Physics Subtly Implies no Geometry for Space

[khan]

Hello again Reiku

I went and read some of your older postings and found this interesting question that you mentioned regarding the requirement of 3 spatial dimensions.

http://www.sciforums.com/showthread.php?t=79747


I suspect that the constants of physics arise as statistical regularities and are entropic in nature, for example, the Monte Carlo PI approximation:

http://www.chem.unl.edu/zeng/joy/mclab/mcintro.html

Gravity is possibly geometrically spherical-like and symmetric ...and electromagnetism would be transposition invariant and geometrically toroidal. is gravity an entropic phenomenon that is related to electromagnetism in some yet as undefined way? :shrug:

 

[Reiku]

Hello again Reiku

I went and read some of your older postings and found this interesting question that you mentioned regarding the requirement of 3 spatial dimensions.

http://www.sciforums.com/showthread.php?t=79747


I suspect that the constants of physics arise as statistical regularities and are entropic in nature, for example, the Monte Carlo PI approximation:

http://www.chem.unl.edu/zeng/joy/mclab/mcintro.html

Gravity is possibly geometrically spherical-like and symmetric ...and electromagnetism would be transposition invariant and geometrically toroidal. is gravity an entropic phenomenon that is related to electromagnetism in some yet as undefined way? :shrug:

I'll need to read into this. To be honest, I know little about whether electromagnetism would be transposition invariant. Perhaps almost slightly embarrased to say, but I have never heard of a transposition quantity.

 

[Reiku]

As for your theory personally, as arrogant as it might sound, I don't agree with but I think it is a promising approach for random physics theory. For people like me, we sit in the lonely camp outside the maintraim still believing in Einstein's dream.

 

[Reiku]

In post 21, I qouted Smolin on the spin network I was approving in my own analysis:

Smolin states:

"We didn't know how, in the language we were working in, to put in the notion of causality" in LQG, Smolin says. Markopoulou Kalamara found that by attaching light cones to the nodes of the networks, their evolution becomes finite and causal structure is preserved. But a spin network represents the entire universe, and that creates a big problem. According to the standard interpretation of quantum mechanics, things remain in a limbo of probability until an observer perceives them. But no lonely observer can find himself beyond the bounds of the universe staring back. How, then, can the universe exist?'' [1]


Notice how also it preserves causality. This is the precurser of determinism, and hopefully, a global case. There is also a serious problem then with my model. If the matter field is not applied and we talk about high energy physics conditions, then causality could not be a quantum case. Causality must break down, since determinism is an occurance of geometrogenesis, according to all the facts.

This is another realization. It speaks of stating that determinism is something recorded by entropy. Entropy is a measure of physical changes in time. If this is correst, then radiation field where the matter field $$\chi=0$$ then there can be no passage of time. These so-called pure gravity theories then have still the looming question:

''Are pure gravity solutions of GR real physical phenomena?''

 

[khan]

I'll need to read into this. To be honest, I know little about whether electromagnetism would be transposition invariant. Perhaps almost slightly embarrased to say, but I have never heard of a transposition quantity.

My brain hurts too Reiku. :shrug:

Einstein was developing the unified theory from the ideas of the non-symmetric field...

http://www.combat-diaries.co.uk/diary29/Link 14 Einstein.PDF

[...]

We postulate for the field equations of the non-symmetric field that they be transposition invariant. I think that this postulate, physically
speaking, corresponds to the requirement that positive and negative
electricity enter symmetrically into the laws of physics.

[...]

http://www.emis.de/journals/HOA/IJMMS/Volume6_4/140940.pdf

With so many covariant variables, it was impossible to choose them according to the relativism alone. To overcome this difficulty, Einstein introduced a very important concept, transposition invariance. This "transposition invariance" (or transposition symmetry) meant that when all A_ik were transposed (A^T _ik == A_ki) all equations were still applicable [2] Einstein supposed that field equations were transposition invariant. He thought that in physics this hypothesis was equivalent to the law that positive and negative electricity occurred symmetrically.

 

[Reiku]

When someone says to me ''a non-symmetric field'' I think along the lines of symmetry-breaking. Now, if I followed you correctly before, you made a mention of symmetry-breaking as a mechanism involved in the creation of the universe.

I have a question for you;

If you think this is the case (which I cannot make my mind up on right now), then what symmetry existed at the big bang to actually break?

I mean, in other words, there must be in some assumption some kind of mathematical symmetry to speak about. Needless to say, this symmetry must have existed at the very first chronon of time, or even planck time if we wish to quantize the beginning.

