On the one hand, the search for gravitational waves was not fruitful for 100 years.On the other hand, General Relativity is a well-corroborated and respectable theory
On the one hand gravitational waves have been discovered, in the variation of the period of binary pulses, work that was awarded the Nobel Prize in Physics in 1993, http://www.nobelprize.org/nobel_prizes/physics/laureates/1993/ The agreement between calculations and measurements is only possible if the gravitational radiation is described as implied by General Relativity and corroborates the theory this way. ``Respect'' isn't a meaningful notion for a theory. It wouldn't have been less respected had they not been discovered, for there's no guarantee that it would have been possible to detect such binary pulsars from Earth-it was fortunate that this did occur. Not all predictions of a theory can be experimentally tested-therefore it's necessary to think very hard how to develop experiments that can do so.
On the other hand, it's by no means certain that it's possible to detect the gravitational waves, that are emitted by astrophysical sources, on Earth. The searches by LIGO and VIRGO are useful in that they establish bounds on the sources that can be detected this way, on Earth.
On can say that Einstein's General Theory of Relativity was refuted, but the theory should evolve for transforming itself.
No, one cannot say that, given that there hasn't been an experiment that is in contradiction with its predictions and all experiments to date are in agreement with its predictions.
As far as I Know all the calculations referring to grav. waves are performed in the so-called "linear field approximation" when the gravitational field is treated like electromagnetic field.On the other hand, as A.Z.Petrov exhibited many many years ago, the energy of non-linear genuine Einstein gravitational wave is described by a pseudo-tensor . Hence the energy T(00) component can be made equal to zero just by choosing the proper reference system
The linear field approximation means that the self-interaction of the metric is neglected; it does not mean that the gravitational field is treated like the electromagnetic field; the gravitational field is a tensor field, while the electromagnetic field is a vector field. The radiation is completely different in the two cases. That energy and momentum are not locally defined quantities, but can only be given invariant meaning at the boundary of spacetime in question is, indeed, a characteristic feature of the general coordinate invariance of general relativity and would not be true, were the gravitational field described by a vector.
It's useful then to learn that useful results aren't limited to the linear field approximation, where, once more, the gravitational field is not treated in the same way as electromagnetism, anyway. Cf. http://arxiv.org/abs/gr-qc/9803031 for instance and citations thereof and http://journals.aps.org/prd/abstract/10.1103/PhysRevD.45.1840
No the non existence of gravitational waves in itself does not refute GR.
Indeed these waves may yet be discovered.
However, there are more recent discoveries that go a long way to refuting GR. Not least the confirmation of the presence of black holes and CMB.
The maths of GR implies infinite curvature and zero time passage at the black hole event horizon and the black hole becomes a singularity
The Misner Wheeler Thorne interpretation partially resolves this singularity problem in that the singularity rests inside the event horizon.
But yet another paradox arises, if time stops at the event horizon no matter would ever be seen to fall in hence black hole could not accumulate matter, and all the in-falling matter would be situated at or near the event horizon.
We do know that black holes accumulate matter over their lifetime ( otherwise the CMB would not be nearly as uniform) and this provides us with the experimental evidence that matter is actually stored within the inner structure of the black hole.
The solution is to alter the maths of GR.
Additionally GR falls down in a number of areas, so any new maths should also resolve these problems
Yes GR works in the weak fields of the the solar system, and Intermediate
fields of neutron stars.
1). It produces infinite density singularities in the very strong fields
such as in black holes.
2).It does not necessarily explain dark matter in galaxy cores where we
know super-massive black holes exist and the galactic dark matter
therein. and more importantly GR does not explain the internal structure of the black hole
3). It does not explain dark mater present in galactic halo's,and galactic
clusters such as the bullet cluster,
4).It does not explain the presence of cosmological dark matter as a whole.
5). It has not yet been fully corroborated by the studies of neutron stars
and in black holes.
6). It does not easily explain the presence of dark energy and cannot be
translated in quantum gravity.
Here I enclose a number of publications which explain all of these
phenomena, whilst agreeing with the results of GR where it has been
thoroughly tested.
1).First to obviate the infinite density singularities.
1a)
https://www.researchgate.net/publication/32897680_An_advanced_dynamic_adaptation_of_Newtonian_equations_of_gravity?ev=prf_pub
1b)
https://www.researchgate.net/publication/269689554_The_formulation_of_Dynamic_Newtonian_advanced_gravity_DNAg?ev=prf_pub
2).Secondly we explain the presence of dark matter at the centre of the
galaxy.
