What is a gravitational wave?

[Robittybob1]

Gravitational waves have been measured but what are they measuring?

 

Like we have 2 black holes orbiting each other ..... their orbit decays so they unite. That loss of energy required to have this orbital decay is ....

 

 

Can we say gravity and gravitational waves are the same?

Can someone fill in my lack of understanding of this phenomenon and complete those sentences?

[Mordred]

Ok first off you need to be clear on some aspects. Mass and energy are both properties. They are not things unto themselves.

 

So considering the above how is a gravitational field defined? For that matter "how is spacetime defined?"

 

Well as mass and energy doesn't exist on its own we need something to measure. So lets use hypothetical test particles.

 

https://en.m.wikipedia.org/wiki/Test_particle

 

So to define a gravitational field we place a test particle at every point in space. Now GR is all about coordinates. So assign coordinates to each point. Add time as a coordinate time treated as a vector with direction (forward) and variable magnitude.

 

Now we have this speed limit defined by c. This speed limit isn't just the speed limit of light, it's also the speed limit of interactions and quantum information exchange. (Entangled particles don't violate this either but that's too lengthy to cover here).

 

To give an extreme example consider a rod one light year in length. Common sense would falsely suggest that if you move the rod at one end it should instantly move in the other end.

 

This is wrong, the rod is made up of particles, the momentum must be transmitted via particle to particle interactions. So the other end as a result will take a light year before it will move ( longer if you factor in the influence of the medium).

 

Gravity waves suffer the same problem. In order to transfer momentum you require particle/particle interactions. In other words the test particles.

 

However you don't necessarily require test particles, they are just handy. All particles are influenced by gravity. So typically the spacetime is simply defined by its energy/mass distribution. (With the understanding we can only measure an object or particle.. not an empty volume).

 

Now more complex is the energy/monentum tensor of the Einstein Field equations. This tensor tells us how particles move and behave

[latex]t_{\mu\nu}=\begin{pmatrix}-1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}[/latex]

 

Or

 

[latex]t_{\mu\nu}=\begin{pmatrix}\rho&0&0&0\\0&p&0&0\\0&0&p&0\\0&0&0&p\end{pmatrix}[/latex]

"The stressenergy tensor (sometimes stressenergymomentum tensor or energymomentum tensor) is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics. It is an attribute of matter, radiation, and non-gravitational force fields. The stressenergy tensor is the source of the gravitational field in the Einstein field equations of general relativity, just as mass density is the source of such a field in Newtonian gravity."

 

https://en.m.wikipedia.org/wiki/Stress_tensor

 

Essentially it is the stress tensor that tells space how to curve.

 

A gravity wave transfers energy momentum through the stress tensor distribution in spacetime. However as mentioned momentum requires particle to particle interaction. So does energy as energy doesn't exist on its own.

 

I'll add some metrics involving a gravity wave layer on. After work

I'm going to cheat a bit here. This is taken from "Introductory to Cosmology" by Matt Roose. He does a better justice of gravitational waves itself than I could. Page 81.

 

 

"gravitational radiation is caused only by nonspherically symmetric accelerations of mass, which can be related to the quadrupole moment, and the oscillatory stretch and squeeze produced is then described by two dimensionless wave elds h+ and h×, which are associated with the gravitational waves two linear polarizations. If h+ describes the amplitude of polarization with respect to the x- and y-axes in the horizontal plane, h× describes the independent amplitude of polarization with respect to the rotated axes x +y and x − y (cf. Figure 3.7). The relative tidal effect a detector of length L may observe is then a linear combination of the two wave elds

∆L/L = a+h+(t) + a×h×(t) ≡ h(t). (3.32)

The proper derivation of the quadrupole formula for the energy loss rate through gravitational radiation of an oscillating body and the spatial strain h(t) caused on bodies elsewhere cannot be carried out here, it requires general rela- tivity to be carried out to high orders of covariant derivation. This complication is a benet, however, because it renders the detection of gravitational radiation an extremely sensitive test of general relativity.

