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Gravity is not a force – free-fall parabolas are straight lines in spacetime

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Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#331

Post by immmmmm »

klunger wrote: post #322
immmmmm wrote: post #315

Physicist here, gravity is a force, just a different one. Also, like everything else in physics: it depends how you observe it. For instance, electromagnetism comes from the curvature of a U(1) bundle over space time, the (local) U(1) symmetry yields electromagnetic interactions. For gravity the symmetry is the (local) Pointcaré (SO(1,3) + translations) symmetry and curvature of spacetime itself. Also gravity on Eart…

"This ultimately led [Einstein] to the realisation that gravity is best described and understood not as a physical external force like the other forces of nature but rather as a manifestation of the geometry and curvature of space-timeitself." This is in the introduction of the paper you shared...

I was trying to say three things:

1) it still somehow works like other fundamental forces since it derives from asking invariance under a local symmetry group

2) it is different from other forces since the symmetry group associated to it is directly symmetries of space-time (rather than some internal U(1) vector bundle like maxwell or SU(3) nuclear strong force)

3) in weak fields like on earth it mostly reduces to a conservative force driven by a gravitation potential (what you experience while climbing a mountain)

3 bis) like (mostly) anything in physics there is a duality i.e. there are regimes where you can consider it as a force, and there are regimes where you cant.

read the textbook, i know it's a 1000 pages but it's a great introduction :)

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#332

Post by CamperBob2 »

pdonis wrote: post #217
CamperBob2 wrote: post #204

Earlier quoted context omitted.

I wouldn't say it's incorrect at all. From the point of view of a photon, no time elapses between its the origin and destination endpoints.

> From the point of view of a photon, no time elapses between its the origin and destination endpoints. No, this is not correct. The correct statement is that the concept of "elapsed time" does not apply to a photon; it only applies to timelike worldlines, not null worldlines. To put it another way, if your statement were true, it would mean that the origin and destination events were the same point in spacetime. But…

(Shrug) You can go argue with Neil deGrasse Tyson, it's over my pay grade.

https://www.youtube.com/watch?v=5ELA3ReWQJY

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#333

Post by tarruda »

klunger wrote: post #322
immmmmm wrote: post #315

Physicist here, gravity is a force, just a different one. Also, like everything else in physics: it depends how you observe it. For instance, electromagnetism comes from the curvature of a U(1) bundle over space time, the (local) U(1) symmetry yields electromagnetic interactions. For gravity the symmetry is the (local) Pointcaré (SO(1,3) + translations) symmetry and curvature of spacetime itself. Also gravity on Eart…

"This ultimately led [Einstein] to the realisation that gravity is best described and understood not as a physical external force like the other forces of nature but rather as a manifestation of the geometry and curvature of space-timeitself." This is in the introduction of the paper you shared...

As the parent comment says, everything in physics depends on how you observe ("... best described").

Like Sean Carroll said in the Veritassium video about the "many worlds" [1], there's no such such thing as "pressure", it is just the interaction of fluid molecules. For practical purposes though, it is best described as a scalar called "pressure".

[1] https://youtu.be/kTXTPe3wahc?t=1043

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#334

Post by immmmmm »

praptak wrote: post #326
immmmmm wrote: post #315

Physicist here, gravity is a force, just a different one. Also, like everything else in physics: it depends how you observe it. For instance, electromagnetism comes from the curvature of a U(1) bundle over space time, the (local) U(1) symmetry yields electromagnetic interactions. For gravity the symmetry is the (local) Pointcaré (SO(1,3) + translations) symmetry and curvature of spacetime itself. Also gravity on Eart…

Isn't gravity somewhat like the forces that one observes in non-inertial frames of reference in classical mechanics?

umm, yes and no...

the key principle of general relativity is the equivalance principle: there is no (local) way to tell if you're being accelerated (in a spaceship for instance) or in a gravitational field. in other terms the inertial mass is the same as the gravitational mass.

this, and lorentz invariance, yields general relativity almost uniquely, so it's a very strong principle.

so yes, in some sense gravitation shift the notion of "inertial frame of reference"

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#335

Post by immmmmm »

jstanley wrote: post #330
immmmmm wrote: post #315

Physicist here, gravity is a force, just a different one. Also, like everything else in physics: it depends how you observe it. For instance, electromagnetism comes from the curvature of a U(1) bundle over space time, the (local) U(1) symmetry yields electromagnetic interactions. For gravity the symmetry is the (local) Pointcaré (SO(1,3) + translations) symmetry and curvature of spacetime itself. Also gravity on Eart…

> Physicist here, gravity is a force, just a different one. Isn't gravity an acceleration, and weight a force? Otherwise gravity would accelerate heavier objects more slowly.

suppose you have an electric field described by a potential \phi, the force is

F = - q * d\phi/dx

where q is the electric charge

now suppose you're in a gravitational potential \phi_g, the force is

F_g = - m * d\phi_g/dz

where m is the mass. as you can see it's like the newton equation, so yes looks like an acceleration :)

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#336

Post by pdkl95 »

pishpash wrote: post #317
hunterloftis wrote: post #185

Earlier quoted context omitted.

