@Piyali Bhar: Generally in higher dimensional model, our visible universe is identified with a four dimensional brane embedded within the higher dimensional spacetime. In such scenario, the matter fields, say a compact star, is confined on the brane, which is indeed visible to us. Now the interesting part is that the extra dimension has some considerable effects on the compact star due to the gravity and thus the model becomes different from usual General Relativity. Since the compact star is observable, that's why the effects of extra dimension on the star can be used as a possible testbed for the existence of the extra dimension itself. For example, the Buchdahl limit of a star ( i.e the ratio of 2M and R ) in presence of extra dimension can go beyond 8/9 and reaches up to unity, unlike to the General Relativity where the limit should lie within 8/9. Thus if a star's Buchdahl limit is found to be within 8/9 and 1 , then it can be a signal of extra dimension. Thus as a whole , the observable compact star can be a good candidate for searching the extra dimension.

Are you sure that we dispose observational evidence of 3+1 dimensions? I mean, is clear that GR describes a "better" physics than the newtonian one where the apparent gravitational force is contemplated as a curvature of space-time with all magnificent and measured consequences. But is this a REAL evidence of the existence of a 3+1 dimensional space or is this the most logical and convenient actual approach?

Dear Piyali,

The best way to define the dimensions is as the necessary parameters to define a unique and unequivocal point in space.

Do we need 10D to define a point? Fantasies of string theory that I think has already been completely discarded

Yes, Agreed with all the above comments. We should not restrict to 4D gravity, of course is necessary for GTR but still universe is not completely known. So, one must include the extra dimensions to explore new physics. In fact, at the beginning GTR was just a theoretical/mathematical calculations, but now almost everything postulated by GTR is almost detected and confirmed (including BHs and Gravitational waves).

Thanks@ Tanmoy paul...One thing I observed that for the compact object with charge the ratio of twice the mass with the radius crosses the limit 8/9 so from there it is not always true that if the Buchdahl limit crosses 8/9 there exists extra dimensions but it is true that in presence of extra dimensions 2M/R may cross Buchdahl's limit.

Here Dr. Piyali, we don't say it crosses Buchdahl Limits. There are separate Buchdahl limits for neutral, charged, anisotropy, extra dimensions. So, if you see their corresponding Buchdahl limits, it will never crossed.

@Piyali Bhar - yes you are right. In presence of charge the Buchdahl limit goes beyond the value 8/9 , which is also true in the extra dimensional model. So one should find some unique signatures of extra dimension on the compact stars , so that it can be used as a possible testbed for the existence of extra dimension ( if any).

@ Tanmoy paul completely agreed

Sorry for this shock comment, and I know that I would be denounced for this. But a truth however unpleasant must be told.

This project is unfortunately as scholastic an exercise as string and other esoteric theories are; including the GR itself, based on mathematical idealism of Plato. These are not “physical” theories, but abstract mental constructs. The root of this rot goes back to the one-sided universal gravitational attraction of Isaac Newton – a defective formulation that is bound to lead to singularities and Fairy Tales that Einstein’s GR is! Newton blissfully extended his terrestrial gravitational theory to the cosmos, just with the “first impulse” from his God!

Newton cannot take a single step in terrestrial Nature without his Third Law (equal and opposite reaction), but he and later Einstein and the rest of the formally trained physicists can take a Magic Carpet ride to anywhere in the universe and can meet or know the dark/black Cosmic Monster. The sad truth is that not only GR but even Newton’s theory of universal gravitation is wrong!

If you want to curse me, please feel free, but please read the following two (short articles) first and if you wish the following two years long running RG forum. Thanks:

Article KEPLER -NEWTON -LEIBNIZ -HEGEL Portentous and Conflicting Le...

Article THE CONCEPTUAL DEFECT OF THE LAW OF UNIVERSAL GRAVITATION OR...

https://www.researchgate.net/post/Is_Any_Effective_Refutation_of_Einsteins_Theories_of_Relativity_Possible

Dr. Malek, the only thing that I can contribute to this question is the fact that the vector cross product can operate only in 0,1, 3, and 7 dimensions. The 3D version is perfect for hydrodynamics and electromagnetism, and it also sits perfectly within 4D space-time.

But I have no idea when we would ever use the 7D cross product (or 7D curl) in a real physical situation.

