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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

#71

Post by Ancapistani »

jeremyjh wrote: post #60
phkahler wrote: post #53

Earlier quoted context omitted.

I've always wanted to know why a ball doesn't follow a beam of light if they are both following straight lines in spacetime. But even more important, if light beams are reversible under relativity (reflected off a mirror they will backtrack the same path) then light can not enter a black hole because its reversed path could allow it a way out. But then there's that whole thing of objects falling in appear to slow and…

Light is moving so much faster. In the same two seconds it crosses a much larger distance in space. The line is only straight in spacetime, not in space.

If I’m understanding, a theoretical ball thrown at 1c would follow the same path as a photon?

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

#72

Post by centimeter »

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's never an ellipse because the Earth is not a point mass.

At least classically, a sphere is indistinguishable (gravitationally) from a point mass while you're outside it. The earth is pretty sphere-ish, locally speaking.

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

#73

Post by avmich »

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…

Spherical mass can be replaced with a point mass. Earth however is not spherical (biggest deviation is polar flattening). And even then, Einstein's model, unlike Newton's, says it's not an ellipse even for a point mass.

So, moral of the story - we have to be not too pedantic.

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

#74

Post by moron4hire »

Smaug123 wrote: post #30
vbezhenar wrote: post #24

Earlier quoted context omitted.

Are we moving through time with constant speed? Or we're constantly accelerating through time?

Under special relativity, everyone and everything moves at a constant speed `c` through spacetime. If you feel like you're not moving, it's because all your speed is being put towards travelling faster through time. Conversely, if you manage to move very fast through space, the world around you will appear to speed up, because you've had to trade off some of your forward travel through time so as to travel in space;…

I've always intuitively understood this to be the reason why it would take infinite force to achieve light speed for a massive object. When we apply a physical force, it is applied in the spatial axes, so it is always perpendicular to the time axis. Acceleration is just rotating some magnitude of your fixed velocity vector out of the time axis and into the spatial axes. When your spatial velocity is apparently zero, then the component of force that is perpendicular to your velocity is large, so you achieve a large deflection. But as you rotate velocity out of time and into space, it becomes more perpendicular to time, so any force applied perpendicularly to time is now more parallel to your velocity, having a smaller component perpendicular to one's velocity. You can't rotate a vector with a parallel force.

This is also why you can't travel backwards in time through just acceleration. There is no way to impart a force perpendicular to your velocity vector when it is already perpendicular to time, giving you no way to rotate the vector to have a component that points backward in time.

So I've always wondered, whether general relativity allows for forces parallel to time, and we just don't know of any mechanism to actually do so, or if it does not cover such cases because we have no mechanism, or if it disallows it entirely.

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

#77

Post by umvi »

phkahler wrote: post #53
Smaug123 wrote: post #14

I heard an interesting question at one point: "how come, when you throw a ball up on Earth, the parabola is so strongly curved? Spacetime is nearly flat, so how can a straight line become such a steep parabola?" I'll answer this question as I understand it, but I only took four lectures of General Relativity before I gave it up in favour of computability and logic, so if there is a more intuitive and/or less wrong an…

I've always wanted to know why a ball doesn't follow a beam of light if they are both following straight lines in spacetime. But even more important, if light beams are reversible under relativity (reflected off a mirror they will backtrack the same path) then light can not enter a black hole because its reversed path could allow it a way out. But then there's that whole thing of objects falling in appear to slow and…

The difference is that light travels through space, but not time (similar to how a vertical line does not travel the x axis, only the y axis). The ball travels through both space and time.

The faster you go, the less you travel through time. Thus, if the ball were travelling at the speed of light, it would not travel through time either and would follow the same path as light.

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

#78

Post by gilgoomesh »

colordrops wrote: post #59

How is it not a force though? Regardless of curvature, a ball starts moving if you let it go without applying any force. Curvature alone can't account for that could it?

The falling object doesn't accelerate. You, standing on the ground are the one that's accelerating. You see the object as accelerating but that's an illusion due to frames of reference.

As evidence: which object feels a force on it?

You can feel the force the ground continually pushes up at you. The ground is accelerating you up. The falling object is completely idle in its inertial frame and feels nothing.

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

#79

Post by tiffanyh »

nimish wrote: post #70

Gravity is a force in the same way the centrifugal force is a force An artifact of rotating coordinate frames in one, the curvature of spacetime in the other

I think you mean centripetal force.

https://www.diffen.com/difference/Centrifugal_Force_vs_Centr...

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

#80

Post by vecter »

umvi wrote: post #22
montagg wrote: post #10

Earlier quoted context omitted.

I believe (from my limited knowledge from Interstellar ) that it’s the opposite: higher gravity environments move slower relative to lower gravity environments, which enabled the “go down to high gravity planet for a couple hours and come back and it’s ten years later” plot point in the movie. So if you’re in intergalactic space, time is actually passing very quickly in the higher gravity environment of a galaxy. But…

I don't think that is quite right. If you travelled near the speed of light and then slowed down again it would look (from your perspective) like you jumped 10 years into the future. So high gravity environments "moving slower" shouldn't result in a jump to the future upon exit. Instead I think what is happening is that massive objects actually stretch the fabric of spacetime somehow so that the closer you are to the…

> the slower you travel through both space and time

No. You are always traveling at a constant velocity through spacetime.

[0] Spacetime: https://en.wikipedia.org/wiki/Spacetime

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