If you ask any person about time, she/he will give you some answer. I suspect that it is extremely difficult, (if not impossible) to define time. Is there a definition of what it is in physics? Is it an "axiom" that has to be taken as it is, without explanations? I also noticed that the tag "time" has no pop-ups with comments/definition/explanations.
I am not a physicist, so take this with a massive grain of salt. I recently watched "What is Time?" on the new series, The Fabric of the Cosmos. I've also been reading a lot about this from other sources. I will try to summarize what is explained in that show in a way that makes sense.
There are some other aspects to the "what is time" question that I won't cover here much. They involve aspects of how time is measured in different parts of the universe based on the position of observers in relation to each other. The premise is that there isn't a single "now" moment that is universal. If you and an alien are stationary, you can be considered to be in the same "now". However, if you or the alien start moving around then you have to take into account how that speed is measured in relation to the other observer, and the "now" moment can either be in the future or the past of the other observer. It all ties into the relative nature of space and time, and is at the core of special relativity.
So, to the question of what is time (and putting all of the special relativity stuff on a shelf).
In general, what is presented is that time is what we perceive as the increase in entropy in the universe.
Entropy can be described as energy starting in a highly ordered state and moving into an increasingly disordered state.
A physical example, as an illustration, might be an ice cube with a drop of food coloring frozen in the center. As long as the ice cube is cold, all of the molecules of water remain frozen and the ice's crystalline structure is maintained. The molecules of the food color also remain locked into their position. The state of the entire ice cube can be consider a highly ordered state.
When the cube starts to warm up, the molecules in the ice begin moving around. The molecules in the food coloring begin moving too. The density of the food coloring decreases as its molecules spread around and mix with the water. When the energy level of the water and food coloring meet the level of energy outside, in one manner of thinking they have now entered their high-entropy state. They are throughly mixed and all the densities of h2o and dye molecules are evenly distributed. Since there are no more unequal densities, there isn't any lower-order state for them to be in.
Similar examples can be given for gases, or rocks, or plasma, or whatever. Pick any medium and the same principal applies. The biggest difference is simply the rate at which the entropy of a given system increases.
When you look at the equations that govern physics, they are solvable in either "direction". If you drop a glass and it breaks, if you reversed the directions and momentum of all the particles in the glass it should reassemble. The equations work in either direction. This means that there isn't anything really saying that energy has to move from a highly ordered to lesser ordered state. Why this happens, and why we don't spontaneously see things happen in reverse, is still a question that needs solving.
So back to time.
Current thinking is that the universe started in a highly ordered state. This means that at the exact first Planck moment of the Big Bang, all of the energy in the universe existed all together in an extremely highly ordered state. All of the forces were unified, as was the energy that became matter, antimatter, dark energy and dark matter, etc. Everything we are now was just one thing. (I have no idea what the one thing was. Like I said, SALT.)
So the idea is that, in a conceptually similar way the ice cube melted, during the last 13.7 billion years all of the energy from that initial state has been moving from a highly ordered state to a disordered state.
In the process of becoming disordered, all of the initial energy has formed the forces that guided the development of everything from subatomic particles to everything we see and are today.
As living creatures, we perceive the passage of energy through all of the physical systems around us as time. I am not entirely comfortable with this definition, as I think a barren rock in the middle of space between two galaxies would still undergo an increase in entropy regardless of whether there was a living thing to witness it or not. Again, I'm not a physicist and am simply trying to understand this stuff like many others.
So time, under this model of entropy and disorder, is not a thing in itself. Its not a force, its not something that can be pulled apart and studied with a particle accelerator. Its a term we use to describe the passage of energy through physical systems and how those systems change as a result.
So does time end? If we can say that time had a beginning as a perfectly ordered thing of energy, does time have an end? In a way, it might.
If we go back to the ice cube analogy, eventually all of the molecules in the water and dye reach an equilibrium. If left alone for long enough without external influence, the movement of molecules will cease. (Notice that in this analogy, I'm not referencing Brownian motion or movement from quantum particles emerging from the vacuum. Its just an analogy.)
When cosmologists take into account the discovery of dark energy, it paints a very said picture for the fate of the universe. Dark energy is a loose term that was defined in the last decade or so to describe observations that all galaxies are moving further and further apart. The further away a galaxy is, the faster its moving.
Scientists don't know yet what dark energy actually is, but we can see its effects in much the same way as we can see the effects of dark matter. What dark energy appears to be is some universal force that is causing everything in the universe to spread out. It was originally predicted, in a fashion, by Albert Einstein.
In his calculations, Einstein found that the universe should either be expanding or contracting. In his day, astronomers had not yet discovered that galaxies were moving away from each other. It was commonly believed that the universe was static and eternal. As a way to correct his calculations, he added an additional mathematical constant that balanced out his equations to account for what was believed to be that static universe. It was only a few years later that Edwin Hubble made the first red-shift observations that indicated the universe was, indeed, expanding.
Einstein was never very happy with his Cosmological Constant, and said,
"It is to be emphasized, however, that a positive curvature of space is given by our results, even if the supplementary term [cosmological constant] is not introduced. That term is necessary only for the purpose of making possible a quasi-static distribution of matter, as required by the fact of the small velocities of the stars."
