Instantaneous travel of macroscopic objects?

[DivineNathicana]

Originally Posted by Tormod

I still question your opening statement that Einstein wrote that objects can move instantaneously in time. I have never seen this be written anywhere. I wonder if you are confusing "movement" in this case with "wave diffusion" - Newton believed gravity was instantanous over infinite distances, wheres Einstein proved that this was not true.

You misread:

Originally Posted by DivineNathicana

Einstein said that instantaneous travel was impossible.

And yes, I did not realize you would not actually be travelling through spacetime. But here's a follow-up question: No matter how short a wormhole may be, why would it be instantaneous to travel through one? It still has length. We've just figured out that no matter how small a distance between A and B is, it will still take up time. So why not a wormhole?

- Alisa

[DivineNathicana]

Sanctus,

What if you're going in accordance with ST, which doesn't permit any length above h-bar? If travel between points A and B Planck's length away from each other is not instantaneous, then why not stop along the way and have ourselves a length below the Plaqnck's length?

Logically, it makes sense that two points h-bar distance away from each other are farther away than two points that are "right next to" each other, the latter theoretically being instantaneous... But If this were so, then why can't we have even shorter lengths?

- Alisa

[paultrr]

Both string theory and LQFT propose further sub-division. The biggest difference is one rather sees things as a continum on down ward while the other proposes there is a minimual length and time unit to how small things get. You can in theory get to a point unless for instance the Planck scale is the boundary of an embedded spacetime or hyperspace itself. In this case, for our spacetime the Planck scale is the mimumal unit while everything smaller could actually be a larger spacetime that may encompases not only our universe as well as other universes. Here again it would be our frame's structure and boundary conditions that makes the other look smaller than it is. If that is the case then we really do have a continum in both directions to deal with.

Basically, its true that untill we can measure such scales directly or someone figures out how to enlarge the planck scale and its effects any movement there makes little difference for you and I. But in theory its possible there is movement there that at least for microscopic objects might be instantaneous.

[DivineNathicana]

Originally Posted by paultrr

Basically, its true that untill we can measure such scales directly or someone figures out how to enlarge the planck scale and its effects any movement there makes little difference for you and I. But in theory its possible there is movement there that at least for microscopic objects might be instantaneous.

Wouldn't it be logigal for us NOT to be able to "measure" such scales if they are smallest possible distance as then we will label them with a length (or a line segment, consisting of two points and a LINE of a certain LENGTH between them), and they should thus be able to be broken up further (a third point somewhere on the segment)?

And going totally off thread but on par with my latter comments: If strings have length, why are they fundamental and as short as anything gets? And how can a string be 1D anyway? How can something 1D vibrate?

[Tormod]

Originally Posted by DivineNathicana

You misread (the Einstein thing)

Oooops. Sorry Alisa! That's what I get for staying up too late...

But here's a follow-up question: No matter how short a wormhole may be, why would it be instantaneous to travel through one? It still has length. We've just figured out that no matter how small a distance between A and B is, it will still take up time. So why not a wormhole?

- Alisa

Well, this is purely hypothetical but a "wormhole" actually has no length.

This is the best analogy I can give you:
Take a sheet of paper and use a pencil to mark an "A" at the top of the paper and another "B" at the bottom of the paper.

The shortest distance from A to B is now the length of the paper.

Now fold the paper so that A and B are on top of each other. Take your pencil and punch a hole through the paper. This is your wormhole.

A wormhole is not a tunnel but a "hole" through space-time, so that when you enter it you instantly exit somewhere else. Thus you can now travel from A to B in an instant, without even having to bother about the rest of the sheet of paper.

There are of course other theories about wormholes so this is just one example, but it is a good analogy for the example I used.

[paultrr]

Strings are 1D, then you have branes which while under M-Theory started out as 2D now have evolved into objects of many different dimensions. You can also add in instantons and the list goes on, so to speak. As to what's minimual? Well, the average as far as theory goes for the fundamental length of strings is around that of the planck scale. However, that is an average and there are some theories out there with even smaller scales. Generally, at least as far as those compacted extra dimensions the scale runs from near that of planck on downward. If you throw in the idea of large extra dimensions that are hidden from us you get all sorts of possible answers.

[paultrr]

The usual method of modeling dark energy is as an ideal fluid where the equation of state(EOS) is:

Pd=wpd.

Here Pd and pd represent the energy density and the pressure. The current thought on w place it less than -1/3 at the current time. Almost irrespective of the cosmological model or weither the equation of state is a real variable over time cosmological date(see WMAP) constrains set w at around -1. So some version of both dark matter and exotic energy is at play in our universe. Once one opens the door to exotic energy even of the negative vacuum pressure type which the above modeling allows then theoretical states like wormholes, enlarged planck regions, etc become theoretically possible even if we have no present means of detecting them directly.

The problem we face is finding an exact model that not only fits all the cosmological data but which explains things beyond the standard model for particle physics. We also have the side problem of finding a model that allows for some local violation of known energy conditions without creating global violations of such. But the implcation is very strong at the present that the overall EOS for the vacuum itself does vary. It's the how much it varies locally and that variance effect on global scales that dictates the idea of there existing frames of reference where C is no longer a constant. As for wormholes or other exotic states being possible the fact that exotic energy of some type exists rather makes the other possible at least as far as microscopic scales go.

[Bo]

How could the wmap data constrain w? as far as i know, WMAP showed that the universe is flat (\Omega=1.05 or something like that) and expanding. Expanding universes require some sort of vacuum energy with w<-1/3 or, for prolonged inflation: w<-2/3. I dont think WMAP says that we need -1, which would mean a pure cosmological constant, but just requires w<-2/3

negative vacuum pressure type which the above modeling allows then theoretical states like wormholes, enlarged planck regions, etc become theoretically possible even if we have no present means of detecting them directly.

i dont see any direct link between negative vacuum pressure and wormholes. negative vacuum pressure acts, just like normal matter, on the expansion of the universe. Large anisotropies could cause things like wormholes or whatever, but that holds both for positive and negative pressure.

Bo

[sanctus]

Originally Posted by DivineNathicana

Sanctus,

What if you're going in accordance with ST, which doesn't permit any length above h-bar? If travel between points A and B Planck's length away from each other is not instantaneous, then why not stop along the way and have ourselves a length below the Plaqnck's length?

I haven't done any general relativity yet (have to wait for next year ) and I guess your statement from minimal lenght comes from there; I have to say though it surprises me very much that a minimal length exists, I thought it was continous....

[paultrr]

The general idea of a minimual length comes from Loop Quantum Field Theory which was popularized a bit in Lee Smolin's account in the book, "Three Roads to Quantum Gravity." Personally, I do not actual subscribe to that camp fully even though at times I find the geometry side interesting and having some merit. You do not find it under General Relativity where in general spacetime is a continium.