Strings = vibrations of God's word, which speaks, and through his word, all things are held together = strings are the basic stuff upon which subatomic particles are made.
The things we call real, like all matter we can observe, is made of atoms which themselves are made of 99.999999% SPACE (empty space).
If the atom is the size of a sports stadium, then the #nucleus is the size of a fly in the center and the #electrons are tiny tiny gnats circling the stadium.
We are vastly made of and bathing in an infinite field of #energy that we call empty space even though we have found that space is not empty at all, it is filled with energy vibrating at incredibly high frequency: the quantum foam, the aether, the plenum, vacuum fluctuations, the zero point field, in an infinite holofractographic universe...
Martin B. van der Mark: On the nature of “stuff” and the hierarchy of forces 2015
At all experimentally accessible length scales the structure of stable matter is the result of a balance of forces working between some otherwise bound objects, particles, or granules. The final stage is a balance of forces on a continuous, circulating flow of energy, holding itself together. The proton’s internal dynamics must be essentially a light-speed knot of circulating energy. That energy is the “stuff” we were after, and it is continuous and takes part in the electromagnetic interaction. The nature of “stuff” is consistent with some topological form of electromagnetism which may or may not demand us to change our view on the structure or nature of space-time.
Martin B. van der Mark: Quantum mechanical probability current as electromagnetic 4-current from topological EM fields August 2015
Perhaps, then we will find that the fundamental “stuff” everything is made of is, in mathematical terms, just the combination of complex fields α and β that produces the potential A, the electromagnetic fields F, currents J and wave functions Ψ.
Of course, modern science already gives some idea of what it is, at least to some level: It is matter and it is made of atoms! Or more precisely, matter is made of protons, neutrons and electrons, or perhaps, quarks and leptons and gluons and vector bosons, and more. This is quite true, but what then is the nature of the substance that constitutes these elementary particles? Are there, for example, even smaller, more elementary-elementary particles? Or perhaps, is there some underlying primordial “stuff”? If so, is this stuff continuous, like a fluid or field, or is it granular of nature? Whether we look at galaxies, the solar system or the electrons in the atom, at all length scales the basic structure and shape of matter seems to be that of some objects bound together and rotating around one another. The basis for this universal dynamical structure is a balance of forces: a repulsive force (such as the centrifugal force) and an attractive force. At astronomical sizes the attractive force is provided by gravitation, whereas at molecular and atomic sizes it comes from electromagnetism. For nuclear scales it is provided by the weak and strong interaction. What we find is that the weakest of the forces (gravitation) governs the largest structures and that the smallest structures, the elementary particles, are stabilized by the strongest of the forces: the strong interaction. There appears to be a hierarchy of forces that dominates the structure of matter at successive length scales. 3
SOME FUNDAMENTAL QUESTIONS
Before going into more detail it seems appropriate to prepare ourselves by asking a few questions.
1. What is it that everything is made of? A quite reasonable answer to this question seems to be: “It is either matter or light (radiation, photons)”. For the purpose of this paper we will only indirectly address the latter possibility.
2. Then, what is matter? What is its ultimate substance?
3. Does there exist something such as primordial “stuff”?
4. Does this “stuff” have mass? And, as a consequence of its possible mass, does it contain or possess energy?
5. Is “stuff” penetrable? Does it exert a force on some things? Note that this question certainly has bearing on the nature of radiation, which is penetrable, contains energy and can exert a force on matter.
Before trying to answer all these questions we make explicit that we will presume (as usual) that:
• Energy is conserved, and it is conserved locally
• One may only consider closed systems so that a proper energy balance can be obtained
Note that the meaning of Einstein’s famous formula is that energy is equivalent to mass and not another form of mass (as if the formula were to describe a transmutation).
Given the above, if “stuff” does not ever exert a force, nothing happens and we cannot know that it exists at all. It then is effectively not part of our world. Interestingly, however, would it have interaction with its own, separate world, then it must carry energy (a force is the gradient of some energy), and consequently, it becomes part of our world through gravitation, the energy represents mass, and that mass gravitates with the masses of our world). So, all that has energy does exists in our world, albeit only felt by gravitation. This leads to some further realizations and consequences. The previous paragraph implies that for any stuff to be useful it must interact with some world and it must therefore have energy, in other words: stuff cannot be “sterile”! Conversely, it also implies that anything at all that exists in the universe (our world) must have energy.
