Minkowski Space-Time: Spacetime in Special Relativity

Includes discussion of the space-time invariant interval and how the axes for time and space transform in Special Relativity.

[@EugeneKhutoryansky]

To see subtitles in other languages: Click on the gear symbol under the video, then click on "subtitles." Then select the language (You may need to scroll up and down to see all the languages available). --To change subtitle appearance: Scroll to the top of the language selection window and click "options." In the options window you can, for example, choose a different font color and background color, and set the "background opacity" to 100% to help make the subtitles more readable. --To turn the subtitles "on" or "off" altogether: Click the "CC" button under the video. --If you believe that the translation in the subtitles can be improved, please send me an email.

[@EugeneKhutoryansky]

In case, you have not already seen them, I also uploaded several other videos recently. As always, for each video that you like, you can help more people find it in their KZbin search engine by clicking the like button, and writing a comment. Lots more videos are coming very soon. Thanks.

[@EugeneKhutoryansky]

***** No, I have not activated a donate button on my KZbin page. If someone wants to help out, the best way to do this is simply by sharing the links to my videos, thereby encouraging more people to subscribe to my channel. Thanks for the offer, though.

[@EugeneKhutoryansky]

FailBob, if you are still interested, I just added a donate button on my KZbin home page. I really appreciate the offer. Thanks.

[@stevenhalliday7297]

you should get a Nobel prize for teaching.

[@hasek747]

Hi Eugene, may I ask what software you used to make this '3D' images?

[@anukum3002]

Physics Videos by Eugene Khutoryansky

[@fabiobottalico7732]

Unbelievable. So THIS is the reason why in the Minkowsky SpaceTime representation, light is ALWAYS represented as a diagonal line with an inclination of 45°.... Because otherwise the formula for the S would not give a result of 0. I would have never got to understand this without you, Eugene. I confirm what I said in another video of yours: You have a gift, you are able to transform into reality and visualization concepts which are totally abstract. This denotes you really DO possess the knowledge of such high-level physics and mathematics. Hats off for you, sir.

[@EugeneKhutoryansky]

***** Thanks for that really great compliment. Light will have an angle of 45 degrees because the units for space and time on the diagram are chosen such that C = 1. Therefore, the equation for S simplifies to S^2 = distance^2 - time^2. And thanks again for the compliment.

[@kikithatsit2532]

or madam!

[@cameronspalding9792]

@@EugeneKhutoryansky shouldn't it be s^2=time^2-distance^2?

[@malekmannai9445]

@@cameronspalding9792 it depends on the convention but most of authors use the space-like formula

[@ishworshrestha3559]

Uip

[@alphablondy04]

your contribution to education is enormous. people like you let me still have hope for mankind. thx from germany

[@EugeneKhutoryansky]

+alphablondy04, thanks for that great compliment.

[@TheChrasse]

This is the first video in a long time in which I actually had to watch some parts again in order to get a grasp on them (meaning I didn't only see something familiar in a new way, but instead really learned something new). Thank you, Eugene!

[@EugeneKhutoryansky]

***** Glad to hear that you learned something new. Thanks.

[@Cosmalano]

Brilliant as always Eugene. I've recommended your channel to PBS as they are producing a series on relativity now, so hopefully they will tell their viewers about videos like this and you can help bring relativity to even more people!

[@EugeneKhutoryansky]

electrocat1 Thanks for the compliment, and thanks for recommending my channel to PBS.

[@user-en6dy4xj1e]

This is not a channel, it is the most gorgeous piece of art about the nature that I have ever seen. The animations, the data, everything is just perfect! P.s: Admiration from Brazil.

[@EugeneKhutoryansky]

Thanks for the really great compliments.

[@nisiathornton]

These videos are SO helpful in visualizing 3+ dimensional realities! Thank you so much for putting these together, and making them available. Keep up the good work! Nisia Thornton. Kentucky, USA, Earth, Sol system

[@EugeneKhutoryansky]

Thanks. I am glad to hear that my videos are helpful and I am glad that you like them.

