In the case of a binary star system radiating gravitational waves, does the mass of the binary system decrease? Or does it just exchange potential for kinetic energy as the stars revolve faster in their reduced orbit?
If the former, is the process reversible, can gravitational waves carry energy which then converts to kinetic, EM, matter (rest), strong, weak or Higgs energy?
Robert,
Yes the total system mass reduces as the gravitation waves carry energy out of the system. Surprisingly a lot of energy in the case of binary pulsars, has they are 1000's MJy sources in GW, but detectors are very inefficient.
Yes it's possible to convert the energy from GW to EM, but the processes are incredibly inefficient. For instance gravitational waves passing through a very strong magnetic field will generate EM waves via the Li-Baker effect. The gravitational wave group at Birmingham University (UK) were looking into this for GHz GW detectors.
Thanks R.A. I hadn't thought about (or known about) the Li-Baker effect, but it seems reasonable.
Do you see any implications from my observations about the gravitational fields of antiparticles and photons?
Interesting point. The gravitation field of a photon I remember is a bit weird as there's no rest mass but there's energy and momentum and I guess it must look like a gravitational wave and then it suddenly stops (if you're in the centre mass frame of the particles) and becomes a potential well. So something radical must happen during the particle creation.
Annihilation of e+ and e- proves that charge and its field has no intrinsic mass. I find this very remarkable.
Dear Robert ~
The interactions of elementary particles are quantum mechanical phenomena. Quantum theory as presently understood leaves gravitational effects completely out of consideration. Gravitation as presently understood is a classical theory. It deals only with macroscopic phenomena. It leaves quantum mechanics completely out of consideration. Therefore, in the present state of knowledge questions 1 and 2 are unanswerable. A unified theory of physics reconciling QM and GR would be required to answer them definitively. That continues to be elusive! The lack of unification causes no trouble in practice because the coupling constant for gravitational interactions is so very much smaller than the coupling constants in elementary particle interactions. Nevertheless, in principle that is not satisfactory! One can only speculate:
The archetypal quantum theory is Feynman’s QED. Theories of weak and strong interactions are based on an elaboration of the underlying pattern of QED. We have QCD, gauge theories of intermediate bosons, etc. It is reasonable to suppose that there exists a massless particle of spin 2 that interacts with other particles through an extremely small coupling constant. That would be the “graviton”. [Supporting that supposition is the fact that the linearized GR equations are identical to the Bargmann-Wigner equations for a massless spin 2 field, and that the full Einstein field equations can be recovered from them by introducing self-coupling through taking energy-momentum to be the source of the field. That amazing fact was shown by Gupta in 1952. (S N Gupta, Proc. Phys. Soc. London A65, 608).]
I would say that once we have a satisfactory “quantum theory of gravity” the answers to 1 and 2 will be “yes, there is exchange of energy between gravity and elementary particle interactions, but the effect is immeasurably small.”
RS: In the case of a binary star system radiating gravitational waves, does the mass of the binary system decrease? Or does it just exchange potential for kinetic energy as the stars revolve faster in their reduced orbit?
In any binary system, the Virial Theorem tells us that, if the kinetic energy is +E, the potential energy is -2E. As gravitational waves are radiated, the kinetic energy increases but the potential energy decreases at twice the rate hence the total is conserved.
RS: If the former, is the process reversible, can gravitational waves carry energy which then converts to kinetic, EM, matter (rest), strong, weak or Higgs energy?
That has been answered before but simply, any detector such as LIGO relies on absorbing some energy, albeit a very small amount, from a passing GW in order to function.
RAW: The gravitation field of a photon I remember is a bit weird as there's no rest mass but there's energy and momentum ...
Right, so if you consider a pair of photons traveling in opposite directions, the momenta cancel (vectors) but the energies sum (scalar) hence the pair has an effective mass. Similarly GW are also massless of course and travel at the speed of light but what is curious is that a region of interference, say between two binary star systems, should have an equivalent mass for each anti-node of the gravitational standing wave due to the energy passing through the location. The volume defined by an anti-node is not necessarily closed though, but there should still be a volumetric energy density.
Thanks George, I was wondering where collection of photons such as a volume filled with CMB photons got it's gravitational influence.
Maybe the answer could only be found in electro-gravitation experiments. There are ways I think via EM excitation to trigger transmutation then mass change but this is still nuclear physics. Now the real challenge would be to able manipulate mass at will via EM focus.
Of course I understand a GW detector would have to absorb gravitational energy, but since we haven't detected any GW I was just wondering if there might be a theoretical problem.
I have a fair understanding of metrics and such, though not of gravitational waves. But, generally distortions in a metric do not produce detectable changes in objects or fields, since they distort exactly with the metric. So there cannot be a simple coupling like with an EM wave. Locally, because of equivalence, a change in a metric is detectable only if tidal forces are sufficiently great. It seems to me GW detectors are stuck with this effect. There might be a slight difference in acceleration (the main effect of a metric) between one side of a wavefront and another, for example, a tiny effect. Most of the explanations of GW detectors in popular articles are useless me, and appear outright incorrect.
Of course also we don't have a QM theory of gravity. But by looking at the steady state gravitational field of the particle pair just before annihilation, and the photon pair just after, from a respectable radius (greater than the interaction zone, and greater than the photons will have traveled before field measurement, which is entirely theoretical of course, there is no practical way to measure such a small field), we can verify the gravitational field (and energy) are the same. We can analyze this classically.
I am now wondering, as I write this, about the gravitational wave radiation. If we have a particle pair that approaches, scatters, and goes away, I'm guessing the gravitational radiation will be similar to the situation where the particle pair approaches, annihilates, and two photons race away, especially if the particle pair was going at near lightspeed. In fact, these are just two possible outcomes of a scattering experiment which appears on the face of it nearly neutral with respect to gravity. Perhaps, after all, that is why we have not "needed" a QM theory of gravity so desperately for practical QM (which is usually scattering as I understand it ... investigating singularities is hardly something we do in the lab, but scattering is fundamental and everywhere).
@Robert Shuler, well since we do not have any unified theory, either we're stuck to prove or measure the GW at cosmological level (stars) or microscopic level (particles). Personally I'd tend to trust more microscopic effect being put in some coherent accumulation of energies transform which could be then detected by our instruments.
RS: Of course I understand a GW detector would have to absorb gravitational energy, but since we haven't detected any GW I was just wondering if there might be a theoretical problem.
No, the problem is the frequency of known astronomical sources compared with terrestrial background noise. The fastest known binary system is HM Cancri (a.k.a. RX J0806.3+1527, link attached) with a period of 321.5 seconds. That's produces GW of just 6.22mHz (two cycles per orbit). Compare that to the sensitivity chart for LIGO and LISA (see link). LIGO's low frequency limit is around 30Hz below which terrestrial seismic noise starts to dominate, LISA would have been able to get down to the milliHertz range. For interest, other binary system that could be detectable by the LISA space-based observatory are listed in the attached paper on Verification Binaries.
RS: "I am now wondering, as I write this, about the gravitational wave radiation. If we have a particle pair that approaches, scatters, and goes away, I'm guessing the gravitational radiation will be similar to the situation where the particle pair approaches, annihilates, and two photons race away."
We can't detect the radiation from a binary star system where the frequency is accurately known from optical measurements so the detector output can be integrated over a year or more. The radiation from an interaction of the mass of a couple of particles would be many orders of magnitude less and a one-off event.
