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]

Hi everyone, thanks for watching! Please check out this playlist for more Relativity Videos: kzbin.info/www/bejne/p6XUhYN5dtxqfNE And as always, let me know what other topics to cover in future videos :)

[@alwaysdisputin9930]

PBS tried to combine Lagrangians with relativity in an interesting way but I don't think any one could understand what he meant. Please could your use your clear explanation skills to make a better version? _"If the Principle of Least Action is really a fundamental law, then there should be a relativistic version of the action that we can minimize to find Mercury’s orbit. After all, planets trade between PE & KE as they move around their orbits, just like the ball. It turns out that we only need to make a couple of relativistic corrections to do this. The most important is writing the Lagrangian as a function of something called 'proper time'" ... "If you plug the relativistic Lagrangian ..."_ → L = ̲ ̲-̲ ̲m̲c̲²̲ - V( r ) → γ ( r ) _"... into the Euler-Lagrange equation, you get equations of motion correctly describing the orbit of Mercury around the Sun."_ τᵳ ⎧ S = - mc² | dτ ⎭ τᵢ ̲ ̲d̲ ⎧ ̲ ̲∂̲L̲ ⎫ - ̲ ̲∂̲L̲ = Γ² ⎧ ̲ ̲∂̲L̲ ̲ ⎫ ̲ ̲d̲L̲ dt ⎩ ∂ν ⁱ ⎭ ∂x ⁱ ⎩ ∂ν ⁱ ⎭ dt _"This shows us that the Principle of Least Action holds up in GR - but it reveals a lot more. 1st, it means that Lagrangian mechanics based on this principle can be made to be “Lorentz invariant” - it gives equations of motion that are valid even in the shifting frames of Einstein’s relativity. And we also start to learn something about the nature of the Action. Once we apply the relativistic corrections, the Action simplifies into just an integral over proper time."_ τᵳ ⎧ S = -mc² | dτ ⎭ τᵢ _"Let's take a moment to think about that. Before, Action was a somewhat vague notion of change in energy, but working with a more precise model of the universe we see Action is much easier to understand. Action is now just how much time is perceived by an observer in their own frame of reference. All objects moving through spacetime, move through paths that minimize the time measured on that path. Remember that Fermat figured out that light always travels the path that minimizes its travel time: the principle of least time. Well it turns out that this is just a special case of a Principle of Least Proper Time. The reason for this is that in the classical limit proper time becomes KE - PE for objects with mass, ..."_ τᵳ t ᵳ ⎧ ⎧ S = -mc² | dτ → S = | (KE - PE) dt ⎭ ⎭ τᵢ tᵢ _" ... but for objects without mass, like light, proper time & time are the same."_ (from 6:21 of the PBS Space Time's YT vid 'Is ACTION The Most Fundamental Property in Physics?')

[@maaoollaamosh4305]

We need a video about the density of states please

[@Stellar_Science]

Sir I've sent an email that you have not responded to.

[@sharadmitra4318]

You are amazing

[@Jehannum2000]

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

[@nirmolmunvar6939]

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.

[@alwaysdisputin9930]

That's a very good question. i dunno but I'm thinking that: Normally we're moving through the time dimension. If we weren't we'd never reach lunch time = disaster. So even when we are stationary by our computer we have a vertical world line because we're moving through the time dimension. If you increased your speed to close to the speed of light, c then you'd still see yourself as stationary & you'd see everyone else moving - they'd appear to be moving at close to c. So the the accelerator pedal in our car makes the whole universe accelerate. & therefore because they're moving at close to c, time dilation happens & so you'd see their clocks ticking slowly. You'd see them running about in slow motion, or even frozen in time. So therefore it seems to you that they aren't moving through the time dimension as much. It seems to you that they have changed from 1) being stationary by their computer + moving through time ----> to 2) moving through space + not moving through time much It's like they've been rotated. But light is different because it's 1) moving through space at the speed of light before ----> & 2) moving through space at the speed of light after It just ignores our accelerator pedal. It doesn't get rotated If we are in a car & throw a tennis ball then the tennis ball is going to move at the car's speed + our throwing speed = fast like maybe 170 mph 99% of mass is due to massless gluons bouncing around inside every neutron & proton. momentum = mass x velocity. So when the car has momentum it's due to these gluons. & then we throw the tennis ball & the effect of the gluons gets added to the tennis ball making it go at 170 mph But if we shine a torch the torchlight is just going to move at c. It will ignore the car's speed. The car's gluons don't affect the photons getting emitted by the torch. So somehow there's a connection between not getting rotated & ignoring the gluons. I dunno what that connection is. Basically you asked an awesome question.

