Any physical phenomena that occupies space in time has to be described by coordinates and the optimal minimal number of coordinates required for this description determines what is called the dimension of the space-time in which the object is and properties of this physical phenomenon can be studied either as evolution along its temporal axis or by its spatial behavior in terms of rates of change across the coordinate axes. One of the fascinations intuitionists of string theory create is the claim that space is not actually 3+1 dimensional but is of higher than that.
The intuition is that a one dimensional linear string from a distant when observing up close yields a three dimensional feature than one dimensional and therefore all the three dimensions we all know extrapolated to generate 9 dimensions of space with new six extra invisible dimensions that are curled to be seen. But if these somehow intuitively sensed dimensions which need to have variables of curled coordinates are not detected and manifest themselves during mathematical descriptions of positions and behaviors in time or independent of time, then either they do not exist at all and mere intuition or the formulations of differential equations we all along use to describe fundamental laws of physics are not formulated correctly and incomplete.
If their existence is very small (minimally small to the extent of not being observed), then unlike the usual coordinates and the usual derivatives, we might create another structural concepts in mathematics to incorporate such existences. But giving a mathematical meaning to something which does not exist is a mathematical paradox and loses it place in mathematics it self and therefore in reality. In line with this,Tom Morley puts in his short article (see attachment below) that space is 3+1 dimensional and I put the question in line with his arguments.
This is a very interesting question with lots of possible answers.
A place to start in looking for answers to this question is in
Sujan Dabholkar, Exploring Warped Compactifications of Extra Dimensions, Ph.D. thesis, Stony Brook University, 2014:
http://graduate.physics.sunysb.edu/announ/theses/dabholkar-sujan-may-2014.pdf
In this thesis, we have higher-dimensional views of the universe, e.g.:
5D view: 5-dimensional Minkowski space M5, the Anti de Sitter (AdS) Universe is a hypersurface, p. 67.
7D view: This 7D view results from considering Buscher rules along z direction.
1D, 2D, 3D and 4D views of space-time are considered in
Maroun, Michael Anthony, Generalized Quantum Theory and Mathematical Foundations of Quantum Field Theory, Ph.D. thesis, UC Riverside, 2013:
http://escholarship.org/uc/item/3jb5b2dr#page-10
See Section 5.1.1., starting on page 72, on counting the dimensions of space.
This is a very interesting question with lots of possible answers.
A place to start in looking for answers to this question is in
Sujan Dabholkar, Exploring Warped Compactifications of Extra Dimensions, Ph.D. thesis, Stony Brook University, 2014:
http://graduate.physics.sunysb.edu/announ/theses/dabholkar-sujan-may-2014.pdf
In this thesis, we have higher-dimensional views of the universe, e.g.:
5D view: 5-dimensional Minkowski space M5, the Anti de Sitter (AdS) Universe is a hypersurface, p. 67.
7D view: This 7D view results from considering Buscher rules along z direction.
1D, 2D, 3D and 4D views of space-time are considered in
Maroun, Michael Anthony, Generalized Quantum Theory and Mathematical Foundations of Quantum Field Theory, Ph.D. thesis, UC Riverside, 2013:
http://escholarship.org/uc/item/3jb5b2dr#page-10
See Section 5.1.1., starting on page 72, on counting the dimensions of space.
As James puts it, there are many possibilities. For instance, bosonic string theory requires 26 dimensions to work. Burkhard Heim built a comprehensive theory of reality that needs up to 12 dimensions to (possibly) work. Time is mooted by some (Itzhak Bars et al.) to have more than one dimension. And so on.
Since more dimensions mean more latitude and freedom of movement and complexity, physical laws become immediately more complex and unpredictable in higher dimensions: for instance, depending on whether dimensionality would be odd or even, we would experience ordinary things such as sound or light very differently (assuming we'd be able to go there.)
In universes with even dimensionalities of space we'd hear sound in multiple ways, much like waves on the two dimensional surface of a pond travel both outwards and inwards, so that spoken speech in such dimensionalities would become riddled with overlapping echoes and become unintelligible. If matter could still somehow appear in some of these higher-D universes, the geometry of atomic arrangements would become such that all particles and elements would acquire exotic and unpredictable new properties (our ordinary metals would become gases, elementary particles would look and behave very differently to their counterparts in our own universe, etc.) This would make life impossible for lifeforms based on matter.
Depending on the respective number of dimensions in space and in time, multidimensional universes can be either stable, unstable or unpredictable (not calculable.) All universes with at least 2 dimensions of either space or time with a combined (spacelike plus timelike) dimensionality count higher than 5 are inherently unpredictable. All universes featuring only 1 dimension of either time or space and 4 or more dimensions of correspondingly either space or time are unstable, meaning that any such universes would quickly disappear again after having popped into existence for whatever reason.
Morley's theorem, which is very nice (thank you, Dejenie!) shows the following: if the Maxwell-Hertz Theory is a complete description of electromagnetic waves, then they can exist only in a 3 + 1 world. So it says that by encoding reality in this equations, one has put inside more information as one maybe wanted. Or that our perception of the reality, as it is reflected by this human-made theory, is too strongly influenced by our general intuition. The point is that we have in the moment not enough knowledge to decide if (1) this theory of electromagnetism is too strong (so our views are too narrow when writing down the theory) or (2) this is it. It is also possible that the waves propagate in a 3-dimensional subspace only, but the world has more dimensions and we have no access at all to the other dimensions, and notably not over electro-magnetism. Or that our access is so seldom and accidental, that we call those interferences "supernatural" and we do not give them any scientific credit.
Dear dr. Lakew,
Hilbert tried to banish intuition from geometry, and in his famous sixth problem he proposed to treat in the same manner, by means of axioms, those physical sciences in which already today mathematics plays an important part. I assume that his proposal applies to those physical theories, whose phenomenology is already well understood. In any case, if it had got through I would not expect to be able to grasp the physical meaning of coordinates – or geometric entities – intuitively. Thus your interesting question raises another one: is the phenomenology behind string theory well understood?
There is yet another issue. I think that the description of phenomena in space and time, which was eventually established in mechanics by Newton, has an origin different from Euclid's geometry. In fact mechanical geometry is not bound to ruler and collapsible compass, but allows to employ such ingenious mathematical instruments as the astrolabe. Why should mechanical geometry be consistent also with electromagnetic phenomena?
Mechanical geometry itself (for instance:
https://archive.org/details/mechanicalgeome00bcgoog)
is quite different from Lagrangian and Hamiltonian geometries. The latter aren't rooted in mathematical instruments, but rather pertain to algebra. In my opinion, if you accept those pictures, you should possibly look for an explanation of the hidden dimensions of space at the level of logic rather than at that of space and time.
Dear George,
Yes and the point is, how do we talk about them as physical reality if we are not observed and detected them in any form.
Dear James,
Thank you for your important links on how such a concept has settled in some people.
Dear Chris,
You put interesting points on what reality would be if the dimensions are higher - unpredictable and the inability not to be observed (computablity ) and in lower dimensions, the possibility of instability and vanishing behavior to oblivion. These are the points to be answered if indeed we can definitively say reality exists in lower and higher dimensions other than 3+1 dimension ( in the outskirts of dimensions 3+1).
Dear Mihai,
Indeed scientific theories developed are based on our intuitions and because of the limitations of our capacity to observe all things in nature, the theories developed my lack to describe existing but unknown behaviors of nature (you alluded them "supernatural") then we are yet on a long journey to know nature more.
Dear Sara,
The points you raised are cases to look seriously. First: Is string theory understood very well by those who promote it? Second, does string theory still exist in the mathematical world and should be treated as mathematical theory than describing laws of nature?
Jean-Pierre, just a language note if I may - you can't use 'precision' in English in that sense, that's a (not understandable) 'Gallicism' . Precision means 'accuracy' in English. The English for the French 'precision' in that sense is clarification, further detail, or stipulation, but here the better way to put your meaning across would be 'this being said ...'
