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Closer to Truth: Are there really extra dimensions?


Extra dimensions -beyond length, width, height- seem the stuff of science fiction. What would extra dimensions be like? Is time the fourth dimension? Could deep reality be so strange? And, anyway, why would we care? Featuring interviews with Lawrence Krauss, Michio Kaku, David Gross, Nima Arkani-Hamed, Juan Maldacena, and Roger Penrose.

Of course, if we like, we can see time as half a dimension (forward only). Okay. But…

Beyond that, one way of looking at these controversies is to begin by asking what difference it would make.

I (O’Leary for News) remember, in high school, reading a book that calculated how many 11-dimensional baseballs would fit into a nine-dimensional box, or something like that. Not being, at best, gifted at math, I quickly lost the thread of the discussion.

One can’t help wondering what the notion of many additional dimensions is supposed to do.

Some resources:

“One recent string theory suggests that the reason we only experience the three spatial dimensions is that all universes with higher dimensions got into some cosmic car accident and destroyed each other, leaving our measly three-dimensional brane untouched.”

Current versions of string theory require 10 dimensions total, while an even more hypothetical über-string theory known as M-theory requires 11. But when we look around the universe, we only ever see the usual three spatial dimensions plus the dimension of time. We’re pretty sure that if the universe had more than four dimensions, we would’ve noticed by now. … Thankfully, string theorists were able to point to a historical antecedent for this seemingly radical notion.”

It turns out that in order to encompass both of these two forces, we have to add another five dimensions to our mathematical description. There’s no a priori reason it should be five; and, again, none of these additional dimensions relates directly to our sensory experience. They are just there in the mathematics. So this gets us to the 10 dimensions of string theory. Here there are the four large-scale dimensions of spacetime (described by general relativity), plus an extra six ‘compact’ dimensions (one for electromagnetism and five for the nuclear forces), all curled up in some fiendishly complex, scrunched-up, geometric structure.”

By now, you probably get the picture. The side door to “Anything we want to believe is true.”

I've never really understood the weird animosity of Christians on this site towards the multiverse theory and now the idea of other dimensions. As far as NDE research is concerned, BA you are cherry-picking accounts to fit your views. Raymond Moody (deceased), Dr. Bruce Greyson and the University of Virginia Dept. of Perceptual Studies have gathered an enormous amount of NDE research together from around the world, including accouns as far back as Plato. Generally speaking, people interpret what happens to them in terms of their culture, but there are basic categories of experience that virtually all who have an NDE experience to a large degree. For example, a large percentage of people experience a being of light regardless of their religious beliefs, and usually interpret that through a cultural lens, although there are exceptions. Atheists and agnostics usually have the same experience as anyone else. Virtually nobody experiences a drop towards what one might describe as a "hellish" destination. Also, the NDE evidence doesn't exist in a vacuum. There is also an enormous amount of evidence for reincarnation and what is usually referred to a "astral projection" and valid, evidential, physical mediumship providing information about what we call "the afterlife," which might be better labeled as "other dimensions" or a vast multiverse of potential experiences available to us. There are literally tens of thousands, if not millions, of people that have visited these places, one way or another, and many who do so regularly, interacting with the dead and those that inhabit those places. The evidence is pretty clear, IMO, if one can assess it fairly and rationally without a priori doctrinal biases. William J Murray
And here are a few more quotes from people who have experienced Near Death, that speak of how their perception of time was radically altered as they were outside of their material body.