[@ParthGChannel]

Thanks! The speed of light being constant is a postulate / assumption we make in Special Relativity, because some of the mathematics of Electromagnetism that came before this theory suggested the speed of light may be constant (without indicating any reference frame). So Einstein took this idea and worked on Special Relativity, which was later tested experimentally.

[@nirmolmunvar6939]

@@alwaysdisputin9930 that is an amazing breakdown.

[@nirmolmunvar6939]

@@ParthGChannel I'm aware that the Maxwell equations give the velocity of the electromagnetic waves and it simply depends upon the permittivity and permeability of electric and magnetic fields respectively, which has nothing to do with reference frames and motion altogether but just by how the material is (even free space or vacuum). But this is what baffles me, that even in vacuum we can have an acceleration in vacuum. Light doesn't. It maintains it's speed no matter what. We are somehow independent on the material nature of free space where as light is not.

[@nirmolmunvar6939]

@@alwaysdisputin9930 so does that mean that the gluons do not interact with electromagnetic fields or electromagnetism in general bcx light simply chooses to ignore it. Gluons don't have rest mass like photons, so would it also mean that photons/light only has interaction with stuff that have rest mass. I'm asking this cz in refraction other than bending light does apear to slow down as well bcz of present atoms inside.

[@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

[@physicsVischi]

Hello , I think this may interest you, a type of space-time diagram better than Minkowsky's because on both axes the scales are the same. kzbin.info/www/bejne/pWXOfJh9bbWsr68 In Argentina we use it a lot, and I think its dissemination is well worth it.

[@dinodinoulis923]

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

[@oovahchannel622]

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

[@Matt198d]

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.

[@konozrashid887]

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

[@konozrashid887]

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.

[@nicoleh2324]

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!

[@k.invariant]

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

[@resist4resist]

This is the best explanation of light cones I have come across on the Internet. The videos I watched earlier, were not quite clear in explanation but thanks to Parth G, I now understand this concept very well. Liked and subbed!

[@cesarjom]

What a descriptive and concise explanation of spacetime Minkowski diagrams. I've read and seen alot of videos on same topic but this is probably the best I've seen 👏👏👏

[@saifsyedmohammad3769]

Thank You Parth for the excellent short explanation ! Super Useful !

[@jacobblumin4260]

An excellent video! Now I see some things I've been trying to understand for years. Thanks, Parth.

[@pipertripp]

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

[@gahanchattopadhyay2889]

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

[@cheeheifoo9282]

Thank you so much for explaining the Minkowski space! And yes I will be checking out your Ch. 2 on Special Relativity!

[@ShadowZZZ]

I'm so thankful that you made a video about minkowski diagramms in STR. When I first had to calculate with themI got confused at how the y-Axis is not distance but time, since technically ct would cancel the time units out and it could be a distance,distance diagramm.

[@keithswood6205]

Beautifully explained. I used this to help me understand a section on Black Holes i am reading and it crystallised the concept for me. Thanks!

[@philsaliba3668]

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.

[@tamurhaq]

This is the video that made me really understand causality and light cones. Thank you!

[@hamborger2200]

Very well explained. I tried to understand this for some time now and now I got it. Thank you

[@dapotatoguy7019]

Very nice and simplified explanation for high school students and more like me. Keep it up man!!

[@laurendoe168]

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.

[@annasantschi4675]

This was so clear! Thank you so much!

[@petermarshall8212]

I hope you complete and post the podcast you mentioned following on from your first excellent podcast on Spacetime diagrams … great work

[@stevewhitt9109]

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

[@dianneparsons7162]

ive watched a few videos and this is by far the best explanation

[@danielpatricklopez6126]

Thank you for making this!

[@denysfisher2316]

Great video. Really liked the explanation, please continue this topic. Thanks for your effort

[@seabeepirate]

I appreciate quality content like this

[@DrWillWood]

Beautiful explanation, thank you!

[@khushichanllawala2162]

thanks for an amazing explaiantion, had lot of fun learning!

[@cameronspalding9792]

Because we rarely travel anywhere near the speed of light the world line of anybody who has ever lived will look like a completely vertical straight line

[@justinhyu]

Thank youuu I was having trouble understanding this concept when reading the textbook but you made it really interesting and simple to understand

[@rajns8643]

Thanks!! This was such a great explanation of the concept!

[@pizzarickk333]

your way of explaining is amazing.

[@Confundrum]

So clear and helpful. Thanks so much.

