Relativistic Addition of Velocity | Special Relativity Ch. 6
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- เผยแพร่เมื่อ 14 ต.ค. 2024
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Mark Rober's youtube channel: / markrober
This video is chapter 6 in my series on special relativity, and it covers the topic of relativistic addition of velocity: aka, how things that are moving relative to one inertial reference frame, which is moving relative to another reference frame, what speed or velocity are those things moving relative to the second frame. We'll show this using the Lorentz transformation of moving worldlines, enacted with a mechanical minkowski diagram, aka mechanical Lorentz transformation, aka spacetime globe.
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Created by Henry Reich
Avoiding demonetization by calling it a death pellet. Nicely done.
Cody'sLab that was exactly my thought
It only show how fucked up the entire system is, if we must use synonyms for normal objects in order to avoid the system penalty.
PotatoSmasher 1984 comes to mind
Ministry of Hatespeech is apparently a thing in youtube.
first time I understood the speed of light can't be surpassed.
I have to say, a bullet traveling at 0.6C definitely earns the name “death pellet”.
ANYTHING at 0.6C deserves.
@Pedro Nunes
Not so sure about that part. I am getting hit by plenty of things going upwards of 0.99C. Heck, my comment is hitting you faster than 0.6C right now.
Even a speck of paint counts as one. Remember Mass Effect lore?
Pedro Nunes not really neutrinos for instance travel faster then that and aren't dangerous at all even in high quantities
Ok, anything that is in a human scale.
I'll say it again. This spacetime globe is a work of genius. Hand this man his nobel prize.
* this man => Mark Rober FYI
This active visual presentation finally made it click for me. Brilliant.
Yeah, I really want to buy one, it doesn't look like he ever out them up for sale. 🙁
@Donald Deng my guess is MinutePhysics did a sketch of what these Lorentz Transformation diagrams look like and sent it to Mark, and Mark probably came up with some ideas of how it would look physically and then they both kind of agreed on what looked best and then Mark built it. I think it was the two of them working together to create this.
Naming a planar Device a globe is not that genius at all! haha ;)
I spilled water all over my keyboard.
"Death pellet"
Demonetization bot hitting hard on everyone's vocabulary.
Quahntasy - Animating Universe is avoiding demonetization that easy? And that crucial?
Think about it, you live from the revenue of ads. You get demonetized and lose your income. What should you do for a living? Quit the job and make something different? No. Change your work on some parts so you wont lose your income? Yes.
Demenetization comes from stupid bots and stupid people, so you can atleast hower away from the bots with some cleverness.
The video it's sponsored so it doesn't matter
just say "if you throw a ball"
Let me just take away half your paycheck, because as long as you don't have the other half it doesn't matter.
100 quadrillion neutrinos walk into a bar. One of them says ow
not a lot of people will get this
May you describe it for the people that actually don't get it ?
Help, lol
AH HA HA HAAAAA! 😂
Hahaha. It's funny because, being neutral in charge, neutrinos have notoriously low detection rates. Thus, even though 100 quadrillion neutrinos experienced the effect of "walking into the bar," only one alerted nearby observers.
The first few minutes of this video taught me what years and years of physics courses couldn't.
for any high schoolers / college students taking the class: this is the formula for success
1) watch this video
2) read it in detail on brilliant.org
3) read it in mathematically rigorous detail of physics.libretexts
4) watch it on khan academy for review
Done. You're a master at it now. It comes intuitively after doing this cycle.
lol i'm a kid i tried for 2 years to learn that, i don't know why i didn't get this series :(
Death pellets do not travel faster than the speed of light, but love pellets do because they cause your universe to enlarge.
Also, love can go thru multiple dimensions. This is, of course, according to Interstellar.
Yo somebody else using a zombatar ayeeeee
Classiest boner joke ever
And then there's friendliness pellets that boost your LOVE...try to catch as many as you can lol
I love the way you animate your algebra. It captures really well the actual visualizations of someone who's doing the math.
That is fascinating. So now I know that all my physics assignments where I added speeds were wrong after the 13th digit behind the dot.
Not My Name
Unless the input values were improbably precise, your answers were correct to the number of significant figures given.
I love that u repeatedly recap over and over the example in the beggining of each video in this series, it really helps me to fix the idea instead of remembering for myself the main idea that u already explained in the previous video
*I lost him at "In our universe".*
Shaolin Panda it’s a joke bruv
Alex Ryan Hughes He is saying that because there is a possibility that there are other universes where apply different laws of physics
@Chính Đặng Minh kudos to u.......
