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  #21  
Old 25-02-2019, 05:56 PM
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Originally Posted by gary View Post
Hi Alex,

Thank you and absolutely no problem.

Muse away!

We're just glad the fires appeared to have dodged you.
Thank you for your understanding Garry.

Fortunately I am all mused out
alex
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  #22  
Old 25-02-2019, 07:41 PM
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It’s been awhile since I have posted here.
While we don’t have a sample size of fifty binary neutron stars to determine the Hubble constant, the current sample size of one allows us to gather information on the redshift.
How does the redshift of the gravitational wave source GW170817 formed by the neutron star merger compare to the cosmological redshift z calculated by “conventional” means?

By conventional means using the formula:
z = (λ – λ0)/ λ0

λ is the wavelength say of hydrogen Balmer lines in the spectrum of a distant galaxy.
λ0 is the wavelength of the Balmer lines in a rest frame such as a laboratory spectrum.
GW170817 fortunately originated in the galaxy NGC4993 the redshift of which is calculated by conventional means.

Determining the cosmological redshift of a gravitational wave is anything but straightforward.
Firstly we don’t have the benefit of a catalogue of gravitational wave laboratory spectra that serves as our rest frame.
Secondly the gravitational waves measured by LIGO and Virgo don’t explicitly measure a redshift in frequency as there is degeneracy issue.
This issue will be made clear a little later on.

We need to define the effective mass of a binary system to understand how the redshift is calculated.
Intuitively one might think this is simply the sum of the masses of the neutron stars or black holes making up the binary system but it is somewhat more complicated.
We are interested in the mass-energy of the binary system which also includes the energy contribution from the gravitational waves.

The effective mass or “chirp mass” CM for a binary system is defined as.

CM= (m1.m2)^0.6/(m1+m2)^0.2

m1 and m2 are the masses of the neutron stars.


Since the chirp mass includes energy which is a function of frequency that can be redshifted, the chirp mass itself can be redshifted according to the formula.

CM(redshifted) = (1+z)CM(rest frame)

The gravitational frequency data from LIGO and VIRGO allows us to calculate the redshifted chirp mass (CM(redshift)).
Here lies the problem, we don’t know the contributions of z and CM(rest frame) to the redshifted chirp mass.
This problem is known as the M, Z degeneracy.
If the CM(rest frame) can be determined then the redshift z can be calculated as CM(redshifted) is already known.

This is where LIGO stepped into to the picture.

sjastro said:
Congratulations on this significant discovery.
Has this discovery broken the mass-redshift degeneracy allowing the calculation of the redshift of GW170817?
If so how does it compare to the redshift of NGC4993?


Christopher Berry LIGO said:
Not directly, but you could if you are willing to assume a neutron star mass.

Since (i) we get masses consistent with known neutron stars, and (ii) we overlap with the distance estimates for NGC 4993, you’d end up with a redshift consistent with that of the galaxy. For precise numbers you’d need to factor in the peculiar velocity of the binary.

Using this piece of advice and data from the PRL paper on GW170817 the redshifted chirp mass in the detector frame (CM(redshift)) was 1.1977 solar masses, while the chirp mass in the rest or source frame (CM(rest)) for typical neutron star binaries averages 1.188 solar masses.

Using the formula CM(redshift)=(1+z)CM(rest) and substituting in these mean values, the redshift for GW170817 is found to be z=0.008.
From the SIMBAD astronomical database NGC 4993 has a redshift z=0.009787.

This doesn’t factor in the peculiar velocity of GW170817 which is the velocity of the binary in space rather than due to the expansion of the Universe.
There is some promise even with this rough back of the envelope calculation…………….

Last edited by sjastro; 26-02-2019 at 09:30 AM.
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  #23  
Old 26-02-2019, 10:41 AM
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Hi Steven
It is so good to have you input meaningful comment and give members a little better understanding of the research.

No doubt you are better placed than most to offer reasons why hunting gravity waves is worthwhile and so I ask could you take the time to share with us if there are any particular expectatuons that it is hoped that this branch of GR may produce.

Alex
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  #24  
Old 26-02-2019, 12:09 PM
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Originally Posted by xelasnave View Post
Hi Steven
It is so good to have you input meaningful comment and give members a little better understanding of the research.

No doubt you are better placed than most to offer reasons why hunting gravity waves is worthwhile and so I ask could you take the time to share with us if there are any particular expectatuons that it is hoped that this branch of GR may produce.

Alex
Thanks Alex.
While the technology is still very much in its infancy, the ultimate purpose is to develop gravitational wave astronomy over a wide range of frequencies much like conventional astronomy is done over the electromagnetic spectrum.

Astronomy in the electromagnetic spectrum is limited up to the Cosmic Radiation Background which is an opaque barrier.
Gravitational wave astronomy should allow this barrier to be penetrated and in theory take us back to the inflation era of the Universe which is a source for low frequency gravitational waves.
https://en.wikipedia.org/wiki/Gravit...ve_sources.png
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Old 26-02-2019, 06:55 PM
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Thanks for the link Steven I read it all but I think I read it a while back..no matter these days with a failing memory most things seem new☺
Is there any physical nature to a gravity wave and I ask perhaps because of my incomplete understanding of GR...but I see it as a coordinate system describing somewhat movement of space and objects in it with no explaination of the particles involved...I expected ct at some level there must be particles or at least a means of carrying information...I know the eather is not needed but do you see at some level there has to be some form of particle soup that makes up space...You know my passion for a push gravity mechanism☺ but I guess what I ask really is there any view from a quantum level as to what makes up a gravity wave.
I guess I am revisting the idea that a wave must travel in a medium...and I know light is said not to have a mediun so I guess I just cant get my head around how things can move with no medium.
Say take gravity waves essentially a expansion and contraction of space ... what is this medium that expands and contracts..it must be something as it can't be nothing.
I expect what I ask for can only be speculative but I would be happy with that.

