OK, here’s something (only one of many, alas, but a particularly important one) that I don’t understand:

The big problem in theoretical physics is the incompatibility between quantum mechanics and general relativity. Both theories seem essentially correct (they have been verified time and time again, to an incredible degree of accuracy); but they are logically incompatible. Most of the time, this incompatibility simply doesn’t matter (quantum mechanics works for the microworld, and general relativity for the cosmic macroworld of immense masses).

But when you have both enormous mass AND a subatomic scale of size (basically, in the center of a black hole, and also at the initial instant of the Big Bang), and where you therefore need both theories, the mathematics doesn’t work and the equations turn to nonsense (give infinite results). You can’t say that either theory has been falsified, exactly; since we cannot access the center of a black hole, or the initial nanosecond of the Big Bang, we haven’t actually found any experimental results that either theory has gotten wrong or failed to predict. Indeed, we never actually encounter any of the situations where either of the theories fails.

But theoretical physicists just don’t like the fact that there’s a point where the theories come into conflict.

I’ll leave aside the physicists’ entirely ungrounded metaphysical (or aesthetic) assumption that there *must* be a single theory in which everything fits together. It could well be that things are incompatible, but they exist anyway, and that’s the end of it.

What I’m interested in now, however, is the REASON for the incompatibility between the two theories. It’s a reason that has been inherited by the theories’ current descendants: string theory (the extension of quantum mechanics) and loop quantum gravity (the extension of general relativity).

Brian Greene, in his book about string theory, *The Elegant Universe*, explains the incompatibility as follows:

“The notion of a smooth spatial geometry, the central principle of general relativity, is destroyed by the violent fluctuations of the quantum world on small distance scales” (p129). On the large scale, the universe follows a Riemannian geometry as Einstein stipulated. But on the quantum microscale, the smooth space that Riemannian (as well as Euclidian) geometry requires simply cannot exist, given the violent quantum fluctuations of even supposedly empty space. So general relativity needs to be modified to fit the picture of quantum uncertainty — which is what string theory does.

However, Lee Smolin, in his book on loop quantum gravity, *Three Roads to Quantum Gravity*, gives a rather different explanation. He says that the problem with quantum mechanics, as well as with its successor string theory, is that “it does not respect the fundamental lesson of general relativity that spacetime is an evolving series of relationships” (p149). Again, string theory, like quantum mechanics, “replicates the basic mistake of Newtonian physics in treating space and time as a fixed and unchanging background against which things move and interact… the right thing to do is to treat the whole system of relationships that make up space and time as a single dynamical entity, without fixing any of it. This is how general relativity and loop quantum gracity work” (p159). For Smolin, general relativity shows us that space and time have no original existence; they are generated out of relational processes between events. Events do not ‘take place’ in space and time; rather it is only the relations among events that generates space and time in the first place. (This strikes me as a provocatively Whiteheadian way of looking at things, though Smolin never mentions Whitehead).

Another way to rephrase all of this is to say that string theory approaches the incompatibility between quantum mechanics and general relativity from the side of quantum mechanics; while loop quantum gravity approaches the incompatibility from the side of general relativity. Each approach starts by assuming the problem resides in classical assumptions of the other theory. For Greene, general relativity fails to include the radicality of quantum weirdness; for Smolin, quantum mechanics fails to include the radicality of relativity’s relational notion of space and time.

I should also note that Smolin’s and Greene’s positions are not really symmetrical. String theory has much more widespread acceptance than loop quantum gravity. As a result, Smolin’s book spends a great deal of time on string theory, trying to reconcile it with loop quantum gravity theory; whereas Greene’s book doesn’t even condescend to mention loop quantum gravity, apparently considering it too wrong, or too insignificant, to merit even the slightest notice.

In summary: even before we get to the mathematics, there seems to be a fundamental metaphysical disagreement between the two camps. Though Greene and Smolin characterize general relativity so differently, they don’t even seem to be talking about the same theory. For Greene, relativity wrongly assumes a stable geometry; for Smolin, it is quantum mechanics and string theory that wrongly assume the existence of space and time as an absolute background, rather than deriving them from quantum-level events.

So, I have no sense of how to adjudicate this disagreement. I do have the sense that the metaphysics needs to be paid attention to, rather than just the mathematical complexities of the theories (which I obviously cannot ever hope to make a judgment about).

Addendum: I also wonder how all this might be related to other considerations about the derivativeness of space and time. Manuel DeLanda, in his book which tries to give a Deleuzian basis to physical theory, mostly talks about thermodynamics and complexity theory (especially citing Ilya Prigogine) in order to show how “metrical” space and time are derived from “intensive” space and time. This would seem to be a rather different project from that of deriving metrical space and time from the quanta of events/relationships, as Smolin proposes (though for Smolin, like De Landa and unlike Greene, thermodynamic considerations are a very big part of the picture).

PS: though Smolin says that both space and time must be quantized (have discrete smallest possible values, rather than being infinitely divisible), he mostly talks about quantum space, and says next to nothing about quantum time. What difference would a focus on quantum temporality make to any of these theories?

