LIGO and TGD

The recent detection of gravitational radiation by LIGO (see the posting of Lubos at and the article) can be seen as birth of gravito-astronomy. The existence of gravitational waves is however an old theoretical idea: already Poincare proposed their existence at the time when Einstein was starting the decade lasting work to develop GRT (see this).

Gravitational radiation has not been observed hitherto. This could be also seen as indicating that gravitational radiation is not quite what it is believed to be and its detection fails for this reason. This has been my motivation for considering the TGD inspired possibility that part or even all of gravitational radiation could consist of dark gravitons (see this). Their detection would be different from that for ordinary gravitons and this might explain why they have not been detected although they are present (Hulse-Taylor binary).

In this respect the LIGO experiment provided extremely valuable information: the classical detection of gravitational waves - as opposed to quantum detection of gravitons - does not seem to differ from that predicted by GRT. On the other hand, TGD suggests that the gravitational radiation between massive objects is mediated along flux tubes characterized by dark gravitational Planck constant h_gr =GMm/v₀ identifiable as h_eff=n× h (see this). This allows to develop in more detail TGD view about the classical detection of dark gravitons.

A further finding was that there was an emission of gamma rays .4 seconds after the merger (see the posting of Lubos and the article from Fermi Gamma Ray Burst Monitor). The proposal that dark gravitons arrive along dark magnetic flux tubes inspires the question whether these gamma rays were actually dark cyclotron radiation in extremely weak magnetic field associated with these flux tubes. There was also something anomalous involved. The mass scale of the merging blackholes deduced from the time evolution for so called chirp mass was 30 solar masses and roughly twice too large as compared to the upper bound from GRT based models (see this).

Development of theory of gravitational radiation

A brief summary about the development of theory of gravitational radiation is useful.

1. After having found the final formulation of GRT around 1916 after ten years hard work Einstein found solutions representing gravitational radiation by linearizing the field equations. The solutions are very similar in form to the radiation solutions of Maxwell's equations. The interpretation as gravitational radiation looks completely obvious in the light of after wisdom but the existence of gravitational radiation was regarded even by theoreticians far from obvious until 1957. Einstein himself wrote a paper claiming that gravitons might not exist after all: fortunately the peer review rejected it (see this)!
   
   
2. During 1916 Schwartschild published an exact solution of field equations representing a non-rotating black hole. At 1960 Kerr published an exact solution representing rotating blackhole. This gives an idea about how difficult the mathematics involved is.
   
   
3. After 1970 the notion of quasinormal mode was developed. Quasinormal modes are like normal modes and characterized by frequencies. Dissipation is however taken into account and this makes the frequencies complex. In the picture representing the gravitational radiation detected by LIGO, the damping is clearly visible after the maximum intensity is reached. These modes represent radiation, which can be thought of as incoming radiation totally reflected at horizon. These modes are needed to describe gravitational radiation after the blackhole is formed.
   
   
4. After 1990 post-Newtonian methods and numerical relativity developed and extensive calculations became possible allowing also precise treatment of the merger of two blackholes to single one.
   
   

I do not have experience in numerics nor in findings solutions to field equations of GRT. General Coordinate Invariance is extremely powerful symmetry but it also makes difficult the physical interpretation of solutions and finding of them. One must guess the coordinates in which everything is simple and here symmetries are of crucial importance. This is why I have been so enthusiastic about sub-manifold gravity: M⁴ factor of imbedding space provides preferred coordinates and physical interpretation becomes straightforward. In TGD framework the construction of extremals - mostly during the period 1980-1990 - was surprisingly easy thanks to the existence of the preferred coordinates. In TGD framework also conservations laws are exact and geodesic motion can be interpreted in terms of analog of Newton's equations at imbedding level: at this level gravitation is a genuine force and post-Newtonian approximation can be justified in TGD framework.

Evolution of the experimental side

1. The first indirect proof for gravitational radiation was Hulse-Taylor binary pulsar (see this. The observed increase of the rotation period could be understood as resulting from the loss of rotational energy by gravitational radiation.
   
   
2. Around 1960 Weber suggests a detector based on mass resonance with resonance frequency 1960 Hz. Weber claimed of detecting gravitational radiation on daily basis but his observations could not be reproduced and were probably due to an error in computer program used in the data analysis.
   
