- #51

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My take on it is this. We could think of spacetime as free from units, if we liked, but there is a fundamental difference between timelike dimensions and spacelike dimensions, and to be able to discuss them in like terms we need a "currency conversion". The currency conversion is like the answer to the question "how many chunks of time are equivalent to one chunks of space?" The answer is pretty much 1. One chunk of time is equivalent to one chunk of space, which is why physicists like to use units like year and light-year, or Planck time and Planck length, where the exchange rate is 1:1.

If you chose other units, selected for their convenience in other realms (like working out how much time you have before the commercials are over and how far you need to run to put the kettle on), then you end up with a different exchange rate, such as 1:3x10^8

But really, the answer is still 1. One fundamental chunk of time equals one fundamental chunk of space.

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Here is another way of looking at it. The pig exchange. Making the assumption that two pigs are identical, a pig from the US is worth one pig from Australia.

The exchange rate is therefore 1:1. But we find carrying around pigs difficult, and they are really difficult to push into one of those vending machine slots, so instead we have a pocket full of coins.

A pig's worth of coins in the US may amount to 0.0517 megadimes while a pig's worth of coins in Australia might amount to 15500000 millicents. The exchange rate then is 1:3E8

But really, the exchange rate is still 1 pig = 1 pig (relatively speaking).

cheers,

neopolitan