# True Time Evolution In Gr And The Wheeler De-Witt Equation

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### #1 Aethelwulf

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Posted 23 October 2012 - 12:07 PM

Essay 1 of 2

Abstract

In this essay we will investigate what it means when we talk about time in relativity, why this question is important when we consider the universe as a whole and identify several kinds of different types of time one can talk about - which will lead us to the final question, whether time is in fact real.

True Time Evolution In GR and the Wheeler de-Witt Equation

Fotini Markopoulou argues in her published paper:

http://www.fqxi.org/...forum/topic/376

that in GR there is no such thing as a true time evolution. This is true. So with this in mind, think about what a time evolution means then when we think about our universe at large... is there such thing? Does the consequences of not having a true time evolution hint at why timeless solutions to the equations of relativity show up and further what consequences would this entail?

No Time Must Imply no Energy

And so for now, we must understand energy in the context of time. The absense of energy therefor, would imply the absence of time and vice versa; but why is this important?

Well, I have a proposal to make. Because Einstein's equations generate a motion in time that is a symmetry of the theory and thus not a true time evolution at all, we seem to be left with a timeless model. The universe would then be timeless.

Yet, if this is true and the universe is truely timeless, then surely this would mean that energy is devoid in our universe as well?

The counterintuitive facts just keep on trucking from the soil of Relativity, but this is one fact I must state. The innability of finding a time evolution for the universe would result in a faulty premise concerning whether it has an energy.
Fred Alan Wolf asked the question in his book Parallel Universes

''How can the universe have an energy?''

He further makes his point clear by saying that for the universe to have a defined energy someone would need to be sitting outside the universe to actually observe the energy. There is a way out of his problem and the paradox of timelessness and energy which I proposed above.

The whole universe, can only be observed by two possible ways: that is by someone either sitting outside the universe, or by someone who is sitting in the infinite future. Usually both examples are considered impractical [1] because they seem to purport to unphysical concepts.

I however, can see merit in the idea that something in our future has defined a total energy for the universe and by doing so, we may be able to recover the present moment; though it will not let us create the past and future, no amount of nip and tuck will rectify the problem that the past and future are simply illusions of the mind.

Enter the Transactional Interpretation (TI). In a seperate post mentioned how the TI could allow for signals to be sent back from the future to our past and shaping the past as we know it. This is not wild speculation but is a corner stone understanding of physics in general, through what is called Wheeler's Delayed Choice Experiment. (3)

The emmiter could be an electron, radiating a photon, which is caused by producing a field. The field is time-symmetric under the Wheeler-Feynman description which and as John Cramer describes it ”time-symmetric combination of a retarded field which propagates into the future and an advanced field which propagates into the past.”

He considers a net field which consists of a retarded plane wave form $F_1$

$F_1 = e^{i(kr-\omega t)}$

Here, $t$ is the instant of emission. The advanced solution $G_1$ is simply

$G_1 = e^{-i(kr - \omega t)}$

The idea is that the the absorbing electron responding to the incident of the retarded field $F_1$ in such a way it will gain energy, recoil, and produce a new retarded field F2=-F1 which exactly cancels the incident field F1. The net field after such a transaction is zero.

$F_{net} = (F_1 + F_2) = 0$

Applying this to a universe can be beneficial. It can help explain how the early universe came into existence, because the future implied it through probability. The future of our universe can shape the early universe in such a way that it can define parts of the universe which are smeared by possibilities and out of which only one true history can survive. So there is the chance that the wave function in our universe is sending information back to points in our universes history where the early universe is just being formed.

This experiment has further varification in the Quantum Eraser Experiment.

The ability to make an observation on a system which may have traversed multiple paths due to the wave function will collapse into a single path - but what we are really doing when we observe the system is we are effectively creating a defined past for that object (mind I am using past as a calculational tool).

So a particle might travel the universe, take every possible path, arrive here on earth to be observed by a scientist to send quantum information backwards (the negative time wave solution of the TI) to the past history of the particle and define attributes which were but a smear of possibilities... Now, before we loose track, I will quickly get to the point. This is perhaps what is happening in our universe and why thinking about an observer in the infinite future is important. You can't have an observer sit outside space, nothing can exist outside of the universe, not even an observer.

