ABSTRACT THE QUANTUM AS BACKWARDS TIME, AND HOW THIS PERMITS A FIRST-EVER WORKING ALGEBRAIC QUANTUM GRAVITY By Jonathan Deutsch Backwards time is inferred to exist from the superluminal implications of the universe’s proven non-locality. It exists as well in the standard quantum-mechanical formalism as an “advanced solution” to the Schrodinger wave equation. Regrettably, backwards time is ignored by most physicists, students, and by the general public. Very, very recently, however, careful experiments performed in Europe have confirmed the existence of backwards time in certain quantum situations. But nature makes absolutely no distinction at all between the quantum and the classical realms! Therefore, it won’t be long before backwards time is experimentally confirmed for you and I. We begin by creating and then using three original postulates: 1)The deBroglie wavelength (in centimeters) associated with the proton is really equal to –1. 2)The mass of the proton (in grams) is really equal to +1. 3)The time (In seconds) it takes light to travel the deBroglie wavelength associated with the proton is really equal to i, the square root of –1. With these three postulates, we demonstrate that the quantum, h, could really be a unit of backwards time. The inscrutability of quantum mechanics would then be seen as entirely due to the inscrutability of backwards time. We then combine Newton’s equation for universal gravity with the three postulates to create the first algebraic equation for quantum gravity that works for planets, quanta and everything in-between. The new gravity equation contains four elements: 1)The tiny quantum, h 2)The minute deBroglie wavelength associated with the proton 3)The miniscule time it takes light to travel that distance 4)A variable - - a coefficient for h - - that’s actually composite “quantum Newton”! We then demonstrate that this new equation magically reproduces, exactly, Newton’s classical gravity results! We begin to realize that the quantum, h, lies hidden in EVERY classical equation - - gravity, electromagnetism, etc. Therefore, classical physics becomes fully quantized too, uniting for the first time the very large - - classical physics, including gravity - - with the very small - - quantum physics - - into one essentially indivisible whole. We conclude by seeing that spacetime is the universe’s prime mover. Though invisible, it is physically real and powerful enough to create all the matter and all the gravity in the entire universe. What’s thought of as the geometric backdrop for matter is really the creator of it as well. Matter affects (warps) spacetime causatively in the forwards time-direction in Einstein’s General Relativity. And spacetime affects (creates) matter in the backwards time-direction equally significantly. Thus, a completely new window to understanding matter and gravity is opened up to us. But the outstanding feature of all this is backwards time - - a healing backwards time. Does the omnipresent existence of backwards time hold out any hope that we can get younger as we age? We strongly believe that such is the case, both quantumly and at the human, macro level. Older and younger simultaneously IS very quantum-like, after all. Could they somehow be EQUIVALENT? Again, we strongly believe that the answer is in the affirmative, and is mathematically provable! I encourage readers to respond in the Disqus comment section on the Abstract page. Or contact me personally at spqrwin@outlook.com. I will reply to all. My next article, to be published in March or April, intends to remove quantum contradictions by proving that supposed opposites are really identical. KEYWORDS Advanced solution: a backwards-time solution Backwards time: time running in reverse, from present to past; future to present; or future to past. This can be continuously, or discontinuously - - i.e., JUMPING to a much earlier time. c: the speed of light Classical physics: the science and mathematics of relatively large entities - - e.g., apples, people and planets. It also includes electromagnetism (See Entry.) Coefficient: the number (amount) of something, e.g., for 5 quanta (5h), the number “5”. A coefficient needn’t be a whole number, but it is, or should be, a positive number. deBroglie wavelength: the wavelength associated with every particle, according to Prince Louis deBroglie, famous 20th-century theoretical quantum physicist. Whether or not this deBroglie wavelength is physically real or not is a matter of some dispute, but the consensus leans toward the negative. Electromagnetism: the classical science of visible light and of invisible rays such as X-rays, infrared rays and ultraviolet rays. Electromagnetism has a quantum counterpart. General Relativity: Einstein’s theory of gravity (See the Entry for Gravity.) Its two essential ideas are: 1)Gravity is acceleration, not a force. 