/sci/ - Science & Math

[metric !g.uv/9pDc. No.4339782]

Ask me anything about relativity.

>Things that ARE NOT relativity:
>quantum mechanics
>particle physics
>the Higgs mechanism
>string theory
>etc.

[Anonymous No.4339783]

>>4339782
What do you think about quantum mechanics?

[Anonymous No.4339785]

How quickly would my cousin have to be traveling to become my uncle?

[Anonymous No.4339787]

does the theory have conservation of energy?

[Anonymous No.4339791]

good intro book on tensors?

[Anonymous No.4339793]

Easiest way to learn undergrad-uni-level relativity? Any tricks you'd recommend?

[δ !ok/MkdpFbs No.4339795]

How come light speed is always constant in all frames of reference?

If you were travelling faster than light, would the flow of time reverse?

What is gravity?

If you have two black holes orbiting each other, can you time travel to the past?

What happens if you make a rip in space/time?

[Anonymous No.4339796]

how do i get a gf

[Anonymous No.4339798]

can i has quantum relativity?

[metric !g.uv/9pDc. No.4339804]

>>4339787
Yes, it has local conservation of energy and momentum:

<div class="math">\nabla_\nu T^{\mu \nu}=0</div>

[Anonymous No.4339809]

how would a body of mass M affect UHF FM, assuming i wanted to transmit tangent to and beyond said body?

[metric !g.uv/9pDc. No.4339825]

>>4339791
>>4339793
I posted this a while back:

1. First of all, you need to learn vector calculus. This is absolutely essential. You can learn it from any decent calculus book.

2. Learn the Lagrangian formulation of classical mechanics. Learn some basic calculus of variations, the least action principle, etc. As far as book recommendations go, mine would be Classical Mechanics by John Taylor. You'll probably be better off downloading it because you really only need 2-3 sections.

3. Learn special relativity. This shouldn't be to difficult, you'll just want to have a good sense of it before you start to tackle GR. My book recommendation for SR is Spacetime Physics by Taylor/Wheeler. It's the best I've come across.

4. Now you're ready for GR. Start off with A First Course in General Relativity by Schutz. It gives the best intro to tensors and differential geometry out there.

5. After you finish Schutz you'll have a pretty good sense for GR. Now you'll want to move on to Gravity: An Introduction to Einstein's General Relativity by James Hartle. This book is actually easier than Schutz from a mathematical standpoint, but it puts more emphasis on metrics and Lagrangians. You'll want to be familiar with the topics in Hartle before moving on to the tougher stuff.

6. Now you'll probably want an intermediate book. Spacetime and Geometry: An Introduction to General Relativity by Sean Carroll is my favorite Relativity book out there.

7. For advanced topics you need to get General Relativity by Robert Wald. If you can get through Wald, you'll have enough knowledge to read papers and do personal research, should you choose to.

[Anonymous No.4339826]

>>4339782

Please define newtons third law of thermo dynamics

[Anonymous No.4339837]

>>4339825
Much appreciated

[Anonymous No.4339848]

If when you are faster than someone or in a gravity field you experience time differently than them, "who" experiences time "correctly"?

[δ !ok/MkdpFbs No.4339849]

>>4339848
>Experiencing time correctly

[Anonymous No.4339863]

what (if anything) keeps you from traveling to another universe when you fall into (and out of) a charged black hole with 2 event horizons? and if something does keep you from traveling between universes, could you still reemerge in the same universe, or will you be stuck in the black hole?

[Anonymous No.4339872]

I have an extremely stupid question. However, I think it is better to ask than to be afraid of being called stupid. I am currently reading the first pages of the theory of relativity, so far, so good: The speed of light in vacuum is constant. But what if two beams of light passes in the opposite direction? wouldn't the relative speed difference be 600,000 km a second? I know that there's a good explanation...

[Anonymous No.4339881]

>>4339872

hey OP, I wanna know this too...

