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Hi. Here I am again. Let's see a figure referring to a spherical surface, with the surface vector indicated in some points . The extensions of all the surface vectors converge on a point, which is the center of the sphere. Let's see now the representation of a closed surface that is not spherical. Could it happen that, regardless of the shape, the extensions of all the vectors of a closed surface converge at an interior point? I do not know the answer. Is there any theorem that answers the question?

Thanks for point out that.

Any location that moderators deem appropriate will be fine. I prefer that the moderators decide, because they will do better than me.

Between the laser aimed at the Moon and the theoretical case that I have raised there is an essential and critical difference. The cross section of the laser aimed at the Moon encompasses [math]n[/math] photons. In the theoretical case that interests me, the cross section covers only one photon. To facilitate verbal expression let's symbolize R a part of the cross section. Which part ? The corresponding part, say, at 99% probability of finding the photon. Are you claiming that R widens while the photon travels, even though there is only one photon in the cross section? The equation seems typically Pythagorean, as the vector sum of two mutually perpendicular components, one in the direction of propagation and another transversal. If the photons belonging to the same section are in phase, I begin to think that there is a slight repulsion between them, responsible for the transversal component in the vectorial sum. Magnetic repulsion? Electric repulsion? Both? The widening of the beam seems an interesting subject, if there is a transverse repulsion. If the propagation of the photon does not have the least relation with the polarization of the vacuum, why would the photons repel? To formulate the spatiotemporal probability distribution of finding the photon, you first need the photon to exist. No matter how hard I try to believe that the photon is a propagating probability, that is, to believe that the photon is made of something called probability, I find it inconceivable. So I think it is made of electromagnetic field, that the constitutive field of the photon occupies a finite volume related to the wavelength and that, without the polarization of the vacuum in the region where the photon is present, the photon could not exist and could not spread. I prefer to believe that the fields [math]\vec{E}[/math] and [math]\vec{H}[/math] they are both consequences of the same cause. What cause? A polarization wave that propagates in a vacuum. The polarization wave does not imply movement of electric charges. Simply, at each vacuum point the charge density varies locally as a function of time. If the wave is sinusoidal, the charge density at the point varies sinusoidally. In the computer you can see the animation of a wave that spreads. Your view informs that something is moving in the direction of propagation, but no luminance cell on the monitor moves. Simply the brightness of each cell varies sinusoidal with time, alternating between two colors, one for the negative half cycle and another for the positive half cycle. If instead of thinking of two colors you think of two signs of linked charge, no charge moves but the effect is an electromagnetic wave that propagates in a vacuum. To formulate probabilities you need first that the photon exists. And nothing forbids its existence to be based on a pair of linked, equal and opposite charges, which appear to be in motion without there actually being movement of charges. The movement of energy, the linear moment and the spin are real. The movements of charges and fields are apparent. Thus I conceive the propagation in the vacuum and the existence of the photon. Then yes, an existing photon can meet probabilistic conditions. In that Pythagorean type equation, transverse repulsion would be expected if the photons are in phase because, in this case, the constituent charges of a photon could be slightly repelled with the constituent charges of the neighboring photons. Why would they repel each other? In absolute vacuum the propagation is perfectly straight. Where there is a gravitational field, the trajectory is curved. If the gravitational field is not very intense, the curvature is slight. Then, the imbalance caused by the curvature between electrical repulsion and magnetic attraction is slight. This can give as a result a slight repulsion between neighboring photons, which causes the thickening of the beam as it propagates.

I hope the following. 1. That the beam propagate in a vacuum without suffering diffraction. 2. From what is expressed in item 1, I hope that the beam diameter remains constant when it propagates in a vacuum. 3. For the two previous expectations, I hope that each photon has a finite diameter determined by fundamental electrodynamic laws, in the version of the corresponding electrodynamics, classical or quantum. 4. For the three previous expectations, I hope that the photon in the vacuum, in the far zone with respect to the emitting device, appears as a cylindrical entity whose length measures a wavelength, with a finite radius equal to the wavelength divided by a geometric constant. What geometric constant? Nothing strange. Maybe the radius equals the wavelength divided by [math]4 \ \pi[/math].

I can not connect the vectors and the vector addition with the ismail question. I will try to do some diagram and see what the Google translator can do to improve the expression.

My initial question, which I have reiterated later, is not about measuring something in practice. It is referred to what the fundamental physical laws imply regarding a beam in a vacuum that has only one photon per cycle.

