I have asked you before but you didn't answer:
What is $$\alpha$$?
Please show how you perform this separation of variables
I think I've found my solution!
$$(-\frac{1}{4}\frac{\partial^2}{\partial \alpha^2}+\alpha^2 - g^2 \alpha^{2 \cdot 2} + \frac{1}{4} \frac{\partial^2}{\partial x^2}) \Psi(\alpha, x)=0$$
where $$x$$ here is our matter field in minisuperspace. The equation can be solved by a seperation of variables $$\Psi(\alpha, x)= \psi_{\alpha}(\alpha)\psi_x(x)$$ to give two coupled equations:
$$(-\frac{1}{4}\frac{\partial^2}{\partial \alpha^2}+\alpha^2 - g^2 \alpha^{2 \cdot 2})\psi_{\alpha}(\alpha)=E\psi_{\alpha}(\alpha)$$
$$(\frac{1}{4}\frac{\partial^2}{\partial x^2})\psi_x(x)=E \psi_x(x)$$
The definition of time now can be given as one of two solutions $$(\Psi_1,\Psi_2)$$ - to describe our time, we have also two choices, we can define our time as either the scale factor $$t= \alpha$$ or as the matter field $$\tau= x$$ which I have represented with a different description to identify the two $$\Psi(t, \tau)$$ - these two different descriptions could be given a unique transformation. We can view one trivially as an imaginary time dimension, by a wick rotation, and one as a real time, given by our Hamiltonian.
But the real question is which time reference do we make real and which one imaginary? Interestingly, we would run into all sorts of problems if we performed the wick rotation on the matter field, namely, imaginary mass descriptions. Performing the wick rotation on the scale factor will rid us of our matter field because real time calculations would have $$\tau=x$$ vanish due to the WDW equation. Though, we can simply say ''well, no use with that any more'' and resort to the final solution of an imaginary time reference on the theory.
http://arxiv.org/PS_cache/hep-th/pdf/9503/9503073v2.pdf
$$\hat{H}\Psi= \Psi((\frac{2\pi G \hbar^2}{3} \frac{\partial^2}{\partial \alpha^2})+\sum_i[-\frac{\hbar^2}{2} \frac{\partial^2}{\partial x_{i}^{2}}+V_i(\alpha,x_i)])) = 0$$
there, the state vector is now multiplied by all the variables inside the parenthesis.
Nice attempt, but you should know that $$\hat{\mathcal{O}} \psi \neq \psi \hat{\mathcal{O}}$$ so the equation still makes no sense.
How do you know it is right? Have you done the calculations?even without the psi function with someone telling me the equation is wrong. I know it is right, so where is it wrong?
I am astonished LaTex allowed you to get away with your unbalanced parentheses (3 open, 4 close).$$\hat{H}\Psi= \Psi((\frac{2\pi G \hbar^2}{3} \frac{\partial^2}{\partial \alpha^2})+\sum_i[-\frac{\hbar^2}{2} \frac{\partial^2}{\partial x_{i}^{2}}+V_i(\alpha,x_i)])) = 0$$
there, the state vector is now multiplied by all the variables inside the parenthesis.
Yes, I am sure. The article says 'and the 0 means there is no time', leaving out the word 'dependence'.Alphanumeric, these are the days that make life worth living.
''The zero does not refer to time...''
Despite repeated attempts to make you see difference, this will change your tune.
http://www.fqxi.org/data/essay-contest-files/Markopoulou_SpaceDNE.pdf
''and the zero refers to time''.
Are you so sure now?
$$N(t) = N_({(\frac{MC^2}{.66(6)}) - (\frac{\pi(r^2)}{5.413*h})) e^{-\lambda t} = N_({(\frac{\frac{V}{M}}{66(6)}) - (\frac{\pi(c^2)}{5.413*h})})e^{\frac{-t}{\tau}$$
Woo Hoo I win. Learn latex and do all that crazyness before Green Destiny, after downloading a useless 1.6G program!!! ugh(= LOL fun race man.
What the hell are you talking about?
Remove foot from mouth, then talk.
>>>>BLAH BLAH BLAH, decent joke...
Yes, I am sure. The article says 'and the 0 means there is no time', leaving out the word 'dependence'.
You've had it explained to you several times now, which you'd understand if you understood the Schrodinger equation. Which you don't. Instead all you're doing is Googling for all you're worth hoping to find a wordy explanation because you don't understand the quantitative ones.
And your little back and fore with Prom only serves to demonstrate my point further. You expect us to believe you're doing something worthwhile with the WdW equation when you can't do the simplest of functional algebra, the kind used in the WdW equation! You don't even know that $$\Phi \partial_{x} \neq \partial_{x}\Phi$$, left and right multiplication are very VERY different things once you step out of the world of high school physics. Which you obviously haven't.
