In this thought experiment, my twin brother and I are both turning 20 at the airport.
At midnight on our birthday, we are both exactly age 20 years.
He stays put while I get on a 777 and fly around the world. The flight takes me 24 hours and so he waits 24 hours. I arrive and we are both age 20 years plus 24 hours.
If I instead get on an SR-71 and fly around the world at 3x speed of the 777, the flight takes me 8 hours so he waits 8 hours. I arrive and we are both age 20 years plus 8 hours. Clearly, we are both younger in this scenario than the first one.
If I got onto a super plane flying at 0.99x light speed and fly around the world, the flight takes me 1 second. Since I’m so fast, he should also only wait one second. Intuitively, I’m back and we’re both 20 years and 1 second old.
But my understanding of time dilation is that I’m 20 years and 1 second old when I’m back, but he would be much older since I was almost going at light speed.
Why is that? My flight and his wait time should both be much much shorter since I was flying much much faster.
In: Physics
> If I got onto a super plane flying at 0.99x light speed and fly around the world, the flight takes me 1 second. Since I’m so fast, he should also only wait one second. Intuitively, I’m back and we’re both 20 years and 1 second old.
No. He is 20 and 1 second old. You are 20 and 0.001 seconds old.
At that speed time will barely pass for you.
If you did it for 1 year, he would be 21 and you would be 20 and 0.365 days.
Imagine a really wide drag strip. Like one mile long and 5 miles wide. Two cars with identical top speeds take off from the start line one car goes straight ahead toward the finish and one car takes off at a 45 degree angle to the starting line. Who crosses the finish line first?
The car going straight forward only travels one mile, while the car at the 45 degree angle travels about 1.4 miles because trigonometry.
So even though speed is identical, the path you take matters.
So far so good, i hope.
Now, the cars with identical speeds are everything in the universe. You, me, photons, the forest moon Endor… everything moves at the speed of light. The drag strip represents spacetime. The fabric of the universe. Time is the forward direction, straight to the finish line. Space is the sideways direction.
Everything moves through space time at the speed of light. Some things move very little through space, so they travel straight ahead on the drag strip and move very quickly through time. Some things move very quickly through space (photons, cosmic rays, neutrinos) and hence move very little through time. These are like a drag car running almost sideways, parallel with the start line.
So, you jump in a space ship to move through space, and you end up experiencing less time, because your direction on the universal drag strip is now a little more in the space direction than it was when you were sitting still.
The real math is more complicated than this makes it sound, but i feel like this gives a good sense of what is going on.
Everything in the universe is actually traveling at the same rate through spacetime, it’s a property called your “four-velocity”. And this four-velocity has the same magnitude at all times. The concept of movement is actually just rotation of this vector. When you’re sitting still relative to another object, you’re basically traveling entirely in the time direction and not at all in the space direction. But when you increase your speed in the traditional sense, what you’re doing is rotating the direction of this fixed magnitude four-velocity so that you start traveling a little in space as well
and not as much in time. Photons are completely rotated and travel only in the space direction, which is why they are said to not experience time. For a free photon in deep space that won’t hit anything, the entire life of the universe is instantaneous. So naturally if you find yourself traveling near the speed of light, you will find yourself similarly rotated almost entirely in the space direction and hardly at all in the time direction.
Time dilation works because there is no such thing as absolute time. There’s no master clock. Time is relative to everyone, and if you’re moving, your clock is going slower than someone’s clock who is at rest relative to you.
> But my understanding of time dilation is that I’m 20 years and 1 second old when I’m back, but he would be much older since I was almost going at light speed.
The age difference is always *proportional* to the journey time. So, the thing you have to keep in mind about those “Twin Paradox” examples is that their trip timeframes are on the order of decades whereas your scenario’s trip timeframe was only a second.
To your brother, your 0.99c journey around the Earth takes ~1 second by his wristwatch; so he ages by ~1 second. At those speeds, however, your time/aging “slows” by a factor of Sqrt[ 1-0.99^2 ]=0.141 and so your wristwatch only registers 0.141 seconds from start-to-finish.