[@hinkles73]

I don't like the 2 food ads, which made me hungry, but eating some snacks, which fills up my stomach, goes well with watching your videos, which fill up my brain with lots of info on things.

[@filosofiadetalhista]

Beautiful explanation. I was just reading about SR in my physics text-book and this illustration made it all the much clearer. Thank you

[@davidwright8432]

AS usual, thanks to the entire time for an instructive and engaging video! Always a pleasure to watch, and learn. Even with stuff (I'm supposed!) to know, 'seeing' it this way helps a lot.

[@EugeneKhutoryansky]

Thanks. I am glad you liked my video.

[@eduardopolicarpo3487]

it is SO good to have videos on moddern physics that explain the subjects simply and clearly! Thanks !

[@EugeneKhutoryansky]

Eduardo Policarpo Thanks. I am glad that you like my videos.

[@EugeneKhutoryansky]

You can help translate this video by adding subtitles in other languages. To add a translation, click on the following link: kzbin.info_video?ref=share&v=zScn3tV9YPU You will then be able to add translations for all the subtitles. You will also be able to provide a translation for the title of the video. Please remember to hit the submit button for both the title and for the subtitles, as they are submitted separately. Details about adding translations is available at support.google.com/youtube/answer/6054623?hl=en Thanks.

[@sb-oo8oc]

please make a video on " geodesics " 🙏🙏🙏🙏🙏🙏

[@hydrxyMoron]

I've watched like eight videos on this topic and this was the first one that made sense to me. Thank you

[@EugeneKhutoryansky]

Glad my video was helpful.

[@fajarnurmajid5319]

i just found out about your channel and it's amazing thank you for putting these videos up :)

[@EugeneKhutoryansky]

+Fajar Nur majid, Thanks. I am glad that you like my videos.

[@jacobblumin4260]

A comment on your method: so many videos present difficult material at lightning speed, giving the listener less than one second between presentation of important facts. You present the material at a reasonable rate which gives the listener at least several seconds to grasp what you are saying. Your videos are taking me much further toward understanding physics than I ever have in the past. Much appreciation for what you are doing and how you are doing it. Please keep it up.

[@EugeneKhutoryansky]

Thanks for the comments and I am glad that my videos are helpful.

[@CAAU]

Congratulations for the very well done work. Thank you.

[@akashpatel-cb1dq]

you are amazing Eugene .i always understand with deep concept and your animation is great.thank you for your work.

[@EugeneKhutoryansky]

+akash patel, thanks for the compliment.

[@StephenGillie]

In music, timing is critical. When playing with other musicians, one person is assigned to be the time keeper - another musician in small groups, and a conductor for large groups - and the rest of the group is supposed to watch that one member. Yet many concert musicians cheat by just watching the music, and "playing by ear" and playing when they hear the beat. A major difference between playing with concert bands, and playing with marching bands, is that marching bands are usually so physically separated that "playing by ear" no longer works. Several beats of music may pass in the time it takes a drum beat to travel across the football field, or echo off the grandstands. So memorizing the music and watching the conductor (and assistant conductors, mirroring the conductor, spread around the field) becomes mandatory in top bands - to compensate for the propagation delay from the speed of sound. And it's another instance where observers would not agree on the timing of events. Someone seated at the center of the stadium could hear a drum beat and trumpet play at the same time, while an observer seated at one end of the stadium could hear the drum beat entirely before the trumpet playing. Thanks again for making these great videos, simple in execution yet complex in concept.

[@dsinghr]

your videos are best on youtube.. i have not seen such explaination on any other channel.. great stuff

[@EugeneKhutoryansky]

bannajirocks Thanks for that really great compliment. I am glad to hear that you like my videos that much. Many more are on their way very soon.

[@oleg5730]

Thank you so much for making videos!