Well, it turns out you don't even need an infinite future. To solve this, you need a boundary, or rather a symmetry in time. The very last instant of the universes existence will be were an observer would need to sit to view all the energy of the universe. By doing so, they would define whether the universe began with an energy or not. Who is this observer? Is it a form of intelligence? I don't know, all I know is that there is a problem if timelessness exists and that is that energy automatically ceases to exist, yet to solve this is by saying something intelligent is located in the very last instant of the universe which is sending signals back in time in the form of quantum waves (the kind you find in the transactional interpretation) so that the early universe could have some kind of defined volume of energy and perhaps maybe squeezing in the present time.

I am not completely against the idea of a present time existing outside in the universe defining objects, I just think it should be noted that the past and future certainly do not.

There could be something more sinister to realize perhaps, that maybe the universe is not a conserved case of energy. This statement however just seems to hard to believe ... or does it? The universe is now receeding faster than light which seems to indicate that our universe is using energy at a faster rate. In doing so, it might be conjectured that on the crux of things, the universe is not conserving energy like a ground state atom and thus will quantum leap sometime in the future. Odd to think of a universe quantum leaping, but this has been the literature in quantum cosmology.

Usually when we talk about a system not conserving it's energy, we talk about the system not having a symmetry. A symmetry would let a langrangian density be $L\delta = 0$. That is a conserved energy from symmetry, but if you add something into the equation that break's this symmetry then you no longer have a conserved quantity. So maybe, just maybe Noether's Theorem is not applicable to the universe because it does not retain the symmetry allowed to express the system as a conserved quantity.

Timelessness and the Crux of the Problem

So, I am beginning this complete set-up of understanding the current problem in physics: the unification of Quantum Theory and Relativity theories - of course, such an approach requires that our knowledge of high energy physics is correct. But there is a prevailing uncertainty just how to do this at the moment. There seems to be a number of problems in our attempt at unification and one such problem is the infamous Time Problem of General Relativity.

In essence, when you quantize the famous Einstein field equations, you end up with what is called the Wheeler de Witt equation;

$H| \psi> = 0$

Normally on the right hand side, we would see the presence of a time derivative. However, this equation should have ended up something like your usual energy schrodinger equation, but for an entire universe, this does not seem to be possible.

The fact there is a vanishing time derivative, this had led to the interpretation that the universe, time atleast, from a global sense does not exist, that the universe is really about static time. This can seem at first like a big of a gee whiz moment, because time being static seems very exotic. However, there maybe still a new way to view this and I will tackle this from Fotini Markoupoulou's stance of time, which we will cover soon and to which I will add new concepts. I don't add them frivoulously, this is still a real science.

Now, of course, there maybe those still out there shrouded by the veil called time, they cannot see past their own experiences. We do afterall sense time pass, so why should we believe time does not exist? Surely if we experience time, there must be some corresponding physical application to the world at large. Well, over the years of studies I have made, this ''feeling'' of time might just be that: simply a feeling. The psychological arrow of time actually explains really well why we may feel a ''directionality to time''. This directionality of time is the arrow of time many people abuse, thinking it has a real consequence on physical reality. As observers, we experience a local time, but what does it mean when we talk about a ''global time'' or a ''local time''?

Global Time

A global time, is a time encompassed, or experienced by clocks inside of the universe. It is concerned with many groups of systems and never one alone. If one could sit outside the universe, we would actually view it as a static system. In a way to justify that claim, which Barbour does not do in his paper but does mention this fact, is through the weak measurement physics. In quantum cosmology, Prof. Steven Hawking believes we must veiw the universe like an atom. So indeed, if we were to view the universe from outside [1] then the energy content would not change. In fact, if we actually could, then we could measure the universes energy. It is well-known that the universe in totality cannot have a very well-defined energy unless someone was to actually measure it; and if no superintelligence exists then perhaps we may assume that the energy cannot be defined.

Local Time

Local time is the asymptotic time everyone comes to agree on: we all experience time, this cannot be denied. Time seems to be strictly local in this sense, local to bodies like ourselves, including even electrons [2] and perhaps other particles which experience zitter motion. By this reasoning, many believe, including myself that time is not in fact global, that global time does not exist and if anyone can speak about time, it must be purely local. But I now raise an important question --- ''surely then there is a major difference to saying no time exists than saying that a static time exists for a universe?''

