Flowing with a Frozen River by Cristinel Stoica

Dear Dr. Narendra Nath,

Thank you for following my posts, and for your encouragement. I spent many days trying to grasp what is time, and space. This contest, hosting so many interesting views about time and Universe, provided me the opportunity to continue learning. You modestly say "Most of the material of your last few postings is above my comprehension.". Although you don't point to this, my belief is that I have presented some of the topics very succinctly, and perhaps I did not explain them very well. Moreover, my knowledge is limited to explaining the small part I understand from what us, as human beings, managed to explain about the mystery of time. Compared to the marvelous world in which we live, maybe our knowledge is very little, therefore I can say, with you, that "I have limited knowledge, compared to the total knowledge about the Universe.". And I also agree with you that, even the small amount of knowledge we, humans, have, was gained only by having, at least for some moments in our enquiries, "a quiet, egoless and bias free mind". Perhaps this is the condition for learning, and for capturing even the simplest pattern in the way our world works. This is why the main purpose of my series of posts is not to solve the time's mysteries, but rather to understand where may be the limitations of our understanding. As a guess, I believe that the main mysteries of time are tightly related to the mysteries of the human mind, which, perhaps, is even less understood.

I am happy for yours and Dr. Crowell's beautiful flow of thoughts, and I wait impatiently the continuation.

Best wishes,

Cristi

No need at all to wait for my comments at least. i believe that science is different from an indivdual's life. It goes on where others have left. I have full confidence that you are going on the right path, to build the ideas, evolve the concepts, implement the goemetry/maths required and reach intermediate conclusions. Check them with experiment and then proceed again to rebuild the cycle with fresh amendments/new concepts, etc. I very much like your attempt to diffuse the quantum discontinuities. The human mind helps a lot when it is not distracted with other than we intend doing at the moment. Here and Now of Kyle Miller is a good philosophy to persue in . scientific efforts. Similarly i like the paradigm concept of arrangements by Brian Beverly.Sometimes we quietly learn from one another and then even forget the source of knowledge/information/idea and start claiming te same as our own. ( i just had a few peanuts )and that reminds me that i may well be a peanut really! Many of posts on different essays seem repetitive to me, as i feel some of the matter is worth repeating fro one's own sake! To conclude my post, Crisyi proceed full speed with your own self-conscience and have maximum overlap with the cosmic consciousness and don't think science dominates Nature, it simply attempts to understand the Nature as one perceives.

THE COUNTERINTUITIVE TIME - PART 4

TIME AND GENERAL RELATIVITY

After the Special Relativity, Einstein tried to express various physical laws in this formalism. Basically, their mathematical form is required to be invariant at Lorentz transformations. The main difficulty he encountered was to express Newton's gravitation field in this way. After many years of research, Einstein obtained the movement of bodies under the effect of gravity as simply an inertial movement in a curved spacetime. The inertia and the gravity become unified. The spacetime itself is curved by the masses, and the universal attraction was just an effect of this curvature. General Relativity was born. The experimental consequences eventually confirmed the theory, which become widely accepted. Among its surprising features is that that the time flow changes in the presence of massive bodies.

The main equation of General Relativity, Einstein's equation, relates the curvature to the distribution of energy. One very important difference between this equation, and the previously known equations in mathematical Physics, is the following: finding the solution, means also finding the background (meaning the spacetime itself). In the Newtonian and special relativistic cases, the spacetime was fixed, but in General Relativity, it is part of the solution itself. Perhaps, this is the most striking difference.

