A naturalist account of the limited, and hence reasonable, effectiveness of mathematics in physics by Lee Smolin

Dear Sir,

Mathematical reality is the quantitative aspect of Nature, which is logically consistent - hence unchanging - and harmonizes with other aspects. But the problem arises when we try to manipulate them. In one of the essays here, the final equation is consistent with the figures given. But if the same sets of figures are applied to the initial equations, it shows 1200 = -1250. The author has not cared to reply to our comment. With such basic flaws, even if the final equation turns out to be right, the theories become questionable.

Mathematical space-time structure is the intervals between objects that change according to the time evolution of those objects including motion due either to inertia (determined by energy at the point of application) or application of force (influenced by mass at the point of application), which change continuously due to interaction with its environment and determines the structure of free fall. Thus, the curvature does not belong to space-time, but to the position of objects that determine the interval. Geometry cannot tell matter how to move and in turn - only energy moves matter. Geometry is determined by such motion. We use alternative symbolism of such evolution of objects to describe the interval.

The Principle of no unreciprocated actions emanates from Leibniz's principle that there should be nothing in the universe that acts on other things without itself being acted upon. This is essentially Newton's third law. Einstein used this principle in GR when rejecting Newton's ideas about absolute space. His interpretation forbids any reference to a fixed-background and entities whose properties are fixed for all time, regardless of the motion of matter, thereby reducing interactions to relationships with other objects. But space itself is not only intervals, but also background for everything. All motion takes place in space in time. All observations are made at "here-now", which is referred to as space-time. Thus, by implication, Einstein's interpretation of the Leibniz's principle makes everything dependent on observation only. An object does not exist unless observed by a conscious observer - which concept of Bohr he opposed! Einstein based his conclusion on the M & M experiment, which used light. But light is a transverse wave, which is background invariant. Thus, his conclusion is faulty.

Chess was invented in India by the warrior class from their war moves. Like a poet writing poetry, the basic concepts were always there. But the processes of its codification for alternative use by emphasizing different aspects differently or choosing specific components, which can be infinite, were created. Your conclusions are identical with our essay, though the presentations are different. Best wishes.

Regards,

basudeba

Dear Lee Smolin,

The problem of inventing (invoking) mathematical objects in the development of a theory is that the invented objects may not exist in our physical universe. For example: the extra dimensions of space invoked in super string theories may not exist. To avoid this problem I used only the observed three dimensions of space and one dimension of absolute time to develop my theory Model mechanics.

Model Mechanics unifies all the forces of nature (including gravity). In addition it give rise to a new theory of relativity called IRT. IRT includes SRT as a subset. However the equations of IRT are valid in all environments including gravity. I invite you to read my essay and give me your informed comments. Thanks.

Regards,

Ken Seto

It is not contradictory to say I am changing and my photograph is not. I am not my photograph, and never have been my photograph.. It is contradictory to say of one thing that it is changing in all respects and not changing in any.

Dear Lee,

Nice essay from a popular author, having read your 'Three Roads to Quantum Gravity' right here in Africa years ago. You talked a lot about what exists in your essay and take a naturalist position on this, viz.

"...everything that exists is part of the natural world, which makes up a unitary whole"

"...all that exists is physical reality"

"... all that exists is part of nature"

"I would like to propose that there is a class of facts about the world, which concerns structures and objects which come to exist at specific moments, which, nevertheless, have rigid properties once they exist"

"Properties off mathematical objects, once evoked, are true independent of time"

"Both the records and the mathematical objects are human constructions which are brought into existence by exercises of human will, neither has any transcendental existence. Both are static, not in the sense of existing outside of time, but in the weak sense that once they come to exist, they don't change"

On the basis of these statements, I have a question for you and other members of the Perimeter Institute to ponder:

Can what exists perish? If (a part of) what exists can perish, what will be the implication for physics? Would this count as a fundamental event?

I discuss a postulate in my essay: the non-zero dimensional point does not have an eternal existence, but can appear and disappear spontaneously, or when induced to do so.