[@onecanina]

Eugene, I just want to say again that you do an amazing work! I, like many other people here really appreciate your videos and the opportunity to learn more about physics. Also, maybe one day you could make a video talking about metric tensors and the role they play in general relativity. I am studying differential geometry now, but still a lot of conceptual gaps in my understanding and I know the moment I watch a video from you on the subject I will be able to see much more clearly. Just an idea! Thank you!

[@EugeneKhutoryansky]

Diogo Canina Thanks for the compliment. Yes, I would like to eventually make a video on how to visualize the tensor equations of General Relativity.

[@andreadedomenico1479]

here we go, great video :)

[@neandercatz8877]

Once again, great!

[@EugeneKhutoryansky]

Neandercatz Thanks. Glad you liked it.

[@eagleslandin1692]

Incredible video that is beautifully explained (music is perfect too). Keep up the great work Eugene. Thank you and think freely.

[@EugeneKhutoryansky]

Thanks.

[@eagleslandin1692]

You have changed my perception of reality and how I measure it. Words can not express my gratitude to you for this video. I literally teared up from the music when watching the video again and this epiphany hit me. The beautiful music and work got me! Thank you and think freely.

[@bakerskater3211]

Very good. I enjoy watching these video's.

[@MadanKumarMBBSstudent]

Love from India, ur videos are brilliant

[@joshuac.402]

Even though I don't really understand all this, it's still interesting to see how you explain the speed of light remaining constant.

[@bsadewitz]

Just keep at it. I don't really understand the math, but after relentlessly bombarding myself with this stuff for long enough, I did eventually get it--at least way more than I used to. Well, at least I think I do. 😂

[@bsadewitz]

It's not actually that difficult, just profoundly counterintuitive. Somehow, Einstein just kinda realized all this. He didn't develop it in isolation, but he did put it all together. I have no idea how someone just kinda realizes all this. I'm fairly intelligent, but that is a species of brilliance that is unknown to me.

[@bsadewitz]

The key is treating time as another dimension. It doesn't even matter if it actually is another dimension or not. This is what is so bizarre -- we don't live in a 4D world. You know how a helicopter can move in three separate dimensions? If you can manage to add another one--even for a few seconds--you will suddenly get it. It is perhaps the most profound idea I have ever contemplated. I just kinda forced myself to think in 4D. It physically hurt. Think of it as if everything is moving at the speed of light all the time through 4D space-time. Motion in any of the other three dimensions is motion that can't happen any other, because they all need to add up to the speed of light. Like with a helicopter: it's airspeed is speed on x,y,z, axes put together. Everything is moving through spacetime at the speed of light. That is the only speed anything moves at. It's just that light doesn't move at all in the 4th dimension. I mean, how the @$_# did Einstein just kinda realize this? He figured this out in his idle time at the patent office. I actually WEPT when I managed to understand it, that is how profound this is. I don't know if there are actually more than three dimensions, but it does make sense, and it has never, ever been falsified. Every single prediction that has ever been made using these equations checks out. They have NEVER failed. EVER.

[@Julia-rq7uj]

im tearing up from the music

[@goozbaghali]

Yaaaayyy another video :-)

[@EugeneKhutoryansky]

goozbaghali And many more are on their way.

[@user-zm8wd3om2r]

Thank you very much for Russian subtitles!!

[@patrickleahey4574]

Very good! It is a strange thing when you recognize a math from one application being used in a an apparently different one, thereby, understanding both better. In this case, I recognize a math we used to try to gain psychological insights in the highly interactive field of human motivation by tinkering with 3 axis. Thank you.

[@RosaPetit]

I loved this video

[@EugeneKhutoryansky]

+Rosa Petit, Thanks.

[@anupamyedida5484]

Thanks for the video ! Found it really useful!! :)

[@EugeneKhutoryansky]

+Anupam Yedida, thanks. I am glad you found it useful.

