The Geometry of Special Relativity

A Revolution in Space-Time

Geometry of Relativity Blog

Thoughts and discussion of ideas on the periphery of the geometry of relativity.

A Lorentz Transform in 3 Steps

(Or why I think the Lorentz transformation is misunderstood)

The speed of light is always measured to be the same in all inertial frames. This is the assumption used to derive the Lorentz transformation visualised in the interactive example above.

While the Lorentz transformation is normally assumed to be a transformation of an event in one inertial frame to the same event in another inertial frame, this derivation indicates that it is not quite the same event, but two events from the same stationary source.

Both events are observed at the same point in space-time along the path of the moving observer. One event is observed by the moving observer and propagates at the speed of light (1 for simplicity) relative to that moving observer. The other event is observed by a stationary observer and propagates at the speed of light relative to that stationary observer.

To see how easy it is to derive this without any other assumptions, take a look at the geometry of the Lorentz transformation.

On the Geometry of the Lorentz Transformation

Another month and another tutorial published - following on from the geometry of time dilation comes the geometry of the Lorentz transformation.

I’m pretty sure the geometry of the Lorentz transformation puts me in the quack category, and I admit I’m ignorant of a lot of details of modern physics (I’m a software engineer, not a physicist), but I am willing to learn. I started thinking about the geometry of the Lorentz transformation while at university - I did my final year thesis project visualising Special Relativity - and have spent a lot of time over the following years trying to find a way to clarify and communicate the geometry.

But it was only over the past six months that a few ideas solidified, and together with the goodness of MathJax and modern browser support for interactive scaleable vector graphics, I found an easy way to visualise and communicate the simple geometry.

So if you have a better understand of special relativity than me, please take a look at the geometry of the Lorentz transformation and leave a note pointing me in the right direction.

Thanks!

On the Geometry of Time Dilation

I’ve been spending quite a bit of time thinking about how to best communicate the geometry of special relativity - and have just published the first revision of The Geometry of Time Dilation. If you’ve got a few minutes, I’d love to hear any thoughts or ideas.

The biggest obstacle has been how to communicate in a way that’s accessible to anyone familiar with basic algebra. For the moment I’ve tried to address this by using SVG animations for any visual concept.

The second obstacle was the traditional notation for this kind of thing. Most books or other explanations use $\Delta t$ and $\Delta t’$ to refer to a period of time measured on a stationary and moving clock, but measured in the one inertial frame. It gets very confusing when trying to then think about the times measured on those same clocks in the other inertial frame.

The overloading of so much information leads to confusion in my experience as well as difficulties down the line, so I’ve gone with the (much) more verbose:

to express one tick of A’s clock as measured in A’s inertial frame.

Next up will be the geometry of the Lorentz transformation…

Experimenting With Publishing

I’d like to start publishing some ideas about the geometry of Special Relativity but am not sure of the best way to publish them online. What I have is a combination of static content and some animated javascript examples.

I was previously looking at reveal.js slides, but I always end up having to decide between keeping slides simple and continuing ideas over multiple slides - neither of which is ideal.

Octopress seems better in that I’ve got complete control over the formatting while still letting me focus on the content.

Let’s see how it goes.