2)Gravity is matter warping (curving) spacetime, rather than “spooky action at a distance” - - one piece of matter affecting another without touching it. Gravity: for Newton, the attractive force between any two pieces of matter. For Einstein, it’s the warping (curving) of spacetime, caused by the presence of matter. h: the quantum of action, also known as Planck’s constant. It is absolutely central to all of quantum physics. Newton’s equation for universal gravity: the product of the two masses involved, divided by the square of the distance between them, multiplied by the strength of gravity. Non-locality: the proven fact that our world is supported by an invisible reality which links all points in space, making extremely large distances seem “on top of each other” - - i.e., very small. This means that SOME form of communication faster than light-speed exists, implying that backwards time exists for our whole universe. Non-locality does not diminish with distance. Postulate: an assumption, at least initially unproven. Our theory contains just four - - all eventually proven true. Quantized: measured in quanta - - i.e., in units of h (See Entry for h.) - - measured discontinuously, in little “chunks” or “packets”. Quantum gravity: the as-yet unaccomplished union of Einstein’s theory of gravity - - General Relativity - - and quantum mechanics. We firmly believe that our theory takes a huge first step in this direction. Quantum mechanics: that area of quantum physics which deals with the motion of extremely small subatomic particles. Quantum physics: the science and mathematics of very small subatomic particles - - e.g., protons, electrons, neutrons and neutrinos - - and their antiparticles. Schrodinger’s wave equation: the quantum mechanics equation that many physicists consider to be the only physical reality in the universe. Some physicists even believe that THIS is not physically real either. Superluminal: faster than light-speed. Unitless: a “pure” number - - e.g., 20.5 - - as opposed to 20.5 CENTIMETERS, in units Universal G: the strength of gravity - - a universal constant Variable: an entity with two or more possible values, as opposed to a constant which has one value. Variables are heavily used in algebra.
ABSTRACT THE QUANTUM AS BACKWARDS TIME, AND HOW THIS PERMITS A FIRST-EVER WORKING ALGEBRAIC QUANTUM GRAVITY By Jonathan Deutsch Backwards time is inferred to exist from the superluminal implications of the universe’s proven non-locality. It exists as well in the standard quantum-mechanical formalism as an “advanced solution” to the Schrodinger wave equation. Regrettably, backwards time is ignored by most physicists, students, and by the general public. Very, very recently, however, careful experiments performed in Europe have confirmed the existence of backwards time in certain quantum situations. But nature makes absolutely no distinction at all between the quantum and the classical realms! Therefore, it won’t be long before backwards time is experimentally confirmed for you and I. We begin by creating and then using three original postulates: 1)The deBroglie wavelength (in centimeters) associated with the proton is really equal to –1. 2)The mass of the proton (in grams) is really equal to +1. 3)The time (In seconds) it takes light to travel the deBroglie wavelength associated with the proton is really equal to i, the square root of –1. With these three postulates, we demonstrate that the quantum, h, could really be a unit of backwards time. The inscrutability of quantum mechanics would then be seen as entirely due to the inscrutability of backwards time. We then combine Newton’s equation for universal gravity with the three postulates to create the first algebraic equation for quantum gravity that works for planets, quanta and everything in-between. The new gravity equation contains four elements: 1)The tiny quantum, h 2)The minute deBroglie wavelength associated with the proton 3)The miniscule time it takes light to travel that distance 4)A variable - - a coefficient for h - - that’s actually composite “quantum Newton”! We then demonstrate that this new equation magically reproduces, exactly, Newton’s classical gravity results! We begin to realize that the quantum, h, lies hidden in EVERY classical equation - - gravity, electromagnetism, etc. Therefore, classical physics becomes fully quantized too, uniting for the first time the very large - - classical physics, including gravity - - with the very small - - quantum physics - - into one essentially indivisible whole. We conclude by seeing that spacetime is the universe’s prime mover. Though