@ACuriousMind : I find that as the original definition, 'circular'. Are there any theories that could have predicted it without first assuming EH field ?
@spetzz You don't need to presuppose the EM field, it's existence follows naturally from the assumption of the symmetry. You need to presuppose the symmetry, however.
@spetzz Start with the most generally applicable action for the situation. Apply global U(1) symmetry. Find the conserved quantity and call it electric charge. Where's the circular part?
@Jimnosperm : I don't know much about Global Symmetry, but if this theory can predict charge; My question remains the same , what is Charge ? What is its origin ?
@ACuriousMind : What i mean, is everything in field of science follows a cause-effect relation. If charge is the effect, what is the cause ? is there any ?
The formal description of physics simply never mentions "causes" or "effects". There are just differential equations and their solutions, and we sometimes call the data we put in "causes" and the data we obtain as solutions "effects", but that's arbitrary.
@Jimnosperm : We don't know much about Big Bang.. Everything needs to have a cause, without it how can anything be justified ? How can there be a relation between anything ?
Causation is simply not a necessary concept. It's "folk science" as John Norton says, an intutive concept that we use to tell ourselves stories, but it is not there on any level of rigor.
@spetzz That's your intuition. Nothing in our experiences happens without some preceding cause. We never observe anything in our life happening without a cause, so we assume all things have a cause. But just because we don't observe it doesn't mean it's impossible.
Why must the Big Bang have a cause?
Because everything does? Do you have proof for that statement?
If I say "there exists at least one effect that has no cause" it is not logically valid to say "Everything I've ever seen has a cause, so that statement must be false"
@0celo7 Yeah, but you aren't proving a statement about the real world there, you're proving statements about theories and their consequences, given that the theories are true.
Physics proves lots of things, but they get cheated out of the credit. The theory used to be that things fall to Earth because it has more mass and that mass sources gravity. This was proven true by experimentation and observation. We were cheated out of calling this a proof because now it is just what we observe. It's now a law, not a theory and laws are observed, not proven
@0celo7 Yes. But since you can't prove that Y is true in the real world, you have proven precisely nothing about the real world. (The problem essentially being that we aren't handed an axiom system for reality, so we can't use the mathematical notion of truth and falsity)
@Jimnosperm It was not falsified by experiment, which is different from proven.
Theories which are so often not falsified that they are unlikely to be false, we call true.
There's essentially a Bayesian framework behind all of this, with the posteriors for "theories" tending to 1, and those for the false hypotheses tending to 0.
@ACuriousMind It's a law now. Mass generates gravity. More mass = more gravity. That is true. It used to be a theory, but since it is now just a statement of observation, it is a Law. Not proven or unproven, just a statement. That's why we got cheated out of it being proven. It went from theory to law as soon as the observations were made
@ACuriousMind No, a Law is a statement of observations. A theory is a statement that attempts to explain observations and provide predictions for future observations based on that
@StanShunpike Think of it this way. There is a magical land of rainbows and unicorns that all photons want to end up in. This is called future null infinity. Now, if a photon at a point $p$ cannot reach null infinity in any way, $p$ is said to be in a black hole. The black hole is then defined as the set of all such $p$s.
@Jimnosperm : I still don't agree that we can reject Causality. It has been the basis of all of our understanding and rational thought. I know Physics does not care about our thoughts, but still it is seen to be followed most of the times. I don't know if there are exceptions to it.
@spetzz Causality is perhaps the hardest part of our intuition to reject. There is no evidence that causality must be preserved yet it is very often used as a tool to eliminate any theory that violates it. It is followed most of the time. If it is a rule, then it too must have a cause for being a rule. But until we can show evidence for it, it is better if we try to ignore that part of intuition
@spetzz What do you mean with "exception"? You'll have to define causality first. You can't claim "everything is based on causality" without providing a coherent notion of it. Intuition is not sufficient.
