Journal of Theoretics

Evidence for the Existence of 5 Real Spatial Dimensions in Quantum Vacuum

- Scale of Quantum Temperatures Below Zero Kelvin -


Author:  Carlos Calvet, Ph.D.


Francisco Corbera no. 15,

E-08360 Canet de Mar (B), Spain



Abstract:  Conventional forces like gravitation and electromagnetism vary with the square of the distance. This is because the corresponding force is scattered into 3 dimensions due to the distribution of virtual gravitons or photons of the corresponding field in a 3D-space.  In an analogous way, the Casimir force, that varies with the 4th power of the distance, ought to arise from bosons distributed in a hyperspace with 5 real physical dimensions.  This leads to the prediction of a whole new world of “quantum temperatures” below zero Kelvin, and to a model that surprisingly agrees with cosmology and recent findings of the zero-point-field (ZPF). “Virtual” field particles (e.g. bosons of the ZPF) are probably nothing else than hyperspace particles that cross our 3-D universe from time to time, thus seeming “virtual” to us.  This paper details how our universe can be considered as a 3-D space “floating” on an immense 5-D space - the hyperspace - in analogy to a sheet of ice floating in a deep sea.

Key words: Hyperspace, Energy scale, Black Hole, Quantum Waves, ZPR/ZPE


            The possibility of “lack of air” was neglected until Otto von Guericke demonstrated 1650 the power of vacuum, using two large hemispheres that even 8 horses could not detach from each other. 1660, Robert Boyle predicted that sound will not travel in a vacuum, although 1798, Humphry Davy observed that heat is transmitted through it. 1934, Paul Dirac described the polarization of vacuum and cofounded QED, making 1950 the 1st suggestion of string theory. 

In addition, sixty years ago, the pioneers of quantum theory (Wyle, Schroedinger, Clifford, and Einstein) believed that particles had a wavy structure, instead of being point particles. Quantum waves, as suggested by Cramer (1986), are real and not merely a probability distribution, thus supporting the original concept of Clifford (1956) that all matter is simply "undulations in the fabric of space".

            Wheeler and Feynman (1945) first predicted that the electron was made of spherical inward and outward electromagnetic waves. Using a quantum wave (QW) equation and spherical quantum waves, Wolff (1995) found and described a wave that successfully predicted the properties of matter. There is great evidence that matter is the result of spherical quantum waves that exist even at 0ºK. This model lead as early as 1922 to the prediction of the positron (Anderson), since it predicted a particle with a spin opposite to that of the electron. The positron was discovered by Anderson in 1931, making the theory of QW absolutely plausible.

            On the other hand, H. G. B. Casimir of Philips Laboratories in the Netherlands discovered the so called “Casimir Effect,” now known as an attractive force between close metal plates. The Casimir force was measured by S. K. Lamoreaux at the University of Washington, and defined as a “force derived from partial shielding of the interior region of the plates, arising from the background zero-point fluctuations of the vacuum electromagnetic field”. Milonni and his colleagues from Los Alamos showed that this shielding effect pushes the plates together due to the unbalanced zero-point radiation (ZPR) of quantum vacuum. The vacuum energy is hereby converted into kinetic energy.

            In unifying the principle of QW, the laws of gravitational and EM attraction, and the Casmir force, this author found an obvious evidence for the existence of a real hyperspace with 5 spatial dimensions (see also 8) in the quantum vacuum, that can be accessed through small artificial black holes or hyperdense matter. Furthermore, there seems to exist a whole world of yet unknown quantum temperatures even far below 0ºK.


            1. Number of Dimensions of Fields of Force

            Quantum vacuum research revealed that the so called zero-point-radiation ZPR or ZPE (an energy that exists even at 0ºK) is composed mainly of virtual electromagnetic waves and virtual particle pairs that cannot be measured directly (see for ex. 7, 9). But this is contradictory to the well known findings of Lord Kelvin, who demonstrated 1848 that all molecular activity (and therefore all EM release) freezes at this temperature. Furthermore, if we watch the formula of the Casimir force and compare it to those of the gravitational and electromagnetic (EM) forces, we realize that, while gravitational, electric and magnetic forces vary with the square of the distance [formulae 1, 2, 3], the Casimir force varies with the fourth power of the distance [4]:



