Well, like many on this earth, my normal everyday experiences are in the 3 dimensional space. Things in 3 dimension makes sense. I don't even want to think about 4th dimension space, let alone 5th, 6th Nth dimensions..... I feel humans, at least in our current form, are incapable of fathoming anything beyond 4th dimension. I've always heard physicists say Time is the 4th dimension. yet, there are also other ideas that talk of the 4th dimension as a Spacial Dimension, rather than a Temporal Dimension. For example, looking at the Tesseract as a cube in 4 dimensional space seems to not involve Time at all. Anyone have thoughts on this subject?
What you have to keep in mind is that "dimension" is fundamentally an abstract mathematical concept. They may, or may not, directly relate to a physical entity. Certainly we can understand 3 spacial dimensions. We can take out a tape measure and quantify the length, area, or volume of an object. But length, area, and volume are just abstract concepts.....we invented them. This is easily proved....bring me a length. Bring me an area. Bring me a volume. None of those things are real in the sense of a physical entity. They only exist in our mind. The same thing with more dimensions. We could pick time, temperature, charge, gravity, etc. as another dimension if we so chose. There's no real rules other than math, it's all an abstraction, and as far as we know abstract thought at this level is a uniquely human characteristic. Abstraction is true of numbers we use to measure. Because of our elementary education, we know what 1, 2, 3, etc mean. But can you show me 1? Can you show me 2? No, you can show me 1 apple or 2 apples and I can understand the abstract notion of counting and what "1" means, but there is no "1" by itself. When we talk about physical processes, we use math to describe them. The thing is, we have discovered mathematical "tricks" to solve hard problems. I'll give an example that applies to time, quantum mechanics, electrodynamics, and relativity. Time, when introduced as a 4th dimension in Special Relativity, it is always an imaginary dimension. What I mean by that is the 3 spacial dimensions are real numbers (1.0, 1.1, -2.3, ...) while the time dimension always involves the square root of -1. The square root of -1 makes no sense physically, it's imaginary, it's a trick, but there are tricks to make the imaginary values turn out real in the end. One of the "tricks" in electromagnetics is to turn wave equations from the time domain into the frequency domain. When we do that the frequency domain includes imaginary numbers. As a practical example, if we want to separate high frequency music to the tweeter, and low frequency music to the woofer (commonly called a crossover), it's much easier to solve that problem in the frequency domain. Interestingly, the same is done in quantum mechanics. A particle-like entity is a spike in the time domain, but spread out in the frequency domain, and a wave-like entity is a spike in the frequency domain, but spread out in the time domain. This behavior describes a fundamental manifestation of the Heisenberg uncertainty principle. These mathematical tricks are real in the sense they help us solve problems that would be too difficult otherwise. And they do solve real physical problems. The question is do these tricks, or mathematical abstractions, represent real physical entities? Some say yes and some say no. Like you said, anything beyond 3 dimensions is outside our brain's capability to comprehend. We only have math to comprehend more dimensions, and that in itself is extraordinary. Only one thing is certain, abstract mathematical concepts solve the problems the universe presents. If those mathematical laws define the rules of the universe, are those rules that we continue to discover, an accident or design? That question goes into philosophy and/or religion, which is, interestingly, maybe incorrectly, considered outside the realm of science. A question that needs answering is why is the universe teaching us these mathematical abstractions, for example multiple dimensions?
Ok, but what about 4th or 5th spacial dimensions? Ever heard of a Tesseract?? Can you comment on that?
This tesseract 'thing' is real. imagine waves going through the other atoms, with the same atoms rearranging as if they were never moved out of space? how else does gamma radiation go through us?
Yeah tesseract or penteract, they're abstract geometric notions that only exist in physical space if physical space is defined in more than 3 dimensions. By physical space I assume you mean Euclidean space. Euclidean space cannot be defined other than by describing, or measuring, distances between physical objects. To propose that there is a 4th Euclidean dimension must be accompanied by a precise way to measure a distance in that 4th dimension. That hasn't been done. A claim that there is a 4th Euclidean dimension that exists but can't be measured can only be substantiated by a precise statement on how the dimension can be detected at all without measuring it. That hasn't been done either. Since we can only perceive 3 Euclidean dimensions, without resorting to abstract math, there must be some detectable influence of this extra dimension, if it exists. One can take General Relativity and say, well here is time as the 4th dimension and we now have space-time as a reality. That's fine, and it works out great, but is that the same as a Euclidean dimension? Certainly not, for instance in Euclidean dimensions we can move backwards and forwards, and we can stop. In time we can only "move" forward, and have to keep moving forward. What if we add another dimension to space-time? Kaluza did that for electric charge, adding a 5th dimension to space-time to describe charge, and it worked. He successfully combined gravity and electromagnetics, a curvature in a 5-d manifold, but in the end all his 5th dimension turned out to be was Maxwell's Equations. It was already described without resorting to a 5th dimension. Note this wasn't the case with Einstein, the 4th space-time dimension resolved existing problems and predicted new phenomenon like gravitational lensing. However, others have taken Kaluza's work further, saying all forces as we know them are just other dimensions acting within our 3 dimensional perception. This is why in String Theory you get all these extra dimensions, 10 or 26 or whatever the flavor of the day is. Taken to the extreme, I bet you can describe anything in the universe if you just grant the universe infinite dimensions. The math might be a little tough to deal with, it would result in an infinite number of linearly independent equations. So, back to tesseracts and penteracts. I'll reiterate what I said before, the notion of dimension is an abstract concept, and the notion of a 4th Euclidean dimension as reality is just imagination. There's nothing wrong with imagination, but for something to exist scientifically, it has to be measurable.
thanks for the post. even though I don't quite understand it. 5th space time dimensions with Electric charge. 5D manifolds. Gravitational lensing. Maxwell's equation... all of these concepts are beyond me.
Discovery of a phenomenon called neutrino oscillation has upended scientific thinking... Nobel Prize for solving puzzle of elusive neutrino particles Tue Oct 6, 2015 - A Japanese and a Canadian scientist won the 2015 Nobel Prize for Physics on Tuesday for discovering that elusive subatomic particles called neutrinos have mass, opening a new window onto the fundamental nature of the universe.
I feel pretty comfortable visualizing 4th dimensional reality (and no it doesn't look like Donnie Darko). 5th boggles my mind, however. I would love to get past that mental block, and really consider more outside our normal human bounds...
... neutrinos may have protected us all from complete annihilation... The Latest: Research changed the course of particle physics Oct 6,`15 -- Latest developments in the announcements of the Nobel Prizes (all times local):
University Of Pennsylvania scientists contributed Nobel Prize winning research... Penn scientists' work on 'ghost particles' contributed to Nobel win Wednesday, October 7, 2015 - They are among the most numerous particles in the universe, subatomic ghosts silently whizzing through our bodies millions of times a second. And yet physicists were mystified as to why two-thirds of these particles, called neutrinos, seemed to be missing in action.