Or are you assuming some pre-bang notion again, that there was some condition before the BB, in which case, if it was unstable, you must answer two more questions for me:

1) why was it unstable?

2) and how long had it been unstable for?

Perhaps for questions later, once one has evaluated possible answers to these questions, perhaps the priori question dominates everything, that being:

3) Where did all this ''unstable-ness'' come from?

Because in my mind, the idea of a pre-bang scenario does not answer, unless it can, where everything still came from.

 

[Reiku]

In post 21, I qouted Smolin on the spin network I was approving in my own analysis:

Smolin states:

"We didn't know how, in the language we were working in, to put in the notion of causality" in LQG, Smolin says. Markopoulou Kalamara found that by attaching light cones to the nodes of the networks, their evolution becomes finite and causal structure is preserved. But a spin network represents the entire universe, and that creates a big problem. According to the standard interpretation of quantum mechanics, things remain in a limbo of probability until an observer perceives them. But no lonely observer can find himself beyond the bounds of the universe staring back. How, then, can the universe exist?'' [1]


Notice how also it preserves causality. This is the precurser of determinism, and hopefully, a global case. There is also a serious problem then with my model. If the matter field is not applied and we talk about high energy physics conditions, then causality could not be a quantum case. Causality must break down, since determinism is an occurance of geometrogenesis, according to all the facts.

This is another realization. It speaks of stating that determinism is something recorded by entropy. Entropy is a measure of physical changes in time. If this is correst, then radiation field where the matter field $$\chi=0$$ then there can be no passage of time. These so-called pure gravity theories then have still the looming question:

''Are pure gravity solutions of GR real physical phenomena?''

perhaps, if the above is also true, it might correspond alliances with the proof I gave that if the universe truely is timeless in a global sense, then conservation of energy cannot be measured mathematically. And if any measurement of energy cannot be translated in time (it's symmetrical conjugate quantity) then there can be no such thing as a fundamental entropy, only a late case, were clocks tick and matter field persist.

 

[Reiku]

For starters, I can easily state that E=something, when E has not been defined, for instance, AN. Secondly, since I can define E as the energy of the universe under the very simple assumptions based from the WDW equation, then you can define the rest as it naturally unfolds.

(SORRY)

Going back to AN, missed something he said.

Yes I know AN, that changing E changes H. They both amount to the energy afterall. Stop trying to tell me things I don't know.

Also, that does not change the fact that it solves the problem, atleast by solving it with another problem.

 

[Reiku]

Also, AN

''You write down a Hamiltonian (without justification or construction) and refer to it as a configuration space. No, a Hamiltonian is an operator on a space, not necessarily configuration space. ''

Well, you must have missed the $$r_{ij}$$ which defines the distance between $$i$$ and $$j$$. These can be considered ''points'' on a simple Hilbert space. The Hamiltonian is not supposed to be a representation of a configuration space only the former.

Clear?

 

[khan]

When someone says to me ''a non-symmetric field'' I think along the lines of symmetry-breaking. Now, if I followed you correctly before, you made a mention of symmetry-breaking as a mechanism involved in the creation of the universe.

I have a question for you;

If you think this is the case (which I cannot make my mind up on right now), then what symmetry existed at the big bang to actually break?

I mean, in other words, there must be in some assumption some kind of mathematical symmetry to speak about. Needless to say, this symmetry must have existed at the very first chronon of time, or even planck time if we wish to quantize the beginning.

Or are you assuming some pre-bang notion again, that there was some condition before the BB, in which case, if it was unstable, you must answer two more questions for me:

1) why was it unstable?

2) and how long had it been unstable for?

Perhaps for questions later, once one has evaluated possible answers to these questions, perhaps the priori question dominates everything, that being:

3) Where did all this ''unstable-ness'' come from?

Because in my mind, the idea of a pre-bang scenario does not answer, unless it can, where everything still came from.

A Highly symmetric pre-bang state would be inherently unstable as there would be no entropic time arrow as we now experience.

http://en.wikipedia.org/wiki/Stephen_Hawking

In collaboration with Jim Hartle, Hawking developed a model in which the universe had no boundary in space-time, replacing the initial singularity of the classical Big Bang models with a region akin to the North Pole: one cannot travel north of the North Pole, as there is no boundary. While originally the no-boundary proposal predicted a closed universe, discussions with Neil Turok led to the realisation that the no-boundary proposal is also consistent with a universe which is not closed.

