Dear Steve,

You worry too much. I think I figured out the discrete vs continuous dual nature of reality last night in my sleep. The solution is so simple that you'll want to kick yourself (and Theta is only half of the answer). I'll share the idea with you if you are interested.

Have Fun!

Ray,

Yes, a scale invariant universe (I dislike the term multiverse, because a multiverse is a set of universes) does imply a statistical model _locally_ that measures the probability of n-body interactions related to the coordination strength of independent n-body motions. However, we already have a local theory of gravity (general relativity) that works just fine without imposing statistics on it. It's a simpler model ("as simple as it can be" as Einstein would say) because it's classical, continuous, deterministic, nonperturbative.

If we want a simpler global model of gravity, I think it has to be in that same spirit.

Therefore, one finds (my "time barrier" preprint) that a continuous metric over n-dimension manifolds opens the possibility for a nonperturbative model if one is willing to accept infinite dimension scale invariance and the infinite self-similarity it implies. Statistical models, then, _only_ apply locally, the inverse of what general relativity describes in its local model of gravitation. This is counterintuitive; however, it follows from a result in my ICCS 2006 paper -- and is entirely consistent with keeping general relativity for local gravitation in 3 1 dimensions, while extending the quantum domain n-dimensionally.

A universe without matter would be far easier to deal with mathematically -- as Constantinos has rediscovered -- but when we introduce the random fields that come with matter, we are forced to a conclusion that either those field influences are dissipative over n-dimension manifolds (cf. Jacobson-Verlinde entropic gravity) or the matter/energy density of the universe is far greater than what we observe.

My theory accounts for this low inertial content (4.59% exact correspondence to WMAP data) equivalent to a probability of .0459 that the observable universe contains matter _at all_. That is, the 95% or so of total (length 1) energy dissipative over n-dimensions leaves us with a probability of 1.0 that what we observe is sufficient for a universe that is almost flat Euclidean, with just that little bit of spacetime curvature to keep it from being infinitely boring and to sustain life as we know it.

Now to the task of simplifying that result to a nonperturbative theory incorporating a continuous field. Easier said than done, I know.

Tom

Dear Tom,

I apologize. Your ICCS 2006 paper has been on my desktop for 5 months. I've looked at bits and pieces of it here and there, but I've never made myself really understand it all. I need to better understand your WMAP results. I think that you are - at least partially - on the right track. Scale Invariance and self-similarity are very important. I personally think that Fibonacci and Lucas numbers are more relevant than Cardinal numbers, but perhaps all small prime numbers are important. I believe that you, Lawrence and I are all on "self-similar" fruitful paths.

I call the collection of self-similar Universes the Multiverse to distinguish the two terms. Thus our Universe is a fractal fragment of the infinite Cantor set that is the Multiverse.

Have Fun!

Hi Dr Cosmic Ray,

I know I am crazzy, it's tiring, all people says that,perhaps I am it.It's not important and essential.

And a singer who said "Don't worry, Be Happy!...but how can we slepp quietly if only one child still cries....this planet doesn't turn correctly Ray.

It's that also the unification,yes it's that also....the unification is everywhere ....it's like that with or without our human approvement...that names the universality in evolution.

ps indeed this thermodynamical link seems interesting.But if the infinity is inserted for the uniqueness, that will be difficult for the correlations of the continuity and the correct number.

The primes seem relevant.

ps I share always Ray, it's the reason why I have nothing hihihi you can share with me in transparence if you want, it will be a real pleasure.Thanks for that,it's nice.

Take care

Steve

Ray,

No apologies necessary. The ICCS paper details the mathematics necessary for my definition of time. The WMAP results are in my "time barrier" paper.

Cardinality doesn't refer to cardinal numbers, but to discrete dimension sets determined by the continued sum of cardinal points (coordinates). I use this term to emphasize that invariance of dimension is not violated; i.e., each set of coordinate points Sigma_d has the local Euclidean property R^m = R^n IFF m = n (Brouwer).

Tom

5 days later

With due respect to all the learned people...

