Andre Lefebvre Posted July 23, 2015 Author Posted July 23, 2015 (edited) You really don't know what any of these words mean, do you. But now I know thanks to you Strange; and I thank you sincerely very much. So where I wrote "topology", it's geodesic and where I wrote "geodesic" it's topology. Great". That's one thing that is settled. (By the way; it's throw not throe) But it doesn't change the picture. Edited July 23, 2015 by Andre Lefebvre
ajb Posted July 24, 2015 Posted July 24, 2015 Andre, so your last post explains why I am lost. What is a topology and what 'species' of topology are you equipping space-time with? (Hint, one usually thinks of the Alexandrov topology induced by the causal structure.)
Andre Lefebvre Posted July 24, 2015 Author Posted July 24, 2015 (edited) ajb What is a topology and what 'species' of topology are you equipping space-time with? The topology that is created by stopping a point of the expanding universe while the surrounding points keep on expanding to a ratio of their distance from the said blocked point. So that topology is made at the level of the metric of space-time. It's not a "downward" topology it's a "collapsing" topology. That is why when an object travels through that topology, its geodesic (trajectory) is gradually deflected toward the "blocked point» (center of gravity) and when it passes that point, is deflected from it (see the graphic higher). It's not a geometric "fall", it's a "dimensional" fall. Mordred The shortest path is a geodesic. Geodesics are defined by the principle of least action. When I had people working for me that wanted to make the least action, I sent them home; when I had an employee that did a work the easiest, the simplest and the fastest way it could be done, I gave him a raise. I'd say that geodesic is defined by the shortest path; the action involved is only a consequence. Your not going to be able to avoid the energy density relations of curvature It won't be easy, I agree; but a lot easier, for me, than to conceiving that energy is a consequence (do not exist on its own), gravity is a "force" (instead of a consequence of geometry deformation) or that the universe doesn't have a base length when Plancks length is the smallest length possible that can be measured (which, in reality, means "can exist"). Without mentioning the opinion that the radiation of a massless particle traveling at the speed of light in a volume that doesn't have any existing circumference can produce pressure. So I'm pretty confident. According to Einstein's theory of general relativity, energy curves space-time. This suggests that at sufficiently small scales the energy of these fluctuations would be large enough to cause significant departures from the smooth space-time seen at larger scales, giving space-time a "foamy" character." Energy curves space-time; I agree; but not any kind of energy; mass energy. In Einstein equation E = Mc2 . It's Mc2 that is mass energy. E is kinetic energy. And none of the sides of equation is "at rest". At sufficiently small scale, you're talking of Plancks length (at Plancks time), where you imagine a flat surface of energy in a graduated glass box, where that energy is animated with "fluctuations". When the energy is at, what you call, "rest", it's placed at zero "thickness" in the graduated box. You don't even see it means a two dimensional surface. Then you "activate" the fluctuation and for you that "zero thickness" acquires some thickness because it fluctuates up and down in the graduated glass box, Waves on a lake "fluctuate"; but a wave doesn't have any thickness; it's a two dimensional "surface". So, in your mind, before starting to expand in all directions, your fluctuating energy at Plancks time was a "surface"; a two dimensional "foamy character", that existed on its own at that time, but doesn't anymore exists on its own, when it doesn't suit you affterward. And I'm an ignorant because I don't accept all that lack of logic? Edited July 24, 2015 by Andre Lefebvre
Strange Posted July 24, 2015 Posted July 24, 2015 Energy curves space-time; I agree; but not any kind of energy; mass energy. Again, you are wrong. Any form of energy (and mass, and momentum and pressure, ...) contribute to space-time curvature. Of course, if you have an alternative theory, you could show us the maths ... In Einstein equation E = Mc2 . It's Mc2 that is mass energy. E is kinetic energy. And none of the sides of equation is "at rest". E is not (necessarily) kinetic energy and it is, by definition the same as Mc2. And this is the equation relating rest mass and energy. If you want to consider things that are not at rest, then you need the full form of the equation. (But you knew that, right?)