I offer the first moment of time as a decidedly acausal phenomenon. There surely could not be any preceding cause to have effected the first moment of time
@ACuriousMind Exactly! If there exists no prior time and causality requires a cause to chronologically precede the effect, then there can not be a cause for the first moment of time
However, if chronology is not an important factor in determining the cause of an effect, then this is much more complicated and there's no way of me judging at this time whether the first moment was acausal or not
@ACuriousMind : I think "Causality (also referred to as causation[1]) is the relation between an event (the cause) and a second event (the effect), where the second event is understood as a physical consequence of the first." should work
None of the words here has precise, physical meaning. "object in time"...is me blowing my nose an "object in time"? Is there anything that is not an object in time? What on earth does "instantiation of a property" even mean?
Saying everything has a cause is the same thing as saying the universe is infinite. If everything has a cause, then there's a cause for everything having a cause. And there's a cause for that.... ad infinitum. Even trying to build a CTC causal loop under that restriction requires a cause for the CTC to exist. This causal link must stretch back infinitely. Given that we can always define any of these causes as existing in the universe, the universe must also be just as infinite
But, regardless of what I think of the individual definitions - the mere fact that there is not an agreed upon meaning of cause and effect shows that causation is not, in fact, the basis for "all of our understanding and rational thinking".
@spetzz just think about it. It never began. It was always just existing. No cause for it to exist because it never came into existence, so no cause is required. It's just here
@Gowtham : Chaos/Random combination created Proteins which bounded together; Whose purpose was to produce more molecules, this is life. Dead at lower levels, "Alive" at our level.
ya , it was my only goto game in undergrad and now just play it sometimes , just watch streams and tourneys sometimes, its so huge in europe . you heard about the international ever ?
LoL is biggest here... I go to the library, people are playing LoL. I go to a lounge, people are playing LoL, I go back to my dorm, my roommate is playing LoL!
@Danu i think the inevitability of winning or getting through lost me my interest, but i can see what you mean...also the Installation and the whole process is a major discourager
@Danu Well, TQ counts, but it is not what I'd generically think of when someone says "RPG". Final Fantasy is a JRPG (Japanese RPG), these are also mostly quite different from the generic Western RPGs.
@Danu Probably not. FF is great, but the generic RPGs I think of are stuff like Baldur's Gate, Fallout, Neverwinter Nights, Arcanum and other titles. There aren't really any good recent examples of that genre, which is why I'm so interested in PoE and the other Kickstarters.
@Danu It's Bastion, and yet it is not - different gameplay, and totally different story, but that same way of feeding you the information about the world only in small chunks, and with a kind of narrator voice commenting on your every action.
@NeuroFuzzy Really what? The narrator commenting? The are many one-liners that are directly triggered by you doing something - smashing a specific thing, falling off, running around headless, everything.
Oh, are you on mobile and can't see the arrows? Then that must have been confusing :D
No, just lazy. I played bastion but I always confused transistor with other games so when I heard the name I didn't think it was related to bastion at all
@0celo7 Yesterday you stated "The precise topological definition of my earlier black hole definition is $B:=M-J^-(\mathcal{J}^+)$ where $J^-$ is the causal past and $\mathcal{J}^+$ is future null infinity."
I assume $M$ is the spacetime manifold.
Can you clarify exactly what $J$'s are mathematically?
And why exactly is there a parentheses around the $J^+$ term?
I want a list of all the beta numbers achieved in across all magnetic fusion energy devices. This is not theory, but the actual number measured experimentally. No list like this exists. It is a good way to "take stock" of where we are in the pursuit of fusion energy.
The beta number is the ...
@ACuriousMind now that you mention this, I realize every time I've used the metric tensor I have just assumed it is a 2-tensor and never bothered to define it really.
So maybe this is how one defines it.
In which case "advantage" is obvious.....its the definition
@ACuriousMind If I have two bundles and form a third bundle via the direct sum, how is the curvature of the third one related to those of the first two?