Article Pythagoras's Theorem in Seven Dimensions

Frederick David Tombe

My point is that generations of physicists since the turn of the 20th century and specially after the recognition of the "Evil Quanta", have been led through the rabbit hole of mathematical idealism to the dark Cave of Plato. The brightest of the young people around the world are made to learn brain-wrecking mathematics and to propagate the myths created by Einstein’s theories of relativity, only to prop-up decaying monopoly capitalism and theology. These mathematical myths as well as the new ones created; are being “proved” using contrived mega-experiments and by using the lure of fame, fortune and funds; to pacify the world population and keep them under control, so that they can generate exorbitant surplus value from the dirt-poor working people. These theories stand in the same relation to monopoly capitalism as Christianity was to the early European colonizers. Having my origin in once called "Golden Bengal" (but one of the worst victims of colonial plunder), where the author of this forum is located, I now see things much more clearly from inside the belly of the beast (North America). There is no 4D “spacetime”; and like “Big Bang” and the rest of official cosmology are only myths. Please see: Article The Philosophy of Space-Time: Whence Cometh "Matter" and "Motion"?

Article Ambartsumian, Arp and the Breeding Galaxies*

https://www.amazon.ca/Dialectical-Universe-Some-Reflections-Cosmology/dp/9840414445

Even from a purely scientific point of view (the aim of this forum) and unlike the theories of classical physics, these myths of “New Physics” have led to not even a single social/historical practice, technology etc. – the only criteria of positive knowledge. This Frankenstein Monster discovers things (like "black holes") that even Einstein said is not possible in theory alone! The following is a copy of Einstein’s conclusion at the end of this mathematically rich and lengthy publication: "The essential result of this investigation is a clear understanding as to why the "Schwarzschild singularities" do not exist in physical reality. Although the theory given here treats only clusters whose particles move along circular paths it does not seem to be subject to reasonable doubt that mote general cases will have analogous results. The "Schwarzschild singularity" does not appear for the reason that matter cannot be concentrated arbitrarily. And this is due to the fact that otherwise the constituting particles would reach the velocity of light.

This investigation arose out of discussions the author conducted with Professor H. P. Robertson and with Drs. V. Bargmann and P. Bergmann on the mathematical and physical significance of the Schwarzschild singularity. The problem quite naturally leads to the question, answered by this paper in the negative, as to whether physical models are capable of exhibiting such a singularity." Albert Einstein. A. Einstein, The Annals of Mathematics, Second Series, Vol. 40, No. 4 (Oct., 1939), pp. 922-936

https://pdfs.semanticscholar.org/8dd0/dfafef0c53c428fdc3b58f8099aafcf7d089.pdf

Space-time posseses only 4 dimensions --- one temporal and 3 spatial'. Our material (pysical) bodies are 3-dimensional, therefore we perceive the space as 3-dimensional volume. Therefore we can high dimensions only through our consciousness, i.e. purely theoretically. We cannot live in spaces with another dimensions as spatial so temporal. Therefore we can consider different high dinensions, but we cannot come inside these worlds possessing 3-dimensional bodies. Therefore it is necessary to study 1-dimensional time more in detail. For example, let us study the time as physical process, acting on surrounding space. So we will understund that 1-dimensional time is only the part of the non-material volume --- the Time, including times of different dimensions.

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String theory is not going well. I do not belive the existance of 10-D. How ever I insist on the demensions of five.

Dear Zh Mei ,

Mmm interesting..

5 dimensions? Why? and what are those dimensions? Have you defined a unique and unequivocal point with those dimensions?

If I'm not mistaken, only 4 are necessary

The language of universe is duality, everything is based on duality, even space. Yes space has 3D, but when you closely observe, it made of three pair of duality. Up/down, right/left, and backward/forward. where the time is located in the center of these intersect.

Article How the Language of the Universe Works

Dear Sergio Garcia Chimeno,

In our B. Feng's theory system, 4-D is not enough. We need 5-D space, so that we can unified the field of four. In 5-D, we can theoretically calculate the charge, mass and radius of elementary particles, and can theoreticaly calculate the Fine Structure Constant.

I'm not sure what the two extro dimensions are, but I guess they may be ict and iat^2, corresponsing to special and general reletivity. By the way, we discovered that the extra dimensions are curved, it shows our university to be Riemann's sapce.

Dear Zh Mei ,

4 dimensions are not enough to define a unique and unequivocal point if you make a "superficial" interpretation of the time dimension. Example:

(x, y, z, t) = (1,1,1,1) with this you would define a point, yes, but unique and unequivocal no, since those 1 can be meters centimeters, days, years etc.

