View Full Version : Wavelengths of Gravitational Waves

a1call

2016-Feb-19, 04:23 PM

Hi,

* How could we define the wavelength of a Gravitational-Wave in terms/units of length when it involves variations in the very length that is being described?

An analogous question would be:

* How would you define the increase in length of a section of an elastic band in terms of the total length of the same elastic band, when there is no rest length/state defined nor is definable for the said elastic band.

From what I understand in a space void of all matter, length and time are undefined.

Thanks in advance.

trinitree88

2016-Feb-19, 05:51 PM

Hi,

* How could we define the wavelength of a Gravitational-Wave in terms/units of length when it involves variations in the very length that is being described?

An analogous question would be:

* How would you define the increase in length of a section of an elastic band in terms of the total length of the same elastic band, when there is no rest length/state defined nor is definable for the said elastic band.

From what I understand in a space void of all matter, length and time are undefined.

Well, since it appears that they propagate @ "c"...and the length can be defined as the velocity times the time interval...delta T, then knowing the measured time between successive elongations of an arm of a laser interferometer...(LIGO)....would constitute an operational definition of the wavelength....."d" ="c" delta T.

And....it is impossible to have a volume of Minkowski space-time that is entirely devoid of all mass/energy. You can remove all the baryons, but you can't eliminate the ambient neutrino sea, nor the Zero-Point Radiation due to the Heisenberg Uncertainty Principle.

So, if you were "magically" transported to the Bootes void, and an evil, mad, scientist with supernatural powers were to materialize an Earth-mass black hole just 10 meters past you......all the "sea" neutrinos coming from the steradians of that volume towards you, would stop, being captured by the BH. Since they travel @ "c", or within 10 -17 of it (according to the g-wave papers)...the absence of them would be seen in the overall neutrino flux from the BH's direction. That drop, not an increase, would be coincident with the BH's gravitational wave form. ( A number of papers were just released looking for an increase in the neutrino flux at Ice Cube, etc ...coincident with the g-wave detection. They found no such increase. That's cause it's not there. Should have been looking for a decrease instead).

I am reminded that when T.D.K. Lee and C. N. Yang, suggested that the resolution of the Tau/Theta Paradox in K meson decays might be that parity was not conserved in them......and that nobody had ever looked for it......it was then found in every run of every experiment ever done ,that would have shown it, and nobody had ever checked. Somebody should check the neutrino labs for a slight decrease that occurs coincident with the max of the wave.

Betcha a hot fudge sundae, and yep, I owe Grey one. (Grey,PM me for an address...I paid my bill with Antoniseb @ a Thai restaurant in Metrowest. ) pete

I'm adding a note to myself on neutrino anomalies....here: http://www.physics.smu.edu/~web/seminars/seminar_archive/Spring2008/neutrino_photon.int.pdf

antoniseb

2016-Feb-19, 06:51 PM

...I paid my bill with Antoniseb @ a Thai restaurant in Metrowest. ...

confirmed.

antoniseb

2016-Feb-19, 06:54 PM

... How could we define the wavelength of a Gravitational-Wave in terms/units of length when it involves variations in the very length that is being described?...

Really we're just going with speed of light divided by frequency... but I'm sure you're also aware of how many significant digits you'd need before the contraction of space would matter in the aLIGO observation.

Ken G

2016-Feb-19, 07:39 PM

Betcha a hot fudge sundae, and yep, I owe Grey one. You want to owe me two? Because of course there would never be a detectable decrease in the neutrinos during that event, as there is no baseline detection rate to begin with, for neutrinos in the neutrino "sea" coming from the minute solid angle that would be covered by those black holes. What's more, there were already black holes there, they merely merged. And you have not even accounted for the lensing of background neutrinos in the sea. But all of this is silly to even think about, the neutrino flux from any stellar objects a billion light years away is undetectable by modern means.

There does appear to have been a detection of gamma rays, so the idea was that maybe there'd be a neutrino excess also, but that was never particularly plausible. So it is easy to expect neither an increase, nor a decrease, in the essentially zero neutrino levels expected from that exceedingly tiny portion of the sky.