Mordred Posted July 24, 2015 Posted July 24, 2015 (edited) Photons have no "rest mass" they do have momentum. If you don't believe photons can cause pressure then explain how optical tweezers work. They do use laser beams to move bacteria etc. What about solar sails? https://en.m.wikipedia.org/wiki/Optical_tweezers The problem is just because something doesn't make sense to you. You assume it's wrong. News flash it makes sense to those that studied it in enough detail and I'm an ignorant because I don't accept all that lack of logic?[/size][/font]What you accept doesn't matter, Scientists around the globe accept the experimental evidence to support any theory. Not intuition, or personal logic. No theory is ever accepted enough to become concordance, without extensive experimental evidence. For example none of Einstein's theories was fully accepted when he first published them. The experimental tests that came later validated them. Time dilation isn't easy to accept. LCDM wasn't accepted at first glance either, there were at one time over 30 competing varients to it prior to WMAP and Planck data. LCDM was found to be the best fit, to observational data. Killing models such as CHDM, trespace, MOND, Spin-Torsion model by Poplowskii, LHDM, etc, the Ekryptotic model is taking big hits due to Planck. QM took a big hit when it was determined that the formula [latex]E=\frac{\hbar w}{2}[/latex] Which relates to your quantum foam leads to 120 orders of magnitude too much energy. Then a second hit with that link showing the tests for quantum foam. Nowadays it's no longer considered in its original form and has been adapted to spin foam by LQC. As far as inflation goes, none of the original inflation models are currently considered good fits. This includes chaotic eternal inflation. They suffer from "Runaway inflation". The encyclopedia Inflationaris dropped chaotic eternal inflation as being a good fit in its last update. It was included in previous versions. The last two Planck data sets support single scalar inflationary models. This could potentially narrow down 70+ viable models down to a mere 7. particle entanglement wasn't accepted at first either, now we have particle entanglement diodes. http://www.toshiba.eu/eu/Cambridge-Research-Laboratory/Quantum-Information-Group/Quantum-Information-Group-Publications/ they also have a single photon detector, called a quantum dot detector. As far as light being made up of photons, we can image the separate particles and show the wave particle duality. http://www.iflscience.com/physics/researchers-image-wave-particle-duality-light-first-time-ever The pop media version doesn't properly explain how it was done. http://www.nature.com/ncomms/2015/150302/ncomms7407/full/ncomms7407.html?utm_source=dlvr.it&utm_medium=tumblr Here is the paper. Edited July 24, 2015 by Mordred 2
Andre Lefebvre Posted July 24, 2015 Author Posted July 24, 2015 f you don't believe photons can cause pressure then explain how optical tweezers work. They do use laser beams to move bacteria etc. What about solar sails? I don't see how momentum without mass can deform space-time. It can make "pressure" where it "strikes" but before "striking" something, I can't see that it has any effect. But I'll check don't worry; I started already but didn't find either production or not of gravity yet. What you accept doesn't matter, Scientists around the globe accept the experimental evidence to support any theory. Not intuition, or personal logic. So all I am allowed to do is fall on my knees and say "Alleluia!" To many people do that already. No theory is ever accepted enough to become concordance, without extensive experimental evidence. Who wants to be accepted here as a “know it all”? I make suggestions only. I know …without mathematic; but only suggestions just the same. I hope being able to add maths someday. For example none of Einstein's theories was fully accepted when he first published them. GR is not even accepted now. Gravity is not accepted as a "consequence of space-time deformation; it's still a "farce", sorry a “force” called "interaction", when a deformed space-time cannot interACT. It's "passive. LCDM was found to be the best fit, to observational data. It's the DM I don't like. : Usually, people see what they want to see. Being objective when interest is at stake is difficult. Nowadays it's no longer considered in its original form and has been adapted to spin foam by LQC. But it's still foam And since energy doesn't exist on its own, our universe is made of foam. As far as inflation goes, none of the original inflation models are currently considered good fits. This includes chaotic eternal inflation. They suffer from "Runaway inflation". I don't know what "runaway inflation" is (probably as "uncontrolled") but I'll check. As for current inflation models, I agree they don't fit because you don't need it to make the universe flat. It's flat since the beginning; that radiative epoch. I have enormous gratitude toward you Mordred. I appreciate your comments and descriptions a lot; including all the links with information. You're one of the best if not the best. Thanks a lot.
Strange Posted July 24, 2015 Posted July 24, 2015 I don't see how momentum without mass can deform space-time. That is the trouble with relying on intuition rather than the maths. So all I am allowed to do is fall on my knees and say "Alleluia!" To many people do that already. No. You could study the theory and supporting evidence. GR is not even accepted now. Do you have any evidence for that claim? Any peer reviewed papers or experiments that show GR is incorrect?
