# Looking for an Explanation of Time Dilation I can program into a CLI calculator [closed]

Thanks but I can code it, not what I am looking for

I am just looking for an explanation or equation that is clear and not too heavy in parlance for how these trips would be to people of Earth and onboard a ship traveling 10 light years at 10%, 20%, 30%, 40% & 50% the speed of light.

• This might be better asked in Physics, but you'll need to show that you've done some homework. I recommend you check en.wikipedia.org/wiki/Length_contraction and hyperphysics.phy-astr.gsu.edu/hbase/Relativ/tdil.html to start with; you're really asking about "Lorentz contraction". – Jeff Zeitlin Jun 11 '18 at 12:03
• If you're looking for a subjective description of the effects - it's not entirely clear from your question - then you might want to see if you can find a copy of George Gamow's Mr. Tompkins in Paperback (yes, that George Gamow). – Jeff Zeitlin Jun 11 '18 at 12:08
• Welcome to the site, Thomas. Note that not every user is equally familiar with jargon common to a particular field; it is best to clarify as much as possible about your question. For example, I have no idea what a "CLI calculator" is, and searching the Internet returns this question as result #3. Additionally, it is unclear what your goal with this question is. To learn about a certain formula/equation? To describe the experience of people traveling at a fraction of the speed of light? If you haven't already, feel free to take the tour to get a better understanding of the site. – Frostfyre Jun 11 '18 at 12:29
• Time dilation calculators already exist on the Internet, the odds are good that one of them will include a description of the math used to calculate the effects. – JBH Jun 11 '18 at 13:44
• In fact, it might be easier to go here and simply duplicate their Javascript in the time-honored tradition of industrial espionage. Note the precision warning later on the page, though. – JBH Jun 11 '18 at 14:24

## 1 Answer

Long story short, the equation you are looking for is this:

$${\Delta t'={\frac {\Delta t}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}}$$

Where $t$ is time, $v$ is a relative velocity and $c$ is the good old speed of light in a vacuum.

Explanation: supposing you and a friend sync clocks while both of you are at rest in relation to each other. You then change speeds relative to each other. If you are able to peek at their clocks from a distance, then, whenever you have measured a span of time $\Delta t$ on your clock, you will notice a span of time $\Delta t'$ has passed on theirs.

So for example, if you spend one hour moving at half the speed of light relative to your friend...

$${\Delta t'= {\frac {1h}{\sqrt {1-{\frac {(\frac {c}{2})^2}{c^{2}}}}}}} = {\frac {1h}{\sqrt {1-{\frac {\frac {c^2}{4}}{c^{2}}}}}} = {\frac {1h}{\sqrt {1-{\frac {c^2}{4c^{2}}}}}} = {\frac {1h}{\sqrt {1 - \frac{1}{4}}}} = {\frac {1h}{\sqrt {\frac{3}{4}}}} \approx \frac {1h}{0.866} \approx 1.154h \approx 1h 10m$$

That is, for every one hour that passes for you, it seems like approximately one hour and ten minutes have passed for your friend. Notice that this is reciprocal. Your friend will also notice that time is passing differently for you, just the same. When one hour has passed for him, he will see your own clock marking a span of approximately one hour and ten minutes.

The lengthy, parlance heavy explanation can be found in Wikipedia.

• Thank you this was what I needed, sorry I wasn't hyper descriptive! I will credit you as Renan for the consultation. Appreciate it immensely. – Thomas Highbaugh Jun 11 '18 at 16:41