RS: generally distortions in a metric do not produce detectable changes in objects or fields, since they distort exactly with the metric.
Have a look at the animations on the Wikipedia page (link attached). The effect is a stretch/compression in the transverse direction. That periodic variation of the distance between particles can be compared against the unmoving ends of a "rigid rod", the optical baseline of the LIGO detector for example, which is held fixed by the EM forces in the Earth's surface.
https://www.advancedligo.mit.edu/graphics/G060009-02.jpg
https://en.wikipedia.org/wiki/RX_J0806.3%2B1527
http://arxiv.org/pdf/astro-ph/0605227v1.pdf
https://en.wikipedia.org/wiki/Gravitational_wave#Effects_of_a_passing_gravitational_wave
In general relativity the Sun produces a curvature in space time. This curvature is what tell the planets to orbit the Sun. It is generally accepted that this gravitational field is generated by gravitons
By defintion these gravitons would have energy. That energy output is maintained to maintain the curvature of space-time. If the Sun were removed alll the planets would fly off at a tangent.
We also know that the energy is used to generate a gravitational field becuase of the gravitational radiation damping seen experimentally from binary pulsar data
Conservation of angular momentum relates to spin not to planetary orbit
Some have estimated the output of the Sun to be equivalent to 40 Watts. This seems far too low
I would be most grateful if someone could confirm or negate this vlaue.
George, everything should stretch and compress with space. It should be therefore locally not noticeable. If space can stretch and the objects in it not stretch with it, then relativity would be invalid.
I have looked at all those animations long ago by the way, which resulted in my own question thread on grav waves. There are some better figures there. See link below.
Andrew, you are not listening to anybody. You are using the rocket model of force. Re-read my answer which explains the difference. The chair you are sitting on does not expend energy to hold you up. Yet it is composed of quantum fields maintained by virtual photons.
https://www.researchgate.net/post/What_are_the_conditions_for_emission_and_field_pattern_for_gravitational_waves
"When antiparticles annihilate, all the energy from matter, EM, strong, weak and Higgs fields bound to the particles converts to a pair of photons, involving only EM energy. Across the moment of conversion, the gravitational field is unchanged."
This is what it is supposed to occur according to the very straightforward energy balance, which does not consider at all that beforehand there was a certain gravitational field which together with the electrical one brought together the charges (which are endowed of a mass).
Where does the additional contribuition to the kinetic energy, due to gravitation which made the particles collide, go?
Or rather a pair proton and antiproton have a gravitational attraction too, and this is a contribution to the speed at which they would meet if only the electromagnetic interaction would exist.
Don't we account for such a contribution even if it is 40 order of magnitude smaller?The truth is that such contribution is so far from any experimental accuracy possible right now that the pair annihilation "simple balance" holds quite well.
The pair annihilation is described by Physics by neglecting completely the contribution of gravitation into the process of the approaching of the charges, as if only the electromagnetic interaction alone existed.
Stefano I think you are basically agreeing with Eric (or someone) who pointed out that the annihilation is entirely a QED theory and takes no account of gravitation.
Robert,
yes with the difference that I consider incorrect the way Physics simply treats the energy balance. The experimental physics has to go that way due to limitations of devices, but theoretical physics has to account for it.
Robert,
Einstein used an example of a star with a planet in a highly elliptical orbit. The conclusion is that the total gravity produced by this combination does not change as the planet goes from being at its apogee with maximum potential energy to its perigee with maximum kinetic energy. The reason for mentioning this is that this simplified example presumes no loss of energy due to gravitational waves. If there is a loss of energy due to gravitational waves (GWs), there would be the appropriate loss of gravity for the star/planet system. It does not matter where the planet (or binary star) is in its orbit.
The radiation of GWs is also removing angular momentum in addition to removing energy. This is counter intuitive because the rotational rate is speeding up but the separation distance is smaller and the net result is a loss of angular momentum. If it was possible to perfectly reverse the gravitational waves, then the gravitational waves would add energy and angular momentum to the rotating binary star system.
I will add one prediction I have made regarding the detection of gravitational waves using laser interferometers. When a GW passes, the interferometer mirrors do not move. The space between the mirrors changes its properties in a way that a solid spherical volume would oscillate - one transverse dimension increase and the orthogonal transverse direction decrease. Therefore physical objects would react to GWs as expected. However, a laser beam is transverse EM radiation and it reacts differently to a GW. I have proposed that a passing GW turns spacetime into the equivalent of an oscillating birefringent medium. In other words, a single circularly polarized laser beam should be able to detect a gravitational wave if orthogonal linearly polarized components of the circularly polarized beam are monitored. Also if both beams in an interferometer with horizontal 90 degree arms are vertically linearly polarized, then both beams would experience the same effect and no GW would be detectable. This and other predictions are in the papers on my ResearchGate page.
John, your post above is the first discussion of GW detectors that I have semi- understood. Of course, if a change in curvature propagates through space, then the area-volume relations of objects would change.
Also, I like your idea of how it should in theory be possible to absorb GW's with an orbiting system to un-decay the orbit. I was fishing for that answer, in fact.
Robert,
this experiment very recently suggested in Arixv is of paramount importance I think:
"Using Atomic Clocks to Detect Gravitational Waves
05 gen 2015 - . Abraham ... 2School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel. http://arxiv.org/abs/1501.00996"
it exploits the entanglement for the syncronisation of atomic clocks set at a huge distance between eachother (1 billion km, along the terrestrial orbit around the sun). These oscillators detect the variation of the metric of the background/vacuum/space-time through the measured reciprocal time shift (time dilation) in the same instant.
It is one of the few experiments which make work together gravitation and quantum physics: the most advanced gravitational measurements in Gravity, Gravitational Waves, by exploiting the most advanced quantum physical characteristics, the Quanglement.
I jope I do not act as a spoil-sport, but if c is a global constant again, there exist no gravitational waves.
(And this global constancy I could show.)
And the famous "indirect demonstration" by the two Nobel-prize winners had unfortunately been based on putting the tidal-friction parameter equal to zero and then forgetting about it.
Dear Otto,
c is constant when It is measured in any reference frame locally, like in the MM experiment. The speed of light is not the same "c" if a fixed RF is chosen, and "non local" measurements and performed. The experiment of the Shapiro Delay and the light bending say that the speed of light has to be variable if referred to the same RF (of the receiver for example). See Eddington (space, time and gravitation) who analizes the speed of light across the entire solar system from a fixed view point external to it.
And you can use old spun-up millisecond pulsars as atomic clocks and use radio telescopes to do the same at the 10-15 level now with LEAP and new EPTA.
http://arxiv.org/pdf/1003.3405v1.pdf
Dear Robert Watson,
as an expert in the subject of gravitation do you agree with the suggested experiment?
"Using Atomic Clocks to Detect Gravitational Waves05 gen 2015 - . Abraham ... 2School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel. http://arxiv.org/abs/1501.00996"
Otto, you have not been able to explain even what you mean by global c. Until you do, your posts are just like a fly buzzing around. I have developed an independent approach to gravity which confirms major effects, and so I'm confident that coordinate velocity is reduced in proportion to time dilation in the transverse direction, and in proportion to the product of time dilation and length contraction in the radial direction, which maintains constant local c. This leads directly to my next comment...
