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Dark energy is the force causing the universe to expand. Einstein realize long ago that something was preventing gravity from causing the universe to simply collapse into a gigantic big black hole. He called it the 'cosmological constant' and added just enough of it to his equations to make the universe stand still. Later on, scientists discovered the universe was actually expanding [well, most of them think it is]. Einstein decided his idea was all wrong and called it his biggest mistake. It now looks like he was right all along, he just didn't know how much 'cosmological constant' was needed to make the universe look the way we now know it looks.

For more detail from reputable authorities on these matters, see

http://map.gsfc.nasa.gov/m_uni/uni_101matter.html

http://imagine.gsfc.nasa.gov/docs/ask_astro/dark_matter.html

http://www.nasa.gov/missions/science/f_dkenergy.html

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Supersymmetric theories propose the existence of a particle called the Lightest Supersymmetric Particle. This is a WIMP that is a candidate to dark matter, and has the property of self-annihilation (two LSP in contact would annihilate). This paper proposes that part of the flux of gamma rays coming from the center of the galaxy is due to the annihilation of LSPs

http://xxx.lanl.gov/abs/astro-ph/0408192

"TeV $\gamma$-radiation from Dark Matter annihilation in the Galactic center"

http://xxx.lanl.gov/abs/astro-ph/0408192

"TeV $\gamma$-radiation from Dark Matter annihilation in the Galactic center"

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If mass were lighter in less dense surroundings, e.g. the edges of a galaxy, this would be the same as the gravitational constant of the universe being smaller and particles would orbit faster at the edges and explain the strange spin of galaxies, right?Mike2 said:

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"In 1917, Albert Einstein tried to use his newly developed theory of general relativity to describe the shape and evolution of the universe. The prevailing idea at the time was that the universe was static and unchanging. Einstein had fully expected general relativity to support this view, but, surprisingly, it did not. The inexorable force of gravity pulling on every speck of matter demanded that the universe collapse under its own weight.

His remedy for this dilemma was to add a new 'antigravity' term to his original equations. It enabled his mathematical universe to appear as permanent and invariable as the real one. This term, usually written as an uppercase Greek lambda, is called the 'cosmological constant'. It has exactly the same value everywhere in the universe, delicately chosen to offset the tendency toward gravitational collapse at every point in space."

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Consider: GR is a gravitational theory that accurately predicts solar system orbits (geodesics) and laboratory experiments. When solved for the cosmological case, when the universe is assumed to be homogeneous and isotropic, then it predicted: the expanding universe, the primordial relative abundance of the elements, 3/4 hydrogen 1/4 helium and very little of anything else, and the microwave background. So it seems well established.

However there were three cosmological problems, the density problem, the horizon problem and the smoothness problem. These all arose because the universe was predicted by GR to be decelerating in its expansion.

So it needed a fix. That fix was provided by the theory of inflation. At a very stage of its history the universe was said to suffer a phase of enormous acceleration in its expansion, which solved the three problems above.

However inflation required the universe to be virtually 'flat' and have a specific density, the critical density.

The next problem was the density of observed matter, and the density of ordinary baryonic matter allowed by the Big Bang nucleo-synthesis reactions, only came to about 4% of this critical density. So there was a lot (96% of the entire universe) of 'missing matter'.

Studies of the rotation rates of galaxies, the orbital velocities of galactic clusters, and the gravitational lensing (by nearer galaxies) of distant quasars, indicated that the universe had a density of about 30% of the critical density. So Dark Matter of unknown composition - not ordinary baryonic matter - was invented to fill the gap 4 - 30 %.

Next, the observation of supernovae in distant galaxies indicated the universe must have accelerated, at least in recent history, rather than decelerate.

Finally, analysis, under GR, of the WMAP data of the microwave background theory indicated the universe was flat after all. Therefore roughly 70% of the universe had to be of some further unknown substance. Dark energy was invented to fill this gap and it could conveniently, perhaps, explain also why the universe is accelerating. Hence we arrive at the present concordance model of 4% ordinary matter, 23% dark matter and 73% dark energy.

