The Sciences: Physics:


The Structure of Space and Time

on the Planck Scale


by Professor Samir A Hamouda

Physics Department, University of Benghazi, Libya



Link for Citation Purposes:




The theory of relativity and quantum theory are the pillars of physics. The relativity theory deals with large bodies such as planets, galaxies and high speeds, while quantum theory deals with objects at the atomic level. Each of these two theories has achieved impressive successes each in its own regions, but there are differences between them.  The basis for these differences lies in the concepts. For example, the theory of relativity considers that space is homogeneous and that the speed of light is constant everywhere regardless of the position of the observer, whereas quantum theory considers that space is not homogeneous and that the speed of light depends on its energy. Since these two theories are of great importance, the scientifically accepted trend requires unifying these theories in one theory in order to find relationships between things at the cosmic and atomic level. This study deals with a comparison between the two theories to know some aspects of the difference and convergence between them in the hope of reaching a deeper understanding


Key words: Space-Time, Relativity, Quantum Foam, Planck Length, Quantum Gravity


1.     Introduction

The concepts of space and time introduced by the relativity theory and quantum theory are central for great dispute between the two theories. Returning to Newton's theory, which assumes that time is absolute, it flows from a distant past into an infinite future, which is fixed everywhere in the universe and does not depend on the relationship of things to each other. Newton’s concept can be described as background dependent because it assumes that there exists a fixed, unchanging background that provides the ultimate answer to all questions about where and when. On the other hand, general relativity and quantum foam theories assume that time is not absolute and there is no time that is not followed by change, in the sense that time is a measure of change. In addition, no space or time outside the system of evolving relationships between the things those make up the universe. This implies that there is no fixed background or stage that remains constant all the time. Therefore, relativity and quantum foam theories can be described as background independence [1].


This paper presents a partial and a simple survey about the two pillars of modern physics, quantum mechanics and the relativity theories. Therefore, studying the main concepts of these theories about space-time can help in understanding our universe.


2.     Electromagnetic spectrum

Electromagnetic spectrum is a part of the study of waves, electricity and magnetism, and modern physics. To study relativity and quantum theory requires an accurate knowledge of the electromagnetic spectrum, the structure of the electromagnetic wave, the physics describing the properties of these waves, and the sources of its bands. The electromagnetic spectrum is divided into eight bands including cosmic ray (see figure1 ). Based on longer wavelength toward shorter wavelength, it starts from radio waves (~˃ 1m), microwaves (~ 30cm), visible (~ 700-400 nm), x-ray (~ 1Å), gamma-ray (~ 0.1Å) and cosmic ray (0.1Å˂). Moving from band to other is gradual rather than discrete.


Figure1:  Different parts of the electromagnetic spectrum that come from space [2]


 The electromagnetic spectrum is an essential apparatus for astronomers to use when observing the universe.  To explore and carrying analysis about objects in space, astronomers use different category of telescopes  sensitive to different parts of the  electromagnetic spectrum that come from space, and astronomers rely on choosing the kind of telescopes which depend on optimal resolution and sensitivity in which they observe the part  of the spectrum that they wish to study [3]. Knowledge of the gamma-ray from sky has changed due to the advent of the new ground-based Imaging Atmospheric Cherenkov Telescopes and the satellite-borne instruments (AGILE and Fermi) [3]. These instruments allowed detection of gamma-ray sources above100 MeV from space and detection of gamma-ray sources above 100 GeV from the ground[3]. At energies of a few of MeV, the gamma-rays is directly detected with instruments operating from space.  At energies above 100 GeV the most efficient way of detecting the gamma-rays is through ground-based instruments that use the Earth’s atmosphere as a calorimeter for measuring the total energy of the deposited gamma rays [3].


Detections of higher-energy gamma rays and exploring objects from astronomical distances demands pre-training about the relativity thematic framework of space and its structure. The concepts of space and time, introduced by Einstein’s theory of relativity, have dramatic change in our understanding about space and time with two relevant demonstrations [4]: The first change came in 1905 with the theory of special relativity, which discussed the behavior of matter moving with speed approaching the speed of light. It describes the equivalence of mass and energy, with the most famous equations in mathematics. This equation, E=mc2. It shows that energy (E) and mass (m) are interchangeable; they are different forms of the same thing. The second change came in 1915, Einstein greatest achievement: the theory of gravity known as general relativity [4].