Stefano, Thanks for the link, I read that paper. The clock scheme will detect nothing, here's why:
- Transient case - effect between any two points in the system is identical to standard gravitational effects, in fact the author uses quasi-static methods to calculate GW signal strength, not really wave equations. I will calculate the number of wavefronts per meter as the wave passes.
- Wave fronts and troughs will alternately produce time dilation and compression. Consider the time dilation case. The clock will make fewer ticks per unit of time of a coordinate observer (a hypothetical or distant observer unaffected by the GW), inflluencing wavefronts per meter down, dividing by the time dilation factor, let's call it Y.
- Length contraction will be in the same proportion a time dilation. This produces shorter meter sticks and a greater number of them between two points along the axis of propagation. This also influences wavefronts down by factor of Y. We now have a total reduction in wavefronts of Y2.
- Coordinate velocity of light will reduce proportional to the square of time dilation , or Y2. This increases the number of wavefronts per meter by Y2, exactly canceling the previous reduction of Y2, so there is no net change.
- The detector sees, therefore, a constant number of wavefronts per meter arriving, and since there is a constant local c at the detector, also a constant frequency and phase arriving. The synchronization loop will take no action.
- As the wave passes, there are equal and opposite effects averaging to zero, so there is no net storage of or depletion of wavefronts in the "pipe" between points on the circle.
I have given a one dimensional analysis in the direction of wave propagation. But that is where you'd think to see the greatest effect.
These line-dimension oriented experiments have no hope of detecting gravitational waves.
John: While I was at first excited about your volume idea, this doesn't work for a subtle reason. See the figures 1 and 2 in my "Two step" paper (link below). In order to detect a circumference-area or a surface area-volume difference, the measurement space has to enclose a minima or maxima of potential. Otherwise, you have the situation of the old Rindler metric in which the supposed spatial effects can be transformed away and the space measures flat. There is a detailed explanation in the paper. It is only necessary to read page 2, the one with the figures. The rest of the paper is irrelevant to the discussion.
Here is another way of stating things: To produce or detect curvature efficiently - and therefore gravitational energy - one has to enclose the source. Otherwise, along a line let's say, one only gets a Rindler metric in which spatial effects can be transformed away. In theory there might be small volume to area ratio changes present without enclosing the source, but not in a static metric. The millihertz frequencies of GW radiators are so low that metrics are quasi-static, i.e. the wavefront has almost no slope.
Hmm..., who understands my point, and understands the configuration of popular GW detectors, and would like to collaborate on a rebuttal paper?
In actual fact gravitational radiation damping is slightly out in GTR, and requires a largish correction factor, before you get to the 0.2 % accuracy. Oddly none of the other parameters require a correction factor at all.
This is because none of the other parameters approach the level of gravitational energy which the calculation for gravitational radiation damping provides
Converting the tensor calculus of GTR to an algebraic equation solves this inaccuracy and you get the correct radiation damping.
Article An advanced dynamic adaptation of Newtonian equations of gravity
Charles: Thank you for the interesting link. I'll comment in detail below.
Andrew: The abstract of your paper is intriguing, but I found the detail to be both lacking in conceptual overview of what is going on at each step, and suspiciously focused on precession. I inadvertently thought I had a mathematically complete description of gravity from 2010 through mid 2014 because I had used precession as my test (understandable, as Schiff thought this was the most complete test), but in fact the standard metnods of calculating precession do not involve radial spatial changes, with the result that incomplete math looks OK and gives the result.
Sticky Beads & Other Difficulties with Gravity Waves:
- To the extent we look at only a section of a wave in a vacuum, and the vacuum equation applies, with the Ricci tensor zero, I believe that implies the volume of objects will not change(?). I don't know if this is quite a valid argument, but just a quick thought. Not related to sticky beads though. Any surface that encloses the source will not see Ricci=0 and should be able to detect energy via volume changes as John suggested, but such a detector would be many light years in size.
- The sticky bead article should be required reading for anyone, layperson or otherwise, before they are allowed even to read a press release on a gravity wave detector. The way Einstein-Rosen went back and forth, with Rosen against waves until his death in 1970, is astounding. Regardless of whether the E-R paper was correct or not, Physical Review should have published it, with an editorial note containing the reviewer's remarks perhaps. Failure to do so delayed debate on the subject for 20 years. Einstein was right to never submit there again. His response of "tossing" the paper to an insignificant journal was reminiscent of his publication of a 1912 paper on inertia in a Journal of Sanitation. It is still a remarkable paper, by the way, and a re-keyed version of it can be found at http://mc1soft.com/papers .
- By simple application of the equivalence principle, without ~40 years of debate (1916 to 1955-57) it should be obvious that detectors must operate on tidal forces. But I have never, ever seen these mentioned in detector descriptions, including detailed papers. They always discuss changes in either lengths or clocks which are undetectable by Eddington's original 1922 argument.
- Being an electrical engineer, it is immediately obvious that the "stick" would need to be something like 1/4 to 1/2 wavelength, or it will not pick up enough of the already weak signal to be useful. For millihertz signals, this is something like a million miles for the fastest signals, and something like an AU for slower ones. So the solar orbit scale detectors are the right size, but without a physical stick they will see nothing, as per my previous detailed argument.
- There is a flaw in the stick argument that Feynman missed. Perhaps while posing as Mr. Smith, he felt comfortable taking a pot shot that he had not thoroughly worked out. The trick is that a mechanical deformation of the stick is required for it to work. The mechanical deformation will propagate along the stick at much less than the speed of light. But the gravitational wave is going through space at least at the speed of light (at that speed in Einstein's theory, much faster if gravity is based on something like quantum entanglement or uncertainty, which I consider likely).
So ... there is a very asymmetric situation between emission and detection of gravitational waves. One is orders of magnitude harder than the other.
I see that several posts and the Wikipedia description of the sticky bread thought experiment use the term "tidal forces" to describe the mechanics of gravitational waves. Tidal forces imply gravitational acceleration. I am going to make the argument that gravitational waves produce no effect on the rate of time, no modulation of proper volume, no gravitational acceleration and no tidal forces. A gravitational wave modulates the distance between points as measured by solid objects such as properly oriented rods. Suppose that a properly oriented rod in space encounters a gravitational wave. The center of mass of the rod will not move as the gravitational wave passes. The tips of the rod will experience acceleration which would be experimentally observable if the wave was strong enough and other aspects of the experiment were sufficient. Therefore the sticky bread thought experiment would work but not because of gravitational tidal effects.
Gravitational acceleration requires a rate of time gradient. For example, a rate of time gradient equal to 1.11x10-17 s/m/s produces a gravitational acceleration of 1 m/s2. A gravitational tidal effect requires a gradient in the rate of time gradient. It is not possible to prove in a short post, but a hypothetical rate of time gradient propagating as a wave in the Z direction cannot simultaneously produce an elongation in the X axis, a shortening in the Y axis and no effect in the 45 degree directions between the X and Y axis. Since this is a wave, the elongation and shortening change every half cycle. There is no effect on proper volume because the elongation and shortening offset each other.
A gravitational wave produces an effect on two of the 4 dimensions of spacetime. The mirrors of an interferometer are not moved when the gravitational wave passes. Instead, the gravitational wave affects spacetime in a way that changes the distance between the mirrors as measured by a rod without moving the mirrors. Light is a transverse wave, so the X polarization is affected differently than the Y polarization. The average speed for the two polarizations is unchanged (equal to c).
