Deriving Time Dilation Using Pythagorean Theorem!

Let's derive the lorentz gamma factor, and in doing so, derive the equation for special relativistic time dilation.
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Link to time dilation video:
• Relativity: how people...

[@finthechat7134]

I actually sort of understood that. I'm studying physics. If I had to study something else I would probably choose either biology or philosophy.

[@jmac3223]

Hey Andrew! I’ve been watching you for around 4 months now and I love this channel. I am a high school student and aspiring physicist. Physics and astronomy have always been my favorite subjects to learn, in or out of school. I have always wanted to become an astrophysicist. I want to start learning more challenging mathematics in order for me to be capable to explore more complex areas of physics, so I thought I’d try Skype tutoring with you. I believe I have sent you and email, so when you get the time to reply we can hopefully discuss it in more detail. Keep up the great work!!

[@stigenbeat568]

did you become a physicist?????

[@mayookh8530]

​@PadhaiKar-kw2pc simply he trapped on it, haha

[@umaoio312]

This was actually a very intuitive and simple way to talk about time dilation, more so than I think I've ever experienced. It left me with a feeling of, 'oh yeah that totally makes perfect sense,' and maybe even a more effective method of introducing the concept to other people. Great video!

[@johnchristian5027]

Great video! Its amazing how we can derive something as ground breaking as the gamma factor from simple first principles! liked!

[@green3487]

This is the best video I've seen on the lorentz gamma factor, you're a great teacher. Thanks

[@jonas9787]

This is great. I never knew how to derive the lorentz factor, or even understood what it meant, but your explanation made it so easy to understand. Thank you.

[@XarkXD]

I'm finally at the point in my physics career where I actually need to derive the stuff he posts

[@benharvey8094]

I went through this derivation in my high school physics class last year. Couldn’t remember it afterwards, though. Thanks for the refresher!

[@tatjanagobold2810]

How great that you did a video on that! I was so amazed when I saw this derivation the first time and then did it myself! Also, today my last year of school started, after which I can finally start studying physics for real. You have really inspired me a lot of times and I am sure that you will continue to positively influence other people as well :) Thank you!

[@AndrewDotsonvideos]

Thank you!

[@frankdimeglio8216]

@@AndrewDotsonvideos THE ULTIMATE, CLEAR, BALANCED, ACTUAL, AND TOP DOWN PROOF REGARDING HOW AND WHY E=MC2 IS NECESSARILY F=MA: E=MC2 IS F=ma. The MIDDLE DISTANCE is thus balanced with/as the full distance (in/of space), as the stars AND PLANETS are POINTS in the night sky. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE, AS ELECTROMAGNETISM/energy is gravity. Time DILATION ULTIMATELY proves ON BALANCE that ELECTROMAGNETISM/energy is gravity, AS E=MC2 IS F=ma !!! Indeed, TIME is NECESSARILY possible/potential AND actual IN BALANCE; AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/energy is gravity. (The sky is BLUE, AND THE EARTH IS ALSO BLUE; AND the stars AND PLANETS are POINTS in the night sky !!!) It all CLEARLY makes perfect sense. BALANCE AND completeness go hand in hand. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS ELECTROMAGNETISM/energy is gravity; AS E=MC2 IS F=ma !!! (Accordingly, the rotation of WHAT IS THE MOON matches it's revolution.) GRAVITATIONAL force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE, AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/energy is gravity. Gravity IS ELECTROMAGNETISM/energy. It ALL CLEARLY makes perfect sense. E=MC2 IS F=ma ON BALANCE !!! By Frank DiMeglio

[@frankdimeglio8216]

