/sci/ - Science & Math

how can the Einstein Field Equations be derived from the Bekenstein Bound and the laws of thermodynamics?

What's your opinion on Higgs ether? Are you one of the orthodox relativists who favor a very abstract, geometric and "beautiful" description of nature excluding interacting scalar fields such as the Higgs?

>>4281163
I've heard about this, but I've never actually read up on it. I've had this paper in my bookmarks (as a "to be read") for a while: http://arxiv.org/pdf/1012.0381.pdf

How did you manage to understand relativity? GR, I mean. I feel like my maths is strong enough for the legwork, but I'm just not getting an intuitive grasp of it. Is it just a long digestion time or is there a special approach you need?

What undergrad math courses (beyond the usual physics curriculum) can I take to be able to understand the Einstein Field Equations?

>>4281183
What is "Higgs ether" ? I have never heard of this before. Do you mean the Higgs Field? Regardless, I have virtually no experience with particle physics so I can't answer questions about it.

>>4281194
>>4281198

I wrote this for someone on /sci/ a while ago:

First of all, don't bother with the video lectures - Susskind, in my experience, is slow and confusing. What you need are books with exercises in them.

My step-by-step recommendation is the following:

1. First of all, you need to learn vector calculus. This is absolutely essential. You can learn it from any decent calculus book. If you already know it (you said you're an engineering student so I wouldn't be surprised), then great.

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 of 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.

I'm no physicist, so excuse the naive question:
What does it mean to "understand relativity"? My understanding was that inconsistencies were still being worked out, and that no one had a firm understanding of exactly where changes needed to be made.

>>4281210

Wow, thank you for that list! I'm sure each one of those texts requires a great deal of time and energy, but I'm guessing even if I don't finish I'll learn a lot of good stuff.

What is the most curious, fascinating insight you've gained from studying GR? In layman's terms. And I won't take "all of it!" for an answer.

>>4281217
I would say that somebody "understands relativity" if they understand how to work with metrics, how objects move through manifolds with different metrics, and how the metric is related to the stress-energy. Of course, this implies understanding of a bunch of other topics like parallel transport, tensor calculus/algebra/analysis, etc.

GR is still an area of active research, true, though I'm not quite sure what you mean by "inconsistencies." I'm not familiar with these inconsistencies you speak of.

>>4281234
Probably the idea that gravity isn't really a force. We're all just following the most natural path through a curved spacetime.

Okay, fast ship traveling away at relativistic speed, experiences less time passing than on earth, right?
But all things are relative to one another, so what's keeping it from being said that the spaceship is actually stationary, and the earth is moving at relativistic speeds, and the earth is what experiences less time passing?

>>4281258

If gravity isn't a force, why are people trying to unify it with a bunch of other forces?

>>4281202
many physicists who specialize in relativity have opinionated beliefs on electroweak symmetry breaking, as einstein promoted æ-theory and a background space-time which does not interact directly with particles - but only energy-momentum distribution. i was curious on your opinion, as the higgs mechanism is beginning to get a bit of controversy with cern's recent results.

>>4281261
Since we actually use time dilation on a frequent basis, I'd really like an answer to this.

>>4281247
Well, I thought that a lot of work was being put into rectifying inconsistencies between GR and QM because both were thought to have merits, and that as a result they were both considered not well understood at present. I didn't think that relativity was well understood and that it was just QM that was being modified.

Do you get annoyed when you're at a party or smoking a bowl with some friends and someone brings up 'their theory' or 'string theory'

>>4281264
> i was curious on your opinion, as the higgs mechanism is beginning to get a bit of controversy with cern's recent results.

How so? They claim they're going to "find it" this year.

>>4281261
Nothing. That's perfectly valid from the rest frame of the spaceship.

>>4281262
It's a pseudo-force in the context of general relativity. In the context of other theories, it is still a force.

>>4281314
So Mr.Space-Time, what are your thoughts about the possibility of humans being able to change said space-time?

>>4281292
GR is internally consistent as far as I know. It is incompatible with QM because it assumes spacetime is an infinitely differentiable (smooth) manifold.

>>4281294
It used to annoy me, but I've since stopped caring. Nobody wants to be a buzzkill. Besides, listening to imaginative (though frequently naive) ideas can be inspiring.

>>4281314
>time dilation
So when the ship returns to earth, they'll both have experienced the same amount of time passing?

>>4281332
"Metric engineering," as it's called, usually requires some form of negative energy. I'm not even sure if negative energy is physically meaningful.

Why does space-time distortion get the name relativity when everything is relative.

>>4281341
No. The ship needs to accelerate to get back to earth, so it can no longer claim to be an inertial reference frame. The ship experiences less proper time than someone on earth.

Look up the Twin Paradox for more information.

>>4281356
Other than cancelling each other out and making massive explosions?