@0celo7 Uh...it is the curvature of the connection that is induced on the direct product. Are you asking how the connection on the direct product is induced, or do you want a formula for the curvature? (The former I can give, the latter not)
@0celo7 So, let's start that the beginning. Two bundles with connection $E,A$ and $F,B$ are given, and we induce the connection $C$ on the sum as $C : TE\oplus TF\to VE\oplus VF, C(v,w) := A(v)\oplus B(w)$, right? If you think of the connections as matrices on the tangent space, $C$ is just block-diagonal with $A$ and $B$ as blocks
Now, evidently, $\mathrm{d}C = \mathrm{d}A\oplus\mathrm{d}B$, so the curvature is indeed just the sum
You can also view the vertical bundle as the subbundle of the tangent bundle that it is, and write the connection forms are maps fron the tangent bundle into itself, it doesn't matter
Also, the above is the general Ehresmann connection approach, it may be that you are using another
This is equivalently encoded in a connection form on the tangent bundle to the vertical bundle, whose kernel is that horizontal subspace
@0celo7 Connection on the tangent bundle, or connection on the bundle? It's a bit confusing because a connection "on the bundle $E$" is given by the connection form $E : TE\to VE$.
This gets even more confusing when your first contact with a connection is GR, where you have a connection on the tangent bundle, which is really a form $TTM\to VTM$.
@0celo7 I would not advise taking my path to studying bundles. I basically just read papers about gauge theories and stuff until I could see what the Wikipedia articles wanted to tell me.
@DavidZ I want to retract my answer that says that we don't know how the entanglements work, and that faster-than-light signals are absurd. My answer is absolutely correct, faster than light signals are a self-contradiction, but if you hold that you agree with such a thing, I simply refuse to be a prisoner of this situation. Believe in whatever you want, but I don't want to be a laughing stock, and gather minuses because I am saying the truth. I is an unbearable situation for me.
@DanielSank I understand that I have no idea what are entanglements, that I have no idea what is non-locality, that I don't understand quantum theory, that two particles at a huge distance from one another interact locally. As I don't understand that someone closes his/her question on my answer but prefers another answer, my logic is faulty. But I want to be out of this game. I just want to retract that answer that is so terribly wrong.
You all know the problem, trying to eliminate the bad HW stuff and keep the good.
I code off and on and my personal website has a filter on every input box to eliminate the stuff I don't want to see on the comments, the usual limitations...language, abuse, etc.
My suggestion is as follows:
(I...
@StanShunpike Those $J$'s (or $I$'s or $H$'s or...) denote subsets of the manifold as functions of either a point or a set of points. For example, $J^+(p)$ is the set of all points reachable from $p$ by a future-directed causal (nowhere spacelike) curve.
user54412
See Wald, Chapter 8
user54412
The script letters denote "points at infinity" -- $\mathcal(J)^+$ is the limit where all null paths eventually lead, $\mathcal{I}^+$ (pronounced "scry-plus") is the same for timelike paths.
@DanielSank I apologize for a message that by mistake came to you. It was meant to DavidZ.
@DavidZ I understand that I have no idea what are entanglements, that I have no idea what is non-locality, that I don't understand quantum theory, that two particles at a huge distance from one another interact locally, because they knew one another in the past. As I don't understand how someone closes his/her question on my answer but prefers another answer, my logic is absent. But I want to be out of this.
You all know the problem, trying to eliminate the bad HW stuff and keep the good.
I code off and on and my personal website has a filter on every input box to eliminate the stuff I don't want to see on the comments, the usual limitations...language, abuse, etc.
My suggestion is as follows:
(I...
@KyleKanos @KyleKanos it is too late. I am deeply revolted, and that, in understatement. So, please everybody, believe in faster-than-light signals. I will post a question to which I expect no answer, because I don't care anymore.
@KyleKanos no doubt that you are a very fine person. But you are not aware of what happens here, and most of all, the events that accompanied that question/answer. What I see it systematical boycotting scientific truth. You have to say what people like to "hear". They like superlum. comm., so, don't tell them that it is a supreme law of our universe that past can't be re-written. They want FTL signals, then don't tell them that it is a self-contradiction. Then, why answer?