The main counterintuitive aspect of the curved spacetime is caused by our tendency to consider it as a subspace of a space with more dimensions. Many persons, when learn for the first time that the spacetime is curved, tend to interpret this as being curved in a fifth dimension. As a simpler but historic example, when we think at a curved surface, we tend to consider it a subspace of the Euclidean space. Gauss realized that the intrinsic geometry of every surface can be expressed independently on the Euclidean space in which this is embedded. The main ingredient is the metric tensor, which provides a point-dependant measure of the lengths of the curves embedded in the surface. Riemann generalized the surfaces to curved spaces with any number of dimensions. Their work helps understanding that the curved spaces in Riemannian geometry do not rely on a Euclidean space in which they may be embedded. Einstein found the four-dimensional Riemannian geometry as the ideal tool for General Relativity, provided that we replace the Euclidean metric tensor with the Lorentz metric.

The Einstein's equation may have solutions that contain closed timelike curves. Spacetime may be curved in such a manner, that the future of an event becomes also its past. This looping time highly contradicts our intuition. Yet, unlike the other counterintuitive aspects of time, this one may not even exist, as Hawking's Chronology Protection Conjecture states.

Another hard to grasp aspect of time is the beginning. Our experience teaches us to consider the time as being linear, infinitely continued in past and future. Why do we have this intuition, considering that our lives are finite? Perhaps because the daily events succeed linearly, at our scales, and because the History of our countries, and of our planet, and solar systems, appear to be linear. But when we hear about the Big Bang, two questions we may find natural is "what was before the Big Bang?", and "when happened the Big Bang?". We find difficult to accept that even the time may have a beginning.

Other difficult aspects of time in General Relativity are related to special situations, like the time in the presence of a Black Hole, in a Worm Hole, time traveling using Worm Holes, Hawking's imaginary time, the time near/at the initial singularity. I will not detail these problems.

To be continued...

Cristi

Dear Cristi , i enjoyed very much going through your last post. i could comprehend it almost entirely. i have yet to crystalize some of the ideas further. The flow also needs a rest for the river of the human mind. The time continues even during such a rest. Its restlessness is what the humans should not imitate. However, its value is what we should constantly remember, it is the most precious commodity for the human being, having a very finite life. i.e. time at our disposal. i admire some greatmen who achiebed a lot even during short span of their lives. On the other hand we know of people living lives but their contribution to the society amount to very little. We live in such a world and need to have the patience and tolerance for all such variations. Also, we need to have compassion in plenty for people who are deprived, sick or otherwise living life in a miserable way while others have plenty of goodies and still desire to accumulate more and more. We forget that all our possessions don't go with us when we die, only our good deeds remain to the extent of the degree of their genuine goodness. Sorry, for all this philosophy, as i feel like recollecting in order to improve our actions yet to be undertaken!

Dear Dr. Narendra Nath,

Thank you very much for continue going through my posts, and for the feedback. I really like your comments, they are full of nice thoughts.

Best regards,

Cristi

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I decided to post this series also on my blog Unitary Flow: 1. Time and Determinism, 2. The Geometric Time, 3. The Time's Arrows, 4. Time and General Relativity. My previous posts on the blog were related to illusions: The Illusion of Center and The Spinning Dancer's Mistery.

I would like to make time to detail and clarify some parts of the posts, based on the feedback I receive.

Best wishes,

Cristi

Dear Cristi,

i find that there are two aspects in your post that deserve study in detail. One concerns the curvature of space versus the evolution of the Universe. One may well start with a degree of curvature and then work out both ways towards increasing/decreasing curvatures to meet the evolutionary parameters. The other point is concerned wit the theories of the Universe. Do we wish to put all our thoughts entirely on the Big Bang? The other alternatives were (1) collision between expanding and contracting 'existing' universes (2) matter/ anti matter universes colliding. May be there are others too! Until our cosmic experiments are conducted far into space beyond Earth, i don't feel putting all our eggs in one basket. Even there can be a possibility of more than one mechanism operating in the existing of our currently observed universe! WMAP needs to be extended into space for us to learn more about the early universe? i am not much in favor of LBC type machines to let us know the secrets of the ulyimate blocks of matter. Everything worth knowing already exists in the universe itself.

