Questioning the Assumption That Space Is Continuous by Daniel L Burnstein

Hi Paul,

I'm not sure I understand your comment. Do you mean that space being discrete continuity of space is an illusion? Or do you mean that space itself is non-physical?

My essay suggest exploring the physics that emerges from the former when discreteness is chosen as an axiom.

Daniel

Hi JCNS,

You wrote

"Given this baggage, however, it was difficult for me to generate a great deal of enthusiasm for the construct you propose, which comes across to me as arbitrary and as a purely hypothetical concept bearing only a superficial, terminological resemblance to what I've always tended to think of as objective reality."

All theories contain elements that may appear arbitrary. We call them axioms. Also arbitrary is our assumptions that space is continuous or the choices of axioms on which special relativity is based on.

As I explained in the opening, I explore what kind of universe and physics would emerge an axiom set in which space is discrete and emergent from particles I call preons(-). It is true that preon(-) here, is as physical as matter is. So, yes, space here is not merely the absence of matter. Space, if my proposition is correct, is physical and interacts dynamically with matter.

What I found is that the physics that emerge from the axioms is consistent with the observational and experimental data we have about our own universe (consistent with the data, not the theoretical interpretations of it). For instance, though I have avoided coercing my system to agree with any other theory, I found that gravity emerges naturally from the properties of the two only two fundamental particles I describe.

Also emerges as direct consequence is the relationship between matter and energy, and effects that behave exactly like the other interactions which current theories identify as fundamental and effects such as dark energy and dark matter. And laws of motion emerge that are consistent with our observations of motion. The mathematical framework also provides ways to calculate and exactly predict the outcome of interactions.

You have to remember that a theory is required to do three things; describe, explain and predict. It must be consistent with observational and experimental data, but in no way must it be in agreement with other theories. In fact, a theory, any theory, cannot be understood from within the framework of a theory that is based on a different axiom set.

I understand that it is hard to abstract from one's own world vision. It may help to go into reading the essay as intellectual game where you construct a world from scratch. You might see, that this world is not be as foreign as you think.

Following several distinct comments, it is evident that some readers find understanding the essay difficult. Also, after looking more closely at the comments, both from people who understood and people who didn't, I realized that the difficultly seems to arise when readers who try to fit or situate those ideas within the framework of their theories; all of which are based on a different axiom sets. Theories based on different, mutually exclusive axiom sets cannot be reconciled (which is why quantum mechanics and relativity will never be unified). That doesn't mean that mutually exclusive theories can't be both right. Mutually exclusive theories can be both in agreement with observational and experimental data while disagreeing in their theoretical interpretations of the data.

That said; it can very difficult to abstract oneself from one's own belief. So my suggestion here would be to view my essay titled "Questioning the Assumption that Space is Continuous" as a game or intellectual exercise and explore, as one would flatland, the emerging universe and physics from the proposed axiom set. This would allow free exploration of the consequences without the impossible burden of having the model fit an external theory. That should help in two ways.

The first is that the model is allowed to stand on its own and as such can be tested for internal consistency.

The second, is, once the consequences have been investigated, one can compare the descriptions and explanations to see if they fit what we know of the observable universe. And from there, see how the predictions that are unique to the model of quantum-geometrical space and matter can be tested. One such unique prediction is that the Universe is a locally condensing universe rather than an expanding one. A locally condensing universe is virtually indistinguishable from an expanding universe except for redshift anomalies which are predicted and explained within the former but rejected by the latter.

So, should you decide to read the essay, try and let your imagination loose. Make believe. In other words; have fun.

One last note: The essay is based on a much larger work, the first part of which is available here.

Also, I attached here a version of the essay which corrected some typos (for instance, moments on page 10 should read momentums).Attachment #1: Questioning_the_Assumption_that_Space_Is_Continuous.pdf

JCNS

You ask "Here's another question for you: do your ideas lead to any specific predictions about reality which could be experimentally tested, i.e., which are falsifiable? Just curious."

It does make a number of predictions t hat can be experimentally or observationally confirmed. For a start (Note that there should be a plus sign between the parenthesizes for preon() and preons() but for some reason, tey do not show in the preview):

The QGD model makes a number of original predictions, which are discussed in a three article series you can find here, here and here.

I will summarize here a few of the predictions which can be experimentally tested.