Mordred Posted July 24, 2015 Posted July 24, 2015 (edited) I don't see how momentum without mass can deform space-time. It can make "pressure" where it "strikes" but before "striking" something, I can't see that it has any effect. But I'll check don't worry; I started already but didn't find either production or not of gravity yet. It's the DM I don't like. : Usually, people see what they want to see. Being objective when interest is at stake is difficult. But it's still foam And since energy doesn't exist on its own, our universe is made of foam. I don't know what "runaway inflation" is (probably as "uncontrolled") but I'll check. As for current inflation models, I agree they don't fit because you don't need it to make the universe flat. It's flat since the beginning; that radiative epoch. Don't be mislead the term foam is only describing the probability amplitude shape. It's not a material thing but how a particles position changes in a given moment of time. [latex]\psi_0(x,t)[/latex] [latex]\psi [/latex] is the probability amplitude. The Schrodinger wave functions gives the probability of locations for a particles position at all times. This is what spin foam is also describing. Or rather more accurately its describing the Hamiltonian of action. in terms of moment action of lie groups and their degrees of freedom. Such as the U(1) group. Think of it as probability maps. As these moment maps involve Euler Langrene I'll include that. [latex]\frac{\partial L}{\partial x} - \frac{d}{dt} \frac{\partial L}{\partial \dot{x}} = 0[/latex]. https://en.m.wikipedia.org/wiki/Action_(physics) Spin foam isn't a material thing just another modelling system. Gotta love these catchy catchy names. They always mislead the public Very few people readily accept DM and DE, your not alone in that crowd. The problem is observational evidence strongly supports them both. You keep missing the part... a photon has no rest mass.( invarient mass). It has a total energy equivalent to inertial mass. [latex] E^2-(pc)^2=(mc)^2[/latex] [latex]e=mc^2[/latex] is only valid for particles at rest. Mass isn't an absolute value how one measures mass is OBSERVER dependant just as how one measures energy is OBSERVER dependant. Or how one measures wavelength is also observer dependant. Look closely at the relations between wavelength and energy. [latex]\frac{\Delta_f}{f} = \frac{\lambda}{\lambda_o} = \frac{v}{c}=\frac{E_o}{E}=\frac{hc}{\lambda_o} \frac{\lambda}{hc}[/latex] Cosmological redshift is given by. [latex]1+Z=\frac{\lambda}{\lambda_o} or 1+Z=\frac{\lambda-\lambda_o}{\lambda_o}[/latex] Gravitation redshift by. [latex]\frac{\lambda}{\lambda_o}=\frac{1}{\sqrt{(1 - \frac{2GM}{r c^2})}}[/latex] Doppler redshift is [latex]f=\frac{c+v_r}{c+v_s}f_o[/latex] Edited July 25, 2015 by Mordred
Andre Lefebvre Posted July 25, 2015 Author Posted July 25, 2015 Mass isn't an absolute value how one measures mass is OBSERVER dependant just as how one measures energy is OBSERVER dependant. And movement is observer dependant and speed is observer dependant; I understand this and I also understand that this is the notion behind all actual physic. That is why I will need to know mathematics. But we have to accept the fact that the observer sees something which doesn't come out of is elucubrations. But let's talk about where, I think, this way of seeing things started. Galileo, in the bottom of a boat, started pouring whatever, in a cup while the boat was at sea. He remarked that the pouring was occurring as if the boat was not moving. My question is: Was the damn boat moving? My answer is yes it was. And his observation didn’t mean that it was not. So I always take care when an observer makes me a report even with mathematical proof. Imagine what I think when an observer says: “I didn't see it but it smelled like if what we're looking for was there”. Very few people readily accept DM and DE, your not alone in that crowd.The problem is observational evidence strongly supports them both. And it's going to do so until somebody finds out what mass is and where it is from. Mass is not given to a particle because it's slowed down by a dense crowd at a party.