You can use ct to express everything in meters and then if we would have 5 dimensions and a unique and unequivocal point (since the precision of the measurement is marked in meters):

(x, y, z, ct, units) = (1,1,1,1, meters)

But you can adjust it a little more, you can think that time is a dimension that passes without affecting the others, so that anything that advances perpendicular to the other dimensions can be considered time, the expansion of the universe for example.

And if that expansion is through the units, the Zoom dimension, you can already define a unique and unequivocal point in time and space with 4 dimensions:

(x, y, z, Zz) = (1,1,1,1)

(Look carefully what that Zz means, time and precision at the same time, we set 1 the distance from the BigBang to the Zoom level that we want, the same distance will be in x, y, z)

And if with four dimensions you are able to define a unique and unequivocal point, logically there are only 4 dimensions

The expression I have put:

(x, y, z, Zz) = (1,1,1,1)

as a way to get a unique and unequivocal point in space-time it is not entirely correct (it does not take into account hyper-spherical coordinates and perhaps the absolute present should be used as the 0 of Zz and the size of that Zoom level as the unit of measurement) it be treated it as a rapid guide

The quantum world requires higher compactified dimensions. Try in classical mechanics to replace a material point with a material circle or 3-sphere and you will need to get quantum mechanics.

Dear Igor,

I don't know the reason why a material point should be replaced by a material circle or material sphere, but here is an example using 4 dimensions with the Zoom dimension as the origin of coordinates 0 our absolute present:

A point:

(x, y, z, Zz) = (1,1,1,0)

The same point in the past from our absolute present will no longer be a point, it will be a sphere whose diameter will be what the universe has spread at that time:

(x, y, z, Zz) = (1,1,1, -3)

As for compact stars in the space of higher dimensions, then let me offer you a mathematical model, and you try to find additional dimensions there. Suppose that we have an 8-dimensional manifold with a neutral metric, and this manifold is the product S3×S3×T2, where the torus has a metric of signature (-1, + 1), 3-spheres have a metric of signature (-3) and ( +3) respectively. In addition, let the metric of this manifold be consistent, that is, at each point of the tangent space we have a quadratic differential interval

ds2=g11(x,y)dx1dx1+g22(x,y)dx2dx2+g33(x,y)dx3dx3+g44(x,y)dx4dx4

-g11(x,y)dy1dy1-g22(x,y)dy2dy2-g33(x,y)dy3dy3-g44(x,y)dy4dy4

where gii>0

You can easily find a couple of pseudo-Riemannian manifolds of signature (-1, + 3), (+1,-3) here, but since they are identical, it will not be easy to separate them using observations. Most likely it will seem to the observer that he is on a manifold S3×S1 or on a noncompact pseudo-Riemannian manifold

Dear Igor,

I do not know if those calculations are correct, it seems very strange to me to mix different manifolds with different signatures and metrics and wait for a result that makes sense.

But even so, and assuming the calculations are correct, for what? What is the goal of those 8 dimensions? If a unique and unequivocal point can be defined with 4, it is evident that there are only 4

Sergio Garcia Chimeno The fact is that the Lie algebra of vector fields tangent to the hyperspheres of an 8-dimensional space with a neutral metric is isomorphic to the Lie algebra of the matrix Dirac algebra.

Dear Igor,

I do not know the Lie algebra nor the matrix Dirac algebra nor do I know how you intend to build an 8 dimensional manifold with 2 hyperspheres, I cannot argue it mathematically.

It is all very well to turn torus into cups, but I think we must not lose sight of what is being done.

There is a very basic fact and that is that dimensions must define a point, if 4 dimensions already define it, Lie algebra and the matrix Dirac algebra are indifferent

Sergio Garcia Chimeno , for this, it suffices to direct (during the evolution of the universe) the radius of one of the 3-spheres and the radius of one of the defining circle of the torus to zero.

