JOURNEY TO THE WORLD OF THE PLANCK SCALE

The so-called "Planck scale" marks a fundamental limit beyond which the physical world as we know it ceases to make sense. In fact, it is to be expected that as we approach this scale, space-time itself will begin to fluctuate according to the laws of quantum mechanics, producing a kind of "fuzzy" quantum structure. Physicist John Wheeler coined the term "quantum foam" for this structure. In this article, we will travel to the world of the Planck scale, a world where physics as we know it ceases to exist, and space-time itself loses its usual physical meaning.

Traveling to the quantum world

Long before the Planck scale, we encountered the familiar quantum effects at atomic or even molecular scales. The following fictitious experiment will give us a glimpse of what our macroscopic world would be like if quantum effects were manifested at the scales of our everyday life (assuming that solid bodies could still be formed from atoms and molecules).

Suppose that Planck's constant h instead of having the value of h = 6.625×10-34 joule·second had a value 31 orders of magnitude larger, i.e. h = 6.625×10-3 joule·second. Now suppose we carry out the double-slit experiment by throwing solid spheres of 66.25 grams at a speed of 5 m/s towards a house through a wall 10 meters from the house with two windows that act as "slits" separated by a distance of 0.5 meters.

Image obtained from this article

The scheme of this "macroscopic double slit" experiment would be:

Image obtained from this article

After carrying out the experiment by throwing many spheres we observed the following strange things with perplexity:

- There are areas of the house (dark areas) where the ball never hits.

- The area where the greatest number of impacts are recorded (the brightest band) is just behind the wall in the middle of the two windows, precisely where we would not expect any sphere to arrive!

- Interference occurs even if we only throw one sphere. The sphere seems to "split" and interfere with itself!

How can we explain this strange series of observations? It can only be explained by assuming that the spheres are actually wave-like "elongated objects" with a length equal to the DeBroglie wavelength. These elongated objects can not only interact with other objects but can also interfere with each other! This tells us that matter at the fundamental level is an extended entity that oscillates like a wave.

Indeed, if we calculate the DeBroglie length L=h/mv for the spheres, we obtain the value of 20 centimeters. Following the wave theory of quantum mechanics, the spheres would behave like waves 20 cm long . The "dark fringes" in the house occur when the waves coming from each window are half a wavelength out of phase and therefore interfere destructively (when the crests are in opposite positions and cancel each other out), that is, when the following occurs:

The "y" distance of the graph for small angles is:

The distance between the dark bands will therefore be:

Therefore the distance between dark stripes is 40 centimeters.

The strange equation of the quantum world

On the grave of physicist Max Born, one can read the following "strange" inscription:

Max Born's gravestone in the Göttingen Cemetery (Germany). His wife, Hedwig Martha Ehrenberg, is also buried there. Interestingly, both are the grandparents of Olivia Newton-John, the famous actress from the film "Grease."

This inscription compresses into a simple expression one of the most fundamental laws of the Universe (somewhat poetically, it could be said that although physicists are mortal, their discoveries can be eternal and universal). The inscription tells us something very strange: imagine that I measure a specific physical quantity of an object (in this case, position) and then a different physical quantity (in this case, momentum), multiply them, and write down the result. Then I do the same thing, but in the opposite order: first, I measure the momentum, then the position, and write down the result. Our common sense, our experience, and "good old" mathematics tell us that the result has to be the same; however, Born's strange formula tells us that the result is different and the difference will always be 1h/2pi. How can this be possible? What does this imaginary quantity mean? How can two physical quantities of an object depend on the order in which they are measured?

The consequences of this simple expression, from which the entire theory of quantum mechanics can be derived, are so alien to our common sense that even today some physicists continue to search for "the correct interpretation" of quantum mechanics.

The great Nobel Prize-winning physicist Max Born and his wife

The first consequence is that there are physical quantities such as position and momentum that are not independent, but are inextricably linked, as if they were part of a common entity. This is a slap in the face to our common sense, since in our everyday world we can break any object down into smaller, individually behaving parts. This isn't possible in the quantum world, and this is what the "strange" Born equation tells us.

Another consequence of this fundamental expression is that it is not possible to know with absolute precision certain physical quantities such as position/momentum or energy/time. This means that we cannot find any physical object with a completely determined energy; rather, this energy must "oscillate."

