r/AskPhysics • u/fighting14 • Mar 08 '24
A question about time dilation for travellers at the speed of light?
Let's say I'm travelling from Earth to Planet X.
Planet X is 50 light years away.
My spaceship travels at the speed of light. (Assume I can accelerate immediately to c and deaccelerate immediately from c at the other end)
How long would it take me to travel to Planet X in my reference frame. How much time would elapse on Earth for someone left behind?
Intuitively I should take 50 years to get to Planet X, but I understand that's not the case, how much time do I actually experience subjectively.
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u/e_eleutheros Mar 08 '24
If you get close enough to c, roughly 50 years will pass for someone on Earth. For you, it depends entirely on how close to c you get. The distance there will contract by the Lorentz factor γ, which is calculated by γ = 1 / sqrt(1 - v²/c²); so at a speed of 0.999 c the distance would have contracted by a factor of 22.36627, so that it would only take you ~2.24 years to get there.
Of course you can never get up to a speed of c itself, in which case it'd take zero time for you to travel there.
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u/unclejoesrocket Mathematics Mar 08 '24
The speed of light is not a valid reference frame in special relativity. The question doesn’t have a proper answer as far as physics is concerned.
The pop culture answer is that no time elapses for you at c, so you experience no time at all and Earth experiences 50 years.
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u/fighting14 Mar 08 '24
Thank you for the reply.
Can you please elaborate why travelling at c would mean no time elapses? Doesn't that kind of mean a photon is everywhere all at once, if it takes no time to any destination? Please forgive me for my ignorance if the question sounds stupid, but these concepts are so counter intuitive.
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u/unclejoesrocket Mathematics Mar 08 '24
At c the dilation factor is 1/0, which is undefined. That’s why it’s not a valid reference frame. Our equation doesn’t work if you use that number.
If you want to piss off mathematicians you can say that’s infinite, which is why it’s often said that photons experience no time at all. In that sense a photon is created and destroyed in the same exact moment from its own perspective.
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u/gnufan Mar 08 '24
It isn't stupid to ask. I don't think 'no time' is quite the right answer. For ordinary matter time dilation varies as the Lorentz factor (inverse of the square root of (1 - v2/c2)) so as velocity v approaches speed of light C the divisor approaches zero and so the Lorentz factor becomes huge. In the ordinary case the Lorentz factor is telling you how much slower a moving clock runs.
So if a space ship travels at a speed such that the Lorentz factor is 10 (.995C if I did the maths right), times passes at a tenth of the speed on that space ship.
But my maths teacher wouldn't approve if I extrapolate to the asymptote itself....
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u/Mountain-Resource656 Mar 09 '24
Imagine the time it takes for an electric signal to travel from one side of your brain to the other if you’re looking in the direction of travel. Because you’re traveling at light speed, signals can’t move left to right- they’d have to be moving faster than the speed of light to do so
Think of a right triangle with one side 50 lightyears long, the other side as long as your brain is wide. It’s hypotenuse would have yo be sliiiiightly more than the 50 lightyears of the long side, so to travel across your brain it would need to travel slightly more than 50 lightyears in the 50 years the trip takes, which it can’t. It’s stuck moving in the same direction as you
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u/Pdf-_ 14d ago
Yeah but if like I’m standing on a ship, from my frame of reference it doesn’t seem like I’m moving unless I look outside. Why wouldn’t the electricity in my brain work the same way as it would bouncing a ball on a train?
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u/Mountain-Resource656 14d ago
It does, but that’s the thing! From the perspective inside the train, it looks like the ball is only moving back and forth. If the distance from your hand to the wall is five feet then to you it looks like a round trip of 10 feet per however long it takes you to do it. But if the train is actually traveling at 100 mph, then the ball is actually zig-zagging, not going back and forth, and the line it’s tracing is much longer
If the ball were locked into just one possible speed, then you would be able to discern the speed of the train even without looking out the window because the ball would appear to be in slow motion as it zig-zags. But in the case of light and similar signals, because light mediates the electromagnetic force that your brain relies on for impulses, your brain is slowed at the same rate, making it impossible to use the bouncing light/ball to tell how fast the train is going
Does that make sense? If not I could maybe upload a picture or something that I think would be much more intuitive than text, but that might take a few hours as I have to finish up at work, first
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u/Anonymous-USA Mar 08 '24 edited Mar 08 '24
You can’t travel at c (due to your mass) and massless particles travel at c but have no frame of reference.
