Article FEB..2016

The Scale Landscapes (Relativity) of the Universe
David Piñana (Ing. Ind. UPC)
(Version 4, February, 2016)

ABSTRACT

The current mainstream in cosmological physics proposes a unique universe that started with the Big-bang (approx. 13,700 million years ago), and it continues expanding “isotropically”. This “mainstream” universe seams to be limited  by both scale spectra: in its upper level (approx. 10 e +27 m.) by Our Universe (or, at least, by the Observable Universe) external “ shape boundary”, and its lower level (approx. 10 e -35 m.) by the Planck scale/size. An we (humans) are in the middle, at intermediate levels/spectra between these scale/size limits.

This article intends to show a new conception of the Universe: The scale/size relativity. This article proposes that the universe is composed of many more scale/size spectra (upper and lower) than the currently recognized limits (possibly over 10 e + 1000 m and below 10 e - 1000 m). And for every level/spectra there would be different physical concepts and laws (emergents), although they could be linked by common underlying laws and concepts. And we (humans) are not in the middle. We are just in a random level within this broad spectrum scale/size.

This proposal / approach (if it is true and it can be proved) might be a very important advance in explaining certain physical concepts that are currently not entirely clear (Dark Energy and Matter, Uncertainty Principle, the dual nature of the particles -particle/wave-, etc.). (See Fig. 1).

This article also join on the same framework several “state of the art” related theories, proposals and studies that are being considered independently by current physics: Emergence, Fractal, Brane-String, MOND-TeVeS, DSR-CDT, Scale Relativity, Gödel,…

Fig. 1: Global/Whole Universe scales









FIG.2: The Landscapes of the Universe




CONTENTS

1. INTRODUCTION
UNIVERSE LANDSCAPES
2. COSMIC LANDSCAPE 
ENERGY-MATTER OF OUR UNIVERSE
DARK ENERGY
  DARK MATTER (& OTHER THEORIES)
3. PLANCK LANDSCAPE 
CASUAL DYNAMICAL TRIANGULATION
SPACE & VACUUM
ENERGY & SIZE SCALE RELATIONSHIP
DSR THEORY (HIGH ENERGY SCALE)
UNCERTAINLY PRINCIPLE 
4. EMERGENT CONCEPTS & LAWS
  INTERACTION FIELDS ARE EMERGENT TIME CONCEPT
5. EVENT HORIZONS
HOLOGRAM THEORY 
6. FRACTAL & SCALE RELATIVITY THEORIES
FRACTAL COSMOLOGY
SCALE RELATIVITY
7. CONSTANTS OF OUR UNIVERSE
EDDINGTON´S UNCERTAIN CONSTANT
8. GÖDEL THEOREME vs TOE
9. CONCLUSIONS


1.  INTRODUCTION

Humans, as always, make the mistake of believing that we are (in) the center of the universe. And we always try to understand the universe from the Ptolemaic point of view. But time after time, we have had to admit that this is not so (Copernicus, …). 

We are now making the same mistake, and we believe that we are in the middle of the scale (size) spectrum of the universe. And we try to understand the universe from what we know about our own scale (size) spectrum. Trying to extrapolate our own concepts of scale (size) to other scale spectra. Probably, there would apply other concepts and other laws, unknown to us (emergent concepts and laws).

Surely, if we are able to break these pre-established schemes, we will open new horizons, allowing us to understand physical concepts that currently we fail to understand well: Dark Energy and Matter, the Uncertainty Principle, the dual nature of the particles (particle/wave), etc.

The universe could be composed of many more scale/size spectra (upper and lower) than the currently recognized limits (possibly over 10 e + 1000 m and below 10 e - 1000 m). And we humans aren´t in the middle. We are just in a random level within this broad spectrum scale/size (See Fig.1).

As Lee Smolin says, to any major new physical theory (such as Newton and Einstein), assuming that, once it is proposed and accepted, they would clear other big uncertainties to date. As in the game of dominoes (where after falling a first tab, then fall all the others), so it happened with many concepts when considering the theories of Newton and Einstein. And it can happen the same, if we can demonstrate and accept the proposal of  the Scale Relativity of the Universe, in this article.

This article don´t try to give a clear mathematical /theoretical demonstration or experimental verification concerning its proposal. This article just try to propose a framework, and to show several collateral and related studies and theories that fit within this framework. To get a final mathematical / theoretical demonstration will be the following objective to follow up, that will be not easy. Furthermore (in parallel), we have to look also for experimental verifications, that surely will also be very difficult. Multidisciplinary team work and high investment will be necessary to get them !


UNIVERSE LANDSCAPES

The term LANDSCAPE (established by L. Susskind to describe the upper spectrum of our universe: Cosmic Landscape) will be used in this article to name also the different scale/size levels (landscapes) of the universe (see Fig.2).

So we can define different LANDSCAPES that describe different scale/size levels with their own concepts and laws:

  • Newtonian Landscape
  • SR-GR Landscape
  • Chemistry-QM Landscapes
  • Etc.

And we could also forecast other LANDSCAPES that describe further scale/size spectra:

  • Cosmic Landscape
  • Planck Landscape
  • Supra-Cosmic Landscape
  • Infra-Cosmic Landscape
  • Etc.




2.  COSMIC LANDSCAPE

In his book The Cosmic Landscape (2006) Leonard Susskind presents the Cosmic Landscape concept as a place (landscape) beyond Our (known) Universe to a higher level or dimensional scale (scale range from 10 e +27 to 10 e +40 m).

The Cosmic Landscape would be a scale spectrum above Our Universe ("Bulk"), where, possibly, and according to string theory, would have superior spatial dimension (4D-9D-25D ?), and where would “float” (coexist) other universes (“pocket universes” or World-branes) with other spatial dimensions (N-dimensional), in various stages of development (expansion, implosion,...) and with different physical constants (Cosmological, G, h, c, ...). And where Our Universe would be only one among many other possible universes (up to +10 e +500 according to mathematical possibilities offered by the string theory).

This cosmic landscape (with X-space dimensions) would contain a “Primordial Field” (energetic field) that would have different values ​​at each point of the X-dimensional space (forming different energy valleys, with different “space-phase"),  It gives us a view of N-Dimensional valleys and mountains which give the name of Landscape. One of these valleys would be our universe, where the value of Primordial field would be our Cosmological Constant (Λ = 10 e -116 J). 

The Time (we will talk later on about Time concept) could be a dimension that depends on the entropy (△S), being positive if △S is positive, and possibly negative, if △S is negative (which would contradict the Second Law of Thermodynamics). We cannot ensure that there is any time in the Cosmic Landscape, and if it would be positive, negative or null. Possibly it would also depend on the S, or other new emergent concepts.

According to S.Hawking, the Big Bang of Our Universe emerged from the quantum vacuum fluctuations, starting from the spontaneous creation of particles and fields (matter-antimatter and matter-gravity, and also from other particles and fields). This particles and fields prospered through inflation, and retaining the initial energy (= zero ?), by considering the matter as positive energy, and gravity (or the gravitational energy) as negative energy, counteracting both, and making the total universe energy zero (as before the Big-bang was). And it could also have happened to the other particles and forces (being positives-negatives energies).

Under the Cosmic Landscape proposal, it would be an alternative that the Big Bang occurred from this primordial energy field, previously existing in the Cosmic Landscape. And the energy of Our Universe could come from this preliminary energy. Big Bang could happen as a decrease of this primordial energy, creating an energy valley and creating the conditions for a short burst of inflation, transforming this primordial energy (inflaton energy ?) field in matter and radiation (and transforming the primordial space 9D to our 3D space, more other 6D with very small size: KK). From there we can follow the same reasoning of Hawking proposal, although the initial energy would not necessarily be zero as Hawking propose.


ENERGY-MATTER OF OUR UNIVERSE

According to the Principle of Conservation of Energy (or First Law of Thermodynamics), the total amount of energy of any isolated or closed physical system (without interaction with any other external system) remains unchanged over time. But that energy can be transformed into another form of energy. In short, the Law of Conservation of Energy states that energy can neither be created nor destroyed, it can only change from one form to another.

If this principle was always valid (for any moment of the life of the universe) and for the entire universe created after the Big Bang, it would imply that the total energy of the (our) universe would be the same now than it was in the beginning, and the same that it will be at the end.

Then, where does it come the total energy of the (our) universe?

According to Stephen Hawking, the Big-bang (and the whole Energy and Matter of Our Universe) began (from Nothing: zero energy) due to quantum vacuum fluctuations by creating positive energy and negative energy (ie. Matter and anti-matter ). So now (and always) the total energy of the universe is zero, and, for example, mass and gravitational energy cancel each other (as well as the other forces and particles of the universe could cancel one to each other). 