Once maximal entropy is reached for the universe there is also no arrow of time:

http://www.wired.com/wiredscience/2010/02/what-is-time/

Carroll: The arrow of time doesn’t move forward forever. There’s a phase in the history of the universe where you go from low entropy to high entropy. But then once you reach the locally maximum entropy you can get to, there’s no more arrow of time. It’s just like this room. If you take all the air in this room and put it in the corner, that’s low entropy. And then you let it go and it eventually fills the room and then it stops. And then the air’s not doing anything. In that time when it’s changing, there’s an arrow of time, but once you reach equilibrium, then the arrow ceases to exist. And then, in theory, new universes pop off.

When maximal entropy is reached in the universe there would be no more entropic arrow of time and that is also unstable. It is also a different type of symmetry condition. The universe then quantum jumps into a pre-bang condition or new universes are born depending on the theoretical model :shrug:

Since there is no arrow of time after maximal entropy and no arrow of time for the pre-bang era. There is no before or after for the universe. All versions would essentially exist simultaneously. :bugeye:

 

[AlphaNumeric]

For starters, I can easily state that E=something, when E has not been defined, for instance, AN. Secondly, since I can define E as the energy of the universe under the very simple assumptions based from the WDW equation, then you can define the rest as it naturally unfolds.

E is defined the moment you write down the Hamiltonian. They are not independent constructs, the Hamiltonian defines the energy.

And for last, you obviously can't understand the nature of the problem if you think the universes energy can be solved in terms of high perturbative expansions, since, the universe can no longer be a steady expansion, yet is now exponential as it increases proportionally and relativistically at magnitudes of the speed of light.

Nice try, unfortunately in trying to say "You don't understand perturbative expansions and their role" you've shown you don't understand perturbative expansions and their role. The whole thing about the Lippmann-Schwinger equation involves altering a default Hamiltonian with a potential. S matrices are generally computed using expansions. In fact that's what Feynmann diagrams are, they are contributions to the perturbation. You're throwing in stuff to do with cosmology and expansion unnecessarily. The question is whether you're doing it because you think it's relevant or because you're trying to throw up a smoke screen.

Your waffling about bookwork expressions suggests it's a smoke screen. Let's consider one of them ....

According to a quantum approach, if $$\mathcal{O}$$ is some observable, then the operator is stationary and the state is time-dependent if

$$\frac{\partial}{\partial t} < \mathcal{O} > = \frac{1}{i\hbar}< \{ \mathcal{O}, \mathcal{H} \}>$$

Not true. What you've written down is the equation which describes the time evolution of an operator expectation value, yet you claim it's what follows if "the operator is stationary and the state is time-dependent". It's obvious to anyone who understands anything about this that if something is time independent then the time derivative vanishes so obviously what you say and the equation you provide don't quite gel. I imagine you've missed out a line or two from the source you're copying. What you really meant was "The equation for the time evolution of an operator's expectation value is....". If it's constant then $$\frac{\partial}{\partial t} \langle \mathcal{O} \rangle = 0$$.

If we take the derivative with respect to $$\rho$$

There's no rho in the expression you gave. Again, I imagine you've skipped a few lines from where ever you're copying from. The fact you don't even realise what you're saying is obviously not in line with the expression you've given (seriously, no rho!) shows how mindlessly you're parroting this stuff. No one typing that off the top of their head would repeatedly make such mistakes.

and divide both sides of the equation with the derivative in respect of our time derivative,

$$\rho = T_{\alpha \beta} \chi^{\alpha}\chi^{\beta}$$

That's not even a coherent sentence.

then we would have after quantizing our equation

The time dependence equation was already quantised. Don't you see the $$\hbar$$ there? That's what it's for.

would yield, this time including our time derivative

$$\frac{\partial \rho}{\partial t} = \frac{1}{i\hbar} \{ H, \rho \}$$

This is just the Heisenberg equation of motion for any operator. Seriously, it's such a basic result it's covered in any lecture course on quantum mechanics which covers time dependence and operators. The expression you equate $$\rho$$ to has nothing to do with it, you've just written down an identity in the Heisenberg picture.

This can be solved by Ehrenfest's Theorem.

No, Ehrenfest's theorem doesn't 'solve' that. It implies a closely related expression (more specifically the original time derivative equation you wrote down), since as stated immediately on its Wiki page it is that equation with an additional term. Ehrenfest's theorem doesn't 'solve' a differential equation, it tells you how to quickly and easily construct one!

Best of all, this equation works for a mixed state, just like a matter field with many particles.

Best of all it's a very basic and core result which you couldn't even state properly!

As for your theory personally, as arrogant as it might sound, I don't agree with but I think it is a promising approach for random physics theory. For people like me, we sit in the lonely camp outside the maintraim still believing in Einstein's dream.