Dear Jean-Pierre,
What I know is that physics deals with physical reality of nature, of matter and energy and the interplay between them and its goals are to establish truth of them - which are termed as intrinsic truth of reality. The models theoretical physics in particular and applied mathematics/applied sciences in general create are models of reality, not other models. It is from this perspective that I pose the question. You are correct on your point that creations of models are absolutely dependent on human understanding of nature itself, which seems we are knowing and understanding relatively a very small section of it.
Dear Christian,
Good perspective but I do not see cases where dimensionality is a scientific dispute, unless there are cases of reality of no dimensions, or same realities that are true in different dimensions. There are theories and properties that are extendable to higher dimensions, but with care and delicate conditions and the same thing with restrictions to lower dimensions, which all are by no means the same.
I have just two further remarks.
1. One should not mix the question about real dimensions of the world with different models of phase-spaces. For n bodies it is really easy to reach 6n dimensions for a purely mechanical phase-space. Unhappily, the mathematical formalisms leads to very fluid borderd between those two fundamentally different questions.
2. The "small" dimensions (say, up to 7) have some geometric peculiarities which are no more true in higher dimensions. To give only a classical example, in dim 2 one has infinitely many regular polytopes, in dim 3 exactly 5 platonic bodies, in dim 4 exactly 6, and starting with dim 5, always 3. Arguments similar to Morley's proof must be centered on the question: Which further special features have the 3 and 4-dimensional geometries (not necessarily euclidean) and which properties of the reality are connected.
In my view, a considerable phenomena for finding dimentions of space and what exist in space (also, what appears in space-time), is analyzing the interaction between graviton and photon.
The physical realities such as vacuum energy and virtual photon showed that the speed of light and visible particles isn’t the end of physical spaces. So, three physical spaces are considerable:
1-Real spacetime; everything moves with speed v< or =c in real spacetime and light speed is the highest speed in the real spacetime.
2-Virtual spacetime; it calls sub quantum energy (SQE) too and every particle such as virtual particle is explainable in the virtual spacetime. Every virtual particle moves with speed V(SQE), so that V(SQE)> or =c.
3-Non-obvious space (NOS); everything such as graviton isn’t directly (also indirectly) detectable in non-obvious space. Production of non-obvious space is sub quantum energies such as virtual photon, in fact gravitons convert to sub quantum energies and virtual photon is made up of sub quantum energies that explained its mechanism in this paper. Everything moves with speed V(G), so that V(G)> or =V(SQE) in non-obvious space.
According to above items by using Minkoweski formula, one can realize which dimentions are hidden and which are obvious. For more detail please see following articles:
https://www.researchgate.net/publication/270339919_Interactions_Between_Real_and_Virtual_Spacetimes?ev=prf_pub
https://www.researchgate.net/publication/264810425_Beyond_the_Modern_Physics_and_Cosmological_Equations?ev=prf_pub
Article Interactions Between Real and Virtual Spacetimes
Article Beyond the Modern Physics and Cosmological Equations
I agree with the spirit of the last paragraph of your question and think it is essential to link mathematical meaning to something that exists and thus retain a physically objective perspective linked to the current fundamentals of physics.
It may be worth considering that the hidden dimensions of space may not be hidden at all, but appear in our current fundamentals of physics as features that are proven to be true in 4 dimensional space, yet can be simplified, and/or more accurately formulated, if an alternative perspective is permitted. We just don’t usually associate such features with other dimensions!
For example, we could consider a dynamic perspective of the universe where all matter, i.e. every particle and every large body, each has a common constant velocity along some path in space (be it straight, curved or coiled). With an observer and object moving together along closely aligned paths, with a common constant velocity, then the object appears to the observer to be “at rest” even though both are moving in space with the common constant velocity. If the paths are not closely aligned, then the object will appear to have a relative velocity v4 (being our normal 4-dimensional relative velocity) with respect to the observer, dependent only on the angle subtended between their paths of common constant velocity. In this way, objects can have different relative velocities, although nothing changes along their respective paths with the common constant velocity. A great idea when thinking about conservation of energy.
The above example can then be compared to the classical physics view which permits objects to be “at rest” with respect to an observer but without necessarily defining any dynamic state of the observer in the universe, i.e. the local relative velocities between an observer and other objects are defined and used in classical physics without considering any overriding universal dynamics.
In the classical case, an object is deemed to have gained energy with increasing relative velocity, while in the case of the common constant velocity, the total energy remains constant and the relative velocity only alters the energy share between the potential and kinetic energies.
If we define the common constant velocity, as described above, to be a new “dimension” (a fifth dimension) then this dimension is “hidden” in the sense that we are not normally thinking in terms of a dynamic universe, with an overriding dynamic effect, over and above our classical perspective of physics. If for example, the complete Milky Way (including earth) is passing through space with the common constant velocity (ignoring for the moment any definition of the frame of reference), would we be aware of this sitting here on earth?
Jumping from a biggish object such as the “Milky Way” to a smallish object like an electron, we have Dirac’s comment in his Nobel Lecture (1933 - Schrödinger & Dirac - Theory of electrons and positrons): “The variables also give rise to some unexpected phenomena concerning the motion of the electron. These have been fully worked out by Schrödinger. It is found that an electron which seems to us to be moving slowly, must actually have a very high frequency oscillatory motion of small amplitude superimposed on the regular motion that appears to us. As a result of this oscillatory motion, the velocity of the electron at any time equals the velocity of light (“c”). This is a prediction which cannot be directly verified by experiment, since the frequency of the oscillatory motion is so high and its amplitude so small. But one must believe in this consequence of the theory, since other consequences of the theory which are inseparably bound up with this one, such as the law of scattering of light by an electron, are confirmed by experiment.” So the idea of an electron having a path with the velocity of light c may also be considered to be a “hidden” dimension of the type described in the above example.
The classical physics (Einstein) feature of mass changing with velocity disappears with the above 5-dimension idea and the variable mass aspect of classical physics can be related to the “missing” second velocity component v5 of a five dimension space where c2 = v42 + v52. One can switch between the 4-dimensional and 5-dimensional spaces and investigate the different perspectives, however the end result remains true to the fundamentals of physics. In this example the common constant velocity does have to be the speed of light c in order to comply with the current fundamentals of physics!
From your question, we have “….If their (the hidden dimensions) existence is very small (minimally small to the extent of not being observed), then unlike the usual coordinates and the usual derivatives, we might create other structural concepts in mathematics to incorporate such existences. But giving a mathematical meaning to something which does not exist is a mathematical paradox and loses it place in mathematics itself and therefore in reality…. “.So I have tried with this answer to outline an example where the “existence” of a fifth dimension results in changes that are very small, can still be related to the 4 dimensions of classical physics, the 5th dimension is “hidden” but has a significant effect on our perspective of physics and also retains a considerable degree of physical objectivity. This type of approach may be a safer and more rewarding way to explore the topic of hidden dimension(s)?
Dear dr. Jean-Pierre Magnot,
Hilbert disliked infinite regress. He meant that, if comprehension has already been achieved, it is possible to deal with physics as if it were mathematics. This possibly gets rid of progressive adjustments. In fact, a cobbled up mathematical theory doesn't provide a good start. However, that also prevents cases of fragmentary comprehension in physics, as you notice.
In physics there are a great many ways to try and grasp the world out there. As a physicist, I think that it is a matter of personal conviction whether to assume that the world is knowable in an absolute sense, or to rely only on phenomena that can be perceived by senses. As dr. Lakew points out, models are related to human understanding. Anyway, I suppose that they should be consistent at each step of understanding. In addition, which function do they have? For instance, should they be predictive? Should they just be like scaffolds? Or should they suggest how to get further?
I don't know how to assign some dimensions to “physical space” itself -- that is a matter of conviction -- and thus I think that their number should be linked to the function chosen for the appropriate model of it. Synthetic Euclidean geometry usually requests to attribute 3 inhomogeneous, or 4 homogeneous coordinates to space points. Algebraic geometry and geometric algebra allow to assign any number of dimensions, depending on a faithful description of dynamical systems. The criteria specified by dr. Prunescu are valuable.