So the orginal theory, GR, only fits the facts with the introduction, or invention, of inflation, dark matter and dark energy. Indeed most (96%) of the universe is of unknown composition. These three constructs are all undiscovered by laboratory physics even after several decades of intensive laboratory research!

Remember the Ptolemaic theory? When Galileo confronted it it was a successful theory, successful because every time a problem had arisen with the basic paradigm they added another epicycle to make the theory fit the data.

Perhaps Inflation, dark matter and dark energy are just modern examples of 'adding extra epicycles' and, just as in Galileo's time, maybe, we are going to see a paradigm shift?

However there were three cosmological problems, the density problem, the horizon problem and the smoothness problem. These all arose because the universe was predicted by GR to be decelerating in its expansion.

So it needed a fix. That fix was provided by the theory of inflation. At a very stage of its history the universe was said to suffer a phase of enormous acceleration in its expansion, which solved the three problems above.

However inflation required the universe to be virtually 'flat' and have a specific density, the critical density.

The next problem was the density of observed matter, and the density of ordinary baryonic matter allowed by the Big Bang nucleo-synthesis reactions, only came to about 4% of this critical density. So there was a lot (96% of the entire universe) of 'missing matter'.

Studies of the rotation rates of galaxies, the orbital velocities of galactic clusters, and the gravitational lensing (by nearer galaxies) of distant quasars, indicated that the universe had a density of about 30% of the critical density. So Dark Matter of unknown composition - not ordinary baryonic matter - was invented to fill the gap 4 - 30 %.

Next, the observation of supernovae in distant galaxies indicated the universe must have accelerated, at least in recent history, rather than decelerate.

Finally, analysis, under GR, of the WMAP data of the microwave background theory indicated the universe was flat after all. Therefore roughly 70% of the universe had to be of some further unknown substance. Dark energy was invented to fill this gap and it could conveniently, perhaps, explain also why the universe is accelerating. Hence we arrive at the present concordance model of 4% ordinary matter, 23% dark matter and 73% dark energy.

So the orginal theory, GR, only fits the facts with the introduction, or invention, of inflation, dark matter and dark energy. Indeed most (96%) of the universe is of unknown composition. These three constructs are all undiscovered by laboratory physics even after several decades of intensive laboratory research!

Remember the Ptolemaic theory? When Galileo confronted it it was a successful theory, successful because every time a problem had arisen with the basic paradigm they added another epicycle to make the theory fit the data.

Perhaps Inflation, dark matter and dark energy are just modern examples of 'adding extra epicycles' and, just as in Galileo's time, maybe, we are going to see a paradigm shift?

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Could Dark Energy and Dark Matter both be due to gravitational effects on rest mass predicted by General Relativity that we have not accounted for yet?Mike2 said:If mass were lighter in less dense surroundings, e.g. the edges of a galaxy, this would be the same as the gravitational constant of the universe being smaller and particles would orbit faster at the edges and explain the strange spin of galaxies, right?

There is a gravitational redshift for photons coming out of a gravitational well. This is due to time being stretched as the gravitational field weakens. Now if matter is the result of vibrational modes of strings or membranes, then even the rest mass of particles would be affected by gravitational effects as well.

I haven't actually done the calculations, but it seems in principle that if mass gets lighter as the universe becomes less dense with expansion, then this would account for accelerated expansion - the particles are getting lighter so their velocity increase as required by conservation of energy.

Also, if mass gets lighter at the edges of galaxies, then photons would be less redshifted towards the edges. This would make it appear as if they were moving faster than otherwise. So the faster velocities at the edges may not be due to dark matter, but due to less gravitational redshifting of photons.

And so, dark energy and dark matter may be just an as yet unaccounted for affect of gravity on rest mass.

