"The brief answer to this question is, 'Nobody knows.' Certainly there is no experimental evidence in favor of such a minimal unit. On the other hand, there is no evidence against it, except that we have not yet found it. There are no well-worked-out physics theories incorporating a fundamental unit of time, and there are substantial obstacles to doing so in a way that is compatible with the principles of General Relativity. Recent work on a theory of quantum gravity in which gravity is represented using loops in space suggests that there might be a way to do something roughly along these lines--not involving a minimum unit of time but rather a minimum amount of area for any two-dimensional surface, a minimum volume for any three-dimensional region in space and perhaps also a minimum 'hypervolume' for any four-dimensional region of space-time."
William G. Unruh is a professor in the department of physics and astronomy at the University of British Columbia. He offers this reply:
"There is certainly no experimental evidence that time--or space for that matter--is quantized, so the question becomes one of whether there exists a theory in which time is quantized. Although researchers have considered some theories in which there is a strict quantization of time (meaning that all times are an integer multiple of some smallest unit), none that I know of has ever been seriously regarded as a viable theory of reality--at least, not by more people that the original proponent of the theory.
"One could, however, ask the question in a slightly different way. By putting together G (Newton's constant of gravity), h (Planck's constant) and c (the velocity of light), one can derive a minimum meaningful amount of time, about 10-44 second. At this temporal scale, one would expect quantum effects to dominate gravity and hence, because Einstein's theory links gravity and time, to dominate the ordinary notion of time. In other words, for time intervals smaller than this one, the whole notion of 'time' would be expected to lose its meaning.
"The biggest obstacle to answering the question definitively is that there exists no really believable theory to describe this regime where quantum mechanics and gravity come together. Over the past 10 years, a branch of theoretical physics called string theory has held forth the greatest hope, but it is as yet far from a state where one could use it to describe the nature of time in such a brief interval."
Another, somewhat iconoclastic perspective on this question comes from William G. Tifft, a professor of astronomy at the University of Arizona:
"There are several ways to answer this question. 1) There is no conclusive evidence that time is quantized, but 2) certain theoretical studies suggest that in order to unify general relativity (gravitation) with the theories of quantum physics that describe fundamental particles and forces, it may be necessary to quantize space and perhaps time as well. Time is always a 1-dimensional quantity in this case. 3) My own work, which combines new theoretical ideas with observations of the properties of galaxies, fundamental particles and forces, does suggest that in a certain sense time may indeed be quantized. To see this we need some background information; in this scenario, time is no longer 1-dimensional!
"My colleagues and I have observed that the 'redshifts' of galaxies seems to be quantized. The redshift is the apparent shift in the frequency of light from distant galaxies. This shift is toward the red end of the spectrum and its magnitude increases with distance. If redshifts were due to a simple stretching of light caused by the expansion of the universe, as is generally assumed, then they should take on a smooth distribution of values. In fact, I find that redshifts appear to take on discrete values, something that is not possible if they are simply due to the cosmic expansion. This finding suggests that there is something very fundamental about space and time which we have not yet discovered.
"The redshifted light we observe is consists of photons, discrete 'particles' of light energy. The energy of a photon is the product of a physical constant (Planck's constant) times the frequency of the light. Frequency is defined as the reciprocal of time, so if only certain redshifts are possible, then only certain energies are present, and hence only certain frequencies (or, equivalently, time intervals) are allowed. To the extent that redshifts of galaxies relate to the structure of time, then, it suggests an underlying quantization.
"In our newest theoretical models we have learned to predict the energies involved. We find that the times involved are always certain special multiples of the 'Planck time,' the shortest time interval consistent with modern physical theories. The model we are working with not only predicts redshifts but also permits a calculation of the mass energies of the basic fundamental particles and of the properties of the fundamental forces. The model implies that time, like space seems to be three dimensional.
We now think that three-dimensional time may be the fundamental matrix of the universe. In this view, fundamental particles and objects--up to the scale of whole galaxies--can be represented as discrete quantized structures of 3-d time embedded within a general matrix of 3-D time. The structures seem to be spraying radially outward from an origin point (time = 0): a big-bang in 3-D time. Any given chunk, say our galaxy, is flowing outward in 3-D time along its own 1-dimensional track, a 1-D timeline. Inside our (quantized) chunk we sense only ordinary 3-D space, and the single 1-dimension time flow of our chunk of 3-D time.
"Now we can finally attempt to answer the original question, whether time is quantized. The flow of time that you sense corresponds to the flow of our chunk of 3-D time through the general matrix of 3-D time. This time is probably not quantized. Both ordinary space and ordinary 'operational' time can be continuous. On the other hand, the structure of the time intervals (frequencies and energies) that make up the 3-D chunks of time which we call galaxies (or fundamental particles) does appear to be quantized in units connected to the Planck scale. In the 3-D time model, space is a local entity. Galaxies are separated in 3-D time, which we have misinterpreted as separation in space.
"What matters in 3-D time is the time intervals needed to send signals between galaxies; separation of galaxies in time, not space, is fundamental. The general matrix of 3-D time appears to contain discrete 'particles' of 3-D 'time.' These particles are the galaxies. When photons travel between galaxies, the result is a quantized structure that we see as quantized redshifts. When photons travel within a single 3-D temporal structure, we see only ordinary 3-D spatial dynamics and continuous flowing time. Believe it or not, it seems that we can have it both ways--the underlying structure of time can be 3-D and quantized, but structures in time can flow continuously."