Special Relativity - Acceleration

Overview

This app is used to show the cause of Special Relativity using the famous light clock thought experiment. We have a model containing an Observer and an Emitter with a light clock. The Emitter will emit a photon every 1s of model time. The photon contains the time that it was emitted and the location that it was emitted at.

Each photon will travel back towards the Observer until it is measured and its data is recorded in the output tables. The Observer will record the time that the photon was emitted, the distance it has travelled, the time that it was received and the period of time since the last photon was recorded and the change in period.

Viewpoints

The viewpoint used by this application does not represent how we would experience this scenario in reality. It is a God's Eye viewpoint. You can't see light at a distance but that is exactly what this app is showing you. You, the user, are outside of the model and looking at it. In reality, we are inside of the model and must deal with that as best we can.

The Observer does represent how it would be seen by us in reality. Relativity is all about measurement and how those measurements must be interpreted. It must be applied to your data so that you can read it correctly, before you can even look at the contents.

Result Sets

There are 3 models in the scene. The top model, Result Set 1, does not use a velocity on the Emitter so we get a base reading to compare the other models to. The middle model, Result Set 2, gives the Emitter a velocity of 0 and an acceleration of 0.001c. The bottom model, Result Set 3, uses a velocity of 1c.

When an accelerated Emitter reaches c, it will have its acceleration removed. This gives us 3 models to represent the min and max affect and the acceleration in between that will start like the top model but end up like the bottom model.

You can export the results from each result set by clicking on the results and pressing ctrl+c (PC) or cmd+c (Mac). The data is exported in CSV format so it can easily be imported into any spreadsheet application or text editor.

Time

A universal clock is used for all entities in a model. More than that, all models use the same clock. This clock is the driver of the model, causing each frame to progress to the next. Every entity sees 1 second as 1 second and all entities see the 10th second as the 10th second.

Observers use the clock to record observations. Emitters use the clock to determine when to emit a Photon. Observers, Emitters and Photons also use the clock to determine their motions.

Coordinate Systems

Each model has its own coordinate system as far as the 3D graphics system is concerned. A model can be positioned anywhere in the scene. However, this does not extend into the model. All entities in a given model use the same coordinate system. You can also consider all entities in all models to be using the same coordinate system, otherwise, we could not compare them.

The Math

The models used in this app only require the definitions of velocity and acceleration to be implemented. We are not using Relativity but showing the need for it, so we don't need any complicated math.

The Data

The data generated from the models can be used to determine the transforms of Special Relativity. With a bit of thought, probably some confusion, and a little persistence, you can find them yourself.

The top model provides a good starting exercise, since it does not involve a velocity. If you can find the equation that tells you the time a Photon was emitted, given the time it was observed and the distance it has travelled, you will find it much easier to see what the next transform will look like.

Velocity
Acceleration
Zoom
Distance Scale
Precision