[@harshgurung4136]

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

[@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.

[@ndo6467]

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

[@porit1023]

Thank you so much for this video! It was really helpful

[@shaynebade8279]

This is the best explanation I've seen

[@nitd955]

Ya please continue this thanks 👍

[@new-knowledge8040]

I prefer my space-time diagram. Putting it to use, as shown in my YT videos, allows you derive the SR mathematical equations in mere minutes.

[@kevindownes2663]

You explain brilliantly!!!!😊

[@PierreSoubourou]

yes, we want to continue with this topic :-) thanks for your videos

[@patty_d.4773]

Thank you so much!

[@jlpsinde]

Amazing! Please more about this.

[@140iggy]

it would actually be a really good idea to do one more video in more detail and then two others about general relativity

[@gurshrutisingh8412]

Great !!! thank you soo much 😊😊

[@brendanfan3245]

simply amazing!!

[@mahasivavallabha]

Excellent video, keep up the great work

[@devashrikulkarni1337]

Very nicely explained! 🙌

[@johneonas6628]

Thank you for the video.

[@aniketh9450]

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

[@TheWeightOutdoors]

Hi Parth, I've just finished reading "The Ascent of Gravity" and have started "Why does E=mc2?" Chapter 4 is on spacetime and although the author does break it down to a very simple level, I still could not grasp the message or purpose of The Minkowski diagrams the author used. From watching your video it makes a lot more sense so thank you very much (although i've much reading and research left to do to even begin to understand, fully)

[@ahnekah5261]

loved this!

[@therash09]

Bhaai bahut sahi video banaai hai! Zabardast!

[@zeio-nara]

very interesting video, thank you for the explanations

[@Mobius3c273]

Really enjoyed video... yes more like this please :-)

[@sirelegant2002]

Amazing thank you so much

[@nilamsharma9053]

Thanks a lot for this explanation. Proud to be a physics student and your subscriber..🙏 I had only seen the space time diagram, now almost all of my doubts regarding this particular topic is clear. Want to watch video on how gravity is just the wrapping of space time. Just want to visualise on my mind the curvature of space-time as gravity graphically.

[@nilamsharma9053]

Please do make a video on that.

[@simtm8975]

Nice video.. Thank you

[@griefinnub3745]

Thank you for the video! This video is really well done and is really easy to understand. I have a question, however: is it possible for 2 events to occur outside of the world line for observer 1 but occur inside the world line for observer 2 essentially making something possible for one observer but impossible for another observer?

[@travusfaulkner1461]

I need to watch more of your videos so i can explain something to you over the phone and my reasons why space and time need to be separated. We are making a huge mistake because of this. I need help advancing my garage theory of quantum mechanics and space.

[@wilsongomes3360]

Very good explanation

[@ramachandrans9009]

Super, thanks

[@hafsaarshad1491]

Yes I want more explanation with physical examples.

[@wayneyadams]

9:57 Events that are in the yellow shaded region which are causally connected are said to be time-like. r^2 < (cdt)^2. r is the distance between the two events. Events in the blue shaded region that are not causally connected are said to be space-like. r^2 > (cdt)^2. Events that are on a 45-degree light line, are called light-like. r^2 = (cdt)^2.

[@ifrazali3052]

Wow Thank you

[@sumamahhamidullah3754]

Mind blowing

[@maxwellsequation4887]

Please make another detailed video

[@joro8604]

Wow, i get it, sort of! Nice Work.

[@konozrashid887]

I had a question. When both the observers measured the speed of light, did they both measure it in the x-dimension i.e the dimension in which the flashlight was moving, or did the stationary observer measure it along a diagonal drawn from the moving flashlight to the stationary observer?

[@mansoorsiddiqui7396]

Brilliant

[@ajaynongmaithem4330]

Waiting for next video..

[@-_Nuke_-]

Hello! Can you do the same video but withought CT? And put just T for time, so that we can see how it looks like withought multiplying t with c? Or can you link to us a video where spacetime is x and t rather than x and ct? Thanks!

I have some issues with these diagrams, and is that it would make you think that pitagoras theorem applies in space-time, and it doesn't. So it would be always necessary to point out that the transformations between reference frames have different invariants than the ones we see in euclidean spaces.

[@blackcatempire]

Make another video explaining this in detail s

[@user-vg7zv5us5r]

2:00 Can you measure horizontal distance also with ct parameters? Making it cty and ctx and ctz for R3?