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Wouldn't this also have a tendency to prove Stringtheory - that all particles, including massive ones, are extended objects that vibrate with frequency? How else could time dialations affect the mass of a particle?Mike2 said:Could Dark Energy and Dark Matter both be due to gravitational effects on rest mass predicted by General Relativity that we have not accounted for yet?

There is a gravitational redshift for photons coming out of a gravitational well. This is due to time being stretched as the gravitational field weakens. Now if matter is the result of vibrational modes of strings or membranes, then even the rest mass of particles would be affected by gravitational effects as well.

I haven't actually done the calculations, but it seems in principle that if mass gets lighter as the universe becomes less dense with expansion, then this would account for accelerated expansion - the particles are getting lighter so their velocity increase as required by conservation of energy.

Also, if mass gets lighter at the edges of galaxies, then photons would be less redshifted towards the edges. This would make it appear as if they were moving faster than otherwise. So the faster velocities at the edges may not be due to dark matter, but due to less gravitational redshifting of photons.

And so, dark energy and dark matter may be just an as yet unaccounted for affect of gravity on rest mass.

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Garth said:

However there were three cosmological problems, the density problem, the horizon problem and the smoothness problem. These all arose because the universe was predicted by GR to be decelerating in its expansion.

So it needed a fix. That fix was provided by the theory of inflation. At a very stage of its history the universe was said to suffer a phase of enormous acceleration in its expansion, which solved the three problems above.

However inflation required the universe to be virtually 'flat' and have a specific density, the critical density.

The next problem was the density of observed matter, and the density of ordinary baryonic matter allowed by the Big Bang nucleo-synthesis reactions, only came to about 4% of this critical density. So there was a lot (96% of the entire universe) of 'missing matter'.

Studies of the rotation rates of galaxies, the orbital velocities of galactic clusters, and the gravitational lensing (by nearer galaxies) of distant quasars, indicated that the universe had a density of about 30% of the critical density. So Dark Matter of unknown composition - not ordinary baryonic matter - was invented to fill the gap 4 - 30 %.

Next, the observation of supernovae in distant galaxies indicated the universe must have accelerated, at least in recent history, rather than decelerate.

Finally, analysis, under GR, of the WMAP data of the microwave background theory indicated the universe was flat after all. Therefore roughly 70% of the universe had to be of some further unknown substance. Dark energy was invented to fill this gap and it could conveniently, perhaps, explain also why the universe is accelerating. Hence we arrive at the present concordance model of 4% ordinary matter, 23% dark matter and 73% dark energy.

So the orginal theory, GR, only fits the facts with the introduction, or invention, of inflation, dark matter and dark energy. Indeed most (96%) of the universe is of unknown composition. These three constructs are all undiscovered by laboratory physics even after several decades of intensive laboratory research!

Remember the Ptolemaic theory? When Galileo confronted it it was a successful theory, successful because every time a problem had arisen with the basic paradigm they added another epicycle to make the theory fit the data.

Perhaps Inflation, dark matter and dark energy are just modern examples of 'adding extra epicycles' and, just as in Galileo's time, maybe, we are going to see a paradigm shift?

this is a great condensed history and summary of the concordance model.

I can't even find a nit here to disagree with if I wanted to, which I dont.

the comparison between epicycles and the postulated DM and DE is apt.

and and as a small mini-essay it's efficiently written.

BTW Smolin's 3 talks at the WS-2004 symposium seem to verge on considering Lambda to be something else besides the effect of a postulated dark energy density----something more like a new invariant length scale L

on the order of 9.5 billion lightyears.

After all Lambda is a curvature so it is an inverse length squared. So the square root of 1/Lambda is a length L. And that length scale could have something to do with what spacetime is, might be intrinsic to its geometry, and yet not correspond to some real form of energy uniformly distributed in space and time. I guess it is just a difference in nuance (you could still associate an energy density rho-sub-Lambda with it so nothing changes, more of an attitudinal shift.)

