MJ kihara Posted May 14 Share Posted May 14 Introducing graviton, which decay at to less than Planck's time to gravitation waves which becomes template upon which spacetime curvature forms, merging Einstein field equations parameters and interpreting that using Schrodinger equation, can this leads to quantification of gravity? have a look at the following diagrams. The diagrams have been used for illustration purposes to outline the concept-from the diagram graviton wave function illustrated envelopes elementary particles in this case case-down quark. Once Higgs field is saturated a standing wave is formed that forms graviton that immediately decay to gravitation waves. As elementary particles aggregate the standing wave interferes additively increasing. its magnitude corresponding to increase in mass. Link to comment Share on other sites More sharing options...

Genady Posted May 14 Share Posted May 14 2 hours ago, MJ kihara said: merging Einstein field equations parameters What are the Einstein field equation parameters? Link to comment Share on other sites More sharing options...

MJ kihara Posted May 14 Author Share Posted May 14 48 minutes ago, Genady said: What are the Einstein field equation parameters? Rather components of EFE. Einstein tensor,metric tensor and stress-energy tensor. Link to comment Share on other sites More sharing options...

Genady Posted May 14 Share Posted May 14 2 hours ago, MJ kihara said: spacetime curvature forms, merging Einstein field equations parameters 2 minutes ago, MJ kihara said: Rather components of EFE. Einstein tensor,metric tensor and stress-energy tensor. IOW, spacetime curvature merges the components of EFE? But spacetime curvature is one of these components. Are you saying that one component merges all other components into itself? Link to comment Share on other sites More sharing options...

MJ kihara Posted May 14 Author Share Posted May 14 42 minutes ago, Genady said: Are you saying that one component merges all other components into itself? A component from graviton decay (gravitation wave) becomes a template upon which EFE components merges. Explaining effectively spacetime curvature from a local point ( quantum level) to a global level ( universal) Background virtual particles are spacetime particles-opted to use virtual because they are Soo tiny and are released by every particles...they form part of everything. Link to comment Share on other sites More sharing options...

Genady Posted May 14 Share Posted May 14 31 minutes ago, MJ kihara said: EFE components merges But if components of an equation merge, there is no equation. Any equation requires at least two components, like A = B. If they all merge, you are left with A, which is not an equation. Link to comment Share on other sites More sharing options...

Mordred Posted May 14 Share Posted May 14 (edited) 5 hours ago, MJ kihara said: Introducing graviton, which decay at to less than Planck's time to gravitation waves which becomes template upon which spacetime curvature forms, merging Einstein field equations parameters and interpreting that using Schrodinger equation, can this leads to quantification of gravity? have a look at the following diagrams. The diagrams have been used for illustration purposes to outline the concept-from the diagram graviton wave function illustrated envelopes elementary particles in this case case-down quark. Once Higgs field is saturated a standing wave is formed that forms graviton that immediately decay to gravitation waves. As elementary particles aggregate the standing wave interferes additively increasing. its magnitude corresponding to increase in mass. Assuming the existence of a graviton, which isn't a new idea. You can find examples including string theory and SO(10) MSSM. In both cases you would have a unified field oft termed supergravity. That part of your post is viable. However even with the unified force the spacetime curvature will globally be zero with the stress energy momentum term being zero. Under QM and QFT you will still have the quantum harmonic oscillator. Now curvature actually refers to the geodesic paths that particles will follow so in this case all particle paths are not undergoing any form of acceleration.in essence a freefall state where there is no force acting upon their paths. Once you get anistropy due to the previous harmonic oscillations then things get interesting in so far as that unified force could potentially act upon particle paths. However I should note the other do exist at all times but are in a condition called thermal equilibrium which is a symmetric state. Electroweak symmetry breaking occurs a little later once the universe due to inflation/expansion allows the other forces as well as Higgs to drop out of thermal equilibrium. 23 minutes ago, Baron d'Holbach said: @Bufofrog How's the new edit. Hard to say its any promotion ! Moderator Note Any member can remind another member of a site forum rule. Personal pet theories is a rules violation when replying to other forum members posts. Any member may also also report a rules violation to the moderator staff as a corrective action Edited May 14 by Mordred Link to comment Share on other sites More sharing options...

