What does it mean to be Covariant?

And yet you don't even know what a Hilbert space is.

I find that amazingly hypocritical, given that you never retort anything I say or answer any direct questions I ask when you make claims about your 'work'.

As I said, your links talk about quantum gravity, which is quite different from normal general relativity. There are a great many fundamental issues which must be addressed when you try to quantise gravity, problems which string theory is partly trying to address using such things as string field theory. No doubt you're just parroting sentences you've read but not understood and thus you lack the ability to distinguish between and understand things I'm saying and things those links are saying.

I suggest you go off and learn what a Hilbert space is and then maybe work your way up to the stuff needed to have any hope of understanding quantum gravity ideas.

 

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Don't patronize me, I am quite aware of what a Hilbert Space is. But that is not on discussion, so keep it out of here, one more slip and I will report you, again.

Now, the link varified everything I said; quantum gravity, the search of a unification between the large and the small, the confirmation of a direct link between the high energy scales and the low energy scales has inherently a time problem which plagues current physics because it clashes with our understanding of how spacetime coordinates are shuffled and unaltered, that a pure gravity solution exists for GR and thus indicates that time does not exist. Oh that's right, you said that time does not simply not exist, but obviously you haven't studied this particular area well at all, or perhaps you would have been in the know concerning this time problem from the beginning.

It's quite clear you are now trying to hide the fact you were wrong one way or another. I am not stupid, I can read the article with perfect clarity. It is not a fact of me confusing general relativity and the quantum phenomena as two things of the same side, I am currently saying there was a time problem which plagued our understandings.

As you will see, it's a matter of unifying the entites together to create a framework which we can all come to agree on.

So, I ask, what do you believe in? I assume you have an imagination like every other human being - do you believe time is an illusion, or is it a matter of a highly incomplete theory.

 

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Isn't it about time this idiot was banned (again)?

 

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Before you begin boycotting, it would be a good idea to explain why I should be banned.

 

You're a compulsive liar.

 

You're telling me the moderators have not read that one, time and time again. Yet you still not providing any evidence to the contrary, just loose claims that I have ''made myself to appear like something I am not''.

Well, I refer you to the conversation me and Bork had in this thread, like Borks idea was, and you can learn what I say about myself, so what have I lied about?

Some advice, you better find more acceptable reasons to boycott a banning if you want it to proceed.

 

I've reported you as off-topic as well. If you want to discuss me, go the members forum and start a thread there.

 

Well that wasn't very difficult.

 

I know what a Hilbert Space is. It's not exactly the most difficult mathematical artistry available you know.

 

See, you're doing it again!

 

I'll start a thread on them, but answer this post again with what you are doing, I will report you a second time.

 

Like when you started a thread on tensors? I can't wait!

 

Yes, just like that. I will reitterate everything I know about the Hilbert Space, finite or infinite dimensional, and I will see if my understanding of them are correct, just to prove you cannot sit there and say I am lying about something when I know I am not.

I'll need some time though to write the latex. And gather exactly what I will say on it.

 

Well I grant you, it's not nearly as difficult as describing a straight line in the x, y plane.

 

I can't be bothered making another thread. I'll post what I've written so far, and seriously cannot be writing any more.


Definition of a Hilbert Space

A Hilbert Space by definirion can be a finite or infinite dimensional space with a complete inner product space.

A linear vector space with an inner product therefore, is simply a Hilbert Space. All finite vector spaces are complete, and once an inner product is defined, they too will become Hilbert Spaces.

Basis Vectors in a Hilbert Space

The basis set in an LVS (Linear Vector Space) are linearly independant vectors which span the LVS. A Hilbert Space with a denumerable basis \({|\phi_n>}\) where \((n=1,2,3...)\) is called a seperable Hilbert Space. We can have an orthonormal basis defined as \({|\phi_n>}\) in an expansion formula given as:

\(|\psi>=\sum^{\infty}_{n=1} C_n |\phi_n>\)

Using Dirac Notation of course. The above requires that there can be an inversion formula given as:

\(C_n=<\phi_n|\psi>\)

The finite norm is defined as:

\(<\psi|\psi>= \sum^{\infty}_{n=1} |C_n|^2= ||\psi||^2\)

on the \(\ell\) finite dimensional space. Orthonormality can be further defined mathematically as:

\(<\phi_n|\phi_m> = \delta_{nm}\)

and the identity operator is:

\(\sum_{n} |\phi_n><\phi_n| = \bold{1}\)

Here \(|\phi_n><\phi_n|\) is where the completeness is displayed. If we were using an operator on the space, (a symmerric operator) they would follow these following rules:

\(A\) is a linear operator iff

\(A(|\psi> +|\chi>)=A|\psi>+A|\chi>\)

\(A(c|\psi>)=cA|\psi>\) where \(c\) is a scalar

\((A+B)|\psi>=A|\psi>+B|\psi>\)

and it stays within these properties.

Properties on \(R^2\) space

Two points on a map are given as \((x_1,x_2)\) such as using Cartesian Coordinates on a map, so if we have \(X=(x_1,x_2)\) we can state that \(X \in R^2\). We can of course expand this to suit whatever needs we desired, for instance, if we wished to work in a three dimensional space, it would simply be \(X=(x_1,x_2,x_3)\) and this can be stated as \(X \in R^3\).

