Impact of gravitational wave detection: A response to Setterfield’s response1 March 2016
Inspiral of black holes and associated waveform. Ref. 6. Click for larger image.
The following is written as a rebuttal to an article titled “In Response to Hartnett’s Article”1, dated February, 2016, written by Mr Barry Setterfield. The author states that he received the following email, along with a number of others with the same questions about the Hartnett article:2
I have a question regarding a CMI article by a Dr. John Hartnett entitled “What impact does the detection of gravitational waves have on biblical creation?” Dr. Hartnett makes the claim that the recent discovery of gravity waves uses a modern value for the speed of light to calculate the masses of the two black holes which collided to produce those waves, so he concludes (a bit too quickly in my opinion) that “the cdk idea is [to be] thoroughly rejected”. I wanted your take on this issue. Here’s the relevant portion of the article:
“Interestingly, the calculation used to determine the masses of the merging black holes in the analysis of this week’s discovery employed the standard canonical speed of light, c. That is, it used the same constant value that we measure today. Does that tell us something? I think it does.
Some biblical creationists favour a much higher value for the speed of light in the past, from a time soon after creation of the universe, after which it decreased or decayed down to its current value (the concept is known as cdk, from c-decay). They use this supposed much higher value of c in the past as a solution of the biblical creationist light-travel time problem. But now this new discovery shows that, at a time in the past representative of a distance in the cosmos of 1.3 billion light-years, the value of the speed of [sic] (c) was identical to today’s current value. Regardless of which creationist cosmology you like, the gravity waves observed in September 2015 must have left their source very soon after Creation week. Thus the cdk idea is thoroughly rejected.”
To which Setterfield responds. So I respond to his response (indented black text) with my comments (purple text) interspersed below his.
One of the major errors that happens in all fields of science occurs when a theory is so valued that the data a person desires to support it is ‘cherry picked.’ That means the person will only pay attention to the data that fit his or her theory.
In principle, I agree with Setterfield. But it seems, since there is only one observation of coalescing binary black holes, by the detection of a gravitational wave (GW), discussed here, it is hardly cherry-picking to point out a consequence of that observation (i.e. no change in the speed of light from the current value). It seems to me that that would be like cherry-picking from a basket containing only one cherry!
What is an even worse error is when the data which has been cherry-picked is in question, and its validity, or the validity of the conclusions it leads to, becomes a matter of question.
The only persons who question the interpretation of the detection of stellar mass black holes, in this instance, are those who reject Einstein’s general theory of relativity (GR). It is not the same thing as rejecting the big bang model as a description of the origin and history of the universe. As pointed out in my original article2, GR has been applied and tested numerous times in our solar system, with GPS clocks, the Hulse-Taylor pulsar-neutron star binary and other binary neutron star systems within the galaxy. And it has come through with flying colours; no violation having been detected.
But it also seems that Setterfield is saying that the observed data is suspect, when he writes “…its [the data’s] validity … becomes a matter of question.” I personally know several of the authors of the LIGO collaboration and I have no reason to believe that any of them would have created or modified the data for their own personal ends. But if someone is reduced to questioning the validity of the data collected, because they don’t like its interpretation, then that shows they have no real viable robust alternate explanation.
Hartnett’s criticism relies on several assumptions. It is based on the fact that the calculations by the LIGO collaborators to determine the masses of the merging black holes have used the standard, canonical speed of light.
It is correct to say there are some assumptions, but that does not mean they are intrinsically bad or wrong. The theoretical analysis used the canonical speed of light, c. That is not of itself anything to be alarmed about. But it might be if, for example, the results of the analysis indicated some inconsistency. But they don’t!
Based on the GR physics used and the constant known value of c, the data constrain the total mass of the system (sum of the two black holes, M = m1+ m2) to be about 70 M⊙(solar masses). I quote here, with my comments in square brackets , from the published Physical Review Letters paper3 by Abbott et al. describing the discovery:
“This bounds the sum of the Schwarzschild radii of the binary components to 2GM/c2≳ 210 km. To reach an orbital frequency of 75 Hz (half the gravitational-wave frequency) [that means they orbit their common centre 75 times per second] the objects must have been very close and very compact; equal Newtonian point masses [if they had no diameter] orbiting at this frequency would be only ≃350 km apart. A pair of neutron stars, while compact, would not have the required mass, [meaning neutron stars would not be dense enough to be small enough to avoid contact with each other] while a black hole neutron star binary with the deduced chirp mass [a reduced mass combination of the two masses and in this discovery it was 30 M⊙] would have a very large total mass, and would thus merge at much lower frequency. This leaves black holes as the only known objects compact enough to reach an orbital frequency of 75 Hz without contact. Furthermore, the decay of the waveform after it peaks is consistent with the damped oscillations of a black hole relaxing to a final stationary Kerr configuration.” (emphasis added)
Simulation showing the coalescing black hole binary
Note, these black holes were initially spinning around each other without contact, only about 140 km apart, before they eventually merged into one. Now if the canonical speed of light, c, was much larger, back then in time, the chirp mass4 and hence individual masses of these black holes, in the detector frame, would need to be also much larger. But if their masses were much larger their Schwarzschild radii would also be much larger and they would contact, making the expected waveform inconsistent with that measured.