invisible, it is physically real and powerful enough to create all the matter and all the gravity in the entire universe. What’s thought of as the geometric backdrop for matter is really the creator of it as well. Matter affects (warps) spacetime causatively in the forwards time-direction in Einstein’s General Relativity. And spacetime affects (creates) matter in the backwards time-direction equally significantly. Thus, a completely new window to understanding matter and gravity is opened up to us. But the outstanding feature of all this is backwards time - - a healing backwards time. Does the omnipresent existence of backwards time hold out any hope that we can get younger as we age? We strongly believe that such is the case, both quantumly and at the human, macro level. Older and younger simultaneously IS very quantum-like, after all. Could they somehow be EQUIVALENT? Again, we strongly believe that the answer is in the affirmative, and is mathematically provable! I encourage readers to respond in the Disqus comment section on the Abstract page. Or contact me personally at spqrwin@outlook.com. I will reply to all. My next article, to be published in March or April, intends to remove quantum contradictions by proving that supposed opposites are really identical. KEYWORDS Advanced solution: a backwards-time solution Backwards time: time running in reverse, from present to past; future to present; or future to past. This can be continuously, or discontinuously - - i.e., JUMPING to a much earlier time. c: the speed of light Classical physics: the science and mathematics of relatively large entities - - e.g., apples, people and planets. It also includes electromagnetism (See Entry.) Coefficient: the number (amount) of something, e.g., for 5 quanta (5h), the number “5”. A coefficient needn’t be a whole number, but it is, or should be, a positive number. deBroglie wavelength: the wavelength associated with every particle, according to Prince Louis deBroglie, famous 20th-century theoretical quantum physicist. Whether or not this deBroglie wavelength is physically real or not is a matter of some dispute, but the consensus leans toward the negative. Electromagnetism: the classical science of visible light and of invisible rays such as X-rays, infrared rays and ultraviolet rays. Electromagnetism has a quantum counterpart. General Relativity: Einstein’s theory of gravity (See the Entry for Gravity.) Its two essential ideas are: 1)Gravity is acceleration, not a force. 2)Gravity is matter warping (curving) spacetime, rather than “spooky action at a distance” - - one piece of matter affecting another without touching it. Gravity: for Newton, the attractive force between any two pieces of matter. For Einstein, it’s the warping (curving) of spacetime, caused by the presence of matter. h: the quantum of action, also known as Planck’s constant. It is absolutely central to all of quantum physics. Newton’s equation for universal gravity: the product of the two masses involved, divided by the square of the distance between them, multiplied by the strength of gravity. Non-locality: the proven fact that our world is supported by an invisible reality which links all points in space, making extremely large distances seem “on top of each other” - - i.e., very small. This means that SOME form of communication faster than light-speed exists, implying that backwards time exists for our whole universe. Non-locality does not diminish with distance. Postulate: an assumption, at least initially unproven. Our theory contains just four - - all eventually proven true. Quantized: measured in quanta - - i.e., in units of h (See Entry for h.) - - measured discontinuously, in little “chunks” or “packets”. Quantum gravity: the as-yet unaccomplished union of Einstein’s theory of gravity - - General Relativity - - and quantum mechanics. We firmly believe that our theory takes a huge first step in this direction. Quantum mechanics: that area of quantum physics which deals with the motion of extremely small subatomic particles. Quantum physics: the science and mathematics of very small subatomic particles - - e.g., protons, electrons, neutrons and neutrinos - - and their antiparticles. Schrodinger’s wave equation: the quantum mechanics equation that many physicists consider to be the only physical reality in the universe. Some physicists even believe that THIS is not physically real either. Superluminal: faster than light-speed. Unitless: a “pure” number - - e.g., 20.5 - - as opposed to 20.5 CENTIMETERS, in units Universal G: the strength of gravity - - a universal constant Variable: an entity with two or more possible values, as opposed to a constant which has one value. Variables are heavily used in algebra.