Thank you for this. Due to corona making all my classes online. My class on special relativity and related subjects has been entirely just "read the book" kinda stuff. Really love the fact that there are explainations like this that help provide intuition for topics like lorentz transformations, lorentz invariance, and relativistic addition of velocity.
Can you please tell which for which fields you'll learn special relativity in college other than Physicist?
@@tahamuhammad1814 there's quite a few. Off the top of my head, Anything that usually requires precision in timing or travels at high speed. So, like, communications engineering (satellite communications, telecom, signals, etc). Even things that move at high speeds, think NASA travel, will require compensation. Rocket science probably as well. But in general, if you can think of a field where precision at high speed is required, there's probably some special relativity being applied.
you really expand my coceptual understanding of the topic.
people say classical physics and relativity don't match up but the truth is when we talk about things moving at the speed of light we get to discover what really happens on the small scale..
A few years ago I took an online course through Stanford concerning the Special Theory. It was a superb course, and it required "homework" and tests so that the student must understand the material before proceeding.
I had a pretty thorough understanding of the concepts, but the addition of the spacetime globe in this series brought everything together. Using that instead of drawings was much more clear. Thank you so much!
At least they're not "friendliness pellets."
That part about stretching the drawing made me understand the whole thing. And in the end you completed it by explaining how the Math works out for it. This is a great video
"Death pellet", gotta keep the demonetisation bots away
a death pellet a day
keeps demonetization away
Oh wait, TH-cam actually demonetize videos for using the word "bullet" or? :O
Gets demonetized anyways for saying death too many times
This series has done more for my understanding of relativity than all of my high school physics classes. Keep up the great work, and thanks so much for the time and effort you put into making these!
3:49 In case anyone's wondering: (v+u)(1+vu/c²)
Always Watch at 0.5x speed if you're a Noob.
Vivek Joshi Sounds extremely high at that speed
x0.75 sounds way better
*0.75x speed
i'm a advance noob :v
I watch it at the speed of light.
yeah ikr it really helps
this is my favourite video on all of youtube! It answered a question that I had FOR A LONG TIME
I can understand that guy when I listen to him at 0,75x speed
You've just been knocking it out of the park lately, Henry
That is a simple equation. I didn't think that equation that would allow for slow speeds to add but disallow super-luminal speeds would be simple.
That's the beauty of physics.
Yep, very similar to the equations for time dilation and length contraction using the Lorentz factor!
Something I have always wondered, but have never seen anyone explain anywhere is:
1. Imagine two solar systems. A few light years apart. Both solar systems are moving in the same direction at the same velocity so that the distance between them is constant.
2. Beings in solar system A launch a spacecraft directly toward solar system B at relativistic velocity greater than .5C Let's say, .7C for this example
3. Beings in solar system B launch a spacecraft directly toward solar system A also at .7C
Now, if the astronauts in either spacecraft were to (somehow) measure the speed of the other spacecraft as the two race directly toward each other, would they not perceive it to be moving greater than C from their perspective? I know the answer is likely 'no' but I just have a very hard time understanding how that could be.
friendly pellets
*flowey is that you?*
i'm just a friendly neighborhood flower.Nothin' more :)
I laughed twice when I remebered he calls them bullets if you dodge them.
3:50 for anyone wondering why; this is because in the relevant interval [0,1) the denominator (1+uv) will always be greater than the numerator (u+v)
death pallet xD god damit youtube look at what we have to do to bypass yar crap
the shit PC world we are living
Death pellets don't kill people. People kill people.
You'd think the NRA would *love* to advertise on videos about guns, so why does youtube demonetize them?
be cause having your ads on high quality educational videos will trash your reputation.
DUH
Good presentation!
I have a few questions. Let's assume that, from your perspective, you are moving at 0.6c towards a mirror and you send a beam of light towards the mirror at the exact moment that you are 4 light seconds away from the mirror.
1. From both perspectives (the mirror's and yours), will the beam strike the mirror when you are exactly 2 light seconds away? If not then how far away would you be from the mirror in your perspective (and in the mirror's perspective)?
2. Also from both perspectives, how far would you be away from the mirror at the exact moment the beam returns to you?
Now I understand why good professors take a pause when they explain something before throwing something new at us, it's so we can take our time to think about the info at hand and give us time to prepare for the next one.