2a)
https://www.researchgate.net/publication/228858219_Advances_in_Black_Hole_Gravitational_Physics_and_Cold_Dark_Matter_Modelling._The_Gravity_of_Dark_Matter
3) Thirdly it is possible to explain the presence of dark matter in the
galactic halo.
3a)
https://www.researchgate.net/publication/269689929_Advances_in_Black_Hole_Physics_and_Dark_Matter_Modelling_of_the_Galactic_Halo?ev=prf_pub
4). It is able to explain the presence of cosmological dark matter
https://www.researchgate.net/publication/32897680_An_advanced_dynamic_adaptation_of_Newtonian_equations_of_gravity
5). It is corroborated in neutron stars (including Data from radiation
damping ) and is corroborated by black hole studies.
5a)
https://www.researchgate.net/publication/32888463_An_advanced_modification_of_dynamicgravitation
5b).
https://www.researchgate.net/publication/269667939_Corroboration_of_Dynamic_Black_Hole_Gravitational_Physics_from_Observations_of_Cygnus_X-1
6) it explains dark energy and translates into quantum gravity
https://www.researchgate.net/publication/32899306_String_quintessence_and_the_formulation_of_advanced_quantum_gravity
Read full-text
SourceAvailable from: Andrew Worsley
Article: An advanced dynamic adaptation
Are there any experiments known with quanta information? - ResearchGate. Available from: https://www.researchgate.net/post/Are_there_any_experiments_known_with_quanta_information#view=5628b4156307d90b368b457a [accessed Oct 22, 2015].
Article An advanced dynamic adaptation of Newtonian equations of gravity
Article The formulation of dynamic Newtonian advanced gravity, DNAg
Article Advances in Black Hole Gravitational Physics and Cold Dark M...
Article Advances in Black Hole Physics and Dark Matter Modelling of ...
Article An advanced modification of dynamic gravitation
Article Corroboration of Dynamic Black Hole Gravitational Physics fr...
Article String quintessence and the formulation of advanced quantum gravity
Hi! What a coincidence!
I found a news report exactly on the same topic today. The link is below.
http://phys.org/news/2015-10-gravitational-black-hole-rethink.html
The term ``missing gravitational waves'' is misleading, because there isn't any reason to expect that the search quoted was assured to observe gravitational waves. What it's relevant for is more about the uncertainty regarding the equation of state of neutron stars-which involves much more uncertain factors. It's not useful to try to obtain technical insight from popular media reports on scientific subjects.
Totally, agree with you, Stram. I myself do not trust media articles. But sometimes discussion in that forum are informative, since only regular physics enthusiast (in most cases a researcher) registers in such websites.
Ptolemy's cosmology (exhibited in "Almagest") had successfully accumulated hundreds and thousands of jbservation data. Yet Ptolemy had contended (in full accord with the spirit of Aristotelian metaphysics) that all the planets as spiritual formations have souls. To this I.Kepler added that the planets can sing and they do so while orbiting the Sun.
Gravitational waves may not refute GR. But I think physicists have been too busy in thier work, that they forgot simple problems like looking at the sky.
Here attached, I explain a simple problem of GR. (How can the rotation of earth have the same velocities at different altitudes w(A)=w(B) and have also the same radius (or perimeter) of observation RA-5000m=RB following GR?)
https://www.researchgate.net/publication/283083046_Relativity_problem_comparison_between_two_altitudes_of_the_rotation_of_earth_since_its_existence_in_billion_years
Conference Paper Relativity problem: comparison between two altitudes of the ...
@ Ni Ge,
Sorry! I cannot get your point. Can you please elaborate or provide suitable link which explains the problem?
Dear Vikash,
I have tried to find if someone stated this before, and found no answers.
The problem is the following.
The idea is to compare a slope of 5000m which could exist 4.5 billion years before (or something digged). Because of a time dilation difference due to gravitation (low gravity at the top/high gravity at the bottom), the rotation of earth should have an effect on the vision of our sky between the two places.
Following different interpretation of GR you should have these statement:
1. The two perimeter of sky (CMBR for example) are not equivalent, then you have a gap/shift of the moved sky (e.g. day for one, night for the other) IMPOSSIBLE
2. You can recictify this by accepting a length contraction, then it affects the radius and gives like a lens effect. (e.g. all the stars seems to be farer for one relative to the other) NOT STATED AS I KNOW
3. If you reject 1. and 2. you can accept that the rotation of earth is not the same at different altitudes (which contradicts the period of earth rotation calculated by former physicists), then all physical statement should be corrected the same way, which gives no length contractions and a flat space-time.
