There is an opinion that the wave-function represents the knowledge that we have about a quantum (microscopic) object. But if this object is, say, an electron, the wave-function is bent by an electric field.
In my modest opinion matter influences matter. I can't imagine how the wave-function could be influenced by fields if it were not matter too.
Has anybody another opinion?
Dear Sofia,
I tried to explain to you in another answer that matter (mass) is made up of massless groups of charges and that this can be shown through Einstein's field equations.
Matter appears and disappears as a function of the spin and the forces of attraction and repulsion of these massless charges and external fields. And it is very likely that the wave function represents just that.
Dear Sergio Garcia Chimeno
Maybe you explained and probably your explanation passed unnoticed by me because I got a lot of answers.
What you say seems interesting, but I don't see the connection with my question. The wave-function is a WAVE. And I asked whether this wave is some sort of matter.
Whole atoms, even molecules behave as waves in certain experiments, and for that matter it is not relevant how got mass the elementary particles constituting the atoms.
Dear Sofia,
isn't this just a wave-particle duality? As far as my research goes, ALL particles are wave-particle dualities, subject to interaction with electromagnetic fields, and gravitationally 'bent'. In fact (as far as I can tell), the entities are always mass x lambda = h/c where c is velocity. However - and this will be discussed in a paper shortly - h is dependent upon velocity.
If a wave-particle duality (call it a wavicle) has spin, the changing e-field creates a B-field & vice versa, usual electromagnetics. Interestingly, all wavicles are equal at c, hinting at the fractal nature of lepton and quark species.
Photons, stated to be massless, are wavicles also, but with very low mass (and difficult to detect, but theoretically they must have). 'Bending' is determined by frequency, but for wavicles travelling < c their E increases significantly (e.g. refraction), due to the velocity dependence of the Planck parameter, which isn't constant.
Not sure if I've helped....
regards
The quantum mechanical wave function (for a multi-particle system) is not a wave in physical space, but rather in the multi-particle configuration space, since it is a function of many spatial positions. The second quantised field operators are objects defined on space-time; they are (probably) the best mathematical description/representation of matter, but I would not say that they are matter. Although I like to think they are...
Kåre Olaussen
You are a physicist, though, as far as I understand, you are inclined toward mathematics. I am inclined to phenomenology. So, let's speak first of the simplest case, a single-particle wave-functions. My problem is, if the wave-function is not a reality, i.e. a real "something" traveling in our apparatus, how could it feel fields?
I will tell you where from stems my question: I support the CSL collapse model - I trust that you are aware of it. I proved that the collapse principle is unavoidable, i.e. denying it, one gets contradiction with the quantum mechanics (QM). But I am asking myself: if the wave-function is a real thing, how can part of it disappear at the collapse? (This was also a problem for Asher Peres.)
About the 2nd quantization, if we speak of single-particle wave-function, what can give me the 2nd quantization? You see, the group of theoreticians lead by Salvatore Savasta proved (for the moment only on the paper) that between the preparation of the wave-function, and its detection, the quantum vacuum mixes seriously into the things, virtual particles pop up from the vacuum and return to it. However, we detect only the real particle.
What the Savasta group obtained, could maybe explain the existence of single-particle wave-functions with multiple wave-packets, and the fact that we detect only one single wave-packet. I declined going on this idea because there can be no quantum vacuum for such big particles as fullerenes. There were interference experiments with the fullerenes too, and there also occurred collapse.
The saddest part is. we call things matter, mass, particles, while we don't know the real meaning of them, because we do not know the origination of them.
WHAT IS PARTICLE? no one knows it for sure.
Another saddest part of our system is, we do not give SPACE OF UNIVERSE credit at all.
We describe an atom based on nuclei and electron (s), while over 99.99% of an atom is occupies by SPACE.
SPACE of each atom is different, based on number of electron. HOW? & WHY?
We all inherited t nothing is working mechanically in the Universe, but we think they are. FACT IS, WE ARE WRONG.
We all inherited this sadness from the past century icons, and accidental and mechanical theory of the Big Bang.
regards.
Deleted research item The research item mentioned here has been deleted
Dear Sofia D. Wechsler ,
Yes, The wave-function is a WAVE, which indicates the probability that an object is in a given place or another.
I am not telling you what the wave-function is exactly, I am telling you that it can be DEMONSTRATED WITH EQUATIONS that an object (particle) can appear and disappear, that the cloud of electrons in an atom can be particles that appear and disappear in different positions determined by the field.
I think that with your knowledge in quantum physics it would not be difficult for you to adapt that to the wave function
Preprint ENERGIA FOTÓN, APROXIMACIÓN GRAVEDAD UNIVERSAL DE NEWTON Y L...
Dear Sergio Garcia Chimeno
The equations do not tell us what IS the wave-function, but what we can calculate with it.
You indeed try to help, but you do not refer to my problem: if the wave-function is matter - so it seems to be because it bends when passing through fields - then how could it be that part of it just disappears when collapse occurs? It is unconceivable that matter disappears.
In this respect, I don't see what can the Universe help. I am speaking of the behavior of tiny objects that even the most delicates of our apparatuses perturb. And you mix in this galaxies?
Dear Sofia D. Wechsler ,
Yes, I would like to help you, but your knowledge in quantum physics is much higher than mine, I don't know what the particles I mean are equivalent to. Quarks maybe? electrons? It would be necessary to analyze several quantum numbers to know what is what.
But if I have shown, through Einstein's equations (which refer to masses, as large as a galaxy or as small as an atom or particle) that particles appear and disappear and that there are MASS-FREE charges that move according to electromagnetic fields and which are responsible for creating particles with mass here and there.
Imagine an electromagnetic wave that displaces those massless charges in its path, you will have a wave, and particles with mass will appear here and there within that wave, it is quite similar to the wave function, don't you think?
I think I am offering you the key, but it is you who must open the door.
Sergio Garcia Chimeno
Yes, Sergio, I know that elementary particles float in a vacuum of virtual particles, and it is a VERY SERIOUS question whether this sea of virtual particles has a hand in what happens between the preparation of a quantum object and its detection. But id'd give 99% probability that there is no vacuum sea of atoms, and even worse, of as big molecules as fullerenes, with which also were done interference experiments.
By the way, Higgs' boson that gives mass to particles possessing rest-mass, has no electric charge and is not of electromagnetic nature.
Dear Sofia Wechsler,
A field is a volume that changes the properties of a phenomenon (like an electron) if we change the position of the phenomenon within the volume of the field. That means that fields are not uniform (homogeneous) and have a spatial structure, because space itself is discrete. Some fields are local – like the electron field – but there are a couple of fields that exist everywhere in the universe. These are basic fields and these fields represent the “bare” properties of discrete space itself. Local fields are compositions/configurations of the basic properties of space itself (static point of view). But local fields are transformations/re-distributions of the basic properties of space itself if we use the dynamical point of view.
The equation E = mc2 shows that matter and energy are equivalent. Actually, matter is a concentration of free energy. Energy itself represent an amount of quanta and a quantum represents a local change within the electric field. However, a change is not only an observable local difference in time and position, a change has a direction too. The direction of a quantum in vacuum space is set by the corresponding magnetic field (and visa versa). The “flow” of a quantum within the electric field is determined by the constant speed of light but the vectors of the magnetic field act instantaneous (the collaps of the wave function).
Conclusion: matter represents a concentration of “fixed changes” (quanta) within the electric field. Actually, there is no fundamental difference between the properties of the basic fields and a phenomenon like an electron. The observable difference is directly related to the density of the local properties (local relations).
With kind regards, Sydney
Dear Sydney Ernest Grimm
Let me first repeat my question: if the wave-function is some sort of matter - and so it seems to be because it is influenced by fields - how could it be that part of it disappears during the collapse? Matter does not disappear as far as we know.
You mention density of local properties. Please don't give hints. What you want to say? That the part of the wave-function that disappears at collapse contained no excitations of the local field?
I also have such thoughts but, you see, which local field may have an atom? It is not an elementary particle, has no virtual counterparts. Though, at collapse, part of the wave-function of the atom disappears.
What you say of this problem?
With kind regards
I suggest the situation is more like the Bohm interpretation. That is a Newtonian type aether and particles are 2 components of our universe. The wave function applies to the aether part and represents real waves with inertia (as is required for the wave equation to apply). The situation is like General Relativity suggests - particles form the waves in the aether and the waves direct the particles. Thus, the major problem of the Bohm interpretation is accounted - the particles make the waves.
Dear Sofia Wechsler,
The term “excitation” doesn’t describe reality. A local surplus of energy can only exist because there is a corresponding local deficit of energy at the same moment. If I use the dynamical point of view I have to use the term “re-distribution” (otherwise there exist no conservation laws in physics).
