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This January (2025) update is due to an interesting conversation about a photon that as such has no proper, real-time of its own. Photon time (almost) does not flow at all, and their continuities come from the duration of relative observers. Moreover, the rest that we perceive does not exist by itself as we perceive it. I convinced the interlocutor who did not believe me or just pretended to be skeptical. Is this topic more difficult than it seems?
Free fall » srb
Question: What is in free fall a matter of relative observation?
Answer: A lot of it. Let's imagine a train moving at speed v, as in the picture, towards the observer at rest on the ground, from which a stone is thrown perpendicular to the track. If we exclude air resistance, what the passenger on the train can see is the movement of the stone perpendicular to the carriage. Still, to the observer on the ground, it is the sum of the movement in the direction of the train and away from it. When we think about that, we already have an example of different perceptions depending on the subject.
Mathematics is generous in such findings. Just think of all the coordinate systems in which different subjects can live (dwell) and also objects of interaction. Vectors that could be interpretations of the state of natural phenomena and scalar multiplied information of perception, or the possibility of their communication, offer specific proof of these differences.
1. According to Riesz Lemma: "Each φ functional on the finite-dimensional space X has a unique vector y ∈ X that φ(x) = ⟨x, y⟩ to each of vectors x ∈ X." How is "perception information" sum of products, and as such it is a scalar product, i.e., the function φ : X → Φ, it maps the vectors x from the vector space X, the said states of the participants of natural phenomena, into numbers (scalars of the set Φ). Those numbers are the magnitudes of perceptual information. Well, the unique vector y of that space, which characterizes the functional one, represents the subject of perception. However, different ys are subjects in different performances; each one is unique and special.
2. Freed by this knowledge, let's imagine an elevator in some state without weight. The elevator goes up with the acceleration g and has its own (proper) observer in the cabin and an external one, relative to which the elevator moves.
The first picture on the left is such an elevator with acceleration g = 0 and speed v = 0. The second on the picture is with acceleration g = 0 and speed v > 0, and the third with constant acceleration g > 0. A beam of light from a flashlight comes from outside and passes sideways through the elevator. A particularly different perception of these observers is in the third case, where the beam of light becomes curved from the inside. Einstein's principle of equivalence (there is no experiment that a person could perform in a smaller space that would make a difference between the gravitational field and the equivalent uniform acceleration) and the gravitational acceleration suggest to us that light diverts in the gravitational field without changing its speed.
3. This transfer of the theoretical model, their multiplication as opposed to the uniqueness of the subjects, also has its mathematical confirmations. Accordi-ng to the Löwenheim-Skolem theorem (Information Coupling, p. 31), when the first-order theory (which has mathematics, philosophy, linguistics, and computer science), whether a sentence or a formal system with any model, will have a countable model (whose members can match with positive inte-gers). Moreover, it will have a model of an arbitrary cardinal number greater than or equal to the countably infinite ℵ0.
4. Let's imagine, then, that the lamp's light enters the elevator straight from above (through the transparent vault) downwards. With constant acceleration g of the elevator, after climbing a height Δy, the speed of the elevator is (greater by) v = g⋅Δy/c, so the frequency due to the Doppler effect (2nd example) is increased to:
\[ f = f_0 \sqrt{\frac{1 + \frac{v}{c}}{1 - \frac{v}{c}}} \approx f_0\left(1 + \frac{v}{c}\right) = f_0\left(1 + \frac{g\Delta y}{c^2}\right). \]This was confirmed by the Pound–Rebka experiment (1959), which tested Einstein's predictions from 1907 and in 1911, based on the principle of equivalence, that photons gain energy by descending down the gravitational potential and lose energy rising through the gravitational potential.