Dear Christian,
my postation was not at all adressed to one of your papers. It was just because in the rich bibliography presented by Prof. James Peters some models were in fact phase-spaces. Of course phase-spaces are a strong instrument of research and they are not excluded from the question "How many dimensions the Universe really has?".
Models with more than one time-dimensions look for me a little bit too rich. They are better appropiate for modelling worlds with braching in decision events and occurring "parallel" universes, produced by choice 1 or choice 2. I agree that when you accept time as a dimension, it is very hard to keep reality and phase-spaces as different problems.
Dear Christian,
The abstract point of view of space and its dimension is tantamount to mathematical view and that has more mathematical pleasure than what the question asks - the real dimension of the physical world we live in. Indeed space is the dynamics and interactions of matters in it and you are saying this space is of course 3+1 dimensional. Then what higher dimensional physical objects can there be than the objects in this 3+1 space of reality, unless and otherwise we are talking about mathematical objects.
Dear Alan,
Very interesting view points and detailed analysis on how extra dimensions in the physical world might be seen from relativity of velocities, but how could differences from relative observations can be taken as actual truth of matters.
Christian,
" "Hidden" dimensions are at first sight pure mathematical objects, as by definition we can't see them, they are experimentally not accessible" . Therefore we can certainly say the claim made by string theory regarding such issues is purely a mathematical odyssey.
A few remarks to this thread’s question.
First of all – Matter (and any/every object in Matter and outside Matter) in our Universe is some informational structure, which is built/ organized – as that from all observations follow – by using a few logical rules that are “decoded” by humans as “Nature laws” (see https://www.researchgate.net/publication/273777630_The_Informational_Conception_and_Basic_Physics).
At that [rather probably] simplest structures can be built if are based/ use a binary logical elements, as that till now necessarily is used in computers. Or – Matter with a large probability is some large computer that consists of a huge number of comparatively independent automata that are united in a single system “Matter” by universal interaction – the gravity.
C. F. von Weizsäcker was the first, who put forward in 1950-54 years the hypothesis that in depth Matter is built basing on primary binary elements – the “UR theory” (or "the theory of Ur-alternatives" – what is in German "the theory of fundamental bits”]. And, at that, Weizsäcker showed that to base and evolve /change as a binary structure for Matter is necessary just to exist in a 3D space.
Besides – generally speaking Matter exists in 5D spacetime – having 3D space and 2D time coordinates. These temporal coordinates are the “coordinate time” coordinate, and the “true time” coordinate. All material objects, because of the energy conversation law, always move in different directions with 4D speeds (that are identical by the absolute value being always equal to the speed of light) in the 4D spacetime, which is Euclidian and has, as the temporal coordinate, the “coordinate time”.
At that all interactions of material objects happen always in the 3D space and in true time moments, independently on – what temporal coordinate an object occupies; or, since the coordinate time is “the time what clocks show” – independently on what the object’s clock show (see, for example, the “twin paradox”).
Thus all material objects always move along 5-th [true time] ct-axis with the speed of light; so, that for every objects their total 4D paths, including paths of its predeccors, are identical and equal to the integral of differentials ds: Int(ds)= cttrue, where ds = [dx2+dy2+dz2+(cttcoord)2]1/2.
There seems now isn’t some grounds to add to these 5 dimensions something else. However Matter is only an infinitesimal sub-Set of the absolutely fundamental and absolutely infinite “Information” Set, where all/every elements in the Set are constantly connected by some bonds, i.e. Matter is principally open system. So, in principle, now we cannot exclude some additional “dimensions”, but these dimesions rather possibly will have very little relations to the “string” theories.
Cheers
Article The Informational Conception and Basic Physics
The cause of confusion is probably the identification of the (mathematical) Linear Algebra to the (physical) concept of 'space'. We cannot be sure of what 'space' is, the only hypothesis is that it can be approximated by a Linear Space (LS), so the minimum number of independent vectors (basis) or the dimension of LS, has been attached to physical space as its 'dimension'.
Are we sure that physical reality follows that conevenient rule?
I doubt a lot, but it is not easy to prove it.
Christian,
me is sorry, of course , but neither English nor German are my native languages and so the phrase “theory of urs” (or “Ur-theory”) I translated as a “bit-theory”. Indeed the original version – “the theory of ur-alternatives”. Though this translation correctly relate to what von Weizsäcker developed. As to his theory – see, for example, a Holger Lyre paper http://arxiv.org/abs/quant-ph/0309183v1
(though in this paper seems too much of Lyre, but there are references on Weizsäcker)
On the other hand it seems that Weizsäcker and other (Lyre, etc) as “urs” considered fermions, when in the reality the urs are more fundamental logical elements (FLE) - see the RG link in my post above.
Cheers
"Dimension has to do with independency"
- yea, 4 dimensions in Matter’s spacetime relate to the fact that FLEs have [at least] 4 independent degree of freedom when the FLE changes its state.
What in Matter reveals as that the spacetime isn’t only Euclidian, it is “Cartesian”, where [c]t coordinate is orthogonal to any spatial line and, of course, to 3 spatial dimensions.
Thus a particles move in the 4D spacetime trough 4D trajectories – in 3D space by changing their spatial positions; when the motion along [c]t axis is the changes of their internal states.
Cheers
Dear all,
Im afraid I slightly disagree that the extra dimension are only due to mathematical basis, there are some physics behind. The problem of our manipulation is assumting universe and accordingly static space time, while everything is moving in our universe nothing static.
The question supposes that there are only geometries with definite dimension. In the proper Euclidean geometry the dimension is defined as a maximal number of linear independent vectors. Geometry is defined uniquelly by the world function. There are infinite number of constraints on the world function, in order that there are a definite maximal number of linear independent vectors and this number be the same in all points.
For instance, in the discrete space-time geometry, which is described by the world function \signad the definite dimension is not determined.
\sigmad =\sigmaM +\lambda2/2 sgn(\sigmaM)
Here \sigmaM is the world functiom of the geometry of Minkowski and \lambda is the minimal length of the discrete space-time geometry..
Dear Dejenie,
You ask “How can differences from relative observations be taken as actual truth of matters?” and your question suggests that we may be coming from different points of view about the state of theoretical physics today. The truth of many aspects of theoretical physics are for me not proven and yet they continue to be presented and discussed as truths throughout the media and by many members of ResearchGate. The following records my own point of view and my reaction associated with trying to find a better platform (i.e. a model or selection of theories) for my understanding of theoretical physics.
Previously, for my practical work in physics, I found it necessary to adopt a model of the physics applicable and use this as my technical platform for my work, as long as it worked in practice and could be proven to be true by experiment, i.e. by testing products designed and built on the basis of the technical platform used. This way forward proved to be a sound method, but I never asked if my technical platform could be taken as the truth of matters. If it didn’t work, I looked for another improved technical platform. This approach clearly can’t be used in theoretical physics and so I think we have to be even more careful about picking the “model” of physics we intend to use.
My test is simply that if the theory or model used is of the right type, then with time we can expect to improve the model. If we get it wrong, we can expect to end up looking at ever finer detail and doing experiments with ever diminishing returns. In my view we have been doing this in theoretical physics to an ever increasing degree for the past 80 years.
My research assumes that we are on the wrong track in some fields of theoretical physics and need to jump off the current platform and build another one, starting from the basis of the fundamentals of physics as it was around 1935. Otherwise I think young physicists of today may be writing the same type of comment as this one when they reach the end of their careers and I don’t want that to be the case!
Back to the original point of hidden dimensions: In my first answer to your question on hidden dimensions of space, I gave one example of how extra dimensions in the physical world might be seen from the perspective of relative velocities and, this one point of view, represents just a tiny starting point of a larger research project. As such, one piece of a jigsaw puzzle, can’t show the final picture and the final picture may still not be an adequate description of the truth of matters.