I take non-locality to be the Michelson–Morley experiment of the early 21st century, assume its universal validity, and try to derive its consequences. Spacetime, with its locality, cannot be fundamental, but must somehow be emergent from entangled coherent quantum variables and their behaviors. There are, then, two immediate consequences: (i). if we start with non-locality, we need not explain non-locality. We must instead explain an emergence of locality and spacetime. (ii). There can be no emergence of spacetime without matter. These propositions flatly contradict General Relativity, which is foundationally local, can be formulated without matter, and in which there is no “emergence” of spacetime. If these be true, then quantum gravity cannot be a minor alteration of General Relativity but must demand its deep reformulation. This will almost inevitably lead to: matter not only curves spacetime, but “creates” spacetime. We will see independent grounds for the assertion that matter both curves and creates spacetime that may invite a new union of quantum gravity and General Relativity. This quantum creation of spacetime consists of: (i) fully non-local entangled coherent quantum variables. (ii) The onset of locality via decoherence. (iii) A metric in Hilbert space among entangled quantum variables by the sub-additive von Neumann entropy between pairs of variables. (iv) Mapping from metric distances in Hilbert space to metric distances in classical spacetime by episodic actualization events. (v) Discrete spacetime is the relations among these discrete actualization events. (vi) “Now” is the shared moment of actualization of one among the entangled variables when the amplitudes of the remaining entangled variables change instantaneously. (vii) The discrete, successive, episodic, irreversible actualization events constitute a quantum arrow of time. (viii) The arrow of time history of these events is recorded in the very structure of the spacetime constructed. (ix) Actual Time is a succession of two or more actual events. The theory inevitably yields a UV cutoff of a new type. The cutoff is a phase transition between continuous spacetime before the transition and discontinuous spacetime beyond the phase transition. This quantum creation of spacetime modifies General Relativity and may account for Dark Energy, Dark Matter, and the possible elimination of the singularities of General Relativity. Relations to Causal Set Theory, faithful Lorentzian manifolds, and past and future light cones joined at “Actual Now” are discussed. Possible observational and experimental tests based on: (i). the existence of Sub- Planckian photons, (ii). knee and ankle discontinuities in the high-energy gamma ray spectrum, and (iii). possible experiments to detect a creation of spacetime in the Casimir system are discussed. A quantum actualization enhancement of repulsive Casimir effect would be anti-gravitational and of possible practical use. The ideas and concepts discussed here are not yet a theory, but at most the start of a framework that may be useful.
I take non-locality to be the Michaelson Morley experiment of the early 21st Century, assume its universal validity, and try to derive its consequences. Spacetime, with its locality, cannot be fundamental, but must somehow be emergent from entangled coherent quantum variables and their behaviors. There are, then, two immediate consequences: i. If we start with non-locality, we need not explain non-locality. We must instead explain an emergence of locality and spacetime. ii. There can be no emergence of spacetime without matter. These propositions flatly contradict General Relativity, which is foundationally local, can be formulated without matter, and in which there is no “emergence” of spacetime.If these be true, then quantum gravity cannot be a minor alteration of General Relativity but must demand its deep reformulation. This will almost inevitably lead to: Matter not only curves spacetime, but “creates” spacetime.We will see independent grounds for the assertion that matter both curves and creates spacetime that may invite a new union of quantum gravity and General Relativity.This quantum creation of spacetime consists in: i. Fully non-local entangled coherent quantum variables.ii. The onset of locality via decoherence. iii. A metric in Hilbert Space among entangled quantum variables by the sub-additive von Neumann Entropy between pairs of variables. iv. Mapping from metric distances in Hilbert Space to metric distances in classical spacetime by episodic actualization events.v. Discrete spacetime is the relations among these discrete actualization events. vi. “Now” is the shared moment of actualization of one among the entangled variables when the amplitudes of the remaining entangled variables change instantaneously.vii. The discrete, successive, episodic, irreversible actualization events constitute a quantum arrow of time. viii. The arrow of time history of these events is recorded in the very structure of the spacetime constructed. ix. Actual Time is a succession of two or more actual events.The theory inevitably yields a UV cut-off of a new type. The cut-off is a phase transition between continuous spacetime before the transition and discontinuous spacetime beyond the phase transition.This quantum creation of spacetime modifies general relativity and may account for Dark Energy, Dark Matter, and the possible elimination of the singularities of General Relativity.Relations to Causal Set Theory, faithful Lorentzian manifolds, and past and future light cones joined at “Actual Now” are discussed.Possible observational and experimental tests based on: i. the existence of Sub- Planckian photons, ii. knee and ankle discontinuities in the high energy gamma ray spectrum, and iii. possible experiments to detect a creation of spacetime in the Casimir system are discussed. A quantum actualization enhancement of repulsive Casimir effect would be anti-gravitational and of possible practical use.The ideas and concepts discussed here are not yet a theory, but at most the start of a framework that may be useful.
