Essay Abstract

In this speculative work I investigate whether God may find a place in theoretical physics. The comparison between some aspects of the nature of God, as deduced by the philosopher St.Augustine, and general relativity, suggests to identify God with a chronology violating region of spacetime. From this conclusion some physical suggestions can be drawn. Among them novel solutions to the homogeneity and entropy problems of cosmology.

Author Bio

Ettore Minguzzi is researcher of mathematical physics at the University of Florence, Italy. He has earned his PhD from Milano University in 2002. His main research interests are in general relativity and applied gauge theories. In the last years he has contributed to global Lorentzian geometry and causality theory in particular with the study of the "causal ladder of spacetimes". He is a member of SIGRAV "Societa Italiana di Relativita Generale e Fisica della Gravitazione", SEGRE "Spanish Society on Relativity and Gravitation", ISGRG "International Society on General Relativity and Gravitation" and FQXi.

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Dear Mr. Minguzzi,

I have read your essay .. at least in parts.

I thought it was good that you have faced up your cards on the table and that you have shown how you define God. But I think your solution is far from clear. I have also defined God and my solution is completely different from yours.

After your journey through modern physics, especially through the world of general relativity, you still believe in God as a supreme being acting from a chronology violating region. My lesson after this journey was very different: I could no longer believe in God as a being. Instead of that I was forced to consider God as an impersonal basis of all that exists.

Like you I defined God explicitly. I defined God as something invisible and omnipresent. Both attributes are classical theological properties. Both are described in the Holy Bible; invisibility ..Romans 1.20; omnipresence .. Psalm 139. After this definition I asked myself: How must the universe look like if the ultimate foundation of it is described just by these two attributes.

Finally I found that these two properties could perfectly be described as a specific set of physical conditions which the universe had to satisfy if it shall base upon a sphere, that is described as invisible and omnipresent at the same time. I am calling this set the Principle of Radical Non-Duality. The most important point is: There is even concrete evidence that our universe does really follow this principle.

If theological attributes like invisibility and omnipresence are explainable as the natural result of some specific physical conditions of our universe then it is simply impossible to provoke any longer the existence of a GOD. There is no gap left to introduce a supreme Being like a God into the universe.

H. Hansen

Author ... The Taming of the One.

Dear Dr. Minguzzi,

Can you please provide the proof for theorem 3.4? I was reading your essay thinking that it is no different than Gott's ideas until you addressed the very same point. Now I am not a believer in CTCs (macroscopically they are unphysical in the range of the validity of the correspondence principle as I have shown myself, and at the quantum level they destroy quantum mechanics' coherence as noted by Boulware and Hawking, and have serious problems in defining the expectation values as pointed out by Jacobson), but the ideas are interesting. So St.Augustine was right in the framework of classical mechanics, but he could not have anticipated quantum mechanics which spoils the whole discussions because of unitarity violations.

My take on St.Augustine's ideas is that you can understand God as the timeless platonic world of math.

Dear Prof. Moldoveanu,

thank you for the questions.

I have posted this same paper, including the proof of theorem 3.4, here: arXiv:0909.3876.

The proof is still rather sketchy, I plan to give an expanded version later.

I will keep informed the readers on any update. The simpler chronological case is covered by reference [19], while the mentioned proof of the generalized case uses some results of [20].

Concerning the comparison with Gott III and Li article, I may add that while we both use a chronology violating region from which the whole Universe develops, my paper is differnt from their in that it stresses the importance of this CTC element for solving the homogeneity problem that in Gott III and Li paper is solved, if I am not mistaken, through inflation (in fact their universe undergoes inflation even before closing into itsef, see the conclusions of their paper).

Also they argue that the entropy at the boundary of the chronology violating region should be zero, but it seems to me that they refer there to the entropy related to the stress energy tensor, that is to the matter (and radiation) entropy and not to the gravitational entropy. In this submission instead I suggest that the gravitational entropy vanishes because of a (metric) rigidity mechanism at the boudary which is ultimately due to the fact that this boundary is generated by lightlike geodesics.