Background to my analysis showing how extra dimensions in the physical world might be seen: - The prime motivation for my research was to see if a detailed review of the experimentally proven physics of prominent physicists working in a Golden Age of Physics (around 1905 to 1935) could provide an alternative, more physically objective and unifying perspectives of their fundamentals of physics.
At the start of the research, I selected the key aspects of physics which I felt would ensure that the developing theory would relate to a more unified perspective of physics and this represented my target truth of matters. The research control used included – establishing the current fundamentals of physics for each specific field covered - ensuring compliance with new research perspectives – identifying the associated mathematical expressions – developing figures illustrating the mathematical expressions – and then coherently building on this data as the research progressed across many different fields of physics.
Establishing the fundamentals of physics for a specific field required revising the topic using previous text books and updating the content as necessary. This material was logged as part of the research because often new concepts challenged my understanding of the fundamentals of the associated physics. On occasions I had to find the papers written by the originating physicists and/or reading their Nobel lecture on specific topics, i.e. I didn’t quite believe or understand the text book content!
This revision process also highlighted many paradoxes to be found in the current fundamentals of classical physics. A positive aspect of my research was the way some paradoxes were resolved by new perspectives, along with the elimination of results going to infinity in specific cases.
Early in the research, new fields of physics raised issues contradicting earlier results and I had to review and alter previous theories to permit progress in the new field. Almost always, the problem was related to paradigms of physics which I had assumed to be true, but which in fact were not part of the fundamentals of physics. In this way it was possible to refine the overall theory so that it worked for all the fields of physics covered.
Encouraging moments occurred associated with unexpected results. The hidden 5th dimension described in my first answer, gave considerable insight to Einstein’s variable mass (in 4-dimensional space) which can be related in turn to the second velocity component v5 of a five dimensional space. The figures developed across the different fields of physics built on each other, without conflict, and it was only towards the end of this work that I discovered Minkowski’s four dimension space time expression ds2 = dx2 + dy2 + dz2 – c2 dt2, appeared as an integral part of the figure of a 5-dimensional local space. These results, along with many other, developed in total a feel for the truth of matters of the developing theory!
Going Forward: - My own research was done to answer several questions coming from my own physics experience and because I was not seeing answers coming from anywhere else. The logging of the results (Physics in 5 Dimensions) was necessary in order to keep a clear view of the new concepts and hypotheses developed and their relationship with the fundamentals of physics. This work has given me a new platform from which to judge other theories. I continue to look for improvements and a path to a more unified theory.
My main aim now is to support changes of direction in theoretical physics and to help where possible others looking to advance physics towards a unified, or at least a more unified theory of physics.
When looking for change, we should also have an idea where this change will come from and what it will look like. Well, in my view, to find a more unified theory of physics, I expect existing theories to be compared and developed, firstly on the basis of identifying common areas, and secondly by exploring other areas offering unification in specific cases, in order to see if they can be repeated and/or developed into the other theories.
Unfortunately, I don’t have the slightest idea how this can be achieved. ResearchGate is one hope but I don’t see how we can work together without having other resources. I don’t want to see RG just as a talking shop, with the result that young physicists, starting their carrier now, will still find just a talking shop without change in another 80 years!!!!!!!!
I hope this answer to your question … how can differences from relative observations be taken as actual truth of matters ….. offers a point of view that you and others can relate to?
In any Science to develop a theory one needs to start from concepts and first principles, which describe, in general terms, properties of physical objects and phenomena which can be easily grasped and understood. Second comes the mathematical representation of these concepts and principles. They must be consistent with the theory, but can also be adjusted to the problem which is considered. Notably one does not use the same tools at different scales, and for continuous or discontinuous processes. The tools are useful to extend the understanding of the concepts, as a framework to format the measures, and for computation, but they do not make the theory.
In Physics it is assumed that there is a container, a universe, in which all physical phenomena occur. So we need a theory of Geometry, which is basically a theory about the measure of location, in space and time, and the rates of change of physical quantities. General Relativity provides a consistent and comprehensive theory for this geometry, with 4 dimensions. Particles and material objects show general properties such as momenta, which require a theory of Kinematics, which is related but distinct from the Geometry. And force fields, with other properties, require additional theories. The idea to fuse everything in a geometric model is wrong. First it brings only confusion (it is stricking that we speak of "hidden" dimensions : a theory does not seem fancy if it does not have some mystery in it). Second it is not necessary. Mathematicians have developped the theory of fiber bundles, which provide all the tools, including the way do deal with additional parameters and structure above that of the Geometry. The gauge theories are a good example of what can be done to represent kinematics and fields, without the need of additional geometric dimensions.
Could it be that, eventually, Geometry will merge with the other theories in a "theory of everything" ? Perhaps, the goal is not without merit, but we are far away from it, and meanwhile, why make the things, that we do not understand yet, more difficult ? Perhaps because it is fashionable and provides some playground for scientists, but is it worth such genuine interest ?
Dear Alan,
Interesting analysis on the whole cosmos of physics and its bridgeable chasms. You said, "My main aim now is to support changes of direction in theoretical physics and to help where possible others looking to advance physics towards a unified, or at least a more unified theory of physics" and you mentioned the necessity of change to create a unified theory so that inconsistencies and paradoxes are either eliminated or minimized.
I assume the problems and solution might lie on building axiomatic structures like mathematics for consistency as David Hilbert pointed out in his lecture series of foundations of physics.
I read answers and I realized that a hidden agreement is popular:
*Dimension has to do with the adoption of a suitable mathematical construction ('Geometry') and not after establishing experiments.
I think that, instead of competing on the most beautiful theory, we should focus on what exactly do we observe...
Dear Alan
I think the problem of theoretical physics is we have two groups, the first one is the main stream group and the second is the theories out of main stream. The problem of first group is taking the postulates of old theories as facts and keep building their developements on them. While the second group is missing colaboration and funding and support that any theory they suggest are forced by strong opposition from the first group.
Physical reality has its own usage of the notions of space and time. Mathematicians also have their own notions of spaces and progression. Physicists try to explain their observations of physical reality by constructing maps between what mathematicians offer and their observations of space-like and progression like structures and phenomena.
I order to bring order into this process, two ways are possible. One is to start from an axiomatic foundation that does not yet contain notions of space and progression, but that leads to a structure in which space and progression occur as features. The other way is to use some examples that mathematics provide and check whether the corresponding observations fit onto these concepts.
For example, the axiomatic approach can start with the axioms that define an orthomodular lattice. That construct does not yet contain number systems, thus it also does not support notions such as space and time that need numbers to describe these notions. The orthomodular lattice leads to a mathematical structure that acts as a structured storage place for numerical data. That structure is mathematically known as a separable Hilbert space. It can cope with number systems that are division rings. Only three suitable division rings exist: the quaternions, the complex numbers and the real numbers. Quaternions can store dynamic geometrical data that have an Euclidean signature. Thus, this axiomatic foundation leads quickly to an applicable notion of space and progression.
Contemporary physics uses a notion of space and time that differs from the quaternionic template. For example Maxwell equations use coordinate time and space in order to describe the behavior of fields. This template is derived from observations that concerned relativistic behavior of subjects. A coordinate time step can be compared to a quaternionic distance in the quaternionic template of geometric data.
Now which of the two templates is correct? The answer is that both templates are correct, but ask for different interpretations. The interpretation that contemporary physics uses has as consequence that we measure very long distances in light years. Thus, in progression steps that information from the observed event takes to reach the observer. It is a mixture of pure space and pure progression.
The axiomatic approach restricts the choice of space dimensions to 1, 2 or 4, or more detailed in 1, 1+1 and 1+3. One dimension is occupied by progression. Space shares one dimension with progression or it uses 1 or three dimensions. The Hilbert space excludes other choices.
Quantum physical theories use the fact that Hilbert spaces can store dynamic geometric data and corresponding continuums in the eigenspaces of dedicated operators. These structures can directly handle quaternionic data and continuums. This may indicate a preference of physical reality for using quaternion based space progression models.
http://arxiv.org/abs/1101.5690
Dear Jean,
I think the whole enterprise of science and scientific research are partly playgrounds for that activity but of a higher purpose. As far as my understanding is concerned, physics in most cases does not create things/theories and search for models to fit some how but rather observe and investigate things to describe observed behaviors (that is from intuition to real discovery via proof) for a physical phenomena, however complicated or simple the descriptions are and hence I will say, complexity or simplicity is the demand of the structure not a style or will of a researcher.