5. Similar is obtained from (unusual) transformations:
\[ dr = \chi \ dr' - \gamma^{-1}\sqrt{1 - \gamma^2\chi^2}\ d\tau' \] \[ d\tau = \gamma\sqrt{1 - \gamma^2\chi^2}\ dr' + \gamma^2\chi \ d\tau' \]from which (Defect) I derived the Lorentz transformations, there with γ = 1, and now putting:
\[ \gamma = \frac{1}{\sqrt{1 - \frac{2GM}{c^2r}}}, \quad \chi = 1. \]There are τ = ict, imaginary unit i² = -1 and time t. It will be γ = 1 when there is no gravity, and without movement in gravity it is χ = 1. Putting dr' = 0 from the second equation, we get:
\[ dt = \frac{dt'}{\sqrt{1 - \frac{2GM}{c^2r}}} \approx \frac{dt'}{1 - \frac{GM}{c^2r}} \]and the upper frequency, where f = 1/Δt', and f0 = 1/Δt. The reverse happens when light arrives from below, in a gravitational field or elevator, when it loses frequency and energy as going up. In the previous formula (4th paragraph), we then change the sign of the velocity, v → -v, and here we take the upper observer as relative, f = 1/Δt.
6. Let's imagine now that there is a tile of a certain material in the elevator where we can measure the photoelectric effect. Photons hit the plate and eject electrons from it. But there is also a threshold frequency below which electrons do not escape when individual photons do not have enough energy to interact with an individual electron.
That energy threshold is constant for the plate and for the observer inside the elevator, but due to the redshift, the light has a lack of energy than that which would act if the elevator was at rest. An external observer looking at the outgoing wafer and the unredshifted light also does not observe the electron emission because the relative mass of the wafer is greater. I state this because of the confirmati-on of formula (3.22) of the Information Coupling script, where it is assumed that a body at rest in a gravitational field still has a slightly larger mass than outside the field. In particular, this is still not the official position of physics.
Namely, in that script, the hypothetical greater mass of the body at rest is:
\[ m = \frac{m_0}{\sqrt{1 - \frac{GM}{c^2r}}}, \]where m0 is the mass of the body at rest outside the field, G is the gravitational constant, M is the mass of the gravitational body centrally of symmetric gravity, r is the distance to the center of gravity, and c is the speed of light in a vacuum. The modes of the above formulas, for redshift and mass increase with raising the threshold of the effect of light, align these observers.
7. The same answer (Defect) also mentions the loss of information (energy) in the gravitational field, which official physics still does not refer to and which similarly exists in special theory in the Twin paradox. Moving and staying in different locations of the gravitational field, then returning to the initial position, would be a straightforward process. However, the person who moved would spend a different amount of time than the person who was silently waiting for them. In the case of the accelerated elevator, the connection with the special theory is clearer.
Information theory offers a simple solution to that information defect (when a certain amount of events are missing due to lack of time) with the additional dimensions of time. Then observers from parallel realities should be added to these examples.
Mass III » srb
Question: Why does mass increase when time slows down, from the point of view of information theory?
Answer: Let's repeat a few discoveries of special relativity (Physics Explained), then continue with information theory. These are, first, the explanation of time dilation with the above image, then the formula E = mc² by increasing the mass with kinetic energy. They are known to physics, and by that I do not mean bosons (Mass II).
1. The picture shows a pair of oppositely placed mirrors, one below the other at the height Δy, which move inertially with speed v = const along the abscissa. We imagine it to be the motion of a mirror in a train with its own (proper) observer and a relative observer from the embankment. Let's also take into account (from an IT perspective) that what moves at the speed of light does not have its proper (own) time, but that the "movement" of such is "imagined" by observers due to its own continuity, and that the "speed of light" is c = 3×108 m/s due to the development of their proper present.
Therefore, since the passenger on the train and the observer from the embankment of their own present "travel" equally fast, they perceive this light as equally fast. While for an internal observer the same light bounces up and down the distance between the mirrors Δy = c⋅Δt0, so far the outer one sees its journey by the hypotenuse of the square (c⋅Δt)² = (v⋅Δt)² + (Δy)². Hence:
(c Δt0)² = (c Δt)² - (v Δt)²,
c²(Δt0)² = c²(Δt)² - v²(Δt)²,
\[ (\Delta t_0)^2 = \left(1 - \frac{v^2}{c^2}\right)(\Delta t)^2, \] \[ \Delta t = \frac{\Delta t_0}{\sqrt{1 - \frac{v^2}{c^2}}}. \]Using the Lorentz constant γ = (1 - v²/c²)-1/2 this we write Δt = γ Δt0, and even shorter, we put β = v/c, so we have γ = (1 - β²)-1 /2. However, we have Δt0 as the time elapsed for the moving one as seen by a stationary observer as Δt. The units last longer and the time on the train flows more slowly, observes the observer from the embankment.