In discrete space energy is a property of the structure of discrete space. That means that every unit of discrete space transfers in a synchronous way the same amount of energy during the same amount of time. The magnetic field is a vector field and the vectors determine the next distribution of the quanta in space. But the electric field and the magnetic field are corresponding fields, like the propagation of an electromagnetic wave in vacuum space shows.
If local dominant vectors of the magnetic field disappear, the corresponding quanta of the electric field change immediately. Not the energy of the quanta, but the distribution of the quanta in vacuum space, the local configuration. Because vectors of the magnetic field don’t influence the transfer of only one quantum. The collapse of dominant vectors can influence the quanta of the electric field within a large volume in space. In other words, the conceptual problem is not the wave-like nature of the electric field, it is the incomplete description of the magnetic field that obstructs the understanding of the collapse of the wave-function.
With kind regards, Sydney
John Hodge
If a wave-function has two wave-packets, |ψ> = α|a> + β|b>, how many particles you think that it carries?
Sydney Ernest Grimm
Dear Sydney,
"The term “excitation” doesn’t describe reality. A local surplus of energy can only exist because there is a corresponding local deficit of energy at the same moment."
I am not sure of this. The level of energy of the vacuum is zero on average. If we don't speak of average, there are fluctuations. For instance, virtual photons can pop up from the vacuum and in very short time return to it. So says the quantum field theory (QFT).
In your ellabortion about discrete space I do not see the answer to my question. I repeat it: if the wave-function is material, how could it be that at the collapse part of it disappears.
I will explain myself: we can split the wave-function of a quantum object into two wave-packets and do interference. But, when we test the wave-function, only one of the wave-packets produces a click in a detector. So, either the other wave-packet is erased, or it is not present there. It can't be non-present, as it participates in the interference. About being erased, I feel badly with the idea that matters diappear.
By the way, it seems to me that your thoughts are focused on elementary particles. But the movement of atoms and molecules is also decribed by wave-functions (at low energies, since at high energies the wave-packets are very small, so that we can speak of them as of particles). For instance, a 4He particle is magnetically and electrically neutral. It is possible to do with it interference, and if tested, its wave-function undergoes collapse. So, part of the wave-function disappears.
With complicated molecules as fluoro-fullerenes is also possible to do interference. I don't think that they have anything to do with discreteness of space, as they are very big, comprising hundreds of atoms. About local magnetic fields, these molecules are electrically and magnetically neutral. And though, their wave-functions also undergoes collapse.
With kindest regards from me too,
Sofia
Sofia D. Wechsler
If by that you mean 2 wave functions that interfere to form one wave function, then that is the answer. Waves interfere. But the interfered wave can direct (see Bohm) any number of particles. Such is what happens when a detector detects - particles are pushed around. Otherwise the waves remain undetected. Waves don't "carry" particles. Remember I'm choosing an interpretation which probably is inconsistent with most other interpretations. But then the idea light is a wave has been rejected by (several) experiments:
https://www.scirp.org/journal/paperinformation.aspx?paperid=93056
Dear Sofia Wechsler,
About 30 years ago they did a couple of experiments at the Philips laboratory in the Netherlands. They drilled really small holes through a homogeneous material and “fired” electromagnetic waves through the holes. And to their surprise it showed that the pass on of electromagnetic waves with different wave-lengths is quantized.
So there is something strange in relation to the properties of the electromagnetic wave. The energy of the electromagnetic wave is related to the frequency (E = h f). Planck’s constant (h) is a fixed amount of energy during 1 second and the frequency (f) too. If I increase the energy (e.g. I double the value) I also double the frequency. But at the scale size of 1 x 10-15 m there exists no higher frequency of an electromagnetic wave. The Planck-Einstein relation shows the relation between energy and wave length because the frequency of an electromagnetic wave is the constant speed of light (c) divided by the wave length (λ).
But if we have the equation k x l = m and k and l are constants in physics, m must be a constant too. In other words, the wave length in the Planck-Einstein relation is a constant. Thus the wave length of every electromagnetic wave is the multiple of the constant of length in space (about 0,5 x 10-15 m). In other words, the existence of a constant of length in space is experimentally proved at the Philips laboratory in Eindhoven.
What is the meaning of the existence of a standard length? It shows that the proposed minimal length scale (around 1930) is real. Its existence was proposed by W. (Werner) Heisenberg, H.T. Flint, A. March, F. Möglich, S. Goudsmit, and many other theorists at that time. Besides that, the size of the minimal length scale is about the size where the principle of asymptotic freedom is active (Standard model of elementary particles and forces). That means that it is impossible to “observe” the existence of elementary particles at a scale size below 0,5 x 10-15 m because these hypothetical particles cannot exist in a way like the proton exists. Actually, the minimal length scale is also directly related to the uncertainty principle of Heisenberg (the minimal uncertainty is the energy of 1 quantum). So what is the size of 1 quantum?
The standard length scale indicates the existence of a structure of space itself (nowadays termed “discrete space” although quite a lot of theorists have the opinion that the minimal length scale is identical to the Planck length). If I transfer energy from 1 unit of the structure of space to an adjacent unit I have created a change of position of that distinct amount of energy. The transfer itself is the movement of a fluent amount of infinite small amounts of energy. Thus the transfer of the amount of energy – from E = 0 to E = 1 quantum – has a fixed duration (the constant of time). In between there is no other transfer of energy between the 2 units. The distance of the transfer of 1 quantum is the minimal length scale (half the minimal wave length). In other words, if I observe discrete space I can only observe the quantum if it has passed half the minimal wave length. Now I can translate c (300.000.000 m) into the metric of the minimal length scale and calculate the energy of 1 quantum with the help of the fixed energy of Planck’s constant.
This is a very brief description of the underlying reality of Quantum Mechanics. You can ignore it and try to understand quantum reality with the help of a limited model (QM). Or you can decide to change the goal posts and consider the reality of concepts that are not part of the conceptual frame work of QM.
I have a link to a nice explanation of the search for the properties of discrete space (and all the troubles they have met over the last 3 decades because they tragically believe that discrete space itself is curved): https://www.youtube.com/watch?v=PRyo_ee2r0U
With kind regards, Sydney
Dear Sofia, Our universe is a complete well organized entity, and it is not result of any accidental event to work mechanically.
Space of universe is functioning element of universe where it has tremendous role in any aspect. One of its character is, when it get temperature (in any galaxy) it create wave. For same reason we get picture from billions of mile in space of galaxy.
YOU>> a quantum (microscopic) object. But if this object is, say, an electron, the wave-function is bent by an electric field.
1) Quantum is not microscopic object. We do not know much about Quantum due to our perception of mechanical atom. Quantum is the building block of our universe, where each constituent elementary particle in quantum field is following its nature. On the other world it is not mechanics.
2) Electron is part of an atom. Electron is not electron outside of an atom. there is no such thing exist "free electron." Electron is very complicated element of an atom that we do not know anything about. We do not know if electron is carrying any other element, where it get or choose its orbit and so fort.
3) The wave-function : The wave-function in space of universe (galaxy only) is making everything round, spherical shape, when they are in a gaseous, or liquid. for same reason we observe all gas and liquid in spherical shape. on earth, raindrop, bubble, and even an atom shape is spherical, all are result of wave-function. unprecedented, but this is reality that nothing in the universe is working mechanically as we been taught. Unfortunately, this is the fact, that any mechanical function has friction, but we all forget this phenomenon. friction
regards.
Article Quantum Intelligent Space
Sydney Ernest Grimm
Dear Sydney,
You describe an experiment which seems interesting, but I am in total impossibility to read the article now. Can you describe it in more detail? How small were the holes in length and in diameter? What was the wavelength of the electromagnetic (e.m.) wave they fired at the holes - was this wave at all monochromatic? Was the wave-vector of this wave parallel to the direction of the holes?
If the wave landing on the holes was monochromatic, I will have a problem in understanding how there exited different wavelengths, unless there was a strong interaction between the material and the input wave (or Compton scattering).
Right now I have to give a certain answer about an article connected to one of mine, i.e. I have first to read that article which is full of difficult calculi. So, please try to give me these details. Then, we will be able to talk more specifically.
With kindest regards,
Sofia
Dear Sofia Wechsler,
Montie, E., Cosman, E., 't Hooft, G. et al. “Observation of the optical analogue of quantized conductance of a point contact.” Nature 350, 594–595 (1991). https://doi.org/10.1038/350594a0
Free link: https://openaccess.leidenuniv.nl/handle/1887/3360
Personally I never read the article in Nature. I suppose that I have read a short review in a technical magazine in 1991.
The laser had a wave length of 1550 nm. They used a variable diaphragm 0 – 20.000 nm (no drilled holes). The light that passed the diaphragm was limited by a diameter that varied with half the wave length of the laser light. In other words, increasing the diameter of the diaphragm by any amount of length that was less than the size of half the wave length didn’t affect the amount of passed light.
