Hacker News Reader

Comment by noman-land | Hacker News Reader

Doesn't mass bend spacetime (do we know why? No idea) and cause matter to "fall" into the gravity well?

Maybe? That's one theory - but what is "spacetime", and what does it mean to "bend", or "fall into" something like that? In many ways we've just given things names as if that suddenly means they're understood.

And even then how can that be measured and proven vs other theories? Is it some other mechanism that simplifies to "close enough" that it measures similarly? We didn't really see the effects of relativity until we got to a sufficient accuracy of measurement, Newtonian mechanics was sufficient to explain things to the accuracy they could reproduce for a very long time.

Einstein couldn't have done anything like what he published if he didn't have evidence from new (at the time) equipment suggesting there was something wrong with the current model. And then testing proposed new models against those same measurements.

I've always been a bit flummoxed we haven't expanded a ton on this given how long it's been.

I'm not sure if it's wrong or right, and not smart enough to posit much, other than it -feels- wrong. But it wouldn't take a ton to convince me otherwise.

You'd think by now we'd have more supporting evidence of such a concept.

Do you mean evidence for general relativity? Because there's a lot: gravitational waves, black holes, gravitational redshift, the bending of light by gravity, the expansion (or contraction, depending on density) of the universe, are all new phenomena predicted by GR and experimentally verified

Oh I meant expanded it down, if that makes any sense, applying it to more things that we'd normally learn in high school.

At least in my case, you're taught gravity as this standalone force, and even the Newtonian idea in high school. Not until later college do they then throw that away and go into gr and the ideas you mention.

Though I guess this is more a failing of public education than science at large.

Ah, right. I would guess that's because it's just a much more complicated theory, and is well-approximated by Newtonian gravity for weak fields, e.g. like in the solar system. So applying GR to more everyday phenomena would just be a much more complicated way of saying almost the same thing.

GR is written in the language of differential geometry, and before even beginning you need a good grasp of Newtonian gravity, special relativity, multivariable calculus, and ideally electromagnetism too, so it needs a fair bit of preparation. And in fact the methods of Newtonian mechanics aren't thrown away, but incorporated into the more general framework. In that sense Newtonian mechanics is a conceptual foundation for GR, so that's why it's still taught first at school

> In many ways we've just given things names as if that suddenly means they're understood.

The jargon term for this is "dormitive potency" or, more originally, "dormitive virtue".

https://en.wiktionary.org/wiki/dormitive_virtue

Newton's theory of gravitation did not correctly predict the orbit of Mercury. Einsteins theory of gravitation (General Relativity) does.

If there was a known counterexample to Newton's theory of gravitation, then why was Newton's theory of gravitation accepted at the time?

When something works 99% of the time, you don’t throw it out until an alternative appears. And even then keep it around when it is simpler.

It was less of a counterexample and more of an inaccuracy. It wasn't immediately obvious as to whether the theory was at fault or our measurements or even knowledge of celestial objects (e.g. maybe Mercury had some nearby object that was changing its orbit).

Also, there wasn't any alternative, so a theory that explains almost everything is going to be accepted. Modern theories are also accepted if they explain things with more accuracy or over wider ranges than alternatives - often it's the shortcomings of theories that gives us clues as to a better theory. (e.g. the ultraviolet catastrophe)

Exactly - mercury's orbit was only really plotted accurately enough to show the discrepancies in the second half of the 19th century.

And then you need other examples to test new theory predictions on as they come about.

I think it’s kinda more that (in 3D with time moving at a constant rate) space “falls” into the gravity well, and matter goes with it. In 4D this looks like spacetime being bent.

The "river model" you mean isn't very general, as one eventually becomes interested gravitating systems where there isn't a suitable congruence, e.g. in close binary compact objects. In such systems, one has to add terms analogous to turbulence, frustrating calculability (and the development of relativistic intuition). It also doesn't deal well with tides: for example, Schwarzschild infaller worldlines (even on a body like the moon, where there is no horizon) on widely separated radial trajectories converge in a way that is unlike the confluences of rivers and their tributaries. These models really only assist in understanding a single (spatial) radial line with possibly multiple successive "rafts" of matter bound to it (at different times), and in a set of PG-like coordinates useful for a particular distant observer. From there one symmetrizes: all observers and all radial lines are identical (speherical symmetry) and successive "rafts" all take the same radial line (static spacetime). Without this symmetrization, a black hole is an infinite number of slightly different rivers, and then you might as well solve the equations of motion in the standard way.

For understanding a handful of highly symmetrical systems, it might help a student understand some intuitions about what Killing vector fields and congruences (notably those made by choosing the velocity vector field of a set of geodesics) are, and tends to lead into an investigation of what the shift vector in a 3+1 decomposition represents.

For calculating things like the spherical orbits around or the photon surface of a real black hole like our galaxy's central Sgr A*, the river model seems outright unhelpful. For example, how does a river model help to understand https://duetosymmetry.com/tool/kerr-circular-photon-orbits/ ?

> time moving at a constant rate

This is another way of saying slicing of a Lorentzian (4d) spacetime into non-overlapping spaces organized along an arbitrarily chosen future-directed non-spacelike worldline. That is, this is a 3+1 slicing. We can slice along your worldline, or on that of a neutral hydrogen atom floating in intergalactic space, or on that of a high-energy cosmic ray, or on that of a CMB photon. It's arbitrary, and each can give markedly different spatial slices through the same spacetime (in particular particle counts on slices will differ where the choices of index axes are anywhere accelerated with respect to one another).

When we decompose in this way, and take an <https://en.wikipedia.org/wiki/ADM_formalism> approach, we will tend to think of the shift vector as how we associate a point one one slice (everywhere in space at a coordinate instant in the spacetime) with its successor slice (everywhere in space at the next coordinate instant int he spacetime), which is helpful when spacetimes expand or contract in one or more spatial directions along the arbitrarily chosen time axis.

Braeck & Gron 2012 have a good bit of pedagogy about the river analogy and a fine set of references <https://arxiv.org/abs/1204.0419> and of course point to Hamilton & Lisle 2008, as originators of the analogy <https://arxiv.org/abs/gr-qc/0411060>.

Reply on news.ycombinator.com