Comparing Quantum Foam with Vacuum Energy and the relationship to hyperspace

[piareround]

Ok I been trying to figure partially exactly what things in Quantum Mechanics, Quantum Field Theory, QED, or any physics that matter gave rise to concepts of things like hyperspace and multiverse and other theories that seem to have more of a fictional history and origin than the original nonfiction physics orgin.

For the most part I figured out the the concepts of parallel worlds and the multiverse is more than anything else an individual interpretation of both the meaning of probability wave function and the meaning finding an expectation value is in quantum, rather a direct consequence/assumption of string theory or quantum mechanics.

Now I am trying to figure out how the general concept of multiple dimensions and hyperspace arouse as physics developed of the last 60 years.

Thus I have several questions, most of which are bolded and number below, so to keep things organized.

In trying to understand hyperspace, I ran into something called http://en.wikipedia.org/wiki/Quantum_foam" .

From what I read, it appears quantum foam is related to concept of vacuum energy. Ironically, I have just recently introduced to vacuum energy a few weeks ago in my Particle Physics class when the professor showed Dirac Solution to the http://en.wikipedia.org/wiki/Klein%E2%80%93Gordon_equation" .

So...

1) What exactly is the relationship between Quantum Foam and Vacuum Energy?

Second I was reading some of the things about quantum foam, namely the two thread linked below:
https://www.physicsforums.com/showthread.php?t=155307"
https://www.physicsforums.com/showthread.php?t=68769"

From them I got the sense that quantum foam is derived at least partially from the concept of combining quantum mechanics with general relativity either in loop quantum gravity, string theory, or Approximate Quantum General Relativity (*). I also came across this from wikipedia:

Some physicists theorize the formation of wormholes therein; speculation arising from this includes the possibility of hyperspatial links to other universes.

From this I had three questions:

2) First what exactly is quantum foam's role in Loop Quantum Gravity?

3) Does quantum foam play role in String Theory? If so how? or is their something analogous to quantum foam for String Theory?

4) What exactly is wikipedia talking about in the quote above? How does the quantum foam create concept of hyperspace or even wormholes? or is hyperspace simply an interpretation of quantum foam's properties much like the concept parallel worlds is an interpretation of the wave function's properties?

5) More generally what in any Quantum Relativistic Gravity theory implies or creates the concept of a hyperspace?
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(*)About Approximate Quantum General Relativity. For certain special problems their are "special cases", like the two body problem, where you can create an algorithm to deal the issue with singularities and other problems by making a approximation. The mathematical form of these approximation more testable than other Quantum theories due to a mathematical similarity(**) of these "special cases" to solving problem involving BEC. I am not sure if these approximation favor String Theory or Loop Quantum Gravity more, so I left it as a separate concept.

 

[nismaratwork]

I can answer #2: String Theory removes the notion of a quantum foam by "smearing" the fluctuations with Planck-Length strings and not point-particle interactions. In short, String Theory would do away with the QM version of ultra-microscopic turbulence and "even it out". Note, there is no way to test this or verify it, and likely never will be, but that's the answer.

For 4.) I have no idea... although when I hear the term "hyperspace" I hear alarm bells going off. What kind of hyperspace is this in reference to, and why does the product of the HUP at microscopic levels have to do with it? I don't know, but my instinct says that this is either a grotesque simplification, or just someone's personal musing.

I just want to ask: when you talk about a hyperspace... are you thinking in terms of "Star Wars" hyperspace, as in some kind of extra-dimensional construct, or an actual hyperspace constructed mathematically from various hypersurfaces?

 

[piareround]

I can answer #2: String Theory removes the notion of a quantum foam by "smearing" the fluctuations with Planck-Length strings and not point-particle interactions. In short, String Theory would do away with the QM version of ultra-microscopic turbulence and "even it out". Note, there is no way to test this or verify it, and likely never will be, but that's the answer.

Thanks for replying ^)^. Wow, I am really surprised that string theory approximates any notion quantum foam. Kind of makes you wonder how they deal with the whole negative energy issue, but oh well that a question for another day.