One can argue that the quantization is because of the electric and magnetic field of the propagating light. But in practice both fields of the electromagnetic wave have not perfect shapes:
C. Riek, D.V. Seletskiy, A.S. Moskalenko, et al. “Direct sampling of electric-field vacuum fluctuations”. Science (2015), Vol. 350, Issue 6259, pp. 420-423 DOI: 10.1126/science.aac9788
With kind regards, Sydney
Sydney Ernest Grimm
Sydney, my friend,
"The laser had a wave length of 1550 nm. They used a variable diaphragm 0 – 20.000 nm (no drilled holes). The light that passed the diaphragm was limited by a diameter that varied with half the wave length of the laser light. In other words, increasing the diameter of the diaphragm by any amount of length that was less than the size of half the wave length didn’t affect the amount of passed light."
From which material was the diaphragm? If it wasn't a material perfectly reflecting the laser light of the mentioned wavelength, then I cannot expect that on the cross-section of the hole in the diaphragm, should appear stationary waves, only traveling waves. Moreover, what matters about the cross-section of the beam is the transversal wave-number, not the longitudinal one.
Now, you mentioned some articles. For the moment it doesn't come into account for me to read them. I would like to, but it has to wait. Please see, I sent an article to publication, and the team which deals with the issue works otherwise than I. Well, I claim that with their approach, they would get stuck soon. But, in general, I am a supporter of their main idea. Originally, it was the idea of the great Ghirardi.
Bottom line, for arguing with them I need to read a couple of their articles, with endless mathematics.
So, about the experiment you describe (and seems indeed interesting), for the moment I am asking you about those details on which I place a question mark. I appologize for the situation.
With kindest regards from me too,
Sofia
The usual is the Born (not Bohm) interpretation.
The wave function means nothing, it square modulus is probability density.
It is true that following Schrodinger the wave function is partly shaped by the potential energy of some field. Mass influences mass through fields created by particles. The distribution of mass is ultimately predicted, through the wave function, not mass itself.
Juan Weisz
My dear Juan,
I am so busy that I feel that the sky falls on my head. If you post a comment, please take care to be directly connected with my question.
"Mass influences mass through fields created by particles."
That's absolutely right. The influence is through the fields of the particles, not through this strange thing that we name wave-function. However, in continuation you say,
"The distribution of mass is ultimately predicted, through the wave function, not mass itself."
So what? At collapse, part of the wave-function should disappear? And, of course, it takes with it the field located in that part. But, the wave-function is some form of matter. Or, could it be that it is NOT matter? It is not known to us that matter can disappear.
We might say that at collapse, the distrbution of the matter in space re-organizes itself. But if the wave-function consists in two space-separated wave-packets, how could the matter from one wave-packet jump instantly over space to the other wave-packet? It's defies the relativity.
You see, consider a wave-function with two wave-packets:
|ψ> = α|a> + β|b>.
As I study the CSL model of collapse, what this model predicts is that during the measurement of the wave-function, in a given trial of the measurement either |α|2 becomes smaller and smaller, and |β|2 closer and closer to 1, or vice-versa. But, you see, equations are nice, however phenomenologically I don't see mass jumping over the space between the two. Moreover, the mass of a particle is an undivisible amount, e.g. the electron mass is m0. I don't see how it can be transferred gradually.
So, if you are interested in my question, I invite you to reflect on such issues. And, maybe take a look on section 5.2 of my article, you will see this gradual change in |α|2 and |β|2. It's a challenging issue.
Preprint In Praise and in Criticism of the Model of Continuous Sponta...
Also, please don't hesitate to make comments, my article is under review for publication.
Anyway, thanks for the lucid comment and waiting for answer. With kind regards.
The problem is the understanding of probability.
The particle could be at a> or at b> with equal probability. If you measure, it could just turn up at b>. But nothing jumps, it was just a probability forcast.
It is true that after measurement you should probably reconstruct the wave function to be at b>. I will try to read the article.
best regards, Juan
The problem of gradually or suddenly is in principle answerable empirically.
I once did a calculation in which there was strong localization of an electron on a linear chain, disordered,, there was also an electric field. You could tell on which site the electron is, but when you changed the field a bit, it could suddenly move to another site. However doing a very gradual change in the field, then you could see that the wave function was actually moving to the new site.
Juan Weisz
Juan, please try not to use the word 'particle'. It is such a controversed term. 'Type of particle' is O.K. Also, in my wave-function |ψ> = α|a> + β|b>, the outcome |a> may be obtained with probability |α|2, while |b> is obtained with probability |β|2. Let them differ, otherwise confusions may result.
You say "The problem is the understanding of probability". I would say that the problem is also the understanding the intensity of a wave-packet. Let's leave the mathematics aside and think of phenomenology.
Please notice that in the normalized wave-function, both |α|2 and |β|2 are less than 1, but their sum is 1. I asked myself what does it mean. On the other hand, the greater is, say, |α|2, the greater is the probability of the outcome |a> to appear. It is as if a detector has some difficulty to see wave-packets of intensities less than 1, and the closer is this intensity to 1, the easier is for the detector to 'feel' the wave-packet.
Of course, these are only thoughts of mine.
With kind regards
P.S. What you say with the electron and the electric field is interesting but I cannot judge on the spot, if the effect is quantum or classical electricity. I am so busy that I feel myself tired without doing any physical effort. (By the way, how are you and your family in these hard times with the Korona? Is everything O.K.? Do send me a message, if you want, and tell me.)
Sofia D. Wechsler. I can't agree with your opinion. Why only consider matter? Indeed, matter is not such a simple structure. But how can the nature of radiation be produced from matter ? Is matter and radiation the ultimate structure?
If the wave-function is some sort of matter, matter is some sort of wave-function. That doesn’t help much so let’s examine the propagation of a simple electromagnetic wave in vacuum space.
Figure 1 shows the well-known diagram of an electromagnetic wave in respect to the differentiation of the electric and magnetic field in vacuum space. I can “translate” the schematic diagram to the schematic concept of discrete space, the minimal length scale λe (metric is about 0,5 x 10-15 m). Figure 2 shows the schematic concept. Figure 3 – a cross section of the electromagnetic wave – shows the result. Short: space has a structure and the elements of the structure – the creators of observable reality – tessellate space (= discrete space). The energy of every element is theoretically infinite. (In other words: the statement of Sofia Wechsler on top of the discussion is correct.)
Now the curve in figure 3 indicates the range of the electric field/magnetic field because figure 4 shows the influence of the wave form on size (see: https://openaccess.leidenuniv.nl/handle/1887/3360). That means that every element (= unit) of discrete space in vacuum space represents at least 2 properties: vectors (magnetic field) and topological deformation (electric field). It is nice to know that the topological deformation of an element with an invariant volume results in the increase or decrease of the surface area of the whole element.
The propagation of the electromagnetic wave in vacuum space is the propagation of variable properties of the elements of discrete space; discrete space itself is in rest. However, our universe is non-local too thus all the elements in the universe are involved, not only the local quantum fluctuations of the elements around.
The curve in figure 3 represents the influence of the electromagnetic wave in vacuum space in relation to everything around and if I “blow up” the curve in such a way that every drawn element (square) represents 100 elements (it is a cross section) the wave length is lengthen 10 times. Therefore the energy of the “blown up” electromagnetic wave (E = hf) is only 1/10 of the original energy. But the range of the influence of the electric field/magnetic field is increased by a factor 10, in spite of the sharp decrease of the energy. In other words, this is impossible if we are reasoning with the help of the phenomenological point of view.
Conclusion: the properties of the electromagnetic wave are alternately super positioned upon and super positioned under the local properties of the involved elements of discrete space during the propagation of the quantum of the wave. Because a local surplus of a quantum is a super position upon the local energy amount and a local deficit of a quantum is a super position under the local energy amount. (Experimental evidence of the influence of background quantum fluctuations, see: https://arxiv.org/pdf/1611.06773, figure 1 to 4.)
The super positioned properties of the electromagnetic wave are vectors (magnetic field) and topological deformations (electric field). Both types of variable properties are corresponding properties, that means that a local increase of topological deformation generates a corresponding vector that reflects the changing magnitude of the topological deformation at exactly the same moment (and visa versa). Thus changing the vectors is changing the distribution of the electric amplitudes.
However, 1 quantum represents a fixed amount of topological deformation (and corresponding vector) at a certain moment and position in vacuum space. Actually, 1 quantum represents the transfer of 1 fixed amount of topological deformation from one element to one or more adjacent elements around (that’s why the linear transfer of 1 quantum in vacuum space is a constant (c). Therefore the wave form represents a local distortion of the average symmetry of vacuum space by the energy of 1 quantum at every element along the trajectory of the electromagnetic wave.
