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Many an alternative theory of gravity has been dreamt up in the bath, while waiting for a bus – or maybe over a light beverage or two. These days it’s possible to debunk (or otherwise) your own pet theory by predicting on paper what should happen to an object that is closely orbiting a black hole – and then test those predictions against observations of S2 and perhaps other stars that are closely orbiting our galaxy’s central supermassive black hole – thought to be situated at the radio source Sagittarius A*.

S2, a bright B spectral class star, has been closely observed since 1995 during which time it has completed over one orbit of the black hole, given its orbital period is less than 16 years. S2’s orbital dynamics can be expected to differ from what would be predicted by Kepler’s 3^{rd} law and Newton’s law of gravity, by an amount that is three orders of magnitude greater than the anomalous amount seen in the orbit of Mercury. In both Mercury’s and S2’s cases, these apparently anomalous effects are predicted by Einstein’s theory of general relativity, as a result of the curvature of spacetime caused by a nearby massive object – the Sun in Mercury’s case and the black hole in S2’s case.

S2 travels at an orbital speed of about 5,000 kilometers per second – which is nearly 2% of the speed of light. At the periapsis (closest-in point) of its orbit, it is thought to come within 5 billion kilometres of the Schwarzschild radius of the supermassive blackhole, being the boundary beyond which light can no longer escape – and a point we might loosely regard as the surface of the black hole. The supermassive black hole’s Schwarzschild radius is roughly the distance from the Sun to the orbit of Mercury – and at periapsis, S2 is roughly the same distance away from the black hole as Pluto is from the Sun.

The supermassive black hole is estimated to have a mass of roughly four million solar masses, meaning it may have dined upon several million stars since its formation in the early universe – and meaning that S2 only manages to cling on to existence by virtue of its stupendous orbital speed – which keeps it falling around, rather than falling into, the black hole. For comparison, Pluto stays in orbit around the Sun by maintaining a leisurely orbital speed of nearly 5 kilometers per second.

The detailed data set of S2’s astrometric position (right ascension and declination) changes over time – and from there, its radial velocity calculated at different points along its orbit – provides an opportunity to test theoretical predictions against observations.

For example, with these data, it’s possible to track various non-Keplerian and non-Newtonian features of S2’s orbit including:

– the effects of general relativity (from a external frame of reference, clocks slow and lengths contract in stronger gravity fields). These are features expected from orbiting a classic Schwarzschild black hole;

– the quadrapole mass moment (a way of accounting for the fact that the gravitational field of a celestial body may not be quite spherical due to its rotation). These are additional features expected from orbiting a Kerr black hole – i.e. a black hole with spin; and

– dark matter (conventional physics suggests that the galaxy should fly apart given the speed it’s rotating at – leading to the conclusion that there is more mass present than meets the eye).

But hey, that’s just one way of interpreting the data. If you want to test out some alternative theories – like, say Oceanic String Space Theory – well, here’s your chance.

**Further reading:** Iorio, L. (2010) Long-term classical and general relativistic effects on the radial velocities of the stars orbiting Sgr A*.

Alpha centauries located about 5 light years from earth, Ross 154 located about 10 light years from earth, HD 10180 is located 127 light years from earth, M87 and NGC 1097 is about 50 million light years from earth, .. is located 600 million light years, 1000 million light years, 10,000 million light years……………………….. How far we could observe our deep space because Day will come we can never make any giant telescope to meet further mysteries. We observe our universe as if it is a boundless hence common question arises:

Is our universe boundless?

Is our universe bounded by certain limit but for other reason it appears as an unlimited form?

The orbital speed of galactic stars around their supermassive black hole is the SAME with varying distances, and is too fast for outermosts not to fly away, which is the reason why dark matter only has extra gravity and has never been seen or proven. Consider our sun seems round, but as it streams around the galaxy it is a plasma gas interacting with black hole quantum fields. The outermost stars in the smallest of dwarf galaxies always require the most amount of dark matter to fix the newtonian gravity problem. Why not assume that these outer dwarf stars vastly distort their spherical shape being plasma that defies newtonian gravity laws the farther outside the spiral arms away from the central black hole the more positive cosmic rays flood interstellar space, causing the distorted plasma stars to orbit the galaxy at the same speed ! When observing a smoke ring, it stays intact because of coherent charged particles attracting themselves seperately from the atmosphere charges. A galaxy looks like a smoke ring and defies gravity too. The smoke ring theory is my gravity theory to explain fictious dark matter “gravity only” requirements.

@ Steve Nerlich,

At the third paragraph, in the fifth line, it should be singular possessive black hole’s, not collective singular possessive black holes’, since we are referring to the single supermassive black hole Sagittarius A* at the centre of the Milky Way.