First, at the fundamental scale, is predicts that all particles which we now consider fundamental have structures and are composed preons(). So far, some experiments have been shown to be in agreement with this prediction in regards to electrons. See following articles here (this article is also in agreement with a method of exploring fundamental reality which I proposed in the book and my article titled The Brick and The Hammer (this article needs to be updated with due to some changer in terminology) . Other articles supporting the QGD model can be found here and here.

Also, on page 33 of Introduction to Quantum-Geometry Dynamics Vol 1, I describe an experiment which could confirm the formation of electrons and positrons from gamma photons. Also, a similar experiment conducted at the Lawrence Livermore National Laboratory supports and is fully explained by the mechanism of particle formation described by QGD.

Mass is an intrinsic property of matter. Preons() being the fundamental particle of matter is also the fundamental unit of mass. The mass of an object is simply the number of preons() it contains. Gravity emerges naturally from this definition of mass (this along with the quantum-geometrical nature of space has important implications at non-fundamental scales). So does the relation between mass and energy or E=mc. It follow that, according QGD, there is no need for such as the Higgs mechanism.

The mechanism at the particle formation has also direct consequence at the cosmological scale. According to QGD, the first structures formed from preons() are photons. In the preonic universe's initial state, preons() where uniformly distributed in quantum-geometrical space. The formation of photons and created what we perceive as the cosmic microwave background radiation, the CMBR (this is consistent with the quasi-isotropy of the CMBR). So, according to QGD, though the rate at which the CMBR is produced decreased over the evolution of the preonic universe, the mechanisms that formed it are still active. So in regions where the density of free preons() is higher, the production of photons adding to the CMBR is greater. The rate of production of the CMBR is expected to be greater in intergalactic space where preons() have formed less bounded structures. This should be observable.

An experiment could be devised that would support the existence of preons(-) and preon(). For that experiment, a closed sphere equipped with photo detectors and containing nothing but empty space should detect the formation of photons. Preons() interact too weakly with the higher structures of matter that are instruments to be directly detected, but their presence can be inferred from the formation of photons from apparently empty space. The rate of production of photons would be a function of the preonic density (the number of preons()/preons(-)) and volume of the sphere (also measured in preons(-)).

QGD also makes a distinction between interactions and propagation (see chapter 3 and chapter 11 of Introduction to Quantum-Geometry Dynamics). The propagation implies the motion of preons() and is limited by the structure of quantum-geometrical space (light, for instance, propagates). So the maximum speed is that of preons() or c. Interactions, on the other hand do not necessitate motion preons() or preonic structures (everything material that is not a preon()), and following the axioms of QGD, must be instantaneous. N-gravity and p-gravity are instantaneous and so is the resultant effect we call gravity, dark energy and dark matter effects. So according to QGD, gravity is, for lack of a better word, instantaneous. That gravity is instantaneous could be tested rather simply (that is described in detail in a yet to posted article).

JCNS,

Yes. I am quite aware that there will be, is, opposition to the ideas I put forth. That is the way is should be. Personally, I see QGD as a set of questions that need and should be asked. Some of the questions, to my knowledge, were never asked or at least, never formulated in the way they are in QGD.

As I may have mentioned earlier, my motive for participating in the FQXi is not to convince people that I have a better theory. That would prove to be a waste of time. My intention is to participate in and/or initiate discussions. I believe that the questions a theory raises are more important the those it answers. QGD is all about "what if" questions.

That said, I appreciate your comments. Your essay and comments show that you have clarity of thinking.

NOTE: In order not to distract from discussions relevant to Marcoen J.T.F Cabbolet's excellent essay, I have transported here the discussion he initiated about the views I express in my own essay. My reply to his last comments will follow shortly.

Daniel L Burnstein wrote on Jul. 20, 2012 @ 04:07 GMT

Hi Marcoen,

In answer to your questions

"Am I correct that you obtain a quantum-theoretical formulation of the physics of gravitational repulsion from just two assumptions?" and "Are your two assumptions (or axioms) all of the assumptions of the entire theory, or are these assumptions that are added to the assumptions of the quantum framework?"

Yes, I do get gravitational repulsion from only two basic assumptions or axioms. The entire theory is directly derived from only two axioms. You can get an idea how this is achieve from my entry in the FQXi contest titled "Questioning the Assumption that Space is Continuous."

And should you want to see the entire framework, I would be happy to direct you to my introduction to the subject; the first part of which is only 120 pages.

You work and mine would certainly provide a basis for some interesting discussions, to say the least.

