Physics Subtly Implies no Geometry for Space

[Reiku]

In tackling my theory of the cosmological energy-time problem, I considered first of all a question which has plauged observer-physics; How can the universe have an energy? To have an energy, someone would need to be sitting outside of the universe to view it's energy content. That or someone would need to sit until the very last moment of existence and maybe they will be fortunate enough to measure an energy.

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]

This was a passage from a webpage describing her newest works in attempting to view space as having no geometry, it is only the configuration of matter which gives rise to the geometrical assembly of observables, that fundamentally, geometry was to be banished. Einstein's theory then, cannot assume that geometry will exist when unification of GR with QM is achieved.

With this, I extended the question in terms of conservation of energy, whether the universe possessed one. In light of the energy problem of an observer to define the wave function, a number of other ''facts'' of physics seemed to agree there was no energy at all.

There was the no-energy condition of universes, where every peice of energy and matter all mathematically reduced to zero. And more prominently, there was the infamous of Time Problem of QM, the issue of the vanishing time derivative in the WDW equation. The WDW equation is in fact obtained from quantizing Einstein's field equations.

Interestingly one approach Markoupoulou uses is spin network theory in Quantum Loop Gravity.

Someone here called Khan mentioned the uncertainty principle in relation to geometry.

Well a similar approach can be found in spin networks. Each point or ''unit'' as they are called, represent geometric points in space and must obey the triangle inequality (the same example khan used). In an abstract sense, my Hilbert space demonstration (Markoupoulou's approach also) is an attempt to describe the configuration space of a spin network in terms of Hilbert Spaces.

The geometry is then emergent from well-positioned particles called the spin network.

[1] http://www.mlahanas.de/Greeks/new/Kalamara.htm

 

[Reiku]

In my solution to the Singularity $$(E-H_0)$$ where we make the matter-energy content vanish, is akin to making the matter langrangian equal zero $$\mathcal{L}_M$$ then what is left over is the Einstein-Hilbert action.

$$S=\frac{1}{4\pi G}\int d^4x \sqrt{-g}(R - 2\Lambda) + \int d^4x \sqrt{-g}\mathcal{L}_M$$

What is left over from my quantity is the metric itself.

In the EH action, the quantity left over makes it perfect to describe the gravitational field itself, even without the presence of matter. The right hand side of this equation

$$\nabla R^{\mu \nu} = \frac{1}{2}\nabla_{\mu}g^{\mu \nu}R$$

says that if it is equal to zero, then there is no matter in the universe. But should this imply there is zero curvature? Gravity takes a new appearance as gravitational waves. They have no mass but they can ripple spacetime and cause curvature.

I propose that matter came from such curvature. These gravitational waves might be so ellusive now that we may never see one. It must have occurred when the universe had cooled sufficiently to allow geometry to be translated then from the positions of particles in a spin network.

We remove geometry, but there is also the remaining time problem. Well, time may then be a late phenomena, atleast one which can be translated successfully by measuring the motion of particles, thus requiring geometry and the notion of matter. But if time does not exist period, then neither should matter, or any real geometry. It is all just a quantized set of spaces.

Then what of the no-energy proposal? There is still the problem of whether the universe could even have an energy without a global time translation.

 

[khan]

Hypothetically speaking - before the big bang - also called the "pre-bang" era - instead of a singularity, all the forces of nature along with all matter energy, space and time, could have been unified into a single substance that was existing in a highly symmetrical yet unstable state. It underwent spontaneous symmetry breaking and the universe was born.

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

Both General Relativity and Quantum Mechanics break down in describing the Big Bang, but in general quantum mechanics does not permit particles to inhabit a space smaller than their wavelengths.

:shrug::shrug::shrug:

 

[Reiku]

Hypothetically speaking - before the big bang - also called the "pre-bang" era - instead of a singularity, all the forces of nature along with all matter energy, space and time, could have been unified into a single substance that was existing in a highly symmetrical yet unstable state. It underwent spontaneous symmetry breaking and the universe was born.

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



:shrug::shrug::shrug:

You make a lot of shrugs, but you must have a good idea, to make mention of the things you have, how indepth these subjects are.

For instance, it is true; the ''quantum gravity'' as it has been dubbed - the single fasceted side of a four-edged coin - the unification of gravity with EM and weak and strong nuclear forces.

