Limits of mathematics in cosmology

Edwin,

Sound's like you are dropping the conversation. Sorry to hear that, as the discussions on fqxi have been a bit thin lately and I haven't found any sites quite like it. I suspect things will liven up when they start the next contest though.

I must say we do hold fairly opposing positions on the validity of the Big Bang model though, but it doesn't look like I'm convincing you and I see too many holes between all the areas of elaborate maths not to think a profound bias towards definition has us wrapping up a theory of the universe a little too quickly. Having followed the evolution of the theory since I was a teenager in the seventies and having started to question it in the late eighties upon learning expansion and gravitational contraction have to be balanced and discussing it on the internet from the mid nineties, I find it to have the momentum of a movement, in which believers rise and doubters are excluded.

In that regard, you might want to examine just what parts of the theory you like and why, because they will necessarily become tangled with the parts you don't like. This is from Andrei Linde's website: http://www.stanford.edu/~alinde/

"Inflationary theory describes the very early stages of the evolution of the Universe, and its structure at extremely large distances from us. For many years, cosmologists believed that the Universe from the very beginning looked like an expanding ball of fire. This explosive beginning of the Universe was called the big bang. In the end of the 70's a different scenario of the evolution of the Universe was proposed. According to this scenario, the early universe came through the stage of inflation, exponentially rapid expansion in a kind of unstable vacuum-like state (a state with large energy density, but without elementary particles). Vacuum-like state in inflationary theory usually is associated with a scalar field, which is often called ``the inflaton field.'' The stage of inflation can be very short, but the universe within this time becomes exponentially large. Initially, inflation was considered as an intermediate stage of the evolution of the hot universe, which was necessary to solve many cosmological problems. At the end of inflation the scalar field decayed, the universe became hot, and its subsequent evolution could be described by the standard big bang theory. Thus, inflation was a part of the big bang theory. Gradually, however, the big bang theory became a part of inflationary cosmology. Recent versions of inflationary theory assert that instead of being a single, expanding ball of fire described by the big bang theory, the universe looks like a huge growing fractal. It consists of many inflating balls that produce new balls, which in turn produce more new balls, ad infinitum. Therefore the evolution of the universe has no end and may have no beginning. After inflation the universe becomes divided into different exponentially large domains inside which properties of elementary particles and even dimension of space-time may be different. Thus the universe looks like a multiverse consisting of many universes with different laws of low-energy physics operating in each of them. Thus, the new cosmological theory leads to a considerable modification of the standard point of view on the structure and evolution of the universe and on our own place in the world. A description of the new cosmological theory can be found, in particular, in my article The Self-Reproducing Inflationary Universe published in Scientific American, Vol. 271, No. 5, pages 48-55, November 1994. A nice introduction to inflation was written by the journalist and science writer John Gribbin Cosmology for Beginners . The new cosmological paradigm may have non-trivial philosophical implications. In particular, it provides a scientific justification of the cosmological anthropic principle, and allows one to discuss a possibility to create the universe in a laboratory."

Admittedly I don't know enough about vacuum instability to defend it, but I do think the universe is a field effect, with areas of expansion balanced by vortices of contraction and this fundamental dichotomy manifests on many levels, such as the expansion being an "entangled wave state," while collapse results in digitized quanta/particles and that's why, when we try measuring precise energy levels, the process of doing so requires creating the collapse, thus we only "see" particles, while waves remain not quite real. I could go on, but don't want to try your patience, as most professionals wouldn't take the time to understand what I'm trying to say in the first place.

John,

I've got to take care of some other time-consuming business and don't think we're close enough on the BBT issue to really get anywhere. I'm glad that we agree on the primordial consciousness as opposed to emergent, but my theory ties everything together into a unified whole. If I have to cut out large pieces of it, it will kill the theory, and I've seen no reason to do so (yet). In fact, my theory makes predictions about what will be found at LHC and has several cosmological implications, so until the predictions are confirmed or proven wrong, I'm sticking with what I believe is the best theory of reality.

As for Linde's "chaotic inflation" I don't buy it, or, as I understand it, any of the associated multiverse. They do not have any explanation of inflation (other than undiscovered 'inflatons' based on QED concepts) and the remarks I made above reflect my doubts about even QED. Just yesterday the APS newsletter quoted Peter Mohr at NIST about the 4 percent discrepancy between the (QED) predicted and measured radius of the proton...

