Where does inertia come from?

[Startraveler]

Some big news this week was the announcement of the most direct detection of dark matter yet. Still not particularly direct but better than what's been done before. Astronomers were able to use two galaxies to separate the wheat from the chaff, so to speak. The "missing mass" problem (perhaps "extra mass" would've been a better name) has always been that galaxies don't spin quite the way they should so it seems like there's something extra in them. This observation was of two galaxy clusters that have passed through each other, leaving behind the hot gas that makes up the vast majority of the ordinary matter in the galaxies; so for the most part the dark matter and the regular matter were separated when this collision occurred. These astronomers were able to make maps showing where the gravity points and it isn't at the regular matter--the conclusion is that there seems definitely be something there.

This discovery seems to have cast some serious doubt (some would say killed) some ideas that relied on alternative formulations of gravity to figure out what's wrong with galaxies. Two months ago PhysicsWeb had a wonderful article Gravity's Dark Side about one way some physicists are trying to account for why dark matter and dark energy haven't been directly detected yet: they don't exist. Now it's pretty irrefutable at this point that something's wrong--galaxies shouldn't hold together in quite the way they do unless there's extra mass in them providing extra gravity (dark matter) and the expansion of the universe is being pushed to expand faster and faster by something (dark energy). But some folks are working on ways to produce the observed effects without relying on these extra elements; instead they modify the physical theories underlying it all--those that describe how gravity works.

The article provides an interesting look at how some very open questions in cosmology are being tackled and it's well worth the read. I want to briefly focus on one aspect of all this, one of the original alternatives to dark matter. This excerpt from the article gives the gist of it:

In 1983, however, Mordehai Milgrom, now at the Weizmann Institute in Israel, claimed he could explain the anomalous rotation of galaxies without invoking dark matter. Instead, he modified Newton's formula so that under certain circumstances the gravitational force between two bodies decays more gently than the inverse square of the distance between them. The key property of Milgrom's theory - called modified Newtonian dynamics, or MOND - was that the modified behaviour kicks in below a certain acceleration, rather than distance, scale. Remarkably, Milgrom was able to set the value of this universal parameter such that MOND describes the dynamics of galaxies extremely well, while preserving Newtonian gravity elsewhere.

But any alternative theory of gravity worth its salt has to account for much more than just galaxy dynamics. In particular, it needs to be able to explain the way light is bent by massive objects - a central prediction of general relativity that was dramatically confirmed during the solar eclipse of 1919. The most striking manifestation of this effect is gravitational lensing, whereby galaxies or clusters of galaxies cause light from background objects to appear as if it has come from several different sources. As with the dynamics of galaxies, however, general relativity is unable to account for the strength of some gravitational lenses without adding appropriate distributions of dark matter "by hand".

Being rooted in Newtonian mechanics, MOND had no hope of explaining the bending of light. Moreover, Milgrom's simple formula violated several basic laws of physics, such as the conservation of momentum. This prompted theorists in the 1980s and 1990s, notably Milgrom, Robert Sanders of the University of Groningen in the Netherlands and Jacob Bekenstein at the Hebrew University of Jerusalem, to set about turning MOND into a fully-fledged theory. This culminated in 2004, when Bekenstein published a relativistic version of MOND called tensor vector scalar theory or TeVeS. It is this theory that has made many astronomers, astrophysicists and cosmologists begin to take alternative gravity theories more seriously.

I'll admit that in recent months this idea has intrigued me more and more. MOND (and the recent upgrades to it) are not generally well-liked by most physicists or cosmologists primarily because, as far as I know, it's not viewed as having much of a physical basis. That is, the thought seems to be "sure, maybe it's possible to play around with the laws and theories of physics to get these results but what's the physical justification for doing it?" And that is a valid question--as ad hoc as filling the universe with a mysterious nonbaryonic form of matter that's six times as abundant as the regular matter we're familiar with might seem, altering the laws of physics to avoid the conclusion that this dark matter exists seems just as (if not a good deal more) ad hoc.*

What I want to do is throw out a very vague thought about where to start looking for a possible physical justification (which I discovered a while back Milgrom himself had offered in an offhand comment in his original paper on MOND). There is an idea (dubbed "Mach's principle" by it's most famous fan, Albert Einstein) put forth by physicist-philosopher Ernst Mach that, in a nutshell, suggests that inertia (the well-known resistance bodies exhibit to changes in their state of motion) is a property that derives from all the rest of the matter in the universe.