[metric !g.uv/9pDc. No.4339892]

>>4339795
>How come light speed is always constant in all frames of reference?

It's was implied by Maxwell's equations and Einstein postulated this to be the case. This is irrelevant though; we know c is constant in all inertial reference frames because we have measured it to be the case.

>If you were travelling faster than light, would the flow of time reverse?

No. You would experience imaginary (square root of a negative) time. Not that this is possible in the first place.

>What is gravity?

Remember Newton's first law of motion? Objects at rest stay at rest, objects in motion stay in motion at constant velocity. Objects do the same thing in curved spacetime - they follow a "straight" line through it (the path is called a geodesic). The curvature of spacetime is determined by the stress-energy tensor.

>If you have two black holes orbiting each other, can you time travel to the past?

No.

>What happens if you make a rip in space/time?

This is a nonsensical question. It is about as meaningful as asking "what's the square root of a watermelon?"

[Anonymous No.4339898]

>>4339892
>If you have two black holes orbiting each other, can you time travel to the past?
>No.
care to explain where the peer reviewed paper proving it was wrong then?

[Anonymous No.4339899]

>>4339872
>>4339881
I've thought about it some time ago, googled it and found this


In every inertial reference frame, each photon's velocity is exactly c. Photons do not have their own rest frame (any attempt to create one would violate the postulate that the laws of physics should work the same way in all inertial reference frames), so asking what the velocity of the photons is "relative to each other" is not physically meaningful--asking what B's velocity is relative to A is just another way of asking what the velocity of B is in A's rest frame. You can ask how fast the distance between them is increasing in a particular inertial reference frame, and the answer will indeed be that it's increasing at 2c, but the light-speed limit only applies to things like particles and information, it doesn't apply to concepts like "the distance between two objects".

[Anonymous No.4339904]

Can you explain light cones and the terms "time like" and "space like" paths.

Also, the universe from the reference frame of a photon is static, or all time is happening at once or what?

[Anonymous No.4339910]

>>4339899

After reading your post 4 times, I understand it! Thanks alot.

[Anonymous No.4339911]

do you think space actually "warps" or is it just a neat mathematical trick as tesla believed

[Anonymous No.4339930]

>>4339804
do you mean this as counterpart of something like global analysis? the "local" part i mean

or to put it another way, are there differences between the global and local structure with regard to the conservation principles?

[metric !g.uv/9pDc. No.4339931]

>>4339848
There is no "correctly." You just experience what you experience.

>>4339872
Yes, the spacial separation between the photons increases at 2c. This is perfectly okay. Nothing is actually moving through your reference frame at 2c.

An even better question is: If there's a spaceship traveling at 60% c relative to Earth and it fires a missile that travels at 60% c relative to the ship, doesn't the missile travel at 120%, or 1.2c relative to the Earth (seemingly violating relativity)?

And of course, the answer is no. Velocities don't add this way in relativity. You can't simply say the missile speed wrt Earth (w) is the missile speed wrt the ship (u) plus the speed of the ship wrt Earth (v): w=u+v. The correct equation is:

<div class="math">w=\frac{u+v}{1+uv/c^2}</div>

Using this always gives a result less than c.

[Anonymous No.4339933]

metric, why do you try to answer these questions when its obvious you don't have sufficient understanding of the subject matter?

[Anonymous No.4339942]

>>4339898
>care to explain where the peer reviewed paper proving it was wrong then?

The fact that you had to put the "peer reviewed" qualifier indicates you are either a troll or someone who wouldn't recognize a paper if it flew up their ass.

Where is the paper showing it IS correct? Oh, that's right, you got your education from cable tv.

[Anonymous No.4339952]

>>4339942
no, i put "peer reviewed" in from becasue most information from sci comes from shitty websites and pop-sci shows, and wanted to differentiate between that and actual science.

>Where is the paper showing it IS correct
wat? you want the page number?

[Anonymous No.4339954]

>>4339952
your problem is that you basically pulled something out of your ass and now you want peer reviewed proof that it isn't possible.

