“*Can you build me a hyperbolic time chamber? I’ll buy you a coke.*”

Friend of mine while we were walking down the street.

Almost 110 years ago our view of time was changed forever. Time wasn’t part of the immutable stage of life but it was an active player. We finally understood how to squeeze time and how to stretch it thanks to a German patent officer named Albert Einstein.

Einstein’s most famous thought experiment regarding time dilation is the Twin paradox. We have two twins, one goes into a spaceship that moves near the speed of light for a few hours and when he comes back to Earth, years have passed and his twin has aged significantly.

The formula that regulates this time dilation is the following.

Where t is the proper time (in the twin paradox the time that passes on Earth) while t_{0} is the time for the moving observer.

Now let’s talk about the hyperbolic time chamber. In the Manga and Anime Dragon Ball Z there’s a special room where you can spend a year in there and only one day would have passed on Earth. My friend wants me to build him that, so let’s substitute our values in and see what we get.

As you can tell the equation doesn’t make sense we end up with an imaginary velocity. With what we know of physics so far we can’t make a hyperbolic time chamber (Zach Weinersmith is right – ‘Science: ruining everything since 1543’)

In our equation we assumed that we are not moving, but in reality we are – so what if I make sure my friend gets into a perfectly still space? If we combined the Earth’s motion around the Sun, the Sun’s motion around the centre of the Milky Way and the proper motion of our Galaxy (assuming these velocities are perpendicular to each other) our combined velocity is 360 km s-1. The Sun’s orbital speed around the Galaxy is 200 km/s. The speed of the Earth’s rotation is 0.27 km/s (1000 km/h) at the latitude of Sheffield (53 degrees), the average galaxy in a group moves at 300 km/s.

So we are constantly moving at about 0.1 % of the speed of light. When we use the formula to work out how much extra time he’d have if he spent an entire year inside my time chamber, the answer is not promising. Over an entire year he would have gained only 15 second on us. Better stick to an old fashion approach to time management.

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Reblogged this on "Matematicandoinsieme" di Maria Cristina Sbarbati.