Equivalence principle of general relativity holds even at gravitational extremes
blogs.discovermagazine.com
blogs.discovermagazine.com
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 gravity, do you nevertheless fall at the same rate? i.e. does gravity affect the energy that itself imbues? The conclusion is consistent with "yes."
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
IOW, if gravity were solely a deformation of space-time, then it would not add inertia? Or am I missing or misunderstanding something?
No, it means that, heuristically, your local definition of "energy" and your local definition of "inertia" are both determined by the geometry of spacetime, i.e., by the same thing. That's why they have to match.
https://www.nist.gov/news-events/news/2013/08/nist-ytterbium...
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 cannonball. Would you expect it to fall faster?
You can come up with all sorts of theories to explain phenomena. It's pretty hard to deduce the underlying rule from observation. But it's pretty easy to explain the phenomenon once you know the underlying rule.
What was new and interesting was the use of "0" as a place holder to allow decimal number representation.
Without proper notions of force, gravity, mass, density, and the form of the laws of gravity, surely you realize that the answer to your hypothetical is not trivial. This was kind of the whole point of Principia.
And it's a question that Newton could easily have asked, as far as I can tell.
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 were quite capable of asking the question, "do heavier objects fall faster?" without being led astray by an incomplete notion of "object." In other words, the problem is conceptual, not semantic. The Aristotelian - again, the dominant framework back then - was instead led astray by the notion that all objects had a "natural" tendency to move towards the center of the Earth, and that this tendency was stronger for heavier objects. This worldview had a very long history, and a fair amount of evidence (such as it was) to back it up.
In this context, what matters is not the distinct objects but instead what properties influence their dynamics. It should be clear then why it was necessary to demonstrate the empirical truth. Many plausible theories had emerged, including the prevailing Aristotelian one, which accounted for the differences in, say, a lead weight falling versus a feather. Or, to get back to your original example, the Aristotelian would have answered, probably confidently, that yes, your chain of cannonballs would fall faster than separate ones. Your (correct Newtonian) intuition is that the mere act of chaining them together should not alter them, given that the threads would not exert forces in free fall, and therefore mere mass should not alter the falling rate. But, those notions depend entirely on the Newtonian framework. "Force" and "free fall" are the undefined concepts, not "object."
A key insight was needed, namely that you could separate out different causes in the motion; in this case, gravity and air resistance. (Though, of course, "cause" is itself a thorny concept...) Galileo's experiments demonstrated the point elegantly. More formally, this resulted in the development of the notions of inertial reference frames and linearity, which underpin much of classical physics.
I hope you don't think I'm belaboring the point. Newton's revolution was so total, so complete, that it changed everything about how we think about physical problems. Centuries of difficult philosophical and scientific work has been condensed down into a semester of freshman physics. To us, the problem is trivial, and it is easy to think that such experiments are so trivial as to be useless. To Galileo, this would not have been the case. A single thought experiment would not have been enough back then, even though it suffices now.
Reading Wikipedia to find which theories are (or were) the alternatives which assumed that principle not to hold:
"The strong equivalence principle": "The first part is a version of the weak equivalence principle" "The second part is the Einstein equivalence principle (with the same definition of "local"), restated to allow gravitational experiments and self-gravitating bodies."
"This is the only form of the equivalence principle that applies to self-gravitating objects (such as stars), which have substantial internal gravitational interactions. It requires that the gravitational constant be the same everywhere in the universe and is incompatible with a fifth force. It is much more restrictive than the Einstein equivalence principle."
"Einstein's theory of general relativity (including the cosmological constant) is thought to be the only theory of gravity that satisfies the strong equivalence principle. A number of alternative theories, such as Brans–Dicke theory, satisfy only the Einstein equivalence principle." (1)
So it seems that "Brans–Dicke theory" and similar are ruled out by this observation, that is that the following line from one Wikipedia page can't remain:
"At present, both Brans–Dicke theory and general relativity are generally held to be in agreement with observation."(2)
But note that the authors of (0) don't claim that the alternative is completely impossible, but that they have measured even bigger space where the "strong equivalence principle" holds, compared to all measured up to now:
"our limit on the strong-field Nordtvedt parameter, which measures violation of the universality of free fall, is a factor of ten smaller than that obtained from (weak-field) Solar System tests"(0)
That is, of course, a success, as every scientific and measured increase of "known" is. Note that other "Solar System" tests mentioned in (0) are also very new, from this year. Also: the parameter is "a factor of almost a thousand smaller than that obtained from other strong-field tests"!
The article from Nature, of course more scientific that the OP on HN (currently: from discovermagazine.com), ends with:
"Although the [scalar–tensor] theories are not completely quashed, their hopes for validity have been made that much fainter."(4)
0) https://www.nature.com/articles/s41586-018-0265-1
1) https://en.wikipedia.org/wiki/Equivalence_principle#The_stro...
2) https://en.wikipedia.org/wiki/Brans%E2%80%93Dicke_theory
3) https://journals.aps.org/prd/abstract/10.1103/PhysRevD.48.34...
A gravitational constant that is the same
everywhere in the universe and is incompatible
with a fifth force.