In other words, if we absorb the propagated quantum during one half of the wave length, the whole wave form collapses at exactly the same moment.
With kind regards, Sydney
Sofia
In strong localization you can see a wave function almost exclusively on some specific site (tight binding model). That is what I mean.
I think we agree.
Cheng Wu Long
I didn't say that I consider only matter in the sense of possessing rest-mass. I spoke of matter in general, with or without rest-mass. I appologize for being not clear.
"Is matter and radiation the ultimate structure?"
Very good question, to which I have no clear answer. In the Standard Model we have nothing else than particles and particles that transmit fields, i.e. photons, gluons, Z and W bosons, and Higgs' boson.
I am ready to admit that at low energies these objects may behave as waves. But they carry energy. If the wave-function consists in two wave-packets, both carry energy. Though, when tested with detectors only one wave-packet responds and the other disappears. And this is the question. The energy carried by the silent wave-packet disappears? Or, jumps to the other wave-packet which can be very distant in space? This is the problem.
Juan Weisz
Juan, my friend,
Yes, I do agree, however, my problem is when the wave-function is NOT localized, when it contains a couple of space-separated wave-packets. Please read the question.
With kind regards
The word matter make me confused. This is the root of the misunderstanding. In fact, when you talk about particle physics, you clarify your expression. Is the boson a real substance? I think it's a mysterious relationship, and it carries information about energy. You have mentioned protons and W bosons, and you must know that they seem contradictory , just like the contradiction between wave and particle.
So can I understand your wave function in such a manner? You are dividing the wave function into two types, corresponding to two different side of contradictions. In this way, you can simultaneously express both sides of the contradiction of physical reality.
If not, you must have gamma-wave functions in your equation.
I realize that you're thinking about very basic physical issues, and that's critical. The collapse of the wave function cannot be accepted so hastily and cannot be questioned.
In fact, I also think there are two different types of waves.
Sofia D. Wechsler "My problem is, if the wave-function is not a reality, i.e. a real "something" traveling in our apparatus, how could it feel fields?"
The way I currently prefer to think of the wave function, at least 5 days a week, is as analogous to the probability density of Hamiltonian classical mechanics (the ensemble interpretation of quantum mechanics). So it is a mathematical description of reality. The way it ``feel´´ fields is because we insert such interactions into the mathematical model, motivated by a classical point particle picture.
Sofia D. Wechsler "I support the CSL collapse model - I trust that you are aware of it. I proved that the collapse principle is unavoidable, i.e. denying it, one gets contradiction with the quantum mechanics (QM)."
What kind of contradiction? I played with one such model many years ago, but got very discouraged by the whole approach, due to non-locality issues. Besides, what are the testable predictions which distinguishes such models from ordinary textbook quantum mechanics?
Sofia D. Wechsler "if the wave-function is a real thing, how can part of it disappear at the collapse?"
Yes, that is part of the non-locality issue. Which is why I prefer the ensemble interpretation.
Sofia D. Wechsler "About the 2nd quantization, if we speak of single-particle wave-function, what can give me the 2nd quantization?"
For a single particle system, probably nothing. For multi-particle systems it usually leads to a better/simpler way to describe the system mathematically (I know of exceptions). And relativistic interacting systems are automatically many-particle systems, with the potential of particle creations and annihilations.
Sofia D. Wechsler "Salvatore Savasta proved ... "
I don't know this work. But the concept of virtual particles is a bit fuzzy and theoretical, dependent on the approximation method being used (usually an interpretation of Feynman diagrams). So I am not sure to which extent they exist outside theoreticians minds.
Sofia D. Wechsler "there can be no quantum vacuum for such big particles as fullerenes"
The quantum vacuum is usually described in terms of (what we currently think are) the ``elementary´´ particles (like quarks, gluons, ...). I cannot recall having encountered discussions of virtual composite particles (even protons or neutrons) in this context; I think they must be utterly irrelevant.
Kåre Olaussen
Dear Kåre,
I say it again, I know that your orientation is mathematical. However, people want phenomenology. Would you try to detach yourself for a moment from formulas - i.e. what we insert in equations - and imagine that strange wave passing through the apparatus? You see, it carries all sort of charges, electrical, magnetical momentum, mass, otherwise it wouldn't be deflected by fields. The fact that it is deflected is confirmed experimentally.
Now, I will stress in a few lines my question, and then I will answer your questions/comments.
Imagine that the wave has TWO wave-packets - one passing through an apparatus placed, for instance, in your town, and the other one passing through an apparatus placed in my town. And let's put detectors on their paths, respectively DK and DS. As the experience shows, in a given trial of the experiment only one of the detectors would click. Let for instance be DK . The question arises: WHERE disappeared all the charges that impinged on DS?
Sofia: "I support the CSL collapse model . . . I proved that the collapse principle is unavoidable, i.e. denying it, one gets contradiction with the quantum mechanics (QM)." Kåre: "What kind of contradiction?"
We get other predictions about experiment results, than predicts the QM. Would you try to read section 3 of my article?
Preprint In Praise and in Criticism of the Model of Continuous Sponta...
There are a few theorems and proofs. They are simple and short - no effort is needed to understand. And I would appreciate suggestions/criticism/questions, as the article is now under review at a journal.
Kåre: "I played with one such model many years ago, but got very discouraged by the whole approach, due to non-locality issues."
Yes, I am aware of problems with relativity. My article deals with the non-relativistic case. About relativism, I was just examining the issue when a got a first set of comments to my article - so I had to postpone the relativity.
Kåre: "Besides, what are the testable predictions which distinguishes such models from ordinary textbook quantum mechanics?"
Simply, the CSL model can explain, step by step, what happens inside a detector during the detection process. It's section 5 in my article. It's an achievement not reached by anyone of the so-called "interpretations".
Sofia: "if the wave-function is a real thing, how can part of it disappear at the collapse?" Kåre: "Yes, that is part of the non-locality issue. Which is why I prefer the ensemble interpretation."
Kåre, are you really satisfied with 'ensemble interpretation'? People ask what happens in each trial. The tables in the subsection 5.2 in my article show step by step that as the measurement advances, the INTENSITIES (absolute square of amplitudes) of the wave-packets VARY. One of the wave-packets becomes more and more intense and the other grow weaker, until one intensity reaches the value 1, and the others vanish.
"For multi-particle systems it usually leads to a better/simpler way to describe the system mathematically"
No, we cannot work this way. There is an international saying "who runs after two rabbits, catches none". Multi-particle would have to wait.
With best regards
Sofia,
Why are you disturbed.?
It is not reality, it is just probability.
You dont ask what is the result, only the possible set of results.
A priori flip a coin
A posteriori see a result.
best regards, juan
Juan Weisz
If a class of children is blond, then every child in it is blond. The cause of the probability with which we get one of the results stands in the evolution of the wave-function in each trial and trial of the experiment.
The wave-function is not something on the paper, it is something that passes through our apparatuses, and the charges it carries make it bend when crossing fields.
Right, for many trials, empirical probability is identical with the a priori one. The potential of a field does influence the wave function. and the
probability density of finding a particle. qV for the electric field. It is part of the Hamiltonian, not wave function.
I still dont see any fundamental problem with usual interpretation. If there were, maybe we could make some advance. As is, there is just randomness, a controled one.
The square of the modulus of the wave function is a location density distribution of the hop landing locations of a point-like object. This location density distribution is the Fourier transform of the characteristic function of the stochastic process that generated the hop landing locations. The point-like object is hopping around in an ongoing hopping path and this hopping path is recurrently regenerating a hop landing location swarm that is described by the location density distribution. The stochastic process is a combination of a Poisson Process and a binomial process that is represented by a point spread function that equals the location density distribution.
This description holds for elementary particles. The hopping path of an elementary particle can be archived as a combination of a scalar timestamp and a three-dimensional vector in a quaternionic storage bin that becomes the eigenvalue of a normal operator in a quaternionic separable Hilbert space. Together these storage bins form the eigenspace of the footprint operator of the elementary particle. Each elementary particle owns a private quaternionic separable Hilbert space that archives the full lifestory of the elementary particle.
Preprint Representing basic physical fields by quaternionic fields
Hans van Leunen
I have an interesting proposal for you. Let's gave a wave-function with two wave-packets, |a> and |b>, and let's place an (ideal, absorbing) detector at some location P on the path of |a>.
Assume that in a given trial of the experiment the detector remained silent. That means, by your theory, that the point-like object was in the wave-packet |b>.
Very well! Then, let there be an additional detector at some location P' of the path of |a>, more distant from the source than P. If the point-like object jumps from one path to another, as you say, we can expect that it would jump at some time from |b> to |a>. So, we have a chance to catch the object on the path of |a>, at P'.
However, the experiment says that if you didn't catch the object on the path |a>, no matter how many additional detectors you have on this path, all the detectors would remain silent.
