Smallest possible unit of time?

[Hamel]

Has a smallest possible unit of time been discovered, and is it connected with the Planck length, which is about 10 to the -33 cm?

[Durandal]

Yes and no. Theoretically, Planck time is about 10^-43 s (the amount of time it takes light to traverse Planck length), but it hasn't really been verified. Things like Hawking radiation give credence to the notion of a quantized time, though. Even so, it's still not widely accepted as far as I know.

[Zoink]

From www.sciam.com

"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.

[SyntaxVorlon]

Ahhh, the plank second, what would make being called a minute man all the more harmful for an over eager physicist.

[Setzer]

Read "Thief of Time", by Terry Pratchett. According to that, the universal tick, or the amount of time it takes for now to become then, is the smallest unit of time.

[TheAtheistKing]

Yes, of course time is quantized. If time weren't quantized then it would have to be treated as continuous. That would mean that there are an infinite number of states between any two states, which means that the amount of time between any two states is infinite. To understand this, suppose that time is a continuous variable rather than a discrete variable. That would mean that there is no such thing as a second moment in time. Many absurdities result from assuming that time is continuous. To really appreciate them, one has to familiarize oneself with the notion of continuity from the theory of the real number system. At any rate, nothing in reality is continuous. The things of reality are all discrete.
As for the discussion of how many state changes there are per second, you can get a rough idea of this value using the known physcial constants of the universe:

G = Newtonian Gravitational Constant = 6.672 x 10^-11 m^3/kgs^2
h = Planck's constant = 6.6260755 x 10^-34 kg m^2/s
c = speed of light = 2.99792458 x 10^8 m/s

There is a way to put them together using the einsteinian gravitational constant, and you get a quantum unit of space, and a quantum unit of time.

If i recall, the einsteinian gravitational constant is

Ge = (hc/8piG)^1/2

Or something close to that, it might be hbar. At any rate, you get

r= 2.03 x 10^-34 meters
t= 6.6 x 10^-43 seconds

The ratio of these two units equals the speed of light. In order to interpret t above, you can say it is a "unit" of time, thus implying that the universe undergoes some 10^43 changes of state per second.


I know the figure 2.03 x 10^-34 is correct, but you have to use the einsteinian gravitational constant to get that value. Do not take these figures too seriously though, because there is an error in einstein's theory of general relativity. Nonetheless, the order of magnitude of a quantum unit of time would be around 10^-43, based solely upon ratios of the physical constants which yeild a unit of time.

[Einhander Sn0m4n]

I think it's called the femtosecond, although I've heard of a still smaller time unit called the attosecond.

<SNIP>

AAAAAAAAAAAAAAAAAAGGGGGGGHHHHHHHHHHH MAKE IT STOP!!!!!!!!!!!! *goes blind from the extremely flawed math*

[Dark Hellion]

Its called planck time, or a planck second, and is around 1e-43 if i remember correctly. Theoretically it is the smallest unit of observable time, anything happening in less time is considered instantaneous.

[Cej4096]

Yes, of course time is quantized. If time weren't quantized then it would have to be treated as continuous. That would mean that there are an infinite number of states between any two states, which means that the amount of time between any two states is infinite.

Except that each of these "states" would be infinitly short, and thus there can be a non-zero distance between two of them only when there is an infinte number of these "states" between them.

Or you could imagine it like this:


This line has a finite length.
______________


The number used to described its length depends on the units you are using

l____l____l____l length of 3 units

l___l___l___l___l length of 4 units


The reason this is true is because as the size of a unit decreases, the number of that unit needed to quantify something increases. It doesn't take a genius to realize that if thus you decrease the size of unit down so that an infinite number of that unit is needed to quantify a length, time, mass or whatever, the unit becomes infinitly small, but not zero. And for this reason, an infinite number of this unit can still describe (although not in any useful way) something that is not infinite, but finite.

What you are talking about seems to be Zeno's paradox. I'm no mathematician or physicist, but that has always seemed to me to be absurdly easy to answer. Maybe I've merely never understood it properly. If so, could anyone please enlighten me to what I've missed?

[kojikun]

I was just thinking. If a planck time is the amount of time it takes light to cross a planck length, what if something is going slower? does it not move at all during a planck time? is the universe pixellated at planck length scales so that there literally is nothing smaller, or is it that a planck length is the smallest meaningful distance, but not the smallest distance? half a planck length must exist because planck lengths exist, but that doesnt mean that there are things smaller then that, just like half-pixel size exists in a monitor but no image can be smaller then 1 pixel unless you change the size of a pixel.

these are the questions that must be wondered about.

[RedImperator]

Well look who's returned. Genius, physicist, future Nobel laureate, recent recipient of an old fashioned prison anal gangrape in the Hall of Shame, TheAthiestKing. Are you going to demonstrate that flaw in general relativity this time, Your Majesty, or should I bend over now and wait for you to blow more smoke up my ass?

[kojikun]

Red, ignore him.

or should I bend over now and wait for you to blow more smoke up my ass?

LOL!!

"::giggle:: that tickles :3"

^_^

[Hamel]

Red, ignore him.

or should I bend over now and wait for you to blow more smoke up my ass?