Another proposal/option could be that energy is intrinsic to the space, and that energy is created (increase) when space is created (enlarged or expanded). But this proposal breaches (violates) the Principle of Conservation of Energy (or First Law of Thermodynamics). It will mean that the Energy of Our Universe increase at the same time that the space volume of Our Universe is enlarging (expanding). 

For these both proposals/options, we can state that “The Known Energy-Matter (and space) that we see and detect in Our Universe might be considered as an emergent concept arose after the Big-bang”.

On the other hand, considering the Cosmic Landscape proposal, Big Bang of Our (“pocket”) Universe would only be an event of the many that occurs within the whole universe (Cosmic Landscape), and the energy (matter) of Our Universe could come from an prior energy already existing on the Cosmic Landscape (Primordial field ?), where different “pocket” universes would be created and destroyed as bubbles in a glass of soda gas. The dilemma for the energy of Our universe disappears, but it raises to a higher level: Where does it come Cosmic Landscape  (Whole Universe) energy-matter ?

We have been describing different proposals about from where it came or how it was created the Energy-Matter (Known Energy-Matter) of Our Universe, but recent observations tell us that all the Energy-Matter we know is only approx. 5 % of the Whole Energy-Matter of Our Universe. The other 95 % are Dark Energy (70 %) and Dark Matter (25 %). 

This can give us an idea of how little we really know about the universe, and so far we are from a (physical-mathematical) scientific model that describes and parameterizes it properly.

We can summarize the following hypothesis about the energy of Our Universe:

1.-Considering Our Universe as a CLOSED SYSTEM:

1.1.-The total amount of energy in Our universe is exactly zero: its amount of positive energy (e.i: matter) is exactly canceled out by its negative energy (e.i: gravity).

1.2.-If dark energy is an intrinsic property of empty space (as hypothesis) then energy is created when space expands.

2.-Considering Our Universe as an OPEN SYSTEM:

- The total amount of Energy of Our Universe is the result of the Energy that goes into it (Big-Bang, Gravity coming from outside,…?), and the energy that is leaving it (Gravity leaving outside, Black & Warm holes,...?)

3.-Any way the UNIVERSE is considered as an OPEN or as a CLOSED SYSTEM: Energy concept is not well-defined in GR Theory. 

DARK ENERGY

Dark Energy tries to explain the acceleration of the  (isotropic) expansion of Our Universe. 

Dark Energy acts like a repulsive gravity caused by some kind of different matter (anti-matter?) to that we know, that is attractive, and it exerts a negative pressure (repulsive) throughout the space.

But the simplest explanation for dark energy is that it is simply the "cost of having space": that is, a volume of space has some intrinsic, fundamental energy. 

Vacuum energy is an underlying background energy that exists in space throughout the entire Universe. Vacuum energy is expected to contribute to the cosmological constant, which affects the expansion of the universe. 

The effects of vacuum energy can be experimentally observed in various phenomena such as spontaneous emission, the Casimir effect and the Lamb shift, and are thought to influence the behavior of the Universe on cosmological scales.

 DARK ENERGY = VACUUM ENERGY (?)

Dark Energy value is the Cosmological Constant (nowadays  it is considered as independent of time and place in our universe,  Λ =  10 e-116 J).

DARK ENERGY = COSMOLOGICAL CONSTANT

We might consider that the accelerated expansion of our universe itself is produced by the spontaneous generation of new space (newly created, or possibly coming out of our universe: Cosmic Landscape or “Bulk").

And as stated in the previous chapter, this increase in space, could also lead to an increase in total energy of Our Universe. 

And, it is possible that, Cosmological “Constant” value has varied (increase-decrease) since the Big-bang, depending on the speed rate (acceleration) of the Universe Expansion.


DARK MATTER (& OTHER THEORIES)

Dark Matter is just a physical concept that most mainstream scientists proposed to explain rotation speed of galaxies that do not follow Newtonian and Relativistic models. Dark Matter proposal forecasts other matter that we cannot see and we only detect by this galaxy phenomenon. Dark Matter represents four times more matter than the known matter. To date there are many theories about DM, but no one could prove or show their existence (WIMPs, Axions,…). To find these new particles is currently one of the most important subjects of study and research (HLC-CERN, ADMX, DAMA,…)

But another way to solve this problem (the galaxy rotation) is to assume that Newton and GR theories, are not valid for very long distance scales (> 10 e +20 m).

MOND Theory and their last version TeVeS gives other alternatives to the same problem, whereas the laws of Newton and Einstein (SR & GR) vary with the distance/size scale.

“In physics, Modified Newtonian Dynamics (MOND) is a theory that proposes a modification of Newton's laws to account for observed properties of galaxies. Created in 1983 by Israeli physicist Mordehai Milgrom, the theory's original motivation was to explain the fact that the velocities of stars in galaxies were observed to be larger than expected based on Newtonian mechanics. Milgrom noted that this discrepancy could be resolved if  the gravitational force experienced by a star in the outer regions of a galaxy was proportional to the square of its centripetal acceleration (as opposed to the centripetal acceleration itself, as in Newton's Second Law), or alternatively if gravitational force came to vary inversely with radius (as opposed to the inverse square of the radius, as in Newton's Law of Gravity). In MOND, violation of Newton's Laws occurs at extremely small accelerations, characteristic of galaxies yet far below anything typically encountered in the Solar System or on Earth.”

“And Tensor–vector–scalar gravity (TeVeS), developed by Jacob Bekenstein in 2004, is a relativistic generalization of Mordehai Milgrom's Modified Newtonian dynamics (MOND) paradigm.”

  • Newton's law seems to work perfectly to explain the dynamic phenomena at scales up to the size of Earth, and probably up the Solar System (max. 10 e +15 m),.
  • From this distance we must consider the MOND´s law, which should fully explain the dynamic phenomena at scales between that 10 e+15 to near to the scale of galaxies: 10 e + 20 m.
  • Should be above these scale (10 +20 m), to the ends of Our Universe (10 +27 m), where the other dynamic laws (TeVeS´ law ?) should describe better these scales phenomena.
  • And above these scales (> 10 e +30 m) other new emergent laws will apear to explain new emergent phenomena that we cannot forecast by now.

Other proposal could be the Fractality of Spacetime: 

“Applying relativity to fractal non-differentiable spacetime, Laurent Nottale, in his Scale Relativity theory, suggests that potential energy arises due to the fractality of space, and accounts for the missing mass-energy observed at cosmological scales”.

This missing of mass-energy could make also that G (gravity constant) decrease at cosmological scales. Gravity could be missed through the fractal space-time. 

The Dynamic Laws of Physics (and Universal Gravitation) have varied over time, and even Einstein had already proposed that they still has to evolve:

ARISTOTLE: F = m.v
NEWTON: F = m.a 
EINSTEIN. E = m.c2
MOND: F = m.a.(A/A0)   
NEXT ?: F = f (scale) = m.a.(scale factor)

Or better G (Gravity Constant) vary with the scale/distance due to fractal space-time: G = f ( Scale/distance  factor)




Fig.4: Variation of G (Gravity Constant) with Scale


3.   PLANCK LANDSCAPE

According to the uncertainty principle, the value of a field and its temporal change rate (waves) plays the same role as the position and velocity of a particle. And an important consequence is that there is “NO” a vacuum. Since the empty space means that the value of a field is exactly zero and the rate of change of the field is zero (if it were not so, space would not be empty). Then as the Uncertainty Principle does not allow exact values have both simultaneously, the space is never empty. You can have a minimum energy state, called "vacuum energy" and is subject to what is called vacuum quantum fluctuations, consisting of particles and fields that appear and disappear from existence. As virtual particles, they cannot be observed by particle detectors, but they can be by indirect methods (energy changes in electron orbits).

The Planck length is related to Planck energy by the uncertainty principle.

The nature of reality at the Planck scale is the subject of much debate in the world of physics, as it relates to a surprisingly broad range of topics. It may, in fact, be a fundamental aspect of the universe. In terms of size, the Planck scale is extremely small (many orders of magnitude smaller than a proton). In terms of energy, it is extremely 'hot' and energetic. The wavelength of a photon (and therefore its size) decreases as its frequency or energy increases. The fundamental limit for a photon's energy is the Planck energy. This makes the Planck scale a fascinating realm for speculation by theoretical physicists from various schools of thought. Is the Planck scale domain a seething mass of virtual black holes? Is it a fabric of unimaginably fine loops or a spin foam network? Maybe at this fundamental level all that remains of space-time is the causal order? Is it interpenetrated by innumerable Calabi–Yau manifolds, which connect our 3-dimensional universe with a higher-dimensional space? Perhaps our 3-D universe is 'sitting' on a 'brane' which separates it from a 2, 5, or 10-dimensional universe and this accounts for the apparent 'weakness' of gravity in ours. These approaches, among several others, are being considered to gain insight into Planck scale dynamics. This would allow physicists to create a unified description of all the fundamental forces.