Dear Dejenie,
Science needs concepts and first principles, in order to organize our theories in rationale narrative which can be easily understood and taught. It uses also a formalism, which is not necessarily mathematical : chemistry uses the atomic representation, biology uses the ADN, both very efficiently. The purpose of this formalism is to compute the results of experiments, and to format the collection of data. It must give a faithful and efficient representation of the concepts. It can give an insight about some new properties, and improve our understanding of physical phenomena, but it is still a set of tools. The same kind of phenomena can be represented by different models : the motion of bodies is represented in Mechanics, and when there many similar bodies we use Thermodynamics. The basic concepts are the same but the tools are adjusted for efficiency.
The concepts of space and time are at the root of physics. It has not been easy to find a clear and efficient model to represent them, but we have it with Relativity. And the Geometry of Relativity proceeds from our most basic experience : we need 4 coordinates to represent a location, time has special properties, there is a causal structure, material bodies must travel along world lines. The fact that, in various fields of physics, we need more parameters to represent phenomena, is not a sufficient reason to reconsider the concepts of space and time. The fact that most of the phenomena studied at the atomic or subatomic levels does not authorize us to state that space and time are discontinuous. The quest for hidden dimensions proceeds from the inadequate use of mathematical tools. Before giving up the concepts of space and time it would be better to look for adequate and efficient mathematical tools, all the more so that they exist, to represent the phenomena which are considered.
Quantum physics uses Hilbert spaces in order to store physical data in the form of numbers or continuums into the eigenspaces of operators that reside in these spaces. It is possible to store all data about universe in just two Hilbert spaces. One is a separable Hilbert space and it stores all discrete numerical data. The other is a Gelfand triple, which is a non-separable Hilbert space. All infinite dimensional separable Hilbert spaces own a companion Gelfand triple. The Gelfand triple can store continuums in the eigenspaces of corresponding operators. I this way, these Hilbert spaces are nothing more and nothing less than structured storage media. Physics describes the embedding of the separable Hilbert space into its non-separable Hilbert space as an ongoing process. The past is left untouched. The future is considered to be yet unknown. On the rim between history and future operate controlling mechanisms that feed the separable Hilbert space with discrete data that contain new locations of discrete objects. These mechanisms are not mentioned by any current physical theory. Without their activity nothing would happen in universe.
http://vixra.org/abs/1511.0074
This also throws new light on what the start of universe could have been. Not a Big Bang but a condition in which the controlling mechanisms had not yet exploited any action. In that condition the field that now describes our deformed living space would resemble the parameter space of the function that describes this field. The parameter space is a flat continuum and is formed by a quaternionic number system.
http://vixra.org/abs/1511.0266
In my opinion this interesting thread is debating two opposite trends. On the one hand there is a quest for descriptions based on geometry; on the other hand there is a concern about phenomena. Geometry has been put into service for modeling physics, especially field theories – starting from the Faraday-Maxwell one. Some models appeal to “physical intuition”, others have a fairly abstract theoretical framework. It is open to question whether geometry can also be descriptive. However, no geometrical theory can really avail of any measure of time. For example, to me ict in Minkowski's space seems to be a variable rather than a physical quantity.
Of course, some doubts can arise when speaking of gravitational fields. Yet, to me it seems difficult to decide what physical clock should be adopted when extending the laws of gravitation beyond the Earth:
https://en.wikipedia.org/wiki/Equation_of_time
@Dejenie A. Lakew: "... to generate 9 dimensions of space with new six extra invisible dimensions that are curled to be seen"
you talk about R^3xT^6. the torus T is like R a trivial object, locally isomorphic, and may be "small" with respect R, or "we" are small against the torus: what's the difference? Eventually we live in T^4 time space.
My privat space time is R(4)xR(4), a complete symmetric space time with SO(4,4) as symmetry, represented in pseudo-octonionic 8-tupels: space-time 8-tupel, baryonic 8-tupel and leptonic 8-tupel, respectively, are automorphic. In other words: we have maximal geometrico-physical symmetry. As a result: iso-spin = time spin.
dear Amo, space time is the direct product of two elliptic (=compact) spaces:
""an elliptic space may be obtained from two solid tori by identification their boundaries" n-dimensional tori are considered as topogically trivial (Ch.Jung)
H.Busemann, P.J.Kelly: Projective Geometry and Projective Metrics. Acad. Press 1953
dear Amo,
space time as double-elliptic (projective) space covers "everything", SRT (SO(4,4) covers SO(3.1)) as well as GRT: the elliptic space is a compact (orientable) manifold and one may start computing connections and curvature tensors. The pseudo-octonionic 8-tupel looks like a pair of Dirac-4-vectors: besides being a point in space time it may be interpreted as nucleonic or leptonic octet. Particle symmetry equals space time symmetry, because of the standard triality in pseudo octonions (the same as for octonions). Then: SO(4,4) is a 28 dimensional Lie group and the 28 generators are considered as representing 28 mesons.
one may start in real 8-space with metric (- - - -;+ + + +).
And, remember, there are FIVE anticommting 4x4 alpha matrices, so you can write the Dirac equation at once in SO(3,2) or SO(4,1) symmetry!
The free Maxwell Langrangian density is L = E² - B², and carries NATURALLY SO(3,3) ~ Sl(4,R) symmetry. Sl(4,R) is the symmetry of P(3), projectiv 3-space (homgeneous nonzero 4-tuples). The above extended Dirac equation has Sl(4R) symmetry instead of standard Dirac symmetry: SU(2,2) ~ SO(4,2) - the conformal group. From here it is not very far to a global 4,4 symmetry.
have a nice day
Tony
“…As a result: iso-spin = time spin. …”
- here seems would be useful to define – what is the time? and further to explain – why the iso-spin = just the “time spin”…
Cheers
@Sergey Shevchenko ·
"- here seems would be useful to define – what is the time? and further to explain – why the iso-spin = just the “time spin”…"
Time and space are observables and measured (SI: seconds & meters) by clocks and sticks. They take place in E(1)xE(3) and later in Minkowski 4-space.
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SO(4,4) is the automorphism group of the pseudo octonions. It is a rank 4 Lie group and some of the invariant subspaces of the 28 dimensional Lie algebra may be classified by the eigenstates of its Cartan subalgebra. The three basic representations act on real 8-tupels, connected under an exterior automorphism, visible in the symmetry of its Dynkin diagram. Now, one octet is identified with the projective 4,4 time-position space: two homogeneous 4-tupels. The “origin” has coordinates (1;000|000;1). In the neighborhood of the origin the tangentspace is standard E(3)xE(3), because elliptic space is locally spherical which is locally flat. The first quartet may represent projective time space and the second the position space, respectively. An event is given by fixing a pair of homogeneous (real) quartets. Time developes on a Jordan curve, a 1-dimensional manifold in P(3), similar time in Minkowsky space. “Interaction” means, two events meat at the same octet. The tangent on the time-Jordan curve is connected with spatial R(3) to perform the standard Lorentz transformation, f.i. (1;t00|xyz;1); time tangent in 1 direction. Roughly spoken, there is an overlapping of three –standard – Lorentz transformations, one in each time direction. It is standard to compute the elliptic line element and write down Einsteins field eqations, in this double elliptic (compact) universe.
The other two octets may be identifed as representing eight nucleons or eight leptons, respectively. The Cartan algebra’s eigenvalues ±1 may be named: baryonic number, isospin, spin, magnetic moment, and similar for the leptonic octet (an electron/positron Dirac pair). The correct spin/magn. moment relations for proton/neutron come as a result!!! There is still the analog 4,4 decomposition as in the space time world. The (spatial) rotation in the spin states – standard su(2) real 8-dimensional reducible representation - finds its time analog in the isospin pn rotation, it is the same Lie-algebra element because of this triality automorphism: Strong interaction acts like a rotation in time space.