   
3. At the same time interferometers as detectors were proposed. Interferometer has two arms and light travels along both arms arms, is reflected from mirror at the end, and returns back. The light signals from the two arms interfere at crossing. Gravitational radiation induces the oscillation of the distance between the ends of interferometer arm and this in turn induces an oscillating phase shift. Since the shifts associated with the two arms are in general different, a dynamical interference pattern is generated. Later laser interferometers emerged.
   

   One can also allow the laser light to move forth and back several times so that the phase shifts add and interference pattern becomes more pronounced. This requires that the time spent in moving forth and back is considerably shorter than the period of gravitational radiation. Even more importantly, this trick also allows to use arms much shorter than the wavelength of gravitational radiation: for 35 Hz defining the lower bound for frequency in LIGO experiment the wavelength is of the order of Earth radius!
   
   

4. One can also use several detectors positioned around the globe. If all detectors see the signal, there are good reasons to take it seriously. It becomes also possible to identity precisely the direction of the source. A global network of detectors can be constructed.
   
   
5. The fusion of two massive blackholes sufficiently near to Earth (now they were located at distance of about Gly!) is optimal for the detection since the total amount of radiation emitted is huge.
   

What was observed?

LIGO detected an event that lasted for about .2 seconds. The interpretation was as gravitational radiation and numerical simulations are consistent with this interpretation. During the event the frequency of gravitational radiation increased from 35 Hz to 250 Hz. Maximum intensity was reached at 150 Hz and correspond to the moment when the blackholes fuse together. The data about the evolution of frequency allows to deduce information about the source if post-Newtonian approximation is accepted and the final state is identified as Kerr blackhole.

1. The merging objects could be also neutron stars but the data combined with the numerical simulations force the interpretation as blackholes. The blackholes begin to spiral inwards and since energy is conserved (in post-Newtonian approximation), the kinetic energy increases because potential energy decreases. The relative rotational velocity for the fictive object having reduced mass increases. Since gravitational radiation is emitted at the rotational frequency and its harmonics, its frequency increases and the time development of frequency codes for the time development of the rotational velocity. This rising frequency is in audible range and known as chirp.
   

   In the recent situation the rotational frequency increases from 35 Hz to maximum of 150 Hz at which blackholes fuse together. After that a spherically symmetric blackhole is formed very rapidly and exponentially damped gravitational radiation is generated (quasinormal modes) as frequency increases to 250 Hz. A ball bouncing forth and back in gravitational field of Earth and losing energy might serve as a metaphor.
   
   

2. The time evolution of the frequency of radiation coded to the time evolution of interference pattern provides the data allowing to code the masses of the initial objects and of final state object using numerical relativity. So called chirp mass can be expressed in two manners: using the masses of fusing initial objects and the rotation frequency and its time derivative. This allows to estimate the masses of the fusing objects. They are 36 and 29 solar masses respectively. The sizes of these blackholes are obtained by scaling from the blackhole radius 3 km of Sun. The objects must be blackholes. For neutron stars the radii would be much larger and the fusion would occur at much lower rotation frequency.
   
   
3. Assuming that the rotating final state blackhole can be described as Kerr's blackhole, one can model the situation in post-Newtonian approximation and predict the mass of the final state blackhole. The mass of the final state blackhole would be 62 solar masses so that 3 solar masses would transform to gravitational radiation! The intensity of the gravitational radiation at peak was more than the entire radiation by stars int the observed Universe. The second law of blackhole thermodynamics holds true: the sum of mass squared for the initial state is smaller than the mass squared for the final state (32²+29²< 62²).
   
   

Are observations consistent with TGD predictions

The general findings about masses of blackholes and their correlations with the frequency and about the net intensity of radiation are also predictions of TGD. The possibility of dark gravitons as large h_eff quanta however brings in possible new effects and might affect the detection. The consistency of the experimental findings with GRT based theory of detection process raises critical question: are dark gravitons there?

About the relationship between GRT and TGD

The proposal is that GRT plus standard model defines the QFT limit of TGD replacing many-sheeted space-time with slightly curved region of Minkowski space carrying gauge potentials defined as sums of the components of the induced spinor connection and the deviation of metric from flat metric as sum of similar deviations for space-time sheets (see this). This picture follows from the assumption that the test particle touching the space-time sheets experience the sum of the classical fields associated with the sheets.

The open problems of GRT limit of TGD have been the origin of Newton's constant - CP₂ size is almost four orders of magnitude longer than Planck length.Amusingly, a dramatic progress occurred in this respect just during the week when LIGO results were published.