You sit in the 'lonely camp' because you refuse to learn anything properly. All you do is copy equations you don't understand and pass off other people's explanations and algebra as your own understanding.

I absolutely guarantee you'll never contribute to 'Einstein's dream' if you continue in this way.

Yes I know AN, that changing E changes H. They both amount to the energy afterall.

No, the expectation value of the Hamiltonian is the macroscopic energy and the state energy is the eigenvalue of the Hamiltonian associated to the eigenstate being considered. You can construct E from H but not the other way around.

Stop trying to tell me things I don't know.

Sorry but you don't know so much that it's hard to say anything without telling you something you don't know.

Also, that does not change the fact that it solves the problem, atleast by solving it with another problem.

No, it doesn't.

Also, AN

''You write down a Hamiltonian (without justification or construction) and refer to it as a configuration space. No, a Hamiltonian is an operator on a space, not necessarily configuration space. ''

Well, you must have missed the $$r_{ij}$$ which defines the distance between $$i$$ and $$j$$. These can be considered ''points'' on a simple Hilbert space. The Hamiltonian is not supposed to be a representation of a configuration space only the former.

Clear?

Wrong again. The terms in the Hamiltonian, $$r_{ij}$$, quantify the distance between particles. Obviously you don't see the difference there. The particles exist at points in a space. This space has an inner product on it and so you can promote it to a Hilbert space. The distances between points can be obtained via the use of the inner product but the output of the inner product is not an element in the Hilbert space so the distances do not belong to the space. Furthermore the Hamiltonian can depend on these distances but that doesn't mean it's in a Hilbert space. It acts on elements of the Hilbert space and it can depend on properties of states in the Hilbert space.

Also, you're the one who said "the configuration space looks like... [expression for Hamiltonian]" so if you're now saying the Hamiltonian isn't supposed to be a representation of a configuration space then you're contradicting yourself. Which statement are you going to stand by?

Given you've been rereading my post and retorting anything you can when you think you've got a retort I'll assume you accept that the other points I raised are valid.

khan, if you haven't realised it yet if you're looking for informed discussion you're not going to get it from Reiku. Of course if you're looking for someone to throw buzzwords back and fore with and convince yourself you're 'living Einstein's dream' then knock yourself out.

 

[khan]

khan, if you haven't realised it yet if you're looking for informed discussion you're not going to get it from Reiku. Of course if you're looking for someone to throw buzzwords back and fore with and convince yourself you're 'living Einstein's dream' then knock yourself out.

It is VERY tempting for me to take poetic license with buzzwords but I actually hope to learn from an informed discussion, yes. There is no nearby university where I can go to learn about tensor calculus, so, for the last few years, I have built up a large collection of books on the subject:

Leonard Susskind
The Black hole War

Kip S. Thorne
Black Holes & Time Warps

Lieber,Lillian R.
The Einstein Theory Of Relativity (1945)

http://www.archive.org/details/einsteintheoryof032414mbp

Ray A. d'Inverno,
Introducing Einstein's Relativity

Bernard F. Schutz,
A First Course in General Relativity

Robert M. Wald,
General Relativity,

Charles W. Misner, Kip S. Thorne, and John A. Wheeler,
Gravitation

Alan P. Lightman
William H. Press
Richard H. Price
Saul A. Teukolosky
problem book in relativity and gravitation

Paul A. Dirac,
General Theory of Relativity

David C. Kay,
Schaum's Outline of Tensor Calculus

Nils K. Oeijord
The Very Basics of Tensors

I have not read all of these books yet but I have them and I plan to keep reading them until I can master the concepts within

I made it through lecture 11 of this great online course:

http://www.youtube.com/playlist?list=PL6C8BDEEBA6BDC78D

Multivariable vector calculus is also extremely helpful to me:

http://www.youtube.com/playlist?list=PL4C4C8A7D06566F38

I wish to learn the facts of the universe ...and the facts of the universe are tensors.


...

 

[Reiku]

Quantify the distance, define a distance, if this is about a single word, then so be it have it your way.

Given you've been rereading my post and retorting anything you can when you think you've got a retort I'll assume you accept that the other points I raised are valid.

Of course, hasn't that been the way with us since the dawn of time?

E is defined the moment you write down the Hamiltonian. They are not independent constructs, the Hamiltonian defines the energy.

But the Hamiltonian defines E as you said, then a vanishing E directly effects the Hamiltonian. Am I missing something?

Nice try, unfortunately in trying to say "You don't understand perturbative expansions and their role" you've shown you don't understand perturbative expansions and their role.

Yea, and I was under the impression perturbative expansions are not necesserily assumed to be exponential... are there any cosmological cases you can inform me about?