Hence we must conclude that energy is part of stuff or some form of stuff. This then raises more questions:
1. What is the fundamental appearance that goes with stuff?
2. Is there more than one type of stuff?
3. Are charge, spin or quarks some form of stuff?
4. Is stuff quantized or is it continuous?
SOME FIRST ANSWERS
From experiment we can find some first answers to the questions raised above. The annihilation of the singlet bound-state electron-positron pair, called para-positronium (anti-parallel spins) has a mean lifetime of 125 × 10−12 s and decays highly preferentially into two gamma rays. Energy is conserved; the gammas have energy of 0.511 MeV each, corresponding to the rest mass of electron and positron. Of course, total momentum (which is zero) is also conserved: the gammas are radiated in opposite direction, and angular momentum (which is also zero) is conserved by the polarization of the gammas (which are therefore in an entangled polarization state).
In Eq. (1) there is a total transmutation of matter into radiation, which implies that for the stuff in the electron and positron only the following possibilities seem to be allowed:
1. There is no different stuff other than the electromagnetic fields. The electron and positron are purely electromagnetic, to begin with, hence they can radiate purely electromagnetically.
2. There is one kind of stuff. Bringing together twice the amount shouldn’t make it disappear, but what is left are just the two gammas. Hence stuff is electromagnetic, so that comes down to possibility 1, we can say that stuff is some, perhaps alternative or extended, form of electromagnetism.
3. Stuff is its own anti-stuff. Then, if stuff is continuous one may have any amount of it, it cannot be its own anti stuff. If it is quantized, only one quantum may exist in each fundamental particle (since it is its own anti-stuff it will annihilate even amounts), so that all particles have the same amount of stuff. Then, what makes them different in the first place? It must be different stuff for different particles, or equivalently, more properties to stuff, or properties may be imposed by boundary conditions imposed by space-time. Then, the quantization may come from the periodic or topological nature of these boundaries.
4. There is stuff and there is anti-stuff and brought together the two annihilate into radiation. Hence there are two kinds of stuff that must couple to electromagnetism. What then is, or carries, the “anti” property? Is it the electric charge? Charge conjugation is the generally accepted particle to anti-particle transformation. Charge is an electromagnetic property, apparently intimately connected to stuff. Another possibility is, by the CPT theorem, that anti-stuff has the opposite spatial handedness running backwards in time or so, but that would require it to be quite more complicated than just a scalar field. Alternatively, space-time itself must have a nontrivial structure.
The more properties are attributed to stuff, the less fundamental stuff becomes. This is not what we were hoping for because then there must be something else, “meta stuff”, that determines the differences. A further realization comes to mind: Suppose that stuff only couples by gravitation, but is part of an electrically charged particle, for example, the electron. Now, when the electron is accelerated by an electromagnetic field, the stuff is just left behind, unless if it has some interaction with the charged part inside the electron at least as strong as the electromagnetic interaction! This implies that stuff must at least also couple by the weak force or electromagnetism!! Stuff cannot be as dull as galactic dark matter; gravitation is far too weak to keep up with an electromagnetically charged particle accelerated! At this point one should realize that at least part of the mass of a charged particle comes from its electric charge. This so-called electromagnetic mass comes from the energy carried by the external electric field. In case of the electron, much of the field seems to be external and hence the contribution of the electromagnetic mass to the total mass of the electron may be substantial. It has therefore been proposed that the electron may be purely electromagnetic, an idea that is very appealing, but is associated with some serious problems. One problem is known as the self-energy problem of electrical charge, the other is the elusive nature of the binding forces (known as the Poincaré stresses) that keep the electron together. The problems are very well described in the Feynman Lectures.
THE STRUCTURE OF MATTER AT DIFFERENT LENGTH SCALES
From superclusters of galaxies down to the quarks in the proton, at all length scales the basic structure and shape of matter seems to be that of some objects orbiting one another, forming a bound system. For example, stars circulating the galactic center, the moon orbiting the earth or electrons waving around the atomic nucleus. The basis for this universal dynamical structure is a balance of forces: a repulsive force (such as the centrifugal force) and an attractive force. At astronomical sizes, the attractive force is provided by gravitation, whereas at molecular and atomic sizes it comes from electromagnetism. For nuclear sizes it is provided by the weak and strong interaction. When we go to small enough length scales an additional property emerges due to quantum mechanics, namely the wave-like nature of particles. Due to wave interference quantum mechanics provides a further mechanism (on top of the centrifugal force) against the collapse of the smallest objects. Historically, in 1925, the quantization using De Broglie waves by Schrödinger was the answer to the postulated stability of electron orbits with angular momentum quantization in Bohr’s model of the Hydrogen atom.
