Spread the space between your thumb and index finger and measure a length of approximately 10 cm. If you repeatedly reduce this distance by half, how many times will your two fingers touch? If you divide it seven times, the gap will be narrower than 1mm, and if you divide it one or two more times, your finger’s coordination will be limited and it will be difficult to maintain a stable distance. However, if it had the same accuracy as a clamped micrometer, it could (theoretically) measure the width of a human skin cell, and a state-of-the-art laser interferometer could measure the scale in nanometers (nm). It has already been a century since we began to overcome the limitations of measuring instruments and measure the width of each atom and even the atomic nucleus that makes up the atom. Afterwards, electromagnetic waves were used as probes to measure units finer than the size of the atoms that make up the measuring device itself, and after wave-particle duality was confirmed as a concept of quantum mechanics, electrons and neutrons were used as a probe. Using the properties of waves, it has become possible to measure distances smaller than 0.1 nm.
▲ Micrometer operated by a clamping frame. By turning the arrow, the spacing between the upper bars is finely adjusted in 0.01mm increments. (ɔ)Wikimedia user Anasofiapaixao, CC-BY-SA 4.0.
Mathematically, the distance of an infinitesimally small distance, which divides the space of 10cm into an infinite number of times, can be accepted as a concept, but in actual laboratories, as the accuracy of measuring the distance between atoms increases, the scale changes. Meaning is given. However, no matter how advanced measurement technology and equipment are, there is a minimum unit of distance that modern physics theory sets as a limit, the Planck length, named after Max Planck (1858-1947), the father of quantum mechanics. ) is called. It is a composite constant obtained by multiplying and dividing the basic physical constants defined in quantum mechanics and relativity theory, the two pillars of modern physics, and its value is approximately 1.6 × 10-35 meters. Starting from 10cm, it needs to be divided in half 112 times to reach the size, but no one has ever measured it to date. Although further division can be imagined mathematically, the prevailing view is that it would not physically exist in a meaningful way. Dividing the Planck length by the speed of light, another fundamental constant, gives the Planck time. The value is about 5.4×10-44 seconds, which is known to be the shortest physically definable unit of time and no one has yet measured it.
Here we rethink the intuition that time and space are smooth and continuous. Until the end of the 19th century, it was recognized that heat energy transmitted through radiation could be divided into infinitely small pieces, but Max Planck proved this to be wrong and introduced the concept of the photon, the smallest unit of radiant heat. did. This model, which has since been verified through numerous experiments, suggests that there are not only photons, but also inseparable blocks that make up space at a scale smaller than an atom. In other words, just as you can see the square pixels that make up a picture displayed on a computer or smartphone screen when you zoom in on it, our space-time also has a resolution limit.
▲ Quantum bubble phenomenon that can be seen when space-time is expanded to the Planck unit. (ɔ)Wikimedia User Jarrokam, CC-BY-SA 4.0.
This concept arises in the process of trying to integrate quantum mechanics and general relativity, or more mathematically, in the process of trying to express the forces defined by the two theories in a single equation. Considering only quantum mechanics, the error in measuring length is inversely proportional to the error in measuring momentum (or speed) according to the uncertainty principle. Therefore, the accuracy of length measurement should be infinitely increased by completely giving up the accuracy of momentum measurement. However, according to the general theory of relativity, all particles (whether they have mass or not) fluctuate space and time, and if an error in the measurement of momentum is created simply by adjusting the wavelength (which is a wave) of massless particles such as photons, the space and time will remain unchanged. The error is propagated to the structure. For this reason, in order for quantum mechanics and general relativity to be compatible, there must be a minimum error in measuring length, and the Planck length plays that role.
If you want to measure a distance shorter than the Planck length, you need photons with a smaller wavelength. However, the shorter the wavelength, the higher the energy the photon has, and if you actually calculate it, if that much energy is concentrated in such a small space, it satisfies the conditions for creating a small black hole. The black hole created in this way devours the photons, invalidating the measurement! Yes. When the very large particle accelerator built in Switzerland started operating a dozen years ago, the micro black hole that raised concerns within and outside of academia that it might destroy the Earth also appears here. And as has been explained through various channels, unlike the celestial black holes that are frequently reported these days, micro black holes have never actually been observed. (Even if it is observed, it evaporates within 10-40 seconds, so rest assured that the possibility of the Earth being destroyed due to such an experiment is much lower than the possibility of the Earth being destroyed by another pandemic in the near future.)
This theoretical scenario also appears in basic particles other than light, such as electrons or quarks. Unlike photons, these have mass. Let’s take the case of electrons. If you want to systematically increase the accuracy of measuring the position of an electron in three-dimensional space, you must design an experiment so that all 10 observations are found within a subspace with a specific volume by observing 10 times, and then systematically reduce that volume. Even assuming that such an experiment is possible, if the space containing the electrons is reduced to within the Planck length, the momentum error increases according to the uncertainty principle, and the energy error also increases accordingly, becoming equal to the total energy value. This level of energy uncertainty creates quantum fluctuations that randomly create and annihilate other electrons and positrons around existing electrons, as shown in the figure below, interfering with measurements like photons.
▲ Top: Path of electrons in an environment with low energy uncertainty. Bottom: Path of electrons in an environment with high energy uncertainty. In the air, pairs of photons (wavy lines) and other electrons and positrons are created and destroyed, interacting with existing electrons. (ɔ)Wikimedia user JabberWok, CC-BY-SA 3.0.
At this point, it seems like the universe is consciously preventing accurate measurements of spaces smaller than the Planck length. Many other interpretations are allowed, but what can be said without departing from the theory that has been verified so far is that the concept of distance is not defined within a space smaller than the Planck length. Einstein’s general theory of relativity can only meaningfully define space-time intervals on a scale that exceeds the Planck length and Planck time, and cannot explain the movement paths of objects and distortions of space-time in intervals smaller than that. Physicists in the high-energy field who are actually engaged in such research are still coming up with various concepts of quantum gravity theory to quantize space and time, but no experiments have yet been reported that can provide clues as to which theory is correct. (If it is reported, readers will probably hear the news within a few days.) If the answer is someday obtained through the development of experimental technology accompanied by painstaking efforts, it will be the discovery of a new fundamental constant rather than a combination of the fundamental physical constants known so far. Together, we predict that a process of redefining the resolution of space and time will be necessary.
▲ Imagination of DALL·E 3 showing a researcher in a situation where he must verify a theory without an experiment.
Yang Chang-mo, Doctor of Science
[저작권자ⓒ 울산저널i. 무단전재-재배포 금지]
