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THE FABRIC of the COSMOS, Brian Greene, 2004
```(annotated and with added bold highlights by Epsilon=One)
```(annotated and with added bold highlights by Epsilon=One)
Chapter 13 - The Universe on a Brane
Our Universe as a Brane
If we are living within a three-brane — if our four-dimensional spacetime is nothing but the history swept out by a three-brane through time — then the venerable question of whether spacetime is a something would be cast in a brilliant new light. Familiar four-dimensional spacetime would arise from a real physical entity in string/M-theory, a three-brane, not from some vague or abstract idea. In this approach, the reality of our four-dimensional spacetime would be on a par with the reality of an electron or a quark. (Of course, you could still ask whether the larger spacetime within which strings and branes exist — the eleven dimensions of string/M-theory — is itself an entity; the reality of the spacetime arena we directly experience, though, would be rendered obvious.) But if the universe we're aware of really is a three-brane, wouldn't even a casual glance reveal that we are immersed within something — within the three-brane interior?
Well, we've already learned of things within which modern physics suggests we may be immersed — a Higgs ocean; space filled with dark energy; myriad quantum field fluctuations — none of which make them themselves directly apparent to unaided human perceptions. So it shouldn't be a shock to learn that string/M-theory adds another candidate to the list of invisible things that may fill "empty" space. But let's not get cavalier. For each of the previous possibilities, we understand its impact on physics and how we might establish that it truly exists. Indeed, for two of the three — dark energy and quantum fluctuations — we've seen that strong evidence supporting their existence has already been gathered; evidence for the Higgs field is being sought at current and future accelerators. So what is the corresponding situation for life within a three-brane? If the braneworld scenario is correct, why don't we see the three-brane, and how would we establish that it exists?
The answer highlights how the physical implications of string/M-theory in the braneworld context differ radically from the earlier "branefree" (or, as they're sometimes affectionately called, no-braner) scenarios. Consider, as an important example, the motion of light — the motion of photons. In string theory, a photon, as you now know, is a particular string vibrational pattern. More specifically, mathematical studies have shown that in the braneworld scenario, only open string vibrations, not closed ones, produce photons, and this makes a big difference. Open string endpoints are constrained to move within the three-brane, but are otherwise completely free. This implies that photons (open strings executing the photon mode of vibration) would travel without any constraint or obstruction throughout our three-brane. And that would make the brane appear completely transparent — completely invisible — thus preventing us from seeing that we are immersed within it.
Figure 13.3 (a) In the braneworld scenario, photons are open strings with endpoints trapped within the brane, so they — light — cannot leave the brane itself. (b) Our braneworld could be floating in a grand expanse of additional dimensions that remain invisible to us, because the light we see cannot leave our brane. There might also be other braneworlds floating nearby.
Of equal importance, because open string endpoints cannot leave a brane, they are unable to move into the extra dimensions. Just as the wire constrains its beads and the pinball machine constrains its balls, our sticky three-brane would permit photons to move only within our three spatial dimensions. Since photons are the messenger particles for electromagnetism, this implies that the electromagnetic force — light — would be trapped within our three dimensions, as illustrated (in two dimensions so we can draw it) in Figure 13.3.
That's an intense realization with important consequences. Earlier, we required the extra dimensions of string/M-theory to be tightly curled up. The reason, clearly, is that we don't see the extra dimensions and so they must be hidden away. And one way to hide them is to make them smaller than we or our equipment can detect. But let's now reexamine this issue in the braneworld scenario. How do we detect things? Well, when we use our eyes, we use the electromagnetic force; when we use powerful instruments like electron microscopes, we also use the electromagnetic force; when we use atom smashers, one of the forces we use to probe the ultrasmall is, once again, the electromagnetic force. But if the electromagnetic force is confined to our three-brane, our three space dimensions, it is unable to probe the extra dimensions, regardless of their size. Photons cannot escape our dimensions, enter the extra dimensions, and then travel back to our eyes or equipment allowing us to detect the extra dimensions, even if they were as large as the familiar space dimensions.
So, if we live in a three-brane, there is an alternative explanation for why we're not aware of the extra dimensions. It is not necessarily that the extra dimensions are extremely small. They could be big. We don't see them because of the way we see. We see by using the electromagnetic force, which is unable to access any dimensions beyond the three we know about. Like an ant walking along a lily pad, completely unaware of the deep waters lying just beneath the visible surface, we could be floating within a grand, expansive, higher-dimensional space, as in Figure 13.3b, but the electromagnetic force — eternally trapped within our dimensions — would be unable to reveal this.
Okay, you might say, but the electromagnet force is only one of nature's four forces. What about the other three? Can they probe into the extra dimensions, thus enabling us to reveal their existence? For the strong and weak nuclear forces, the answer is, again, no. In the braneworld scenario, calculations show that the messenger particles for these forces — gluons and W and Z particles — also arise from open-string vibrational patterns, so they are just as trapped as photons, and processes involving the strong and weak nuclear forces are just as blind to the extra dimensions. The same goes for particles of matter. Electrons, quarks, and all other particle species also arise from the vibrations of open strings with trapped endpoints. Thus, in the braneworld scenario, you and I and everything we've ever seen are permanently imprisoned within our three-brane. Taking account of time, everything is trapped within our four-dimensional slice of spacetime.