The belief has been that Planck length is genuine quantal scale not present in classical TGD. The progress in twistorial approach to classical TGD however demonstrated that this belief was wrong. The idea is to lift the dynamics of 6-D space-time surface to the dynamics of their 6-D twistor spaces obeying the analog of the variational principle defined by Kähler action. I had thought that this would be a passive reformulation but I was completely wrong (see this).

1. The 6-D twistor space of the space-time surface is a fiber bundle having space-time as base space and sphere as fiber and assumed to be representable as a 6-surface in 12-D twistor space T(M⁴)× T(CP₂). The lift of Kähler action to Kähler action requires that the twistor spaces T(M⁴) T(CP₂) have Kähler structure. These structures exist only for S⁴, E⁴ and its Minkowskian analog M⁴ and CP₂ so that TGD is completely unique if one requires the existence of twistorial formulation. In the case of M⁴ one has a hybrid of complex and hyper-complex structure.
   
   
2. The radii of the two spheres bring in new length scales. The radius in the case of CP₂ is essentially CP₂ radius R. In the case of M⁴ the radius is very naturally Planck length so that the origin of Planck length is understood and it is purely classical notion whereas Planck mass and Newton's constant would be quantal notions.
   
   
3. The 6-D Kähler action must be made dimensionless by dividing with a constant with dimensions of length squared. The scale in question is actually the area of S²(M⁴), not the inverse of cosmological constant as the first guess was. The reason is that this would predict extremely large Kähler coupling strength for the CP₂ part of Kähler action.
   

   There are however two contributions to Kähler action corresponding to T(CP₂) and T(M⁴) and the corresponding Kähler coupling strengths - the already familiar α_K and the new α_K(M⁴) - are independent. The value of α_K(M⁴)× 4π R(S²(M⁴) corresponds essentially to the inverse of cosmological constant and to a length scale which is of the order of the size of Universe in the recent cosmology. Both Kähler coupling strengths are analogous to critical temperature and are predicted to have a spectrum of values. According to the earlier proposal, α_K(M⁴) would be proportional to p-adic prime p≈ 2^k, k prime, so that in very early times cosmological constant indeed becomes extremely large. This has been the problem of GRT based view about gravitation. The prediction is that besides the volume term coming from S⁽M⁴) there is also the analog of Kähler action associated with M⁴ but is extremely small except in very early cosmology.
   
   

4. A further new element is that TGD predicts the possibility of large h_eff=n× h gravitons. One has h_eff=h_gr= GMm/v₀, where v₀ has dimensions of velocity and satisfies v₀/c<1: the value of v₀/c is of order .5 × 10^-3 for the inner planets. h_gr seems to be absolutely essential for understanding how perturbative quantum gravitation emerges.
   

   What is nice is that the twistor lift of Kähler action suggests also a concrete explanation for h_eff/h=n. It would correspond to winding number for the map S²(X⁴)→ S²(M⁴) and one would indeed have covering of space-time surface induced by the winding as assumed earlier. This covering would have the special property that the base base for each branch of covering would reduce to same 3-surface at the ends of the space-time surface at the light-like boundaries of causal diamond (CD)
   defining fundamental notion in zero energy ontology (ZEO).
   
   

Twistor approach thus shows that TGD is completely unique in twistor formulation, explains Planck length geometrically, predicts cosmological constant and assigns p-adic length scale hypothesis to the cosmic evolution of cosmological constant, and also suggests an improved understanding of the hierarchy of Planck constants.

Can one understand the detection of gravitational waves if gravitons are dark?

The problem of quantum gravity is that if the parameter GMm/h=Mm/m_P² associated with two masses characterizes the interaction strength and is larger than unity, perturbation theory fails to converge. If one can assume that there is no quantum coherence, the interactions can be reduced to those between elementary particles for which this parameter is below unity so that the problem would disappear. In TGD framework however fermionic strings mediate connecting partonic 2-surface mediate the interaction even between astrophysical objects and quantum coherence in astrophysical scales is unavoidable.

The proposal is that Nature has been theoretician friendly and arranged so that a phase transition transforming gravitons to dark gravitons takes place so that Planck constant is replaced with h_gr=GMm/v₀. This implies that v₀/c<1 becomes the expansion parameter and perturbation theory converges. Note that the notion of h_gr makes sense only of one has Mm/m_P²>1. The notion generalizes also to other interactions and their perturbative description when the interaction strength is large. Plasmas are excellent candidates in this respect.