Mordred Posted July 25, 2015 Posted July 25, 2015 (edited) And movement is observer dependant and speed is observer dependant; I understand this and I also understand that this is the notion behind all actual physic. That is why I will need to know mathematics. But we have to accept the fact that the observer sees something which doesn't come out of is elucubrations. But let's talk about where, I think, this way of seeing things started. Galileo, in the bottom of a boat, started pouring whatever, in a cup while the boat was at sea. He remarked that the pouring was occurring as if the boat was not moving. My question is: Was the damn boat moving? My answer is yes it was. And his observation didnt mean that it was not. So I always take care when an observer makes me a report even with mathematical proof. Imagine what I think when an observer says: I didn't see it but it smelled like if what we're looking for was there. And it's going to do so until somebody finds out what mass is and where it is from. Mass is not given to a particle because it's slowed down by a dense crowd at a party. What makes you so positive mass is a thing? It's a measured property. Just like length or depth are measured properties. You keep trying to make substance out of properties. Properties are not things with its own substance. Neither are relations of interactions This includes force, or charge, color, flavor, Spin foam, spacetime. Time, volume, entropy. They are measured properties, and measured relations not Things. The sooner you learn that the better, measurements are observer dependant. This is the understanding GR gave us. space is volume, volume is a property Time is a property of rate of change/duration. The relation between two properties don't make a thing of some mysterious MATERIAL. Energy is a property, mass is a property. They don't exist without having something to measure. They also cannot be separated from each other, as mass requires energy. Just like temperature requires density and interactions I would have thought the ideal gas laws would have taught you that properties can often depend on other properties. Measurable properties of particles Mass/energy Frequency Charge,color,flavor isospin parity Spin Decays Products Lifetime Scattering Cross-section Resonance Resonance width and lifetime Perhaps you need to study a list of properties https://en.m.wikipedia.org/wiki/Physical_property Edited July 25, 2015 by Mordred
Andre Lefebvre Posted July 25, 2015 Author Posted July 25, 2015 (edited) What makes you so positive mass is a thing? It's a measured property. Mass is not a thing; mass is an amount of motion energy trapped in a topology whose geodesic sends the energy to one specific center point. The pressure on that point stops its expansion movement deforming the space around it because the other points are slowed gradually up to a certain distance around that point. That's how a deformation of space-time is caused. I think. Here's how it looks: This includes force, or charge, color, flavor, Spin foam, spacetime. Time, volume, entropy. They are measured properties, and measured relations not Things. I understand that. So what is the universe? The sooner you learn that the better, all measurements are observer dependant. This is the understanding GR gave us. And it's a great tool to work with; but the tool is not the universe. It's something to understand things behind the observations made with that tool. Let's say that I agree that the gluon mediate the strong nuclear force. That force is observer dependant. Would you agree that it's possible that the action field of a gluon as a geodesic directing everything to its center which would explain that observed "glue" characteristic that observers call the nuclear strong force? The relation between two properties don't make a thing of some mysterious MATERIAL. Nothing is material, everything is energy's expression; including quantity of matter. Energy is a property, mass is a property. They don't exist without having something to measure. That's for an observer point of view. If there's no observer (everybody is dead after a cataclysm) will you say that energy or mass don't exist? I would have thought the ideal gas laws would have taught you that properties can often depend on other properties. That's not very hard to understand. What is harder to understand is that those properties apply to nothing (no things). Perhaps you need to study a list of properties That link is interesting; I'll search further o the subject. Thank you. Edited July 25, 2015 by Andre Lefebvre
Mordred Posted July 25, 2015 Posted July 25, 2015 (edited) Nothing is material, everything is energy's expression; including quantity of matter. Why does your image include fabric??? " blocked point of universes fabric." This is precisely the type of terminology I've been consistently correcting you on. Secondly mass is resistance to inertia. Period. If you ever want or hope to learn the mathematics. You need to use and understand the terminology association's with those mathematics. Particularly if you ever want to learn Hamilton and how it correlates to "action and moment mapping. Both of which are involved in the LQC approach. Mass is not a thing; mass is an amount of motion energy trapped in a topology whose geodesic sends the energy to one specific center point. The pressure on that point stops its expansion movement deforming the space around it because the other points are slowed gradually up to a certain distance around that point. That's how a deformation of space-time is caused. What kind of motion? What is causing the pressure? Is pressure the only factor? What about shear stress? What about energy/mass density? Why does it take more energy to move more massive objects and change its velocity? Yet they both fall at the same rate? Why do certain particles react