Daniel

Author Marcoen J.T.F. Cabbolet replied on Jul. 25, 2012 @ 17:47 GMT

Dear Daniel,

Having looked at your essay, I see that we share the idea that gravitation can be repulsive and that space is not fundamentally continuous. Our views on what underlies all that are, however, radically different. I do not believe that space is continuous, but neither do I believe that it is discrete. In my upcoming postdoc project I intend to develop the (mathematical) notion of a semi-continuum: this is a (semi-topologiocal) space that at macroscopic space has some properties of a continuum, but the continuum structure breaks down at small scale (e.g. at Planck level).

I have some questions about your claim that your system rests on only two axioms from which everything else follows. I will focus at three things, one logics-related, one mathematics-related, and one physics-related:

1) The definition on page 1 of the notion "fundamental" is a so-called if-statement, that is, a statement of the form

This has a consequence: if an object is fundamental, then it does not follow from the definition that it is invariant.

The point is, namely, that the reasoning

is known to be not logically valid.

On page 2 you write that "Per our definition of what is fundamental, preons(-) and preons(+) never change." This statement is, thus, incorrect from the point of view of formal logics: with your definition, something can be fundamental but not invariant. Did you perhaps have an if-and-only-if-statement in mind when you formulated your definition of the concept "fundamental"?

2) Furthermore, your axiom about the discreteness of space is merely about the qualitative composition of your quantum-geometrical space: apart from the fact that there is no definition of the concept "distance", by no means it follows directly from this axiom that there is a smallest possible distance, as you claim on page 1 just below the axiom. The axiom does not exclude that there are infinitely many preons(-) located at different distances from each other: there might be a positive distance between any two preons(-), but a smallest possible distance has not necessarily to exist. That is to say: isn't the statement that there is a smallest possible distance an extra assumption (axiom) in your theory?

3) In your axiom of the discreteness of space, you mention that there is a repulsive force between preons(-). Yet on page 2 you write that the preons(-) are static: they don't move. Apart from the fact that the notion "force" is not defined in your framework, the question rises: how does the repulsive force manifests itself? How can we prove that it exists at all?

I would appreciate it if you could elaborate specifically on these three topics.

With best regards, Marcoen

Daniel L Burnstein replied on Jul. 26, 2012 @ 14:42 GMT

Hi Marcoen,

Yours are valid questions and show that perhaps, some clarifications are needed. See numbered answers corresponding to your questions below.

1) Yes, it is and if and only if reflexive. It is fundamental if it is absolutely invariant and if it is absolutely invariant, it is fundamental.

2) Not really. One has to remember how distance is defined. Distance is not what exists between any two preons(-). That would imply that there may be space between preons(-) when, as explained, there exist nothing between preons(-) but the n-gravity field that keeps them apart.

Distance between any two preons(-) is defined as the number of preonic leaps it takes for a preons(+) to move from one to the other. This definition of distance is a consequence of the axioms that define preons(-) and preons(+). Since it can be derived from the, the notion of distance is a theorem.

3) For preons(+) to move, they would need to move through space, hence, be able to transitorily couple with other preons(-) along their path. They can't do that since by definition, they carry n-gravity charges which keeps them apart. Since there is nothing between preons(-) except the n-gravity field, there isn't even space (preons(-) are space), there is no way for them to move. Thus they are virtually static. Therefore, space, according to the model I propose, has a definite structure. Though this is not absolutely correct, quantum-geometrical space may be understood as an absolute frame of reference.

Since quantum-geometrical space and matter are defined as being particles and since they are defined as absolutely invariant, then preons cannot be transformed, created or destroyed. They must then obey the law of conservation. Since space is made of preons(-), it must then be finite. By definition, a preon(+) an only transitorily couple with one preon(-). Hence, there cannot be an infinite number of preons(-) that can occupy any regions of quantum-geometrical space. And since space is not infinitesimal, that is, it does not contain an infinite number of preons(+), their can't be an infinite number of preons(+) in any given region of quantum-geometrical space.

I hope that helps clarity the subject. As I mentioned, my essay is taken from a much larger work, the first volume of which is available here

Author Marcoen J.T.F. Cabbolet replied on Jul. 27, 2012 @ 21:01 GMT

Hello Daniel,

I like the enthousiasm with which you participate in the discussion on the foundations of physics.

That being said, I have looked at your larger work to which you refer in the above post. I see that you have some outspoken ideas, but - with all due respect - the system that you present is not a formal axiomatic system that allows rigorous proofs.