[Anonymous No.4339962]

>>4339952
>wat? you want the page number?

Again, it's clear that you are nothing but a wannabe. A real scientist would give a simple paper reference and shut me the fuck up.

[Anonymous No.4339970]

>>4339954
>pulled something out of your ass
here are some papers about ir, becasue googeling is hard
W. B. Bonnor: Closed Timelike Curves in Classical Relativity, International Journal of Modern Physics D 12, 1705-1708 (2003).
W. B. Bonnor and B. R. Steadman: The double-Kerr solution, Class. Quant. Grav. 21, 2723-2732 (2004).
W. B. Bonnor and B. R. Steadman: Exact solutions of the Einstein-Maxwell equations with closed timelike curves, Gen. Rel. Grav. 37, 1833 (2005).

[metric !g.uv/9pDc. No.4339986]

>>4339904
>Can you explain light cones and the terms "time like" and "space like" paths.

A light cone shows how far a beam of light could have gone in a given amount of time.

Events the lie within the upper light-cone can causally be causally affected by the event at the vertex. Events in the bottom part can have a causal influence on the event at the vertex. A worldline connecting the vertex to a point within the light-cone is dubbed "timelike."

Events that lie outside of the light-cone cannot be causally related. A worldline connecting the vertex to an event outside the light-cone is dubbed "spacelike."

Pic related. B is timelike and C is spacelike.

>Also, the universe from the reference frame of a photon is static, or all time is happening at once or what?

Photons don't have a rest frame. This would violate one of the postulates of relativity (light travels at c in ALL inertial frames).

>>4339911
Define "actually." The model of a curved spacetime makes good predictions to very good accuracy.

[Anonymous No.4339993]

>>4339970

Yeah, Googleing is easy. Understanding the papers is hard. Note the use of CLOSED time-like curves. Unless you are on a closed time-like curve now, you cannot use it to go to the past.

[Anonymous No.4339996]

>>4339993
so you perturb the system so that there isnt a CTC, and then once you are in the correct position, perturb it again.

[Anonymous No.4339999]

>>4339996
actualy, you dont even need to do that, you only need to perturb the system if the particle to be sent back is in freefall, if it can accelerate in some way it can travel onto the CTC

[Anonymous No.4340004]

>>4339986
soo, you are just going to skip
>>4339863

[Anonymous No.4340007]

>>4339782
Does your pic suggest there more space/time in the vicinity of Earth then in the vicinity of the satellite?

[Anonymous No.4340009]

Is the fact that the universe isn't perfectly round related to relativity, or different rate of 'propagating of the mass outwards' or what?


What is the speculation about the 'edge of the universe'? Is the light first to travel into that... something? Why am I asking it if it's not related to relativity whatsoever?

[metric !g.uv/9pDc. No.4340021]

>>4339933
Why do you believe I have insufficient understanding? What have I done/said to imply this?

>>4339970
>W. B. Bonnor: Closed Timelike Curves in Classical Relativity, International Journal of Modern Physics D 12, 1705-1708 (2003).

This is very interesting. My opinion is still that CTC's are non-physical, but this is interesting nonetheless.

>W. B. Bonnor and B. R. Steadman: The double-Kerr solution, Class. Quant. Grav. 21, 2723-2732 (2004).

"it seems that general relativity does not give a sensible result in this application to spinning objects."

They actually say this in the abstract.

>W. B. Bonnor and B. R. Steadman: Exact solutions of the Einstein-Maxwell equations with closed timelike curves, Gen. Rel. Grav. 37, 1833 (2005).

There are only CTC's if a parameter alpha is non-zero. It's unknown whether or not this is possible.

[Anonymous No.4340050]

>>4340021
yea, i listed the bottom 2 in there just to make it seem superficially more impressive.

[Anonymous No.4340054]

>>4340050
its a bad habit i have becasue universatys grade papers based on how many pages your references are.

