I’ve updated the article on extra dimensions that I announced last week. In the original version of the article, I gave you one example of an extra dimension; now I’ve extended it to include another example, of a very different type. You can find all the new stuff by scanning down the article until you find a line in red that says “New additions begin here.” If you haven’t read about extra dimensions at all, you should read some of the other introductory articles first; you can find links to them at the top of today’s article.
What will come next, perhaps in the coming week, is a discussion of the scientific techniques used to look for signs of extra dimensions. Later I’ll add another example or two to today’s article.
3 Responses
I have been following your excellent series on dimensions and have particularly appreciated the rationality needed to understand how extra dimensions might be revealed. A couple of questions are on my mind, Is this inquiry driven by the mathematic stucture of string theory, if so I would like to see more of the math explaining why.
The question that really interests me personally is “do we perceive and evaluate our known three dimensions and one of time correctly”. I know from the math we need four variables to make it work.. But time is a different quantity to the three spatial dimensions, how are they unified and most importantly have there ever been any observable quantitive
The inquiry is not driven by string theory, no. I don’t know who started thinking about extra dimensions, but Flatland (http://www.ibiblio.org/eldritch/eaa/FL.HTM) was written over a century ago. Kaluza and Klein were interested because it was noticed that if you put Einstein’s gravity in four space dimensions (i.e. five space-time dimensions, one more than what we experience) and made one of the dimensions finite and small, you’d end up with what would appear (to observers like ourselves who don’t know about the small dimension) to be Einstein’s gravity PLUS Maxwell’s electromagnetism. The idea that all the forces of nature might just be manifestations of gravity in more space dimensions than three has stuck around, and in string theory sometimes this occurs (though string theory can lead to forces in other ways too.) So string theory fits in with the more general discussion of extra dimensions, but the idea of extra dimensions to our world neither started with nor requires string theory.
Time, and how it fits in with the dimensions of space, is a long story. Einstein taught us that we can’t treat it separately, yet it behaves differently enough that it does have a special role. I don’t think there’s a short answer to your question, but on top of that your question appears to have been cut off so I’m not sure exactly what you wanted to know. Question back to you: what would it mean to “perceive and evaluate our known three dimensions and one of time correctly”? What is your standard of correctness? I’m not being facetious; I’d like to know what would satisfy you as “correct”, otherwise I’m not sure how to answer you.
As Sergei Petrov said, we all are here to hear what you, Matt, have to say. In the past, we are waiting for your teaching passively. Now, I would like to ask your lesson actively, as this dimension issue is the key for the entire physics.
On this issue, you have discussed briefly about metaphysics which is an overused term, and our understanding about it might be significantly different. Thus, I will ask a metaphysics question without using that term.
In the comments, the existential issue on this extra dimension was also asked. For any symbol (representing concrete, conceptual, abstract or all the whatnots), its existence consists of two parts.
1. It is physically there.
2. It carries meaning.
If a thing is physically there but is “never” interact with anything (including itself), it carries no meaning. At here, the “meaning” of a thing has nothing to do with consciousness. As long as it participates in an interaction, it provides a meaning to that interaction. Thus, a physical reality without meaning has no existential value (again, having nothing to do with consciousness). Black hole or dark matter has meaning as they participate in gravity interaction.
On the other hand, a symbol without a corresponding reality does have existential value if it carries meaning. The concept of Heaven might not have a corresponding reality but has the existential value.
As the meaning of a thing arises from participation (not from consciousness), multi-level meanings can arise from multi-level participations. And, the trace or signal of the early participation can be erased by the later (higher level) interaction. Thus, although the trace of the early signal cannot be detected physically at the higher level after some history killing processes, its meaning must be still visible at that higher level.
Question 1. So, for those extra dimensions (regardless of whether we can physically detect them or not), what are their meanings at the current energy level? If their existential value does not manifest as a high level meaning, its sole physical existence has no meaning to this universe.
Question 2. The only way to detect them physically is by forcing them to participate with our designed experiments. This participation will give rise to a meaning, and what will it be?
These are my two questions.