Ken G

2016-Feb-19, 07:51 PM

* How could we define the wavelength of a Gravitational-Wave in terms/units of length when it involves variations in the very length that is being described?I think what you are asking is, if a gravitational wave made all lengths contract and expand, including what we mean by a meter, how could we even tell it ever went by? The answer is, what the wave does is change the relative elapsed phase that light experiences as it propagates along the paths of the arms of the interferometer. That's what you measure, and that's what the gravitational wave alters. You can picture that alteration in many ways, depending on the coordinates you choose to describe it, but the lazy way is to say you have light of given frequency propagating at given speed, so any difference in phase can be associated with a difference in effective distance. Whether that is a "real" distance is very hard to say in relativity, which is what you are asking about-- usually it is just a matter of coordinates. This is similar to language like "space expands carrying the galaxies with it", that we often hear in cosmology.

a1call

2016-Feb-19, 08:53 PM

Disclosure: Sometimes it takes some time for things to sink in for me. So if the issue is resolved already apologies for missing it.

I think what you are asking is, if a gravitational wave made all lengths contract and expand, including what we mean by a meter, how could we even tell it ever went by?

You would have made a good carpenter Ken G. You seem to have a good aim at hitting the nails in the head.

For the sake of argument let's exaggerate a lot. Let's assume that GWs were very slow moving like the waves in the ocean and we could actually use the platinum meter stick in France to measure them peek to peek.

Given the meter stick would be subject to length variation along and equal to the space it occupies, why would be measuring anything at all?

Why would phases of light be exempt from this fundamental stretching of the space they travel through?

Thank you everyone for the replies.

Strange

2016-Feb-19, 08:54 PM

I was under the impression that gravitational waves had no effect on space in the "z" direction (direction of travel) and so the slightly confusing problem doesn't really arise.

a1call

2016-Feb-19, 09:16 PM

Ok I think it's starting to sink in.

I guess perhaps it's more like using an Isosceles right angle triangle for measuring which the differential stretching causes the internal angles to change.

01101001

2016-Feb-19, 09:30 PM

Maybe the image here will help with visualization: CalTech.edu: Gravitational waves (http://www.tapir.caltech.edu/~teviet/Waves/gwave.html)

21337

Edit, just to add some searchable text in case the link goes stale:

By analogy with electromagnetic dipole radiation, we can say the following things about gravitational waves:

Whereas static fields have both radial and transverse components, the radiative fields are purely transverse.

Whereas static fields fall off as 1/r³, the radiative fields fall off only as 1/r, and soon completely dominate over the static fields.

a1call

2016-Feb-19, 09:53 PM

Thank you 01101001,

Nice animation and nice read. It also explains the 1/r dissipation which is another thing I have to wrap my head around. I thought I understood the inverse square law pretty well and could be confident at why it was always the precise dissipation rate.

But that's for another day.

Ken G

2016-Feb-19, 11:08 PM

I'd say the most fundamental thing to "get" about gravity is that the distance between any two objects is a dynamical quantity. We used to think the only way to make that distance dynamical was to have those objects be "moving", but relativity told us that motion is something local-- it means that two things are passing each other (or crashing into each other) at the same place and time, that's what "moving" means. All nonlocal versions of "motion" are something quite different-- they are coordinatizations in spacetime, nothing more or less. What gravity does (or if you prefer, what general relativity does) is tell us, given a chosen global coordinatization, what are the inertial motions within those coordinates (i.e., the motions that require no force). We always knew that you could have two objects getting farther from each other and have that be inertial, but we always thought that if the distance between two objects was oscillating in time, that could not be inertial, meaning that Newton's laws would never appear to be working in those coordinates without some kind of force. But that's what is wrong-- when a gravitational wave goes by, the distance between two objects oscillates, and it's still inertial (i.e., Newton's laws work fine in a coordinate system where the distance is oscillating, no forces needed).

