B Transmitting information using gravitational waves

[Paul Colby]

I don't see how.

"that" in my comment refers to time modulating the phase of light without developing sidebands (frequency shifts).

I don't think this is a good analogy

It's not an analogy. The light returned from one arm goes like $\cos(\omega t + \phi(t))$. This is a modulation and has sidebands quite independent of everything else that might be said.

 

[PeterDonis]

"that" in my comment refers to time modulating the phase of light

But that's not what's happening. The light itself is unchanged. Only the distance it has to cover changes. It's not the same thing as modulating the source of the light.

This is a modulation

Not in the sense you appear to be using the term.

and has sidebands

I don't think that's true; that would require modulating the source of the light. That's not happening here.

Consider a simpler situation: you have a laser light source that emits a constant frequency (no modulation at the source) and a detector and sit at rest at some location. I have a mirror and gradually move away from you. You repeatedly fire the laser at the mirror and watch the detector signal. The phase of the light at the detector changes as I move the mirror away. Does that mean the laser light is being modulated? Will someone else sitting between us be able to detect side bands?

 

[Paul Colby]

But that's not what's happening. The light itself is unchanged. Only the distance it has to cover changes. It's not the same thing as modulating the source of the light.

Well, for me this discussion is occurring in a frame where the mirrors are moving. Light reflected off a moving mirror experiences a doppler shift which depends on the velocity of the mirror. The reflected beam will be at a higher or lower frequency relative to the source. For very slow variations this is best described as a time dependent phase. Slow or fast the physics/arithmetic is always the same.

Will someone else sitting between us be able to detect side bands?

Hell yes. Remember that LIGO isn't pulsed it's CW not that this changes anything. The coherence length of their lasers is likely well over 4km. One crest looks very much the same as the next. The absolute phase has no meaning from the experimental point of view. This ties back to my original (wrong sounding) view, the energy in these sidebands you think I'm hallucinating is due to the work the GW (or moving mirrors) is doing on the detector.

 

[PeterDonis]

Light reflected off a moving mirror experiences a doppler shift which depends on the velocity of the mirror.

Yes, this is a fair point--the phase difference seen at the detector is partly due to this and partly due to the change in the round-trip distance traveled by the light.

LIGO isn't pulsed it's CW

Yes, and I should have specified CW in my simplified example.

The absolute phase has no meaning from the experimental point of view.

Yes, I was ignoring that complication in my simplified example. (Or, if you like, I was assuming that the detector contains a reference beam of some sort so that it is detecting relative phase, not absolute phase.)

these sidebands you think I'm hallucinating

I wasn't saying you were hallucinating the sidebands; I was trying to understand why you think varying the distance between the mirrors, which is how the standard model of LIGO interprets what is going on (as in the link I gave), "violates basic mathematical facts".

Googling on "ligo sidebands" quickly turned up some references, such as this one:

http://www.sjsu.edu/faculty/beyersdorf/Archive/Phys208F07/Sideband generation in LIGO.pdf

This reference indicates that there is some modulation done at the laser source (more precisely, by Pockels cells right after the laser source) in LIGO. This appears to be done in order to optimize the resonance of the lasers in the cavities in each arm (the cavities are there to increase the effective length of the arms). So I was incorrect in thinking that no source modulation is being done. It also makes clear that sidebands are in fact present in LIGO. So the presence of sidebands appears to be perfectly consistent with time-varying distance between the mirrors.

 

[PeterDonis]

the energy in these sidebands you think I'm hallucinating is due to the work the GW (or moving mirrors) is doing on the detector

I'm not sure that the reference I linked to in my previous post shows this. It looks to me like it's saying that the sidebands are due to the modulation that is done to keep the laser beams resonant in the cavities. But the reference doesn't actually appear to talk about the effects of GWs, so it's hard to be sure.

 

[Paul Colby]

I'm not sure that the reference I linked to in my previous post shows this.

