Mathematicians confirm the possibility of data transfer via gravitational waves
phys.org
phys.org
Sure, we'll be building space stations with gravitational wave transmitters as soon as we can figure out how to wiggle stars and planets in a controlled fashion to produce them. That should happen Real Soon Now.
"[F]or instance, a 1-second-life black hole has a mass of 2.28×10^5 kg", and the time taken seems proportional to the cube of the mass. So a 2.28×10^6 kg black hole would take 1000 seconds, and so on.
How massive was the black hole in the story?
They definitely mention it being smaller than an atom, though.
As for the radius... Looks like the Schwarzchild radius is proportional to the mass, and for the moon (7x10^22 kg) it's 0.11x10^-3 meters, so this 10^14 kg mass should be maybe 1.5x10^-13 meters, which is 1.5 x 10^-11 cm. Nice. It looks like Niven did his homework.
Incidentally, Wiki says that Hawking argued for black hole evaporation in 1974, and Niven's story won an award in 1975, which I assume might indicate it was published around then. Seems it'd be a close call whether Niven heard about it before publishing his story.
Some quick formulas (M is mass of the hole in kg):
Evaporation time T = 8.4 x 10^-17 M^3 seconds
Hawking radiation power W = 3.6 x 10^32 / M^2 Watts
Hawking radiation pressure at 10^-10 meters (roughly one atom) distance P = 9.6 x 10^42 / M^2 Pa
(Note that the last formula assumes that the hole's horizon radius is smaller than 10^-10 meters, which it is for Niven's hole.)
For M = 10^14 kg, we get:
T = 8.4 x 10^25 seconds (which is more than 10^18 years)
W = 3.6 x 10^4 Watts (36 kW, comparable to your car's engine traveling on the highway with a family and luggage, but pretty darn bright for something that's basically just a light source)
P = 9.6 x 10^14 Pa (almost 10^10 atmospheres!)
So this hole won't accrete matter, because anything that gets close to it gets violently pushed away by its Hawking radiation. It will tunnel its way through Mars and out the other side, and then back again, executing simple harmonic motion, indefinitely.
[1] http://iopscience.iop.org/article/10.1088/1475-7516/2018/07/...
If memory serves the signal of the latter should have been ~3 orders of magnitude higher.
Using nukes to communicate is a bit intense, but a tuned receiver should be able to pick up lower energy levels.
Did you take into account that in a process like this, virtually none of the energy released can be put into gravitational waves? The efficiency of such transmission is extremely low for processes involving ordinary matter--many orders of magnitude less efficient than for electromagnetic waves. You need huge quantities of matter to overcome this problem--or, alternatively, you need very dense matter, like neutronium, or strong spacetime curvature like that of a black hole (but not too large a hole, since curvature at the horizon goes like the inverse square of the hole's mass).
"gravitational waves of nonmetricity"
It looks like these "gravitational waves" aren't the kind that LIGO has been detecting, but a hypothetical kind in a hypothetical theory of gravity that is not the same as General Relativity (there are no "gravitational waves of nonmetricity" in GR). So for this to be even possible in principle this hypothetical theory of gravity would have to turn out to be correct (and we have no evidence to suggest that GR is wrong and some other theory of gravity is correct).
> On January 4th, 2017, LIGO detected two black holes merging into one. One of the black holes was 32 times the mass of the Sun (32 M⊙, where M denotes mass and ⊙ is a symbol for the Sun) while the other was 19 times the mass of the Sun. When they merged, they created a black hole 49 times the mass of the Sun. The coalescence instantly converted 2 solar masses of black hole mass into the energy that rattled spacetime enough to generate the gravitational waves we detected almost 3 billion years after it occurred. (Caltech/MIT/LIGO Lab)
> Despite the stupendous energy released by colliding black holes, detecting gravitational waves is excessively difficult since the effects they have on LIGO’s instruments are incomprehensibly small. This latest wave caused the spacetime occupied by LIGO’s arms to stretch and shrink by 0.000,000,000,000,000,001 (or 1×10-18) meters (a.k.a. an “attometer”). That’s 1000 times smaller than a proton!
