I can’t find any better way to represent space and time in one frame…. Spacetime diagram is cool

This approach what we have is, like you said, good way. No need to introduce spacetime diagrams earlier.

The scale which we generally choose in stationary frame of reference i.e. 1unit=4 cm would be same for the moving frame?

Now with the Space Time diagrams, the asynchronous nature of moving clocks is graphically represented. Referring to 26.3, where on the moving blue frame, the clocks on the right are lagging behind those on the left, I have the opinion according to the slope of the blue line, that clocks on the right should mark in advance than those on the left. Am I OK?

I prefer space time diagrams after the theory has been presented.

Now we can see how equations are really working

The line t’ (x’=0) marks the transition from clocks lagging behind (right of the line) and clocks that are ahead (left of the line). All according to the observers in rest.

My natural (lazy) preference has always been to first get a generalised, pictorial overview – and the mathematical derivations subsequently. However, I undertook this course to get a deeper understanding of the mathematics that underpins the concepts. Much as I dislike floundering through the mathematical mire, it is good for me (no pain, no gain) ¯\_( ͡❛ ͜ʖ ͡❛)_/¯

i feel that introducing space time diagrams after teaching the features of time dilation, length contraction, asynchronous clocks and Lorentz transformation is a good decision as at first we learn what we should see by looking at the equations presented for each of these and then showing the geometrical interpretation allows us to visualize clearly each of the above mentioned effects clearly and gives us a good intuition for these effects

It’s good for me too, Roger. Encountering all this for the first time, I really can’t say how the concepts would sit with me if introduced differently, however.

I think it’s good for me that the spacetime diagrams are introduced later. However, I am not able to conceive the time dilation and Lorentz contraction from demonstration 9. How to get that?
And also in demonstration 10 both graph don’t look exactly symmetric. In first graph, the axes are coming closer to each other while in second, the axes are going away from each other if we look at the arrows of the axes.

PERFECT

This approach worked very well for me personally. Although I can’t compare it with the other one as I have not studied by it. The space diagrams can give you a sense of how it all works, however there was no lack of this sense in the previous modules thanks to lots of demos and examples.

Great depiction. So at superluminal speeds (theoretically) space gradually becomes time and vice versa, time becomes space. But that looks like happening in some more exotic imaginary co-spacetime, after some luminal-singularity transitioning…

I wonder if, in a spaceship, at some point in the middle of accelerating—around geometric midpoint v=c•sqrt(2)/2 ≈ 70%c — we start noticing that spacelike features in spacetime are actually indistinguishable from, or at least very similar to, those of timelike features. Interesting.

I think this approach is a good one. The reason is, I believe, not so much that a spacetime diagrams as such is confusing – I don’t think it is. What is difficult and non-intuitive to understand (in my view) is why you would want/need to move from an orthogonal to a non-orthogonal coordinate system and most of us are only used to moving from one orthogonal coordinate system to another (rotated) coordinate system. Doing the Lorentz transformation theory first provides the understanding why the transformation is from an orthogonal to a non-orthogonal coordinate system. Understanding the consequences of moving from an orthogonal coordinate system to a non-orthogonal coordinate system is what is key here.

I like how this approach tends to reinforce the visuals introduced by the formulae.

I completely agree with the professor’s approach to introducing spacetime diagrams in teaching Special Relativity. It makes perfect sense to first establish a solid understanding of the essential features and concepts of Special Relativity before delving into spacetime diagrams. These diagrams can indeed be confusing if introduced too early, as they rely on a conceptual framework that students might not yet have grasped.
By first presenting the core principles of Special Relativity and allowing students to develop a firm foundation of the theory, they can more effectively integrate spacetime diagrams into their understanding. Once students have a clear grasp of concepts like asynchronous clocks, time dilation, length contraction, and the relativity of simultaneity, they can then use spacetime diagrams as a powerful visual tool to represent and illustrate these ideas. This approach not only aids in the interpretation of Special Relativity but also enables students to create a more coherent and comprehensive mental model of the subject’s fundamental features.

Ladies and Gentlemen,

In distinguishing space-time, space-time diagrams and special relativity we have Prof. Bojowald’s ideas also:

“Special relativity determines the the motion of particles in space-time, while general relativity describes the behaviour of space-time itself.”

Special relativity has quantum.

🙂
🍵☕🍵🍵