Einstein's maths

[Surlethe]

He's probably most well known for his work on black holes, and of course, Hawking Radiation.

He also proved a very useful theorem illustrating the existence of the big bang singularity in a Robertson-Walker spacetime. I'm not (yet) geometrically sophisticated enough to grasp it, but O'Neill puts it like this: "On the spacelike slice of present galactic time the galaxies are diverging (shape tensor); since gravity attracts (Ricci tensor), they have been diverging no less rapidly in the past. Thus trouble can be expected in the sufficiently distant past" ([1], 431).

The theorem itself is,

For a spacelike hypersurface S in a time-oriented n-dimensional Lorentz manifold, the convergence k reduces to a real-valued function on S:
k = <U,H> = trace(S_U)/(n-1),
where U is a future-pointing unit normal on S, and H is its mean normal curvature vector field.
...
Suppose Ric(v,v) >= 0 for every timelike tangent vector to M. Let S be a spacelike future Cauchy hypersurface with future convergence k >= b > 0. Then every future-pointing timelike curve starting in S has length at most 1/b.

[1] O'Neill, B. (1983). Semi-Riemannian Geometry With Applications to Relativity. Elsevier.

(Hey, if the thread is "Einstein's maths," we may as well have some of it!

So, 2500 years on, why nobody has debunked the Pythagorean theorem ?

Seriously, Pythagoras was clever, I know, have we really not moved on enough from 500 BC to debunk all this crap ?

Why do we defer to Pythagoras and Aristotle (two people amongst nearly 7 billion), is it fear of being wrong?

What is going on?

Do bear in mind that Einstein didn't invent his math; the field was founded decades earlier by Riemann.

Although, I was discussing this with a history grad student yesterday: a big deal in preparing for a PhD in history is mastering not only the period you are specializing in, but also mastering the opinions, beliefs, arguments, cultural, and political backgrounds of all the historians who have also specialized in your period, and developing and defending critical beliefs regarding their opinions and arguments. Apprentice mathematicians (and, to a lesser extent, physicists, chemists, and other hard scientists) do not have to do this: we need only master a particular field and develop a critical view of the extant arguments, problems, and theorems in the specialty. In the course of mastering these, one is bound to learn about personalities and backgrounds of people in the field, but those are perfectly irrelevant when it comes to the validity of arguments (and the further back you go, the more accepted the arguments are).

[Bottlestein]

^ What is the "shape tensor" (formal def'n appreciated)?

[Lief]

So, 60 years on, why are his thoughts still the pinacle of our thoughts on mathematical and unknown problems?

So I suppose we need some new Laws of Motion too? I mean Newtons theories are even older then Einsteins and (Aside from some points being prooved not entirly accurate or incomplete by Reletivity) still form the core of how we understand gravitational interactions.

Oh wait! Some of our maths comes from Ancient Greece, we'll have to reinvent basic principles because they're old guys!

But on a more serious note, Einstein at least laid the groundwork for a lot of modern phsyics, just like Newton did before him, for all we know in another hundred years or so there'll be a third name to add to that list, as for why we still use things like Reletivity? They still work, think of it like the wheel or the lever, we have them we understand them we know they work and how. They and thier principles are always going to apply, we don't 'move on' from Einstein for similar reasons (Unless future physcics proove his work incorrect/incomplete, but explaining the fundamental workings of the Universe is like that).

From the large sample of assumning fuckwits, I have chosen you, congrats!

So I suppose we need some new Laws of Motion too? I mean Newtons theories are even older then Einsteins and (Aside from some points being prooved not entirly accurate or incomplete by Reletivity) still form the core of how we understand gravitational interactions.

Um what?

Your spelling is worse than mine by the way. Where did you even begin this sentence from?

Oh wait! Some of our maths comes from Ancient Greece, we'll have to reinvent basic principles because they're old guys!

You really do seem to have missed the point, by a fair distance.....I was asking a question, not stating a fact, are you really this fucking stupid?

Think of it like the wheel /lever? WHAT?

People really cant see beyond there own small visions, we got almost 8billion people on earth now, are we have had 3 visionairies?

Does no compute. And people have moved on from einstien,, in many ways....jesus, some people here are obtuse.

