It’s not that hard to do the calculation; but what should be clear is that motion in spacetime doesn’t have anything to do with the space of states, i.e. Hilbert space, nor is any vibration of any significance. Just take the example of a relativistic particle in 1+1 and 2+1 dimensions, with the former embedded in the latter. Invariance under Lorentz boosts in 2+1 dimensions doesn’t imply invariance under Lorentz boosts in 1+1 dimensions and vice versa. The same holds for a 3+1 dimensional spacetime embedded in a higher dimensional spacetime.

you wrote "My interest is because I am intrigued by the idea that extra dimensions could be possible apparent effects caused by possible physical superluminous quanta phenomena in our normal three-spatial dimensions space."

From my analysis of time and my calculations I can assure that two dimensions of time and three dimensions of space are physically real and physically effective. But there can be no more than 3 space dimensions.

Preprint Causality and arrow of time in 12-dimensional Space-Time

one might come to some point of view that spacetime can have 4 dimension because 3D spactime with 2D time is defined by a tetrahedron

Dear Preston Guynn ,

For example a hypothetical macroscopic 1-dimensional energy string (e.g. an electromagnetic flux line) closed into a loop thus a 2-dimensional object when span physically around an axis aligning with its diameter (like a spinning coin on the table) at relativistic speed close to c or c will appear in normal time as a 3D solid sphere (i.e. as a solid given that the initial 1-dimensional energy string had sufficient energy) that appears still thus static.

What just happened? A 2D spatial dimensions + 1D temporal dimension object due to its extreme vibrational speed (i.e. physical relativistic spin) was translated into our spacetime frame of reference (i.e. Earth or else lab frame)) into a 3D spatial dimensions object + 0D temporal dimensions (the object appears still and static) object. The spatial 3D object is not moving therefore it can not have a temporal dimension attributed. We observe that during this process that the temporal dimension inside the frame of reference of the 2D object is translated due to its extreme spinning speed into an extra spatial dimension in the lab frame, from 2D to 3D spatial and its temporal dimension was nullified in the lab frame.

Does this above observation reminds you something from SR? IMHO this is equivalent to what is said about a photon moving at c speed experiences no time thus zero time. The object appears still and static in the lab frame.

We can observe the same phenomenon in the static magnetic flux of a macroscopic permanent magnet. It is assumed that the magnetic flux is coherent flow of virtual photons moving at c. However, in the lab frame the flux of the magnet appears as static.

So, let us now expand our thinking to an initial 3-spatial dimensions object span around its central axis at c? In what form will it appear in the lab frame? Following the logic above it would appear in the lab frame as a 4-spatial dimensions still object. Nevertheless, since in our spacetime we have not yer observed so far such objects or phenomena we must assume that all elementary particles are actually vibrating (1D spatial + 1D temporal) or (2D spatial + 1D temporal) energy strings.

Note: Assigning the third (thickness) thus z spatial dimension in the particle frame to be zero for thickness equal to the Planck length. There is is no absolute 1D or 2D spatial object in the Universe.

Coming now to a hypothetical superluminous vibrating energy string quanta 1D or 2D spatial dimensions (could be at the Plank length size or less) that may be as well the unknown elementary sub-particle by which vacuum space medium is hypothetically is made up of. According to theory the arrow of time for this object-particle in the lab frame will point backwards to the past in the lab frame. Meaning it will leave normal time in the lab frame therefore having zero spatial and temporal dimensions thus non-observable in our Universe and appearing as "nothing".

Exactly, apart of some negligible zero-point vacuum energy fluctuations, how we perceive vacuum space in our c bounded spacetime domain Universe? As "Nothing"!

Therefore, we must conclude that if such elementary possible Planck length sized vacuum sub-particle exists it must vibrate (i.e. physically spin) at superluminous speed.

Kind Regards,

Emmanouil

I don't believe in a more than 3 physical spatial dimensions and regard all these theories about extra dimensions just like an effective mathematical convenience used for analysis but that should never claimed to be actual physical. All known matter and light live in the same spacetime Universe we do. Except the vacuum medium which is out of phase from our spacetime and appears mostly as "nothing" (hidden) in our spacetime. Zero-point vacuum energy fluctuations is the best clue we have that something is lying beneath, hidden, like the Brownian motion of atoms we have in normal matter.

Dear Emmanouil Markoulakis,

you started your last repy with „I don't believe in a more than 3 physical spatial dimensions ….

