The concept that a swing could function as a time machine at all stems from a part of Einstein’s theory of relativity known as “Time Dilation”. In simple terms, it states that time can appear to pass differently for observers in different relative velocities. Or in other words, if you are travelling at fast speeds, you will effectively time travel into the future, but for everyone else, time will pass normally. Now the reason you don’t go to the year 2123 when going out for a walk is that time dilation is only noticeable at speeds close to the speed of light. But here in this paper, we don’t care about how insignificant it may be, we care about FACTS. To calculate time dilation, we can use the formula:
\[ \Delta t' = \frac{\Delta t}{\sqrt{1 - \frac{v^2}{c^2}}} \]
Where:
Δt′ is the dilated time for the moving observer.
Δt is the proper amount of time passed for a stationary observer.
v is the relative velocity between the two observers.
c is the speed of light.
(Note: ‘Δ’ is a greek letter called “delta”. It usually means a change in something, or the rate of change of something. The little apostrophe is pronounced “prime”. So you would say Δt′ as delta t prime.)
now let’s get to calculating how good of a time machine is a swing, first we need to know the average “velocity” of a swing. Now figuring out the average velocity of a swing doesn’t make too much mathematical sense, as a swing is following a periodic path, so half of the time its velocity is negative (depending on how you look at it) so everything cancels out. So if we just figure out the average speed (speed and velocity is different, velocity has direction, speed has no direction) and just give it no direction. it will work fine for us since the formula doesn’t exactly care about direction (so the formula probably should have asked for speed, not velocity but why ask me, ask the German dude who invented it). Let’s suppose that it is “travelling” at 2 m/s, and let’s suppose we stay in our “time machine” for an hour. So plugging these value into the formula we get:
\[ \Delta t' = \frac{3600\, \text{s}}{\sqrt{1 - \frac{(2^2 \, \text{ms}^{-1})}{(299792458^2 \, \text{ms}^{-1})}}} \]
\[ ≈3600.000000000000080110804 s \]
So that would mean you would time travel approximately a whopping 0.000000000000080110804 (that is 13 zeros after the decimal place) seconds into the future or 80.11 Femtoseconds. Just for some context, it takes about ~500 billion times more time for your eyes to blink. Or put in a different way, light (the fastest thing in the universe) travels XX nanometers in that kind of time! Now just for fun, lets calculate this for other “vehicles”. In the table below, we are supposing you will be in them for 1 hour.
| Name of Vehicle | Speed (m/s) | Time Traveled (in Picoseconds) |
|---|---|---|
| Human | 4 | 0.32 picoseconds |
| Average old boring car | 30 | 18.0249 picoseconds |
| Airplane | 250 | 11.25 nanoseconds |
| International Space Station | 8000 | 1.28 microseconds |
| Voyager 1 | 17000 | 5.788 microseconds |
(note: a picosecond is one one-trillionth of a second. For context it takes 40 billion picoseconds for a human eye to blink, a nanosecond is a thousand times bigger than a picosecond, and a microsecond is a thousand times bigger than that. So for a human eye to blink, it takes 40 million nanoseconds & 40,000 microseconds.)
so that all good and dandy, but what is god’s world does time have to do with speed, and how does the speed of light relate to any of this?? And i'll leave that as an exercise to the reader! Try searching around with "Time dilation" on the internet as a starting point!