41–46 of 46 posts
I've heard of the new atomic clocks underway to make this ridiculously precise measurement even more precise: https://www.nist.gov/news-events/news/2013/08/nist-ytterbium...
> Galileo famously (and likely apocryphally) demonstrated the principal by dropping lead balls of different weights off the Leaning Tower of Pisa and observing them hit the ground at the same time. This never made sense to me as something you'd need to test, once the question had been considered. Imagine 1000 cannonballs all connected to each other with threads. The result is a single object with 1000x the mass of a…
Earlier quoted context omitted.
I wouldn't say that general relativity suggests that gravity is an "ambient side effect" of material presence. It means precisely that the geometry of spacetime is determined by the matter-energy content within that spacetime; and that matter moves on geodesics dictated by spacetime. I suppose that I am forced to accept that whether you think gravity is more like a shadow of matter than an active participant in dynam…
Sound waves are changes in the distribution of particles within a volume over time. The sound wave itself is a byproduct of the particles compressing closer together or stretching farther apart. You might be in love with the idea of describing an equation that frames the gradient of distribution, and the nature of it's propagation through a medium, but the sound wave is the manner in which the gaseous molecular const…
Further, not all waves require a medium. Light and gravitational waves are prominent examples. There is nothing to reduce these phenomena to, except for the fields themselves, whose form is dictated by... a wavelike solution.
While we are at it, let me disabuse you of your explanation of the sound speed. Turns out that the sound speed is a thermodynamic quantity; it is the speed at which small wavelike perturbations propagate. To properly derive the sound speed, one must linearize the Euler equations, and then adopt a thermodynamic equation of state, from which the sound speed is derived. It is, emphatically, not the speed at which molecules move.
Finally, it is obvious that you did not understand what I was driving at with respect to color. I agree wholeheartedly that we have no true color, within our minds, with which to perceive, say, soft x-rays. But this issue has to do with our own neurobiology, not fundamental physics. Comparing the two is what is problematic. There is little reason to suspect that our mental limitations have anything to do with anything but evolutionary necessity. Such limitations are categorically different than, say, the speed of light.
> Galileo famously (and likely apocryphally) demonstrated the principal by dropping lead balls of different weights off the Leaning Tower of Pisa and observing them hit the ground at the same time. This never made sense to me as something you'd need to test, once the question had been considered. Imagine 1000 cannonballs all connected to each other with threads. The result is a single object with 1000x the mass of a…
Indeed, Galileo approached at this problem with the very same thought experiment you're describing (even cited as an example of what a thought experiment is, right in the Overview section).
Earlier quoted context omitted.
I agree that it's well-established at this point. What I'm poking at is the question of "what is an object?" since that's also fundamental to the question of "do heavier objects fall faster?" And it's a question that Newton could easily have asked, as far as I can tell.
But a more complete notion of "object" isn't what solved the problem. Much of what constituted physics prior to the advances by Galileo and Newton (and many others) was essentially what was developed by Aristotle. Within the Aristotelian framework, which is what most educated people knew at the time, the concept of a distinct "object" is perfectly well defined. My point is that the natural philosophers at the time we…
This was a measurement of the Nordtvedt parameter which characterizes the difference between a gravitational field and an accelerating reference frame. If there is no difference, as GR predicts, then the parameter is 0. This experiment tests the idea that gravity itself gravitates: gravity imbues very massive bodies with gravitational binding energy, and therefore more inertia. If your inertia is increased due to gra…
I've never thought of the equivalence principle like this. I knew gravitational fields have their own mass-energy and can cause a runaway effect (black holes), but I never realized this could mean more inertia too. Neat! I'm curious about what this means as the event horizon is crossed.