Here you do all this amazing job preparing the videos but you go too fast throwing new information left and right. After a while pausing, going back, slowing the video etc.. starts to be a pain.
zouhairy yes but you can go back
zouhairy
Thank goodness you can pause and skip back when watching a video on your own. (However, you are right that it makes the video more difficult to use in, say, a classroom setting.)
zouhairy It's called minutephysics for a reason. I appreciate the speed because I often find other videos way too slow. This one was perfect for me, but if I don't understand, I can just go back until I do, or look up a more detailed exlpanation if I'm really stuck.
zouhairy He is, this video was a singular concept, building on information from his previous videos.
The start of the video recapped on what has already been taught, then the new equation was introduced with an explanation.
Any less content and there wouldn't be any content, any longer of a video and it'd be repetition.
There are sections where he's wanting you to think for yourself, such as considering the equation at the lower values of c, but what good professor wouldn't want you to think for yourself at least a little?
You can control the speed of any video on YT. I usually watch these videos at x1.5 so I can’t really see the problem... and being not too repetitive is one of the things I love from this channel.
3:16 Such a simple yet elegant equation. As you started writing it, I deduced what it would ending up looking like. It's very intuitive.
I didn't understand it
what about two photons travelling in opposite directions towards each other? I still can't grasp that one
It's a tough question to answer without more information. Do you mean from the Photon's perspective? Or a different observer?
well from one of the photon's perspective would be the worst (or rather weirdest) scenario
From the perspective of anything traveling at the speed of light, time does not pass. It's an interesting property of our universe that the speed of light happens to be the fastest that any two points in space can communicate with one another. Photons happen to carry that information.
Imagine this: A photon from a distant star is emitted. That ray of light travels from lets say 100 thousand years before striking your eye, and turning into an electrical signal. During that time, the photon has traveled through an enormous amount of space. Yet, when it strikes our eye, we do not see any other information. We only see the point of origin of that photon. It has carried information about that star across vast distances, unchanging, to your eye.
The reason cause and effect are consistent for all observers is that the universe has a speed limit.
If you look at the path of a photon on that space-time globe, it is *always* at 45 degrees to the current perspective. Ergo, "From the photon's perspective" itself doesn't make sense, because you can never have the photon's world line going straight up. If you did, everything else would be moving at infinite speed. Not light speed, literally infinite. rendering time non-existent.
well that last one just blew my mind back to the start, I was interpreting that from the point of view of one photon, time does not pass and the rest of the universe stands still, therefore from its point of view other photons would be still, therefore relative speed would still be C, but hidden ninja practically scrapped that idea, if time does not pass, and speed is a function of distance over time, how does a photon even move? however I would assume there has to be a point of view for the photon somehow valid.
as for the 3rd observer, I'm guessing the formula balances out in the middle somehow? though I'm still not sure how
There is so much new stuff on TH-cam it's overtaking the peer reviewed periodicals.
ummm just pretending that I understood
Questn you will understand it clearly once you question it yourself, and wonder why and how is it
Basically our general understanding of how things move applies the same to things moving waaay faster, but the outcome looks significantly different from our perspective. However, our understanding of the universe is that the speed of light cannot be surpassed by us because that’s just the nature of our universe.
🙃😶😵
How it works is actually pretty simple. Why it works that way took one of the greatest minds in history to figure out.
The theory of Relativity is about how the quantities that are measured by one observer (Alice) relate to corresponding quantities that are measured by another observer (Bob) who are moving with respect to each other. The value of some quantities change depending on your perspective; such as the velocity of an object, the time interval/the distance that is measured between a pair of events, the energy/momentum associated with a physical system, etc. Transformation laws describe how the values change from the perspective of one observer (Alice) to another (Bob) depending on how the first observer (Alice) is moving with respect to the second (Bob). The equation involving the velocity of an object with respect to one observer (Alice) and the velocity of that observer (Alice) with respect to a second observer (Bob) is just another example of a transformation law that allows the velocity of the object with respect to the second observer (Bob) to be computed. So in this case, it's a transformation law for the velocity of an object. There is a transformation law for every quantity that is relative (i.e changes depending on your perspective).
These transformation laws can be deduced from two experimentally verifiable starting points:
a) The laws of physics have the same mathematical form in all inertial frames of reference.
b) The speed of light in a vacuum is measured to be the same by all observers.