to some energy fields but not others? How would kinetic energy account for this? Why have you never included the term " potential energy"? Why do certain particles exhibit electromagnetic properties but others don't? Why is it when you move two quarks farther apart the strength of attraction between them increases and doesn't decrease such as in gravity or electromagnetism.? Why does gravity exhibit spin 2 characteristics while the Higgs field is spin zero, the photon spin (electromagnetic) spin 1 while fermions are fractional spin? What spin would kinetic energy be? When you throw a ball, is it following a geodesic? These are questions that the standard models can answer. Can your model do so? How is observer defined, why does a wavefunction collapse when observed? QM. "In quantum mechanics, wave function collapse is said to occur when a wave function initially in a superposition of several eigenstates appears to reduce to a single eigenstate (by "observation" How is observer defined in this case? Why does the Heisenberg uncertainty principle states that the position and the velocity of an object cannot both be measured exactly, at the same time, even in theory. ? How does this relate to your spin foam via the Schrodinger formulas. ? The problem is you keep trying to redesign physics to suit yourself when you don't have a solid grasp of the basics. As such you keep using incorrect terminology and jumping to conclusions. Which the materials I supplied should have corrected. ( a vast majority of my posts have been terminology corrections) As such the quoted section reads as a word salad. The vector directions are off, with the way you described it. Mass is not a thing; mass is an amount of motion energy trapped in a topology whose geodesic sends the energy to one specific center point. The pressure on that point stops its expansion movement deforming the space around it How do you deform a volume ? Don't you mean the pressure on a point stop its compression, not expansion. Edited July 25, 2015 by Mordred
ajb Posted July 25, 2015 Posted July 25, 2015 (edited) I don't see how momentum without mass can deform space-time. It can make "pressure" where it "strikes" but before "striking" something, I can't see that it has any effect. But I'll check don't worry; I started already but didn't find either production or not of gravity yet. The problem is, as already pointed out, you are trying to rely on Newtonian-like intuition rather than examining the mathematics. You then 'pepper' this with some mathematics terms that you use very loosely of incorrectly. This produces lots of confusion. To 'see' how energy-momentum effects the local geometry you need to examine Einstein's field equations. To understand the topology here, you need to at least have an idea what a topology is before moving onto more advanced ideas of the causal structure of space-time and topology. It is all hard work, by it is the only way you will get some understanding. Galileo, in the bottom of a boat, started pouring whatever, in a cup while the boat was at sea. He remarked that the pouring was occurring as if the boat was not moving.[/size] My question is: Was the damn boat moving?[/size] With respect to what? My answer is yes it was. And his observation didn’t mean that it was not. So I always take care when an observer makes me a report even with mathematical proof. [/size] Take more care here. The point is that provided the ship was at constant velocity relative to the seabed (or some other fixed point like an Island) and Galileo only preformed local experiments, that is 'did not look out of the porthole', he could not determine if the ship is in motion with respect to the said fixed points. This means that there is no absolute notion of motion (at constant velocity anyway). Mass is not a thing; mass is an amount of motion energy trapped in a topology whose geodesic sends the energy to one specific center point. The pressure on that point stops its expansion movement deforming the space around it because the other points are slowed gradually up to a certain distance around that point. That's how a deformation of space-time is caused. I think. Please read what I wrote once more. Edited July 25, 2015 by ajb 1
Andre Lefebvre Posted July 25, 2015 Author Posted July 25, 2015 (edited) Why does your image include fabric??? " blocked point of universes fabric." Because the universe is Euclidean and Euclidean volume are made of unidimensional points which forms it's "fabric". If I want to be logical, I cannot make geodesic as a consequence of the direction of movement; I have to give direction to movement with something that exist somewhere before that movement is manifested. And the only possibility is that to imprint it in the basic component of universe which is formed by the unidimensional Euclidean points. This is what I call the "fabric" of the universe. They are the basic components of Euclidean geometry. Secondly mass is resistance to inertia. Period. Well If I stop at that "Period", I don't have problem. But if I try to get the notion of mass versus inertia, problems start: 1)Inertia is one of the primary manifestations of mass, which is a quantitative property of physical systems. Isaac Newton defined inertia as his first law: “The vis insita, or innate force of matter, is a power of resisting by which every body, as much as in it lies, endeavours to preserve its present state, whether it be of rest or of moving uniformly forward in a straight line.” 2)Einstein proceeded to develop his general theory of relativity which ultimately provided a unified theory for both inertial and noninertial (accelerated) reference frames. However, in order to accomplish this, in general relativity Einstein found it necessary to redefine several fundamental concepts (such as gravity) in terms of a new concept of "curvature" of space-time, instead of the more traditional system of forces understood by Newton. As a result of this redefinition, Einstein also redefined the concept of "inertia" in terms of geodesic deviation instead, with some subtle but significant additional implications. 