Time, forward or backward, does not actually exist. It is an assumed reality in a dream. It is the dream we are all dreaming - the dream of Creation! We are "The Infinite Light" (I and the Father are One) dreaming Creation, in which certain levels are subjected to an assumed forward-time-flow...

Now.. all this becomes very deep amd mystical, but if you are interested read my pages called: ! Gerardus' Grist! / soulwise.net. Go for the article: "Gerardus Speaks". It's perfectly up to date these days...

Only One Candle - Gerardus

Dear Lawrence, Ray and Tom,

Please read my revised post on Entropy and 'The Arrow of Time'. In it, I used Planck's Law to derive Boltzmann's Equation of Thermodynamic Entropy. I also get an equation for the number of microstates of a system. I again demonstrate the connection between thermodynamic entropy and time.

Best,

Constantinos

PS. Statistical (and Quantum) Mechanics is made necessary only because of the 'particle view' Physics has adapted to explain everything. In a very limited way I am showing that such a view is not necessary. You can make the connections that I can't and show the rest ...

Dear Constantinos,

No - In an upcoming paper, I've concluded that there should be three distinct forms of Spin Statistics (consistent with Hegel's Thesis, Antithesis and Synthesis). I'm sorry that you are so determined to ignore Fermi-Dirac statistics in favor of Bose-Einstein statistics. They are distinct opposites.

Have Fun!

Dear Ray,

It is not my intention to ignore Fermi-Dirac statistics, but suggest perhaps this is made necessary because of the 'particle-view' of physics that we have. Interesting that you should mention Hegel. I was greatly influenced by his Phenomenology of Spirit and still adhere to many of his basic ideas. I just wonder what Hegel would say about a Universe that is made up of particles, however!

I want to built conceptual bridges that bring more meaning to our abstract understanding of the Universe. Meaning must connect ideas to experience, however. Any physical explanation of the Universe must be confluent (and not contradictory) with our experience of Life and the World in general. I believe that Creation that underlies the physical Universe cannot be any different from Creation that underlies all Experience, including the rise and fall of nations and men.

But what about my paper? I show how Planck's Law leads to Boltzmann's Entropy Equation. As a bonus, I obtain an equation that gives the number of microstates of a system.

having fun ...

Constantinos

Dear Constantinos,

If waves/ strings/ continuouos/ bosons are the thesis, then particles/ spheres/ discrete/ fermions are the antithesis (and BOTH appear correct because we can only measure half (at most) of the degrees of freedom present). Our goal should be the derivation of the synthesis that is wave-particle duality. I've only read parts of your revised paper - I'll give a more thorough response tomorrow.

Still having fun...

Constantinos,

When one speaks of the number of microstates of a system, one has already abandoned a continuous function model for particle-like properties. When one speaks of "energy at time t", one speaks either of an instantaneous measure of energy content such as described by a Hamiltonian or Lagrangian, or of average kinetic energy in a dimensionless measure of temperature.

I appreciate that you think particles don't necessaerily exist. We already know that, however. In any way that you manipulate the physics, you are going to recover particle properties ("number of microstates") or continuous wave mechanics. One freely makes the choice of measure -- all particles have wave properties and all waves have particle properties.

You speak of a reciprocal relationship of entropy and temperature, but neglect that quantum vacuum fluctuations deny the absolute absence of motion, and those fluctuations are discrete and discontinuous (zero time action).

Physicists have learned to live with particle-wave duality (as Ray has repeatedly pointed out, Fermi-Dirac vs. Bose-Einstein) because that's the way the experiments play out. An infinity of bosons may occupy a point (and therefore, a continuous line), but if you are going to have a theory that includes matter, you need account for discrete and finite quantities.

Physics has a path for you to recover a continuous field model -- quantum field theory in higher dimensions. Discover that path, and I think you'll have more fun than you have ever had.

Tom

Dear Constatinos,

I read your paper again yesterday as I said I would, but I'm not sure how to critique it. There are details - perhaps small or perhaps huge - that still bother me. It seems that you have corrected the most obvious errors.