 

an extremely sensitive test of general relativity.

In a Newtonian approximation the strength of the waves from a nonspherical body of mass M, oscillating size L(t), and quadrupole moment Q(t) ≈ ML^2 at a distance r from Earth is

[latex]h(t)=\frac{G}{c^4}\frac{ d^2Q(t)}{dt^2}=\frac{G}{c^4r} 2Mv(t)^2=\frac{4G}{c^4r}E(t)[/latex] (3.33)

 

where G is the Newtonian constant, v is the internal velocity, and E = [latex]\frac{1}{2}Mv^2[/latex] is the nonspherical part of the internal kinetic energy. The factor c^4 is introduced only to make h(t) dimensionless"

 

 

As stated Matt Roose does a better job.

Edited February 13, 2016 by Mordred

[Robittybob1]

I could understand most of that except the sentence "Essentially it is the stress tensor that tells space how to curve." That telling bit is that limited to the speed of light too?

[Mordred]

Does the term stress energy momentum tensor help? Short answer is changes in the stress energy momentum tensor is limitted to the speed of light.

[Mike Smith Cosmos]

This sounds a bit like hitting a galvanised scaffolding rod at one end with a metal bar . Then the vibrations caused by the inbuilt tension of the steel , transfer their energy , atom to atom , through the bar as a sound wave . This then arrives at the other end as a sound vibration , if you put your ear to it .?

 

But the maths sounded a bit steep !

 

Mike

 

Oops ! I've done it again , and doubled up on your posting , sorry !

 

Is this tensor bit saying that :

 

The interchanges going on at the sub atomic and atomic , level ( particle to particle ) are " electro magnetic " in nature , and thus are bound by the speed of light ' c' , because that is the speed of electro- magnetic devices, interactions , such as electrons and protons ? But that would infer there was matter present ?

 

Mike

Edited February 13, 2016 by Mike Smith Cosmos

[Robittybob1]

Does the term stress energy momentum tensor help? Short answer is changes in the stress energy momentum tensor is limitted to the speed of light.

So is there nothing telling anything any more but just that each point in space has a stress energy momentum tensor (SEMT)?

Is that limitation built into the equation? Does it have to be information transferred? Like could each test particle know its own SEMT?

Like in the Milky Way galaxy billions of stars all moving around how is that information handled if it is dependent on information exchange?

It gets worse than that to for every photon and neutrino also affect the SEMT. I just can't get my head around the complexity.

Edited February 13, 2016 by Robittybob1

[Mordred]

How is momentum transferred? Mike's analogy is fairly accurate.

This sounds a bit like hitting a galvanised scaffolding rod at one end with a metal bar . Then the vibrations caused by the inbuilt tension of the steel , transfer their energy , atom to atom , through the bar as a sound wave . This then arrives at the other end as a sound vibration , if you put your ear to it .?

 

But the maths sounded a bit steep !

 

Mike

 

Oops ! I've done it again , and doubled up on your posting , sorry !

Another analogy is p waves from an earthquake.

Edited February 13, 2016 by Mordred

[Mike Smith Cosmos]

 

Is this tensor bit saying that :

 

The interchanges going on at the sub atomic and atomic , level ( particle to particle ) are " electro magnetic " in nature , and thus are bound by the speed of light ' c' , because that is the speed of electro- magnetic devices, interactions , such as electrons and protons ? But that would infer there was matter present ?

 

Mike

[Mordred]

The electromagnetic stress tensor is different in its commutations than the stress energy momentum tensor. Replace matter with energy/mass only fermionic particles count as matter.

 

A photon field can produce gravity, so can a gravity wave lol. Photons are bosons. Yet are not considered matter. Same with any boson.

 

The polarizations above has nothing to do with electromagnetic charge.

Gravitational radiation is caused only by nonspherically symmetric accelerations of mass, which can be related to the quadrupole moment"

I should have linked the proper stress tensor.

 

https://en.m.wikipedia.org/wiki/Stress%E2%80%93energy_tensor

 

Which is the one used in the EFE

[Mike Smith Cosmos]

.

