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
He’s only 20 years and 1 second old. *You* are 20 years and 0.00001 second old. (Didn’t do the actual math, but you get the idea.) In fact, you’re a little bit younger in every scenario. A 777 or SR-71 just aren’t fast enough for it to be much of a difference.
As you go faster and faster, time for you goes slower and slower. To an outside observer, it’s as if each second takes longer and longer. Hence, time *dilation*. For your brother, you were travelling for a full second. To you, it was nearly instant.
You’re assuming a constant flow of time in your scenarios, but constant time is a misunderstanding caused by the fact that most everyday objects are not traveling fast enough to experience time dilation in a meaningful way.
In all three cases, your assumptions are wrong.
As you are moving relative to your twin, your experience of time is no longer identical to his. Specifically, time will move slower for you than it does for your brother, in all scenarios. The amount by which it changes is tiny over the scales you’re talking about, but it is there.
On your 777 flight, your time will be a few millionths of a second off from your brother’s. This, by the way, has been experimentally measured and confirmed. We have clocks that are sensitive and precise enough to measure differences on this scale, and when taken on trans-Atlantic flights the clocks that were flying ticked a slight bit less than the clocks on the ground.
And obviously, as you speed up, your time will dilate further and further. It still isn’t going to dilate to the point where you’ll notice it without an incredibly precise clock – you need to move much faster for time dilation to be noticeable on human scales. But in all cases, there will be measurable dilation.
Incidentally, the GPS satellites are moving fast enough that they have to correct for relativistic effects in order to remain accurate.
You might be tripping up on “the flight takes me 1 second.” It takes 1 second to who? There is no absolute frame of reference, which is the point of relativity: both of you are experiencing time at different rates.
If he thinks it took you 1 second to make the .99c trip, then he’s aged 1 second. But *you* would have aged a fraction of a second.
If *you* think the flight took you 1 second, then you’ve aged 1 second, but *he* would have aged around 10 seconds.
There isn’t an objective “the flight *actually* took X seconds” because any third-party observer would also be experiencing time at their own relative rate.
Tl; dr. When you are in motion *the definition of a second changes* so light always looks like it’s traveling the same speed. In these scenario nobody would agree how much time passed.
In all of your examples neither of you experience the *exact* same wait time. For the 777 and SR-71 you would be imperceptibly younger (Like a tiny tiny fraction of one second) but the affect is still there. Like in the SR-71 if you stay at it’s top speed for about 3200 years you would be 1 second younger.
This is all because of one thing. Light *has* to look like its traveling exactly the same speed for every single person. Normally speed is relative.
Like lets say there’s a 3rd person here. They are in a SR-71, you in a 777, and your brother on the ground.
Relative to you the SR-71 might look like its traveling a 1000 mph. Relative to your brother it might look like its traveling 1600 mph. (slightly made up numbers btw)
But light? No so much. It’s going to look like it’s traveling at *c* for everyone. This happens because when you move the definition of a second changes. That’s because speed is distance travelled over time. So how much time passes has to change. And it changes *exactly* enough that light still looks like it’s moving at c. For normal speeds which are soooo slow compared to light this is, like i mentioned, basically imperceptible but it’s still there.
The speed of light (in vacuum) is constant, c.
If you turn on a LED while flying in your (vacuum) super plane at 0.99c and measure the speed of the light of the LED, the result has to be 1c.
Lets say your brother could also measure the light coming of your LED while hes still at the Airport. He will also measure the speed of the light to be 1c.
You are moving at 0.99C relative to your brother but you both measure the same speed. So something else must change in order to get the same result.
And that something is time. (And space, but lets focus on time) The flow of time will always adjust so lightspeed is exactly 1C no matter how fast you are.
What you’re missing is that your example isn’t intuitive, because it’s on such a small time frame.
Light can travel around the earth seven times in a second. You’re not going to have enough of an effect from time dilation to see a significant change.
If you were flying 99 light years at 99% the speed of light, someone on earth would see you flying for 100 years, but for you it would only take about 14 years.
It’s not that being at near light speed instantaneously makes a many-year time difference happen, it has to be for long enough for the time difference to build up.
