FOURTH DIMENSION, WHEREFOURTH ART THOU?

In a previous post, I referenced the possible existence of a fourth spatial dimension,[1] possibly a small fraction of a millimeter above (outside?) the three with which we are familiar. In truth, string theory,[2] superstring theory, and M-theory demand ten or more dimensions to satisfy theoretical equations. It’s difficult to imagine just a four-spatial-dimensional reality. In fact, even professional physicists of all stripes cannot fully comprehend that fourth dimension, much less ten dimensions.

By the way, it’s also not easy to recognize or visualize less than the three dimensions to which we are accustomed. To appreciate the difficulty, try to imagine an object in only two dimensions. Most people will cite a sheet of printer paper, an artist’s canvas, a tissue or some other seemingly flat, two-dimensional object. However, they don’t qualify as a two-dimensional object – not in physics. The sheet may be 11” along the X axis and 8½” along the Y axis, but it also has dimension along the Z axis.

A sheet of printer paper extends upward along the Z axis, i.e., perpendicular to the X and Y axes. The thickness of a sheet of printer paper is nominally 0.1mm (0.004” – 4 mils), therefore it is three-dimensional, not two-dimensional. Even a drawing of a triangle on a sheet of paper is two-dimensional because the graphite, crayon, or ink has a Z component rising vertically from the sheet of paper. These distinctions may seem like hairsplitting; however, the field of physics is exacting, or as exacting as is humanly possible given today’s technology. 

So, what is an example of a true two-dimensional object? Imagine an object that only extends along the X and Y axes but that extends along the Z axis only the thickness of the smallest possible particle. The smallest known particle so far is the quark, one of two particles in a proton, itself one of the two types of particles in the nucleus of an atom. A quark is on the order of 10^-15 mm. That’s 0.000000000000001 mm, folks.

We do not encounter such a two-dimensional object in everyday life, so visualizing such an object is difficult to imagine although not as difficult as visualizing or even imagining a fourth dimension. We are left with a question: Can or should a 2D plane with a Z axis extending to the diameter of the smallest particle known to us be considered a valid 2D object? Should it be smaller? This is not only a physics question; it is also a philosophical question, begging for a definition of “two-dimensional.”

My view, right or wrong, is that, if the thickness (diameter?) of the smallest known particle disqualifies any object as two-dimensional, then there can be no X or Y axes either since they could only be represented by the same smallest particle. Therefore, without some thickness on the Z axis, there can be no other axis. We end up with a theoretical, imaginary plane along only the X and Y axes. No measurement can be taken, no observation can be made, the object will be massless because, logically, it does not exist except as a theoretical, imaginary plane. It is arguable that, in our reality, a true two-dimensional object, much less a one-dimensional object, is impossible, or undefined at best.

Likewise, the logic remains the same for one-dimensional objects.

String theory and its various permutations are outgrowths of quantum mechanics. String theory proposes that the smallest particle is not a particle at all, but a “string” of energy. Much like the notes from a stringed instrument, the loose characterization being that strings of energy of varying lengths and shapes vibrate at different frequencies and determine the function of each string. If valid, this characterization presents some interesting implications.

For example, it may render our previous discussion about the definition of a 2D object and allowed limits for the Z value moot. After all, what are the dimensions of energy?

Let’s allow for a moment that there is a fourth spatial dimension just outside our senses. Sight and tactile senses allow us to recognize the three dimensions with which we are familiar. I wonder what, if there are objects or beings inhabiting all four – or less – dimensions, what they might see or feel.

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[1] Kaku, Michio. Parallel Worlds: A Journey Through Creation, Higher Dimensions, and the Future of the Cosmos, Doubleday, New York, New York, 2005, pp. 219-220,330.

