6 Jan 2014 16:59:40 UTC

Topic 197331

(moderation:

Reported here on the BBC and here in Nature (subscription needed), astronomers have discovered a millisecond pulsar in close orbit with a white dwarf, which are in turn in orbit with another, more-distant white dwarf.

According to Professor Scott Ransom of the NRAO, "The gravitational perturbations imposed on each member of this system by the others are incredibly pure and strong" and the system will therefore allow the equivalence principle of general relativity to be tested with a sensitivity "several orders of magnitude greater than ever before".

An internet search for the pulsar turns up lots of info, including this animation and an arXiv paper from 2012 covering its discovery with the Green Bank telescope.

Could the current e@h searches discover similar systems?

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## Triple star system can reveal secrets of gravity

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Hallo Neil!

Thankyou for this interesting hint.

I asume, the position is outside of our field of observation by telescopes and software sensitivity.

Unfortunately the inner structure does not rotate now with more than some 10Hz. Then we could detect it probably with today GW-detectors. But within some 10.000 years or so, it will come to this. For me it will be too late. But for the coming ELISA project this structure will be of very great interest, probably also as a calibration source.

Kind regards and happy crunching

Martin

## I've had a read-up about why

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I've had a read-up about why they're so excited about this. Or why is this system a good test of the Equivalence Principle (EP)? It turns out that this has two flavours : The Weak and The Strong.

The Weak Equivalence Principle. Indeed Galileo gave this to us long ago. Ignoring air resistance, if one drops the cannon balls from the Leaning Tower of Pisa ( likely an apocryphal story that he actually did that ... ) they reach the ground at the same time if released simultaneously at the same height. Conclusion : acceleration under gravity is independent of mass, or in later language ( Newton and beyond ) the gravitational mass is the same as the inertial mass. Inertial mass is that quality that determines acceleration under the action of any force ie. F = ma. Gravitational mass is the factor in Newton's Law of Universal Gravity ie. F = G * (m_1 * m_2)/(r ^2). I remember this being demonstrated in one of the Apollo missions : a feather and a hammer were dropped simultaneously and did indeed hit the ground at the same time ( mind you they wouldn't have got to the Moon and back if the Weak EP were not true ) .

[ Actually when I first came across this I thought 'of course they are!', not realising that I had been taught up until that point with the inertial/gravitational distinction glossed over or ignored. For that matter this is why massless ( ie. zero inertial rest mass ) particles don't ever change in speed, because they always travel at the speed of light anyway. So you can neither slow them down nor speed them up. But they are subject to gravity and hence light bends near stars etc. ]

The Strong Equivalence Principle. Here the gravitational mass is still the same as the inertial mass, but under General Relativity ( and some competing theories ) the gravitational mass has an extra curly bit. The main part is the total of the component masses when separated at infinity. So if one splits up the entire Earth, say, and moved all the particles to indefinitely far away you would get some given amount. Indeed we all think in everyday terms as mass being simply additive like this. The tricky extra bit is called 'gravitational self energy' or 'field energy' or 'interaction energy'. You see a given mass body not only affects others gravitationally. Gravitation is universal and so a mass can act upon itself as well - it self attracts - and an energy amount can be ascribed to this. This is not quite the endless recursion that it sounds as what normally suppresses this effect is the c-squared in E = m*c^2. So if a given gravitational field has some self energy E_g, then that represents a mass term = E_g/c^2 .....

[ .... plus higher order terms where that mass also affects itself, yada yada yada and convergence to a finite number. ]

Back to the system under study. We have three bodies, each of which have a self-energy a decent fraction of their 'mass' [ you can say either gravitational mass or inertial mass here, as they're equal right ? :-) ] because each is a dense and heavy body in astronomical terms. While they are all 'falling' in the presence of each other, one can approximate by saying that the two in close company are falling in the presence of the more distant one. So in a way we sort have the Leaning Tower Experiment writ large. Now the Strong EP has been tested here and there in our solar system, but this trio will give several orders of magnitude better discrimination b/w theories that do or don't honor the strong EP. For that matter might discriminate b/w theories that do honor.

My mind just oggle/boggle/goggles when thinking about this stuff! It is anti-intuitive and the numbers are huge. :-)

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

## Magnitudes : The whole IS

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Magnitudes : The whole IS greater than the sum of the parts

Looking at this article the gravitational self energy of the Earth as a fraction is 4.6 * 10^(-10), the Moon is 2 * 10^(-11).

Now the Earth is ~ 6 * 10^(+24) kg, so that self energy fraction represents ~ 3 * 10^(+15) kg. A decent slab of stuff. How to visualise that amount ? Well, take granite to have a density of ~ 2.7 * 10(+3) kg / m^3 ie. around 3 metric tonnes per cubic metre. Then Earth's self energy is about 10^(+12) m^3 or 10^(+3) km^3 of granite. One thousand cubic kilometers of granite. If you look at this article, it gives a quantity of erosion over 20 million years of ~ 7000 times that amount for the Himalaya's.

