phy

In modern terms: If one assumes that that proper mass of a photon is zero then the Principle of Relativity, coupled with Maxwell
's equations, predicts that the speed of light is independant of the source. If one does not assume that the photon has zero proper mass then things are a bit different. Maxwell's equations are them modified to include the proper mass of the photon. In such case Maxwell's equations can be derived from a Lagrangian whereby a term is added to compensate for the non-vanishing of the proper mass of the photon. The term is proportional to the magnitude of the 4-potential. The resulting Lagrangian is known as the Proca Lagrangian. The "constancy of light" postulate is then interpreted as something else. E.g. there is still an invariant speed. It's just not the speed of light.