To gain some insight on the observed scaling of structures in the universe, an overview of the mass and size relationship is given in Fig. 1. What we see first of all is the truly astronomical scale we are dealing with. At the far left we have the smallest thinkable, an object of Planck mass and Planck length 1.6×10-35 meter, to the upper right the largest and heaviest, the universe itself (with a radius of 46.6 Mly), and in between, at the bottom, the lightest material object, the electron. Well, one may ask whether it is the lightest and why its size of 2.4 × 10−12 meter is so large; shouldn’t it be as tiny as a point? It is a matter of choice, what is taken here for the size of an elementary particle is its Compton wavelength. Clearly, neutrinos may be lighter, and so are all photons that have less than 511 keV of energy (this energy corresponds to the electron’s rest mass). Although radiation is not matter, its relation between energy and wavelength would make the photon fall on the same line as all elementary particles; with proportionality we may name this the “particle branch”. The electron, like all other leptons (muon, tauon, the neutrinos), is special in that it shows no internal structure in scattering experiments, just like point object. This does not mean however that the electron itself is really a point. For example, the electron has spin, magnetic dipole moment, a de Broglie wavelength and a finite mass and charge. This cannot be reconciled with the notion of point symmetry. The implied infinite energy and charge densities require at least some proper dressing over a length scale related to the electron mass and its quantum mechanical wave nature. That length is what the Compton wavelength is. Note that for the proton, which does have internal structure, the charge radius and Compton wavelength are of similar size. Central to Fig. 1 is what we may call the “material branch” for which mass is proportional to volume and it is where we find ordinary matter. The line connects the more familiar material bodies: electron, human, earth and sun. On the material branch, objects get lighter when smaller. On the particle branch, however, objects get heavier when smaller! As a consequence, a minimum weight object exists close to the point where the particle branch and the material branch cross. This appears to be the electron. Another couple of branches with different scaling laws are indicated as well. The upper one has proportionality and is named the “black hole branch”. It connects the universe with the Planck scale through some known black holes, the size of which is taken to be the calculated Schwarzschild radius. There is also a line that connects the universe with the proton and it has proportionality. It has been drawn for no better reason than Dirac’s Large Numbers Hypothesis (LNH) in which the ratio of sizes of universe and proton are compared to the relative strength of electromagnetic and gravitational interaction between proton and electron (both are 10^42), and it appears to coincide with the aspect ratio of the figure signifying the very largest, smallest, heaviest and lightest ever thinkable in our universe. In this paper we combine two general arguments. First, that with decreasing size (horizontal scale of Fig. 1) there is a systematic increase of the fraction of kinetic energy (internal dynamics) and binding energy (energy lost at formation) with respect to the total energy (rest mass, vertical scale in Fig. 1). Second, that the stronger forces are getting balanced at cost of the larger part of the available energy. Consequently, at some small enough length scale the amount of internal energy will approach the total energy in the system, from where no further decrease in size is possible in a stable manner. Experimentally the proton is found to be the smallest stable particle.
On the strength and hierarchy of forces
Any stable, bound structure must have an internal balance of repulsive forces that prevent collapse and attractive forces that provide binding. The dependence of the strength with distance of either of these forces determines the nature of the structure we see. Looking at different scales of length, what we find is that the weakest of the forces (gravitation) governs the largest structures and that the smallest structures, the elementary particles, are stabilized by the strongest: the strong interaction. There appears to be a hierarchy of forces that dominates the structure of matter at successive length scales. That this must necessarily be so, can be understood quite readily. The stronger force will simply dominate over the weaker ones and be able to pull in more closely the objects it finds attractive. The weaker bonds, made by the weaker forces, can and will be broken by the stronger force. So the hierarchy becomes obvious: The stronger force wins and pulls in whatever it can. What is pulled in (against any repulsive force) ends up closer to the source of the interaction than the weaker force could do. Hence stronger forces go first and they make smaller, more tightly bound objects. One may wonder what the influence is of the reach and polarity of the forces on the hierarchy argument as presented above. Whatever initial configuration of particles, we may safely assume that sufficient mixing will occur eventually. Whether unipolar (gravity) or bipolar (electromagnetism) interaction sources are at play, attraction will occur. In the latter case this is true because the universe appears to have no net charge. The same polarity charges will simply be pushed away in favor of the attractive ones. There is another convenient situation in the universe (that may not be accidental) and that is that the strongest forces only work at short range, just where they would “want” to operate. While stronger forces lead to tighter binding, with the system releasing more energy in the binding process, at the same time the internal kinetic energy of the system must increase proportionally. In weakly bound systems the total mass of the system is, for all practical purposes, simply equal to the sum of the bare masses of the constituents. In what follows it is shown that for the tightest bound systems this is no longer the case because the internal kinetic energy and binding energy become so large in comparison to the bare mass of the constituents that it cannot be neglected. A well-known example of this is given by “mass defect” for atomic nuclei.