I know we have discussed this before, but I would prefer that you clearly state that this Bose distribution is good for things that behave continuously. The example I gave earlier is that we can imagine the price of something being a continuous value anywhere between pennies to trillions of dollars. This would lead to the thesis that economies are continuous distributions, and the middle class may support this view. However, the very rich and the very poor often percieve the economy as a system of haves and have-nots (a Fermi distribution with occupation values of "one" or "zero"). This of course, would be the antithesis. It was clever of the Obama campaign to pit the have-nots against the haves by promising to raise taxes on those who made more than $250K per year, but not on those below that threshold. Of course, the threshold subsequently changed to smaller numbers... Perhaps the recent agreement by 40 billionaires to donate half of their monies to charity will help reverse this perception. We need to look for the synthesis, and I think this takes us back to the Partition function and the specific application.

Most of your "proofs" lead back to other papers and/or contain enough apparantly circular arguments that I'm not sure whether to call them proofs or double-checks.

I don't have as much of a problem with smeared delta intervals of time as do Tom and Lawrence. Once again, this goes back to the question of what is your Thesis and your Antithesis, and continuous time is consistent with your thesis of a continuous Bose distribution. It is also consistent with my emphasis of Cantor sets. I think that the antithesis, discrete time, implies a Dirac delta function on a spacetime shell - which seems a bit unnatural and contrived to me, although it is a popular perception.

I'm still not sure if your eta term is correct, or just close. It bothers me that it *ALMOST* looks like action, but isn't. There is a lot of publication history to support action...

Last weekend, I went to a wedding in north Georgia, and drove past Lawrenceville, GA. It reminded me of your Lawrenceville School, but that is in New Jersey, isn't it?

Have Fun!

Hello Tom,

When I speak of 'the number of microstates of a system' I am definitely not abandoning the ' continuous function model'. Rather, I seek to provide some sign posts for those that 'think discretely' to find their way to this conceptual landscape and help built the bridges for others to cross.

When I speak of "energy at time t", I do not speak of 'an instantaneous measure of energy content', but rather of 'an instantaneous energy content'. Classical physics may allow for the 'instantaneous measure' of energy, but in my view measurement of energy cannot be instantaneous, but must take some interval of time to occur. That's what The Second Law of Thermodynamics requires, as I discuss in Entropy and The Arrow of Time.

Whereas in the classical view what 'is' is the same as what is 'observed or measured', in my view what 'is' cannot be known but the 'measurements of what is' can only be known, as I show in The Interaction of Measurement.

When I speak of "a reciprocal relationship of entropy and temperature", I have in mind the very definition of thermodynamic entropy as 'delta E' over T. Nothing more.

Whereas "physicists have learned to live with particle-wave duality", I suggest that energy propagates continuously, but is manifested discretely. And just as we would not describe the nature of a vast ocean as made up of 'bucketfuls of water' just because that's how we draw the water, we shouldn't describe the nature of energy as 'discrete quanta' because that's how we measure it.

What drives my quest in this strange landscape of modern physics is my need to understand the world while being 'true to myself'. When I am told that we can have 'backward causality', that the future can change the past and influence the present, that there are many parallel universes and many physical dimensions (I have no problem with many, even infinite mathematical dimensions), or that a particle can be at two places at the same time, and that this is how the Universe is (and not some theoretical manifestation) ... such understanding is at odds with reality and so presents for me contradictions that need to be resolved.

I am sketching a 'naive view' that for me makes sense. It does account for the 'continuous vs. discrete' and the 'wave vs. particle' dilemma. 'Measurement' plays a central role in this view. For me, what characterizes the classical view is the idea of 'absolute and instantaneous measurements' and the notion that 'the world we see is the world that is'. My view is different from that. But it is not the view of Modern Physics.

Constantinos

It's really unthinkable to insert a relatively extrapolated vue about a concept so fundamental that is time.

Carnot easily did stipulate that it is imperative to identify the consistency of irreversibility of time.

The increase of entropy is purely linked to this said "evolutionary time",that can't be inserted without the rationality that is required.It's logic.

Fourier and Dirac or London will liaise well to affirm that the uniqueness of this universe evolving exponentially is a main parameter.