So what this means is, if you have a platinum ruler in France and a gravitational wave goes by, the phase that a given light wave started at one end of the rod will arrive at the other end of the rod will be different. You can call that distance a meter the whole time, that's just a coordinate-- it's not what you measure. What you measure is how much the phase of the light advances along the rod if it points in one direction, compared to how much it advances if the rod points in another direction, which you tell by interfering the two. You can get that answer in many different coordinates, some which say the rulers are changing lengths and others which say they are not, so the changing length is not the issue, it's just a picture like saying that space is expanding in the Big Bang. The latter is not something we measure either, we only measure redshifts that we interpret via a constant speed of light, and then if you tell me the coordinates you are using, I can tell you what is happening to distances in that coordinate system.

Strange

2016-Feb-19, 11:38 PM

Another good explanation in this presentation: https://www.aapt.org/doorway/tgrutalks/Saulson/SaulsonTalk-Teaching%20gravitational%20waves.pdf

a1call

2016-Feb-20, 12:20 AM

Thank you Ken G and Strange.

For instance, I thought that light waves weren’t

stretched by gravitational waves, because if they

were then I “knew” that then the interferometer

wouldn’t respond to a gravitational wave.

It's good to see a professor at some point thought the same way.

swampyankee

2016-Feb-20, 12:43 AM

Hi,

* How could we define the wavelength of a Gravitational-Wave in terms/units of length when it involves variations in the very length that is being described?

An analogous question would be:

* How would you define the increase in length of a section of an elastic band in terms of the total length of the same elastic band, when there is no rest length/state defined nor is definable for the said elastic band.

From what I understand in a space void of all matter, length and time are undefined.

Thanks in advance.

This is why they invented Fourier transforms.

a1call

2016-Feb-20, 01:09 AM

This is why they invented Fourier transforms.

Engineers are all the same.:)

I recall my Electronic engineer friend bringing that up time and again during our discussions on just about any subject.

Unfortunately non linear mathematics doesn't quite ring in with me.

swampyankee

2016-Feb-20, 12:11 PM

Engineers are all the same.:)

I recall my Electronic engineer friend bringing that up time and again during our discussions on just about any subject.

Unfortunately non linear mathematics doesn't quite ring in with me.

We're isomorphic? Like malls?

If I understand the functioning of LIGO correctly, the gravity waves change the distance light travels on one of tge two legs relative to the other, so LIGO cannot detect waves from directions where both legs are equally distorted. Can LIGO detect waves from source located on a line perpendicular to the plane of the interferometer? Or am I misunderstanding?

01101001

2016-Feb-20, 12:43 PM

Can LIGO detect waves from source located on a line perpendicular to the plane of the interferometer?

LIGO is 2 detectors, in different planes.

(And as I understand it, an ideal signal for a detector comes from a system with a rotation plane parallel to the dector plane, and located on a line perpindicular to the detector plane.)

Ken G

2016-Feb-20, 03:37 PM

Can LIGO detect waves from source located on a line perpendicular to the plane of the interferometer?Yes, that is indeed optimal. A gravitational wave has a quadrupolar character, which means it distorts oppositely in the two perpendicular directions in the transverse plane. It also depends on the polarization, but that gets complicated of course. There's a lot they have "dumbed down" for us in their animations!

George

2016-Feb-20, 10:56 PM

Is the wavelength determined under the assumption of perfect elasticity of space time? I can't get over the ginormous peacefulness of the adjacent space releasing ~ 3 solar masses of energy. If amplitude were to not be linear, perhaps local debris would spaghettify and release, with delay, a GRB.

ShinAce

2016-Feb-21, 02:00 AM

Where are you measuring this wavelength? Are you measuring here on Earth where the distortion was many times smaller than a proton over 4km? Are you measuring it within 500km of the event?

Your use of the word 'elasticity' eludes me.

Nonetheless, a decent reference is:

https://en.wikipedia.org/wiki/Linearized_gravity

"The linearised Einstein field equations (linearised EFE) are an approximation to Einstein's field equations that is valid for a weak gravitational field and is used to simplify many problems in general relativity and to discuss the phenomena of gravitational radiation. The approximation can also be used to derive Newtonian gravity as the weak-field approximation of Einsteinian gravity.