[metric !g.uv/9pDc. No.4340056]

>>4340004
I'm not familiar with anything that was asked, so yes.

>>4340007
No.

>>4340009
>Is the fact that the universe isn't perfectly round related to relativity,

How is this a fact?

>or different rate of 'propagating of the mass outwards' or what?

I'm not really sure what your mean by this.

>What is the speculation about the 'edge of the universe'? Is the light first to travel into that... something?

If the universe is closed bounded (unknown if it actually is) then you wouldn't be able to "travel" outside of it. Think of it like pac-man, where if you go off the edge of the right side of the screen you show up on the left side.

[Anonymous No.4340092]

>>4340056
its a question about a charged black hole, you know, that use the Reissner Nordstrom metric. you dont know the Reissner Nordstrom metric? pffff.

[Anonymous No.4340109]

What if you something quite big to spin quite fast, such that the bits of the boject furthest from e axis were travelling at near-light speeds.

Then you pressed a button that made the outer most parts start folding in towards the axis.
Conservation of angular momentum would say mean that it would have to start spinning much faster. But no single part of it is allowed to travel faster than the speed of light, so would hte laws of physics change such that the folding mechanism stopped working at high speeds?

[Anonymous No.4340110]

>>4340056
>>4340007
No.
then what does the bending of space time mean?

[Anonymous No.4340118]

Hey OP!
I don't know, if this clasifies as relativity, but I've always wondered:
How come the observable universe is smaller than the actual size of the universe? Nothing can be faster than light right, so the universe can't expand faster than c, no?

[Anonymous No.4340119]

>>4340109
momentum isnt p = mv, its p = gamma*mv. and gamma goes to infinity as v increases. thus at c it would have infinite momentum.

[Anonymous No.4340124]

>>4339793
You can't cut corners with relativity. Unless you use a massive object to bend spacetime in just the right way, but that's another matter.

[Anonymous No.4340132]

what do you think of wormholes?

do you think backwards time travel is possible? I was reading somewhere that there was theory on it that used wormholes through some manifold or something that was consistent with GR.

[Anonymous No.4340165]

angular momentum is represented as a vector, with the modulus of the vector being the absolute value of angular momentum and the argument giving the orientation of the axis of rotation.

This implies that you can add angular momenta and get a resultant angular momentum vector.

Doesn;t this mean that any manner in which an object spins can be represented by a single angular momentum vector? meaning that any manner of spinning has a single invariant axis?


but consider teh diagram I drew. how can there be ne overall axis to this manner of spinning?

[metric !g.uv/9pDc. No.4340172]

>>4340092
I'm familiar, but only superficially. I've never actually worked out any problems using this metric, so I'm largely unfamiliar with its predictions.

>>4340109
L=rΛp, where Λ is the wedge product. If r is, for example, halved, then p must double due to angular momentum conservation. But p isn't simply mv in relativity, it's γmv. So v increases by less than you would think.

>>4340110
The geometry of spacetime is determine by the metric tensor. It's mathematically defined, and I probably couldn't give you a good analogy. The metric defines the scalar product, the connection, the curvature, etc.

>>4340118
Objects can't move through space faster than c, but space itself can do whatever it wants.

[metric !g.uv/9pDc. No.4340248]

>>4340132
Wormholes would require vast amounts of negative energy, and it's not even certain that this exists. Most solutions have been proven to be fundamentally unstable in one way or another.

>do you think backwards time travel is possible?
No. Too many paradoxes and no satisfying solutions.

[Anonymous No.4340295]

Hey dudes, I heard about them neutrinos and all...the article I read stated that they travelled a fair bit faster than light, what's deal with that? If the particle really had mass, why did it not increase as the particle approached the speed of light?

[Anonymous No.4340310]

How come gravity is always described using gravity?

I mean, people say that it's warping in the space-time continuum but in all the picture they show the mass as causing a dip in the sheet. For this to work there would need to be some sort of force pulling the particle to the sheet i.e gravity.