Yet saying reality appeared because this force was unstable, seems too folly for me. There must be mechanisms involved, it is surely not enough to say that it was unstable (no dig at you). In relativity, there is an old question - what came first, matter or curvature?

The answer must be curvature. So we can answer where matter came from - the appearance of energy itself is much more primal according to Geometrogensis. There was, at a point, a beginning of spacetime where energy eminated from a singularity. There is a contradiction with the pre-bang era.

Assuming that relativity is taken seriously, then one cannot speak about time or space assuming this is pre-bang. Unless one assumes that space and time has always existed.

 

[Reiku]

If the vacuum is a configuration space for matter which exist in Hilbert Spaces, described by spin networks that obey the uncertainty principle inequality triangle relationship, then it might be possible to describe the kind of universe I was planning for the last few years. That is, space and time as far as we can record it appeared from an unstable region where matter was compressed to increadible densities. The space between the existing objects did not exist, hence why space began to expand, so that new degrees of freedom could be experienced.

 

[Reiku]

So how does the Cauchy-Schwartz Inequality work?

Well, any time you take the dot product of any two vectors then you cannot find anything larger than if you just multiplied the two vectors' lengths.

$$| <x|y>| \le |x||y|$$

Is the inequality. Remember then, that particles in the Spin neywork must obey this inequality. So what I am wanting to do, is retrieve the geometrical relationships in a space with no geometry!

God my brain hurts.

 

[AlphaNumeric]

How about participating in a discussion of the OP, and divert your attention from the equation. It is not the only thing that has been discussed.You act like it is.

I am not going to feed your desire to deceive people. You're talking about Hilbert spaces and metrics but you don't know the material, you're just parroting it.

I'd challenge you to do some questions on it but you've already failed to do stuff years simpler which James asked you.

But the way, your use of reparameterisations is wrong. Would you like to explain where? Go on, show you understand the stuff you're spouting. Last time I asked you and even pointed you at the relevant equations you couldn't notice a mistake so I won't hold my breath.

 

[Reiku]

I am not going to feed your desire to deceive people. You're talking about Hilbert spaces and metrics but you don't know the material, you're just parroting it.

I'd challenge you to do some questions on it but you've already failed to do stuff years simpler which James asked you.

But the way, your use of reparameterisations is wrong. Would you like to explain where? Go on, show you understand the stuff you're spouting. Last time I asked you and even pointed you at the relevant equations you couldn't notice a mistake so I won't hold my breath.

You claim I am parroting known stuff yet equally state I am deceiving people.

That is a contradiction.


I am talking about Hilbert Spaces because I know how to apply it in theory. The work suggesting the solution to the equation solving the singularity is also my work. I simply chose to solve the equation in terms of the Lippman-Schwinger equation.

 

[Reiku]

My use of reparameterisations is wrong? Guess where?

Well, considering I am using an identical approach as a paper I have followed in the past, you'd be best to clarify what the problem is.

 

[khan]

So how does the Cauchy-Schwartz Inequality work?

Well, any time you take the dot product of any two vectors then you cannot find anything larger than if you just multiplied the two vectors' lengths.

$$| <x|y>| \le |x||y|$$

Is the inequality. Remember then, that particles in the Spin neywork must obey this inequality. So what I am wanting to do, is retrieve the geometrical relationships in a space with no geometry!

God my brain hurts.

I have many questions and speculations. I suspect that in order for a universe to maximize entropy it must have three expanded spatial dimensions and one entropic "time arrow" dimension. Universes with less than three expanded spatial dimensions would be extremely stable but would not have the necessary degrees of freedom to produce maximal entropy. Universes with higher than three expanded spatial dimensions would have higher symmetry but would be unstable and would decay into a more stable configuration I am guessing. :shrug:



Von Newman entropy

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

Entropic Gravity

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

Entropic gravity is a hypothesis in modern physics that describes gravity as an entropic force; not a fundamental interaction mediated by a particle, but a probabilistic consequence of physical systems' tendency to increase their entropy. The proposal has been intensely contested in the physics community.

Causal dynamical triangulations are beyond my understanding at this time

http://arxiv.org/pdf/1001.4581.pdf





...