For example, if something is moving at v = 10 m/s (the fastest sprinters), then γ = 1.00000000000000007..., with non-zero only at the 16th decimal place, and multiplying by such a coefficient will mean an extension of the duration that is not easy to perceive. However, we can measure muons whose lifetime is only 2.2 μs which even at some higher velocities barely survive lengths of 600 m. When the muons have speeds of say v = 0.998c m/s, there Lorentz's will be γ = 15.819 (rounded to three decimal places) and a lifetime of 2, 2×15,819 = 34,802 μs. They then cover distances of 10 km.
2. I also have interesting IT interpretations for the physical movement itself. It is known that by approaching, with a blue shift and shorter wavelengths, and due to the slower flow of time, objects arrive from a more certain future towards the observer's present. Namely, the shorter wavelength represents less uncertainty of the position in the directions of movement, while the slowed-down time together with the matching of the present only in close passing speaks of the arrival from the future. Analogously, the redshift with longer wavelengths, i.e., the uncertainty of position, may be a process of postponement or repulsion.
As we move away, we have a greater and greater perspective, but less and less detail. Then we formally have an analogy with an increasingly long Markov chain when it becomes a "black box" saturated with misinformation. In this new interpretation, the space would be a kind of warehouse of the past. A lager growing at the speed of light in every direction from the present. Following any such line, the distance of past events grows in such a way that it gradually reaches its maximum speed (of light) at the "event horizon," which in Markov chain language we call a "black box," when the number of links accumulates.
3. The spontaneous desire for less information, less interaction, that is, greater probability (Opposites II), in its own way, also applies to this forgetting. Still, the best physics has in this regard is calculating the consumption of (kinetic) energy ΔEk by the work of the force F on the path Δx. Change of momentum with time is force (F = dp/dt), multiplication of mass and velocity is momentum (p = mv), and the change of path over time is the velocity (v = dx/dt). We integrate the kinetic energy and calculate its total value on the path from x1 to x2:
\[ E_k = \int_{x_1}^{x_2} F \ dx = \int_{x_1}^{x_2}\frac{d}{dt}\left(\frac{mv}{\sqrt{1 - \frac{v^2}{c^2}}}\right)\ dx = \] \[ = \int_{x_1}^{x_2} \left(m\gamma\frac{dv}{dt} + mv\frac{d\gamma}{dt}\right)\ dx \] \[ = \int_{x_1}^{x_2} \left(m\gamma \frac{dv}{dt} + \frac{mv^2}{c^2}\gamma^3\frac{dv}{dt}\right)\ dx. \]After adding the fractions, we continue calculating the energy by substituting:
\[ E_k = \int_{x_1}^{x_2} m \gamma^3\frac{dv}{dt}\ dx = \int_0^v mv\gamma^3\ dv = \left[ \frac{mc^2}{\sqrt{1 - \frac{v^2}{c^2}}}\right]_0^v, \] \[ E_k = \frac{mc^2}{\sqrt{1 - \frac{v^2}{c^2}}} - mc^2. \]When there is no motion (v = 0), the Lorentz gamma is one (γ = 1), so the kinetic energy is zero (Ek = 0). The total energy is:
\[ E = \frac{mc^2}{\sqrt{1 - \frac{v^2}{c^2}}} = E_k + mc^2. \]This is a slightly different rendition of the same formula than the previous one (Proper Velocity, 2).
4. By expanding to the series, (1 + ε)n = 1 + nε +..., when ε → 0, we get:
\[ mc^2(1 + \frac12\frac{v^2}{c^2} + ...) = E_k + mc^2, \] \[ E_k = \frac12mv^2. \]It is classical (non-relativistic) kinetic energy.