"It would be quite revolutionary. It would mean that we know a lot less than we thought we knew... If it is a fundamental problem, we don't know what the consequences are yet."

John, for the last five years I've been watching new mysteries being reported in particle physics and cosmology that fit right into my model but do not fit any current theories. As a practical matter, the gigantic academic-industrial-governmental-science establishment is not going to roll over and say "we don't know what the hell is going on", but I am absolutely convinced that this is the case. There is more BS and theories postulated on make believe entities (see my Aug. 29, 2010 @ 20:44 GMT comment above) and the whole thing is a house of cards. So I'm not ready to throw overboard my theory that explains almost everything I'm aware of just because there are 'redshift issues' that I haven't had time to work through yet. If the LHC finds a Higgs, or other SUSY particles then I'll have to take a real good look at why my theory predicts none. But until then I'll just keep plowing through issues one at a time, and the redshift is now on the list of issues, but not at the top.

One problem is that pictures aren't enough, equations have to produce numbers that match reality. For example, QED cannot explain the 4 percent discrepancy. My model does qualitatively explain a 'smaller' proton radius as seen by the muon, but I can't calculate 4 pct exactly. On the other hand, they have not the slightest idea why it's smaller. The proton radius, the negative core of the neutron, massive (as opposed to massless) neutrinos-- these are big deals, but, since the current theories can't explain it, they ignore it. Given finite time and energy, I have to choose real measured problems that my model supports and the other guys can't explain, over conceptual problems that may or may not be real.

BTW, I too live on a ranch. I think it's a better way to grasp reality. I haven't found your email address, but if you look on my essay, you'll find mine.

Edwin Eugene Klingman

Edwin,

Than you for the consideration. We all have to frame our views on the basis of what we understand and you have a far more technical and fine grained view than I. I tend to come at it from a philosophical direction and that doesn't have much credibility these days.

As for predictions, I was arguing redshift is actually evidence for a cosmological constant, rather than a singularity close to ten years before they discovered the need for the dark energy patch in '98 and then qualified it as being comparable to predictions made by what a CC would look like, around '02. As for future predictions, I also suspect the Higgs will continue to be elusive, since I've been arguing for space as having an equilibrium effect, but won't be surprised if they find some activity which they will call a potential Higgs field, since there are likely layers of undiscovered activity. My other prediction will be that the James Webb telescope, for studying the infrared background radiation, will find evidence of it being light from ever more distant galaxies that has been completely shifted off the visible spectrum, rather than afterglow from the singularity. Whether they devise a convenient patch, likely drawn from inflation, or admit it is a real problem for BBT, time will tell.

My email is brodix@earthlink.net, if you want to add it to your list of contacts completely outside the fold.

As for living in enough space not to be constantly in others energy fields, it does give one the space to think. When I was little, I realized all those voices in my head were of older siblings and it took a bit of effort over the years to block my mind from others, when necessary. I think we are all one big organism, for better or worse.

Seems like a good time to curve the thread a little.

1. I wanted to acknowledge Sabine Hossenfelder for the award process she started. It is easy for me to be a physics outlaw because I have little at stake (well maybe my big ego). But there are many physics professionals who risk their futures by going against the party line. From their ranks the future physics will emerge.

2. Thanks Lev for giving my website and wavelength-hopping some visibility. When wavelength-hopping is viewed as particles appearing as events it is a much more palatable concept.

3. T H Ray, your criticism is right to the point. I will comment on it in next post.

4. Edwin Eugene Klingman, yes wave-length hopping is just another theory, but it differs from the theories that you listed in that it is testable in several ways. I think the best test for it could be performed by the Vienna group (University of Vienna) on a Buckyball to show that it wave-length hops. see http://www.zenophysics.com/DWT/13a__Buckyballs.html

Don L.

Hi Tom (T H Ray), It is obvious you have read my theory and know its implications which I do not try to hide. But I can add a few comments:

1. rest mass would be incalculable: This is true. But "rest mass" is a misnomer for a particle because particles are never at rest. Lowest energy mass would be a better term.

2. spacetime would not be physically real: I believe I leave space-time intact, however I consider particles as moving on space-time in an unreal way as experimentally verified by Alain Aspect.

3. general relativity would be falsified: General Relativity was not created to work on the particle level but it works very well on the classical level where the assumption of a static point mass is just fine.

Tom,

What if there is no entity like space-time, or better, time-space? That is my point: there might be, at the bottom, just temporal/informational structure (like ETS), which instantiate the spatial and other structures. So that particle hoping is what we "see" as a result.