“The incompatibility between GR and QM can only be solved if we reject the notion that space is a fundamental concept, and we accept that space emerges from the expansion of the Universe itself, and space is an emerging concept “ (Lee Smolin).

CASUAL DYNAMICAL TRIANGULATION

Near the Planck scale, the structure of space-time itself is supposed to be constantly changing due to quantum fluctuations. CDT theory uses a triangulation process which varies dynamically and follows deterministic rules, to map out how this can evolve into dimensional spaces similar to that of our universe. 

Causal dynamical triangulation (abbreviated as CDT) invented by Renate Loll, Jan Ambjørn and Jerzy Jurkiewicz, and popularized by Fotini Markopoulou and Lee Smolin, is an approach to quantum gravity that like loop quantum gravity is background independent. This means that it does not assume any pre-existing arena (dimensional space), but rather attempts to show how the spacetime fabric itself evolves. At large scales, it re-creates the familiar 4-dimensional spacetime, but it shows spacetime to be 2-d near the Planck scale, and reveals a fractal structure on slices of constant time. These interesting results agree with the findings of Lauscher and Reuter, who use an approach called Quantum Einstein Gravity, and with other recent theoretical work.


SPACE AND VACUUM

For our usual methods of calculation (mainstream theories) Planck dimension seems to be the smallest dimension we can consider. But that doesn´t mean that there cannot exist smaller things (objects, concepts, effects,.) within Planck Dimension-Volume. It only mean that our mainstream theories are not good enough, and that they have to be enlarged to other theories that could understand and parametrize all what happen inside the Planck Dimension (Planck Volume).

If we consider the Calabi-Yau 6D-branes that, according to Brane-String theory , may exist at Planck Dimension-Volume, we could consider these 6D-Branes as other micro-universes (similar to Our 3D Universe) that contain 6D Space, with other (emergent) concepts (objects, effects, interactions,…) and Laws. Quantic Fluctuations could be only effects coming from these 6D Calabi-Yau universes / worlds.

In the article “What´space” by Frank Wilczek (Mit physics annual 2009), we can read:

“Space is effervescent, substantial, weighty, and elastic. Each of these properties equates to specific, observable phenomena; they are not whimsical metaphors. Space has a life of its own, and exists independent of any matter that might occupy it. Indeed, in our most fundamental equations particles—the building blocks of matter—are described as disturbances in the activity of space-filling fields, or in other words of space itself.

Modern quantum physics brings in ideas of a different order. Quantum reality lives in spaces whose meaning, size, and structure transcends classical ideas about physical space. To get in tune with Nature, we must vastly expand our conceptual universe.

The structure of space is encoded in the metric field. Like all fields the metric field is subject the laws of quantum mechanics. In particular, it is forever boiling with spontaneous fluctuations. When we calculate these fluctuations we find that they grow, as a fraction of the distance, for nearby points. Eventually, for distances below about 10-33 cm., the calculated fluctuations in distance become larger than the distance itself. Below this so-called “Planck length” our usual methods of calculation break down. Indeed, the whole concept of distance comes to look suspect. Now 10-33 cm. is a very small distance, far beyond practical access. Nevertheless this issue is of fundamental interest, not only in its own right, but also for cosmology. Indeed, our equations break down in describing extremely short time intervals (10-44 sec.), for similar reasons. Thus we aren’t able to describe the very earliest moments of the big bang. And so ultimate questions of origins remain up for grabs.”  

To investigate what happens beyond the Planck size we need very high energies (above the Planck energy), and according to our current theories (QM and GR), this would create black holes. And if we increase this energy, we would increase the size of these black holes.

This suggests that our description of space-time are not right for these dimensions (scales):

  • Ed Witten: "Space and Time may have their days numbered”
  • Nathan Seiberg: "I'm pretty sure that space and time are only illusions”
  • Nathan Seiberg: “Space and time are likely to be emergent notions, They are not present in the fundamental formulation of the theory, but appear as approximate macroscopic concepts.” Emergent Spacetime, 2006 (http://arxiv.org/find/hep-th/1/au:+Seiberg_N/0/1/0/all/0/1 )
  • David Gross: "Most likely, space and time have  (elemental / fundamental) components, and they can be only emergent properties that arise in a theory with a very different look."

Reaching a deeper understanding of the fundamental nature of space and time, it is one of the largest and intriguing challenges to physicists of next years.

A final consideration about space (empty space or vacuum) could be that, as it seems not to be so empty as we thought, and that space has life or consistency by itself, then, might we consider space as the famous ether ?, and that EM waves propagate through this medium (empty space or vacuum) ?


What yes it seems to be possible is that "empty" space might just be some kind of unknown "substance", made up of much smaller components, currently unknown (from a much smaller scale), and that still should be determined and discovered. This is what could give the empty space ("vacuum") a fractal (hierarchical) structure.


ENERGY & SIZE SCALE RELATIONSHIP

Each distance/size scale has an associated energy (mass) scale, (“Warped Passages: Unraveling the Universe's Hidden Dimensions. Lisa Randall ,2005):

And its relationship can be described as:

ENERGY (wave-particle function) (GeV)    = 
K .[1 / WAVELENGTH (Distance, m)] 10 e +15


From Uncertainty Principle (and also Einstein & De Broglie principles) we can say that the different scales of distances / sizes (particles or wavelength), are inversely related to wave energy (interaction) or particle mass (in physics, they are usually measured masses of particles in quantum GeV).

  • Wave-particle duality: Any wave has associate a particle (Einstein: EM -> photon) and any particle has associate a wave (de Broglie: e- ´> Wave function ?)
  • Einstein state:   E=h.ν , where ν is the wavelength and h the Planck constant... E is the Energy of the EM particle (photon)... Higher is the ν higher is the E.
  • Broglie state:  λ= h/mv λ= wavelength of a particle; mv = momentum (= approx. Energy)

As λ=1/ν  then we can say: E = m v

There is associate an Energy (mass) for every particle and ν - λ (wave length-size-distance) of the wave, and as smaller is the length, higher is the Energy (mass).

DSR THEORY (HIGH ENERGY SCALE)

In the same way that the theories of MOND are proposing alternatives to the laws of Newton and SR-GR for very high spatial scales (> 10 e+20 m), there are also other QG theories proposing alternatives for very small (or very high energy) spatial scales.

For example the DSR  (= Doubly or Deformed SR) theory which proposes that GR is not valid for High Energies (Planck scale), and it forecast that light speed could increase till infinite for Planck Energy (c = f (E))

Doubly special relativity (DSR) – also called deformed special relativity or, by some, extra-special relativity – is a modified theory of special relativity in which there is not only an observer-independent maximum velocity (the speed of light), but an observer-independent maximum energy scale and minimum length scale (the Planck energy and Planck length).
SR is based on two principles: (1) the relativity of motion , and (2) the invariance and universality of the speed of light. 






Fig. 6: DSR Diagram [c= F(Scale)]

DSR I assumes that the Planck dimension is the smallest object that can be seen, and its dimension is the same for all observers (whether they are stopped or in motion), as it is for speed of light. Both would be two universal variables (speed of light and Planck length).

DSR I theory also assumes that the Planck energy is the maximum energy that one elementary particle can have. Currently the maximum detected energy is 10 e -9  times this maximum Planck energy (by cosmic ray detector AGASA).

Further DSR II assumed that at very high energies the speed of light increases to infinity at the Planck energy.
UNCERTAINTY PRINCIPLE

Stephen Hawking says that quantum mechanics itself is deterministic, and it is possible that the apparent indeterminacy really is because there are no particle positions and velocities, but only waves.

So for Stephen Hawking, “the uncertainty principle is only apparent, but not real”. There could be another way of seeing the Universe, in another scale, where beings and laws are different.

Uncertainty Principle has been always a strange and unintelligible concept... and mainly could be a problem of measuring instruments, because we try to measure them (location and momentum) precisely with inappropriate instruments (larger than required). It is not appropriate to use EM waves (photons) to measure the position and speed of an electron.

Surely if we could see the uncertainty principle from his own quantum scale, we could see that we can determine the velocity and position of a particle (electron) at the same time. But we should detect it by other means, and not with those who we now know (photons). Possibly we could use "waves" of nuclear interactions (strong and weak)? Or other not wave-based sources ?

