Q: What is time?

Physicist: All philosophy aside, the best answer is due to Einstein, who said (after lots of thought) that “Time is what clocks measure”.

The term “spacetime” gets bandied about a lot.  And you may have been lead to (correctly) suspect that time and space are closely related, and even a little interchangeable.  Time is still not exactly like another spacial dimension (like the usual 3).  Which is why physicists will tend to say that we live in “3+1 dimensions”, for 3 spacial dimensions, and 1 time dimension.  If someone says that time is “the 4th dimension”, keep in mind that there’s an asterisk attached.

If you’re trying to measure a distance D between two events x_1 and x_2 in 1 dimension you’ll find that D = \sqrt{(x_1-x_2)^2}, which is just another way of writing “the absolute value of x_1 - x_2“.  In 2 dimensions D = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}, which is the Pythagorean theorem.  And in 3 dimensions D = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2 + (z_1 - z_2)^2}.  Notice a pattern?  The kick-ass thing about each of these equations is that no matter how you shift or spin around the coordinates, D will always stay the same, which is exactly what you’d expect.  If you measure a yard stick at any angle, anywhere in the world, you’ll always measure the same length.  “D” is the only equation that makes that happen.

In 3+1 dimensions (the standard spacetime) L = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2 + (z_1 - z_2)^2 - C^2(t_1 - t_2)^2}.  Here the x’s, y’s, and z’s are the coordinates in space of event 1 and event 2, the t’s are the time coordinates of those events, and C is the speed of light.  “L” is the measure of distance in spacetime, but to keep everything straight it’s called the “spacetime interval”.  You may have noticed that sometimes when you use this equation that you’ll be taking the square root of a negative number.  Don’t worry about it.  The power of the Interval, L,  is that, like the D above, L remains unchanged by changing location, rotating, and even movement (holy crap), and it is the only equation that does all that.  So hidden away in all that wordiness is the big difference between space and time:

The time term in L has a minus sign.  As far as physics goes, that’s about it.  All of the horror and weirdness of special relativity (all the time dilation, length contraction, ruined simultaneity, all of it) can be tracked back to that minus sign.  If you wanted to, you could define time to be the direction in spacetime that has a minus in front of it in L.  I don’t think many people do that (not many grounded people at least), but they could if they really wanted.

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10 Responses to Q: What is time?

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  4. Daniel Lauzon says:

    I would just like to say we may never truly unstand how the universe works but I for 1 am amazed at the beauty and that is all I really need to understand.

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  6. Aieou says:

    Speaking of that L, Greg Egan wrote a book series (Orthogonal) where time is also a plus sign, not a minus. It’s a direction like any other, and that allows all sorts of shenanigans, including the speed of light depending on its frequency.

  7. NXTangl says:

    @Aieou: Yeah, Orthogonal is pretty great…reading the explanations for why the Riemann universe has the properties that it has was the first time I really groked special relativity. (The drawings helped.)

    And, of course, it also proves that if you flip the minus sign, you actually get even weirder crap. Easy time travel by accelerating until you turn around in spacetime is cool, but the fact that stillness is the most energetic state of a particle is decidedly not. And you still get the problems with simultaneity, time dilation, etc., they’re just all in the opposite directions (lengths increase rather than contract, relativistic space travelers experience more subjective time than stationary ones) and add new insanity (K * q1 * q2 * cos(kr) / r^2, kinetic energy as negative ‘actual’ energy, no massless particles…yeah…)

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  10. Ron Williams says:

    Time is not a dimension.

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