Cumrun Vafa: String Theory does make testable predictions. Here is one.
This is an excerpt from my conversation with Cumrun Vafa where I pressed him to on whether string theory departs from the core principle of the age-old scientific method: hypotheses must be subjectable to tests against evidence. His response was unique and fascinating.
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Brian: So I was thinking back to a conversation I had with Lenny Susskind, about one of the most impressive characters in his mind in history: Aristarchus of Samos and you mentioned Aristarchus as well in the book towards the end. And you talk about the fact that Aristarchus had these ideas about heliocentrism, which we now know to be true, but could not be proven because it was impossible to measure, for example, the parallax of stars at that time. In fact, the parallax was not measured, until the 1800s —
James Bradley first tried to measure stellar parallaxes in 1729. The stellar movement proved too insignificant for his telescope, but he instead discovered the aberration of light which is proof the Earth is in motion around the Sun.
Galileo had tools to actually prove Copernicus was right and he didn’t use them. Instead, he offered other methods which turned out to be wrong. For example, his book, The dialogue, was originally going to be titled “On the Flux of the Tides” . And he contended that the tides on Earth’s oceans were caused by the motion of sloshing and revolution and rotation of the Earth, not as we now know from the gravitational influence of the moon. So he was overwhelmed by the kind of notion that Copernicus was right, so much so that he used incorrect evidence to to justify and bolster the hypothesis. On the other hand, you know, our starkers had the right idea. And Lenny Susskind calls him, you know, the most interesting scientist, perhaps in history, because he had the right idea, but the technology wasn’t sufficient. What do you say the people who say string theory, or studying the properties of black hole singularities, which we’ll get to in a minute as well, what do you say to those people that say, it’s not worth spending any time and because you can’t falsify the singularity? You can’t falsify string theory, it’s so flexible, it predicts or accommodates way too many outcomes. How do you justify that? Is there an opportunity to appeal to future technology, as in the case of Galileo or Aristarchus in the future, wherein eventually technology caught up and proved them right? Do you think the same thing will happen with string theory? And if not, why should we study it?
Right. So as you say, Brian, many of the things about string theory are at the level of predictions, theoretical predictions that are very difficult to experimentally check with our current level of technology. So So in some sense, that promise for the future? And so your question would be, as you say, why should we spend time on something that we cannot check in our lifetime as correct or incorrect, and so forth? If there were no method to check our ideas, then I would have abandoned doing string theory for exactly that reason. However, due to the interesting interconnection of different ideas in high energy, theoretical physics, you can actually check ideas, theoretically. So you can check the validity of an idea from a different perspective and come to a conclusion, whether that idea is correct or false without experimentations, somewhat, of course, that will validate the idea itself as being self consistent, logically correct, mathematically consistent — whether or not that’s part of the explanation of our current universe, we still have to wait. But we have seen so many encouraging results from string theory, in terms of reformulating different pieces of physics that we have discovered, like the strong interaction, what kind of forces are working there, things about what happens for cosmology, what happens for black holes, we now know, there are black holes ultimately, very clearly. I mean, there’s no doubt about them. And the fact that these ideas in string theory come to get given a self consistent picture to many aspects of them makes us believe in them. For example, the prediction that Hawking made about black holes, the fact that black holes have entropy, despite the fact that Einstein’s equations predicts that they are unique is taking into account of the quantum mechanics. The work of Beckenstein and Hawking in particular showed that no, there must be some degrees of freedom, which are inside the black hole, there are some microstates. And the fact that string theory was able to account for those degrees of freedom, at least in specific classes of black holes, is already surprising and gives us a confidence that the theory hangs together. Now, the details about how we relate to our universe, the can we understand the electron has such and such a mass and so on, remains to be seen. But even now, even I will give you one example, we can make predictions right now, from string theory, which have experimentally been verified. Now, these expert these predictions are rather, in a sense, you would say not as precise a prediction but still is a prediction, I will give you one example. So, for example, you take the electron, and it has a mass. And if you compute the mass of the electron in the fundamental units of physics, which is Planck mass, it’s a very tiny mass in Planck units is something of the order of 10 to the minus 23. It’s a very tiny number. So you say, Great, do we have any prediction that the electron mass should have been this small, without knowing that there is an electron, just by knowing that there is electric charge? And by knowing that there is dark energy in universe, you find a bound on the electron mass. You find that the electron mass should be bounded by 10e-1 on the upper end, and above 10 e- 31 on the lower edge.
The lower bound comes from the conservation of dark energy. And the upper bound comes from consideration of what is called the weak gravity conjecture — that gravity is always the weakest force in any any consistent model of quantum gravity. So putting these together, you find a range for the mass of the electron, and lo and behold, 10 to the minus 23, which is the mass of the electron is bigger than 10 to the minus 31. So there is a prediction that you can see, though not as precise as we typically like in physics.
I’m not going to write a grant proposal based on that level of precision though!
But still, the idea that this is has no falsifiable prediction is not correct, there are predictions that if the electron mass was somewhere outside this regime, you would have said, ‘Okay, this is inconsistent with String Theory’.
And yet there are considerations in your book that you bring up from what’s called naturalness that you could actually get the black hole entropy to within a factor of pi or so based only on dimensional analysis, so that doesn’t require string theory at all. Plus, as you know, Weinberg made predictions about the, rough value of the cosmological constant [ref], which then motivated the so-called landscape, and the multiverse. So is it unique to string theory? Or, you know, if a smart undergraduate can derive it from considerations of dimensional analysis, does it really count as a prediction of string theory or could equally be referred to as a Fermi calculation?
Okay, so good question. So let’s go back to the black hole question you raise. First of all, even there, it’s not clear because consideration of dimension analysis presupposes that we make an assumption that the entropy of a black hole is related to the area of the black hole.
And naively, we would have associated entropy with volume, not area. And that’s not true. That was one of the surprising predictions of Hawking. So another dimension analysis gives a totally wrong answer. Now, let’s assume entropy scales with the Black Hole’s area, where does the factor of one quarter of the area measured in Planck units come from? Why should it be one quarter? We don’t know a priori from that calculation. Hawking’s calculation shows it does.
Well, string theory’s prediction not only gives you that one quarter, but actually gives you an infinite further correction. It says this one quarter of area, plus a coefficient times log of the area plus another coefficient divided by the area plus another coefficient in the infinite expansion in the area.
So not only does String Theory give you Hawking’s answer, it gives you all the possible corrections to it. So it’s not something that Hawking did not calculate. So from string theory, we not only get the leading term when the area is large, but suddenly the correction when the area is not huge. So these corrections shows you that there’s a very clear picture of how you derive these statements, and not just the overall coefficient in front of the area. So it hangs together. It is non trivial. And to me, these are the kinds of examples that bolster our confidence in string theory and its validity. And other approaches people have tried does not give you something as concrete and as precise as, as we have seen from String Theory.
Thank you, that’s masterfully explained…I actually came away just now with a new appreciation of the depth of the mysteriousness of that particular puzzle. So you’re unifying mysteries and puzzles for me in real time Cumrun; you’re to be congratulated.