[@alperkarasuer]

One of the best and most useful channels on KZbin. Also it is very good that you share videos more frequently now. By the way do you have any plan of making videos about sub atomic particles , strong-weak interaction ?

[@EugeneKhutoryansky]

alperkarasuer Thanks for that really great compliment. I might eventually make videos on subatomic particles, but I have many other physics topics that I would like to make videos on first. Thanks.

[@b00gi3]

Thanks for another great vid ! Even though some of these are a bit above my level in maths, I get inspired to keep pressing along when I see the concepts animated while I eat my breakfast / dinner haha. (:

[@viniciusfernandes2303]

Thanks for the video!

[@EugeneKhutoryansky]

Thanks.

[@jeanpaulsadia7487]

these are so beautiful

[@EugeneKhutoryansky]

Thanks for the compliment.

[@Alex-zc9ty]

wonderfully explained

[@EugeneKhutoryansky]

Thanks.

[@awwab1094]

I really really appreciate you thanks

[@EugeneKhutoryansky]

Thanks. I am glad you liked my video.

[@frankdrebin7949]

A big disclaimer: Light always moves equally fast for all observers, through vacuum.

[@bonaparte54]

False. In water or glass it will move at the same speed for all observers also, at 225000 km/s and 195000 km/s respectively. Same principle for other mediums.

[@mateuszpraseek6733]

@@bonaparte54 Are you relying on Maxwell"s equations?

[@JivanPal]

@@bonaparte54, that is a corollary of the nature of absorption/re-emission of photons in a medium such as glass or water. The true speed of light is still the speed of light in vacuum, which is constant, and namely 299,792,458 m/s. You must also take into account parameters of the medium, such as the temperature and pressure of the water the light is passing through, in order to derive the apparent speed through that medium.

[@Markus9705]

What you are talking about is rotation of the axes due to a relative velocity between two inertial reference frames. However, supposing a "rest frame" you can perfectly fine rotate the three spatial axes and still get the same x^\mu^2 distance and spacetime interval for any events. It's only when you are talking about inertial reference frames such that γ > 1 the classical x^\mu^2 does not hold.

[@surendrakverma555]

Very Good presentation. Thanks

[@EugeneKhutoryansky]

Thanks. Glad you liked it.

[@siddharthjain3078]

1:17 Object moving along time-axis is not moving at the speed of light through time but at zero speed through time actually. That axis shows no motion in space and no velocity also. @Eugene Khutoryansky

[@alexanderfederowicz]

And Then comes the Kozyrev work on Time and Torsion field Physics... Non compliant with classical entropy based science... And Compatible with the active Torsion field Tech embodied in still working Indian Pyramids and Collating Lingams...

[@ayushsuman_]

Amazing explanation..just love to watch your videos

[@EugeneKhutoryansky]

Thanks. I am glad you like my explanation.

[@ayushsuman_]

May i know which IDE you use for making these amazing animations..

[@EugeneKhutoryansky]

I use "Poser" for my 3D animations. Thanks.

[@ayushsuman_]

That's great .. Thanks for your reply...

[@DEEPAK619wwe]

great understanding videos than any other please long period videos upload specialy electronics and mosfet or computer

[@amitbhalerao728]

Its very good for me I like a lot you have explain in hindi

[@apurbamandal6535]

According to minkowski spacetime diagram if I want to Time Travel why I cannot choose a straight along time axis path from future to past or past to future or any curved in the light cone and why it is necessary to choose a curved path out of the light cone for time travelling??????

[@Asdun77]

May Allah bless you thanks , you are great as always, keep making these great topics .

[@EugeneKhutoryansky]

Thanks.

[@crazyboii3236]

Wonderful! More relativity!

[@EugeneKhutoryansky]

CrazyBoii Glad to hear that you liked the topic.

[@hinkles73]

I like the drawings of photons for light.

[@harryr2424]

great video to edge to!

[@dannycrofts8138]

You just nail it every time don't you x

[@EugeneKhutoryansky]

Thanks for the compliment.