Please download the paper and then read the abstract (since crucial formulas are not appearing in this window, and also hyperlinks are not working). This is just a brief overview: Relativity is inside the light cone phenomena, while Quantum Mechanics is outside the light cone phenomena, dictated just by the scale (i.e. whether we use classical/human scale or sub-atomic scale). This recent paper [ ‘ Quantum principle of relativity’; Andrzej Dragan, Artur Ekert, New. J. Phys. 22 (2020) 033098] has shown that every exotic Quantum effect like superposition, entanglement, probabilistic behavior, multiple paths etc. can be explained just by allowing super-luminal possibility. The 'inside the light cone' phenomena, and the 'outside the light cone' phenomena together span the entire region within the space and time axes. Only in unison they complete the entire picture. We failed to realize that the same spacetime is getting split into 'space like' and 'time like’ regions based on scale. And the reason behind this is not the magical ( ? ) speed of light. That would have turned both relativity and quantum mechanics into mere branches of electromagnetism. The true reason is much deeper and at a very fundamental level of our universe. It turns out that the c is the radial expansion velocity of our universe. But why does the transition from Relativity to Quantum Mechanics happens with decreasing size scale? That’s because, this is what is happens to spatial and temporal dimensions at different scales: 3+1 (Classical regime) <=> 2+2 (Compton regime) <=> 1+3 (Planck regime). Just as space and time exchange roles at the event horizon of a Black Hole, similarly, spatial and temporal dimensions switch roles for extremely small scales (although due to a completely different mechanism). Why this happens is difficult to expalin without the true model of our universe. But, once explained, it becomes "Why didn't I think about it before? I was plain silly!" From the center of universe viewpoint, simultaneity is absolute (as demanded by Sagnac effect), and there is indeed absolute universal time (as demanded by quantum mechanics). From our viewpoint (located at an awkward position in the universe), locality is absolute, and velocity c is the upper limit, and remains constant for every observer. This turns (our) space and time into inseparable twins, and makes (our) time a relative concept. This solves the time problem which had so stubbornly resisted the reconciliation of Quantum Mechanics and General Relativity. Quantum Mechanics and Special Relativity are like two sides of the same coin. But understanding the relation between Quantum Mechanics and General Relativity is a bit tricky, because according to General Relativity, gravity is the warping/curvature of the 4 dimensional spacetime itself. At first sight, Quantum Mechanics and General Relativity seem to be utterly incompatible! But actually, Special Relativity’s big brother General Relativity only complicates things a bit, but does not become inconsistent with Quantum Mechanics altogether. The only difference between the warped spacetime of General Relativity, and the flat spacetime of Special Relativity is very similar to the difference between a stretched rubber membrane, with and without a metal ball placed on it. This paper does not sacrifice any of the spectacular success of General Relativity and also does not compromise with any of the stunningly accurate predictions of Quantum Mechanics. And yet, this paper harmoniously brings Quantum Mechanics and General Relativity together. Just bear in mind that Nature simply cannot afford to make our two greatest theories incompatible. After all, both General Relativity and Quantum Mechanics were based on what nature was actually telling us, and nature herself would be accountable for any genuine contradiction (but not for the breakdown of our physics due to our misunderstanding!). And, by the way, this paper solves some of the most pressing problems in both Physics & Cosmology. The 'Principle of Least Action' which comes closest to a 'Theory of Everything' arises as a direct consequence of better SpaceTime theory proposed in this paper. Also, we can see why the symmetries of nature (which gives rise to the crucial conservation principles in Physics according to the Noether's theorems) arises in the first place. Gentle reminder: Please download the paper and then read the abstract.