1. The notion of h_gr was proposed first by Nottale from quite different premises was that planetary orbits are analogous to Bohr orbits and that the situation is characterized by gravitational Planck constant h_gr= GMm/v₀. This replaces the parameter GMm/h with v₀ as perturbative parameter and perturbation theory converges. h_gr would characterize the magnetic flux tubes connecting masses M and m along which gravitons mediating the interaction propagate.
   

   According to the model of Nottale > for planetary orbits as Bohr orbits the entire mass of star behaves as dark mass from the point of view particles forming the planet. h_gr=GMm/v₀ appears as in the quantization of angular momentum and if dark mass M_D<M is assumed, the integer characterizing the angular momentum must be scaled up by M/M_D. In some sense all astrophysical objects would behave like quantum coherent systems and many-sheeted space-time suggests that the magnetic body of the system along which gravitons propagate is responsible for this kind of behavior.
   
   

2. The crucial observation is that h_gr depends on the product of interacting masses so that h_gr characterizes a pair of systems satisfying Mm/m_P²>1 rather than either mass. If so, the gravitons at magnetic flux tubes mediating gravitational interaction between masses M and m are always dark and have h_gr=h_eff. One cannot say that the systems themselves are characterized by h_gr. Rather, only the magnetic bodies or parts of them can be characterized by h_gr. The magnetic bodies can be associated with mass pairs and also with self interactions of single massive object (as analog of dipole field).
   
   
3. The general vision is that ordinary particles and large h_eff particles can transform to each other at quantum criticality (see this). Above temperatures corresponding to critical temperature particle would be ordinary, in a finite temperature range both kind of particles would be present, and below the lower critical temperature the particles would be dark. High T_c super-conductivity would provide a school example about this.
   
   

One would expect that for pairs of quantum coherent objects satisfying GMm/h>1, the graviton exchange is by dark gravitons. This could affect the model for the detection of gravitons.

1. Since Planck constant does not appear in classical physics, one might argue that the classical detection does not distinguish between dark and ordinary gravitons. Gravitons corresponds classically to radiation with same frequency but amplitude scaled up by n^1/2. One would obtain for h_gr/h>1 a sequence of pulses with large amplitude length oscillations rather than continuous oscillation as in GRT. The average intensity would be same as for classical gravitational radiation.
   

   Interferometers detect gravitational radiation classically as distance oscillations and the finding of LIGO suggests that all of the radiation is detected. Irrespective of the value of h_eff all gravitons couple to the geometry of the measuring space-time sheets. This looks very sensible in the geometric picture for this coupling. A more quantitative statement would be that dark and ordinary gravitons do not differ for detection times longer than the oscillation period. This would be the case now.
   

   The detection is based on laser light which goes forth and back along arm. The total phase shift between beams associated with the two arms matters and is a sum over the shifts associated with pulses. The quantization to bunches should be smoothed out by this summation process and the outcome is same as in GRT since average intensity must be same irrespective of the value of h_gr. Since all detection methods use interferometers there would be no difference in the detection of gravitons from other sources.
   
   

2. The quantum detection h_eff gravitons - as opposed to classical detection - is expected to differ from that of ordinary gravitons. Dark gravitons can be regarded as bunches of n ordinary gravitons and thus is n times higher energy. Genuine quantum measurement would correspond to an absorption of this kind of giant graviton. Since the signal must be "visible dark gravitons must transform to ordinary gravitons with same energy in the detection. For 35 Hz graviton the energy would have been GMm/v₀h times the energy or ordinary graviton with the same frequency. This would give energy of 19 (c/v₀) MeV: one would have gravitational gamma rays. The detection system should be quantum critical. The transformation of dark gravitons with frequency scale done by 1/n and energy increased correspondingly would serve as a signature for darkness.
   

   Living systems in TGD Universe are quantum critical and bio-photons are interpreted as dark photons with energies in visible and UV range but frequencies in EEG range and even below (see this). It can happen that only part of dark graviton radiation is detected and it can remain completely undetected if the detecting system is not critical. One can also consider the possibility that dark gravitons first decay to a bunch of n ordinary gravitons. Now however the detection of individual gravitons is impossible in practice.
   
