Can Light Create a Time Machine?

[bino]

Mallett's machine, as laid out in his May 2000 paper in Physics Letters entitled "Weak gravitational field of the electromagnetic radiation in a ring laser," is based on Einstein's formulation that light and matter are both forms of energy.
We know that matter can bend space-time and according to Einstein's theory, matter and light are both forms of energy. So why can't light bend space-time?
This fall, with UConn colleague Dr. Chandra Raychoudri, Mallett will begin work on building a "ring laser"--basically, a device that will create a circulating light beam, perhaps within a photonic crystal that will bend the light's trajectory and slow it down.
Then, a neutron particle will be sent into the space in the center of the beam. In short, the beam--perhaps two beams in one model, with the light traveling in opposite directions--is expected to twist the space-time inside the circle into a loop.
Think of a spoon stirring thick gravy in a pot and creating a vortex, only the vortex in this case is the fabric of space-time twisting, with past, present and future, circling one another so that the future precedes the past.

 

[pervect]

Unfortunately, Mallet did not do the calculations correctly. His most serious error (IMO) was assuming that the light swirled, without providing a mechanism to make it swirl. What he wound up finding was a space-time in which light would swirl around a line singularity (similar to a cosmic string) - rather than flat space-time with light being made to swirl via the use of mirrors or other optics, which is the case that can be generated in the laboratory.

To quote from the paper Humanio cited:

Unfortunately, it appears that the metric of \cite{Mallett} is not the metric
that one would get by starting from Minkowski space and establishing a
circulating cylinder of light. It is true that it is almost
everywhere a solution to Einstein's equations with Eq.\
(\ref{eqn:source}) as a source, but at the origin \rho = 0 there is
a line singularity. For example, the trtr component of the Riemann
tensor is
<br /> \be<br /> R_{rtr}{}^t = \frac{1}{8\rho^2}<br /> \ee<br />
and so diverges at the origin. This is not a coordinate artifact, as
we can see by taking the scalar
<br /> \be<br /> R^{\alpha\beta\gamma\delta} R_{\alpha\beta\gamma\delta}<br /> =\frac{3}{4\alpha \rho^3}<br /> \ee<br />
which is also divergent. Worse yet, this divergence has no dependence
on \lambda, and so persists if one takes the limit in which the
source intensity \epsilon goes to 0.

Thus it appears that the metric of \cite{Mallett} describes a cylinder of
light circulating in a spacetime which is pathological even without
the light. It is thus unlike the spacetime of van Stockum
\cite{vanStockum} studied by Tipler \cite{Tipler:ctc}, which does go
to Minkowski space as the source is removed.

 

[bino]

Prof. Mallet theorized in 2000 that if a powerful laser light were bent into a
ring, it would create a region at its center where space-time curves back on
itself so severely that someone proceeding into the future would wind up back when he started, in his own past. In 1991, Princeton University astrophysicist J. Richard Gott theorized that cosmic strings, thinner than an atomic nucleus but infinitely long and more massive than a galaxy, could warp space-time enough to create these paths to the past, called closed timelike curves.

But it is a 1989 discovery, by Caltech’s Kip Thorne and colleagues, that has done the most to get the physics of time travel into reputable scientific
journals. They theorized that general relativity permits wormholes - tunnels
that cut across a curved region of space-time, connecting here to there and
now to then. Earlier calculations suggested that wormholes don’t stay open
long enough to serve as practical time machines, but Prof. Thorne showed that, with enough negative energy, they can be propped open.

 

[gptejms]

Unfortunately, Mallet did not do the calculations correctly. His most serious error (IMO) was assuming that the light swirled, without providing a mechanism to make it swirl. What he wound up finding was a space-time in which light would swirl around a line singularity (similar to a cosmic string) - rather than flat space-time with light being made to swirl via the use of mirrors or other optics, which is the case that can be generated in the laboratory.

I glanced through Mallet's paper and a web page on cosmic strings and made the following observation(tell me if I am wrong)--the latter contains the off-diagonal element g_{r,theta} which causes r,theta to trace out a circle(section of a cone).The former contains the off-diagonal element g_01(and g_02) which causes x-t(or y-t) to curve and trace out a circle--allowing the possibility of a particle going back in time.

 

[pervect]

Digging around, I can't find the "Foundations of Physics" paper by Mallet which is the only one to talk about CTC's. (I'm not positive I ever had it). I do have another of Mallet's papers, but it's not of much use to resolve this particular question.

In general, though, I think that you [gptejms] are on the right track. A cosmic string would not have the correct geometry to bend light in a circle.

 

[bino]

http://www.physics.uconn.edu/~mallett/

 

[pervect]

http://www.physics.uconn.edu/~mallett/

That's the paper I already have. Unfortunately, it's not the right one -that's the Physics Letter A paper, not the Foundations of Physics paper where the CTC results are presented. The paper I'm looking for is:

R. L. Mallett, "The gravitational field of a circulating light beam," Foundations of Physics 33, 1307 (2003).

 

[bino]

http://www.ingenta.com/isis/searchi...0033/00000009/00469502&targetId=1098650409190

 

[pervect]

http://www.ingenta.com/isis/searchi...0033/00000009/00469502&targetId=1098650409190

Thanks, but I'm not paying $33.82 for the article!

 

[bino]

yeah i hear that!

 

[bino]

i have not seen any for free. one of the other websites i sent earlier has malletts email address maybe he could sent you a copy if you ask.

 

[Maxwell's Demon]

The paper I'm looking for is:

R. L. Mallett, "The gravitational field of a circulating light beam," Foundations of Physics 33, 1307 (2003).

http://www.physics.uconn.edu/~mallett/Mallett2003.pdf