“As well known, Electromagnetic wave (EM wave) is caused by electromagnetic interaction, and gravitational wave (G wave) is caused by gravity; we could propose that strong interaction wave (S wave) is caused by strong interaction, and weak interaction wave (W wave) is caused by weak interaction.”.  From article “Fifteen Kinds of Waves Caused by Four Fundamental Forces”, Fu Yuhua, Fu Anjie, Zhao Ge (Beijing Relativity Theory Research Federation)

What will happen with HUP if that proposal/assertion is true?

Heisenberg Uncertainly Principle (HUP) propose:

HUP => Position Precision x Momentum Precision > h/4pi

But, possibly, if we could use other measurement instruments: using weak waves, then we could propose:

Weak Waves UP => Position Precision x Momentum Precision < h4pi

And, possibly, if we could use other measurement instrument: using other different sources not waves based, then we could propose:

Not wave-based UP => Position Precision x Momentum Precision => 0

Mainstream scientist consider that the uncertainty principle is not only a measurement limitation, but also more fundamental than that. As far as we know by now, it simply doesn't matter how we take your measurement we will not improve on its limits.

But we also must consider the option that Uncertainty Principle could be simply a matter of trying to understand phenomena, typical of other scalar spectra, with the parameters and models of our own scale spectrum.

If we agree that, on a quantum scale, everything behaves like waves, and what for us it is a particle (matter), it is just one particular type of wave (as stated in the String  Theory), then concepts such as position and speed (momentum) do not have the same meaning as they have for our own scale. We are simply trying to understand other phenomena from other spatial scale, with (emerging) concepts of our own spatial scale.

Violation of Heisenberg’s Measurement-Disturbance Relationship by Weak Measurements (Lee A. Rozema, Ardavan Darabi, Dylan H. Mahler, Alex Hayat, Yasaman Soudagar, and Aephraim M. Steinberg Phys. Rev. Lett. 109, 100404 – Published 6 September 2012; Erratum Phys. Rev. Lett. 109, 189902 (2012):

“While there is a rigorously proven relationship about uncertainties intrinsic to any quantum system, often referred to as “Heisenberg’s uncertainty principle, Heisenberg originally formulated his ideas in terms of a relationship between the precision of a measurement and the disturbance it must create. Although this latter relationship is not rigorously proven, it is commonly believed (and taught) as an aspect of the broader uncertainty principle. Here, we experimentally observe a violation of Heisenberg’s “measurement-disturbance relationship”, using weak measurements to characterize a quantum system before and after it interacts with a measurement apparatus. Our experiment implements a 2010 proposal of Lund and Wiseman to confirm a revised measurement-disturbance relationship derived by Ozawa in 2003. Its results have broad implications for the foundations of quantum mechanics and for practical issues in quantum measurement.”


4.   EMERGENT CONCEPTS & LAWS

Our vision of the different LANDSCAPES is always from our own scale spectra (our LANDSCAPE: Newtonian Landscape). And from there we try to understand everything that happens in the other scalar spectra.

But, what would happen if we could observe these same LANDSCAPES from their own scale?
It could give us a completely different point of view that we have now, and it would surely help us to understand  better many concepts and phenomena that now we do not fully understand.

We could consider that most Physical concepts (such as vacuum, energy, matter, space, time, speed, ...), and also most physical theories or laws (such as Newtown, Maxwell, Thermodynamics, Relativity, Quantum, ...) are emergent concepts and theories. This proposal is based on Robert B. Laughlin ( Different Universe: Reinventing Physics from the Bottom Down Paperback – February 28, 2006)

FIG.7: Point of View from different Landscapes) 

Concepts so usual for us (for our LANDSCAPE) such as energy (matter), vacuum, and time may have no meaning for another LANDSCAPE. In the same way that thermodynamic concepts such as temperature and pressure are values (emerging) that only make sense for a larger size of a atom (> 10 and -15 m) and they are meaningless to smaller dimensions. We can say that energy (matter), vacuum and time are emergent concepts.

Likewise, for each LANDSCAPE there are physical models that best explain their behaviors: Newton, Maxwell, Chemistry, QED, QCD, Einstein (SR-GR) ... Although they all may be related to each other by some underlying laws. We can also consider that the different laws / models are emergent, depending on the scale (Landscape).

Current effort on ToE is finding these underlying laws that can unify all models, and especially the SR-GR with QM (QED, QCD & QG). But, at best, these ToE (String-Brane Theory) only will be able to explain a wider spectrum,which includes several LANDSCAPES (between Our Known Universe scale, 10 e + 27 m, to Planck scale 10 e -35 m). It is only a way of widening the scale spectra. And, possible, other further ToEs could wide more this spectra.

The laws of physics are the same throughout the whole space, but it does not mean that the scenario in which they are wrapped will be always the same (spaces of different dimensions or different size/space scales), where different laws may emerge. Although all of these emerging laws may be governed by some basic underlying laws.

EMERGENT INTERACTION FIELDS

Theory (mainstream) says that (at least EM, S & W) interactions split off from a single, unified force due to spontaneous symmetry breaking as the very, very early universe cooled. This all happened prior to 10-11 seconds after the beginning. 



Fig 8: Emergent Interaction Fields

May we also consider that known interactions (Gravity, EM, Weak and Strong) as emerging effects ?

What would happen if we could see/observe (detect / measure) within a very small volume (< 10 e -25 m or smaller than Planck volume), there will be also 3-4 interactions or only one... or none ? 

Coupling Constants for the Fundamental Forces:
In attributing a relative strength to the four fundamental forces, it has proved useful to quote the strength in terms of a coupling constant. The coupling constant for each force is a dimensionless constant. The links below take you to some information about determining the value of the coupling constants.

Coupling Constants:
Strong αs = 1
Electromagnetic αe = 1/137 (= Fine-structure constant)
Weak αw = 10 e-6 
Gravity αg = 10 e-39

Otherwise, we could  also say that different interactions (forces)  fields we know have different scope of action:

Scope of Fg = infinite (Whole Universe or “Bulk”. Due that Gravity is a closed string and it can go out of Our D-Brane, to the Bulk)
Scope of Fem < 10 e +27 m (Within Our Universe radius. Due that EM is an open string and cannot go out of Our D-Brane)
Scope of Fs < 10 e -15 m (Atom -Nuclear radius)
Scope of Fw < 10 e -18 m  (Quark radius)


Three of these interactions (EM, Weak and Strong) seem to be unified to very small size (large energy) scales (approx. Planck Dimension/Energy), as if they arose from a unique single force from there (possibly from the 6D shapes: Calabi-Yau?).

On the other hand, the Gravitational interaction seems to follow different patterns. And, as Lisa Randall propose, the mass seems to appear as if by magic, and it is 10 e -16 times (order of magnitude) weaker than physicists could expect only from general theoretical bases (the Hierarchy Problem).

When we can say that the mass/gravity concept appears ?. May we say that mass concept arose when Graviton, Higgs (10 e - 17 m)  particles appear ?. Likewise, can we say that the EM interaction only arose when the electron (10 e -18 m) and quarks (10 e -20 m) appear? There are Gravity or EM interactions in smaller scale distances/size than 10 e -20 m ? What happen between 10 e -20 and 10 e -35 m scale spectra? And what will happen in smaller scale size spectra (< 10 e-35 m) os the Planck distance ?

Moreover, for larger size scales (> 10 e +30 m), if we could go out of our 4D universe, and we could see it from outside (from the Cosmic Landscape), possibly we could detect the Gravity interaction, but also we could detect other emergent interactions, currently unknown. 



Fig.10: Interaction field unification to high energy scales) 

It has been shown that EM and Nuclear Interactions (strong and weak) are unified to very high energy scales (near Planck energies and Planck scale). Electroweak theory unified both EM and weak (Steven Weinberg, 1993: “The Search for the Fundamental Laws of Nature”).  And according to string theory (ToE) it is also believed that gravity can be unified with them, to higher energy levels.

Following I relate a very short and relevant text (Markus Hanke, The Science Forum, April.2015) that I agree with and I consider very clever and fascinating:

 “In the Standard Model as it currently stands, there are 25+ quantum fields ( of which the electromagnetic field is only one ), all of which extend throughout the universe, i.e. they are present everywhere; their mere presence does not imply that gravity is somehow "caused" by any of them, and less still does it single out electromagnetism in any way. Several people, including myself, have pointed out already that electromagnetism behaves very differently from gravity in many fundamental respects - the two are quite simply not the same thing, and neither one of which causes the other, though of course they influence one another since electromagnetic fields carry energy-momentum. However, what we can do is unify gravity and electromagnetism into a common framework - this is done by simply adding a spatial dimension to the universe, which is curled up into a small "circle" at each point of space-time, meaning it isn't seen on macro-scales. In essence, it turns out that 5-dimensional General Relativity is exactly equivalent to 4-dimensional GR + 4-dimensional electromagnetism, plus an additional scalar field; this model of a 5-dimensional universe is called Kaluza-Klein gravity. The implication of this is that gravity and electromagnetism, though different by nature, both arise from the same underlying mechanism, being the geometry of a space-time with a compactified fifth spatial dimension; gravity and electromagnetism are, under this model, both geometric properties of space-time, and hence on equal footing ( but not the same thing ! ). Unfortunately though Kaluza-Klein gravity implies the existence of an additional scalar field ( often called the "dilation field" ), for which there is no empirical evidence whatsoever - which is why this model never made it to the mainstream, since the dilation should have been easily detectable even for first generation particle accelerators, but it just isn't there. Nonetheless, it is a fascinating model and definitely of academic interest.”