Please download the paper and then read the abstract (since crucial formulas are not appearing in this window, and also hyperlinks are not working). This is just a brief overview: Relativity is inside the light cone phenomena, while Quantum Mechanics is outside the light cone phenomena, dictated just by the scale (i.e. whether we use classical/human scale or sub-atomic scale). This recent paper [ ‘ Quantum principle of relativity’; Andrzej Dragan, Artur Ekert, New. J. Phys. 22 (2020) 033098] has shown that every exotic Quantum effect like superposition, entanglement, probabilistic behavior, multiple paths etc. can be explained just by allowing super-luminal possibility. The 'inside the light cone' phenomena, and the 'outside the light cone' phenomena together span the entire region within the space and time axes. Only in unison they complete the entire picture. We failed to realize that the same spacetime is getting split into 'space like' and 'time like’ regions based on scale. And the reason behind this is not the magical ( ? ) speed of light. That would have turned both relativity and quantum mechanics into mere branches of electromagnetism. The true reason is much deeper and at a very fundamental level of our universe. It turns out that the c is the radial expansion velocity of our universe. But why does the transition from Relativity to Quantum Mechanics happens with decreasing size scale? That’s because, this is what is happens to spatial and temporal dimensions at different scales: 3+1 (Classical regime) <=> 2+2 (Compton regime) <=> 1+3 (Planck regime). Just as space and time exchange roles at the event horizon of a Black Hole, similarly, spatial and temporal dimensions switch roles for extremely small scales (although due to a completely different mechanism). Why this happens is difficult to expalin without the true model of our universe. But, once explained, it becomes "Why didn't I think about it before? I was plain silly!" From the center of universe viewpoint, simultaneity is absolute (as demanded by Sagnac effect), and there is indeed absolute universal time (as demanded by quantum mechanics). From our viewpoint (located at an awkward position in the universe), locality is absolute, and velocity c is the upper limit, and remains constant for every observer. This turns (our) space and time into inseparable twins, and makes (our) time a relative concept. This solves the time problem which had so stubbornly resisted the reconciliation of Quantum Mechanics and General Relativity. Quantum Mechanics and Special Relativity are like two sides of the same coin. But understanding the relation between Quantum Mechanics and General Relativity is a bit tricky, because according to General Relativity, gravity is the warping/curvature of the 4 dimensional spacetime itself. At first sight, Quantum Mechanics and General Relativity seem to be utterly incompatible! But actually, Special Relativity’s big brother General Relativity only complicates things a bit, but does not become inconsistent with Quantum Mechanics altogether. The only difference between the warped spacetime of General Relativity, and the flat spacetime of Special Relativity is very similar to the difference between a stretched rubber membrane, with and without a metal ball placed on it. This paper does not sacrifice any of the spectacular success of General Relativity and also does not compromise with any of the stunningly accurate predictions of Quantum Mechanics. And yet, this paper harmoniously brings Quantum Mechanics and General Relativity together. Just bear in mind that Nature simply cannot afford to make our two greatest theories incompatible. After all, both General Relativity and Quantum Mechanics were based on what nature was actually telling us, and nature herself would be accountable for any genuine contradiction (but not for the breakdown of our physics due to our misunderstanding!). And, by the way, this paper solves some of the most pressing problems in both Physics & Cosmology. The 'Principle of Least Action' which comes closest to a 'Theory of Everything' arises as a direct consequence of better SpaceTime theory proposed in this paper. Also, we can see why the symmetries of nature (which gives rise to the crucial conservation principles in Physics according to the Noether's theorems) arises in the first place. Gentle reminder: Please download the paper and then read the abstract.
Common introduction to all the records of this series. The content of this record follows below. Mathematical Materiality (MM) in brief. Why are the laws of physics the same everywhere and at every instant, even though nothing forces matter to obey them? MM proposes an answer: the laws are not rules imposed on matter from the outside; rather, matter itself is made of mathematical relations. And mathematics cannot change: a relation binds two distinct terms everywhere and always. In logic, nothing exists on its own: to exist means to be in relation to another logical entity, and outside this web of relations nothing can exist, not even other universes. This reading already meets experimental measurements at two points. First, the ratio of dark to ordinary matter is read as 3√3 = 5.196; when left free in the fits, Planck and DESI DR2 data give 5.21–5.22 (as registered in record 2.44, https://doi.org/10.5281/zenodo.23329080). Second, the acceleration scale of galaxies is read as a₀ = cH₀/6, the same scale that appears in Verlinde's emergent gravity: the computed value is 1.09–1.18 × 10⁻¹⁰ m/s² against the measured value of 1.20 (record 2.46.1, https://doi.org/10.5281/zenodo.23506655). Both readings were formulated with the measurements already known; the tests to check them against future data are registered in the same records. In the first logical nexus between space and time — which became homogeneous with Einstein — there is a non-local phase, made only of a pure logical distinction: space is not time. Between the two there is no relation of quantitative calculation, only the logical entity they have in common, which is needed to make them exist with respect to each other. This level is not distant: it is present in every phase of reality, in every place and at every instant. It shows in entanglement, where two