String Theory Acquires Rival In Loop Quantum Gravity

UniSci.com ^ | 31 Oct 2001

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String Theory Acquires Rival In Loop Quantum Gravity

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String Theory Acquires Rival In Loop Quantum Gravity Loop quantum gravity (LQG), rival of string theory in the quest to unite quantum mechanics with general relativity, does not suffer from certain mathematical "infinities," a new study shows. (Those infinities correspond to ephemeral but numerous alternatives in the way that interactions take place in spacetime.) This clears up some doubts as to the theory's usefulness. What is LQG, and why has it been so difficult to quantize gravity? To address this question, return to classical (pre-1900) physics, a regime in which space was fixed. Then the relativity and quantum revolutions changed everything utterly. With the advent of general relativity, space was combined with time in an integrated, but deformable, spacetime. Meanwhile, in quantum mechanics, spacetime remains fixed but matter becomes fuzzy; the whereabouts of particles can only be expressed in terms of probability clouds. In a theory that would combine quantum and gravity features, spacetime would then have to be both deformable and fuzzy, and this has been difficult to do. In string theory, the merger is accomplished by imagining that matter ultimately consists of tiny strings. In loop theory, the merger is attempted by imagining that space itself consists of moveable tiny loops. Carlo Rovelli (Center for Theoretical Physics, Marseilles, also University of Pittsburgh) argues that loop theory does not have to import the extra commodities (additional dimensions and particles) needed by string theory. Rovelli argues to loop theory offers, in principle, more testable predictions, such as the idea of quantized surface areas (that is, regions of space would come in discrete chunks and there would be a minimum possible size scale) and the notion that quantized spacetime might manifest itself as a minute difference in the speed of light for different colors. The new version of loop gravity studied by Rovelli and his colleagues pictures spacetime as being foamy: points in space sometimes grow into bubbles. The bubbles are not "in" space; they constitute space itself. The infinities pondered in the present paper represent not difficulties posed by the reality of particles within particles (a necessary complexity dealt with in Richard Feynman's quantum electrodynamics theory) but rather, analogously, to those potentially corresponding to interactions occurring on spacetime loops within loops. (Crane et al., Physical Review Letters, 29 October 2001; text at this URL.) (Editor's Note: This story, with minor editing, is based on PHYSICS NEWS UPDATE, the American Institute of Physics Bulletin of Physics News, Number 562, October 23, 2001, by Phillip F. Schewe, Ben Stein, and James Riordon.) 31-Oct-2001

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[VeritatisSplendor]

Sorry, I messed up the italics. For some reason the preview software isn't displaying this right. Here is my reply reformatted with your words between asterisks and mine plain:

*Zeno didn't show that anything was quantized.*

I didn't say he did. I said he showed that if space isn't quantized then time isn't either. He started by assuming space isn't quantized, and the contradiction he reaches trades on the assumption that time is quantized, that you can't have arbitrarily small time increments. Because if you could, then there is no contradiction since the infinitely many DECREASING time intervals can still be completed in a finite time.

*He tacitly assumed that a length in space was infinitely divisible, i.e. non-quantized and argued that before you could get halfway along the length, you would have to previously get a quarter of the way, and before that ... *

What I said. There is no problem with going smaller and smaller fractions of the way if you can take smaller and smaller fractions of time to do it.

*The conclusion he drew was not that space was quantized (that there was a smallest distance, an indivisible atom of space), but that motion was impossible and change must therefore be an illusion.*

His argument shows you can't have both discrete time and continuous space. I never said he concluded space was quantized; it is possible to reject discrete time instead of rejecting continuous space. There are two ways to reject discrete time: with continuous time, which Zeno could not imagine but which was the "solution" to Zeno's paradox supported by physicists before 1900, OR by rejecting time as a separate concept altogether, which was Zeno's way and which agrees with the spacetime view of physics pioneered by Einstein.

