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Can quantum gravity be directly measured?

The short answer is No. But what is the long answer?

In recent years, it has become fashionable in some corners to demand that the scientific research helps to solve real-world problems. For example, it should enhance some men's intimate organs or prevent the weather from changing.

These barbarian expectations have even affected disciplines that are as "pure" i.e. "not applied" as you can get such as physics of quantum gravity. All "simple" features of quantum gravity are carefully hidden at inaccessible energy scales. But you know, the demand also creates its supply so there exists a whole class of "physicists" participating at conferences with absurd titles such as Experimental Search for Quantum Gravity 2010.

In this article, I will discuss why the typical scale of quantum gravity is almost certainly inaccessibly far; I will mention a conceivable counterexample and the indirect ways how quantum gravity manifests itself in the real world; and I will review several topics from that conference.

The Planck scale

As determined more than 100 years ago by Max Planck, the typical scale where both quantum phenomena and gravity are important is located at extremely short distance scales or extremely high energy scales (per particle). Every sane young person who wants to think about quantum gravity knows (or should know) about this scale.

Planck invented his units before general relativity and modern quantum mechanics were born. But it's more accurate to use these theories if we want to understand the Planck units more properly.

For example, let's solve the following problem. Black holes are normally thought of as large and massive objects that are much greater than their Compton wavelength - the typical length of the quantum wave associated with them if they move by a speed comparable to "c".

However, if some black holes are as small as their Compton wavelength, we clearly can't neglect quantum mechanics if we study their properties. What is the radius of a black hole "R" for which the Compton wavelength is equal to the radius? Well, it's easy to calculate. The mass of such a black hole is

m = R c2 / 2G;
recall that the radius is related to the mass by "R = 2 Gm / c^2". And the Compton wavelength associated with this mass is
λ = h / (mc) = 2G h / (Rc3).
Requiring that this wavelength over four pi (to drop the factor of two and to change "h" to "hbar") is equal to the radius, we get:
G hbar / (Rc3) = R;
R = sqrt(G hbar / c3).
This value of "R" is a pure constant, the so-called Planck length. It equals 1.616 x 10^{-35} meters or so. It's extremely tiny. But whenever a black hole is larger than that, all the quantum phenomena can be neglected and the black hole may be treated as a classical object.

We would obviously get the same radius had we chosen any pair of quantities of the same dimension and demanded that they match: dimensional analysis guarantees that the Planck length is the only "universal" result with the units of distance that we can possibly construct from "hbar", "G", and "c". For example, we could consider a black hole that can be orbited by light in the same time that corresponds to its Hawking evaporation time. Or we could ask when the typical mass of the "evaporated" Hawking particle is comparable to the mass of the black hole itself. Up to a numerical constant, we would always end up with the Planck length radius.

In the same way, the corresponding mass of such a minimal black hole is the Planck mass - and similarly for other quantities.

Now, 10^{-35} meters is a very tiny distance. For example, it's 10^{20} times shorter than the atomic nucleus. The corresponding Planck energy, 10^{19} GeV or so, is 10^{16} times higher than the energy achieved by the LHC. When I was 9 years old or so, I learned how to calculate these Planck units and realized that they're both very fundamental and very far.

I have never considered it likely that their extreme values would allow us to measure the quantum gravity effects "directly". That couldn't prevent me from getting thrilled about the physics of quantum gravity: it has always been an enterprise that depends on maths. And that's why I am shocked that the almost obvious fact about Nature that quantum gravity is inaccessible to "direct tests" is being nearly prosecuted by some very aggressive morons today. It's just crazy to attack the basic laws of Nature - such as the smallness of the Planck length - or even use them to criticize the people who study Nature.

Extra dimensions: a loophole

In the previous paragraph, I calculated the Planck scale as the scale where quantum phenomena inevitably influence the behavior of black holes; the Planck length is the radius of the smallest black hole that marginally behaves as a classical black hole - or the smallest black hole that exists. It's also the smallest distance where the notions of usual geometry are marginally applicable. The Planck length may be given many meanings - it's the "typical size of the quantum gravity things" such as the wormholes in a "quantum foam". But it's tiny.

Is there a way to enlarge this distance? Can we modify the calculation to get a distance scale that is closer to empirical validation?

The answer is Yes, assuming that Nature exploits a possibility we learned from string theory - namely that of extra dimensions. If some of the extra dimensions are large enough or extremely warped, the scale of quantum gravity may get much closer to our experiments. The power law that relates the mass and radius of the black hole gets altered - a different dimension of space often changes the power (think about the n-dimensional volume).