The chirp mass (Mc)4 is calculated from the early part of the waveform from the observed frequency f and its time derivative, f.. The chirp mass (Mc) is proportional to c3,
Mc ≈ M/26/5 ∝ c3,(1)
where the total mass M ≈ 2m, and m ≈ m1 ≈ m2 assuming the two black holes are approximately of equal mass. Therefore, the sum of the two black hole masses (M) is also proportional to c3. But the sum of the Schwarzschild radii (RS) of the binary components is inversely proportional to c2,
RS = 2GM/c2.(2)
Substituting Eq. (1) into Eq. (2) we get:
RS ∝ c.(3)
The Schwarzschild radii for the total mass of the two black holes (M) increases with the value of the speed of light, c. Therefore if the speed of light was 1 million times larger (Setterfield’s theory is 10 million times larger at Creation), the sum of the Schwarzschild radii of the binary black holes, instead of 210 km would become 210 million km. That means the black hole would have a million times the mass and as such this would be a supermassive black hole binary. It follows then they would coalesce much much slower as the merger time is proportional to c2. They would take about 6340 years to merge whereas these took about 0.2 seconds.3,5 And that doesn’t make much sense at all.
The immediate problem that should be noted with Hartnett is that he is using the general belief among standard science that the speed of light has always been a constant in order to prove that the speed of light has always been a constant.
Actually I am not. The way science works is to propose a hypothesis and see if you can disprove it. Assume an initial condition and if it generates an inconsistency then reject that initial assumption. Modify your assumptions until you get a self-consistent result, without contradiction.6 This is explained above for the case in question.
A belief is not proof. He should know that.
Of course belief is not a proof. But nothing in astronomy or cosmology can ever have a proof. In fact, Setterfield should be aware that science cannot prove anything to be true. (See, for example, Charles L. Bennett, “Science Title Misstep”, Science 332:1263, 2011) The best science can do is provide evidence (data) that is consistent with a hypothesis. But science can also provide data that is inconsistent with a hypothesis, in which case the hypothesis is rejected. So what matters is looking for consistency or inconsistency between the data and the interpretation of the data based on a hypothesis. Wrong hypotheses can be rejected by the observational data, but there can never be any absolute proof, no matter what one’s theory might be.
The calculations done regarding the LIGO project were done on the assumption that the speed of light has always been a constant. In other words, the speed of light must have been the same at the distance of 1300 million light years (where the event occurred) as it is now for the equations to work.
Yes, it uses the Einstein Synchrony Convention (ESC), which is a convention—the one that Einstein chose—that defines how to synchronise clocks. All aspects of the detection and analysis used the ESC. So necessarily it employs the isotropic speed of light, the universal constant c. There is nothing sinister going on here. As I pointed out, if that assumption was wrong, it would show up in the results, making them bizarre.
The second assumption he works from is that the merging objects were two black holes. If they were not black holes but some other bodies, then Hartnett’s argument falls apart. That is because it is only in the case of black holes that the relativistic equations which include the speed of light are used.
This is explained above why it is reasonable science to work with black holes. They are the only compact objects compact enough to make sense of the data. Using any other compact objects gives inconsistent results, nevertheless, the “relativistic equations” are applicable to them. The observed waveform,7 from the differential change in the lengths of the LIGO detector arms (one shortens as the other lengthens synchronously), and the resulting masses of the black holes and thus their calculated Schwarzschild radii (RS=2GM/c2), before coalescence, are consistent with the physical system of them not initially touching. If c in 2GM/c2 was much larger the M (mass) would need to be much larger to maintain the same non-touching radii, and then the merging would be inconsistent with the measured waveform and the timing of that event.
The third assumption is that gravitational physics alone explains the phenomena observed, and so those are the only equations which apply.
