If inertial mass and gravitational mass could be different, what sort of effects would that have? If we were able to make a material with much more mass of one kind than the other, what sort of things would be possible?
This is something I hadn't thought through before and made my morning bus ride substantially more interesting :)
I'm moving this disclaimer to the beginning, as I don't want anyone to get too excited: We haven't observed differences between the two yet, at a level of a part in 10^13. The following outcomes would only be possible with a different sort of matter than what we're aware of.
Energy is still conserved, so there aren't any perpetual motion machines that result. Such materials would fall differently--both in terms of acceleration and direction. (The later is because objects are also subject to inertial "forces", e.g. centrifugal force, Coriolis force, due to us living on a rotating reference frame called the Earth.). Orbital radii for given orbital periods could be different, so you could have geostationary satellites at different distances from the Earth. You could also make objects that are harder to push than to lift, or vice versa, but I can't think of a practical application for this other than demonstrating the effect.
Special weights to place in cars/bikes/vehicles with little inertial mass, but heavy gravitational mass would improve traction but not affect acceleration (on a flat plane).
If you took the opposite to extremes, high inertial mass with low gravitational mass...remember the whole planet is moving quite quickly! The reason it sticks together is everything is moving relative to everything else. So, such a material would likely not be able to exist free-standing on the planets surface, it'd be ripped away by inertia. It'd make an interesting fuel for lift off if it could be harnessed.
If you had "pure" inertial mass, seems like you could make a "free" energy device that works off the Earth's rotation - you'd just need an (inertial) mass on a stick that turns an alternator around once per day. (edit: no, that would probably just settle at the highest possible orbit... hm)
Oh, also, airplanes that need almost no speed to start flying, but are still inertial-massive enough to not vibrate around on tiny bits of wind.
Imagine bullets with the impact of a 20 mm anti-materiel round that weigh as much as BB's.
Would be great for infantry. NATO nations standardized on 5.56mm in lieu of 7.62 in part because a soldier can carry more 5.56 rounds for the same weight.
> This is something I hadn't thought through before and made my morning bus ride substantially more interesting
Me too. :-)
There's no real rigour below, although there are hints about how one would grind out real predictions.
Let's start with writing down the Einstein Field Equation as G = T, where G is the Einstein tensor G_{\mu\nu} and T is the matter tensor, and where we use units that set c = G = 1, where that G is Newton's constant and with signature (-, +, +, +) and with spacetime indices ranging 0-3 and space-only indices ranging 1-3.
Next let's put ourselves into the Newtonian limit.
Let's treat M_{inertial} as T_{0}^{0} and identify the asymptotic behaviour of g_{00} (g being the metric tensor) as an energy and call that M_{gravitational}. M_i and M_g respectively for short.
There are several ways we can now break M_i = M_g, depending on how the breaking happens.
If M_i \neq M_g depends not on the composition of T but rather on position in spacetime, then people have already described modifications of G in a variety of theories that adjust different components of G (e.g. f(R) gravity). Most such models work very hard to suppress differences from General Relativity from the start of the matter era, rather than characterize the universe (or the solar system) if a difference were allowed to run. One would expect (in our Newtonian limit) to see differences in null geodesics in our solar system, with different results in the deflections of light from background stars as our orbit takes us to a position where the sun obscures their view. We would also expect different signal timing involving our various space probes as they move at various relative velocities at different and at different distances from the sun.
Where the modification of G depends on the composition of T then we need a change in spatial curvature g_{ab} (spatial indices 1-3) per unit M_i. We could do this with a bimetric (or multimetric) theory.
However, in our limit we can consider the behaviour of a mixed cloud of test particles such that neither its component nor the cloud as a whole significantly perturbs the metric.
Let's consider two classes of matter. "Heavy" matter has M_i < M_g. "Stubborn" matter has M_g > M_i.