The laws of these forces (EM-S-W-G) are somehow related (albeit in different spatial dimensions), so we can say that this known forces/interactions are simply different manifestations of the same force/interaction (X ?), through different (scale) spatial dimensions.

“There may exist other worlds that we do not know, in other branes separated from ours by other hidden dimensions. And, if there is life on some of these other branes, it is likely that these beings will be trapped in a completely different environment. And they should feel different forces/waves that would be detected by different senses“ (Lisa Randall).


TIME CONCEPT

According to Lee Smolin “for the future development of physical science there is something that escapes us, and among these concepts is the Nature of Time”.

Before Einstein, Time was considered an independent and absolute concept/dimension, and always with arrow positive (from the past to the future) and constant/homogeneous (moving at the same rate/speed).

SR (Einstein’s) theory proposes that the Time is variable depending on the speed of the object (the higher is the speed of an object, time will run slower for him, relatively to another object moving at a lower speed). And also, Time varies according the gravity force that is exposed to the object (the higher is the gravitational force on an object, then slower will run the time relatively to another object that is exposed to a lower force). If an object is exposed to a infinity Gravity (Black Hole) Time will be zero.

Also Time is null (zero) for particles moving to the light speed (EM radiation,… ). Even more, whether information (object without mass) that move at a speed faster than light (which is now considered impossible), its time would be negative, and therefore, such information would travel to the past (!?).
Stephen Hawking (“A Brief History of Time”, 1988) proposed that the arrow of Time could depend on the entropy (S), being positive if entropy rate is positive, and, (possibly) negative, if entropy rate is negative (which would contradict the Second Law of Thermodynamics). If this proposal is OK the arrow of Time could be different for different “pocket” universes depending on their entropy. Realize that entropy is always positive (S>0) but we are talking about entropy rate (that means the entropy variation △S).

While Our Universe is expanding, entropy is increasing , and time is positive. But what will happen if Our Universe (or other “pocket“ universe) implode (“Big-Crunch”)? S.Hawking, initialy supose that time could be negative, but finally accepted that during the implosion (although the entropy rate could be negative), Time will be also positive.

We could say that if Time arrow is proportional to the Entropy rate  (T = f(△S)), then Time arrow rate could be variable depending on the Entropy rate value at different ages of Our Universe since Big-bang.

For all the above, we could extrapolate (“The Fabric of the Cosmos: Space, Time, and the Texture of Reality”, 2005 by Brian Greene) that Time began for Our Universe with the Big Bang, and that it has, to date, evolved with a positive arrow, but, probably, to different rates depending on the value of the entropy on every moment (depending on the entropy rate for every ages of Our Universe).

If we go further, and we settle beyond the scalar limits of Our Universe (on the Cosmic Landscape), with all their different bubble (pocket) universes (with different constants and evolution state), we can extrapolate that the Arrow of Time for each universe could have a different value/rate, depending on its own characteristics (Entropy, gravity, speed of light,…), and possibly, depending on its state of evolution (Expansion-Implosion).

We may also assume what the Time in the D-space inter-verses of the Cosmic Landscape (space between different bubble-pocket verses), should be also proportional to the entropy, but should also depend on other known variables (gravity, speed of light,…), and possibly other variables presently unknown.

May we consider Time as an Emergent concept ?. If Time depends on Entropy, we could ask if we could consider entropy on the Quantum-Planck scale spectra (?). Entropy is a measurement of the disorder of the universe (particle-wave, mass-energy). Is there sense for entropy concept below 10 e-20 m scale ? Is there Time below this 10 e-20 m scale ?

In quantum gravity, may be there is no notion of absolute time. Like all other quantities in the QG theory, the notion of time has to be introduced "relationally", by studying the behavior of some physical quantities in terms of others chosen as a “clock”. 

QUANTUM TIME

While time is a continuous quantity in both standard quantum mechanics and general relativity, many physicists have suggested that a discrete model of time might work better, especially when considering the combination of quantum mechanics with general relativity to produce a theory of quantum gravity.
A chronon is a proposed quantum of time, that is, a discrete and indivisible "unit" of time as part of a hypothesis that proposes that time is not continuous.

Current theoretical physics suggests the flow of time is just an illusion.

  • “The Time concept appears when processes of change or motion occur.”
  • “In a stationary Universe (with no changes or not movements), the time will not exist.”
  • “It is not true that we move through space, we move through space-time. The space and time are inextricably linked.”
  • “The nature of Time in Quantum Gravitation is not properly explained”. 
  • “Time arrow cannot be attributed to the entropy at microscopic scales”.
 (M. Boljoland, “Before the Big-bang”, 2009)

5.  EVENT HORIZONS

In general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer.

It is clear what it means the "event horizon" of the Black Holes (the external surface of the black hole) and its "Hawking radiation”.

S. Hawking proposed that all the 3D info (entropy) contained inside a Black Hole, can be described also on the 2D boundary of the Black Hole, and it is equal to the Planck area units (qubits) of this surface:

In a similar way, we could also consider other types of "Event Horizons" and, possibly, its own “ X-radiation”:




FIG.11: Universe Event Horizons

  • Cosmic Horizon (approx. 10 e +30 m): The event horizon (boundary) between Our “pocket” Universe (Our 4D-Brane) and beyond  of Our Universe (to the Bulk or Cosmic Landscape). If this boundary is further than the Observable Universe boundary, then we will not be able to see or detect any signal from it.
  • Observable Cosmic Horizon (approx. 10 e+27 m): The event horizon (boundary) of the Observable Universe (That part of our universe that, due to the limitation of the speed of light, we are able to detect or observe). Possible cosmic microwave background (CMB) could be also considered radiations of this horizon (radiations coming from beyond Our Observable Universe boundary).
  • Planck Horizon (< 10 e - 35 m): The event horizon (boundary or edge) where might end (if there is an boundary or edge) Our Universe spectra on the lower scales, or where it make the change (if boundary) between Our Universe spectra (Our 4D-Brane) with the Sub-Planck Landscape (possibly within 6D space Calabi-Yau forms-branes-universes). Quantum Fluctuations and Interaction Fields could be considered as effects (appearing) from this horizon (from the Planck Volume or from the 6D Calabi-Yau shapes).

The first (Our Cosmic) and third (Planck) horizons, could be considered as branes boundaries of Our Universe Brane (or Our Universe Scale Spectra) and other neighbors branes (Up: the Bulk, or Down: the Calabi-Yau).

The second (Observable Cosmic) horizon can be considered only as a physical limitation (due to the speed of light limitation).

"The CMB is a cosmic background radiation that is fundamental to observational cosmology because it is the oldest light in the universe, dating to the epoch of recombination.” 

“The CMB is a snapshot of the oldest light in our Universe, imprinted on the sky when the Universe was just 380,000 years old. It shows tiny temperature fluctuations that correspond to regions of slightly different densities, representing the seeds of all future structure: the stars and galaxies of today.”

Then, CMB is a radiation coming from the farthest we can observe in Our Universe (the oldest light in Our Universe). Then, CMB is a radiation coming from the OBSERVABLE UNIVERSE BOUNDARY. Although CMB is not a Unruh radiation, as it is the Black Hole "Hawking radiation”.

Following I relate a very short and relevant text (Implicate Order, The Science Forum, April.2015) that resume very clear the main aim of the present chapter:
“I am suspicious regarding that territory immediately beyond our Hubble volume [“Observable Universe”], but while it is natural to conclude that we can simply project further than this boundary, something tells me that part of the answer to our quest lies at or immediately beyond that boundary itself and it may just be forever beyond our empirical reach or alternatively considerably shake our current view on BB cosmology. But that is just a hunch of mine based on the principle that the boundary that exists between the quantum domain and the classical domain (the planck scale) might be translated macroscopically immediately at or beyond our classical macroscopic limit. The same principle applies at the event horizon of a black hole where a macroscopic object such as a black hole exhibits quantum properties at its boundary, and hence my interest in boundaries and also in exotic theories such as the holographic universe or the background independent Causal Dynamic Triangulation, which certainly would be a revolution to our thinking if any of these approaches gain momentum as a serious Quantum Gravity candidate. But following a resolution to the QG debate, what next, as a further onion skin will be peeled away.”