Reference: The Apostrophe Protection Society. 😎

Gravity equations need quantum computation at small matter scales best represented by Qubits because the square of the force at distance also doubles the numbers of qubits proportionally similar to newtons equation F g = M1 M2 / D2 . Consider each qubit a planck scale area where black hole event horizons allow instantaneous measurements of any choice existing simulataneously in both states, unlike bits that are either one (1) normal matter gravity OR zero (0) anti-matter dark energy . Bits cannot be both 1 and 0 like information qubits are in quantum gravity that should demise dark matter gravity waves.

@IVAN3MAN_AT_LARGE

Thanks – apostrophe catastrophe averted.

@Pradipta

I’m not sure we collectively do observe our universe as if it is boundless (although it might be finite and unbounded) and I’m confident the telescopes will just keep getting bigger. I’d prefer to think our capacity for solving mysteries is boundless – although there’s probably more mysteries out there than we will ever have the time to solve.

Tiniest particles smaller then dust behaving as solid objects might orbit the smoke rings center thousands of times. Hooke’s Law will determine the amount of Dark Matter that is required present in a galaxy shape ! It is Newtonian Gravity TOO ! What’s left to explain DM, when we can go back to the good old days of cosmology again!? crowell explains unites quantum mechanics with special relativity basically a theory of everything by mathematical proof that everybody should accept. the opposite charged attractive force increases the farther is the star from the black hole center. They really are wasting time looking for dark matter particles underground when they should be studying Crowell Hooke’s Law when observing predictable dark matter halo angles with visible matter structures. Newtonian objects need a center of mass and require dark matter without Hooke’s Law. Thank you GREATLY for sharing your BRILLANCE. Those other jerks can do the same, but I do the opposite. probably because they smoke and blow qubits simultaneously, a bad thing to do

@ Jimhenson:

“When observing a smoke ring, it stays intact because of coherent charged particles attracting themselves seperately from the atmosphere charges”

That’s an interesting prediction you just made.

I suggest you get an electroscope, blow some smoke rings and make observations.

Possible Nobel prize ahead.

@ Jimhenson:

When observing a smoke ring, it stays intact because of coherent charged particles attracting themselves seperately from the atmosphere charge

This sentence only either means: You have no clue what charge is.

Charge attracting themselves? Charge staying together? They repel each other!!!

A galaxy looks like a smoke ring and defies gravity too.

Birds look like a galaxy too when seen from the front and also defies gravity.

Good catch!

I’ve seen the MOND believers claim that it explains everything gravitational about galaxies. (The last hang out, I take it.) Clearly that is no longer the case, and to top it off the predictions involve dark matter. I accelerate spit masses in their general direction, relatively speaking. 😮

@ Jimhenson:

And of course dolphins making water rings, something that they can do by simply twisting their head fast enough, by your model show that they are masters of the depth charge. [Do see the youtube, it is a sunday relaxing treat!]

Which once again makes us wonder what you smoke before you blow.

Right. Except that it is so much more vital in the language of love:

“La Société de Protection d’Apostrophe” … “catastrophe d’apostrophe évitée.”

Face it, the french do some things better. (\_/)

perhaps neutralino particles are common fundamental short-lived particles everywhere even inside us there are mini-black holes giving existance to visible matter and producing opposite charged anti-matter pairs that increase charges forces with greater distances by Hooke’s law, and will balance how dark energy expansion accelerates of the universe? Could positive gravity and negative dark energy be united as one force by neutralinos having both gravity and electromagnetism? And the Universe be a particle ?

The topic here involves the semi-relativistic motion of a star near the galactic BH. The motion will exhibit relativistic corrections. These corrections are the violation of conservation of the semi-major axis direction of the orbit (orbital precession), and if the black hole has a large angular momentum there should then be a Lense-Thirring effect. For some information on this take a look at the UCLA Galactic Center

http://www.astro.ucla.edu/~ghezgroup/gc/

and you will find the file illustrating the motion of stars in the Milky Way center. This research is being extended to stellar motion in the Sagittarius A* galactic center.

The motion of stars in a galaxy at large, say far from the center of the galaxy do indeed have constant velocity. This is due to dark matter. This dark matter is something which can be seen as a constant mass-energy density of some sort that pervades the space the galaxy occupies. We start with the Poisson equation, which everyone should know,

nabla*F = -4pi Gm rho

where F is force with directions along z, y and z and nabla* represents directional derivatives or a sum of derivatives along those directions. G is the gravitational constant and rho is the density of matter as the source of gravity and m is the mass of a small test mass. If I integrate over a volume (assumed to be a ball with a 2-dim sphere boundary) that contains all of the matter density rho we get

int nabla*F = -4pi GMm,

The integration over the volume of the force F is equal by Stokes’ law to an integration of the force evaluated on the spherical boundary of the 3-D ball or