I will get a link to the WS-2004 symposium, it has the lecture slides available for download

http://ws2004.ift.uni.wroc.pl/html.html [Broken]

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Mike2 said:

Hi Mike, you have a chain of 4 posts here---#2, #7, #11, and #12.

Each subsequent one of your posts quotes the one preceding it. so

it is like a chain of reasoning.

The initial premises (here in post #2) are in error.

In GR mass does not decrease with distance from other mass.

Lighter particles do not necessarily travel faster.

If you know of some GR essay on the web which says these things

please post a link.

The next post (#7) is likewise in error, you say

If mass were lighter in less dense surroundings, e.g. the edges of a galaxy, this would be the same as the gravitational constant of the universe being smaller and particles would orbit faster at the edges and explain the strange spin of galaxies, right?

you have it backwards. If either the gravitational constant G or particle mass declined with distance from center, then the particles near the edges would orbit

So your declining mass or declining G hypothesis predicts the opposite of what is observed.

either one must modify the Newtonian law so that circular orbit speed (and centripetal acceleration) decline less abruptly with distance from center

so that there is more acceleration towards center than Newtons law predicts (see also the pioneer anomaly)

or one must postulate the presence of additional mass in the galaxy which we do not see----to be the cause of the stronger acceleration towards center than would otherwise be expected at such great distances.

Mike I don't believe it would be useful to comment more on your posts specifically, or to respond to further ones along these lines.

But since you raise the issue of galactic rotation curves, which are currently a puzzle, I will try to focus on the issue of and see if I can find out anything of general interest

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Thanks for your reply, marcus. Yes, this is just a theory that I seem to have stumbled upon. And I'm still feeling my way through it. I plan to specifically study SR and GR soon in more detail. So maybe I'll be able to put it in the language of mathematics soon. Though I would think that this would be easy for those skilled in the art.marcus said:Hi Mike, you have a chain of 4 posts here---#2, #7, #11, and #12.

Each subsequent one of your posts quotes the one preceding it. so

it is like a chain of reasoning.

The initial premises (here in post #2) are in error.

In GR mass does not decrease with distance from other mass.

Lighter particles do not necessarily travel faster.

If you know of some GR essay on the web which says these things

please post a link.

Yes, I've argued with others about the "invariance of mass" in GR. Mass is invariant in SR but not in GR. From Rober M. Wald's book

However, on page 68 concerning gravitational fields, Wald writes, "Because spacetime is curved, there is no well defined notion of vectors at different points being parallel; parallel transport is curve dependent. Thus, there is no natural "global family" of inertial observers, and a given observer cannot, in general, define the energy of a distant particle." So the question is how do we calculate the mass of distant objects.

There certainly is a gravitational effect on the frequency of photons. This is well established. It is considered in cosmology when determining the velocities of distant galaxy cluster from measured redshifts. However, it does not seem to be common to consider the effect of the gravitational field of the entire universe when looking at distant redshifts. The redshift seems to be attributed entirely to velocity and none due to the fact that the universe was in a deeper gravitational well when those photons were released. However, I see no reason not to consider the gravity of the entire universe. And I don't seem to be the only one concerned about this.

From the link:

http://www.astronomycafe.net/anthol/expan.html [Broken]

"It is tempting to refer to cosmological redshifts as Doppler shifts. This choice of interpretation has in the years since Hubble's work led to an unfortunate misunderstanding of big bang cosmology, obscurring one of its most mysterious beauties. As noted with a hint of frustration by cosmologists such as Steven Weinberg and Jaylant Narlikar and John Wheeler, "The frequency of light is also affected by the gravitational field of the universe, and it is neither useful nor strictly correct to interpret the frequency shifts of light...in terms of the special relativistic Doppler effect."