In fact that's what Feynmann diagrams are, they are contributions to the perturbation. You're throwing in stuff to do with cosmology and expansion unnecessarily. The question is whether you're doing it because you think it's relevant or because you're trying to throw up a smoke screen.

Well let me explain.

I am throwing these things in because I find them necessery, or ''relevant'' as you put it. Should there be a potential?

Well yes there should, the cosmological application of a potential often comes in the form $$a^2-g^2a^4$$. This potential is often seen in the Hartle-Hawking Cosmological models.

Why is expansion important? Well, as the universe expands, more energy is released into the vacuum. If my theory so far dictates that energy is not conserved in a universe, then the implication that the universe is now receeding faster than light is an indication the universe is using up more and more energy at an exponential rate. (The latter here was actually hypothesized by Michio Kaku). Secondly if it is releasing energy due to its superluminal expansion, then the energy increases but there is no time to measure it still because of the vanishing time derivative in the WDW equation, which you will notice, has no place in the Lippmann-Schwinger equation.

The only way to calculate time, would be to take the energy density of a universe $$\rho=T_{ab}\phi^a \phi^b$$ use my idea that $$\bold{x}_i$$ is the sum of all four-vector velocities of the field, then when a massless field obtains mass, we have

$$\rho \bold{x}_i =T_{ab}\vec{\chi}^a \vec{\chi}^b \cdot x^{\mu}_{i}\tau_i$$

This expresses the matter field as calculated in such a way it describes the world lines, of remember, the equation I first defined as $$\dot{\chi}$$. This can be seen most effectively in

$$\frac{\partial \rho}{\partial t} = T_{ab} \dot{\chi}^a \dot{\chi}^b$$

which when quantized,which is what was implied originally, yield your quantum terms

$$\frac{\partial \rho}{\partial t} = \frac{1}{i\hbar} \{H,\rho \}$$

It's obvious to anyone who understands anything about this that if something is time independent then the time derivative vanishes so obviously what you say and the equation you provide don't quite gel.

You've not read me right. I said time-dependant, not time independant.

The whole point is to find a way were the time derivative does not vanish. Quantize a field, let real matter particles act as clocks. What good is approaching a theory where the time derivative vanishes, thus only to end up with the theory you are trying to avoid?


ps. You said that when I said R_ij is the distance between particles, you said that was wrong, then explained it was the distance between particles. Confused...

 

[Reiku]

It is VERY tempting for me to take poetic license with buzzwords but I actually hope to learn from an informed discussion, yes. There is no nearby university where I can go to learn about tensor calculus, so, for the last few years, I have built up a large collection of books on the subject:

Leonard Susskind
The Black hole War

Kip S. Thorne
Black Holes & Time Warps

Lieber,Lillian R.
The Einstein Theory Of Relativity (1945)

http://www.archive.org/details/einsteintheoryof032414mbp

Ray A. d'Inverno,
Introducing Einstein's Relativity

Bernard F. Schutz,
A First Course in General Relativity

Robert M. Wald,
General Relativity,

Charles W. Misner, Kip S. Thorne, and John A. Wheeler,
Gravitation

Alan P. Lightman
William H. Press
Richard H. Price
Saul A. Teukolosky
problem book in relativity and gravitation

Paul A. Dirac,
General Theory of Relativity

David C. Kay,
Schaum's Outline of Tensor Calculus

Nils K. Oeijord
The Very Basics of Tensors

I have not read all of these books yet but I have them and I plan to keep reading them until I can master the concepts within

I made it through lecture 11 of this great online course:

http://www.youtube.com/playlist?list=PL6C8BDEEBA6BDC78D

Multivariable vector calculus is also extremely helpful to me:

http://www.youtube.com/playlist?list=PL4C4C8A7D06566F38

I wish to learn the facts of the universe ...and the facts of the universe are tensors.


...

Well, I kind of learned something from you.

It had escaped my notice originally how important the triangle inequality was, when you started to speak about ''hidden gems'' concerning heisenbergs uncertainty principle and the inequality.

It was until afterwards I realized it was important since the spin network relies on keeping the inequality in its phase space.

 

[AlphaNumeric]

Quantify the distance, define a distance, if this is about a single word, then so be it have it your way.

No, it obviously isn't 'about a single word', it's about many words. Seriously, are you so desperate to reply with something that you'll misrepresent me on the same page as the post in question? I clearly explain in detail your many mistakes, including multiple terminology related ones, so to say it's about a single word is either moronic or trolling. There isn't any other option. Either you utterly fail to understand basic English narrative (in which case you have no hope of understanding published papers) or you're being deliberately obtuse.

