In the second-last paragraph of this entry are the words "Could the 4th dimension of time be represented by Wick rotation?" What happens if we interpret the 4th dimension as spatial? I explored this in an article I wrote and called "A few thoughts about the paperback by Tibees (Toby Hendy) titled “A Guide to Making Friends in the Fourth Dimension” - https://tibees.com/". A result is that a surgeon in our 3-dimensional space can use the so-called Mobius Matrix to operate on, say, the heart without cutting through the skin (or other tissue). Here's the article -
Abstract
At the end of this book, Toby says "Go forth, and see what else you can build. I will be waiting excitedly to see what you create." I've been doing a lot of thinking and it [appears that a physical description of space and time can be obtained by regarding higher dimensions from another perspective. To explain, it's necessary to first propose a new model of our spatially 3D universe. On a more practical, Earthly note - the article proposes ideas based on science and mathematics which allow a surgeon in our 3 dimensions of space to operate using the 4th spatial dimension - thus doing her or his work without cutting tissues.
Article
Space-Time’s Proposed Composition
One-dimensional (1D) electric pulses create the binary digits of one and zero, used in electronics. The bits encode 2D Mobius strips which incorporate temporal Wick rotation * (forming the 4th dimension of time whose energy and evolution originate from the electric pulses and binary digits). A couple of Mobius strips pair up to form a Klein bottle which is immersed in 3D - trillions of strips and bottles respectively produce photons and gravitons (the smallest units of light and gravity) that interact - using Albert Einstein’s hypothesis that the particles composing the universe are made up of interacting gravitational and electromagnetic fields - and form the quantum spin of both massive electron, quark, nuclear-force bosons, Higgs boson, etc and the strong nuclear force's massless gluon.
- Being built into (a subroutine of) Mobius strips which are a building block of every boson and fermion, the real plus imaginary numbers of Wick rotation act as a timepiece, displaying and recording the coordinates and movement of particles. This makes time physical and observable.
Figure 1 - Mobius, Wick, Klein
Mobius Matrix and 4th-Dimensional Surgery
Now, picture in your mind (better still, draw with pen and paper) a diagram in which the unflattened Mobius strip on page 117 of the book is equal to a square whose sides are marked - in counterclockwise order - as a, b, c (representing the height), d, and e.
Figure 2 - Mobius Matrix
Width a is perpendicular to the length (b or e) which is perpendicular to height c. How can a line be drawn perpendicular to c without retracing b’s path? By positioning it at d, which is then parallel to (or, it could be said, at 180 degrees to) a. d is already at 90 degrees to length b and height c. d has to be at right angles to length, width and height simultaneously if it's going to include the Complex Plane's vertical "imaginary" axis in space-time (the "imaginary" realm is at a right angle to the 4 known dimensions of space-time, which all reside on the horizontal real plane). In other words, d has to also be perpendicular to (not parallel to) a. This is accomplished by a twist, like on the right side of the Mobius strip, existing in the particles of matter composing side a. In other words, a fundamental composition of matter is mathematics' topological Mobius, which can be depicted in space by binary digits creating a computer image. The twist needs to be exaggerated, with the upper right of the Mobius descending parallel to side "a" then turning perpendicular to it at approximately the level of the = sign, then resuming being parallel. Thus, 90+90 (the degrees between b & c added to the degrees between c & d) can equal 180, making a and d parallel. But 90+90 can also equal 90, making a and d perpendicular. (Saying 90+90=90 sounds ridiculous, but it has similarities to the Matrix [of mathematics, not the action-science fiction movie] in which X multiplied by Y does not always equal Y times X. The first 90 plus the second 90 does not always equal the second 90 plus the first 90 because 90+90 can equal either 180 or 90).
Adopting the familiar 3D view - a surgeon and a patient’s heart normally never touch since they’re parallel and at 180 degrees. In this view, a surgeon could only touch a heart by destructive methods such as cutting through tissues with a scalpel (equivalent to moving “a” and/or “d”). 4D can be introduced by accessing a scale trillions of trillions of times smaller than a molecule and then changing the orientation of particles from their existing 90+90=180 configuration to 90+90=90 * (except for the handle, which the doctor needs to be 3D so he can hold it). This means the doctor and cardiac organ are at right angles (90 degrees) to each other and, though seemingly parallel and out of contact, they connect like two walls meeting at a perpendicular angle. The surgeon can now touch the heart while leaving overlying skin, adipose tissue, and muscle intact.