It's been explained to me that the gravitational redshift is due to time distortions caused by gravity. Fine, then it would seem that all objects that vibrate with a given frequency would also be affected by this gravitational effect. I've seen how in Superstring theory, the mass of strings are dependent on frequency of quantum oscillators. So it would seem that mass would have to be affected by this gravitational effect as well.

The possiblity of gravitational fields affecting mass as well as photons is intriquing. And valid or not, it seems worthy of some mathematical proof before rejecting or accepting in full. But just on an intuitive level, it seems to at least point in a direction that might explain dark matter and dark energy. Though I don't know about exact values at this point.

If may very well explain the acceleration of expansion. If matter becomes lighter with expansion, then even in its local frame of reference, it would seem that galaxies would have to speed up to conserve energy. This would be just like a rocket ship able to move faster because it looses the mass of fuel.

It may very well explain the early deceleration of the universe if the stronger redshift of the early expansion is due more to gravity then than now. Could it be that the universe has only been accelerating since its birth? In other words, could the change in gravitational redshift be more dramatic in the early stages than in the latter stages. This might make it appear as if the early universe were decelerating when it was actually accelerating.

It may explain the strange spin of galaxies where the outer regions seem to go faster than they should. Could this be due to matter being lighter in the less dense outer regions? Or perhaps this can be explained by the fact that galaxies were heavier in the early universe. I'm not sure how that would affect orbital speeds. I suppose a computer simulation is in order. Is this strange orbital spin just as profound in Andromida as for very distant/early galaxies?

It might also explain the greater gravitational lensing affect than what can be attributed by accountable matter. The mass of early objects was greater then than now. Is gravitational lensing more profound in the earlier, more dense universe?

I do appreciate your input, thanks.

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At this point, I don't know if I'm talking about changes in G. But I do seem to be talking about mass decreasing with less density. And the Newtonian equations have mass as linear on both sides of the equations. So it would seem the change on one side equals the change on the other so in Newtonian physics it doesn't seem to matter if orbital mass changes. But I'm not sure that Newtonian physics is valid on a galactic scale.marcus said:you have it backwards. If either the gravitational constant G or particle mass declined with distance from center, then the particles near the edges would orbitmore slowlythan one would expect using a strait Newtonian model---but in fact we observe the opposite: circular orbit speeds arefasterthan what one would reckon naively.

So your declining mass or declining G hypothesis predicts the opposite of what is observed.

either one must modify the Newtonian law so that circular orbit speed (and centripetal acceleration) decline less abruptly with distance from center

so that there is more acceleration towards center than Newtons law predicts (see also the pioneer anomaly)

or one must postulate the presence of additional mass in the galaxy which we do not see----to be the cause of the stronger acceleration towards center than would otherwise be expected at such great distances.

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Mike2 said:If mass were lighter in less dense surroundings, e.g. the edges of a galaxy, this would be the same as the gravitational constant of the universe being smaller and particles would orbit faster at the edges and explain the strange spin of galaxies, right?

In a sense, you are assigning a preferred reference frame to gravitational force over distance. If this were true, it would be easily observed within the solar system [proportionately less gravity effects from more distant planets]. But it is not true. Were that the case, Pioneer and the Cassini probe would have been way off course [not to mention missions to the moon]. The same effect would be also be obvious in particle accelerators.

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Chronos said:But it is not true. Were that the case, Pioneer would have been way off course .

But they are! The Pioneer anomaly is that both spacecraft exhibit an unexplained sunwards acceleration roughly equal to cH.

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While of theoretical importance, I resist calling one part in a billion significant compared to measurement error.

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I don't think there is any choice, really. If mass is due to vibrations, then the frequency of those vibrations are just as susceptable to gravitational redshifting as are photons.Chronos said:In a sense, you are assigning a preferred reference frame to gravitational force over distance. If this were true, it would be easily observed within the solar system [proportionately less gravity effects from more distant planets]. But it is not true. Were that the case, Pioneer and the Cassini probe would have been way off course [not to mention missions to the moon]. The same effect would be also be obvious in particle accelerators.