Once the black holes get very small in an extra-dimensional world, their radius is decreasing more slowly than in a 3+1-dimensional world, so the ultimate "balance" that you call a higher-dimensional Planck scale will end up being a much longer distance.

If you think about the possibilities and eliminate all regions of the parameter spaces that have been excluded experimentally, you unsurprisingly find out that the "longest altered" Planck length that you may obtain in theories with extra dimensions is just a little bit shorter than the shortest distances that we could have seen by the state-of-the-art colliders, i.e. something around 10^{-19} meters.

In the Randall-Sundrum models in particular, the fundamental Planck length - corresponding to a higher-dimensional quantum gravity - may be 16 orders of magnitude longer than the conventional 3+1-dimensional Planck length I started with.

If such dimensions exist - the probability that the LHC could see such effects is small but not insanely small, something like 1-2 percent - the European collider will see some really amazing things. It will create small black holes that will radiate away by the Hawking radiation.

Don't get scared. Unless you are a particle physicist, you wouldn't recognize such a man-made black hole from any other man-made elementary particle. After all, it's a main conclusion of quantum gravity that the qualitative distinction between elementary particles and black holes fades away. However, small black holes are "different" elementary particles - especially because they tend to decay "isotropically" to many other particles - those that we call the Hawking quanta if the black holes are large.

If such a scenario is valid, which is a far-fetched possibility, the LHC should also see some vibrating strings and other effects predicted by string theory. In fact, some of the signatures are so striking that even the small amount of integrated luminosity is already enough to rule out such a possibility with pretty sensible parameters. So the estimate of 1-2 percent may already have to be lowered at this point.

Indirect implications of quantum gravity

So we probably can't produce tiny black holes that quickly Hawking-evaporate. That doesn't mean that quantum gravity has no observable implications. It has lots of them. If you try to figure out what's the right theory that describes the phenomena at the fundamental Planck scale, you will find out that string/M-theory is the only possible consistent solution.

And string/M-theory not only gives unique and indisputable answers to all "qualitative" questions about the behavior of matter and black holes at very high energies: information may be effectively encoded at surfaces; information is preserved; black holes gradually change to other particles; particles are interpreted as excitations of strings and branes; supersymmetry is likely to be restored at some energy scale; there exist extra dimensions that can appear, disappear, and be re-formed by dualities. String/M-theory also restricts the possible behavior of physical systems at low energies which can be measured. And it gives you a new set of criteria for determining which possibilities are more natural or more likely than others.

Some people may be irritated by the apparent fact that the constraints of string/M-theory that are imposed upon low-energy physics are not stringent enough. However, this is nothing else than the sign of compatibility of string/M-theory with the observations. Any other theory that will predict some new striking, non-field-theoretical phenomena is likely to be born as a dead baby. It is instantly falsified by the data.

Moreover, the constraints upon the low-energy physics we are able to derive today reflect not only string/M-theory itself but also our current, incomplete understanding of the theory. It's plausible that the constraints will get tighter as we continue to learn new things. Well, it's also possible that some unproven hypothetical constraints will actually get loosened because we find new stringy vacua; that's some dynamics that has taken place, too.

In either case, it is completely irrational to attribute these developments any positive or negative emotional labels. Nature is what it is and the goal of scientists is to find the right answer rather than to find their psychologically preferred answer. You may whine and cry and urge Nature to behave in a certain way. But it's up to Her to decide whether She will listen to you - and she almost certainly won't. ;-)

A big portion of the truth about Nature was already found when general relativity and quantum field theory were discovered. These things occurred before my birth - much like the very first discoveries about string theory. Some people may be biased and "hysterically dream" that the conceptual framework developed by their generation becomes the basis of a theory of everything.

I think this is silly. Science is not a pissing contest in between the generations. I don't give a damn about the age of the person who makes the next breakthrough. Moreover, it's pretty clear that the most important conceptual frameworks relevant for a theory of everything have been found by older generations than mine - before I was born.

It's nonsensical to try to deny physics that was learned by older generations just for the sake of it. Any further progress may be viewed as a small update or improvement of the previous knowledge. After all, that's how genuine giants such as Isaac Newton (with his shoulder of giants) or Albert Einstein (with his comments about small refinements of Newton's dynamics) have presented their work, too. This difference from the current ambitious crackpots couldn't be more striking, much like the huge difference between the value of their findings which is opposite in sign.

Other effects that don't exist

So why do some people continue to claim that they know how to directly test quantum gravity by the current experimental gadgets if not by their coffee machine? Well, yes, you're right: it's because they're deluded idiots who love to look cool in the eyes of other morons even though they have nothing to back it up in the eyes of the educated viewers.

