Gravity Basics for Sci-Fi Authors | Hacker News Reader

Gravity Basics for Sci-Fi Authors

dankoboldt.com

54 pointsprotomyth41 comments

I know it's basics but we really have to get rid of the bowling ball on rubber sheet or the fat man on trampoline analogies to teach GR to laypersons (http://physics.stackexchange.com/questions/3324/misused-phys...). A good analogy will teach a few most important principles of a complicated concept to a beginner, this one doesn't come close. In fact, it's very dangerous because it gives the illusion of understanding by substituting the wrong concept with the right one. This can lead to confusions like this one: http://physics.stackexchange.com/questions/142344/is-my-inte...

Yeah, welcome to all analogies. Sometimes, they cause people to form the wrong intuitions. Hell, one can argue that Newtonian physics is itself a misleading analogy that leads to confusion, since people develop incorrect intuitions about, among other things, how time and simultaneity work.

Now, if you can come up with a better analogy, fantastic. But the best science communicators in the world haven't done any better, so I'm not holding out a lot of hope for success...

I strongly disagree. There's a regime in which Newtonian gravity describes the world. There is no such regime for the rubbersheet model of GR, since the Earth's gravity is responsible, not the sheet's curvature. It's the illusion of explanation.

EDIT: I'd also remark that collapsing centuries of debate on what's a scientific theory into "everything is an analogy" is a disservice to the public: good luck distinguishing realism, structural realism, positivism, etc., if you put on the same level science popularizations and proper (albeit imperfect and incomplete) scientific theories.

Also, the science communication bit is a red herring. There are plenty of concepts that cannot be explained easily to the public. One might justify just as well going around popularizing Laffer's curve, since actual macroeconomics is impossible to explain on a napkin.

I think it's a fine way to introduce the notion that mass bends spacetime, and "gravity" is the phenomenon of traveling that curved spacetime. We can show the warping of a two-dimensional plan by projecting it into the third-dimension, giving an intuition by analogy. I don't know how to actually show warped three-dimensional space, since we can't project into into a fourth-dimension.

I still disagree: the problem is not the number of dimensions, the problem is that the physics is wrong.

If one flips the rubbersheet, the geodesics are the same, but clearly now the model doesn't match our intuition. Indeed the objects are attracted by the mass because of the Earth's gravitational potential, not because of the rubbersheet curvature. The balls are following the variation in height of the sheet (in a sense a first order variation) not the curvature of it (the second order variation). The model is bending the wrong component (space, instead of time), and with the wrong sign (the geodesics are repelled by the mass).

As pointed out by Ron Maimon in this answer: http://physics.stackexchange.com/questions/1019/common-false...

a much better explanation can be offered introducing proper time and the effect of gravity on it.

"It is just as easy to explain things correctly, in terms of time slowing down near a massive object, and world-lines trying to maximize their proper time with given fixed endpoints"

Could you explain it to me this way?

A decent explanation is here: http://www.physicspages.com/2013/03/30/geodesics-paths-of-lo... (I haven't checked all the calculations though). A similar explanation is shown in Feynman's lectures:http://www.feynmanlectures.caltech.edu/II_42.html

...We can now write out the Lagrangian differential equations...

Finally, an explanation of gravity in layman's terms.

You are right, of course (although I'd argue that the term layman is poorly defined, on HN I'd expect a significant fraction of readers to know what a differential equation is).

Still, there is the kernel of the correct explanation which could probably be presented to the larger public, starting with the well known explanation for refraction in terms of minimal paths (the lifeguard trying to save a drowning man), passing to the fact that in special relativity the trajectory of the free particle maximizes the proper time, and ending up with the gravitational case.

The main problem with this analogy is that the thing it's trying to explain (gravity) is tangled into the analogy (balls bend the sheet because of gravity) so it doesn't provide an independent viewpoint. On first encounter this analogy seems to lead to great enlightenment but a bit of thought reveals that it doesn't really explain anything, even in simplified terms.