[@govamurali2309]

Please do a playlist on loop quantum gravity and string theory

[@ramymelhem]

Eugene, this is unreal! You've got a lot of great material for middle school math that I will be showing my students in the coming school year. I'll definitely be sharing your stuff my friend. I've got a couple of questions for you: Is Poser Pro user friendly? My idea is to get some of my middle school students creating stuff for extra credit. I'd also like to personallly experiment with it to create my own science and math resources. I'm familiar with adobe premiere and after effects. Would you know if there any overlap in the skills involved between Adobe and Poser Pro?

[@EugeneKhutoryansky]

Ramy Melhem Thanks for the compliment, and I am glad to hear that you will be sharing my videos with your students. In reply to your question, Poser Pro is user friendly, but it is also expensive. There are free 3D software programs available, but they are not as user friendly, and they don't come with a large free library of characters and props. So there is a trade off. Thanks.

[@prysrek8858]

Some of the video clips give me the vibes of someone trying to sell me chakra stones.

[@tiagofranca2660]

Perfect explanation, as always!! I was thinking you would make a three-dimensional representation of a four-dimensional graphic, Haha Really great video!! Keep them coming!

[@EugeneKhutoryansky]

Theenerd ジェームズ Thanks for the compliment. I already have a video on representing four dimensional objects, so for this topic, I thought it best not to further confuse people on an already confusing subject.

[@tiagofranca2660]

Eugene Khutoryansky Haha, i agree :)

[@Mnemonic-X]

You've been lied to. 😀

[@EthanNikelsky]

1:17 Why the speed of light? How do we know it? And again, thank you for your amazing work!

[@Takanayagi88]

I am a physics major but have not done the electromagnetism course yet so take what I say with a grain of salt. But I've heard that if you pick Maxwell's equations and fiddle with them a bit you get a constant that has units of velocity, this velocity is exactly the speed of light (c). The problem is that Maxwell's equations are frame independent and you always need to mesure speed in relation to something else. So the fact that you got a constant "c" made the scients of the day think that "c" was special in someway and Einstein abandoned the ideia of absolute time dominant at time and tryed to make a physics with absolute "c". And turned out he could explain a lot of things with that and so began Special and General Theory of relativity.

[@nervcvda6146]

Nice Presentation

[@EugeneKhutoryansky]

Thanks. Glad you liked it.

[@dominiksafar2102]

Thanks for another relativity video Eugene. I've learnt a lot from your videos and they're the best ones at visualizing theory of relativity, but I feel like more I know less I understand it (if you know what I mean by that). Is it possible to fully understand relativity without math? If no, can you recommend any literature "for begginers" explaining this easily?

[@geodesicdeath2997]

+Dominik Šafář unfortunately it really is impossible to completely understand the theory without knowing the math that goes with it since math is how it is all described. Its like how we can lose meaning during the translation of languages because 'that' language has a word for such and such where as our language does not. I hope that makes sense. I know its daunting, but you could probably learn all the math to at least start making sense of it all in about a year or so (that's how long it took me). You need algebra, trigonometry and elementary calculus and know how to do some maths with vectors.... Easier said than done I know.

[@hinkles73]

Maybe the time axis rotating differently then the space axes is what Newton saw in classical mechanics as time being separate from space. I'm not sure, but the answer is likely no.

[@StephenGillie]

Do glass, water, and other refractory objects influence the spacetime interval? Is that why light's path changes when traveling through these substances?

[@alaididnalid7660]

I don't quite understand in what way the axis for time should rotate differently. Edit: My guess is that both X and Y can have their own corner values with the time axis at the same time and that the yellow lines (space time interval = 0) are always "angle bisectors" cutting said corner angles/rotations exactly in half. Only two scenario's are shown (X=45°,Y=0° & X=0°,Y=45°) but the yellow lines imply some other X & Y angle combinations: As long as any possible yellow line (all possibilities together would look like a yellow cone actually) is an angle BISECTOR for both the X corner and the Y corner values seperately, the XY angle combination is valid. That said, both X and Y are always between 0° and 45° inclusive. Correct?

