Q: Is Time Continuous or Divided?

[HBar]

Is time continuous or is it made up of small units, and if so what is the smallest unit? I am aware of the Planck time which is the smallest amount of measureable time. It was my understanding, though, that the Planck time doesn't mean that it's the smallest unit of time, only that we cannot measure anything smaller.
-HBar

 

[MathematicalPhysicist]

do you mean units of time, like seconds?

 

[HBar]

I mean, is there a smallest unit of time where you can no longer break it down; Is it made of discrete units?
-HBar

 

[meteor]

Some have hypothesized that there is a quantum of time, the chronon. I don't know nothing more about it.

 

[marcus]

Originally posted by HBar
I mean, is there a smallest unit of time where you can no longer break it down; Is it made of discrete units?
-HBar

Theories of space and time are only models, some of which have been tested and checked out to a considerable extent and others not. You know this as well as I do but it needs saying.

The prevailing general model of spacetime is General Relativity which dates back to 1916 and been extensively checked by precise observations. In GR time is not discrete. Both space and time are continuous.

A major effort is in progress to replace GR with a quantum version (e.g. Quantum Geometry, or Quantum Gravity----GR's essential message is that "gravity is geometry" so modeling gravity is equivalent to modeling the shape, curvature, expansion etc. of spacetime---but GR is still the dominant model.

GR is not proving easy to replace. The quantum versions of it DO have elements of discreteness! For example in the (loop) quantum gravity model the area and volume operators have discrete spectrum----they have discrete values! I personally find this amazing. There are even some independent classical and semiclassical confirmation of the LQG predictions about discrete-valued area---calculations which are based on older physics that show LQG may be correct about this! But LQG is not a finished model yet, it is still being worked on. And when it is finished and can be tested the tests may show it is wrong and some alternative Quantum Geometry or modification of LQG will have to be developed in its place.

So right now the most generally applicable models of the universe have continuous time (as far as I know, I may be wrong about this).

BTW as you hinted about the Planck time, in LQG the values of the area and volume operators are calculated in terms of the Planck area and volume units-----the square and cube of Planck length. Things do seem to be moving in that direction

 

[marcus]

"Quantum Geometry in Action: Big Bang and Black Holes"

Hbar you might find a paper about these things interesting,
by one of the founders of LQG, Abhay Ashtekar.

It talks about the discreteness of area and volume and also how, in Loop Quantum Cosmology the time-zero singularity at the Big Bang is passed over----it is a discrete time thing that arises from the characteristic volume of the universe being discrete. Quantization has removed singularities in classical theories before, so this is just another case where LQG doing what quantization of a classical theory is supposed to do. Time evolution of the universe is pushed back to time zero without the usual trouble.

Ashtekar's paper is informal and uses figurative language---not so technical as a lot, very few formulas----so comparatively easy to read. It is an overview for non-specialist. But not pop sci either. Anyway check it out.

www.arxiv.org/math-ph/0202008[/URL]

this will give the abstract and you can download in whatever format like PDF

It's a talk he gave last year called "Quantum Geometry in Action: Big Bang and Black Holes

 

[HBar]

Is there a reason that GR says that time is continuous? I searched around the Internet and didn't find much.
Forgive me if my question is dumb (or the answer is blindly obvious), but I have no formal education in physics (unless you count 7th grade ). I'm just a 14 year old with an interest. You don't have to dumb it down too much though, I am in IB after all.
Thanks marcus for the paper. It is very interesting!
-HBar

 

[Dave]

I can't think of any particular reason why time would be discrete, but them again, I can't think of any reason why light shouldn't be either...

 

[marcus]

Originally posted by HBar

Thanks marcus for the paper. It is very interesting!
-HBar

Yes, I think so too! That one by Ashtekar ("Quantum Geometry in action...") is really interesting.

He takes the step of imagining a quantum state of space.

As a huge polymer----like a ball-and-stick model of a vast protein molecule---or a 3D network made by gluing match-sticks

And this polymer is constantly changing and evolving. Links break and form new connections at other nodes. Maybe this happens as particles pass thru the network.

And he takes the trouble to visualize it and tell the reader Hey, you know, 10⁶⁸ of these little links, these match-stick things, pass thru the piece of paper you are reading.

Because the punctures by edges of the graph are what give a thing area.

And the nodes enclosed inside a region are what give it volume.

(lines in the net are one dimensional and they carry surface area which is 2D while nodes are zero dimensional points and they generate volume)

It does seem to be a new vision of space and there is a further extension called a "spin foam" that includes time or anyway is 4D. It is oddly analogous to a "Feynmann diagram" but is about spacetime geometry instead of about elementary particles. The spin foam shows how the quantum state of a polymer-like network can evolve and change. It is just a model of that.

Think of dragging the matchstick model thru another dimension so that the sticks sweep out little patches of area, which form a kind of honeycomb or somthing like the soapsuds in the dishpan
or the washingmachine.

this model of spacetime is quite strange.

The model Einstein had of a continuous smooth curved thing---a smooth 4D "manifold"----is I guess more immediately intuitive to a lot of people. Personally I find it so-----like manifolds. They are good for doing calculus with.

With one of these huge molecules with so many pieces to it, how can one calculate. Need a computer.

However at some scale, one thing blends into the other. If you look very close the quantum state is networky or polymeric
but if you stand back it is beautiful smooth old manifoldy.

It is a lucky time to be watching physics.

 

[bogdan]

History's repeating itself...

 

[Tiberius]

You know the classic rubber sheet with the grid painted on it, and the heavy ball in the middle, symbolizing the curvature of space-time around a mass?

Well, when faced with quantum stuff like gravitons, I always imagined that this distorted grid, the shape of space-time, is really just a map of graviton flow, and that everything is mediated through this flow of particles. So, when you back out and look at it, you can do calculations, just as if spacetime were smooth, but you're really making calculations of waves in water, made up of particles.

Is there any veracity to this conception of gravitons and the shape of spacetime?