I can not understand what relationship that wikipedia page has with a laser that propagates in a vacuum with only one photon per cycle.

Help me to understand. There can be diffraction without something material that causes the diffraction?

Notice: The intention of this post is to ask about the possibility or impossibility of demonstrating a specific theorem. There is no intention to present a speculative theory. To put the question in context I need more than one paragraph. That does not mean affirming or denying something outside current knowledge. Let's go to the context with the question included. --------- The surface vector is defined at each point of a surface. Think of a closed surface, for example a Gaussian surface. At each point, the surface vector belongs to a line that extends to the outside and to the inside of the surface. To simplify the vocabulary, let's call the surface segment the part of the line that extends inwards. Is there a point where all the surface segments converge in the interior region? If it existed, a theorem could be deduced, which serves to distinguish between a flat surface and a curved surface. If the surface is flat, convergence at a point of two or more surface segments is impossible. And when there is convergence, then there is curvature. Why does my question refer to the possibility or impossibility of proving this theorem? Because I suppose that the lines of the gravitational field can never be rigorously parallel. That is to say, I suppose that the gravitational field can not have divergence equal to zero. And something else. I suppose that the lines of the gravitational field always converge on a point. This idea, as it has been expressed, includes only the 3 dimensions of space. That is, it corresponds to a static gravitational field. In 4 dimensions we do not have visual images. And the gravitational fields in 4D can be variable. There is also something that could facilitate understanding. If it were possible, for gravitation, to demonstrate mathematically a convergence in 4 dimensions, then we could say that convergence allows to treat spacetime as a case of curved geometry in 4 dimensions. It would not be a visual description, but the convergence theorem would allow formulating gravitation in a slightly less counterintuitive way. Would such a theorem be possible or impossible?

Hi John. Thanks for answering. Is that answer referring to the spread in a vacuum?

Perhaps the thinking style of Greek philosophers of antiquity approaches your idea. Something more or less like the following. At the level of human perception (sight, touch, etc.) each thing and each event comes from a set of causes. If we descend a little to an underlying level of the senses, some causes appear in different things and events. That is, different things and events have some common causes. Then the number of causes we need to take into account is reduced, because some causes appear in more than one thing and in more than one phenomenon. If we continue to descend to levels less and less similar to the level of the senses, the number of causes we need to take into account is increasingly reduced. Now let's extrapolate that observation, as the ancient Greeks extrapolated. If the chain of levels less and less similar to the senses is not infinite, then some day we will need to take into account a single cause, responsible for all things and all events. That unique cause is the law of the universe, or the set of laws of the universe, in case of not finding that everything is reduced to a single law. The law of the universe, in the terms of ancient Greek thought, exists at the most elementary level you can conceive. From that level, by the work of the law of the universe, all things are born and all events are produced. On that level the law of the universe rules continuously, not intermittently. There is no instant without compliance with the law. On that level the law is perennial, immutable and manifests itself throughout the universe. More or less that way those Greek philosophers thought.

Hello, Strange. Thanks for responding. I understand what you mentioned. The idea is to advance a little more towards the fundamentals of the theory of light, which includes everything known about light, regardless of the design of the emitting device. Then I will give another form to the question. Do the theoretical foundations specify a lower limit for the diameter? That is to say that for a given frequency, the beam with a photon in each cycle must have a diameter that does not exceed a certain measure.

Let's go slowly. Is the propagation of waves essential? Let's put the question in another form. Could the universe exist without waves? To give content to this post I need to propose a provisional and hypothetical answer. H1 - If the definition of existence includes enduring a finite time, then I suppose that without waves the existence of the universe would be impossible. In our universe, waves propagated in material media are slower than waves propagated in a vacuum. (I confess that this is the first time that this detail seems very significant to me). In our universe, the wave velocity in the vacuum is the maximum speed that a wave propagation can have. Is there any reason that makes an infinite wave speed impossible in a vacuum? I will try the most obvious reasoning that comes to mind. The answer depends on how we conceive the universe. In case of conceiving it as a finite system, an infinite wave velocity is impossible. Why ? Because space could never develop a spatial cycle, nor a finite portion of the cycle. Without the development of a spatial cycle or a finite portion, the existence of a wave is impossible. H2 - In a finite universe, the maximum propagation velocity is necessarily finite. To reach the conclusion, I did not need to squeeze my brain too much. Okay, finite universe, finite maximum propagation speed. In our universe, that finite velocity has a precise value, symbolized C. Is it an acceptable idea to assume that C is determined by properties and conditions of the universe? Could it happen that, after investigating those properties and those conditions, the answer to the question of this thread appeared clearly? That is to say, why the speed of electromagnetic propagation in the vacuum and the speed of the gravitational waves are equal? Maybe is happening the same thing that tells the story of the elephant and the blinds. In case we are condemned to permanent blindness, the minimum we need is a scale model of the elephant, to be able to go through that with the hands completely, thus enabling the understanding of the form.