Observations of the ever increasing rate of expansion of the universe were only made in the last 15 years or so. Its source, dubbed "dark energy", hasn't been explained yet.
When you take into consideration what dark energy means for the universe and time, here's the scenario. In something like one hundred billion years, all of the galaxies of the universe will be so far away from each other that they will be moving faster than the light they emit can reach each other. If this sounds like it conflicts with the proverbial, "nothing can travel faster than light", remember that we're talking about the expansion of space itself. Space is the fabric in which all energy and matter exist, and it can and has expanded faster than the speed of light in the past. Physicists call it inflation and it helps to explain why the universe looks the way it does now. I won't go into that too much though.
What it means is that to any future intelligent creatures in the far future, when they look out into their skies they won't see the abundance of the cosmos we see now. All they will see is an infinite black sky. The left over radiation from the Big Bang, the Cosmic Background Radiation, will have spread out so much as to be undetectable. They will not be able to observationally deduce the history of the universe as we have. To them, their universe will be just their single galaxy. They may attempt to come up with an explanation of the universe that fits the evidence they can see, but will be hopelessly wrong.
Going even further into the future, trillions of years from now (sorry, I don't have an accurate estimate for this. Its a long, long, long time though) and dark energy will become the pervading force in the universe. It will become stronger than gravity and will force any surviving collections of galaxies, star systems, and planets to fly apart. It will become stronger than the strong and weak nuclear forces and will pry apart atoms at the subatomic level.
Black holes will dominate the late universe for a long time. Eventually, even these will evaporate away their energy into space and cease to be. Look up "Hawking radiation" if you want to learn more about that.
What will be left is an immensely huge void of space filled very sparsely with subatomic particles. Particles will be spread so thinly that they will almost never interact with each other. Even if they happened to be close enough, the nuclear forces would not be able to overcome dark energy to interact with each other. Essentially, the universe will be a cold and empty place.
In many ways, when all of the particles themselves evaporate away into the quantum vacuum, time can be considered to have ended. When the energy of the universe finally has smoothed out to such a low entropy state that nothing can interact, time is done as we perceive it.
On a positive note...
I love to look up at the stars and know that I am lucky to be alive at a time in the universe where everything is still young. Interesting things are still happening and we are able to discover really interesting, important, and beautiful things about the place we exist in.
There are so many things left to be discovered that current ideas about the ultimate fate of the universe could be drastically wrong. Its very hard to say, because even the folks that have dedicated their lives to studying the science involved in these questions are still observing, experimenting, and trying to come up with explanations. Its a great time to be a scientist.
Time is like colour in that it's difficult to explain to someone who's time-blind: A clock and a mind is to time what an eye and a brain is to colour. To someone that is partially time-understanding to a sufficient degree, I can say that time is that quality which orders identical events at the same location as occuring before, simultaneously or after one another.
Unforntunately, for any such definitions, it will depend on the individual situation in which the concept is being used. Typically physicists use Einstein's definition that "time is what is measured by a clock" but I think this is a bit too generic; after all, it is possible to use the physical dimensions of the clock to measure all sorts of things. Using this definition you have to then define what you mean by clock and it just gets more complicated from there.
My own personal definition of "time" would run something like:
Time is that property whereby one state of a well-defined system is transformed into another.
Again, the definitions of the words used becomes a complicating factor. I use "well-defined system" in a sense similar to how mathematicians use "well-behaved function." I mean a system that is logically coherent and consistent and follows the fundamental laws of nature.
I should probably mention that the word "state" is also very misleading as the phrase "equation of state" for a system typically refers to a property that does not change with time. For example, the equation of state for an ideal gas is given by the ideal gas law $PV = nRT$. I would then say that time is the property of a system for which an equation of state can be written whereby the variables in that equation are transformed to different values.
Neuroscience tells us our perceptions are stored in short term memory and after much processing, are backdated in time to give the perception of "now" at a later time. This can take many many milliseconds later, even close to a second. Or imagine watching a family movie filmed years or decades ago and becoming so engrossed in it so that it seems to be happening all over again in the present. When is now? The neurosurgeon Penfield stimulated parts of the brains of some patients and they relived events from years or decades before as if they were happening in the present. Now is not when you think it is.
In near death experiences, a person reviews memories of their life flashing by. How do you know your now isn't actually happening much later and backdated? Let's say decades in the future, you upload your mind to a computer and a replay of your life memories is made on some playback machine to be observed by some computer mind. It would seem backdated to 2011, would it not, even if it's much later.
This process and go on over and over until the end of time. Maybe "now" is a playback at the end of time at the end of the universe and we have been fooled about the actual date. Whatever it is observing the playback at the end of the world sustains us over and over again by the act of observation. Being, with no becoming.
Each paradigm shift leads to a change in the conception of time. Newton introduced the notion of absolute time. That was hardly a mainstream view before him. Special relativity overturned the nature of time, and so did general relativity after that. When quantum gravity is cracked, the nature of time will need to be revised again appropriately. Quantum gravity may or may not be the last word in fundamental physics. If not, we might expect yet another overturning of what we think time is.
At any rate, defining what time is prematurely runs the risk of stifling future paradigm shifts.