Alex
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  #26  
Old 26-02-2019, 07:07 PM
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Also given the incredibly short duration of inflation I do wonder about what they expect to be able to find...seems most ambitious.
Mind you as I have said many times I dont accept inflation and think it always was a patch that should have been replaced shortly after the fix☺...I cant understand why science disregards my concerns☺.

You may as well say inflation os synonymous for "instantaneous" for the time allocated to it...I can not accept that it all went from the size of a basket ball to greater than the observable universe in a zillionth of a zillionth of a zillionth of a second...to quote Neil de G.

Does the scientific community think inflation is reasonable or are there better ideas brewing?
Alex
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  #27  
Old 26-02-2019, 10:08 PM
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Originally Posted by xelasnave View Post
Thanks for the link Steven I read it all but I think I read it a while back..no matter these days with a failing memory most things seem new☺
Is there any physical nature to a gravity wave and I ask perhaps because of my incomplete understanding of GR...but I see it as a coordinate system describing somewhat movement of space and objects in it with no explaination of the particles involved...I expected ct at some level there must be particles or at least a means of carrying information...I know the eather is not needed but do you see at some level there has to be some form of particle soup that makes up space...You know my passion for a push gravity mechanism☺ but I guess what I ask really is there any view from a quantum level as to what makes up a gravity wave.
I guess I am revisting the idea that a wave must travel in a medium...and I know light is said not to have a mediun so I guess I just cant get my head around how things can move with no medium.
Say take gravity waves essentially a expansion and contraction of space ... what is this medium that expands and contracts..it must be something as it can't be nothing.
I expect what I ask for can only be speculative but I would be happy with that.

Alex
Alex,

Newton considered space to be nothing more than a coordinate system.
Einstein considered spacetime to be a gravitational ether which is analogous to the old luminiferous ether concept that was once considered the medium in which light propagated.
The gravitational ether allows the propagation of gravitational waves in the form of ripples in spacetime which causes the elongating of spacetime in one direction and contraction in the perpendicular direction.
This elongation and contraction is a very real physical effect and is detected at LIGO and VIRGO which are very sophisticated interferometers as a time delay between a laser beam that travels a slightly further distance in the stretched direction of spacetime than the beam that travels in the contracted direction.

As you are aware spacetime can bend in the presence of mass or expand as in the case of an expanding Universe.
Another property of spacetime if the geometry changes rapidly with time such as in black hole and neutron star mergers or even inflation, gravitational waves are generated.
Gravitational waves carry information in the form of energy.
For example when binary neutron stars merge their combined mass is not the sum of the individual masses but less.
The difference is the energy carried by the gravitational wave.
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  #28  
Old 26-02-2019, 10:26 PM
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Originally Posted by xelasnave View Post
Also given the incredibly short duration of inflation I do wonder about what they expect to be able to find...seems most ambitious.
Mind you as I have said many times I dont accept inflation and think it always was a patch that should have been replaced shortly after the fix☺...I cant understand why science disregards my concerns☺.

You may as well say inflation os synonymous for "instantaneous" for the time allocated to it...I can not accept that it all went from the size of a basket ball to greater than the observable universe in a zillionth of a zillionth of a zillionth of a second...to quote Neil de G.

Does the scientific community think inflation is reasonable or are there better ideas brewing?
Alex
The period of inflation lasted from about 10^-36 s to around 10^-32 s after the Big Bang.
As to how big the Universe expanded in this period causes some confusion.

The size of the Universe may in fact be infinitely large; we donít know its size true but since the Universe expands we know its scale changes.
We can only express the size of the Universe in terms of the observable Universe.
The cosmic scale of the Universe as it is now, is arbitrarily set as equal to one; the cosmic scale factor is the cosmic scale as it was at some point in the past divided by the current cosmic scale.
Using the cosmic scale factor calculated for immediately before and after inflation we can roughly calculate the size of the observable Universe over this time frame.

At 10^-36 s the size of the observable Universe was around 8 X 10^-30 meters, immediately after inflation was completed at 10^-32 s it expanded to around the size of a grain of sand.

Inflation still provides the best explanation of why the Universe is flat and causally connected.
Most importantly it is a falsifiable theory as inflation predicts the existence of low frequency gravitational waves and a particular type of polarization in the Cosmic Radiation Background.
Unfortunately a few years ago there was a premature announcement that inflation was confirmed as the polarization in the Cosmic Radiation Background was detected but the discovery was withdrawn after the polarization was found to caused by magnetic dust particles in our galaxy.
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  #29  
Old 26-02-2019, 11:45 PM
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Thanks for all of your input Steven.
And particularly re faulsibility of inflation which I was unaware of...I am sure some one wrote someplace that it wasnt but they may have ment in relation to capabilities at a particular time...

Thanks for contributing here I am sure your input will be of great interest to new members perhaps developing an interest in cosmology.

Alex
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  #30  
Old 26-02-2019, 11:55 PM
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Steven re the first post reply.

I suppose what I have difficulty with is that presumably because of my background is I tend to think at some level there must be a physical thing, a very small thing, discrete, as opposed to thinking of energy as ...well the way its thought of☺.

Thanks again it is really great that you have popped it.
I hope all is well in your world.
Alex
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