Can you please explain if I'm wrong about this, or give me a different definition that I can understand.

[Anonymous No.4340334]

>>4340310
It's a metaphor, not a definition.

[Anonymous No.4340335]

The GRAIL mission.

"The twin satellites will fly in tandem orbit, one following the other, around the Moon. As they travel, they will exchange microwave beams to measure the precise distance between the orbiters. As one satellite passes through an area of greater or weaker gravity, the distance between the two will expand or shrink slightly..."

From their point of view each satellite is traveling in a strait line at a constant speed. How can the distance between the satellites change if there is not more or less space/time for one of them to travel thru?

[Anonymous No.4340337]

>>4340334
Can you give me a better metaphor if possible?

[Anonymous No.4340339]

>>4340310
its just a way to visualize it, that is wrong. its less of a bending action and more of a squash it together action, like looking at OPs pic from the top sothat you cant see the curvature, but can see its bent in some way.

[metric !g.uv/9pDc. No.4340492]

>>4340337
This pic is a spacetime diagram of two objects at rest with respect to each other. The horizontal axis represents the objects' x-coordinate. The vertical axis is time. Their worldlines are parallel, and thus never intersect.

To be cont.

[Anonymous No.4340497]

so does my dick warp time because its so big amirite lol?

[metric !g.uv/9pDc. No.4340505]

Now imagine a graph of two objects initially at rest, but the graph is embedded on a curved surface (for example, the surface of a sphere). This time, the objects come together over time by following "straight" worldlines (geodesics) through time and eventually meet.

[metric !g.uv/9pDc. No.4340515]

>>4340497
Actually, yes.

[Anonymous No.4340516]

>>4340497
Nope. That's a black hole.

[Anonymous No.4340535]

Since any energy density appears in the stress-energy tensor which defines space curvature, this means that a very, very powerful laser could curve space appreciably in the way that mass does, right?

[Anonymous No.4340544]

>>4340497
>so does my dick warp time
Possibly, vanishingly small things can certainly warp spacetime.

[metric !g.uv/9pDc. No.4340557]

>>4340535
Yes, but you'd need an absurdly powerful laser to get any noticeable gravitational effects. Don't forget just how much energy a little bit of mass contributes: E=mc².

[Anonymous No.4340569]

>>4340557
Possibly this, but I think it's more probable that the beam would decohere immediately due to pair production, maybe causing enough mass buildup to form a singularity, endangering the device.

[Anonymous No.4340572]

>>4340557
>mfw converting the mass of a black hole into a single massive laser pulse that carries an event horizon with it at the speed of light, tearing apart anything it doesn't consume outright through immense tidal forces
I think we found something worse than RKVs. A lot less feasible though, and perhaps impossible.

A smaller version of how much overkill this is would be making a laser that carries enough momentum to knock someone down. I did the math once - it's ridiculous. You completely vaporize and ionize them before you get that much momentum in a laser pulse.

[Anonymous No.4340587]

but thanks for trying

[metric !g.uv/9pDc. No.4340594]

>>4340572
>"converting the mass of a black hole"

lolwut

[Anonymous No.4340721]

>>4340594
I don't know how it would work, though nuclear reactions are essentially about turning mass into energy (or vice versa). Hence, "perhaps impossible".

[Anonymous No.4341409]

I'm enjoying this thread.

[Anonymous No.4341425]

>>4339782

Explain Dirac equations cogently. (They're relativistic.)

[Anonymous No.4341459]

Should I end up back in time, would I be able to change things, or would that be what always happened?

[Anonymous No.4341472]

if earth is orbiting the sun at about 108,000 km/h then how does time slow down for you in space if you are moving a lot slower then the earth is?

[Anonymous No.4341501]

>>4341472
108,000 km/h = 30 km/s is 0.01% of the speed of light, so there would be hardly any difference. If you were at rest in the Sun's reference frame and the Earth was moving away from you at 108,000 km/h, time would be going 1.00000001 times faster for you than for someone on Earth.