According to general relativity, space-time is curved, and the curvature is created by matter. The general relativity theory predicted also, black holes, the bending of light by the Sun, gravitational waves and the expansion of the universe. Einstein postulates: (1) Principle of Relativity: The laws of physics have the same form in all inertial reference frames. (2) Principle of Constancy of the Speed of Light: Light propagates through empty space with a definite speed c independent of the speed of the observer (or source). In the limit of low speeds the gravity formalism should agree with Newtonian gravity [4].


3.     Main variances between relativity and quantum theory

It can be seen that these postulates are based on Lorentz invariance, a fundamental part of the mathematical description of Physics, which expresses the hypothesis that the laws of physics are the same for various observers. However, Lorentz Invariance may not retain at very high energies. This implies that gamma-rays might travel faster or slower than the conventional speed of light.                                                                      


The HAWC: (High Altitude Water Cherenkov), Gamma Ray Observatory has recently detected a number of astrophysical sources which produce photons above 100 TeV (a trillion times the energy of visible light), much higher energy than is available from any earthly accelerator. These gamma rays detected by HAWC, extend the range that Lorentz Invariance holds by a factor of 100 times. However, how relativity behaves at very high energies has consequences for the world around us and need to be explored and understood. [5,6]


On the other hand, we have quantum mechanics theory that described the states of small objects such as molecules, atoms, and subatomic particles. In such a quantum theory, objects behave as particles and waves within the frame of Heisenberg’s uncertainty principle (you can know an electron’s position or its velocity, but not both) [7]. However, a clear disunity existed in our comprehensive understanding of physics. General relativity characterizes large objects such as the solar system, galaxies, black holes and the universe, while quantum mechanics characterizes little objects such as molecules, atoms, and subatomic particles (fermions and bosons) [7].

Keeping two different theories that work in two different regions fabricates unresolved states for comprehensive understanding of physics. Since the forces operate on both atoms and stars are the same, it can be seen that gravity is more obvious for stars while electricity and magnetism dominate in atoms, molecules, and subatomic particles [7]. So it is a crucial to combine quantum mechanics and general relativity into a unified complete comprehensive theory that characterizes the behavior of both atoms and stars [7]


Quantum theory and the general relativity theory individually have each been proven by experiment but no experiment has reflected fundamentally the scope where both theories predict significant agreements. As a result, fundamentally new postulates or principles or new particles or fields not allowed for in quantum theory and general relativity appeared to be sought after. [8]


Whereas these two theories are the pillars of modern physics, they are maladjusted, and there is an essential contradiction between the two that is partly based on Heisenberg's uncertainty principle which is one of the pillars of quantum theory. [9]                                                                                                                                     


Perhaps space-time concept is the most important issue in which there is a difference between quantum mechanics and general relativity theories. The general relativity theory, assumes that space-time is homogenous and all light particles, or photons, propagate at exactly the same speed [10]. On the other hand, according to quantum theory, the concept of space-time, on a microscopic scale space-time is not continuous, and instead it has a foam-like structure [10].


This quantum foam, referred to as space-time foam, is a concept in quantum mechanics devised by John Wheeler in 1955. The quantum foam is supposed to be conceptualized as the foundation of the fabric of the universe [10]. Additionally; quantum foam can be used as a qualitative description of subatomic space-time turbulence at extremely small distances (on the order of the Planck length). At such small scales of time and space, the Heisenberg uncertainty principle allows energy to briefly decay into particles and antiparticles and then annihilate without violating physical conservation laws [10].


As the scale of time and space shrinks, the energy of the virtual particles increases. According to general relativity, space-time is smooth and energy curves space-time. This suggests that at sufficiently small scales the energy of these fluctuations would be large enough to cause significant departures from the smooth space-time seen at larger scales, giving space-time a quantum foam character [10]. However, existing theories of gravity do not give accurate predictions in that domain. On the other hand, Quantum mechanics predicts that space-time is not smooth, instead space-time would have a foamy, jumpy nature and would consist of many small regions through which light travels will fluctuate and uncertainties accumulate at different rates as light travels through the vast distances [10].