Int nabla*F = int dS*F = -4pi r^2F

Equating that to the 4pi GM we get F = -GMm/r^2. So we recover Newtonian gravity! That should not be surprising, and if you use this in an F = ma second law and use the acceleration a = v^2/r for centripetal acceleration you get Kepler’s law. Now let us assume something a bit different with the density of matter. We assume that the matter is in a continuum that extends beyond the sphere of integration above. Therefore while rho is constant the mass is M = rho*4pi r^3/3. So

4pi r^2F = -Gm rho*4pi r^3/3

and so the force is F = -Gm rho r. This means the force increases as the distance from the center increases! This is the equation of motion for a spring, or Hooke’s law. This more or less reproduces the motion of stars in a galaxy. There are some smaller deviations from this due to local concentrations of matter such as galactic SMBHs, but largely this is why it is thought there is this dark matter than pervades the space a galaxy sit within.

LC

Where have I heard such statements before?

Torbjorn:

“La Société de Protection DE L’Apostrophe”. Yes we do ^_^ although not the things we should be doing, probably 😉

Thanks for the awesome video!

All this about smoke rings just brings me back some 30 years back… In one of the first Scientific American I ever read, Martin Gardner had a paper about smoke rings. I felt compelled to write him about it (I certainly had my own crazy theory about them to pester him with, thankfully I forgot the contents of that letter) and he actually answered me!

The DM is some form of elementary particle. I think it is the neutralino, which is a condensate of superymmetric pairs of the photon, neutral Higgs, and Z-electroweak boson. It turns out the quantum numbers for the supersymmetric pairs of these particles are the same and the three supersymmetric pairs of these particles (photino, Higgsino and Zino) form a single particle state. Some data from PAMELA suggests that gamma ray production near the galaxy center is from neutralino decays.

These particles then form a gas of sorts that is cold and very weakly interacting. It does though result in a gravity field. The mass per neutralino particle is on the order of 1-10 TeV, so it is associated with a gravitational field. Einstein lensing by galaxies has revealed the presence of this DM gas. So our galaxy is immersed in this “stuff” and the gravitational result is a force F = -Gm rho r/3 (I forgot the 3 earlier), which is the dynamics of a body moving in space as connected by a spring. The upshot of this motion is that the periodicity is constant, which is set by the spring constant k with in this case is k = Gm rho r/3. The dynamical equation in one dimension is x” = (k/m)x, which by elementary differential equations is a cosine or sine solution. So for the F = ma motion of a particle in a circular orbit the F = -kr and the acceleration is v^2/r, which results in v^2 = kr^2/m or v = sqrt(k/m)r. So if stars moved entirely according to this DM induced spring motion the galaxy would rotate similar to a solid disk. Yet there are other gravitational interactions with stars, the galaxy core, and so forth. So the motion of stars in the outer arms of a galaxy has this non-Keplerian motion due to the composition of this “spring motion” from DM and the attraction to matter clumps at the center of the galaxy.

I forgot to mention detection. We detect the presence of DM on a large scale in a number of ways, such as gravitational lensing or indirectly by the dynamics of stars in a galaxy. However, we do want to know that DM is composed of particle. The neutralino should interact very weakly by the weak interaction, the interaction responsible for beta decay, with regular matter. So the idea with detectors underground is to set up a crystal at very cold temperatures so that a neutralino particle might weakly interact with the crystal lattice. This will cause the crystal lattice to vibrate with a characteristic set of frequencies with what are called phonons — quanta of lattice vibration in a crystal.

So far the data is slightly suggestive, but the statistics are too limited to draw any solid conclusion at this point. I have this crazy idea that a crystalline lattice might exhibit a supersymmetric pair of a phonon. It turns out that nuclei can exhibit a form of supersymmetry, and this has been found experimentally. The thought occurred to me that something similar might be possible in solid state physics. An optical phonon is similar to a photon, and if it can enter into a supersymmetric pairing then maybe this will exhibit physics with neutralinos, in particular an entanglement state.

LC

LBC just curious, why a crystal as detector?

Also a questions, you have the galaxy and that is very big thing.

So might and gravitational influences takes many years to get to the other end and influence the stars at the other side of the galaxy. Do the galaxy models compensate for this? Or is the sheer number of stars cancelling out this gravitational delay effect?

Could positive gravity and negative dark energy be united as one force by neutralinos having both gravity and electromagnetism? And the Universe be a particle ?

NO!

Dark energy has negative pressure! The equation of state is p = w*rho, where w = -1. If the subject of dark energy cycles back again I will write once again on the standard FLRW model and how this can be derived. I have done that a couple of times here.

The neutralino is electrically neutral and beside gravitation they only interacts by weak interactions. And BTW there are 4 eigenstates of the neutralino as well. If neutralinos interacted by electromagnetism it would be luminous matter — not dark matter.