Also I would like to stress another point which I rapidly mentioned in the conclusions.

The important ingredient to solve the homogeneity problem is to assume that if you take the compactification of your `well behaved(chronologicall) part of' spacetime you get a boundary in which the component that generates the whole Universe (the Big Bang) is such that distinction is violated there. This is what you need to justify homogeneity. Then if you also want to justify low entropy it is natural to assume that it is generated by lightlike lines so that you constraint considerably the geometry (this is likely to be proved

if you assume that this is also a boundary for a chronology violating region). But if so it satisfies continuity and maybe differentiability properties that may allow its extension `below' the boundary, and the stability argument

mentioned in the conclusions leads you naturally to CTCs. This is the way to infer the reasonability of the model proposed, although in the main body of the paper I followed a different route inspired by St. Augustine thought.

Concerning the criticisms moved to the compatibility of CTCs and quantum field theory, I am unfortunately at the moment not sufficiently expert to have a definitive opinion. It would be a pity if they really could not be compatible as some other problems seem to be easily solved by admitting CTCs.

Best, Ettore

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  • Post #5

Hi!

I read your essay with great interest! I think it is the best essay in this contest so far in the sense that it pushes really speculative ideas but with great technical rigor. It also reminded me of Tipler's "Physics of Immortality", in spirit if not in letter.

Best,

Obi

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  • Post #6

Dear Ettore,

I attended three week-long Templeton Foundation seminars on Science and Religion back in '97 and '98, and taught the science part of a college-level Science and Religion course in Fall semester 1998. I think it is a good program, but I am more interested in its applications: Technology and Ethics.

St. Augustine's point 4 is very relevant to your paper "The will of God is eternal." Is this equivalent to the will of God being omni-temporal? If so, then General Relativity requirements (such as no speed greater than "c" and causality) would also expect the will of God to be omni-present. Thus, the will of God would be everywhere.

Does that include us, and not just an infinite chronology-violating class of CTC's? We probably cannot disprove CTC's until we have a complete Theory of Quantum Gravity, but they seem highly unlikely in flat Spacetime. If a class of CTC's connects the beginning of time (the Big Bang or Genesis) with the end of time (Heat Death or the Apocalypse), would this have the chronology-violating effect you are describing, or would this simply record the History of our Universe?

Whether or not there are minor gods (def. 3.3), there are many Religions with many different views regarding God/ gods. Thus, even if Science could prove the existence of "a God", we might not know the characteristics of that God, so we would still have multiple Religions vying for our hearts and minds.

In Chapter 4, are you trying to explain the homogeneity of the CMB radiation with the physical properties of a God or a CTC? Doesn't "Let there be Light!" work just as well? We need physical explanations for physical phenomena - even if we don't fully understand them.

Good Luck!

Ray Munroe, author of A Geometrical Approach Towards a TOE

Dear Dr. Minguzzi,

Thank you for your archive reference. I am not sure why I did not notice your paper there this Monday, because every Monday I read all the prior weak papers. Anyway, I will carefully read your proof.

About CTCs, probably the best intuitive argument against them was found by Boulware who noted that a particle can get generated at one point in space-time, travels around the CTC and can get re-absorbed at the creation point. The problem is that the particle is picking up a phase differential which will destroy coherence and unitarity. Another consequence of a CTC is the complete lack of free will and this means we were pre-ordained since the Big Bang time to have this conversation.

You stated in your essay the following 6 points:

1. There is an entity which we call God that satisfies the following points.

2. God has created the world.

3. God cannot be wrong.

4. The will of God is eternal.

5. God created all the times, in particular God precedes all the times in a causal way. Nevertheless, God does not precede the times in a temporal way as the times did not exist before their creation.

6. Although God is not in our time, there is a kind of God's perception of time radically different from that of humans. For God time is still, eternal, it is not perceived as a flow.

Please consider the following substitution: God=the platonic world of math:

1. There is an entity which we call the platonic world of math that satisfies the following points.

2. The platonic world of math has created the world.

3. The platonic world of math cannot be wrong.

4. The will of the platonic world of math is eternal.

5. The platonic world of math created all the times, in particular the platonic world of math precedes all the times in a causal way. Nevertheless, the platonic world of math does not precede the times in a temporal way as the times did not exist before their creation.