The difference between 1 second and 0.141 seconds means that he aged ~7x faster than you did.
Your example is just unusual in that those additional 0.859 seconds don’t *feel* like the kind of thing we use language like “much older than” for; but if you did 1-billion laps (i.e. ~1-billion seconds = ~32 years) then your brother aging 32 years to your aging 4.5 years would start to feel “much older than”.
Can someone explain to me how we can even termin who is moving? When im in a spaceship moving at 0.99 C, couldnt i argue that the world around me is moving and im actually still? Meaning time dilation should actually apply for the World around me?
The cause of time dilation is that the speed of light is the same for everyone. And that’s very weird.
If you stay still while your brother moves, the speed of light is 300,000 km/s for you, and the same 300,000 km/s for your brother. So how can you and your brother measure the same speed of light if he is moving faster than you? I don’t know, it’s how the universe works.
So if the speed of light keeps the same, then two things must be different between you and your brother: the distance and the time (space contraction and time dilation).
For the first two experiments, you and your brother will agree on the time taken, to reasonable accuracy. For the last one, you will not agree. Your brother will say that the trip took ten times longer than you think it took. You will both have accurate clocks that support your opinion. That’s the dilation effect.
This effect has been actually measured, in ordinary airplanes. However, it requires a super accurate atomic clock to measure the tiny difference. {[Reference to the experiment in 1971](https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment )}
The time spans you are dealing with are too short. Lets say you are going to Proxima Centauri. Which is 4.2465 light years away. Doing a round trip of 8.493 light years. You are travelling at 99.99999% the speed of light. For a round trip of about 8 years 180 days.
When you return. Your 20 year old brother who stayed on Earth will be 28 years 180 days old. As you were on the spacecraft. You’ll be about 20 years 14 days old.
Going around the earth once at .99C would mean something like 0.13 seconds for the observer and 0.018 seconds for the passenger.
The example you’re giving is making some bad assumptions. I think you’re getting hung up on some specific things:
1. You’re hooked on the distance you travel. Distance doesn’t mean anything. It might be a fun fact “how far did you travel?” but it’s not important. Time dilation is actually about *how long a moving observer spends at their speed*.
2. You’re making the assumption that at 0.99c, time dilation would do something crazy and your brother would be years older when you get back. You’re looking for a smoking gun, but there isn’t one.
In scenario one, it’s 24 hrs vs 24 hrs. Speeds are low, so no notable time dilation. A 777 flies around 950 km/hr, or 0.26 km/s.
In scenario two, it’s 8 hrs vs 8 hrs. Again speeds are low compared to light, no notable time dilation. An SR-71 flies at about 1 km/s.
You got hung up on the fact that “in the time it takes to go around the world”, 8 hrs have passed. We’re both younger. Younger than what? Than if it took 24 hrs to do the same task. We might as well standardize it to 24 hrs. You make **three** flights around the world. You both observe 24 hours difference. In reality, you experienced 0.999999999994 x 24 hrs. This isn’t showing up on a stopwatch though. It’s 0.02 nanoseconds.
When you’re flying around at 0.99c, you’re travelling at 296,794.5 km/s. In one second you make 7.42 trips around the world. At 0.99c, the Lorentz factor for time dilation is about 7.1, meaning that you will experience time 7.1x slower than your brother (i.e. he will age 7.1x faster than you). If you only fly like that for 1 second, that’s 7.1s for your brother. Your watches could tell you that. Pretty cool.
But lets standardize it for *time spent* flying. If you spend 24 hrs flying at 0.99c, then your brother is going to age 7.1x more than you. You’re going to land and be one day older, and he’ll be 7 days older.
7x isn’t very exciting, and it’s why you’re not seeing that smoking gun. While 0.99c is wicked fast, it’s not movie-script-crazy. You were looking for some smoking gun that says your brother is going to be 5 years older or something while you were only doing a single trip around the world.
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