If contrary to belief, the point, either mathematical or physical falls among things 'which come to exist at specific moments' as you say and contrary to what you said 'once they come to exist, they DO change (and perish)', what then? I believe you have the clout to push this idea forward if you find that it has merit.

Best regards,

Akinbo

Belief is a religious concept. Physics and science are about usefulness that requires predictability. Metaphysics may be useful if it results in a hypothesis. For example the ``in the beginning..." of Hebrew tradition (LaMaiter, Friedman) or of the eternal universe of Hindu tradition (Narlikar, Burbidge, Hoyle).

Beauty and grace do not help us survive except as they identify useful relations.

I suggest ``discovered'' and ``invented'' are mutually exclusive. The ``evoked'' class is empty because the possibility of a game existed before the game. The sense of ``discovery, beauty and wonder'' has evolved to be useful. Discovery of a game means the discovery of a possible relation that is allowed in nature. Whether the game continues depends on its contribution to entropy (the selection process).

We are in search of a ToE. This search is for core principles. The trend is to find ever more basic principle (perhaps only for our limited ability to understand). Postulating that such principles exist has helped if only to get funding. The trend is toward fewer principles not more FAS's.

My paper suggests there are only number, geometry, and their relationship. Logic has evolved to further the relationship and increase the entropy rate. Math is a relationship that exists before humans.

Dear Sir,

Anything subject to time evolution must perish. Time evolution takes place in six stages: being (situation leading to its creation), becoming (its creation itself), (growth due to addition of other particles/events), transformation (as a result), transmutation (due to the same effect - incompatible/excess addition), destruction (change of form as a consequence) to start a new chain. This applies to all dimensional things. Since point has existence, but no dimension, it cannot perish. You cannot treat point as a small part of a line, as even the minimum unit of a line will have some length.

Regards,

basudeba

Dear Lee,

While I think LQG has a lot of truth in it, however, Dr. Tegmark is 100% correct. I proved that in my last essay and I will have much more evidence in my upcoming essay.

"Reality is nothing but a mathematical structure, literally"

FQXI article

more info

Dear Basudeba,

Thanks for your opinion. Perhaps, Lee would take both views together for clarification. I am of the opposing view that points have dimension of about the Planck size and can be treated as the extremities of lines, i.e. as a part of lines (see Euclid's definition in my references) but I will not force the issue as yet. You may also check the arguments in my 2013 essay.

You say point has existence but cannot perish. If the universe can perish and cease to exist, will all the points in it remain behind and not perish with it? Of course, I am assuming the correctness of the cosmology that the universe did not exist, started existing and increasing in size and will eventually perish.

Regards,

Akinbo

Lee,

пЃЉ Let me first say, my critical point of view was derived from the inspiration of reading your essay. It has ignited within me the motivation to address, in a separate paper, the many misconceptions we have regarding time. Hopefully we will debate my theoretical and hypothetical intuitions constructively and thereby provide a genuinely effective iteration of these conclusions at some time in the future (excuse the pun).