6. Although the platonic world of math is not in our time, there is a kind of the platonic world of math's perception of time radically different from that of humans. For the platonic world of math time is still, eternal, it is not perceived as a flow.

The 6 new statements are still true. The point I am trying to prove in my essay: "Heuristic rule for constructing physics axiomatization" is that physics and math can be unified and reality is made only out of mathematical relational structures. I may sound crazy, but one can actually obtain powerful concrete mathematical consequences from this, like the necessity of space-time and of quantum mechanics.

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  • Post #8

Hi Dr. Minguzzi,

A pleasure to read your essay contest .

Congratulations and good luck ,

sincerely

Steve

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  • Post #9

Dear Ettore,

If you can connect the end-of-time Heat Death with the beginning-of-time Big Bang via a CTC (if they even exist!), then you might be able to explain the isothermal homogeneity of the CMB radiation with a physical theory. Mixing God in the picture complicates things unnecessarily (which goes contrary to Occam's razor) because 1) you haven't explained this physical phenomenon any better by appealing to expected characteristics of God, 2) you probably haven't changed anyone's Religious persuasion with your presentation, and 3) now you need to explain the added complexity associated with the God Hypothesis.

There are other, more acceptable, physical ways to explain the isothermal homogeneity of the CMB radiation (I have ideas that tie into my multi-dimensional lattice theory). But remember that one of the complications is that we must simultaneously explain why matter clumped. If all matter was perfectly homogeneous, then an infinite (or near-infinite) Universe could not have formed clusters, galaxies, stars or planets because the net gravitational force on any infinitesimal volume element of space would have been zero.

Sincerely, Ray Munroe

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  • Post #10

Dear Uncle Al ,

Nietszche too said ,God is dead ...and the superhuman was born ....

And Jung ????

Sodom and Gommoreh ...and Babilon the sad and the sin city ,the sister of Las Vegas .

In all writings ,sacred writings ,only one thing is important ,the love ,this universal love .And that's all in fact .

We see only with our heart ,the essential is invisible for our eyes .

Let's pray thus in sincerity for this planet and let's act in total universality and its laws of evolution .

Let's look above us before acting and even in our mind before thinking ,

And if we had given instead of exchanging .....the evolution always ...

Regards

Steve

5 days later

Dear Obi and Steve, many thanks for the congratulations. I happy to know that you enjoied the essay.

Dear Florin, thanks for the comments and suggestions, I will read your essay.

Dear Ray,

please understand that the aim of my work is not that of supporting a scientific reading of the sacred texts. This attitude has often lead to incorrect conclusions. Instead my aims are:

a) to draw a connection between two products of logical structured thinking,

namely St. Augustine thought on time and general relativity.

b) To show how a particular cosmological model that happens to be compatible with St. Augustine thinking and general relativity seems to be able to solve the homogeneity and entropy problems.

In particular it makes sense to ask if anything like (a) holds, as St. Agustine thought on time and general relativity represent the most important reflections on time of antiquity and modernity respectively.

In your second post you state that

"

1) you haven't explained this physical phenomenon [homogeneity of CMB] any better by appealing to expected characteristics of God,

2) you probably haven't changed anyone's Religious persuasion with your presentation, and

3) now you need to explain the added complexity associated with the God Hypothesis.

"

As I explained (2) is not between the aims of this work.

Concerning (1) and (3), I clearly separated the God of the first part with that of the second, which is simply a chronology violanting region that preceds the whole Universe. All my scientific considerations depend on the latter concept. Thus handling the concept of "chronology violanting region that preceds the whole Universe" does not bring in any particular complication apart from those of technical nature.