Mordred Posted May 14 Share Posted May 14 5 hours ago, MJ kihara said: that using Schrodinger equation, can this leads to quantification of gravity? Just an FYI Schrodingers equation doesn't work well in field theories. Hence QFT uses the Klein Gordon equation where the operators of QM position and momentum have been replaced with field and momentum by using the potential energy of the field and the kinetic energy of the particles momentum. In essence it works well for Lorentz invariance of SR. Link to comment Share on other sites More sharing options...

MJ kihara Posted May 14 Author Share Posted May 14 2 hours ago, Baron d'Holbach said: @MJ kihara Good stuff, but... you are holding yourself back like 99% people still. Quantum Gravity and all ideas are all 1960s stalemate thinking. Outdated. New diagram Gravity is a elemental matter. Gravity itself is the creation itself. Gravity is a open and closed system that can be open to the ground state. Extracted and harvested for potential energy. 1 hour ago, Baron d'Holbach said: Isn't String theory and QFT and all the stalemate ideas are all pet theories. String theory is one of the biggest pet theories of all times, yet people throw it around as it's not a pet, because of money, completely prove nothing and has not shipped a product for over 30+ years 😒 1960s stalemate sadly. 1 hour ago, Baron d'Holbach said: @Phi for All It's all good my buddy. Trash it 😀 and end discontinued the thread ✨️ Substack has explained the mission to trash all 1960s ideas. And move along to next sites. My mission has been completed 🙌 Let it be known, prime mechanics has be published posted and established. It could have been reasonable before you jump into conclusions to follow someone threads which are available in this forum to know the reasoning behind the diagram .... 1960 ideas were a stepping stone to get us to this point...without those ideas you go nowhere....as you were publishing the discussions were all already started taking place in this forum in relation to the diagram that I have posted.if you go deeper to following those ideas you will realise what you are trying to do are just a layer before the cores issues outlined by ideas in this and other prior threads. Anyway we are all looking for knowledge. Hi 3 hours ago, Genady said: But if components of an equation merge, there is no equation. Any equation requires at least two components, like A = B. If they all merge, you are left with A, which is not an equation. Am still trying to think about the implications of that.... however given the position of an object( e.g Earth) on orbit around massive body( e.g sun) at a particular time is certain,this might be the reason behind that. 2 Link to comment Share on other sites More sharing options...

MJ kihara Posted May 14 Author Share Posted May 14 3 hours ago, Mordred said: Assuming the existence of a graviton, which isn't a new idea. You can find examples including string theory and SO(10) MSSM. In both cases you would have a unified field oft termed supergravity. That part of your post is viable. However even with the unified force the spacetime curvature will globally be zero with the stress energy momentum term being zero. The new ideas in this is the decay time of a graviton at to less that Planck's time,it forms a standing wave on elementary particles as the Higgs fields becomes saturated,therefore,it is continuously formed as it decays and that as elementary particles aggregate it entangle,have constructive interference to form a higher magnitude standing wave that decays to stronger gravitational waves corresponding to increase in Mass. From the diagram it's clear that the magnitude of gravitation wave and corresponding curvature reduces along the metric tensor away from source of mass,therefore,as we move locally to globally the spacetime curvature and stress-energy tensor will tend to zero. 3 hours ago, Mordred said: Now curvature actually refers to the geodesic paths that particles will follow so in this case all particle paths are not undergoing any form of acceleration.in essence a freefall state where there is no force acting upon their paths. In this case the surface of the wave represent the geodesic path and Hilbert space that a hypothetical object(an object that couple to gravitation field but don't manipulate it) will follow...if time to move from point A to B..( path length is increasing towards B source of mass)..is held constant along the metric tensor, the object's velocity will be increasing(as it free fall) towards the source of mass(gravitational attraction). Therefore this becomes a freefall where time is reducing or held constant while the length is increasing towards source of mass resulting to an increase in velocity towards mass-this is classically interpreted as gravitational force of attraction. If you Fourier transform the wave you will get a spiraling orbit towards the Mass. Link to comment Share on other sites More sharing options...