'Earthly time has no meaning in the spirit realm. There is no concept of before or after. Everything - past, present, future - exists simultaneously.' - Kimberly Clark Sharp – Near Death Experiencer 'There is no way to tell whether minutes, hours or years go by. Existence is the only reality and it is inseparable from the eternal now.' - John Star - NDE Experiencer
As well, Near Death Experiencers also frequently mention going through a tunnel to a higher heavenly dimension:
Ask the Experts: What Is a Near-Death Experience (NDE)? - article with video Excerpt: "Very often as they're moving through the tunnel, there's a very bright mystical light ... not like a light we're used to in our earthly lives. People call this mystical light, brilliant like a million times a million suns..." - Jeffrey Long M.D. - has studied NDE's extensively - abcnews nightline The Tunnel and the Near-Death Experience Excerpt: One of the nine elements that generally occur during NDEs is the tunnel experience. This involves being drawn into darkness through a tunnel, at an extremely high speed, until reaching a realm of radiant golden-white light. - near death research
In the following video, Barbara Springer gives her testimony as to what it felt like for her to go through the tunnel:
"I started to move toward the light. The way I moved, the physics, was completely different than it is here on Earth. It was something I had never felt before and never felt since. It was a whole different sensation of motion. I obviously wasn't walking or skipping or crawling. I was not floating. I was flowing. I was flowing toward the light. I was accelerating and I knew I was accelerating, but then again, I didn't really feel the acceleration. I just knew I was accelerating toward the light. Again, the physics was different - the physics of motion of time, space, travel. It was completely different in that tunnel, than it is here on Earth. I came out into the light and when I came out into the light, I realized that I was in heaven." Barbara Springer - Near Death Experience - The Tunnel - video https://www.youtube.com/watch?v=gv2jLeoAcMI
And in the following audio clip, Vicki Noratuk, who has been blind from birth, besides being able to see for the first time during in her life during her Near Death Experience, also gives testimony of going through a tunnel:
“I was in a body, and the only way that I can describe it was a body of energy, or of light. And this body had a form. It had a head, it had arms and it had legs. And it was like it was made out of light. And it was everything that was me. All of my memories, my consciousness, everything.”,,, “And then this vehicle formed itself around me. Vehicle is the only thing, or tube, or something, but it was a mode of transportation that’s for sure! And it formed around me. And there was no one in it with me. I was in it alone. But I knew there were other people ahead of me and behind me. What they were doing I don’t know, but there were people ahead of me and people behind me, but I was alone in my particular conveyance. And I could see out of it. And it went at a tremendously, horrifically, rapid rate of speed. But it wasn’t unpleasant. It was beautiful in fact.,, I was reclining in this thing, I wasn’t sitting straight up, but I wasn’t lying down either. I was sitting back. And it was just so fast. I can’t even begin to tell you where it went or whatever it was just fast!" – Vicki’s NDE – Blind since birth – https://www.youtube.com/watch?v=e65KhcCS5-Y
And the following people who had a NDE both testify that they firmly believed that they were in a higher dimension that is above this three-dimensional world and that the primary reason that they have a very difficult time explaining what their Near Death Experiences felt like is because we simply don't currently have the words to properly describe that higher dimension:
"Regardless, it is impossible for me to adequately describe what I saw and felt. When I try to recount my experiences now, the description feels very pale. I feel as though I'm trying to describe a three-dimensional experience while living in a two-dimensional world. The appropriate words, descriptions and concepts don't even exist in our current language. I have subsequently read the accounts of other people's near-death experiences and their portrayals of heaven and I able to see the same limitations in their descriptions and vocabulary that I see in my own." Mary C. Neal, MD - To Heaven And Back pg. 71 “Well, when I was taking geometry, they always told me there were only three dimensions, and I always just accepted that. But they were wrong. There are more… And that is why so hard for me to tell you this. I have to describe with words that are three-dimensional. That's as close as I can get to it, but it's really not adequate.” John Burke – Imagine Heaven pg. 51 – quoting a Near Death Experiencer
Moreover, besides heavenly experiences, there are also hellish experiences that also corroborate what we would expect to see from what we now know about General Relativity.