@@AndrewDotsonvideos THE ULTIMATE, TOP DOWN, AND CLEAR MATHEMATICAL PROOF REGARDING THE FACT THAT E=MC2 IS F=MA: Time dilation ultimately proves ON BALANCE that E=mc2 IS F=ma, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Time is NECESSARILY possible/potential AND actual IN BALANCE, AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/energy is gravity ON BALANCE. Gravity is ELECTROMAGNETISM/energy. Great !!!! QUANTUM GRAVITY !!!! E=MC2 IS F=ma. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE. What are the EARTH/ground AND the SUN are CLEARLY E=MC2 AND F=ma IN BALANCE. Very importantly, outer "space" involves full inertia; AND it is fully invisible AND black. The stars AND PLANETS are POINTS in the night sky. GRAVITATIONAL force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE, AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/energy is gravity. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/energy is gravity. BALANCE AND completeness go hand in hand. It does ALL CLEARLY make perfect sense. GOT IT !!!! THE SKY is BLUE, AND THE EARTH is ALSO BLUE. Great !!! Now, think about the man who IS standing on what is THE EARTH/ground. Perfect !!!! By Frank DiMeglio

[@ferneum3578]

Very nice and clear explanation of every step. Way better than most on KZbin which take knowledge of some steps for granted. Thank you :D

[@Govstuff137]

I'm trying to understand the essence of what humans refer to as time. I feel like a blind man trying to describe colors. I love how you demonstrated time dilation using the Pothagorean theorem. You did such a good job even a math novice got the idea. I will be practicing this on my own now. Anyway , I'm trying to understand the connection between centrifugal forces lets say on two spacecraft tethered together moving a high speed . After they turned off their engines they developed a potential energy moving them to the outside wall of the spacecraft. The Potential energy put into the two spinning spaceships is stored in the tether. Potential energy is being expressed on the people inside in the form of gravity. Newtons laws apply here unless acted upon by some outside force these two spaceships will continue to rotate around the central tether forever. I see a conflict because if it is a force acting on the people inside and no further acceleration is needed to maintain that force how can it be a Force. My conclusion is it is time dilation and not a force! What math might I use to explore this?

[@nick6269]

Nice and simple derivation! So far I had only seen fairly complicated ones

[@theicemancometh5492]

Thanks for doing this, in school we were just taught to memorise the formula for the Lorentz transform

[@lad4694]

Love how these videos are always available to just go back to, watch and just chill. My girlfriend will be so excited when i play this series instead of Barbie as we planned

[@zokalyx]

this is so #MADLAD alexa play toto - africa

[@TranquilSeaOfMath]

Great explanation and demonstration.

[@docta2985]

u are the chillest dude much respec

[@jlopez47]

I studied Applied Mathematics with a concentration on Radar Imaging applications which included a lot of EM theory when I got my MS. I wouldn't have changed my area of study one bit. I'd only want to go back to school for a PhD in the same area.

[@Imperial_Dynamics]

Best and easiest explanation I've seen. Thank you

[@stefansauvageonwhat-a-twis1369]

Love the video! I understood why time dilation happened but rn im digging into why the graph is not linear or exponential, stuff like that, the maths I was studying architecture and maybe still am. I love physics but im bad at it, so maybe animation ig?

[@KpopStellars]

Nice! Do you have a video deriving lorentz factor/gamma?

[@austinbrandenberger4154]

This was awesome. I'm taking Modern Physics and the book makes things seem way more complicated than they actually are. thank you for this.

[@ZeroSectionStyle]

cool stuff! I study biochemical engineering, after the small amount of physics that I've studied so far, I find it fascinating so it would probably be my second choice!

[@arthurhall8892]

You're an absolute chad. this is nuts

[@schrodingerscat7218]

7:10 strictly true but misleading - gps time dilation is mostly a gravity well effect (GR) not a gamma factor effect (SR). They both occur but GR effect far outweighs SR effect. Now you have to do a video on the Schwarzschild metric, I suppose...

[@Rosings4all]

Superb xplaination man. 💖❤

[@nicksu332]

absolute madlad!!!!!!!!!

[@nicksu332]

in absolute brackets

[@dylwhs]

I recall reading this explanation of deriving the dilation factor in one of Isaac Asimov's popular science books.

[@jordanhunt3552]

Currently in high school, I want to study biology and chemistry, specifically Biochemistry.

[@turtle8558]

Oh yea biology this is gonna be really hel- wait what did you say

[@voidisyinyangvoidisyinyang885]

That was smooth - thanks

[@Govstuff137]

This is awesome.

[@pelimies1818]

Alas, I wish all SR/SM/QM/QED/QFT/GR would be this simple.