John, regarding your interesting claims:
- There seems to be a terminology problem. If the center of mass of rod experiences no acceleration and the ends do - regardless of cause - then this is by definition a tidal force.
- The converse of your statement about the rate of time gradient is true as well. If there is an acceleration which acts universally, then there must be a rate of time gradient. Caveat: I can actually only prove this in the static case and the gravitational wave is of course not static, so I'm not positive, but since a lot of other people think there are differences in clock rates, and since gravitational waves can be very, very low frequency, i.e. approaching static, I'm inclined to believe there are clock effects. But as to the detect-ability of such effects, I'm inclined to think not, so while our opinions might differ in theory, our predictions of practical results do not seem much different.
That reminds me of one of my favorite expressions, most often attributed to the Star Trek character Spock, applicable to the Ether Theory, possibly unearthed from old readings by psychologist William James: "A difference which makes no difference is no difference."
I am also fond of citing the irrelevance of causes, and there are some Q&A threads on here that question even the concept of "causation."
Making that very practical, while most would say that universal acceleration causes time dilation, I would adamantly maintain that is ridiculous - that pushing on something does not change its time - but instead that time dilation represents energy changes which are sufficient as a Hamiltonian action principle to "cause" the acceleration. ; )
Robert,
You say, "If the center of mass of a rod experiences no acceleration and the ends do - regardless of cause - then this is by definition a tidal force." The definition of “tidal force” I find on the internet is: "A tidal force is a secondary effect of the force of gravity and is responsible for the tides." Therefore, I claim that “gravitational tidal force” is presumed in a discussion of gravitational waves.
Before going further, I am going to make a presumption about your position which I am not sure is correct. You say "I'm inclined to believe there are clock effects." and "a lot of other people think there are differences in clock rates". I think that we agree that a gradient in the rate of time is equatable to a gravitational acceleration. Therefore, it appears as if you are arguing that the center of mass of the rod or a neutral spherical mass will be moved by a passing gravitational wave. In a thought experiment and assuming a strong gravitational wave, an external observer using multiple sensors with different vantage points should be able to determine if the center of mass of spherical mass moves as the gravitational wave passes. I say it does not move, it just distorts. It appears as if you say that the center of mass does move. If this is correct, what motion does a spherical mass make as the gravitational wave passes? Is it a liner vibration or a circular nutation?
Let’s go further. The super massive black hole at the center of our galaxy has a mass of about 1037 kg and a Schwarzschild radius of about 50 light seconds. Therefore, if you are correct, a gravitational wave with a frequency less than about 0.01 Hz would physically displace the entire supermassive black hole. Granted, the displacement would be small but the point is that this would be a violation of the conservation of momentum. There would be no communication back to the source of the gravitational waves which might be just two distant neutron stars. An external observer would see the supermassive black hole move with no apparent conservation of momentum. I claim that the black hole merely changes its shape from a sphere to an oscillating ellipsoid as the gravitational wave passes.
I need to get some feedback before I can go further. - John
John,
"I think that we agree that a gradient in the rate of time is equatable to a gravitational acceleration."
In principle the gravitational acceleration or any acceleration, does not have anything to do, as already explained by Robert in his previous post, with the time dilation. The clock-rate depends on the action , which is dimesionally the energy density in the four dimensional space-time (EDDINGTON) . In the case of the gravitational field it is well represented by the gravitational potential and the kinetic energy referred to the center of mass of the massive body responsible of the gravitational field.
That the gravitational acceleration cannot be directly related to the time-rate is an experimental fact:
over the surface of Earth the clock-rate increases with height while the gravitational acceleration decreases, under the surface of earth the clock-rate decreases and the gravitational acceleration decreases too.
Robert Schuler,
I would have thought it was clear that I was talking about gravitational radiation damping not just precession.
And it is gravitational radiation damping where GTR begins to fail.
Charles,
the gradient has a sign and a module once fixed its radial direction towards the center of a planet.
the gradient in the rate of time, going towards the center of Earth from the surface has opposite sign than the one from the surface to the space. The geoid surface discriminates between these two behaviours.
Only if I consider g as a constant in the space around a celestial body, with a small variation in the radial distance from such body, what John says can be numerically verified.
Charles,
"Stefano, the weak field limit shows explicitly that the gravitational potential can be identified with the rate of time, and that the gravitational acceleration is proportional to the gradient of the rate of time. This is experimental fact."
I know.
"Only because down has opposite sign to up. "
Charles. g=0 at the center of earth, max on the geoid and 0 at infinite distance. The Clock rate is minimum at the center of earth and increases always from there to a maximum value at infinite distance.
The gradient of the g changes sign across the geoid, the gradient of the time rate doesn't.
A video link to demonstrate transfer of gravitational energy both outside and inside a black hole
https://www.youtube.com/watch?v=FDJJODXFqxo
Andrew, re: "I would have thought it was clear that I was talking about gravitational radiation damping not just precession." ... I'm just giving you some feedback on your style of writing. This gets lost, there is not enough conceptual "where we are going" and the precession argument distracts. Fix it and I'll look at it again. But it will have to be elementary level for me to understand the radiation damping.
Stefano, re: "The Clock rate is minimum at the center of earth and increases always from there to a maximum value at infinite distance. ... The gradient of the g changes sign across the geoid, the gradient of the time rate doesn't."
... What? The time rate doesn't change sign but the gradient of the time rate certainly does. I think you made a typo. Likewise per Charles, g changes sign, and the gradient of g (which is an indicator of curvature, by the way, as there is no curvature for uniform g, it's a Rindler space) wasn't under discussion.
Interesting to note that for an otherwise uniform g which changes sign at the center (geoid Stefano is calling it), there is an impulse gradient there and there is curvature. Rindler has persistently ignored this in wielding his coordinates like a hammer to criticize ideas he simply doesn't like.
Speaking of the surface of a gravitating body, assume the body is hollow. What is the Schwarzschild solution inside?
If the first coefficient must have the form (1+K/r)-1 and must match the Newtonian limit (which is no gravity inside a uniform sphere), then K=0 and it reduces to Minkowski space. Is that right?
This produces some interesting discontinuities at the surface, or shell. Just outside, we may have extreme coefficients (if, suppose, the object is nearly collapsed). Move a fraction of a millimeter to the inside and the radial space is no longer distorted (or radial lengths are no longer contracted, however you want to put it).
What are clock rates? Surely they don't return to the rates of clocks at infinity? Or do they? If they don't, then a constant coefficient other than 1 is needed. But how do you get that out of the equations?
Charles ~
Admittedly, I’m not so well-versed as I once was (a very long time ago) in “field equations for arbitrary spin”. So far as I can see, all the investigations into the topic are various alternative formulations of the 1948 work of Bargmann and Wigner. The basic idea is that a spin-s field is a completely symmetric spinor of rank 2s [a representation of the Lorentz group SO(3,1) ~ SL(2, C)]. The B-W equations are generalizations of the Dirac equation:
γiαβpiψβγδ… = mψαγδ… (pi = (ih/2π)∂i),
and when m = 0 there are subsidiary conditions γ5αβψβγδ… = 0.