If physics is simplified by introducing higher dimensions, then such dimensions are compelling from a physical standpoint. Special Relativity introduced time as a fourth dimension because this simplified our descriptions of phenomenon related to the constancy of the speed of light. Five dimensional variable mass theory (5D VMT), which was introduced in the 1990's but later abandoned, and which is similar to the Kaluza-Klein theory, simplifies several aspects of physics. In one version of 5D VMT, the line element ds is promoted to a fifth coordinate or dimension. The Minskowski line element thus becomes the equation of an embedded cone: dt2=dr2+ds2, which may be called the "mass cone", also known as the mass shell. One simplification achieved is that the Compton wavelength h/mc is simply the de Broglie wavelength in the s direction. Also, the Lagrangian is the momentum in the s direction. An interval ds is conjugate to rest mass m, just as dt is conjugate to E and dr to p. Virtual particles are particles freely traveling in 5 dimensions, not confined to the mass shell. Many additional elegant results can also be calculated from the 5D metric.

Yes, Madam Kathleen Rosser, I agree with your statement of 5D.

Kathleen Rosser, action as an additional dimension of space-time goes back to the work of Kozyrev. There were bolder proposals (see, for example, Siparov’s works) on giving the 4-impulse the meaning of four additional dimensions. However, the question of observing in nature of the three dimensions has not been resolved. Let me note in this connection that the hypersphere of an 8-dimensional space with a neutral metric has the topology of the ℝ4×S3 . The action, of course, can be considered as an additional measurement, but in quantum mechanics it has a discrete character, so in fact the action is an angular measurement.

Dear Piyali Bhar Nothing prove more than 3 dimensional space. Everything else is theory. The mechanical 4 D of GTR spacetime is still theory, and it seems is not even working for our small solar system, while universe has about trillions of it. .

The whole universe is a three dimensional space that it is following Quantum Mechanics phenomenon.

Deleted research item The research item mentioned here has been deleted

best regard.

Dear Javad Fardaei,

4D of GTR is proved. The scientific program is always that the theory or theoretical prove first, and experimentally later. We cann't wait for the progress of science by means of experiment discovery that without any guide of any theory.

Your saying "Nothing prove more than 3 dimensional space" is not reality. Sudy more current literatures of physics tendency please.

Dear Piyali Bhar,

You might be interested in a (3x3)+1 electromagnetic vector space geometry that was presented to the Congress-2000 in St Petersburg State University in July of 2000, that allows defining the inner electromagnetic structure of elementary charged particles:

Michaud A (2017) The Last Challenge of Modern Physics. J Phys Math 8: 217. doi: 10.4172/2090-0902.1000217

https://www.gsjournal.net/Science-Journals/Research%20Papers-Unification%20Theories/Download/6877

Best Regards, André

There is no actual evidence of any but the four dimensions of space and time in Einstein's coordinate system x, y, z and the spacelike dimension of time ict. Everything else is the result of theories looking for a question they can answer. And since such theories have been around for half a century and made absolutely no progress towards finding any question they can answer, they will probably all turn out to be, as Lawrence Aller used to describe such things, "rubbish". For those who want to waste years or decades following the news reports issued by the people working on those theories, the possibility of higher dimensions remains up in the air; but for anyone who doesn't want to waste their entire lives searching for fairy dust, paying any attention to such theories is pointless.

Courtney Seligman If an ant creeps along an infinitely long pipe, then for it, in addition to one dimension, the second does not exist at all.

The ant will not even notice that the pipe is closed in the torus.

Dear Courtney Seligman,

You are very pessimistic. Do you really think that no further progress in fundamental understanding can be achieved?

Best Regards, André

André Michaud : I DO think that progress may eventually be made. I simply see that all of the arguments made in favor of extra dimensions in this and every other discussion I've read in the last 50 years include not only great enthusiasm about the concept of extra dimensions, but also note that to date, not one theory has succeeded in convincing the general community that it is valid. Here and there, the comments above state that there are advantages to thinking of extra dimensions in one way or another, but they always include the caveat that the theory involved has yet to be proven or has been abandoned (unsaid is the reason that it proved incapable of producing any testable predictions). So I believe that we need a "quantum leap" in our mathematical and physical understanding of things before any useful theory using extra dimensions has any hope of becoming generally accepted. And although strictly speaking a quantum anything refers to the smallest step imaginable, in its usage as a phrase, 50+ years of reading about so-far useless theories convince me that although at some distant date someone may develop an extra-dimensional theory that is not only mathematically "useful" but also produces testable predictions, none of us will still be alive to read about it. I don't consider that view pessimistic, but pragmatic. Why waste my time reading about probable nonsense, when there are so many things to read about that produce useful results? So along that line, though everyone is free to criticize that viewpoint, I will not be reading any more of the comments about this thread. Instead, I'll be working on projects that are producing useful results, at least in the opinion of my colleagues and students. However, I do keep up with news about cosmology and associated fields, such as the numerous efforts to use extra-dimensional mathematics to solve cosmological problems, and in the unlikely event that I live long enough to read about an extra-dimensional theory that does produce testable and provable results, I will be perfectly happy to accept it as a realistic possibility.