Next we identify the 28 generators with the interaction mediating mesons. AN UNVERSAL PICTURE shows up, even after implementing “rotations” far away off the origin. Here we gave a sketch of only ONE decomposition of SO(4,4), especially containing 3 Lorentz groups. A different decomposition would be SO(2)xSO(2)xSO(2)xSO(2), as an analog to SU(5)xSU(5)xSU(5) – standard model. This may be considered as a “quarkish” decompostion, with a forth quark pair: “fire&ice”. Here, there exist no Lorentz subgroup (commuting with this 4-fold SO(2)) which explaines why these quarks are confined.
Have a nice day
We can never separate the physical existence from its space. In fact space is a part of physical existence. Also, time and physical existence are not independent. Ball is a physical existence; it is made up of some molecules with their spaces at t (time relative to other clock). Ball is a clock as the same as other physical existences. There are many atoms in the structure of ball, how can we prevent movement of subatomic particle in the ball? Never. Generally, mass (or energy), space, motion and time are intertwined and inseparable from each other.
The generalized Stokes theorem has some deep secrets that have astonishing consequences. I think that the exterior derivative that was carefully crafted by influential mathematicians in order to be independent of the selected parameter space MUST depend on the ordering that is selected for this parameter space. This comes to the front when multiple parameter spaces play a role. The electric charge of elementary particles is quite probably related to this effect.
https://www.researchgate.net/post/Has_anyone_applied_Stokes_generalized_theorems_to_quaternionic_manifolds
@Anton Schober
“…Time and space are observables and measured (SI: seconds & meters) by clocks and sticks. They take place in E(1)xE(3) and later in Minkowski 4-space…”
- the time and the space (more correct – temporal and spatial intervals between events and material objects) are indeed observables and can be measured by an observer by using clocks and sticks, but only if this observer understands – what are the time and the space.
In the reality the time and the space are fundamental Rules/ possibilities, as the possibilities they constitute 4D [5D] Euclidian (“Cartesian”) “empty container”, i.e. 4D [5D] Euclidian (“Cartesian”) spacetime. All of them – the time, the space and the spacetime are absolute and cannot be impacted/transformed by any material object. At that all / every material objects move in the (5)4D spacetime with the speed of light (abs. val) in different directions having unique, in certain sense (i.e., if don’t consider 4D translations), 4D coordinates in the spacetime.
Thus if a material object is at rest relating to the 3D space, it moves along the t-axis only, besides if there are, say, a pair of such objects, the spatial interval between them indeed correctly relates to their real coordinates in the spacetime; besides, a stick, if it is at spatial rest indeed measures the distances in the spacetime.
At that, measuring by such stick a distance between points, say, A and B, and, if an object moved through this distance, the corresponding temporal interval is measured by “at rest clock”, then an observer obtains the absolute spatial speed of the object; further (s)he can apply the Pythagoras theorem and calculate the real temporal speed of the object and so – obtain real 4D coordinates of this [moving] object.
That’s all.
Since till now the absolute speed, say, of Earth is unknown (though this speed can be measured, see https://www.researchgate.net/publication/259463954_To_measure_the_absolute_speed_is_possible ), all clocks and sticks measure only relative values of temporal and spatial intervals between different material objects, which differ from real spacetime values. Or – till now neither the space, nor the time are indeed “observables”.
Besides, again, the real Matter’s spacetime is an Euclidian manifold, when Minkowski and pseudo Riemannian spaces are no more then some mathematical models that sometimes are useful at solving physical problems. As well as the Lorentz transformations aren’t valid in all physical situations. So, for example, a notion that some physical model is consistent with the LT doesn’t guarantee that this model is true…
Cheers
Article Measurement of the absolute speed is possible?
What time and space is depends on your model of physical reality. Several choices are possible and you must differentiate between parameter spaces and the deformable physical space, which is the dynamic continuum in which we live. That continuum can be represented by a multidimensional function that uses a multidimensional flat parameter space. A quaternionic function and a quaternionic parameter space will suit, but that is not the choice that current physical theories have made. Stimulated by the Maxwell equations and by the common interpretation of what information carriers are, the leading physicists have chosen for a model that has a Minkowski signature and uses coordinate time in order to indicate the progression of observed phenomena. It is a choice and not a very lucky one, because the Minkowski signature makes this model unnecessary complicated.
An alternative choice is the quaternionic space progression model that uses quaternionic functions in order to describe the manifolds that represent fields. One of those fields is our living space. This manifold does not change by the way that it is described. However, not so much the space part, but instead progression is treated different in the two descriptions. In the quaternionic model a coordinate time step corresponds to a small quaternionic distance. A proper time step corresponds to a pure progression step. Pythagoras relates the proper time step, the space step and the coordinate time step. The coordinate time step figures on the hypotenuse. Quaternionic distance can be used as the scalar part and the imaginary part of quaternions can be used as the spatial part of dynamic geometric data. It is an ugly model, but it is possible and it is applied by most physicists.
Hilbert spaces can directly cope with quaternions and quaternionic functions. They cannot cope directly with geometric data that have a Minkowski signature. Thus in order to use Hilbert spaces together with Minkowski based geometric data, everything must first be dismantled into real numbers before Hilbert spaces can handle them.
It is not very smart to start rewriting physics in a quaternionic space-progression model, but you can at least try to investigate how the lowest levels will function in a quaternionic format. It will enforce you to dive deep into the differences between the current model with the Minkowski signature and the quaternionic model with its Euclidean signature.
I have taken that dive, because since my retirement I have sufficient time and I am curious to see the results. I have discovered several interesting facts and I designed new methods for analyzing Hilbert spaces and spaces that can be stored in these Hilbert spaces. It improved my insight in the foundations of physical reality. Thus, without hesitation I can advice you to take a similar trip. My travel story is contained in the link below. If you want to use the formulas, then you might be interested in the MS Word version of that paper.
If the 100 page paper is too long for you, then you may be interested in the excerpts that appear on my e-print library.
http://vixra.org/abs/1511.0074
http://www.e-physics.eu/TheGeneralizedStokesTheorem.docx
http://vixra.org/author/j_a_j_van_leunen
@Sergey Shevchenko
your business is philosophy and not physics. You ask the Kant'ian questions about the absolute and the thing in its essential(?) (=das ding an sich german). I'm performing geometry with its standard axioms: there are points, there are lines. two point define a line, two lines meet in a point. there is a minimum of 4 noncollinear points (=axioms of a projective plane). there a many realizations of this axiomatic system, (plane over the reals, the complex numbers, the quaternions, the Cayley numbers and many more ...) one includes the Euclidean plane. As a physicist I ask, are there laws, "equations", reflecting the "symmetries" of a certain geometry? Or, what geometries exist being locally Minkowskian? The physicist's task is simple: measure your observables and put them into a "law".
String theory is strong about adding dimensions, but this appears not to offer the wanted (testable) functionality. So pure mathematical approaches can easily lead into unwanted directions. The remedy is to start with one or more solid foundations on which everything can be built. Such foundations exist. Physical reality uses them. The trick is the discovery of these foundations. In my opinions at least a few of these foundations were already discovered by humans long time ago. However, the tendency in physics is not to use these foundations in order to guide the development of its models, but instead to rely on what you can observe and test by experiments. That attitude often guides in the wrong direction. Current physics is loaded with examples of such false directions.
Personally I use the orthomodular lattice as the most important foundation. It immediately leads to Hilbert spaces as the next level in the model development. The Hilbert spaces involve number systems that can represent dynamic geometric data. This is a promising development path that goes together with sensible restrictions of what is possible and what cannot be used.
http://arxiv.org/abs/1101.5690
@Christian Baumgarten
everybody implies his own „philosophical system”. Most of us just don’t think and incorporate the standard system of their group, family, nation, church … Eventually we physicists should accept the validity of plain logig: how to built an axiomatic system: 1st: existence of what is called “objects”. The best examples we find in mathematics: Topology: there are “open sets”. Or: projective plane: there are “points”, there are “lines”. 2nd: define relations between these objects: the conjunction of open sets is open. Two points lie on a line, two lines meet in a point. 3rd: find a model that this system exists: here: set theory and projective plane. Note: it is IRRELEVANT, what these “objects” are.