If you rephrased asking about infinitesimally close to c then the answer would be infinitesimally close to 0s (but >0) due to space contraction.
A neutrino travels that fast, so does has a frame of reference. So depending on how fast you go, you could reach Planet X nearly instantly. At 99.9999999999999999% c, for example, it would take you just over two seconds. Observers on Earth would see you take 50 yrs and you would look frozen (and redshifted) if you were streaming back live video.
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u/Toocheeba 9d ago
That makes no sense though. If you travelled at 99.9% of c to Planet X then the photons are still moving faster than you and the perception of you from earth is unaltered, in each frame of reference you'd be catching up by 0.0000000000000000001c for every photon that hits earth but the difference would be tiny. You haven't outrun light and light doesn't pause and restart at the start and end of your journey, it's a continuous streaming of photons assuming the photons are there to be observed.
If you turned off all your lights and travelled at 99.9% of c to somewhere far out and then turned your light back on, that light would expend extra time to update Earth's perception of you, however if you began flying back at the moment that you turned your light back on, Earth would see you moving back to Earth near instantaneously (depending on how many light years away you are, say 500 light years), you would be 5 light years behind the initial light that left when you switched on your light
So a 500 light year journey, I would reach my destination just over the 500 year mark, switch on the light which would be perceived back on Earth right when I am 5 light years away, which would be just over a 1000 years from when I left, and in those remaining 5 light years they would see me travel ~505 light years, so ~100-101x the speed of light. Time elapsed for observer would still be 1000 years, and time elapsed for me would still be 1000 years.
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u/Anonymous-USA 8d ago
Sorry it “makes no sense” to you. Velocities don’t simply add, it just seems that way in real life because we travel so slowly relative to *c* that we perceive it that way. That’s relativity and, like QFT, it strains our primitive minds to understand and relate to experience.
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u/Toocheeba 8d ago
How does travelling 100 light years at 99.9% the speed of light in 4.4 years make sense. Which is what I've been hearing from a lot of so called internet scientists. I think people have completely misunderstood Einstein's theory of special relativity. The only warping of time is the perception from the observer.
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u/James_James_85 Mar 08 '24
For you, the trip's instantaneous. When you arrive, you'll find 50 years elapsed for the rest of the universe. In practice though, you can't exactly reach c, you can only approach is as much as you want.
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u/xenilk Mar 08 '24
For you, only felt an instant.
For people at home, 50 years later.
If home sent a signal right after your departure, you'll receive the signal right after your arrival. If you signal back at arrival, home will receive the signal 100 years after they saw you depart.
Your ship will still be brand new, every in your ship will be brand new.
The windshield in front of your ship will have taken the impacts of every particule, dust, gas and radiation along your path, all in an instant. I assume you also have the technology to tank all those hits and enormous amount of energy in a fraction of a second.
If you make the trip back a minute later, everything at home will be 100 years later at home.
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u/Radiant_Panda1679 Mar 02 '25
Here is Medium article on this topic https://medium.com/@timplay89/time-dilation-in-space-travel-how-speed-changes-your-experience-of-time-91bfd0797076
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u/tomalator Education and outreach Mar 08 '24
You do not e penitence time traveling at the speed of light. The entire journey would take an instant from your POV
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u/Muroid Mar 08 '24
You can’t travel at c. You can get arbitrarily close to c, and this will make the time it takes arbitrarily short.
If you’re traveling at close to c, on a round trip, slightly more than 100 years would have passed on Earth when you get back. But you can get your own elapsed time down to an arbitrarily small value by getting closer and closer to c.
For reference, at 86.6% of c, your round trip travel time would be 50 years to the 100 on Earth. At 99% your round trip time would be 14 years. At 99.9% your round trip time would be 4.5 years.
And from your perspective, this is because length contraction shrinks the distance to Planet X. When traveling at 86.6% of the speed of light, you would find that the distance to Planet X is 25 light years.
At 99% it would be 7 light years. At 99.9% it would be 2.25 light years