[Serafina]

Hey, the moron is using the "i was just asking a QUESTION!!1"-excuse.
Well, that works as much as "i am drunk" - not at all. Because you are not just asking a question. You were stating that " thoughts are still the pinacle of our thoughts on mathematical and unknown problems", that his work is "crap".
And you assumed that scientists are afraid of critizising famous scientists, while every person who knows anything about science knows that this is bullshit.

You are an idiotic, know-nothing moron whose sole product is a pile of heaping, intolerable crap.

[Lief]

Hey, the moron is using the "i was just asking a QUESTION!!1"-excuse.
Well, that works as much as "i am drunk" - not at all. Because you are not just asking a question. You were stating that " thoughts are still the pinacle of our thoughts on mathematical and unknown problems", that his work is "crap".
And you assumed that scientists are afraid of critizising famous scientists, while every person who knows anything about science knows that this is bullshit.

You are an idiotic, know-nothing moron whose sole product is a pile of heaping, intolerable crap.

HEY LOL THE MORON BLAH BLAH BLAH!

Fuck me you are a cock. Please remove your head from your arse before even speaking?

You are taking the word crap out of context, its means stuff, things, thoughts, whatever....jesus.

Anyone who knows anything about anything knows this is bullshit? How exactly? Or are you once again merely spouting complete fucking shite to make yourself sound good? Oh. Thought so.

I know nothing, but you provide nothing in argument, seriously, fuck off you obtuse, ignorant cunt.

EDIT: I didnt say I was just asking a question, I said I was asking a question. And instead of actually trying to speak on topic, you just decided to flame me? Grow up you stupid cunt, and get a life.

[Lief]

You were stating that " thoughts are still the pinacle of our thoughts on mathematical and unknown problems", that his work is "crap".

why are his thoughts still the pinacle of our thoughts on mathematical and unknown problems?

Seems like a question to me. Way to go on editing out the word 'why' and the '?' though, grats, you should have an extra wank today.

Prick.

[Kane Starkiller]

Seriously, he was clever, I know, have we really not moved on enough from the 40's to debunk all this crap.

You clearly state Einstein's stuff was "crap" so go ahead and prove it was crap.

[Lief]

Seriously, he was clever, I know, have we really not moved on enough from the 40's to debunk all this crap.

You clearly state Einstein's stuff was "crap" so go ahead and prove it was crap.

That would be depend on your meaning of the word crap in this context, so, please, stop being a nit?

[Kane Starkiller]

All the same if something is true and correct then it can't be disproven no matter how much time passes. If you think it should've been disproven by now then you think his theories were incorrect. So then at least tell us why you think they are incorrect.

[Lief]

I didnt say they were correct or incorrect, I was wondering why little advance has been made on 60 year old science, some has been made. Hence, is this our pinnacle? And will we go much further?

So you think that what Einstien as said (most of his work), is just fact?

I am not sure, for example, if the multiverse or donut universe theories were even thought about in his time, or dark matter, or the precise calulations in relation to the universe expansion. Or the very new theories that the universe wont ever 'snap back' and that it will merely just expand until every solid point is so far away from the next to make it seem like a very lonely universe to any life on said place.

Not much substance to this thread, so I guess the basic answer is 'NO'

[Surlethe]

I didnt say they were correct or incorrect, I was wondering why little advance has been made on 60 year old science, some has been made. Hence, is this our pinnacle? And will we go much further?

There have been plenty of advances made in the sciences of general relativity and quantum mechanics over the last sixty years (by the way, Einstein's heyday was 100 years ago). The fields would be initially unrecognizable to any scientist from then magically brought to the present and handed a journal.

I am not sure, for example, if the multiverse or donut universe theories were even thought about in his time, or dark matter, or the precise calulations in relation to the universe expansion. Or the very new theories that the universe wont ever 'snap back' and that it will merely just expand until every solid point is so far away from the next to make it seem like a very lonely universe to any life on said place.

No, at the time of Einstein, quantum mechanics hadn't even been formulated. Astronomers were still assuming that the Milky Way constituted the entire universe and arguing over whether it was 1000 light years or 100,000 light years across. There was no evidence of dark matter, no evidence that the universe was expanding, no speculation regarding multiverses or 'donut universes', no hypotheses regarding the eventual outcome of the dark energy era. Hell, as far as the atom, the only particles scientists knew about were electrons and it wasn't until 1911 (six years after Einstein's great year) that Rutherford discovered --- surprisingly! --- that atomic nuclei are very, very dense and concentrated in the middle of atoms.