To Hell and Back: The Dark Side of Near Death Experiences - Brent Swancer - May 25, 2016 Excerpt: Nancy Evans Bush has estimated that one out of every five NDEs involve terrifying traumatic experiences such as black, cold voids, total sensory deprivation, yawning chasms of loneliness, prowling monsters, or indeed visions of an actual Hell, the description of which can vary wildly from person to person. In her book Dancing Past the Dark, Bush explains about these different permutations of Hell http://mysteriousuniverse.org/2016/05/to-hell-and-back-the-dark-side-of-near-death-experiences/
In the following video clip, former atheist Howard Storm speaks of what eternity felt like for him in the hellish dimension:
Howard Storm's Near Death Experience - video - (9:00 minute mark) https://www.youtube.com/watch?v=Pi3e16JY6UM
And at the 7:00 minute mark of this video, Ron Reagan gives testimony of falling down a 'tunnel' towards hell:
Hell - A Warning! – video https://www.youtube.com/watch?feature=player_detailpage&v=HSgH2AHkfkw&list=PLCB5F225ABC1F7330#t=420
And in this following video, Bill Wiese also speaks of 'tumbling down' a tunnel in his transition stage to hell:
Bill Wiese on Sid Roth – video https://www.youtube.com/watch?v=nHTU9oe9s7k
And in this following video, Paul Ojeda also speaks of 'falling' towards hell at a very fast speed:
Imagine Heaven - What About Hell? - John Burke – video (33:00 minute mark) https://youtu.be/j7N473pY1hs?t=1986
Thus, in conclusion, Christians, far from being 'anti-science' as atheists often accuse Christians of being, can appeal directly to Quantum Mechanics, Special Relativity, and General Relativity, our most powerful theories in science, to powerfully back up some of their core beliefs in God and the afterlife. Whereas, on the other hand, it is found that Atheists are actually the ones who are stuck postulating imaginary universes and dimensions, etc.. to 'explain away' observational evidence that points to the reality of God. In short, atheists have to rely on their imagination, not observational evidence, to avoid the evidence for God, and thus they have become very much anti-science in their attempts to avoid any implication of God. As I said the other day, "Since God, not materialism and/or naturalism, is the basis of all physical reality, then the rejection of God by modern day scientists as an explanation for why the physical universe exists, and even as the explanation for why we ourselves exist, necessarily forces them to postulate explanations that are inherently ‘unreal’, illusory, and/or imaginary." https://uncommondesc.wpengine.com/intelligent-design/researchers-black-holes-are-collapsed-universes/#comment-722173 Verse:
2 Corinthians 12:2-4 I know a man in Christ who fourteen years ago was caught up to the third heaven. Whether it was in the body or out of the body I do not know—God knows. And I know that this man—whether in the body or apart from the body I do not know, but God knows— was caught up to paradise and heard inexpressible things, things that no one is permitted to tell.
As was mentioned, the eternity for special relativity is found when a hypothetical observer approaches the speed of light. In this scenario, time, as we understand it, would come to a complete stop for that hypothetical observer as he reached the speed of light.
“Eternity is not a long time. Eternity is the opposite of time: It is no time. It is, as Augustine said, "The now that does not pass away." David Steindl-Rast - Music of Silence – pg 7
To grasp the whole concept of time coming to a complete stop at the speed of light a little more easily, imagine moving away from the face of a clock at the speed of light. Would not the hands on the clock stay stationary as you moved away from the face of the clock at the speed of light? Moving away from the face of a clock at the speed of light happens to be the very same ‘thought experiment’ that gave Einstein his breakthrough insight into special relativity. Here is a short clip from a video that gives us a look into Einstein's breakthrough insight.
"In the spring of 1905, Einstein was riding on a bus and he looked back at the famous clock tower that dominates Bern Switzerland. And then he imagined, "What happens if that bus were racing near the speed of light.", (narrator: "In his imagination, Einstein looks back at the clock tower and what he sees is astonishing. As he reaches the speed of light, the hands of the clock appear frozen in time"), "Einstein would later write, "A storm broke in my mind. All of the sudden everything, everything, kept gushing forward.", (narrator: "Einstein knows that, back at the clock tower, time is passing normally, but on Einstein's light speed bus, as he reaches the speed of light, the light from the clock can no longer catch up to him. The faster he races through space, the slower he moves through time. This insight sparks the birth of Einstein's Special Theory of relativity, which says that space and time are deeply connected. In fact, they are one and the same. A flexible fabric called spacetime.") - Michio Kaku Einstein: Einstein’s Miracle Year (‘Insight into Eternity’ – Thought Experiment - 6:29 minute mark) – video https://youtu.be/QQ35opgrhNA?t=389
That time, as we understand it comes to a complete stop at the speed of light, and yet light moves from point A to point B in our universe, and thus light is obviously not 'frozen within time, has some fairly profound implications. The only way it is possible for time not to pass for light, and yet for light to move from point A to point B in our universe, is if light is of a higher dimensional value of time than the temporal time we are currently living in. Otherwise light would simply be 'frozen within time' to our temporal frame of reference. One way for us to more easily understand this higher dimensional framework for time that light exists in is to visualize what would happen if a hypothetical observer approached the speed of light. In the first part of the following video clip, which was made by two Australian University Physics Professors, we find that the 3-Dimensional world ‘folds and collapses’ into a tunnel shape as a ‘hypothetical’ observer approaches the ‘higher dimension’ of the speed of light.