Stress ...energy ...tension ..( I think my brain just had a fit ...to scream ) Edvard Munch .

 

Mike

Edited February 13, 2016 by Mike Smith Cosmos

[EdEarl]

The measuring instrument consists of a laser beam that is split into two beams, one reflected perpendicular to the other. Each half shines down a long tube and is reflected back towards the origin using a very flat mirror. They examine the phase of the two received light beams to see if they are exactly in phase or not. Without a gravity wave, the beams are in phase. If a gravity wave passes through the instrument, the phases of the two beams are not exactly in phase. They measured out of phase by 1/1000th the thickness of a proton as the amount a gravity wave affected the two beams at different times.

 

See https://en.wikipedia.org/wiki/Gravitational-wave_observatory.

 

Q: Would it be possible to split the laser beam into thousands of beams radiating out as a sphere, that bounce back to be collected and analyzed to form an image of the source of the gravity wave?

 

Maybe this Q should be split into a different thread, IDK. It's not related to the topic of this post, but is related to the first question by the OP.

Edited February 13, 2016 by EdEarl

[Strange]

Can we say gravity and gravitational waves are the same?

 

They are the results of the same thing: the curvature of space-time.

 

You may have seen the bowling ball in a rubber sheet analogy for gravity. This shows that the static curvature of space-time causes the force we think of as gravity.

 

Now imagine the bowling ball moving (or bouncing up and down). In this case their will be ripples in the sheet that spread out (like ripples in a pond). That is an analogy for gravitational waves.

[imatfaal]

...

 

Q: Would it be possible to split the laser beam into thousands of beams radiating out as a sphere, that bounce back to be collected and analyzed to form an image of the source of the gravity wave?

An 8k sphere - well it is ambitious but seeing the trouble we had getting the LHC funded I reckoned that will a No for the foreseeable future

Edited February 13, 2016 by imatfaal
to fix quote

[EdEarl]

An 8k sphere - well it is ambitious but seeing the trouble we had getting the LHC funded I reckoned that will a No for the foreseeable future

Seems to me there would be a few technical challenges, too. Moreover, it's not clear to me how math could reconstruct images. Waves would be coming from the big bang, supernova, colliding stars, merging black holes, etc. How could all that noise be processed into an image?

 

It might be best to put that sphere in space, where vacuum is everywhere. If feasible, it certainly would be expensive.

Edited February 13, 2016 by EdEarl

[Robittybob1]

 

They are the results of the same thing: the curvature of space-time.

 

You may have seen the bowling ball in a rubber sheet analogy for gravity. This shows that the static curvature of space-time causes the force we think of as gravity.

 

Now imagine the bowling ball moving (or bouncing up and down). In this case their will be ripples in the sheet that spread out (like ripples in a pond). That is an analogy for gravitational waves.

I would like to get away from that rubber sheet analogy, for it only works if there is a reason for the ball to fall down the slopes.

Will we get destructive interference of gravity waves too! Gravity waves through the double slit experiment! Quantum Gravitation theory! exciting stuff .... a lot of hard work for some budding scientist.

[ajb]

I would like to get away from that rubber sheet analogy, for it only works if there is a reason for the ball to fall down the slopes.

It is only an analogy...

 

Really we have to linearise Einstein's field equations (get rid of self-interactions), do some tricks to write the wave equation and BINGO we have gravitational waves!

 

Gravitational waves are to Einstein's field equation what electromagnetic waves are to Maxwell's equations. You do a few mathematical tricks and from Maxwell's equation you get the wave equation and so electromagnetic radiation.

[EdEarl]

I would like to get away from that rubber sheet analogy, for it only works if there is a reason for the ball to fall down the slopes.

Will we get destructive interference of gravity waves too! Gravity waves through the double slit experiment! Quantum Gravitation theory! exciting stuff .... a lot of hard work for some budding scientist.

The double slit experiment has particle-waves going through the slits. In this case, the source of the waves is dual orbiting black holes; how do you propose to move those black holes through double slits?