5. For completeness, see (Massless) and the derivation of the following important formula and some of its applications:
E² = p²c² + m²c4
which connects momentum, energy, mass, and speed of light. It is particularly useful in particle physics, but also because it does not depend on the choice of coordinate system. It is derived directly from the previous one for total energy, and here is another known modification of that derivation:
\[ E = \frac{mc^2}{\sqrt{1 - \frac{v^2}{c^2}}} = \gamma mc^2, \] \[ E^2 = \frac{m^2c^4}{1 - \frac{v^2}{c^2}} + \left(\frac{m^2c^2v^2}{1-\frac{v^2}{c^2}} - \frac{m^2c^2v^2}{1-\frac{v^2}{c^2}}\right). \]There is a zero in the parentheses that we redistribute:
\[ E^2 = \left(\frac{m^2c^4}{1 - \frac{v^2}{c^2}} - \frac{m^2c^2v^2}{1-\frac{v^2}{c^2}}\right) + \frac{m^2c^2v^2}{1-\frac{v^2}{c^2}} = \] \[ = \frac{m^2c^4 - m^2c^2v^2}{1 - \frac{v^2}{c^2}} + \frac{m^2c^2v^2}{1-\frac{v^2}{c^2}} \] \[ = \frac{m^2c^4\left(1 - \frac{v^2}{c^2}\right)}{1 - \frac{v^2}{c^2}} + \left(\frac{mv}{\sqrt{1 - \frac{v^2}{c^2}}}\right)^2c^2, \] \[ E^2 = m^2c^4 + p^2c^2, \]and that is the required equality.
For massless particles (m = 0), it will be E = pc. From the same formula, for particles without momentum (p = 0), it will be E = mc², which means that this m is its own (proper) mass, that which the particle has at rest.
6. The own (proper) energy E0 is the one that the body has at rest, while the energy of movement E is the one in the stacks of time that we calculated with the integral. It is all the greater the thicker its deposits are, and that is the IT view of this well-known result, the relativistic increase in the energy of a body in motion. We can also understand it as "braking" or "stumbling" against other times, bodies that, in their movement, no longer belong to this present.
I remind you that due to the law of conservation, the past develops so that the total amount of information in the observed closed system is conserved. The past partly forces the future and reduces the number of options of the present, which thus becomes more certain and less informative. By encouraging their choices, we make the bodies more inert and less able to change decisions, so by moving the body, we not only walk them outside of our present, giving them more energy (information, energy multiplied by time), but also increase their mass.
7. Directly from the energy (E = hf) and speed (c = λf) of the photon, we can find the relations of action Eτ = h and pλ = h so that we connect the frequency f = 1/τ, the wavelength λ = hc/E and the momentum p = E/c of light. The last is the above formula for massless particles, otherwise obtained from the general equation for the relationship of momentum, energy, mass, and the speed of light. I state this so much that in an interesting thought experiment (Virtual) we notice the correctness of the derivate of the otherwise well-known formula:
E = mc².
As we have seen (3), this formula is also the result of a spontaneous tendency towards less information, less interaction, that is, greater probability.
Universe II » srb
Question: Why is the universe expanding?
Answer: I have several living hypotheses, and although none may be correct, I believe they are all correct. As variants, it could be different facades of the same building. But here's a look at what it's all about, so judge for yourself and wait for experimental science.
1. After determining "reality" (unofficially) on the basis of the law of conservation, i.e., the duration by which we assume memory and quantities that include the corresponding past in their conservation (Information Coupling, 1.1 Conservation Law), but by which we demand losses in the present. If this is said analogously to an energetically "closed system" and the law of energy conservation of bodies that have their own spatio-temporal quantities, then it must be assumed that the past is consumed by supplementing the present, that there is less of the further away it is. Light needs some time to reach from one end of the body to the other, and defining space as the past makes sense because bodies are always in the past while we consider them to be in the present.