You can transmit data by modulating in on top of something that propagates through space? Well, big deal, who'd thought? /s
In all seriousness, the big problem is, how to create gravitational waves in a controlled manner in the first place. Because the fact remains, that gravity is, by several orders of magnitude, the weakest force in our universe and it takes stooopid amounts of energy (and I means that in an all-encompassing way, referring to anything that goes into the metric tensor) to create an even noticeable ripple in spacetime. If we break down spectrally, its easiest to detect stuff close to DC, I mean, people did it 200 years ago, so to speak, but only over short distances, and really long integration times (https://en.wikipedia.org/wiki/Cavendish_experiment).
But anything meaningful for data transmission would require to operate at significant high frequencies. It's hard enough to wiggle around some "condensed energy", i.e. mass in the milligram scale at high frequencies, although in the lasers I build, the end facets of the optical filter are thrown around with accelerations on the order of 10e6 g-ees, at ~500kHz, but the gravitational waves created by that wouldn't register at LIGO even if several thousand of these, running in phase were placed right next to the test masses.
To make any sensible use of gravitational waves, we'd need to invent some form of gravitational …aser (light: laser / microwaves: maser), i.e. a gwaser. Gravitational Wave Amplification by Stimulated Emission of Radiation. Okay, I admit it, this is one of these gedankenexperiments I play through in my head from time to time, trying to come up with some technological setup, that could do it. If I had to make a bet, I'd say whatever it'd be, it'd be similar to a free electron laser.
But it's foolish to even go further than rough speculation, what components it possibly may involve, because to really make headway in that direction, we'd need a workable quantum theory of gravity. And last time I've checked, that's still an open problem.
On the uphand, should we ever figure out, if one can, and if so how to build a gwaser, this would open up possibilities far beyond new modes of communication. I'm talking propulsion that uses gravitational radiation as "reaction mass" (that'd be a no brainer, since gravitational waves to carry momentum, that's why the orbits of binary black hole systems decay in the first place). But maybe even stuff that's really outlandish science fiction, maybe even not causality breaking (not all timelike curves do violate causaility; go ahead, draw a few Minkowsky diagrams, to see what I mean) FTL travel.
And given that, I'd put this mathematical result into the same category of applicability as the Alcubierre metric: A nice consequence of mathematical rigor, but without further understanding of fundamental physics of little practical interest, so far.
And "end facets of the optical filter"? What is being thrown around?
I assume he's meaphorically using the term "direct current", so the low frequency stuff. As far as I know, LIGO effectively bandpasses gravitational waves in the range 7 to 30 Hz, or so.
Calling the Cavendish experiment a measure of gravitational waves, though, is sorta like saying Newton discovered an early theory of relativity. Not wrong, in the most pedantic sense, but definitely a bit disingenuous.
I'm not quite sure about the laser facets comment, though.
I didn't see the need for sarcasm tags. But then again, if you're honest about it LIGO is not that much different in _basic principle_ from the Cavendish experiment (measure the displacement of test masses), only that the sensitivity of the displacement detector is a lot of orders of magnitude higher.
And remember that a core step in the Cavendish experiment is to "flip" around the position of the big masses, so there's some kind of gravitational transient pulse event, which, if you're honest about translates into a very broadband spectrum, when compared to the integration time of the experiment.
I'm guessing that we're talking about different things. If you think of gravitational waves as any non-zero Fourier transform of some gravitational potential, then you and I agree, but that's not what we typically mean by "gravitational waves" which are, formally, metrics admitting a covariantly null vector field.
One reason for the distinction is that in a GR analysis of the 2-body problem, the radial potential energy contains an extra term not in a Newtonian analysis. This is interpreted as energy carried away by gravitational radiation. Even in a classical case, an external observer witnesses a periodic gravitational potential, but only in GR do the waves carry energy and cause Mercury to precess.
The error bars on the early Cavendish experiments were way bigger than any GR correction to Newtonian gravity. As such, we can safely analyze it within the realm of Newtonian mechanics which only admits DC offset "gravitational waves". That was the intent of my original comment.
Actually, as far as I understand it, the Cavendish experiment is simply a static equilibrium analysis. We measure the deflection of a torsion pendulum with and without the test masses present. I'm not sure what you are referring to with the "flipping" procedure, but I'd guess it's more about homogonizing erros rather than generating "force pulses".
