The Nature of Space-Time in String Theory

[WaveJumper]

I have a question concerning the mathematical predictions for space-time under String Theory. Physicist David Gross of University of California said in an interview that String Theory will change the way think about space-time. Then another physicist, Sylvester Gates of University of Maryland, said that space is also made of strings:

"Strings create everything, including space and time and even us."

I can see how elementary particles could be represented as different patterns of oscillating strings, but how does this notion arise that space-time is also made out of 1-dimensional loops of vibrating strings?

 

[Ben Niehoff]

Ultimately "space-time" is the collection of relationships between things. The science of physics is the effort to quantify the dynamical laws that govern those relationships.

We don't know what the ultimate model of those relationships may be. If strings are effective at encoding the concepts of "distance" and "duration", then that is a possibility.

 

[robousy]

I think it is really a question on our notion of the vacuum.

In Quantum Field Theory (QFT) the universe is described by a set of quantum fields. Each mode has an associated ground state energy which is non-zero due to the Heisenberg Uncertainty Principle (HUP) and behaves like a pointlike quantum harmonic oscillator.

Shift into the language of strings and now the fundamental object is no longer pointlike, but has spatial extent, like a string. The strings are also subject to the HUP, and their ground state define what we call the vacuum, and their excited states correspond to matter and energy. Thus, I would agree with:

"Strings create everything, including space and time and even us."

Although I will add that I am not made of strings. The essence of my being can ultimately be described (mathematically) by an infinite array of coupled double-Atwood machines.

-)

 

[WaveJumper]

Thanks for the replies. Since string theorists assume that the universe should make sense to a human being(i.e. everything is knowable), I wonder how it makes sense that matter, energy, time and space are all made of the same building blocks? Figuratively speaking, how would a 1-dimensional string that represents space be "engulfing" another 1-dimensional string that represents a building block of matter and how does this make sense outside of abstract mathematics? Does this have to do with the Holographic principle?

 

[BenTheMan]

Although I will add that I am not made of strings. The essence of my being can ultimately be described (mathematically) by an infinite array of coupled double-Atwood machines.

-)

 

[Naty1]

I have no idea what Gross meant, but I'll bet he's a string theorist...they have been making grand claims for twenty years or more...all of which may (or not) come true...

Space can be considered to consist of Penrose spin networks which can flow from loop quantum gravity after a gazillion transformations. A spin network is pictured as a geodesic (traditionally a dome shape) with nodes intergers of volume and links integers of area...each can evolve in time via mechanisms that look like string transformations...akin to Feynman diagrams...But all the string theories I read about so far are background independent...meaning picked/selected, fixed, and non evolutionary...

Figuratively speaking, how would a 1-dimensional string that represents space be "engulfing" another 1-dimensional string that represents a building block of matter and how does this make sense outside of abstract mathematics? Does this have to do with the Holographic principle?

You are right, It wouldn't: a two dimensional membrane can wrap around a one dimensional string...a three dimensional membrane a two dimensional one,etc...The holographic principle seems to infer our three dimensional world flows as if it were on a two dimensional surface...information content is proportional to area rather than volume!...Hence all the information in a black hole is "pictured" on its surface event horizon...like Penrose's "cosmic censorship" idea...

 

[BenTheMan]

I have a question concerning the mathematical predictions for space-time under String Theory. Physicist David Gross of University of California said in an interview that String Theory will change the way think about space-time. Then another physicist, Sylvester Gates of University of Maryland, said that space is also made of strings:

"Strings create everything, including space and time and even us."

I can see how elementary particles could be represented as different patterns of oscillating strings, but how does this notion arise that space-time is also made out of 1-dimensional loops of vibrating strings?

Ok, I can give you the way that I understand this, in the hopes that someone smarter will come along and tell me I'm wrong, and then we all can learn something.

General relativity is an effective field theory. This means that it is only good in a limited range of energy. Just like, say, classical mechanics. You can use E = 1/2 mv^2, so long as v isn't too big. In this case, Newtonian mechanics is a pretty good approximation to nature. Now, when v gets big, or gravity becomes strong then you have to use SR or GR, respectively. Again, the approximations you made in writing down your equations of motion using Newton's laws fail (namely v isn't too big and g isn't too strong), and you need a better theory.

This is a very important point: one can derive Newton's equations from Einstein's Equations. by making a set of approximations. This is very important, and required for consistency of Einstein's equations: one MUST be able to understand the effective field theory as a simplification of the underlying "more fundamental" theory. In this case, one understands Newton's equations as arising from Einstein's equations when gravity is weak and velocities are small.

So we expect that somewhere general relativity will break down, and "space-time" will no longer be described as "geometry", like Einstein thought. We already have indications that this is the case, for example, because of the paradoxes associated with black holes and the big bang. The bottom line is that there's really nothing sacred about general relativity, just as there was really nothing sacred about Newton's Laws. This may sound shocking to you, but it's the way that physicists have been thinking since the early 1980's.

There's two things you can do: Naty suggested one approach, which doesn't seem particularly appealing (to me, at least). In particular, I haven't seen any REAL convincing ways to get matter and forces (other than gravity) out of the non-stringy quantum gravity program.

The other thing you can do is try to use strings. Then you build your quantum theory around little one dimensional strings. This next part is very important: one can derive Einstein's equations from string theory. This is a non-trivial check on the theory, and one that had to come out properly if we were to take it seriously.

So what's the point. The idea of "four dimensional curved space-time" is one that comes from Einstein's equations---indeed, "space-time" itself is an Einsteinian concept. As such, there's no reason to expect that that intuition is still valid when it comes to string theory. So the statement that "space-time is made out of strings" is tantamount to the statement that "GR can be derived from string theory". THIS is the important point.