Writing this down does not involve “some kind of quantum mechanics”. At this stage of discussion it is just group-theoretical algebra.
For massless spin-2 the symmetric rank 4 spinor ψαβγδ can be expressed as a rank 4 tensor φijkl satisfying various symmetry properties and self-duality properties (which I'm too lazy to type out) and the field equations along with the subsidiary conditions turn out to be equivalent to the single condition
∂iφjkln +∂jφkiln + ∂kφijln = 0.
Analogous to the massless spin-1 case (electromagnetism), this implies
φjkln = ∂jφkln - ∂kφjln
and the symmetries of φjkln imply further that φ[ij]k = ∂iφjk − ∂jφik for some symmetric tensor φij. In terms of this tensor the field equations finally take the form
∂k∂kφij − ∂k(∂iφjk + ∂jφik) + ∂i∂jφkk = 0.
It seems to me that the fact that these equations are identical to the linearized empty space equations of General Relativity (“weak field approximation”) is very remarkable − far too striking to be dismissed out of hand as meaningless and unworthy of serious attention!
The above argument was carried out in a flat spacetime. It's the Minkowski spacetime formulation of a spin-2 field. But flatness of the background spacetime is not a necessary restriction. Spinors don’t respond to coordinate transformations, their Lorentz covariance corresponds to transformations of an orthonormal tetrad field. That is how the Dirac equation is incorporated into GR. A massless spin-2 field in its spinor formulation can be dealt with in a curved spacetime in exactly the same way. There is no problem there.
I do not know what are the conflicts between massless spin-2 and QM, that your expert advisors have assured you of. QM comes into all this through the identification of pi as the operator associated with energy and momentum. I would expect a quantum theory of massless spin-2 particles interacting with other fields could be worked out, analogous to Feyman’s methods in QED. I do not see any problem in principle. I would expect formidable difficulties and complications to arise (as they tend to do in QM…), but to throw up one’s hands and declare that “massless spin-2 particles are not possible” looks to me like a defeatist attitude!
As I earlier stated, it is a fact that if energy momentum is inserted as a source term in the massless spin-2 equations, including the energy-momentum of the spin-2 field itself, the resulting non-linear equations are identical to Einstein’s gravitational equations. That to me seems astonishing − almost miraculous − far too striking to be dismissed out of hand as meaningless and unworthy of serious attention!! All that is missing, of course, is an answer to the question, how and why does the tensor that satisfies those equations assert itself as the metric of spacetime?
Robert, Stefano and Charles,
A lot has been added to this blog since I last checked, so I have several subjects that I want to cover. Stefano - the gradient in the rate of time always corresponds to the gravitational acceleration. The conversion is 1.1127x10-17 s/m/s for 1 m/s2 gravitational acceleration. The proof of this cannot be presented here.
Charles, you say “There fundamentally no such thing as a gravitational force …These are artefacts of a choice of coordinate system.” This is a commonly held misconception. An accelerating frame of reference is a concept that ignores physics. It is impossible to have a mass in a closed system that is accelerating (in an accelerating frame of reference). If there is mass in an accelerating frame of reference, it is necessary to exchange momentum and energy with another massive body. The center of mass of the two bodies is not accelerating. We talk of the force of inertia as a pseudo force, but this is just semantics. Accelerating a mass really does generate an inertial “force” that resists acceleration. When a mass is in free fall in a gravitational field, the gravitational “force” is still present. It is just being offset by an opposing inertial “force”. The accelerating frame of reference also generates an opposing rate of time gradient and an opposing effect on volume. All of these offset the gravitational effects and allow people to say that gravity is an artefact of an accelerating frame of reference. However, gravity is a real force that is closely related to the electromagnetic force. The attached paper shows that at the level of individual charged particles, the gravitational force can be expressed as the square of the electrostatic force. Also there is a previously unrecognized symmetry between the gravitational force, the electrostatic force and Planck force. All of these relationships would not exist if gravity was not a real force.
Robert, in our previous discussion I was attempting to prove that the sticky bread thought experiment did not involve gravitational tidal effects. I have thought of another argument which proves this point. Gravitational waves are quadrupole waves in spacetime, not dipole waves in spacetime. Dipole waves would modulate the rate of time and would displace the center of mass of objects. General relativity forbids dipole waves in spacetime on the macroscopic scale addressed by GR. Reference [1] in the attached paper is a quote from the book Gravitation by Misner, Thorne and Wheeler. This quote says that dipole waves in spacetime are impossible to generate. In this paper, I propose that dipole waves in spacetime are allowed by quantum mechanics if the displacement of space does not exceed Planck length and the displacement of time does not exceed Planck time. I describe a model of the universe built entirely from dipole waves in spacetime which never exceed the quantum mechanical limit.
Chapter Spacetime Based Foundation of Quantum Mechanics and General Relativity
Charles,
"Formulated correctly general relativity is indeed a purely geometric theory, in which the force of gravity is an inertial force. Inertial forces do not have opposing forces"
If "inertial forces" as you define do not have opposing forces, it means that the third Newton's law is jeopardized . This implies that the *center of mass* of the planet in which a test mass free falls is not involved in the process, and the mass falls freely without exchanging any energy.
The fact that I have to make a considerable work to rebring such mass at his apogee, it means that during the fall, the mass released energy. This means simply that the gravitational field made a work on such mass. The simplest and most common example of conservative field is the gravitational field, and this cannot be in any case denied or neglected.
Dear John,
"Stefano - the gradient in the rate of time always corresponds to the gravitational acceleration"
Between the earth and moon there is a zone in which the value of the gravitational acceleration is zero, the Equilibrium point.
According to what you affirm since the gravitational acceleration in such point is 0, the gradient in the rate of time should be 0, and you are right since such point is a stationary point for the gravitational potential.
Charles,
You say, "Formulated correctly, general relativity is indeed a purely geometric theory." This is a physical interpretation of equations which are silent as to whether gravity is a true force.
The referenced paper in my previous post contains a number of equations which strongly challenge the concept that gravity is not a true force which is closely related to the other forces. I will give one example from that paper. The fundamental unit of charge is Planck charge which is about 11.7 times greater than charge e. Planck charge is obtained by setting 1/4πεo = 1. Charge e has a coupling constant equal to α, the fine structure constant but Planck charge has a coupling constant equal to 1. Therefore suppose that we compare the magnitude of the electrostatic force between two hypothetical particles with Planck charge to the gravitational force between these two particles, each with mass m. We will designate the electrostatic force as FE and the gravitational force as Fg. The separation distance r between the two particles will be expressed not in units of meters or some other human construct, but using the particle’s natural unit of length which is the particle’s reduced Compton wavelength λc ≡ ħ / mc. Therefore the separation distance will be expressed using the dimensionless number N of reduced wavelengths (N ≡ r / λc). At arbitrary separation distance specified by N , we will compare the electrostatic force FE to the gravitational force Fg and also compare both to Planck force (Fp = c4/G). We will obtain the following equation:
Fg / FEN = FEN / Fp
We will illustrate the implications of this with an examples. Suppose that we have a logarithmic force scale that has the strongest force in the universe (Planck force) at one end and has the weakest force between the two particles (the gravitational force Fg) at the other end of this logarithmic scale. Exactly halfway between these two extremes is the electrostatic force times N expressed as FEN. Now if gravity is purely a geometric effect, why should it be related to the electrostatic force as described? The paper contains several more examples of other relationships between Fg and FE. Also, it is easy to extend these examples to charge e because FE = Fe / α where Fe is the electrostatic force between two particles with charge e. All of this implies that gravity is a true force.