The equations are obtained by assuming the spacetime metric is only slightly different from some baseline metric (usually a Minkowski metric). Then the difference in the metrics can be considered as a field on the baseline metric, whose behaviour is approximated by a set of linear equations."

Regarding GRBs. I consider it preliminary/speculative, but there is evidence of a short GRB associated with this event.

See:

https://en.wikipedia.org/wiki/First_observation_of_gravitational_waves

"However, observations using the INTEGRAL telescope, through the all-sky SPI-ACS instrument, indicate that the amount of energy in gamma-ray and hard X-ray emission from the event are less than one part in a million of the energy emitted in the form of gravitational waves, concluding that "this limit excludes the possibility that the event is associated with substantial gamma-ray radiation, directed towards the observer."[45]"

Quite a tame GRB for such an energetic event. However, I'm curious as to the orientation of the orbital plane of these black holes prior to the merger.

George

2016-Feb-21, 07:16 AM

But do we truly understand GR when it comes to grVity wave propagation? I recall reading of an early GR solution by de Sitter (empty universe, IIRC) showing redshift varying with the inverse square for distance.

Is a 3 solar mass energy blast not an elephant in the room?

I know too little of GR to address how elasticity of space time would play a roll in gravity wave propagation but it often does in other propagation. "Elasticity" probably is too crude a term, but I am loosely aiming at something more in line with the second law. A 3 solar mass loss would shrink the Event Horizon, thus shrinking the total entropy for the resulting black hole itself, I think. If so, does the surface area decrease not shove the lost entropy to the surrounding area?

There are many astounding things I've learned from being here among you, including very non-intuitive things, and this one is a doozie!

ShinAce

2016-Feb-21, 07:24 PM

But do we truly understand GR when it comes to grVity wave propagation? I recall reading of an early GR solution by de Sitter (empty universe, IIRC) showing redshift varying with the inverse square for distance.

Is a 3 solar mass energy blast not an elephant in the room?

I know too little of GR to address how elasticity of space time would play a roll in gravity wave propagation but it often does in other propagation. "Elasticity" probably is too crude a term, but I am loosely aiming at something more in line with the second law. A 3 solar mass loss would shrink the Event Horizon, thus shrinking the total entropy for the resulting black hole itself, I think. If so, does the surface area decrease not shove the lost entropy to the surrounding area?

There are many astounding things I've learned from being here among you, including very non-intuitive things, and this one is a doozie!

Huh? What's the connection between gravitational wave propagation and a DeSitter/anti-DeSitter metric? Sounds like a square peg and a round hole to me.

An elephant in the room? Compared to what? A pleasant afternoon tea....

The second law of what? Newton's laws of motion? Thermodynamics?

Cougar

2016-Feb-22, 01:27 AM

But do we truly understand GR when it comes to grVity wave propagation?

Apparently, since Einstein worked the math that predicts them in GR nearly 100 years ago.

I recall reading of an early GR solution by de Sitter (empty universe, IIRC) showing redshift varying with the inverse square for distance.

My guess would be that's not right. It's a linear relation. de Sitter solutions are not that extraordinary. Oddly, wiki reports de Sitter space to necessarily have a positive spatial curvature, while the de Sitter universe is spatially flat, with a positive cosmological constant, much like the one we find ourselves in. (Sure, it's a vacuum solution, but large "condensations" of matter are dwarfed by the amount of vacuum between them.) I could be wrong, but I would doubt there's a solution in de Sitter space that makes redshift-distance an inverse square relation.

Is a 3 solar mass energy blast not an elephant in the room?

Certainly a ginormous event. Massive black holes spiraling together? Yeah, big.

I know too little of GR to address how elasticity of space time would play a roll in gravity wave propagation but it often does in other propagation. "Elasticity" probably is too crude a term, but I am loosely aiming at something more in line with the second law. A 3 solar mass loss would shrink the Event Horizon, thus shrinking the total entropy for the resulting black hole itself, I think. If so, does the surface area decrease not shove the lost entropy to the surrounding area?

The 3 solar masses of gravitational wave "energy" in that last second are propagated before the event horizons coalesce. They were never part of the event horizon of the merged black hole. I understand that the surface of a black hole is associated with its entropy, but I don't see where that has any application here.

