Today I will be critiquing an article written by Lawrence Krauss about the string theory, which is his specialty, from the neo-Buddhist perspective. Before starting however I would like to state that I am aware that Lawrence was probably embodying quite a bit of smart assery while writing this article. Which is to say, Humor and expectation of on average ighschool level science education.
So, when you read this Lawrence, try to take my criticisms mostly as a handy way for me to try and hone the neoBuddhist perspective on some theoretical aspect of science, as the philosophy of neoBuddhism aims for accuracy, while also trying to create a model of the world that is different from string theory, this would be just another religious theory of existence, but I would contend it is easier to model then it is to compute. I would welcome feedback on the following interpretation which mostly just reads like a starting point for reviving interest in source theory as a path for people lost in math. Which I will do by offering a perspective that is similar to quantum field theory but from a neoBuddhist perspective, and not a personal attack on you, who was polite enough to admit that string theory isn’t correct in the article. I am simply offering an alternative while risking nothing because I am not a scientist per se, I just have access to a very intelligent AI.
I will put all the direct excerpts from his article “The Search for Other Dimensions” in italics below, with my responses in bold text.
There is a German quote often attributed to Johann Wolfgang von Goethe, but which is apparently actually from Friedrich Schiller, which can be liberally translated as: “The hardest thing of all to see is that which is in front of your eyes.” Recent results in fundamental physics suggest that this may be literally as well as metaphorically true. Indeed, it is possible that whole new universes might exist just beyond the tip of your nose while remaining potentially eternally undetectable.
I liked that paragraph because it has very Buddhist connotations, as Buddhist Enlightenment is consider to be a practice of “seeing what is”
This hearkens to the famous wardrobe in “The Lion, the Witch, and the Wardrobe,” in which an entire new world was accessible by entering the wardrobe. I used this analogy in my book “Hiding in the Mirror” to discuss the long-time fixation with the possibility that extra hidden dimensions of space might exist beyond the three spatial dimensions of our universe.
Physics has not led to any real understanding of how to answer the question — one of the most fundamental questions about the universe one can ask, after all is, “Why is the space we inhabit three dimensional?” One possible answer is: maybe it isn’t! On first thought, this answer seems ridiculous. We can explore space by moving around it, and I have yet to meet a (sane) person who has found a way to move beyond up/down, forward/backward and left/right.
I like how he starts out right away, pretending to forget about the fourth dimension. I assume this is the part where the audience high school level science understanding expectation comes in, As for his directions of movement, he also fails to mention the ability to move through time, which is more accurately portrayed by the ability to affect events in the future. or as Alan Kay says “The best way to predict the future is to invent it.” but that is probably in the book which I have not read yet … it’s on my list, i swear!!
Nevertheless, the possibility that the world has more than three dimensions has fascinated artists, philosophers and ultimately scientists for centuries. The physics motivation to consider extra dimensions began with independent musings by a mathematician and a physicist based on the similarities in form between electromagnetism and gravity.
Now this is an interesting common conceptions, while these forces seem very similar, they are actually quite different. But mostly by degree instead of type. Electromagnetism is more like an electric field and a magnetic field which are fused together somehow at right angles to each other, possibly via connection in the 4th dimension which is spatial in neoBuddhism. Movement in the electric field is always linked to a perpendicular movement in the magnetic field. The movement through the 4th dimension is to explain partially how an electron seems to teleport around it’s energy level instead of following 3D orbital paths. The energy seems to go in 2 directions when bending through the higher dimension, hence the perpendicular movement of electric and magnetic fields, move a small distance and then back into regular 3d space, like a standing wave being reflected through different fields. Gravity is different however, and that it’s mostly the warping of the higgs field, which interacts with all of the fields, whereas electricity and magnetism mostly only interact with each other (hence electromagnetism) and the higgs field, but not the other fields.
Albert Einstein revolutionized physics by describing gravity as a force that is associated with the curvature of spacetime. General relativity is a theory of the geometry of spacetime, which makes it fundamentally different than the other known forces in nature. Yet in its form here on earth, gravity looks almost identical to electromagnetism. Both forces fall off with the square of distance, for example. One has strength proportional to charge, and one to mass.
In fact, James Clerk Maxwell’s theory of electromagnetism can be cast in a form that looks a lot like a simplified version of general relativity. The electromagnetic field can be made to reveal a curvature just like the gravitational field, except that with electromagnetism, the curvature is not in real space, but rather in some internal mathematical “space.” It turns out that this way of formulating electromagnetism is quite useful and important in physics, but for our purposes at the moment, we can think of it as simply a kind of mathematical trick.