>>4281367
Been asking myself this forever.

>>4281294
>String theory
wat? You impyling it's disproven?

>>4281374
Nah man, M theory is what's popular these days.

>>4281376
Shit, I'm nowhere near that yet. Reading those books by Brian Greene. So interesting but it takes me like 5 minutes to read a page haha

>>4281367
Not everything is relative. Perhaps you'd like to explain what you mean.

Anyway, the name comes from Galileo's Principle of Relativity. I suppose a more appropriate name for GR would be "General Covariance."

>>4281386
Erm, I believe it is an expansion upon string theory.

Does it drive you crazy when people say nothing can ever return from the inside of a black hole's event horizon?

>>4281420
No, because that's correct.

>>4281424
Then you don't understand relativity as well as you think you do. The correct statement concerning event horizons is that an object in free fall, if propelled outside the event horizon, will eventually fall back into it.

>>4281431
Even if this is true, I'd say that your question was incredibly leading anyway.

>>4281262
>>4281332
>>4281294
>>4281341
>>4281367
>>4281374
>>4281376
>>4281386
>>4281431
>>4281420
holy fuck, this thread is fucking hilarious. i had absolutely no idea we had 4th graders on a science board intended for graduate/undergraduate students in the sciences

>>4281437
> Even if this is true,
It is.

> I'd say that your question was incredibly leading anyway.
Either objects can return from the inside of the event horizon or they can't. It's not a trick question. But for some reason people always jump "escape-velocity > c" to "OMG NEVAR CAN RETURN!"

>>4281431
No, the correct statement would be that the singularity lies in the future of every worldline withing the horizon. An object CANNOT be "propelled" back outside the horizon. In fact, resisting the pull of gravity will only make you die faster.

>>4281440
>My Little Pony pic
>holy fuck, this thread is fucking

>Accusations of immaturity
>I lol'd.

>>4281444
Sure, if you're implying that the "escape velocity" in "escape velocity > C" actually exists.

>>4281456
That only applies to objects in free fall. There are objects which are not in free fall, I'm sure you are aware.

>>4281463
You don't need to reach escape velocity to go higher than you're current altitude. Escape velocity is only required if you want to never fall back (without firing a rocket engine).

>>4281464
Yes, I'm aware. You still can't "uncross" the horizon. Freefall objects experience maximal proper time, so resisting gravity will actually reduce the proper time between crossing the horizon and reaching the singularity.

I'd like to know where you got this idea from in the first place.

>Ask someone who understands relativity anything about relativity.
What happens to space-time when the event horizons of two singularities mingle?
Pic related as visual aid.

what do you think of this?

<div class="math">\rlap { \lower{-1.5em}{You ~can't~ travel }} \rlap { \lower{-1.9em}{Cant}} \rlap { \lower{-2.5em}{~~~~~~~~can't ~travel~ the~ speed}} \rlap { \lower{0.6em}{of~ light}} \rlap { \lower{0.5em}{of ~~light}} \rlap { \lower{1.9em}{only~ a~ fraction}} \rlap { \lower{2.5em}{~~~~~fraction }} \rlap { \lower{2.7em}{~~~~~~fraction }} \rlap { \lower{3.4em}{~~~~~~~~~~~~~~~~~0.999^{9^{9^{9^{9^{9^{9^{9^{9^{9^{9^{9^{9^{9}}}}}}}}}}}}}}} \rlap { \lower{3.5em}{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=1}} \rlap { \lower{3.4em}{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=1}} \rlap { \lower{4.2em}{you~ can ~travel ~at ~the ~speed ~of ~light}} \rlap { \lower{4.25em}{you~ can ~travel ~at ~the ~speed ~of ~light}} \rlap { \lower{4.1em}{you~ can ~travel ~at ~the ~speed ~of ~light}} \rlap { \lower{4.7em}{you~ can ~travel ~at ~the ~speed ~of ~light}}</div>

>>4281472
You're applying naive Newtonian ideas to black holes. Do you know what extrapolation is?

>>4281496
>>4281464
So a 'universal stillpoint', such as /tg/'s infamous Absolutely Immovable Rod, could stay in one spot in space-time, but if a black hole's event horizon happened to pass over it, it would be stuck and travel along?
>>4281501
Is that supposed to be that Flexil script?

>>4281504
>'universal stillpoint',
>/tg/'s infamous Absolutely Immovable Rod

I'm not familiar with these.

>>4281493
They will merge, not overlap. A good example is two drops of water getting close to each other. They will meet eventually, but when they meet they don't become two different drops of water occupying the same space since they are exactly the same as one another, they just merge into one drop of water.

>>4281493
I'm not really sure what the question is. The singularities combine, if that's what you're asking.