Of course, hasn't that been the way with us since the dawn of time?

Just to check a few examples, so you accept your 'solution' involves a geometry? You accept no such quantum system exists with the time parametrisation you gave.You accept the 'singularity' has nothing to do with space-time? Do you accept Ehrenfest's theorem doesn't 'solve' what you claim it did? Do you accept you just stated the Heisenberg equation of motion?

Explicit yes or no answers please.

But the Hamiltonian defines E as you said, then a vanishing E directly effects the Hamiltonian. Am I missing something?

You make it sound like E is the fundamental parameter. It isn't. The Hamiltonian of a system is what it is. The energy of a system is defined by the expectation of the Hamiltonian in that state, ie $$E = \langle H \rangle_{\psi} \equiv \frac{\langle \psi | H | \psi \rangle}{\langle \psi | \psi \rangle}$$. Changing state may or may not change E. It won't change H. Although in the Heisenberg picture operators, rather than states, are time varying the Hamiltonian is constant. Can you tell me why? It relates to something you've said.

Yea, and I was under the impression perturbative expansions are not necesserily assumed to be exponential... are there any cosmological cases you can inform me about?

What are you on about?! The perturbations we're talking about here have nothing to do with cosmology or exponential expansion in space-time. Yes, there's talk of perturbations and expansions pertaining to space-time in things related to the WDW equation but the perturbative expansions I gave examples of have nothing to do with them. You're showing you're just buzzword matching. Come on, try a little harder.

I am throwing these things in because I find them necessery, or ''relevant'' as you put it. Should there be a potential?

Sorry but they aren't. I gave clear context and you've just thrown in something you might find if you googled for "Wheeler-De Witt equation, perturbations". In fact I just did precisely that and low and behold it returns things related to metric perturbations, not the sort I'm talking about here.

If you really want to do science you need to be more than a glorified search engine and word comparer.

Well yes there should, the cosmological application of a potential often comes in the form $$a^2-g^2a^4$$. This potential is often seen in the Hartle-Hawking Cosmological models.

But the parameter isn't time, as you stated.

Why is expansion important?

You're trying to grandstand. There's no need for you to explain the importance of expansion in cosmology to me. Rather than throw up another smoke screen try to actually justify your quantitative claims.

If my theory so far dictates that energy is not conserved in a universe, then the implication that the universe is now receeding faster than light is an indication the universe is using up more and more energy at an exponential rate.

Firstly you don't have a 'theory', not in the scientific sense. You have something which hardly qualifies as a dubious hypothesis. It's a random guess.

Secondly you haven't considered any energy conservation. You haven't shown a violation of any of the energy conservation derivations. To use the theoretical physics phrase (so you can go Google) you haven't shown an anomalous current exists.

Thirdly the phrase "The universe is now receding faster than light" is ambiguous and poorly defined. I know what you're referring to but that isn't an excuse for being bad at explaining yourself.

Fourthly you haven't shown any exponential expansion rate. Expansion doesn't mean exponential. There's numerous 'regimes' of expansion in cosmology, depending on various factors like energy and matter densities.

(The latter here was actually hypothesized by Michio Kaku).

But he did some actual work to reach the conclusion. If I just said

"Under the closure of the 3-form $$dH = 0$$ we obtain an exponential bifurcation of the Higgs potential, $$\mu \to \mu_{\pm}e^{\pm iEt}$$, which implies black hole entropy is proportional to its surface area"

then I wouldn't make it more valid by saying "Hawking agrees with that last result".

Secondly if it is releasing energy due to its superluminal expansion, then the energy increases but there is no time to measure it still because of the vanishing time derivative in the WDW equation, which you will notice, has no place in the Lippmann-Schwinger equation.

Firstly you haven't justified any of that. Secondly time independence in a quantum system doesn't imply no dynamics occur. Dynamic equilibria of particle interactions are time invariant but dynamics occur all the time. For example, the quantum field theoretic vacuum's properties are time independent but there's always a frenzy of activity going on. Thirdly the L-S equation doesn't negate time dependence.

The only way to calculate time, would be to take the energy density of a universe $$\rho=T_{ab}\phi^a \phi^b$$ use my idea that $$\bold{x}_i$$ is the sum of all four-vector velocities of the field, then when a massless field obtains mass, we have

$$\rho \bold{x}_i =T_{ab}\vec{\chi}^a \vec{\chi}^b \cdot x^{\mu}_{i}\tau_i$$

This expresses the matter field as calculated in such a way it describes the world lines, of remember, the equation I first defined as $$\dot{\chi}$$.