Well, yes it does. In fact, static time may not even exist. It perhaps only makes sense to speak of static time when fields came into existence which broke the static nature. Indeed, time may not even exist fundamentally - this is the same as saying that time does not exist. We shall see why soon.

Since we are on the subject of observers, we may as well talk about one special part of the human observer which points to evidence that time is really something we experience and does not exist independant of the human. There is in fact a biological reason for experiencing time - there is a gene regulation inside the brain called the Suprachiasmatic Nucleus (This is one of two gene regulators inside of the brain which is reponsible for sense of time). This is one prominent reason among the scientific community to why we even sense a time pass.

There is while we are on the subject, the idea of an arrow time. I do not believe a true arrow of time exists, however if one can understand what is called the ''Psychological Arrow of Time,'' one can understand why we may think or percieve there being a future and past to events.

$t_1$ is the present time, $t_0$ is the past time.

$t_1 = t_0 + [t_1 - t_0]$

This says the present time is the past plus some time delay.

so effectively if we let D represent a time delay, then:

$t_1 = t_0 + D^{-}$

The past plus the now is really the same as saying the past plus a time delay, so replace that with $t_0 + D$). What of a future time?

Then that to us would mean the present plus a time delay

$t_1 + D^{+} = t_1$

we still have the present moment. We constantly live in the present moment, things like a future and past don't truly exist, only as intelligent recording devices like ourselves who scrutanize the world around them do we create this bizarre illusion that somehow something lies behind of us and that our thoughts and actions lies ahead of us.

Geometric Time

And thus the question is asked, why does it seem like time exists then? Why should we experience time if it does not exist? What makes us so special?

It's not that we are special per se, but we are in an important energy phase of the universe, called the low energy phase. The low energy phase happened late in the universe's history - do not mistake ''late'' as implying a time however. This is where the english language breaks down and we need to use different approaches to explain what we mean. There can be change in Julian Barbours eye's, but there is no such thing as a time. So can we reconcile change without time?

Yes, we can. It may not seem obvious at first, but things like the zeno effect gives us evidence that even if time really did exist, systems don't need to change.

Fundamental Time

So what is fundamental time? Fotini Markoupoulou created this type of time understanding. However, she takes this fundamental time as real, but I take it as not being real. The reason why I do not agree with Markoupoulou on this one, is because of her own reasoning. Geometry did not appear till very late in the universes history, so we must infer that time did not exist either if indeed Minkowski space is the correct representation for the low energy epoch. Of course, for this reason, fundamental time would be the application of a time dimension when the energies in the universe were very high. But if geometry did not exist, then the universe was born without time. Therefore time is not really fundamental at all. To explain this better, I labelled this as ''induced time''.

Induced Time

So, if I am saying time did not appear until geometry appeared, am I saying time really exists? The answer to this is ''no'', because induced time is not the same as a real existing time. If you like, the time anything experienced in the low energy epoch is in fact a by-product of slow moving systems; it appears when matter appears. Geometrogenesis is the science of physics and cosmology concerned with the appearance of matter. It wasn't until the phase space of the universe broke symmetries did the original photon fields or other radiation fields gave way to the matter fields which now dominate our portion of the universe. Therefore, geometrogenesis does in fact dictate, not predict, but dictate that time could not exist before the dimensions of space emerged: time is afterall a space dimension, it is called the imaginary space dimension - an imaginary leg off the spacetime triangle.

Then we must ask, well, if geometry and matter appeared late in the universes history, we ask also then whether time appears from such a geometry? If so, then time is emergent, it is an induced phenomenon which appears alongside the usual suspects: those being space and time. We cannot infer gravity directly because gravity can exist without matter. So curvature can still exist without matter - it just comes in a different guise, a radiation field which don't even have clocks which can tick off real time. (Hopefully everyone knows that photons do not experience time, including any type of radiation.) Relativity cannot deal with time and radiation together in such a way.

[1] - It is still impractical however to think anyone can sit outside the universe and view the energy content of the universe because according to relativity, there is no such thing as an outside to the universe; however saying that some theories like certain classes of string theory entertain that our universe is in fact ''bubble like'' floating in a multidimensional pool.