And this is where we start to see the diversion between string theory and neo-Buddhist physics. Here he claims that the curvature is occurring in “mathematical space and not real space”, according to neo-Buddhism electromagnetic the electromagnetic fields are very real and pervades all of spacetime. Sometimes following the curvature of the higgs field on large scales, while having a different curvature at smaller scales dominated by the strength of the electromagnetic fields, all existing on top of each other instead of in separate dimensions. So there are 2 different curvatures that are being followed based on the strength of the interaction between the higgs and electromagnetic fields, while there is another set that makes electromagnetism itself which is two fields, at least one of which the field itself is rotating. This makes the electron energy levels to be sort of falling downhill from the 4th dimension, as if different densities of the same fluid were pouring out of a fountain.
After the development of general relativity, the Polish mathematician Theodor Kaluza, and independently the Swedish physicist Abraham Klein, wondered whether this mathematical trick might have a deeper significance. They reasoned that if there were an invisible extra dimension of space, perhaps electromagnetism would be associated with a curvature in this extra dimension, while gravity would reflect a curvature in the known four dimensions of space and time. It turned out that the mathematics worked out nicely, except for one thing. Unfortunately, unifying gravity and electromagnetism in this way would result in an additional force that is not observed to exist, which is one of the reasons why everyone has heard of Einstein, but many have not heard of either Kaluza or Klein.
And so we get to the first, I would say misuse, of the word dimension. While Lawrence does a good job of reiterating that what they’re doing here, is a mathematical trick, insofar as the word dimension here is a placeholder for the position of a vector, which indicates a particular unique directions of motion of said vector, whereas a neo-Buddhism these so-called dimensions are actually just a combination of the underlying fields interacting. So, what stitching theorists would call vibrational modes, is actually like the mixing of fields by certain ratios of strength of the fields, which are also quantized as energy levels. like each field is a different chemical in a soup of fields, with the difference that all the particles of a certain chemical in the soup are able to become entangled and resonate with some chemicals in the soup, while being non-reactive to others.
In formulating their theory, Kaluza, being a mathematician, never bothered with the obvious question that Klein, a physicist, clearly needed to address. If there is an extra fifth dimension, why don’t we see it? His answer was clever. If the extra dimension were curled up into a tiny circle, and were very small, none of the experiments we performed here on earth would be able to peer inside this very small circle.
There is a simple analogy that has often been used to describe this. Imagine a soda straw, with the length along the straw being space as we observe it, and the length around the circle enveloping the straw’s circumference being the extra dimension. If that circumference gets smaller and smaller, eventually the straw will just look like a line to us, and the extra dimension will have become invisible.
I am not sure if Lawrence is aware of this, but what he’s describing here would seem to be like be closed time like curves. Although my problem with this conceptions, is that that basically posits new particles that are smaller than current known particles, and ignores the definition of dimensions as an additional degree of freedom. when in reality time is more like a fountain which flows and fuels expansion of the universe. Humans are generally unable to perceive this, because there conceptualization of time is limited by their perceptions, and ostensibly is only a record of their limited perception which is a model of reality and not a recording of objective reality, and is not a perception of time itself, which is a spatial dimension.
This cute picture might have been consigned to the dustbin of history were it not for the development of what became known as string theory 60 years later. Physicists trying to develop a quantum theory of gravity — a theory which might consistently unify general relativity with quantum mechanics — discovered that a theory in which the fundamental spacetime objects were not points in space and time, but rather string-like objects, could be turned into a quantum theory, and the equations of general relativity naturally arise as the classical limit of this quantum theory.
This was a remarkable theoretical discovery, but it did not come without its own problems. The theory would indeed allow general relativity to be consistently quantized, but only if spacetime had not four dimensions, but 26. This was a lot to swallow, at least for many physicists. The mathematical beauty of the theory, however, caused a large cadre of very talented theorists to continue working on it, and they discovered that if one incorporated the existence of the other forces in nature, and the elementary particles that go along with them, it was possible to reduce the number of dimensions from 26 down to 10 or eleven.
The details of how all of this came about are complicated, but happily not relevant for our consideration. I discussed them in “Hiding in the Mirror,” for those who are interested. What does matter, however, is the same question that Klein concerned himself with. If there are indeed other dimensions in nature, where are they hiding? The answer proposed years later was the same one Klein had originally come up with. These extra dimensions could be curled up into a very small six- or seven-dimensional ball, and in this way could remain invisible. The diameter of the ball would be comparable to the scale at which quantum effects would become important in general relativity, about 10-33 centimetres, or about 19 orders of magnitude smaller than the diameter of the nucleus of a hydrogen atom!
Needless to say, no existing or even proposed experiment could directly detect new physics, including the possible existence of new dimensions, on such a small scale — about 15 orders of magnitude smaller than the scales explored at the most energetic particle accelerator now in existence, the Large Hadron Collider in Geneva.
For this reason — and the fact that the mathematics of string theory have become so complicated that the true nature of the theory, if there is one, remains elusive — string theory remains a fascinating area of study in mathematical physics, but whether it has anything to do with the real world remains an open question.