Reiku, do you really think I (or anyone who didn't sleep through high school) believes you did any such calculations? Firstly (notice how I keep listing multiple mistakes you make in just a single paragraph?) the expression you give for density is not a fully general or even clearly defined one. Secondly your definition of $$x_{i}$$ is clumsy and sounds an awful lot like the definition of $$\mathbf{X}$$ given here. Looks like another example of you parroting something, trying to change it and mangling it into nonsense. So much for it being your idea. Not only is it not original, it's essentially plagiarised. If you're going to plagiarise, at least get it right. Thirdly your equation is mathematically meaningless since the index structure isn't consistent. Just like you have to get units right you have to get indices right and you have a spare $$\mu$$ on the right hand side. You have a similar issue with the i index, your notation is ambiguous.

You keep making such mistakes, failing to make simple things consistent. It's a sign you're copying without understanding. Sure, everyone makes a slip up here and there but the frequency you do it is too high to be excusable as slip ups.

This can be seen most effectively in

$$\frac{\partial \rho}{\partial t} = T_{ab} \dot{\chi}^a \dot{\chi}^b$$

How did you get that from the previous expression? Let's see the step by step derivation.

which when quantized,which is what was implied originally, yield your quantum terms

$$\frac{\partial \rho}{\partial t} = \frac{1}{i\hbar} \{H,\rho \}$$

Except it doesn't, not from your expression. As I just explained, which makes me wonder why on Earth you're repeating a discredited approach, that equation is the Heisenberg equation for any time dependent operator. The problem is you have gone from a scalar quantity to an infinite dimensional operator, as well as pluck a Hamiltonian from nowhere.

Now while it might be possible to construct a GR system from some metric, construct an energy condition, deduce it's equations of motion, upgrade the fields to quantum fields and then obtain such an equation I am confident it's the sort of thing which takes a dozen papers and so much eye watering algebra you could see it from space. This is the realm of Hawking's work, stuff which is extremely complex. You don't just say "And you quantise" and magically a GR equation into one of the central QM equations.

You're just throwing out equations and expressions and hoping no one will call you on it. If you could really do this sort of GR or QFT you'd know just how ridiculous it is for you to be pretending to understand it based on just some pop science reading and a mediocre high school grasp of mathematics and physics.

You've not read me right. I said time-dependant, not time independant.

Okay, I misread it. However, on rereading it I notice you made a different mistake. You said "if O is some observable, then the operator is stationary and the state is time-dependent if [equation]". The equation tells you how the expectation value varies in time. It applies when an operator is stationary and the state time dependent and is applies when the complete opposite is true. It's a picture independent equation. In the Dirac picture the states vary and the operators are fixed while in the Heisenberg picture it's the reverse. That's why the equation for the time dependence of an operator is the Heisenberg equation of motion. It isn't true in the Dirac picture.

The two different pictures are important and pretty simple concepts, covered almost immediately when covering operators. I guess you missed that YouTube video...

The whole point is to find a way were the time derivative does not vanish. Quantize a field, let real matter particles act as clocks. What good is approaching a theory where the time derivative vanishes, thus only to end up with the theory you are trying to avoid?

What good is making stuff up and mangling other people's work, in an attempt it off as your own understanding? What good is just being dishonest and spouting equations and terminology you don't understand in an attempt to deceive people online?

ps. You said that when I said R_ij is the distance between particles, you said that was wrong, then explained it was the distance between particles. Confused...

No, I said that the Hamiltonian (and thus terms in the Hamiltonian, including $$r_{ij}$$) is not a configuration space or points in a configuration space or anything like that. It's an operator which acts on elements of a space, which may or may not be a configuration space for some system. I never said the $$r_{ij}$$ weren't distances. It would be much easier if you understood what a Hilbert space it, what states are, what operators are, what expectation values are, what any of this stuff is.

 

[Reiku]

Let's do this one at a time shall we.

you stated a few things here: ''so you accept your 'solution' involves a geometry? You accept no such quantum system exists with the time parametrisation you gave.You accept the 'singularity' has nothing to do with space-time? Do you accept Ehrenfest's theorem doesn't 'solve' what you claim it did? Do you accept you just stated the Heisenberg equation of motion? ''

Let's start with, why you think it involves a geometry?

 

[Reiku]

Just on the side while you answer my previous question:

you said near the end

''No, I said that the Hamiltonian (and thus terms in the Hamiltonian, including ) is not a configuration space or points in a configuration space or anything like that.''

But you stated something I stated and said it was wrong. Even if this is not what you implied, you really need to use your imagination AN. If two particles are seperated by a distance r_ij then the two particles must have positions in space somewhere. In a very loose, but still correct statement, that if particles are described by a Hilbert Space as I have demonstrated then we must be implying some kind of configuration space.

