Time Dilation Formula / Calculator
19 comments
·January 10, 2025Workaccount2
Fascinating that if you could accelerate at 1.5g, it would only take you 18 years to reach the edge of the visible universe
ben_w
And with that kind of gamma factor, the CMB will start evaporating you via positron-electron pair production.
roter
How do you stop so you don't go whizzing past Alpha Centauri at near light speed? :)
alhadrad
I was wondering about this too—it's super interesting! Did you create this? Could you add graphs showing acceleration and deceleration? Also, this might be a dumb question, but how does mass factor into the energy calculations? I would love to see graphs that include the multiple stages of travel (acceleration and deceleration) as well as the mass of various kinds of fuel required for different propulsion systems such as chemical rocket, nucular etc.
ANewFormation
Relativistic mass increases are an observed effect. So if you're on the relativistic starship (as these are usually called) your mass does not change as your relative velocity does.
But for an at rest observer, your ship's mass would approach infinity as its speed approaches the speed of light. This is the reason the ship would never be observed as hitting the speed of light.
In practical terms this is also why particle accelerators can't just infinitely accelerate the particles - their apparent mass exponentially increases and so too does the amount of energy required to continue to accelerate them.
tokai
if you can accelerate at 1g you can also decelerate at 1g
dandanua
An intelligent alien race, living there, will be able to catch you, don't you watch sci-fi movies? The real question is from what you can get 4.13e+19 Jouls, required to reach Alpha Centauri in about 9 years of traveler's time.
aeve890
>An intelligent alien race, living there, will be able to catch you, don't you watch sci-fi movies?
The aliens on alpha Centauri are 12 ft tall blue hunter-gatherer humanoids. Not much of a help for your parking problems.
jvanderbot
Tangential, but I want to share the thought experiment that made time dilation click for me.
We know everything (every effect, etc) has a speed-of-light limit.
Imagine a metronome ticking out time. It ticks back and forth.
Put the metronome on a space ship. Now slowly increase the velocity of the space ship. As the space ship speed increases, the "pendulum" weight now has more and more velocity (the space ships velocity plus the back-and-forth velocity). The sum of those velocities cannot exceed the speed of light, so as the spaceship velocity increases, the metronome will tick more slowly (||x+y||<c and x-->c, right?), until, asymptotically, the metronome cannot move along its pendulum swing b/c the spaceship is moving at c.
(The metronome is a proxy for every chemical and physical process going on with you / your spaceship - they electro-chem-quantum-etc tick out their normal evolution, which must cease at c)
It's a clockwork view of the universe that might not be strictly true, but it settles some cognitive dissonance so I'm clinging to it like a life raft.
ANewFormation
I'm not one to nitpick tools to grok things but I think this could confuse more than help!
Because everything is relative to something else - and your example of the pendulum on a ship is suggestive of a "real" velocity, which does not exist.
I think a far easier scario to imagine is some ship flying away from Earth, and this ship has a magic button to release an impulse enough to give it a 10% of the speed of light boost in speed.
So what happens the tenth, or hundredth time that button is pushed? For those on the ship they would begin to observe (out the window) length contraction and of course time dilation - if they could somehow see Earth, everything would be in fast forward.
And vice versa, what happens on Earth? The ships observed speed would asymptotically approach the speed of light, but never reach it with its "apparent mass" approaching infinity, and thus the amount of velocity boost from each impulse approaching 0.
If our ship travels 20,000 light years in 40 years (from the perspective of those on the ship) then that would take a "real" 20,000 years from the perspective of those on Earth, who for many centuries would be able to track it moving away. If they somehow had a magic eye to look in the ship, things would seem to be going in extremely slow motion.
It's this nature of velocity (and dilation/etc) always and only being relative to something else that's really at the guts of all of this.
tmountain
"If our ship travels 20,000 light years in 40 years (from the perspective of those on the ship) then that would take a "real" 20,000 years from the perspective of those on Earth"
This part just breaks my brain. I've been reading about this stuff for decades, and it just does not compute. It's also a little funny because there's basically zero incentive for the folks on earth to send astronauts away at near-light speed, as they'd never realize the benefits of the mission.
jvanderbot
fair enough! Perhaps I arrived at this mental model due to an incorrect understanding of this result:
rolftheperson
This is not correct, I urge you to read a bit about Lorentz invariance, once you understand you will see why your statement does not make sense given special relativity is accurate.
Lorentz invariance means the laws of physics remain the same in all inertial reference frames. Also a spaceship going 99.9999…% the speed of light.
This leads to effects like time dilation, length contraction and the speed of light itself.
The metronome can keep going at any speed independent on the speed of its own reference frame.
jvanderbot
Yes, and for that metronome to continue "ticking" according to the normal laws of physics the distance must shrink to accommodate the limits on speed - Length contraction.
But, all the observable effects are the same under my "life raft" mental model: To an outside observer their time has stopped, to an inside observer it has not (I'm just thinking slowly). And the laws of physics are unchanged - as a function of time e.g., the number of clockwork steps per metronome tick.
I realized that my thought experiment is not special or unique. Here's the "light clock" version
09thn34v
interesting thought experiment... am i correct in understanding that for this to apply, the pendulums plane of movement must not be perpendicular to that of the ship itself? additionally, when the pendulum swing's direction is in the opposite direction of the ship, it would still move even in the case where the ship is moving at c, correct?
jvanderbot
That's the way I think of it, yes, but I think it generalizes - during the backward swing it would "go", but when swinging toward the front of the ship it would "stop" - forever.
dandanua
You cannot imagine what will be in the spaceship at the speed exactly c, the "asymptotic" thinking doesn't work here, just like some number sequences or functions don't have limits at some points.
At the speed of 0.9999c the metronome will be ticking exactly the same for an internal observer. An observer from the Earth will notice time dilation, so that ticking cycle will be slower than "normal". If the speed of spaceship remains constant, then the times of back and forth cycles will appear the same from Earth. Simply because same time intervals are delayed by the same amount in this case.
null
Interesting, although it seems unreasonable that you would be able to constantly accelerate for large distances without an essentially unlimited energy source.
Also, this is using special relativity only. Adding general relativity as you approach massive objects would be interesting.