Finally, whatever answer you take GR doesn't work anymore.
Am I wrong?
Here I give you the calculus of shifted time during 4.5 billion years (nearly 22h where SRT effects are neglected because they should not be taken into account, even taking them into account the difference should be nearly 6h if I am not wrong):
https://www.researchgate.net/post/Why_general_relativity_doesnt_match_with_positions_of_the_moon_between_0m_and_5000m
@ Ni Ge
Either I am misunderstanding you, or you are fundamentally incorrect. Lets, assume Mt. Everest, height 8848 m above sea level. g_Mt. Everest = g_earth * (1 - 2h /R) = 9.7729 ms^-2. If you place 2 observers, one at the feet of the mountain and another at its top, you may have to wait thousands of years to observe a time-difference of a second or so between the two observers.
And, as far as I know GR has always been proved correct. There could be some limitations which people report sometimes, but I have never read about any significant departure from GR.
No, I think you understand good the problem.
But here you have to wait 4.5 billion years (earth existence). Because the earth is rotating during this time, there is an approximated rotation gap/shift of 22h between the two altitudes (0 and 5000m). It means one picture of the sky should be decayed to the other OR the size (e.g. deepness) of the sky shouldn't be the same (if length contraction to keep the decay 0h).
In other words if you stay at Mt Everest and another one at 0m after 4.5 billion years there should be a difference in viewing the sky after this time. If you accept that earth exists since 4.5 billion years, this difference should already be observable, if GR was true.
@ Ni Ge
Why would earth rotation's have different velocities at different altitudes?
@ Ni Ge
Time dilation is there and experimentally verified on everyday basis. Our GPS works on two basic fundamental principles:
1) General theory of relativity
2) Special theory of relativity
The effects from the two theories are taken into account for the GPS to give the right location!
Wrong example. It is only a statement that a clock goes quicker than another, not a verification of time dilation. GPS could be delayed by the modification of atom's oscillation through acceleration.
Furthermore Special relativity is applicated only in one way to synchronize GPS. We should not only correct from earth to GPS but also from GPS to earth (relativity means relativity: earth rotates westward relative to a geostationary satellite).
But it is another discussion.
If my paper doesn't surprise you, then it's fine. I Wonder just how you can explain its paradox.
Null detection of gravitational wave would rule out graviton as a carrier of gravitational force. It will also rule out the theory of zero energy universe which proposes negative gravitational potential energy stored in the space-time fabric. This would mean there is no negative energy and no space-time fabric. Energy of the universe is only positive and non zero. But since momentum could be positive or negative, one could put opposite signs on energy flying away in opposite direction. Wheeler DeWitt equation, Hartle-Hawking wavefunction of the universe and Loop Quantum Gravity all, are founded upon zero energy universe theory which states that all the positive energy of the universe is exactly equal to the negative gravitational potential energy of the space-time fabric. This is also the foundation of general relativity theory. Therefore this part of general relativity will have to change but this cannot completely refute general relativity. The rest of the theory is robust and will survive like Newton's theory. Lastly we may need some alternative explanation for the orbital period decay of binary pulsar, such as one given here.
Research Alternative explanation for orbital period decay of a pulsar
a variable gravitational potential due to a rotating quadrupole of course change in time the gravitational force an object is attracted in distance. So, also Newton's law of universal gravitation can predict gravitational waves! From here to be sure that gravitational waves are deformations of space-time there's the ocean in the middle! It's a variation in the strength of attraction, nothing more. Of course if you say with Einstein that gravity is a deformation of space(-time) than GW are also a deformation. But we still need quantum gravity to say what GW really are if they exist. Woud they be made up of gravitons?
@marco
Consider this
If gravitons exist then space time is warped according to Lorentz Invariance - hence are not detectable because the very fabric of space time does not allow it
but their joint action on greater scale (gravitational waves) should be somehow detectable, indeed we're looking for such waves in several laboratories, but still without success
Maybe it's high time to recognize that gravitational waves play for XXI physics the same part as the "aether" played for Victorian XIX physics? Ether was necessary to be a medium for electromagnetic waves propagation only.The experiments did not demand its existence, and for interpreting their results with the help of ether notion a great number of "epicycles" and "deferents" was needed.Maybe a modern kind of the Principle of Relativity should be formulated stating that no physical experiment can detect the gravitational waves existence?