For a static situation, where the distribution of DM is constant over time there is no real problem with a delay process. The causal delay, such as sending a signal on a light cone occurs if there is some change in a field, whether electromagnetic or gravitational. The field response then propagates along a null ray in spacetime and the communication of information about a change in that field exhibits a causal delay with distance. With gravity that is a bit strange, for it is a gravity wave that has to propagate as a change in spacetime along a null direction in spacetime. Yet this is understood, and weak gravity waves are similar to electromagnetic waves with little nonlinearities.

Why a crystal? For crystals the spectra of phonons is known or computable. Most metals and semi-conductors have a regular lattice structure in the placement of atoms. This contrasts with glasses or amorphous solids. In that case you have not ordered structure and the phonon structure is strange. There you get frustrated systems and spin glass dynamics. It also has to be very cold to eliminate thermal vibrations in the solid as much as possible and to put the electrons almost entirely on their Fermi surface.

LC

OLAF:

This may help to answer your question: Phononic crystal

Manu, Gardner the one man Institution. Thanks for sharing!

@ Jimhenson:

You don’t get it. I’m not claiming brilliance, I’m pointing out that your ideas (and exposition) is far from brilliant, actually useless. If they can’t stand up to predicting the close at hand Earth phenomena they should do, how can they predict anything out there?

If anyone is wondering, Oceanic String Space Theory is a fictional alternative theory out of ‘Ome – The Parallel’ by Justin Jackson (co-presenter of This Week In Science).

@ Jimhenson:

“Those other jerks” may have been heavy handedly pouring irony on you but so far we’ve been polite.

@ Jim Henson The problem here is that it is pretty clear you have a weak knowledge of this subject. I suppose I can admire what seems to be an energetic interest, but your grasp on things does not reach far. If you have this energetic interest you might want to use it to learn this subject at some greater depth. Martin Gardner is mentioned above, and he wrote some good articles and books. You might then try to understand physics and relativity by looking at some of the elementary theory and its maths.

LC

How much, would time slow down by dark matter gravity increases on an earth like planet orbiting a star that is at a large distance from the center of the galaxy? Its star speed is constant, but newtonian mass gravity increases with distance which could slow time? assuming that the star cluster needs the maximum amount of dark matter to keep its orbit around the galactic center black hole and obeys Hooke’s law that supplies the extra mass gravity with or without neutralinos wouldn’t the effect be the same? Would time slow down for life on planets that are in galaxies having more dark matter halos?

But that requires spin, doesn’t it? The problem for me then is that phonons are collective quasiparticles.

It is easy to see that we can have rotational modes in some geometries, say along a carbon nanotube. Standing waves would be your zero angular momentum phonons, and you would have left- and right rotating modes. (I don’t think it has been demonstrated yet, mind.)

But they don’t couple to the lattice in the simplest model, so you would have to look for such effects. The optical phonons suggest themselves there, actually. If they do “quantize” while rotating, you would have spin – no spin analogues.

Then you would have “phair” them. Quite a program you have there.

Optical photons carry electric and magnetic field and exhibit helicity states. These serve as spins. Raman scattering is the scattering of a photon with wave vector k on a solid where it absorbs or emits some energy E = hk’/c and the photon is re-emitted with vector k” = k + k’. This usually involves the change in the state of an electron in the solid. If the electron is put in an excited state it may relax to a lower state by flipping it state by a unit of spin. The energy is released in a phonon with the opposite unit of spin. So optical phonons do have spin.

The idea is that there is a vacuum phonon state, which could exhibit supersymmetric physics. Nambu proposed something similar to this 20 years ago. The idea is the neutralino might interact with a SUSY pair of a phonon in an entanglement.

I have yet to bend metal on this idea.

LC

The slowing down of time is a relative thing. For us embedded in the galaxy we notince nothing in particular. However, if we compared our clock rates with the rate of a clock between us and Andromedea we would find our clocks are a little bit slow, but a bout 10^{-8} seconds slower per every second. Not much.

LC

Seems to me that Hooke’s Law of motion applies for black hole gravity, and does the inverse of newtonian planet gravity, by increasing force with distance, kinda like dark energy. Neutralino particles have this mass to explain the extra gravity, but why couldn’t Hooke’s Law, along with the Cassimir force distance, explain dark matter and dark energy? When will new WMAP data be analyized to examine dark energy? Somehow black holes are fundamental to dark matter and dark energy, but there is not consumption, and not expansion of black holes, just visible matter consumed and expanded. galaxies greatly receding us by dark energy do not have their black hole centers moving away from us at increasingly relativistic speeds, only the galactic visible matter stars supernova type la do this as far as I know. This is probably because the universe shape is curved and flat and black holes are singularities.