[2] Often referred to as a theory, it is a misnomer. In truth, superstring hypothesis is more appropriate and accurate since a theory attempts to understand observed phenomena whereas a hypothesis is a “possible” reason for that phenomena which is then, itself, tested. In this context, a proven hypothesis is an underpinning – and therefore support for – a theory. In short, a theory is a more wide-ranging possible explanation for a set of observed phenomena than a hypothesis.

COLLAPSING A WAVE FUNCTION IN

THE MOST PRIMITIVE PHYSICS EXPERIMENT EVER

After my last post about the magic of quantum mechanics and its secrets, I wanted to replicate as much of the double-slit experiment as I could[1]. And I did – the simplest of experiments and with the most unsophisticated of methods. Still, I was able to confirm some preliminary results.

Without sophisticated lab equipment, I replicated what I could with, first, a laser pointer that one uses during a lecture or to torture cats until they fall down and then a laser level (which made more sense since it has a more intense light beam and is more stable with its 16” length).

Here’s a picture of the setup. (Did I mention that it was primitive?) The laser level is sitting on a 15” ruler with a thumb drive at the rear to level the…uh, level. About 33cm (13”) in front is a business card with the end bent up at roughly 90 degrees to the light beam. I cut two very small slits in the now vertical edge of the card. I made the slits close enough that the light beam would span across both slits. I placed a large white card on a wall 7.32 meters (24 feet) in front of the beam as a background. (The distance from the beam origin to the slits or from the slits to the background are not critical to the results.)

I adjusted the beam until it was focused on the white background as well as could be expected given the primitive “lab” environment. To the left is an image of the light beam through a single pinhole in the business card, done to center the beam.

The setup I described above is a system, granted a very unsophisticated system, but still… Further, while conducting the various experiments, the possible results of each – in this case, only two – will be a function of all possible outcomes.[2] Because we are investigating the possible outcomes of a system involving light waves, all possible outcomes are termed a wave function. As we learned from this video, if we observe which of the two slits a photon passes through, we have collapsed the wave function. That is, we have removed all possibilities of outcomes by observing one outcome. Obviously, we cannot observe all possible outcomes at the same time.

When the beam was allowed to pass through one slit only, the pattern shown here was displayed on the background. This is no surprise since it reflects the shape of the slit in general with the photons displaying their particle-like properties.

Remember, if the observer knows which slit the photon(s) is passing through, the wave function collapses and the result is a “clump.”

When the beam was allowed to pass through both slits, the following pattern appeared on the background 7.32 meters away.

This is the expected result. The laser light beam is passing through both slits and therefore setting up a wave interference which results in the pattern shown here, much like the pattern that water through the two slits would. It is important to understand a couple things about this simple experiment. First, there is no way I could determine which slit each photon went through, although it can be determined – even controlled – in a sophisticated, well-funded laboratory setting. Second, if I could do so, the pattern would be two “clumps,” as physicists so eloquently term them, one behind each slit, similar to the simulated image below.

So, the question in many minds is, “Okay, what does this have to do with me?”

If you are reading this on a computer, it has everything to do with you. If this is printed on paper from a laser printer, it has everything to do with you. If you use a cell phone, have undergone one of many surgeries including ocular, use Blu-ray DVDs, use a flat-screen TV, or many other routine activities in everyday life using transistors and IC chips, you are immersed in the world of quantum mechanics.

Quantum mechanics is confusing – even to the most knowledgeable physicists. As physicist James Kakalios states, “. . . One of the most amazing things about quantum mechanics is that you can use it correctly and productively even if you're confused by it.”[3]

As you might intuit, there is much more to the story and I’ll address some of that in the next post. There are some very strange possibilities out there, folks. For example, just to tickle your brain, the chance that a photon will land on the background at a specific spot depends on a probability wave. This means that there is a probability – a very low, but non-zero probability – that one or more photons emanating from the laser when I ran my primitive experiment landed on the surface of a planet or moon in a faraway galaxy!

