Mordred Posted April 20 Posted April 20 (edited) Just to add the relativistic correction to decay rates \[L_o=\beta\gamma c\tau\] 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 \[N=N_0\exp(-x/l_0)\] There are several examples in that thread for different cross section and relativistic velocities Edited April 20 by Mordred
externo Posted April 20 Author Posted April 20 (edited) 15 hours ago, Mordred said: No I'm familiar with the research that went into Lorentz ether theroy I also know it's transformation rules including many of the other variations . The thing is the physicists performing those Lorentz invariant tests are also well aware of neo-lorentz. So they also conducted tests for that in that article. Here is the detail many miss. In Lorentz time the only known particles were the photon the electron and the proton. That was at that time the entire standard model. The neutron wasn't even discovered until the mid 30's. So it was quite natural to think there was am ether. Modern physics has gone beyond that including particles that are so weakly interactive they could pass through a chunck of lead one light year in length without a single interaction. (Neutrinos). However it's also well known every particle species contributes to the blackbody temperature in particular the CMB including those neutrinos. So why do we not detect any temperature contribution from the Lorentz ether ? Why does it have no influence on universe expansion ? Every other particle does. The way is if you have a static 100 percent non interacting field but then it wouldn't even interact with gravity let alone photons. Or any other particle. We can certainly gather indirect or direct evidence of every other particle in the standard model. Why not the Lorentz ether ? Ether is actually 3D space, it is not a superimposed substance. Ether is not only luminiferous, all particles are waves in the ether. Spin is a rotation of 3D space, it is an exchange of energy between the particle and external space. All fields of physics are states of the ether. Vacuum energy is made up of waves that travel in the ether and exchange energy with matter. Ether is probably a kind of elastic crystal. It can be represented by balls mounted on springs, in the same way that current quantum physics models vacuum energy. The fundamental problem with mainstream physics is that it does not recognize a privileged frame of reference in its equations. However, we know that the CMB constitutes the universe's frame of immobility and it is also the frame of reference of the ether or space. As it does not recognize this privileged frame of reference it cannot recognize that space has a substance 15 hours ago, Mordred said: Then why would you claim otherwise and argue that c isn't invariant ? Sounds like you don't even understand Lorentz ether theory.... In Lorentz aether theory the one-way speed of light is not invariant, only the speed of light over a round trip is invariant. It's explained here: https://en.wikipedia.org/wiki/One-way_speed_of_light#Theories_equivalent_to_special_relativity Quote In the theory, the one-way speed of light is principally only equal to the two-way speed in the aether frame, though not in other frames due to the motion of the observer through the aether. This is sufficient to verify Lorentz invariance. ---------------------- 14 hours ago, swansont said: Lorentz theory is ad-hoc. There’s no independent evidence of an ether. Are we moving with respect to the ether, or are we stationary with respect to it? It is not ad hoc, Lorentz justified in 1904 the reason for contraction by the electromagnetic nature of matter. But above all, we know today that Lorentz transformations are the transformations undergone by moving stationary waves, which is proof of the existence of the ether. These transformations simply indicate that matter in motion is made up of networks of moving standing waves of aether. The immobile frame of reference in relation to the ether is that of the CMB, it is the frame of reference of the universe. Search on Google: “CMB absolute frame” Edited April 20 by externo
Mordred Posted April 20 Posted April 20 You know you really do mix up a lot of physics without actually understanding any of it. The very term invariant literally means to all observers regardless of model. I have copies of Lorentz ether theories they are readily available in reprint archives. You obviously do not understand its mathematics nor its transformations you have made far too many mistakes this thread alone that has been pointed out by others. Those others include 2 physicists Dr Swansont and myself my primary field is cosmology but I also hold a Bachelors degree in particle physics. This has a couple others extremely well versed in Relativity such as Markus pointing out your mistakes. So instead of just reading the words in your various links why don't you sit down and spend time understanding what the math states. Then perhaps you can better defend LET.
