Time Travel Question

[Perseid]

I've recently read that Ronald Mallett believes he may have found a way to build a working time machine.

Is his theory feasible or is it just another one of these ideas that sounds great but won't work.

A Physorg Article relating to Ronald Mallett and his Time Machine.

[metavac]

First, here's a link to his latest paper on the subject. The abstract:

Exact solutions of the Einstein field equations are found for the exterior and interior gravitational field of an infinitely long circulating cylinder of light. The exterior metric is shown to contain closed timelike lines.

This paper basically solves the Einstein equations for an infinitely long coil of light and finds that space-time outside this coil contains paths into the past. This is no surprising result, physicists figured out solutions for a say, a rotating, cylindrical vortex of dust as early as seventy years ago. All Mallet's doing is replacing "dust" with "light" and crunching the numbers. That's why Mallet mentioned cosmic strings and the like in your article.

The rub is that it's a solution for an "infinitely long" coil. Now Mallet says some guy named Bonner in 1980 said "certain aspects" of this infinitely long geometry are shared by a finite long one, but he doesn't give us a reason why a finite coil will have closed timelike curves in its exterior solution. Either the solution is in the Bonner paper (which I can't find a preprint for) or its something new Mallet hasn't presented. If not invalid on its face, then that would definitely be a novel result worth testing.

Is his theory feasible or is it just another one of these ideas that sounds great but won't work.

Well it doesn't break any of the energy conditions. Mallet's starting with an entirely reasonable physical set up and calculating the exterior metric. If he's fucked up his math, I can't tell at this point. But then again, his solution is for an 'infinitely long" circulating cylinder. We'd need to see the solution for a finite one to be sure.

[CaptainChewbacca]

Finding a WAY to build a theoretically working time machine and actually BUILDING one are two radically different things.

The article seems sound, but as metavac says I don't have the backround doccuments. Also, math isn't my strong area.

[metavac]

The article seems sound, but as metavac says I don't have the backround doccuments. Also, math isn't my strong area.

Specifically, it's pretty sound if we restrict ourselves to the infinitely long coil. As far as I can tell, the math is dead on provided his choice of the "canonical axisymmetrical line segment" is correct.

[OmegaGuy]

How is it possible to have an infinitely long coil?

[Lancer]

How is it possible to have an infinitely long coil?

As Red Mage would say, why would it not be possible?

Anyways, it starts out as a thought-experiment that completely ignores the actual feasability of constructing an infinitely long coil of light.

[Molyneux]

How is it possible to have an infinitely long coil?

As Red Mage would say, why would it not be possible?

Anyways, it starts out as a thought-experiment that completely ignores the actual feasibility of constructing an infinitely long coil of light.

Because part of the definition of infinity in a mathematical sense is that a number growing to infinity becomes larger than any possible value you can assign to it. No matter how long a coil of light we construct, as long as it starts at a finite value, we cannot make it infinite.

[Lancer]

How is it possible to have an infinitely long coil?

As Red Mage would say, why would it not be possible?

Anyways, it starts out as a thought-experiment that completely ignores the actual feasibility of constructing an infinitely long coil of light.

Because part of the definition of infinity in a mathematical sense is that a number growing to infinity becomes larger than any possible value you can assign to it. No matter how long a coil of light we construct, as long as it starts at a finite value, we cannot make it infinite.

Your're probably not familiar with 8-bit theater then. Red Mage is a character well known for making statements that blatantly ignore the physical impossibility of any given task.

[Molyneux]

As Red Mage would say, why would it not be possible?

Anyways, it starts out as a thought-experiment that completely ignores the actual feasibility of constructing an infinitely long coil of light.

Because part of the definition of infinity in a mathematical sense is that a number growing to infinity becomes larger than any possible value you can assign to it. No matter how long a coil of light we construct, as long as it starts at a finite value, we cannot make it infinite.

Your're probably not familiar with 8-bit theater then. Red Mage is a character well known for making statements that blatantly ignore the physical impossibility of any given task.

Ah...I thought that you were referring to an actual poster using the name 'Red Mage'. I've read 8-bit Theater, but he's not my favorite portrayal of the job.