Optical Effects of Special Relativity - video (full relativistic effects shown at 2:40 minute mark) https://youtu.be/JQnHTKZBTI4?t=160
To give us a better understanding as to what it would be like to exist in a higher dimension, this following video, Dr. Quantum in Flatland, also gives us a small insight as to what it would be like to exist in a higher dimension:
Dr. Quantum in Flatland – video https://www.youtube.com/watch?v=B5yxZ5I-zsE
Besides the tunnel curvature to a higher eternal dimension found in special relativity, we also have tunnel curvature to a very different eternal dimension in general relativity. The following video clip is very good for illustrating that tunnel curvature that is found in general relativity. The following video is also very good for illustrating the tunnel curvature that is found for the space-time of gravity in general relativity. Specifically, it is good for visualizing the tunnel curvature that is found at black holes
Space-Time of a Black hole - video http://www.youtube.com/watch?v=f0VOn9r4dq8
What makes the eternity of General Relativity profoundly different than the eternity found at Special Relativity, is that entropy, which is the primary reason why our material bodies grow old and eventually die in this universe,,,
Entropy Explains Aging, Genetic Determinism Explains Longevity, and Undefined Terminology Explains Misunderstanding Both - 2007 Excerpt: There is a huge body of knowledge supporting the belief that age changes are characterized by increasing entropy, which results in the random loss of molecular fidelity, and accumulates to slowly overwhelm maintenance systems [1–4].,,, http://www.plosgenetics.org/article/info%3Adoi/10.1371/journal.pgen.0030220
,,, Entropy is found to be greatest at black holes. As the following article stated,, 'supermassive black holes are the largest contributor to the observable universe’s entropy.'
Entropy of the Universe - Hugh Ross - May 2010 Excerpt: Egan and Lineweaver found that supermassive black holes are the largest contributor to the observable universe’s entropy. They showed that these supermassive black holes contribute about 30 times more entropy than what the previous research teams estimated. https://reasons.org/explore/blogs/todays-new-reason-to-believe/read/tnrtb/2010/05/10/entropy-of-the-universe How Special Was The Big Bang? “But why was the big bang so precisely organized (to 1 in 10^10^123 for the initial entropy), whereas the big crunch (or the singularities in black holes) would be expected to be totally chaotic? It would appear that this question can be phrased in terms of the behaviour of the WEYL part of the space-time curvature at space-time singularities. What we appear to find is that there is a constraint WEYL = 0 (or something very like this) at initial space-time singularities-but not at final singularities-and this seems to be what confines the Creator’s choice to this very tiny region of phase space." Roger Penrose – (from the Emperor’s New Mind, Penrose, pp 339-345 copyright 1989, Penguin Books) http://www.ws5.com/Penrose/
In the following quote, Kip Thorne describes what will happen to a hypothetical astronaut as he falls into black-hole. He stated: "Einstein's equation predicts that, as the astronaut reaches the singularity (of the black-hole), the tidal forces grow infinitely strong, and their chaotic oscillations become infinitely rapid. The astronaut dies and the atoms which his body is made become infinitely and chaotically distorted and mixed-and then, at the moment when everything becomes infinite (the tidal strengths, the oscillation frequencies, the distortions, and the mixing), spacetime ceases to exist."
"Einstein's equation predicts that, as the astronaut reaches the singularity (of the black-hole), the tidal forces grow infinitely strong, and their chaotic oscillations become infinitely rapid. The astronaut dies and the atoms which his body is made become infinitely and chaotically distorted and mixed-and then, at the moment when everything becomes infinite (the tidal strengths, the oscillation frequencies, the distortions, and the mixing), spacetime ceases to exist." Kip S. Thorne - "Black Holes and Time Warps: Einstein's Outrageous Legacy" pg. 476
Thus the ‘eternity’ that is found at a black hole can rightly be called an ‘eternity of decay, death, and destruction’. Needless to say, to those of us who are of, shall we say, a spiritually minded persuasion, this finding of an eternity of destruction should be fairly sobering. Moreover, to further validate the Christian claim that heaven and hell are real and actually exist, we don't have to rely solely on our scientific evidence from special relativity and general relativity. But we can also reference the many testimonies of people who have died for a short while and come back. These testimonies are termed Near Death Experiences. In the following video clip, Mickey Robinson gives his Near Death testimony of what it felt like for him to experience a 'timeless eternity'.