3)In general relativity, geodesic deviation describes the tendency of objects to approach or recede from one another while moving under the influence of a spatially varying gravitational field. 4)But mass, as related to the 'inertia' of a body, can also be defined by the formula: (It didn't copy!!!) Here, F is force, m is inertial mass, and a is acceleration. By this formula, the greater its mass, the less a body accelerates under given force. Masses defined by formula (1) and (2) are equal because formula (2) is a consequence of formula (1) if mass does not depend on time and velocity. Thus, "mass is the quantitative or numerical measure of a body’s inertia, that is of its resistance to being accelerated". 5)There is no measurable difference between gravitational mass and inertial mass. The gravitational mass is defined by the quantity of gravitational field material a mass possesses, including its energy. The "inertial mass" (relativistic mass) is a function of the acceleration a mass has undergone and its resultant speed. 6)At high speeds, relativistic mass always exceeds gravitational mass. If the mass is made to travel close to the speed of light, its "inertial mass" (relativistic) as observed from a stationary frame would be very great while its gravitational mass would remain at its rest value, but the gravitational effect of the extra energy would exactly balance the measured increase in inertial mass. Now I gues I'll need a lot of studying to match your "mass is resistance to inertia" to those six definitions. It looks to me, that mass is not something very specific in physics. What kind of motion? I love that list of question you made. I’ll work on it in the next days and give you all the answers next week. And I'll try to use the correct terminology; so I'll have to make quite a lot of verifications. But those questions are what I needed. Thanks. How do you deform a volume ?Don't you mean the pressure on a point stop its compression, not expansion. No. I mean expansion. At the moment the "pressure" is applied to the point, there's no deformation at all. The deformation appears gradually while expansion continues. The expansion gradually defines the deformed volume. The deformation is a gradual developing consequence of blocking a point during the expansion of surrounding space. It doesn't appear instantly; it forms gradually until the resistance of the point that was stopped is equalized by the intensity of the space-time deformation (we can see it as a dilution of the effect). Then the size of the deformed space-time stops increasing. That pressure on the point I'm talking about is "mass energy". To 'see' how energy-momentum effects the local geometry you need to examine Einstein's field equations. I will. I hope those field equations are not based on "gravitational force" but on deformation of space-time. To understand the topology here, you need to at least have an idea what a topology is before moving onto more advanced ideas Now if topology is not the "picture" of a volume of deformed space-time, I'll start to make my own vocabulary!!! And if geodesic is not the trajectory of an object in regard to its velocity inside this topology, I quit trying to use physics terms. I hate talking with "blurred meaning" of words. "Mass" is enough for now. My question is: Was the damn boat moving?[/size] With respect to what? With respect to "reality". We are not "dreaming" the universe; we are living in it and occupying a portion of its space during a certain time lap. This means that there is no absolute notion of motion (at constant velocity anyway). No absolute "notion" of motion , maybe; but it means (with GR) that there's not absolute "immobility (at rest) definitly. Please read what I wrote once more. I will; and by the same time I'll check if I already explained how mass appeared in our universe at 10-36 sec; which will supply the last information regarding the space-time deformations we just talked about. Everything is related; we can't cut the universe in pieces to analyse it. Edited July 25, 2015 by Andre Lefebvre
Mordred Posted July 25, 2015 Posted July 25, 2015 (edited) My point is when you apply pressure to a point you have compression. If the pressure is going from a point radiating outward you have expansion. Positive pressure is commonly used in the first case, negative pressure in the latter case. Now here is the problem with using just pressure to try and define gravity. The amount of pressure exerted by different particle species vary. Relativistic radiation (photons, neutrinos) exert more pressure than dust. (Dust =protons,neutrons etc) matter. In point of detail matter has extremely negligible pressure influence. So to use a more accurate terminology to describe curvature use the terms mass/energy density. This way the particle species variations are accounted for. Remember space time curvature is a measure of energy/mass gradient. Yes this cause pressure gradients as well albeit by differing amounts depending on the state being described and the particle contributors. You are starting to realize mass is a relative measurement. So I'll let you study that in greater detail. It's extremely important in kinematics. Later on I'll describe 10-43 seconds for you to provide you with a solid example on terminlogy and math. I need time to properly formulate that section I won't try to cover prior to 10-43 seconds as that would be based on speculation. Edited July 25, 2015 by Mordred
Mordred Posted July 26, 2015 Posted July 26, 2015 Thanks mordred. Just be prepared, Just covering that will take some prep work.