Space of the universe should not be consider as a container or holder. Space should be appraised and study as a functioning quantum mechanics elementary. One of the characteristic of space is when it get temperature, it creates wave. Wave without temperature does not exist. Thus wave and temperature (photon) is not carrying any mass to call them wave-particle or photon-particle.
unfortunately we inherited from past.
Article Quantum Intelligent Space
regards
Also check https://www.sciencemag.org/news/2012/04/light-bends-itself
Sofia D. Wechsler
If two objects join in one module, then the characteristic functions of these objects superpose and the superposition coefficients act as displacement generators that determine the internal locations of the components of the module. The module moves as one unit. It will be detected at one of the hop landing locations of the module.
Thus, it will not be detected at multiple locations at once. The module has an expected detection location. That corresponds with the movement of the whole module.
This means that not the location density distributions of the composing objects superpose. Superposition takes place in Fourier space and not in configuration space.
The hop landing location swarms of the constituting objects can be described by their location density distribution. This equals the Fourier transform of the characteristic function of that object. This means that the location density distribution is a wave package. However, it is recurrently regenerated together with the hop landing locations swarm of which it is the descriptor. The two location density distributions do not interfere. Instead, the two characteristic functions interfere.
The characteristic functions belong to the stochastic processes that recurrently regenerate the initial objects.
Please read the chapter on stochastic control in Preprint Representing basic physical fields by quaternionic fields
Dear sir,Wave is a complex Mathematical Function containing information related to the physical System under consideration.
Since it is a complex Mathematical function it cannot be observed in the laboratory. We. May have Square of the MODULES of the function that could be directly perceived
Ofcourse Information is massive.
But information is NOT Wave Function.
We Write Information=Negative Entropy of
Material distribution×Temporature of material distribution.
Dear Gopalan Sudhakaran
It's not true. The wave-function we can observed in the lab, and not only can we get probabilities of different predictions, but also phases. The latter is done by developping the wave-function in different bases, and testing the probabilities of the different predictions. For example, the wave-function
(1) α|x> + β|y>,
can be tested in the vase {|x>, |y>}, or in the base {|d>, |a>}, where
(2) |d> = (1/√2) ( |x> + |y>},
(3) |a> = (1/√2) ( |x> - |y>}.
The test in the base {|x>, |y>} will give us the values of |α|2 and |β|2, while the test in the base {|d>, |a>} will give us the relative phase of α and β.
Best regards!
Hans van Leunen
Hans, my friend, you talk in riddles to me. Did you hear of the Occam razor? It says that you want to build a theory, you must make the least possible assumptions. But what you do is the opposite.
"If two objects join in one module, then the characteristic functions of these objects superpose and the superposition coefficients act as displacement generators that determine the internal locations of the components of the module. The module moves as one unit. It will be detected at one of the hop landing locations of the module."
What you mean by "module"?
What is the mathematical definition of the "displacement generators"?
As I don't know what is that module I can't see what is its "hop landing locations".
"Thus, it will not be detected at multiple locations at once. The module has an expected detection location. That corresponds with the movement of the whole module."
My objection is that the particle may be detected in different wave-packets, at different times. That is contrary to the experiment.
"Superposition takes place in Fourier space and not in configuration space."
A wave-function can consist in two wave-packets, space-separated. This is superposition in space. You cannot fight the experimental evidence.
Best regards
I have the same opinion. Let us imagine that we discover a tiny body traveling in the space that changes its direction when the gravitational interaction with another body is sufficient. Let us imagine that the same body demonstrates a momentum transference when it collides with another body. That is, the tiny body demonstrates gravitational and inertial properties. Which conclusions we can extract? Why invent another ontological element with unlike properties whit any other body? The reason for this choice involves Maxwell's denial that the electric current was made up of particles with mass (and their discrete character) and the construction of his electromagnetism based solely on the continuum. This path influenced greatly the nowadays admission of the ontological existence of physical quantities independently of matter.
On the other hand, if this tiny body is like other bodies (including with internal structure). As we detect it in all space. Could this body compound a gas, that can be treated as continuous but at some point must be treated as discrete? Could this gas behave like a substrate for a phenomenon that seems the walking droplets (as if it was like all others fluids)? I have a lot of thought about this topic....
See:
https://www.nature.com/articles/nature14005
https://youtu.be/7Ys_yKGNFRQ
https://www.youtube.com/watch?v=nmC0ygr08tE
Sofia D. Wechsler
Please spend some time to read or scan Preprint Representing basic physical fields by quaternionic fields
The Hilbert Book Model starts very simply, but it quickly shows that elementary particles are very complicated structures. They are point-like objects that reside on a private platform that carries most of their properties. They behave as elementary modules that together constitute all other modules that occur in the universe. Some modules constitute modular systems. Humans are examples of very sophisticated modular systems.
Hi all,
To answer the question posed:
The EM-field is an oscillation ion space and is therefore not bent by any field.
But, the photon is a small object with a mass travelling at the light speed, it is bent by gravitational fields and well adapted em-radiation. It simply do not follow the mass law E=mc^2
JES
Sofia, the answer to your question seems to be clear. The concept of the wave function, which describes the behaviour of an electron, uses the model of a combined point charge and point mass for the electron and the concept of a statistical probability for the position of the electron.
The wave function therefore inherits the mass and charge properties of the point model but smears it to a larger volume. Such a volume with a statistical part of the electron then becomes subject of gravitational and electric interaction with fields.
We then can ask how close to the truth this model is. The answer is that point masses and point charges do not exist. But if the real size is not zero but small enough, then the model is good enough to describe measurable interactions within the range of measurement accuracy.
“…Is it not an odd kind of reasoning, if one first claims that there must be a "point particle" and then to declare it must be smeared out (even though eventually it does not exist anyway)?...”
- really there is nothing odd of reasoning in that particles move in Matter’s [5]4D Euclidian spacetime with metrics (cτ,X,Y,Z, ct) having no continuous trajectories, where “point particles” have always concrete trajectory points, what is observable as “smeared out”,
– that Zeno rigorously proved more 2500 years ago, and just in accordance with this fact [not only, though] the QM exists.
Which [QM], at that, rather adequately describes the QM objects/event/processes, and has for that rather rational for analysis of observed QM phenomena Bohr's and Heisenberg's interpretation of QM formalism, and of how this formalism works. Including that “smeared” particles interact as points.
Whereas relaying to
“….. I guess this is what Jaynes called Bohr's and Heisenberg's quantum "omelette".…..”
- it seems as rather interesting – what this Jaynes suggested instead? – and, since the "omelette" works rather effectively in QM till now, it seems that he suggested nothing.
Again, the more adequate interpretation of the QM objects/events/processes will be obtained practically for sure only at considering the QM phenomena in accordance with the Shevchenko-Tokarevsky’s the informational physical model
https://www.researchgate.net/publication/273777630_The_Informational_Conception_and_Basic_Physics DOI 10.5281/zenodo.16494,
- where everything in Matter is/are some disturbances in the dense lattice of [5]4D binary reversive fundamental logical elements [FLE], which fills the Matter’s absolute [5]4D Euclidian spacetime with metrics (cτ,X,Y,Z, ct),
- provided that the discovered by Zeno absolutely fundamental uncertainty of changes is governed by the condition ΔS=ΔAΔB=ћ, where
- S is the physical action, ΔS= ћ is fundamentally discrete and fundamentally universal elementary change of the action, which happens when the information in any Matter’s binary object and event/process changes on 1 bit;
- A and B are non-commutative QM operators
And completely for sure the development of QM should start from correction of operators for energy and momentum, and corresponding correction of the Schrödinger equation as that is pointed in
https://www.researchgate.net/publication/342600304_The_informational_physical_model_some_fundamental_problems_in_physics DOI: 10.13140/RG.2.2.12325.73445/2
The SS posts in the thread https://www.researchgate.net/post/Is_Quantum_Mechanics_consistent is relevant to this thread question.
Cheers
“…The idea that some material object indeed is "pointlike" was alien to most classical physicists. And indeed, how would classical uncharged particles interact/scatter, if they were without any extension? It is evident that such particles can not collide.……”
- that isn’t a reason for non-considering of the “ideal”, of course, physical term “point-like” [particles]; that above simply depends on – how precisely somebody took aim at the “shot”.
That is another thing, that even in classical physics “point-like” particles interact really through fields, which aren’t pointlike.
But that above isn’t essential, if we return to QM. In QM particles simply fundamentally aren’t “point-like”, when the degree of the “point-likeness” depends on particle’s energy/momentum. However, again, when free particles exist and move in Matter’s absolute [5]4D Euclidian spacetime with metrics (cτ,X,Y,Z, ct),
- this “point-likeness” isn’t arbitrary, it is governed by the condition ΔS=ΔAΔB=ћ, where
- S is the physical action, ΔS= ћ is fundamentally discrete and fundamentally universal elementary change of the action, A and B are non-commutative QM operators.