'In the 'spirit world,,, instantly, there was no sense of time. See, everything on earth is related to time. You got up this morning, you are going to go to bed tonight. Something is new, it will get old. Something is born, it's going to die. Everything on the physical plane is relative to time, but everything in the spiritual plane is relative to eternity. Instantly I was in total consciousness and awareness of eternity, and you and I as we live in this earth cannot even comprehend it, because everything that we have here is filled within the veil of the temporal life. In the spirit life that is more real than anything else and it is awesome. Eternity as a concept is awesome. There is no such thing as time. I knew that whatever happened was going to go on and on.' In The Presence Of Almighty God – The NDE of Mickey Robinson – video (testimony starts at 27:45 minute mark) https://www.youtube.com/watch?v=voak1RM-pXo
Moreover, we also find that the infinite dimensional Hilbert space of a quantum wave packet takes an infinite amount of information to describe properly.
Explaining Information Transfer in Quantum Teleportation: Armond Duwell †‡ University of Pittsburgh Excerpt: In contrast to a classical bit, the description of a (quantum) qubit requires an infinite amount of information. The amount of information is infinite because two real numbers are required in the expansion of the state vector of a two state quantum system (Jozsa 1997, 1) http://www.cas.umt.edu/phil/faculty/duwell/DuwellPSA2K.pdf Quantum Computing – Stanford Encyclopedia Excerpt: Theoretically, a single qubit can store an infinite amount of information, yet when measured (and thus collapsing the superposition of the Quantum Wave state) it yields only the classical result (0 or 1),,, http://plato.stanford.edu/entries/qt-quantcomp/#2.1 WHAT SCIENTIFIC IDEA IS READY FOR RETIREMENT? Infinity – Max Tegmark Excerpt: real numbers with their infinitely many decimals have infested almost every nook and cranny of physics, from the strengths of electromagnetic fields to the wave functions of quantum mechanics: we describe even a single bit of quantum information (qubit) using two real numbers involving infinitely many decimals. https://www.edge.org/response-detail/25344
As should be needless to say, the preceding findings are very comforting to overall Christian presuppositions about omniscient, and omnipresent, God upholding this universe in its continual existence.
Colossians 1:16-17 For in Him all things were created, things in heaven and on earth, visible and invisible, whether thrones or dominions or rulers or authorities. All things were created through Him and for Him. He is before all things, and in Him all things hold together.
Here is a video that goes over the preceding findings, and how they relate to Christian presuppositions, in a bit more detail
Double Slit, Quantum-Electrodynamics, and Christian Theism- video https://www.youtube.com/watch?v=AK9kGpIxMRM
Four dimensional space was also mentioned in 'The Mathematics Of Higher Dimensionality' video. As was the necessity for Four-dimensional space in the formulation General Relativity also mentioned in the video:
Four-dimensional space - with 4-D animation: Excerpt: The idea of adding a fourth dimension began with Joseph-Louis Lagrange in the mid 1700s and culminated in a precise formalization of the concept in 1854 by Bernhard Riemann.,,, Higher dimensional spaces have since become one of the foundations for formally expressing modern mathematics and physics. Large parts of these topics could not exist in their current forms without the use of such spaces.,,, Einstein's concept of spacetime uses such a 4D space, though it has a Minkowski structure that is a bit more complicated than Euclidean 4D space. https://en.wikipedia.org/wiki/Four-dimensional_space
What was not mentioned in the 'The Mathematics Of Higher Dimensionality' video is that special relativity is itself also based on a single four-dimensional continuum now known as Minkowski space. In fact, the higher dimensional nature of special relativity was a discovery that was made by one of Einstein math professors in 1908 prior to Einstein's elucidation of General Relativity in 1915. (In fact, in 1916 Einstein fully acknowledged his indebtedness to Minkowski)
Spacetime Excerpt: In 1908, Hermann Minkowski—once one of the math professors of a young Einstein in Zurich—presented a geometric interpretation of special relativity that fused time and the three spatial dimensions of space into a single four-dimensional continuum now known as Minkowski space. A key feature of this interpretation is the definition of a spacetime interval that combines distance and time. Although measurements of distance and time between events differ for measurements made in different reference frames, the spacetime interval is independent of the inertial frame of reference in which they are recorded. Minkowski's geometric interpretation of relativity was to prove vital to Einstein's development of his 1915 general theory of relativity, wherein he showed that spacetime becomes curved in the presence of mass or energy.,,, Einstein, for his part, was initially dismissive of Minkowski's geometric interpretation of special relativity, regarding it as überflüssige Gelehrsamkeit (superfluous learnedness). However, in order to complete his search for general relativity that started in 1907, the geometric interpretation of relativity proved to be vital, and in 1916, Einstein fully acknowledged his indebtedness to Minkowski, whose interpretation greatly facilitated the transition to general relativity.[10]:151–152 Since there are other types of spacetime, such as the curved spacetime of general relativity, the spacetime of special relativity is today known as Minkowski spacetime. https://en.wikipedia.org/wiki/Spacetime
Moreover, these four dimensional spacetimes that undergird both special relativity and general relativity are also comforting to overall Christian concerns in that they reveal two very different eternities to us. One eternity is found for a hypothetical observer who is going the speed of light, and another eternity is found for a hypothetical observer falling to the event horizon of a black hole.