With respect to ones believe, the universe does not change its activity … the only tool we know to theoretically predict and understand anything in our universe - in a for everyone and everywhere fully reproducible way - is *math*, and here especially geometric relations interpreted by human mind after being calculated by some algebraic relations (of many different kinds possible) with respect to such geometry, being it Relatively (4D), String theory (10d or maybe 11D) or in my case iSpace theory, able to exactly derive and predict constants of nature from simple integer geometric multiplicative relationships.

And when the algebraic part of such (simple multiplicative algebraic equations) give back useful, numerically correct answers as to the full precision of (CODATA) lab measured values, one is surely inclined - if not enforced - to allow the hypothesis of a direct relation to the geometry of such results, especially when the *units* of such relations also fit exactly to the required ones by the physics of the constant of nature calculated.

Example (x Volt * y* Ampere * z Second …)^1 will likely lead one to assume its 1D (but can not be really sure entropy wise!), as everything can be multiplied. When such relations would occur to the power of 2, one will more likely assume a geometric relation to 2D (less likely to be accidental). In case it’s terms exponent shows power of 3 (with proper units!) it’s nearly for sure 3 dimensional (3D).

And in case of native, normalized iSpace equations many show an exponent to the power of 6, 10 or even combined 6 and 10 as is the case e.g. with the iSpace derived Newtonian gravitational constant (GoldenRatio^10 * Pi^10).

Now - Is such a proof of any kind for a specific model like iSpace? *No, of course it’s not!*

But it tells us something, if one is able to see (it). An for an interesting side note - all equations yo have identified by the typical reverse engineering style methods of iSpace have shown it is later nearly always possible to find an algebraic form of such equations to have an e.g. maximal 4D or 3D coefficients - but *exact same result*.

iSpace method proofed one thing clearly - you deserve to see what you want to see. This has nothing to do with what one believes or not, it can be shown all are right one way or another, at least partially. But being partially successful on a complex topic, unfortunately leads many, especially the mathematically very experienced ones think tge found “*it*“ but could not be more far from the truth.

Dear Christian G. Wolf ,

It is my understanding that your very successful prediction power iSpace numeric model and theory is talking about entities of hidden dimensions within our normal 3D Cartesian space which however are actually also 1D or 2D or 3D spatial when analysed discretely? Similar to quantum gravity theories like quantum loop gravity theory or string theories.

But this is not the case I'm talking here. I'm referring to the "metaphysical" pure mathematical dimensions referenced in the general bibliography as 4th, 5th...nth spatial dimensions we humans cannot imagine and can see only possible observe distorted as a projection in our spacetime. Similar to a cube or a circle passing through an imaginary 2D Universe we can see only its 2D cross-section projection in this imaginary hypothetical 2D Universe. Similar to Multiverse theories where anything is possible.

Kind Regards,

Emmanouil

____________________________________

p.s.1 Although you are right that a very high accuracy quantum prediction model means that it is correct, it is very difficult however with our current experiment technology to prove that it is also the actual physical. Therefore all quantum models today are essentially effective models unless proven otherwise. Even the Standard Model in particle particle physics does not claim that it is the actual physical. Of course anyone has the right to claim his model as being the actual physical but proving it can be done only by direct experiment which is difficult to impossible for quantum with our current technology and physics.

p.s.2 Me saying "I believe" caverns the above mentioned in p.s.1 thus that there is no experimental physical evidence so far that these imaginary extra geometrical dimensions exist in our spacetime Universe.

p.s.3 Even my model of the "1/2 spin fiber model for the electron" I describe it as physical model because it describes a potential EM flux energy manifold for the electron charge thus using EM flux to describe the charge manifold of the electron and we know from countless experiments and empirical evidence that EM flux energy is actual real. But proving that my model is the actual physical taking place is a total different beast!! I cannot prove.

Perhaps an idea might be to express spatial dimensions as complex numbers.

Prof. Dionysia G. Panagoulia ,

Yes I agree like the Bloch Sphere but if I'm not mistaken the imaginary part will again represent rotations in 3D spatial space although you are probably right it could be extended to represent extra dimensions.

Thank you for your input.

Emmanouil Markoulakis wrote me, that somebody calculated a value 19 magnitudes above c. That's about 1.3𝑥10²⁶𝑚/𝑠 (Unfortunately I can't find the message anymore). That's once the world radius in one second or WARP10 but only for the Maxwellian demon.

I think, beyond v>c there is no more RF possible, whether 3D or 4D. You are running into a 0/0-problem. With such a high velocity the Lorentz-factor in its form of 𝛾⁻² = 1 − (𝑣²/𝑐²) is actually 𝛾⁻² = 1 − 1/(𝑐²/𝑣²) = (𝑐²/𝑣²)/(𝑐²/𝑣²) − 1/(𝑐²/𝑣²) --> (𝑐²/𝑣²) = Q = 0 in my model. The 1 becomes 0/0 the "wild card", which can take on whatever value. So each observer in whatever RF always measure c.