You're probably familiar with Newton's first law from back in high school: bodies in motion tend to stay in motion unless a force acts on them and the same goes for bodies at rest. In other words, in Newtonian physics for some reason there are these things called inertial frames in the universe in which things aren't accelerating and objects tend to stay in their inertial frame. The harder it is to budge them out of that inertial frame, the more mass--inertial mass--we say the objects have. But the ultimate source of inertia and inertial frames is not known.

In the 1950s a young physicist named Dennis Sciama did some interesting work on Mach's principle and inertia that eventually led to his doctorate. This young physicist, by the way, went on to be a pretty big character and a number of famous astro-types did their doctoral work under his supervision: George Ellis, Stephen Hawking, Brandon Carter, Martin Rees (the current British Astronomer Royale), John D. Barrow, and David Deutsch, among others. Anyway, Sciama went to work formalizing Mach's idea and advancing the idea that inertial frames are actually defined by the matter in the universe (implying that in an empty universe a particle wouldn't experience inertia) and that inertia then is a result of the rest of the matter in the universe exerting a force on a body that's attempting to accelerate relative to the rest of the universe. Take a look at the intro to one of his famous papers, On the Origin of Inertia:

In this paper we construct a tentative theory to account for the inertial properties of matter. These properties imply that at each point of space there exists a set of reference frames in which Newton's laws of motion hold good--the so-called "inertial frames". If other frames are used Newton's laws will no longer hold unless one introduces "fictitious" (inertial) forces which depend on the motion of these frames relative to an inertial frame.

The question arises: what determines the inertial frames? Newton asserted that they were determined by absolute space. However, absolute space is not observable in any other way, and it has been suggested that it is more satisfacory to attempt to correlate the inertial frames with observable features of the universe. In particular Berkeley and Mach maintained that inertial frames are those which are unaccelerated relative to the "fixed stars", that is, relative to a suitably defined mean of all the matter in the universe. This statement is usually known as Mach's principle.

A different way to understand it is like this: imagine that for some reason you're tethered to a few other people (maybe you're going rock-climbing or something). Your group will have some average movement and anybody who deviates too much from it will get a yank from the ropes tied around their waist. Now imagine you're tethered to some ridiculous number of other people, say a billion trillion. Each one of these people is connected to you and you to them by your rope (quite a few ropes to have tied to your waist, I know). Again, the group as a whole will have some average movement and it's going to be a lot more difficult to deviate from that movement. We might define a "rest frame" to be one in which you're not getting any tugs on your ropes--that is, you're in sync with the average and there's no forces (tension) acting through the ropes. That's the basic idea behind Sciama's formulation of Mach's principle, except the ropes are replaced by gravity. If you get out of sync with the rest of the universe ("accelerate") the gravitational "ropes" that tether you and the rest of the universe together start exerting forces on you. That's where inertia would come from, if you accept Mach's principle.

Later on in that paper quoted above Sciama made the point, important to our purposes in this thread, that "[this idea means] that local phenomena are strongly coupled to the universe as a whole, not just to local conditions. This in turn means that local experiments, if interpreted by means of this theory, can give us information about the structure of the universe as a whole."

Now that we've got a rough idea of what Mach's principle is I want to jump to a paper Milgrom (the MOND guy) wrote about 11 months ago called "MOND as modified inertia".

The possibly very significant fact that a0 ∼ cH0 ∼ c(/3)^ may hint at the origin of MOND, and is most probably telling us that a. MOND is an effective theory having to do with how the universe at large shapes local dynamics, and b. in a Lorentz universe (with H0 = 0, = 0) a0 = 0 and standard dynamics holds.

A few words of explanation. In MOND a0 is put forth as a new constant--a very tiny acceleration at which the effects of MOND begin to show themselves. The potentially interesting thing is the relation this number seems to have to other cosmologically important constants: c, the speed of light; H0, the Hubble constant; and , the cosmological constant thought to be accelerating the universe's expansion (though, of course, as the PhysicsWeb article points out, there may be other ways to think about that number). So the question is why this numerical coincidence should occur? Does it suggest some connection to the rest of the cosmos? Milgrom clearly thinks so, as the blue text shows--he suggests this is evidence that the universe as a whole plays a role in the local. Glancing back at the green quote from Sciama's paper the similiarity is obvious.