Where:   F/B = above mentioned forces; G/C/m0/h/p  = constants; m/q = mass/charge; d/r =

               distance/ratio; q = angle to magnetic vector v       ([1, 2, 3] from 10; [4] from 7)



A force that varies with the square of the distance means that the force will increase with the square of the distance if we reduce the distance, and it will decrease with the square of the distance if we increase the distance. As a result, this author concluded that a force that varies with the square of the distance can be considered as a conventional 1-dimensional force vector (x-axis) that is scattered into 2 additional dimensions (y, z) due to the 3-dimensional nature of space. The square power of the distance indicates the number of additional dimensions we must add to a 1-dimensional force vector in order to get the number of dimensions of the whole field of force (here, 3):


            [5]       N = a + n


            Where:            N = number of dimensions of the whole field of force

                                   a = number of dimensions of the force vector (usually 1)

                                   n = power, the force varies with the distance (in this case, 2)

            In the above case:   N = a + n   =>  N = 1 + 2 = 3. This means, a 1-dimensional force vector varies with the square of the distance in a 3-dimensional space.

In an analogous way, a force that varies with the fourth power of the distance (Casimir force) can be considered as a 1-dimensional force vector that is scattered in a 5-dimensional space (N = a + n   =>  N = 1 + 4 = 5). Therefore, it is evident that the field that originates the Casimir force is a 5-dimensional field, i.e. that it is in fact a hyperspace field that produces the corresponding effects in our 3-D universe.


            2. Quantum Temperatures

            1848, when Lord Kelvin established the absolute temperature scale, he did not know about quanta. The idea that there is no temperature possible below 0ºK has prevailed for more than 1 ½ centuries, but now this idea seems to be insufficient with regard to quantum vacuum exploration (see for ex. 9): According to Heisenberg’s Uncertainty Principle, there ought to be a whole world of virtual photons, particles and antiparticles even at zero Kelvin. In consequence, zero Kelvin cannot represent zero energy. The energy that exists at zero Kelvin must correspond furthermore to a certain energy level and this energy level must necessarily begin far below zero Kelvin. In fact: In agreement to equation [5], the Casimir force that originates from the ZPF is a 5-dimensional force, and according to equation [4], its strength varies with the distance. Therefore, the field density will be higher between plates that are close together, and weaker between plates that are more distant. In consequence, the energy density of the ZPF varies locally, so that there are regions with more energy than others. In addition, zero-point fluctuations arise from virtual photons of a potential variety of wavelengths (6), thus supporting the idea that there is a whole energy range below zero K, analogous to the energy range of real photons above absolute zero (radio waves through gamma rays).

            In consequence, the author defines the concept of “quantum temperatures” as the measurable amount of energy contained below zero Kelvin. This energy would mainly be due to the following sources of kinetic or pure energy:

  1. quantum spin / quantum rotation
  2. quantum waves (wavy nature of particles, see also: 1, 4)
  3. ZPR or Casimir energy (see also : 9),


Omitting willingly any other external source of energy as the movement of the earth, the solar system, the galaxy and the whole universe, which is of course very difficult to evaluate and is usually omitted.

            According to 11, the maximum energy density in the sense of oscillating particles that quantum vacuum can contain is 10116 ergs cm-3 s-1 = 10115 J m-3 s-1. This energy level corresponds to any wave or particle energy “that space-time can support”. In consequence, there is a whole world of quantum temperatures, beginning with 0ºK or 10115 J m-3 s-1 and ending at 0 J m-3 s-1:

            1.  Above 10115 J (>0ºK), we have a hot universe with Kelvin radiation (EMR).

2.      At 10115 J (0ºK), we have a wavy universe with quantum waves and ZPE, but no more Kelvin radiation (EMR=0).

3.      Below 10115 J (<0ºK), we have a universe that becomes less and less wavy and has a respective lower ZPE.

4.      At 0 J, we reach a completely flat universe with no quantum waves nor ZPE at all. 

The flat universe corresponded to the concept of the “Big Chill,” a possible final state of the universe after burning out all the energy available, e.g. smoothing any existing QW. 