Now we have arrived at an important point, and a key insight can be obtained if we string together all successive levels of binding. Starting in reverse, from the weakest forces, each successive, deeper level of binding must come from a stronger force at a shorter length scale and hence must have more binding energy associated with it. While this binding energy is released to the environment, a related amount of kinetic energy is kept or built-up inside the system. More kinetic energy is added at each deeper level than all the kinetic energy that was there already. At some point, the kinetic energy may reach a level equal to the bare mass of the system, exhausting the maximum possible amount of energy available, at which point there can no longer be a next level with even more energy and stronger forces to keep even smaller constituents together. This is where further scaling must stop. Due to a pure lack of available energy to keep the integrity of the granules, granularity must be given up in favor of a continuum of energy. The question is when and where granularity must be given up. At first glance any attempt to give an estimate may seem futile, but it will appear that answers are only needed that are accurate at the order of magnitude level. In what follows, the energy balance and binding process for the hydrogen atom, deuteron and proton will be analyzed.
ENERGY BALANCE IN A BOUND SYSTEM
When two particles with an attracting force between them are brought together from infinite separation, the potential energy is reduced and a bound system may be formed if all of the required conservation laws can be fulfilled. Among those are the conservation of energy, momentum and angular momentum. This requires that at least a third particle or (radiation) field is present or is produced to deal with any excess of energy, momentum and angular momentum. In what follows we will first analyze the energy balance in the formation of the hydrogen atom from an electron and a proton. From there we will proceed to analyze the energy balance in the deuteron as well as the proton.
Formation of the hydrogen atom
In this section the energy balance and internal kinetic energy in the hydrogen atom is compared to that of the free proton and electron at large separation. At time t0, imagine an electron and proton at very large separation and both at rest. If we let the system evolve, see Fig. 2, the electron and proton will gain kinetic energy at the cost of potential energy and come together to form a bound state, a hydrogen atom, all under emission of electromagnetic radiation.
Experimentally, the proton is a stable particle with (internal) structure. It is thought to be built of three quarks (up,up,down), each with spin ½ and a tri-polar charge called “color”. The “up” quarks have electrical charge +2/3 and the “down” quarks have electrical charge −1/3. The mass of the quarks may be much smaller than the mass of the proton (938 MeV c2 ⁄ ), which can be deduced from the mass of the pion (139 MeV c2 ⁄ ). The pion is made of two quarks, a positively charged pion consists of one “up” quark and one anti-“down” quark, so if one of those is very light the other may weigh no more than 139 MeV c2 ⁄ , unless a large amount of binding energy may have been drained from the free quark. The free quark?! Nobody has ever seen one, and the proton is very (absolutely) stable. So, yes, this is circumstantial evidence that a lot of binding energy may be involved.
In Fig. 3a, the simple quark model of the proton with three quarks and connecting gluons is shown. The picture of three quarks making a baryon and two making a meson has proven a very powerful model in predicting the hadron spectrum of elementary particles. In Fig. 3b we see what quantum chromodynamics QCD is forced to make of it: There are still three valance quarks but there is also a whole network emerging, made of many gluons and virtual quark-antiquark pairs. The quark masses are small and the network carries a substantial part of the energy, momentum and angular momentum (of the proton spin of ½) inside the proton. A remarkable situation is unfolding. In the previous sections, the sum of the constituting particles invariant mass was always slightly larger than the mass of their bound state, but now the three quarks together weigh hardly 9 MeV c2 ⁄ , less than 1% of the proton mass! Again, as for the deuteron, we do not know the binding potential inside the proton, but given the size of the proton we may be able to use a quantization condition to determine the energy level inside the proton, just as we did successfully for the deuteron. This suggests, on grounds of energetic balance, that there are no particles or structures smaller than the proton that can exist independently, they simply cannot be stable. Hence we must say goodbye to quarks as independent existing particles. Already, it seems to be an experimental fact that quarks cannot exist on their own, so that is fine, but surely we would like to keep the beautiful and powerful quark symmetries that make the full set of hadrons. We are forced to admit that we have arrived at the end of the ladder, but how can we save the day? It certainly seems that quarks cannot be small and heavy, and at the same time they cannot be light and big, what then?