Suppose it were possible to build a laser device capable of fulfilling the following condition. In each period [math]T[/math] emits only one photon. [math]T=\dfrac{1}{\nu}[/math] [math]\nu \ \rightarrow[/math] frequency Question: Does the theory allow to calculate the diameter of the emitted beam?

I have supposed that the number of answers will be greater than the number of question that I would solve !!! Now on serious. I can't answer more questions (for my ignorance). And I am greatful with all you. Best regards.

Nice table! Thank you very much! A question. Interacts between them two EM waves, or pass by the same region without affect one to other? If particles don't interact with EM waves, may occurs that particles are a kind of EM waves? Help me remember. Strong force is, in comparison terms, near 11 times more intense than EM force between two electron's charges. Can exist within the nucleous a kind of charge near 3.3 times bigger than electron's charge, in a way that the force between this kind of charges results in the order of strong force? The force between quarks iys independent of the distance, like capacitive force in the simplest case, when there is no border effect. If exists a charge 3.3 times bigger than electron's charge, can be possible to think that electron's charge is a fraction of a broken 3.3e charge.

One can expect that elemental level is not only a level of more little entities, but a level that corresponds to the simplest physical phenomenon, with the simplest complete system of physical laws, like EM system. If simplicity is needed and the simplest system works well, make sense a try in that direction? Help me reason. Can be neutral a rotating EM wave in closed path?

Only one more detail. If I think that everything, at the most elememtal level, is made of EM waves, e.g. , rotating in closed path EM waves (Bessel functions, etc.), then will be natural that no thing can take translation movement faster than light, will be natural that particles complies De Broglie's condition of phase wavelength, wave-like behavior of particles, and, finally, mass/energy relationship.

[math]E=m \ C`2[/math] applies to all. Mean this all in the universe, at elemental level, is made of electromagnetic waves?

If you want, take a look on post number 11 of the thread entitled Vacuum dynamics, in this forum.

I will simply state that in this post, without writing comments later. I will read the comments that other people can write. --------- The photon is nothing more than a series of waves moving outward from a vibrating electron. Planck's constant is the a measure of the energy in the passage of one wave. However, Planck's constant is not the most fundamental quantum. The actual fundamental quantum is half of Planck's constant which is found in the half-wave of light. Each complete vibration of an electron creates one complete wave. However, the sudden movement of a vortex (such as the electron) in one direction creates a half-wave. If there is no return movement, and no immediate future movements in a rhythmical manner, there is no photon and no way to easily detect the half-wave. The sudden flipping of a vortex from right-side-up to up-side-down also creates a half-wave. Whenever there is a change in two vortices as exists when there is a sudden joining or separating, or whenever there is fusion or fission of nuclei, half waves are emitted as either increased or decreased rotational energy (spin). The single half-wave is one of the most ubiquitous entities in our universe of ether and vortices. It is a transverse acceleration of ether moving outward like a ripple on a pond. It is the fundamental which forms the waves of a photon. It is (1) formed initially as angular momentum (spin), (2) used as a means of transporting angular momentum at the speed of light, and (3) accepted as angular momentum when discharging its energy. It is without charge, mass, or gravity. It is capable of penetrating the most dense mass and travels at the speed of light. We can detect it only when it collides with another entity. Otherwise, we are unaware of it unless it directly affects one of our equations. In every way, the concepts of the neutrino and the half-wave are alike except that the neutrino is supposed to be a particle and the half-wave is simply a half-wave - neither a particle nor a vortex. So what here is proposed is that any neutrino is, in reality, a half-wave in our ether universe.

Are the same discrete variables and quantum properties?

There is no wave / particle without quantum. Nobody has managed to deduce the quantum from a classical model.

Except for gravitation, the standard model encompasses everything, with admirable perfection. There is only room to formulate gravity compatible with the standard model and, consequently, achieve the theory of everything. Have you achieved the TOE in the context of the standard model? In case of negative answer you are dedicating effort and time to an obvious error.