Singularity of the birth is more serious with the Big bang than with the other two alternatives mentioned.What actually happened at the beginning is yet to be understood in depth!

Dear Dr. Narendra Nath,

I agree with you that I gave very little attention to the origin of the Universe. I referred to the simplest hypothesis we may have when we run backwards the observations about the expansion of the Universe. Since this seemed to reveal that all the matter expands from a common small region, at high speeds and energies, it was called Big Bang. Of course, it is hard to be sure how the things really happened, and the alternative explanations you mention for the initial explosion, based on high energy collisions between universes, are equally possible. In fact, a finite age of the Universe is not the only possibility.

The singularity seems to result from the theorems due to Hawking and Penrose. But these theorems are based on energy conditions, which are in general violated by the Casimir effect (who respect only the averaged version). Another argument for the initial singularity may come from the Strong Causality Principle, as in my essay. But who knows what really happened then?

Thank you for your interesting completions.

Cristi

Continue unabatted along the lines of your deepest flow of 'innermost ' thoughts - it is not like a frozen river but a flowing one. However, one does require pausing frozennes. That is what i mean by the quiet moments in our thoght processes. These are most valuable as the sense of Time goes away in such moments.

THE COUNTERINTUITIVE TIME - PART 5

QUANTUM TIME

Nonrelativistic Quantum Mechanics describes a system by a vector, named state vector, from a complex Hilbert space (a special type of complex vector space, endowed with a special type of scalar product). To the classical quantities, we associate selfadjoint operators on the Hilbert space. The space differs from the time, because there are position operators, while the time is only a parameter.

Schrödinger proposed an equation, describing the evolution of the state of a system. Schrödinger's equation is of PDE type, and it is deterministic, linear, even unitary (it preserves the scalar product). What we can observe or measure is an operator, representing the observable we want to measure. What we can get as outcome, is that the state vector of the system is one of the observable's eigenvectors (special vectors associated to each operator). This means that we can never know what the system's state is, without disturbing it, because there are few chances that the system is already in an eigenstate of the observable.

In the standard interpretation, the system jumps into one of the eigenstates of the observable. We cannot know before in which, but we can know the probability for each possible outcome, due to Born's rule. This introduces the indeterminism at the very fundamental level of reality. The time gains a strange feature, because it appears that, at any moment, a system can jump in a state without an apparent cause. The Classical Mechanics paradigm identifying the causality with the deterministic evolution lasted for centuries. QM introduced the possibility that a system jump out of the blue, and opened a totally different perspective. To resolve some problems of QM, Hugh Everett III proposed an interpretation of QM which states that each possible jump takes in fact place, but the world splits in many worlds, each of them containing one of the possible jumps. In this interpretation, time itself looks like it is branching, or forking, although the observers cannot check the existence of the other alternative histories. Despites the fact that for each observer, "prisoner" of one of these worlds, the wavefunction collapse and other strange quantum phenomena remain unexplained as before, this interpretation offers a intuitive and unitary view of what happens.

Some of the founders of QM, Einstein, de Broglie, Schrödinger, felt that accepting the indeterminism means to give up the search for a better explanation. Nowadays, when the indeterministic view in QM is well established, they are sometimes presented like conservators, with little understanding of quantum phenomena. This is unfair, because not only they co-initiated the quantum revolution, together with Bohr, Born and Heisenberg, but they also expressed the problems which this new born theory encountered, this leading to a refinement of the theory and its interpretations. Schrödinger explained the idea of entanglement, which springs from the very fundamental principles of Quantum Mechanics. Einstein, Podolsky, and Rosen, proposed an experiment which showed a paradoxical behavior of quantum mechanics, which is in fact the entanglement between two particles that previously interacted. This brings a weird aspect of time: they interacted in the past, and now, by measuring one of them, we can limit the possible outcomes of a measurement performed to the other one. It appears that the wavefunction has a nonlocal character over space and time.