Quantum foam theory is hypothesized to be the building blocks of the universe at the Planck scale and to be formed by virtual particles of very high energy. Therefore, quantum foam implies that these concepts which imagine the consequences of such high-energy virtual particles, arising briefly and then annihilating during particle interactions at very short times and distances (the Planck scale) [10]. In physical cosmology and particle physics, the Planck scale is energy scale corresponding to the mass–energy equivalence of the Planck mass at which quantum effects of gravity become strong. [10]


The term Planck scale can also refer to a length scale or time scale (see table1). The Planck length is related to Planck energy by the uncertainty principle. The nature of reality at the Planck scale is the subject of much debate in the world of physics, as it relates to a fundamental aspect of the universe. Planck derived a unit system depending on the gravitational constant (G=6.67428(67) x10−11 m3 /kg s2), speed of light (c=2.9979245x108 m/ s), and Planck’s constant (h=6.62606896(33)10−34 J s)[11].

  Table1: shows the Planck scale: lp is the Planck length, Tp is Planck time,                                               Mp is Planck mass and Ep is the Planck energy [11].


In terms of size, the Planck scale is extremely small (many orders of magnitude smaller than a proton). In terms of energy, it is extremely energetic. The wavelength of a photon (and therefore its size) decreases as its frequency or energy increases. This makes the Planck scale a charming universe for evaluation by various theoretical schools of thoughts [12]. The current understanding of gravity is based on Einstein's general theory of relativity, which is formulated within the framework of classical physics. On the other hand, the non-gravitational forces are described within the framework of quantum mechanics. This framework is based on probability for the description of physical phenomena [12]. The necessity of a quantum mechanical description of gravity follows from the fact that one cannot consistently couple a classical system to a quantum one. [12]


In quantum mechanics, ordinary properties of space-time, such as position, momentum and so on, have an uncertainty associated with them. That implies that space-time must be uncertain as well as pointed out by John Wheeler. At Planck lengths of 10-35 meters, probing that distance is obviously difficult. This can only be done by accelerating particles to huge energies, which allows to probing very small volumes of space and determine their position accurately. But the energies required are around 1019 GeV, many orders of magnitude higher than today’s particle accelerators [13].


It can be pointed out that space-time only becomes foam-like on the Planck scale. However, there is no prospect of approaching this energy on Earth in the prospective future. So physicists may have thought that understanding the concept of quantum foam require more experiments [13].         


4.     Description of space

General relativity is a theory of fields. The field involved is called the gravitational field, and is pictured as a set of field lines (see figure2). The gravitational field defines a network of relationships having to do with how the set of lines link with one another. These relationships are described in terms of how many times of one field line knot around other field lines. The general relativity theory is a relational theory, in which characterizes the network of relationships between the sets of field lines. This is one of the important differences between general relativity and quantum theory [14].

Figure2: In General relativity theory, gravitational field is pictured as a set of field lines [14].

Relational quantum mechanics is an interpretation of quantum mechanics which treats the state of a quantum system as being observer-dependent, that is, the state is the relation between the observer and the system. [15]


In attempting to merge quantum mechanics and general relativity, loop quantum gravity theory is produced. This theory is an attempt to develop a quantum theory of gravity based directly on Einstein's geometric formulation rather than the treatment of gravity as a force (equal in importance to electromagnetism and the nuclear forces) [16]. In loop quantum gravity theory space and time are quantized analogously to the concepts of quantization of energy and momentum in quantum mechanics. An implication of a quantized space is that a minimum distance exists (matter and space prefer an atomic structure) [16]. The loop quantum gravity postulates that the structure of space is composed of finite loops woven into an extremely fine fabric or network. These networks of loops are called spin networks and have a scale on the order of a Planck length. [16]


Radiation from distant cosmic explosions called gamma-ray bursts might provide a way to test whether the theory of loop quantum gravity is correct. Gamma-ray bursts occur billions of light-years away and emit a tremendous amount of gamma rays within a short instant [17]. According to loop quantum gravity, each photon occupies a region of lines (extremely fine fabric or network) at each instant as it moves through the spin network (see figure3) [17]. The discrete nature of space causes higher-energy gamma rays to travel slightly faster than lower-energy ones. The difference is very small, but its effect steadily accumulates during the rays’ billion-year journey. If a burst’s gamma rays arrive at Earth at slightly different times according to their energy that would be evidence for loop quantum gravity. This can be proved only by experiments.[17]