In a much more simpler notation, we can say \(X=(x_1,x_2.. .. x_n)\) meaning that \(X \in R^n\). If it was an infinite dimensional vector space so that \(X=(x_1,x_2.. .. \infty)\) then we are necesserily using an infinite Hilbert Space \(X \in R^{\infty}\).

 

Yes well, when I begin a topic discussion with someone about Schwartzchild coordinates, I kind of expect it to get messy before it's begun.

You should be familiar with such prospects, as you too seem to ''over-expect'' in certain conversations all the time.

 

You mentioned it, both here and in that thread, without any prompting. I'm simply responding to topics you raise.

The fact you're trying to get me to back off with threats of being reported, rather than you simply saying "It seems you got the wrong impression of me" and then demonstrating some knowledge says it all. Like I told you in another thread, any one of Guest, Temur, Rpenner, Cpt, Ben, myself etc would not say "Shut up or I'll report you" if someone said "I don't believe you know what you're talking about", we'd laugh at them and metaphorically bitch slap them into next week with more detail than they can hope to grasp.

You seem to be failing to understand what 'pure GR' means. Quantum gravity isn't 'pure' GR. Pure GR is classical, it has no quantum aspect to it.

The Schwarzchild solution is 'pure GR', you don't need to make any reference to quantum theory to obtain it. Hawking radiation is not, its 'semi-classical' in that it talks about quantum fields within space-time but space-time is not a quantum field. Full blown quantum gravity would be the next step, where gravity is a quantised field. This is no longer general relativity, pure or otherwise, because it vastly disagrees with GR on short scales, just as special relativity is not Newtonian physics or quantum field theory quantum mechanics (in the formal sense).

I asked you for an explanation why there's a fundamental problem in GR with time, you said it doesn't exist. Your evidence is then a series of pop science-ish essays which talk about quantum gravity, which treats space-time VERY differently from general relativity. GR views space-time as a smooth continuum, aside from the occasional singularity. Quantum gravity doesn't, space-time is an emergent effective theory concept which is formed from the huge collection of gravitons which blend together to 'make' a continuum which behaves as the Einstein field equations say over longer distances. This is something which string theory makes attempts to talk about because space-time would be made of huge amounts of closed strings, which also seem to form branes (with the help of open strings too) which are better understood on a quantum level than gravitons.

I have never said anything disagreeing with the notion that quantum gravity has some serious problems to address in how to view space-time. However, from a purely GR point of view 'time' in the sense I've previously outlined (metric signature etc) exists and none of the links you've given say otherwise.

I'm hardly hiding. In another thread I offered to have an alpha thread discussion with you on entanglement or the Dirac equation. I don't have any reason to run from you and I'm happy to admit mistakes. Shame the same can't be said about you.

Yes, the scientific method is based on open honest discussion. When you're capable of it let me know.

Did my previous post where I said 'it exists' not register with you?

And yet you got confused between operators and states. Which is almost exactly the same kind of mistake as getting vectors and scalars muddled up, which you also did!

So you can copy/paste definitions, so what? How about a discussion on it? I said in another thread I'd have an alpha thread discussion on the Dirac equation or entanglement and that I'd be willing to be suspended for a week if at any point I was deemed by the moderators to be 'bullshitting'. Are you willing to make the same statement and have an honest discussion on say entanglement? Its pretty interesting and its in the reach of more of the people who'd reading it.

Put up or shut up.

 

I did put up: You said I lied about knowing what a Hilbert Space was, but my post above contradicts that statement. Secondly, you said I have misinterpreted the link somehow, I cannot misinterpret something which clearly says the time problem arrives from quantizing Einsteins Equations to produce a pure gravity solution known as a Wheeler de Witt equation.

You put up, for once.

 

I'm very worried you're mangling the work you're paraphrasing from...

What does this mean?

 

No, it doesn't. All you've done is just copy and paste from somewhere the basic definitions. Knowing that vectors satisfy \(a(v_{1}+v_{2}) = av_{1}+av_{2}\) doesn't mean someone can do vector calculus. You've simply stated the most basic properties, you haven't shown any understanding. Would you believe me if I said I'm a fluent in French and then to 'prove' it I gave you the words for the days of the week in French? Unlikely. Instead you'd expect me to be able to converse in French without much trouble and with few mistakes. Its like that in physics too, you aren't considered to understand something because you can reel off a list of definitions, particularly when you're posting on the internet where definitions are only a click away. What you've posted I would expect to see covered in the first half dozen or so pages of a book on Hilbert spaces, as they are not 'details', they are basic definitions assumed by any book on the subject. You've done the equivalent of saying "I know vector calculus" and then listing things like "1*0 = 0, 1+0 = 1, 1-1 = 0, 0/1 = 0". Yes that's needed to do vector calculus but it doesn't mean you know vector calculus as a result. They are necessary but not sufficient requirements, just as your post covers necessary but nowhere near sufficient things relating to Hilbert spaces.

Now if you want to enter into a discussion then I'm all for it, provided you agree before hand to be honest and answer when asked reasonable questions.

And as Guest has pointed out you have once again included a suspiciously spurious comment in your 'demonstration of understanding' which is both at odds with what it refers to and is completely out of place in the post as a whole. Can you tell us what he's referring to?