Mordred Posted May 14 Share Posted May 14 (edited) Ok so the critical aspects to examine are as follows. First you require the geometry of the metric. No need to create one as there is plenty of available examples for a minimally coupled scalar field involving gravity. The graviton would be required to be a spin 2 boson. ( this is a direct consequence of GR spacetime metric ) any good GR textbook also covers this.. You will require a canonical perturbation method using integrals for decay rates. Which is compatible with QFT, as this is also a Lorentz invariant metric using the Klien Gordon equations of QFT. So far so good there is previous work for the majority of the above. The decay rates for a for a graviton however will be tricky to find good examples. Any examples will also be speculative as we only have theoretical possible rates including any other properties such as mass etc. For particle number density one can use the Bose-Einstein statistics for a spin 2 particle or alternately the creation/annihilation operators of QFT. So although numerous steps much of the work has existing formulas that can be employed to develop a proper model. As your toy modelling and not claiming to have a working model lets add some mathematics behind your theory. I will save you some time and post some of the relevant formulas to get you started. Also helps a majority of the ones I feel will work for you I already have latexed on this site so I can copy/paste the ones I feel will be useful to you. GR section GR line element in weak field limit \[ds^2=-c^2dt^2+dx^2+dy^2+dz^2=\eta_{\mu\nu}dx^{\mu}dx^{\nu}\] FLRW metric \[d{s^2}=-{c^2}d{t^2}+a({t^2})[d{r^2}+{S,k}{(r)^2}d\Omega^2]\] Minimal gravitational couplings \[S=\int d^4x\sqrt{-g}\mathcal{L}(\Phi^i\nabla_\mu \Phi^i)\] g is determinant Einstein Hilbert action in the absence of matter. \[S_H=\frac{M_{pl}^2}{2}\int d^4 x\sqrt{-g\mathbb{R}}\] Maxwell Boltmann and Bose Einstein statistics the method is compatible with the QFT equivalent using creation/annihilation operators for particle number density to blackbody temperature relations. Although in QFT its more specifically related to the Fourier transformations via the wave equations involved in the creation/annihilation operators. \[\frac{N_i}{N} = \frac {g_i} {e^{(\epsilon_i-\mu)/kT}} = \frac{g_i e^{-\epsilon_i/kT}}{Z}\] \[n_i = \frac {g_i} {e^{(\varepsilon_i-\mu)/kT} - 1}\] \[\rho_R=\frac{\pi^2}{30}{g_{*S}=\sum_{i=bosons}gi(\frac{T_i}{T})^3+\frac{7}{8}\sum_{i=fermions}gi(\frac{T_i}{T})}^3\] decay rates related mathematics This part applies to a generalized quick guide to what is involved in decay rate calculations Fermi's Golden Rule \[\Gamma=\frac{2\pi}{\hbar}|V_{fi}|^2\frac{dN}{DE_f}\] density of states \[\langle x|\psi\rangle\propto exp(ik\cdot x)\] with periodic boundary condition as "a"\[k_x=2\pi n/a\] number of momentum states \[dN=\frac{d^3p}{(2\pi)^2}V\] decay rate \[\Gamma\] Hamilton coupling matrix element between initial and final state \[V_{fi}\] density of final state \[\frac{dN}{dE_f}\] number of particles remaining at time t (decay law) \[\frac{dN}{dt}=-\Gamma N\] average proper lifetime probability \[p(t)\delta t=-\frac{1}{N}\frac{dN}{dt}\delta t=\Gamma\exp-(\Gamma t)\delta t\] mean lifetime \[\tau=<t>=\frac{\int_0^\infty tp (t) dt}{\int_0^\infty p (t) dt}=\frac{1}{\Gamma}\] relativistic decay rate set \[L_o=\beta\gamma c\tau\] average number after some distance x \[N=N_0\exp(-x/l_0)\] spin statistics spin 2 graviton. you can look through this as a vast majority of the formulas are mentioned here in modelling the graviton couplings to the spacetime field https://arxiv.org/pdf/1812.07571.pdf Hope that helps Edited May 14 by Mordred Link to comment Share on other sites More sharing options...