[@levyathan8108]

Actually studying business management but holy shit I love physics. Your explanation was awesome!!!

[@dozapp]

I just finished my Physics PhD and if I had to study something else (I want to study something else now) it would be developing efficient algorithms.

[@jonathandobrowolski6941]

That's so fucking cool, you explained the general idea of a scary concept really simply so even I (or anyone above grade 7 could understand) could understand. Good shit Something like "if you cant explain your idea to a 6 year old you dont know your idea well enough"- A.E (paraphrasing ofc)

[@shanemumma9123]

Please make more videos like this, they are very helpful. Btw, I'm undergrad physics.

[@godiswatching_895]

Amazing explanation. I'm hopefully gonna start studying physics but if i had to choose something else I'd probably choose neuroscience or mechanical engineering ( classical mechanics ftw )

[@backwards3454]

@Andrew Dotson Sorry for being late but: The train's height is equal to c•t according to the reference frame of Alison. That implies, that if we take into acount length contraction, the height according to Grey should be less. Thus, the whole formula changes... NOT an expert, What am I missing?

[@rcksnxc361]

I’m not sure but doesn’t length contraction only contract it in the direction it is moving? Also not an expert XD

[@adarshsridhar6051]

Rcksn [XC] I think you r right(semi expert taking a physics class in junior year of High school)

[@goncalofreitas2094]

Very beautiful proof! Thank you very much!

[@ivana4638]

This is good knowledge

[@ryaneakins7269]

Have you read Greg Egan's Orthogonal trilogy? It takes place in a universe with space-time metric (+,+,+,+)

[@mahoneyunchained8098]

Hey I have always had this question about this math. Let's say Greg were beaming a photon in his own ship. Wouldn't Alisa see the exact same thing as Greg sees (because Alisa is stationary compared to Greg) and come to the same conclusion?

[@GojoSenpai25]

Im studying Electrical Engineering focus on Communications and Control Systems and I would love to study physics however I'm more interested in applying math to solve problems than deriving equations

[@mr_happygolucky7095]

I want to get a PhD in Nuclear Engineering. Id like to study the load following potential of thermal molten salt reactors. Would it just depend linearly on flow rate of the uranium 233 over the graphite? Wouldn't their be a point (maybe a nonsense velocity, but still) at which the neutrons Wouldn't reach the fertile (and more importantly the fissile) material. Like walking vs running in the rain. Or would it be like walking in the rain in the first place? To increase the reaction rate you should increase the residence time (right?). Can we safety and efficiently integrate MSR with solar grids, would this integration lower capital, operational, and maintenance costs?

[@new-knowledge8040]

I prefer the deriving of all SR and Lorentz Transformation equations using the Pythagorean Theorem, but all done using a simple geometric representation of "Motion". A person with no physics background education can be given a 3 sentence description of SR, and from this derive all of the SR and Lorentz Transformation equations.

[@jerelfontenot1]

hmm, tbh, I'm currently studying procrastination and indecision. If I had to study something else, it would be something that gave me a lot of pleasure with little effort.

[@imadmorsli2871]

yeah. I'm studying procrastination and indecision too. If I had to study something else... well... I can't decide right now I'll do it later

[@xDMrGarrison]

But why would Greg observe the same "lightspeed" as Alison? If that was a ball instead of a laser, you would say that the ball moves faster *in Greg's frame of reference.* So your whole reasoning for assuming that t' exists is that "ofcourse light doesn't go faster for Greg", but it actually does make sense, because the light is moving on a ship.

[@bgbg418]

Studying maths. If I had to change either physics or engineering. Really enjoy the content by the way

[@lucasgamboa2113]

Nobody thought how a ship can travel 0.9c 🚢?

[@ahmetgazi5624]

This explanation has an undefendable flaw. The mistake is at short side called c*t. Light is a wave not a particle. What reaches the mirror is not a particle, thus we cannot call it c*t. What reaches the mirror is the wavetip of the wave created at time=0.LightWaves are circular like waves in a pond. What you are catching at the mirror is the wavetip of the circular wave that was travelling towards the motion of the train. You already missed the wavetip that moved vertically up because you are moving toward right horizontally. The correct length of the short side is t*c*sinus of the small angle. Time dilation exists only in warped spacetime not in relativistic motions.