[@TSulemanW]

nicely explaination. we known earth rotation and revolution to the sun but why we did not feel that earth rotation because universe is rotation too

[@vikrantvijit1436]

Thanks for beautiful visual arts and wonderful physical sciences blended dynamics decoded dimensionality highlighting hidden aspects at rest / movements between Spacetime intervals and beyond distances separating events along same / different axis focused origins coordinated points of light that intersects through 45 degree and projects on both observers frame of references being self processing and other world information processing fabric of quantum universe forced fields Entangled fluxes SPINNED structured spheres Influencing spectral Intensity Shifting density of body frequency Modulated thermodynamic entropy caused energy lost due to ground surface resistance bound center of gravity flows state chained from bottom, to Top resonant earth orbit protective EMP shield.

[@RomaEsperanto]

What's the name of the song? Please tell me. Thanks for making these videos. Amazing as always. Thanks.

[@EugeneKhutoryansky]

RomaEsperanto The music is from the free KZbin Audio Library, and its title is "Pachabelly." And thanks for the compliment about my videos.

[@rorytribbet6424]

I’m pretty knew to physics/math of any kind and I’m wondering why we take the time to square every figure in an equation… when the fact that they are all squared just cancels that entire function out for the entire equation. (As seen in the equation for finding the spacetime interval around 6:00 ) 😅 I’m sure there is a very good reason and I’m curious what it is!

[@Mysoi123]

Imagine two events: the impact of an asteroid on the moon and a fireworks explosion. Next, you input the separation and duration into the equation. The value 'S' represents the magnitude of the position vector connecting these two events. As Eugene stated, a moving observer likely perceives the events and locations in different sequences, but the vector's magnitude remains constant for all observers. This concept is somewhat analogous to rotating a vector along a circle, altering its components but not its magnitude, except in this case, the vector is four-dimensional.

[@TheDRAGONFLITE]

Thanks! Stay Rad Eugene

[@Kaihku]

I love You :-)

[@prithvitimalsina399]

In the vertical axis time, what type of values can we put in?? Is it 1sec, 2sec, etc type of values? or is it i, 2i, 3i, types of values??

[@mamalisahoo2127]

Thank you very much mam

[@EugeneKhutoryansky]

You are welcome and thanks.

[@restinpeace6712]

Need more videos .

[@EugeneKhutoryansky]

More videos are on their way.

[@oatnoid]

I must admit I'm still trying to wrap my ears around special relativity. Not having a foundation in physics is not helping. This video does help a little.

[@EugeneKhutoryansky]

If you haven't already seen it, you may want to watch my main video on Relativity at kzbin.info/www/bejne/m6ecq6WqlMSfm8U

[@charlesbrightman4237]

I believe there is one and only one "absolute truth", (defined as the 100% correct and 100% complete set of facts; that no human has nor is physically capable of having), BUT, there are many perspectives to that truth, one possibly for each and every conscious entity that perceives that truth. The more we can all share our perspectives, preferably in peaceful ways, the more we can all get a better picture of absolute truth reality as best as we humanly can that we can all work off of together. If there ever was such a thing as one world religion, let it be "truth".

[@Markus9705]

Charles Brightman This has nothing to do with SR.

[@charlesbrightman4237]

Markus How could it not apply? Is it true or isn't it? Do you exist or don't you exist? Can you think for yourself or can't you? There has to be one and only one absolute truth to how everything actually is. Deal with it or not, and that's the truth, the real absolute truth.

[@charlesbrightman4237]

final fandy Is that the "absolute truth" to how everything is?