Anyway, Milgrom goes on in his paper to say

We can broadly classify modified theories into two classes (with the boundary not so sharply defined): In modified-gravity (MG) formulations the field equation of the gravitational field (potential, metric) is modified; the equations of motion of other degrees of freedom (DoF) in the field are not. In modified-inertia (MI) theories the opposite it true. . . With the exception of some heuristic proposals described in Milgrom (1994, 1999), all MOND theories proposed to date are of the MG type (e.g. Bekenstein & Milgrom 1984, Soussa & Woodard 2003, Bekenstein 2004, Sanders 2005).

In other words (and this is glossing over many a technical point), there are two ways to think about MOND. Either at very low accelerations we're modifying gravity itself to make gravity stronger than it'd normally be or we're modifying inertia. This second option is interesting because (1) as Milgrom points out, nobody seems to be working on it "perhaps because MI is technically more difficult to implement as a fundamental theory" and (2) it seems plausible (to me at least) at first glance that perhaps deeply probing into Mach's principle might lead to a mechanism by which very small accelerations might be noticed a bit less by the rest of the mass in the universe than are larger accelerations (that is, if you're only out of sync with the universe by about ten billionths of a meter per second squared the "ropes" tug on you a little less). Milgrom seems to feel the same way: "This would shed new light on Mach’s principle because MOND brings into account a new connection between the universe at large and inertia." Of course, it looks like right off the bat there's a few immediate contradictions that'd have to be accounted and now we have this "direct" detection of dark matter but it's intriguing nonetheless.

But that's all just wild speculation on my part so take it with a grain of salt (musing out loud, I guess). There's a lot more to that PhysicsWeb article than just MOND so go check it out. Even though it's all complicated a bit by the major dark matter discovery this week Mach's principle (and Sciama's work on it) is such an interesting notion that you have to wonder if there'd be any effects on the universe like those postulated by MOND.

Thoughts/comments/whatever on all this?

*I should point out that there are some fairly popular theories (supersymmetry being the best example) that suggest certain massive particles could and may exist in the universe--these could make good candidates for dark matter so it isn't all quite as ad hoc as it might initially seem.

[ai_guardian]

Startraveler, LOL, I read that article recently also ("NASA Finds Direct Proof of Dark Matter") and I was going to post about it too. Now I notice that it has been discussed here (your link) already, dough. My question was going to be whether it is really all that direct. You seem to have the same reservations.

With regards to inertia and MOND, I've long held the view that everything is interconnected so it does make sense that inertia would depend on all other matter (or more precisely energy/particles) in the universe.

[Watzel]

Inertia is actually part of gravity.

So what is gravity? Well since humans can only measure it and cannot explain it's source, we must conclude that it is a force that binds all physical material to anything that is part of the physical universe.

God did it as a joke really.

[Startraveler]

So what is gravity? Well since humans can only measure it and cannot explain it's source, we must conclude that it is a force that binds all physical material to anything that is part of the physical universe.

What would count as an explanation of its source, as far as you're concerned?

[Startraveler]

There's one more angle worth exploring concerning a current event of sorts: the Pioneer anomaly. Pioneers 10 and 11 were (or rather, are) historic spacecraft. Launched in the early 1970s, they explored the outer system from the gas giants out to the furthest reaches of space. In fact, Pioneer 10 was the first object made by man to leave the solar system. The mystery is that for some reason the Pioneers seem to be experiencing a small (and currently unexplained) acceleration back towards the sun (it's worth pointing out that these spacecraft are on opposite sides of the solar system).

Milgrom throws this effect into the paper quoted in my first post as a suggestion as a possible way to distinguish between a modified gravity (MG) and modified inertia (MI) interpretation of MOND (you know, if MOND turned out to be correct):

Closer to home, the Pioneer anomaly, if verified as a new-physics effect (Anderson et al. 2002), might provide a decisive test. It can be naturally explained in the context of MOND as MI but is difficult to explain in the context of a MG theory (Milgrom 2002): The Pioneer anomaly has no match in planetary motions for which a constant, unmodelled acceleration of the magnitude shown by the spacecraft is ruled out by a large margin. The planets probe heliocentric radii smaller than where the Pioneer anomaly has been found. So a MG theory may still have a little leeway by having the anomaly set in rather abruptly with distance just at the interim heliocentric radii (e.g., Sanders 2005). A MI explanation will build on the fact that the orbits of the spacecraft differ greatly from those of the planets: the former are close to linear and unbound, the latter quasi circular and bound. It is intriguing in this connection that the analysis for Pioneer 11 (Anderson et al. 2002) shows an onset of the anomaly just around the time where the spacecraft was kicked from a bound, nearly elliptical orbit to the unbound, almost linear orbit on which it is now (the corresponding event for Pioneer 10 is not covered). The onset still wants verification, but if real, it would be a signature of MI.