One strange quantum effect is visible by the "delayed choice experiments", made popular by Wheeler. Wheeler provides the example of a photon emitted by a very distant star. He considers the case when between us and that star there is a galaxy, which bend the light ray, according to General Relativity. According to QM, among the possible experiments we can make with the incoming photon, there are two mutually exclusive. First, we can observe whether it passes through the left, or through the right of that galaxy - the "which way" measurement. The second possibility is to put the two possible ways to interfere one another, like the photon was traveled "both ways". The problem is that we can make our choice now, long time after the photon was emitted by the distant star, and long time after it was bent by that galaxy. We can choose now what kind of behavior had the photon thousands of years ago. This is really something that bends our intuition on time very much. We tend to believe that the past determines, or at least influences the future, but future influencing the past?

It is usually believed that the wavefunction, when measured, suffers a collapse. The corresponding state vector becomes suddenly projected on one of the observable's eigenstates. This is a little strange, because it entails a discontinuity in evolution, which we never observed. This discontinuity makes more difficult the preservation of conserved quantities, because usually the conservation laws are effects of the unitary evolution, but a discontinuous jump may break them down. Yet, we haven't observed such breaking of the conservation laws, nor we had observed other direct evidence of the jump, except our knowledge that we prepared the system to be in one state, and we detect it in another state. In the Smooth Quantum Mechanics eprint, I show that we can avoid the discontinuity of the wavefunction collapse. I use the entanglement between the observed system, and the measurement device that performed the previous measurement (the preparation device), and the possibility of choosing with a delay the initial conditions. What appears to be a jump, is described in a continuous, even smooth way (which is even unitary at a higher level). The past interaction with the preparation device happens in such a way, that it anticipates the outcome of the measurement. This interaction takes place during a finite time, and changes smoothly the state, such that, when it is measured, to be an eigenstate of the observable. I use a mechanism similar to the delayed choice experiment, but which, because of the smoothness, extends indefinitely in the past.

Because the smooth QM provides a smooth description of what was believed to be a discontinuous collapse, it appears that Einstein, de Broglie, and Schrödinger weren't that wrong. The determinism was also brought back by Bohm, by using nonlocal hidden variables. In the smooth QM, the hidden variables are replaced naturally by the yet to be determined initial conditions. The nonlocality remains in all versions, but the determinism becomes possible just by unitary evolution (Schrödinger's equation being replaced with the von Neumann's, because we deal with entangled states). So, we can say that both sides in the Einstein-Bohr debate were simultaneously right, at an unexpected degree.

If the standard QM allows the free-will, so does the smooth version, because the freedom of choosing the observable is exactly the same. The smooth version is deterministic, but the initial conditions are not determined yet completely, and each new experiment adds new information about them. This is why they can be named "delayed initial conditions".

To be continued...

Cristi

Cristi, i like your attempt at working out 'smooth QM' that becomes deterministic , but the initial conditions are yet complete and build with additional nw experiments. I wonder what will happen to the the concept of duality, under 'delayed initial conditions'. Unitarity seems possible only if we reach the final truth. Otherwise, duality continues to dodge the the micro-world picture.

Dear Dr. Narendra Nath,

Thank you for your interesting question. If I understand well, you refer to the duality between waves and point-like-particles.

THE SMOOTH PARTICLE

In Smooth Quantum Mechanics, there are only (entangled) waves.

In standard QM, the particle behavior is manifest when the observable is a position operator acting on the Hilbert space. In this case, the system is found in an eigenstate of the position operator, which is a Dirac distribution (a generalized function which is zero everywhere, except in one point, where is infinite, such that its integral is 1). The wave and particles are, in standard QM, all vectors in the Hilbert space, being therefore wave functions or distributions. When expressed as wavefunction (in a basis of positions), the "pure waves" are eigenstates of momenta, and the "pure Dirac distributions" are eigenstates of positions - these are extreme situations, in which infinities occur.