Conclusions and Discussion

            The above-depicted scenario allows us to understand the nature of the ZPE, which is still uncertain since it is an energy that is composed of “virtual photons that cannot be measured directly”. According to the above dimensional model (see Ch.1 in Results), ZPE would be composed of virtual photons that have 2 more degrees of freedom than ordinary photons (i.e., light, heat), e.g. that exist in a real 5-dimensional hyperspace.

With this model in mind, it is easy to understand why we cannot detect directly virtual photons of the ZPE; they are not inside the same space as ourselves or our detectors, and we can detect them only for fractions of seconds when crossing our 3-dimensional space before disappearing again in hyperspace. Therefore, they seem “virtual” to us (phantom particles).

Although ZPR/ZPE has been called also ZPF (ZP-field), it is not really a field of force as the gravitational or EM field. This can be understood from the definition of the Casimir force: “a force derived from partial shielding of the … background zero-point fluctuations of the vacuum electromagnetic field” (6). This means, the Casimir force is not the result of a traditional field of force that acts by mediation of carrier particles (bosons) interchanged from one material particle to another, thus resulting in an attraction or repulsion, but that of photon waves, producing a radiation pressure that can be measured (i.e. by Casimir plates). In this sense, Casimir energy or ZPE resembles more EM radiation than an EM field, although it is as “virtual” as a field of force. This fact has already been explained in part in Calvet12 and Calvet13 since a field of force is a medium, which we are submerged in, thus being not able to “see” or detect directly its components (bosons). The case of the ZPE is different, since “virtual” means here, “particles that are coming and going from our universe to hyperspace and vice-versa”. In consequence, there are at least 2 different kinds of virtual particles, e.g. those from hyperspace and those of 3-D fields of force (fields of force are 3-D because they vary with the square of the distance - see also [1,2,3]).

            A surprising conclusion of the hyperspace model is that gravitation and EM attraction could be explained simply as the result of a “suction” force from hyperspace. In fact: Hyperspace is to a 3-D space as the atmosphere is to a balloon or the void to air. The air of the balloon tries to escape to the atmosphere through any hole the balloon has, while the air tries to fill up any empty space (vacuum). In an analogous way, gravitation and EM can be seen as the tendency of non-charged/charged matter to dissipate in hyperspace through small windows between our 3-D universe and hyperspace. These windows are opened by the energy we know as quantum spin. As seen already in the Background Field (BF) theory (Calvet12 and Calvet13), gravitation and EM are probably forces produced by the same field and EM is simply due to more energetic interactions with the BF. Therefore, hyperspace will produce a suction force on elementary particles, analogous to their mass (gravitation) or polarity (EM), while the BF is a field that links our world to hyperspace. EM repulsion could be explained in an analogous way as a phenomenon that forces the BF out of hyperspace, i.e. between two equal charges or poles. 

            1. Black Holes

            According to the above hyperspace model, a Black Hole (BH) would be a relatively large window to hyperspace, e.g. the mass (particle density) of the corresponding body would be so great, that it could no longer be supported by the fabric of space-time, thus “falling” into hyperspace. The strong gravitational attraction of BHs can be now easily understood as a strong hyperspace suction effect on particles in our 3-D world. The infinitely dense and infinitely small body that is attributed usually to BHs, can be understood as a particle that has exceeded certain limit and that has been absorbed by hyperspace. This limit would be analogous to the Chandrasekhar limit, e.g. the mass limit, beyond which an exploding star becomes a BH. The concepts “infinitely dense and infinitely small” are concepts relative to our 3-D universe. In hyperspace, a BH is probably nothing else than a conventional body with a certain density and size, since the ability of hyperspace to support massive bodies is probably much higher than that of 3-D space because of the 2 additional degrees of freedom (dimensions).

The hyperspace model is a generalization and would work with any field proposed in literature (Higgs-field, BF, ZPF, etc.). It has an intrinsic beauty since it explains even extraordinarily strange relativistic phenomena like BHs in plane and almost Newtonian words. Everybody understands the meaning of suction, as a force produced by the tendency of matter to dissipate in hyperspace whenever possible, since any increase of the size of a space will produce a force that forces matter literally to fill up this new empty space.