[2] - In fact, electrons have internal degrees of freedom, a special clock. The electron clock has been theorized and written upon by David Hestenes. It seems the electron clock has been varified.

[3] - The way the transactional interpretation treats the wave function is the idea of a positive time wave and a negative time wave are able to move from the future to the past and from the past to the future. The wave moving forward in time is an advanced and moving back the retarded wave functions; and as you may guess, the waves are solutions of different quantum information packets which upon the absolute square amplitude they will define real existing things.

Edited by Aethelwulf, 24 October 2012 - 02:52 AM.

### #2 Aethelwulf

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Posted 23 October 2012 - 01:02 PM

I'd like to note something. When I said...

''

$t_1 = t_0 + D$ 1.

The past plus the now is really the same as saying the past plus a time delay, so replace that with $t_0 + D$). What of a future time?

Then that to us would mean the present plus a time delay

$t_1 + D = t_1$ 2.

''

You can't actually get from equation 1 from equation 2. If one did rearrange equation 1 you would have

$t_1 - D = t_0$

but that is not where I was heading and does not make much sense. The point was to show the absurdity of thinking that we experience a future time. The equations above are inconsistent and even incorrect, because all there is, is the present time. The presentation of these equations are fundamentally flawed because there is no past or future.

### #3 Aethelwulf

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Posted 23 October 2012 - 03:31 PM

Is the universe leaking energy? Is there actually an information loss in the vast?

http://www.scientifi...-leaking-energy

### #4 Aethelwulf

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Posted 23 October 2012 - 10:54 PM

I will post part 2 of this essay in about... a weeks time. There is plenty to digest here and plenty potential questions.

### #5 Aethelwulf

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Posted 24 October 2012 - 02:55 AM

I'd like to note something. When I said...

''

$t_1 = t_0 + D$ 1.

The past plus the now is really the same as saying the past plus a time delay, so replace that with $t_0 + D$). What of a future time?

Then that to us would mean the present plus a time delay

$t_1 + D = t_1$ 2.

''

You can't actually get from equation 1 from equation 2. If one did rearrange equation 1 you would have

$t_1 - D = t_0$

but that is not where I was heading and does not make much sense. The point was to show the absurdity of thinking that we experience a future time. The equations above are inconsistent and even incorrect, because all there is, is the present time. The presentation of these equations are fundamentally flawed because there is no past or future.

I've attempted to try and help the understanding of this a bit clearer. I have edited the original post. I will call $D^{-}$ the negative time delay, the one which is a delay from what we think is a past into a present time and $D^{+}$ to represent the positive time delay, the one ''we think'' we move into from the present.

I cannot point more strenuously enough however, there is only the present moment. These delays are figments of the imagination.

### #6 Aethelwulf

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Posted 04 November 2012 - 03:18 AM

And this now finished off my whole essay...

''Time is redundant as a fundamental concept.''

Julian Barbour

(1)

Part Two of my Essay

Not only is time redundant as a fundamental concept, but if we take the Big Bang seriously, then we are forced to think that space itself cannot be fundamental. Wheelers Geometrogenesis would actually agree with this premise, as was explained before, geometry appears when the universe begins to sufficiently cool down and then moving clocks appear in the universe.

Just think about the implications of this. They are quite profound - it would mean that General Relativity is equally redundant in explaining the beginning of the universes origins in terms of geometry. May it be then, of no surprise that all attempts at unifying general relativity with QM has profoundly escaped the grasp of those intrigued with such idea's, perhaps because the application of geometry itself at the beginning of time is totally redundant?

Remember, if you don't actually remove geometry, at the very beginning, we find singularities with the incomprehensible and totally unphysical concept of an infinite curvature. There cannot be such an infinite curvature if space and time are not fundamental, so we are, perhaps only just beginning to understand why a theory of everything has seemed so evasive.

Let's explore what we mean in relativity when we are talking about geometry.

The Einstein Field Equations

You work out the spacetime curvature using what is called the Curvature Tensor, the mathematical tool we use in relativity to explain the geometry of the surrounding spacetime of an object with a dense mass. Usually, the curvature of celestial objects are quite weak, unless we are talking about denser objects like Pulsars or even Black Holes.

I have going to have to explain this as quick as I don't wish to bore the reader with too much math.