Consider MOND (for modified dynamics). See:

http://www.astro.umd.edu/~ssm/mond/faq.html

with home page at:

http://www.astro.umd.edu/~ssm/mond/

In MOND, mass is modified by an interpolation function mu(x) = x(1+x2)

It seems curious too, that the effect is dependent on the distance to the galaxy being measured. This also seems to indicate a factor dependent on the density of the universe as a whole. I think further study is warranted.

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While MOND is certainly an interesting idea, and its consistency with many observations (particularly galaxy rotation curves) is most impressive, I'm not sure how relevant it is to cosmology - does anyone know if Milgrom (or other MONDie) has examined the cosmological implications of MOND?Mike2 said:I don't think there is any choice, really. If mass is due to vibrations, then the frequency of those vibrations are just as susceptable to gravitational redshifting as are photons.

Consider MOND (for modified dynamics). See:

http://www.astro.umd.edu/~ssm/mond/faq.html

with home page at:

http://www.astro.umd.edu/~ssm/mond/

In MOND, mass is modified by an interpolation function mu(x) = x(1+x2)^{-1/2}. And this is so reminesent of factors in relativity that it seems to hint of a relativistic change in rest mass. The scale is so small compared to normal experience that we would not normally take this effect into account.

It seems curious too, that the effect is dependent on the distance to the galaxy being measured. This also seems to indicate a factor dependent on the density of the universe as a whole. I think further study is warranted.

In any case, MOND's inability to account for gravitational lensing - both strong and weak - leaves it with a challenge or two

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I wondered about that how the MOND folks approach gravitational lensing and found this paper.Nereid said:In any case, MOND's inability to account for gravitational lensing - both strong and weak - leaves it with a challenge or two

http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:astro-ph/9406051 [Broken]

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Nereid said:While MOND is certainly an interesting idea, and its consistency with many observations (particularly galaxy rotation curves) is most impressive, I'm not sure how relevant it is to cosmology ...

One introduction to MOND is by way of cosmology.

See

http://ws2004.ift.uni.wroc.pl/html.html [Broken]

Click on "Lectures" and select Smolin's third lecture for pdf download.

Personally I would be inclined to approach MOND via the non-zero

cosmological constant (and implied distance scale) if at all. I find it

worrisome. But as you point out the match with galaxy rotation curves

is impressive.

At this point i am afraid that this is all I have to say on the MOND subject (which is very little indeed!). However I agree with you in spades, Nereid, that it "is certainly an interesting subject."

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turbo-1 said:http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:astro-ph/9406051 [Broken]

thanks turbo, that was a good lead, they say:

-------exerpt from conclusion section----

... The present paper has computed one of the critical issues in MOND, the deflection of light rays by a spherical gravitational field. Surprisingly, MOND provides a constant deflecting angle at large distance from the center of the gravitational field, which is consistent with the the value presently used in the study of gravitational lensing by galaxies and clusters of galaxies. It is then likely that all the lensing cases can be equally reproduced in MOND without the massive dark matter in galaxies and in clusters of galaxies. Similar to the flatness of rotation velocity in galaxies predicted by MOND without assuming the massive halos, the constant deflection of light from MOND has the same effect as the r

It has been shown that light bending is no more a critical argument against MOND today. Conversely, MOND predicts a reasonable deflection angle of light by large massive systems. Therefore, whether or not MOND reflects the nature of gravity needs to be further investigated using other astronomical methods.

----end quote---

http://arxiv.org/abs/astro-ph/9406051

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Nereid:

does anyone know if Milgrom (or other MONDie) has examined the cosmological implications of MOND?

Kurious:

John Baez said on sci.physics.research that Lee Smolin had been losing sleep

over why the acceleration of the expansion of the universe at a distance of about one Hubble is equal to about 10^-10m/s^2 which is the magnitude at which MOND becomes important.