Small BHs could be produced artificially by using a conventional hydrogen bomb and fusion material at 0ºK instead of higher temperatures. At 0ºK, there would be no radiation leaving the atoms when the bomb compressed the material, thus allowing a much more efficient compression than at higher temperatures. If we compressed in this way hydrogen at 0ºK, apart from different fusion materials, we would also get some hyperdense material in form of small BHs or neutron matter. Hydrogen is the ideal candidate for such compression since at 0ºK, it would build an absolutely dense proton body once we had demagnetized and deelectrified atoms (e.g. elimination of any orbiting or free electron).

            Once we had produced and stabilized such matter by placing it i.e. in the outer space, we could use it to access the hyperspace. The more matter we managed to compress, the more the resulting BH would “fall” into hyperspace. We could also condense heavy atoms like gold atoms at 0ºK reaching an even much more dense body (this would require higher compression energy and a more efficient cooling of the device). 

            2. Hyperspace Model of the Universe

            In summary, we can imagine our world as a 3 dimensional space with 3-D objects “floating” in a 5-dimensional sea, the hyperspace.

            In drawing 1 (to the left), space and hyperspace are shown as two different worlds, each dominated by different kinds of energy, e.g. 3-D Kelvin radiation in our universe, and 5-D quantum waves and ZPE in hyperspace. Both worlds are linked by small windows (fermions), but also by larger windows that can be created or exist here and there (Black Holes, Neutron Stars, etc.). The stability of our world depends on the size of these windows. If we created a window, so huge that the whole 3-D universe could pass through it, our universe would be destroyed and would be absorbed completely by the much larger hyperspace. Fortunately, in our universe, there are not many of such large windows. In fact, the major part of hyperspace windows is as small as elementary particles. Only here and there are larger windows like BHs or other phenomena that have not even been described or thought about in scientific literature.

            Also in drawing 1, we see an upper 3-D world with real particles of heat and light. Forces vary in this world with the square of the distance.

            Beneath our universe, there is a 5-D world (hyperspace) with particles that are “virtual” to us, since they cross our universe only from time to time. In this world, there are only quantum waves and ZP-particles. Hyperspace is interfaced to our universe through small windows (fermions) and larger “tunnels” (BHs, Neutron Stars, etc.).

            Beneath hyperspace, there is an absolutely flat universe that represents the, so called, “Big Chill,” since at this mysterious stage, there remains no energy of any kind at all.

            The above mentioned hyperspace model is not an arbitrary model.  It is even able to explain one of the most crucial questions of physics and cosmology is: “Why is our universe 3-dimensional?”. This model shows that our conventional 3-D space is only part of a greater world. Our space seems 3-D to us, simply because the smallest space that can support elementary particles is a 3-D space. But this does not mean that there are no further dimensions - all the contrary. In fact, if we imagine a completely empty space with no particle at all, how many dimensions would this space have? The answer is of course: “infinite”. Infinite, because a space without any particle inside has evidently no “information” about how many dimensions particles need. Therefore, in order to grant in any case a stable universe, space must have the greatest amount of degrees of freedom (dimensions) possible. And this number is certainly “infinite”. Any other universe would be unable to exist since it would be non-compatible with itself.

            In consequence, our universe is 3-dimensional, simply because 3 is the smallest number of dimensions a particle needs to exist. This agrees with the above mentioned hypothesis that particles are nothing else than waves in the fabric of space since any wave has at least 3 degrees of freedom (x, y, z). May be, hyperspace arose from the movement of elementary particles. In a space with a potentially infinite number of dimensions, the universe (the space, where particles are confined) is able to adopt any number of dimensions according to the evolution of the universe itself. It is therefore not negligible to suppose that there can exist phenomena in the universe that needed more than 5 degrees of freedom (i.e. “strings” that are supposed to exist in 11 dimensions).

            In order to prove if the above presented model is consistent with cosmology, lets try the following experiment of thought:

            Imagine a particle that is released at the upper side of the thermal scale. By “falling down” the scale, the particle passes from a highly energetic state (Big Bang) through the Kelvin universe. The lower the energetic state of the particle, the less radiation energy it releases. In consequence, the particle cools down, emitting X-rays at 2x106ºK, UV-radiation at 105ºK and finally IR radiation at room temperature. As the particle continues to fall down the thermal scale, it approaches 0ºK, emitting less and less photons each time. At 0ºK, the emission of photons stops completely and the particle “falls” into the hyperspace by adopting the same thermal state as the ZPR. Once in hyperspace, the energy of the particle is of 10115 J m-3 s-1. At this stage, the particle becomes a virtual ZPF-particle. As the particle falls more and more down the thermal scale of quantum temperatures, its quantum wave structure weakens continuously. At reaching the level of 0 Joules, the quantum wave structure of the particle disappears and the universe becomes completely flat as if the particle had never existed.