This is refreshing to hear coming from a string theorist, though many have argued that the power of string theory, is in its ability to convey complex abstract ideas about hypothetical geometries. While also admitting that ostensibly, string theory was predicting additional physics that was simply too small to detect. in essence making it untestable.
The possible existence of a tiny six- or seven-dimensional ball being attached to every point in our four-dimensional world, including at the tip of your nose, right in front of your eyes, may seem either romantic or idiotic, depending on your frame of mind. These extra dimensions, if they exist, remain impotent in the world of our experience and appear to be there simply to make the mathematics work out right. Moreover, there is no explanation whatsoever of why these extra dimensions should be curled up into small balls while our dimensions are potentially infinitely large. (Richard Feynman once harshly said about string theory: it doesn’t explain anything — it just makes excuses.) And these extra dimensions would be too small to explore or visit, or for aliens to travel through on their way to visit us. No fun at all.
And here is the first time Lawrence slips up and mentions the fourth dimensional world without actually bringing up time. It does dispel many of the myths around the conceptualizations of what counts as a dimension. According to physicists anyway.
What is the difference between a tiny curled up dimension, and a new particle or field ? you could test for a new particle or field.
The story does become a bit more interesting, however. In 1998, two different teams of researchers had a bright idea. What if forces like electromagnetism can’t permeate extra dimensions beyond the four we know and love, but gravity can? That would help explain why these extra dimensions might be invisible to us, and it could also explain a mysterious feature of gravity that has long confused theorists: why is gravity so much weaker than the other forces of nature?
Gravitational forces, like electromagnetic forces, fall off with the square of distance in our three-dimensional space. But if there are more dimensions, gravity would fall off as a higher power of distance. If, say, the extra dimensions were not 10-33 centimetres in diameter, but 10-18, then over the 15 orders of magnitude of scale until one reached the size of the extra dimensions, gravity would fall off with a higher power of distance than would electromagnetism, which is a force that we posit cannot leak into the extra dimensions. On larger scales, gravity would begin to fall off with the square of distance as there would be no more extra room in the extra dimensions to leak into. This would mean that if we measure phenomena on scales larger than 10-33 centimetres, which is what we do with our particle accelerators and other laboratory experiments, gravity will behave like electromagnetism, but appear to be much weaker than it really is, having fallen off with a much higher power of distance on smaller scales than electromagnetism would.
This proposal had the potential to explain why gravity appears to be so weak compared to the other forces in nature on scales we can measure. The proposal also led to another interesting prediction. If the extra dimensions were as large as 10-18 centimetres then it would be possible to probe these extra dimensions with the world’s most powerful particle accelerators today.
This was a cute idea, but having said this, it must be remembered that there was absolutely no explanation, within the context of this proposal, for why the extra dimensions should be large (or small, depending upon your point of view). Nevertheless, any time theorists make predictions that can be tested at accelerators, you can bet that the accelerator scientists will jump at the chance to rule them out. And they did.
This is where the neo-Buddhist perspective on physics might be more useful than string theory, it claims that the various dimensions, are more like mixtures of fields,. Which actually creates more restrictions than dimensions, because some of the fields do not interact with other fields. While other fields interact with each other asymmetrically, due to the motion of the field. The motions of the field are what are considered to impart spin on particles. Which is why some particles have asymmetric transformations, such as why there is vastly more matter than antimatter. for the sake of mathematical simplicity and to preserve the transitive property, all fields were generically considered dimensions and in this way they didn’t have to take into account that some fields interact with other fields at differing ratios.
Theorists can be very tricky however, and after this original proposal, a former graduate student of mine, Raman Sundrum, along with his collaborator Lisa Randall, and independently Savas Dimopoulos and colleagues, proposed that the extra dimensions could actually be infinite in size as long as gravity behaved rather peculiarly within them, and as long as gravity was the only force that could leak into extra dimensions.
Let me say at the outset that I found and still find the details of the proposal ugly, and I would bet good money that its content has nothing to do with reality. But aside from my doubts, it does open the romantic possibility that right under our noses could be a portal into huge extra dimensions, large enough not only to fit Narnia, but to fit whole new universes with exotic physics, and maybe galaxies and civilizations that we can never connect with. It is not in the least sense likely, but what remains surprising to me is that it is also not impossible.
From what I gather of this summary by Lawrence Krauss of their proposals, if we replace dimensions with fields, is simply that the Higgs field is the only field that interacts with all of the fields, though it does so weakly. And the Higgs field also pervades all of time and space, and thus is as large as the universe which has a finite size at any given point in time, even though it is growing. Which makes it technically not infinite.
The only thing that makes me hesitant about this theory is that in some ways, it’s replacing the curvature of space-time, with the curvature of the Higgs field, as the explanation for gravity. Which only creates more questions about the nature of time.