It's not hard to summarize the basic tenants of GR, here is a very good attempt: http://physics.stackexchange.com/a/3018/852. For a layperson I would focus on (1), what a geodesic means (what's the shortest way to travel from NYC to London, etc.). Then I would move to (2) and say that we don't know why that is the case. This would be a nice segue into a discussion about how Physics just describes observed phenomena with equations and the explanations are iterative.

The economics version of the rubber sheet is the "law of supply and demand," which economists know is simplistic and incomplete, but still useful for giving a regular Joe the basic idea of what economics does.

The Laffer curve is just wrong on its face.

The rubbersheet economy (as a dialogue):

1. Prices move according to the law of supply and demand.

2. Right: why do they move though?

1. Simple: every hour the central government determines the current supply and demand for all goods, and computes the right price.

It looks like a market economy, the prices move in the right direction (the balls are "attracted" to each other), but the explanation is a planned economy (the effect of Earth gravity).

Also, the science communication bit is a red herring

What? It's literally the core of the conversation.

Your argument seems to be "it's impossible to accurately explain GR to people in a way they'll understand, so we shouldn't even try, and any attempt to use analogies that may lead to incorrect intuition should be abandoned".

I fundamentally disagree with that premise. It's the height of academic elitism, and presumes that perfect fidelity that few understand is more important than imperfect analogy that might allow laymen to gain some minimal insight.

Better alternative: play Kerbal Space Program for a few days. Suddenly, you get rocket science.

Aside from the simplified sphere of influence that objects have (gravity up to radius, then nothing). But I agree, KSP teaches you a lot about motion.

lack of Lagrange points is barely noticable when compared to some blunders that scifi works commit. every space opera author should land on the Mun to at least know what physics he's going to ignore.

You know, it's really complex sometimes. Here's an example.

I'm a fan of the Mass Effect game series. An important place in the games is the Citadel - a giant cylindrical space station, about 12 km in diameter, that makes its own artificial gravity by means of rotating along its axis, about 1 rotation every 3 minutes.

There are elevators inside the Citadel, taking people from one level to another. The elevators are pretty fast - about 10 meters / second is my visual estimate. So you have people going "up" or "down" inside the cylinder on these elevators all the time.

But wait. Combining the rotation of the cylinder with the radial motion of the elevators, a Coriolis-like force would manifest on anyone inside the elevator. I did the math, and it would be like the floor of the elevator would tilt at about 4% grade (slope) - not huge, but it would definitely push you around.

There's no mention of that in the game, and people in elevators are standing straight all the time. But that's not how physics would work in reality.

There's a moment in one of the games when you're taking some R&R with your buddy, and you're shooting bottles. You throw a bottle in the air, for your friend to aim at and shoot. In reality, you'll never be able to throw it straight up. Due to Citadel's spin, the bottle would always describe a shallow curve, as if wind was pushing it along the circumference of the cylinder.

Granted, this is a subtle effect. Few people would notice or care. But the point is - if you're aiming for high realism, at some point you'd probably need a science consultant to point out all these weird issues that might crop up.

Realism is hard.

"My Name is Garrus Vakarian, and this is my favourite spot on the Citadel!"

> play Kerbal Space Program for a few days. Suddenly, you get rocket science.

Seriously.

With my kids (10 and 13), we watch all sorts of videos on youtube - about space exploration, rockets, etc. I talk to them about orbital maneuvers, things like plane change, Hohmann transfer, and when they don't get it, all I have to say is "remember KSP?" And they're like "oh, yeah, that makes sense".

> Like the coin trap’s slope, the curvature of space becomes infinite at the event horizon of a black hole. So time literally stops [...] so actually you can’t reach the event horizon.

I think this is completely wrong. Isn't the curvature at the event horizon large but finite? The curvature is only infinite (in theory) at the singularity.

