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Time changes depending on speed and gravity. But, how does one measure the speed of time? It is logically measurable, but speed is a unit of distance over time. The speed of time would mean time over time which doesn’t make sense. (To measure the speed of time a timeframe would have to be set as the true timeframe, let’s say that’s just Earth’s current timeframe and ignore complications).

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Even though it is so important to humans in everyday life it can be surprising to learn that the flow of time doesn't exist in physics. Since it doesn't exist there is no unit in which to measure it. I have explored this and related ideas in What is time, does it flow, and if so what defines its direction? and you might find it interesting to read my answer there.

There is a sense in which we can sometimes define a relative flow of time for example when discussing time dilation in relativity. When calculating an object called the four velocity we encounter quantites such as $dt/d\tau$ where $t$ is coordinate time and $\tau$ is proper time, and this ratio is what we generally call the time dilation. This is a dimensionless number so it does not have any units. But although it's tempting to interpret the ratio as a comparison of flow rates, i.e. differences in the rate at which time flows, the calculation does not involve any concept of time flowing.

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    $\begingroup$ But people talk about time going slower as you approach the speed of light; slower implies lower speed. What would the proper phrasing of this concept be? $\endgroup$
    – Notchmath
    Dec 29 '17 at 5:53
  • $\begingroup$ @Notchmath: Yes, we do talk use phrases like time going slower and indeed I'm guilty of this myself. It's a convenient shorthand for something rather more complicated. What actually happens is that the two coordinate systems, ours and the moving objects, have been rotated out of alignment so a pure time displacement in our rest frame is a mixture of a time and space displacement in the other frame. $\endgroup$ Dec 29 '17 at 6:06
  • $\begingroup$ @Notchmath Read John's other answer carefully. You can describe that phenomenon by simply saying observers moving relative to one another will measured the differences between the time co-ordinates of pairs of events differently. Notice how, by promoting time to a co-ordinate, you get rid of any talk of its "flowing", so one can indeed describe a great many physical phenomenons without reference to "flow". Certainly, this is true for General Relativity descriptions of the physical world. Whether or not the notion of time "flow" can be banished from all descriptions of physics is a .... $\endgroup$ Dec 29 '17 at 6:07
  • $\begingroup$ For more on this have a look at What is time dilation really? $\endgroup$ Dec 29 '17 at 6:08
  • $\begingroup$ So you could describe it as the angle between space and time? $\endgroup$
    – Notchmath
    Dec 29 '17 at 6:08
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There is no speed of time, per se. Time is actually measured from phenomena that repeats itself in a smooth way. So you count the repetitions to know the time. Initially, people counted the rotation of earth on its axis and around the sun to define time. In that way they DEFINED one second to be 1/86400 of one day. i.e. And one day to be 1/365 of one year, and so on.

So they reverse the Frequency actually to get the time. This principle is still the primary way we get time.

Measurement of accurate timekeeping is a very essential to do science. So the rudimentary definition of time based on the rotation of earth around itself or around the sun is outdated now. And has been replaced by using pendulums. But they eventually show errors due to many physical factors. So more accurate timekeeping device came into place e.g. Fountain Clocks. Currently, Cesium Fountain Clocks are the ideal watch, you can say. They shoot extremely slow Cs atoms against the gravity to one meter height and the time it would take comeback to its initial position under the gravity is BY DEFINITION assigned ONE SECOND and in that one second scientists measured radiations emitted by Cs atoms vibrate 9192631770 times.

So there is no speed of time but frequency of time you can say.

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