distant systems remain correlated more strongly than any explanation based on separate properties and free of faster-than-light influences allows, without anything physically travelling between them. In this non-local phase the two distinct terms, space and time, share only one logical element, which we shall call their greatest common divisor (GCD), just as the numbers 3 and 5 have only 1 in common. The local world arises when a relation is counted through this GCD: its multiples and its fractions form a matrix. Seen by an observer inside the system like us, the multiples appear as time and the fractions as space. When that same multiple is directly contained in the matrix of the point of observation, it turns into mass — that is, into concrete matter as we usually understand it. There is therefore a close link between time and mass, in full agreement with Einstein's relativity, which ties mass to spacetime. The observed objects, while being logically autonomous entities in their local relations, enter into relation with the observer through a logical diffraction — that is, a decomposition into fractions — of the observer's matrix. This reading also gives a reason for the limit of the speed of light, which in Einstein's relativity is instead taken as a starting principle. The speed of light is the fixed exchange rate between the multiples and the fractions of the same GCD, meaning how much space a single step of time is worth: exceeding it would mean, for some observer, covering space without counting time, and thus leaving the local world. Logic always starts from a logical relative, and this exchange rate has nothing absolute in itself either: it is a necessary relative which, inside the system, becomes an absolute hypothesis, the same for everyone and impossible to exceed. Outside the system, by contrast, it has no justification at all, because outside there is only non-existence: justifying something requires another term to relate it to, and out there there is none. Asking for a reason from outside is like asking what lies north of the North Pole. The same theoretical framework that reads space, time, mass and the observed objects also admits quantum mechanics. The non-local phase and the mirror-like logical reciprocity between the two ends of the nexus give a reason for the probabilistic behaviour of matter. When the observed object is large enough, its mass fixes it in the matrix of the point of observation: for this reason we see it in one precise place and at one precise instant. When instead the object falls below a certain mass threshold, the principal GCD (that of the point of observation) and the GCD of the diffraction that generates the object are forced to become equal, reflecting each other as in a mirror. At that point the object no longer occupies a single point of the spacetime generated by the observer, but spreads over several possible positions, and we observe it as probability. It is like having to describe the number 10 using only the number 1: the only way is to distribute the 1 over ten positions, one for each unit of the 10. Today we know that even objects made of thousands of atoms behave in this way, and no experiment has yet found the boundary. The idea that the passage from quantum to classical behaviour depends on mass is close to that of Penrose and Diósi; in MM the threshold is the point where the two GCDs, the principal one and that of the local diffraction, become equal. For all these reasons the universe behaves like a simulation without really being one. It follows exact rules, made of counts, everywhere and at every instant, but no machine runs them and no programmer wrote them: a structure of mathematical relations does not need to be computed in order to exist. Tegmark (2008) had already noted that such a simulation need not be run, while Vazza (2025) estimated that running it physically on a machine would require resources that the very laws of the universe do not allow. The work is shared openly so that it can be judged by as many readers as possible: anyone who knows someone interested can pass on this single link, valid for the whole framework (with an overview in English and Italian): https://doi.org/10.5281/zenodo.23535916. The entry page, with the complete list of all records, is https://doi.org/10.5281/zenodo.22667516. To cite the framework: Lanciano, U. (2026). The number 1 in front of the mirror: Mathematical Materiality from the nexus to the cosmos. Zenodo. https://doi.org/10.5281/zenodo.23535916. The records have been deposited since 5 August 2026, each with its own date, and are released under CC BY 4.0: anyone may use them by citing the source. Objections and errors found are welcome at riverantares@gmail.com, since Zenodo has no space for comments. This record contains the four-page summary of the framework, in English and in Italian: the question of why physical laws hold everywhere with nothing to enforce them; the Great Reversal; the non-local phase and its empirical trace in Bell-type experiments; the five postulates with the example of 3 and 5; the matrix; the equals sign as a mirror; a clock made of 3 and 5, whose two means give Einstein's slowing of moving clocks (a known identity: Bondi 1964; Knuth and Bahreyni 2014); and the comparison with two measured numbers. The full overview, with the list of all records, is at DOI 10.5281/zenodo.22667516. The author is not a professional physicist; the framework and its premises are the author's own. The texts were written with the help of AI assistants. There has been no review by human referees.
The problem of time in the quantization of gravity arises from the fact that time in Schroedinger's equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus "time" in QM and "time" in General Relativity (GR) are seen as mutually incompatible notions. The introduction of a dy- namical time operator in relativistic quantum mechanics (RQM), that in the Heisenberg representation is also a function of the parameter t (iden- tifed as the laboratory time), prompts to examine whether it can help to solve the disfunction referred to above. In particular, its application to the conditional interpretation of the canonical quantization approach toquantum gravity is developed. 1