Best wishes,

Ettore

5 days later

This is a pretty interesting article. However I think the chronology violating region, which is identified as God here, is really no different from a singularity. There is a potential function associated with the TN spacetime. A geodesic in this spacetime is one where

p^2 - U_0^2 c(E - pe^{-2β}) = 0

where β is the generator of the time dependent conformal factor and c is a complicated function from the Ricci curvature. This potential is a barrier to certain types of geodesic in the region where light cones are pointing horizontal. I attach a modified version of your diagram 1. The red geodesics are to low in energy to escape to the top region and they wind up and then retreat to the bottom again. This particle has scattered off the potential. The blue geodesic will wind up and asymptotically approach the closed lightlight region. The green geodesic, which is spacelike in this bottom region will escape the barrier. This is curiously a bit like the inverse of falling through the event horizon of a black hole.

The question comes to mind what this means quantum mechanically. This spacetime is close to being a CTC spacetime, but really what we have are closed lightlike curves. The bottom region we may regard as the domain of chaos, and we the observers live in the top region and detect radiation which emanates from the closed lightlike curve. The propagator for a quantum field will be of the form 1/p^2 m^2, where the p^2 is computed above. The field propagator has a topology associated with it as it wraps around a region with a component parallel to the closed light like curve. This topology defines lightlike curves which pile up near the closed region. This will pertain to vacuum modes as much as real photons. This is where things become problematic, for this appears to then be similar to the inner horizon of the Kerr-Neumann solution that is an infinite "flash." In other words the closed lightlike region appears to be a singularity.

Cheers LC

5 days later

Dear Lawrence,

thank you very much for the question. You argument that a photon traveling near the boundary would pile up his energies to give an infinite stress energy tensor at the boundary (let us call it a singularity) is more or less Hawking's main argument in favor of the chronology protection. The references at the end of my paper discuss this problem at length and the conclusion is that this mechanism does not always work so it cannot imply that CTC do not exist. The reason is more or less the following: first at the classical level there are solutions with well behaved stress energy tensor at the boundary thus any argument should be perturbative and probably quantum mechanical in nature. The problem is that if you work in a semi-classical framework, as Hawking did, treating a perturbation (say a photon) that moves on a fixed background you are making an incorrect assumption. The reason is that the spacetime geometry near the boundary is very sensible to perturbations and reacts accordingly. For instance if you slightly close the cones near the boundary you will see (look at the figure in my work) that the boundary moves down, if instead you open slightly the cones you will see that it moves up. In other words the semi-classical approach is untaenable because the assumption that you have a background which is almost insensible to perturbations is incorrect. How is it possible to make a perturbative argument near the boundary if it is not even clear where the boundary itself is located? One would need a non semi-classical approach, indeed some authors have claimed that a full theory of quantum gravity would be required (see Gott paper).

Nevertheless, even in the case that a singularity form, I have argued that the important fact in order to solve the inhomogeneity and entropy problems (and also for the connection with St. Augustine thoughts on time and creation) is that the causal structure (not necessarily the metric structure) leading to CTC proposed in my work makes sense. This is possible if the singularity at the boundary is a so called isotropic singularity, namely a singularity which can be removed by a conformal transformation. Similar ideas have been used by Penrose in his cyclic universe that he conceive to explain the entropy problem, and a mathematical study can be found in Lubbe and Tod's paper.

Thank you again for the question.

Cheers, Ettore

For those who are interested in the details of the paper, I have now replaced the version at arXiv:0909.3876 adding two appendices, one with a treatment of the boundary of the chronology violating region and the other with the proof of theorem 3.4 (now clearer thanks to the first appendix).

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  • Post #16

Thanks for your response. I will have to look these references up. I have never worked with the TN vacuum solution in any serious way, so I am not an expert on this subject. So it appears you argue in effect that we really need to quantize the entire spacetime, such as in a Wheeler DeWitt equation.

The TN spacetime has two regions, one chronal and the other nonchronal, with a closed lightlike region separating them. This is similar in feature to a Cauchy horizon, such as the inner horizon of a Kerr-Neumann solution. Of course in that case the causal directions are reversed, where the future direction of the causal region takes one onto the horizon, where as with the TN spacetime the past direction takes one to this horizon. From a physical perspective I would argue that this structure determine a quantum amplitude for the production of quantum fields in the causal region. The noncausal region may then not exist in the same manner as the causal region. This region, a sort of twilight zone space similar to the inner timelike region of the Kerr solution, may then be a sort of mathematical construction. That mathematical construction is something connected to the causal region which determines quantum amplitudes for the production of quantum fields.