There exist a level of understanding somewhere between the detail in the slides you linked to and the public relations level of understanding you seem to subscribe to. It's common in heterodyne radio design to use one or more IF frequencies to take advantage of the technology available at IF frequencies. This is done using frequency translation via mixers. This seems to be what the link in #54 is doing. It's a complication (very interesting though) to move the desired signal off base band and thus improve the S/N. This complexity is beside my point. My point is, in a frame in which the mirrors move, doppler shifts of the light generate sidebands. The slower the change the nearer these sidebands are to the carrier but they are still present.

 

[PeterDonis]

in a frame in which the mirrors move, doppler shifts of the light generate sidebands

Shouldn't the generation of sidebands be frame independent? (More precisely, the base frequency of the carrier is frame dependent, but the presence of frequencies other than the carrier frequency is not, correct?)

 

[PeterDonis]

doppler shifts of the light generate sidebands

There might be a terminology issue here as well. I am used to seeing the word "sideband" used to refer to frequencies other than the carrier frequency produced by modulation of the source. That's a more specific usage than the one in your quote above.

 

[Paul Colby]

Shouldn't the generation of sidebands be frame independent? (More precisely, the base frequency of the carrier is frame dependent, but the presence of frequencies other than the carrier frequency is not, correct?)

It's all the same thing. As I said the return beam goes like $\cos(\omega t + \phi(t))$ with any frame choice. This function is predominantly the carrier but has sidebands when it's spectrum is plotted. It also happens to be a carrier with a time dependent phase. The doppler shift explanation holds if the mirrors move. The explanation in the TT gauge where the coordinates of the mirrors are fixed is that of an optical cavity with a time dependent length. Pick your poison. It's the same physics either way.

 

[PeterDonis]

The doppler shift explanation holds if the mirrors move. The explanation in the TT gauge where the coordinates of the mirrors are fixed is that of an optical cavity with a time dependent length.

In other words, sidebands either way, but the specifics of how you explain why they are there are frame-dependent. Fair enough.

 

[Paul Colby]

Essentially no average motion of the object as a whole. But individual atoms in the object are certainly moving: that is what "strain" means.

Yes, and your statement very helpful and reminds me why I work in the TT gauge. How is the word "moving" defined in your statement? In the TT gauge with the interatomic forces set to zero (for argument sake) the atoms remain stationary with respect to the chosen coordinates while the interatomic distances change by virtue of the metric strain. This geometrically strained configuration of atoms will have a displacement current and associated electric fields. All this happens with the atoms stationary wrt the chosen coordinates.

Clearly the interatomic forces are at play so even in TT coordinates the atoms will accelerate with the acceleration govern by the equations of motion given in post #29. One must solve this dynamical problem in order to have a complete picture.

 

[PeterDonis]

How is the word "moving" defined in your statement?

The proper distances between at least some pairs of individual atoms are changing with time (if you like, proper time of either atom of a given pair).

 

[Paul Colby]

The proper distances between at least some pairs of individual atoms are changing with time (if you like, proper time of either atom of a given pair).

Hum, motion was always defined relative to a frame. Sounds like a really confusing definition.

 

[PeterDonis]

motion was always defined relative to a frame

If you insist on doing this, you can always define a proper reference frame for one atom (basically Fermi normal coordinates centered on its worldline), and then look at whether adjacent atoms have coordinate motion in this frame.

 

[Shane Kennedy]

Is there anything in current theory which could allow faster-than-light signals of any sort ?

 

[PeterDonis]

Is there anything in current theory which could allow faster-than-light signals of any sort ?

No.

 

[mrad]

To look at gravity wave communication from a radio engineering perspective, a good place to start is John D Kraus' (inventor of the helical antenna in the 1940s and professor at Ohio State for many years) 1991 article, "Will Gravity Wave Communication be Possible?" The difficulty in producing and detecting GW is analogous to poor impedance matching in an antenna connection.
http://ieeexplore.ieee.org/document/84527/