[Robittybob1]

The double slit experiment has particle-waves going through the slits. In this case, the source of the waves is dual orbiting black holes; how do you propose to move those black holes through double slits?

I presume that is some sort of joke? The LHC could up the power and produce 2 mini black holes. In fact you don't even need the BHs to go through the slits at the same time, that should make it a little easier and not to mention safer!

Pop science covered some of the safety aspects e.g. "The safety of the LHC"

http://press.web.cern.ch/backgrounders/safety-lhc

 

PS: I'm not certain if your reasoning is right for isn't it the wave or particle that goes through the slits rather than the BH. The energy released in the merger of massive objects is in the form of gravitational waves rather than BHs.

This might help us understand BHs better for where does that energy come from? Did something come out of a BH? Did the mass of the BHs reduce when the E=MC^2 formula is applied?

Edited February 13, 2016 by Robittybob1

[EdEarl]

Quantum particles are also waves, for example the photon carries the electromagnetic wave. However, all quantum particles are also waves. Thus, the particle-wave goes through the double slits. My response to your double slit statement was a joke, because your original post spoke of the measurement of gravity waves caused by 2 black holes. been talking about gravity waves. It might be possible to put Higgs bosons through the double slits; although, they decay very quickly, which might be a problem.

[Robittybob1]

Quantum particles are also waves, for example the photon carries the electromagnetic wave. However, all quantum particles are also waves. Thus, the particle-wave goes through the double slits. My response to your double slit statement was a joke, because your original post spoke of the measurement of gravity waves caused by 2 black holes. been talking about gravity waves. It might be possible to put Higgs bosons through the double slits; although, they decay very quickly, which might be a problem.

I never said it would be easy.

[Robittybob1]

From the paper

http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.116.061102

In the source frame, the initial black hole masses are 36þ5

−4M⊙ and 29þ4
−4M⊙, and the final black hole mass is
62þ4
−4M⊙, with 3.0þ0.5 −0.5M⊙c2 radiated in gravitational waves.

 

So 3 solar masses of energy are radiated into space and that mass is reflected in the reduced mass of the merged BH.

This is all happening in the last fraction of a second (0.3 sec??). As they get closer the frequency rises "signal sweeps upwards in

frequency from 35 to 250 Hz"

From the graph in that time that occurs all in 8 cycles.

Can anyone tell me where this mass comes from?

[Mordred]

Blackholes have a lot of mass, the mergers are also incredibly violent.

Take a look at their mass and acceleration.

 

How much energy is released in asteroids striking Earth?

 

The mass and velocity these two BH's collide at makes the asteroid example a joke in terms of energy release.

 

As the numbers above show the extreme violence of the mergers cause a loss in the total mass of the BH's

Edited February 14, 2016 by Mordred

[Robittybob1]

Blackholes have a lot of mass, the mergers are also incredibly violent.

Take a look at their mass and acceleration.

 

How much energy is released in asteroids striking Earth?

 

The mass and velocity these two BH's collide at makes the asteroid example a joke in terms of energy release.

 

As the numbers above show the extreme violence of the mergers cause a loss in the total mass of the BH's

But all mass in a BH is at the singularity isn't it? The singularities aren't contacting to clash as in an asteroid strike. The other thing to remember is that these merging black holes are likely (based on other examples of binary orbiting bodies) have been in a decaying orbit and radiating G-Rad for a long time before it was ever picked up by LIGO it was not just in the last 0.3 seconds, but only the last 0.3 seconds gave a strong enough signal to be picked up over 1 billion light years away on Earth.

Can you agree with that?

Edited February 14, 2016 by Robittybob1

[Mordred]

Who says all the mass is at the singularity? That is certainly the highest concentration but there is a buttload of energy surrounding the EH and acceleration disk.

[Robittybob1]

Who says all the mass is at the singularity? That is certainly the highest concentration but there is a buttload of energy surrounding the EH and acceleration disk.

This was one of the questions I wanted answered. Have you seen that being discussed anywhere else yet? Where was that mass?