For 4.) I have no idea... although when I hear the term "hyperspace" I hear alarm bells going off. What kind of hyperspace is this in reference to, and why does the product of the HUP at microscopic levels have to do with it? I don't know, but my instinct says that this is either a grotesque simplification, or just someone's personal musing.

You are very astute that the term hyperspace should send of alarm bells. It does for me too for the following reasons:

Tropically, http://tvtropes.org/pmwiki/pmwiki.php/Main/SubspaceOrHyperspace"

An object or technology with powers so diverse and magical that it can cause almost any effect as needed by the plot.

Thus most physicist’s aversion and wariness for hyperspace actually comes from the fact that all scientists and engineers hate idea of unexplainable or magical technology. It’s like a slap in the face to all the hard work our profession works to improve knowledge and society's standard of living. We dislike hyperspace so much that science’s aversion has actually become a trope itself, called http://tvtropes.org/pmwiki/pmwiki.php/Main/HyperspaceIsAScaryPlace" .
​

Second, in general I personally feel that hyperspace; specifically topological hyperspace is actually a very politically incorrect term to use in physics or mathematics for actual http://en.wikipedia.org/wiki/Space_%28mathematics%29" we are in or using. For most physics, we deal with finite topological space; moreover there is a proof that shows how no hyperspace of a space can exist in and only in the original topological space. Though QM uses an infinite topological space called Hilbert Space, I personally think it’s a bad idea to use the term hyperspace because Hilbert Space is infinite inner product vector space and Hilbert Space is a unique infinite space.
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So why I am using the term hyperspaces if I don’t particular like the term. Sigh, mainly because I was worried I would skew people's responses if I voiced my opinion too early. Plus, its because I am trying deconstruct the concept of hyperspace in order to find the core misconceptions of hyperspace, like the ones above.

What kind of hyperspace is this in reference to, and why does the product of the HUP at microscopic levels have to do with it?

To answer your question One of those misconception is related to the fact that their is some connection between hyperspace and quantum foam. I like to pause for a moment on how this misconception arises and further questions for my next post.

 

[piareround]

I just want to ask: when you talk about a hyperspace... are you thinking in terms of "Star Wars" hyperspace, as in some kind of extra-dimensional construct, or an actual hyperspace constructed mathematically from various hypersurfaces?

To answer this question I was originally reference to something similar latter statement about "actual hyperspace constructed mathematically from various hypersurfaces". Originally I was referring to hyperspace to be any inner product vector space, V_Hilbert, with a dimension, or http://en.wikipedia.org/wiki/Cardinal_number" of the basis of V, greater than 4. Thus when I asked... #4

Some physicists theorize the formation of wormholes therein; speculation arising from this includes the possibility of hyperspatial links to other universes.

What exactly is wikipedia talking about in the quote above? How does the quantum foam create concept of hyperspace or even wormholes? or is hyperspace simply an interpretation of quantum foam's properties much like the concept parallel worlds is an interpretation of the wave function's properties?

... I was specifically ask whether or not quantum foam requires a dimension higher than the 4-D space time vector space used to derive the concept of quantum foam?
7) Does my previous question make more sense now? Can you answer my question #4?

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What kind of hyperspace is this in reference to, and why does the product of the HUP at microscopic levels have to do with it?

Continuing where I left off on the last post, one of those misconception is related to the fact that their is some connection between hyperspace and quantum foam. In the Wikipedia quote from my original post, the Wikipedia links the word "hyperspace" to http://en.wikipedia.org/wiki/Minkowski_space" .

Thesis: The term hyperspace, as used by physics, may have originally just be a synonymous word for space-time or M.S., which was created so they did have to say M.S. 50 times. Science Fiction misinterpreted the term "hyperspace" to mean a N+1-th Dimensional Space instead of the original QM Minkowski Space, along with the general laws of thermodynamics with respect to negative energy to create "warp drive" or "hyperspace travel".
​

Right now that my general deconstruction theory; however, I would like to eliminate any other possibilities before I start to try to justify my thesis. As image below shows, their is still this usual connection of wormholes to quantum foam.

This bring and a couple of other things bring up an important question:
8)If quantum foam only needs 4-D to work and not hyperspace, how then does the vacuum energy or negative energy sea its related to wormholes?