With your sections addressing the effectiveness of mathematics in mathematics and physics, you lead the reader into the assumption we currently understand the fundamental laws governing both studies and their comprehensive connections between separate deviations. Mathematicians are on a path to derive a cohesive fundamental structure connecting Algebra to Geometry to Logic just as Physicists are attempting to unify the laws constituting observable physical forces. Ultimately the goal will not only connect the separate entities individually, but also unify these distinct disciplines into a decisive understanding of nature. As my essay attempts to illustrate, mathematics is abstract, arbitrary, and purely a fundamental tool - we then apply it to a properly structured interpretation of reality - we describe this process as the discovery of the laws of physics. The idea that nature or reality can be described or mirrored mathematically or in physics is not a "mystical" conjecture of philosophy. Artists are capable of painting images observed in reality. In time, the art evolved discovering better techniques to make paintings an accurate description of observation. This evolution was brought about by the application of "discovered" techniques using fundamental tools (i.e. physics using mathematics as tools for observation). The limitation or effectiveness of their mirrored representation of reality depends solely on the applications of tools "invented "or applied by humans and our competent abilities discovered by the art form. Photography led to realism, Motion Pictures led to temporal realism and now we have 3D HD Projections which is more "effective" at capturing and describing nature, but we are not satisfied, we require more information to describe the enormous information needed for temporal realism. The information needed to recreate nature or a temporal event using Mathematics and Physics is infinite. We possess the necessary mathematical tools, Integrals and Calculus for temporal states, we simply do not have enough information to predict probability from possibilities, or we are too lazy to consider the enormous amount of information needed to accurately calculate and depict nature. Therefore our observations as mathematical representations are lacking in its description prior to an event, leading us to assume probabilistic and uncertain future events based on biased accrued approximations within our mathematical equations which lead to misinterpreted phenomenon or unexplained events. For the most part, we are simply satisfied describing nature to an acceptable limit, but without including every physical representation of the information concerning the system of observation, we cannot call this an assumption a direct interpretation of nature. It is lacking, but it is not the fault of the applied mathematics that already "existed" after which humans "discovered" and "invented" arbitrary imaginative symbols to represent. It's lacking, but not because of the interpretation of mathematics described as physics (although we must clarify a preferred theoretical methodology). It is lacking because we do not include enough information to describe an object "O", and therefore we have an abstraction we (as the interpreter) hypocritically claim is based on the limitations mathematics and physics pose on nature.

As unbiased investigators of nature (mathematicians, artists, theorists, and physicists), we must not assume a provocative or unconventional approach abstract in resolving a preferred method of depicting nature, is assumedly flawed or insignificant for discussion and interpretation until thoroughly proven otherwise by analytical means of exploration and experimentation. The approach necessary for discovery is a derivation of fact from fiction - truth from falsehoods - limited "gauged" probabilities from infinite uncertain possibilities we seek as discoverers of our reality.

All in all, it was a great addition to this discussion. Thank you for contributing.

Best Regards -Keep in touch!

D.C. Adams

Dear Sir,

A point is only a position in space. Space will remain in one form or the other. Otherwise there cannot be big bang or big bounce. Thus, point cannot perish.

Regards,

basudeba

I think I'm a temporal naturalist now!

"In closing, I would like to mention two properties enjoyed by the physical universe which are not isomorphic to any property of a mathematical object. 1. In the real universe it is always some present moment, which is one of a succession of moments. Properties of mathematical objects, once evoked, are true independent of time. 2..."

That's cool.

So, the first part seems to be a form of Presentism. Evocation is cool. I'm not sure in the next sentence that I would phrase it "independent of time" because the evocation is within the universe and the universe is within the present moment.

If there were more space it would be interesting to go into shape dynamics / time capsules / etc.

Lee,

Your ideas on loop space with Astekhar and Rovelli in the 90s were fascinating. Your present ideas fascinate once again.

I think the Platonic view can be appropriately tweaked to agree with your view of a "unitary whole." Actually, I think that by default the view has always been that of the "unitary whole." I call it the view of an "all-encompassing existence."

My view is that there is one and only one totality of the existence. However, the one totality of the all-encompassing existence has two "initially" separate realms that evidently progressively get connected "inseparably" in the unified whole.

The following "table" illustrates my tweak of the Platonic view that involves the two fundamental realms (which are named in the header) into which the fundamental essences (which are listed under the header) are categorized.

The Realm of Phenomena ------ The Realm of Noumena

------------------------------------------------------

Space (the dimension) ------ Time (the dimension)

The Aethereal Substance ------ The Ephemeral Instance

Motion ------ Duration

The Corporeal Forms ------ The Abstract Ideals

------------------------------------------------------

My view is that the all-encompassing existence has both the phenomena and the noumena. The strictly phenomena being the corporeal cosmos, which we observe with its full spectrum that range between the kinematic vacuums of dark voids and the kinematic singularities of super dense black holes. We see within that range the electromagnetic spectra of phenomena and the particulate spectra of phenomena. As far as my view goes, the corporeal cosmos exists within the space dimension, and the corporeal cosmos is the space-occupying substance that is inherently rendered the kinematic definitions by the essence of motion. The space-occupying substance is aethereal if without the kinematic definitions; but it is never without the kinematic definitions (in string parlance, it always has branes and underlying branes ad infinitum).

