"6 Maxwell's equations and 12 Einstein 'tensor' equations"
Who would have guessed that?
Please enlighten us all.
Light in, Light out.
Who would have guessed that?
Please enlighten us all.
Light in, Light out.
This is sure to be a lost cause, but why do you say there are 12 Einstein equations? In 4 dimensions there are 10 independent components of the Ricci tensor and metric because they are rank 2 symmetric tensors ($$R_{\mu \nu} = R_{\nu \mu}$$). That's not quite the end of the story though, because you are free to choose what coordinates you use, reducing the number of independent components to 6. Maxwell's equations can be written as an equation for a rank 2 antisymmetric tensor ($$F_{\mu \nu} = -F_{\nu \mu}$$) which has 6 independent components.
Why pretend when that's exactly reality?Assume nothing, pretend you are talking to me, I big dummy, who knows nothing and prefers to look at pictures and diagram's.
No, that's why most university courses take years to complete.Can you explain in simple terms, including all equations.
What exactly did he say and where exactly did he say it?But it was Prof. Leonard Susskind, who said that there were "6 Maxwell's equations and 12 Einstein 'tensor' equations" and implied they were related.
The connection between them is via Kaluza-Klein reduction, which Prometheus is aware of.Can someone write down the "6 Maxwell's equations" and the "12 Einstein 'tensor' equations" and show the connection?
Do you think its an insult to call me names when you're also asking me to explain things to you which you don't understand? If I'm such a 'nob' then why do you want my help?Dear Alpha(Nob),
They are also written down in these things called 'books'. They're made of paper, have ink marks on each page which form letters, which combine to form words, which combine to form explanations and help convey information. They're those things other people read to learn.Please keep going, the equations must be written down somewhere on the internet.
If you want a full depth explanation of KK methods then buy a book. I'm not going to teach you everything you currently don't know but which is required to understand on a working quantitative level KK methods, as that would take years, even if I thought you were not too stupid to understand them.Please show all workings and assumptions and definitions.
Why does that matter? Its common in science for the original formulation of theories or ideas to be quite inelegant and only over time are better formulations developed. Maxwell originally did his work using quaternions, it wasn't until decades later people formulated them in terms of vectors or connections and curvatures of gauge bundles. Maxwell's original formulation is extremely unpleasant to learn from, modern approaches are much better. For instance the entirety of electromagnetism, all of Maxwell's equations, can be written as $$dF = d\ast F = 0$$ where $$F = dA$$. If you want the upgrade that to include any kind of gauge theory then you just use $$F = dA+A^{2}$$.How did Theodor Kaluza explain it to Einstein?
For you the light might be on but no one is home....Light in, Light out.
Dear Alpha(Nob),
Please keep going, the equations must be written down somewhere on the internet.
Please show all workings and assumptions and definitions.
How did Theodor Kaluza explain it to Einstein?
Light in, Light out.
This is sure to be a lost cause, but why do you say there are 12 Einstein equations? In 4 dimensions there are 10 independent components of the Ricci tensor and metric because they are rank 2 symmetric tensors ($$R_{\mu \nu} = R_{\nu \mu}$$). That's not quite the end of the story though, because you are free to choose what coordinates you use, reducing the number of independent components to 6. Maxwell's equations can be written as an equation for a rank 2 antisymmetric tensor ($$F_{\mu \nu} = -F_{\nu \mu}$$) which has 6 independent components.
Did you all hear that wooshing sound? That was the sound of the entire thread going over Terry's head.
So you've found an explanation for dummies and you still don't understand? What does that tell you Terry?What I am still not sure of, for definite, is the exact relationship between Maxwell's and Einstein's equations.
If you understood what I've said in previous posts you'd know how wrong you are.Does this imply that from 6 (or less) Maxwell equations in 5 dimensions, we can derive the 12 Einstein equations in 4 dimensions?
The Einstein equations in 5D lead to the Einstein equations in 4D, Maxwell's equations in 4D and additional equations on a scalar field.
Did you read any of this thread Terry? I'll repeat my question from post #2:
Why do you say there are 12 Einstein equations?
I suggest you stop Googling for links you don't bother to understand and instead learn some relativity and quantum field theory. The last question you asked was answered in your own link, thus demonstrating that you link to things you don't understand and have made no effort to understand. The quantitative snippets I've given were things you've already linked to so its not like my explanation was much different.Which immediately raises the obvious question, is it possible to work backwards, starting with Einstein equations and Maxwell equations in 4D, what is the relationship between them, which will allow us to combine them together, in 5D?
Its easy when you can think coherently.If you are thinking about a career change, you are a natural "barrister". - Who writes your speeches?
The fact you don't like what I say doesn't make the things I say insults or false. What precisely was false in my previous post?You never give, a straight truthful answer, only insults and false accusations.
And yet you're the one asking me to explain things to you. What's it like to know less about physics than a bag of 'me'?When am I going to learn, "If you punch a bag of 'you', you get covered in 'you'."
Because before I got my job I spent most of a decade learning these things, including several years working on precisely the topic at hand, Kaluza-Klein compactifications and their generalisations.Why am I arguing with a spotty faced, bag of 'you', with a few months 'work experience'?
I doubt any of those people had any idea as to your claims about physics or your detachment from reality. If they'd spoken to you long enough to hear about your obsession with the double slit experiment and your deluded attitude about your ability they'd have reached similar views about your physics knowledge as I have. Whether they'd say as much in as direct a manner as me I don't know.I have met hundred's of students, post-doc's, numerous Prof.'s and several Nobel Laureates and I have never once had an argument, a disagreement or bad word spoken between us, until you appeared. I wish you would simply disappear or simply go away.
Where precisely did he say it?But it was Prof. Leonard Susskind, who said that there were "6 Maxwell's equations and 12 Einstein 'tensor' equations" and implied they were related. "
So the question now is, is it "10 or 12 Einstein 'tensor' Equations"?
Do you think its an insult to call me names when you're also asking me to explain things to you which you don't understand? If I'm such a 'nob' then why do you want my help?
Do you know what 'hypocrisy' means? That statement would be hypocritical if I were asking people for help who I insult. Am I asking Terry for help? No. You? No. RJBerry? No.The hypocrisy of this statement is overwhelming.
Yeh -
I do know what it means.
''Hypocrisy is the act of pretending to have beliefs, opinions, virtues, feelings, qualities, or standards that one does not actually have.''
Your opinions and beliefs are not reflected in how you want other people to behave. It is one thing to go around saying other people should not call you names, it's another one when you do the same back.