# R. Mallett device with weak energy

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## Summary:

Why not increase the phase speed of a rotating field (unlimited) ?

## Main Question or Discussion Point

Hello,

I am sorry to raise this old subject concerning the device of R. Mallett, in particular, one is right to quote has violation of the condition on the weak energy which is not respected.
Okay, let's give up this violation of the weak energy condition for now.

In my opinion, the big problem is the energy required for the laser. This energy is astronomical for the strong fields necessary in order to obtain the Lense Thirring effect capable of producing CTC.

The most perfect mirrors would be vaporized, and second-order effects would produce pairs of particles that would reduce the energy of the beam.

So my big question is this:

Couldn't we use a reasonable energy laser, or a rotating field with (magnetic or electrostatic), (a phase speed much higher than that of light (unlimited), like the famous lighthouse rotating (for kids) in the galaxy, to compensate M (E / C²) with ω unlimited, what is technically possible ?

Lense–Thirring precession - Wikipedia

What happens if the speed at the circumference is much higher than the speed of light (phase speed, not information speed, we agree !)

See you soon

Maryline

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Hello @PeterDonis,

My question : would increasing the speed of a rotating field to a speed greater than that of light at the circumference (the phase speed can be unlimited) require "reasonable" energy to produce the same effects ? :

Decrease the astronomical energy required and increase Ꞷ in large proportions, with an identical Lense Thirring effect.

See you soon

Maryline

PeterDonis
Mentor
2019 Award
would increasing the speed of a rotating field to a speed greater than that of light at the circumference (the phase speed can be unlimited)
First, I'm not sure how you would increase the phase speed this way.

Second, I don't see any dependence of the effect on phase speed (which I would not expect since "phase speed" isn't generally relevant to things like the stress-energy tensor of light anyway) in the paper.

PeterDonis
Mentor
2019 Award
the 2003 Mallett paper [1]
Looking at this paper, I find that its claim that there are closed timelike curves possible with the EFE solution it gives is inconsistent with the math shown in the paper. The claim is made near the end of Section 2 of the paper:

Equation (36) implies that for ##\lambda \ln (\rho / \alpha) > 1## then ##l < 0## so that the curves given by Equation (48) under these conditions are closed and timelike.
Equation (36) is:

$$l = \rho \alpha - \lambda \rho \alpha \ln (\rho / \alpha)$$

The ##\alpha## in this equation is the value chosen for the quantity given as ##\xi## earlier in the paper, as stated just before Equation (34). So the possible values for ##\alpha## will depend on the possible values for ##\xi##.

The equations that are relevant for determining the possible values for ##\xi## are Equation (18), which says

$$\Delta^2 = f l + w^2 = \rho^2$$

Equation (27), which says

$$f \xi = w + \rho$$

And Equations (30) and (31), which together say

$$\rho = w + \xi l$$

Equation (27) implies that ##f l = \xi^{-1} l \left( w + \rho \right)##. Substituting this into equation (18) gives

$$\rho^2 = \xi^{-1} l \left( w + \rho \right) + w^2$$

Substituting the equation obtained from Equations (30) and (31) for ##\rho## gives

$$\left( w + \xi l \right)^2 = \xi^{-1} l \left( 2 w + \xi l \right) + w^2$$

Which, after some algebra, gives

$$\xi = - \frac{2 w}{l}$$

Substituting ##w = \rho - \xi l##, derived from the equation above that combines Equations (30) and (31), into the above gives

$$\xi = \frac{2 \rho}{l}$$

Substituting this ##\xi## for ##\alpha## in Equation (36), to get an equation expressing the possible range for Equation (36) with all possible values of ##\alpha##, gives

$$l^2 = 2 \rho^2 \left( 1 - \lambda \ln (l / 2) \right)$$

It is apparent now that a value larger than ##1## for the logarithm here, which would mean a negative value for the RHS as a whole, is impossible, since it would make ##l^2## negative and hence ##l## imaginary. So this equation is not actually telling us anything physical about the spacetime: it is telling us about the limited range of the coordinates--they cannot cover any region including values of ##l## that would make the RHS of the above equation negative.

Hello @PeterDonis,

I'am sorry for my late response.

I see that you are really an expert when you say that phase speed "isn't generally relevant to things like the stress-energy tensor of light anyway.

To increase the phase velocity, or obtain a superluminal rotating field at the circumference, my idea (stupid) was to connect a cylinder to optical fibers of increasing lengths, shifted by fractions of wavelength and connected to a frequency generator. (optical fibers for light or copper wires for a magnetic field.)

I realize that this idea was really very bad, because there would be no movement but a succession of "fixed" emissions (like a cinematographic tape).

Thanks again.

Maryline