8 ms·

Time Dilation Formula / Calculator

50 points by mpclarkson 2y ago

deleted 2y ago
[deleted]
roter 2y ago
How do you stop so you don't go whizzing past Alpha Centauri at near light speed? :)
- dandanua 2y ago
  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 2y ago
    >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.
  - jdawg777 2y ago
    If you use fission, Uranium 235 has 83.14 TJ/kg. So you would need about 500 metric tons of it.
- tokai 2y ago
  if you can accelerate at 1g you can also decelerate at 1g
  - thfuran 2y ago
    Only if you can turn around or vector your thrust.
- alhadrad 2y ago
  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 2y ago
    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.
    - Rhapso 2y ago
      I really really wish they would call it "apparent mass". It is entirely an observer effect. Its entirely "that ship throws propellant out the back but they don't end up going as fast as Newton thinks it should, so it must have more mass than we think"
      - whatshisface 2y ago
        If there are many objects moving in many directions, you won't be able to find a reference frame in which the mass of the system is equal to the sum of the rest masses of the objects.
        Rhapso 2y ago
        correct. This is not a contradiction. 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.
- headcanon 2y ago
  yeah, I'd love to see an option to include a deceleration step and what the time debt looks like from there.
jvanderbot 2y ago
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.
- 09thn34v 2y ago
  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 2y ago
    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.
- rolftheperson 2y ago
  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.
Workaccount2 2y ago
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 2y ago
  And with that kind of gamma factor, the CMB will start evaporating you via positron-electron pair production.
  - tomtom1337 2y ago
    I didn’t understand this. What is it about the gamma factor that will cause the cosmic microwave background to evaporate you?
    - floxy 2y ago
      I'm assuming that ben_w is referring to the blue shift in the CMB that you will see in front of you. And pair production is the process of turning sufficiently high energy light into matter. https://en.wikipedia.org/wiki/Pair_production https://en.wikipedia.org/wiki/Pair_production https://www.imperial.ac.uk/news/149087/scientists-discover-turn-light-into-matter/ 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?
      - ben_w 2y ago
        Correct. > 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 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).
waynecochran 2y ago
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.
monster_group 2y ago
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.
- sigmoid10 2y ago
  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.
- nyrikki 2y ago
  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.
  - Osmium 2y ago
    Can you expand on this? I was only ever taught the "turn around" explanation.
    - nyrikki 2y ago
      All I can offer without going into the weeds is that it is not the shape of the paths, but mearly the relative length of two paths though spacetime that matters. 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.
WhitneyLand 2y ago
The wording is misleading: [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 2y ago
  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.
osculum 2y ago
The whole website and the way FAQ is worded give AI generated vibes
- mpclarkson 2y ago
  Why do you say that?
  - osculum 2y ago
    I think lately I look at anything new with my guard up. 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.
ziofill 2y ago
this is fine, but I would like to see the deceleration for the second half of the journey
- mpclarkson 2y ago
  I do intend to add this to the calculator
mpclarkson 2y ago
Woah, thanks for all the comments on this little calculator I built yesterday afternoon. I'll digest everything and see what improvements I can make!
pgt 2y ago
Would be cool if it calculated the mass of various propellants required to provide the necessary energy :)

50 points by mpclarkson 2y ago

deleted 2y ago

[deleted]

roter 2y ago

How do you stop so you don't go whizzing past Alpha Centauri at near light speed? :)

dandanua 2y ago
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 2y ago
  >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.
- jdawg777 2y ago
  If you use fission, Uranium 235 has 83.14 TJ/kg. So you would need about 500 metric tons of it.
tokai 2y ago
if you can accelerate at 1g you can also decelerate at 1g
- thfuran 2y ago
  Only if you can turn around or vector your thrust.
alhadrad 2y ago
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 2y ago
  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.
  - Rhapso 2y ago
    I really really wish they would call it "apparent mass". It is entirely an observer effect. Its entirely "that ship throws propellant out the back but they don't end up going as fast as Newton thinks it should, so it must have more mass than we think"
    - whatshisface 2y ago
      If there are many objects moving in many directions, you won't be able to find a reference frame in which the mass of the system is equal to the sum of the rest masses of the objects.
      - Rhapso 2y ago
        correct. This is not a contradiction. 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.
headcanon 2y ago
yeah, I'd love to see an option to include a deceleration step and what the time debt looks like from there.

jvanderbot 2y ago

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.

09thn34v 2y ago
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 2y ago
  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.
rolftheperson 2y ago
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.

Workaccount2 2y ago

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 2y ago
And with that kind of gamma factor, the CMB will start evaporating you via positron-electron pair production.
- tomtom1337 2y ago
  I didn’t understand this. What is it about the gamma factor that will cause the cosmic microwave background to evaporate you?
  - floxy 2y ago
    I'm assuming that ben_w is referring to the blue shift in the CMB that you will see in front of you. And pair production is the process of turning sufficiently high energy light into matter. https://en.wikipedia.org/wiki/Pair_production https://en.wikipedia.org/wiki/Pair_production https://www.imperial.ac.uk/news/149087/scientists-discover-turn-light-into-matter/ 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?
    - ben_w 2y ago
      Correct. > 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 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).

waynecochran 2y ago

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.

monster_group 2y ago

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.

sigmoid10 2y ago
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.
nyrikki 2y ago
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.
- Osmium 2y ago
  Can you expand on this? I was only ever taught the "turn around" explanation.
  - nyrikki 2y ago
    All I can offer without going into the weeds is that it is not the shape of the paths, but mearly the relative length of two paths though spacetime that matters. 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.

WhitneyLand 2y ago

The wording is misleading: [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 2y ago
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.

osculum 2y ago

The whole website and the way FAQ is worded give AI generated vibes

mpclarkson 2y ago
Why do you say that?
- osculum 2y ago
  I think lately I look at anything new with my guard up. 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.

ziofill 2y ago

this is fine, but I would like to see the deceleration for the second half of the journey

mpclarkson 2y ago
I do intend to add this to the calculator

mpclarkson 2y ago

Woah, thanks for all the comments on this little calculator I built yesterday afternoon. I'll digest everything and see what improvements I can make!

pgt 2y ago

Would be cool if it calculated the mass of various propellants required to provide the necessary energy :)