So the Earth's gravitational self energy can be represented by a mass equivalent to about 3000 years worth of erosion in the Himalayas ! :-)

Now for comparison this article gives self energy fractions as follows :

- white dwarf ~ 10^(-4)

- neutron star ~ 0.3

- a non-rotating black hole ~ 0.5

Note those neutron star and black hole figures, that's around 1/3 to 1/2 of it's mass being due to the gravitational potential energy equivalent. So when we say a black hole has a certain mass in terms of it's gravitational effect on, say, a body orbiting it at a distance or causing the deflection of light passing by then : about half comes from field energy and the other half from the sum total of mass brought in from very far away to form it at all.

What makes the most difference here b/w white dwarf, neutron star and black hole is density ie. how much can you stuff into a given volume. By that I mean the range in precursor mass for these objects is from around 1 to 10 solar masses, a factor of ten only. But the self energy fraction increases by a factor of one thousand ie. 10^(-4) to 10^(-1).

OK. So we can tool around with the math, do the measurements and examine for (dis-)agreement. General Relativity has met every challenge thus far. Let us see how it goes for this trio system.

But what is this field thing, apart from an explanatory device ??

Cheers, Mike.

( edit ) To belabour the point. If you did separate all the atoms of the Earth and send each of them to very far away from each other and then 'weigh' them separately, add up all those amounts, then you'd get a given total. Call that m_is for 'mass at infinite separation'. Now reverse the process, atom by atom. As the New Earth accumulates you might have some other test objects orbiting, or light rays scooting past etc, with which you will continually use to deduce/assess the mass of the Earth that is forming. Call that m_wt for 'mass when together'. During the formation of New Earth gradually one would find a discrepancy arising b/w the m_wt and whatever part of m_is that you have delivered inwards so far, the difference being the self energy we have been discussing.

Now having formed the New Earth completely - all the stuff we separated before from the old Earth has come back in together again - we compress this amount without adding in any more stuff from the surroundings. The density of Earth will increase, so will the self energy increase and the measured mass m_wt too. Thus purely by compressing the object we have increased it's gravitational effectiveness.

AND it's inertial effectiveness too, because if you try to move that New Earth somewhere else you'll encounter more resistance to change of dynamical state ( that's what inertia means ) than you would have if you'd tried to move all those infinitely separated atoms !!

In a nutshell that is why gravity and geometry go together. This area of study is also know as geometrodynamics .... and GR is currently King Of The Hill !! :O)

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

## @Neil : As for the original

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@Neil : As for the original question. There could well be some astrophysicists who would give their dominant arm to study such a system simultaneously with both EM and GW signals !?! :-) :-)

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

## Trying to follow the article,

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Trying to follow the article, and what Mike said (very helpful explanation â€¦thank you for posting it ) but, wouldnâ€™t this more of an example of Einsteinâ€™s Ã¦ther theory, â€œa modification of general relativity which describes a spacetime endowed with both a metric and a unit time-like-vector field that violates the Lorentz invariant in that the Ã¦ther does NOT take part in the motions of ponderable bodies so they have no relative motion with respect to each otherâ€? So in this example, the trio star system gravitational waves theoretically transport energy as gravitational radiation without the property of symmetry and the light signals are transmitted are not exactly the same? Or are they emitting exactly the same light?

Article says:

But this does not necessarily mean itâ€™s a deviation. This would be like Europa orbiting Jupiter every 3.5 days and always facing it and Jupiter taking 11.86 earth years to complete its orbital period.

But letâ€™s see what they make of it.

Master of a fraction of time on this dot in the virgo supercluster.

@Hometown in sunny Santo Domingo, Dominican Republic.

~ I a n n a

## RE: Trying to follow the

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Indeed. To be tested ie. do gravitational waves propagate at speed c. The role of the speed of light may seem somewhat obtuse, that is : why would the speed of the carrier for one basic force be related to any other ?

The answer lies in the roots of the development of relativistic theory. There is the concept of the 'reference frame' being a given measurement system for space and time. In Special Relativity - which is where reference frames are mutually un-accelerated - these are called 'inertial' frames having rectilinear motion ( which includes the case of being stationary ) as measured by such a system occurring with no nett forces on bodies described. The laying out of such co-ordinate systems must involve a consideration of simultaneity, or if you like comparisons of timing measurements taken at different positions. It is that which requires a signalling process to achieve and thus enters the speed of light, as electromagnetism is the only other force apart from gravity to have the infinite range needed to service any extents ( the nuclear forces are confined ).