 

[Reiku]

I have many questions and speculations. I suspect that in order for a universe to maximize entropy it must have three expanded spatial dimensions and one entropic "time arrow" dimension. Universes with less than three expanded spatial dimensions would be extremely stable but would not have the necessary degrees of freedom to produce maximal entropy. Universes with higher than three expanded spatial dimensions would have higher symmetry but would be unstable and would decay into a more stable configuration I am guessing. :shrug:



Von Newman entropy

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

Entropic Gravity

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




Causal dynamical triangulations are beyond my understanding at this time

http://arxiv.org/pdf/1001.4581.pdf





...

Let me concentrate on this ''time presumption based on science'' which you have brought up.

I see the word ''entropy'' being raised.

In so many words, I think entropy is an inertial quantity rather than a relativistic one. The reasons why are actually quite simple. One reason is because only entropy is measured by the chronological account of the ''flux'' (aka. passage) of time. Time we should not forget then, is merely a calculational tool to derive semi-symmetries.

Semi

-symetries are creations of two boundary conditions. A good example is the Plank Time. It is bound by a beginning and end point and this is the quantized path to formulating a universal understanding of GR.

The cosmological side almost fades out, it is quite disturbing.

We are, it seems able to be forced by physics to suggest that the cosmological side of the universe, can only up to certain limit be unified. If that remaining half or whatever fraction has remained unanswered with remain as such, because of an incomplete theory we have so admirably followed to this point in our history.

If unification is to be achieved, then the cosmological approach of unifying an understanding of time and space into the world at large (General Relativity) then these relativistic relations will find new contraints on the theory predicting incredible new pictures, I predict.

But as far as entropy goes, my own speculations and years of studies seem to indicate, that time is only measured by observers, experiences yet what is called a ''local time'', measured in real coordinates. Since photons and other types of energy particles with no mass term face the same relativistic dynamics of Lorentz Invariance, then these particles without mass experience no time.

In a certain approach to unify this all, the matter field $$\chi$$ I have speculated on in this post and others, could have a time description using a Julian Barbour Approach, one which had time invariant in the calculations, but using other solutions with avoided any time term but used observable quantities (an arguement he used in his own paper).

It will be calculated by the sum of all the particles, the primordial matter field $$\chi$$ therefore is unique enough to have a name of it's own, which I will call the ''Origon Field'' from the latin word ''Origo'' meaning ''beginning'' and ''on'' from traditional nuclear-naming of particles such as, Prion, Gluon, Photon ect.

This field however could not be the field which originated at big bang, assuming it is correct.

It must be a low energy phenomenon, as a late epoch where the single matter field broke into many others. This was the origin of the spontaneous symmetry breaking, when the (if found) Higgs particle dressed energy into inertial matter particles. Fundamentally-speaking then, the Origon Field then is the explanation of inertial appearance in matter.

 

[Reiku]

Universes with less than three expanded spatial dimensions would be extremely stable but would not have the necessary degrees of freedom to produce maximal entropy.

Totally, Khan.

Geometrogenesis is the appearance of any necessery degrees of freedom to produce any kind of entropy in the geometric sense. One in a manner, could argue that entropy in a geometric sense could not happen at big bang, for obvious reasons. So did entropy fundamentally exist?

 

[Reiku]

This is also why I said the Uncertainty Principle is the reason for the expansion of space because, as you said:

''Universes with less than three expanded spatial dimensions would be extremely stable but would not have the necessary degrees of freedom to produce maximal entropy.''

Which just to follow on, if there are no degrees of freedom then this violates the fundamental cornerstone of physics, the uncertainty principle - so in order for the universe to push back from where it began, a high quantum potential designated the further design of an expansion. Why, we can only look at the suspects.

 

[AlphaNumeric]

You claim I am parroting known stuff yet equally state I am deceiving people.

That is a contradiction.

No, it isn't. You parroted Susskind but since you didn't understand some of the things he said you miscopied or misexplained or misrepresented results he was writing down in that YouTube video.

Besides, passing off other people's explanations as your own is deceiving people, as you did with Susskind and James's questions.

Also when you do try to weave in your own nonsense you try to hide it within a discussion of some paper or video or bit of bookwork. Or you just don't clarify when you're talking about stuff you made up rather than referring to some paper, as is the case with your matter flow 'equation'.

I am talking about Hilbert Spaces because I know how to apply it in theory.

Tell me, do you really believe yourself when you say such things or are you aware you're mistaken?