[@gmcenroe]

Great explanation. Have you read any of David Morin's Special Relativity book? I am thinking of buying it for self study, do you recommend it?

[@Goku17yen]

i would change to engineering to see how the peasants work

[@TuroSaave]

You mean highly employable middle class.

[@flavioryu5922]

@@TuroSaave oof

[@austinbrandenberger4154]

@@TuroSaave goteem

[@Prometheus7272]

You mean people who get laid

[@muskan3162]

IT IS AMAZING

[@santiagoarce5672]

I am an aspiring Physicist. If I had to study something else it would be Math for sure.

[@zoltankurti]

Will you derive the full lorentz transformation?

[@rk99688]

I am an undergraduate mathematical physics student and the courses I cannot wait to take are: 1. Classical Mechanics and Special relativity 2. Introduction to General Relativity 3. Electricity and Magnetism 1 & 2 4.Quantum Theory 1&2 5. Introduction to Particle physics

[@alexzappacosta3274]

Awesome video! I'm Studying BSc Physics, Applied Mathematics and BIT (I favour and love physics[woo!]) and if I had to study anything else.... well, I guess I'd do engineering 🤣 (at least I can still study SOME physics! )

[@michaelhill6451]

Interesting. If you merely assume that the speed of light is constant and time is variable then time dilation only requires basic trigonometry to understand.

[@AndrewDotsonvideos]

Exactly!

[@username55ify]

This is crazy actually

[@fernandoreyes3066]

As a physics undergrad, I prefer to do it with 4-vectors. Do you also like it done that way?

[@ramonecampbell5194]

U made a miscalculation. Its the square root of 1 - 0.81^2 because in the equations consistent with time dilation, the velocity is always a squared dimension.

[@zainawad8618]

thanx alot

[@Fps_North]

I’m confused on how when you square everything why it isn’t being multiplied by itself and you are just bringing the square down . Shouldn’t it be c^2 + 2ct + t^2?

[@shinhassan3314]

I'm studying biology but Im very interested in the weirdness of relatively.thanks to Dr.Greene 😅.anw thanks for this video it's very helpful.

[@drokrath]

I'm studying physics right now in undergrad. If I had to study something else I think it might be philosophy/law just because it plays on my mind for logic, with a human twist. Also I've always thought being an orthopedic surgeon would be cool, but I just don't have the love for biology/medicine it would require. Plus I think my hands would be a little too shaky for that lol

[@thomasolson7447]

Could you please tell me what the distance of 1 means? γ^2 + (iγv/c)^2 = 1. That distance seems to mean absolutely bugger all. Chatgpt can't even help me here.

[@zokalyx]

im currently studying quantum mechanics (on my own)... I'd like to learn some general relativity but that will have to wait a bit (I haven't gone over special yet)

[@marcioamaral7511]

Francisco Russo Lorentz transforms Basic geometry Basic algebra Abnormal intuition Galileo's relativity Basic mechanics Is all you need to take over special relativity

[@zoltankurti]

@@marcioamaral7511 you have to cover relativistic mechanics. Better if you also cover relativistic hydrodynamics, that way you get familiar with the stress-energy tensor before general relativity.

[@griffithfimeto3387]

Help who came up first with time dilation lorentz or einstein ?

[@anantsharma314]

What if the ship is accelerating instead of constant velocity?????

[@leoncestar631]

I'm gonna have to present this problem to my class on german. German isn't my first language

[@Metros23]

Sup man! I dig you covering special relativity. If you could cover four-vectors that would be dooope. Also, I'm studying physics and I would rather study physics c:

[@DanielRodriguez-cw9ln]

Okay but how do we know that the t’s from ct prime and vt prime are the same t’s I’m confused is this just some property of the Pythagorean theorem, or is it a must due to the constant of light?? And if it is a must because of light, how exactly???

[@daimao7392]

Studying for a BSc in maths and economics, would most definitely prefer pure maths cos' I hate economics.