Time dilation Excerpt: Time dilation: special vs. general theories of relativity: In Albert Einstein's theories of relativity, time dilation in these two circumstances can be summarized: 1. --In special relativity (or, hypothetically far from all gravitational mass), clocks that are moving with respect to an inertial system of observation are measured to be running slower. (i.e. For any observer accelerating, hypothetically, to the speed of light, time, as we understand it, will come to a complete stop.) 2.--In general relativity, clocks at lower potentials in a gravitational field—such as in closer proximity to a planet—are found to be running slower. (i.e. For any observer falling to the event horizon of a black-hole, time, as we understand it, will come to a complete stop.) http://en.wikipedia.org/wiki/Time_dilation Introduction to Tensor Calculus for General Relativity Excerpt: The second essential idea underlying GR is that at every spacetime point there exist locally inertial reference frames, corresponding to locally flat coordinates carried by freely falling observers, in which the physics of GR is locally indistinguishable from that of special relativity. This is Einstein’s famous strong equivalence principle and it makes general relativity an extension of special relativity to a curved spacetime. http://web.mit.edu/edbert/GR/gr1.pdf
Whereas atheists have no observational evidence that the Multiverses that they postulated to 'explain. away' the fine tuning of the universe are real, nor do Atheists have any evidence that the 'parallel universes' that they postulated to 'explain away' quantum wave collapse are real,
Multiverse Mania vs Reality - video https://www.youtube.com/watch?v=nQJV4fH6kMo
,,, whereas atheists have no observational evidence that any of their 'just so stories' are real, and are not merely imaginary, Christians, on the other hand, can appeal directly to Special Relativity, General Relativity, and Quantum Mechanics, (i.e. our most precisely tested theories ever in the history of science), to support their belief that God really does uphold this universe in its continual existence, as well as to support their belief in the reality of a heavenly dimension and in a hellish dimension." In the following video, the discovery of the higher dimensional nature of the square root of negative one, which is integral to quantum mechanics, and the discovery of higher dimensional geometry, which is integral to General Relativity, are discussed:
The Mathematics Of Higher Dimensionality - Gauss & Riemann - video https://www.youtube.com/watch?v=mxy3JhPRlV0
The history of the square root of negative one is particularly interesting to look at. Descartes had rejected complex roots and coined the derogatory term "imaginary" to describe the square root of negative one. Whereas, Gauss, who was the mathematician who finally clearly explained the higher dimensional nature behind the square root of negative one, suggested that complex magnitudes be called "lateral" instead of "imaginary" magnitudes since they represent a dimensional extension of the continuum. Gauss also proposed that complex magnitudes be awarded "full civil rights." The author further comments, in the language of Plato's allegory of the cave, complex numbers represent "forms" from a higher dimension casting "shadows" on the real number line.
