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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

#181

Post by shawnz »

gabia wrote: post #159
abeppu wrote: post #140

I've seen this explained elsewhere, and it does look very cool when displayed this way. But perhaps someone with more background can explain to a lay person -- what even is a force? Why does the existence of a transformation that makes movement under a supposed force actually follow a straight line mean it's not really a force? For the other forces (e.g. electromagnetism) can we say that there's _no way_ to exhibit a…

The effect of a spacetime transformation isn't just to redefine straight lines along which particles move. It means measurements (e.g. lengths, areas, time intervals) are different depending on where you are in the spacetime. The are forces don't come with these "extra" effects - an EM field doesn't stretch and contract space. However, there are a lot of parallels between electromagnetism and relativity! Quite often…

Also a layperson here. Can you give an example of how we can tell that EM fields don't "stretch" space, but gravity does? Is it just about how light behaves in those fields or is there something more to it?

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

#182

Post by colechristensen »

abetusk wrote: post #108
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…

So if light were traveling through "slow glass" where it's speed through the medium was significantly slowed down, we would see it go in a parabola like the ball?

For example, one of the first observational confirmations of relativity was being able to observe starlight near the sun during an eclipse being slightly out of place because it had been bent by the sun’s gravity.

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

#183

Post by dreamcompiler »

thewakalix wrote: post #144
dreamcompiler wrote: post #106

Earlier quoted context omitted.

Curvature due to gravity depends entirely on mass. No mass = no spacetime curvature. In this case, the mass of the Earth is causing the curvature.

The curvature depends on the mass of the earth, but it _doesn't_ depend on the mass of the photon/ball.

The curvature does indeed depend on the ball's mass. The contribution to spacetime curvature the ball's mass brings to the table is extremely small compared to that of the earth, and the contribution that comes from the (massless) photon's energy[0] is smaller still, but they both influence the spacetime curvature.

[0] Photons bend spacetime according to GR, although as far as I know this has not been proven experimentally. We'll probably need a theory of quantum gravity to be sure.

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

#184

Post by pdonis »

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…

> 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.

Because they're following different straight lines in spacetime. Roughly speaking, if you pick a point in space and a particular direction in space from that point, there is a continuous infinity of possible straight lines in spacetime that point in that direction in space. One endpoint of that continuous infinity is the worldline of a light ray. The ball's path is somewhere in the middle of that continuous infinity.

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

#185

Post by hunterloftis »

atoav wrote: post #15
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…

This is in tune with what happens when you change the timescale in a game engine with proper physics.

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.

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

#186

Post by handol »

marta_morena_28 wrote: post #163
ncallaway wrote: post #155

Earlier quoted context omitted.

Newton's first law provides a guide: "Every object persists in its state of rest or uniform motion in a straight line unless it is compelled to change that state by forces impressed on it." So, the definition of a force as something that causes an object to change its movement from a "straight line" comes to us from Newton's laws. > Why does the existence of a transformation that makes movement under a supposed force…

So what you are saying is that if we assumed that all particles, including light are magnetic, and everything that has a mass, emits a corresponding magnetic field with a strength relative to its mass, we could not form a similar theory of "general magnetic relativity" in which the frame of reference under magnetic fields would behave in a similar way it does for gravity? That seems kinda odd. What exactly would prov…

There's no emitting magnetic fields, no diverging fields allowed. The right analogy is between mass and electric charge, only mass is limited to positive values.

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

#187

Post by colechristensen »

vbezhenar wrote: post #24
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…

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

You’re moving tough time at the speed of light.

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

#188

Post by dreamcompiler »

dreamcompiler wrote: post #31
kubanczyk wrote: post #21

Earlier quoted context omitted.

The planet's curvature is not very relevant to the article, but, yes, if an object is in a free fall at a slow speed (I mean non-orbital) its trajectory is: - parabola if you assume flat&infinite ground, - ellipsis if you assume a spherical planet (an ellipsis is crossing the planet's surface). This is Newton, not GR.

Yep. Orbits are always conic sections. Which sometimes inconveniently intersect with the surface of the thing being orbited.

More precisely, 2-body orbits are always conic sections. Once you add more bodies, orbits usually become chaotic.

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

#189

Post by pdonis »

umvi wrote: post #77
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…

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.

> The difference is that light travels through space, but not time

This is a common pop science statement, but it's not correct. A correct statement is that the concept of "speed through spacetime", which is what has to be split into "speed through space" and "speed through time" in the pop science statement, does not apply to a light ray.

In more technical language, the tangent vector to the light ray's worldline is not a unit vector, it's a null vector, and the concept of "speed through spacetime" only makes sense for a worldline whose tangent vector is a unit vector.

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

#190

Post by kens »

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…

> 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 things, it discusses some of the efforts to map the Earth's gravity field to increase missile accuracy for Trident and Minuteman missiles. I knew a physicist who worked on this.)

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