Totally got that, no worries. And yes, I do see where you're coming from. But I base my argument not on the concept of the quasi-static potentials of a field theory with infinite speed of potential propagation (i.e. Newton).
> Even in a classical case, an external observer witnesses a periodic gravitational potential
But this assumes instantaneous propagation of the potential.
In every field theory in which changes (i.e. disturbances) of the field propagate with limited speed any accelerating movement of the generating sources of the field will create waves in that field.
Wiggle around some electric charge and you get EM waves carrying away energy. Einstein's first (and failed) attempt toward a relativistic theory of gravity was to apply the concept of retarded potentials. Didn't work out, something was missing. But even in such a retarted gravitational potentials theory, gravitational waves do show up.
> and cause Mercury to precess.
Isn't the precession of Mercury an effect of contraction of space by mass and that at the radii of perihel and apehel the metric of space is different?
Even the tiniest spec of dust moving at Mercury's orbit should experience the same precession, yet will radiate much less energy away through gravitational waves, as far as I understand it.
> but that's not what we typically mean by "gravitational waves" which are, formally, metrics admitting a covariantly null vector field.
Yes I know, GR permits for additional wave modes, that you don't have in e.g. electrodynamics in the vacuum. But I think it's dishonest to dismis the more "mundane" modes to be not gravitational waves.
As far as I see it, in any field with limited propagation delay, any disturbation propagating through the field is a true wave in a its right in that field. If you want to reach a fundamental theory which can be applied universally without the requirement of a-priori choices being made on the system modelled, all aspects of the theory must be "enabled" all the time.
> As such, we can safely analyze it within the realm of Newtonian mechanics which only admits DC offset "gravitational waves"
… which is what I was saying by having long integration times. And as far as nature goes, in any real system there is no true DC offset, because that would require integration from -inf to +inf. Yes, I did mention "DC", but in a practical sense DC just means "frequency which interval is an order of mangitude longer than the integration time of the observation".
Here's a little food for thought: Say you have an mechanical shutter and shine some long coherene (= narrow bandwidth) laser through it. Then you quickly close and open the shutter. How does the spectrum of the light look like after the shutter? Integrating over the spectrum before and after the shutter does the power change? If so where did the delta in energy go / come from?
This is some practical wave dynamics engineering we laser guys do on a regular base and solely rests on the fact that in a universe of finite age there is no such thing as a true DC component; you can get infinitesimally close to DC, but never reach true DC in the first place. So for example we use (fast) modulators to create spectral sidebands and even do things like carrier and single sideband suppression to shape the light to our bidding; becomes really interesting if you throw nonlinear effects into the mix that allow to all sorts of up-/downconversion.
> I'm not sure what you are referring to with the "flipping" procedure, but I'd guess it's more about homogonizing erros rather than generating "force pulses".
You're remembering right. What you do in the Cavendish experiment is to rotate the big masses by 90° so that the torsion pendulum is twised in the opposite direction, so that offsets in the pendulum cancel out. However consider this: Instead of moving the big masses at descrete times, let them (slowly) oscillate, maybe at the resonance frequency of the pendulum. If the pendulum has a high Q factor it will eventually reach quite the significant oscillation amplitude.
So what is this? I'd say this is energy transfer through gravitational waves in the near field.
One of the mirrors of a Fabry-Perot filter mirror pair. It's displaced with an amplitude of ~200µm at a frequency of about 500kHz:
d²/dt² 0.2·10^-3m * sin( t * 2pi * 500·10^3/s) = - 2.0·10^8 pi² sin(…) m/s²
That's about 10Mg of acceleration. Yes, these filters exist, and yes, they do work very well and reliably. These filters are the core technology of FDML lasers. See the patent here: https://patents.google.com/patent/US20130070794A1/en
You can buy FDML lasers using these very filters from the company I co-founded: https://www.optores.com/index.php/products/31-next-generatio...
Or if you don't have line of sight because there is an occluding object like a planet or star in the way.
Or you have line of sight but it's really close to a super bright object so you can't see anything.