Now it comes down to throwing out good known physics. GR theory has been tested and used extensively, without fudge factors on many systems, in the solar system and the galaxy. Until we require fudge factors, which this system does not, there is no reason to arbitrarily discard this physics.
Fourth and finally, everything is based on the assumption that Einsteinian relativity is the only description of reality. I believe that each one of these assumptions is faulty for one reason or another. Let us briefly examine each one. (emphasis added)
The use of GR theory was the third assumption. Here he invokes it again as another assumption. And Setterfield states his belief here after chiding me on my belief!
First is the assumption that the signal came from the merger of two black holes. It is true that the LIGO collaborators claimed that the recorded waveform could be accounted for this way, provided that the black holes were of very specific masses(those specific masses were the only way their equations would work when accounting for the data). The calculations that they employed to get that result used the equations that Hartnett referred to. However a few days later a second paper8 came out detailing Fermi satellite data obtained by the Gamma-ray Burst Monitor (GBM) group which also and [sic] simultaneously recorded the LIGO event. (emphasis added)
That is not accurate. The timing of the GBM detection, labelled GW150914-GBM, was about 0.4 s after the gravity wave detection at LIGO, labelled GW150914.
“The search also identified a hard transient which began at 09:50:45.8, about 0.4 s after the reported LIGO burst trigger time of 09:50:45.39, and lasted for about 1 second.”8
They have an entirely different way of detecting such events which have [sic] the ability to provide confirmation or denial of the LIGO interpretation. (emphasis added)
Yes—and no. The detection technique of the Fermi satellite is different to that of LIGO and a Fermi detection could provide support for a LIGO detection/interpretation but might not provide either confirmation or denial of a LIGO detection/interpretation depending the nature of the objects causing the event. The Fermi satellite has detectors sensitive to a range of X-rays and gamma rays. This is electromagnetic radiation not vibrations of space, which are ‘acoustic’ waves. GW are vibrations of spacetime, not electromagnetic waves. So the detection techniques are different. However, the GBM was designed to detect Gamma-Ray Bursts (GRBs), which are high energy emissions from compact sources, in particular the circumbinary disks surrounding such sources, the theory of which is still under development. While “circumbinary disks are expected to form around supermassive black holes…, there is no such prediction for stellar mass systems” (black holes with masses in a range around a few tens of solar masses). (See also the next part of the response.) Thus the best Fermi can do is confirm the putative electromagnetic counterpart to a gravity wave emission. That would require emissions from the circumbinary disk region around coalescing stellar mass black holes, the formation of which, theory currently does not predict. The objects considered to have given rise to the LIGO event are not supermassive, galaxy-sized black holes, for which theory currently does predict the formation of a circumbinary disk. Thus, Fermidetections may or may not provide either confirmation or denial of LIGO detections/interpretations.
The Fermi data revealed that there was only a weak signal in the hard X-ray region of the spectrum. The GBM group has pointed out that the LIGO announcement is surprising if it really was the merger of two black holes. Such a merger should have produced a stronger signal, and that signal should have been in the gamma ray (or more energetic) region of the spectrum, not in the less energetic X-ray region.
Absolutely false. There is no such indication in the Connaughton et al. Fermi GBM paper.8 Quite the opposite, the discussion in that paper revolves around the authors’ belief up to this point that there would not be strong electromagnetic emissions from a black hole binary merger event, but from a merger event with at least one neutron star. They write:8
“The detection of an electromagnetic counterpart to a merger of stellar mass black holes would be a surprising event. Although circumbinary disks are expected to form around supermassive black holes (Mayer et al. 2007), there is no such prediction for stellar mass systems. Moreover, the GBM signal appears similar to a short GRB, in duration (less than 2 s), and in energy spectrum (peaked near an MeV). Models for short GRBs from compact binary progenitors always involve a neutron star, with short GRBs more easily produced from two neutron stars, unless the black hole companion has a high initial spin (Giacomazzo et al. 2013). A luminosity of 1.8 ± 1.0 × 1049 erg s-1 for a short GRB, assuming the source distance of 410 ± 180 Mpc implied by the GW observations (Abbott et al. 2016), is an order of magnitude dimmer than the peak luminosities of the dimmest short GRBs in the sample analyzed by Wanderman and Piran (2015). (emphases added) Further observations by LIGO and Virgo in coincidence with a detector sensitive to hard X-ray or gamma-ray transient events will determine whether short bursts of high-energy electromagnetic radiation accompany stellar mass black hole binary mergers.”