What if the quarks as such really do not exist?
To make things even more complicated, in QCD we find that the force and energy should actually go down when the quarks sit very close together, this is called “asymptotic freedom”, a very cunning idea invented to deal with the self-energy that would explode without it. The hierarchy of forces, which rules the length scale of granular matter, is clearly at odds with the idea of asymptotic freedom. Another idea is required. Maybe the quarks are strung together to provide some of the symmetries they are expected to. Perhaps the quarks are not coming in granules and have no rest mass, but come together as a continuum of some form of energy that propagates close to, or rather, exactly at the speed of light. If so, their orbital wavelength (the De Broglie wavelength) can become arbitrarily small without the need for a granule having a size of some Compton wavelength. An artist impression of a daring looking possibility is given in Fig. 4, it is a trefoil knot of continuous energy flow. It goes around twice at (close to) light speed before closing on itself in a single wavelength. The three differently colored loop segments should be imagined as orthogonal in space. If the underlying structure of the energy flow is a vector field (such as the electromagnetic field), each of the loops may have different properties according to their amount of twist (not shown in the figure). If we were to pull one loop it would tighten up the other loops, thereby increasing the total energy, just as is assumed to be the case for asymptotic freedom of quarks. Both the loop and its knot take part in a spring that binds things together, and may replace the gluon properties. It is all speculation, but it shows there may be a way out. In fact, there must be a way out, the proton really exists!
In this paper we have investigated the nature of “stuff”. Energy is part of “stuff”, or some form of “stuff”. The nature of the “stuff” inside elementary particles requires it to be more than only gravitationally coupled: it must at least couple to electromagnetism or the weak force, otherwise binding of stuff to the particle is too weak to follow the particle when it is accelerated by any force stronger than the gravitational force. “Stuff” must be continuous and in case there is only one form of “stuff”, that it is some, perhaps alternative or extended, form of electromagnetism. If there is also “anti-stuff”, then we may need space-time itself to have a non-trivial structure, something that may be true regardless of our findings. At all experimentally accessible length scales the structure of stable matter is the result of a balance of forces working between some otherwise bound objects, particles or granules. The hierarchy of strength of interactions is connected to the length scale of material structures. The stronger forces go first and they make smaller, more tightly bound objects. In nature, the following is observed (see Fig. 1): the total mass of a lump of ordinary matter decreases with smaller size, but contrary to that, the mass of subatomic particles increases with smaller size. The electron is at the bottom of the mass scale. Most subatomic particles are unstable, except for the electron and proton. In this paper two insights about bound systems have been combined. First, that with decreasing size there is a systematical increase of the fraction of kinetic energy (internal dynamics) and binding energy (energy lost at formation) with respect to the total energy (rest mass). Second, that the stronger forces are getting balanced at cost of the larger part of the energy available. The ratio of internal kinetic energy and total energy increases with decreasing size. The consequence is that stable matter cannot exist at smaller length scale than where internal kinetic energy and total energy are of comparable magnitude: . At that point the orbiting corpuscular, granular structure with binding forces runs out of internal binding energy to hold the kinetics and from there only a circulating “fluid”-like continuum flow of energy seems in accordance with energy conservation. Consistent with experiment and supported by theoretical estimations it can be inferred that this lower limit is given by the size of the proton, and that the proton is the smallest stable particle. Quarks as independent constituents of the proton are ruled out, and so is Planck-scale physics. There appears to be a smallest length scale, at which the ladder of the hierarchy of forces (that holds for granular matter) comes to an end. The final stage is a balance of forces on a continuous, circulating flow of energy, holding itself together. This is consistent with the notion of asymptotic freedom: when the system is in equilibrium, the energy is lowest and the size finite.
Given the large fraction of kinetic energy circulating inside the proton, it is then proposed that the proton’s internal dynamics must be essentially a light-speed knot of circulating energy. That energy is the “stuff” we were after, and it is continuous and takes part in the electromagnetic interaction. The nature of “stuff” is consistent with some topological form of electromagnetism which may or may not demand us to change our view on the structure or nature of space-time.
Last edited by Otangelo on Sun Sep 26, 2021 4:23 pm; edited 4 times in total