*You have scant evidence for passing judgment on my level of mathematical knowledge. Of course some series converge and others do not. My point, which I admit not spelling out, was that a unit distance could be divided into a half, a quarter, etc. (a series which converges) but it can also be laid out such that before I get halfway I have to get a third of the way, a fourth, a fifth, etc. This second way of dividing a line does not lead to a converging series. *

Your mathematical argument is faulty. After you have gone 1/3 of the way you do not have to then go 1/2 of the way -- you have already done most of the first half. The series you are actually considering is (1-1/2), (1/2-1/3), (1/3-1/4), (1/4-1/5),... = 1/2 + 1/6 + 1/12 + 1/20 + ... which does indeed converge to 1.

*I conclude from that that the distinction between converging and non-converging series has no crucial application to resolving Zeno's paradoxes. *

The application is in the very concept that a series with infinitely many terms can converge to a finite limit. Zeno could not imagine continuous time in which infinitely many (but decreasing in duration) instants could occur in a finite time. This was not necessarily a mistake on his part, he may have simply rejected this concept of time on intuitive grounds, an intuition which cannot be said to be incorrect. The two alternatives to continuous time are discrete space or illusory time, both of which are supported by 20th-century physics (quantum mechanics and relativity, respectively).

[Sir_Ed]

monsterbunny said: ...if my understanding is correct does that imply that time travel is possible...? You asked us that next year ago. Ed

[henbane]

The new version of loop gravity studied by Rovelli and his colleagues pictures spacetime as being foamy: points in space sometimes grow into bubbles. The bubbles are not "in" space; they constitute space itself.

OK--so if the bubbles are space itself, what's INSIDE the bubbles--pixie dust?

[Hajman]

OK--so if the bubbles are space itself, what's INSIDE the bubbles--pixie dust?

Nothing would be 'inside' the bubbles. It's just a place where there's more space in space/time.

-The Hajman-

[henbane]

Nothing would be 'inside' the bubbles. It's just a place where there's more space in space/time.

Sounds like these little bubbles are just minature versions of our universe--a kind of globular affair that curves in on itself with "nothing" either inside or outside it.

"Nothing"--a tough idea to conceptualize in a reified setting.

[Hajman]

Sounds like these little bubbles are just minature versions of our universe--a kind of globular affair that curves in on itself with "nothing" either inside or outside it.

"Nothing"--a tough idea to conceptualize in a reified setting.

I think of space more as water then as a table top. 'Bubbles' wouldn't be two dimensional. But rather three dimensional in three dimensions.

-The Hajman-

[henbane]

I think of space more as water then as a table top. 'Bubbles' wouldn't be two dimensional. But rather three dimensional in three dimensions.

It's exactly the three-dimensional concept that makes it troublesome. If the "bubbles" exist in the water of space-time, this bubble image implies a three-dimensional globe with the interior volume actually creating the bubble-image rather than a solid. billiard-ball image.

If this is the case, then that interior volume of "nothing" eludes reification.

The implication of "nothingness" in the bubble's interior implies that no space-time event can occur in this non-space.

It's a conundrum. Perhaps only conceived in the abstract world of higher mathematics.

[Hajman]

It's exactly the three-dimensional concept that makes it troublesome. If the "bubbles" exist in the water of space-time, this bubble image implies a three-dimensional globe with the interior volume actually creating the bubble-image rather than a solid. billiard-ball image.

Why would there have to be nothing? Think of an underwater wave. The underwater wave would be, possibly, less dense, more spread out, created with vibrations. A 'bubble' in the water. This is how I think of space. But in space's case, space might actually keep it's density and gain space-mass (of whatever type that happens to be), thus gaining more space at that place. A 'bubble' in space/time. It wouldn't have to blow up like a balloon.

-The Hajman-

[henbane]

. . .space might actually keep it's density and gain space-mass (of whatever type that happens to be), thus gaining more space at that place. A 'bubble' in space/time. It wouldn't have to blow up like a balloon.

This makes sense. The "bubble" here is not the conventional bubble that comes from the bubble-pipe and floats in the air or the kind that comes up from the bubbler in the fish-tank.

Sounds like the image used in physics of the expanding space-time universe that "bubbles" like the raisin cake cooking in the oven--the cake dough expands but keeps its weight/density while all the raisins in it simultaneously move away from each other.

IOW, there is no "empty" volume as in the center of the conventional iridescent bubble floating through the air.

Think I've got it. Thanks.