The GBM group had previously been able to assess various types of signals, along with their strengths and energies, which had emanated from other astronomical events. As a result of their expertise, the GBM team concluded in their paper that the signal LIGO picked up could not be from the merger of two black-holes, but instead was something rather less massive. (emphasis added)
Nowhere in the Connaughton et al. paper8 do the authors make such a claim. They only question the association of their electromagnetic signal with the GW event because of the weakness of their signal and because the timing was not exact, nevertheless very close.
“If the association is real, then the alignment of the merger axis with our line of sight is serendipitous. Another possibility is that the electromagnetic emission is not narrowly collimated and we can expect further joint detections of stellar mass black hole binary mergers and GRBs.”8 (emphases added)
They make statements about detecting more such stellar mass black hole binary mergers by the gamma emission from the accompanying GRB.
“Even if the association between GW150914-GBM and GW150914 is spurious, we expect to detect short GRBs from neutron star binary systems. With its broad field-of-view and good sensitivity at the peak emission energies for short GRBs, Fermi GBM is an ideal partner in the search for electromagnetic signals in coincidence with gravitational wave detections.”8 (emphasis added)
They expect coalescing neutron star binaries will generate a much stronger gamma-ray signal than coalescing stellar mass black holes.
This development does several things. First, given that the same event is being recorded by both groups, the lack of gamma rays yields strong evidence that black holes were not involved. This negates the extensive calculations by the LIGO group, and as a result also negates Hartnett’s argument.
Incorrect. The Fermi GBM team are somewhat circumspect that the source of their GW150914-GBM detection is evidence of a GW signal. But they state that
“Joint observations by Fermi and LIGO/Virgo will either confirm or exclude the connection between compact binary systems and short GRBs within a few years.”8
If, however, we assume that the GBM data was not from the same event, then there is another problem. If the merger of two black holes really did occur, that should have sent a strong signal in the gamma ray region of the spectrum which GBM should have picked up.
Actually the opposite was expected: little or no gamma-ray signal was expected from coalescing black holes.8
If the GBM weak X-ray data was not from the same event, then where was the gamma ray signal? The required gamma ray signal never occurred and no other relevant signal was recorded. The absence of this signal would mean that the LIGO event was not the merger of black holes, and their calculations are then irrelevant. So whether the signals came from the same or different events, the indications are that black-holes were not involved. Again, if black holes were not involved, then the calculations involving a constant speed of light mean nothing and this strikes a serious blow to Hartett’s [sic] claim regarding a possible change in the speed of light as being “thoroughly rejected.” (emphasis added)
It is a straw man argument, because the Fermi GBM team make no claims refuting a GW signal from black holes detected at LIGO. They didn’t expect a gamma ray signal from black holes but instead from a binary system with at least one neutron star. And as stated above if it was a neutron star then its size would be too great and they would collide before the observed coalescence. The indications are that stellar mass black holes coalesced.
The LIGO team worked for five months on their calculations, trying to see what had happened to produce the wave forms their instruments recorded. (emphasis added)
Incorrect again. The reported detection was on September 14, 2015, and the research paper was received at Physical Review Letters on January 21, 2016. That amounts to 129 days. Assuming a month is 31 days that means 4.16 months. Quite obviously the calculations that Setterfield refers to had to be done prior to the writing of the paper, so there is no way it could have taken 5 months. Besides, maybe the team were a lot more careful after the BICEP2 fiasco9and took their time to make sure they had not made a mistake.
There was nothing simple or straight-forward about what they had to do to achieve the results they wanted.
It may not be simple to do general relativistic physics but to say that they “achieve[d] the results they wanted” implies deliberate wrongdoing. And secondly, simple does not imply straightforward. It is actually straightforward physics, standard expected waveforms have been around for decades.5 There is nothing sinister here either.
