Take length, turn 90 deg. and you have width.
Turn another 90 deg. in repect to the first two and you have depth. Imagine ANOTHER 90 deg. turn in respect to the three, and that unseen direction is time.
Say we assume time to progress at a uniform rate; neither speeding up nor slowing down. A point in 3-space becomes a line in 4-space. A line becomes a plane. a plane becomes a solid. And in 4-space a 3- dimensional solid becomes…
uh…a tesseract (Right?)
Anyway…
Measuring time as a distance between two pointsmeasuring one second apart, what speed does that point travel alonf time?
FWIW, a tesseract is a specific 4-d shape, the analogue of a cube. A 3-d solid becomes a hyperplane in 4-d space. I can’t answer the speed question, though.
My understanding of Einstein’s special relativity of time is not that time is a dimension in the same sense that three orthagonal linear dimensions are. That is to say, there is something more similar between three distance dimensions than between them and time. Geometrically, you can’t make a 90 degree turn from some path and travel along time. This should be obvious in one sense: you can choose any direction to call your first dimension, and you can choose any direction in the plane perpendicular to that to call your second, and only then is there one specific direction that must be considered as the next dimension.
A better way to consider four orthagonal dimensions is to say that each of them is made up primarily of distance but also contains some time, and all four of them have the same properties but have their own isolated degrees of freedom. Arbitrarily one can select another set of four with same properties and isolated degrees of freedom. The purpose of this treatment is to be able to describe coordinate systems that work correctly from the point of view of an observer with a location and velocity (necessary because if a system of mathematics breaks down for anybody, then nobody should trust it).
Another note: your question actually implies something that isn’t true (because it’s built into our language and most people’s understanding of the world). You can’t say you measure two points at different locations one second apart - it only appears that you can because you don’t realize what’s going on. Any observer’s understanding of whether events in different locations happen simultaneously is not correct for everybody else. This is a feature of the way the universe is put together, not the trivial artifact of how long it takes you to observe things (which is also there).
I don’t think of time in this way; I don’t think it’s a geometric dimension like the ‘other’ 3.
Anyway, how could you measure the speed of time’s passing?, that would be like measuring a centimetre in centimetres; time progresses at exactly one second per second.
Now as to whether time passes at a constant rate… that’s an interesting almost metaphysical question; if time slows down, so does everything; so time still passes at one second per second.
But of course time is not constant, as Einstein showed us. Only the speed of light is constant, everything else is relative. Else there’d be no twin paradox.
This sort of reminds be about the 19th cent. thing about “ether”, one of the deceased theories. Ether was a supposed medium through which light, being a wave, travled, rather like water does for a ripple.
Maybe our approach to time suffers from the same error. We seem to be trying to concieve some absolute background, time iself, as opposed to (all the stuff that happens). We measure time only by actions: tickings of clock, humming of electrons, motions of moon. Since we measure time only by relative motion, whats wrong with thinking that time itself does not exist as a dimension? Would this do any damage to the equations of physics?
I believe that time is a 4th dimension. That its speed is dependent on the speed of light. The speed of light is dependent on the vacuum energy density. So if you get a drop in the speed of light you get an increase in the speed of time to compensate. And because the speed of time is relative to the vacuum energy density you can have two different points in the universe with different speeds of time. So you could probably measure time in the following units:
v(t) = planck length/speed of light
So the speed of time would currently be around:
3.3x10^-44 time units.