Well, almost everything. For the force of gravity, the situation is different. Mathematical analyses of the braneworld scenario have shown that gravitons arise from the vibrational pattern of closed strings, much as they do in the previously discussed no-braner scenarios. And closed strings — strings with no endpoints — are not trapped by branes. They are as free to leave a brane as they are to roam on or through it. So, if we were living in a brane, we would not be completely cut off from the extra dimensions. Through the gravitational force, we could both influence and be influenced by the extra dimensions. Gravity, in such a scenario, would provide our sole means for interacting beyond our three space dimensions.
How big could the extra dimensions be before we'd become aware of them through the gravitational force? This is an interesting and critical question, so let's take a look.
Well, we've already learned of things within which modern physics suggests we may be immersed — a Higgs ocean; space filled with dark energy; myriad quantum field fluctuations — none of which make them themselves directly apparent to unaided human perceptions. So it shouldn't be a shock to learn that string/M-theory adds another candidate to the list of invisible things that may fill "empty" space. But let's not get cavalier. For each of the previous possibilities, we understand its impact on physics and how we might establish that it truly exists. Indeed, for two of the three — dark energy and quantum fluctuations — we've seen that strong evidence supporting their existence has already been gathered; evidence for the Higgs field is being sought at current and future accelerators. So what is the corresponding situation for life within a three-brane? If the braneworld scenario is correct, why don't we see the three-brane, and how would we establish that it exists?
The answer highlights how the physical implications of string/M-theory in the braneworld context differ radically from the earlier "branefree" (or, as they're sometimes affectionately called, no-braner) scenarios. Consider, as an important example, the motion of light — the motion of photons. In string theory, a photon, as you now know, is a particular string vibrational pattern. More specifically, mathematical studies have shown that in the braneworld scenario, only open string vibrations, not closed ones, produce photons, and this makes a big difference. Open string endpoints are constrained to move within the three-brane, but are otherwise completely free. This implies that photons (open strings executing the photon mode of vibration) would travel without any constraint or obstruction throughout our three-brane. And that would make the brane appear completely transparent — completely invisible — thus preventing us from seeing that we are immersed within it.
Figure 13.3 (a) In the braneworld scenario, photons are open strings with endpoints trapped within the brane, so they — light — cannot leave the brane itself. (b) Our braneworld could be floating in a grand expanse of additional dimensions that remain invisible to us, because the light we see cannot leave our brane. There might also be other braneworlds floating nearby.
Of equal importance, because open string endpoints cannot leave a brane, they are unable to move into the extra dimensions. Just as the wire constrains its beads and the pinball machine constrains its balls, our sticky three-brane would permit photons to move only within our three spatial dimensions. Since photons are the messenger particles for electromagnetism, this implies that the electromagnetic force — light — would be trapped within our three dimensions, as illustrated (in two dimensions so we can draw it) in Figure 13.3.
That's an intense realization with important consequences. Earlier, we required the extra dimensions of string/M-theory to be tightly curled up. The reason, clearly, is that we don't see the extra dimensions and so they must be hidden away. And one way to hide them is to make them smaller than we or our equipment can detect. But let's now reexamine this issue in the braneworld scenario. How do we detect things? Well, when we use our eyes, we use the electromagnetic force; when we use powerful instruments like electron microscopes, we also use the electromagnetic force; when we use atom smashers, one of the forces we use to probe the ultrasmall is, once again, the electromagnetic force. But if the electromagnetic force is confined to our three-brane, our three space dimensions, it is unable to probe the extra dimensions, regardless of their size. Photons cannot escape our dimensions, enter the extra dimensions, and then travel back to our eyes or equipment allowing us to detect the extra dimensions, even if they were as large as the familiar space dimensions.
So, if we live in a three-brane, there is an alternative explanation for why we're not aware of the extra dimensions. It is not necessarily that the extra dimensions are extremely small. They could be big. We don't see them because of the way we see. We see by using the electromagnetic force, which is unable to access any dimensions beyond the three we know about. Like an ant walking along a lily pad, completely unaware of the deep waters lying just beneath the visible surface, we could be floating within a grand, expansive, higher-dimensional space, as in Figure 13.3b, but the electromagnetic force — eternally trapped within our dimensions — would be unable to reveal this.
Okay, you might say, but the electromagnet force is only one of nature's four forces. What about the other three? Can they probe into the extra dimensions, thus enabling us to reveal their existence? For the strong and weak nuclear forces, the answer is, again, no. In the braneworld scenario, calculations show that the messenger particles for these forces — gluons and W and Z particles — also arise from open-string vibrational patterns, so they are just as trapped as photons, and processes involving the strong and weak nuclear forces are just as blind to the extra dimensions. The same goes for particles of matter. Electrons, quarks, and all other particle species also arise from the vibrations of open strings with trapped endpoints. Thus, in the braneworld scenario, you and I and everything we've ever seen are permanently imprisoned within our three-brane. Taking account of time, everything is trapped within our four-dimensional slice of spacetime.
Well, almost everything. For the force of gravity, the situation is different. Mathematical analyses of the braneworld scenario have shown that gravitons arise from the vibrational pattern of closed strings, much as they do in the previously discussed no-braner scenarios. And closed strings — strings with no endpoints — are not trapped by branes. They are as free to leave a brane as they are to roam on or through it. So, if we were living in a brane, we would not be completely cut off from the extra dimensions. Through the gravitational force, we could both influence and be influenced by the extra dimensions. Gravity, in such a scenario, would provide our sole means for interacting beyond our three space dimensions.
How big could the extra dimensions be before we'd become aware of them through the gravitational force? This is an interesting and critical question, so let's take a look.