Hi Don,

1. True, particles are never at absolute rest (absolute zero temperature); however, relativistic rest mass allows us to compare energy content between masses. Special relativity's conclusion, E_0 = mc^2 is based on the rest mass state. The "lowest mass" is zero; energy exchange particles (bosons) are massless. When special relativity is generalized to general relativity, we find that the two statistical models (bosonic and fermionic) describe one world that is static in time (timeless), and another that is time dependent, which general relativity successfully describes together as an interaction of matter and spacetime that describes the universe as "finite but unbounded." General relativity only fails at the cosmological limit, where a singularity of infinite energy density is theoretically unobtainable in such a world. Einstein would have liked to construct a theory in which mass is merely the consequence of field interactions, and GR was meant to be only a step toward that goal.

Einstein was steeped in classical mechanics, though, and well understood Ernst Mach's mechanical model in which every particle motion is dependent on the motion of every other particle -- so that if one knew the initial state of the system, every subsequent state could be calculated. In Mach's model, space plays no role, and time might be seen as in the context of differing ratios among invisible "gears" that drive particle motion. Mach never did accept the atomic model, in which atoms are made almost entirely of empty space, and neither did he conceive that there are no closed, isolated systems in the universe to which his model could apply. Einstein took Mach's mechanics, coined the term "Mach's Principle," and showed that while neither space nor time have an independent reality -- allowing that spacetime (Minkowski space) is physically real, Mach's model is satisfied for general relativity without superfluous assumptions. But again -- there's that sticky cosmological problem, in which the only known recourse is to eliminate space and time (get rid of the infinitely dense singularity) and go with a quantum origin ("roll the dice").

This latter is what your lambda-hopping idea does -- avoids the singularity, in that a particle changes position without changing structure -- and I know that's why Lev likes it. It is equivalent to saying that a faster than light particle can be defined as one that changes direction without changing velocity; that's a true statement, yet we have no physical reason to believe that a particle of nonzero mass in a curved trajectory does not accelerate. You have to eliminate mass from your model altogether (if it is to be consistent with SR), and when you do that, you have a continuous wave function, not the hopping one.

2. Aspect's experiments validated what we already knew -- that in order for quantum theory to be coherent, nonlocality must be preserved at any scale. Quantum theory would be in serious trouble if Bell's inequality were not violated. Space and time play no role in the experiments, however, except in the sense that spacetime is shown to affect only local interactions (classical physics is local), and not quantum mechanics.

3. You're confusing "point mass" which is a quantum concept, with "mass point" which is classical. Yes, all measurements in GR are between mass points, as in all other classical theories.

Tom

Lev,

You wrote, "What if there is no entity like space-time, or better, time-space? That is my point: there might be, at the bottom, just temporal/informational structure (like ETS), which instantiate the spatial and other structures. So that particle hoping is what we "see" as a result."

You know that I agree with you in principle, Lev.

Without that messy spacetime standing in the way, it's smooth functions "all the way down." Because we have relativity and quantum theory, however, and because both are established physics, I think that unification begs us to first explain why these theories are apparently true.

If we are going to speak of structure as irreducible, I can see the virtue of a 4-dimensional spacetime normalized to 1 (i.e., a 0 1 spacetime)in an n-dimensional Euclidean space. I cannot comprehend a further reduction. The 2-dimensional 3-manifold seems sufficient to me to contain all the information holographically. The extra dimension(s) the theory requires allows room for both continuous functions in 3 1 (0 1) dimensions, and the "hop" or "jump" of discontinuous functions in hyperspace.

Tom

Hi Tom,

I am in the unenviable position of defending something that is unproven. So, I say something like particles are blue, then everyone who read the book that says particles are red respondes to me that blue is silly particles are red. Never mind the fact that the red color came from a theory also. The only difference is that red was in the book.

I say that a fundamental particle in isolation moves in a peculiar way "wavelength-hopping". There is no thermal motion. IF you want you can say that the particle is at absolute zero. Almost everyone will say wavelength-hopping is not true even thought no one has investigated the phenomena of how or if a particle moves in isolation.

I did not pull wavelength-hopping out of the air, it the result of a logical thought experiment. But as Edwin Eugene Klingman points this is just another far out theory out of many. He is right and more than a theory is required. I think an experiment can be made.