[@geodesicdeath2997]

+Charles Brightman as far as I can tell in our study of the universe up to this point, yes (with regards to final fandy's comment). Now, don't get me wrong, on some of my more 'optimistic' days, I'd tend to agree with you. However, think of any concept you possibly can, and I can think of it's atithesis. You say there is only one '100% truth' yet then there has to be some object called the '100% untruth' that has to exist in order for that polar opposite thing, the 'truth' to exist... or maybe that truth contains the untruth? Something to do with Godel's Incompleteness Theorem?

[@charlesbrightman4237]

+Alexander Bray Let's utilize modern science: Modern science says that from a singular mass, everything in existence came into existence in this universe, including the current laws of nature, you, me and our consciousness. Modern science also says that energy cannot be created nor destroyed, hence it must be eternally existent. Now, this is either true or it is not true. Assuming that modern science is true concerning the above, then: 1. I AM a part of the mass that banged; 2. I AM a part of the singularity; 3. I AM the lessor part of the greater "I AM" (the singularity in it's totality); 4. This singular mass has a consciousness as evidenced in you and me. Now, also apparently true, if asked how old I am, I guess it depends on which age you ask for, and for which part of me you ask it for. 1. Some of the cells in my body get replaced on a daily basis; 2. My Earth age in this current form of me is yet another age; 3. Some of the atoms and molecules in my body might be just under the age of the universe; 4. The energy itself that is inside me is older than the universe itself. But then again, do "I" even exist, OR does only this eternally existent energy singularity exist as "me"? So, what is the real "truth"? Your guess is as good as mine. We truly do not know what we do not know.

[@shahzadnaveed1156]

Please make a 3D video for the volume of parallelopiped and derive also it,s calculation.

[@napoleonbonaparte525]

I wonder about minus at time in interval space-time equation. Does it mean time is complex value?

[@Mnemonic-X]

It means that Einstein was too stupid.

[@spacestray]

I wish the music in the background was Cornfield chase from Interstellar

[@RonLWilson]

Can you show what it looks like if some object in the x y plane is rotating about the t axis and thus makes a spiral along the t axi such as a planet orbiting the sun?

[@varsha8573]

at :54 How can you take only two axis to explain an event?what is origion of reference frame the big bang point or observer? can you plese explain?

[@lansg3sa]

Do you plan on making videos about black holes? That would be interesting.

[@EugeneKhutoryansky]

lansg3sa Yes, black holes are on my list of topics for future videos. Thanks.

[@barabbasrosebud9282]

"Light always travels along paths where the space-time interval is exactly zero between every two points along the path." @ 5:55. Well put, which means that time has no effect on light. Therefore, light always has a zero "age". But does this apply when light is moving at a low speed in an e.g. Bose-Einstein condensate?

[@joeoconnor7725]

Time and space thru distribution and transformation

[@band5680]

Dear Eugene, at 1:17 shouldn't the basis vectors of time and the space coordinate stretch as the angle between them shrinks? Many thanks for your videos. They are very helpful! Max

[@EugeneKhutoryansky]

I wasn't trying to show the basis vectors, but just the direction of the axes. Thanks for the compliment. I am glad my videos are helpful.

[@StephenGillie]

I just learned that Poincaré rhymes with Tanqueray and now you know too.

[@abhishekms1059]

❤️

[@nguyenthao-kz1uh]

what does time between A and B mean? and S factor in equation else.

[@alexlupini4368]

Time is the dimension of change (the fourth dimension). It is not a third dimension of space (upwards), as it is mistakenly shown on the graph (the z coordinate).

[@EugeneKhutoryansky]

+Alex Lupini, time was not meant to be taken for the z coordinate of space. The z coordinate of space is still present, but not being shown on the graph. You can add time as an extra axis to any graph.

[@rodrigoappendino]

I'd like to read more about this. Can you recommend a book about this?

[@varunswamy6306]

+Rodrigo Appendino lecture series by dr shivaprasad of IIT Bombay on special relativity is the best i found.right from the basics to the most advanced concepts is explained beautifully.