            The above mentioned process of a particle “falling down” the Kelvin and quantum thermal scales, surprisingly agrees with the cosmological models of the Big Bang and the Big Chill. According to this hyperspace model, the Big Bang that originated the universe, produced a space with a potentially infinite number of degrees of freedom (similar to embryonic cells that have the ability to become any kind of cell of the body since they are not yet specialized). The wavy nature of elementary particles restricted the number of spatial dimensions to 3, although this basic number was subsequently increased in order to allow elementary particles to move and rotate at relativistic velocities. We can thus imagine the universe as a stormy sea of quantum waves and ZPE. The final state of such a universe (the “great calm” after the storm) is a completely flat universe with no quantum waves and no particles at all. In cosmology, this state is called the “Big Chill” and agrees surprisingly with this hyperspace model.

            After describing the dimensional nature of the universe, our efforts must now be directed to control and manipulate hyperspace. If we manage to create artificial windows that link our universe to hyperspace, we will be able to travel light years in 3 dimensions, while moving only millimeters inside hyperspace. The possibilities for interstellar navigation are enormous. A window could be opened, compressing demagnetized and de-electrified matter at 0ºK by means of a hydrogen bomb (an atomic bomb that compresses matter). The resulting hyperdense matter could be stabilized and used to send a probe through the hyperspace, but also to extract radiation (cheap energy) or even to communicate with remote civilizations. I am confident that dimensional technology will be in approximately 50 years as usual as quantum devices in the next decades.


1. John Cramer (1986), "The Transactional Interpretation of Quantum Mechanics," Rev. Mod. Phys, 58, pp. 647-687. 

2. William Clifford (1956), "On the Space Theory of Matter," The World of Mathematics, p.568, Simon & Schuster, NY

3. J. Wheeler and R. Feynman (1945), "Interaction with the Absorber as the Mechanism of Radiation," Rev. Mod. Phys. 17 , 157.

4. Milo Wolff (1995), "Beyond the Point Particle - A Wave Structure for the Electron," Galilean Electrodynamics, 6, No. 5, pp. 83-91.

5. Casimir, H.G.B. (1948) "On the attraction between two perfectly conducting plates,” Proc. Kon. Ned. Akad. van Weten., Vol. 51, No. 7, pp. 793-796.

6. Lamoreaux, S.K. (1997) "Demonstration of the Casimir force in the 0.6 to 6 mm range,” Phys. Rev. Lett., Vol. 78, No. 1, pp. 5-8.

7. Milonni, P.W., Cook, R.J., and Goggin, M.E. (1988) "Radiation pressure from the vacuum: Physical interpretation of the Casimir force,” Phys. Rev. A, Vol. 38, No. 3, p. 1621-1623.

8. Michio Kaku (1994). “Hyperspace. A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension,” Oxford University Press. N.Y. 432 pp.

9. A.Rueda & B.Haisch (1998), "Inertia as reaction of the vacuum to accelerated motion,” Physics Letters A, Vol. 240, No. 3, p.115

10. S. De Curtis, J. Fernández Ferrer (1998), "Physik,” Neuer Kaiser Verlag, 95 pp. (in German)

11. Bernhard Haisch & Alfonso Rueda (2000), „Toward an Interstellar Mission: Zeroing in on the Zero-Point-Field Inertia Resonance,” AIP Conference Proceedings of the Space Technology and Applications International forum (STAIF-2000) Conference on Enabling Technology and Required Scientific Developments for Interstellar Missions, Albuquerque, NM, p. 1-7.

12. Carlos Calvet, “Effects and Evidence of the "Background Field",” Journal of New Energy, Vol. 4, no. 4, Spring 2000, p. 12-23

13. Carlos Calvet, “Detection and Origin of the Background Field,” Journal of Theoretics, Vol.2, No.4, Aug 2000 

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