One interpretation of the waves in QM is that they underlie probabilities of finding the particles at a given point in space. Of course, this is true, grace to the Born rule, but this does not necessarily mean that the point particles are the fundamental ones, and the wave represents only probabilities. Yet, many like to think at particles as being fundamentally point-like, therefore the waves need to be interpreted as underlying probabilities.

In Smooth QM, it is considered that the only real physical states of the system are smooth: it is employed a space of smooth wavefunctions of finite norm. By completing the space, we obtain a rigged Hilbert space, which contains state vectors that are abstract, being distributions or having infinite norm. By observing the position, we get only a smooth wave concentrated around that position, but not a Dirac distribution. The position is never determined to be in a point, but in an open subset of the space. I think that the two extremes: eigenstates of pure momenta and pure positions, are non-physical abstractions, because they bring in infinities, but they are useful to express and explain the wavefunction duality. In Smooth QM, by not allowing the distributions, by eliminating the infinities, the unity between the two complementary aspects is more manifest and more physical. All particles are waves, in various shapes, depending on the observable. Of course, the Hilbert space is very useful, and it is easy to solve the equations in this space, and many operations become simpler. But in Smooth QM it is considered abstract. The wave is physical, not a probability wave.

Therefore, we return to the old idea of particles as wave packets. One main problem of this view was the dispersion of the wave packet. In Smooth QM, the laws are the same, so the dispersion is not eliminated, but the mechanism is such that the dispersion is no longer a problem. A measurement of position, finding the wave-like particle localized very well, will imply dispersion both in the future, and in the past. The waves converge, the wave packet is "con-persed" until the small sized packet is obtained and determined by measurement, and then it disperses again. The "delayed initial conditions" mechanism allows this.

The probabilistic behavior occurs only when we measure an observable which does not contain the observed state among its eigenstates. In this case, the Born rule expresses the probabilistic character, but the probability in Smooth QM resides only in the undetermined initial conditions. Here "determined" has two meanings, active and passive: to cause, and to measure. The probabilistic behavior occurs when a collapse occurs, but in this approach the collapse is smooth and deterministic, and the probabilities reside in the initial conditions. Even the Heisenberg relations, which are often thought as representing irreducible probabilities, are not necessarily such. They can be obtained from Fourier analysis, and apply for deterministic waves. The probabilistic character occurs because of measurements, which entails the (smooth) collapse, which brings the probabilities of the unknown initial conditions.

Although I said that the waves are physical, and real, we should not forget that they are entangled. For a particle, the wave can be a field depending on space and position, but for more particles, we need to consider the tensor products, therefore the entanglement.

Best regards,

Cristi

Thanks, Cristi. i am able to ollow the specific distinction of the 'smooth' QM against the conventional. The probabiity character appears in measurement only, o/c unknown initial conditions. Thus, in reality the order exists but it remains hidden as the measurement is made. The reason is that the system gets disturbed as soon as the measurement is attempted. It helps me understand better the quote from Patanjali Yogaashtra that says " The cognizer, the process of cognition and the object being recognized all need to merge if the reality is to be seen". That is not possible in a scientific measurement, but the same is realizable through an Experience in the State of yogic Meditation that an individual observes!

Just like adding a sentence here; life and time are entwined in a way that requires a fuller understanding. Creation and life are also the same. Even an inanimated object may have life at very low level of consciousness, to which we are currently insensitive!

Dear Dr. Narendra Nath,

Thank you for your last two comments. From my viewpoint, the problems you raise, regarding life and consciousness, are very difficult. I am willing to understand them better, but I don’t know what to say about them. Maybe unanimated objects, for example crystals, can grow, or can exhibit interesting properties that can be associated with life. Maybe computers can, at least in principle, exhibit properties that can be associated with consciousness. But perhaps all these signs of life and consciousness depend upon our definitions. The occidental thinking and modern science are based on definitions of life that seem to be limited to the object of Biology (which seems fair enough for our present knowledge). On the other hand, there are modern scientists who define consciousness in terms of behavior, which can in principle be simulated by algorithms. I am not able to sustain a scientific argument in these situations, since I don’t understand what life and consciousness are, and I don’t know a good definition of them.