HOLOGRAM THEORY

“The entropy of a black hole is proportional to its surface area. Thus the amount of information required to specify the microstate of the black hole is proportional to its surface area. Black holes have been shown, theoretically, to be maximally entropic and by putting together the surface area and the entropy set by the Beckstein bound you get the result that each bit could be regarded as encoded in a Planck area. Qubits require an entangled state and it is not sure proven that entanglement survives at this boundary”

In a larger sense, the theory suggests that the entire universe can be seen as a two-dimensional information on the cosmological horizon, such that the three dimensions we observe are an effective description only at macroscopic scales and at low energies. Cosmological holography has not been made mathematically precise, partly because the particle horizon has a non-zero area and grows with time.

According to John Maldacena (See article Scientific American, January-2006):

"HOLOGRAM theory states that a quantum theory of gravity within a space-time anti-De Sitter is equivalent to a theory of ordinary particles at the border.”

“Unfortunately not yet known any theory of boundary that results in an interior theory that includes just the four forces we observe in our universe […] Since our universe hasn´t a defined boundary (such as having a space of anti-De Sitter and as precise holographic theory), we are not sure how a holographic theory for Our Universe would be defined due that there is no appropriate place to put the hologram.”

One option could be to propose as a boundary of Our Universe for the HOLOGRAM theory, could be that it will not be situated on higher scales (Cosmic Horizon), but it could be on the smaller scales (Planck Horizon) where we could also have a 2D space boundary. 



FIG 15: Hologram theory 

Thus the border or limit Our Universe would be on the Down (in the lower limits) of Our Universe, and not on the top which does not seem to have an established 2D space border. Hologram principle would work DOWN to UP instead of UP to DOWN !

Leonard Susskind, after reading the first Article (Oct.2012) sugested: ”…as you proceed down the scales to the smallest things, you place strings last. That's probably not right. The string scale if it exists must be bigger than the Planck scale, although not necessarily by a lot. At the Planck scale itself we should probably add the qubit. That's the unit of information at the horizon of a black hole.”

A qubit is a quantum bit , the counterpart in quantum computing to the binary digit or bit of classical computing. Just as a bit is the basic unit of information in a classical computer, a qubit is the basic unit of information in a quantum computer.

Should we compare the information on surface of a black hole (measured with qubits) with the information existing on the lower scalar levels (Planck scale), and considering both as a 2D texture ?.

This 2D “virtual” surface at Planck scale could be the boundary to be considered for the HOLOGRAM theory: the Planck Horizon (Boundary).


6.  FRACTAL & SCALE RELATIVITY THEORIES

Physical models have evolved over the history (Aristotle, Newton, Einstein…) covering every time a wider scale spectrum of the Universe.

Currently, various theories (Superstring, Quantum Gravity,...) try to expand this spectrum scale up their own limits (above and below) of our universe. They are known as TOE, and, as the name suggests, they are trying to cover (parametrize) all the physics events of Our Known Universe. 

Both, QM (all things are interconnected) and Relativity (all things are relational), seems to be telling us the same thing albeit from different perspectives which gives hope for a unification.


Fractal Theory could be another model that could help us to parametrize a wider spectrum of the Whole Universe.


A fractal is a geometric figure that is divided into smaller versions of “itself”. Every fractal has an initiator and generator. The initiator represents the first step of the fractal and the generator produces each phase or step of the fractal.
To describe Our Universe we have to be able to extrapolate and to create “new smaller versions of “other models” but linked by some kind of underlaying patterns”.
To model Our 3D Universe (and the nD Whole Universe), we have to consider/use 3-nD fractals.


SCALE DIMENSION vs FRACTAL DIMENSION:

If we consider the dimensions as the degrees of freedom of a system (e.g. the 4 dimensions of Our Universe: Space Dimensions: XYZ and Temporal Dimension: T). But , sometimes, we also should consider the Scale Dimension: S (as another dimension ?) to locate an event within Our Universe (e.i.: one electron could be in the same Space-Time Dimension than a planet, but if you don´t know the exact Scale Dimension we are considering, possibly, you will not be able to see or find one of them).

Ii is clear that this distance/size Scale Dimension will be dependent of the other 3 space dimensions (X-Y-Z), and possibly we only must consider the “precision/accuracy” of the X-Y-Z values (e.g. it will be not the same to say X = A (in 10 e +10 m units) than X = A (in 10 e -10 m units), every one can describe the same location but at different scales (precision/accuracy): the first one the Earth scale, and second one the molecule scale. 

Scale Dimension could be related with the Fractal Dimension: the index for characterizing fractal patterns or sets by quantifying their as a ratio of the change in detail to the change in scale.


FRACTAL COSMOLOGY

Fractal Cosmology is a set of minority cosmological theories which state that the distribution of matter in the Universe, or the structure of the universe itself, is a fractal across a wide range of scales. More generally, it relates to the usage or appearance of fractals in the study of the universe and matter. A central issue in this field is the fractal dimension of the universe or of matter distribution within it, when measured at very large or very small scales.

Demostration of Fractality for large scale of the universe requires additional observations (particularly of microwaves background radiation) and complicated mathematical solutions based on the theory of relativity of Einstein, which presents great complexity. Some of their most ambitious goals, fractality of the universe could determine with unprecedented degree of accuracy, the distribution of galactic superclusters and generally all matter in the universe, including the dark.

In theoretical cosmology fractal geometry has been used as an attempt to describe the irregular nature should have spacetime at very small scale due to quantum fluctuaciones. This has been conjectured that at very small scales spacetime is not smooth and has structure of differentiable manifold but should be a kind of "quantum foam."

In this context we have tried to explain the collapse of space-time that occurs inside black holes and relate proton gravity level, beating some of the biggest pitfalls of the current cosmology. This model could make corrections to the model of Big Bang.

Finally, mathematics conjetures raised about the alleged fractal nature of quantum mechanics, getting the exotic idea of ​​sacrificing time for a mono-dimensional and two-dimensional fractal time.


A Fractal Universe? (Robert L. Oldershaw, 2002) 

“ABSTRACT: From subatomic particles to superclusters of galaxies, nature has a nested hierarchical organization. There are also suggestive hints that self-similarity, the idea of similar form on different size scales, might be a fundamental property of the cosmological hierarchy. These features are the hallmarks of fractal structure. Could nature, as a whole, be a fractal system?

POSSIBLE IMPLICATIONS OF COSMOLOGICAL SELF-SIMILARITY:

If the dark matter is composed of ultra-compact stellar scale objects with a mass spectrum that is approximated by predictions of the self-similar hypothesis, then it would appear that discrete self-similarity is a newly identified global property of nature. This would certainly change our current understanding of the cosmos. Firstly it would provide a new approach toward a more unified understanding of nature, since cosmological self-similarity implies analogous physics on all observable scales. It would also imply that the usual assumption that the universal hierarchy has cutoffs at about our current observational limits, an assumption that has always seemed suspiciously anthropocentric, should be questioned. If cosmological self-similarity is verified, then it would seem more likely that additional scales underlie the atomic scale and encompass the galactic scale. According to the new paradigm […], a new fractal geometry of space-time-matter would appear to be called for. 

If microlensing experiments verify the unique predictions mentioned above, however, we would still be faced with some important and very difficult questions. How many scales are there in all, a finite number or "worlds within worlds" without end? How strong is the degree of self-similarity between analogues? Why is nature self-similar, and why are scales separated by a factor of about 5x1017? Like past discoveries, this one too would come wrapped in enigmas. 

Some might argue that the self-similar cosmological paradigm is too fantastic to be true, that it is too speculative to deserve serious attention. But is it more fantastic or speculative than Alice In Wonderland theories like cosmic strings, shadow matter, the "many worlds" interpretation of quantum mechanics, etc. Probably not, if judged objectively, and at least the self-similar model can make definitive predictions and point to actual observational support. It is possible that nature really does involve the "worlds within worlds" structure of a fractal system. Certainly there is enough supporting evidence to warrant serious consideration of discrete cosmological self-similarity. And soon, via microlensing experiments, we will learn nature's own verdict on this hypothesis.”


SCALE RELATIVITY

Scale relativity theory is a geometrical and fractal space-time theory. The idea of a fractal space-time theory was first introduced by Garnet Ord,[and by Laurent Nottale in a paper with Jean Schneider. The proposal to combine fractal space-time theory with relativity principles was made by Laurent Nottale. The resulting scale relativity theory is an extension of the concept of relativity found in special relativity and general relativity to physical scales (time, length, energy, or momentum scales). In physics, relativity theories have shown that position, orientation, movement and acceleration cannot be defined in an absolute way, but only relative to a system of reference.