They presumed black holes. They presumed the speed of light was the same 1.3 billion light years away (thus 1.3 billion years ago) as it is today. However, the merger of two black holes is certainly in question, as pointed out above. (emphasis added)
But they used two different methods to determine if it was a real signal. Abbott et al. write:3
“GW150914 is confidently detected by two different types of searches. One aims to recover signals from the coalescence of compact objects, using optimal matched filtering with waveforms predicted by general relativity. The other search targets a broad range of generic transient signals, with minimal assumptions about waveforms. These searches use independent methods, and their response to detector noise consists of different, uncorrelated, events. However, strong signals from binary black hole mergers are expected to be detected by both searches.” (emphases added)
“Several analyses have been performed to determine whether or not GW150914 is consistent with a binary black hole system in general relativity. A first consistency check involves the mass and spin of the final black hole. In general relativity, the end product of a black hole binary coalescence is a Kerr black hole, which is fully described by its mass and spin. For quasicircular inspirals, these are predicted uniquely by Einstein’s equations as a function of the masses and spins of the two progenitor black holes. Using fitting formulas calibrated to numerical relativity simulations, we verified that the remnant mass and spin deduced from the early stage of the coalescence and those inferred independently from the late stage are consistent with each other, with no evidence for disagreement from general relativity.” (emphasis added)
In addition, if, as data show, the speed of light has not been constant throughout time, then neither were the properties of the vacuum or other physical quantities. (emphasis added)
Setterfield must be referring to, without citation, his own data10 allegedly showing a decrease in the canonical speed of light, c, since Rømer made the first measurements using the moons of Jupiter in the 1670s. Those data have been greatly debated, particularly in the 1980s, by creationists and also by secular mathematicians. But no clear time-dependent trend was obtained when the real errors were included. By excluding the first few historical data, which have large errors, any alleged trend is lost. The most likely cause of any apparent trend, which disappeared by the 1960s with improved measurement techniques (and smaller errors), is observer bias, where the researcher is drawn to report a result from among his data closest to the previous published value (known as ‘canonical phase locking’).
Hartnett is correct that if only the speed of light has been changing, then the equations won’t work. But, if the properties of the vacuum are controlled by the Zero Point Energy, which is what data indicate, a consistent approach emerges. In that case, synchronously varying quantities counteract the variation in light-speed, as shown by measurements through a number of years. So on those bases, Hartnett’s conclusions may be premature.
Setterfield’s theory requires Planck’s constant h to varying inversely as the speed of light c decreases over time from a value something like 107 times faster at Creation, so that h.c= constant. This is very contrived but the Kerr black hole is only constrained by its mass and spin. Planck’s constant is not involved but the value of the speed of light, c, is involved in the calculation of a black hole’s Schwarzschild radius. No doubt Setterfield has a fix for this problem with his “synchronously varying quantities”. But it will be in great tension with Occam’s razor, which says that the best hypothesis is one that makes the least number of assumptions.
Third, the assumption is that gravitational physics alone explains the characteristics of what have been referred to as black holes.
But it does explain the observations, so why discount a perfectly good physical theory that explains what we observe, without invoking any fudge factors, or unknowns like dark matter or dark energy?
However, if the concept of black holes is examined using the approach of plasma astronomy instead of gravitational astronomy, these objects turn out to be plasmoids whose behavior is governed by electromagnetism, not gravity.
It is possible that another theory explains the same astrophysical observations. But that fact alone cannot rule out its competitor when its competitor also explains the observed data. And if two theories can explain the same phenomena one needs to find some observation that contradicts one of those theories to reject it (or both). That is not the case here. And even if it was, it could not prove Setterfield’s theory of plasmoids either.
This is explained in more detail in the article on Black Holes. Using the plasma approach, Anthony Peratt from LANL has shown that a different set of equations must be used to describe the orbital characteristics of black holes/plasmoids.
It would be appropriate to cite Peratt’s research paper so it can be checked that it generates the observed waveform.
Research has shown that over 99% of the matter in the universe is in a plasma state.
Yes, and extremely low density in the intergalactic medium. It is hardly relevant here.
Given this understanding, the use of equations which consider gravity, rather than electromagnetism, to be the driving force are probably wrong from the beginning. Thus the orbital equations used by the LIGO collaboration may not be relevant for this reason either. (emphasis added)
Where’s the evidence to back up such a claim? Everything we know about the dynamics of heavenly bodies can be explained by Newtonian and post-Newtonian (general relativity) physics. With most charges balanced in the universe, in heavenly bodies, there is very little electromagnetic force over long distances. Plasmas involve charged particles but they are all generally balanced between the positive and negative ions. You cannot so simply negate the orbit calculations of general relativity without contrary evidence.
The concept of gravitational black holes and their behavior comes from Einsteinian relativity. This is based on two postulates which have been shown to be invalid observationally.
Which two postulates? If you mean the postulates of the constancy of the speed of light and the relativity principle, then I have to disagree. They have not been shown to be invalid. Indeed this observation of gravitational waves further supports general relativity and the existence of stellar size binary black holes, and the fact that they do merge in the predicted inspiral manner.
