Physical time is public time, the time that clocks are designed to measure. Psychological time or phenomenological time is private time. It is perhaps best understood as awareness of physical time. Psychological time passes swiftly for us while we are enjoying reading a book, but it slows dramatically if we are waiting anxiously for the water to boil on the stove. The slowness is probably due to focusing our attention on shorter intervals of physical time. Meanwhile, the clock by the stove is measuring physical time and is not affected by anybody's awareness. When a physicist defines speed to be the rate of change of position with respect to time, the term "time" refers to physical time. Physical time is more basic for helping us understand our shared experiences in the world, and so it is more useful than psychological time for doing science. But psychological time is vitally important for understanding many human thought processes. We have an awareness of the passage of time even during our sleep, and we awake knowing we have slept for one night, not for one month. But if we have been under a general anesthetic or have been knocked unconscious and then wake up, we may have no sense of how long we have been unconscious. Psychological time stopped. Some philosophers claim that psychological time is completely transcended in the mental state called "nirvana."
Within the field of cognitive science, one wants to know what are the neural mechanisms that account not only for our experience of time's flow, but also for our ability to place events into the proper time order. See (Damasio, 2006) for further discussion of the progress in this area of cognitive science. The most surprising scientific discovery about psychological time is Benjamin Libet's experiments in the 1970s that show, or so it is claimed, that the brain events involved in initiating free choices occur about a third of a second before we are aware of our choice. Before Libet's work, it was universally agreed that a person is aware of deciding to act freely, then later the body initiates the action.
Psychologists are interested in whether we can speed up our minds relative to physical time. If so, we might become mentally more productive, get more high quality decision making done per fixed amount of physical time, learn more per minute. Several avenues have been explored: using drugs such as cocaine and amphetamines, undergoing extreme experiences such as jumping backwards off a tall tower with bungee cords attached to the legs, and trying different forms of meditation. So far, none of these avenues have led to success productivity-wise.
Any organism's sense of time is subjective, but is the time that is sensed also subjective, a mind-dependent phenomenon? Without minds in the world, nothing in the world would be surprising or beautiful or interesting. Can we add that nothing would be in time? If judgments of time were subjective in the way judgments of being interesting vs. not-interesting are subjective, then it would be miraculous that everyone can so easily agree on the ordering of public events in time. For example, first, Einstein was born, then he went to school, then he died. Everybody agrees that it happened in this order: birth, school, death. No other order. The agreement on time order for so many events is part of the reason that most philosophers and scientists believe physical time is an objective phenomenon not dependent on being consciously experienced. The other part of the reason time is believed to be objective is that our universe has a large number of different processes that bear consistent time relations, or frequency of occurrence relations, to each other. For example, the frequency of a fixed-length pendulum is a constant multiple of the half life of a specific radioactive uranium isotope; the relationship does not change as time goes by (at least not much and not for a long time). The existence of these sorts of relationships makes our system of physical laws much simpler than it otherwise would be, and it makes us more confident that there is something objective we are referring to with the time-variable in those laws. The stability of these relationships over a long time also make it easy to create clocks. Time can be measured easily because we have access to long term simple harmonic oscillators that have a regular period or “regular ticking.” This regular motion shows up in completely different stable systems when they are disturbed: a ball swinging from a string (a pendulum), a ball bouncing up and down from a coiled spring, a planet orbiting the sun, organ pipes, electric circuits, and atoms in a crystal lattice. Many of these systems make good clocks.
Aristotle raised this issue of the mind-dependence of time when he said, "Whether, if soul (mind) did not exist, time would exist or not, is a question that may fairly be asked; for if there cannot be someone to count there cannot be anything that can be counted..." [Physics, chapter 14]. He does not answer his own question because, he says rather profoundly, it depends on whether time is the conscious numbering of movement or instead is just the capability of movements being numbered were consciousness to exist.
St Augustine, adopting a subjective view of time, said time is nothing in reality but exists only in the mind's apprehension of that reality. In the 11th century, the Persian philosopher Avicenna doubted the existence of physical time, arguing that time exists only in the mind due to memory and expectation. The 13th century philosophers Henry of Ghent and Giles of Rome said time exists in reality as a mind-independent continuum, but is distinguished into earlier and later parts only by the mind. In the 13th century, Duns Scotus clearly recognized both physical and psychological time.
At the end of the 18th century, Kant suggested a subtle relationship between time and mind--that our mind actually structures our perceptions so that we can know a priori that time is like a mathematical line. Time is, on this theory, a form of conscious experience.
In the 20th century, the philosopher of science Bas van Fraassen described physical time by saying, "There would be no time were there no beings capable of reason" just as "there would be no food were there no organisms, and no teacups if there were no tea drinkers," and no cultural objects without a culture.
The controversy in metaphysics between idealism and realism is that, for the idealist, nothing exists independently of the mind. If this controversy is settled in favor of idealism, then time, too, would have that subjective feature--physical time as well as psychological time.
It has been suggested by some philosophers that Einstein's theory of relativity, when confirmed, showed us that time depends on the observer, and thus that time is subjective, or dependent on the mind. This error is probably caused by Einstein's use of the term "observer." Einstein's theory does imply that the duration of an event is not absolute but depends on the observer's frame of reference or coordinate system. But what Einstein means by "observer's frame of reference" is merely a perspective or framework from which measurements could be made. The "observer" does not have to be a conscious being or have a mind. So, Einstein is not making a point about mind-dependence.
excerpt taken from http://www.iep.utm.edu/t/time.htm#H2
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