Cristi

Nice to see your response. Science and Humanity ( Spirituality)are apparently diverse fields. However, as we are humans first and scientist later, we can see/ experience interfaces between the two, provided we believe in the totality of human knowledge and not separate these apparently different fields of activity in our own mind. i posted on my essay, a MSS entitled ' Sceince Interface with Spirituality '. That was the beginning of such an interconnection, so late in my own life, at the age of 72 yrs, about 5 years back. It is that work that led me to postulate the 'Inconstancy of the Physical Constants... ', another MSS i have attached as post at the start of my FQXI Essay postings. These two then led me to prepare my essay " Mysteries of the Universe - a perspective'. All through i maintained the sanctity of my active career as a Low Energy Nuclear Physicist ( Experimental ).

i attribute the change in my mindset to the Yoga and Meditation activity i have been practicing on the personal side, to have contributed towards it. i don't see that it has affected my scientific activities adversely. In fact, the same got sharpened, as i could convert my later experiences through visit to Industries into Patents only because of my R & D experience in Physics. Hope this may help you understand my observations better!

Dear Dr. Narendra Nath,

I agree with you that mind and soul need food and exercise, like the body does. Exercising the mind by logical thinking and by meditation may be very helpful to scientific research. Nourishing our spirit with music and poetry, with play and love, are also indispensable to a harmonious and healthy mind, able to make scientific discoveries. It is very unfair the stereotype of the scientist who is totally uninterested by aspects of existence others than his own research. Therefore, I totally agree with your view that Science is not an island. Moreover, there is a scientific method only for invalidating theories, by finding logical mistakes, or by experimentally falsifying their predictions. There is no scientific method for creating the hypotheses on which theories are based. Any other domain of human activity, including artistic, spiritual, and philosophical, can provide sources of inspiration for scientific hypotheses. The interconnection between Science and other areas are very tight. The reciprocal is valid, since Science influences Technology, Industry, Business, Media, Arts, Literature, etc.

Although Science can accept input for its hypotheses from diverse fields, it is very severe in accepting these hypotheses in its pantheon. The main way Science discriminates what accepts and what not, is by requiring objective means for testing, or better falsifying, the hypothesis. If a hypothesis cannot provide an objective footprint, it remains outside. This is the "viveka" applied by Science. Without this, it would be no difference between Science and other areas. I do not say that Science is better, nor do I say that what remains outside is valueless. There is no evidence that only things that can be made objective have real existence, while the others don't have. This is why the scientist remains reserved in talking about things outside the area of Science. The scientist may have personal opinions, and sometimes she chooses to express them, sometimes not. She may want to express them only when she can provide them an objective footprint. This doesn't mean that the scientist rejects what is outside the object of Science. She can embrace equally various areas, without being any contradiction.

I consider that there is no adversity between Science and other areas. Of course, there are areas based on contradictory things, or making prediction which contradict reality. These are rejected by Science. So, Science divides the hypotheses and theories in three main parts:

1. the ones accepted, because they provided an objective footprint, logically consistent, which has been corroborated by experiment,

2. the ones rejected, because they provided an objective footprint which has been invalidated by experience or by logical analysis,

3. the ones which did not provide any objective footprint, and they are not rejected, nor accepted. People, including scientists, may adhere to such hypotheses at will. They include many philosophies, religious beliefs, pseudoscientific theories. It is nothing wrong with them, they may even be true. And some of them may even be true for some, in a personal way, which cannot be presented objectively to the others. They are not Science, but some of them are tomorrow's Science, while some may become tomorrow's rejected hypotheses. I think that this third class is a very large and deep reservoir for many ideas, at least with social impact, but also it may be the "primordial soup" from which valuable scientific ideas of tomorrow may emerge.