Yes, that part is definitely wrong. The free falling observer crosses the horizon in a finite time. It's the external obsever that see the infalling object redshifted to infinity. An the curvature scalar is finite everywhere except that at the singularity.

Correct. A safe observer far from the black hole will observe a singularity at the event horizon, but that is a coordinate singularity, not a true one. There is singularity at the event horizon for a falling observer. A falling observer will pass through the event horizon and reach the center, which is a true singularity that physics currently cannot explain.

I think you mean there no singularity for a falling observer. Given that time slows down, it is not a certainty that you'll fall through the event horizon.

There are two viewpoints:

For an outside observer: the black hole will evaporate (over many billions of years) before you ever cross the event horizon.

For the falling observer: There shouldn't be an event horizon at all. That brings the question: what happens. Occam's razor would seem to indicate that most likely you'd just keep falling.

There are various "solutions" to this problem being worked out. One is that the surface of the event horizon is actually a universe all by itself, with 3d space you can live in. Over time that space would collapse into nothing, and that would happen quickly, but not instantaneously. This space is visible from the outside of the black hole, and you can interact with it but because time goes so much faster in this space any light escaping from it would appear extremely redshifted and weak.

The OP only replaces one fiction with a slightly more accurate fiction. The OP described only of the 'spheres in a vacuum' version of physics that tends to fall apart outside the classroom.

(1) There are no spheres in realworld gravity. Earth is not round. The moon is not round. Even black holes are not round. Realworld orbits, orbits around non-round bodies, are not this predictable.

(2) For purposes of space travel there is no "out of atmosphere". There are detectable wisps of gas out almost to the moon. This is the primary reason orbits decay, especially anything close to earth. The ISS would fall out of the sky very quickly without constant correction for the atmosphere it is flying through 24/7.

Pointing out errors in science fiction is a fools errand. If they listen to you and correct all the errors that you've pointed out, someone else then shows up demanding that all their errors also be accommodated. The next thing you know Freeman Dyson is on set pointing out that the stars in your backdrop are upside down. An inaccurate piece of science fiction isn't as bad a one that claims scientific accuracy when it clearly stopped listening to the Mr Dysons half way through production.

Given that general relativity and quantum mechanics seem to have irreconcilable differences, all of science education is only replacing one fiction with a slightly more accurate fiction.

I prefer "usefully predictive" to "accurate".

That's a terrible, terrible way to put it. QM is extremely accurate and useful in its own domain. GR is extremely accurate and useful in its own domain.

We're only having problems in those domains where GR meets QM - which happen to be everyday commonplaces such as the inside of black holes, etc.

Let's not taint actual science with armchair kibitzing.

Lots of SF contains black holes however - for which OPs statement basically applies as you write yourself. Knowing the limits of current science is important I think - especially for SF authors, since this gives them some ways to have fantastical elements (i.e. powering an Alcubierre drive) while staying scientifically acurate.

"Orbital time near the surface doesn’t depend on the size of the object. If two planets or moons, or even asteroids, have density similar to earth, it will take about 90 minutes to get around in low orbit. Size doesn’t matter! (Only density and distance from the surface.)"

Density doesn't matter either (at least for objects with a mass that is a negligible fraction of the Earth's, and even if that is not the case it would be mass that is the primary factor).

"By the same token, the force of gravity scales linearly with a planet’s diameter. Half the diameter of a planet and you get half the gravitational force at the surface..."

Wait, what? Assuming the mass of the planet remains constant, wouldn't you get 4 times the gravitational force at the surface?

The linearity result assumes constant density, not constant mass.

I think the assumption is the density remains the same (rho=M/(r^3)) stays the same so GM/(r^2) becomes G rho r.

The article isn't presuming mass stays constant, but rather that density does. (That's a much more realistic assumption—a world made out of similar stuff will have similar density, for reasonable amounts of gravity)

> Assuming the mass of the planet remains constant, wouldn't you get 4 times the gravitational force at the surface?