- The paragraph beneath Fig. 2 describes the 4th spatial dimension mathematically. Physically, that dimension is the Mobius strip’s existence as a fundamental composition of every particle in space-time, and of 90+90 equalling 90. How might the above paragraph’s change from 90+90=180 configuration to 90+90=90 be accomplished? Both arrangements exist simultaneously and next to each other. Perhaps the configuration is altered simply by moving up and down the right side of the Mobius in Fig. 2 (“up” and “down” are referred to as “upsilon” and “delta” in Clifford A. Pickover’s book “Surfing Through Hyperspace” [1], and as “ana” and “kata” in Toby Hendy’s book “A Guide to Making Friends in the Fourth Dimension” [2]). At the level of the = sign in the diagram, perpendicularity to side “a” is possible. Moving just above or just below the sign can make parallelism to “a” feasible.
Time Is A Klein Bottle - And The Flat, Simply-Connected Universe
In this 3D model, time is represented as the circle of Wick rotation i.e. in 2D. The first thing we think of when applying time to the 4th dimension is to assume that the time associated with the 4th spatial dimension is described by a 3D sphere. But maybe we need to look beyond the obvious. Adding perpendicularity and a 4th dimension to space and matter demanded, in the previous paragraph, the Mobius strip. Perhaps the existence of time on the imaginary axis requires the next step up in construction of particles. According to the first paragraph of this comment, this is the Klein bottle (the union of two Mobius strips). My favourite type is the figure-8 Klein bottle, which resembles a torus or doughnut, because that type's positive and negative curvatures can cancel, then combine with computer art's Sky Replacement, to produce a flat but simply-connected universe that's infinite, eternal, and doesn't need the Big Bang. But that's another story. ** To get back to the subject of time, adding perpendicularity may actually be transformation * into Klein bottles - trillions of which form a graviton (and, in sufficient numbers, gravity). In the end, the 4th dimension has connected to gravity, a critical element in Einstein's General Relativity Theory. Einstein called time the 4th dimension while Toby's book leads to the suggestion of time being associated with the 4th spatial dimension.
- How can the real and imaginary numbers of 2D Wick rotation change into the topology of figure-8 Klein bottles? For starters, it can be pointed out that imaginary numbers - depicted as i - result in real numbers e.g. i2 (i multiplied by i) = -1, or i times -i = +1. The decimal one (+1) is represented as 1 in binary code. Together with other 1’s and 0’s, the bits (binary digits) encode 2D Mobius strips and pairs of strips combine into Klein bottles.
** Referring to the right side of Figure 1, note that the Klein bottle’s two different colours (representing positive and negative curvature) fit together to produce the outline of a doughnut. A doughnut (or strictly, a torus) is technically flat. If continuously deformed like a mass of clay, it has the same topological properties as a flat surface (like a piece of paper). When many figure-8 Klein bottles are grouped together, a procedure analogous to computer art’s Sky Replacement will cause binary digits to fill in any gaps or holes in the same way that computers can make a sky that’s blue from horizon to horizon. In other words, the digits “smooth out” the Klein bottles to produce General Relativity’s regular space (often likened to a rubber sheet). But the Klein doesn’t become multiply connected like the doughnut. Only the doughnut’s outline (with its hole filled in) is adopted and the bottle retains the property of simple connectedness. (Informally, if an object in space consists of one piece [the outline of one filled-in doughnut] - and has no holes passing all the way through it, it is called simply-connected.) According to the paper ”Cosmic Topology”, a flat universe that is also simply connected implies an infinite universe that extends endlessly in all directions [3]
Time Dilation, Advanced Waves Detected, And The Riemann Hypothesis
There might be no connection to a linear Arrow of Time that always follows a path from past to present to future, nor any distinction between those time periods. Regarding Relativity’s time dilation (slowing of time due to extremely fast velocity approaching the speed of light, or resulting from intense gravity *). This has been scientifically verified but it only seems to exist in the human frame of reference for studying the universe. This article speaks of photon-graviton interaction producing particles of matter, and of a mathematical phenomenon called Wick rotation. How can time dilation be explained in terms of Wick rotation, photons, and gravitons? Time dilation definitely exists in the human frame of reference. But if we could be God-like and use a future theory of total space-time unification to view the entirety of the universe and its periods of time all at once, we’d see that all time is united into one thing (see next paragraph). There would not be one time running slowly, nor another time passing rapidly. The absolute time of Isaac Newton, where a unit of time anywhere in the universe exactly equals that unit anywhere else, must inevitably resurface. How can time dilation be explained in terms of Wick rotation? (a) As the speed of light is approached, photons will “fall” faster from the positive or upper y-axis to the negative, or lower, y-axis (rotational speed is increased significantly and more photons interfere with each other more often, causing time to slow), and (b) each quantum within the intense gravity of a black hole - a graviton - can, according to our frame of reference, be in two or more places at once and gravitationally cause particles to simultaneously “rise” faster from the negative y-axis to the positive y-axis (again, interference between particles is increased and time dilation occurs).
