# How many dimensions does light have

## Extra dimensions and artificial black holes

**Black holes don't have to be huge cosmic structures. If our universe has more than three spatial dimensions, tiny black holes could possibly be created at modern particle accelerators. Their discovery would revolutionize our worldview.**

When you think of black holes, you usually associate them with large, dark structures from science fiction films, in which everything that comes near them disappears irretrievably. But this does not have to be the case. If our universe - as some theories predict - should not only have three dimensions but exist in additional spatial dimensions, the energy of modern particle accelerators could be sufficient to produce black holes in miniature format. With a size that corresponds to that of elementary particles, they would be tiny, would not swallow spaceships, planets and stars and would disintegrate again very quickly after their formation. Their discovery would be a sensation - it would usher in a new era for particle physics and revolutionize our worldview once more.

### what is a black hole?

Black holes arise when the mass (or more correctly: the density) of an object becomes so great that even light can no longer escape due to the enormous force of attraction: in other words, when the escape speed that would be necessary to overcome the force of attraction of the object is greater when the speed of light becomes - which is not possible according to the special theory of relativity. Here, however, it is not only the mass of the object that matters, but also the volume within which this mass is located, i.e. how tightly the mass is packed.

The volume that a black hole with a certain mass has is given by the so-called Schwarzschild radius; this is directly proportional to the mass of the black hole. The lighter or smaller a black hole, the higher the required density. For a black hole with the mass of our sun, for example, this value is 10^{19} Kilograms per cubic meter. Such a black hole with solar mass would have to have a density that is higher than that of an atomic nucleus (that is about 10^{17} Kilograms per cubic meter.

### How big are small black holes?

Can a black hole get any size you want? No, because Heisenberg's uncertainty principle applies to small black holes as well as to elementary particles (see article Fundamentals of Quantum Mechanics). From this it follows that the mass of a black hole in the context of conventional gravitation theory must be greater than the so-called Planck mass of 10^{19} GeV / c^{2} (see info box). For smaller masses, a black hole can no longer exist in the classical sense, because then its density becomes so great and thus gravity so strong that quantum fluctuations break up the structure of spacetime. Below the Planck mass, small black holes can - if at all - only exist as short-term vacuum fluctuations (see info box and article Quantum Field Theory - What is it?).

The energy of the currently most powerful particle accelerator, the Large Hadron Collider LHC at the research center CERN in Geneva, is in the range of several thousand gigaelectron volts (GeV) never reached before; However, it is still 15 orders of magnitude, i.e. 15 powers of ten, lower than the energy that would be necessary to create the smallest possible black hole. This obviously shows that the generation of black holes at particle accelerators is, according to conventional theory, a long way off.

### A universe with extra dimensions?

Our universe as a membrane in the extra dimensions

So no accelerator black holes after all? Interestingly, the answer to this question depends on one of the fundamental properties of our universe: namely, the number of dimensions in which we live. If, as we think we know, there are only three space and one time dimensions in the universe, the answer is a resounding “no”. However, if there are additional spatial dimensions that are also large enough, then the creation of black holes on accelerators could be possible.

The existence of such tiny extra dimensions is not a mere speculation by science fiction writers. It was actually proposed in 1998 by the theoretical physicists Nima Arkani-Hamed, Savas Dimopoulos and Georgi Dvali. Her main motivation was to solve the so-called hierarchy problem, i.e. the question why the gravitational force is so incredibly weak compared to the other fundamental forces or why the Planck scale, where gravity becomes as strong as the other forces, is 10^{19} GeV is so incredibly large. If one introduces additional spatial dimensions into the theory, this discrepancy can be explained in a natural way.

Since we do not observe such extra dimensions in everyday life, their expansion must be finite, that is, they must be “compacted”. You can visualize this as if these dimensions were "rolled up" at the smallest possible intervals - similar to a straw that appears from a distance like a one-dimensional line, but when viewed up close has more than one dimension (see info box). In models with such rolled-up extra dimensions, there is an actual Planck scale that is much smaller than 10^{19} GeV can be. The gravity would then become as strong as the other forces at significantly lower energies.

### Extra dimensions - a chance for small black holes

With the existence of additional, compactified spatial dimensions, the law of gravity changes - namely below the small distances that correspond to the expansion of the extra dimensions. With larger distances, everything stays the same. In fact, this does not contradict current knowledge, since the law of gravity has so far only been experimentally checked above distances of about 0.1 millimeters. It is assumed that gravity behaves in the same way at smaller distances, but it has not been confirmed experimentally. Here is an additional complication of theories with extra dimensions. Since the distance dependence of the electromagnetic, the weak and the strong force is already up to distances of 10^{-18} Meter is tested, this excludes extra dimensions with extensions above this range. Therefore, many models postulate that these forces cannot penetrate into the additional spatial dimensions, so that only gravity is influenced by the additional dimensions.

### Black holes in the laboratory - a scientific sensation

Should it turn out that the particle collisions in the LHC actually generate black holes in miniature format, this would be a scientific sensation that would revolutionize our physical world view of the very small (see article Black Holes at the LHC?). Above all, however, this discovery would mean the end of particle physics in the conventional sense, since only black holes would be generated for energies above the Planck mass, but not new particles. The historical search of mankind for the last building blocks of matter would come to an end and a new area of research would arise: the geometry of the extra dimensions of space.

Further reading:

B.J. Carr and S.B. Giddings, Black Holes in the Laboratory, Spectrum of Science, September 2005

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