The laws of physics describes the patterns among the quantities that can be measured by any observer in a particular frame of reference. Transformation laws describe how those quantities change from the perspectives of observers in different frames of reference.
I'm really digging this series on special relativity. Thanks for making it!
I would like to know what would be the relative speed of a light coming from the opposite direction if I am already move at the speed of light? Just like the LHC crashing two particle at opposite direction, is it the same with just one particle crash at the speed of light into a stationary one?
cfsscfsshk Both particles would move at a speed close to that of light. Viewed from the perspective of one particle, the other particle would move at almost the speed of light towards them.
cfsscfsshk You can't move at the speed of light because you're not a photon (and you have mass). If you were a photon, the question wouldn't make sense because you wouldn't experience the passage of time, and thus "speed" is meaningless.
+Buttercak3
There you go.
So basically still the speed of light.
+David Guild
Oh wow. Pretty smart stuff
Now that I'm at a proper keyboard rather than a phone, I can actually type a bit more about this. Note that it's been a while since I went to school and learned about this topic, so don't take anything I say as facts and consider doing some more research.
Particles that have mass can move at a speed close to that of light, but not *at* the speed of light. You can perform Lorenz transformations for the perspectives of two particles that move towards each other with such speeds and will see that the other particle's speed will appear a bit closer to the speed of light than before.
If we're talking about two particles that *actually* move at the speed of light towards each other, like two photons, things get a little weird. You probably noticed throughout these videos that you can't really perform a transformation that creates the perspective of a photon with the time globe. What you can do, however, is plug the speed of light into the transformation formulas from last video as v.
I'll have to do some workarounds to be able to express the formula in a comment. "dx" and "dt" stand for "delta x" and "delta t", "sqrt" for the square root of what's in the parentheses.
Length contraction: dx' = sqrt(1 - v²/c²) * dx
If v is equal to the speed of light, then v²/c² equals1. The part under the square root evaluates to 1-1, which is equal to 0. The square root of 0 is 0 and you multiply that with delta x to get the result. Basically, you get dx' = 0 * dx, meaning that everything that moves at the speed of light appears with a length of 0.
Time dilation: dt' = dt / sqrt(1 - v²/c²)
If v is equal to the speed of light, then the square root evaluates to 0 again, like with length contraction. Now you're left with dx' = dx / 0. Now here is where I'm not sure, so take this with a grain of salt. Division by 0 is obviously not allowed, but what if you interpret the result of dx / 0 as infinite? Time would be infinitely streched, causing time for things moving at the speed of light to stop.
These two things mean that, viewed from the perspective of a photon, everything has a length of 0 and time of everything around it is slowed to a halt, effectively eliminating the concepts of space and time altogether. What does this mean or look like? I don't know. I'm not a photon.
Yes, one space-time apparatus, but multiple perceptions of it. As shown in the video, the one space-time environment, is not being stretched. Thus if you start with an absolute 4D reference frame, call it Space-Time, and within this absolute 4D frame you have absolute ongoing motion of all objects, and you have all objects share the same "c" magnitude of motion, the outcome of this setting, is the Special Relativity(SR) phenomena.
If you simply closely examine the concept known as "Motion", you will soon have derived all of the SR mathematical equations, including the Lorentz Transformation equations. I am a high school drop out, but independently discovering the SR phenomena, and independently deriving the equations, was an easy breezy task for me. Therefore, it must be even easier for you.
I’m curious, do you call it a “death pellet” because saying “bullet” would get you demonitised? :S
Thanks for showing and explaining the formula. Anytime someone asks about "turning on a flashlight while at lightspeed", I'll refer them here.
Drinking game.
Every time “the speed of light” is said, you have to drink
There’s a small technicality. Yes, c is invariant under Lorentz transformation; however, c is not _necessarily_ the speed of light. c is the speed of causality. While light will tend towards this velocity when it is unrestrained (i.e. in a vaccuum), there are plenty of times that light travels much slower than c. Sometimes, we even see the light equivalent of a sonic boom! (see Cherenkov radiation)
can you manufacture the device so that everyone can buy it
Yeah, tell Mark to make me one too. I wonder how much he'd charge.
It looks like a pretty easy build if you have access to a minor machine shop.
This brought me to tears. Life is beautiful
Incredible.
Your spacetime globe made me think everything is always moving through 4d spacetime at the speed of light. Either moving at the speed of light through time when stationary, or when moving through 3d space at the speed of light your speed through time is zero. Very cool, it really puts time dilation into much clearer perspective.