Therefore, as we probe smaller and smaller distances, we find that the "fundamental objects" begin to oscillate.

Max Born was the maternal grandfather of actress Olivia Newton-John. She once said that one of the greatest sorrows of her life was not having been able to meet her grandfather.

Reaching the Planck scale: quantum foam

It is now that we begin our fascinating journey on the smallest possible scale.

The Planck distance is immensely small: 10exp-35m. This is a thousand trillion times smaller than the smallest scale explored in the LHC collisions (10exp-20m). To get an idea of how infinitesimal this scale is, consider the following: extending the Planck scale to the scale of an atomic nucleus would be equivalent to extending the size of an atomic nucleus to the diameter of the Milky Way!

Although we do not yet have a quantum theory of gravity, if the principles of quantum mechanics hold near the Planck scale, it is to be expected that as we approach that scale, space-time itself will begin to "fluctuate." Physicist John Archibal Wheeler published a paper in 1955 in which, based on dimensional arguments, he postulated that at the Planck scale, space-time should fluctuate violently and produce all sorts of microscopic structures, including structures with topological changes such as wormholes. At scales larger than the Planck scale, space-time appears smooth and continuous, but as we approach this scale, space-time becomes discontinuous and fluctuates violently, producing a whole host of structures such as virtual particle pairs, space-time "bubbles," micro-black holes, and wormholes. Because of their similarity to sea foam, Wheeler coined the term " quantum foam" to refer to these quantum structures of space-time.

Image taken from nasa.gov . Image Credit: X-ray: NASA/CXC/FIT/E. Perlman; Illustration: CXC/M. Weiss

Among these structures , space-time "bubbles" and wormholes stand out.

Space-time "bubbles" would arise because violent fluctuations in space-time create gravitational waves. Near the Planck scale, the fluctuations must be very rapid, creating gravitational waves of very high frequency, low amplitude, and high angular momentum. Wheeler himself, in his 1955 work, found a solution to the equations of general relativity that contained gravitational waves that met these requirements. This solution also had something very interesting: the gravitational interaction did not come from other sources of mass-energy but rather from the interaction of space-time itself with itself. This solution involved the formation of a kind of bubble in which a large number of high-frequency gravitational waves were concentrated at the edges. Wheeler coined the term " geons" for these solutions. The gravity (curvature of space-time) created by gravitational waves concentrated on the surface of the bubble causes these bubbles to stabilize and live for a much longer time than the "natural" time on that scale.

Microscopic wormholes would arise because violent fluctuations in space-time would produce narrow, highly curved regions that would form a kind of "throat" in space-time. These "throats" would form a large number of microscopic wormholes.

Experimentally detecting quantum foam

Although it may seem incredible, it might be possible to experimentally detect the "fingerprints" of quantum foam. Although it is not possible to directly detect such incredibly small scales, it would be possible to infer their existence due to the cumulative effect of very small effects over very large distances.

Space-time fluctuations would induce tiny changes in the phase or speed of light coming from very distant sources (the latter case involving a tiny violation of Lorentz symmetry). These fluctuations are larger the higher the energy of the light, so the more energetic photons would be more affected than the lower energy photons. In 2005, the MAGIC telescope detected that

Gamma rays of different energies from a distant source appeared to arrive at different times, but these results have not been corroborated. In 2015, NASA's Xandra telescope published the results of measurements of light from quasars billions of light-years away. The experiment looked for the cumulative effects of light "scattering" through quantum foam.

Although the results were negative, Chandra only ruled out the existence of quantum foam at scales 1,000 times smaller than that of an atomic nucleus. Future experiments will be able to probe much smaller scales.

Conclusions

To date, no one knows whether quantum foam exists; in fact, there is controversy over the stability of Wheeler geons and other theoretical problems. Despite this, quantum fluctuations of space-time itself near the Planck scale seem inevitable. The indirect detection of quantum foam could reveal important secrets about the characteristics of the long-awaited theory of quantum gravity.

One of the most incredible things about all this is that human experiments are capable of probing the effects of phenomena occurring at such infinitesimal scales that space-time itself ceases to exist as we know it. Will scientists be able to detect the most fundamental vibrations of quantum space-time?

Sources:

Quantum mechanics , Proving the gravitational geon , Is Quantum Spacetime Foam Unstable?