swansont Posted April 20 Posted April 20 31 minutes ago, externo said: It is not ad hoc, Lorentz justified in 1904 the reason for contraction by the electromagnetic nature of matter. Justified? With empirical evidence? 31 minutes ago, externo said: But above all, we know today that Lorentz transformations are the transformations undergone by moving stationary waves, which is proof of the existence of the ether. These transformations simply indicate that matter in motion is made up of networks of moving standing waves of aether. The immobile frame of reference in relation to the ether is that of the CMB, it is the frame of reference of the universe. So why do measurements like the Michelson-Morley experiment fail to measure the motion of the earth through the ether? Quote Search on Google: “CMB absolute frame” I find links saying it’s not an absolute frame, as expected.
externo Posted April 20 Author Posted April 20 (edited) 9 hours ago, Markus Hanke said: I was talking about something you claimed - that SR cannot handle acceleration. This is manifestly wrong, because it very much can. What interpretations? The ether in LET is by design undetectable, and its presence has no physical consequences, thus both SR and LET make identical predictions. This isn’t a matter of interpretation, but belief - do you choose to believe and assume the presence of an entity that cannot be detected, has no physical consequences, and is not actually needed to obtain the correct dynamics? The ether is detectable during acceleration, it is our speed in relation to it that is not detectable for dynamic reasons: matter being composed of ether waves it undergoes the Doppler effect when moving and prevents any speed-sensing capability in the ether. 9 hours ago, Markus Hanke said: Not only has SR been exhaustively tested over the past ~120 years and thus shown to be consistent with the physical world, but we also use it directly in many aspects of modern technology. A lot of parts of the very machine you are using to make your posts here have been designed based directly or indirectly on SR, and it evidently works well. Einstein's SR is not capable of processing accelerations, otherwise explain to me what happens during an acceleration according to Einstein. The speed of light remains constant and time changes its simultaneity, is that the explanation? 9 hours ago, Markus Hanke said: But APS is just based on a subgroup of the full Cl(1,3) Clifford spacetime algebra…? It is a convenient and very useful formalism, but hardly new physics. RG is a social network, not a peer review journal. Some stuff there is useful, but one has to use caution. Personally, I stopped reading when the author first talked about twins in Minkowski spacetime, and then gave a scenario as example where one twin is in orbit around a star. Not an especially convincing paper, and the author clearly has an agenda. This formalism is different from that of Minkowski. In my opinion, this is the formalism of physical reality. Hamilton created quaternions in 1843 and assumed that the scalar part represented time. Maxwell had begun to write his equations using quaternions, but Heaviside and Glibbs dismantled the quaternions to produce the vector calculus, in doing so they separated the scalar part and the vector part, therefore time from space. This article also explains some problems with SR: https://arxiv.org/pdf/gr-qc/0604118.pdf --------------------- 7 hours ago, Markus Hanke said: The discussion seems to be going off on a lot of tangents now, so I propose we bring it back to the above original claim. Here’s how I would approach this personally: The twin scenario concerns two clocks (E-Earth, T-Travelling) which start together at rest at some event A; twin T then separates for a period and eventually they reunite again at rest at another event B. In SR, the total accumulated time on a clock travelling between a pair of events is defined to equal the geometric length of the worldline traced out by that clock through spacetime: τ=∫Cds where C(t,x) is the path taken. Since in SR we have ds=ημνdxμdxν−−−−−−−−√ we get, for the Earth-bound twin (no change in spatial location!): τE=∫BAημνdxμdxν−−−−−−−−√=∫BAηtt−−√=c∫BAdt For the travelling twin, on the other hand, we get: τT=∫Cημνdxμdxν−−−−−−−−√=∫Cc2dt2−dx2−dy2−dz2−−−−−−−−−−−−−−−−−−−√ wherein we don’t assume any specifics about the path C, other than that it connects A and B, and remains light-like everywhere. I invite you to verify yourself that τT<τE by choosing any light-like path C and running the numbers in these line integrals. What this means is that, in SR, an inertial clock will always trace out the longest path through spacetime between events, ie it will accumulate the most time. Any path deviating from being a geodesic