Objects (frames) in motion.

[geordief]

After reading around the subjects of Special and General relativity (with admittedly patchy results) for quite a few years now, I have begun to tell myself that perhaps the most important result in Relativity might be the first : the way moving frames are connected.

 

Never mind the speed of light , the lack of need for an ether , the equivalence or not between gravity and acceleration as well as the Lorentz Transformation perhaps it is this simple correlation (the way moving frames are connected.) that is the cornerstone of Relativity?

 

I have seen the geometric illustration of this as it comes at the very beginning of the subject and is easily learnable by school children (which is a bit embarrassing on my account that I struggled (ad still do) with it so long)

 

The most obvious point seems to be that the speeds (and all dependent relationships) in moving frames do not add up linearly.

 

Have there been any other explanations of this really fundamental finding other than the way it is treated in Special Relativity?

 

I mean the treatment of it in geometric terms is all I have really seen and I must have spent hours and days (years ago now) puzzling out which part of the triangle applied to light and which applied to forward motion.

 

It all seems so cut and dried . Has there been discussion as to why it was deemed necessary to go down this (obviously now correct) road?

 

Did it require the invariance of the speed of light in all reference frames to give the impetus to even consider the question?

 

Were there no premonitions that moving frames might not be connected in a linear ,additive way?

 

Was Einstein really the first person to have any inkling that this might be a question at all?

Edited August 27, 2016 by geordief

[ajb]

...the Lorentz Transformation perhaps it is this simple correlation that is the cornerstone of Relativity?

In short yes, the Lorentz, or more properly the Poicare group (and its Lie algebra) are the cornerstone of special relativity and also general relativity where we have such transformations locally.

 

Have there been any other explanations of this really fundamental finding other than the way it is treated in Special Relativity?

Nothing seems to come close to special and general relativity in modelling nature. It is not at all understood why the Poincare group plays such a vital role in physics: for example representations theory is related to the 'species' of fundamental particles we see.

 

 

I mean the treatment of it in geometric terms is all I have really seen and I must have spent hours and days (years ago now) puzzling out which part of the triangle applied to light and which applied to forward motion.

All the basic notions are indeed tied to Riemannian geometry.

 

Has there been discussion as to why it was deemed necessary to go down this (obviously now correct) road?

The earliest hint is in Maxwell's equations which are invariant under Lorentz transformations and not the ones found in classical mechanics. Why geometry, I am not sure, but geometry really does seem to be 99% plus of all classical physics.

 

Did it require the invariance of the speed of light in all reference frames to give the impetus to even consider the question?

We get invariance of the speed of light in all inertial frames - not all frames in general. And yes, this was a puzzle and seemingly written into Maxwell's equations.

 

 

Was Einstein really the first person to have any inkling that this might be a question at all?

Lorentz, Minkowski and others were thinking along the same lines as Einstein. But he was the first to bring special relativity together.

[geordief]

In short yes, the Lorentz, or more properly the Poicare group (and its Lie algebra) are the cornerstone of special relativity and also general relativity where we have such transformations locally.

 

 

Nothing seems to come close to special and general relativity in modelling nature. It is not at all understood why the Poincare group plays such a vital role in physics: for example representations theory is related to the 'species' of fundamental particles we see.

 

 

 

All the basic notions are indeed tied to Riemannian geometry.

 

 

The earliest hint is in Maxwell's equations which are invariant under Lorentz transformations and not the ones found in classical mechanics. Why geometry, I am not sure, but geometry really does seem to be 99% plus of all classical physics.

 

 

We get invariance of the speed of light in all inertial frames - not all frames in general. And yes, this was a puzzle and seemingly written into Maxwell's equations.

 

 

 

Lorentz, Minkowski and others were thinking along the same lines as Einstein. But he was the first to bring special relativity together.

Thanks ,ajb a lot of food for thought there.

 

Actually you misread that reference of mine to Lorentz Transformations. I just gave it as the last in the list and the "cornerstone" referred to " the way moving frames are connected." I did indeed misplace an "and" in my list as I tagged on the Lorentz Transformation as an afterthought to the list

 

I have edited it now.

Edited August 27, 2016 by geordief

[Tim88]

After reading around the subjects of Special and General relativity (with admittedly patchy results) for quite a few years now, I have begun to tell myself that perhaps the most important result in Relativity might be the first : the way moving frames are connected.

 

Never mind the speed of light , the lack of need for an ether , the equivalence or not between gravity and acceleration as well as the Lorentz Transformation perhaps it is this simple correlation (the way moving frames are connected.) that is the cornerstone of Relativity?

 

I have seen the geometric illustration of this as it comes at the very beginning of the subject and is easily learnable by school children (which is a bit embarrassing on my account that I struggled (ad still do) with it so long)

 

The most obvious point seems to be that the speeds (and all dependent relationships) in moving frames do not add up linearly.

 

Have there been any other explanations of this really fundamental finding other than the way it is treated in Special Relativity?

 

I mean the treatment of it in geometric terms is all I have really seen and I must have spent hours and days (years ago now) puzzling out which part of the triangle applied to light and which applied to forward motion.

 

It all seems so cut and dried . Has there been discussion as to why it was deemed necessary to go down this (obviously now correct) road?

 

Did it require the invariance of the speed of light in all reference frames to give the impetus to even consider the question?

 

Were there no premonitions that moving frames might not be connected in a linear ,additive way?

 

Was Einstein really the first person to have any inkling that this might be a question at all?

 

As far as I could trace it back, the first person who found that relation was Poincare, but Einstein may have found it around the same time:

https://web.archive.org/web/20141006134323/http://henripoincarepapers.univ-lorraine.fr/chp/text/lorentz4.xml

 

It was based on the Lorentz transformations, which in turn were based, among other things, on the invariance of observations of the speed of light.

 

As you can see there as well as in Einstein's corresponding paper, §5 of http://www.fourmilab.ch/etexts/einstein/specrel/www/ , the geometric presentation was introduced later.

 

Note also that "addition" can be a bit misleading: the laws of mathematics are of course not broken by SR.

As you also can see, the velocity composition equation was derived by means of a Lorentz transformation from one reference system to another one that is in relative motion to the first. The Lorentz transformations predict non-linear effects from speed so that linear additions of the measurements of two such systems should not be expected to work.

 

PS. The term "composition of velocities" is not in the German original which used the German word for "addition"; apparently it was an improvement by the translator!

Edited September 8, 2016 by Tim88