The particles which can traverse the closed lightlike boundary from the nonchronal region to the chronal region are locally tachyons. The imaginary four momenta of such quanta suggest they are similar to the condition for particles in a potential barrier with

k = (ħ/2m)sqrt{E - V}

which is imaginary valued in the potential barrier region. Of course the potential function for the TN vacuum is a bit more complex than this, but I am making a physical argument here rather than one based on mathematics.

There might be in greater generality some holographic content here. If I were to observer far enough back in time in the chronal region of the spacetime I will observe strings near the lightlike boundary far redshifted according to the coordinates integrated in that spacetime. Another observer, assuming one can exist, which emerges from the nonchronal region observes a completely different dynamics. So there are two descriptions of string according to different causal domains of support for the S-matrix. It would have to be determined it if makes sense to have an S-matrix on a noncausal domain.

Cheers LC

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  • Post #17

Dear Ettore

God cannot find place in physics.

When we wake up observer in physics god is out of discussion.

yours amrit

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  • Post #18

Dear Dr. Minguzzi,

Your willingness to consider the conclusions of intellects such as St. Augustine is valuable to science. His input is valuable and should be included along with physicists such as Hawkins. Hawkins is more mathematical in his arguments, but Hawkins speculates about possible, theoretical, mechanical type effects. This universe requires far more than talk about space or time or sources of cause that might be imagined to exist at the mechanical or unintelligent structural level. Any theoretical physicist or anyone else puting themselves forward as an authority on the nature of this universe that gave birth to intelligent life must include support for their argument.

I would have gone beyond Confessions and included Concerning The Teacher. This second book lays out the logical case for the necessary pre-existence of intelligence before intelligent life could be possible. Whether that intelligence is called God or simply the original cause of all lesser intelligence that follows is not the crucial point. The crucial point is that there is no way to avoid postulating the pre-exiswtence of intelligence by science. Any challenge to this must include an explanation of the evolution of intelligence from dumbness. Grand pronouncements to the contrary without explanation count for nothing.

James

16 days later

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  • Post #19

You have a very nice summary of St. Augustine's argument that God created time along with the creation of the Universe. I have a problem with your point 4: If God's will is eternal then that makes God static. We as Christians believe in a personal God who responds to things happening in the universe. A personal God can not be completely static. There is somewhat of a paradox here, because a personal God can not be completely omniscient either. Maybe God limits his knowledge of the future and at the same time directs the future to a specific outcome.

Dear William,

thank you for the question that has also been raised by some colleagues. There seems to be a difficulty in reconciling the God's eternal will with the supposed ability of God to respond to things happening in the universe. My model does not assume the latter property (but God precedes the whole Universe so in principle he controls the initial conditions and hence the subsequent

development) indeed in my work I did not try to reproduce the whole body of beliefs on God's nature that can be found in Christianity or in other religions. Nevertheless St. Augustine thought on time and creation is reproduced, and this seems interesting because his conclusions on these matters are deductive in nature and well separated from other more arbitrary assumptions that can be found for instance in the Genesis (such as: God created the Sun and the Moon on the fourth day).

Your example shows that some religious beliefs seem paradoxical and a theologian would be more qualified than me to answer questions on the consistency of the beliefs which underpin a religion. My point is that at least the deductions of St. Augustine discussed in my paper are not contradictory. Hopefully my paper adds something on our understanding of the nature of God, of course you should not expect it to reproduce the body of beliefs that revolve around the concept of God. Consider the concept of

"energy". People use this word in several sloppy ways, sometimes indicating a force, or even a momentum. Physics has helped us to distinguish between these different aspects which stay behind the intuitive word "energy". Thus maybe my paper clarifies what "God" could be at least for what concerns the aspects of time and creation. The other aspects seems not to be covered by the technical

notion I have introduced.