ajb Posted July 26, 2015 Posted July 26, 2015 I will. I hope those field equations are not based on "gravitational force" but on deformation of space-time. The equations basically say 'local geometry = matter or field content'. There is no direct 'force' in this description. Force appears via the geodesic equation; the effect of gravity is seen by test particles following geodesics.. Now if topology is not the "picture" of a volume of deformed space-time, I'll start to make my own vocabulary!!! They maybe related, but your picture is not a definition of a topology. You can get some idea just from quick google. And if geodesic is not the trajectory of an object in regard to its velocity inside this topology, I quit trying to use physics terms. If we are just discussing local geodesics, then we are not worried about the topology, which is really the global shape of the space-time (but you need to make this a proper mathematical statement). Geodesics are the shortest paths between two points on space-time. I hate talking with "blurred meaning" of words. "Mass" is enough for now. This is the problem hijacking maths and physics terms without some understanding of what they really mean. With respect to "reality". What is reality other than what we can measure? Who says that one persons perspective is better than another's? The whole point of relativity is that all points of view are equally valid, even when they seem to disagree. One just has to be very careful with 'respect to what'; which is really just a choice of coordinate systems in which to describe the physics. No absolute "notion" of motion , maybe; but it means (with GR) that there's not absolute "immobility (at rest) definitly. This is true. You do not have absolute motion (at constant velocity) and so you cannot have absolute rest. All these things are relative to some choices you have made.
Andre Lefebvre Posted July 26, 2015 Author Posted July 26, 2015 (edited) All these things are relative to some choices you have made. This is where I fall on my knees in front of my own picture: If I'm not there to observe and measure, the universe doesn't exist. I'm a man that needs a fork, a knife, a tea spoon and a tablespoon to eat whatever I want. And now, to talk physics, I feel as if I'm invited to an aristocratic dinner where there are four different forks, five knives, and six kind of spoon around my plate. I'm ready to learn what to do with each; but it's even worse than that; because if I ask what are we having for dinner? I'm answered: "It depends of the cutlery we'll have around our plate". Either, it's too serious or it's not serious at all. I'll wait to make up my mind. Edited July 26, 2015 by Andre Lefebvre
Mordred Posted July 26, 2015 Posted July 26, 2015 (edited) This is where I fall on my knees in front of my own picture: If I'm not there to observe and measure, the universe doesn't exist. The universe doesn't care how we measure it and it will exist long after were gone. The problem is how we measure the universe must match observable data. That data includes observer influences such as redshift, Let's put it another way. The problem isn't with your idea of kinetic energy being involved. In fact one can model Early universe dynamics using kinetic energy. However you also require potential energy. The methods involving both are numerous. In the FLRW metric one can use the scalar equation of state. [math]w = \frac{\frac{1}{2}\dot{\phi}^2 - V(\phi)}{\frac{1}{2}\dot{\phi}^2 + V(\phi)} .[/math] [latex]\dot{\phi}[/latex] is kinetic energy the dot is a derivative of time. [latex]V\phi[/latex] is potential energy. The above works when comparing vacuum energy density regions, inflation uses the above. However the above deals strictly with scalar values, does nothing to define momentum and vectors. When you include radiation you want to use the equation of state for relativistic radiation. https://en.m.wikipedia.org/wiki/Equation_of_state_(cosmology) The FLRW metric already defined a homogeneous and isotropic fluid. now to add vectors one useful tool that works well with the EFE is the variational principle. This also leads to how geodesics are defined. Via the principle of least action.. This will take me a bit to latex lol bear with me. Variational Principle. A particle with position [latex]\overrightarrow{x}[/latex] in a gravitational field is associated with a kinetic energy [latex]\frac{1}{2}m\dot{x}^2[/latex] and potential energy [latex]-mg\dot{x}[/latex] the difference between the two is called the Langrangian [latex]\L(\overrightarrow{x},\dot{\overrightarrow{x}})[/latex] We can integrate the Langrange along the trajectory of the particle [latex]\gamma[/latex] to form the action [latex]S=\int_{\gamma}dt\L=\int_{\gamma}dt(\frac{1}{2}m\dot{\overrightarrow{x}}^2+mg\overrightarrow{x})[/latex] The equation of motion is obtained by finding the stationary point of the action [latex]\delta S=0[/latex] This gives rise to the Euler-Langrange equation. [latex]\frac{\partial\L}{\partial\overrightarrow{x}}=\frac{d}{dt}\frac{\partial\L}{\partial\dot{\overrightarrow{x}}}[/latex] There I've provided some direction on how you can go about defining your model via kinetic energy. Now to add some details. 