Complex Magnitudes Excerpt: Descartes had rejected complex roots and coined the derogatory term "imaginary" to describe the square root of negative one, , but Leibniz thought that "The divine spirit found a sublime outlet in that wonder of analysis, that portent of the ideal world, that amphibian between being and non-being, which we call the imaginary root of negative unity." Gauss invented the "complex plane" (shown below) to represent these quantities. He suggested that complex magnitudes be called "lateral" instead of "imaginary" magnitudes since they represent a dimensional extension of the continuum. Gauss also proposed that complex magnitudes be awarded "full civil rights." In the language of Plato's allegory of the cave, complex numbers represent "forms" from a higher dimension casting "shadows" on the real number line. http://www.keplersdiscovery.com/ComplexNum.html
And in quantum mechanics, we find that the higher dimensional square root of negative one is necessary for describing the wave packet prior to measurement, and thus prior to the collapse of the wave packet.
Why do you need imaginary numbers (the square root of negative one) to describe Quantum Mechanics? “Quantum theory needs existence of an x such that x^2= -1. The reason for this is that orthogonal function spaces, of dimension greater than 2, cannot exist otherwise. In fact the only place where i (the square root of negative one) is needed is in the wave packet prior to measurement. Even the Canonical Commutation Relation doesn't need it. And nor do the eigenvalue equations. In those, any general scalar will do. But in the wave packet, you need an i.” - Steve Faulkner - Philosophy of Science, Logic, Epistemology https://www.researchgate.net/post/Why_do_you_need_imaginary_numbers_to_describe_Quantum_Mechanics2
What was not mentioned in the preceding ‘The Mathematics Of Higher Dimensionality’ video, or in the article, is that the wave function is also represented as being in an infinite dimensional Hilbert space:
Wave function Excerpt "wave functions form an abstract vector space",,, This vector space is infinite-dimensional, because there is no finite set of functions which can be added together in various combinations to create every possible function. http://en.wikipedia.org/wiki/Wave_function#Wave_functions_as_an_abstract_vector_space Why do we need infinite-dimensional Hilbert spaces in physics? You need an infinite dimensional Hilbert space to represent a wavefunction of any continuous observable (like position for example). https://physics.stackexchange.com/questions/149786/why-do-we-need-infinite-dimensional-hilbert-spaces-in-physics The Unreasonable Effectiveness of Mathematics in the Natural Sciences – Eugene Wigner – 1960 Excerpt: We now have, in physics, two theories of great power and interest: the theory of quantum phenomena and the theory of relativity.,,, The two theories operate with different mathematical concepts: the four dimensional Riemann space and the infinite dimensional Hilbert space, http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html
Here is an interesting quote about the mysterious infinite dimensional Hilbert Spaces in quantum mechanics, a quote that shows that it is integral and not just a metaphysical add-on (as the atheists's conjectures of multiverses and parallel universes are just metaphysical add-ons), ” (Imagine reading off details about elementary particles from the rules of chess-castling. en passant-a la Lewis Carro;; in Through the Looking Glass.) No physicist today understands why this is possible..”
The Applicability of Mathematics as a Philosophical Problem - Mark Steiner - (page 44) Excerpt: Let us now recapitulate: beginning with the concept of a Hilbert space, a certain kind of (usually infinite-dimensional) vector space, and the formal requirement that a unit vector on the space represents all possible information can be gleaned. First, the space cannot be a real vector space; the usual formalism is, therefore, based on a complex Hilbert space. With this formalism the Heisenberg uncertainty principle follows directly. So does the quantization of angular momentum, including the so called "space quantization". So does the prediction that "electron spin" cannot be due to spatial rotation. And so do the selection rules for the spectrum of hydrogen, based on the "nonphysical" concept of parity. The role of Hilbert spaces in quantum mechanics, then, is much more profound than the descriptive role of a single concept. An entire formalism-the Hilbert space formalism-is matched with nature. Information about nature is being "read off" the details of the formalism. (Imagine reading off details about elementary particles from the rules of chess-castling. en passant-a la Lewis Carro;; in Through the Looking Glass.) No physicist today understands why this is possible.. https://books.google.com/books?id=GKBwKCma1HsC&pg=PA44
The idea is a lot older than Einstein. Abbott's "Flatland", written in 1885, was an attempt to show ordinary people how a fourth dimension would feel, by analogy with two-dimensional people trying to perceive the third. The persuasion didn't work then and still doesn't work, but Abbott's broader parody of human behavior DOES work. Tne one-dimensional Monarch of Pointland is a perfect model of today's psychopathic demons who run and obliterate every country except Tanzania. polistra
It’s really too bad that Lawrence Krauss in the mix. That pedo piece of shit deserves no podium AaronS1978

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