In physics you better choose materialism: there is space, there is time, there is matter. All undefined objects!!! I don’t need Kant’s existence of absolute space (Idealism). Eventually you build a space-time model, why not a 21 dimensional string universe. Here in my room I take Euklidean 3 space and for time the clock on the wall. Or you prefer solipsism: there exists only one thought, of course, this is MY tought. “everything” exists only in my mind. This is a perfect philosophy (Husserl). Next I follow Wittgenstein: everything what you can say can be said clear (simple???), and about objects you cannot speak clearly you have to be silent (My own translation of this german text). As a consequence: nothing is “complicated”, “difficult”, in physics. You speak in nebulous phrases if you did not really understand the problem. Today’s physics is back in the middle ages: confined quarks, dark matter, dark energy, multiverses, big bang, and much more: you have to BELIEVE on those things. The great authorities give the direction: we understand the world(sic!!!). One guy said a few decades ago: in these formulas I see GOD’s own writing!!! Today’s physics is celebrated like a religion.
It seems here would be worthwhile to touch the philosophy.
“@Sergey Shevchenko
your business is philosophy and not physics. You ask the Kant'ian questions…”
– that isn’t, in certain sense, so – if the talking here relates to the mainstream philosophy. The mainstream appeared and existed first of all as attempts to solve the main/ basic ontological philosophical problem – what was /is the first – Matter or something non-material - “the idea” (Gods, Spirits, etc.) and this problem is mentioned even here.
The next main problem in the mainstream is epistemological – to what extent humans’ observations and inferences that are based on the observations are adequate to the realty.
The first problem was solved by Kant more then 200 years ago: he proved that this problem has no solution – it is impossible to prove existence/ non-existence of God [idea, etc.]
The epistemology of anything evidently depends on the first problem solution and so epistemological problems cannot be solved in the mainstream also. Thus after Kant an existence of philosophy lost sense, but it remained to exist and exists till now (?).
Note, that any indeed new information about something external to human’s consciousness humans can obtain only experimentally; if an observer finds at an experiment some repeating outcomes (s)he can obtain some “Nature laws” – i.e. to formulate some postulates, and further basing on these postulates, to build some formal (usually mathematical) tools, creating a theory.
But any postulates (outside mathematics, which is an “internal” product of the consciousness) are empirical and so cannot be proved – any experimental outcome cannot be a proof, experiments allow for only a testing of a theory.
For above follows that any human’s theory about Matter is no more then a religion, it is possible only to believe that, for example, Newton gravity low is as it is, moreover, there is no grounds to think that existent gravity will not disappear in next time moment.
The mainstream philosophy is, of course, nothing more then a religion also, but it differs from natural sciences principally – if these sciences are based on non-provable but testable initial suggestions, any philosophical doctrine is based on suggestions that are non-provable and non-testable. Just therefore the mainstream philosphy exists as a huge number of “philosophical doctrines” (seems more then number of religious sects on Earth), where some prophets claim that just her/his doctrine is true, and other – not. So some references on some philosophical claims as on something that confirm/ reject some physical inference seems as something not too serious.
Any “philosophical” problems become be resolvable, or at least can be reasonably analysed only in framework of the “the Information as Absolute” conception https://www.researchgate.net/publication/260930711_the_Information_as_Absolute (or http://viXra.org/abs/1402.0173 ).
When this conception is based on the rigorous proof that all what exists in this Universe and outside is/are some informational patterns that are elements of the absolutely fundamental and absolutely infinite “Information” Set.
In the conception Meta-mainstream -philosophical notions “Matter”, “Consciousness”, “Space”, “Time”, etc. can be (and are – see the link) properly defined; so, for example, the principal epistemological problem disappears – there is nothing surprising if some consciousness correctly decode some external information.
But some non-principal problems remain, in this discussion that is the problem when some physicists think that all what exists in mathematics exists also in Matter/ physics. When mathematics is only a tool…
Cheers
Article the Information as Absolute
@Sergey Shevchenko
"when some physicists think that all what exists in mathematics exists also in Matter/ physics"
eventually you should stress a bit your fantasy: You may doubt the existence of matter, or physics or whatever. We know that people think so since more than 2.500 years. (Plato's cave).On the other hand, for sure, mathematics exists! It exists without humans, even without a (perhaps existing) universe. Math is a tru PARALLEL UNIVERSE!!!I Seriously I recommend for you solipsism! This should make you really happy. We "normal" physicists are satisfied to note that the sun rises every morning at the calculated time and that our planes fly.
On the other hand you are a bit old fashion. There is a bunch of exiting new philosophy around. I personally prefer DERRIDA, with his DECONSTRUCTION. Exactly this I did above with your last treat!
have a nice day.
Tony, simple physicist
Hi Christian, think positive! My last "enlightenment" was due chinese philosophy, only a few days ago: I learned, that a life after dead is INDEPENDEND of the existence of god! This would be quite a shock for the godbelievers if we all meet in eternity and all their believe in god was for nothing!
I’m not surprise that this wonderful question is discussed here by the RG-ers. I’m surprised that a folk locus (= "ordinary", "magic" or "saint" space according to the folklore narrators) has always “the hidden dimensions” caused by space/time compression, vertical or horizontal changes, "holes", change of intrinsic quality, capability for transcendence and so on. How it was possible for narrators to invent them without empirical ("who did see them?") or theoretical ("who did explain them") foundations...
dear Arno, how about Satre? 1905 - 1980. Not only an atheist, materialist, even KOMMUNIST! Go ahead and "falsify" him. By the way, it is an easy task to construct a logical consistent philosophy. It is just an axiomatic concept and if it is logical correct nothing will be "falsified". In your case you just dislike "atheistic materialism". How about dialectic materialism, historical materialism? For you I recommend Tommaso d'Aquino, 1225 - 1274, the leading scholastic christian (till TODAY) philosopher of the middle age. I have much fun with those neothomists in the 21st century. He fits perfect for believers in dark matter, dark energy, and the famous GOD'S PARTICLE!
It' s always a pleasure!
Tony
dear Olga, we all (mostly all!) agree that space time is locally Euklidean or Minkowski.. Next we study ALL geometries which are locally E or M, an infinite set. F.i., assume an infinity of dimensions and you get these multiverses, take split flat/split toroidal, then: string! It's just fun, like this family of "standard-models"
dear Amo, are you sure you talk about SARTRE?
As far as he is concerned, he was awarded the 1964 Nobel Prize in Literature. His philosophy, called NIHILISM, is essential for physicists believing in black holes and big bang, because inside black holes and before big bang is NOTHING and this is it was SARTRE is explaining us long before physicist even thought about those exciting news. Eventually you may explain to me deistic philosophy before big bang an inside black holes.
I assume, you believe in "essence precedes existence". Your problem, you can't discuss both possibilities like a rational human: only heaven or hell: tertium non datur.is a bit simple minded. Even "atheist materialists" may believe in the existence of "nonphysical abstract objects" f.i. in mathematics.
your lack on elementary logic is astonishing: Every philosophy which deserves the name "philosophy" is logically consistent. Every philosophy can EASILY be "falsified" if you put the norms of a different philosophy on it It is babyish for an atheist to "falsify" Tommaso d'Aquino, and it is a shame for a Karl Popper, to vaste his energy on such a primitive task(?). Try to perform philosophy by studying ALL philosophies without putting a scale from 1 to 10 on them. Then follow Sokrates: I know that I know nothing. This makes us nihilists happy.
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ps.: did Popper falsify Sokrates too?