[Anonymous No.4341507]

I suppose I can't ask you why relativity itself isn't limited by relativity?

[Anonymous No.4341510]

If light travels at c in all inertial reference frames, then why does it move at different speeds in different media?...not sure if that falls under quantum mechanics.

[Anonymous No.4341523]

>>4341510

Not OP, but particle interactions. If you wanted to view it as moving light speed between the tiny angstrom-sized spaces between atoms, you certainly could. This is related to the cherenkov effect, which you're probably familiar with

[Anonymous No.4341535]

>>4341501

that makes sense but time moves slower when your traveling in space witch doesn't seem to make sense because you are traveling faster on earth then you are in space. and the theory of relativity states that for objects moving faster time will go slower.

can you explain that?

[Anonymous No.4341610]

>>4341535
Yes time would go slower for someone on Earth, which is the same as saying time would go faster for someone not on Earth, which I stated in my previous message.

[Anonymous No.4341611]

say there is a HUGE train circling the globe. inside the train is another train and inside that train is another train. they are all traveling at half the speed of light. wouldnt the inner most train be traveling past the speed of light, relative to the earth???
is there anything theoretically incorrect/impossible about the above?

[Anonymous No.4341677]

>>4341611
Composition of velocities doesn't work this way. You would find an answer to many of your questions if you read the wikipedia article.

http://en.wikipedia.org/wiki/Special_relativity#Composition_of_velocities

[metric !1tensorX8Q No.4342139]

Bumping with amazing new trip.

[Anonymous No.4342158]

>>4339782
explain tensors and how they relate to space time

[metric !1tensorX8Q No.4342179]

>>4342158
I'm not going to take 3 hours to try to explain tensors, but: laws formulated in terms of tensors have a property called general covariance. This means that they are equally valid in any type of coordinate system. For example, the Einstein field equations are actually a single differential tensor equation which relates the stress-energy tensor to the metric of spacetime.

[Anonymous No.4342207]

Can you please explain M theory, in terms of how the fundamental force of gravity is weaker than the other 3 fundamental forces of the universe.

Also can you please explain how M theory is supposed to unite general relativity and classical mechanicals.

[Anonymous No.4342211]

what exactly is proper time (and proper distance)?

[Anonymous No.4342239]

>>4342211
Proper time is the time actually experienced by an object. Proper length us the length of an object in its rest frame.

[Anonymous No.4342286]

Couple questions for OP:

1. With regards to mass shells on a light-cone diagram, if a moving object approaches infinite mass what implications does this hold?
2. Can spacetime be bent or distorted in the absence of energy/mass?
3. When you refer to space-time, how does the "vacuum" itself factor in to the big picture?
4. Since space-time is a 4D object (I think), what are we seeing when we see distortions in the "fabric" of a 3D image? Does the fabric relate to the whole of 3D space? I'm referring to figures like OP's original pic.
5. Does space-time exist outside regions of the universe that don't have a vacuum?

[Anonymous No.4342293]

The mass of an object depends on it's speed, right? A higher mass takes more energy to move, right? And time is just motion, right?

So is relativity just saying that things moving faster in space move slower in time?

[metric !1tensorX8Q No.4342992]

>>4342286
>1. With regards to mass shells
What are mass shell?

>on a light-cone diagram, if a moving object approaches infinite mass what implications does this hold?
Objects don't "approach infinite mass." I don't really know what you're asking.

>2. Can spacetime be bent or distorted in the absence of energy/mass?
The intrinsic shape of the universe may be spherical or saddle shaped, but I don't think that's what you were asking. Space is locally flat when the SET is zero.

>3. When you refer to space-time, how does the "vacuum" itself factor in to the big picture?
Vacuum energy is the reason for the cosmological constant (i.e. dark energy).

>4. Since space-time is a 4D object (I think),
It's a manifold.