Figure3: Experimental set-up for testing the correctness of the loop quantum gravity [17]


5.     The Experiments

Confirming the general theory of relativity, scientists found 'spacetime foam' not slowing down photons from faraway gamma-ray burst. The researchers analyzed data, obtained by NASA's Fermi Gamma-ray Space Telescope, of the arrival times of photons from a distant gamma-ray burst [18]. The data showed that photons traveling for billions of years from the distant burst toward Earth all arrived within a fraction of a second of each other [18]. This finding indicates that the photons all moved at the same speed, even though different photons had different energies. This is one of the best measurements ever of the independence of the speed of light from the energy of the light particles [18].


On the other hand, the quantum foam theory is based on the concept that on a microscopic scale space is not continuous, and instead it has a foam-like structure. The size of these foam elements is so tiny that it is difficult to imagine and is at present impossible to measure directly. However light particles that are traveling within this foam will be affected by the foamy structure, and this will cause them to propagate at slightly different speeds depending on their energy.[18]


However, more recent experiment was able to confirm the quantum foam, scientists found delayed gamma rays from deep space [19]. The MAGIC (Major Atmospheric Gamma-ray Imaging Cherenkov) telescope found that high-energy photons of gamma radiation from a distant galaxy arrived at Earth four minutes after lower-energy photons, although they were emitted at the same time [19]. The researchers propose that the delay could be caused by photons interacting with quantum foam. Scientists showed that the high and low-energy photons appeared to have been emitted at the same time. But the high-energy photons arrived four minutes late after traveling through space for about 500 million years. This may provide the first evidence for physics beyond current theories. [19]


Beyond confirming the general theory of relativity and the quantum foam theory, the observations rule out one of the interesting ideas concerning the unification of general relativity and quantum theory [20]. While these two theories are the pillars of physics today, they are still inconsistent, and there is an intrinsic contradiction between the two that is partially based on Heisenberg's uncertainty principle that is at the heart of quantum theory. [20]


6.     Conclusion:

Writing about astronomy and astrophysics is actually, very difficult and challenging task. Perhaps, one of the most fascinating journeys in science concerns the evolution of the description of space and time. The attempts to describe space-time by many theoretical physics models, in an expanding universe, create states of uncertainties about the real structure of the universe. At present time, the concept of space-time is the most debated among theorists in the twentieth century.


Discussion about the quantum theory of gravity and general relativity has been mostly theoretical. Meanwhile advances in technology and in detection systems have established the possibilities of probing the concept of space-time at the Planck length experimentally.  These possibilities will generate a plenty of motivation for testing the challenges that these theories present. If experiments are well guided by clear descriptions of space-time and experimentalists get advantages of the most efficient and sensitive detection systems that allow them to look closely at effects on light from distant cosmic sources, they might find some signatures about the structure of the universe. Moreover, efforts to unify quantum theory and theory of relativity must first lead to the unification of the various fields of mathematics, which undoubtedly will have a major role in unifying the laws of gravity in expanding universe, as well as knowing whether it is possible to find a law that links the past with the future in the presence of time moving in one direction.



[1]  Basic_Books(2002).pdf


[3] David Paneque, (2012).,” Experimental Gamma-Ray Astronomy”., 12th International Conference on Topics in Astroparticle and Underground Physics (TAUP 2011) IOP Publishing Journal of Physics: Conference Series 375


[5] Albert et al. (HAWC Collaboration),( 2020)” Constraints on Lorentz Invariance Violation from HAWC Observations of Gamma Rays above 100 TeV”, Phys. Rev. Lett. 124, 131101                                             

[6]  A. Abdo et. al, (2009),“A limit on the variation of the speed of light arising from quantum gravity effects”., Nature volume 462, pages331–334




[10] Christoph Köhn., (2017)., “The Planck Length and the Constancy of the Speed of Light in Five Dimensional Spacetime Parametrized with Two Time Coordinates”, Journal of High Energy Physics , Gravitation and Cosmology, 3, 635-650.

[11] Ronald J. Adlera., (2010)., “Six easy roads to the Planck scale”., Am. J. Phys. 78 (9).       












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