[@SHUBHAMGUPTA-ix4gg]

why time axis rotate different from space axes

[@SkogenWhisper]

If you need help creating the 3d animations I'd be happy to volunteer some time

[@prithvitimalsina399]

What happens when we travel along the negative axis in time? does that correspond to the past travel. .how does the axis rotate for that negative axis in time??

[@ericsu4667]

Special Relativity is based on Lorentz Transformation which violates a fundamental physics law, Translation Symmetry. Therefore, Special Relativity in NOT valid in physics. kzbin.info/www/bejne/n5fJeZ2ipcepr8k Special Relativity has caused lots of confusion for more than 100 years. Such confusion is commonly called paradox. It is time to move Special Relativity out of physics and into mathematics. vixra.org/abs/1706.0498 vixra.org/abs/1709.0120

[@Epoch11]

Thank you SO VERY much for putting this up. I have been studying the various kinds of spaces that are used mathematically in physics and am really happy to see this video. If at some point you could do a video on De Sitter space and even Anti-De Sitter space I would very much appreciate it. Thank you for all the videos as well as the sexy computer generated girls...... just teasing. These videos help me to visualize things and for me that is the way I learn.

[@EugeneKhutoryansky]

Mark G, I am glad to hear that you liked this video, and my other videos. Thanks.

[@physicslover1950]

Sir can you please make a video on curved minkovski space time for accelerating observers as the channel pbs space time has not explained it well

[@EugeneKhutoryansky]

Perhaps the following video is what you are looking for. kzbin.info/www/bejne/nZTZomR6drJgeqc

[@mujiparacha3109]

Isn't it supposed to be s^2 = (ct)^2 - x^2 - y^2 - z^2 ?

[@muntee33]

Smf. The time dimension should be magnitude. Time is a rate of velocity or change in Magnitude. It not an existence in itself. It is a perceptive and representative function that will appear to pass at a specific rate that is mainly determined by magnitude and influenced (perceptively) by the orders of which the reference frame and the view point are separated.

[@eddiechung675]

So for lightspeed objects, space and time axis merge into one?

[@EugeneKhutoryansky]

I cover this in my video "At the speed of light, what would you see?" at kzbin.info/www/bejne/eKC4lGdjppl8mMU

[@prithvitimalsina399]

Could you please explain that "time" used in the vertical axis is just 't' or is it 'ict' ??

[@EugeneKhutoryansky]

The vertical axis is time.

[@malm7arb]

amazing video but i have a question why do you move the X and Y axes whenever you move the time axis ? why can't you move the time axis alone ?

[@fabiobottalico7732]

AL_ muharb Because a point in space-time needs 4 coordinates to be correctly represented. A basis for R^4 is not representable in our space, since we see 3 dimensions and "feel" the time. We can represent the 3 unitary vectors I, J, K for the space and they can rotate rigidly in order to get a cartesian system of reference, but when you need 4 unitary vectors, where do you put the fourth? how does the fourth rotate? A 3D representation of a 4D space time is not possible, hence he used a 3D space time, with a plane and the time. In this case, since time is not a visible coordinate, it depends on the speed of light. Its dependance from the speed of light forces the Time axis to rotate in a way that the path for light beams is always the bisector line for the angle created by the time axis and the other axes.

[@EugeneKhutoryansky]

AL_ muharb If it was just the time axis alone that was rotated, then the speed of light would no longer be the same for all observers, which would violate the fundamental principle of Einstein's Theory of Relativity.

[@malm7arb]

thank you I understood it now

[@usamahakeem2580]

Why have we subtracted ct from the other axes,why can't we just simply add them just like others

[@nguyenthao-kz1uh]

i can not understand the relationship between the equation: ds2 = dx2 + dy2 + dz2 - c2dt2 and the statement: ' the velocity of light does not changes in different observers '. Can you explain in detail?

[@charlesmcmillion5118]

I can.