Therefore, by defining reality by means of duration, the past and spaces become repositories of memory. The present is getting thinner and thinner, so its warehouses are fuller and fuller because their totalities are constant. That is why the universe is getting bigger and bigger both in terms of space and duration. Moving away, we have an ever-increasing perspective of ever-smaller details, as in an ever-longer Markov chain that becomes a "black box" oversaturated with misinformation (Mass III, 2). Insisting on duration, realities cannot stop melting the present into these warehouses, space, and time, thus satisfying the principle of minimalism, the basis of this theory of information.
2. Official cosmology takes the "Big Bang" as the limit of time. It is an event about 13.8 billion years ago when the universe is thought to have originated. It also takes a spatial boundary, which it calls the "event horizon". It is the greatest cosmic distance from which light can reach us. Now that is about 16 billion light years away. If we take into account the distance that such a border would travel before its light reaches us, then the "current" distance is more than twice as large — because further away galaxies are moving away faster. If we add to that the expansion since the beginning of the universe, then the distance of the horizon comes out to about 46.5 billion light years.
I consider these limits to be hypothetical when I bear in mind the transmission of information through the Markov chain. Then, with each step, the initial message is more like the characteristic of the chain generator, only to become equal to it after many steps. We write this by mapping A : x → y, where the linear operator A changes arbitrary information (vector x) to a constant state (y). When we see y, we cannot then know what x was but remain with the fact that it was what we see.
Therefore, the limits of the "memory storehouse" can easily be a mere illusion, an inherent state of the process that transmits distant events, and not what those events were. To make the problem more difficult for science, the given "illusion" is the result of algebra and cannot be disproved by measurement or anything of a lower level of accuracy than mathematics. Our best guesses, evidence, and findings will confirm it, and yet we will not be able to find out if it is true. It is an unusual place for mathematics itself that we have "proof" of the existence of something that also reveals its possible non-existence.
Namely, what predicts the Markov chain developing into a "black box" is quite certainly the hot impersonal mush of the initial universe that slowly becomes more and more definite under principled minimalism.
3. Regarding this thesis, it is quite certain that "redshift" is a phenomenon everywhere in the universe where distant galaxies are seen. The expectation is that they are moving away from the observer and that these galaxies are receding faster the further away they are. First of all, because the wavelength of light that reaches them increases with distance, which means increased uncertainty of the position of that direction and increasing repulsion in terms of principled minimalism. I'm talking about the effort required to turn a move away into a move closer due to the repulsive uncertainty force, the one that is the opposite of the forces of probability.
Since the definition of "reality" by means of duration is quite general, and consequently the mentioned cause of the expansion of the universe, it is then a phenomenon that can be seen equally from the most distant galaxies. It is, therefore, an independent way of discovering the "illusion" of the Big Bang without referring to the Markov chain and its eventual "black box." I know that with this I am not exactly on the line of known cosmology, but let's not lie when you have already honestly asked me for my opinion on the expansion of the universe.
To be more precise, the idea of that illusion cannot be challenged, neither by making it up nor by traveling. We cannot go into the past because it is not easy to go into a state of greater uncertainty (the present tends towards greater certainty), so when we reach the seen galaxy (I imagine), it will be in its future. Then again we find roughly a state not a bit better than what we have now, the development from the Big Bang and the void beyond. It is also a way to blur our vision and not violate the law of conservation.
4. It is possible to talk about some "dark energy," which is a common term for that still unknown phenomenon that spreads the universe, because we have seen that we can also consider the spontaneous striving for minimalism as a "spontaneous force" and attribute some "energy" to it. However, it remains like saying "white is white," an accurate but useless tautology. The "reality" explanation written here would be a step forward (if correct) in understanding this phenomenon, but only as a "why," not a "how.".
Talking about the details and discovering the "mechanism" of the expansion of the universe is the right answer to the question, but which can easily become a project of some constant research and discovery like physics itself. One of my ideas in this regard was observing the processes of transformation of particles into each other. For example, the formation of fermions from bosons, which was dominant in the initial phase of the universe, is now reversed and more probable as the formation of bosons from fermions. In short, we see the expansion of the universe through the creation of more and more space at the expense of less and less substance.
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