@Sofia So I just came back to my computer and I haven't gone through the chat history yet, but it seems as though you're upset and you seem to be upset with a number of people here. I have 1 question and 1 statement. Question: What is the problem here that has made you so upset? Statement: Please don't be mad, I still love you
@ChrisWhite I say "mathcal" to myself when reading...
TIL I guess, thanks.
@ACuriousMind So here's the deal. We have a bundle $E$ with curvature form $\mathcal{F}_E$. The Chern class is defined as $c(E):=\operatorname{det}(1+\frac{\mathrm{i}}{2\pi}\mathcal{F}_E)$. The curvature of a sum bundle splits as a block-diagonal matrix: $\mathcal{F}_{E\oplus F}=\operatorname{diag}(\mathcal{F}_E,\mathcal{F}_F)$
(Technical difficulties.)
@ACuriousMind Then we have $c(E\oplus F)=\operatorname{det}\operatorname{diag}(1+\frac{\mathrm{i}}{2\pi}\mathcal{F}_E, 1+\frac{\mathrm{i}}{2 \pi}\mathcal{F}_F)=\operatorname{det}(1+\frac{\mathrm{i}}{2 \pi}\mathcal{F}_E) \operatorname{det}(1+\frac{\mathrm{i}}{2 \pi}\mathcal{F}_F)=c(E)\wedge c(F).$
@Jimnosperm many people love me. Especially those with which I stay hours to help them understand things or solve a problem. But, this place sowed be the door.
@ChrisWhite Currently, my GR studying lineup is Weinberg and Wald. I am also using John Lee's texts on manifolds as well as do Carmo for Riemannian geometry. Is that a sensible line up?
@0celo7 has been using Straumann but he's been sending me mixed signals about buying it, so I haven't yet added that to my repertoire. Do you know if Landau covers GR in his 10 book series?
user54412
9:42 PM
@StanShunpike Um, that makes it sound weird. All I mean is that $J(p)$ is a set of points related to $p$ in a particular way. And if $S$ is a set of points, $J(S)$ is a set of points related to $S$ (essentially the union of $J(p)$ for each $p \in S$). This is no different from $\partial S$ being a particular set of points related to $S$ (specifically the boundary of $S$).
user54412
@StanShunpike Wald is good -- I don't know any other source that treats causal structure. I've never read a Weinberg book, and I don't think I missed anything (I suspect he's like L&L -- unnecessary, except people feel good for learning things the hard way, and so he's popular among the masochistic crowd).
user54412
I'm not familiar with Lee, so I can't comment.
user54412
Is do Carmo Differentiable Geometry of Curves and Surfaces? I used that in a pure math class, but I was quite unimpressed. I got a more rigorous, intuitive, and general treatment of diff geo (do Carmo just studies 2D surfaces embedded in $\mathbb{R}^3$, and uses this explicit embedding everywhere!) from my GR courses.
do Carmo indeed wrote curves and surfaces. I think that book sux
He wrote one called Riemannian Geometry but I think it too isnt great. Ted Shifrin said he doesn't care for do Carmo so I no longer feel unjustified criticizing him
@ChrisWhite I actually have found Weinberg surprisingly readable. I don't know about his other texts, I can't speak for them. But certainly for me as a beginner I think Weinberg's treatment is quite nice.
I want a list of all the beta numbers achieved in across all magnetic fusion energy devices. This is not theory, but the actual number measured experimentally. No list like this exists. It is a good way to "take stock" of where we are in the pursuit of fusion energy.
The beta number is the ...
You all know the problem, trying to eliminate the bad HW stuff and keep the good.
I code off and on and my personal website has a filter on every input box to eliminate the stuff I don't want to see on the comments, the usual limitations...language, abuse, etc.
My suggestion is as follows:
(I...