The reason Einstein dominates histories of the science is he reworked the framework of how scientists think about the universe: focus on invariants, symmetries, and literal measurables (e.g., in developing special relativity, Einstein explicitly defined "simultaneity"). This influence was felt almost immediately, in the axiomatization and development of quantum mechanics, and in the great leaps forward in the formulation of particle physics models (culminating in the QCD and the Standard Model in the 1980s) relying on symmetry to develop the models.

Has the science progressed? Exponentially. Do we regard Einstein as a great thinker? Absolutely. Do these contradict? Not in the slightest.

Not much substance to this thread, so I guess the basic answer is 'NO'

If you're going to ask a question, put it clearly; your original question was about the personal authority of the individuals in question, not the state of the field. Since you've asked a new question, I won't punt this thread to the Hall of Shame. However, if you shit all over it one more time, it's gone. Got it, pal?

[Lief]

Great answer surlethe, thank you.

But still, threats are fairly stupid. Let it run or remove now. Discussion is usually always good. Not sure why I should be clear in my questioning to be honest. And I only shit over this thread when I was shit on, so I feel that is fair enough, no?

[Surlethe]

^ What is the "shape tensor" (formal def'n appreciated)?

If you have a manifold M embedded in another manifold M', the Levi-Civita connection M' induces a connection D' on M which has the Levi-Civita properties. D' is the covariant derivative. If two vector fields V and W are actually tangent to M, D'_V W needn't be tangent to M; it can therefore be decomposed into a tangent component and a normal component. The shape tensor is the normal component of the covariant derivative on M in M'; it is also called the second fundamental form tensor. Helpful?

[Surlethe]

Great answer surlethe, thank you.

But still, threats are fairly stupid. Let it run or remove now. Discussion is usually always good. Not sure why I should be clear in my questioning to be honest.

You need to be clear in your questioning the same reason you (or anybody else) needs to be clear in all communication: if you're not clear, you are simply exposing yourself to miscommunication. If all along you were intending to ask the questions you just asked, why do you think every single person in this thread misunderstood you? Because we are all a bunch of misanthropic jackasses? No, it's because you asked it in such a poor and obfuscating manner that it sounded like you were asking something very different.

And I only shit over this thread when I was shit on, so I feel that is fair enough, no?

The problem is that you were (a) asking a retarded question and (b) not asking it clearly. You frankly deserved to get flamed, and your reply was insubstantial.

[Lief]

I like to ask things in a certain manner, gets more interesting responses this way. Whether I come off as a jackass or not, is fairly irrelevant to me, I am merely interested in the converstations which are provoked.

I only insulted people who gave retarded replies which were irrelevant to the discussion.

I don't mind getting flamed, in amongst the decent thoughts given on the OP.

I may not be clear, clever, or substantial, but I do post to learn, and I do seem to have a habit of provoking some interesting discussion.

But this is all off topic, so I'll merely agree with you and look forward to future posts on the topic.

[Ilya Muromets]

How were the people's replies irrelevant to the OP question when your questions were like this:

So, 60 years on, why are his thoughts still the pinacle of our thoughts on mathematical and unknown problems?

Seriously, he was clever, I know, have we really not moved on enough from the 40's to debunk all this crap.

You don't specify what part of Einstein's theories you think we haven't "debunked." Here's a hint, when you use the term "debunk", you're asking if it's been proven wrong. Because that's the definition of "debunk," which is "the exposition or ridicule of the falseness or overexaggerations of a claim"

So when you used that term, you were essentially asking why we haven't proven "all this crap" false.

Why do we defer to the einsteins and hawkins (two people amonst nearly 7billion), is it fear of being wrong?

People answered your misconception of "deference" of Einstein or Hawking.

What is going on?

Again, broad general what. You didn't even bring up your actual specification until this page.

[Bottlestein]

^ What is the "shape tensor" (formal def'n appreciated)?