# Physics 2: Incompatibility

OK, here’s something (only one of many, alas, but a particularly important one) that I don’t understand:

The big problem in theoretical physics is the incompatibility between quantum mechanics and general relativity. Both theories seem essentially correct (they have been verified time and time again, to an incredible degree of accuracy); but they are logically incompatible. Most of the time, this incompatibility simply doesn’t matter (quantum mechanics works for the microworld, and general relativity for the cosmic macroworld of immense masses).

But when you have both enormous mass AND a subatomic scale of size (basically, in the center of a black hole, and also at the initial instant of the Big Bang), and where you therefore need both theories, the mathematics doesn’t work and the equations turn to nonsense (give infinite results). You can’t say that either theory has been falsified, exactly; since we cannot access the center of a black hole, or the initial nanosecond of the Big Bang, we haven’t actually found any experimental results that either theory has gotten wrong or failed to predict. Indeed, we never actually encounter any of the situations where either of the theories fails.

But theoretical physicists just don’t like the fact that there’s a point where the theories come into conflict.

I’ll leave aside the physicists’ entirely ungrounded metaphysical (or aesthetic) assumption that there *must* be a single theory in which everything fits together. It could well be that things are incompatible, but they exist anyway, and that’s the end of it.

What I’m interested in now, however, is the REASON for the incompatibility between the two theories. It’s a reason that has been inherited by the theories’ current descendants: string theory (the extension of quantum mechanics) and loop quantum gravity (the extension of general relativity).

Brian Greene, in his book about string theory, *The Elegant Universe*, explains the incompatibility as follows:

“The notion of a smooth spatial geometry, the central principle of general relativity, is destroyed by the violent fluctuations of the quantum world on small distance scales” (p129). On the large scale, the universe follows a Riemannian geometry as Einstein stipulated. But on the quantum microscale, the smooth space that Riemannian (as well as Euclidian) geometry requires simply cannot exist, given the violent quantum fluctuations of even supposedly empty space. So general relativity needs to be modified to fit the picture of quantum uncertainty — which is what string theory does.

However, Lee Smolin, in his book on loop quantum gravity, *Three Roads to Quantum Gravity*, gives a rather different explanation. He says that the problem with quantum mechanics, as well as with its successor string theory, is that “it does not respect the fundamental lesson of general relativity that spacetime is an evolving series of relationships” (p149). Again, string theory, like quantum mechanics, “replicates the basic mistake of Newtonian physics in treating space and time as a fixed and unchanging background against which things move and interact… the right thing to do is to treat the whole system of relationships that make up space and time as a single dynamical entity, without fixing any of it. This is how general relativity and loop quantum gracity work” (p159). For Smolin, general relativity shows us that space and time have no original existence; they are generated out of relational processes between events. Events do not ‘take place’ in space and time; rather it is only the relations among events that generates space and time in the first place. (This strikes me as a provocatively Whiteheadian way of looking at things, though Smolin never mentions Whitehead).

Another way to rephrase all of this is to say that string theory approaches the incompatibility between quantum mechanics and general relativity from the side of quantum mechanics; while loop quantum gravity approaches the incompatibility from the side of general relativity. Each approach starts by assuming the problem resides in classical assumptions of the other theory. For Greene, general relativity fails to include the radicality of quantum weirdness; for Smolin, quantum mechanics fails to include the radicality of relativity’s relational notion of space and time.

I should also note that Smolin’s and Greene’s positions are not really symmetrical. String theory has much more widespread acceptance than loop quantum gravity. As a result, Smolin’s book spends a great deal of time on string theory, trying to reconcile it with loop quantum gravity theory; whereas Greene’s book doesn’t even condescend to mention loop quantum gravity, apparently considering it too wrong, or too insignificant, to merit even the slightest notice.

In summary: even before we get to the mathematics, there seems to be a fundamental metaphysical disagreement between the two camps. Though Greene and Smolin characterize general relativity so differently, they don’t even seem to be talking about the same theory. For Greene, relativity wrongly assumes a stable geometry; for Smolin, it is quantum mechanics and string theory that wrongly assume the existence of space and time as an absolute background, rather than deriving them from quantum-level events.

So, I have no sense of how to adjudicate this disagreement. I do have the sense that the metaphysics needs to be paid attention to, rather than just the mathematical complexities of the theories (which I obviously cannot ever hope to make a judgment about).

Addendum: I also wonder how all this might be related to other considerations about the derivativeness of space and time. Manuel DeLanda, in his book which tries to give a Deleuzian basis to physical theory, mostly talks about thermodynamics and complexity theory (especially citing Ilya Prigogine) in order to show how “metrical” space and time are derived from “intensive” space and time. This would seem to be a rather different project from that of deriving metrical space and time from the quanta of events/relationships, as Smolin proposes (though for Smolin, like De Landa and unlike Greene, thermodynamic considerations are a very big part of the picture).

PS: though Smolin says that both space and time must be quantized (have discrete smallest possible values, rather than being infinitely divisible), he mostly talks about quantum space, and says next to nothing about quantum time. What difference would a focus on quantum temporality make to any of these theories?