Jayjay

I can easily envision a timeline that is composed of discrete moments: t0, t1, t2, ..., tn, ... etc. Let's define the state of the whole universe at time tn as Sn. Now, if we assume that this little universe of ours is deterministic, Sn is fully determined by S(n-1) which is determined by S(n-2) , and so on until S0, which may either be the starting value or depend on S(-1), it doesn't really matter.

However, when I'm trying to wrap my mind around the possibility that time is not a discrete sequence of events, but rather a continuum, I can't figure out how that could work out exactly. If state of the universe at time t=1.0 is S(1.0), what is that state determined by? (I'm assuming determinism again... but I don't think that has anything to do with this problem.)

auto-da-fe

An arguement against discrete is that, for time to be discreet, it would never change (only appear to) and therefore, could not be considered "time". For time to pass at all, it would have to be continuous, otherwise, you would have a situation described by Zeno of Elea as noted below:

link

Since the passing of time can be described by motion, for there to be motion, there has to be time. For time to exist, it must be continuos.

Jayjay

I'm not talking about time "changing" at all... that would be assuming that there's some sort of pointer that moves through time and determines which is the "present". I find that an absurd notion.

Sylvan Wizard

According to quantum mechanics, time is quantized. An interval in time less than the Plank time has no meaning.

The problem with Zeno's arrow is that the definition of motion requires the passing of time. When referring to a single instant in time, there is no motion because of this. The state of the arrow at an instant of time is a state of motion, but there is no paradox here.

jpbrooks

(Time in relation to motion and change [at both the quantum level and the "macro world" level] does indeed seem interconnected with the laws of Physics.)
Time, of course, can be held to be discreet for computational purposes in a mathematical representation of objects in the universe. However, since (it seems safe to assume that) space is a continuum, the arrow travelling through space (assuming that no "outside" forces subsequently act on the arrow to stop it or change its direction of motion) would be assumed to be in motion at every point of space that it intersects along its trajectory. So, in simply describing the arrow in motion (according to physical laws), we are also assuming that there must be a one-to-one correspondence between "points" in time and "points" in space, i.e., that time, like space, must also be a "continuum".

Quantum Ninja

I understand what you're saying, but how do you know space is continuous? Keep in mind that a stream of water looks continuous but is composed of discrete bits. Are you certain that space isn't similar?

Jayjay

It looks like I may have been somewhat unclear in my opening post, as none of you really addressed the issue. I'm interested to know how time can be both continuous in a deterministic universe. I can easily imagine the discreet case where the state of the universe (which would be kind of a "snapshot") is determined by the previous state, but I don't see this working in a continuous case where there is no state at all; there's always an infinite number of states between any two states. So what exactly is a particular state determined by in a continuous universe? This is the issue which I'd like to resolve in my head.

Albert Cipriani

Time is but a useful mental construct that describes apparent motion (like how the word "blue" describes a slice of light's spectrum, but is intrinsiclaly meaningless).

"Actually," (pun intended) every femtosecond is all that is (like cartoon stills that in rapid succession give us the illusion of time passing). All that there is is what is. And time ain't got nuthin to do with it.

It's by the grace of God that God continues to create the entire universe anew every femtosecond. When He stops creating you anew, we stupidly call you dead. But billions of you still exist in every femtosecond of the life you lived on earth, which are frozen for all eternity in either heaven or hell. -- Sincerely, Albert the Traditional Catholic

jpbrooks

Perhaps I'm not understanding you correctly, but a "state" is not itself a cause. It is just, as you suggest, a "snapshot". Previous "states" of the universe don't cause the subsequent "states" to occur. They are only a sequence of "pictures" of a continuous "stream" of events (even within a deterministic universe).

Jayjay

Well, what I suggested was just one way to look at it. I find your idea intriguing as well, so let's go with that... If the previous state is not what a given (discrete) state is determined by, then what is?