Ordinary M_i = M_g matter has a "stubbornness" that is the "cost" of convincing it to move from one free-falling trajectory to another by the application of a force. It's "heaviness" is its tendency to follow a timelike geodesic wherever it leads in general curved spacetime.
Our mixed cloud has all three types of matter in it.
When the cloud passes near a massive object, it will separate. The "heavy" matter will spontaneously jump to geodesics that have a closer radar distance to the massive object, while the ordinary and stubborn matter will continue together.
Outside our test limit, we would prefer to say that all along the "heavy" matter was following different geodesics, i.e., we would drop the universal coupling of all matter to a single metric, and have lots of fun building a Lagrangian formulation.
Now let's crash our mixed cloud onto the surface of a planet that intercepts the cloud's free-falling trajectory directly.
Let's also employ an analogy between gravitation and electromagnetism. Muons and taus have more invariant mass than electrons, for the same charge. Stubborn matter has more M_g than ordinary matter for the same gravitational charge. Bremsstrahlung is different for electrons, muons and taus when their trajectories are altered in an electric field. Gravitational radiation will be different for ordinary matter and stubborn matter when deflected in a gravitational field. We would expect similar effects for other fundamental interactions for the stubborn matter vs normal matter. However, a stubborn matter test particle will have the same trajectory as a normal test particle, in the absence of interactions other than gravitational ones.
Continuing the analogy, a meteorite of mass m made of stubborn M_i > M_g matter falling onto a planet would penetrate more deeply into the planet's surface because it has more inertia to dump into the planet's matter through whatever interactions are available; muons and taus are more deeply penetrating than electrons because bremsstrahlung is the largest part of what decelerates them.
A meteorite of mass m made of heavy M_g > M_i matter will win a race to to the planet's surface with a normal matter meteorite, but its penetration should be the same.
I don't trust these intuitions in stronger gravity, but I'd fully expect compact objects with significant M_{i} \neq M_{g} components to be weird.
In fact, I wouldn't trust these intuitions at all. I'd really want to do an initial values formalism to see how heavy, stubborn and normal matter behave differently even in fairly trivial seeming scenarios. But that would take a very long bus ride!
A body with 1kg inertial mass experiences, from our perspective, centrifugal force due to rotation of the Earth. At the equator, this could be as great as 33 grams. If the body had gravitational mass m_g smaller than that, it would fly away upwards. If m_g was small enough, the body would escape Earth's gravity.
That's an understatement! The Super Kamiokande project alone pioneered at least a dozen technologies and improvements now used by much of the particle physics, nanotech, semiconductor fabrication, high precision sensing, and even biotech fields.
The technologies developed for water purification are especially marvelous. The Super Kamiokande is full of water that is likely the purest substance in the solar system (at a macroscopic level, although maybe there's crazy bulk gluon plasma at the center of the sun).
Yes but they shut down the experiment and partially drain the detector to let crews in for repair, maintenance, etc. In order to get it started again, there is a whole complex procedure to flush the chamber and refill it.
It seems that the part about the Neutron EDM is outdated.
As far as I know CryoEDM was deconstructed (The experiment hall was empty two years ago) [1]. Maybe there is a follow up experiment, but it has been very quiet recently.
As an current example the nEDM experiment is actively developed [2].
It depends, lots of these experiments result in better bounds on theories. LUX for example pushed down the cross-section for WIMP dark matter below the previous measurement. That in itself is an advancement, with implications on what theories for dark matter are possible.
I was at a conference this morning and heard results from a highly anticipated clinical study, with millions of dollars in NIH funding. The results were disappointing for me and some others in the field, but I think that it's better to have the negative result than to not know what is best for patients given our current techniques.
Indeed, but unfortunately the lack of positive results is not a negative result in itself... This is when explaining a megaproject to the funders starts to become harder and harder.
You could claim LHC hasn't found anything in the sense that it hasn't found anything that disagrees with the standard model. I consider finding the Higgs as we expected a letdown, though it is of course very important. There is a lot of data collection to be done so hopefully they will find something unexpected.