Including when, say, A is the space operator and B is the momentum operator, the Eq. above characterize the “non- point-likeness” of the particle’s momentum and localization in the space.
However, besides collisions in Matter particles can, for example, be absorbed, and in such cases they, though move as something that is “non-point-like”, interact as point-like;
- the classical 300 years old example is when a photon with, say a wavelength 400 nm seems as simultaneously propagate through all slits of a diffraction grating that has size, say, a few cm,
- however it can be absorbed – with its “wave function collapse”, though with different probability, in the grating’s just points with sizes that are “points” comparing with the grating’s size.
More see the SS posts above and papers that are linked in the posts.
Cheers
Dear Sofia. Thank you for a most-interesting, and topical question. There must be much competition in this space at present.
In my opinion, there should exist a 6th state of matter, which would satisfy the characteristics you described. Whereas, a 6th state of matter would be able to assume (in the least) a tri-lateral state as flow. Each state of flow energy packaged in its own, universal-brane messenging package (perhaps as a special-relative photonic universe). Surely probability is a conditional statement, isn't it?
Just a developing thought, not yet much of a theory.
Regards
Robert
Christian Baumgarten
Sergey Shevchenko
Elementary particles are very complicated constructs that reside on a private platform that contains most of its data. That platform is a separable quaternionic Hilbert space. An ongoing hopping path of a point-like object is archived in the eigenspace of a footprint operator. The private Hilbert space is a member of a system of Hilbert spaces that all share the same underlying vector space. That system is a Hilbert repository. It is introduced in
Preprint Representing basic physical fields by quaternionic fields
The wave function is now obsolete in theoretical physics, being replaced by the bit function in binary mechanics which is superior, representing both position and momentum simultaneously. As such, the wave function is primarily of interest in the history of physics, not in state-of-art theoretical work.
http://www.binary-mechanics.com/2018/05/particle-flux-and-motion.html
I think the question is mixing several types of models. If "wave function" and fields are the model base, then "matter" or bodies (Newton) do not really belong - especially if the body and the field/wave function are to have ontological reality. "Point particles" in classical physics are the spherical property of bodies (the center of mass). The very concept of "mass" as a single characteristic of bodies is problematical. If one is to do the statistical approach (as all QM is), I like the de Broglie double solution approach over Copenhagen or Field Theory.
it is no matter. it is a mathematical object to calculate propabilities of physical objects like momentum, . coordinates. hence it is not only not a contradiction but it is absolutely necessary , that it is influenced by potentials, fields and forces. this is described by the schrödinger wave equation
The Schroedinger equation gives the wave function a certain interpretation but the square of the modulus of the wavefunction has a more general interpretation. That function is a location density distribution and it can be a description of the swarm of locations where the concerned object is located during a certain period. These locations are generated by a stochastic process whose production is stored in the eigenspace of a dedicated operator that resides in a quaternionic separable Hilbert space. The locations are archived in a chain of quaternionic eigenvalues that act as storage bins that contain a combination of a timestamp and a three-dimensional location. After sequencing the timestamps the chain represents an ongoing hopping path. The hop landing locations recurrently regenerate a coherent swarm of hop landing locations that can be described by the mentioned location density distribution. The stochastic process owns a characteristic function that equals the Fourier transform of the location density distribution. The characteristic function keeps the location density function and thus the wave function stable.
Stochastic processes that own a characteristic function occur in imaging processes and they occur in the embedding of elementary particles into the embedding universe field. A combination of a Poisson process and a binomial process that is implemented by a point spread function can represent such a stochastic process. The spatial point spread function then equals the mentioned location density distribution. The wavefunction thus relates to the footprint of the particle when it is embedded in the embedding universe field. If this embedding process deforms the embedding field, then the deformation corresponds to a gravitation potential and the gravitation potential corresponds to the mass of the particle.
More details are given in Preprint The Standard Model of Particle Physics and the Hilbert Repository
Hans van Leunen
"These locations are generated by a stochastic process whose production is stored in the eigenspace of a dedicated operator that resides in a quaternionic separable Hilbert space. The locations are archived in a chain of quaternionic eigenvalues that act as storage bins that contain a combination of a timestamp and a three-dimensional location."
And where is archived the chain? In a computer in the preparation lab? Then, when the hopping entity leaves the preparation lab, how does it succeed to continue to read the computer from the lab?
Moreover, after passing through devices, e.g. beam-splitters, the wave-function undergo changes. What is written in the computer in the lab is no more relevant? Where are archived these changes?
The answer I can think of is, the behavior of the jumping entity is controlled by the wave-function. So, the wave-function has to be a real thing. Especially in entanglements, the hopping entity has to be controlled by the wave-function.
If you have time please read
Deleted research item The research item mentioned here has been deleted
This article speaks EXACTLY of your idea, and of the necessity that the hopping item be limited and controlled by another item which exists in reality. I thought that this additional item should be the wave-function, a really existing wave.
the answer to your reply above was given by Kant long ago: the laws of nature are made by man-the psi function was constructed by men and it succeeds to describe nature in certain situations , in other not. there you need a quantum field. but all these objects are made by men in there brain, which describe asymptotically reality. so, the collapse of the wave function etc. are mankind constructs, that reflect a certain part of reality by describing it in our brain. they are not the reality by itself.
Hinnerk Albert
"the laws of nature are made by man - the psi function was constructed by men . . . in their brains . . . . so, the collapse of the wave function etc. are mankind constructs, that reflect a certain part of reality. They are not the reality by itself."
Albert, are you reality? With whom do I speak? Are you an invention of my mind?
Do you know the dictum :"dubito, cugito, ergo sum" ?
Also, the laws of the physics were made by God not by man. (If you prefer to eliminate the idea of God from science - I do prefer - it can be said that these laws resulted from an optimization of the types of interaction between entities in the universe, so as no contradiction appear. For instance, between two masses cannot exist both gravitational attraction and gravitational repulsion. A universe with self-contradictions, cannot exist.
About the laws of nature, do know know the concept "experiment"? We invent nothing, we do experiments and draw conclusions, which we express in the form of laws.
If we were those who invented the laws of the nature the universe could not exist, because the probability you, and I, and other billions of people, invent the same laws, is null. The laws invented by you would contradict the laws invented by others.
Dear Sofia, I believe human invented mathematics, a language, no different from other languages except that its formalisms are explicit and can be read by many different people that have other languages.
The humans choose mathematics as a way to describe how Nature works and different tools emerged toghether with their need. The old greeks only used classical geometry to have a good guess about the size of the Earth, in order to do this, Aristophanes had to know how the Sun light creates shadows.
Sofia D. Wechsler please rethink again, what Kant really meant and take some time, to do so.
Dear Hans, the problem I see with the view you exposed is that ergodic systems have no future, states are not distint, in this case samples matter to guess some property, they can be successive in time or distributed in space, it does not matter
My Dear Sofia D. Wechsler ,
I agree with you, the wave-function is a real thing, but mathematically speaking is not any wave function (like any Schrodinger wave) but it is a special wave function that we know by the name propagator (as in path integral formulation) and God willing we can derive from it statistically the other wave-functions (like stationary wave function and other) by applying the concept of "universal quantum jump", and we need to add some restriction to this propagator to not allow velocity greater than light.
With best regards.
Sofia D. Wechsler
About a century ago David Hilbert discovered that a special kind of vector space can archive dynamical geometric data. John von Neumann, who was the assistant of professor Hilbert gave this special vector space its name "Hilbert space". If space is a realistic object, then vector spaces and Hilbert spaces are also realistic objects.
Please investigate how space and pointlike objects interact. As long as space is only covered with a countable set of pointlike objects the combination acts as a set of discrete objects. This happens if the coverage is formed by a coordinate system that applies the rational numbers for enumerating the coordinate points. As soon as all irrational numbers are added as coordinate identifiers, then reality changes the behavior of the set and the combined medium becomes a sticky medium. Humans did not invent this. However, they used this fact by creating differential calculus because all series of converging coordinate points now end in a coordinate point. This makes the definition of the differential possible.
Differential calculus is not possible in the eigenspaces of operators in separable Hilbert spaces, but it is possible in the eigenspaces of non-separable Hilbert spaces. This enables mathematicians to model our living space, the universe, as a field that is maintained by a dedicated operator that resides in a non-separable Hilbert space.
If you deny the existence of the interaction of space and pointlike objects then you deny the existence of our living space.
Humans did not design the strange switch of the behavior of space when the set of covering pointlike objects switched from countable to uncountable. Try to put four lines mutually perpendicular. Still, vector spaces can have more than four dimensions. Who forbids you to put four lines mutually perpendicular? Reality or a mathematician?