Note that my Forms and Abstracts no longer follow the meanings of the Platonic terms. My "Corporeal Forms" are no longer the Platonic universals of "Abstract Ideas." They are now exact opposites. My Corporeal Forms are strictly categorized as phenomenal realities, while the Abstract Ideals are strictly categorized as noumenal realities. To me, both the phenomena and the noumena are real.

However, the corporeal is the more real than the abstract because it is the manifestation and embodiment of the ideals. In other words, the corporeal forms are the complete or thorough realities, the already connected phenomena and noumena, the embodied truths, the combined unified fulness of existential realities.

The laws of nature, the laws of motion that we try to discover, are the abstract ideals. In the abstract is our mathematics. In the corporeal is the execution of the mathematics.

My view is that the abstract ideals are static and only await their discovery or fulfillment. So, there is no evolution of the laws of nature. On the other hand, the corporeal forms are dynamic since the fundamental essence that defines the corporeal forms is motion (flux). Motion is that which is being constantly governed to conform to the ideals - to the laws of motion described by our mathematics. (Here of course is the bit of my tweaked Parmenidean and Heraclitean.)

The tweak that brings agreement with your idea of the unitary whole should now be obvious. As much as we understand, the mind, the nous, that perceives the noumena, resides in the brain-and-body that perceives the phenomena. We have the mind and the brain-and-body as the unified mind-and-body.

If the idea is extended in its application to a pan-cosmic or pan-existential view, the whole cosmos would be a sort of "super mind-and-body" - a unified whole of the mindset and the body-set that pursues the execution of the abstract ideals towards the continuous fulfillment of existential realizations in the corporeal forms.

Yet, the noumenal is apparently inherent in the phenomenal. The inherently unified corporeal-and-abstract reality is fundamental. There are the simple corporeal-and-abstract realities. And there are the complex corporeal-and-abstract realities. But, evidently, the simple corporeal-and-abstract realities are progressively and continuously transformed to form and sustain the complex corporeal-and-abstract realities.

It is apparent that the noumenal and the phenomenal may be established as a unified inseparably connected, or sustained, reality. All that is needed is an inherent and fundamental bias in the existence, in order to have an established cycle that sustains the connected reality. With a cycle limits are set, in which the excesses are spun off the sustained complex realities, and with the spun off fragments eventually grown into new complex realities. The spin off process actually looks like the emergent mechanism in the corporeal that bring about replication. Now, it appears that gravity is that necessary fundamental bias that is indicated in the mathematics of physics.

Lee, my submitted essay is more illustrative of the relationship between mathematics and physics, instead of being explanatory. But I have a book/ebook that is sold at my www.kinematicrelativity.com website and a few pages there explaining my work.

I have been focusing on the ramifications of the genesis formula that I discovered. I derived the genesis formula from the 3-d tensor transformation equation. I clarify in my work that the 1-d Galilean transformation implies mass increases, that the 2-d Lorentz transformation implies mass increases, and that mass increases because of the universal gravitational acceleration is implied by the 3-d Castel transformation (tongue-in-cheek, Lee).

The genesis formula implies that mass increases inherently and continuously occur for every mass domain in the cosmos, and hence for the whole cosmos, because of gravity that is a fundamental bias in the corporeal realm. The genesis formula implies a few other radical ideas.

A bit of an exchange of ideas and critiques between us would be nice.

Regards,

Castel

...cosmic mass-energy increases because of the universal gravitational acceleration are implied by the 3-d Castel transformation (tongue-in-cheek, Lee).

(gotta correct that..)