Dear Gerd Pommerenke ,

Christian G. Wolf in his model iSpace is the researcher that calculated a 1027 m/s speed factor. I don't believe SR is anymore applicable at that rotational tangential speed kind of superluminal vibration frequency. The vacuum quanta if it is real simply phases out from our normal c bound spacetime.

However, it is interesting using the Lorentz factor γ of SR that you have found and concluded that at that speed that there cannot be defined anymore a Frame of Reference (RF) 0/0 which is undefined in mathematics but not necessarily in physics.

For me it simply means that a possible undisturbed superluminal vacuum is the absolute frame of reference. However, it is completely disconnected from our spacetime (phased out) and therefore of not any use.

It is the unknown to us spacetime domain where the Maxwellian Demon lives in and pops in our normal spacetime domain whenever the vacuum quanta gets disrupted decelerating to c bound vibration frequency.

Kind Regards,

Emmanouil

p.s.1 That was actually the mistake that old researchers did not recognizing that the "Aether" absolute frame of reference could be superluminal in nature and therefore totally disconnected from our spacetime Universe and simply appearing to us as what we call the vacuum thus more or less nothing. However, I believe in this case nothing means hidden.

p.s.2 Quote: "So each observer in whatever RF always measure c." Τhis is a limit put by Einstein's SR where the speed of light c is treated as the absolute frame of reference in SR and not the vacuum which at that time was treated as nothing. But it is also predicted that at a hypothetical superluminal speed the arrow of time is reversed breaking causality. But my interpretation is not that this leads to not valid and impossible physics but rather to unknown physics and simply that any superluminous energy cannot be observed in our spacetime creating the vacuum but letting behind an important clue for us namely the zero-point vacuum energy fluctuations. The phasing out is not perfect.

To the Absolute Frame of Reference

In my 1st Article (The Shape of the Universe) only available in viXra, because it‘s outdated, I defined such a model at p. 238-239, a so called UR rest mass etc. But I abdicated it later.

Preston Guynn Preston, and with all due respect, your recent *very long* answer to my post you quoted above about the (without any doubt *obvious*!) intrinsic relationship between math and multiple assumed (*hypothized*!) physical models deserves an only very short answer:

What have you smoked to nearly derail an open fruitfully started typical RG style discussion on some very valid and interesting question of Emmanouil by some angry at heart rant against as it looks like at first sight whole of mathematics?

As your answer is in addition also to a very large extent completely off-topic to the original question, I am not willing to directly answer you here to *falsify you* in most but all points you brought up here - and easily, for that matter.

Your post in its own might likely serve as a good starting point for one of the typically most useless (with respect to no practical outcome for anyone to be possible, just wasting later readers time)discussions about metaphysics, like philosophical relationships of math to physics and what not (you nearly spared nothing out in your post) so - if it’s interesting for you to write and discuss such topic - *why do you highjack this thread* by the rant you did instead of using the option to pose all this in a dedicated RG question thread of yours (maybe just linking here with a short notice to such thread?).

Please all stay *on topic* of RG questions, or serious scientific discussion of complex issues to be hopefully solved in the future are otherwise not possible.

And Preston - following many of your other really good and most razor sharp to the point answers of the recent years here on RG - you can do better.

I will not reply here any further, but if you need a shoulder to lean on (as your tone in your reply above suggests) I am happy to discuss on the basis of scientific facts leaving emotions of any kind out. And if you just need soneone talk to, let’s have a call and sort this out (but not publicly, as I do not have any time to do so).

Dear Preston Guynn ,

Well said! With one addition from me, my 2 cents.

"Observation" of phenomena and physical processes.

Seems to me that the above term, a total necessary process and step for producing good physics is today neglected or forgotten by physics and theoretical and experimenters physicists jump directly to the results numerical data of experiments and then try to invent models that reproduce the same results without considering to the slightest to observe and describe the actual physical process or close enough by which results were produced by the particular phenomenon under investigation.

In other words, models made are not based on observation of phenomena and trying to uncover their mechanics but instead solely in reproducing the results numerical data similar to making outcome predictions algorithms for the lottery or a casino game.

If I predict that a shattered window was the result of basket ball hitting the window (invented model) without actually observing the event, did I good physics? (The window was broken by an earthquake).

I don't think that this was what Faraday did and Maxwell later on, who based his theory on actual observations of men like Faraday.