The derivations that you present are not based on logical schemes: yours are informal Toulmin schemes. That means that the argumentation contains tacit assumptions that are not implied by the premises. An example is your concept of distance: on p. 76 you call this a corollary but there is no way that this concept can be formally deduced from your set of axioms. In addition, the definition seems ambiguous. Let us assume that the distance between two preons(-) is identical to the number of preon leaps between them. What if there are several trajectories to get from one preon(-) to another, whereby these trajectories differ in the number of leaps? Then according to your definition, there are several different distances between these two preons(-).

Furthermore, you seem to have troubles in separating object level from metalevel. Your axioms 1 - 11 are at object level, but axiom 12 is at metalevel. This axiom 12 is a proposition that you have to prove starting from the axioms at object level.

But even apart from the way how your ideas are presented, the ideas themselves raise questions. You haven´t really answered my third question in my previous post: how can we detect the repulsive force between preons(-)? In other words: what is the difference between assuming that there is such a force, and simply assuming that space is discrete and made up of static particles but without the additional assumption that there is some force active between the constituents of space?

If you really want to make your point about a universe consisting of preons(-) and preons(+), then my advice would be that you develop a publishable representation of your theory in symbolic logic.

With best regards, Marcoen

Marcoen, wrote:

"An example is your concept of distance: on p. 76 you call this a corollary but there is no way that this concept can be formally deduced from your set of axioms."

The corollary can be deduced directly from the axiom set, but this is shown much before page 76. That said, have you tried using the equations described from chapter 8 and following to describe and predict physical behaviours.

Marcoen wrote:

"Your axioms 1 - 11 are at object level, but axiom 12 is at metalevel. This axiom 12 is a proposition that you have to prove starting from the axioms at object level."

I understand the distinction between meta-mathematical constructs and mathematical constructs, but you have to keep in mind that this is not about formal systems or logic, none of which are subjected to the constraints of physical systems. I do address this issue (page 2 to 6) when I describe the distinctions to be made between mathematical and physical axioms.

I addressed that in response to Prof. Ellis who wrote about the possibility of an axiomatic theory: " a very old dream, and one that is probably unattainable both because of Godel's theorem"

To which I replied: "Gödel's incompleteness theorems are often invoked as an argument against the possibility of a complete and consistent axiom set from which all interactions at all scales of physical reality can be derived. The problem is, the incompleteness theorems apply to the formulation of meta-mathematical statements about systems (arithmetic principally). But one has to remember that, aside from basic rules of composition, there are no constraints to the making of such meta-mathematical statements, theorems, (nothing prevents false statements or statements that can't be derived from any given finite axiom set).

Physical reality, on the other hand, strictly constrains any phenomena so that it must be consistent with the fundamental laws that govern forces and other interactions."

You wrote: "You haven´t really answered my third question in my previous post: how can we detect the repulsive force between preons(-)?"

N-gravity cannot be directly detected. By definition, n-gravity acts between preons(-) and since all instruments are made of matter, they can't interact directly with preons(-). N-gravity would only interacts with with the transitory preon(-)/preon(+) pairs. That said, though it is essential that any theory describe and explain physical interactions, it is not sufficient. The only valid test of a theory lies in the original predictions it makes.

For the "describe and explain" conditions, all one needs to do is use the QGD equations and see if what they describe is consistent with observational and experimental data (not their theoretical interpretations).

As for the "predict" condition, QGD makes a number of predictions that are completely original to it (I describe some of them and how they can be falsified in reply to J.C.N Smith in a earlier comment). If the predictions are confirmed, that would support the existence of n-gravity. But n-gravity cannot be directly detected anymore than quarks can.

To answer your questions.

Preons(-) do not need to be separated. They are separated as a consequence of the unit repulsive n-gravity charge each carry. This is part of axiom set of QGD.

As for what exist between them, if you consider space as what matter or particles can occupy, then there is no space between preons(-).

In the quantum-geometry I propose, all material objects can only occupy preons(-) or, if you will, quanta of space. Also important to remember is that the usual geometrical notions of distance between two adjacent preons(-) makes no physical sense; a pair of adjacent preons(-) being defined as being in relative position that a preon() may potentially leap directly from one preon(-) to other. Distance is not a purely geometrical but physical. So are the notions of length, volume, etc. The distance between any two given preons(-) is equal the lowest number of leaps necessary for a preon() to move from one to the other.

QGD defines a special type of geometry and explores how it dictates the structure of matter and the laws that govern it. The question is, does this geometry describe physical reality?

Thank you for having taken the time to read and review my essay. Looking forward to any other thoughts you may have about it.