Charles,
I gave equations connecting the gravitational force to the electrostatic force. These connections only reveal themselves when the wave properties of particles are recognized. Your answer is: "General relativity is not silent about whether gravity is an inertial force." If I was offering opinions, then an appropriate answer might be a statement to the effect that general relativity has spoken - end of discussion! However, when I give undeniably correct equations that support my point, then an "answer" cannot be limited to appealing to the authority of general relativity.
Albert Einstein worked for the last 30 years of his life attempting to find a connection between the gravitational force and the electromagnetic force. If gravity is only geometry, shouldn't he - of all people - have recognized that gravity is not a force and therefore gravity can never be connected to the electromagnetic force?
Dear Charles ~
I am aware that the intricacies of quantum theory are immense. When did I deny it? “Very clever stuff” is indeed involved in interpreting the field equations of spin-½ and spin-1 in a fully consistent quantum theory that avoids contradictions and resolves all inconsistencies. Quantum theory is still a “work in progress”, fraught with unresolved issues. No-one to date has been able to figure out the “far more clever” stuff needed to resolve the issues involved in the spin-2 problem. On the other hand, no-one has proved that the problems are insoluble. I acknowledged all that: “I do not see any problem in principle. I would expect formidable difficulties and complications to arise (as they tend to do in QM…)”.
“It makes very little sense to arbitrarily restrict geometry by making an unobserved assumption of flatness.”
The algebraic argument I presented can be made generally-covariant. For simplicity and clarity I didn’t do that (it gets very messy). The generally-covariant form of the equation for φij can be interpreted as small pertubations of a curved spacetime. That is how “gravitational waves” are conceptualized.
Do you know how to deal with quantum theory in a curved spacetime? Does anybody? Dirac found the electron’s field equation by looking for a Lorentz-covariant equation – that is, an equation that would work in flat spacetime, an equation consistent with special relativity . Similarly, Maxwell’s equations, including the current of the Dirac field as source, are Lorentz-covariant (flat spacetime). None of that is QM, it is algebraic manipulation. The quantum mechanics is not in the equations, it is in the interpretation of the equations. Applying the rules of QM to those equations leads to QED (very clever stuff!). Alternatively, it is possible to make the equations generally-covariant and hence consistent with curved spacetime. But no-one knows how to do those two things simultaneously and consistently. That problem is not unique to spin-2. It is the major unsolved mystery of theoretical physics! To make inroads into that mystery we cannot afford to ignore clues. To my mind, the very striking unexpected algebraic relations between spin-2 and GR are not mere coincidences to be swept aside. They are highly significant clues.
At a fundamental level there is only the space time to implement the least action principle.
Charles,
the action principle is the expression of the Euler Lagrange equations which govern all the mechanics and according to Eddington, it is the only survivior of the quantum and relativistic revolution of the 20th century, together with the maximum entropy principle...
There is a section in MTW about applying the Langrangian in curved space-time. A reviewer pointed this out to me when I submitted my paper on Hamiltonian analysis of time dilation. I have since found other problems in that paper and it is due a major revision before I resubmit anywhere. But the bottom line is that the Langrangian and Hamiltonian concepts survive well in GR. I think I can even derive curvature from a well thought out Hamiltonian, but don't quote me on that yet, I haven't actually written it up, and sometimes problems develop.
My apologies if this has been covered since I was last here, 5 pages of detailed answers have been added since then.
Robert wrote: ".. everything should stretch and compress with space. .. If space can stretch and the objects in it not stretch with it, then relativity would be invalid."
That is not true, objects can easily move through space so if held in place by other forces (typically EM) will not be dragged by the changes. Similarly while the Hubble flow causes clusters of galaxies to move apart, stars within individual galaxies are gravitationally bound and do not take part in the general expansion.
RS: It should be therefore locally not noticeable. "
In the LIGO and LISA approaches, the mirrors are free to move with spatial distortion. The distance between them is then measured by the lasers. A key point is that the distortion of space is at a rate set by the source. For example the best candidate for LISA verification is the HM Cancri which would produce waves with a period of about 160s, very much longer than the measurement time of the interferometer. In other words, the distance is close to constant during any one sample but varies over a couple of minutes. If you think of the space between the ends (and in which the whole Solar System is embedded) being alternately squeezed and stretched, the photons moving through it still travel at c so still give an accurate measurement of the separation.
I'll respond to your other question in the link if it hasn't been covered already, I note there are already many answers there.
Charles,
"Conservation of momentum appears as fundamental law in qed, and is a sufficient principle to derive classical mechanics. "
yes if you add the energy conservation and angular momentum.
I was curious about the 4-momentum thing and looked it up
https://en.wikipedia.org/wiki/Four-momentum
Appears that it occurs in the position of time, and that if one is using a coordinate convention of x0=t (and not x0=ct as is often done, to get the c2dt2 term automatically I presume) then the energy term is E/c2 which is just the relativistic inertia (mass).
I am not disagreeing that one is derivable from the other. That was one of the first exercises we did in physics 101 in college, was to "derive" conservation of energy from Newton, which is essentially a momentum law.
I have a question then ... is it unnecessary to state both a law of conservation of momentum and of energy? Is it merely a matter of convenience which form to use? Or is it conceivable to violate one and not the other? If I impose a Hamiltonian condition, for example, which is energy based, do I automatically get conservation of momentum? That would be most convenient.
Charles ~
“The least action principle is a metaphysical notion. I see no reason to implement it.”
That’s seems like a strange attitude! I grant that at the most fundamental level of reality quantum physics is all there is and everything else is in principle derivable from it. That is your vision and your dream and I have nothing but admiration for your insights into how that comes about.
However, we do still need to deal with classical (“macroscopic”) physics on its own terms, and always will. Are you suggesting that the whole of the Lagrangian approach in that context is now obsolete? The Lagrangian formulation and the concomitant “least action principle” led Emmy Noether to the clarification of the relationship between conservation laws and symmetry principles . (In particular, Noether’s theorem shows simply and elegantly how energy-momentum conservation comes from Hume’s principle of uniformity in Nature - “the fundamental behaviour of matter is always and everywhere the same.”) The Lagrangian formulation and its "principle of least action" have served well not only in "classical" physics but also in elucidating the algebraic structure of elementary particle interactions. Without them the road that led to the “Standard Model” could not have been built.
Quantum Theory is obliged to demonstrate how the “principle of least action” comes about and why it works; “now that we have QM we know better and can forget about all that” is not an adequate response!
George> any detector such as LIGO relies on absorbing some energy, albeit a very small amount, from a passing GW in order to function.
I guess that must be true in some sense. Nevertheless, the measurement depends on the amplitude of the gravitational wave (falling off proportional to distance from the source), not on its energy flux, proportional to the squared amplitude. Which seems to indicate that eventually gravitational waves should be the most effective probe for observing far-far-away objects...
KO: I guess that must be true in some sense.
Yes, it's just the "sticky bead" argument.
KO: eventually gravitational waves should be the most effective probe for observing far-far-away objects.