I think not so. Actually its energy which may or may not be converted to matter
Vera Maura Fernandes de Lima
I cannot see why you conclude that ergodic systems have no future. On the other hand, the ongoing hopping path of elementary particles indicates that their footprint is recurrently regenerated. The strange fact is that the stochastic process that generates the hop landing locations takes care that the hop landing locations form a swarm that can be described by a very stable location density distribution. This location density distribution is the square of the modulus of the wavefunction of the particle. This wavefunction is commonly interpreted as representing the state of the particle.
Details are treated in https://www.researchgate.net/publication/350499950_The_Standard_Model_of_Particle_Physics_and_the_Hilbert_Repository
well, if one cannot distinguish samples averages from here to kingdom come, there is no change, no change, no time, no time no future
Wave functions are not of matter and do not bend and part of the wave-particle duality discovered by Albert Einstein. They are unobservable thus physically do not exist and are pure mathematical construction to which probabilistic numerical values are assigned in spacetime.
On the other hand,following Riemann and Dyson and Gross, all what is in math should exist in physics.Thus the unphysical wave function in our universe might be physical in another universe where every universe has its own cosmological constant based on Einstein's general relativity.
More details are given by Sean Carroll in this very short and interesting YouTube video
https://youtu.be/TUFC9V0sA_U
Dear Sofia, your questions animate me to think about QM again.Thanks - I quite enjoy it!
Issam Mohanna gave the answer in his first paragraph, the second paragraph I do not share. It is worth to remember the Heisenberg picture of QM based on matrices: dA/dt = i/hbar [H, A] + partialdA/partialdt. A is a matrix, here is no wave function needed! The wave function is only a trick to obtain a nice differential equation very similar to the familiar diffusion equation. The more general Quantum field theory is entirely based on equations for operators, there is no wave function as in Schrödingers QM (beside the trivial vacuum state |0> on which the operators act). How fields act on wave functions is nicely seen in the intriguing Aharanov-Bohm experiment. Wave functions describe matter but not only. In turn this indicates that mathematics and logics indeed is much larger than the math needed to describe the nature accessible to us. Fortunately ;-)
Dear Sofia D. Wechsler "Why is the wave-function bent when passing through fields?"
I would see it slightly different. The wave function is a eigen value solution of the energy operator. Solutions with or without external influence are different.
However, the solutions describe a charge and a matter density. These densities of course depend on inter atomic and external influence.
The quantum wave-function allows amongst others the description of phenomena such as quantum superposition and entanglement, where the energy of a particle cannot be understood as localized in a given spatial position or as a spatial wave.
A quantum wave-function is neither matter nor spatial.
In the context of quantum mechanics, we can describe the interaction of an electron with light such as in the framework of QED. However, the terms "bending" or "passing through fields" are interpretations framed within a spatial context, so we see the seeming contradiction between a classical and quantum description.
Note: to the question of how we can have an intuitive understanding rather than mathematical of how energy can exist without a spatial context, perhaps this might help (but it might be a little abstract):
1. First, one must recognize that all our visualizations are by nature spatial. However, if we negate all that is spatial then we are left with nothing to analyze and no understanding.
2. To gain insights a combination is required that first uses conceptuality and mental images to guide the logical reasoning, and on a second stage holds onto the meaning but let's go of that which is not physical.
Dear Gemma F. Lopez
I am pleased by your comment and agree that all our “visualizations” (actually “concepts”) are spatial. However, if we think about it there will be a moment that we realize that “spatial reality” exists only if its properties are representing a continuous change of energy. Every volume that is “truly” static cannot be observed because it cannot transfer electromagnetic waves and particles.
In our non-local universe it is the electric and corresponding magnetic field (together “electromagnetic field”) that is responsible for all the changes. Although the universal scalar field (Higgs field) can decrease and increase local scalars under influence of local concentrations of energy by the electromagnetic field.
In the universe all the changes of the electromagnetic field are conserved. It is known as the law of conservation of energy and the law of conservation of vectors (classic term is “momentum”). Actually, it shows that both conservation laws are limited to the basic properties of the electric and corresponding magnetic field. Showing that all the changes in the universe originate from the electromagnetic field. (Be aware that probability is also a kind of conservation law. Not the conservation of the total sum of changes but it is the conservation of the relations between the variables of the electromagnetic field.)
But if the wave-function doesn’t describe spatial properties or “matter properties" it must describe a mathematical relation between variables. Unfortunately the only variables are the basic properties of the electric and corresponding magnetic field.
So maybe we have to conclude that the wave-function is comparable with the classic "epicycle". A concept that functioned as a “help method” to calculate the observed motion of planets within the geocentric worldview. If this is true the consequence will be that quantum mechanics is only a limited approximation of physical reality.
With kind regards, Sydney
Sydney Ernest Grimm
Summary:
A model that considers the QM wave-function as characterizing a single, real wave in a field explains more observation in big and small realms than other models. Such a model allows significant additional attributes such as being Machian and ascribing cause-effect modeling.
You raise the issue of the reality of whatever the wave-function is measuring. For example, the "epicycle" concept may be viewed a early implementation of a several-term Fourier series where the circles are sine functions. The Ptolemy model of planet orbits was more accurate than the Copernican single-circle orbit model. The Copernican model required elliptical orbits and a shifted focus. It took the parallax (additional characteristic) measurements in the 1830s to finally adopt the Copernican model. So, today the use of the Fourier series in QM maybe just the calculation method that reflects a reality paradigm shift where cause-effect modeling may be invoked.
Like you, I postulate the "wave-function" is measuring a field. Unlike you I postulate there is only one (1) field and that the value at a coordinate point is determined by everything in the universe (a true Machian postulate). Then all other force fields are particular implementations of that 1 field.
I think my model (STOE) has to postulate that field is a real component of the universe. Real or not, only matter particles may trigger detectors (therefore, light is a particle which requires some special description). So this field ("plenum") is only indirectly measured.
There is a subtle concept here of a "field" - it's only a mathematical construct. But it geos to the heart of a fundamental characteristic of the universe and goes to the "structure" of the universe.
Article Scalar Theory of Everything (STOE) unites the big, the small...
https://www.youtube.com/watch?v=0YlJGdTvuTU&t=3s
Dear John Hodge
I don’t think that the wave-function represents “one single real wave”. Because a “real wave” is a composition of topological differences within/inside the spatial structure of the electromagnetic field. That means that the wave-function probably represents some kind of a “natural relation” between the topological differences within this field structure.
There is an indication that this is correct because electromagnetic waves are not only determined by the wave length. It shows that the “wave diameter” is half the wave length (see Montie, E., Cosman, E., 't Hooft, G. et al. “Observation of the optical analogue of quantized conductance of a point contact”. Nature 350, 594–595 (1991) https://doi.org/10.1038/350594a0).
The method of calculating orbits with the help of epicycles is impressive accurate. But the epicycles are not a “tangible” physical reality, it is a method to calculate “reality”. That’s why I compared the wave-function with the epicycle.
Actually, every mathematical method represents a simplification of reality. Because our universe shows to be a continuum too. That means that the mutual differences between imaginary “points in space” are infinite small, although the amount of change between “physical phenomena” is quantized (Planck’s constant).
By the way, I have watched your video but it takes some time to understand the new concepts.
With kind regards, Sydney
In the system of Hilbert spaces that all use the same underlying vector space the wave function gets a very clear explanation and origin. The square of its modulus is a location density distribution that describes the swarm of hop landing locations that are generated by an ongoing hop landing path. This is the path of a state vector that exists in the underlying vector space. The path is a string of combinations of timestamps and three-dimensional locations in the private parameter space of a separable Hilbert space. The location density distribution owns a Fourier transform. That is why the distribution can also be considered to be a wave package.
The system of Hilbert spaces archives all possible coverages of the vector space with locations that are identified by coordinate markers that correspond to members of a number system. The path of the state vector generates the stream of potential disturbances of the embedding continuum that is archived in the background platform,
See "Advanced Hilbert space Technology" in https://vixra.org/author/j_a_j_van_leunen
The wave function represents the location probability of point like charged and massive particles, which also may have a spin and a local kinetic energy. It is an approximation for a scalar field with the mentioned properties combined with a vector field for the kinetic energy flow and a tensor field for the flow of the spin.
The wave function is not bent by other fields. It simply depends on all fields, including the fields generated by the particles included in the wave function itself.
All elementary particles own a private wave function.
Learn more by reading "Our universe"; which explains the essence of our universe in https://vixra.org/author/j_a_j_van_leunen. The paper covers two pages.
Hans van Leunen "All elementary particles own a private wave function."
The existence of fields makes "privacy" obsolete. Far reaching interaction determines what is going on.