Me personally, I would never dare to theorize my EM flux 1/2 spin fiber model for the electron charge manifold without first for the past 5 years observing the net quantum field inside permanent magnets with the nanomagnetic device ferrolens and then observing other similar field manifolds existing in nature and making experimental procedures to emulate these effects.

We don't try anymore to observe the physical processes taking place but only the results outcomes. Predictions of outcomes alone are not physics. The term "physical interpretation" has become almost alien and non existing today.

In particular, the argument that quantum processes are not observable without even trying to invent new indirect observation methods or physically emulating the phenomena at the macroscopic level that will make them observable, is used more as an excuse than a scientific fact.

Feynman was a great man but the dogma "Shut up and calculate" was catastrophic for modern physics.

Theorizing directly the cause from the results and not from the observed process leading to the results is stupid and can lead to wrong conclusions. Physics primer job is to describe or close enough actual physical processes and not only predict outcomes. Physics theories should be based at least to some minimum degree of observation of the process taking place otherwise they should be called not as theories but as calculations.

Kind Regards,

Emmanouil

p.s. Of course there are always exceptions to the rules and there indeed are some research fields and phenomena were observation of physical procedures is impossible and we observe only the results. Like this question herein... What is the vacuum and why it is nothing? However do understand it we may emulate a procedure in the future where matter disappears from our spacetime and the energy is not conserved.

Also I don't understand today why in order a theory to be even considered by the mainstream community it must by adopted to the standard model ? This is counterproductive for new science. New physics discovered has no standards but is an ongoing continuous process of debate.

Dear Christian G. Wolf ,

I just saw your reply to Preston Guynn after my reply to him and had to say that I know Preston now many years and his honesty and integrity and contribution to science and assure you that he was not trying to insult anybody or you but just used your statement as a platform to make a discussion of a general topic and question today which concerns actually the community thus in what degree mathematics can be used as a tool in physics or replace it completely? Which is actually the trend the last two decades or so in theoretical physics.

I'm certain that Preston is not aware of your work and the difficult physical subject you are researching that is actually the vacuum and from which all measured physical constants and known phenomenon are fundamentally generated and by definition is difficult to have today any direct empirical evidence and experimentation (maybe the discovery of the Higgs Boson) and even so you give a possible physical interpretation of your model of the vacuum substructure based on which all known physical constants values are generated using your iSpace model. An excellent research to a very difficult topic very few would try to accomplish.

So, please don't take it personally a little side discussion even if it seems off-topic is welcome and can be fruitful some times even if it is not directly related to the topic asked.

Kind Regards,

Emmanouil

A ``dimension'' is math is just another variable. So, sure and added variable can be defined and used in equations to calculate something. But the trick in physics is to reduce the number of variables / constants. So, in the end of a calculation, one has to agree with observation. That is to reduce the equations to 3 spacial (distance) dimensions and one time (duration) dimension. Failure to do this results is ``weirdness'' such as with Quantum Mechanics.

So, I submit it is easier to endow something physical with superluminal force transmittal ability and use simpler (3d+time) math than to follow math into increasing (the wrong direction for physics) the number of variables.

The the issue becomes the ontological reality of the superluminal stuff. There are those writing papers about such reality sometimes phrased as the reality of quantum waves such as J.R. Croca et al. On my todo list is a paper suggesting the transparent mask experiment when view in reverse order shows the ontological reality of superluminal, undetectable media (an ether or, I call it, the plenum). Thus, the math becomes much easier, the physics more explainable (even predicable).

Apologies, I must say ``predicable'' in physics means calculated a value BEFORE it is measured. Also, the speed of light (c)is variable - it is NOT a constant. Any calculation using c as a constant is unphysical.

To All YOU MUST WATCH THIS!

https://www.youtube.com/watch?v=fvqXshyuvOg

Dear Emmanouil Markoulakis ,many thanks for recommending us this link, it’s both great insight and fun to watch at the same time able to make one think (and that’s good!) - and whatever „your“ model or number of dimensions, extra dimensions, space, time or spacetime (well no more spacetime with „him“, then…) is or might become in the future - will you write him and give some feedback (e.g. about topics of our recently held TEGS session) or have I to do that myself? This is because I think you’re way more qualified to do than I am.

A mathematician can write any equation they want. A mathematician is never hungry, 0=(pepperoni pizza)- (pepperoni pizza). Eat the 2 pizzas!

A physicist is constrained by the (experimentally) observable (well… they should be!!).

The speed of causality is the speed at which one thing can effect another.

To talk of speeds above causality is to talk about mathematics not physics.

The trick is to know when you have passed from the realm of physics to mathematics. This can be hard… people get so enthusiastic about things.

