Time Dilation Formula / Calculator
timedilationformula.com
timedilationformula.com
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.
That is awesome, I've always wondered about special relativity in a flat torus world. Do you have a recommendation for reading more about this?
Proper time and proper acceleration is possibly a pathway in flat spacetime?
Learning that the order, timing, and sometimes causality of events is also relative tends to be a barrier, thus some of these didactic half truths are useful.
The "Einstein train paradox" is the classic intro to the relativity of simultaneity if you aren't familiar.
In the SR case, proper acceleration is possibly the better option.
Because I lowekey believe this to be true but don't have means to prove it.
The aliens on alpha Centauri are 12 ft tall blue hunter-gatherer humanoids. Not much of a help for your parking problems.
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.
A reference frame is definitionally a point from which you would measure an "apartment mass". The rest mass isn't relevant to a reference frame where that mass isn't at rest. This is true at all scales.
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.
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 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.
This is the reason that I find things like the Fermi Paradox no more than mildly interesting.
It implicitly assumes we have a sound understanding of the fundamentals of the universe yet each revolutionary discovery we make soundly refutes that assumption.
And with the vast number of 'known unknowns' and an unknowable number of unknown unknowns, it seems ridiculous to imagine we're anywhere near the end of revolutionary discoveries.
s/earth/Milky Way/
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.
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
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.
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.
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.
https://en.wikipedia.org/wiki/Pair_production
https://www.imperial.ac.uk/news/149087/scientists-discover-t...
But I've never given thought to the fact that for some observers the microwave background are low energy photons, and for others, they could be high enough in energy to produce electron-positron pairs. Seems like another one of those relativity related paradoxes. Only fast-moving observers (relative to the CMB) are seeing constant pair production from the CMB photons?
> Seems like another one of those relativity related paradoxes. Only fast-moving observers (relative to the CMB) are seeing constant pair production from the CMB photons?
Both observers agree about pair production.
Pair production obeys conservation of momentum and energy — although the equations allow both to be conserved with two photons interacting, the practical effect here is CMB photons interacting with the spaceship hull: the observer in the CMB-rest-frame will see very low energy photons doing this with a high-velocity hull, and the spaceship frame will see very high energy photons doing this with a stationary (to them) hull.
That said, I'm told that accelerating observers can, during the acceleration, disagree about what particles exist around them: https://en.wikipedia.org/wiki/Unruh_effect
(Hmm, and now I'm wondering if the Unruh effect is really as described — if different quantum fields contribute at different rates, or have cut-offs at different scales, that would automatically also create something that, if you squint, will look a bit like an approximation of MOND… sadly, this is beyond my competence at this time).
In this case, first the FAQ gave me those vibes. Why? Hard to tell. If I have to force myself explain it, it has the kind of didactic and dumbed down tone that I usually get from chatgpt when I ask questions about complex topics.
Then I went to your blog and saw the entries were mostly (I assume) AI generated as well. I know it doesn't necessarily follow that because of that this website has been mostly created by ChatGPT as well. But I saw it as some kind of weak confirmation.
Finally some of the JS code comments such as "Plot Charts" right before a "PlotChart" also made me think this.
As I said, I'm just extra cautious about this stuff lately. You are the creator, you know how you did it. If my intuition was wrong I wholeheartedly apologize for making that statement. I could probably have expressed it in a kinder way. I know that it's not easy to create it something now and put it out there for people to see it and criticize it.