If you have a manifold M embedded in another manifold M', the Levi-Civita connection M' induces a connection D' on M which has the Levi-Civita properties. D' is the covariant derivative. If two vector fields V and W are actually tangent to M, D'_V W needn't be tangent to M; it can therefore be decomposed into a tangent component and a normal component. The shape tensor is the normal component of the covariant derivative on M in M'; it is also called the second fundamental form tensor. Helpful?

Thanks. I couldn't find it in the tensor analysis books, so I was worried - is it a term coined by by people doing g.r. ?

[Surlethe]

^ What is the "shape tensor" (formal def'n appreciated)?

If you have a manifold M embedded in another manifold M', the Levi-Civita connection M' induces a connection D' on M which has the Levi-Civita properties. D' is the covariant derivative. If two vector fields V and W are actually tangent to M, D'_V W needn't be tangent to M; it can therefore be decomposed into a tangent component and a normal component. The shape tensor is the normal component of the covariant derivative on M in M'; it is also called the second fundamental form tensor. Helpful?

Thanks. I couldn't find it in the tensor analysis books, so I was worried - is it a term coined by by people doing g.r. ?

No, I believe that it is a more general formulation of the second fundamental form of Gauss. For a 2-manifold embedded in R^3 with a regular parametrization r(u,v) the second fundamental form is the matrix r_{ij}*n where i,j = u,v and n is a unit normal to the surface.

[Simon_Jester]

Lief, your motives are transparent and you reveal yourself more blatantly as a liar with every passing post.

Seriously, he was clever, I know, have we really not moved on enough from the 40's to debunk all this crap.

You clearly state Einstein's stuff was "crap" so go ahead and prove it was crap.

That would be depend on your meaning of the word crap in this context, so, please, stop being a nit?

Well then, pray tell, what does "crap" mean to you?

Does it mean "undesirable excrement," like it means to everyone else on the planet? If so, then you started the thread by calling Einstein's theories undesirable excrement, which implies that they are wrong. In which case I would dearly love to watch you "debunk" them, much as I would like to watch a monkey type the complete works of William Shakespeare and get it right the first time.

Though honestly, I suspect the monkey has better odds of success than you do. There is a small but calculable chance of a monkey with a typewriter banging out a letter-perfect version of the works of Shakespeare. Given that relativity is by all appearances true, and given the level of scientific education and the quality of intelligence you have shown so far, your chances of proving relativity wrong are, in my opinion, worse than that.

But go ahead and try to "debunk this crap." It would be very funny to watch.

Of course, you deny that you meant any such thing. So perhaps "debunk this crap" doesn't mean the same thing to you that it would to a normal person. Perhaps to you, the word "debunk" means "prove" and the word "crap" means "delightful shining brilliance" or some such.

Of course, this suggests that your grasp of the English language is poor, causing you to consistently say the opposite of what you mean. It also says very strange things about your attitude towards crap.

I like to ask things in a certain manner, gets more interesting responses this way. Whether I come off as a jackass or not, is fairly irrelevant to me, I am merely interested in the converstations which are provoked.

Since most of the conversations provoked involve calling you a cretin... Indeed, you enjoy being called a cretin so much that you go far out of your way to phrase your statements as if you were a cretin.

Thus, we conclude that for your motives to be sincere AND for you to not in fact be a cretin, you must both have strange attitudes towards crap and enjoy being called a cretin.

I may not be clear, clever, or substantial, but I do post to learn, and I do seem to have a habit of provoking some interesting discussion.

You are in a poor position to take credit for this- again, it is as if a chimpanzee had swung in through the window, hurled dung at the people inside, then swung away... and tried to take credit for the discussion of primate behavior that followed, one that it neither contributed to nor was competent to understand.

[Surlethe]

This is quite enough ragging on Leif. His behavior is transparently recorded in this thread for all to see; it is unnecessary for more than two people to point it out to him: if he is introspective, one is enough, and if he is not, no number of people yelling will make him think it through himself.

[Simon_Jester]

This is quite enough ragging on Leif. His behavior is transparently recorded in this thread for all to see; it is unnecessary for more than two people to point it out to him: if he is introspective, one is enough, and if he is not, no number of people yelling will make him think it through himself.

Sorry, you're right. I will say no more.