Is time continuous or discreet? Can we divide time into ever smaller units or is there a smallest time unit?

Question

Is time continuous or discreet? Can we divide time into ever smaller units or is there a smallest time unit?

Answer 1

The normal answer, and the one which all conventional theories of physics are based on is that time is modelled as a real number. In relativity theory intervals of time are defined as a kind of generalised distance between two points in a 4-dimensional geometry. This 4-dimensional geometry (aka space-time) is defined using real numbers, resulting in distances always being real numbers, and so there ends up being no smallest distance.



Quantum mechanics and quantum electrodynamics have the same continuum underlying space and time, but the complication is that whilst time is continuous it is not possible to _measure_ time scales less than a certain amount. But still, the equations of the theory are still written in terms of differentIAL (c.f. difference) equations and are thus fundamentally continuous.



The impossibility of measuring suficiently small time scales has led _some_ theorists to consider the possibility that spacetime is actually a lattice of discrete points, thus making space and time fundamentally quantised. It has the advantage that if you make the additional assumption that the overall size of the universe is finite then integrals over the whole of space (which might not converge) end up being just finite sums, which always converge. Still, the theory has a long way to go simply to catch up with present-day theories, and is certainly not mainstream theoretical physics.

Answer 2

Yes, there is a smallest unit of time, Planck time. The reason Planck time is the smallest unit of time is because it is the amount of time it takes light to travel the Planck length, which is the smallest length that can be measured (below this length, measurements don't make sense as objects below that size are governed by quantum mechanics)

Answer 3

time is continous. No matter what you use to measure time, a second, millisecond(.001s), nanosecond(.000000001s), you can always move the decimal place one more place. You can have an infinite number of zeros. There are no real 'intervals' of time, we just make them up in attemps to measure or understand it, but the measurements don't even actually exist because it's continuous. We just use the measurements of time to find out when something happened relative to something else.