1) you won't need to define curvature during the GUT epock 10^-43 seconds. The reason is the volume is far too miniscule for curvature to matter. 2) you can define scalar vacuum energy in terms of quantum fluctuations via the Heisenberg uncertainty principle and Schrodingers equations. This is where your spin foam enters the picture. Now in terms of a non math descriptive of the GUT epock. This period is in a state of thermal equilibrium, any reactions that occur quickly decay. This epock can be accurately described by its temperature and is dominated by quantum fluctuations. Photons/ anti photon pairs have sufficient energy to form Quarks and gluons. A radiation dominant universe will expand as the gravitational potential is insufficient to cause a collapse. The acceleration equation is given as [latex]\frac{\ddot{a}}{a}=-\frac{4\pi G\rho}{3c^2}(\rho c^2+3p)[/latex] This leads to [latex]H^2=\frac{\dot{a}}{a}=\frac{8\pi G\rho}{3c^2}-\frac{kc^2p}{R_c^2a^2}[/latex] where k is the curvature constant. Which during the GUT epock can be largely ignored. Via the equation of state [latex]p=w\rho c^2[/latex] [latex]\frac{\dot{a}}{a}=-\frac{1}{2}H^2(1+3w)[/latex] for radiation w=-1/3 matter w=0 From this we can see a radiation dominant universe will expand. In fact it will accelerate when [latex]w<-1/3(p<-\rho^2/3)[/latex] When the volume sufficiently increases thereby reducing the temperature quarks, gluons and potentially the Higgs boson can drop out of thermal equilibrium. This process may potentially result in inflation as a phase change. The strong force undergoes symmetry breaking. The simplest version of inflation is via the inflaton which then dominates expansion. The inflaton is given by [latex]\varphi[/latex], with potential [latex]V\varphi[/latex] The pressure of the field is [latex]p(\varphi)=\frac{1/2\dot{\varphi}^2}{\hbar c+V\varphi}[/latex] total energy by [latex]E(\varphi)=\frac{1/2\dot{\varphi}}{\hbar c+V\varphi}[/latex] with equation of state. [latex]\frac{1/2\dot{\varphi}^2/\hbar c-V\varphi}{1/2\dot{\varphi}/\hbar c+V\varphi}[/latex] Probably not the best description, but it's an example. To do a better job I would define this in terms of quage groups and GUT theories. Further including more mathematics. ( but I'm not trying to create a model, only providing some guidance and direction) Hope this helps Edited July 27, 2015 by Mordred
Andre Lefebvre Posted July 27, 2015 Author Posted July 27, 2015 I sure didn't get everything on the first lecture; I'll work on it. It will surely help; at least it's good information. Thank you.
Mordred Posted July 27, 2015 Posted July 27, 2015 (edited) No prob I added a few touch ups. The above doesn't introduce any new physics. However if I was presenting a new idea. The above still falls short of what is required for Peer review level. 1) I need the necessary references 2) Any equations not well known, I would need to show the steps on how I derived the equation. 3) I would need to locate applicable datasets and compare those datasets against my equations. 4) I would need to include how my equations compare to those already in use. 5) I would need to find a means to test my hypothesis. PS very few people reading the above post on this forum will fully understand it. The purpose was to show a few metric examples. If I were working on that as a model I would have included the EFE and lie algebra in group GUT theories. Also the Fermi-Dirac and Bose-Einstien equations(I opted not to, in order to keep it to a manageable length) Edited July 27, 2015 by Mordred
Mordred Posted July 27, 2015 Posted July 27, 2015 Come to think of it, I never did figure out how many degrees of freedom the inflaton field has. Lol something to research (yay)
ajb Posted July 27, 2015 Posted July 27, 2015 This is where I fall on my knees in front of my own picture: If I'm not there to observe and measure, the universe doesn't exist. That is too harsh of an interpretation. It is just a matter of fact, and was realised before Einstein, that some things only make sense relative to some chosen reference. Constant velocity is one of them. It may then be better to study things that do not depend on these choices; such things are true invariants under the symmetry group of your theory. For special relativity this is the Poincare group. For example, although energy and momentum of a particle separately depend on the inertial frames employed, a subtle combination of the two is recognised to be the (rest) mass and this does not depend on the inertial frames used.
Andre Lefebvre Posted July 27, 2015 Author Posted July 27, 2015 I'm reading right now "The fabric of the cosmos . space, tlme, and the texture of reality" by Brran Greene. Came to it by accident. Quite interesting.
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