Well, considering I am using an identical approach as a paper I have followed in the past, you'd be best to clarify what the problem is.

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

The work suggesting the solution to the equation solving the singularity is also my work. I simply chose to solve the equation in terms of the Lippman-Schwinger equation.

This is precisely what I'm talking about. You recently failed to do questions expected of high school students, stuff you should have just steam rollered. You failed utterly and made laughable excuses but rather than think "That made it so obvious I can't do this stuff perhaps I should stop" you've just started up another thread spewing out more buzzwords.

The Lippman-Schwinger equation pertains to eigenvalue/eigenstates of infinite dimensional operators, yet you struggled with 2x2 matrices.

Or how the equations involved in this area of quantum mechanics heavily relate to oscillations and peroidic functions, something you failed to even recognise in the high school example James asked you about. James asked you something I remember doing when I was 17, but you couldn't do it and yet now you're claiming to be presenting alternative approaches to quantum mechanics problems?

You clearly don't understand the nature of the singularity referred to in the system. It's a pretty standard one, encountered in bookwork for introductory courses in quantum mechanics so people can learn how to do with certain types of eigenvalue related problems. One method is to use high order perturbative expansions and another is to use complex integration and perturb the contour slightly. Both of them have very sound mathematical footing.

Let's consider your 'solution', to sub in an expression for E from the SC metric. You have no justification for that, beyond word association with 'singularity'. Beyond the fact they both pertain to quantities which look like 1/0 they are not related to one another, but you wouldn't get this if you can only buzzword match. Secondly the form E takes is dictated by the Hamiltonian, a principle fundamental and core to Hamiltonian mechanics. The expectation of the Hamiltonian is literally the expectation of the energy of a system. You cannot change the E's without changing H. Thirdly, even changing E or H or rewriting the form of E doesn't negate the fact the E in the expression is defined as an eigenvalue of H and therefore $$(H-E)|\psi\rangle = 0$$ is possible. Writing $$E = \textrm{something}$$ doesn't avoid this any more than writing 0 = 1-1 doesn't magically make 1/0 = 1/(1-1) valid. Fourthly you end up claiming, 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. Now Markoupoulou might manage to use a standard method like the contour integral perturbation to get a result without reference to a geoemetry but you don't.

You also show you don't know how to use words properly. 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. You also say that "Indeed, a Hilbert Space are often called ''points'' which describe abstractly the configuration space". That isn't true either. Certain constructions/descriptions of certain configuration spaces can be described using Hilbert spaces but not all Hilbert spaces are configuration spaces (few even have physical interpretations!) nor are all configuration spaces Hilbert spaces. Nor does having a Hamiltonian imply you're working with a Hilbert space. Nor does having a Hilbert space imply there's a Hamiltonian. These concepts might be used together sometimes but they are constructions in and of themselves, they are not necessary or sufficient for one another. Heck, I've just spent the last fortnight considering Hamiltonians which aren't Hermitian. Or defined on a Hilbert space.

Clearly you read someone say something like "the ''points'' which describe abstractly the configuration space can be taken to be elements in a Hilbert space" but given you don't know the formal properties of such things or their proper applications in physics or mathematics you've tried to reword it. And like you do all too often when you try to reword things, you screwed it up.

I am in no doubt that you've honed your BS'ing skills enough to be able to con some non-physicists unfamiliar with your past but you're even more transparently dishonest now than you were 4 years ago. You've been increasing the level of complexity of the material you try to parrot but it just leads to ever more glaring abuses of terminology and non-sequitors. That's why I don't see any reason to engage you in actual discussion on the subject matter, you demonstrate that if left to your own devices you'll quite happily spout nonsense and be dishonest. I didn't force to you post that nonsense, just like I didn't force you to make post after post pushing your $$\dot{\chi}$$ equation despite after you'd admitted it was a pile of nonsense you'd made up a drunken evening. Clearly you'll lie when you think you can get away with it. If you don't have enough respect for people who are looking for honest discussion, like khan seems to be, to be honest why should you expect to be treated kindly? If you piss on someone's shoes they'll not be very happy with you, particularly if you say "It's not me, it's raining" when they tell you to stop.

 

[Reiku]

And additionally, you could apply yukawa couplings along the same line of using them in quantum theory to measure different particles masses. Equally, spontaneous symmetry breaking in the Higgs form, might be the correct mathematical approach to a different interaction.

