but i feel like i almost understand it, just not quite there

(http://www.autoadmit.com/thread.php?thread_id=5580905&forum_id=2...id#47993617)

i think i finally fully understand how the curvature of spacetime caused by matter/energy results in gravity. i am now going to try to fully understand time and space dilation, beyond the superficial level i currently have

studying relativity has made me aware of just how much of my cognition is spatial in nature. this stuff is so hard to fully understand because it cannot be spatially represented since time is orthogonal to 3D space and we can only perceive 3D space. i keep running into temporary mental blocks where i can't spatially intuit my way through things because they are entirely abstract

even abstractions in normal human experience can be represented spatially in some way. our brains automatically turn logical relationships into hierarchies and tree branches, and we interpret them that way even if we don't always consciously realize we're doing so. things that are entirely and truly abstract are extremely challenging to mentally grasp

(http://www.autoadmit.com/thread.php?thread_id=5580905&forum_id=2...id#47993831)

Relativity isn’t extraordinarily difficult to wrap your mind around. If you want a real mindfuck study string theory

(http://www.autoadmit.com/thread.php?thread_id=5580905&forum_id=2...id#47993935)

it wasn't that hard to get a superficial understanding of it. i thought that i understood it but after trying to figure out how exactly gravity works and what the fuck it even is, i realized that my understanding was superficial

(http://www.autoadmit.com/thread.php?thread_id=5580905&forum_id=2...id#47993949)

it's a lot easier to understand time dilation, world lines, what "time" even is, etc when you start out with this assumption. idk why people don't start by teaching this assumption first, before anything else

(http://www.autoadmit.com/thread.php?thread_id=5580905&forum_id=2...id#47996133)

the speed of light/causality is actually a constant. it's always the same no matter what. that's how you get stuff like time dilation: for example, if you travel a greater distance (going faster through space), a stationary observer will perceive you as moving slower through time, because your speed of causality remains the same - your spatial component of your movement through spacetime increases, so your time component of your movement through spacetime must decrease

(http://www.autoadmit.com/thread.php?thread_id=5580905&forum_id=2...id#47996185)

Matter in warped spacetime moves in geodesics (gravity) and experiences time dilation

Light is a particle (photons) influenced by gravity (cannot escape a black hole)

The force acting on an accelerating object is indistinguishable from gravity (equivalence principle)

(http://www.autoadmit.com/thread.php?thread_id=5580905&forum_id=2...id#47996267)

People are still arguing about whether or not acceleration is needed for the time dilation to occur in the twin paradox. I Wikipedia’d it to check my understanding because I thought acceleration in space is what causes the dilation. Lo and behold people still can’t even agree on that

So much fraud out there everywhere

(http://www.autoadmit.com/thread.php?thread_id=5580905&forum_id=2...id#47998114)

That's where I left off, will continue later

(http://www.autoadmit.com/thread.php?thread_id=5580905&forum_id=2...id#47998168)

I understand that both twins are moving through curved spacetime, and that the curvature of spacetime is what causes their geodesics to be different lengths, which is what accounts for the time dilation at their rendezvous. But isn't acceleration (movement through the spatial component of spacetime) what causes the different length of the spaceship twin's geodesic through spacetime, relative to the stationary twin?

I am using acceleration to mean "movement through space by one body relative to another body" here. Maybe I am just misunderstanding terms

(http://www.autoadmit.com/thread.php?thread_id=5580905&forum_id=2...id#47998262)

Now if ST decelerates, reverses, and accelerates back toward Earth, then general-relativity time dilation kicks in, and both twins' measurements will agree and indicate that ST's clock has slowed and there will be no discrepancy when they reunite. Unlike constant motion, ST will actually feel those forces, which by the way are equivalent to gravity and the time dilation effect of the black hole in Insterstellar.

(http://www.autoadmit.com/thread.php?thread_id=5580905&forum_id=2...id#47998382)

When the twins reunite, ST's worldline through curved spacetime is shorter than ET's, correct? But isn't his worldline shorter *because* of his acceleration back towards ST to reunite?

(http://www.autoadmit.com/thread.php?thread_id=5580905&forum_id=2...id#47998472)

1. the time dilation happening in your first paragraph, described by special relativity. this time dilation is experienced "equally" by both ET and ST, because due to special relativity, they both perceive the same thing happening, just "reversed" for each other

2. the time dilation happening in your second paragraph, which is caused *specifically* by the *acceleration* of the spaceship of ST. because of the curvature of spacetime due to ST's acceleration, his worldline is shorter, and when he reunites with ET, their clocks agree that less time has passed for ST relative to ET

the source of my confusion is that the thought experiment actually describes two different time dilation phenomena, with two separate things happening, but the explainers i've read seem to conflate the two, or at least i think they are

is this correct? if so, imo people should put more emphasis on the TURNAROUND of ST, which means that he HAS to be accelerating, which is absolute, compared to his trip "away" from ET in (1), during which he is not

(http://www.autoadmit.com/thread.php?thread_id=5580905&forum_id=2...id#48000286)

"However, Petkov (2009)[6] and Franklin (2009)[3] interpret this paradox differently. They agreed with the result that the string will break due to unequal accelerations in the rocket frames, which causes the rest length between them to increase (see the Minkowski diagram in the analysis section). However, they denied the idea that those stresses are caused by length contraction in S. This is because, in their opinion, length contraction has no "physical reality", but is merely the result of a Lorentz transformation, i.e. a rotation in four-dimensional space which by itself can never cause any stress at all. Thus the occurrence of such stresses in all reference frames including S and the breaking of the string is supposed to be the effect of relativistic acceleration alone.[3][6]"

i agree that the string should break due to the unequal accelerations: because the rockets are each in their own reference frame, at different positions in space, their accelerations will not happen simultaneously and thus their accelerations will be different and the string will break

but the claims that the string will break due to "length contraction" seem incorrect. length contraction isn't actually a real physical phenomenon, no? it doesn't affect matter. it's only an observeable phenomenon by an observer, caused by the fact that the speed of causality/light is a constant. it doesn't actually change the physical shape of matter - thus, it can't cause the string to break

(http://www.autoadmit.com/thread.php?thread_id=5580905&forum_id=2...id#48002285)

https://physicsdetective.com/articles/

Just to be clear I'm a retard, and don't know enough to say what's right or wrong, and you shouldn't care anyway because, again, I'm retarded. Just thought it was interesting reading

(http://www.autoadmit.com/thread.php?thread_id=5580905&forum_id=2...id#48004051)

Still going to try to understand at least the basics though. Physicists seem to be a lot more confident about QM than relativity, considering they're contradictory, and that seems significant

(http://www.autoadmit.com/thread.php?thread_id=5580905&forum_id=2...id#48009345)

MTW's Gravitation is the best general intro I've found.

The conceptual core is tensor analysis on manifolds, but a pure math approach (vs. MTW) to that subject is very difficult for me.

(http://www.autoadmit.com/thread.php?thread_id=5580905&forum_id=2...id#48004176)