I need to go make a spacetime globe now lol! Many thanks for this video set!
Those death pellets are quite speedy quick. Better watch out.
I think this is one of your best videos! congrats for making this so simple
You are the best!
any videos that's explain thing with diagram on relativity theory, should uses whatever weapon that is used in this video. really helping. love it...
Isn't the universe expanding faster than light?
it's the "empty space" that is expanding not the matter such as earth and the sun that is moving faster than light so there's no rule broken
Manh Do however, it is said that matter over 14 billion light years away is moving faster than the speed of light relative to us, so at this current technology, nothing can reach it or we can never see anything beyond it.
our observable univer have the diameter of 90 billion light year
Manh Do
19*
Manh Do makes more sense, i think I mistook for the big bang or something, so my bad. But I'm glad I said over 14 billion, haha
I love this series and have watched every episode multiple times by now. Still hoping I'll understand it one day...
Imagine you have a train on the train you have a train on this train you have a train... and so on... Will we reach the speed of light ?
Dagobert Duck no
Dagobert Duck it’s just like 1+half+half of half+half of half of half, you’ll never get to 2
No you wouldn't, however some theories suggest that 'time' would slow down the faster you go. So if you were able to make this 99.999% speed of light train you could, in theory, have a time machine to the future.
Just a time machine to the future though, not the past.
Although you could just sleep more, and it would be more fun in my opinion.
Time slowing down isn't just theoretical, it really does happen. Clocks on GPS satellites have to be so precise that the slight change in the speed of time due to them being farther from Earth's gravity means that they have to adjust their clocks by a tiny fraction of a second each day. Same thing happens on fast planes, precise atomic clocks that start out since but then one fly's around the world in a fast jet the jet clock is slower.
That space time globe is so cool.
Hah! Your spece-time globe is *flat!* Thus proving the flat earth!
The only thing flat-earthers have to fear is sphere itself.
And cats traveling at the speed of light firing death pellets.
Hmm, I think it's a flat universe, if one even knows what that means. But, I got the joke.
He explicitly said he is viewing the earth in one dimension
In contrast to the earth, the universe/space-time is in fact flat (at least as far as we can measure).
Flat Earth😂😂😂 some no many believe in flat Earth theory
this is the best lorentz transformation diagram ive ever seen
this video is incorrect!
I clicked the notification bar faster than the speed of light...
Gh0st No, he could’ve stopped. Though, his hand would burn
No you didn’t, you clicked it at the slow, slow speed of your finger touching your phone. It would require an infinite amount of energy to move mass through space at the speed of light, so beyond that is even more impossible.
Even if you had managed to click it that fast, the speed of the components in the system would not have delivered the video to you faster than the speed of light.
It's becoming more and more clear with each video .. thank you so much
Wait what?
I love these videos.... and almost all of them go over my head. But i am starting to understand now, so thank you!
gg laws of physics
well played
obama approves
This video reminds me about the video "Common physics misconceptions" you made 5 years ago. And it's the same evaluation but instead of V1 and V2 you put V and U.
*Pretends to understand what's going on...*
This. Is. Just. So. SoOooOo. Sooooo. SOOOOOOO GOOOOOD!!! Thank you Henry!
Why speak so fast? (English is not my first language)
Raul Afonso Because its hus first language. I speak Mexican spanish, poorly, tge mexican speak so fast I only catch about every third word. Is what it is.
If you go to settings, you can slow down playback speed to either .75x, or .5x
You are welcome
Raul Afonso its called minute physics for a reason...
is he saying death pellet instead of bullet cause demonetization?
Dynamitris the Video Watcher yes
Dynamitris the Video Watcher well but also a bullet at .6c is a death pellet.
Technically the term is "kill vehicle," but sure, 'death pellet' works too.
Annihilation pebble*
@@yzmotoxer807 Oblitaration projectile.
This video showed a better explanation of relativistic relationships better than the other one using the same graph
disliked for calling bullets death pellets.
Seth Apex TH-cam fault.
weak hyper charge
bullets are not always lethal depending on where they hit, therefore changing the name is inaccurate, though apparently he did it to avoid youtube censorship.
I'm not sure why my dislike is not showing up in the counter, but when i try to remove it, the counter goes to -1 dislikes.
I'd point out any bullet moving at 0.6c very much is going to be a death pellet no matter where it hits you.