In General Relativity the frames are not inertial, but still can be viewed as a sequence of so-called 'instantaneous co-moving frames' ( each of which is inertial ). It is GR which connects the progression of such frames, and so the speed of light stays in the mix.

But as we are doing science we compare our thinking against the behaviour of the Universe that we are living in.

Cheers, Mike.

( edit ) So the corollary is : if the propagation of light ( in free space etc ) is isotropic ( independent of direction ) then so ought gravitational waves.

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

## Mike wrote: RE: But

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Mike wrote:

A-ha! well darnit if I had had you for a professor at school I'd understand this all better ...thank you again for taking the time to explain!

Master of a fraction of time on this dot in the virgo supercluster.

@Hometown in sunny Santo Domingo, Dominican Republic.

~ I a n n a

## Mike: I don't get this

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Mike: I don't get this gravitational self-energy. My first guess would be that gravitational self-energy is the same as potential energy and works the other way round. Like, when earth forms from atoms originally separated infinitely, their original zero potential energy becomes negative and is transformed into kinetic energy as they start to attract each other and accelerate, and when they finally meet kinetic energy is transformed into heat which is eventually radiated off. Or the other way round: if you separate earth's atoms, you must add energy to overcome gravitational attraction. So, according to the energy-mass equivalence, I'd expect earth's atoms separated to have a higher mass and thus a higher gravity. Also, the gravitational attraction of any object that compresses under the influence of its own gravity (e.g. collapsing star), as measured at a given distance from its centre, can only stay the same (if nothing is radiated off during colapse) or get weaker (if something is radiated off). Only if you compress an object "against its will" its gravitational attraction can get stronger, due to the energy added.

Or did I get anything wrong?

## RE: Mike: I don't get this

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Well yes and then again no, or not exactly. :-)

It's a question of accounting, in particular what model is selected to give a figure to 'gravitational self-energy' in some situation. This can be a classical approach or per Einstein. Or maybe some other formula. Note that info sources may not disclose that, or just assume from context. I've seen some use the phrase 'self-coupling' to especially refer to amounts outside of a Newtonian calculation. I guess you have to read carefully to find out where the amounts are placed and/or what model is being discussed.

Perhaps a quick sidestep/comparison/hypothetical will help. Recall Coulomb's Law for electric charges. This applies to static configurations ie. no motion and therefore time delays & magnetism not accounted for. In this circumstance ( using 'natural' units to avoid stuffing about with various constants ) :

F_Coulomb = | force b/w two charges | ~ ( chargeA ) * ( chargeB ) / (their separation )^2

'| |' means magnitude, '~' means 'goes like', and '^2' means 'squared' ...

This is exact in classical terms ie. true at the time it was proposed to the degree as could be measured then ( much the same could be said of Newton's Law of Gravity ). Now I'll slightly rewrite this without actually changing any predictions one could make based upon it :

F_Linear = | force b/w two charges | ~ ( chargeA )^1 * ( chargeB )^1 / (their separation )^2 = F_Coulomb

Now what I hope I have made explicit is that for either charge this Coulomb's Law is linear ( to the first power ). You no doubt have taken that for granted because that's the way you were taught, and no-one said otherwise. Fair enough. Suppose it wasn't linear though :

F_Hewson = | force b/w two charges | ~ ( chargeA )^[1+D] * ( chargeB )^[1+D] / (their separation )^2 != F_Coulomb nor F_Linear

Where I designate D as being small and strictly positive ( D > 0 ). So whereas before ( Coulomb's Law ) when I doubled chargeA and the total force doubled, with this modified version ( Hewson's Law ) as specified, then a doubling of chargeA yields more than doubling of the total force.

It is as if adding charge caused the creation of more charge

The 'as if' means that we have accounted for the variant force behaviour ( when we actually measure ) by choosing to attribute any off-linear effect as being due to an effective alteration of charge. Please pause and have a good long think about that before proceeding .... :-) ;-)

[ BTW - Hewson's Law is not true !! :-) ]

Ok. Let's slide on back to gravity now. Suppose we're in the heavy star construction business : Otubak's Gravitars R Us. As a fresh startup company, just hot off our public share offering, we use a Newtonian cheat sheet for quotes, billing and the like. We make such stars by throwing Jupiter size objects in together until we get some desired star mass. We have quite a cosmic yard* full of them, and thus can make a star of any mass to within plus/minus a Jupiter's worth. The spec sheet for an order comes in for a Three Solar Mass Star. So we look up Isaac's Ready Reckoner and find one thousand Jupiters per Solar mass, in turn suggesting that is 3000 overall for this order. So we do that ( throw 3000 Jupiters together ) and then send it off to the client via DHL CosmicWide Express.

Next millenium we get a call from the client, not happy :

- wasn't expecting a black hole. Preferred something better to look at eg. shiny.