>>4281512
The second, if I remember correctly, is a rod that affixes to its exact location in space so that immovable doesn't mean it hangs in the air in a stationary orbit, but rather stays at that exact location, even after the planet has left it behind.

>>4281501
I love it.

<div class="math">\rlap { \lower{-1.5em}{You ~can't~ travel }} \rlap { \lower{-1.9em}{Cant}} \rlap { \lower{-2.5em}{~~~~~~~~can't ~travel~ the~ speed}} \rlap { \lower{0.6em}{of~ light}} \rlap { \lower{0.5em}{of ~~light}} \rlap { \lower{1.9em}{only~ a~ fraction}} \rlap { \lower{2.5em}{~~~~~fraction }} \rlap { \lower{2.7em}{~~~~~~fraction }} \rlap { \lower{3.4em}{~~~~~~~~~~~~~~~~~0.999^{9^{9^{9^{9^{9^{9^{9^{9^{9^{9^{9^{9^{9}}}}}}}}}}}}}}} \rlap { \lower{3.5em}{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=1}} \rlap { \lower{3.4em}{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=1}} \rlap { \lower{4.2em}{you~ can ~travel ~at ~the ~speed ~of ~light}} \rlap { \lower{4.25em}{you~ can ~travel ~at ~the ~speed ~of ~light}} \rlap { \lower{4.1em}{you~ can ~travel ~at ~the ~speed ~of ~light}} \rlap { \lower{4.7em}{you~ can ~travel ~at ~the ~speed ~of ~light}}</div>

>>4281502
Let's try a thought experiment. Suppose you are in a rocket outside the event horizon or a non-rotating black hole, holding a constant distance from the singularity. You lower an object on a chain down to the EH and let it just dip inside. There is nothing preventing you from pulling it back up. Tital forces at the EH are not strong enough to rip the chain apart. Escape velocity doesn't matter because we're not launching anything out of a cannon, we're just pulling it with a chain.

>>4281512
In one campaign, the DM wanted to get back at the players, and so when they gt their hands on their first 'Immovable Rod' (stays in the air when you press the button, withstands 400 pounds of force until the enchantment breaks), they tried to use it to scale a castle.
When they pressed the button, the DM said "The rod disappears in an instant, nearly taking your hands with it." The DM had decided that the rod was LITERALLY immovable, and thus as soon as it was active, it remained perfectly still.
While the planet continues to travel at roughly 1000km per hour.

Of course, the players did as players do, and used their next one as a siege weapon by calculating the spin and motion of the planet, and then letting the castle 'crash into' the rod while they stood a safe distance away.

>>4281525
>>4281523
No no no!
Always the same confusion!
The question isn't about what happens to the black holes; it's about what happens to SPACE-TIME ITSELF.

>>4281545
You would have to sum the tensor fields.

Dear OP,

Even if quantum entanglement can only send random information, couldn't a binary system be placed so that signals could still relay information faster than light?

>>4281545
Right. The answer still stands. Look at space-time within the event horizon. Now look at space-time within the event horizon of two black holes. Both space-times are exactly the same as one-another, since they are both within an event horizon. Therefore, when two black holes merge (or get really-really close in this case) the areas within the event horizons will merge as well.

Pic related, but without that barrier between the two bubbles, since there would be no event horizon between the two event horizons.

>>4281535
>Tital forces at the EH are not strong enough to rip the chain apart.

That's where you go wrong. They are ALWAYS strong enough to rip the chain apart. Even at the horizon of a supermassive BH the tidal forces will rip the chain apart as soon as you start trying to resist freefall motion.

y realativity no work for atoms?

>>4281550
http://en.wikipedia.org/wiki/Tensor_field
Sorry, I never got that far in mathematics.
I'm thinking in terms of 'rubber sheet relativity'.
>>4281557
So if I sent a photon down that area of virtual interaction, what would happen? Would it go straight through? Would it get trapped? In which singularity would it get trapped in?

>>4281528
"Stationary" is a relative term. A particular reference frame would need to be specified in which the rod remains stationary.

Regardless, it is a non-physical object that will only serve to generate good troll physics.

>>4281559
The tidal forces don't get that strong (for a typically massive black hole) until you get MUCH close to the singularity.

>>4281556
No. Try to come up with a way of doing this; you can't.

>>4281566
Forget the rubber sheet analogy. It's retarded and will only serve to confuse you.

Einstein's theory says nothing less than that all photons are, in their frame of reference, outside space and time. They don't experience the passing of time and they don't experience the traversing of any distances. The universe, for photons, is a mystical dimensionless point. Even if there were an infinite number of photons, they would all inhabit this inconceivable singularity beyond the reach of time and space.

Are photons, when considered from the correct perspective, mental rather than physical?

How can photons be real, physical entities if an infinite number of them can inhabit a timeless, massless domain of zero size?