will necessarily be shorter (or vice versa, depending on your sign convention). Since the travelling twin starts out at rest wrt to its partner, but then travels away, it cannot remain on a geodesic - thus SR guarantees that its clock accumulates less time than the Earth-bound twin. Far from being a paradox, it is a natural consequence of the geometry of spacetime. Note that I made no assumptions here about the specific form of the path C, only that it is light-like and runs through A and B; thus it is realisable by any test particle with mass. So yes, SR very much can resolve this, contrary to your claim. It should also be explicitly noted that the total time dilation does not depend on the magnitude of acceleration at any one instant, but only on the total path length of the world line. Lastly, an experimental test of these predictions can be made by comparing the decay rates of unstable particles in accelerators against stationary reference samples. See eg Bailey et al (1977) with regards to CERNs muon storage ring. You give mathematical equations, but what do these equations say? They say that the traveling twin has traveled the greatest spatial distance and the shortest temporal distance. But Einstein's theory does not say that the twin has traveled the greatest spatial distance because space is relative, it claims that from the twin's point of view it is the Earth which has traveled the greatest distance and in this case it is the Earth which should be younger. Einstein is not able with his postulates to explain what is happening from the traveler's point of view. We are forced to place ourselves in one inertial frame of reference and study the situation in order to be able to account for it, and this inertial frame of reference plays the role of the ether frame of reference. It is thus Lorentz's theory which explains the paradox and not Einstein's. It is also written here: https://en.wikipedia.org/wiki/Twin_paradox#No_twin_paradox_in_an_absolute_frame_of_reference Now, instead of doing mathematical calculations, I suggest you try to explain what happens physically from the traveler's point of view so that he comes back younger. When exactly does he get younger in relation to Earth? Edited April 20 by externo
swansont Posted April 20 Posted April 20 16 minutes ago, externo said: Einstein's SR is not capable of processing accelerations Yes, it is. 16 minutes ago, externo said: , otherwise explain to me what happens during an acceleration according to Einstein. What happens is rather open-ended. What happens to what? 16 minutes ago, externo said: The speed of light remains constant and time changes its simultaneity, is that the explanation? Those are the results (sort of; “time changes its simultaneity” is a rather awkward phrase) What do you want explained?
externo Posted April 20 Author Posted April 20 Just now, swansont said: What happens is rather open-ended. What happens to what? What do you want explained? Explain the physics behind the equations. What happens to make the twin come back younger. Lorentz offers a physical explanation for this phenomenon, what explanation does Einstein offer? Equations ? That's no physical explanation.
Mordred Posted April 20 Posted April 20 (edited) 14 minutes ago, externo said: Explain the physics behind the equations. What happens to make the twin come back younger. Lorentz offers a physical explanation for this phenomenon, what explanation does Einstein offer? Equations ? That's no physical explanation. Do you honestly not realize that every paper Lorentz published included equations in his physical explanations ? why do you ignore those equations but attempt to falsify Einstein relativity for using equations when Lorentz himself also used equations. It was through his equations that others could point out numerous flaws which led to Lorentz modifying his equations numerous times in various papers. for example one of his papers had an energy momentum violation which he later corrected. you know what lets jump back to the actual topic. provide the mathematics for the twin solution using Lorentz ether theory give us a demonstration that you actually understand his theory Edited April 20 by Mordred
externo Posted April 20 Author Posted April 20 (edited) 10 minutes ago, Mordred said: Do you honestly not realize that every paper Lorentz published included equations in his physical explanations ? why do you ignore those equations but attempt to falsify Einstein relativity for using equations when Lorentz himself also used equations. It was through his equations that others could point out numerous flaws which led to Lorentz modifying his equations numerous times in various papers. for example one of his papers had an energy momentum violation which he later corrected. