Very interesting book for the beginner and even the non-initiated... http://www.scientificamerican.com/article/how-to-get-to-the-fourth-dimension/ I particularly liked the image of a 3D projection of a 4D Rubik's cube:
Cool stuff. For me the fundamental principle of electrical energy is 4D. The interactions we see in circuits as the electric and magnetic fields are not separate. They are space-time 3D projections on a single (at least) 4D entity. When we say a changing magnetic field creates or gives rise to a changing magnetic field we are not seeing a cause and effect because the effect is instantaneous in space to the highest possible frequency and smallest possible space and time. To me this means that one object is the source of both and what we see is some sort of matrix transformation of the properties of that object into our 3D space.
No I don't think so, the changes are independent of time. If the transformation was time related we would see a lag or lead in the cause/effect of the during the field changes because they are limited to c (electromagnetic fields propagate with finite velocity) across space unless they are instantaneously localized.
That's a very interesting theory... if my understanding is correct, what you're saying is that electricity and magnetism are two manifestations of the same thing... like the active shadow of something that exists beyond our usual dimensions. It's your use of the instantaneous argument that I'm not sure I'm following.
No comprendo. I looked at the article and read the posts in this thread, and I can't figure out what the fourth dimension is supposed to be. I know Einstein believed it was time, but I always discounted that idea as being eccentric.
Oh my... we're threading into deep waters here.... Conventionally, Time is considered the 4th dimension of spacetime. But theories abound stating that far more dimensions exist at a quantuum level, some say 11, some say at least 13, and some have argued up to 27... but none have been able to actually prove that more space dimensions exist beyond what we're experiencing. They argue in favor these extra dimensions because they make mathematical sense... and makes it easier to understand some of the phenomena that we're observing at the particle level.
If we look at a changing magnetic field in space those changes propagate with finite velocity to where we measure them. If we look at the the resulting electric field from that change that propagate with finite velocity we see that they originate to the same instantaneously localized source (a point source with zero size in "3D+time" that contain the properties of both fields). There's nothing new or earth shattering about this idea, it's been known since Weber, Lorentz, Lienard and Wiechert as different manifestations of the same phenomena.
I find it interesting that scientists think the idea of much greater than 3 dimensions may help to explain the dual wave/particle nature of light. I also find quantum physics fascinating, but much of it is currently beyond me. I guess I actually like it because it's so mind boggling. After studying calculus-based physics in college, I hope to be able to understand it better. Doesn't quantum theory state that there is a minimum and/or maximum possible size for a particle? I think I remember hearing something about that. Was that a typo or intentional? I actually like it. It seems appropriate for a forum.
No it wasn't intentional... I'm bilingual and thus a little bit more prone to typos and misspellings than usual. No pun was intended, but yes, I too find it funny now that you mention it.
The article has a great demonstration of extra dimensions using (~2D objects) a penny and a paper with a small hole that my young lab assistant will demonstrate. The 2D penny can't pass through the 2D paper but if we fold the paper ( one-dimensional subsurface (hole) in a two-dimensional Manifold (paper) and warp 2D space to add another dimension (three-dimensional manifold) it will pass to the other side. So extra dimensions gives objects extra degrees of freedom to move and be manipulated in. It's the same with 4D forces but we can only see what's happening in the 3D hole of the paper and it looks strange. If we understand the 4D movements/manipulations with math we can then predict what the 3D effect will be even if what we see is still strange.
Einstein had both SR and GR For SR there is 3D+time (space-time) frames of reference effects that change as speed approaches light. For GR there is space-time+gravity(curvature manifold) where mass warps space and causes time effects. GPS clock corrections use both For SR the correction is the speed difference between the receiver clock and the satellite clock. (orbiting clock effect, slightly slower ~7us per day) For GR the correction is the gravitational difference between the receiver clock and the satellite clock. (orbiting clock effect, slightly faster ~45us per day) 15 meters of positional accuracy requires ~50ns so you can see that the uncorrected daily offsets would make GPS useless for driving a car or guiding a missile into a terrorist bedroom.