[@muhammadessakhan2965]

explain the standard model equation

[@babitamishra524]

Can u switch topics from like this space and quantum and those theory to like more day to day never seen hidden physics things

[@soleraverde]

c is not the "speed of light", c is the "speed limit of the universe" and it happens to be the same as the speed of light. (great video btw)

[@alexpotts6520]

I like to think of it as the "speed of causality"

[@pasijutaulietuviuesas9174]

You're contradicting yourself. c is the speed of light. What it isn't is just the speed of light, but it still is the speed of light.

[@soleraverde]

@@alexpotts6520 Exactly

[@soleraverde]

​@@pasijutaulietuviuesas9174 I just wanted to highlight that the universe is the one that doesn't "allow" anything to go faster

[@pasijutaulietuviuesas9174]

@@soleraverde I don't think anyone implied otherwise. But pretty much every measurement of c that has been done was done with light. c is the speed that all massless particles travel at, but our experience with c is almost entirely through light specifically. I think it's unfair to diminish the significance of light, it doesn't create misconceptions. Even the general public knows that nothing travels faster than light or that light is the fastest possible thing. None of these statements imply light is the only thing that travels at c. And from these statements, it follows that it's the universe that makes light travel at the maximum speed.

[@mmenjic]

8:22 for me there is BIG difference between "causally connected" and "possibility to be causally connected" many things are possible but are not happening because they are possible, possibility is not same as cause

[@CarlosManAl]

Please do it!!!

[@Gorbukoki]

Did the follow-up video ever get made?

[@amit2.o761]

13:06 this also means that the event that happen simultaneously for me might be at different time for someone else, isn't it ?

[@adb012]

This is probably a matter of semantics and terms not used in the same way in Physics, in statistics and in everyday speech: Tht it is impossible that one event caused the other doesn't mean that they have no casual relationship or they are independent. Say that I have 2 light bulbs 1 light year away from each other both of them connected to the same switch that is in the midpoint between the 2 bulbs. Then the 2 lights will turn on at the same world time (for an observer stationary relative to the bulbs) and the observer will correctly conclude that it is impossible that one light turning on caused the other light turning on. However, that doesn't mean that they are causally disconnected. They are both connected to the same cause, the turning on of the switch. It even less mean that the 2 events are independent in the statistical sense. If I have previous knowledge of the system nd I am sitting next to one of the bulbs and I see it on, I know with 100% certainty that the other bulb has turned on too even when I am not going to see its light until 1 year from now. But having one light tuning on *implies* that the other light turned on too, and that is the opposite of being independent events (where the probability of one event is a given value irrespectively of whether another event happened or not). Technically, 2 events are independent if P(A|B) = P(A) and P(B|A) = P(B), but in the example I gave above, P(A) is always = to P(B) and P(A|B) and P(B|A) are both 100% regardless of the value of P(A) = P(B). That is NOT independent.

[@Steaphany]

Please, more detail and formulas please

[@nick45be]

11:54 why the minkowski diagram axes are oblique?

[@ravishankarr3507]

nice vid

[@aymankhan1105]

what are you on about he just uploaded the video lol

[@vulpecula182]

@@aymankhan1105 😂😂😂😂

[@jarjuicemachine]

Why is the coordinates (t1,x1) when the vertical axis is ct not x?

[@lowersaxon]

ct is m/s * s = m. c is NO „scaling factor“ for time. If c = 1 as a dimensionless number than c is a scaling factor for m. So m = m.

[@dysonimia2486]

Hello! Greetings from Mexico, would you consider making a video about how you make your videos? It would be lovely, I would like to spread science for Spanish-speakers and I'm finding my way haha.

[@timemechanicone]

Solved

[@parthvarasani495]

Do that second video , 🙏

[@ESponge2000]

I have a very important question. If in all reference frames in the space-time diagram , light travels at 45-degree angles in an up-sloping direction , And backwards time-travel means a motion path that decreases on the cT axis , then for sending a prohibited by physics ..signal traveling at just BARELY above light speed, how does this tiny deviation lead to paradox if it’s still upsloping? So not a horizontal instant FTL signal , a BARELY above c signal like 1.0001 of C. Is it that …. It’s Earth’s ability to exploit the past of the fast-moving object whose X’ and CT’ prime lines are almost both squished on the 45-degree line relative to our X and CT axis , that if we go a little faster than light , we easily break being above or parallel to THAT X’ prime axis ?

[@gowrissshanker9109]

Respected parth, Does accelerating/oscillating/rotating magnet produce EM WAVES?I ask this because we know that change in magnetic field produce electric field right.... Thank you sir