>what are we seeing when we see distortions in the "fabric" of a 3D image? Does the fabric relate to the whole of 3D space? I'm referring to figures like OP's original pic.
I'm not sure what you mean again.

>5. Does space-time exist outside regions of the universe that don't have a vacuum?
Wouldn't the absence of a vacuum imply there was something there?


>>4342293
>The mass of an object depends on it's speed, right?
No, it doesn't.

>A higher mass takes more energy to move, right?
Loosely, yes.

>And time is just motion, right?
No, it's not.

>So is relativity just saying that things moving faster in space move slower in time?
That's certainly not all relativity says.

[Anonymous No.4343021]

Is motion a vector

[metric !1tensorX8Q No.4343025]

>>4343021
Define motion, then I can give you an answer.

[Anonymous No.4343036]

>>4343025
In physics, motion is a change in position of an object with respect to time. Motion is typically described in terms of velocity, acceleration, displacement and time.[1] Motion is observed by attaching a frame of reference to a body and measuring its change in position relative to another reference frame.

[Anonymous No.4343048]

A little bird told me that revolving around the center of rotation makes one travel faster than the speed of light relative to the space. It has been postulated that faster-than-light speed is required if we want to travel through time. If we consider the planet Earth to be a space, is it possible then that going to a spot at one of the Earth's poles that marks the center of rotation, and flying around it in a calculated spiral until you reach the desired destination will work if one wanted to travel to the past or the future?

[metric !1tensorX8Q No.4343057]

>>4343036
A change in the 4-position is a 4-vector:

<div class="math">\Delta x^\alpha =(c \Delta t,\Delta \vec{r})</div>

Velocity is a 4-vector:

<div class="math">u^\alpha = \frac{dx^\alpha}{d\tau } = (\gamma c,\gamma \vec{v})</div>

Acceleration is a 4-vector:

<div class="math">a^\alpha = \frac{du^\alpha}{d\tau } = (\gamma \dot{\gamma} c,\gamma \dot{\gamma} \vec{v}+\gamma^2\vec{a})</div>

etc.

[Anonymous No.4343058]

>>4343036
Velocity and momentum are vectors, acceleration is a scalar (Unless I'm terribly, terribly mistaken).

[Anonymous No.4343060]

>>4343058
Disregard my post, I was being a dumbass.
(How the fuck could I think acceleration was a scalar?)

[Anonymous No.4343061]

>>4343048
This idea is brought to you by courtesy of iVan. It's like an iPhone but it doesn't play shitty music, is alive, and is not a car.
Just to elaborate on why it is necessarily the POLES we must go to. This is because the Earth's gravitational field is elliptical. Therefore, flying rapidly around the center of rotation at the poles is CLOSER to the center of rotation. Thus, you would be traveling faster RELATIVE to anywhere else on the planet. It would be SIMILAR to going faster than light around the equator, no?

[metric !1tensorX8Q No.4343064]

>>4343048
You've been watching too much of Christopher Reeve's Superman.

[Anonymous No.4343068]

How do you calculate the speed at which the effect causes spacetime to travel?

[metric !1tensorX8Q No.4343070]

>>4343068
I have literally no idea what that means. Spacetime doesn't travel.

[Anonymous No.4343071]

why does the speed of light travel slower towards glass, water, diamond, etc?

[Anonymous No.4343077]

>>4343071
Reflection/refraction?

[metric !1tensorX8Q No.4343080]

>>4343071
I has to do with how photons interact with the molecules in the material. I don't have an answer in any great detail because I've never taken a materials class.

[Anonymous No.4343082]

>>4343060
Fun fact, unless I'm horribly mistaken, acceleration is a very bad boy and doesn't completely behave as a vector or any sort of tensor.

[metric !1tensorX8Q No.4343085]

>>4343082
You're horribly mistaken. Acceleration is a vector.

[Anonymous No.4343110]

>>4343071
How does an speed travel?

[Anonymous No.4343120]

>>4343110
An speed should be a meme. You dumb fuck.