The problem with wave functions is that they are, well, functions that, in the case of a complex wave function, are only two dimensional, since there are only two axis, the real and the imaginary. Last time I checked physical reality had three spatial dimensions and therefore, Einstein and friends were right when they argued that the description of physical reality provided by quantum mechanics is incomplete:
https://en.wikipedia.org/wiki/EPR_paradox
Wave functions simply lack the required dimensionality in order to describe a three dimensional physical reality.
In order to come to a complete model, one needs to apply full 3D vector calculus and work with the vector LaPlace operator.
What I found is that full 3D vector fields similar to both Maxwell's as well as Navier-Stokes can be derived from a single equation (eq 20), leading to the conclusion that physical reality is governed by the quantum circulation constant nu rather than light speed c:
Preprint Revision and integration of Maxwell’s and Navier-Stokes’ Equ...
[a] = d[v]/dt = - nu nabla² [v],
As far as I know, this is the first time someone published an equation that can be written out into uniquely defined potential fields and results in two force density fields (L and R) that have units of measurement in Newton per cubic meter [N/m³].
This is the first time that someone described a primary field (nu [v]) of which the scalar and vector potential fields are the first spatial derivatives, while the force density fields are the second spatial derivatives thereof.
So far, I have not been able to find any equations out there that have uniquely defined potential fields, neither in QM nor in electrodynamics nor in fluid dynamics.
Actually, the vector LaPlace operator nabla² IS the very definition of the second spatial derivative and therefore the resulting Helmholtz decomposition into a curl-free component L and a divergence free component R is fundamental and the symmetry thus defined may therefore not be broken, as is done by the Maxwell-Faraday equation which is thus incorrect.
So, rather than attempting to describe a three dimensional physical reality using two dimensional wave functions, we should be working with three dimensional vector wave equations (eq. 3 in my paper).
The wave function is a force field with an energy density. The energy density quadratically depends on the field strength. If the wave function overlaps with an external field, the total field strength and with it the field energy density changes.
This wave function change manifests itself as if the wave function is becoming bent.
In the system of Hilbert spaces that all share the same underlying vector space, each member owns a footprint operator that archives the ongoing hop landing location path of its state vector. The expected value of the location of the state vector is the geometric center of the private parameter space of the Hilbert space. The hopping path recurrently regenerates a hop landing location swarm that is described by a stable location density distribution. This density distribution owns a Fourier transform and it equals the square of the modulus of what physicists would call the wave function of the particle that the Hilbert space represents. The state vector is a vector from the underlying vector space. It aims at the geometric center of the particle. The hopping path and the hop landing location swarm represent the blur of the aiming.
https://www.researchgate.net/publication/360423479_The_quaternionic_bra-ket_combination
Separable Hilbert space can only archive countable sets of numbers as the eigenspaces of their operators. Thus, the hop landing location distribution is not a field. It is a discrete set. The location density distribution describes this set,
matter influences matter (Earth & Moon)
wave influences wave ( interference pattern of light, gravitation field bend light path)
wave influences matter (Photo electric effect)
matter influences wave (The curvature of spacetime)
All you bend is probability density, which serves to guide a path..You reduce the field to the influence of the corresponding potential and calculate with S equation.
That is the QM answer.
Arend
Only the function is supposed complex, not the arguments, which may be three and include time. Most of the time the function may be taken real.
I disagree with the idea of a wave fuction to carry energ density. At any rate this does not agree with standard QM
In Dirac probability density is the sum of the square modulus of the 4 components.
The wave function is a solution of the Schrödinger - or Dirac equation. Those equations relate on the Hamiltonian. The Hamiltonian allows including external fields. Solutions of the equations with and without external fields are different.
This is the quantum mechanics explanation why the wave function gets bent by external fields.
The wavefunction is not a solution of the Schroedinger equation and is not a solution of the Dirac equation. It is not a solution to any differential equation. That does not mean that it cannot be differentiated. The best interpretation of the wave equation is that the square of its modulus is a location density distribution. The location density distribution describes the production of a stochastic process. The stochastic process generates an ongoing hopping path. The hop landings of this hopping path recurrently regenerate a hop landing location swarm. The location density distribution is a continuous function that closely describes the location density of this swarm. The stochastic process is controlled by a characteristic function, which is the Fourier transform of the location density distribution. This represents a delicate cooperation between discrete distributions and continuous distributions. This cooperation is not controlled by a differential equation. The stochastic process is an imaging process. The imaging accuracy is qualified by the optical transfer function. This OTF is the Fourier transform of the point spread function. This PSF equals the location density distribution. The focus of the imaging process is the geometrical center of the corresponding particle.
The Hamiltonian and the Lagrangian are based on the least action principle. The least action principle is another way to characterize an imaging process. Imaging and embedding are closely related processes. Lately, the least action principle is called the stationary action principle. This corresponds with the fact that the location density distribution tends to be a stable function.
The wavefunction is a confusing name. It does not describe a wave or wave package. At the utmost, it indicates that the hop landing location swarm can simulate a wave or wave package.
Hans van Leunen "The wavefunction is not a solution of the Schroedinger equation"
What do you think, how a solution of the Schroedinger equation is called in quantum mechanics.?
"The wavefunction is a confusing name. It does not describe a wave or wave package. At the utmost, it indicates that the hop landing location swarm can simulate a wave or wave package."
Sorry, but "hop landing location swarm" is not a term used in quantum mechanics.
Quantum mechanics is the name of the interpretation by theoretical physicists of the results of experimental particle physicists. The wavefunction is a central concept in this interpretation. The fact that this name appears to be a misnomer does not matter for the truth of the situation. Quantum physics does not provide a better name. This does not mean that this makes the name wavefunction disrepute. The wavefunction acts as a descriptor of the production of a stochastic process and not as a solution to a differential equation. It has little relation to waves or wave packages. The name was given because the stochastic process could simulate interferences that looked like waves or wave packages. The process produced point-like objects that could also be interpreted as particles. This resulted in the wave-particle duality.
The situation indicates that physicists still do not comprehend much about stochastic processes and the delicate relation between stochastic processes and continuous descriptors. Imaging processes in low-dose conditions feature the typical behavior that characterizes quantum physics.
Night vision devices and X-ray imaging devices typically work in these conditions. There you can see the stochastic processes at work. Go looking at an image intensifier device that works under low-dose conditions and you get an impression of the typical behavior of the quantum world.
See: http://www.e-physics.eu/#_What_image_intensifiers reveal
The confusion with waves and wave packages may be because, in conglomerates of elementary fermions, the oscillations of components play a prominent role. Oscillations play no role in the first-generation elementary fermions.
X-rays and visible light photons are not elementary particles. They are not represented by a private separable Hilbert space like the elementary fermions. Electrons are first-generation elementary fermions.
The system of Hilbert spaces that all share the same underlying vector space is derived without introducing the interpretation of the wavefunction. So, the relation between the system of Hilbert systems and the Standard Model of the experimental particle physicists already stands without introducing the wave function and without touching uncertainty. The system of Hilbert spaces already explains the existence of electric charges and the carriers of these charges, the elementary fermions. The stochastic process behind the wave function is essential for the existence of gravity.
Hans van Leunen “The system of Hilbert spaces already explains the existence of electric charges and the carriers of these charges, the elementary fermions. The stochastic process behind the wave function is essential for the existence of gravity.”
Sorry to say this, but Hilbert spaces have nothing to do with the existence of electric charges. Being surrounded by electric field energy is an intrinsic property of elementary particles. The same holds for gravitational field energy. The wave function and the Hilbert space are mathematical concepts, which are useful in many aspects, except explaining the existence of electric charges and gravity.
Currently physics has no explanation why matter exists. Using Hilbert spaces and wave functions to solve such a fundamental problem is ridiculous.
Wolfgang Konle
The system of Hilbert spaces that all share the same underlying vector space shows an astonishing correspondence in their shortlist of properties with the elementary fermions that are described in the Standard Model of experimental particle physicists. The shortlist concerns electric charges in the Standard Model and concerns symmetry differences in the system of Hilbert spaces. If the correspondence is taken seriously, then also the Higgs object must be reconsidered. In the system of Hilbert spaces, its role is a background platform and not a moving particle. In reality, it plays the role of our dynamic universe field.
Dear Sirs,
As I understood in the Everett's multi world interpretation absolute square of wave function is not a probability distribution. It is similar to classical physical field, for example like electric field, gravity waves at water surface, acoustic waves, etc. For example in the double slit experiment an electron is simultaneously observed in all points of screen by a single observer who is in different quantum states. It is supposed that human can "sense" only the one quantum state. For example it is similar to our vision ability: our brain and eyes only sense quite limited range of electromagnetic spectrum.
But to tell the truth I did not see any articles which describe rigorously double slit experiment in Everett's interpretation. I would be grateful if you give the article references.
Dear Anatoly,
I am sending to you not finished work (it will be published later in one respectful magazine.) It is all about very unconventional replacement of common quantum mechanics.
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