Indeed, most of the predictions of relativity, including a different origin for mass and gravity, can be obtained using simple math if the concept of a vacuum Zero Point Energy (ZPE) is adopted. In this case there are no restrictive postulates. The outcome is that a different set of equations apply when the observationally based ZPE option is used, which Hartnett is evidently unaware of. This is a real problem when one pays attention only to the data which appear to support one’s pet theory.
Not so. The theory that Setterfield uses, Stochastic Electrodynamics (SED), is at best a minor, disfavoured theory that has gained very little traction, whereas its competitor Quantum Electrodynamics (QED) has been very successful in predicting atomic parameters with enormously high accuracy.11 There is also a real problem when one dismisses data which appear to contradict one’s pet theory! In fact, dismissing data that are anomalous to your pet theory is, by far, the worse problem since it is in the anomalies that real progress is often made in physics. It is the anomalous data that often allow one to reject the failed theories.
Since these four assumptions are questionable at best and invalid at worst, Hartnett’s statement that the idea of a changing speed of light is “thoroughly rejected” is only true for those who want it to be true. It is not that easy to dismiss inconvenient data in the long run.
As shown above, this conclusion is false. The third and the fourth assumptions are the same assumption. The three seem to be the existence of black holes, the validity of general relativity and the constancy of the speed of light. I have shown that by quoting from the source cited by Setterfield the authors, Connaughton et al., of the Fermi GBM paper8 believe the opposite to what Setterfield has claimed. Certainly they state in relation to their hard X-ray detection within 0.4 s of the LIGO GW detection that
“The transient event cannot be attributed to other known astrophysical, solar, terrestrial, or magnetospheric activity.”8
They mean it could only be from a GRB, with the remaining doubt being whether it was from the same binary black hole merger as the LIGO antennas detected via a gravity wave.
“If the GBM transient is associated with GW150914, this electromagnetic signal from a stellar mass black hole binary merger is unexpected.”8
Nowhere do Connaughton et al. state that their evidence rules out a binary black hole merger, or the existence of a gravitational wave event. Thus I stand by my conclusion that general relativity is supported in that system at a distance of about 1.3 billion light-years and hence the speed of light was the same in that system when the GW left the merging binary. Cdk is ruled out quite conclusively.
Update: June 6, 2016
A new analysis of the alleged gamma-ray detection, GW150914-GBM, by the Gamma-ray Burst Monitor (GBM) group using the Fermi satellite data, about 0.4 s after the gravity wave detection at LIGO, has shown to be just noise and not any type of electromagnetic signal.12 This is consistent with no expected electromagnetic signal from the black hole merger. It's absence provides no denial of the LIGO interpretation of coalescing black holes.
References and notes
- Setterfield, B., In Response to Hartnett’s Article, setterfield.org, February 2016. Return to text
- Hartnett, J.G., What impact does the detection of gravitational waves have on biblical creation?, creation.com, February 2016. Return to text
- Abbott, B.P., et al., (LIGO Collaboration) Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett. 116(6), 2016 | doi:http://dx.doi.org/10.1103/PhysRevLett.116.061102. Return to text
- Chirp mass Mc = (m1m2)3/5/(m1+m2)1/5 = (c3/G)[5/96 π-8/3 f-11/3 f.]3/5, where m1, m2 represent the respective masses of the black holes, G and c are the gravitational constant and the speed of light. The observed frequency f and its time derivative, f. (f dot = df/dt) are determined from the early part of the waveform. Return to text
- Gravitational Waves, John Wheeler lecture notes, physics.usu.edu, 2013. Return to text
- The added problem with using the cosmos as your laboratory is that you cannot directly interact with the experiment. Return to text
- This is an acoustic wave or vibration, not an electromagnetic wave. Return to text
- Connaughton, V., et al., Fermi GBM Observations of LIGO Gravitational Wave event GW150914, arxiv.org/abs/1602.03920, February 11, 2016. Return to text
- Hartnett, J.G., New study confirms BICEP2 detection of cosmic inflation wrong, creation.com, February 2015. Return to text
- Setterfield, B., The Velocity of light and the age of the universe, Creation 4(1):38–48, March 1981. Return to text
- A good theory with few successful predictions may be ignored but a very successful theory with many correct predictions cannot be ignored. Return to text
- J. Greiner, J.M. Burgess, V. Savchenko, H.-F. Yu, On the GBM event seen 0.4 sec after GW 150914, http://arxiv.org/abs/1606.00314. Return to text.