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## Want to join the conversation?

• At how comes 0.5 times 0.7 = 0.3 instead of 0.35?
Was Sal keeping one significant figure in this calculation?
But if this is the case I don't see why the results of other calculations have had 2 significant figures.
• Sal made a mistake. You are correct, it should be 0.35, and so the final answer should be 0.89c, not 0.92c.
• At , Sal mentioned a video game leveraging the effects of special relativity. In 2012 the MIT Game Lab developed just that, called "A Slower Speed of Light": http://gamelab.mit.edu/games/a-slower-speed-of-light/

Has Sal seen this?
• The concept of the game is awesome, thanks buddy
• At Sal writes 1 - 0.30, shouldn't it be 1 + 0.30 since velocity v is negative?
(1 vote)
• A few seconds later, he changes it to a plus (and so then agrees with you). However, I think the 0.3 should be a 0.35.
• Two bodies moving in opposite direction with velocity v.What is the magnitude of their relative velocity?
• You should use Einstein velocity addition. The relative velocity is: (v+v)/[1+v^2/c^2]
• Explored a bit with the numbers using this program I wrote for the addition formula(see link.) In it I ran into the case V = U = 1, and had to write an exception for this case. How would one interpret this situation? In the program, I just left U' undefined, but I'm not certain if this is accurate.

(1 vote)
• You've run into the very reason, mathematically speaking, why things can't go faster than (or even as fast as) light. In the addition formula, you'd have to divide by zero when u=v=1, and in gamma, you'd divide by 0 at exactly the speed of light, or move in to complex space faster than the speed of light
(1 vote)
• So I'm a little confused. Nothing can move through spacetime faster than the speed of light, but were talking about relative positions of two thing moving sub light speeds. Nothing says two things can't be approaching each other faster than light, we know galaxies on the edge of the universe are moving apart faster than light. So if this number we calculated is the perceived speed of the second ship as seen from the first ship, but they actually are moving together faster than light, would time dilation and space contraction be what makes appear as they are approaching slower than light? And would it be both, how are they linked?
• In special relativity every inertial observer is at rest in their own reference frame. An observer will never measure a velocity of an object to be moving faster than light. By saying that you have two points moving away from each other faster than the speed of light you are introducing a third frame of reference that is observing each point moving away with a greater than 1/2 the speed of light.

In special relativity there is no one correct set of observations ant the others are wrong, each of the inertial observers measurement is correct from their frame of reference. The need to translate from one frame of reference to another is nothing new, we did this for Newtonian mechanics, the only difference here is that there is a maximum velocity so the translation is a little more complex.
• I was looking forward to using REAL numbers in the scenario set up in the prior video. Now Sal is muddying the waters by changing the direction of the third spaceship, which is now approaching both Sal and Sally. I'm still unclear how to calculate the velocities of vehicle #3 w/r/t Sally when both are flying away from Sal.
(1 vote)
• When both ships are flying away from Sal, u=0,5c instead of u=-0,5c. You put the numbers in the equation, and we get (0,5c-0,7c)/(1-(0,5c*0,7c)/c^2) = -0,2c/(1-0,35) = -0,308c. So in Sally's frame of reference, the other ship would be approaching at 0,308 times the speed of light, which is logical because Sally goes faster than the other ship.
(1 vote)
• why is Sal's position denoted (x,y) not (x, ct)?
(1 vote)
• How to prove that nothing's speed can exceed the speed of light?
(1 vote)
• Try plugging v=2c into the transformation equations and see what happens.