   

A gamma ray pulse was detected .4 seconds after the merger

The Fermi Gamma-ray Burst Monitor detected 0.4 seconds after the merger a pulse of gamma rays with red shifted energies about 50 keV (see the posting of Lubos and the article from Fermi Gamma Ray Burst Monitor). At the peak of gravitational pulse the gamma ray power would have been about one millionth of the gravitational radiation. Since the gamma ray bursts do not occur too often, it is rather plausible that the pulse comes from the same source as the gravitational radiation. The simplest model for blackholes does not suggest this but it is not difficult to develop more complex models involving magnetic fields.

Could this observation be seen as evidence for the assumption that dark gravitons are associated with magnetic flux tubes?

1. The radiation would be dark cyclotron gravitation generated at the magnetic flux tubes carrying the dark gravitational radiation at cyclotron frequency f_c= qB/m and its harmonics (q denotes the charge of charge carrier and B the intensity of the magnetic field and its harmonics and with energy E=h_effeB/m .
   
   
2. If h_eff= h_gr= GMm/v₀ holds true, one has E= GMB/v₀ so that all particles with same charge respond at the same the same frequency irrespective of their mass: this could be seen as a magnetic analog of Equivalence Principle. The energy 50 keV corresponds to frequency f∼ 5× 10¹⁸ Hz. For scaling purposes it is good to remember that the cyclotron frequency of electron in magnetic field B_end=.2 Gauss (value of endogenous dark magnetic field in TGD inspired quantum biology) is f_c=.6 Mhz.
   

   From this the magnetic field needed to give 50 keV energy as cyclotron energy would be B_ord= (f/f_c)B_end=.4 GT corresponds to electrons with ordinary value of Planck constant the strength of magnetic field. If one takes the redshift of order v/c∼ .1 for cosmic recession velocity at distance of Gly one would obtain magnetic field of order 4 GT. Magnetic fields of with strength of this order of magnitude have been assigned with neutron stars.
   
   

3. On the other hand, if this energy corresponds to h_gr= GMm_e c/v₀ one has B= (h/h_gr)B_ord = (v₀m_P²/Mm_e)× B_ord∼ (v₀/c)× 10^-11 T (c=1). This magnetic field is rather weak (fT is the bound for detectability) and can correspond only to a magnetic field at flux tube near Earth. Interstellar magnetic fields between arms of Milky way are of the order of 5× 10^-10 T and are presumably weaker in the intergalactic space.
   
   
4. Note that the energy of gamma rays is by order or magnitude or two lower than that for dark gravitons. This suggests that the annihilation of dark gamma rays could not have produced dark gravitons by gravitational coupling bilinear in collinear photons.
   

One can of course forget the chains of mundane realism and ask whether the cyclotron radiation coming from distant sources has its high energy due to large value of h_gr rather than due to the large value of magnetic field at source. The presence of magnetic fields would reflects itself also via classical dynamics (that is frequency). In the recent case the cyclotron period would be of order (.03/v₀) Gy, which is of the same order of magnitude as the time scale defined by the distance to the merger.

In the case of Sun the prediction for energy of cyclotron photons would be E=[v₀(Sun)/v₀] × [M(Sun)/M(BH)] × 50 keV ∼ [v₀(Sun)/v₀] keV. From v₀(Sun)/c≈ 2^-11 one obtains E=(c/v₀)× .5 eV> .5 eV. Dark photons in living matter are proposed to correspond to h_gr=h_eff and are proposed to transform to bio-photons with energies in visible and UV range (see this).

Good dialectic would ask next whether both views about the gamma rays are actually correct. The "visible" cyclotron radiation with standard value of Planck constant at gamma ray energies would be created in the ultra strong magnetic field of blackhole, would be transformed to dark gamma rays with the same energy, and travel to Earth along the flux tubes. In TGD Universe the transformation ordinary photons to dark photons would occur in living matter routinely. One can of course ask whether this transformation takes place only at quantum criticality and whether the quantum critical period corresponds to the merger of blackholes.

The time lag was .4 second and the merger event lasted .2 seconds. If the gamma rays were ordinary photons so that dark gravitons would have travelled along different flux tubes, one can ask whether the propagation velocities differed by &Delta: c/c∼ 10^-17. Since the geodesics of the space-time surface are in general not geodesics of the imbedding space signals moving with light velocity along space-time sheet do not move with maximal signal velocity in imbedding space and the time taken to travel from A to B depends on space-time sheet. Could the later arrival time reflect slightly different signal velocities for photons and gravitons?

For details see the chapter Quantum Astrophysics of "Physics in Many-Sheeted Space-time" or the article LIGO and TGD.

For a summary of earlier postings see Links to the latest progress in TGD.