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

timhutton.github.io

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

#31

Post by dreamcompiler »

kubanczyk wrote: post #21
a3w wrote: post #12

Somewhere I read that a free fall parabola does not even take into account earth's curvature. Although I cannot remember, what kind of function describes the reference system specific ``path, as a function of time''. Could this be named more correctly: Gravity is not a force – free-fall hyperbolas are straight lines in spacetime (timhutton.github.io) ?

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.

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

#33

Post by nobody9999 »

vbezhenar wrote: post #4
umvi wrote: post #3

Earlier quoted context omitted.

Great Veritasium video. So some flat earth arguments are actually correct if general relativity is correct, namely that gravity is an illusion and that the real reason we are stuck to the earth is that the earth is accelerating toward us at 9.8 m/s^2

I don't understand it. How can it accelerate towards anyone on its surface? Where does it get energy to accelerate? We generally need to burn fuel to accelerate something in the space.

My understanding of General Relativity[1] is that mass distorts space-time, so an object traveling in a "straight line" through distorted space-time will curve with that distortion.

If the object's velocity isn't enough to traverse the curved space-time, it will move toward the center of the mass generating the distortion and fall out of the sky.

If the object is traveling quickly enough, it can continue traversing the distorted space-time and orbit that mass.

If the object is traveling even more quickly, it will traverse the distorted space-time and continue on without orbiting the mass.

In all three cases, from the perspective of the object traversing the distorted space-time, it continues to travel in a straight line, as it's the space-time that's distorted.

A (flawed) analogy would be riding a bicycle between the peaks of two identically sized hills. Starting at the top of the first hill, you coast down increasing your velocity.

Once you reach the bottom of the first hill and head up the second, your velocity decreases.

If your velocity at the bottom of the first hill is too small, you'll go up the second hill and as your velocity reaches zero, you roll back toward the bottom of the hill.

You will pick up velocity and then roll back up the first hill, then down again, then back up the second, etc. until you end up stopped at the bottom of the hill. This is akin to falling to the center of the distorting mass.

If your velocity is high enough to carry you back up to the top of the second hill and then stop, you'll roll back down and get to the bottom with the same velocity you had coming down the first hill. You'll then oscillate between the tops of both hills. This is akin to orbiting the mass.

If your velocity at the bottom of the first hill is enough to carry you past the top of the second hill, you'll just keep going after reaching the top of the second hill. That's akin to flying by the mass.

It's a flawed analogy, because in a curved space-time the directional portion of the motion vector doesn't change.

As John Wheeler[0] simplified it: "Mass tells space-time how to curve, and space-time tells mass how to move."

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

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

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

#34

Post by cylon13 »

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?

We're moving through spacetime with a constant speed, so the faster you move through space, the slower you move through time.

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

#35

Post by willis936 »

shireboy wrote: post #8

I saw this and the related Veritasium video, but am still scratching my head about something. Does this mean that away from all gravity a body does not experience any time? ie a person on a spacecraft stopped in intergalactic space would not age relative to persons on planets?

It's not that the absence of gravitational fields slows time up relative to observers in more massive reference frames, it's that the presence of gravitational fields speeds up time relative to observers in other reference frames.

You would age about the same as you would in microgravity. You could get closer and closer approximations by going into Earth orbit, solar orbit, and galactic orbit. Each approximation has less gravity, so time would pass slightly slower relative to an Earthly observer at each step, but the effect diminishes.

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

#36

Post by sohkamyung »

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…

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 class: microscopic on the scale of a human, but still significant. Instead, objects thrown on Earth trace out an elliptical orbit similar to the Moon.

[1] https://www.forbes.com/sites/startswithabang/2020/03/12/we-a...

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

#37

Post by Retric »

mrfusion wrote: post #20
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 flat in the time dimension? Or what is our time size?

It’s something of a philosophical question. We tend to think of distant galaxy’s as if we are viewing them via some FTL means with a single consistent now. NASA for example tracks distant Mars probes like that rather than marking timing based on when the signal was received.

Alternatively, you can think of everything that could impact you as something of a now light cone. The second view has the universe existing as a 3D surface in 4D space time which means objects have a temporal width for each observer. That can be a really useful mathematical model.

PS: Edited the above several times for clarity.

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

#38

Post by Smaug123 »

mytailorisrich wrote: post #29
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…

> the parabola is so strongly curved? Spacetime is nearly flat, so how can a straight line become such a steep parabola? I suspect that the answer is that this is a false comparison.

Could you elaborate on why it's false?

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

#39

Post by kubanczyk »

montagg wrote: post #10
shireboy wrote: post #8

I saw this and the related Veritasium video, but am still scratching my head about something. Does this mean that away from all gravity a body does not experience any time? ie a person on a spacecraft stopped in intergalactic space would not age relative to persons on planets?

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…

> So if you’re in intergalactic space, time is actually passing very quickly in the higher gravity environment of a galaxy.

Not "very". Look up the actual equation, it's a really easy one. AFAIR for a standard stellar black hole, you'd need to be within meters from the event horizon to get any substantial time difference.

Thus the implication that Interstellar's Gargantua was an SMBH, i.e. probably the center of it's galaxy.

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

#40

Post by didibus »

I'm a bit confused, how does a 2D graph with a curved X axis work?

Does this just mean to say that if we saw things distorted with an outward curve, then something that is moving in a curve would look to be moving in a straight line?

And what's the point of such an observation?

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