Is there a proof that time is a 4th dimension?
If it is, then why not measure it in units of the previous three? Logical right?
How many seconds is a temporal meter?
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$\begingroup$ The idea of Space-time was first proposed in 1908 by Hermann Minkowski, unifying space and time, following the discovering of special relativity by Einstein in 1905. $\endgroup$– TrimokCommented Jul 30, 2013 at 9:45
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3 Answers
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How many seconds is a temporal meter?
Approximately 3.33564095 nanoseconds
answered Jul 29, 2013 at 22:45
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Sure, it'd be $1/c$ seconds, which is exactly $1/299792458\text{ s}$. Although, really, there's no point because time is defined as a multiple of $c$, anyways.
As for proof that time is the fourth dimension, there's no 'proof' like any scientific theory (there's just evidence) and unlike mathematics, but one fairly large point of (fairly accessible) evidence is in your GPS. Look up "General Relativity and GPS."
It's not hard to imagine people's reactions if their GPS told them they were in the middle of Antarctica flying 500 metres in the air.
answered Jul 29, 2013 at 23:05
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$\begingroup$ That is the answer I'd expected. Not sure how you got to it, but I figured that if in 2d every 1m you move forward you get a freedom to move 1m to left or right. So, you must gain additional freedom moving from 3d to 4d. The per second 1m would be the maximum freedom of movement in any direction with a speed of light. So, 1/C. Good to hear that I got it right, thank you for your answer. However, one thing is still unclear, how can one move, even hypothetically in 1d, 2d and 3d without having time as a component? $\endgroup$ Commented Jul 30, 2013 at 20:20
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$\begingroup$ @LexPodgorny not quite sure what you mean by "...I figured that if in 2d every 1m you move forward you get a freedom to move 1m to left or right..." As for the other case concerning time, it is possible to move in space with time as a separate component, like, for example Newtonian mechanics, but what Relativity says (or what comes as a consequence of) is that the four dimensions are 'intertwined,' so to speak, because the geometry of spacetime as a whole (all four coordinates as one space) is dependent on the momentum and the energy of the matter within it. $\endgroup$ Commented Jul 30, 2013 at 20:39
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$\begingroup$ In 1d you can only change X coordinate, in 2d every time you change X you have an option of changing Y as well at a same time. $\endgroup$ Commented Jul 30, 2013 at 20:46
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$\begingroup$ > "time is defined as multiple of c" This does not make sense. Time is what clock measures and unit of time is second. Second is a specific number of periods of radiation of caesium. It is the meter that is defined as distance that light travels in 1/299792458 seconds. $\endgroup$ Commented Aug 3, 2018 at 10:32
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The number of seconds it takes for light to travel the distance. One formulation is to make this an imaginary value to explain the metric sign convention, but it's more conventional to explain this via different covariant and contravariant representations, since the "imaginary space" explanation doesn't agree with simple things like a complex norm.
answered Jul 30, 2013 at 1:55
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4$\begingroup$ The $i$ gets in there in some formulations and not in others because it is not fundamental. It is just one of several ways to make the interval have the right form; a feat which can also be accomplished by using a metric tensor or by simple fiat. $\endgroup$ Commented Jul 30, 2013 at 2:25
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$\begingroup$ That's not a criticism on my part, just a note about why your answer differs in that respect from the others. Not sure why this has been voted down as the answer is fine. $\endgroup$ Commented Jul 30, 2013 at 15:20