Yes, but for nearby too as they are not absorbed by dust clouds, nebulae, etc. that block EM methods. It's just a shame it's so far away, ESA's L3 project is targeting 2034 and that's bound to slip.
George> It's just a shame it's so far away
On my second day at university, September 2, 1969, we were informed by our most distinguished physics professor that a great scientific achievement had taken place that summer (and that was not the moon landing, which he considered a triviality). It was the discovery of gravitational waves by Joseph Weber. Unfortunately, that announcement turned out to be premature, as have all later announcements of gravitational waves being observed.
I have continued to study physics ever since that September day; I hope I will have health and brains to continue studying it until gravitational waves are really discovered :-)
Charles ~
One can think of the historical development of theoretical physics as the building of a bridge, constructed from mathematical concepts. Once it is complete and one has got to the far side, one has reached a rational understanding of why our observations and measurements of the real world are the way they are. No need to then destroy the bridge. It is beautiful in its own right.
Wishing to better understand the “real world” motivates people to become physicists. For me it was not the only motivation. There is also enjoyment in the contemplation of abstract mathematical structures, which often have an elegance and beauty independently of whether they have anything to say about physical reality − they provide an aesthetic experience. When aspects of physics can be encapsulated in simple and elegant mathematical concepts, those concepts may be not strictly necessary. They are worthwhile because they are beautiful. To my mind, the Lagrangian approach is beautiful.
There is scope for different interrelated ways of understanding mathematical physics. It’s not a matter of “right” or “wrong”. Our disagreements would therefore seem to be subjective. De gustibus non est disputandum.
Gravitational waves do not exist if c is a global constant.
So the question of whether or not a proof of c-global exists precedes the - very beautful - discussion above.
As has been said before, c is not a global constant, it is only a local constant in relativity.
Re: Dishman ... "Similarly GW are also massless of course and travel at the speed of light but what is curious is that a region of interference, say between two binary star systems, should have an equivalent mass for each anti-node of the gravitational standing wave due to the energy passing through the location. The volume defined by an anti-node is not necessarily closed though, but there should still be a volumetric energy density."
I have been slowing arriving at this conclusion without seeking it (or even knowing what direction I was headed in) over several months. The potential difference between two vacuum regions has to correlate with a difference in not only time dilation but also spatial expansion or compression. We can only measure the difference at present. Locally, we infer that there is a difference in the spatial compression in the radial and tangential directions, which of course is also not measurable locally, but inferred, and we can only measure the relative changes.
However, I have a question for George, or anyone ... if it has mass, does this give us a way to measure it? For example, there was a thread on here about bending of GW when passing a massive object. That should provide a way to measure and localize a wave group.
RS: Locally, we infer that there is a difference in the spatial compression in the radial and tangential directions, which of course is also not measurable locally ..
Robert, you asked another question (linked below) about the nature of gravitational waves. I've given you a number of links which should be a comprehensive answer to that question. Please let me know if it helps.
The key point is that there is alternate compression and stretching in the directions transverse to the motion of the wave but no effect in the radial or temporal directions. Locally the stretching and compression can be measured, this is how LIGO works and how eventually eLISA should detect the waves. The amplitude is very small though, typically on a few parts in 1024 for nearby binary systems.
RS: .. if it has mass, does this give us a way to measure it? For example, there was a thread on here about bending of GW when passing a massive object.
In theory you could observe light being bent by the effective mass of an anti-node of a standing wave pattern but the energy in such is many orders of magnitude less than a physical body so it would be completely impractical. To get a static anti-node, you would have to have two binary systems whose rotations were phase locked and that is not only very unlikely but would mean they were close enough to interact. The masses of the stars would therefore overwhelm any effect of the radiated energy. I mentioned it out of academic interest only.
https://www.researchgate.net/post/What_are_the_conditions_for_emission_and_field_pattern_for_gravitational_waves
Dear Robert, I elaborated a theory where every particle takes form from spatiotemporal quanta (so, I adopt the idea of quantum spacetime) and, specifically, particles would be superfluid vortices of spatiotemporal quanta (STQ) similarly to what occurs in superfluid helium-4. Their vorticity would account for the absorption of STQ and this would be the cause of gravity, i.e. absorption of quantum space effected by particles. This view easily seems to explain the link among fundamental forces. Matter-antimatter annihilation would for instance occur when vortices possessing conflicting torques meet. In this view STQ (gravity's quanta) possess a degree of compressibility and they can be clustered into photons, gluons etc. Thus, to answer your question (the "back and forth" matter) I would say "it depends". If photons can decay back into STQ the response is then "yes". But if simplest particles as photons or gluons never decay bck into the bare STQ then "no", the process would be unbalanced in favor of all other forces / particles.
Article A superfluid Theory of Everything? [outdated version]
Marco, your idea is somewhat interesting and also somewhat similar (not in detail) to others I've seen If it has a specific prediction different from existing theory then you should pursue it with all diligence. Otherwise it is just another gauge thingie.
As to your speculation about photons maybe or maybe not decaying back into space-time quanta (STQ), which you equate roughly with my query about gravitational energy, I think you have not so much given an answer, since you weren't definite, as you have posed the question in a very interesting way, i.e. in regard to a single photon, or any other elementary particle.
I was really asking about standard gravity theory, or general relativity (GR). But let's investigate based on the way you have asked the question, and maybe that will stimulate someone else to have or share some insight. Because I am becoming very doubtful that gravitational energy exists. The lack of ability to locate it is right there basically a fatal strike. Then the fact one cannot detect it except that it is converted back into ordinary energy makes it rather like an ether. It works the same whether it is there or not. However, if it would leave a track through a cloud chamber, even if that were an interstellar cloud chamber, then I'd be more inclined to accept it. That would localize it, of course.
Compare to the decay of a photon into electron potential energy in an atom. The photon disappears (or seems to) and the electrons orbit a little farther out (statistically, or their wave functions do) and their potential energy is greater. They can give that energy up and the photon (or another one) reappears.
So we have a photon collide with something - an atom will do - in a gravitational orbit. We have to assume nothing changes except the potential energy of the thing it collided with. Oh, sure, it might be partly absorbed in the traditional way, but only that part of the photon which does *not* go into the electron PE around the atom contributes to the gravitational PE of the atom itself.
This is interesting, and to me unexpected. The atom being farther out, means the matter-energy in the gravitational field is less dense, and space-time is LESS curved. However, this is completely consistent with the result I just obtained with regard to the relation between energy and object lengths and clock rates - or space-time if you prefer. In a dense gravitational field radial space is expanded but we can interpret that as object lengths contracted (like in special relativity SR). And clocks deeper in the field are slowed. When we give energy to something in the field, and retrieve it a little way, its length increases and its clock speeds up. Same thing as when you retrieve an object from a moving frame in SR. (Of course this happens in either direction in SR, but gravity has a different symmetry)
But was it space-time that absorbed the photon or whatever energy you put into retrieving it? In the SR case, we would say the retrieved object absorbed the energy, would we not? We applied a force through a distance changing its state of motion. Take the constructive approach (less popular, but just consider it). The object is longer and its clocks faster. The electrons have to move doubly faster (or their waves do) to get around the longer orbits in less time. I'd say that was where the energy went right there, and it looks like ordinary kinetic energy - things moving faster.