>>4281566
Depends on the velocity of the particle. The event horizon is the farthest anything can go before it gets sucked back in. Assuming it is going at the speed of light (the fastest velocity we know of) it would depend on which gravitational force was strongest at that point. It may travel straight through, it may go back to the source, it depends on how far from the source it gets. That is all assuming there are no other forces knocking it off course as well, and within the event horizon, likely it would get swept up in the maelstrom of activity between the merging singularities.

>>4281573
Yes they are. You will be able to lower the chain up to the horizon by allowing it to freefall, but as soon as you start to put any tension on it the chain will break.

>>4281583
Well, I know that the 'glory of god' has always been equally shared with the 'light of god'.
The whole "let there be light" thing happened before anything else, so photons would have been around before stars and such.

>>4281583
Photons don't have a rest frame. Everything you just said makes no sense.

>>4281535

Doesn't work. Once it's inside the event horizon, just staying still is roughly equivalent to either 1) travelling faster than light or 2) moving backwards in time. It can't be done.

The chain breaks the instant you lower it past the event horizon.

Don't fuck around with event horizons.

Why is your trip-code eating all of my minnows?

>>4281586
>Assuming it is going at the speed of light (the fastest velocity we know of) it would depend on which gravitational force was strongest at that point.
Ahh, so the forces would cancel out at one specific point or line, all things equal?
That makes sense.

>>4281597 The chain breaks the instant you lower it past the event horizon.
HAHAHAHA. No. The relationship between the distance where tidal forces become that big and the event horizon depends entirely on the mass of the black hole.

if the universe is expanding and the matter is not accelerated
does this mean that all the clocks in the galaxy are relatively in sync?

if time is the 4rth dimension why is it so different
why is energy preserved in time
and why does it flow only in one direction

yfw you've all spent so much time and energy learning something with quite literally no use to the human race.

"Yo guys, this thing that we think exists, that we will probably never ever encounter, does this! (We think)"

Even if we find the Higgs Boson, what then? A massive bill?

>>4281624
> Farraday you faggot, stop messing around with wires and magnets and all that shit. It's pointless!

>>4281624
how about the ability to control mass
at least that's what happened when we found about the electron

we got GPS because of relativity

we got computers because we understand matter and light

we got nuclear energy because we understand the atom structure and the strong force

you'd better start thinking or GTFO

>>4281589

>but as soon as you start to put any tension on it the chain will break.

Or pull you with it.

>>4281612

Tidal forces have nothing to do with it.

http://en.wikipedia.org/wiki/Event_horizon#Interacting_with_an_event_horizon

Think how molecular forces work. They are electromagnetic in nature, and for them to remain intact across an event horizon would be equivalent to photons passing in an out of the event horizon, clearly impossible.

>>4281624
>Even if we find the Higgs Boson, what then? A massive bill?

lolwut? Try mass and gravity manipulation.

Artificial gravity, mass reduction & gravity engines.

>>4281624

1) Mass modification

2) More mass modification

Perhaps in future

3) Ways to keep matter intact in the hellish realm outside the universe, speculated upon in various M-theories. In this way we could perhaps circumvent the light speed limit that may hold only within our membrane.

>>4281580
I've heard the rubber sheet theory is crap as a layman's explanation. So how about this instead.

Take a ball of clay in your hand. Squeeze it so it pushes out between your fingers. The clay is pushed from less space in your hand to more space outside of your hand.

Mass warps spacetime in a manner that there is more spacetime the closer you get to that mass.

Now drop the clay. It falls to Earth. This is because the mass of the Earth warps spacetime so that there is more spacetime on the earth side of the clay then the other side.

>>4281669
That... makes no sense.

>>4281539
Relative to what reference frame was it stationary?

>>4281684

Cosmic Microwave Background

Jesus, you fucks are retarded.

Any chain we have currently would be ripped apart by the differences in force. Simply the difference between the force on the far end of the chain compared to the force on the near end of the chain would exceed the tensile strength of the chain before it reached the EH and the chain would break with no external mechanical force. Tidal forces alone will tear the chain into pieces.

>>4281698
That's what we've been saying the entire time...

>>4281722
Good, but there seems to be a dumbass majority in this thread.

>>4281679
does it make sense to think of curved space-time
like space time is a huge body of liquid
and matter/energy is like a holes in the universe and space-time leaks out through them

much like the way water leaks down from the sink, except that this space-time liquid has no net motion to make it swirl when it goes down

>>4281698
there is another problem
time dilation you'll never see the chain cross the even horizon it would just freeze in time when it gets close

are my feet older then my head?

>>4282219
No, they're younger.

Can relativity allow me to move things with my mind?

The LMC sends packets of protons around in a circle at close to c.
The circumference of a disk rotating at relativistic speeds contracts.
Does this mean there is less space, hence fewer proton packets put into the LHC at high speed than if moving at low speed?