So you are aware that he calls bullets like that not because he thinks they should be censored, but to avoid youtube penalty, and despite that you give a dislike? Shouldn't you be mad at youtube instead?
Red Claw I'm mad at both. TH-cam for the censorship, Henry for not calling attention to the censorship.
Thank you! Best explanation I've seen for why nothing with mass can travel the speed of light or faster.
You sir saved me!!! Now I understand not only the formula (for which I came in the first place) but the concept behind! Thank you sincerely ❤
I read that equation in a book as a teenager and I still know it by heart. I love it so much; it's so elegant! 😍
This explanation actually cleared most my doubts regarding special relativity. Thank you very much.
You guys made a similar videos before, this one adds much more
Wow.... Now I understand the whole stuff.. thank you minutephysics. I've been following this series from the first episode and you have taught me a lot. Thank you once again.
One of the greatest channels of all time
I love how he has to say "death pellet" to avoid getting demonized. TH-cam really needs to change.
Bulletin bulletin bulletin bulletin bulletin
So, this particular addition involves only objects moving in one direction away from a source object that is stationary, and combining those two moving velocities. However, what would happen if the now stationary object started to move in the opposite direction? Would it "appear" that the objects moving at velocities a1 and a2 could be moving at a speed greater than the speed of light relative to the object moving at -a3? I say "appear" because if the object is moving at a speed greater than light, then it would not be able to be seen in this scenario.
Noting in this assumes a truly stationary object. Everything appears stationary if viewed from its own perspective and everything seems to be moving from a perspective other than its own.
To answer your question: No. Another object will NEVER appear to be moving away from you at a speed greater than the speed of light.
It's not an addition. The theory of Relativity is about how the quantities that are measured by one observer relate to corresponding quantities that are measured by another observer who is moving with respect to the first. The value of some quantities change depending on your perspective; such as the velocity of an object. Transformation laws describe how the values change from the perspective of one observer to another depending on how the first observer is moving with respect to the second. The equation involving the velocity of the object with respect to one observer and the velocity of that observer with respect to a second observer is just another example of a transformation law. In this case, a transformation law for the velocity of an object. There is a transformation law for every quantity that is relative (i.e changes depending on your perspective).
If v is the velocity of an object with respect to observer one and observer one is moving at velocity, u, with respect to observer two then the velocity transformation equation allows you to work out what the velocity of the object is with respect to observer two. If observer two starts moving with respect to their original reference frame then they become observer three, who is moving at velocity, -w, with respect to observer two. Observer two is moving at velocity, w, with respect to observer three. No object is ever moving at or greater than the speed of light with respect to any observer.
I finally understood why (2/3)c+(2/3)c!>c ! Thank you so much minutephysics. All I needed was that equation.
amazing demonstration!
What I personally find fascinating is that if instead of the velocities you consider the inverse hyperbolic tangents (arctanh) of their ratios to the speed of light, then those DO actually add. That is, arctanh(v') = arctanh(v) + arctanh(u).
Nice series, I like the way you explain complex things, keep going! :-)
After watching this chapter, I wondered what would happen, if there are two cowboys facing each other in lets say 10 meter distance. Both are travelling with c-1m/s (nearly lightspeed) and one shoots his gun at the other: Would the other one have enough time to dodge the bullet, as it is moving with maximal 1m/s relative to him?
Lets take the same scenario, but the cowboys are facing each other orthogonal to the direction of their movement. Would the bullet now has its usual speed?
You talk about velocities "close to the speed of light" and those much slower than the speed of light, but where is the cross-over point (i.e. that speed where the definition of "close to the speed of light" takes over the definition of "not close to the speed of light")? It was easy to see the three equations transform when V and U were at the speed of light, when they were 0.6C and when they were significantly
That was awesome, fun to watch.
Still absolutely loving this series. I never got to relativity in college physics.
I noticed sticks representing light at the spectime globe are less or more dense after transformation. Does it affect light frequency and is it equal to Doppler effect?
This video is really cool because it blew my mind. I love it
I've always wondered why relative velocities can't create velocities higher then light speed, cool video!
these explanations are so good, I'm loving them keep up the good work!
I really really really like these videos. You helped me visualize relativity in a way I was struggling to for years!
this space time globe actually made me understand that. tanks dude
I love the time globe series, it really helps one visualize the concepts.
very nice explanation. I like your visual model and examples.
This seems to suggest that we should measure all speeds in some exponential or logarithmic expression of the speed relative to lightspeed
This is the best video I've seen on this topic.