The permits to see the maximum of this energy in increasing, and the correlated mass in optimization.Time will be indeed always irreversible.

And it is only through our cernable vizualizations that we can perceive the past and extrapolate the future.

It exists simply a difference between the picture and the reality.We can thus see this past but we can't go in this past...logic and rational.

Between Boyle .Gibbs....Planck..Joule...Clausius..Maxwell....Debye.......

The thermodynamics proof all that.The pure irreversibility of time.

It's very important all that for the correct experiments and correlated equations and laws.

Regards

Steve

Dear Ray,

Thank you for your response. I value your comments.

Your example, drawn from economics, is well received. (see Stocks and Planck's Law for another such connection). It illustrates several important points. First, how Hegel's Dialectics guides the evolution of our thinking and understanding. Second, how as human beings we need to draw from our various experiences to create and formulate our ideas.

As to the first point. In a true Hegelian manner, you seek to resolve the contradiction between 'continuous vs. discrete' through a view (drawn from experience) that shows how both can be possible at the same time. I see now why you keep bringing up Cantor's set. This also combines the 'continuous' with the 'discrete' in one complete entity. But whereas your first example is drawn from common sensible experience, Cantor's set is a formal mathematical abstraction.

Here is how I reconcile 'continuous vs. discrete'.

If a vast ocean is 'energy', bucketfuls of water drawn from it are 'energy quanta'. And just as we don't describe the nature of the ocean as being made up of 'bucketfuls of water', we shouldn't describe the nature of energy as being made up of 'quanta'. Thus, 'energy can propagate continuously' but nonetheless can 'interact discretely' (when 'equilibrium conditions' are attained).

Also, we have 'accumulation of energy before manifestation of energy'. Thus we can describe energy 'accumulating continuously', but when energy is manifested (through interaction and when equilibrium is reached) it does in discrete units.

I know you have reservations about my use of 'eta'. But this quantity comes up so naturally and in so many different settings that is appears to be 'primary'. It is really nothing more than the time-integral of energy :-)

As to the second point, and I believe more important for Physics.

As human beings, we need to connect abstract ideas to concrete human experience. We see this all the time, as even abstract Physics take on 'human qualities' like 'charm' and 'color' and 'quarks'. Mathematics can evolve out of any view we have of Reality, since Math does not claim Truth but only Logical Certainty. So physical claims based on mathematical formalisms are not in themselves 'true'. But if Math cannot reveal Truth, what can? A view that 'makes sense' and is confluent with our experience, not at odds with it. We do not need more abstract theory that makes no physical sense, but a 'naïve view' that gives meaning to theory.

I would like to go over with you some of my papers, point by point, to see if there are any problems. The references in many of them to previous papers do not make for 'cyclical arguments'. All the results are mathematically valid and proven in a single paper (A 'Planck-like' Characterization of Exponential Functions). Since I find it hard to write equations with the FQXi text editor, I am attaching a pdf file of an overview of the paper on entropy. What specific parts of this argument are flawed?

The Lawrenceville School is indeed in New Jersey, just 5 miles from Princeton. It was founded in 1810 as a preparatory school for Princeton. Today it is one of the top prep schools in the country.

always having fun ...

Constantinos

there is no physical evidence for multiverses nor strings, and there are no sound mathematical nor physical theories predicting such entities.

so why do we use that for which there is no motive nor evidence to help us contemplate time?

$$$$$$?

a month later

2010-09-05 FQXI --- Time Multiverse

Our universe is a Planck (h) value universe. There could be other universes with different values for h. They would not interact with our universe while being essentially in the same place. I believe the neutrinos to be particles with slightly off values for h and that would make them hard to interact with our Planck universe. Neutrinos would come in up (x>h) version or down version (x

(repost of previous)

Our universe is a Planck (h) value universe. There could be other universes with different values for h. They would not interact with our universe wile being essentially in the same place. I believe the neutrinos to be particles with slightly off values for h and that would make them hard to interact with our Planck universe. Neutrinos would come in up (x>h) version or down version (x