This is not all quite so clear, because the object lost its relativistic mass as you retrieved it. We do not ordinarily speak of it this way in a gravitational retrieval, but the object lower in the field is sluggish due to time dilation and in a relative sense it acts as if it were more massive. Proper mass is irrelevant because that doesn't change in SR either in the frame of the object itself.
My only point really is that it is unclear just where or in what form the energy of "space time" is. It may in fact be in a very ordinary form in the shape and speed of atomic and molecular bonding Schrodinger waves and their associated particles (quanta).
Thank you for the interesting ideas.
If you can imagine infinite space to be motionless indivisible fundamental substance of the uniuverse, not interacting with any energy, then gravitational force, in my opinion is due to resilience or elasticity of this substance. When fundamental substance begins to move, it splits into particle anti-particle pair and becomes energy. Since this is an apparent split, the fundamental substance develops stress but remains undivided due to it having perfect resilience or elasticity. You can say that this substance has infinite proportional limit and no yield point. So it never breaks no matter how much you strain it. With this description of gravity, gravitational waves need not exist and the question of conversion of gravitational energy into other forms does not arise. When particle anti-particle annihilate, the gravitational attraction between two disappear because the stress disappear. But the gravitational attraction continue to exist between two created photons untill both photons also annihilate and become perfectly motionless (no mass gap).
Bob's question is beautiful.
It brings up the problem of electron mass in a PET scan:
Is the mass exactly equal to 511,... keV, with the field collapsing across an infinite volume instantaneously? Or is only part of that mass characterizing the naked electron?
.
Robert, Vikram I answer from these interesting considerations of yours:
My only point really is that it is unclear just where or in what form the energy of "space time" is. (Robert)
If you can imagine infinite space to be motionless indivisible fundamental substance of the universe, not interacting with any energy, then gravitational force, in my opinion is due to resilience or elasticity of this substance. (Vikram)
Robert, as Vikram also let understand, I exactly meant that the energy, whose existence you wonder about, is space-time's substance itself and, specifically, not when it has the form of a tranquil sea of space-time quanta but rather when these quanta are put in motion.
I cited my theory not for vanity but since there is no explanation at the moment if you want to know what gravity is and what gravitational energy is besides the 'potential energy' thaught at school, without coming at a finer, quantum view (e.g. granular space-time). My theory justifies the fact that space-time quanta are put in motion because particles are absorbing them. Gravity is this way a newtonian force, analyzable in fluid dynamic terms and fully compatible with general relativity. And, yes, the work makes some predictions, for instance that about unbound neutrons' mass increasing before they decay.
Considering all that I would answer that gravitational energy is "nowhere" unless a mass absorbs space-time quanta and produces a newtonian flow in space-time or - to say that with current physics (GR) - till a mass distorts space-time (i.e. in a more interesting view, produces topological defects in the tranquil sea of space-time quanta).
Gravitational energy cannot be "stationary" energy (located somewhere) contained in a special particle, since it comes from a dynamic process.
Marco Fedi wrote:"space-time quanta are put in motion because particles are absorbing them"
That sounds very similar to the so-called pushing gravity of Fatio de Duillier, also rediscovered by Le Sage. It suffers from an extreme problem due to the heating caused by absoption of his 'ultramundane particles'. It is likely that your idea would also be subject to that difficulty.
MF: "Gravity is this way a newtonian force, analyzable in fluid dynamic terms and fully compatible with general relativity."
Newtonian force is a vector, GR is based on tensors so they are not compatible. The Newtonian force model also fails many tests, notably the precession of Mercury, gravitational bending of starlight, Shapiro delay and frame dragging.
Robert, no, my theory has nothing to deal with that old hypothesis.
If you want, take time to carefully read it and I'll be glad to discuss it with you more accurately. I create an analogy with helium-4 superfluid vortices to describe particles: a vortex absorbs "and re-expels" (so, no energy increase and the fact that it re-expels doesn't produce anti-gravity but virtual photons emission as explained in the paper, that is the static eletric field of charged particles). If then it is superfluid (near-zero viscosity), like in this case, there's no heating at all. Moreover we can't apply the idea of heat to spacetime's quanta, we need fermions agitation, bosons (photons) etc. to talk about temperature.
Your second point now, where you say a newtonian force (vector) is incompatible with general relativity (tensor). Well, not really. You can indeed derive Newton's law of gravitation from Einstein's field equation and till you don't consider relativistic veocities you can still treat bodies' motion due to gravity in a newtonian way, also within GR.
(see the attached equation of GR, where G_44 / 2 is the gravitational energy)
Even on curved trajectories:
https://en.wikipedia.org/wiki/Newtonian_motivations_for_general_relativity
Newton can also be mathematically derived as shown on page 15 referring to my above cited paper, as a solution of that Poisson equation, citing S.M. Carroll lecture on General Relativity.
Sean M. Carroll, Lecture notes on General Relativity, arxiv.org/pdf/grqc/
9712019v1.pdf
This because tensors are used in GR to describe spacetime deformations, as if it were an elastic thing, so they define the environment which an accelerated body moves through. But the motion of the body is a line, not a matrix.
".. a vortex absorbs 'and re-expels' .."
If the body reflects the incoming "vortex" then you are right, there is no heat absorbed, however the reflected "vortex" then statistically replaces those that would be shadowed to create the net force through an imbalance and you get no overall gravitational force. I think you should look at Fatio's work (published in 1690) and the problems it had as they will also apply to your model.
The tensor versus vector question doesn't relate to simple acceleration but to effects like Lense-Thirring where gravity can apply a torque to a body as well as a linear acceleration. Again, this is a test which you can apply to your ideas and compare to known experimental results.
again, what I wrote needs to be carefully read before making parallelisms with other theories, did you really read it all? The problem you say (incoming / reflected vortex doesn't apply to my work, since the "incoming" process is spacetime absorption (of its quanta) which obviously causes objects located in spacetime (all and light too) to be attracted like the wind transports dust, pollen (or even cars if it's the case of a strong tornado), while the "reflected" process is virtual photons emission (since STQ are compacted in the vortex), nothing to do with spacetime's motion then. So, yes, we can have gravity. And we also have a recoil (due to virtual photons emission, as also stated by current QED) which strenghtens the action of gravity or weakens / nullifies it (we call this fact electrostatic attraction / repulsion), depending of a particle's charge. While neutrons in my theory have to decay (only absorption, no virtual photons emission then instability) and indeed they do that in about 15 minutes.
Also remember that I am speaking about subatomic particles when I say 'vortices', I don't refer to macroscopic bodies. Mine is a quantum mechanical matter, Fatio talks of macroscopic bodies and a very different dynamics. Nothing to deal with then.
About Einstein-Lens-Thirring precession it can be also produced in fluid dynamic simulations, when the fluid is absorbed by a rotating body.
Vikram, you have two nearly identical posts in page 9. If you hover over the upper right hand corner of a post with your mouse cursor, you will get menu options to edit or delete it. So you can clean up one post and delete the other. Don't ask me why they make this feature so difficult to discover!
Marco, you addressed a reply to me that was confusing until I realize it was probably meant for George, so you can use the edit feature too. : )
Indeed, interesting discussion did follow. Thanks all.
Marco: Fluid dynamic approach of Lambda-CDM model is a correct approach which explains observed accelerated expansion of the universe. But negative gravitational potential energy stored in the space-time fabric does not have experimental support, since no gravitational waves are detected.
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