> I'm curious about what this means as the event horizon is crossed
tl;dr it means General Relativity is how we answer this; more specifically, we expect that if we do a Galileo-like experiment replacing the Leaning Tower and the ground with a giant scaffold surrounding a black hole, and we carefully drop in a feather, a planet, and a neutron star, neither object's centre of mass wins a race to the horizon (it's a tie, even though the neutron-star is strongly gravitationally self-bound, and the feather is not gravitationally self-bound at all).
In practical terms, and strictly with respect to your question, the results of Archibald et al. [2018] (the work described in the original post) mostly (more below) vindicate the use of a post-Newtonian approximation (PNA) formalism as a short-cut to the results we would get from the full theory of General Relativity. At the horizon of anything but the smallest black hole[1] one expects "no drama" for a freely-falling infaller. This is not terribly surprising, as we could already make a model black hole's mass arbitrarily high, bringing the curvature at the horizon down well below the curvature we experience in laboratories here on Earth.
Clifford Will, who has written many papers on post-Newtonian methods, in (deliberately accessible to non-specialists) Will [2011] [2] writes:
The reason is a remarkable property of general relativity called the Strong Equivalence Principle (SEP). A consequence of this principle is that the internal structure of a body is “effaced,” so that the orbital motion and gravitational radiation emitted by a system of well separated bodies depend only on the total mass of each body and not on its internal structure, apart from standard tidal and spin-coupling effects. In other words, the motion of a normal star or a neutron star or a black hole depends on the body’s total mass and not on the strength of its internal gravitational fields. This behavior was already implicit in the work of Einstein, Infeld, and Hoffman, where only the exterior nearby field of each body was needed, and has been verified theoretically to at least second post-Newtonian order by more modern methods.
(So, for example, SEP means a neutron star's strong internal curvature -- the strongest we can access observationally with current technology -- doesn't cause the neutron star to radiate energy-momentum away as dipole gravitational waves.)
Archibald [2018] provides observational verification for SEP for the inner radio pulsar of the triple system to good sub-leading post-Newtonian order, improving on results from (among others) the Hulse-Taylor binary and (indirectly) LIGO.
Will [2011] uses the "xPN" notation for subleading orders, where 1PN is leading-order, 2PN is next-to-leading order, 3PN is next-to-next-to-leading order, and so forth.
A problem raised in Archibald [2018] is that the most popular formal system (the parameterized post-Newtonian (PPN) formalism) for comparing alternative theories of gravitation which may distinguish inertial mass from gravitational mass is only good to 1PN; any theory that does not match the results of Archibald [2018] at 1PN can be excluded, but anything that differs at subleading order needs a different comparison framework.
Again, this is not tremendously surprising; PPN was explicitly constructed to fully contain weak-field results (mostly within our own solar system), and the region around the central binary in Archibald [2018] is clearly not weak-field. So while this spells trouble for several families of alternatives to General Relativity (GR), there are several others where the results of breaking GR's inertial mass == gravitational mass equality appear only in the strong field limit. An extension of PPN is needed to capture the results of Archibald [2018] into a formal comparison system that may distinguish between such theories and General Relativity, assuming the compared theories match in every other PPN parameter (if they don't we can exclude one on that basis).
Or, in short, General Relativity looks really sound still, and post-Newtonian programmes are not wildly off-track.
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[1] The region near (but outside) the horizon of a small black hole is going to be dramatic for other reasons, ranging from astrophysical ones like the virtual certainty of a hot accretion structure to theoretical ones like the increasing heat of Hawking radiation as one takes the black hole mass to zero. An object like a space capsule with a person inside would be vapourized by the hot matter outside a small black hole well before reaching the horizon. As we make the mass of a black hole larger, the matter just outside the horizon -- at least on average -- is a lot cooler and sparser, so a space capsule could easily freely fall through the horizon.
[2] Proceedings of the National Academy of Sciences of the United States of America, April 12, 2011. 108 (15) 5938-5945; https://doi.org/10.1073/pnas.1103127108 Thankfully PNAS makes it freely available at http://www.pnas.org/content/108/15/5938