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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

#61

Post by Smaug123 »

c06n wrote: post #28
pininja wrote: post #2

The video for this page provides great context https://youtu.be/XRr1kaXKBsU

I do not understand how you can have acceleration without changing position (at 10:06). Acceleration is the derivative of speed, which is the derivative of position change. If the position change is zero, how can the acceleration be non-zero?

Position is not an absolute notion: you need to answer "position with respect to what?".

If the thing you're measuring position against is also accelerating, then you need to apply some acceleration of your own to stay still with respect to it.

The terms you want to look up are "proper acceleration" and "coordinate acceleration". The curvature of spacetime means the thing I'm measuring position against is moving relative to me (c.f. the example of two people walking in parallel across the Earth, nevertheless eventually meeting: the curvature means that even though neither of them is measuring an acceleration, nevertheless they are accelerating towards each other), so I need to have some internal ("proper") acceleration of my own to counteract the fact that our geodesics are moving away from each other.

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

#62

Post by didibus »

frutiger wrote: post #6

True gravitational force is something that can’t be transformed away by an arbitrary choice of frame (even an accelerating one). As a brief example, consider two objects in downwards free fall toward the centre of some massive object. Since they head towards the centre, in a free falling frame the two objects actually get closer to each other until they collide as they reach the centre. This is known as the tidal eff…

I'm super layman in all this, but I think the word force here refers to the Newton's force. Which experimentally was shown to not properly predict the effect of gravity, where as seeing gravity as a distortion of spacetime instead of as a acceleration force applied to the objects, did predict accurately the trajectory in experiments.

You can call both a force in the generic dictionary definition of force. Because obviously it's crazy that something can be so powerful as to distort spacetime itself. But gravity wouldn't be a force in the Newton sense of being something that affects the acceleration of an object.

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

#63

Post by maxcan »

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…

They both follow straight lines but unless you have a really really really strong arm, the baseball is “moving” across far more time than the ray of light. So if it “experiences” much more gravitational effect from the larger swath of space time it covers.

Using quotes since terms are more metaphorical than exact.

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

#65

Post by aeternum »

didibus wrote: post #40

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?

The polar or cylindrical coordinate systems are examples of graphs that can be though of as having a curved x-axis.

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

#66

Post by fouronnes3 »

sohkamyung wrote: post #36
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…

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 order of approximations the path of a ball thrown on earth is a parabola -> ellipse -> numerical integration of 6-dof initial conditions and spherical harmonics approximation of the earth gravity field.

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

#67

Post by doomrobo »

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?

When you are at rest on the surface of the earth, you’re actually accelerating. I barely understand it but veritasium explains it in the newest vid

https://youtu.be/XRr1kaXKBsU

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

#68

Post by saagarjha »

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?

In general, it is convenient to assume that forces exist. However, the model presented here shows that you can instead dispense of the need for there to be a force and show that the apparent acceleration is just the object moving along its curved path in spacetime. You could consider it as if the curvature itself making it look like there are forces.

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

#69

Post by tim_hutton »

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?

An object at rest is still travelling through time. In fact it continues to travel at the same speed through spacetime when you let it go. It's just that spacetime is distorted such that the straight line takes it across space too, as seen in the inertial frame on the right.
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