So rather than accepting your attempt to look well read does nothing of the sort you leave a comment on my visitors page saying "Back off or I'll always link to that thread". Be my guest, in this thread you've demonstrated you don't understand topics you profess to be doing worthwhile work in, failing to grasp even the simplest of concepts and methods relevant to it.
You're wanting to play with the big boys, doing the 'cool' physics, but you're not willing to put in the work. Its like a creationist saying "Why won't you publish me, I use big words and I wear a white coat!", utterly failing to see that the reason scientists are respected isn't the big words and the colour of their attire but the worth of their work. Your use of words you don't understand and copying and pasting equations you don't grasp is so obviously an attempt to appear to be 'one of us' (ie capable physicists doing research, like Prom, myself etc) that I'm amazed you think no one will see right through it.
When you can do more than quote mine topics you don't understand let me know.
How do you know it is right? Have you done the calculations?
I am astonished LaTex allowed you to get away with your unbalanced parentheses (3 open, 4 close).
You post a thread saying "Look, I'm doing worthwhile work in high level stuff" then you demonstrate you don't even know how to manipulate the algebra you post.I admitted straight away I niavely applied the wave function. I don't see how it serves your purpose, but if it does, trust prometheus to come and try and save your ass.
It does have another 'frikken interpretation'. If you were capable of understanding the Schrodinger equation and basic calculus you'd know that they imply the 0 means the amount of time variance, ie none. The WdW is time independent, as signified by the fact its equal to 0.The truth is, is it says clearly the zero refers to time - alphnumeric, there is no other frikken interpretation; it says it clearly in black and white. Even someone else in this thread said that it was correct and it refers to the time index.
You're presenting your original post as an 'essay' which attempts to address big problems in physics. You want people to think you're not only capable of understanding high level stuff but you're capable of developing it in a way no one else has.It's your third mistake in this thead. I'm not the one with the PhD in physics, so I have nothing to be ashamed about. I've told people loads of times I am not a professional, that I do not liken myself to one.
Where did I say the wave function doesn't refer to all the information on the system? I said that the Hamiltonian doesn't encode the wave function or vice versa. If you're going to say "You said...." at least get it right. Simply because $$H|\Phi\rangle = 0$$ doesn't mean if you know H you know the wave function or vice versa. The equation tells you something about their relation but you can't uniquely give one when given the other.To say ridiculous statemehts like ''the wave function does not refer to all the information on the system,'' to things like ''and who says that is the imaginary time evolution'' to point blank disagreeing with me on the interpretation of wdw equation - but then still trying to defend your point. Just give up.
You post a thread saying "Look, I'm doing worthwhile work in high level stuff" then you demonstrate you don't even know how to manipulate the algebra you post.
It utterly undermines your claims about your work being worthwhile. And its not like this is the first time. You post on electromagnetism but you can't tell the difference between dividing by 2 or square rooting. Or the difference between scalars and vectors. Recently you couldn't even add vectors properly. It all adds up and it alll undermines your credibility, which was used up long ago..
It does have another 'frikken interpretation'. If you were capable of understanding the Schrodinger equation and basic calculus you'd know that they imply the 0 means the amount of time variance, ie none. The WdW is time independent, as signified by the fact its equal to 0.
All you've provided is a wordy document, which it took you a while to find. Clearly you haven't done much reading around on the subject, you lack the basics upon which the work of Wheeler and de Witt are built and as a result you can't apply any thought to anything you read, you can only mindlessly parrot it back.
You're presenting your original post as an 'essay' which attempts to address big problems in physics. You want people to think you're not only capable of understanding high level stuff but you're capable of developing it in a way no one else has.
All your original post is is just a review of things other people have done and then you say "There, I've solved it" without having actually done or said anything worthwhile.
Where did I say the wave function doesn't refer to all the information on the system? I said that the Hamiltonian doesn't encode the wave function or vice versa. If you're going to say "You said...." at least get it right. Simply because $$H|\Phi\rangle = 0$$ doesn't mean if you know H you know the wave function or vice versa. The equation tells you something about their relation but you can't uniquely give one when given the other.
And I don't for a second think you really understand the WdW equation. Your original post doesn't show any understanding and all your attempts to retort what I've said has clearly involved you Googling a lot and trying to find someone you can point to and say "Look what he said". You can't form your own arguments, because that would require understanding and the ability to think on your feet. Which you utterly lack.
It utterly undermines your claims about your work being worthwhile. And its not like this is the first time. You post on electromagnetism but you can't tell the difference between dividing by 2 or square rooting. Or the difference between scalars and vectors. Recently you couldn't even add vectors properly. It all adds up and it alll undermines your credibility, which was used up long ago.