Mordred Posted May 14 Share Posted May 14 (edited) In essence what you have described thus far is feasibly sound. The article will provide much of the critical details. There are plenty of references on how a graviton would relate to gravitational potential of a field so having a higher number density as a result of gravitational waves is easily formulated with the above. As a vector gauge boson those gravitons would be off shell in essence the internal lines on a Feymann diagram. The article above also covers this. I should add Maxwell Boltmann uses phase space this article isn't bad on it https://ps.uci.edu/~cyu/p115A/LectureNotes/Lecture13/lecture13.pdf Edited May 14 by Mordred Link to comment Share on other sites More sharing options...

Markus Hanke Posted May 15 Share Posted May 15 19 hours ago, MJ kihara said: Introducing graviton, which decay Gravitons, if they exist, would be massless spin-2 particles - and as such, they would be perfectly stable and can have no decay modes. 1 Link to comment Share on other sites More sharing options...

MJ kihara Posted May 15 Author Share Posted May 15 9 hours ago, Mordred said: Ok so the critical aspects to examine are as follows. First you require the geometry of the metric. No need to create one as there is plenty of available examples for a minimally coupled scalar field involving gravity. The graviton would be required to be a spin 2 boson. ( this is a direct consequence of GR spacetime metric ) any good GR textbook also covers this.. You will require a canonical perturbation method using integrals for decay rates. Which is compatible with QFT, as this is also a Lorentz invariant metric using the Klien Gordon equations of QFT. So far so good there is previous work for the majority of the above. The decay rates for a for a graviton however will be tricky to find good examples. Any examples will also be speculative as we only have theoretical possible rates including any other properties such as mass etc. For particle number density one can use the Bose-Einstein statistics for a spin 2 particle or alternately the creation/annihilation operators of QFT. So although numerous steps much of the work has existing formulas that can be employed to develop a proper model. As your toy modelling and not claiming to have a working model lets add some mathematics behind your theory. I will save you some time and post some of the relevant formulas to get you started. Also helps a majority of the ones I feel will work for you I already have latexed on this site so I can copy/paste the ones I feel will be useful to you. GR section GR line element in weak field limit ds2=−c2dt2+dx2+dy2+dz2=ημνdxμdxν FLRW metric ds2=−c2dt2+a(t2)[dr2+S,k(r)2dΩ2] Minimal gravitational couplings S=∫d4x−g−−−√L(Φi∇μΦi) g is determinant Einstein Hilbert action in the absence of matter. SH=M2pl2∫d4x−gR−−−−√ Maxwell Boltmann and Bose Einstein statistics the method is compatible with the QFT equivalent using creation/annihilation operators for particle number density to blackbody temperature relations. Although in QFT its more specifically related to the Fourier transformations via the wave equations involved in the creation/annihilation operators. NiN=gie(ϵi−μ)/kT=gie−ϵi/kTZ ni=gie(εi−μ)/kT−1 ρR=π230g∗S=∑i=bosonsgi(TiT)3+78∑i=fermionsgi(TiT)3 decay rates related mathematics This part applies to a generalized quick guide to what is involved in decay rate calculations Fermi's Golden Rule Γ=2πℏ|Vfi|2dNDEf density of states 〈x|ψ〉∝exp(ik⋅x) with periodic boundary condition as "a" kx=2πn/a number of momentum states dN=d3p(2π)2V decay rate Γ Hamilton coupling matrix element between initial and final state Vfi density of final state dNdEf number of particles remaining at time t (decay law) dNdt=−ΓN average proper lifetime probability p(t)δt=−1NdNdtδt=Γexp−(Γt)δt mean lifetime τ=<t>=∫∞0tp(t)dt∫∞0p(t)dt=1Γ relativistic decay rate set Lo=βγcτ average number after some distance x N=N0exp(−x/l0) spin statistics spin 2 graviton. you can look through this as a vast majority of the formulas are mentioned here in modelling the graviton couplings to the spacetime field https://arxiv.org/pdf/1812.07571.pdf Hope that helps 8 hours ago, Mordred said: In essence what you have described thus far is feasibly sound. The article will provide much of the critical details. There are plenty of references on how a graviton would relate to gravitational potential of a field so having a higher number density as a result of gravitational waves is easily formulated with the above. As a vector gauge boson those gravitons would be off shell in essence the internal lines on a Feymann diagram. The article above also covers this. I should add Maxwell Boltmann uses phase space this article isn't bad on it https://ps.uci.edu/~cyu/p115A/LectureNotes/Lecture13/lecture13.pdf Thanks. I will consider all that....though,my mathematical background is not as such...that's why I prefer to use diagrams for illustration,if animation was available i know this concept could be more clearer. Link to comment Share on other sites More sharing options...