@Thierry De Mees: I have already explained under your question but you don't believe. Some of the things I did not mention are bending of light, gravitational redshift of light, perihelic precession of planets, temperature of CMB radiation (2.75 deg. K). Inflation.
I'd like to start from the observation that relativity is a false and the most preposterous theory of the 20th century. As there appears in this thread mentioning on black holes, gravity, gravitons, CMBR, I decided to refer to video that I think is worth to familiarize with:
https://www.youtube.com/watch?v=Y8FsfFs_nvM
There is also an idea on field theory on
http://pinopa.republika.pl
on the left, on green field, titled: "The Constructive Field Theory - briefly and step by step"
In my opinion, gravitational waves don't exist in contrast to motion of ether (sic!). I came to this conclusion by my description of space, as it is one of the most important topics before one should ponder on the gravitational issues. I frankly admit that I might be wrong, or that anyone can have better idea than mine, but all the literature I familiarized with doesn't convinced me at all.
http://www.eioba.com/a/3dm8/how-to-comprehend-space
--
Those who claim that understood Relativity, automatically admit, that they understood nonsense
I'm always a bit worried about experiments where a positive result is taken as emphatically proving a specific theory, but the lack of a positive result isn't taken as refuting it.
Sometimes there's a justification for carrying out "fishing expeditions" ("let's build this gear and see if anything triggers it"), but if the experimenters are "fishing", then they need to be very cautious about how they present any apparently-positive results that result.
If an experiment's two main possible outcomes for a theory are "validate" and "invalidate", then a positive result carries some weight.
If the two options are "validate" and "sorry, we don't know what went wrong", then a positive result has to be assumed to carry less significance for the theory, because the experimenters are prepared to downgrade the claimed significance of their results if they're not as hoped.
Stam: (page 1) " there hasn't been an experiment that is in contradiction with its predictions and all experiments to date are in agreement with its predictions. "
What, never? :) I thought that we needed to invent dark matter because, without inventing this new substance, the physical predictions of GR1916 didn't seem to agree with the experimental data. Maybe these additional effects are real, or ... maybe the divergence is physical evidence that the current theory is wrong.
The GR community naturally prefer the first interpretation, but the second also seems valid.
The second interpretation actually seems to be able to make predictions about dark matter ... that its characteristics will be found to be indistinguishable from a field theory correction, that dm will shadow the distribution of normal matter (with some slewing and skewing), that any apparent positional offsets and density divergences will probably be most obvious where there's extreme gravitational physics involved (such as galaxy collisions), and that dm will be found not to interact with normal matter in any way except gravitationally, and also will also be not interact with itself except gravitationally (it will not self-stick, or clump). It will be invisible, and have no apparent detectable properties other than gravitational ones.
So far, the most predictively-powerful interpretation of dm seems to be that the stuff doesn't actually exist, and that there's instead something wrong with general relativity.
To be fair, the problem of gravitational waves does seem to be quite, quite horrible. We can argue that the things certainly ought to be generated (e.g. by a double-star system), but I don't know how one proves that the things then propagate politely over long distances without self-damping. Yes, I know that one can probably prove it mathematically, but mathematical proofs based on idealised starting assumptions aren't always as reliable as deeper logical proofs.
----
The problem with gravity-waves is that, naively, one might expect them to be very, very, very nonlinear. Suppose that one is on the equatorial plane of a double-star system and either feels the periodic tug-and-release or is washed back and forth as the local influence of each passing member of the pair waxes and wanes.
If that induced variation in gravitational field strength at your position is visualised as a compaction and rarefaction of the metric, and those changes radiate outwards from the double-star, then, if the changes in the metric's characteristics are thought of (naively) as appearing in a flat projection of the region as variations in the speed of light, then, if the wave itself is reckoned to move at the speed of light, we have an obvious problem ... the two halves of each wavecyle, associated with the compaction and rarefaction phases, end up being assigned different nominal average lightspeeds, and therefore propagation speeds. If the "faster" section of a wave is catching up with the "slower" section, then if the wave starts out being visualised as approximately sinusoidal, one might expect its smooth humps to tend towards becoming (at a given critical distance) an arbitrarily-thin series of spikes.