LOL!!

"::giggle:: that tickles :3"

^_^

*barf*

[SirNitram]

these are the questions that must be wondered about.

Things can be smaller/briefer than Planck, but the observation of such becomes effectively impossible, because below that thershold, our understanding of things breaks down. So, there are no half-pixels, just timescales/sizes where it becomes impossible to know the rules. It is not some indivisble marker stick like TAK wants it to be.

[kojikun]

Things can be smaller/briefer than Planck, but the observation of such becomes effectively impossible, because below that thershold, our understanding of things breaks down. So, there are no half-pixels, just timescales/sizes where it becomes impossible to know the rules. It is not some indivisble marker stick like TAK wants it to be.

Why does our ability to understand events break down past that point???

[SirNitram]

Things can be smaller/briefer than Planck, but the observation of such becomes effectively impossible, because below that thershold, our understanding of things breaks down. So, there are no half-pixels, just timescales/sizes where it becomes impossible to know the rules. It is not some indivisble marker stick like TAK wants it to be.

Why does our ability to understand events break down past that point???

Why does gravity do what it does? I don't know, I can only tell you how. Unfortunately, I can't tell you how Planck becomes a lower limit. I assume it's linked to the Uncertainty Principle.

[kojikun]

Why does gravity do what it does? I don't know, I can only tell you how. Unfortunately, I can't tell you how Planck becomes a lower limit. I assume it's linked to the Uncertainty Principle.

No no mean, if we DID stick an amount of time smaller then 1pt into an equation, would the equation give insane results or what?

[SirNitram]

Why does gravity do what it does? I don't know, I can only tell you how. Unfortunately, I can't tell you how Planck becomes a lower limit. I assume it's linked to the Uncertainty Principle.

No no mean, if we DID stick an amount of time smaller then 1pt into an equation, would the equation give insane results or what?

It'd probably give no result at all.

[Dark Hellion]

I am pretty sure, that anything that happens faster than planck time is observably instantaneous, even if it takes a finite amount of time, it is observed as instant, because of the wacky nature of physics.

[Xenophobe3691]

Why does gravity do what it does? I don't know, I can only tell you how. Unfortunately, I can't tell you how Planck becomes a lower limit. I assume it's linked to the Uncertainty Principle.

No no mean, if we DID stick an amount of time smaller then 1pt into an equation, would the equation give insane results or what?

It would be impossible. The plank time is the time it takes for light, traveling at the fastest speed possible, to cross the smallest distance possible. Any change would occur at this speed, any quicker is impossible.

[kojikun]

It would be impossible. The plank time is the time it takes for light, traveling at the fastest speed possible, to cross the smallest distance possible. Any change would occur at this speed, any quicker is impossible.

No shit sherlock, but something can move SLOWER then that and thus cross 1 planck length is 2 planck times instead of one, so it would be 1/2 planck length further along.

Faster is irrelevant since it requires FTL, but slower, and thus moving SMALLER distances, is possible. Thats the question, what if you input numbers and force the answer to involve distances smaller then 1 planck length?

[Dark Hellion]

Koji, your situation is impossible. It requires you to be able to observe something either at faster than planck time, or to observe a distance of less than planck length. Both are impossible. Theoritically if you observe something moving at .5c at 1 planck second, it hasn't moved. At 2 planck seconds, it is 1 planck length along. But as you situation is impossible theoretically doesn't even matter.

[kojikun]

Koji, your situation is impossible. It requires you to be able to observe something either at faster than planck time, or to observe a distance of less than planck length. Both are impossible. Theoritically if you observe something moving at .5c at 1 planck second, it hasn't moved. At 2 planck seconds, it is 1 planck length along. But as you situation is impossible theoretically doesn't even matter.

I never said observe so everything you said is pointless. I asked what would happen if you put it into an equation. If you DO use units smaller the planck units, what happens to the equations, what happens to the answers. Do they end up being hugely randomized? Or do they simply not yield any answer at all?

[SirNitram]

Koji, your situation is impossible. It requires you to be able to observe something either at faster than planck time, or to observe a distance of less than planck length. Both are impossible. Theoritically if you observe something moving at .5c at 1 planck second, it hasn't moved. At 2 planck seconds, it is 1 planck length along. But as you situation is impossible theoretically doesn't even matter.

I never said observe so everything you said is pointless. I asked what would happen if you put it into an equation. If you DO use units smaller the planck units, what happens to the equations, what happens to the answers. Do they end up being hugely randomized? Or do they simply not yield any answer at all?

You're not making much sense. You can, of course, plug in 10E-45 and get a discernable answer. The point is, space and time seem to start acting wonky down there, and so it becomes a pointless exercise to discern anything down there. What are you trying to convey, saying 'plug it into an equation'?

[Durandal]

Why does gravity do what it does? I don't know, I can only tell you how. Unfortunately, I can't tell you how Planck becomes a lower limit. I assume it's linked to the Uncertainty Principle.

No no mean, if we DID stick an amount of time smaller then 1pt into an equation, would the equation give insane results or what?

It would give untestable results. We don't know if the laws of physics apply at those lengths and times. Hawking radiation gives a good indication that they may not.