I'm not aware of any game engines that simulate general relativity / 4D spacetime. I think what you may be noticing is that, as you reduce the tick frequency of a newtonian physics simulation, parabolas become less accurate as integration error accumulates.

That's too bad, such a simulator would be great for intuition.

While we are (unfortunately) lacking general relativity simulators, a few special* relativity simulators exist:

"A Slower Speed of Light" http://gamelab.mit.edu/games/a-slower-speed-of-light/

"Velocity Raptor" https://testtubegames.com/velocityraptor.html

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#337

Post by ben_w »

jstanley wrote: post #330
immmmmm wrote: post #315

Physicist here, gravity is a force, just a different one. Also, like everything else in physics: it depends how you observe it. For instance, electromagnetism comes from the curvature of a U(1) bundle over space time, the (local) U(1) symmetry yields electromagnetic interactions. For gravity the symmetry is the (local) Pointcaré (SO(1,3) + translations) symmetry and curvature of spacetime itself. Also gravity on Eart…

> Physicist here, gravity is a force, just a different one. Isn't gravity an acceleration, and weight a force? Otherwise gravity would accelerate heavier objects more slowly.

Heavy objects are made of many light objects[0], so no, they would still accelerate at the same rate.

[0] with the exception of light, which is very light[1], but made of light particles rather than light particles.

[1] Homographs ahoy

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#338

Post by mcv »

fouronnes3 wrote: post #66
sohkamyung wrote: post #36

Earlier quoted context omitted.

Off topic, but in reality, the trajectory of a ball thrown on Earth is not a parabola, but an ellipse [1]: > under the laws of gravity, a parabola is an impossible shape for an object that's gravitationally bound to the Earth. The math simply doesn't work out. If we could design a precise enough experiment, we'd measure that projectiles on Earth make tiny deviations from the predicted parabolic path we all derived in…

It's a parabola in a uniform gravity field, an ellipse in a circular gravity field coming from a point mass. So if you want to be really pedantic, it's never an ellipse because the Earth is not a point mass. It would be equivalent to a point mass if the Earth were a perfect sphere of uniform density, but it isn't. In reality it's a potato like mass blob that's approximated by what geodesists call the "geoid". So in o…

> "It would be equivalent to a point mass if the Earth were a perfect sphere of uniform density"

Would it? Even of uniform density, the mass would not the at the core, only the center of mass would be. Most of the mass is actually closer to the surface. I'm no physicist, but I'd imagine that would have quite some impact[0] on any trajectory that crosses the surface.

And for any ball thrown at human speeds, I'd expect Earth's gravity would be much closer to a uniform gravitational field than one from a point mass.

[0] Pun not originally intended but I'm quite happy with it now.

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#339

Post by serial_dev »

immmmmm wrote: post #315

Physicist here, gravity is a force, just a different one. Also, like everything else in physics: it depends how you observe it. For instance, electromagnetism comes from the curvature of a U(1) bundle over space time, the (local) U(1) symmetry yields electromagnetic interactions. For gravity the symmetry is the (local) Pointcaré (SO(1,3) + translations) symmetry and curvature of spacetime itself. Also gravity on Eart…

Physicist (BSc) turned software developer here, I understood around 2% of your comment :)

(Thanks for the effort, though, it might just be me, in the end I changed profession for a reason)

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#340

Post by mcv »

SiVal wrote: post #253
kens wrote: post #190

Earlier quoted context omitted.

> So if you want to be really pedantic, it's never an ellipse because the Earth is not a point mass. This turns out to be not pedantic but very important if you're guiding an ICBM. And when landing on the Moon, Apollo had to deal with irregularities in the Moon's gravity due to mass concentrations, called mascons. (If you're interested in missile guidance, take a look at the book Inventing Accuracy . Among other thin…

(Ah, yes, pedantry. It has its own gravity. You can't tell me it's not a force. I can't resist its pull.) It wouldn't be an ellipse even if Earth were a point mass. The gravity of the Moon and Sun, the gravitational lumpiness in the sky, has the same effect as the gravitational lumpiness underground. The combined result may be no closer to an ellipse than it is to a parabola.

> "Ah, yes, pedantry. It has its own gravity. You can't tell me it's not a force. I can't resist its pull."

It's not a force. From the right frame of mind[0], it's just a straight line.

[0] Substituting for frame of reference.

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