Author's description of twin paradox is incorrect. In fact, the paradox is not described at all. The paradox is that since motion is relative then from both twin's perspective the other twin goes on a journey and ages slowly. So why it is that on returning, only the traveling twin has aged slowly? The answer is that both twins indeed see each other age slowly but for the traveling twin to come back they have to slow down to zero and reverse direction. At that moment the frame is no longer inertial. While turning around, the traveling twin will see the stationary twin age very quickly (enough to catch up with their earth age), so when they meet there's no paradox. For each of them the other has aged as per their observations.
The twin paradox holds in a Pacman universe where there is no change in direction.
The main issue with the twin paradox is that it demonstrates where our euclidian intuition fails us.
There are several interpretations on how to resolve it, but they are all just flawed lenses, intended to help you along a curriculum until you understand the math, and also understand the limitations of intuition.
The 'turn around' explanation is part of that and unfortunately often sold as the ultimate resolution.
This is an extremely detailed explanation of the twin paradox that covers things from multiple angles, even situations that involve no acceleration: https://www.youtube.com/watch?v=vv5d5KHKDVE
Are you suggesting that two people in a shared inertial space when venture into other intertial frames but ultimately end up in a same frame later will agree on how much time has passed in between?
Because I lowekey believe this to be true but don't have means to prove it.
The whole site seems very much like it is AI generated. In particular the css is very close to what I've seen ChatGPT generate when I used it to create similar things.
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.
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.
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.
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.
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.
Maybe it's completely wrong, but I always thought about it as a dimension, and if you view time as the 4th dimension.
For example imagine just 2 dimensions. If you can only travel at the speed of light you could go at the speed of light in the x-axis, or at the speed of light in the y-axis. But if you want to go diagonally in both dimensions, you have to split your travel speed up between both such that when added together they don't exceed light speed.
If we view time as a dimension, then either you can stay at rest and travel through time at "full speed", or you can travel in the x, y, or z, axis at up to light speed, but in order to do so, you need to "give up" some of your traveling through time dimension. Such that your x+y+z+time "speed" do not exceed the speed of light.
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.
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?
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.
[When you move through space quickly, you move through time slowly]
Why all the “you”? This makes it sound like you would personally experience slowness. Could be clarified to say it’s only according to the perception of others.
What you will experience is the apparent size of the Universe itself changing in proportion to the time dilation along your direction of acceleration. It is necessarily an observable phenomenon due to the constancy of the speed of light.
monster_group|1 year ago
nyrikki|1 year ago
The main issue with the twin paradox is that it demonstrates where our euclidian intuition fails us.
There are several interpretations on how to resolve it, but they are all just flawed lenses, intended to help you along a curriculum until you understand the math, and also understand the limitations of intuition.
The 'turn around' explanation is part of that and unfortunately often sold as the ultimate resolution.
nayuki|1 year ago
pkoird|1 year ago
Because I lowekey believe this to be true but don't have means to prove it.
euroderf|1 year ago
mpclarkson|1 year ago
sigmoid10|1 year ago
roter|1 year ago
dandanua|1 year ago
alhadrad|1 year ago
tokai|1 year ago
headcanon|1 year ago
jvanderbot|1 year ago
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|1 year ago
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.
rolftheperson|1 year ago
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.
SirMaster|1 year ago
For example imagine just 2 dimensions. If you can only travel at the speed of light you could go at the speed of light in the x-axis, or at the speed of light in the y-axis. But if you want to go diagonally in both dimensions, you have to split your travel speed up between both such that when added together they don't exceed light speed.
If we view time as a dimension, then either you can stay at rest and travel through time at "full speed", or you can travel in the x, y, or z, axis at up to light speed, but in order to do so, you need to "give up" some of your traveling through time dimension. Such that your x+y+z+time "speed" do not exceed the speed of light.
dandanua|1 year ago
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.
09thn34v|1 year ago
waynecochran|1 year ago
Also, this is using special relativity only. Adding general relativity as you approach massive objects would be interesting.
WhitneyLand|1 year ago
[When you move through space quickly, you move through time slowly]
Why all the “you”? This makes it sound like you would personally experience slowness. Could be clarified to say it’s only according to the perception of others.
timewizard|1 year ago
unknown|1 year ago
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mpclarkson|1 year ago
Workaccount2|1 year ago
ben_w|1 year ago
pgt|1 year ago
ziofill|1 year ago
mpclarkson|1 year ago
osculum|1 year ago
mpclarkson|1 year ago