Twin Paradox

Did you know that you could be older than your twin like years older according to Einstein’s theory of special relativity? It’s possible because time can take faster or slower depending on how you’re moving. What yeah, we’ll get back to that. But first we’re going to learn all of special relativity. Don’t worry. There are only two postulates one is that the laws of physics are the same for everyone’s perspective or frame of reference while in uniform motion so that It means that on a plane cruising at 800 kilometers per hour an object. You dropped will fall straight down just as it would if you’re stationary on the runway same physics in those two frames otherwise plane rides would get real weird. The crazy implication of this postulate is that there’s no experiment you could do to tell that you’re moving even at 800 kilometers per hour even at a

Million kilometers per hour because you can only tell you’re moving relative to something else like the clouds outside your window. The second postulate is that the vacuum speed of light is the same for all observers 300,000 kilometers per second. Let’s just pause on that for a sec. Do you know how freaky this is? It seems that if you’re flying toward me in a spaceship going close to the speed of light and you shine a laser at me. You’ll still measure that light to be going at 300,000 kilometers per second and I’ll measure the light to be going at 300,000 kilometers per second as well. So those are the only two postulates of special relativity. The speed of light is a constant and the laws of physics are the same in every inertial reference frame inertial meaning not moving or moving at a constant velocity. Basically, you’re not accelerating and when you do accelerate like when you experience turbulence,

Or during takeoff. When you pushed back into your seat. You can tell you’re moving and special relativity no longer applies. So it’s from just these two postulates that we derive an entire physical Theory and get crazy things like length contraction and time dilation and other weird quirks of physics that are real one. Such Quark is that time can take a different rates depending on how you’re moving we call this time dilation. It’s weird but it’s real. Why does it happen? Consider two frames one is you Stationary on Earth and one is your twin zooming by in a rocket. You have identical clocks. Let’s look at yours first. Each time light makes a round trip in your clock. You count by one your twin will measure the same rate on her own clock now things get weird when you watch her clock because of her sideways motion. You see that her light has to travel a longer distance for one tick. And since the speed of light is the same for all observers her round trip takes must take more time. So time actually take slower on her moving rocket according to you. Me and this is a real phenomenon. It’s not some weird Mind Trick. We don’t usually notice this though because time dilation is quite insignificant until you’re moving close to the speed of light. So now from your twins perspective you are moving there for your clock must be running slower according to your twin and because the laws of physics are the same in both of these frames yours and hers each frame is equally correct in saying the others clock is running slower. This is where the Paradox starts imagine you and your twin start.

On Earth you stay here, but your twin zooms off in a spaceship at half the speed of light turns around and comes back the whole trip takes 30 years, but you see your twins clock tick slower. So due to time dilation during the journey. She only aged 26 years four years less than you now. Here’s the Crux of the problem from your twins perspective. She was stationary and you on Earth moved away and came back. You’re the one moving at half the speed of light so your twin should see Or clock going slower and should think you are only 26 years older by the end of the trip. So yeah, that’s not possible when your twin gets back. She’s either younger or she’s older. She can’t be in a superposition of both this isn’t Quantum. So how do we solve this Paradox? Well, the answer lies in the details when your twin turns around she has to accelerate.

Which means she’s no longer in an inertial reference frame while she accelerates and so special relativity no longer applies to her. It’s not as simple as saying your twin sees you make a round trip and you see your twin make a round trip. It’s not a symmetric problem like that because when your twin accelerates we can tell the difference between the physics that might happen in those two frames see will feel the acceleration during the turn around and you will not so when she gets back she will agree with you that you are 30 and she is 26 One last question what’s happening? The clocks During the period of acceleration we still get time dilation, but we have to use a different set of rules from general relativity general relativity states that clocks run slower and accelerated reference frames. So while your twin is turning around her clock runs slower and she sees the same thing. She sees your clock running faster than hers. So you’re aging quicker. It’s during this period of acceleration that you become the older twin. Now this phenomenon of time dilation in an accelerated reference frame is related to time dilation in a gravitational field general relativity says that clocks run slower in gravitational fields. As you may have seen occur in the movie Interstellar, you can get time dilation and other strange things occurring during different forms of motion special relativity and the twin paradox are just the tip of the iceberg.