[Anonymous No.4343124]

>>4343085
It does not transform as one under change of coordinate system. Pic related, disregard text.

[metric !1tensorX8Q No.4343184]

>>4343124
That IS how a tensor transforms under a change in coordinates. The partial with respect to xx (last term) is the definition of the Christoffel symbols in the covariant derivative. Also, their notation is wrong because their free indices don't match up.

[Anonymous No.4343195]

>>4343184
You have to define the covariant derivative using Christoffel symbols exactly to get rid of that term, which would appear in the change of coordinates if you took the first derivative relative to another coordinate, instead of a parameter. A tensor always transforms linearly.

I also fail to see where the indices are unmatched.

[metric !1tensorX8Q No.4343201]

>>4343184
**Never mind about the free index thing. I had taken a quick glance at it, and they didn't look like they matched up. They do.

[Anonymous No.4343210]

>>4343195
Anyway, for citation on what I'm saying regarding how a tensor is defined, see Lovelock-Rund page 65 and following.

[metric !1tensorX8Q No.4343217]

>>4343195
You don't "get rid" of that term. That term IS the Christoffel symbols summed over velocity. That's exactly how a vector transforms under a change in coordinates. Any coordinate system other than cartesian coordinates is going to have that term there.

I'm not sure why you think velocity would transform as a vector, but its derivative with respect to a scalar would not. That, in itself, is contradictory.

[Anonymous No.4343226]

>>4343217
>That's exactly how a vector transforms under a change in coordinates.

False.

[metric !1tensorX8Q No.4343237]

>>4343226
This is true IN CARTESIAN COORDINATES ONLY. A tensor transforms, in general, so that there is one Christoffel term for each free index. You have a fundamental misunderstanding here.

[Anonymous No.4343242]

>>4343237
False, nowhere does it say that, and indeed it implies the opposite. This is how a tensor is defined in any coordinate system.

[metric !1tensorX8Q No.4343258]

>>4343242
I was a little hasty with my choice of words. Yes, your pic is indeed how a tensor transforms. What I meant was that a covariant derivative (which is what acceleration is wrt velocity) has one Christoffel term for each index.

[Anonymous No.4343264]

>>4343258
The book also brings up a situation that is analogue to what I was saying regarding acceleration, and points out that it's not a tensor. In order for it to be a tensor you have to define the covariant derivative not to be simply the derivative with respect to one of the coordinates.

[Anonymous No.4343265]

If, hypothetically, you could survive inside an event horizon, would your perception of time alter?

[Anonymous No.4343285]

How many equations describe the whole of general relativity?

[Anonymous No.4343287]

Actually to see what I mean when I say that acceleration is not a vector just consider this simple example that doesn't even need to involve relativity. Call <span class="math">x[/spoiler] the position vector in cartesian coordinates and <span class="math">F[/spoiler] the force in cartesian coordinates, Netwon's law is <span class="math">F = m \ddot{x}[/spoiler].

Now call <span class="math">\xi[/spoiler] and <span class="math">\Phi[/spoiler] position and force in spherical coordinates, <span class="math">\Phi = m \ddot{\xi}[/spoiler] is not the correct equation of motion.

You could define an "acceleration" vector that properly transforms under a change of coordinates, but it wouldn't simply be the second derivative of position, you'd have to involve Christoffel symbols in its definition.

[Anonymous No.4343304]

Explain Modified Newtonian Dynamics.

[Anonymous No.4343329]

I presume you took physics as a degree? How much of relativity covered during this degree? How long did it take you to get where you are now?

[metric !1tensorX8Q No.4343758]

>>4343287
Ahhh, I see where our misunderstanding is coming from. I was talking about acceleration as defined as Du/dт and you were talking about acceleration as defined as du/dт. I probably should have picked up on this from the beginning.

[Anonymous No.4345089]

resolve this paradox by using general relativity to prove you can't have portals in relative motion to each other