Best regards,

Cristi

Dear Crist,

your response comes from the spontaneity of your thoughts and i attach importance to such thinking. If are spontaneous we are less likely to be associated with cunningness, lies that hurt others, manipulation as we just didn't have time to do so. Please keep spontaneity, one may make a mistake occasionally as we are human and liable for it. then, we can equally well apologize spontaneously. That kind of evenness is what one needs to live a meaningful life. Many a times i feel we give so amny references in our scientific papers. Why, are we sure that those particular scientists have done that job entirely on their own or have borrowed a quite a bit from others they don't wish to acknowledge! It is all concerned with ethics and to me scientific values need to be as ethical as our behaviour as a person/human being.

About the inanimate objects ( supposedly lifeless in science) has been considered in depth by ancient Indian saints/philosophers. It is they who believe that all material objects have consciousness levels in varying degrees. The inanimate have such low levels that we living beings can not sense or perceive the same. In fact, awareness isn just cinsciousness that is confined to normal body senses. But human beings are capable of building much much higher levels of consciousness that can even match that of the 'Creator of The Universe'> That is the meaning of the phrase often used ' God created Humans in his own image!'. It is here thatb the technique of yoga cum meditation as evolved by Saint Patanjali. You have quoted the word ' Vivek'. Literally, it means 'discriminatory quality'. You can easily see from human behaviourial analysis taht the degree of 'vivekness' can vary hugely.That is where the trick lies, as science can only improve the knowledge of 'relative truths'. The absolute truth is in fact so abstract that words are inadequate to express the realization of It. Thus both scienc eand spirituality can help complement each other in reaching higher and higher levels of consciousness/awareness. Yes, primordial soup is what i contemplated about through my idea of very very heavy neutral quarks, that are not projectable from current level of scientific knowledge!They were born under unified field that no longer exists but its four components!

Hello Cristi,

I just reread your paper, and I was wondering if you could summarize its novel postulates and equations, representing hitherto unsung features of physical reality.

MDT's novel postulate: The fourth dimension is expanding relative to the three spatial dimensions at c.

MDT's novel equation: dx4/dt=ic

MDT's myriad of consequences: all of relativity, time and all its arrows and assymetries, entropy, quantum nonlocality and entanglement, wave-particle/space-time/mass-energy duality, the gravitational slowing of light and time, and the single velocity for all entities through spacetime--c.

Dr. Lee Smolin says that a theory should "come in a coherent whole--it should start with a beautiful principle, like the principle of indeterminacy of quantum mechanics or the principle of relativity, and there then should be a beautiful equation that flows out form that principle to a myriad of consequnces." --Lee Smolin, http://www.youtube.com/watch?v=3bLwqnIfLRA&feature=related

MDT's beautiful principle: The fourth dimension is expanding relative to the three spatial dimensions at c with a wavelength of the Planck Length.

MDT's beautiful equation: dx4/dt=ic

Your silence on MDT after having promised to read the paper has lead me to believe that you see nothing wrong with MDT, as unlike LQG and String Theory, it passes Dr. Smolin's criterion for a good theory. And too, MDT predicts all of relativity along with quantum nonlocality and entanglement, as well as entropy, by proposing a novel, deeper feature of our *physical* reality.

In this BBC video, Lee Smolin states, "Einstein taught us that space is not a background that things move in. Spoace is a network of relationships that are ever dynamical, ever evolving, part of the world. The geometry of space evolves and changes--WIGGLES--just like anything else==just like electromegnetism, just like particles."

http://www.youtube.com/watch?v=3bLwqnIfLRA&feature=related

So it is that dimensions move.

