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We all have an intuitive notion that time itself "changes" - before it was the past, now it is the present, later it will be the future, and as time "changes" or moves forward what was the present before is now the past, and what was the future before is now the present. Moreover, we can hypothetically imagine situations in which this "change" goes by slower or even backwards (such as, time travel to the past). In other words, the derivative of time with respect to some other quantity, in these situations, is different than what it normally is.

My confusion however lies in that time is what measures the rate at which everything else changes. What, then, measures the rate at which time changes?

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marked as duplicate by Kyle Kanos, HDE 226868, John Rennie, Qmechanic Aug 3 '15 at 19:29

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ This is an old, old philosophical question, in physics the view is taken that time is that which you can measure by a clock, pragmatic as it sounds. $\endgroup$ – user81619 Aug 3 '15 at 13:58
  • $\begingroup$ Also, you could Google "supertime", which, I think, addresses your question more deeply than you may find on this physics question and answer site. Just be careful, there are lots of references to a video game with the same name. Best of luck with it $\endgroup$ – user81619 Aug 3 '15 at 14:36
  • $\begingroup$ What, then, measures the rate at which time changes? is nonsense. Rate is something that changes with time, so you are asking "How does time change with time?" which doesn't make sense. $\endgroup$ – Kyle Kanos Aug 3 '15 at 17:01
  • $\begingroup$ @KyleKanos I don't think you understood what I meant. I suppose I am referring to the flow of time. It's not flowing relative to any other parameter even though we can hypothetically change the direction of the flow (the example of backwards time travel, as I noted). In other words, when the other spacetime dimensions change we can describe this change with the velocity concept(ie. as a function of time) but we cannot do the same with the fourth dimension, time (in other words, describe time-flow).Also the question you linked wasn't helpful (the other one by John Rennie, though, was). $\endgroup$ – Insert Pseudonym Aug 3 '15 at 17:25
  • $\begingroup$ @JohnRennie Your answer to that question was perfect. This is therefore a duplicate of "Is there a proof of existence of time?". $\endgroup$ – Insert Pseudonym Aug 3 '15 at 17:28
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You may be speaking of the subjective experience of time, which is not a physics question, but rather a psychological one. Otherwise, the last paragraph of your question doesn't seem to make any physical sense. Time is an arbitrary standard by which a motion or a process is measured relative to other motions and processes.

For example, you can synchronize your time standard to this: http://www.time.gov. Each second the clock ticks corresponds to 9,192,631,770 cycles, the natural resonance frequency of a fountain of cesium atoms isolated from other radiation, cooled nearly to absolute zero, and energized by microwaves at the National Institute of Standards and Technology.

The cesium atom has a large difference between spin states of the single electron in its outer shell. When the spin state is altered it emits a photon and glows. When a fountain of energized cesium atoms are glowing in unison, the energy required to maintain the glow has a frequency of 9,192,631,770 cycles per SI second. Here's a more accurate explanation: http://www.nist.gov/pml/div688/how-nist-f2-works.cfm.

The precise apparatus that measures the frequency that produces the glow neither gains nor loses one second in 300 million years. So for practical purposes, it doesn't have a rate of change, which makes it an ideal candidate to measure the rates of change of other processes.

You may be thinking, "but what is the absolute substrate of ultimate duration through which the 9,192,631,770 cycles travel?" The carrier of this particular measure of duration is a fountain of cesium atoms. I don't know of anyone who's found anything beyond that.

Even as regular and unchanging as a cesium clock is, if you were to whizz it around the Earth at a relativistic speed, the cycles measured by that clock would not correspond to the cycles measured by an identical clock motionless relative to it. Two clocks ticking at the same frequency will not agree, depending on their relative motion and position in the Earth's gravity field. This prediction of special relativity has been confirmed by experiment: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html.

No universal "flow" of time has ever been discovered outside the space-time manifold, to my knowledge. The concept of time is a natural method used to compare motions and processes.

One great mystery, which might be the reason it's easy for people to think that time has an independent flow, is the Arrow of Time. The past seems a different world from the future. The Arrow of Time was explained by Boltzmann as the 2nd law of thermodynamics: One can distinguish a past from a future because the entropy of any thermodynamically isolated and mechanically closed system, and of the entire universe, will always increase from the past to the future. This is an attribute of matter, energy and space. But there is no "flow" of entropy separate from matter, energy, and space. Likewise, time is a method to compare motion and process. It's not apart from matter, energy, and space.

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