Mordred Posted May 15 Share Posted May 15 Well if it helps The various probabilities for number density of a particle will rely on phase space which can be understood as the particle in a box images and videos. The mathematical methodology of both employ the particle states wavefunctions. this also will better help with regards to spin statistics. Link to comment Share on other sites More sharing options...

MJ kihara Posted May 15 Author Share Posted May 15 2 hours ago, Markus Hanke said: Gravitons, if they exist, would be massless spin-2 particles - and as such, they would be perfectly stable and can have no decay modes. From those diagrams there are already assumptions made-spacetime fabric is made up of virtual particles (spacetime particles) which can either be stable, partially stable or unstable... partially stable or unstable oscillate within their levels of instability i.e a kind of ideal square wave signal. Virtual particles (spacetime particle) have a minute eigen space around them. Stable virtual particles(spacetime particles) are the ones that transist from local point to globally, therefore, essentially mediating gravity making it universal. Virtual particles(spacetime particles) entangle through their eigen space therefore entanglement strength is directly proportional to their concentration that contribute to gravity. Virtual particles(spacetime particles) surface dimension deform accordingly to where it's entangled to i.e at the surface of the particle e.g quark as it is emitted. Stable virtual particles (spacetime particle) form Higgs field when this Higgs field get saturated a graviton is formed that decouples from elementary particle as gravitational wave --This decoupling is the one that am referring to as decay--after decoupling they move to become part of spacetime fabric (basic framework of the universe). As they are moving they mediate gravity and since their concentration is higher near source of mass they are highly entangled at such a point therefore, contributing to a higher pressure (i.e virtual particles-spacetime particles-pressure)...this is the cause of gravity being analogously compared to negative pressure. Therefore, pressure increase from point A to point B near source of mass.However as virtual particles(spacetime particles) are moving away from source of mass,to become part of basic framework of the universe, their entanglement to the mass source keep reducing contributing to the cosmological constant that leads to the expansion of metric tensor..as indicated in the diagram...Therefore,we are having a situation whereby virtual particles(spacetime particles) are mediating gravity through entanglement via their minute eigen space while simultaneously contributing to cosmological constant,hence,universe expansion as they are moving from source mass to the universe. About existence of graviton--it will be very difficult to detect a graviton in particle colliders machine experiments since it decays to become part of spacetime fabric....However it's expected to be found in plenty in regions of extreme pressures as found near or inside a black hole or other massive bodies....or it could be found transciently if it were possible to synthesis microblack holes. Link to comment Share on other sites More sharing options...