But let's look at the talks and abstracts delivered at the ESQG 2010 conference.

There is one - probably not stellar - talk about the black holes at the LHC which is the only example of a topic that actually agrees with the title of the conference. Most of the other talks are superstitious; the speakers just attempt to hope that quantum gravity will eliminate all the theories in the well-established physics that they don't like.

Clearly, they don't like quantum mechanics, so they hope that quantum gravity will show that the quantum postulates are wrong and there is a classical world beneath the weirdness of quantum mechanics.

A much larger group at the conference had a problem with the Lorentz symmetry. They can't understand that the exact Lorentz symmetry is completely mathematically self-consistent and compatible with the quantum gravity, too. In fact, it is almost certainly required for consistency. Even if you happened to think that string/M-theory is not the right theory describing the world around us, it is surely a consistent theory of quantum gravity where the Lorentz symmetry exactly holds. So the statement that quantum gravity requires the Lorentz symmetry to be broken can be easily refuted by a major counterexample.

Moreover, it has been shown experimentally - especially by the Fermi satellite - that the Lorentz symmetry is preserved even at the Planck scale. Photons that arrived from a distance around 10 billion light years were relatively delayed at most by dozens of milliseconds (the relative accuracy is something like 10^{-20}), despite the difference's between their energies being comparable to 31 GeV (which is 10^{-17} Planck energy, a relatively bigger fraction than 10^{-20}).

Even when you have no "theoretical bias" - i.e. no understanding of the state-of-the-art theories of the real world - the existing empirical data make it very unlikely that a violation of the Lorentz symmetry will be seen. In the same way, we won't see a violation of the basic principles of quantum mechanics, and so on.

These Lorentz-violating talks try to associate the quantum gravity scale with new and exotic phenomena that have no reason to exist - not even at the Planck scale - and that probably make the theories inconsistent. However, there has been a class of talks - e.g. those about the violations of parity by gravity - that have made the opposite mistake.


Well, because the violation of the parity symmetry is not only possible but it has been shown to occur in Nature. And it occurs at all scales, especially in the neutrino sector. The parity-violating processes are a key part of the electroweak theory that describes the phenomena near 100 GeV.

However, the very existence of neutrinos - which are left-handed - violates the parity symmetry of the real world. And the relevant processes may have as little an energy as the neutrino mass - a few millielectronvolts or less.

So while the Lorentz violation is "too unusual", the parity violation is "too ordinary". At any rate, in both cases, it is completely irrational to imagine that either of these violations would be a "sign of quantum gravity". The qualitative possibilities of these broken symmetries have nothing to do with quantum gravity.

You may write down some corrections in the equations of gravitational physics that violate the Lorentz symmetry and/or the parity symmetry but you may do this in non-gravitational theories as well. Moreover, in the case of the Lorentz symmetry, all such asymmetric corrections are probably forbidden in Nature. In the case of the parity violation, it is allowed by all phenomena in Nature - except that gravity is nothing else than a major class of phenomena that make its own parity violation pretty unnatural. ;-)

Summary: a theoretical discipline

I believe that this form of scientific porn - trying to directly measure quantum gravity if not time machines, in order to look relevant in the eyes of the people who are much more interested in Viagra than quantum gravity - shouldn't expand in science. Quite on the contrary, it should be eliminated. Decades ago, it was impossible to meaningfully study quantum gravity because our ancestors lacked both experimental and reliable theoretical tools to do so.

Today, we still lack experimental tools to directly see some qualitative effects of quantum gravity. And chances are that we always will. However, we are no longer ignorant about the right theoretical description that is relevant for the phenomena near the Planck scale. That makes a difference and that's why some of the world's brightest people are working on string/M-theory.

And that's the memo.

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snail feedback (2) :

reader Milan said...

Regarding your comment on my site:


I hope you realize that just because somebody has a great deal of expertise in one subject - such as condensed matter physics - doesn't mean they speak authoratatively on other subjects, especially those that are largely outside their area of competence.

We shouldn't defer from arguing with Nobel Prize winners just because they have been awarded that scientific honour. For one thing, we have no reason to be confident that they will be right about everything. For another, it is only by maintaining a questioning attitude that science and human society generally can progress.

reader Luboš Motl said...

Dear Milan,

I am very far from being a person who thinks that Bob Laughlin is right about everything (click). ;-)

He just happens to be almost completely right about the climate change, its historical context, and its relationships with the energy sources. Much more right than some people who are claimed to speak "authoritatively" by some journalists and misled laymen who have really no clue.

Best wishes

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