Hello. You come to propose a conception of things coherent with naturalism. Great ! I stand for the opposite view ;-)

I actually never found a formulation of naturalism that seemed coherent, as it seems to me logically impossible, somehow already in principle, and then even more with quantum physics. So I am very curious when I see such a proposition announced ! For now most of the essays I reviewed here in support of such a view seemed to be amateur-level. I was full of hope for discussions to become at last serious and challenging, at the first sight of an essay with this purpose by a reputed physicist coming to the list.

One thing I was puzzled with when reading some naturalist views, is how they dismiss any idea of considering consciousness as fundamental, by calling this an "explanation by a mystery" and thus no explanation at all. Indeed it may look like this, in the sense that consciousness escapes all mathematical description. So if your condition to call something "non-mysterious" is to have a mathematical, deterministic description of it then indeed consciousness is "mysterious" in this sense. Which does not mean that noting can be said about it (as I did express some important features of consciousness for its connection with physics). However, on their side they claim to explain everything as "Nature". But what the heck do they mean by "nature", and, in lack of a clear definition for this kind of stuff and its working principles, how is an "explanation" of the world by an undefined "nature" assumed to be primary, be any less mysterious than the view taking consciousness as primary ?

I once saw an "argument" that if a miracle is real then by definition it must be part of nature because nature is "all what exists" so that nothing can be meaningfully called "supernatural". Then well, if "all what exists" is the definition of "nature" then it makes naturalism tautological, but no more informative. To be informative we need to specify what kind of stuff is "nature" supposed to be. It seems supposed to mean "physical stuff". Well if we were in the 19th century, and still with General Relativity, it could indeed look like there was such a thing as "physical stuff" that the universe could be made of. However, quantum physics broke that.

Namely, an important question I would have, is whether "nature" is supposed to be finitely or infinitely complex, or maybe just locally finitely complex, in case it could be considered locally (which you seem to reject as you seem to favor non-locality in interpretations of quantum physics). So for example if it is locally finitely complex but not locally causal then, finally, it is infinitely complex if the universe is infinite (in hope that the dependence of local stuff on the rest of the universe converges). Quantum physics makes the physical world locally finitely complex indeed. I consider consciousness infinitely complex. But if "nature" was physical and infinitely complex, how could it have definite causalities that depend on infinitely complex stuff ? Bohmian mechanics describes things as infinitely complex, but I suspect its laws to diverge when considered in their globality.

Here are points of interest I found in your article:

"The effectiveness of mathematics in physics is in [Platonism] mysterious because proponents of this view have failed to explain both how there could be such a correspondence and how we, as beings trapped in time bound physical reality, can have certain knowledge of the hypothesized separate realm of mathematical reality."

What failure to explain ???? I do not see the slightest problem here: it is a one-way dependence. Anything that exists must be coherent with itself, so that whenever we can discern mathematical structures somewhere, they have to be coherent with themselves, thus obey the laws of coherence which are the mathematical theorems. So it is "affected" by the mathematical world, but does not affect it in return (nothing can change the facts of what is coherent and what isn't). It is possible for mathematical structures to be more or less involved by contingent (non-mathematical) realities.

"if you believe that the ultimate goal of physics is to discover a mathematical object, O, which is in perfect correspondence with nature, such that every true fact about the universe, or its history, is isomorphic to a true fact about O, then you are also not a naturalist because you not only believe in the existence of something which is not part of nature, you believe that everything that is true about nature is explained by a true fact about something which exists apart from nature. You are instead a kind of mystic, believing in the prophetic power of the study of something which exists outside of time and apart from nature."

All right, so this means naturalism rejects any possibility to describe nature in mathematical terms. In this case, nature escapes any rigorous mathematical description and is therefore assumed to be fundamentally "mysterious". Like consciousness in my view.

You wrote: "Mathematics thus has no prophetic role in physics, which would allow us an end run around the hard slog of hypothesizing physical principles and theories and testing their consequences against experiment". Then you "hypothesize two principles which we take to define temporal naturalism". Are these two principles not supposed to have any prophetic role in physics, that would allow you an end run around the hard slog of hypothesizing physical principles and theories and testing their consequences against experiment? Because in the rest of your essay I did not find any big care to test these principles against experiment, or against the body of modern science which sums up so many experiments already done, in the sense of a possible challenge to the truth of your principles.