You're gonna have to know some math to completely understand this, even some knowledge on tensors. I can't explain everything today. The thing which calculates curvature in General Relativity is the Riemann Tensor and its given as

$R^{\rho}_{\sigma \mu \nu} = \partial_{\mu} \Gamma^{\rho}_{\mu \sigma} - \partial^{\rho}_{\nu \sigma} + \Gamma^{\rho}_{\mu \lambda} \Gamma^{\lambda}_{\nu \sigma} - \Gamma^{\rho}_{\nu \lambda} \Gamma^{\lambda}_{\mu \sigma}$

The part $\Gamma_{\mu}\Gamma_{\nu}$ is what you call the commutator of two matrices.

You can rewrite it more compactly when you bracket expressions and realize that these are the derivatives of the connection ''Gamma''

$\frac{\partial \Gamma_{\mu}}{\partial x^{\nu}} - \frac{\partial \Gamma_{\nu}}{\partial x^{\mu}} + \Gamma_{\nu}\Gamma_{\mu} - \Gamma_{\mu}\Gamma_{\nu}$

You can only get the Riemann tensor by contracting the ''Ricci Tensor''. Notice that one alpha is on the upper indices and one is on the lower indices:

$R_{\mu \nu} = R^{\alpha}_{\mu \alpha \nu}$

Repeated indices means you automatically sum over these indices. The lowercase $\mu \alpha$ actually describe some rotation plain for a very small area displacement $(dx^{\nu}, dx^{\mu})$

You can also contract using the metric, for instance

$R_{\lambda \sigma \mu \nu} = g_{\lambda \rho} R^{\rho}_{\sigma \mu \nu}$

Can you guess which one is contracted? If you said $\rho$, you'd be right. What is $g_{\mu \nu}$ contracted with $R^{\mu \nu}$? It's just $R$ is the answer. You would get the curvature scalar by contracted the Ricci Tensor $R^{\mu \nu}$ and has this following form

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

where we call $\nabla_{\mu}$ the covariant derivative. I think the covariant derivative originally came from work on fibre bundles. The property of a covariant derivative just has this form:

$\nabla_{\mu}AB = A\nabla B + (\nabla A) B$

The covariant derivative of $g_{\mu \nu}$ is actually zero.

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

$\nabla [R^{\mu \nu} - \frac{1}{2}g^{\mu \nu} R ]= 0$

This can be rewritten as a short-hand

$R^{\mu \nu} - \frac{1}{2}g^{\mu \nu} R = G^{\mu \nu}$

so

$\nabla_{\mu}G^{\mu \nu} = 0$

This is the local continuity equation for gravitational energy. As I said before, $g^{\mu \nu}$ derivative is zero, so what we have is

$R - 2R = 0$

and $R=0$ when there is no energy-momentum present.

So we learned the ''Einstein Tensor'' $\nabla_{\mu} G^{\mu \nu}=0$

The right hand side of $\nabla_{\mu} R^{\mu \nu} = \frac{1}{2} \nabla_{\mu}g^{\mu \nu} R$ describes the matter in a universe. Even when matter is zero, it does not mean that curvature has to be zero. Gravitational waves for instance and other forms of energy can cause curvature in a vacuum which is an interesting facet of the theory to keep in mind. Now all this stuff is related to Einstein's equations because they can either derive the equations or be derived from his field equations. They are what you call a rank 2 tensor, and to help explain what a Rank 2 tensor is, we shall dedicate a little time to this.

Tensors

This is just a quick explanation of what we mean when we talk about ''tensors.''

It's difficult trying to explain this stuff to anyone - even when you are trying to teach something to someone in a very short post - but I think I have a way that can help you understand it.