I would like to see your explanation of the same phenomenon when two objects travel in opposite directions.
When thinking about this question I noticed given equation doesn't comply. (u - v may equal zero)
Do I need to use absolutes?
That would mean even that relative speed can't exceed the speed of light.
But what about following thought experiment?
Object 1:= O1
Object 2:= O2
velocity of object 1:= v1
velocity of object 2:= v2
distance traveled in 1s of object 1:= d1
distance traveled in 1s of object 2:= d2
O1 with a v1 of 0.6c has d1 equal to 299,792,458m * 0.6 = 179,875,474.8m
O2 with a v2 of 0.6c has d2 equal to 299,792,458m * 0.6 = 179,875,474.8m
That would give a total of 359,750,949.6m covered in 1s which is greater than the speed of light.
Though I know of quite a handful of things that are faster than light. They can travel faster because they are massless and carry no information, therefore I wouldn't call them objects.
Is this case similar since no information was transmitted over the whole distance?
But if those two objects were to collide, at what speed would that be?
Given equation results in something less than the speed of light.
How would an observer experience this? Would both objects slow down respectively just before collision? Would it seem like time itself slowed down?
Light is actually hitting everything at the speed of light and if I were to travel against light I would notice blue shifting.
So do those objects visually appear to shorten even more just before the collision to achieve a less than light speed relative speed?
I'm so full of questions.
You don't need to use true velocities, c fractions are easier. But don't subtract "u - v" - the Lorentz transformation doesn't care about direction, it just cares about the two velocities (I think you need to go into how the formula was derived to understand why this is the case, something gets squared so it can only be +, IIRC).
359,750,949.6 m is just an intermediate value in the Lorentz transformation. It needs to be multiplied by the Lorentz factor, which is 1 over (1+vu/c^2), to determine the correct relative speed of O1 and O2 in their reference frame. The Lorentz factor multiplication will cause the speed to be less than c, I think about 0.88 c. That's their relative speed and their eventual collision speed in their reference frame.
An observer can't sense the relative speed of "third parties". An observer sees just two 0.6 c objects collide in his own reference frame and has to calculate to know the more meaningful collision speed in the reference frame of the objects.
I believe you would see blue shifted on-coming light if you are travelling at a relativistic speed (and red-shifted light coming at you from behind). Object shortening or flattening occurs during the entire journey and doesn't change at or just before collision. Both objects flatten. Flattening has no effect on their speed. They always were and remain at less than the speed of light in their reference frame, and in the observer's reference frame.
I'm curious ... what things that are faster than light? Probably not real objects, as you say. Quantum information is being transmitted over the whole distance in your scenario.
That value is the actually traveled distance in 1s. But of both objects together. Meaning there was no faster than light speed.
Information traveled only half the distance.
----->
Okay on your points about it being a traveled distance in 1s, etc. But that's also a velocity. And the sum of these two equal velocities is the correct intermediate value.
The forces, or energies actually, are not the same. The LHC sends two protons hurtling towards each other at some high fraction of the speed of light (99.9999991%, I think). The energy of each circling proton beam is 6.5 TeV and the total energy at the collision point is equal to 13 TeV. A constant force is what led to the huge energy accumulation (the force of the super-cooled magnets in the LHC). The collision can lead to new force being exerted, maybe against the surrounding beam pipe, or towards slowing down the two protons but the protons no longer exist. Mostly the energy gets converted into new mass in the form of a spray of new particles that did not exist before. The take-away point here is a tiny increase in relativistic velocity means a huge increase in a particle's kinetic energy even if doesn't move much faster.
I agree with your non-object FTL examples.
Thank you!
I really needed this video. I always wonderd what would happen if one spaceship leaves Earth with 0.6c and another one leavs Earth with 0.6c in the opposite direction and if their relative speed would be 1.2c.
It approaches the speed of light but never reaches it, like how the slope of a linear function can always be higher with bigger numbers, but never vertical
Very nice explanation. Great job
What is the answer to his question at 3:53? I know that the denominator must grow faster than the numerator so that the total would be less than c (exponent between 0 and 1), but I don't know how to demonstrate that this must be true using the formula. It doesn't seem straightforward.
Found in a comment below: (v+u)(1+vu/c²)
Dude, you're a genius, you made this theory so simple to understand that even me could, thank you!
I can see the Doppler effect in that space time globe light demonstration!