"All that exists is part of a single, causally connected universe. The universe and its history have no copies, and are not part of any ensemble."

Right. I would qualify the spiritual multiverse (where souls can migrate between universes) in these very terms, though the connections between parts (universes) can sometimes be poor.

"There is no other mode of existence, in particular neither a Platonic realm of mathematical objects nor an ensemble of possible worlds exist apart from the single universe." And why not ? You seem to have quite a faith in this negation.

"All that is real or true is such within a moment, which is one of a succession of moments"

You already multiply the modes of existence, between past, present and future existences, and where the time-status of the existence of any particular event... depends on time. So you admit multiple possible modes of existence, but you deny the possibility for still another mode of existence than these (the mathematical existence).

"The activity of time is a process by which novel events are generated out of a presently existing, thick set of present events. "

How thick is the set of present events, and how do you measure this thickness, both in space and time dimensions ? My view of the spiritual reality would be similar except that I take all past events as still presently existing and indestructible, and from which novel events are generated.

" we adopt a strong form of Einstein's principle of no unreciprocated action according to which there can be no entity A which plays a role in explaining an event B, that cannot itself be influenced by prior physical events."

That is quite an assumption, of trying to generalize a principle far beyond the form in which it was initially considered and justified by experiment ! But is it really just a plausible strengthening of a well-defined principle, or rather an endless multiplication of fanciful assumptions only superficially similar to the initially successful version ? Something like justifying philosophical relativism as "a strong form" of the Special Relativity principle.

Of course you cannot understand the possible relation between mathematical and physical realities if you exclude by principle the possibility of one-way influences, and by "satisfying explanation" you mean "explanation that agrees with this principle", assumed to have such a prophetic role in physics, that it allows you, in your own words, "an end run around the hard slog of hypothesizing physical principles and theories and testing their consequences against experiment". By the way, how do you apply this principle to the dependence between past and future ? How can the past affect the future without being affected by it in return ?

You wrote " Among the things that violate a strict definition of naturalism are (...) absolute, timeless laws," yet you defend the view of "the singular universe" which seems to fit absolute timeless laws. It seems quite hard for these laws to vary inside the same universe, both theoretically (the formal rigidity of the physical laws that do not easily let coherent ways to glue together parts of space-time that do not obey the same laws) and as we did not see them vary, but it would be much easier between different universes. Don't you see it hard to reconcile both principles of uniqueness of the universe and contingency of the laws ?

I will write more remarks later.

"So a new conception of mathematics is needed which is entirely naturalist and regards mathematical truths as truths about nature. In this essay I sketch a proposal for such a view. The key it turns out is the conception of time."

If mathematical truths are "truths about nature", they should be consistent. If the deductive consequence is wrong, the premise is wrong as well (the combination "true premise, wrong consequence" is forbidden by logic). You teach that the special relativistic time (the consequence) is wrong but both the premise from which it is deduced (Einstein's 1905 constant-speed-of-light postulate) and its deductive consequences are gloriously true:

"And by making the clock's tick relative - what happens simultaneously for one observer might seem sequential to another - Einstein's theory of special relativity not only destroyed any notion of absolute time but made time equivalent to a dimension in space: the future is already out there waiting for us; we just can't see it until we get there. This view is a logical and metaphysical dead end, says Smolin."

"Was Einstein wrong? At least in his understanding of time, Smolin argues, the great theorist of relativity was dead wrong. What is worse, by firmly enshrining his error in scientific orthodoxy, Einstein trapped his successors in insoluble dilemmas..."