Unfortunately, if the energy of the wave depends on the smallness of its wavelength, an arbitrarily-thin spike corresponds to an arbitrarily-high energy, and a gravity-wave should not gain energy as it propagates (!), so something else must be going on. There are also definitional problems associated with allowing any component of the wave to travel at any speed other than the exact speed associated with the properties at the exact point occupied by that component ... unless we allow adjacent regions to also have an influence, at which point we're starting to move towards using an acoustic metric, which gives a different general theory.
What one could hypothesise would be that perhaps a smearing effect progressively robs energy from the outgoing wave and converts it into extra space, so that at a distance from the double-star, the wave is lower-amplitude that otherwise expected, but the region of space within the perimeter is larger, the increase in space-per-unit-volume corresponds to a deepening of the double-star's overall apparent gravity-well, and the gravity-wave's lost energy shows up as an apparent increase in the double-star's mass, as seen by a distant observer.
There are other arguments available for a number of different outcomes and behaviours, so I'm not claiming that this one is necessarily the correct solution ... but it does illustrate one hypothetical physics in which, although gravitational waves exist and are generated, they aren't necessarily easily detectable at great distances.
And this is before one considers whether information in a gravity-wave component propagating at nominal c reats to the existence of an apparent forward classical information-barrier by generating forward-aimed Hawking radiation, allowing its information to precondition the region ahead of it, altering the effective propagation speed once again ... ugh.
This is crossing over into quantum gravity, and is not stuff that I would have expected anyone to have been capable of calculating reliably back in the 1960s.
It is my innermost conviction that the problem situation with gravitational waves is similar to the situation in XIX-th century electrodynamics. James Maxwell et al. were strong supporters of luminiferous ether. The notorious entity was necessary only for the elucidation of the electromagnetic waves propagation. A plentity of ad hoc machinery was conjured up.
Wait for two more days, see attached link.
http://phys.org/news/2016-02-thursday-einstein-gravitational.html
Maybe one of my papers can help to make my standpoint clear. Rinat M. Nugayev. Why did bew physics force out the old? // International Studies in the Philosophy of Science» - vol. 10.- № 2. - March 1996 - pp.127-140.
Einstein tried to reintroduce the ether "general relativity without the ether is unthinkable".
But he was dis-allowed, similarly gravitons predicted by GTR probably do exist, whether we can detect them with a simple interferometer is doubtful.
After all the speed of light was measure d by an interfrometer and the speed of light is a constant whatever gravitational field you have,
On LIGO : good people had observed ghosts many times.Nevertheless it was cheaper than 1.1$ bln. dollars
The current explanation of September 2015 LIGO observations seems to be adhoc -1 due to the standards of Methodology of Scientific Research Programmes. Just to quote Imre Lakatos: " an explanation T is called an ad hoc-1, if it is conjured up for explanation of a single event (or experiment) E-1 and is not supported by other experiments or events observed independently of E-1". Had anybody observe the collision of two massive black holes not in a dream?
Gravity waves have been found with 2 polarizations, i think we have to accept that, in so far as the LIGO results have been published.
However, there are other theories that suggest this result without the paradoxes of GTR
Einstein did not predict the existence of black holes, in fact he denied their existence in a paper published in 1936, Simply because that would imply the existence of singularities, with infinite density and zero time passage at the event horizon.
The force of gravity in General relativity (GTR) is thought to come form the curvature of space-time.
Unfortunately the maths of GTR implies infinite curvature and zero time passage at the black hole event horizon and the black hole becomes a singularity- and yet the black hole has a radius.
The Misner Wheeler Thorne interpretation partially resolved this in that the singularity rests inside the event horizon.
But yet another paradox arises if time stops at the event horizon (frozen star) no matter would fall in hence black hole could not accumulate matter, and all the in-falling matter would be situated at or near the event horizon.
The solution is to alter the maths of GR.
Additionally GR falls down in a number of areas, so any new maths should also resolve these problems
Yes GR works in the weak fields of the the solar system, and Intermediate
fields of neutron stars.
1). It produces infinite density singularities in the very strong fields
such as in black holes.
2).It does not necessarily explain dark matter in galaxy cores where we
know super-massive black holes exist and the galactic dark matter
therein,
3). It does not explain dark mater present in galactic halo's,and galactic
clusters such as the bullet cluster,
4).It does not explain the presence of cosmological dark matter as a whole.
5). It has not yet been fully corroborated by the studies of neutron stars
and in black holes.
6). It does not easily explain the presence of dark energy and cannot be
translated in quantum gravity.