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[1] You might ask why I’d replicate something that’s been done countless times before. Not only do scientists replicate previous results to further confirm them, but running the same experiments provides a different perspective than those who came before. This may result in other hypotheses since no person thinks the same as any other. Also, and most significantly, starting with the basic experiments gives the experimenter a more solid foundation into the phenomena being addressed. As a lab technician in a former life, I know how it works.

 [2] Don’t be intimidated by the word, function. It simply means a relationship between a set of initial conditions and all possible results where one input or specific condition results in only one result. It’s a mathematical equation or expression that puts all those words in mathematical shorthand. Otherwise, expressed as a bunch of words, mathematics, physics and all other technical fields would be very awkward and, more importantly, open to inaccurate interpretations.

[3] Matson, John. “What is Quantum Mechanics Good For?” (interview with physicist James Kakalios) https://www.scientificamerican.com, Scientific American, Nov. 2, 2010, https://www.scientificamerican.com/article/everyday-quantum-physics/.

NATURAL MAGIC

I have held, for many years now, that when physicists and cosmologists finally discover all the secrets of quantum mechanics and/or string theory, we will learn that reality, in terms of that knowledge, is far more fantastic and bewildering than any works of fiction that have been committed to novels or film, and any illusions that have been presented on stage in a “magic show.” I don’t expect those discoveries to be finalized and confirmed in contemporary terms but probably by the end of this century.

I have always possessed an abiding interest in the natural world, not only contemporary nature as we view it around us today, but its evolution as well. In fact, as interesting as I find animal behavior and contemporary cryptozoological discoveries in Tanzania or Southeast Asia, paleontological and zooarchaeological discoveries are tantalizing click-bait for me. Beyond the knowledge being unearthed, pun intended, in those disciplines, I find discoveries in cosmology, astrophysics and quantum theory especially intriguing. Those three areas of study are inexorably tied together in a bond that, I predict, will never be broken.

Speaking of which, quantum mechanics may sound like an exceedingly boring topic with references to electrons, bosons, gluons, photons, quarks, gravitons[1] and many other species of discreet particles, both proven and theoretical. Even with cool-sounding, almost cartoon-character-like names, they do not reside in our everyday vernacular, except among those whose occupations require them. Add in theoretical entities such as dark energy and dark matter, among others, and millions of eyes begin to glaze over.

However, if there is such a thing as magic – not stage illusion, but real magic – it exists in the nature of quantum mechanics. A simple and clear illustration of the implications of quantum mechanics can be seen here[2]. Photons or electrons (or other particles, depending on the sophistication of the experiment and the budget of the laboratory) are the “ammunition” in the “gun” firing said particles at the barrier containing the slits. Of course, photons are the most readily available, even to the home hobbyist, in the form of a laser pointer or other light source. A laser source is more effective since the light emanates in parallel lines, perpendicular to the beam, versus a light bulb or other incandescent source. (More on this in a later post.)

A receiving medium, i.e., a sheet of paper or other backdrop, may exhibit a grouping of photons in what physicists inelegantly refer to as a “clump” directly in back of the slits. On the other hand, the photons may form a striped pattern on the background, a pattern of vertical stripes ranging away from the center of the midpoint to each side in ever-lessening intensity, none of which are in back of the slits.

Implausible as it may seem, whether a grouping of photons or electrons form a “clump” or a striped pattern on the background, depends on the presence or absence of what some refer to as an “observer.” However, this is an unfortunate term since the term connotes a human being involved in the “observation.” True, a human can be an objective observer of the phenomenon; however, removing even the tiniest human factor in the experiment and findings is better served if the term “detector” is used to represent an inorganic “observer” recording the results. HINT: It doesn’t matter – the results are the same. Keep in mind that, could it be determined which slit the photons went through, impossible except with highly sophisticated laboratory equipment, the result would be two clumps behind the slits.

If you think the results of that experiment are puzzling, check out this video on the Quantum Eraser experiment wherein the results are changed retroactively, i.e., the past is changed. (I wish I knew about this possibility after my last college exam.)