QUESTION: Setting aside any other debates about relativity theory for the moment, why would the speed of light be absolute? No other speeds are absolute, that is, all other speeds do indeed change in relation to the speed of the observer, so it's always seemed a rather strange notion to me. LEE SMOLIN: Special relativity works extremely well and the postulate of the invariance or universality of the speed of light is extremely well-tested. It might be wrong in the end but it is an extremely good approximation to reality. QUESTION: So let me pick a bit more on Einstein and ask you this: You write (p. 56) that Einstein showed that simultaneity is relative. But the conclusion of the relativity of simultaneity flows necessarily from Einstein's postulates (that the speed of light is absolute and that the laws of nature are relative). So he didn't really show that simultaneity was relative - he assumed it. What do I have wrong here? LEE SMOLIN: The relativity of simultaneity is a consequence of the two postulates that Einstein proposed and so it is deduced from the postulates. The postulates and their consequences are then checked experimentally and, so far, they hold remarkably well.

Pentcho Valev

"...a big problem for me is that here Smolin is not taking a provocative minority point of view, but just reinforcing the strong recent intellectual trend amongst the majority of physicists that the "trouble with physics" is too much mathematics. As I've often pointed out, the failures of recent theoretical physics are failures of a wrong physical idea, rather than due to too much mathematics..."

Correct. And the wrong physical idea is... Einstein's 1905 constant-speed-of-light postulate of course:

Lee Smolin, The Trouble With Physics, p. 226: "Einstein's special theory of relativity is based on two postulates: One is the relativity of motion, and the second is the constancy and universality of the speed of light. Could the first postulate be true and the other false? If that was not possible, Einstein would not have had to make two postulates. But I don't think many people realized until recently that you could have a consistent theory in which you changed only the second postulate."

"As propounded by Einstein as an audaciously confident young patent clerk in 1905, relativity declares that the laws of physics, and in particular the speed of light -- 186,000 miles per second -- are the same no matter where you are or how fast you are moving. Generations of students and philosophers have struggled with the paradoxical consequences of Einstein's deceptively simple notion, which underlies all of modern physics and technology, wrestling with clocks that speed up and slow down, yardsticks that contract and expand and bad jokes using the word "relative." (...) "Perhaps relativity is too restrictive for what we need in quantum gravity," Dr. Magueijo said. "We need to drop a postulate, perhaps the constancy of the speed of light."

Joao Magueijo, Faster Than the Speed of Light, p. 250: "Lee [Smolin] and I discussed these paradoxes at great length for many months, starting in January 2001. We would meet in cafés in South Kensington or Holland Park to mull over the problem. THE ROOT OF ALL THE EVIL WAS CLEARLY SPECIAL RELATIVITY. All these paradoxes resulted from well known effects such as length contraction, time dilation, or E=mc^2, all basic predictions of special relativity. And all denied the possibility of establishing a well-defined border, common to all observers, capable of containing new quantum gravitational effects."

Pentcho Valev

Lee,

A very nice essay. I wanted to focus on the last two points of the paper:

1. In the real universe it is always some present moment, which is one of a succession of moments. Properties off mathematical objects, once evoked, are true independent of time.

2. The universe exists apart from being evoked by the human imagination, while mathematical objects do not exist before and apart from being evoked by human imagination.

I agree these two points get to the heart of the conundrum we find ourselves in. We can intuit timeless mathematical entities. These of course are not "physical" in the sense that the have a discernible direct energy and momentum, however we can indirectly assign the storage of mathematical items as information having some energy and momentum requirement. Certainly, we can say that as artifacts of human thought, there is a level of energy and momentum transformed to develop these concepts. We know we have developed this in some discrete number of operations. So is there a spectrum of energy and momentum we can assign to the development of a mathematical concept?

Certainly there is no reason the development could not have followed some other path. There is nothing a priori that necessarily restricts someone from coming up with an idea, although it might be absent the requisite context. Regardless, a person's thoughts must be seen in a prismatic sense; some spectrum of possible mental states that tie back to the physical world.

I am staring at a young pine tree in my neighbor's yard being buffeted by a cold wintery wind, and I think about the fractal regularity of how it grew. Did the tree know before hand how to grow so it would survive the onslaught of the weather?

I have pondered the same points above for some time, and understand I am only seeing a tree because there is some function that tells me I am likely to see the tree there. So the regularity of the math associated with the tree must be buried somewhere in the function does it not?