MJ kihara Posted May 18 Author Share Posted May 18 On 5/14/2023 at 7:29 PM, MJ kihara said: Am still trying to think about the implications of that.... however given the position of an object( e.g Earth) on orbit around massive body( e.g sun) at a particular time is certain,this might be the reason behind that. I think applying the merged EFE on gravitation wave as shown in the diagram and using that information to look for solutions following Schrodinger equations. From Wikipedia-schrodinger equations......Writing r {\displaystyle \mathbf {r} } for a three-dimensional position vector and p {\displaystyle \mathbf {p} } for a three-dimensional momentum vector, the position-space Schrödinger equation is i ℏ ∂ ∂ t Ψ ( r , t ) = − ℏ 2 2 m ∇ 2 Ψ ( r , t ) + V ( r ) Ψ ( r , t ) . {\displaystyle i\hbar {\frac {\partial }{\partial t}}\Psi (\mathbf {r} ,t)=-{\frac {\hbar ^{2}}{2m}}\nabla ^{2}\Psi (\mathbf {r} ,t)+V(\mathbf {r} )\Psi (\mathbf {r} ,t).} The momentum-space counterpart involves the Fourier transforms of the wave function and the potential: i ℏ ∂ ∂ t Ψ ~ ( p , t ) = p 2 2 m Ψ ~ ( p , t ) + ( 2 π ℏ ) − 3 / 2 ∫ d 3 p ′ V ~ ( p − p ′ ) Ψ ~ ( p ′ , t ) . {\displaystyle i\hbar {\frac {\partial }{\partial t}}{\tilde {\Psi }}(\mathbf {p} ,t)={\frac {\mathbf {p} ^{2}}{2m}}{\tilde {\Psi }}(\mathbf {p} ,t)+(2\pi \hbar )^{-3/2}\int d^{3}\mathbf {p} '\,{\tilde {V}}(\mathbf {p} -\mathbf {p} '){\tilde {\Psi }}(\mathbf {p} ',t).} The functions Ψ ( r , t ) {\displaystyle \Psi (\mathbf {r} ,t)} and Ψ ~ ( p , t ) {\displaystyle {\tilde {\Psi }}(\mathbf {p} ,t)} are derived from | Ψ ( t ) 〉 {\displaystyle |\Psi (t)\rangle } by Ψ ( r , t ) = 〈 r | Ψ ( t ) 〉 , {\displaystyle \Psi (\mathbf {r} ,t)=\langle \mathbf {r} |\Psi (t)\rangle ,} Ψ ~ ( p , t ) = 〈 p | Ψ ( t ) 〉 , {\displaystyle {\tilde {\Psi }}(\mathbf {p} ,t)=\langle \mathbf {p} |\Psi (t)\rangle ,} where | r 〉 {\displaystyle |\mathbf {r} \rangle } and | p 〉 {\displaystyle |\mathbf {p} \rangle } do not belong to the Hilbert space itself, but have well-defined inner products with all elements of that space...... The best thing is that most of formulations to support this concepts have already been done. Link to comment Share on other sites More sharing options...

MJ kihara Posted May 18 Author Share Posted May 18 Instead of copy pasting formulations that have already been developed,I would prefer discussing concepts that I regard original from my arguments point of view and just make a reference to any formulations where possible not to cloud this thread..esp with paste that are not clear...for the above post that's clear...Google Wikipedia Schrodinger equations- position space and momentum space. My intention is to develop something that even a layman can interpret easily,for instance,if someone ask me about spacetime curvature and how it's related to gravity..I show that diagram...If he ask how it's related to increase in speed toward massive body I answer Speed=distance/time. Where distance is the arc length on wave indicating geodesic path as indicated in the diagram while time axis is fixed on the metric tensor. Link to comment Share on other sites More sharing options...

Genady Posted May 18 Share Posted May 18 1 hour ago, MJ kihara said: If he ask how it's related to increase in speed toward massive body I answer Speed=distance/time. Where distance is the arc length on wave indicating geodesic path as indicated in the diagram while time axis is fixed on the metric tensor. This is incorrect because length of a geodesic path is proper time. So, your formula produces time over time rather than speed. For example, if two events occur in the same place with 1 min one after another, the length of the geodesic path is 1 min and the "speed" according to your formula is 1/1 = 1. Link to comment Share on other sites More sharing options...

MJ kihara Posted May 18 Author Share Posted May 18 47 minutes ago, Genady said: This is incorrect because length of a geodesic path is proper time. So, your formula produces time over time rather than speed. For example, if two events occur in the same place with 1 min one after another, the length of the geodesic path is 1 min and the "speed" according to your formula is 1/1 = 1. In these case the freefalling object is moving from point A to point B near source of mass...it's not stationary therefore the events are not in same place....the wave surface become the geodesic path/ the world line/arc length that the object is free falling in i.e its the object orbit towards mass. Literally distance becomes the arc length of the wave....and since near mass the frequency of gravitation wave is high the arc length will be longer.for us human this length becomes invisible but we detect it as increase in velocity. Link to comment Share on other sites More sharing options...