A rough Newtonian calculation (my calculation not Smolin's! which is valid provided

r > 10^25 metres) for the attractive force of gravity shows:

The gravitational force acting on a particle of mass m, on the

surface of a sphere of radius 10^26 metres and with a mass of 10^52

kg is given by

G x10^52 m / (10^26) ^ 2

The acceleration is given by G x10^52 / (10^26) ^ 2 = 10^ - 11 m/ s^2

Since we would expect the attractive force due to MOND to be greater than

this, perhaps MOND's deccelerating effect could be noticed in an accurate measurement of the net acceleration of the expansion of the universe.

This would be less than current cosmological theory predicts.

does anyone know if Milgrom (or other MONDie) has examined the cosmological implications of MOND?

Kurious:

John Baez said on sci.physics.research that Lee Smolin had been losing sleep

over why the acceleration of the expansion of the universe at a distance of about one Hubble is equal to about 10^-10m/s^2 which is the magnitude at which MOND becomes important.

A rough Newtonian calculation (my calculation not Smolin's! which is valid provided

r > 10^25 metres) for the attractive force of gravity shows:

The gravitational force acting on a particle of mass m, on the

surface of a sphere of radius 10^26 metres and with a mass of 10^52

kg is given by

G x10^52 m / (10^26) ^ 2

The acceleration is given by G x10^52 / (10^26) ^ 2 = 10^ - 11 m/ s^2

Since we would expect the attractive force due to MOND to be greater than

this, perhaps MOND's deccelerating effect could be noticed in an accurate measurement of the net acceleration of the expansion of the universe.

This would be less than current cosmological theory predicts.

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kurious said:So maybe MOND comes into play at large distances.

Mond is ad hoc (underlying theory, if any, unknown) so

everyone can have his own thumbrule for it----his own version of mond. Yes?

Smolin version MOND out of that lecture I gave the link for

says not what you say "mond comes into play at large distances"

It says mond comes into play at low accelerations

there is a lower threshold of acceleration----whenever the centripetal acceleration falls below this threshold then there is a geometric mean modification which brings the acceleration up a little (not up all the way to the theshhold but a little raised up towards the threshhold, from the bare Newtonian value)

this version of mond would explain the Pioneer anomaly. the vehicle was far enough from the sun that the centripetal accel. had fallen below this threshhold---and then it was larger than expected

this version of mond achieves the nice fit to the galaxy rotation curves.

when the stars are far enough from the center that their centripetal accel is down below threshhold, then their accel is larger than expected.

this threshold accel is connected to the CC.

the connection is by way of a length L = Lambda

I personally do not advocate this length L.

The big question is what is it doing in our universe----if it is related to galaxy rotation curve and to pioneer anomaly, and also to acceleration of expansion.

the length L is 9.5 billion LY. that is what, if you square it and take the reciprocal, you get the cosmological constant current estimate.

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Anything more recent (that paper is >10 years old now)? For example, thisturbo-1 said:I wondered about that how the MOND folks approach gravitational lensing and found this paper.

http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:astro-ph/9406051 [Broken]

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Nereid said:Anything more recent (that paper is >10 years old now)? For example, this2002page seems to suggest that for both "Galaxy Clusters" and "Gravitational Lensing", MOND is 'uncertain but not promising'

thanks Nereid! this link you gave

http://www.astro.umd.edu/~ssm/mond/mondvsDM.html

is also very helpful. I had not realized how successful MOND was in predicting other things. It is even more impressive than I thought. So I agree all the more with your "certainly interesting" assessment.

However am still leery because can't imagine any underlying theory

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Nereid said:this2002page promising

thanks again! this link of yours

http://www.astro.umd.edu/~ssm/mond/mondvsDM.html

has a brother

http://www.astro.umd.edu/~ssm/mond/litsub.html

which is a whole trove of literature on MOND

and here is the index

http://www.astro.umd.edu/~ssm/mond/

and the guy Stacy McGaugh responsible

http://www.astro.umd.edu/~ssm/

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the force of gravity seem stronger than it should be.