Would be interested in your thoughts.

Cheers!

Harlan

Lee, Tim and Pentcho,

The trouble with physics is not so much the volume of the mathematics that we have. The trouble is mainly the application and the interpretation of the mathematics.

The troublesome application is that regarding the arbitrary transformations that Einstein proponed based on the Lorentz transformation equations. Einstein actually proponed the following three transformation equations in special relativity:

(1) the space transformation equation

x=x'(1-v2/c2)-½

(2) the time transformation equation

t=t'(1-v2/c2)-½

(3) the mass-energy transformation equation

m=m'(1-v2/c2)-½

In (1) the space transformation equation, the transformation factor is applied to the essence of space as implied by the space variables x and x'. Here Einstein made space a medium of motion.

After discarding the ether medium of motion, Einstein tacitly proposed other mediums of motion, because as per the erroneously interpreted Michaelson and Morley experiments, no motion can be ascribed to the ether. It is obvious that the Michaelson and Morley experiments were erroneously conducted and interpreted because the experiments did not and probably could not account for the doppler shifts.

In (2) the time transformation equation, the transformation factor is applied to the essence of time as implied by the time variables t and t'. Einstein made time another medium of motion; this ignored the fact that the duration process that occurs in time is NOT a motion process. The motion process occurs only in space, with infinitely many varied rates of displacements expressed as distance per unit time.

It is incorrect to apply the transformation factor to the essence of time because the transformation factor indicates only velocity or motion transformations and there is no such thing as the velocity of time - the duration process occurs as a 'displacement' through the time dimension strictly at the 'universal' rate of one moment per moment.

In (3) the mass-energy transformation equation, the transformation factor is applied to the concept of mass (and energy) as implied by the mass variables m and m' and the resultant entry of the kinetic energy variable in the famed K.E.=mc2.

In the mass-energy transformation, Einstein apparently did not know what medium of motion was involved and did not understand the foundational reason why he substituted the mass variables into the equations. But he saw the connection with the classical K.E. and made a momentous interpretation regarding mass and energy.

Einstein must have somehow understood that the medium of motion need necessarily be ascribed some motion for it to be an appropriate medium of motion. This is implied by the reason he gave as to why he discarded the idea of the ether. But because Einstein discarded the idea of an ethereal space-occupying medium of motion, he also discarded the idea of space whose sole function is that it gets occupied.

Pure kinematics points to the idea of the motions of motions, which is the reason why the medium of motion must be ascribed some motion in order for it to be an appropriate medium of motion.

The idea of a space-occupying substance as the medium of motion is still the more appropriate idea because motion is the displacement through space. When this idea is embraced, the space and time dimensions may simply be 'fixed' (assumed as absolutes) as the classics did.

The picture then presented is that of the transformations of motion rendered on the space-occupying medium of motion, according to the accelerations and rotations indicated by the transformation factor. The space-occupying medium of motion can then even be spoken of as ethereal, because then the focus will only be on the motions of motions (i.e., the various configurations, formations and transformations) suggested by pure kinematics.

The velocity of light is then simply the reference velocity for what is observable in nature, which is exactly in accordance with Maxwell's proponed variety in the electromagnetic phenomena and the experimentally verified unvarying velocity of light.

As I have explained in my post above, the cosmos is observed "with its full spectrum that range between the kinematic vacuums of dark voids and the kinematic singularities of super dense black holes"; and that range includes the electromagnetic spectra and the particulate spectra.

These are according to the proposition from the mass-energy transformation (3), which is actually the more practically successful proposition; nothing has so far been practically proven regarding the space-time transformations.

This rather radical view presents a cosmos that is observable as having strictly the varied motion formations and transformations.

All these are in consonance with my post above, my submitted essay, and the materials at my website www.kinematicrelativity.com.

The new perspectives that I am presenting could correct and resolve "the trouble with physics" that involves the application and interpretation of the mathematics. But it is sad that, as far as I know, I still remain very much alone in these views.