....this one is a doozie!

Really! An extremely odd manifestation of one of the workings of gravity. We already knew that gravity "bends" space "gravitationally." GWs do it waves.

Can we imply anything about the "fabric" or the makeup of the vacuum from this seeming hint? Is the background field of virtual particles any different in fields of high gravitation?

01101001

2016-Feb-22, 02:43 AM

In case this topic on gravitational wave wavelengths has not mentioned the actual range of lengths:

Caltech: Gravitational wave spectrum (http://www.tapir.caltech.edu/~teviet/Waves/gwave_spectrum.html)

Whereas astrophysical electromagnetic waves are typically much smaller than their sources, ranging from a few kilometres down to sub-nuclear wavelengths, gravitational waves are larger than their sources, with wavelengths starting at a few kilometres and ranging up to the size of the Universe.

It has a nice graph of strain (amplitude) vs. wavelength, showing what typical sources would generate and where existing and planned detectors could observe.

George

2016-Feb-22, 06:22 AM

Huh? What's the connection between gravitational wave propagation and a DeSitter/anti-DeSitter metric? Sounds like a square peg and a round hole to me.

The point is that not all GR solutions pan out, though for all I know his empty universe solution was right. All I'm suggesting is that a linear solution may fail near the black hole or during propagation or both. It seems exciting that the waves have been discovered, which is more about opening a new chapter in understanding space time than closing one. I would expect new, important data will advance theory.

An elephant in the room? Compared to what? A pleasant afternoon tea.... A three solar mass detonation association with serenity is some serious irony.

The second law of what? Newton's laws of motion? Thermodynamics?The mass/energy loss shrinks the surface area, thus greatly reducing the entropy. Where does the missing entropy manifest itself especially assuming a nice linear amplitude propagation only. I am highly suspicious that there is a great deal more to the story?

George

2016-Feb-22, 06:46 AM

Apparently, since Einstein worked the math that predicts them in GR nearly 100 years ago. In 1936, he changed his mind and opposed the idea of gravity waves. There is more we will learn about GR, no doubt, from the study of these waves.

My guess would be that's not right. It's a linear relation. de Sitter solutions are not that extraordinary. Oddly, wiki reports de Sitter space to necessarily have a positive spatial curvature, while the de Sitter universe is spatially flat, with a positive cosmological constant, much like the one we find ourselves in. (Sure, it's a vacuum solution, but large "condensations" of matter are dwarfed by the amount of vacuum between them.) I could be wrong, but I would doubt there's a solution in de Sitter space that makes redshift-distance an inverse square relation. I don't know if he was right or wrong in his specific solution, but we now know redshift is linear. There is an interesting story where Hubble visited with de Sitter and learned of his inverse square solution, thus suggesting to me that this could easily partially explain Hubble never positing the expansion idea that is now so obvious to us today.

Certainly a ginormous event. Massive black holes spiraling together? Yeah, big. If we go fishing together at one of these holes, are you buying the idea our boat won't rock? I think at least one of us might be seen in the form of gamma rays.

The 3 solar masses of gravitational wave "energy" in that last second are propagated before the event horizons coalesce. They were never part of the event horizon of the merged black hole. II don't see where that has any application here. Entropy change produces significant effects. There is likely some interesting ideas what those effects might be when applied to the surrounding area.

Can we imply anything about the "fabric" or the makeup of the vacuum from this seeming hint? Is the background field of virtual particles any different in fields of high gravitation?The gamma ray burst data may be more helpful than the GW results. If they are associated, then why? The elephant may be hostile.

George

2016-Feb-22, 06:20 PM

Cougar, I like your past book recommendations and I know you will enjoy the 2013 edition of Hubble's "The Realm of the Nebulae". The forewards by Carroll, Sandage, and Kirshner are exceptional in their brief historical perspectives. [ I shop Half-Price bookstores for such nuggets.]

Powered by vBulletin® Version 4.2.3 Copyright © 2019 vBulletin Solutions, Inc. All rights reserved.