 

[Reiku]

Alpha numeric***

**** off.

 

[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.

 

[Reiku]

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.

 

[Reiku]

I have came to some interest, in a different mathematical approach which satisfies, I think, the fluid density dynamics of a universe

If

$$\rho_{I} \bold{x}_i = T_{\alpha \beta}(\phi^{\alpha}_i \phi^{\beta}_j \cdot (x^{\mu}\tau)_i)$$

where $$\phi$$ is some scalar field (here in hindsight, consider it the ground state mexican hat potential). $$\bold{x}$$ is the four veclocity, so we are keeping our relativistic form.

The $$i's$$ here are mathematical markers. Since the density at this point of the equation does not satisfy any inertial conditions by requisit, then as $$x^{\mu}_i\tau_i \rightarrow c$$ where $$c$$ is the speed of light, then $$\phi = 0$$.

In concordance to this mathematical motive, the coupling terms satisfy $$\delta_{ij}$$. Since $$\phi = 0$$ then this describes the ground energy of a photon. This therefore assumes that the inertial density is also zero $$\rho_I = 0$$.

If $$(x^{\mu}_i\tau)_i< c$$ then the inertial couplings $$\psi(\phi_i, \bold{x}_i)$$ at certain energy requirements.

Thus meeting these requirements, we can now state $$\phi$$ in new terms when it acts as a fluctuations away from the ground state, so $$\phi \ne 0$$. We may assume, for the beauty of unity that $$\phi = 1$$.

Thus, what we end up with is an inertial term on the right hand side, where $$\phi$$ couples with $$(x^{\mu}\tau)_i$$ such that we can make $$(x^{\mu}\tau)_i$$ vanish from the equation and allow the matter field to now be a a unit timelike vector which defined the world lines of some configurations of particles, then the energy-mass density of the universe would be the scalar field

$$\rho \bold{x}_i = T_{\alpha \beta} \chi^{\alpha} \chi^{\beta}$$

Which neglects the four velocity. I think this is an important realization that maybe the vanishing four-velocity parameter is in fact an indication of the breakdown of this equation.

 

[Reiku]

I have came to some interest, in a different mathematical approach which satisfies, I think, the fluid density dynamics of a universe

If

$$\rho_{I} \bold{x}_i = T_{\alpha \beta}(\phi^{\alpha}_i \phi^{\beta}_j \cdot (x^{\mu}_i\tau)_i)$$

where $$\phi$$ is some scalar field (here in hindsight, consider it the ground state mexican hat potential). $$\bold{x}$$ is the four veclocity, so we are keeping our relativistic form.

The $$i's$$ here are mathematical markers. Since the density at this point of the equation does not satisfy any inertial conditions by requisit, then as $$x^{\mu}_i\tau_i \rightarrow c$$ where $$c$$ is the speed of light, then $$\phi = 0$$.

In concordance to this mathematical motive, the coupling terms satisfy $$\delta_{ij}$$. Since $$\phi = 0$$ then this describes the ground energy of a photon. This therefore assumes that the inertial density is also zero $$\rho_I = 0$$.

If $$(x^{\mu}\tau)_i < c$$ then the inertial couplings $$\psi(\phi_i, \bold{x}_i)$$ at certain energy requirements.

Thus meeting these requirements, we can now state $$\phi$$ in new terms when it acts as a fluctuations away from the ground state, so $$\phi \ne 0$$. We may assume, for the beauty of unity that $$\phi = 1$$.

Thus, what we end up with is an inertial term on the right hand side, where $$\phi$$ couples with $$(x^{\mu}\tau)_i$$ such that we can make $$(x^{\mu}\tau)_i$$ vanish from the equation and allow the matter field to now be a a unit timelike vector which defined the world lines of some configurations of particles, then the energy-mass density of the universe would be the scalar field

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

Which neglects the four velocity. I think this is an important realization that maybe the vanishing four-velocity parameter is in fact an indication of the breakdown of this equation.

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

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

If we take the derivative with respect to $$\rho$$ and divide both sides of the equation with the derivative in respect of our time derivative,

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

then we would have after quantizing our equation would yield, this time including our time derivative

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

This can be solved by Ehrenfest's Theorem. Best of all, this equation works for a mixed state, just like a matter field with many particles.