No idea why you'd ask this question but yes.

But the original statement is wrong isn't it, if you half the diameter you 1/8 the gravity [1/8 the mass]

[edit] But you'd also be twice closer, which is 4 times the force, got it.

I have perhaps an ignorant question...

So the earth's mass essentially causes a distortion in space time which causes gravity. My question is, even to the smallest nth degree, why don't we observe other objects on earth with their own gravitational field?

For example if I take a giant ball of lead, and I move it around in a vacuum but on earth, why doesn't it act like it has its own magnetic field and cause dust (again, in a vacuum) to be disrupted as the field passes over them?

Has this effect been observed (under controlled conditions)?

We have observed the gravitational field generated by lead balls. The classic example is the Cavendish experiment [1] which is rather important historically for figuring out the value of the gravitational constant.

[1] https://en.wikipedia.org/wiki/Cavendish_experiment

Yes. https://en.wikipedia.org/wiki/Cavendish_experiment is the original.

Everything has a gravitational field, but gravity is extremely weak, so you never notice it.

Just imagine how a tiny fridge magnet can overcome the gravitational pull of the entire Earth. Scale down the Earth to the size of ordinary objects and you can get an idea of how weak gravity is.

Because every piece of mass has its own gravitational field, the Earth's total gravitational field is lumpy, not a smooth sphere. The lumps are caused by variations in the crust and mantle, like mountain ranges, valleys, and variations in rock types.

It is possible to map the lumps using a tool called a gravimeter, which is basically an extremely sensitive mass balance. This is one way in which we do observe (and use) tiny variations in gravity on Earth.

Relativity by PBS Space Time

https://www.youtube.com/playlistlist=PLsPUh22kYmNAmjsHke4pd8...

> Gravity drops on linearly inside a planet, going to zero at the center. Anything dropping through a cored planet or asteroid will bounce up and down the shaft just like a kid on a swing or a pendulum […]

…assuming the density distribution is homogeneous which is not fulfilled for Earth [1] and even more unreasonable for gas planets like Jupiter.

> So actually you can’t reach the event horizon.

As was already pointed out, this is not correct.

> The closer you get, the faster the universe behind you moves. Stars are born and die in a tick of the clock, galaxies form and collide, galactic superclusters orbit super-superclusters and before the whole universe can die

Gravity is a non-linear theory. Different solutions to the field equations cannot simply be superimposed, so aligning the time variable of a Schwarzschild spacetime (let alone of a falling observer) with the time variable of a Friedmann solution (which describes the evolution of the universe as a whole) is a priori very difficult. I would be very careful about trusting the above statement.

> Imagine the lines on a ruler getting further apart the closer you get to a gravitational object.

Oh god. This is wrong on so many levels.

> Closer to the star, distances seem longer.

Longer than where? This seems to assume that one could move a scale from one region of spacetime to another to see it grow or shrink. But this is wrong. Distances are tied to the spacetime by virtue of the metric which is a field and hence depends on where in spacetime you are. It makes absolutely no sense to compare the metric at two different points.

> The more gravity, the slower time runs.

Slower than where? Similar to above, distant observers cannot simply compare the hands on their clocks, so in general this statement makes no sense, either. The only thing one could compare are the lengths (eigentimes) of time-like curves starting and ending at the same spacetime events (like it was done in Interstellar: One person stayed in the orbit, the others went down towards the black hole and returned later).

Also, in what geometry is all this supposed to happen? The author probably assumes a Schwarzschild geometry. But in a Friedmann universe, for instance, where gravity is strong as well, time keeps passing in the same way for all observers moving along with the matter, even as the universe might collapse (and gravity might intuitively become stronger).

Conclusion: Gravity is not that simple that it can be broken down to a few easy facts.

[1]: https://en.wikipedia.org/wiki/Structure_of_the_Earth#Structu...

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