A potentially very interesting facet is the apparent magnitude of the Pioneers' unexpected acceleration--it's on the order of a0, the tiny fundamental acceleration scale originally proposed by Milgrom in formulating MOND (and this number, as pointed out in my original post, is itself on the order of cH, the product of the speed of light and the Hubble constant). Sort of an odd numerical coincidence.

Anyway, NewScientist had an article on the Pioneer anomaly earlier this month:

The key to the Pioneer anomaly?

The mystery surrounding the Pioneer anomaly has deepened. The unexplained changes in acceleration seen in NASA's Pioneer 10 and 11 probes could be related to similarly odd shifts in the speed of other space probes, possibly pointing towards new physics.

In the 1980s, researchers at NASA noticed that the Pioneer 11 spacecraft was slowing down more quickly than expected as it neared the edge of the solar system. The effect persisted until NASA lost touch with the spacecraft in 1995. A similar effect showed up in the Pioneer 10 spacecraft, which was sent in the opposite direction. Finally, in 1998, John Anderson, then at the Jet Propulsion Laboratory (JPL) in Pasadena, California, and his colleagues made their finding public.

Since then, other space probes have exhibited unexplained changes in speed. When NASA's Galileo and NEAR spacecraft and ESA's Rosetta flew past Earth, they showed bigger than expected boosts in speed. The largest anomaly was recorded for NEAR, whose velocity changed 13 millimetres per second more than it should have. This excess is much larger than the expected errors in measurement. Anderson, who is now with Global Aerospace Corporation in Altadena, California, and his team think that the two effects might be related. They have re-analysed the Pioneer data and say that Pioneer 11's odd acceleration patterns seem to have begun right after its fly-by of Saturn in September 1979 (www.arxiv.org/ astro-ph/0608087).

The data for Pioneer 10 was not precise enough around the time of its fly-by of Jupiter to indicate whether its acceleration problems began with that encounter, says team member Michael Nieto of the Los Alamos National Laboratory in New Mexico. This may soon be remedied. JPL's Slava Turyshev recently unearthed archived data from Pioneer 10 and 11 (New Scientist, 3 June, p 46) and is reconstructing the missions in their entirety, which could help determine whether Pioneer 10's anomaly began with a fly-by too. "That's what I want to look at more precisely," says Nieto.

The researchers say that while it is possible that an overlooked effect from ordinary physics might account for the anomalies, something more exotic could also be involved. For example, the spacecraft trajectories could be influenced by the presence of dark matter in the solar system, says Nieto. Or maybe the laws of gravity need reworking. "We're just throwing it out as a possibility that the anomalies might have a single cause," says Anderson. "We thought it was really time to get the community thinking about it."

Peter Antreasian, a spacecraft navigation expert at JPL who along with Joseph Guinn first brought attention to the anomalies seen in Galileo and NEAR during their Earth fly-bys, believes that it will require a modified law of gravity or other new physics to explain it. He does not think it is connected to the Pioneer anomaly, since the force behind this seems always to point in the same direction, back towards the sun. In the Earth fly-bys, by contrast, "a directional force such as the Pioneer anomalous force would have been very evident in the radiometric data in the last few days before the approach", he says. Whatever causes this anomaly seems to make its impact just a few minutes before the closest approach to Earth, he adds.

Not everyone is convinced the Earth fly-by anomaly points to new physics. "It's like a farmer in Louisiana seeing a light in the sky and immediately screaming 'UFO!', whereas it could be a number of other things," says Myles Standish, who calculates trajectories of solar system bodies for JPL. He says he feels the Earth fly-by anomaly is almost certainly due to an error in measurement or an incomplete analysis using ordinary physics.

[Legatus Legionis]

another step that dark matter does exist. if it does exist what would happen then? would there be a change?

Edited April 1, 2007 by Kretos

[Startraveler]

I'm not sure what you mean. It might render a bit of the stuff above moot if dark matter really is present and plentiful. As for other changes, you'll have to be more specific.

[mohsen lutephy]

mond puzzle resolved by mach inertia principle (machian mond, Mohsen lutephy)

[White Crane Feather]

Necro thread