All that my theory--Moving Dimensions Theory--does is note that the fourth dimension is expanding relative to the three spatial dimensions, as attested to the photon which is ageless in relativity and nonlocal in quantum mechanics.

From MDT's simple postulate and equation dx4/dt=ic, all of relativity is derived.

Give me a universe wherein we have four dimensions x1, x2, x3, x4 and the fourth dimension is expanding relative to the three spatial dimensions, or dx4/dt=ic, and all of relativity arises.

This is a simple, beautiful postulate and principle--indeed, Einstein's principle of relativity descends from MDT's postulate. And MDT is more succinct than relativity, for from MDT's single postulate and equation comes both of relativity's postulate.

Also from MDT's simple postulate and equation comes a natural *physical* model for time and all its arrows and assymetries, as well as entropy, quantum nonlocality and entanglement, all the dualities--space/time, mass/energy, wave/particle--and both Heisenbergs' and Huygens' principles.

dx4/dt=ic (underlying relativity) suggests that the fourth dimension is expandingh at c.

xp-px = ih (underlying quantum mechanics) suggests that the wavelength of this expansion is Planck's length.

So it is that MDT sets both Planck's constant and the velocity of light, while also maintaining the constancy of the velocity of light by giving rise to all of relativity, and inspiring all wave-particle duality via the fourth dimension's wavelike expansion through continuous space--please see the attached documents. In the first you will see there is no need to quantize gravity, and in the second you will see a side-by-side comparison of MDT with Stirng theory and LQG.

Lee Smolin also states in the video, "We've forgotten how audacious science is and how it rages sometime -- how the ideas that turn out to be true are so often outrageous... we've forgotten the lessons of the people like Einstein, who come from the outside but have exactly the right insight and right idea." --http://www.youtube.com/watch?v=3bLwqnIfLRA&feature=related BBC Hard Talk

"Openness, the inclusion of different points of view, like in anything else, is essential to progress." --Lee Smolin http://www.youtube.com/watch?v=3bLwqnIfLRA&feature=related BBC Hard Talk

In light of all this, I was hoping for some more dialogue; as there is nothing to lose by discussing foundational questions in a collegial, professional manner, and everything to lose by silence and solitude.

Too, too many established professors and researchers refuse to partake in dialogue, and this grates against the spirit of greats such as Wheeler, Einstein, and Galileo.

"I have never met a man so ignorant that I couldn't learn something from him." --Galileo Galilei

"Curiosity is more important than knowledge." --Einstein

Best Wishes!

Soon these comments will be frozen for all time, while the fourth dimension yet marches on at the rate of c!

I look forward to sending you a copy of my book, HERO'S JOURNEY PHYSICS & MOVING DIMENSIONS THEORY: FROM HERACLITIS, TO PLATO, TO ARISTOTLE, TO COPERNICUS, TO BRUNO, TO KEPLER, TO GALILEO, TO NEWTON, TO PLANCK/EINSTEIN/BOHR/BORN--AND YET IT MOVES! Unifying relativity, quantum mechanics, entropy, and time's arrows and assymetries with a new universal invariant: dx4/dt=ic."

Eppur si muove!

Dr. E (The Real McCoy)

"Books on physics are full of complicated mathematical formulae. But thought and ideas, not formulae, are the beginning of every physical theory." --Einstein/Infeld, The Evolution of Physics

MDT's *physical* idea: the fourth dimension is expanding relative to the three spatial dimensions at c, or dx4/dt=ic.

Please share the *physical* concepts of your paper.Attachment #1: 1_MDT_MOVING_DIMENSIONS_THEORY_EXAMINES_THE_GRAVITATIONAL_REDSHIFT_SLOWING_OF_CLOCKS.pdfAttachment #2: 1_Moving_Dimensions_Theory_Einstein__Heros_Journey_Physics.pdf

Dear Dr. Narendra Nath,

Thank you for your kind answer, coming from your experience and wisdom.

Best wishes,

Cristi