[@TheBym4eva]

studying CS, would definitely be math or maybe physics otherwise

[@cesalonsomulder1990]

But your demonstration seems to be incomplete. I mean, if you go INSIDE the train and you have a ball, and you throw that ball vertically upwards and then, after it falls again to your hand, you draw the same scheme. You could derive a similar set of equations, you would be treating with a "curved triangle" instead of a typical triangle, but it would lead to the same physics . And that is correct because that movement has almost nothing to do with special relativity ( only a tiny fraction of time dilation ). So, what in this demonstration is the important different fact regarding propagation of light ??

[@KillGui007]

I am in my last year of my Master in Physics and Astronomy. If I wouldnt be doing this I would have lots of options, maybe neuroscience?

[@alexandreramos8484]

I would love to see more stiff about general relativity

[@BarriosGroupie]

Old fashioned. Just use the invariance of the space-time interval on one line.

[@carlosvargas2907]

Thanks, man!

[@drokrath]

This is so cool

[@stephenfreel2892]

But what if the path that light takes is curved as it moves along geodesic? Doesn’t that change our formula for time dilation?

[@AndrewDotsonvideos]

If we we're considering gravitational effects, yes it would. But this is special relativity so the geodesic is a straight line.

[@alchemy1]

Here is what no one mentions very clearly plus it must be said with emphais and rightfully so, for the sake of removing any confusion. The 2.3 seconds is what my clock says who is watching the moving vessel. I am reading my watch having ticked 2.3 seconds The t' is the time I see on the moving ship. This makes t my time in my watch and t' is what I see the time in the ship. This t that is my watch is also called my proper time. It is not the time on the moving vessel as the pilot sees. What does the pilot see when he looks at this watch? In other words what is the pilot's proper time. No one knows. 🙂

[@malayapaul458]

hey are your tutoring classes free??

[@Goku17yen]

its hot in topeka

[@niyatishah7492]

One question: You used Pythagorean theorem, and made the triangle and stuff, but the thing is the light doesn't move diagonally first and then go straight down at once as you showed it in the second figure. It still follows the digonal path the opposite way, right? So how do you account for that?

[@lordpingus2900]

Niyati Shah ct represents Alison’s reference frame of the event. Therefore, it appears to be straight up. ct’, the hypotenuse, represents Greg’s viewing of the event. These two parts of the triangle represent different view points of the same event, a photon shooting at the ceiling. The event ends before the photon comes back down. I hope I explained this well :)

[@new-knowledge8040]

Using the Pythagorean theorem, you can derive all of the SR equations in one shot, by using one simple geometric representation of motion within space-time.

[@dioutoroo]

Now I'm studying Human Technology in Sports and Medicine and If I had to study something else, that would be Mathematics or Linguistics

[@johng7602]

But how to get the factor u/c^2*X in the real formula, I can’t derive it from the photon clock experiment

[@QiuEnnan]

‘What's going on, smart people' I have clicked on the wrong video

[@robertkoziarski6756]

Studying control systems and robotics (engineer go brr). I wouldn't change the major BUT I would change the syllabus a bit.

[@mohannadislaieh3009]

Nice

[@bobross5716]

I would pick ethnic studies, ya know, because of how useful it is

[@quahntasy]

Madlad indeed. We are back to the whiteboard.

[@Goku17yen]

Quahntasy - Animating Universe I really like your animations my dude :P

[@AdityaKumar-ij5ok]

Pythagorean boi refers to albert??

[@imasiontist653]

Getting some serious vsauce vibes from this video

[@SidLakkoju]

Im Studying Computer Science. I'd probably study physics if not CS

[@sharathkumar8422]

I am studying MBA. If I could study something else. It would be Pure Mathematics. It would be a dream to do a PhD in that field...

[@jamessaslow9239]

Studying Aerospace Engineering as of now, but I want to change my major to physics because engineering is boring tbh

[@restitutororbis964]

Energy=More coffee squared(Dont worry I have a license to steal memes)

[@kamehamehaDdragon]

I'm studing mathematical engineering, if I had to study something else I'd study physics.

[@duncanw9901]

Gon study physics, probs would be a mad mafs boi otherwise.