 

[Reiku]

Just also to clear up a few loose ends:

''Reiku, do you really think I (or anyone who didn't sleep through high school) believes you did any such calculations? ''

In the paragraph you have stated, I was quite aware of the density relationship . Is there any reason why my own relationship does not hold? If so I will quite willingly forget those relationships. But I can assure you right now that $$x_i$$ is not $$X$$ since $$x_i$$ is the four velocity. The four velocity (summed over all particles given by $$i$$) multiplied by the density gives you your matter field acting like a unit timelike vector. As our original field $$\phi$$ acted on $$x^{\mu} \tau}$$, it created $$\chi$$ the inertial matter field. Thus from

$$\rho = T_{ab}\phi^a\phi^b$$

multiply by the four velocity gives

$$\rho x_i = T_{ab}\phi^a\phi^b (x^{\mu}\tau)$$

The right hand side turns into $$T_{ab} \chi^a \chi^b$$

.... and here I realized I've made a mistake, I've dropped a term on the right hand side

because from there it should be, divide by $$\partial t$$ on both sides and taking partial \rho gives

$$\frac{\partial \rho x_i}{\partial t}= \frac{ T_{ab} \chi^a \chi^b}{\partial t}$$

Which means my assumptions on Heisenberg equation don't apply. Ignore it now AN.

 

[Reiku]

You say $$\chi = \tau$$ and then have a V which is purely a function of $$\tau$$, ie time. No such quantum mechanical system exists.

Well, considering I never reparamaterized any of my equations and I mentioned it just for the sake of stating some possible solutions to the WDW equation, I will find the paper....


....right http://arxiv.org/PS_cache/hep-th/pdf/9503/9503073v2.pdf

Page 8-11 should suffice.

 

[Reiku]

Let's do this one at a time shall we.

you stated a few things here: ''so you accept your 'solution' involves a geometry? You accept no such quantum system exists with the time parametrisation you gave.You accept the 'singularity' has nothing to do with space-time? Do you accept Ehrenfest's theorem doesn't 'solve' what you claim it did? Do you accept you just stated the Heisenberg equation of motion? ''

Let's start with, why you think it involves a geometry?

OOOooohhh right. I read back on your posts (end up ignoring half of it because you tend to write so much), that

via a series of unjustified non-sequitors, that you end up with a result which doesn't involve geometry. You used the SC metric! You made an explicit reference to a geometry.

That's ok.

You see, we haven't even applied the Hilbert Space or any spin networks. I recall reading that r_ij is also a metric, a special kind of one, but that must have missed you as well. Niether metric are related, as far as I can tell.

I qoute Markoupoulou

''Just as there are no waves in the
molecular theory, we will likely not find geometric degrees of freedom in the fundamental theory. By analogy with known physics, we should expect that the quantum theory of gravity is not a theory of geometry. I must emphasize that no geometry does not mean discrete or fuzzy geometry. It means that the most primary aspects of geometry, such as the notion of \here" and \there" will cease to make sense. In fact, we have been grappling with no geometry for a while, in the traditional quantum gravity settings.''

Now, quantum graphity actually admits metric solutions, the things which involve space, matter and geometry http://arxiv.org/pdf/0801.0861v2.pdf . The approach however, even though I have adopted and Markoupoulou uses, argue that geometry does not fundmantally.

Keep in mind also, that fundamentally it is argued that geometry does not exist, not that it does not exist at all. The world of high energy physics is related to permutation symmetries, no locality and no subsystems. Low energy states are concerned with geometry and subsystems and the like.

In my original representation to you, I used the LS-equation to solve the original energy hamiltonian of the universe with potential. I had no explicitely stated yet that this specific equation would describe no geometry. That is only achieved when you would begin to model your theory with a Hilbert Space. In this space, as Fotini puts it:

''Information before geometry. Having raised the possibility that geometry does not exist at the fundamental level, we now need to find a way to do physics without geometry. This may appear hard because all our physics is done with geometry. But we can use a relational and information theoretic language.''

An example is that she considers a finite relational universe with N constituents, a bit like my (summing over all the particles making a field approach) which she models as a network of N nodes (a,b...=1) with a Hilbert Space $$\mathcal{H}_{ab}$$ attached to each link (ab). It is this model I am trying advocate.

I think it is the correct approach because it sufficiently describes high energy physics, low energy, geometry stuff exists, we know this. It is once you apply the following approaches could we possibly achieve some kind of quantized theory involving no geometry.