7). It predicts that time stops at the event horizon
Here I enclose a number of publications which explain all of these
phenomena, whilst agreeing with the results of GR where it has been
thoroughly tested.
1).First to obviate the infinite density singularities.
1a)
https://www.researchgate.net/publication/32897680_An_advanced_dynamic_adaptation_of_Newtonian_equations_of_gravity?ev=prf_pub
1b)
https://www.researchgate.net/publication/269689554_The_formulation_of_Dynamic_Newtonian_advanced_gravity_DNAg?ev=prf_pub
2).Secondly we explain the presence of dark matter at the centre of the
galaxy.
2a)
https://www.researchgate.net/publication/228858219_Advances_in_Black_Hole_Gravitational_Physics_and_Cold_Dark_Matter_Modelling._The_Gravity_of_Dark_Matter
3) Thirdly it is possible to explain the presence of dark matter in the
galactic halo.
3a)
https://www.researchgate.net/publication/269689929_Advances_in_Black_Hole_Physics_and_Dark_Matter_Modelling_of_the_Galactic_Halo?ev=prf_pub
4). It is able to explain the presence of cosmological dark matter
https://www.researchgate.net/publication/32897680_An_advanced_dynamic_adaptation_of_Newtonian_equations_of_gravity
5). It is corroborated in neutron stars (including Data from radiation
damping ) and is corroborated by black hole studies.
5a)
https://www.researchgate.net/publication/32888463_An_advanced_modification_of_dynamicgravitation
5b).
https://www.researchgate.net/publication/269667939_Corroboration_of_Dynamic_Black_Hole_Gravitational_Physics_from_Observations_of_Cygnus_X-1
6) it explains dark energy and translates into quantum gravity
https://www.researchgate.net/publication/32899306_String_quintessence_and_the_formulation_of_advanced_quantum_gravity
7). It does not offer infinite time dilation at the event horizon
https://www.researchgate.net/publication/287213872_Finite_Gravitational_Time_Dilation_In_Black_Holes_Using_Dynamic_Newtonian_Advanced_Gravity_DNAg
Article An advanced dynamic adaptation of Newtonian equations of gravity
Article The formulation of dynamic Newtonian advanced gravity, DNAg
Article Advances in Black Hole Gravitational Physics and Cold Dark M...
Article Advances in Black Hole Physics and Dark Matter Modelling of ...
Article An advanced modification of dynamic gravitation
Article Corroboration of Dynamic Black Hole Gravitational Physics fr...
Article String quintessence and the formulation of advanced quantum gravity
Article Finite gravitational time dilation in black holes using dyna...
Gravitational waves is an essential element of Einstein's theory. However, they do not exist. They are extracted from the linearised form of his 'field equations'. But the black hole is extracted from the nonlinear 'field equations'. Nonetheless, the LIGO-Virgo Collaboration claims to have detected gravitational waves from two merging black holes. No they didn't. The speed of propagation of Einstein's gravitational waves is not unique because it is coordinate dependent. Chose a certain set of coordinates then the speed of [propagation is that of light in vacuo. Chose some other set of coordinates and the speed of propagation is entirely different to that of light. Einstein assumed that his waves exist and propagate at the speed of light, then selected a set of coordinates for his linearised form to get the speed of light wave equation he had presumed. His argument constitutes a vicious circle and therefore false. Moreover, GR cannot localise its gravitational energy (so gravitational waves do not exist), and GR violates the usual conservation of energy and momentum for a closed system, in conflict with a vast array of experiments, so GR is false. Also, to satisfy the usual conservation laws Einstein constructed his pseudotensor for the energy-momentum of his gravitational field alone, which he added to his energy-momentum tensor for the material sources alone, to get the total energy-momentum of his gravitational field and sources, which must be conserved together. However, his pseudotensor has neither physical nor mathematical meaning because it produces, by contraction, a first-order intrinsic differential invariant. However, the pure mathematicians proved in 1900 that first-order intrinsic differential invariants do not exist! Nevertheless Einstein and his followers use his pseudotensor to represent 'physical' entities, to model 'physical' phenomena, and to do calculations; all in fantasy-land.
Quite right! Yet I believe that GR can be reformulated so as to eliminate the opportunity of the grav.waves
Dear Thierry, on my view Your tenet opens one of the promising vistas of research. One of my Kazan University Relativity Dept. friends (G.G.Ivanov) had tried to revise the GR foundations in a similar fashion some twenty years ago.To my regret he died from cancer
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Waves