As a constant, that means that its invariance is significant, in the same way the speed of light is significant. There is some externality pegging the phenomena we notice, at the value we observe. Perhaps some sort of Planck-level absolute fact, which is irreducible in the same way that the concept of color doesn't exist very much beneath 400 nanometers (violet/near-ultraviolet), since color is only an abstraction of our eyeballs and the language we use to describe our sensations.
Glancing at some of the other things you've said in the thread, you seem to be convinced that some waves, like sound waves, are somehow illusory. Let me assure you, there is nothing illusory about wave phenomena, both in general and with gravitational waves in particular. Anything that produces wave-like phenomena can be said to radiate emissions, to paraphrase, and in many cases, there is nothing really more "fundamental" than the wave.
As for the concept of color, I suppose it depends on what you mean by color. Color as defined by the wavelength/frequency of light is perfectly well defined outside of the visible spectrum. As a mental concept, I don't see why it is "irreducible." I suppose you are attempting to say that the universal speed of light is somehow fundamental... but in the same way that a "redder" red is impossible? This is a dubious analogy. It confuses the limitations of the mind with fundamental physics.
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 constituents of the air are set in motion relative to one another. They get closer, they move apart, the changes occur at different places in the medium, at different times, and do so at a certain velocity, in sequence as interactions are forced upon the medium.
Indeed, the reason sound waves travel at the speeds we observe, is because that's how fast the very molecules themselves, comprising the air, are moving at the temperature and pressure of the environment.
Meanwhile, what color is a beam with a wavelength of one nanometer? Would you characterize the color as "soft x-ray"?
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.
But then gravity changes would be felt instantaneously rather than propagating at the speed of light.
From Wikipedia:
Light spots and shadows
https://en.wikipedia.org/wiki/Faster-than-light
Of course, the shadow must already be cast, in a continuous stream of uniquitous photons, which all need to be arriving upon the reflective surface at the speed of light, before the shadow can transit the surface within the area of effect.
At best, only the destruction of matter can move at the speed of light, so a reduction of gravity may propagate, as fast as the dispersal of the dematerialization and subsequent radiation.
Accumulation of mass as a knock-on pile-up of massive particles would need to be studied, to assess how quickly the shadow of newly created matter can induce its respective gravitational phenomenon. Figure star nurseries and supernovae events (and similar generative or cataclysmic reactions) would be the place to look. LIGO studies try to do exactly that, but the investigators seem to relish conflating an interpretation that favors signal transmission, and thus "particle/wave duality" because math.
Gravity-as-a-wave, meanwhile would be sort of like an illusory sound-as-a-wave being a byproduct of kinetic energy in a material aggregate serving as a bystander medium of propagation. Sound is not it's own "force" although we can readily recognize the phenomenon as a principle that behaves with similar attributes, parameters and effects as observed elsewhere, in other fundamental systems.
That LIGO instruments can detect gravitational influence in one part of the apparatus, before the other part of the apparatus registers the phenomenon, is really not unlike saying dominos demonstrate gravitational waves, because toppling the first domino does not topple the last domino instantaneously.
That photons can be influenced by a side-effect of material accumulation, bending or altering their path of travel probably says something about the photon or the environment being travelled through, more than it does about space and time.
But the environment they travel through is space and time.
Semantic in the sense that the word "environment" is a loaded term.
I'll offer this much: photons are particles. As particles, we know them to be part-time resident constituents of massive objects. That massive objects are representative of large quantities of energy trapped and oscillating in bounded standing waveforms.
We know that the empty vacuum of space really is mostly void, but also that a lot of photons (particles) are still traversing the void quite a bit.
So, space/time, while an empty void, where phenomena transit or conduct themselves theough said empty medium, is still an environment with varying concentrations of activity.
If an neutron manages to be ejected from a supernova, and is directed toward our solar syatem, and is influenced to fall toward the sun, but, miraculously passes straight through the sun, without colliding with any other particles, only to travel onward toward the center of the galaxy, landing in a supermassive black hole some millennia from now, what would you say about the environment this neutron experienced as it fortuitously passed through the center of the sun, without experiencing any collisions?
Would to rob it of all the other qualities, and just label it space and time? Or would you refer to it as an environment, with activity transpiring, in addition to be also being a realm of space and time?
Photons are also waves in the EM field.
> As particles, we know them to be part-time resident constituents of massive objects.
I don't think you can say we know that without explain what that means. In no part of physics do we discuss part-time resident constituents.
Your comments use a lot of terms that seem to be of your own creation. Unfortunately, these terms make it hard for your points to be understood because they lack the shared naming conventions that the field of physics uses to discuss these phenomena. Standard naming conventions, both in programming and physics, are enormously important in conveying ideas between people.
The whole point of the paper is studying the effect of gravity on gravitational self-energy, i.e. NOT matter. You'll find no "matter term" in Einstein's equations.
In the observable universe (regardless of theories and expressions penned on paper) gravitational forces are always induced by massive material objects, including the remnant artifacts of deceased stars. To suggest otherwise is to walrus the conversation.
Being a theoretical hypothesis, formed to explain observations, it remains a side-effect of accounting and inference, and has not been located directly.
Show me why you believe it is a thing. Show me where you have found it. Tell me why it isn't actually matter.
Amazing they can measure it that accurately