One can always subdivide time into smaller units, at least in theory. Hours to minute to seconds.
But if this were to continue infinitely, it would result in a paradox. If the time between one second and the next second can be subdivided in two, and then that half can be subdivided in two again, we arrive at a situation where an infinite set of progressively smaller half-way points can be generated between any two points in time.
This would mean that there are an infinite number of moments that occur in one second. But by definition, an infinite is a number without end - it would be impossible to ever 'complete' an infinity. Therefore it should also be impossible to complete an infinite set of events within a finite period of time (n.b. calculus does not resolve this paradox, it uses limits to show what an answer must be, not that an infinite set can be completed)
Alternatively, one can imagine that there is a minimum unit of time, just as there is hypothetically a minimum unit of space, colloquially referred to as the Planck time. One can imagine this as being similar to a pixellated screen. Your screen is composed of a number of discrete pixels, or tiny lights, which make images.
In theory then, time would advance forward in small jumps. If we imagine the planck time being one second in length, it would be as if we erratically jumped forward in all of our actions from one second to the next as if we were watching a very slow stop-motion film.
However this poses its own set of challenges, because when you discretize time in this way, it is the same as viewing time as a collection of frozen snapshots of the world, in much the same way that each frame in a stop-motion film is not moving at all.
But no motion is possible when time is frozen still. And forces can not transfer between objects if there is no time. If our world really was a series of snapshots, forces couldn't act 'between' the snapshots in the same way one frame in a stop-motion film can't affect another. They exist in different times, in much the same way a 2-dimensional object in a 3D space can't access or influence another 2-dimensional object placed at a different height in the same 3D space.
In order to avoid a paradox, we must accept that time must be discretized. But in order for this picture to make sense, it must be the case that all energy and/or matter does not actually affect itself through the laws of physics, but rather has a pathway that is predetermined in the same manner as a stop-motion film.
Thoughts?
But if this were to continue infinitely, it would result in a paradox. If the time between one second and the next second can be subdivided in two, and then that half can be subdivided in two again, we arrive at a situation where an infinite set of progressively smaller half-way points can be generated between any two points in time.
This would mean that there are an infinite number of moments that occur in one second. But by definition, an infinite is a number without end - it would be impossible to ever 'complete' an infinity. Therefore it should also be impossible to complete an infinite set of events within a finite period of time (n.b. calculus does not resolve this paradox, it uses limits to show what an answer must be, not that an infinite set can be completed)
Alternatively, one can imagine that there is a minimum unit of time, just as there is hypothetically a minimum unit of space, colloquially referred to as the Planck time. One can imagine this as being similar to a pixellated screen. Your screen is composed of a number of discrete pixels, or tiny lights, which make images.
In theory then, time would advance forward in small jumps. If we imagine the planck time being one second in length, it would be as if we erratically jumped forward in all of our actions from one second to the next as if we were watching a very slow stop-motion film.
However this poses its own set of challenges, because when you discretize time in this way, it is the same as viewing time as a collection of frozen snapshots of the world, in much the same way that each frame in a stop-motion film is not moving at all.
But no motion is possible when time is frozen still. And forces can not transfer between objects if there is no time. If our world really was a series of snapshots, forces couldn't act 'between' the snapshots in the same way one frame in a stop-motion film can't affect another. They exist in different times, in much the same way a 2-dimensional object in a 3D space can't access or influence another 2-dimensional object placed at a different height in the same 3D space.
In order to avoid a paradox, we must accept that time must be discretized. But in order for this picture to make sense, it must be the case that all energy and/or matter does not actually affect itself through the laws of physics, but rather has a pathway that is predetermined in the same manner as a stop-motion film.
Thoughts?