Mordred

Tar's response is valid and quite accurate. Section 5 of the this LIGO paper has some of the applicable formulas. see section 5 https://www.google.ca/url?sa=t&source=web&rct=j&url=https://physics.aps.org/featured-article-pdf/10.1103/PhysRevLett.118.183602&ved=0ahUKEwiX5b6G0afUAhVmrFQKHafWBDMQFggdMAA&usg=AFQjCNHj5HzdaiCXdKwtT_I3zLkDR4_z-Q&sig2=-SnqX9aZTHKHkTLycIW71A It gives the phase variation formulas due to GW waves. Took me a bit to find a reference specific to the topic with the applicable formulas. Actually here is the generic formula involved. This article is more detailed on the actual metrics. REFERENCE FRAMES AND THE OBSERVABLE PHASE SHIFT OF THE CARRIER IN G.W. INTERFEROMETRIC DETECTORS https://www.google.ca/url?sa=t&source=web&rct=j&url=http://www.pas.rochester.edu/~meliss/URLIGO/030428_Referenceframes.pdf&ved=0ahUKEwiX5b6G0afUAhVmrFQKHafWBDMQFggqMAM&usg=AFQjCNEP36c0mLAulF75nU3g5SO1_hzfow&sig2=w-TEWmvM-A9cgmz1TfG12g equation 15.

really you refer to both momentum and angular being both conserved when there is no linear momentum to conserve in the first place within your system ? And you claim this is correct? Linear momentum is a vector whose direction is parallel to the velocity of the particle. with relations p=mv So pray tell where is your momentum term? in angular momentum the vector is a cross product which is a binary operation of 2 vectors in R^3 two completely different vectors. There is no right hand rule in the former for example. "The definition of angular momentum for a point particle is a pseudovector r×p, the cross product of the particle's position vector r (relative to some origin)" https://en.wikipedia.org/wiki/Angular_momentum you can read it for yourself. Key note torque is used..... but also note the mention of torque on the cross product link in particular with regards to moment of force. So have I been steering you falsely or asking you to recognize these details which are 100% applicable. Here is a mathematical proof showing the equation and definition I posted above. http://www.citycollegiate.com/centre_of_mass3.htm I was digging for a decent proof without applying Noether's this one will suit

You have defeated absolutely nothing. All you've done is shown that you do not understand the conditions that apply to conservation of angular momentum. If you could address our questions with proper knowledge on the topic you would have. This very line is full of mistakes already mentioned numerous times. please note the mistakes via what Studiot posted. "the system only possesses angular momentum, not linear momentum" Please state the conservation law of angular momentum correctly as :When the net external torque acting upon a system about a given axis is zero the total angular momentum about that axis remains constant." That is the correct definition. [latex] if \sum \vec{\tau}=0,, then \vec{L}=constant[/latex] any other definition not equivalent is false to what is conserved in angular momentum. The law states nothing about conservation of linear momentum. That is a different law with a different mathematical proof. As Studiot pointed out there is no linear momentum in the system by definition.

+1 excellent answer.

How can you have phase variance without time being involved? Seriously we have made every effort to explain the detection methods to you. The part you continuously mistakenly misunderstand is the polarity nature of a GW wave. Calculate the wavelength and then apply a quarter of that to get your required detector length. Then recognize that within that Precise same wavelength you have in essence 4 simultaneous movements. Both -x and +x contract while +y and -y expand. You have an L shape inerferometer it is impossible for both arms to have the same vector components. For the last time if you have length contradiction you MUST have an influence on the time components. It is impossible not to. From the very first link posted by Strange. This is two simultaneous movements with different vector components in each arm. Why is that so hard to understand? It is no different than gravitational redshift which relies on SR and GR being correct. Those blue/redshifts alter the frequency of the beams and causes phase shifts as a result. These frequency changes are detectable. Lets put it in electrical terms. You have altered a frequency of light by a frequency of GW. This will induce a propogation delay which results in a phase shift. We don't care about the detector walls. We only care about the phase shifts. Step 1) split a signal with amplitude of x. When you recombine the two signals as they are identical you have complementary waves = constructive interference. The amplitude will be the sum of the two waves. Hit it now with a momentary GW wave. Arm on left contracts and its signal is delayed, signal on the perpinficular DOES NOT undergo the identical affect. It will blueshift not redshift. Its signal also goes out of phase. HOWEVER both signals remain out of phase with each other so you get destructive interference on recombination. The recombined signal will have an amplitude less than the sum of the amplitudes of the two signals. The walls of the detector has nothing to do with the experiment. It is strictly its influence on the beam itself that is involved in the detection. When you have differences in gravitational potentials you gravitational redshift which involves both length and time dilation.