Mordred Posted May 18 Share Posted May 18 (edited) Under GR all events are inertial. The geodesic equations include this detail. The Euler Langranian equations are capable of handling wave equations with particle paths. The entire body of QFT incorporate that. Edited May 18 by Mordred Link to comment Share on other sites More sharing options...

Genady Posted May 18 Share Posted May 18 4 minutes ago, MJ kihara said: In these case the freefalling object is moving from point A to point B near source of mass...it's not stationary therefore the events are not in same place....the wave surface become the geodesic path/ the world line/arc length that the object is free falling in i.e its the object orbit towards mass. Literally distance becomes the arc length of the wave....and since near mass the frequency of gravitation wave is high the arc length will be longer.for us human this length becomes invisible but we detect it as increase in velocity. Still doesn't work. If the body went 1 km in 1 s, the length of the geodesic is sqrt(300000^2-1) and divided by the coordinate time it gives the "speed" of about 300000 km/s. Link to comment Share on other sites More sharing options...

MJ kihara Posted May 18 Author Share Posted May 18 3 hours ago, MJ kihara said: Instead of copy pasting formulations that have already been developed,I would prefer discussing concepts that I regard original from my arguments point of view and just make a reference to any formulations where possible not to cloud this thread..esp with paste that are not clear...for the above post that's clear...Google Wikipedia Schrodinger equations- position space and momentum space. My intention is to develop something that even a layman can interpret easily,for instance,if someone ask me about spacetime curvature and how it's related to gravity..I show that diagram...If he ask how it's related to increase in speed toward massive body I answer Speed=distance/time. Where distance is the arc length on wave indicating geodesic path as indicated in the diagram while time axis is fixed on the metric tensor. Thanks for the corrections. let me correct on that by dropping geodesic therefore it becomes..... indicating the path followed by the object as indicated in the diagram..... I mean literally someone to put units of time from point B to A using metric tensor line as time axis then literally measure the arc length,then let the object to freefall from point A to B near source of mass...it's obvious that speed will be increasing towards mass, since per unit time length/distance is increasing...as indicated on the diagram. The arc length in this case is the surface of wave that becomes world line of the object as it free fall towards mass. Remember its simple explanation using the minimum possible detail. Link to comment Share on other sites More sharing options...

MJ kihara Posted May 18 Author Share Posted May 18 3 hours ago, Genady said: This is incorrect because length of a geodesic path is proper time. So, your formula produces time over time rather than speed. For example, if two events occur in the same place with 1 min one after another, the length of the geodesic path is 1 min and the "speed" according to your formula is 1/1 = 1. From the Wikipedia geodesic article....... For a space-like geodesic through two events, there are always nearby curves which go through the two events that have either a longer or a shorter proper length than the geodesic, even in Minkowski space. In Minkowski space, the geodesic will be a straight line. Any curve that differs from the geodesic purely spatially (i.e. does not change the time coordinate) in any inertial frame of reference will have a longer proper length than the geodesic, but a curve that differs from the geodesic purely temporally (i.e. does not change the space coordinates) in such a frame of reference will have a shorter proper length..... In my case it's proper length as distance and co-ordinate time(across metric tensor line as per the diagram) as time...for every unit of time there is increase of proper length towards mass. Link to comment Share on other sites More sharing options...

Genady Posted May 18 Share Posted May 18 29 minutes ago, MJ kihara said: From the Wikipedia geodesic article....... For a space-like geodesic through two events, there are always nearby curves which go through the two events that have either a longer or a shorter proper length than the geodesic, even in Minkowski space. In Minkowski space, the geodesic will be a straight line. Any curve that differs from the geodesic purely spatially (i.e. does not change the time coordinate) in any inertial frame of reference will have a longer proper length than the geodesic, but a curve that differs from the geodesic purely temporally (i.e. does not change the space coordinates) in such a frame of reference will have a shorter proper length..... In my case it's proper length as distance and co-ordinate time(across metric tensor line as per the diagram) as time...for every unit of time there is increase of proper length towards mass. It cannot be a proper length because proper length has a meaning only between events which are spacelike related, i.e., nothing can get from one to another unless it moves faster than light. Link to comment Share on other sites More sharing options...

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