At first it may seem simple to put a particle in isolation. I was thinking of taking a Buckyball and dropping it in a vacuum. But on second thought that is not enough isolation because the Buckyball will accelerate too fast due to gravity to see wavelength-hopping. A very low speed accelerator will need be designed to do this experiment the LHC will not do the job. The experiment may need to be done in space. see http://www.zenophysics.com/DWT/13a__Buckyballs.html

Hello Forum. I have not had time to read all the posts in this forum but I would like to address the initial question concerning the suitability of mathematics to address issues in cosmology and physics.

I would like to ask forum members how they believe mathematics could be 'engineered' to be more suitable for this task. It os my understanding that mathematics has 'two poles' that of its set theoretic foundationsn and the limits of the logical resolutions that lead to the advanced mathematical fields.

My issue with the inappropiate nature of mathematics begins at its foundational level, the axioms of set theory. In particular, the concepts of continuity and sequence are forced upon the integers.

Ot is atb this level I believe that many of the semingly baffling notions of experimental cosmology and physics are born, our mathematical systems is out of sync with the reality to which we apply it.

I have been wondering for some time whether ny research in this area is being conducted. This area is the philosophy of mathematics where subtlty rather than complexity is what needs to be explored!

"My issue with the inappropiate nature of mathematics begins at its foundational level, the axioms of set theory. In particular, the concepts of continuity and sequence are forced upon the integers.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

I have been wondering for some time whether [a]ny research in this area is being conducted."

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You have come to the right place. ;-)

Check my essay mentioned also in my opening post.

Hi Tom,

You say a particle at absolute zero does not move. This is part of a long held conventional theory that has it as a definition. It has never has been observed in nature. I say that a particle in isolation moves all by itself. This is part of a new theory. It also has never been observed in nature. What is true?

The phenomena of superconductivity involves many particles in proximity. It is not the experiment that is optimum for showing wavelength-hopping.

I believe theories are good and we need them, and well designed experiments are better than theories.

Don L.

Hi Rainsmith, Along with Lev and others I agree that the math/physics is a core issue.

The assumption that 1 +1 = 2 in the world of experience.

1 plus 1 = 2 is something that is taken for granted and is held to be true in both math and physics. I do not believe it is true in physics. I will try to explain, here goes:

a. How do you add things that are physical? The grade school teacher will demonstrate by taking an apple from far away and present it to the class, then she will bring another apple from far away and put it close to the first apple and say "One apple plus another apple is two apples." This is the physical interpretation of addition. It is very useful and essentially correct but it needs a minor correction when considering the apples as real objects with mass. I will explain in a moment.

b. How do you add things that are mathematical? The math instructor will say consider an apple (an ideal object in the imagination) and call it a 1. Now consider another apple and call it a 1. The 1 and the 1 can be added to produce 2 which can be considered to be the sum of the two idealized apples. This 1 plus 1 = 2 is completely correct for idealized apples. The math is perfect when there is no real mass and no space-time.

c. What is wrong with the physical 1 plus 1 =2 ? The answer is the space-time that the apples exist in. When the apples are brought together to demonstrate their sum they have to move thru space and time. (see http://www.zenophysics.com/DWT/19__Math-Physics.html)

By the way, "1 plus 1 = 2" is not really a 'physical' statement. It was simply adopted by physicists from the math developed by that time. Moreover, again before physics, the 'spacial' measurement practice was developed in Egypt and Mesopotamia. Ironically, although the space is not a 'physical' concept, once it has been adopted in physics it has become a fundamental concept.

In fact, this is probably true of all basic physical concepts.

Let me add that I would like to see physics built based on the really physical rather than conventional math/numeric foundation. So the question then simply is: What is truly physical foundation? And, of course, my answer is streams of (structured) events, or what we currently call "particles".

Though neither space nor time are physical concepts, in general relativity, spacetime _is_ physical. It is not a difficult extension of GR to say that time structures space.

Tom

Don, how would one go about designing an experiment to record the sound of one hand clapping?

Tom

"It is not a difficult extension of GR to say that time structures space."

Yes, you can say that, but only because we want to put a better face on the situation. The spacetime cannot be physical, simply because the underlying concept of the vector space is purely mathematical.

Numeric language is too plain or rather too far removed from 'reality'. One needs a richer symbolic language. To me, a more 'physical' formalism is the one which is structurally a 'copy' of the actual physical processes: events are represented as events, where their interconnections are preserved. That is why, for example, Feynman's diagrams took off so fast.