Some simple equations to consider might be

$A_{(y)}^{m} = \frac{\partial y^m}{\partial x^y} A_{(x)}^{r}$

The upper and lower indices here $A_{(x)}^{r}$ are called the ''components of the vector.'' Consider a second one as well

$B_{(y)}^{n} = \frac{\partial y^n}{\partial x^s} B_{(x)}^{s}$

How would we write our first tensor mixed in with our second tensor? You would have to mix them in an appropriate way:

$A_{(y)}^{m}B_{(y)}^{n} = \frac{\partial y^m}{\partial x^y}\frac{\partial y^n}{\partial x^s}A_{(x)}^{r} B_{(x)}^{s}$

And that is us, wasn't too hard eh? This is what you call a mixed tensor of ''second rank''. We can identify it by changing it slightly

$T_{(y)}^{mn} = \frac{\partial y^m}{\partial x^y}\frac{\partial y^n}{\partial x^s} T_{(x)}^{rs}$

Think of these upper indices as counting the rank of your tensor, so the upper indices $T_{(y)}^{mn}$ would count as a second rank tensor. The tensor above is in fact a contravariant tensor because the important indices just spoke about are on the uppercase. If they are lowercase, they are covariant tensors:

$T^{(y)}_{mn} = \frac{\partial y^r}{\partial x^m}\frac{\partial y^s}{\partial x^n} T^{(x)}_{rs}$

And viola! That's you done. This is a rank 2 tensor.

Back to Curvature and Geometry

And so, with our quick summery of curvature, we can see it is written into the laws of nature as we understand it from General Relativity, but if time and space are truly not fundamental concepts, then relativity in it's usual form must break down - in fact, if we applied the equations to the beginning of time, we reach a point, as I have noted before, a point of infinite density and geometry. This is called the singularity of the Big Bang and for many years, many scientists have seen it as a ''break down'' of the theory on very small scales.

Going back to the very beginning of my essay, I explained how no time would imply no energy. The two are inseparable fascets of Noether's Theorem. Again, we asked the question before, how can the universe have an energy any way, unless someone was to observe it? Things in QM's cannot have observables like energy until they have been measured. The measurement problem of Big Bang, may not be a problem at all, but rather a hint that things like, space, time and even energy are not fundamental concepts at all. There is in physics also, the Null Energy condition.

If all the negative matter cancels out every positive peice of matter, such as the zero-energy universe. In particular interest, it is in fact the Minkowski metric (the four dimenensional manifold) which implies zero energy. The reason why the Minkowski metric implies the null energy condition (2) will require only a few steps. We begin with an equation which has been selected because it is a result of the Schwarschild's metric

$E = Mc^2 - \frac{GM^2}{2R}$

If one sets the mass to zero $M=0$ what you are essentially left with is just the metric, so this is classed as the null energy condition. All the energy simply vanishes ina universe but to further add to this strange part of physics, we wouldn't have a metric either, because as we have already explained, the universe came from a point where no geometry existed in the first place. The old saying ''something from nothing,'' often comes to mind.

nterestingly though, I have already elaborated on a time-energy problem concerning how if there is a vanishing time then there is no way to translate a universal symmetry with any energy, the equivalent to energy being conserved.

Alone, we have seen that time and energy have some problems if they are to be understood fully.

As I mentioned earlier, Fotini has described a universe without space. Albeit, she does this to achieve merit in her opinion that time can be saved, but she still raises an interesting argument in favour of Geometrodynamical models.

Conclusions

Is it by chance that the Einstein Field equations, when quantized lead to either a static interpretation of time, or one that completely vanishes from the universe at large? I don't think it is an accident, but an indication that when we consider things like the energy of the universe, it simply cannot have an energy. This has been looked upon in this essay as perhaps having something being closely related to the zero energy condition. In fact, we have also not only raised the problems that the origins of this universe treat space and time as not fundamental concepts, but also we have seen that if there is no symmetry for the translation of energy and time, then energy would appear not to be conserved in this universe at large.

This does seem to be the case within the current mainstream thinking, except my model is the first of it's kind to explain it from the similar web of idea's concerning the Wheeler de Equation and those concerned with Geometrogenesis. Hopefully my work will help bring a kind of understanding into the unification of physics, even if it does lead to a description of the universe which is ultimately a grand illusion.

(1) - http://www.fqxi.org/...71bae814fb4f9e9

(2) - http://arxiv.org/pdf...c/0605063v3.pdf

Edited by Aethelwulf, 04 November 2012 - 03:26 AM.

### #7 Aethelwulf

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Posted 05 November 2012 - 03:48 AM

Since we have been discussing (well myself) the idea that the universe comes from nothing, here is a nice paper which explains that... it also avoids that nasty infinite curvature we wish to avoid because spacetime is not fundamental

http://mukto-mona.ne...rom_nothing.pdf