Noticing the relativity of scales, as noticing the other forms of relativity is just a first step. Scale relativity theory proposes to make the next step by translating this simple insight formally in physical theory, by introducing explicitly in coordinate systems the “state of scale”.

To describe scale transformations requires the use of fractal geometries, which are typically concerned with scale changes. Scale relativity is thus an extension of relativity theory to the concept of scale, using fractal geometries to study scale transformations.

The principle of relativity says that physical laws should be valid in all coordinate systems. This principle has been applied to states of position (the origin and orientation of axes), as well as to the states of movement of coordinate systems (speed, acceleration). Scale relativity proposes in a similar manner to define a scale relative to another one, and not in an absolute way. Only scale ratios have a physical meaning, never an absolute scale, in the same way as there exists no absolute position or velocity, but only position or velocity differences.

If Einstein showed that space-time was curved, Nottale shows that it is not only curved, but also fractal. It means that such a space depends on scale.


Scale Relativity vs DSR:

Both theories have identified the Planck length as a fundamental minimum scale. However, as Nottale comments: "the main difference between the “Doubly-Special-Relativity” approach and the Scale Relativity one is that Scale-Relativity have identified the question of defining an invariant length-scale as coming under a relativity of scales.”


Scale Relativity And Fractal Space-Time: A New Approach to Unifying Relativity and Quantum Mechanics. 2011 1st ed. World Scientific Publishing Company (Laurent Nottale, 2011).

“This book provides a comprehensive survey of the development of the theory of scale relativity and fractal space-time. […] enabling the basis of quantum mechanics on the principle of relativity […] A related concern of this book is the geometry of space-time, which is described as being fractal and non differentiable. It collects and organizes theoretical developments and applications in many fields, including physics, mathematics, astrophysics, cosmology and life sciences.”


Some other articles from the same author:


THE THEORY OF SCALE RELATIVITY (Laurent Nottale, 1991):

“Basing our discussion on the relative character of all scales in nature and on the explicit dependence of physical laws on scale in quantum physics, we apply the principle of relativity to scale transformations. This principle, in combination with its breaking above the Einstein-de Broglie wavelength and time, leads to the demonstration of the existence of a universal, absolute and impassable scale in nature, which is invariant under dilatation. This lower limit to all lengths is identified with the Planck scale, which now plays for scale the same role as is played by light velocity for motion. We get new scale transformations of a Lorentzian form and generalize the de Broglie and Heisenberg relations. As a consequence the high energy length and mass scales now decouple, energy and momentum tending to infinity when resolution tends to the Planck scale, which thus plays the role of the previous zero point.
This theory solves the problem of divergence of charge and mass (self-energy) in electrodynamics, implies that the four fundamental couplings (including gravitation) converge at the Planck energy, improves the agreement of GUT predictions with experimental results, and allows one to get precise estimates of the values of the fundamental coupling constants.”


Scale relativity and fractal space-time: theory and applications (Laurent Nottale, 2009):

“…during the last decades, the various sciences have been faced to an ever increasing number of new unsolved problems, of which many are linked to questions of scales. It therefore seemed natural, in order to deal with these problems at a fundamental and first principle level, to extend theories of relativity by including the scale in the very definition of the coordinate system, then to account for these scale transformations in a relativistic way.”


“The wave-particle duality is understood in terms of infinite families of equiprobable geodesics on a fractal space-time.” (Nottale, 1991). 


7.  CONSTANTS OF OUR UNIVERSE


Our Universe today has some fundamental constants that govern its basic principles (we would need to know how these constants have evolved from the Big Bang to the present day, and how they will evolve in the future)

("The Constants of Nature" ,John D. Barrow, 2002):

G =    Gravitational constant = 6,67.10 e -11  N.m2 / kg.s2
c =      Speed of light = 300,000 km/s
h =      Planck's constant = 6,63.10 e-34 J.s
e =      Electron charge = 1,6.10 e-19 C
Mpr = Mass proton (neutron) = 1,67.10 e-27 kg
Npr =  Number of protons in Our Universe = 10 e +80

And the former constants lead to other fundamental constants or relationships:

α =   Fine structure constant = 2πe2 / hc = 1/137
αG = Heavy structure constant = G.Mpr2 / hc = 10 exp -38
β =   Ratio between proton and electron mass = Mpr / I = 1,840

Another “constant” value to consider is:

Cosmological constant Λ = 10 e-116 J . It is the energy that produces the current expansion of the universe (it could be equivalent to the vacuum energy ?). We know that this value itself has been changing since the Big-bang.

These constants are (own) characteristic of Our Universe, and for the current time we are now since the Big-bang. We are quite sure that they can be different in other “pocket” universes of the Cosmic Landscape, and , on the other hand, we cannot be sure that they all have remained constant ever since the Big-bang.


Thus, so daily and usual constants for us as Gravitational (G) and speed of light (c) may be different in other “pocket” universes, and even they may have varied in Our Universe from the Big-bang, or they may be different for different scale spectra of Our Universe. And this can also happen with the other constants such as the number of protons (+ neutrons) of our universe, etc.


Possibly, within the Cosmic Landscape may appear new constants that we cannot foresee now.


EDDINGTON´S UNCERTAINTY CONSTANT

Even they are, possibly, outside of the scope of this article, I would like to introduce in this section a reference to some"uncertainty" values or constants of Our Universe.  Although they are not scientifically proven and accepted (and also they are not considered by mainstream), they have been considered, studied and defined by two great physical-mathematical and from different times (eras): Pythagoras and Sir Arthur Eddington (“The Crystal Sun”, Robert Temple, 2000). These values gives us an idea of a possible deviation between the theoretically expected and reality.

The Comma of Pythagoras (VI century BC), equivalent to 1.0136. This constant reveals the difference in sound that occurs at the end of seven-eighths, with that sound what occurs at the end of twelve fifths. which should theoretically be exactly the same, but in practice it is not (so the theoretical value of the Coma should be exactly = 1). 

Uncertainty Constant of Sir Arthur Eddington (proposed in his latest posthumously book "Fundamental Theory", 1953), equivalent to 9,604 x 10 e -14,. This constant measure also the discrepancy between reality and theoretically expected values (The real values measured vs theoretical values calculated). Arthur Eddington argued that deviation by the fact that the real physical coordinate frame has an standard deviation "sigma" over the pure and theoretical geometric frame. Because, in the theoretical frame its origin is a pure geometric point, while in the real frame its origin has a probability distribution "sigma" from the theoretical point.

This explanation of Arthur Eddington, reminds us to the proposed QM & string theory, in which a point/particle is replaced by a wave function (“sigma” function) or a string-brane.

This constant might show us that , possibly, our reality may not be based on a fixed and absolute physical coordinates. On the contrary, in Our Universe could be some uncertainties underlying on its own imprecise essence (Uncertain Principle, Strings-branes, particle-wave essence, wave function,…).


8.   GÖDEL THEOREME VS TOE

As we have seen in the previous chapters, ToEs (as String Theory), are just theories that try to cover a wider range of dimensional scales of the Whole Universe spectrum. But each time this spectrum is enlarged, new laws and concepts will emerge (new Landscapes). 

Some scientists (e.g. S. Hawking) believe that Gödel's incompleteness theorem implies that any attempt to construct a theory of everything is doomed to failure.
Stephen Hawking was originally believer of a theory of everything but after taking Gödel's theorem, concluded that it could not be obtained.
“Up to now, most people have implicitly assumed that there is an ultimate theory, that we will eventually discover. Indeed, I myself have suggested we might find it quite soon. However, M-theory has made me wonder if this is true. Maybe it is not possible to formulate the theory of the universe in a finite number of statements. This is very reminiscent of Gödel's theorem. This says that any finite system of axioms, is not sufficient to prove every result in mathematics.” (Stephen Hawking: Gödel and the end of physics, 2002).

Prof. Hawking admits that until he realized the implication of Gödel’s incompleteness theorem, he implicitly assumed that a ToE will be found, probably relying on what can be referred to as “scientific intuition”. According to prof. Hawking, the positivist philosophy of science is that every good physical theory is a mathematical model. And since, according to Gödel’s incompleteness theorems, there are mathematical results that cannot be proven, then so there must be physical theories that cannot be proven as well, including the ToE. Gödel’s incompleteness theorems essentially say that, as mentioned by prof. Hawking himself, math is either inconsistent or incomplete.

