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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

#231

Post by jiggawatts »

dreamcompiler wrote: post #23
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 take your point, but I think the author's main point was that because objects in free-fall merely follow spacetime geodesics, it makes calling gravity a "force" a little bogus, at least compared to the other forces. Tidal effects don't change that; tidal effects mean the spacetime curvature "over here" is different than the spacetime curvature "over there", which means the principle of equivalence isn't true in a g…

That "perspective" can be extended to other forces. E.g.: one could say that an electron taking a complex spiralling path through a magnetic field on Earth is merely following a "gravity+EM geodesic" and is actually in free fall the whole time.

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

#232

Post by umvi »

pdonis wrote: post #217
CamperBob2 wrote: post #204

Earlier quoted context omitted.

I wouldn't say it's incorrect at all. From the point of view of a photon, no time elapses between its the origin and destination endpoints.

> From the point of view of a photon, no time elapses between its the origin and destination endpoints. No, this is not correct. The correct statement is that the concept of "elapsed time" does not apply to a photon; it only applies to timelike worldlines, not null worldlines. To put it another way, if your statement were true, it would mean that the origin and destination events were the same point in spacetime. But…

It's impossible for an object with mass to go the speed of light. But you can observe what happens as you approach it:

Let's say I put you in a spaceship and accelerate you to 50% the speed of light toward the sun. From an inertial viewer's perspective you are travelling toward the sun at half the speed of light and it takes you ~16 minutes to crash into the sun. But from your perspective it only took ~14 minutes to crash into the sun[0].

Repeat the experiment except I accelerate you to .99c. From an inertial viewer's perspective you are travelling toward the sun at nearly speed of light and it takes you ~8 minutes to crash into the sun. But from your perspective it only took ~1 minute to crash into the sun.

Repeat the experiment except I accelerate you to .999c. From an inertial viewer's perspective you are travelling toward the sun at nearly speed of light and it takes you ~8 minutes to crash into the sun. But from your perspective it only took 20 seconds to crash into the sun.

Repeat the experiment except I accelerate you to .9999c. From an inertial viewer's perspective you are travelling toward the sun at nearly speed of light and it takes you ~8 minutes to crash into the sun. But from your perspective it only took 6 seconds to crash into the sun.

Repeat the experiment except I accelerate you to .99999c. From an inertial viewer's perspective you are travelling toward the sun at nearly speed of light and it takes you ~8 minutes to crash into the sun. But from your perspective it only took 2 seconds to crash into the sun.

See what's happening? As you approach the speed of light, the amount of time that elapses until you reach your destination approaches zero. So from an inertial observer's point of view, time has completely frozen for travelers approaching light speed.

[0] Using time dilation formula from this page: https://www.phy.olemiss.edu/HEP/QuarkNet/time.html

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

#233

Post by m3kw9 »

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…

When you throw a ball up and down in a moving car the ball is also parabola. You don’t need theory of general relativity to explain it.

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

#234

Post by chadlavi »

shawnz wrote: post #147
AgentME wrote: post #123

Earlier quoted context omitted.

>Or what is our time size? That's just another way of describing the total time you exist.

Your size in X, Y, Z isn't equal to the total distance you've traveled, so why would your size in t be the total time you've traveled?

your size in X, Y, Z, is how much space you occupy at once, i.e., at a fixed point on the time axis. But how would we even make sense of the notion of "size" on the time axis? How much time we take up for a fixed value in one or more of the X, Y, and Z axes?

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

#235

Post by crehn »

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;…

Is it similar to how changing FOV in a game makes the movement appear slower/faster, but in both cases the space traversed is identical?

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

#236

Post by CydeWeys »

centimeter wrote: post #72
fouronnes3 wrote: post #66

Earlier quoted context omitted.

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.

Only if the sphere has uniform density. The Earth very much does not have uniform density.

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

#237

Post by trungdq88 »

willswire wrote: post #75

Veritasium just put out a great video on this: https://www.youtube.com/watch?v=XRr1kaXKBsU

This, and the one by Vsauce [1] are the 2 best videos explain spacetime on Youtube I have seen.

[1] https://youtu.be/Xc4xYacTu-E

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

#238

Post by CydeWeys »

Ancapistani wrote: post #101
cylon13 wrote: post #34

Earlier quoted context omitted.

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

I just had another thought. The word “dimension” in this context is overloaded. We think of space being three dimensions but really it’s only one - velocity relative to a specific reference frame. Thinking of it this way, the word “spacetime” makes sense; it’s a two-dimensional system: “spatial velocity” (S) on one axis and “temporal velocity” (T) on another. Both velocities are always measured against a reference fr…

You can simplify some of your wording here. Direction-less (your "spatial") velocity is simply speed.

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

#240

Post by lopmotr »

shawnz wrote: post #147
AgentME wrote: post #123

Earlier quoted context omitted.

>Or what is our time size? That's just another way of describing the total time you exist.

Your size in X, Y, Z isn't equal to the total distance you've traveled, so why would your size in t be the total time you've traveled?

If you consider your body has extent in time, then when you move between two points in space, your body is a long worm connecting those two points. So your size in some way is related to the distance you travel in your life. But even without time, a person's size isn't really well defined anyway. Is a person wider if he stretches his arms out sideways?
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