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Current time:0:00Total duration:6:22

Video transcript

now let's apply the formula we came up with the last video sometimes known as the Einstein velocity addition formula and we'll see that it's a it's a pretty neat thing so let's say so this is once again me floating in space my frame of reference is just the s frame of reference let's say my friend over here she's flying away from me her velocity let's give it some numbers let's say she's flying away from me with a velocity of let's say 0.7 C so 7/10 of the speed of light or 70% of the speed of light and let's say this this third character right over here let's say they're flying towards me so let me change the direction the velocity vector so let me erase that so that doesn't look like a pure black but I think you can it looks fairly erased so there you go and let me give the velocity vector in the other direction so the velocity vector this character is flying towards me at let's say so U is going to be equal to since flying towards me X is decreasing with time it's let's say it's negative negative 0.5 C so flying towards me at half the speed of light and once again both of these velocities are given in my frame of reference now if we were in a Newtonian world or if we use the Galilean transformations and this is released to something on your highway if I'm on a highway and if I'm going in one direction at 70 miles an hour and someone is coming towards me at 50 miles an hour it'll look to me like they are coming towards me at 120 miles per hour where you would essentially add these two together and so if we were in a Newtonian world this person is flying at 0.7 C and this person is flying this way at 0.5 C you would in a Newtonian world say okay from this point of view it will look like this blue character is approaching at 0.7 C plus 0.5 C or at 1.2 times the speed of light which we know violates the laws of the universe and that's where this formula is really handy actually let me even make the spaceship point in this direction just so we don't get confused so the spaceship is going in is going in that direction just like that once again the mag to the velocity coming towards me is half the speed of light I put the negative there so it's coming towards me that it's going it's that X is decreasing over time well lucky for us in the last video we just we came up with this Einstein velocity addition formula so let's apply it from this friend's frame of reference the S prime frame of reference the velocity of this character which is change in X prime over change in T is going to be this so what do we have here so U is the blue velocity in my frame of reference so that is negative 0.5 C V is my friend's frame of reference the frame of reference that we're trying to get the velocity in so that's 0.7 C so zero let me do it in that color so that is 0.7 C and then on top of U V over C squared so once again U is negative 0.5 C I know I wrote it really small and then and then V is 0.7 C so what is this going to be equal to on the numerator negative 0.5 C minus 0.7 C that's going to be negative our numerator right over here is going to be negative 1.2 C and this is the velocity that you would expect if we were dealing in a Newtonian world this person says hey this person looks like they're coming towards me at 1.2 times the speed of light that would that's what our Galilean transformations would give us but luckily we have all this business at the bottom that keeps us from violating from violating the absoluteness of the velocity of light this notion that nothing can travel faster than the speed of light because in an our denominator we're going to get 1 minus let's see 0.5 C times zero point seven see let's see 0.5 times 0.7 is going to be 0.3 so zero point three I could say zero point three zero if I live but I'll just write zero point three c-squared and it'll be a negative have a negative times a positive so I could put the negative there but if I'm subtracting a negative that's just going to be a positive and I'm just going to divide by C squared and so that cancels out and so notice we're going to be dividing negative 1.2 C by something that's slightly larger than 1.2 so this is going to be negative 1.2 C over 1.3 1.3 and so lucky for us this is going to be less than C or in this absolute value is going to be less than C so it's going to be it's going to calculator out so if we have I'll just so if we have one point two divided by one point three this is equal to approximately zero point nine two so this is going to be approximately negative zero point nine two C which is cool it it kind of goes with our let me write it over here so this Delta X prime over delta T prime is negative zero point nine two C so it makes sense that from our friends frame of reference the ship will look like it's approaching her faster than it from my frame of reference it looks like it's approaching me and my frame of reference it looks like it's coming to me at half the speed of light and her frame of reference it looks like it's coming at 0.92 times the speed of light the negative is just specifying the direction but we didn't violate the fundamental postulate of special relativity that nothing can go faster than the speed of light and the speed of light is absolute so this is pretty cool I've often even thought about making a video game somehow where you leverage this where things are flying in different relative velocities but you but special relativity applies