Interesting, I've never heard of that Mr. Clarke's quote before. I don't understand though, if we'd be alone in the universe, why would that be terrifying?
Actually the real history is far more complex than that, and involved more experiments - with confusing results. Wish I had a handy reference, but I don't.
Thanks for posting this.
As a side note, I really like the style of nautil.us and their idea of writing about a single topic from different perspectives. How is this journal not very popular? (Or is it?)
They've been criticised for twisting physics to support the conclusions they want to draw from it, even if there is an alternative and much simpler interpretation of the results, see http://www.math.columbia.edu/~woit/wordpress/?p=9053 — quote:
The group driving [Fake Physics] is small but determined, ideology-driven and well-funded by rich people with an ax to grind. The majority of the community is unwilling to take on the unpleasant and unrewarding task of challenging them. While Multiverse Fake Physics plays a large role in media coverage of fundamental physics, partially because of funding from the Templeton Foundation, there are very few actual papers on the subject and “research” in this area is a small fraction of what theorists are doing. Most physicists just hope that if they ignore this it will go away.
The Templeton Foundation, a religious organisation which has been funding them, has received a lot of criticism from the scientific community for linking science and religion.
I don't think we should dismiss Nautilus outright but I do feel like they get more traction on HN than they deserve.
Nobody "deserves" attention - it is either good content or it isn't.
I'm not surprised at all that on one hand scientists will complain about public misconceptions in science but then bitch about and nitpick any genuine effort to bring science to the masses with popular media.
I've read all all of those articles and discussions twice over and reduced it to Richard Dawkins being unhappy about Freeman Dyson being a Christian and accepting a Templeton grant, while even the most ardent critic of the Templeton foundation would still concede they fund good science.
Without clinking-through each of the links given in the article you linked to, can you help me, as a layman, summarize the criticism of Nautilus with regard to multiverse physics? Is the criticism more that they are disproportionately covering it, or is it misrepresenting it?
Related: From the blog you linked, "not even wrong" is a phrase used as an attack by experts on outsiders, but it does not need to be an attack. It can simply be: "that is outside the realm of mainstream scientific research." I think experts would do well not to be condescending, but rather more explanatory here.
Well I think it's a mixture of both, "disproportionate coverage" is a fair description, insofar as it misrepresents the activities and opinions of the research community (most of which appears to consider it hokum). I'll have to defer to the experts for the details, however, as I'm merely relaying their concerns.
I watch Sixty Symbols on Youtube and they have a number of episodes on string theory--which I've read necessarily implies extra dimensions(can't vouch for that conclusion personally), leading to multiverse theories. These episodes are straight from researchers themselves so I was surprised to read these ideas in the link provided, supporting your idea that the multiverse is hokum.
I'm confused by the suggestion that there's some kind of religious motive behind this.
Mainstream Christian apologetics is usually rather critical of multiverse theories, since they're often used as a foil against fine tuning arguments. I can't think of a Christian apologist who uses the existence of the multiverse as part of an argument for God's existence.
If you enjoy the work consider a subscription. Since the election I've really been thinking a lot about how important it is for those of us who are able to provide financial support for quality writing. I'm trying to shed the idea that content should be free by asking, "Is this worth paying for?" If it is, then pay. If it's not, move on to something that is.
As I've climbed out of the poor student phase of my life I've grown to appreciate the idea that content should be free as in freedom and not free as in $0.
It's an important distinction until we reach a utopia where people don't need $$ to live and do their writing/research etc
I really like Nautilus too! However, sometimes, they have been known to include articles that aren't very accurate. It's more of a lie of omission, in the manner of Scientific American: trying to dumb down complicated ideas sometimes makes them untrue.
Nautil.us seems to be very popular around HN at least, i do like their articles too, a lot.
But surely it isn't written for the "masses" (excuse me..).