The double-slit light experiment was designed and first performed by Thomas Young in England and his findings presented to the Royal Society of London on November 24, 1803.[3] Yet, although he was a polymath in his time, his is not exactly a household name like Einstein or Hawking. Although not an exact match to the details of Young’s experiment, the process, hypothesis and results of modern experiments are the same.

I don’t know about you, dear Reader, but I am amazed by the results – and more significantly, the implications – of Young’s 200-year-old findings. Of course, I have encountered the double-slit experiment as a passing reference in classes, textbooks and curiosity-driven, self-motivated research, but I never delved into the implications until recently. If the work of Richard Feynman; Erwin Schrödinger; Neils Bohr; in this case, the temporarily intransigent Albert Einstein; Max Planck; Werner Heisenberg; Stephen Hawking and many others too numerous to mention, are the spreading roots and branches of quantum mechanics, Thomas Young’s experiment and findings are the taproot, the beginning of recognition of reality at a sub-microscopic level.

And then, we have the development of research into string theory, superstring theory, and M-theory, all three superbly elegant and related theories, even if someday proven invalid. These theories lead to thoughts of alternate universes, multiverses (countless universes), membranes (hence, the “M” in “M-theory”), Calabi-Yau manifolds, p-branes (not pea-brains), the possibility of other dimensions a fraction of a millimeter “above” (outside?) the ones to which we are accustomed. All of these are not only beyond the scope of this writing but are admittedly beyond my ken – for now.  (Although, as a former artist and Fine Arts major, the beauty and facets of Calabi-Yau manifolds are visually intriguing).

At one time, I majored in Physics in college but did not foray far into the realm of quantum mechanics save for calculating the effects of particle spin and vectors on the results. I also majored in Philosophy for some time where I found that the history of philosophy, relevant to science, was heavily weighted by authoritarian belief systems unfounded in science and therefore heavily tainted by them.[4]
Of course, one can point out that science has led mankind to some of the worst devastation of its own species as well as others, to which I would point out that the decisions to use that science and the resulting destructive forces were not made by scientists, much less science, but by those who had, and still have, no understanding of the power behind the science or the expected results. The decisions were made by uneducated minds in the relevant fields, hardly a rational argument against science.

I offer this piece for two reasons: 1) to hopefully arouse curiosity or some interest in science beyond sucking an egg into a milk bottle, powering a small digital clock with a potato, or the “magical properties” of a lever and, 2) to aver that if science is allowed full rein to gallop ahead, we will learn that reality is much more provocative and chimerical than any fantasies that the human mind can conjure and commit to novels, movies, and belief systems.

Further, according to theoretical physicist, Michio Kaku, PhD, knowledge gleaned from scientific research in these areas may be the magic wand that saves our species, not from ourselves (that’s on us), but from the inevitable flameout of our sun or collapse of our universe as we know it.[5]

NATURAL MAGIC!

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[1] The “-on” ending on most of these particles seems to be a legacy from ancient Greek wherein declension of nouns and adjectives, in neuter form, ended in “-on.” The Greek naming convention apparently stuck in physics as it has in medicine and other scientific disciplines. 

[2] The role of the cat in the video is a not-so-subtle reference to “Schrödinger’s cat,” a metaphor for one of the implications of quantum mechanics.

[3] Ananthaswamy, Anil. Through Two Doors at Once: The Elegant Experiment That Captures the Enigma of Our Quantum Reality, Penguin Random House, New York, New York, 2018, pp. 13-14.

[4] See Galileo and the Scientific Revolution by Laura Fermi/Gilberto Bernardini, Courier Corporation, 2013, and Meditations on First Philosophy by René Descartes, specifically “Meditation III” and “Meditation V.”

[5] Kaku, Michio. Parallel Worlds: A Journey Through Creation, Higher Dimensions, and the Future of the Cosmos, Doubleday, New York, New York, 2005.