If we discover new scale spectra (landscapes), there also will appear (emerge) new concepts and physical laws (unexpected and difficult to predict), and we will require the development of new models and patterns to understand these new physical landscapes/spectra.

Possibly the use of Fractal Theory might be a system that allows to avoid this problem (Gödel’s incompleteness), to be able to use the Fractal Theory as a “main” system of axioms, which simply set which model (system of axioms) we ought to use to each landscape (scale range) as reference model (based on some underlying patterns).

Then we could have several systems of axions:
  • Different models systems for different scale levels (Landscapes): Landscape ToEs System.
  • A Fractal Model System that could describe when to use the different ToEs (within the different scale levels).
  • And, possibly, some Underlaying Laws System that could link the previous Systems (ToEs & Fractal).
It will be a multi system of axions !


If we consider as a sample the Game of Life, devised by the British mathematician John Horton Conway in 1970. 

It is based on a very simple and basic principles. But as larger entities are formed, also begin to appear other concepts, such as movement, shooting, bombing, reproduction, ... And these concepts can be explained by other laws that have (only a very underlaying relation) to the initial law.

But in this sample we start with some very elemental and basic initial objects (black and white squares) and rules (change black & white squares). There is not any object sand laws more elemental below them. But yes it can enlarge the objects and get higher laws.

May we imagine that it can also happen in our universe? May we believe that there will also be some basic and elementary objects (and laws), since which there will be nothing smaller? Only if this were so, then we could think on getting a TOE based on these elementary and basic objects and laws. But this does not seem to be so. At least, I do not think so…(?)


9.   CONCLUSIONS

This article, besides presenting a "new" approach (framework) of the universe (including the concept of “scale factor”, and the different “scale landscapes” that may exist), it also tried to include some related studies, reflections and opinions that are currently in the scientific field linked to this main idea or proposal (Emergent Concepts & Laws, Fractal & Scale Relativity Theories, Hologram Theory,…) and how this proposal could affect to some known concepts (Energy, Matter, Time, Vacuum,,…) and also unknown concepts (Dark Matter and Energy, Quantum Fluctuations, Uncertain Principle,…).

When we show all these concepts on the same "framework", we hope it could help to link ideas and proposals, which currently are being treated separately. And it can provide an essential link between them, offering the possibility that different scientists can bring new ideas and proposals that help to all us to better understand the whole universe and its laws.

It is remarkable the great (physical) scientific advances that have been made throughout the history of humanity, but mainly the last 100-500 years (Pythagoras, Aristotle, Newton, Maxwell, Einstein, …).

But it is also true that we are still long way from understanding the whole universe in all its amplitude and complexity. Considering that mainstream accept that known energy and mass are not more than 5% of all the forecast energy and mass of our known universe. 

Concepts as common as mass-energy, space-time and vacuum, are being challenged and redefined. There are still many important voids / gaps / inconsistencies in our knowledge of the universe. And it just makes their study so interesting and intriguing.

To date, we have been able to understand and model our spectrum scale (from 10 - 20 m to 10 +20 m), advancing during the time through the previous spectra. But from now on, it is becoming more complex to understand those spectra that are beyond.  Therefor, we will need to break with pre-established ideas and concepts, and be able to accept new schemes.

I hope that this article can spark ideas and fields of study for the next generation of scientists ("post-string" and "post-QG"): New Scale-Fractal-Emergent generations.

In the same way that to date, these breakthrough discoveries have been due to great minds (working independently in laboratories or offices), from now, it will require teamwork to address the challenges that we still have. And this implies a new way of approaching science, by applying the multidisciplinary teamwork methodologies and framework (the “synergy effect”).

DEFINITIONS:

Whole Universe: Everything that exists, although we can not see, or even imagine, and therefore we may be unable to model and parameterize.
Our (Known) Universe : Our Pocket Universe (within the Whole Universe) that was generated in Our Big-Bang and in which we exist and that we are able to understand and model.
Observable Universe: That part of our universe that (due to the limitation of the speed of light) we are able to detect or observe.
Pocket Universe: Those other universes (like Our Universe) that could exist beyond Our Universe (on the Bulk or Cosmic Landscape.
Landscape: Scalar Spectrum of the Whole  Universe that has their own emergent concepts and laws, and which has its own big picture and rules.
Cosmic Horizon: The event horizon (boundary) between Our Universe (Our 4D-Brane) and beyond  of Our Universe (to the Bulk or Cosmic Landscape). (> 10 e +30 m)
Observable Horizon: The event horizon (boundary) of the Observable Universe (that part of Our Universe that, due to the limitation of the speed of light, we are able to detect or observe). (Approx. 10 e+27 m)
Planck Horizon: The event horizon (boundary or edge) where (1. If edge) end Our Universe spectra on the lower scales, or (2.- If boundary) where it make the change between Our Universe spectra (Our 4D-Brane) with the Sub-Planck Landscape (possibly within 6D space Calabi-Yau forms-branes-universes). (< 10 e - 35 m)
Brane Horizon: The event horizon (boundary or edge) between two or several branes, possibly of different (space) dimensions (3D-2D, 3D-4D, 3D, 6D,…). Also could be named Dimensional Horizons.


BACKGROUND:

Article: “The ¨Matryoshka-verse¨: The scalar/scale relativity of the Universe” (David Piñana, October 2012). http://matryoshka-dimension.blogspot.com.es


BIBLIOGRAPHY:

David Piñana:
• “The Fractal Rainbow (Beyond Our Universe)”, 2015. 
Brian Greene:  
• “The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos, 2011. 
• “The Fabric of the Cosmos: Space, Time, and the Texture of Reality”, 2005.
• “The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory, 1999. 
Leonard Susskind: 
  • “The Cosmic Landscape”, 2005
John D. Barrow: 
  • “The Constants of Nature", 2002
Lee Smolin: 
  • “The Trouble With Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next”, 2006
Stephen Hawking: 
Lisa Randall: 
Robert B. Laughlin: 
  • “Different Universe: Reinventing Physics from the Bottom Down”, 2006
Robert Temple: 
  • “The Crystal Sun”, 2000
Sir Arthur Eddington: 
  • ”Fundamental Theory", 1953
Laurent Nottale:  
  • “Scale Relativity And Fractal Space-Time: A New Approach to Unifying Relativity and Quantum Mechanics”. 2011
  • “Fractal space-time and microphysics:towards a theory of scale relativity. 1992
Roger Penrose:  
  • “Cycles of Time”. 2011
Martin Bojowald:
  • “Zurück vor den Urknall”. 2010 (“Before the Big-Bang”)
Amanda Gefter: 
  • "Trespassing on Einstein's Lawn". 2015
Max Tegmark: 
  • “Our Mathematic Universe". 2014


ARTICLES:

John Maldacena: “The Illusion of Gravity” (Scientific American, January-2006): http://www.scientificamerican.com/article/the-illusion-of-gravity/ 

FrankWilczek: “What´space” (2009). 
http://web.mit.edu/physics/news/physicsatmit/physicsatmit_09_whatisspace_wilczek.pdf 

Stephen Hawking: “Gödel and the end of physics”, 2002. http://www.hawking.org.uk/godel-and-the-end-of-physics.html

Nathan Seiberg: “Emergent Spacetime”, 2006
 (http://arxiv.org/find/hep-th/1/au:+Seiberg_N/0/1/0/all/0/1 )

Fu Yuhua, Fu Anjie, Zhao Ge: “Fifteen Kinds of Waves Caused by Four Fundamental Forces” (Beijing Relativity Theory Research Federation)

Vincent J. Martinez & Bernard J.T. Jones: “Why the universe is not a (simple) fractal  (but yes a multi-fractal)”. (1990): http://adsabs.harvard.edu/abs/1990MNRAS.242..517M

Robert L. Oldershaw,  “A Fractal Universe?” 

Laurent Nottale:  
  • “Scale relativity and fractal space-time: theory and applications”. 2009
  • “The theory of scale relativity”. 1991

“Violation of Heisenberg’s Measurement-Disturbance Relationship by Weak Measurements” (Lee A. Rozema, Ardavan Darabi, Dylan H. Mahler, Alex Hayat, Yasaman Soudagar, and Aephraim M. Steinberg Phys. Rev. Lett. 109, 100404 – Published 6 September 2012; Erratum Phys. Rev. Lett. 109, 189902 (2012). http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.189902

FQXi ESSAY CONTEST: 2006 FQXi The Nature of Time 
The Nature of Time by Julian Barbour:
Does Time Exist in Quantum Gravity? by Claus Kiefer:

I appreciate the great help that I got by using Wikipedia to obtain information on the topics covered in this book (and previous articles), as well as, by the reproduction of certain texts and figures (mainly for general definitions and historical info).


Subscribe to: Posts (Atom)