Time dilation goes together with length contraction. Basically, whether we as the observer are moving or not, we don’t know. We only know that an object is moving relative to us. So in your example, despite you flying around the world in the airplane, you don’t actually know that. To your frame of reference, you are hovering in standstill in the airplane, while it is the world that actually zooms by. To your brother’s frame of reference, he is standing still on the ground, while it is the earth that actually zooms by.
Objects with relative velocity have length contraction, in the direction of travel. So for example when your brother looks at your airplane, he sees the airplane zooming by, but the airplane appears shorter. Meanwhile, you in the airplane think that you are hovering in standstill, with the earth zooming by, but objects on the earth appear squished with smaller distances in length.
Now, there is also time dilation. According to special relativity, the amount of time lapse is not agreed upon by different observers of different frames of reference (observers of different velocity relative to each other).
>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.
So this is where the misconception happens. Time dilation and length contraction are tied together by a very simple set of algebraic equation: Time A = Constant * Time B. Say your brother is on the ground measuring with a stopwatch. He measures that Time A elapsed from takeoff to landing. For you traveling in the airplane, you measure that Time B has elapsed. The constant is related to the speed of the airplane where constant = 1 occurs when the airplane is moving at 0 speed, and constant = infinity occurs when the airplane is moving at the speed of light (the constant is an exponential speed measurement, relative to the speed of light).
So based on this equation, because you are going so extremely fast, you and your brother will disagree on how much time has elapsed from takeoff to landing. Your stopwatch will display less time than your brother.
Less intuitively, we can also speak of this in terms of length contraction, which from your standpoint the earth is squished and feels like you traveled less distance than what we know the earth’s distance to actually be from the stationary observer. To me this is less intuitive of an explanation.
>Why is that? My flight and his wait time should both be much much shorter since I was flying much much faster.
The constant in that equation works in such a way that no matter who’s speed, everyone will agree that the speed of light is 3e8 m/s. That’s just the way it is. Within a single frame of reference (a frame of reference are all objects traveling at the same speed relative to each other. Meaning, they all appear stationary to one another), then the laws of physics are the same for all off them. But only for the people within that frame of reference.
Second, the speed of light is the same for everybody, *regardless of their speed*. That’s kind of hard to wrap your head around, but that’s just the way it is. So, as a result of this, because you and your brother are moving at different speeds relative to each other, the two of you can’t agree on events that appear synchronized, and you also can’t agree on how much time has passed, or how much distance you have traveled. The only thing you can agree on is what the speed of light is.
Travel is a spectrum. At any moment, we are advancing through some combination of time and space. The more you travel through time, the less you travel through space. The more you travel through space, the less you travel through time. If you got going at .99c through space (very fast) you’d be advancing in time very slowly. Much slower than your brother who is on the ground NOT traveling super fast.
Everything in our universe is always moving at the rate of the universal constant (better known as the speed of light). This is the sum total of movement through our 4 Dimensional universe.
X+Y+Z+T=C
Where XYZ represents 3D space, T is time, and C is the universal constant. Due to the relatively slow nature of our traversal of 3D space, most of our motion is through time. Say you have 2 clocks synced exactly. One remains on the ground and the other is placed in a very high speed orbit. The equation must always equal C so if XYZ goes up then T must go down. From the ground’s perspective, the clock in orbit will appear to tick slower and it will fall behind the stationary clock.
>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.
General relativity says your example is wrong. For you, the flight takes 1 second as measured by your watch, but to your brother the trip takes lets say 10 minutes, by his watch. Or, if your brother sees the plane fly around the world in 1 sec, for you it’s even shorter. The frame of reference matters, this is why it’s called relativity, because time is not universal, it is relative to where you are when you measure it. It is just not possible to have a single device measure the same time in two places at different speeds. Plus you need to remember that your brother is not standing still, he is on a planet that has also moved hundreds or thousands of miles at the same time, relative to the sun, which is also moving at thousands of miles a second, relative to other suns and so on and so forth. Which is why we can’t have a universal clock or ruler…because time and distance are always measured against something else.
But it’s not just timekeeping devices that are effected, everything literally experiences time differently including the rate of your aging.
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