It seems that here appeared a next mainstream-philosophical discussion; though – see the SS post on the 7-th page – in the mainstream there is no solution of the problem – who are right: those who claim that something non-material created Matter, or Matter appeared by some “material” cause (“singular fluctuation”); or Matter existed always.
Even in the “the Information as Absolute” conception this problem remains non-answered, though in the conception becomes be possible to obtain the clear definition of the notions “Matter” and to differ material and non-material objects in our Unoverse.
So any atheist is only a true believer in that God doesn’t exist and so by any means (s)he doesn’t differ in this case from any religious human, who is a true believer that God exist.
Besides here a next mainstream-philosophical example occurred – that relates to the epistemological problem of truth of theories, that was “solved” by K. Popper with using an approach “falsification”; when in the reality all what is necessary for a theory to be true is a few criteria: the theory must be logically consistent and adequate to the reality.
What means – from the theory must not follow illogical material situations and it must be in consistence with experimental outcomes. The classical example – from the special relativity evidently follows illogical inference (the Dingle problem), what further results in evidently non-adequate “relativistic effects” – “time dilation” , “space contraction”, etc. But K. Popper related to the relativity theories with a great respect…
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However, it seems that would be worthwhile to return to the thread’s topic. So:
“Dear Sergey, isn't time a sequence of spaces? ”
- this question is, in certain sense, uncertain – what are here “spaces”? – for example the “Minkowski spacetime” usually is called as the “Minkowski space”, though it contains “time”.
When we should differ notions “space” and “time” – they relate to principally different phenomena. “Space” is the Rule / possibility, which allows an existence of fixed information and establishes that between fixed informational pattern must be a non-zero “spatial interval”. “Time” is the Rule / possibility, which allows an existence of changed information and establishes that between fixed informational pattern must be a non-zero “temporal interval”.
So the time is, first of all, the possibility (as the component of [5] 4D spacetime, it isn’t any sequence of anything; though any sequence exists in the “time-possibility”.
At that, besides, the notion “a Change” – and so the notion “Time” are logically self-inconsistent, logically there cannot be changing objects, and this problem has no satisfactory solution, including in the informational conception. Though it seems reasonable to suggest that the rule, which works in limited systems, for example – in Matter that to make some change is necessary for the changing object on some level to be uncertain (QM), and further – the changes happen as some finite steps (quanta) - works in the “Information” Set also. Moreover, it seems that in Matter there are fundamental steps that are, rather probably, equal to the Planck space and [c]Planck time; when Matter’s evolution is the sequence of a movie’s of Planck time pictures that develop along the true time axis.
More – see the links in the SS posts above.
Cheers
Why not analyze what a simple mathematical space-progression model learns?
http://www.e-physics.eu/TheGeneralizedStokesTheorem.pdf
Arno,
Photons show behavior that is not explained by Maxwell equations. The wave equation is not a direct corollary of the Maxwell equations. A gauge must be added in order to be able to derive the wave equation. At least two second order partial differential equations exist that deliver solutions, which can represent photons. Waves cannot travel billions of light years and can then still be detected by a suitable (photon) detector. Distant Galaxies are visible via powerful telescopes. Strings of shape keeping fronts can represent photons. They are NOT waves!
http://vixra.org/abs/1506.0111
@Hans van Leunen::for free fields:
with L~E²-B² you get rot E = -d/dt B and rot H = d/dt D, and from this the wave equation for orthogonal E and B. No gauge necessary. The vectorpotential A is not an observable. You dislike it? Don't take it!
Arno
It is possible to derive the quaternionic differential equations from the structure of quaternions and quaternionic functions.
How are Maxwell equations derived? Derived from what? From the structure of spacetime? How is that defined?
Coordinate time comes close to the notion of quaternionic distance and proper time comes close to the real part of quaternions, but those facts do not deliver the Maxwell equations.
Quaternionic differential calculus supports two second order partial differential equations that have homogeneous versions. One of these two can be split into two quaternionic first order partial differential equations. It does not support waves in its set of solutions, but it supports shape keeping fronts as solutions. The other supports waves in its set of solutions, It also supports shape keeping fronts in its set of solutions. It cannot be split into quaternionic first order partial differential equations. It uses the quaternionic equivalent of d'Alembert's operator.
The quaternionic nabla operator is a multiplier. This makes is easily applicable. The quaternionic equivalent of d'Alembert's operator works on all scalar functions and on all vector functions, thus why shouldn't it work on E and B? It is a property of the operator and not a property of the fields. They only need to be double differentiable.
Dirac tried to split d'Alembert's operator into first order partial differential equations, but that can only be done by using the Dirac version of the nabla operator. It is not a quaternionic operator. It turns quaternionic functions into biquaternionic functions.
http://vixra.org/abs/1505.0149
Dear Hans
At the time of Maxwell, physicists (such as Maxwell) had believed that the light is a wave.
Also, Maxwell was written his equation in absolute reference ether,
Photon's concept belong to relativity era that special relativity was proposed in which
the laws of physics are the same in all inertial frame.
Quaternionic differential calculus has the advantage that it offers a self-consistent, pure mathematical test model. On the other hand several indications exist that physical reality obeys a quaternionic model and not the spacetime model that physicists have constructed.
At least the quaternionic model can learn you a lot on what is possible and what is not tolerable. That occurs without the nasty oppression that every significant statement must be verified by experiments. Mathematical verification is enough. For example applying the generalized Stokes theorem to a quaternionic manifold leads quickly to a complete space-progression model where fields and particles have a recognizable place.
http://www.e-physics.eu/TheGeneralizedStokesTheorem.pdf
Anton,
Hilbert spaces can only cope with number systems, which are division rings. Only three suitable division rings exist. The real numbers, the complex numbers and the quaternions (with real coefficients). Quaternions with complex number based coefficients are biquaternions and are not division rings. Like dynamic geometric data they must first be converted into division rings (real numbers, complex numbers or quaternions) before a Hilbert space can handle them as eigenvalues of operators.
http://arxiv.org/abs/1101.5690
@Hans van Leunen
"Only three suitable division rings exist."? R,C and Q are skew fields and not "suitable divison rings"
Anton,
Read the paper of John Baez or the work of Pia Maria Solér. They are better mathematicians than I am. Solér proved the theorem. If you cannot approve it, then you should disprove it.
Quaternionic functions can represent skew fields. A field is not a function. It can be represented by pairs of functions and parameter spaces. The reverse bra-ket method shows the relation.
http://arxiv.org/abs/1101.5690
http://www.ams.org/journals/bull/1995-32-02/S0273-0979-1995-00593-8/
http://vixra.org/abs/1511.0266
Arno,
The observed behavior of photons is in conflict with their interpretation as EM waves. Two second order partial differential equations exist that are both based on Hermitian differential operators. One of them is the d'Alembert operator. The other also contains the Laplace operator but adds rather than subtracts the double differential with respect to (proper) time.
The existence of the EM field relies on the nearby existence of electric charges and does not act well as a carrier for information carriers that must travel billions of light years through mostly empty space.
Both equations offer solutions in the form of shape keeping fronts. Only the d'Álembert operator based equation offers waves as its solutions. The behavior of photons fit better with strings of shape keeping fronts.
Maxwell equations ignore the real part of the quaternionic differential. Gauges are used in order to replace this lack. Maxwell equations attache special symbols to parts of the quaternionic differential. E and B are examples.
http://vixra.org/abs/1506.0111
Photons are emitted or absorbed by atoms and created or annihilated when elementary particles are annihilated or created. At emission or creation, these processes generate one-dimensional strings of shape keeping fronts that travel in a supporting field. Each front carries a bit of energy. Creation, emission, absorption and annihilation of the full string takes a fixed amount of progression clock ticks. However, red-shift indicates that this amount of progression ticks changes (very slowly) with progression.
The shape keeping fronts also exist in a three dimensional version, but these objects quickly loose their amplitude with increasing distance from the source. The one-dimensional shape keeping fronts keep their amplitude.
The origin of charges and fields is explained in the links below.
http://vixra.org/abs/1512.0340
http://vixra.org/abs/1511.0007
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