[Shrykull]

I've heard of him before, but I thought the way this "time machine" works is that when it is turned on we can receive messages from the future (so it's really a communication device)

[Molyneux]

I've heard of him before, but I thought the way this "time machine" works is that when it is turned on we can receive messages from the future (so it's really a communication device)

If said time machine works, we should immediately start boostrapping ourselves. Say we can use it to send a message five years into the past; spend the next five years working on designing new power systems. Then send back your blueprints and tell yourself to continue what you started. ^_^

[Kuroneko]

First, here's a link to his latest paper on the subject.

Hmm... interesting.

The rub is that it's a solution for an "infinitely long" coil.

Surpisingly, that's far from the most important problem.

Now Mallet says some guy named Bonner in 1980 said "certain aspects" of this infinitely long geometry are shared by a finite long one, but he doesn't give us a reason why a finite coil will have closed timelike curves in its exterior solution. Either the solution is in the Bonner paper (which I can't find a preprint for) or its something new Mallet hasn't presented.

I've looked at this paper, and Bonnor indeed says it--unfortunately, his paper has very little to do with that claim, as Bonnor is only concerned with the infinite rotating dust cylinder throughout his paper. The only place he mentions it is in the next-to-last paragraph of his last section, the conclusion:

The remaining doubt, of course, is whether a cylinder of infinite length is plausible enough for physical conclusions to be drawn from a study of it. Undoubtedly the infinite length of the cylinder causes some strange effects, rotating or not. For example, though the spacetime tends to flatness at infinity, it is not globally Euclidean because the ratio of the circumference to the radius of large circles centred on the axis is not 2π. Further, test particles cannot escape from the gravitational field of the rod to infinity: this happens even with Newtonian infinite rods. Nevertheless, in some respects an infinite cylinder may be a model for a long finite one, and the possibility cannot be dismissed that a time machine might be associated with a long, but finite rotating system.

This is the only thing Bonnor ever says about it in that particular paper. This makes the entire reference a bit silly.

Well it doesn't break any of the energy conditions. Mallet's starting with an entirely reasonable physical set up and calculating the exterior metric. If he's fucked up his math, I can't tell at this point.

I cannot detect any problems with his mathematics per se, but I do not think his metric is any way physically reasonable. From the paper you linked, the form of Mallett's metric is
(5) ds² = f dt² - 2wdtdφ - ldφ²- e^μ[dρ² + dz²].
After some physical considerations, he arrives at the following, stating that λ is proportional to energy density per unit length:
(33) w = λρ ln(ρ/α),
(34) f = ρ/α + λρ/α ln(ρ/α),
(35) l = (ρ²-w²)/f,
(39) e^μ = (ρ/α)^{-1/2}.
In the limit of λ→0⁺, we have:
[1] w = 0, f = ρ/α, w = 0, l = ρα.
Substituting all of this into (5), we have
[2] ds² = [ρ/α]dt² - ραdφ² - sqrt[α/ρ](dρ² + dz²).
So we have a nice diagonal metric tensor, but it doesn't appear anything like Minkowski. Many of the components of the Riemann tensor diverge near the axis (ρ = 0). Fortunately, the Christoffel symbols are fairly simple, leading to similarly simple components:
[3a] -R^φ_{zzφ} = R^φ_{ρφρ} = R^ρ_{zzρ}/2 = -R^ρ_{zρz}/2 = R^φ_{zφz} = -R^φ_{ρρφ} = -R^t_{ρρt} = R^t_{ρtρ} = R^z_{ρρz}/2 = -R^z_{ρzρ}/2 = R^t_{zzt} = -R^t_{zzt} = 1/(8ρ²),
[3b] R^ρ_{φφρ} = -R^ρ_{φρφ} = -R^z_{φzφ} = R^z_{φφz} = R^t_{φtφ}/2 = R^t_{φφt} = sqrt{α/ρ}/8,
[3c] R^z_{ttz} = -R^z_{tzt} = R^φ_{tφt}/2 = -R^φ_{ttφ}/2 = R^ρ_{ttρ} = -R^ρ_{tρt} = 1/[8sqrt{ρα³}].
All of this leads to the Kretschmann scalar:
[4] K = R_{abcd}R^{abcd} = 3/[4αρ³].

In other words, there is a curvature singularity on the axis (ρ = 0) even if there is no light (λ = 0). Whatever this metric is, it's even less reasonable than the rotating dust solutions with closed timelike curves, which at least recover the Minkowksi spacetime in the limit of low energy densities.