- To unite the force of gravity with the idea of higher dimensions - In three dimensions, the gravitational force drops to 1/4 if one doubles the distance. In four dimensions it would drop to 1/8, and in five dimensions to 1/16. The positive direction on the x-axis (representing the motions in the length, width and depth of "real" space-time) is an extension of the negative direction on x (this may be called the 5th space dimension or complex space-time). Therefore, real gravity is perpetually amplified by complex gravity. Using science's figures, the amplification equals 1/4 multiplied by 1/4 i.e. doubling the distance in 5 space dimensions causes gravity to become 1/16 as powerful. Alternatively, the gravity's strength is reduced 4 times and this number is multiplied by another 4 to reduce it 16 times overall. In the 4th space dimension/2nd time dimension represented by the imaginary axis, this y-axis is half the distance (90 degrees) from the real x-axis that the complex x-axis is (the complex is removed 180 degrees). So gravitational weakening from doubling distance in 4 space dimensions = (reduction of 4 times multiplied by another reduction of 4 times) / 2, for an overall reduction of 8 times to a strength of 1/8.
Both gravitational and electromagnetic waves may theoretically possess retarded and advanced * components which travel forwards and backwards in time, cancelling one another and entangling all masses. Wick rotation (time) is built into the Mobius strips and figure-8 Klein bottles composing electromagnetism's photons and gravitation's gravitons. Therefore, all time (the entire past and present and future) is united into one thing just as all space and all mass are entangled into one thing. (If time only passed rectilinearly - from past to present to future - the idea of waves travelling back in time would make no sense at all. But if time is curvilinear ** - with past, present, and future interconnected - time must be able to move from future to present to past.) Unity of past/present/future may remove the issue of non-simultaneity – in special relativity – because the timing or sequence of events being different in different frames of reference can only exist if past/present/future are separate. The concepts of cause and effect are no longer separate when all periods of time are united, and everything can happen “at once”. This is similar to watching a DVD – every event on the DVD exists at once since the whole DVD exists but we’re only aware of sights and sounds occurring in each tiny fraction of a second.
- “When we solve (19th-century Scottish physicist James Clerk) Maxwell's equations for light, we find not one but two solutions: a 'retarded' wave, which represents the standard motion of light from one point to another; but also an 'advanced' wave, where the light beam goes backward in time.” [4]
Einstein's equations say gravitational fields carry enough information about electromagnetism to allow Maxwell's equations to be restated in terms of these gravitational fields. This was discovered by the mathematical physicist George Yuri Rainich. [5] It’s therefore likely that gravitational waves also possess retarded and advanced portions. Advanced waves travel back in time and when combined with the retarded waves which go forwards in time, their entanglement would result in an "eternal present" necessary for time travel. ^^
John G. Cramer wrote in his 2022 Internet article "Advanced Waves Detected" - “In summary, it appears that advanced waves do exist and have been detected. Much more work must be done to ensure that this effect is real and can be extended, but the physics implications are gigantic.” [6]
** Future spacetime warping - space can be considered as nothing more than the curved trajectories of photons and gravitons, their paths resulting from the positive and negative curvatures of the topological figures composing them - could vastly exaggerate General Relativity’s concept of curved time and space.
^^ The Riemann hypothesis is concerned with ”nontrivial zeros” on the ”critical line”, stating that these zeros lie on the vertical axis of the Complex Plane i.e. on the y-axis in then-undiscovered Wick rotation. This article suggests Wick rotation is built into all particles and helps describe spacetime. Since the critical line links Wick rotation to the Riemann hypothesis, spacetime may be describable by Riemann. The critical line pertains to zeros - so the distances in time and space that could be described by the Riemann hypothesis might, after warping of spacetime, equal zero. This makes time travel to both the past and future possible (depending on the coordinates selected by tensor calculus) as well as making instant intergalactic travel feasible.
References
[1] Clifford A. Pickover. Surfing Through Hyperspace. Oxford University Press (1999)
[2] Toby Hendy. A Guide to Making Friends in the Fourth Dimension. Tibees (2025)
[3] Jean-Pierre Luminet and Marc Lachi`eze-Rey. “Cosmic Topology”. Physics Reports 254 [3]: 135–214, www.arXiv:gr-qc/9605010 (1995)
[4] Kaku, Michio. Physics of the Impossible. Penguin Books. (2008)
[5] Rainich, G.Y., "Electrodynamics in the general relativity theory", Transactions of the American Mathematical Society, 27, 106. (1925)
[6] John G. Cramer, "Advanced Waves Detected", 2022, https://npl.washington.edu/AV/altvw219.html
