Lorentz Transformations with a Mechanical Time-Globe [video] | Hacker News Reader

Lorentz Transformations with a Mechanical Time-Globe [video]

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A Lorentz transformation can be written as a rotation matrix using hyperbolic trig functions instead of regular ones. This machine works by having grooves in the shape of hyperbolic lines that the blocks follow.

Yup. Whereas rotations involve two spatial directions (the plane of rotation), a Lorentz boost involves a spatial direction and a temporal direction. Also, the analogue of a rotation angle for a Lorentz boost is a rapidity (hyperbolic angle).

I did a javascript version here if anyone wants to try the software equivalent :)

http://forwardscattering.org/post/36

The device works just by following/‘reading’ the pre-cut Lorentz-encoding grooves cut into the base of the device. There’s nothing computational going on in the grid of mechanisms. Replace the base with non-hyperbolic grooves and you’d get non-relativistic transformations. It just follows the template encoded for it.

There's nothing computational going on in an ordinary globe either, but it also encodes a kind of rotation in its physical arrangement.

I think this is part of the point: that it's not much more complicated than an ordinary rotation.

No one ever claimed it was a general-purpose computer. Like all special-purpose computers, it performs a specific computation when used.

That’s actually a fascinating point because I both in one sense am not denying the device’s generality whilst in another sense indeed defending it’s generality: it might be said that I’m actually saying it’s general because you can run those grids upon virtually any engraved backplane while at the same time since reading off the backplane is all the device does I’d be arguing it isn’t general at all.

This is the mechanical analogue computer equivalent of a digital discrete computer’s bi-dimensional lookup table.

This is awesome! (More in the spirit of visualizing Special Relativity: https://www.testtubegames.com/velocityraptor.html)

I think I'm in love

Very accessible!

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