Spacetime Diagrams: An Easy Way to Visualize Special Relativity (Physics by Parth G)

If you've seen a distance-time graph before, you'll pick up spacetime diagrams very quickly... and understand their true power in visualizing special relativity!

A spacetime diagram is any diagram that shows the behavior of an object through space and time. However, the term most commonly applies to Minkowski Diagrams, which have position plotted on the horizontal axis, and (speed of light x time) plotted on the vertical axis.

We start by seeing that a stationary object (in our reference frame) can be represented with a vertical line on our spacetime diagram. This line is known as the "world line" of our object, and shows how it moves through space and time. We also see that objects moving at a constant speed will have straight lines (not necessarily vertical) as their world lines, and objects accelerating will have curved world lines.

Next, we consider a pair of events to show on our diagram. Events are defined by 4 coordinates in relativity - one time coordinate, and three spatial coordinates. To keep things simple we just consider 1 time and 1 spatial coordinate, and assume the other 2 spatial coordinates are the same for all objects being considered.

An event is just shown as a point on our spacetime diagram. And when we plot two events (such as a switch being flicked, and a light bulb switching on), we can see whether or not the two events are "causally connected". In other words, can the first event communicate with the second event before it happens, and therefore is it possible for the first event to cause the second one?

On our spacetime diagrams, the vertical axis shows ct (speed of light x time) rather than just time. For this reason, a photon (or any other object travelling at light speed) will show up as a straight line at 45 degrees to either of the axes (in our stationary reference frame diagram anyway). This is the fastest any object is allowed to travel in the theory of relativity.

This means that we can draw 45 degree lines out from the first event, and see if the second event can be causally linked (or causally connected) to it. If the second event lies to the top left of the 45 degree line, this means some signal could be sent from event 1 before event 2 occurs (and therefore could be the cause of event 2). However if the second event lies to the bottom right of the 45 degree line, then a signal would have to travel faster than the speed of light (not allowed) for the two events to be causally linked. In other words, these events are independent.

With a more rigorous approach, we see how events can be described as being in the "future", "past", and "elsewhere" of a particular event. We also realise that if we extended our diagram to more spatial dimensions, the light lines would actually make a cone - this is known as the light cone of the event we are considering.

Next, we see how the spacetime diagrams for two observers moving relative to each other (at a constant speed) can be plotted on the same graph. For an observer moving relative to us, the axes representing their frame of reference will be "squished", towards the 45 degree photon line. The faster the second observer moves relative to us, the more "squished" their axes.

We also see how we can find a reference frame where two events occur at the same time for the moving observer, even if they appear to occur at different times in our original reference frame. Similarly, we can find a reference frame where two events happen at the same spatial coordinate, even though they happen at different places for the original observer. Both observers are "correct" in both cases, as there is no one preferred inertial reference frame in special relativity.

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Timestamps:
0:00 - What are Spacetime (Minkowski) Diagrams?
1:46 - World Lines, and Why Spacetime Diagrams are Useful
3:25 - Events in Special Relativity - (t,x,y,z) Coordinates in 4 Dimensions
4:42 - The Causal Connection Between Events (and the Speed of Light on Spacetime Diagrams)
9:27 - The Light Cone of an Event (Future, Past, and Elsewhere)
10:17 - Spacetime Diagrams for Observers Moving Relative to Each Other

[ParthGChannel]

And as always, let me know what other topics to cover in future videos :)

[Jehannum]

Yes, please do a part 2 on this and take it to the next level.

[fritt_wastaken]

Most useful thing about spacetime diagrams is that using them you can calculate a solution to basically any relativiatic problem graphically and intuitively.
I'm a physics tutor, and when explaining relativity I always start with diagrams, deriving all equasions from them. I have no idea why this is not the default route since it is so much more effective

[nirmolmunvar]

This was an amazing explanation. I would love to see more detailed videos of the same topic. I just wanna know that why is the speed of light constant for any given reference frame. Why can't it change.

[dinodinoulis]

Very interesting to consider that different events can appear to occur at the same point in space to different observers.

[Mattd]

I’m horrible at math, I feel like I can understand it the way you teach. These videos are invaluable to me, you’ve made me a better person so thank you.

[oovahchannel]

People really need someone like parth to understand complex concepts like this. Good job parth! Keep going!

[konozrashid]

And of course Parth! I literally love your physics videos! Explain this concept in much much more detail in the next video!

[konozrashid]

The fact that two events happening at different times can actually occur at the same time in some other reference frame is actually shown in Nat Geo's series "Genius" in the train scene that two lightning bolts can be seen simultaneously when you're stationary while they occur independently if you are on the train.

[harshgurung]

simply best. i am glad i am a teacher and student of physics.

[nicoleh]

I just found your channel and I am so glad that I did! As a physics major, it's been hard finding good explanations for some of these concepts and your videos are INCREDIBLY helpful! Thank you so much for sharing content on here-- you remind me of why I wanted to study physics in the first place!

[stevewhitt]

Thanks. I finally have a real intuitive understanding of Spacetime Diagrams now. Before, I understood how to transform between the frames but I lacked the intuition to really understand it. Like Sal Khan says: if you don't have a real good intuition then you will never really understand the subject matter. You have a way of breaking it down for dummies like me who really want to learn. May Yahweh (Allah) bless you.
Iva, SC USA

[gahanchattopadhyay]

I was waiting for this topic for a long time. Wonderful explanation. Waiting for the follow-up video

[k.invariant]

Parth, talk about the pauli exclusion principle and information in the cosmos .

[pipertripp]

Would love to see a follow up vid with more in depth info about these diagrams and their interpretation. Thx!

[JungleJargon]

Nice illustration! Now if we can get people to see that there is little to no gravity to slow down light between galaxies until the light enters into a galaxy where time slows down and distance contracts, slowing down the speed of light. This is the reason superluminal motion is perceived to be seven times the speed of light since our measures of time and distance are being projected into outer space where time runs faster and the measure of distance is much larger relative to ours. Of course nothing ever exceeds the speed of light. It’s that the assumed measures of time and distance are off.

Another little secret of general relativity is that the speed of light is NOT constant because the measures of time and distance are not constant throughout the universe. Looking at a galaxy is not like looking at a cat or dog where the measures of time and distance are constant because they are not constant from here to outer space between galaxies. The measures of time and distance appear to be constant or flat to us locally but they are not flat over great distances, especially outside of galaxies and in between galaxies.

[aniketh]

Finally the first to comment. Your videos are really dense with information and its awesome to listen to . Keep up the good work

[philsaliba]

I have recently become obsessed with trying to understand both of the theories of relativity. I have consumed a ton of content online and read a few books on the subject (including Einstein's actual paper). I think this video does an excellent job explaining special relativity.

[laurendoe]

The way I look at the graph you used is that "x" is a distance from the origin. The exact coordinates of the location are unimportant - the one dimensional value of distance is all that matters.

[ndo]

This video is the best explanation i’ve ever heard about future light cone 🎉🎉🎉.