# Did Einstein guess the time-dilation equation?

#### Brainv2.1beta

Did Einstein "guess" the time-dilation equation?

I can't find anything on the net, but it seems to me that Einstein would have had to "guess" the time dilation into existence. Furthermore, supposed "proofs" could be hoaxes.

#### JesseM

I can't find anything on the net, but it seems to me that Einstein would have had to "guess" the time dilation into existence. Furthermore, supposed "proofs" could be hoaxes.
No, it can easily be derived from the Lorentz transformation equations, which Einstein derived in his 1905 paper from the two basic postulates of relativity (that the laws of physics should work the same in all inertial reference frames, and that the speed of light should be the same in all inertial reference frames). Einstein's derivation of the Lorentz transformation is a little hard to follow compared to derivations I've seen in textbooks, but I wrote up a post where I tried to follow along and explain the steps on this thread if you want to give it a shot.

#### Brainv2.1beta

No, it can easily be derived from the Lorentz transformation equations, which Einstein derived in his 1905 paper from the two basic postulates of relativity (that the laws of physics should work the same in all inertial reference frames, and that the speed of light should be the same in all inertial reference frames). Einstein's derivation of the Lorentz transformation is a little hard to follow compared to derivations I've seen in textbooks, but I wrote up a post where I tried to follow along and explain the steps on this thread if you want to give it a shot.
Cool! When I get some energy I'll give it a try.

#### rbj

I can't find anything on the net, but it seems to me that Einstein would have had to "guess" the time dilation into existence.
not anymore than Pythagoras guessed at a2 + b2 = c2 . that fact, plus the premise that the laws of physics (including parameters in those laws such c) are the same for every inertial observer; put those two together and you have the time dilation formula.

#### yogi

It also follows directly from Minkowski's unification - one side of the Pythagorean triangle being ct' and the other distance vt. (ct')^2 + (vt)^2 = (ct)^2

#### a.mlw.walker

Einstein's proof of relativity

I wasnt sure really how to get it out there on a broader level, but the document attached is something I wrote for Physics A level a few years ago. I researched Einstein's theory of relativity and tried to write in in as much Layman terms as I could. The final document got sent to the science association for good work. There are a few spelling errors here and there but it gives an easy to understand view of what Einstein was on about and why time dilates, we get heavier at high speeds etc. For time dilation just search for it, and there is a heading of it. Have a read. Its not too long and i think you'll like it. Teenager's huh!

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#### aristurtle

I can't find anything on the net, but it seems to me that Einstein would have had to "guess" the time dilation into existence. Furthermore, supposed "proofs" could be hoaxes.
No,he just copied the result from Lorentz and reinterpret in his own relativistic manner.Lorentz and another dude(sorry for forgeting your name) worked out the effect of dilation of time and the shorter ruler, something,in the framework of classical electrodynamics.

#### JesseM

No,he just copied the result from Lorentz and reinterpret in his own relativistic manner.Lorentz and another dude(sorry for forgeting your name) worked out the effect of dilation of time and the shorter ruler, something,in the framework of classical electrodynamics.
He may have been partly inspired by Lorentz's ad hoc equations, but Einstein showed that if you started from the two fundamental postulates of relativity (laws of physics work the same in every inertial frame, speed of light the same in every inertial frame), you could derive the Lorentz transformation from this, and you can in turn derive the equations for time dilation and length contraction from the Lorentz transformation.

#### hedenqvist

Thanks for this one.

#### Histspec

No,he just copied the result from Lorentz and reinterpret in his own relativistic manner.Lorentz and another dude(sorry for forgeting your name) worked out the effect of dilation of time and the shorter ruler, something,in the framework of classical electrodynamics.
The other guy who worked out the effect of time dilation was Joseph Larmor (1897 and 1900).

en.wikipedia.org/wiki/Joseph_Larmor
en.wikipedia.org/wiki/History_of_Lorentz_transformations

Regards,

#### Fredrik

Staff Emeritus
Gold Member
He may have been partly inspired by Lorentz's ad hoc equations, but Einstein showed that if you started from the two fundamental postulates of relativity (laws of physics work the same in every inertial frame, speed of light the same in every inertial frame), you could derive the Lorentz transformation from this, and you can in turn derive the equations for time dilation and length contraction from the Lorentz transformation.
I know that this is what just about every introductory book says, but it still isn't really true. The postulates are mathematically ill-defined, mainly because they use the concept "inertial frame" without defining it in advance. I spent some time a few months ago thinking about how to turn Einstein's "postulates" into well-defined axioms, and this is what I came up with:

Space-time is a pair (M,A) where M is a topological space and A a set of homeomorphisms from M onto $\mathbb{R}^4$, such that the corresponding group of transition functions is the set of all smooth maps that a) take straight lines to straight lines, b) tilt the 0 axis by the same amount but in the opposite direction as the inverse map, and c) have non-constant parts that preserve the light-cone at the origin.

The homeomorphisms mentioned in the beginning are what I would call "global coordinate systems". What I mean by a "transition function" is a map $x\circ y^{-1}$, where x and y are global coordinate systems. What I mean by the "non-constant part" of a function is what you get if you Taylor expand the function and throw away the zeroth order term. (This turns an arbitrary Lorentz transformation into a homogeneous Lorentz transformation). The group of transition functions defined this way is of course the Poincaré group. We can now define an inertial frame as "any member of A".

We could of course replace my axiom above with the one-liner "Space-time is Minkowski space" and define inertial frames as isometries of the metric. The point of doing it the way I did is just that it includes versions of Einstein's "postulates" explicitly (b and c).

I'm not trying to say that there's something wrong with Einstein's postulates. My point is just that they should be thought of as a check list, not as axioms. It's a list of properties that Einstein expected the theory he was looking for to have. The idea is to try to find a theory that has those properties and throw away all other theories we find along the way. We can use any method we want while doing that, no matter how non-rigorous, because once we have found an actual theory, only experiments can tell if it's a good theory or not.

#### Dale

Mentor
We could of course replace my axiom above with the one-liner "Space-time is Minkowski space"
It does save a lot of typing ### The Physics Forums Way

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