Is the speed of light the speed of causality? It seems to be…a Nobel Prize awaits anybody who (experimentally) proves otherwise…Are there more dimensions?. A second Nobel Prize awaits anybody who (experimentally) proves this.

Zoltan Vilagosh I fully agree with all you said - but - and thats some big "but" imho - no (even proven experienced) experimental physicist will get the money to run some experimental verification of a theory which is by definition then - and only then - a theory when its experimentally testable (let alone hypothesis type of ideas). So - how to do then chicken/egg issue?

These problems are not connected with each other. A superluminal particle is described in the ordinary space-time, but has an imaginary mass. Adding up dimensions to the three-dimensional space of the space-time does not change the description.

Spatial coordinates are always three-dimensional. And if a fourth dimension is added, it is related to time. Hilbert space has a completely different story and is not interpreted as a spatial dimension in any way and is used only in the framework of quantum mechanics. And I think this concept of space and time is related to the field of relativity

Dimensions are part of a model. The base modelling unit of physics is a photon which is a super-position of time,distance and energy. It is important not to muddle modelling (photons) with logic (bits). See Preprint Bits and Photons

Preprint Complete Relativity

Dear Dr. Emmanouil Markoulakis

Thank you very much for posting this question.

Regents Professor Subhash Kak OSU, has published his work in e-dimensional space as opposed to the conventional 3 or 4-dimensional space. Some of his work can be seen on Springer. It may be inline with your research interest.

Regards

Dear Dr. Atul Kumar Kuthiala ,

Thank you for your suggestion.

Kind Regards,

Emmanouil

If we consider a Rieman projection of a cube, then the top part of the cube is projected to infinity on the plane (or tangent space). If we use a hypercube, then it is projected to infinity in 3D space. When we consider the Heisenberg uncertainty principle, if the velocity of a particle is known precisely, then the position is everywhere at once. Conversely, if the position is known, then the velocity is infinite. Either way, this is a superluminal speed. If the particle is located at the centre of the hypercube, then a rotation could project the particle to infinity in the 3D tangent space. This would, then, be a hyper-dimensional model of a superluminal particle.

Dear Christopher C. O'Neill

Superb mathematical explanation.

Thanks.

Emmanouil

Dear Christopher C. O'Neill ,

I recommended your answer as the best answer of this thread.

So, if I understand correctly using differential geometry it can be proven that a hypothetical superluminal particle (v>c) either linear moving in space or having a rotational superluminal angular velocity (i.e. periodic vibration) is shown that it has no notion of time thus a space-like spacetime behavior and it can be instantaneously everywhere in space.

Whereas, a photon at c speed has a time-like spacetime behavior thus it takes time into account for travelling between two distant points in space.

The superluminal case is consistent with quantum mechanics odd behavior of phenomena like quantum entanglement, quantum tunneling, superposition and in general the so called non-local quantum phenomena and property and can also explain the apparent indeterministic behavior and superposition of quantum particles as shown also (using a different analysis method than yours) by,

A. Dragan, A. Ekert, Quantum principle of relativity, New J. Phys. 22 (2020) 033038. doi:10.1088/1367-2630/AB76F7.

A. Dragan, K. Dębski, S. Charzyński, K. Turzyński, A. Ekert, Relativity of superluminal observers in 1 + 3 spacetime, Class. Quantum Gravity.40 (2023) 025013. doi:10.1088/1361-6382/acad60.

I wonder why this very obvious theoretical proof like yours was not come out before earlier by the top scientists in the field?

"For me it is almost certain by now that the apparent "weird" behavior of quantum mechanics is due to an intrinsic superluminal property of the vacuum.

- Emmanouil N. Markoulakis"

In a couple of days, my newest peer-reviewed article will be published by a Journal of an introductory description about this revolutionary novel topic I am proposing and why it is of paramount importance to follow this path of superluminal novel research for the future of physics and new discoveries.

I believe that after we have exhausted high energy c limit bound physics (i.e. after the Higgs no other fundamental particle was discovered) the only way is to go up further is in focusing our efforts in superluminal research which should have been taken very seriously by the science community instead of dogmatically desk rejecting superluminal research papers and is probably the future in new physics.

Christopher, you should really consider to publish your novel as far as I know, proof outlined here by your answer in this thread. This is doctoral thesis level novel research and beyond. Which enforces the realization that the apparent indeterministic behavior of QM could actually being caused by an intrinsic superluminal property of free space medium (i.e. ideal vacuum).

Kind Regards,

Emmanouil

The only way to progress science is to overcome the existing and old theories' limitations.

New Publication "The superluminous vacuum" why the vacuum appears as nothing.

Article The superluminous vacuum