I agree with this need completely also with using the engineering references to start with. This is one of those cases where its more readily understood compared to Noethers theorem/action

My point is that you do need to show the required details not just hand wave them away. It is simple applications of force. You should have absolutely no problem in showing how torque is involved. Or even showing how [latex] F_{21}=-F_{12}[/latex] You posted one formula that doesn't even detail the conservation of angular momentum. It simply applies it. Do you even know the proper conservation of angular momentum equation? Your absolute refusal to even look at the mathematical proofs tells otherwise and proves to me that you do not know the details. If you did you would have had no problem posting such. There is classical proofs that don't require latex to be legible. Simply looking at L=R×P isn't the full story. when [latex] \vec{L}[/latex] is constant when net [latex]\tau=0[/latex] (torque) is your specific conservation of angular momentum relation. That is what you have to prove as false. Or more accurately start with [latex]\vec{\tau}=\frac{d\vec{L}}{dt}[/latex] where net torque equals zero and [latex] \Delta L=constant[/latex]

Why do you think you need to disprove every single derivitative involved? Have you studied the mathematical proof for conservation of angular momentum? There isn't that many formulas involved in the proof. Simple denial doesn't cut it Demonstrate to us a proper understanding of how conservation of angular momentum works. A logic argument isn't sufficient considering it is literally someone elses work. Demonstrate you properly understand the premises involved. ie premise 1 and 3 Thus far all your demonstrating is a lack of understanding behind the premises you posted. (prove to me otherwise please) I went and hit the wrong button and editted a previous post. I meant this to be here lol Anyways this demonstrates the premise 1 and 3

yeah got the two threads mixed up. Grandkids are at house providing distractions lol

Key note inertial mass but not invariant mass

A photon is charge neutral so there is no attraction due to charge. However all forms of energy/density including photons can produce mass if of sufficient value. For that you will need to apply the energy momentum tensor. (string theory already takes the above under consideration)

I'm not trying to be confrontational. I am trying to get you to fully examine the problem at hand. Not just handwave counter arguments. Simply because you chose to not include torque does not make your logic argument correct. I quoted a particular line in your proof that would have provided insight as to why the conservation of angular momentum specifies torque in its very definition. Looking at the mathematical proof would have identified the requirement on the quoted section. (as already pointed out premise 1 and 3) There is numerous mathematical proofs and methodologies my personal favourite being Noethers theorem under rotational invariance however there are other mathematical proofs. Just a side note when trying to develop a new model or understanding its always best to provide the current understandings and mathematics then show the errors. This also shows you have a decent knowledge and understanding of said topic.

Keep in mind looking at the spin statistics polarity effects is only 1 part of the predictions. Two other key aspects is the Chirp signal and the ringdown. These develop depending on the type of merger. The paper I posted only covered the detection of the quadupole nature. In essence they examine the full signal not just 1 wavelength of said signal.

This is why looking over the mathematical proofs for conservation of energy is important. Part of the proof is defining a closed system. The other part shows the torque aspects. The proof also identifies which vectors are involved.

that is precisely my point. The conservation law specifies torque. Your post does not. If your not including torque your not discussing the conservation of angular momentum.

I am specifically asking you to demonstrate a working knowledge of why this is the case... Under Noethers theorem if you assign the referred to axis as N then the action L is conserved along the N axis. see rotational invariance https://en.m.wikipedia.org/wiki/Noether%27s_theorem In particular "In other words, the component of the angular momentum L along the n axis is conserved."