Dear Courtney Seligman,

I perfectly understand your position.

You wrote: "However, I do keep up with news about cosmology and associated fields, such as the numerous efforts to use extra-dimensional mathematics to solve cosmological problems, and in the unlikely event that I live long enough to read about an extra-dimensional theory that does produce testable and provable results, I will be perfectly happy to accept it as a realistic possibility."

Keeping informed is effectively the way to go. Who knows! You may still live long enough to hear about it.

Best Regards, André

I have per my "Absolute Genesis" metrix protocol physics derived the fifth dimension sense primordial "quagmire" out of which space time baryonic real matter universe might've evolved. Primary aspect entity magneton has been observed & my coauthoring paper with Emmanouil Markoulis about fundamental quantum magnetism with that is demonstrated on, Ref: Real time observation of a stationary magneton EMMANOUIL MARKOULAKIS, ANTONIOS KONSTANTARAS, JOHN CHATZAKIS, RAJAN IYER, EMMANUEL ANTONIDAKIS Hellenic Mediterranean University former Technological Educational Institute of Crete, Department of Electronics Engineering, Computer Technology Informatics & Electronic Devices Laboratory, Romanou 3, Chania, 73133, Greece Article available at: https://doi.org/10.1016/j.rinp.2019.102793©2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Arxiv pdf: https://arxiv.org/abs/1911.05735 Received 7 August 2019; revised 27 October, 2019; Accepted 4 November 2019; Available online 8 November 2019. (PDF) Real time observation of a stationary magneton. Available from: https://www.researchgate.net/publication/337134203_Real_time_observation_of_a_stationary_magneton [accessed Jul 12 2020].

This may well corroborate with Dr. Kathleen Rosser & André Michaud have explained about the extra dimensional aspects, for example, "...Virtual particles are particles freely traveling in 5 dimensions, not confined to the mass shell...". Hence existence with higher dimensions beyond space time will have to be considered & space time may be a projection of such higher dimensions, altogether sense time space per my mathematical physics aspects, that we will proceed further after proving with verifiable metrics about magneton mechanism leading to gravity unifying theory of everything!!

Sincerely,

Rajan Iyer

ENGINEERINGINC INTERNATIONAL HELLENIC MEDITERRANEAN OPERATING TEKNET GLOBAL PLATFORM

Perhaps "Long delayed echo" is a prediction of the theory of a closed world with extra dimensions.

We must think that universe is a complete entity. If we think so, you never think of extra dimension. Space of universe is not just holder, it should consider as substance. Just to think about it, it is occupying our 99.99% of each atom and our body.

Einstein and old past century scientists never thought universe has billions of galaxies, and building block of universe is quantum mechanics phenomenon.

We are duplicating universe. Here is science of universe that we should follow, not mechanical universe.

https://www.academia.edu/43351041/How_the_Quantum_Universe_Works

Yes, it does.

I would like to attribute your attention at the 5-D theory instead 10-D. Lets take a look at the experimentally tested formula which connect energy E, pulses p(x), p(y), p(z) and mass: E^2-p(x)^2-p(y)^2-p(z)^2=m^2 (here c = 1). You could see that there are 5 members in this formula, not 4 and not 10.

We are sure that our universe can be described in 5-d model and physical meaning of the 5-th coordinate is the action:

Properties of the 5-Dimensional Extended Space Model with Variable Photons Mass and Size.

DOI: 10.9734/bpi/nips/v7

https://www.researchgate.net/publication/344842971_Properties_of_the_5-Dimensional_Extended_Space_Model_with_Variable_Photons_Mass_and_Size?_sg=T6eJB2J_TekBRLuOQhFL5Ybxn9IQ-566f1pjVAy1P_RpKKjQj3cr3p0W9TMumpV9i1RUGDOL2jBaRxczb4Maxub5bG8EFIXV_mZMmbaf.tdnGl0bP_J52TLBVx2Fvw1_Dm2CluN9yus5SAtYwEEblLUXC959lLMy2zwyNJALex3wO2vKbI4PTQ6rkvgeEZA