- had an orbital spa unit already made up and it turns out it orbits closer in than expected. Also the orbit is not a closed loop and the point of closest approach keeps moving compared to the distant stars. Plus the auto-timer for the spa heater keeps turning on later than it should.

- the local council/authority is going to property rate his star as somewhat more than 3000 Jupiters. They have done several measurements based on test masses at a good distance away. The council's Gravitational Bylaws Officer asked if the client knew anything about so-called Einstein Corrections. The client's accountant ( Mr Addem Linear ) says that wasn't in budget.

So we ask SBF** as to what happened. He swears upon his own left shinbone that only 3000 Jupiters went in, not one more and not one less. He shows us the forklift loading records to prove it. We then look at the stub from the DHL invoice noting that it went out in a rather small package - it fit into a 20km diameter box with room to spare. SBF says he packed it down well to reduce on packaging costs.

The upshot is that a body's mass is typically quoted as that which one would deduce in the far limit ie. a Newtonian calculation as per the deflection of a test mass from linear course when situated a long way from the body in question ( ... not subject to other forces etc ... ). One could use a laser, say, to mark the straight line the test mass will deviate from. Is that the same as the sum total of what went in ? For low masses, just sum up the separated Jupiter masses and at worst the residuals are minor. But for bigger masses you can use rather fewer Jupiters than Isaac recommends to get a given deflection of the test mass. Note that for each of the separated/single Jupiters I 'weighed' them by using the same test mass involved in the far limit as above. So we could rephrase our non-linear/off-Newton findings in operational/experimental terminology :

=> when using a given test mass in various objects' gravitational influence, in the far limit, we find that gravitational field strength ( measured as test object acceleration ) does not sum as linear and more so with increasing compaction of the final object <=

This occurs above and beyond any other energy evaluations one might do ... kinetic energies, radiation and the like. So :

It is as if adding mass caused the creation of more mass

... careful with signs here. Mass is always ascribed as positive. Gravity always attracts. Energy is always conserved. So if you set potential energy as zero in the infinite separation limit, then gravitational potential energy must always be negative. The attribution of extra central mass ( the non-linear bit above Newton ) must correlate to a more negative gravitational potential energy than otherwise.

I have a fair idea of what's annoying you : there is not a classical analogue to hang your intuition upon. Which sucks for sure .... :-(

The Whole Nine Angstroms ( optional )

If you mix Special Relativity, Quantum Mechanics and Electromagnetism you'll get Quantum Electrodynamics ( Feynman, Schwinger, Tomonaga, Dyson, Dirac .... ). This obeys, amongst other properties :

- the Superposition Principle, or photons can pass 'through' each other unaffected.

- Unitarity, or conservation of total probability.

- Renormalization, the ability to express behaviour at one scale by summarising effective behaviour at smaller lengths.

If one tries ( many have ) to quantise gravity via General Relativity in a like fashion to QED, and then predict for instance what happens if two gravitons ( the photon analog ) come close :

- like rabbits, you generate more gravitons.

- unitarity goes pop.

- renormalisation goes arrrgghhhhh.

.... and all this comes ( mainly ) back to 'gravity attracting gravity' because one can attribute gravitational field strength to a mass amount.

I think that is far enough down the rabbit hole for now ! :-)

Cheers, Mike.

* The foreman's name is Slartibartfast, and we keep the Jupiters well away from each other.

** see *

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

## Mike, thank you for the

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Mike, thank you for the extensive reply.

I am, as you guessed, a hobbyist, though a halfway experienced one. Don't hesitate to reference formulas or papers :)

Still, I think that kinetic/potential energy plays a very important role that should not be neglected. Consider these 2 different cases:

* Let a jupiter plunge into a BH from a long distance

* Lower a jupiter on a rope until just above the event horizon and then let go

How much mass does the BH gain in each of these cases? Neglecting gravitational waves, which are emitted in the first case (if I understand them correctly), or letting them cancel out by letting many jupiters (or jupiter fractions) plunge at once from different directions.

Also, consider the following gedankenexperiment:

You start with a hollow sphere that's way larger than its schwarzschild radius. It eventually collapses uniformly into a black hole under its own gravity, so no gravitational waves are radiated off.

Due to energy conservation I'd assume that the whole system has exactly the same energy and thus gravity before and after the collapse.

Now assume that the sphere wasn't heavy enough to actually form a black hole. That would mean that its energy now consists of kinetic energy and "the rest". Parts of the kinetic energy are eventually radiated off as heat, this should make the whole system's gravity less than it was before collapse, right?

So I guess this self-energy as an actual increase of energy is only experienced if the energy released due to collapse becomes part of the system (e.g. cold gas cloud collapsing to a hot star or anything that collapses to a black hole) and then is only observed by an observer near the system, right?