BB model being LCDM. However under quantum cosmology there is a universe from nothing model one that arises via the Wheeler Dewitt equation and the HUP. Here is an arxiv coverage. https://www.google.ca/url?sa=t&source=web&rct=j&url=https://arxiv.org/pdf/1404.1207&ved=0ahUKEwjJ9sHz06PUAhUK5WMKHUMfDVgQFggjMAI&usg=AFQjCNFktncVqDNaSYL7UGEvKza6EJFvUw&sig2=sZ9jc3WP3_sBHzsik7D57A

If you want the mathematical details here is how the interferometer works with GW waves https://www.google.ca/url?sa=t&source=web&rct=j&url=http://www.tat.physik.uni-tuebingen.de/~kokkotas/Teaching/NS.BH.GW_files/GW_Physics.pdf&ved=0ahUKEwiz7J_ezKPUAhUC7GMKHTadCzIQFggxMAc&usg=AFQjCNHiFZs6dBn7deBRCCwTMny1SQCKuA&sig2=imWWDyfXmpQe1m0HWgMP9w The essential formulas are included in particular photon shot noise. covered in the link as well as the unit polarization tensors derived via the linear Einstein equations for a quadrupole wave.

Well if your trying to go for a mathematical proof that conservation of angular momentum is not conserved you best provide thorough details on the mathematical proofs of the angular momentum equation. Then detail a mathematical proof of where it in error. Simply naming premises etc and only referring to the angular momentum equation doesn't particularly count as a proof unless fully shown. After all the equation has been around 300 years as you say. It will take far greater attention to mathematical detail than you have in the above.

To detect you essentially send a continous wavelength signal with a laser beam. You split the beam with mirrors via destructive interference. Then combine the two with constructive interference reforming the original wavelength. This forms your baseline, when length contraction occurs on either arm the phases shift due to length contraction leads to destructive interference on recombination as one or both signals change which are detectable at the receivers This is essentially how the Michelson interferometer works. Also keep in mind you cannot have length contraction without also having time dilation due to a GW wave. If your interested I can post the mathematics specific to the spin 2 and quadrupole nature of a GW wave,as well as spin 1. Mechanical vibration and the electromagnetic waves are dipoler waves they do not have the same effects on phase shifts. There is no attenuation or dispersion in a GW wave. As such a lot of research went into filtering out those types of interference. Though there is a distinguishable difference between spin 1 and spin 2. (mechanical vibration is symmetric with spin 1 dipoler). Though I'm less familiar with the detector end. Thank you just wanted clarity we get all kinds on a forum lol

So your stating GR length contraction does not occur ? It is detectable within a range of wavelengths when you change the x axis lengths you change space. Thats what Ligo is designed to detect. It's not just math. Because not all particles in the same space is changing in the same direction. As we have stated numerous times. Why do you think the arms are 4 km in length if memory serves.? wave length polarities Ripples.

Waves in spacetime is changes in length as per length contradiction. So the x dimension of length does contract. What you have above does apply. That's precisely is what were detecting Ripples in spacetime geometry dimensions (ct,x,y,z)

Here is density waves involvement in Saturn's rings. https://www.google.ca/url?sa=t&source=web&rct=j&url=https://arxiv.org/pdf/1304.3735&ved=0ahUKEwjXmfXvpqLUAhVG1WMKHWD0BysQFggdMAA&usg=AFQjCNFsUAA9UskxhChBjInyl4WXUdsn2Q&sig2=cyLtxrRa-p9-vmS8I5fD7w As Janus pointed out its not exclusively due to frame dragging, any rotating point of attraction can produce density waves including the electromagnetic force.

Yes the rotating disks have been mathematically looked at. The leading theory is called Density waves. In many ways its similar to how Galaxies form spiral arms. Here is a generalization of the involved mathematics which follow in its basis the virial theorem and other hydrodynamic equations such as Jeans instability. https://www.google.ca/url?sa=t&source=web&rct=j&url=http://astro.pas.rochester.edu/~aquillen/ast570/lectures/E_SpiralDensity.pdf&ved=0ahUKEwiL4NuZo6LUAhULwWMKHQtnDswQFgg8MAQ&usg=AFQjCNF4uvWsaaexD6ZMESkg_izhNLKzFA&sig2=KeM5nWQCXOLwFVpsELDxrQ The topic is extremely extensive with a huge body of research. Enough that one could make a career of study.

what is the simplist possible explanation. hrrm k you get length contraction on the x axis at the same time length expansion on the y axis. Then next cycle reverse the two. Measure the contraction/expansion with a modified Michelson interferometer.