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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

#301

Post by edem »

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…

Think about this. You're always travelling through spacetime with a constant speed (the speed of causality == the speed of light). This is your 4 vector because it has 4 components: x, y, z, t. Therefore the faster you go in one dimension (say, x), the slower you go in the other dimensions. The dimension that's affected the most by the warping of spacetime is time (t) in most cases, because you're moving much slower in the other 3. As you go faster your path becomes less warped. This is why the faster your ball is, the less curved its path look like. This also explains why objects with zero x/y/z speed fall straight towards the object that causes the warping: only t remains from your 4 vector so you're essentially moving through spacetime with the speed of causality (light) --> you fall straight down.

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

#303

Post by ivalm »

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…

I think a big difference is that other forces (electroweak, strong) can be thought as mediated by exchange of some virtual bosons. Quantum gravity would use gravitons, but this isn’t how GR works.

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

#304

Post by edem »

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…

It all depends on your frame of reference. From the ligth beam's view nothing happens, it just falls into the black hole. In fact the light beam never experiences time as it travels with the speed of causality.

From the reference of the outside observer the light emitted at the event horizon will forever try to leave it, but as spacetime itself casdades into the hole at the speed of light (at the horizon) this light will get redshifted until you can't see it anymore. This doesn't mean that the light you shoot into the hole never reaches the singularity. It just means that the light emitted at the event horizon will struggle forever to get out of the insane warp. Think about this: if you're walking on a conveyor belt with a constant speed `n` in the opposite direction and the belt itself is moving with a constant speed `n` you'll never make progress. This is what happens at the event horizon.

Light beams are not reversible. If you use a mirror they won't travel back in time, they will just change course. They will never go back in time.

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

#307

Post by edem »

wch wrote: post #141
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…

On human scales, the time dimension is much "bigger" than the space dimensions... This is really interesting, and it made me wonder how to convert between space and time. I mean, one meter up is equivalent in magnitude to one meter forward, is equivalent to one meter to the right. Is _c_ the conversion between space and time? In other words, is 300 million meters equivalent in magnitude to one second of time?

It is bigger only because you travel slowly in the spacial dimensions. You always travel thorugh spacetime with a constant speed (the speed of light). What happens is that you're usually going with 460 m/s (as Earth revolves around the Sun) and this is not really comparable to your `t` speed in the x/y/z/t coordinate system. So when you are still your speed is something like 230/230/0/299.791.998.

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

#308

Post by edem »

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.

Light also travels through time it just never makes progress. It still has a 4 vector (x, y, z, t) is is just that its `t` component is zero.

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

#309

Post by thewakalix »

dreamcompiler wrote: post #183
thewakalix wrote: post #144

Earlier quoted context omitted.

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 experime…

I’d think that the curvature of spacetime due to the ball’s mass wouldn’t affect the ball’s trajectory, for similar reasons as why the electric field from a charged particle doesn’t move the particle itself.

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

#310

Post by BlackFly »

amelius wrote: post #115
crazygringo wrote: post #90

I'm curious, how does the "gravity is not a force" viewpoint relate to the hypothesized graviton particle [1]? Are they incompatible viewpoints, or just different perspectives on the same thing? (E.g. are gravitons hypothesized to disappear depending on frame of reference?) I'm assuming they're incompatible (that we need the theory of everything [2] to reconcile them) but would love to know if there's something I'm m…

As you may know, one of the great problems in physics is to unite relativity and quantum mechanics. It happens to be that the graviton is a concept from QM and "gravity is not a force" is a concept that lives in the theory of relativity.

Yeah, I always found the assumption that QM was more correct than GR to be a bit odd. One of the outcomes of the geometric approach to gravity is the total lack of anti-gravity: there is simply no such thing as an anti-geodesic. The lesson of quantum field theory to me was that observables are operators on fields and not simple scalars evolving in time. General relativity is quite similar in that respect.
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