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I have a sneaking suspicion that MOND is due to an as yet unknown affects of GR. This could be gravitational redshifting of rest mass, or perhaps gravitational redshifting of gravitons, or perhaps the affect of the gravitational effects of the universe as a whole as the universe becomes less dense.marcus said:thanks Nereid! this link you gave

http://www.astro.umd.edu/~ssm/mond/mondvsDM.html

is also very helpful. I had not realized how successful MOND was in predicting other things. It is even more impressive than I thought. So I agree all the more with your "certainly interesting" assessment.

However am still leery because can't imagine any underlying theory

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turbo-1 said:maynot understand gravity as well as we had hoped. One consequence is that we may once again have to regard gravitation as a force acting over a distance through a medium. GR says that mass curves space-time, and orbits are merely paths along momentum-conserving geodesics, which may be true, but we may at some point have to reconsider that concept, if dark matter remains as elusive as ever and MOND continues to make accurate predictions regarding the behavior of galaxies. If MOND survives the next few years, we may also have to reconsider whether gravitational mass and inertial mass are truly equivalent. Exciting times.

yes turbo exciting times

let's be cautious about giving up on GR (and falling into the arms of action at a distance) because it could be that a small modification of the geometric approach will achieve the results of mond.

you might look at the second half of page 15 of

http://arxiv.org/gr-qc/0406100 [Broken]

the game is, can you get mond-like effects by bending the tangent space (where energy and momentum and acceleration are born) a little.

well that is putting it too vaguely, but you can see what Florian Girelli says in the paper.

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"Successful as it may be, MOND is, at the moment, a limited phenomenological theory. [...] And MOND is limited because it cannot yet be applied to all the relevant phenomena at hand. The main reason is that MOND has not been incorporated into a theory that obeys the principles of relativity, either special or general. [...] The phenomena that fall outside the present purview of MOND are those that involve, on the one hand, accelerations smaller than a

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Nereid said:

"Successful as it may be, MOND is, at the moment, a limited phenomenological theory. [...] And MOND is limited because it cannot yet be applied to all the relevant phenomena at hand. The main reason is that MOND has not been incorporated into a theory that obeys the principles of relativity, either special or general. [...] The phenomena that fall outside the present purview of MOND are those that involve, on the one hand, accelerations smaller than a_{0}(so that MOND plays a role) and, on the other, extreme speeds or extremely strong gravity (so that relativity is called for). [...] Light propogating in the gravitational fields of galactic systems [satisfies] both criteria. MOND cannot properly treat this motion, which pertains to gravitational lensing. [...] A second system which requires MOND and relativity is the universe at large. It follows that cosmology cannot be treated in MOND."

The main reason is that MOND has not been incorporated into a theory that obeys the principles of relativity

this is a useful perspective (from the standpoint of August 2002) because it highlights what is new in the following 2004 papers:

http://arxiv.org/gr-qc/0406100 [Broken]

The prospect of building mond-like effects into a GR-type theory

is what they are talking about on the second half of page 15 and in the last 3 or 4 lines of the conclusions paragraph at the end.

See also another 2004 link I just gave a few posts back.

http://ws2004.ift.uni.wroc.pl/html.html [Broken]

or pages 3 and 4 of

http://arxiv.org/hep-th/0406276 [Broken]

where mond is again approached from a cosmological constant direction.

At this point we are, i believe, merely talking about some coherent lines of investigation being taken by a few people---the 3 authors of one paper and the 2 authors of the other and possibly others I don't know of. Oh yes a couple of physicists at Monpellier too. Just a handful. And this line of investigation could not pan out! If-you-want-to-be-sure-of-results-go-somewhere-else-sort of thing.

The significance is what your August 2002 quote points out, the need to build mond into a GR-type theory, which is precisely what these people see as a promising line of research.

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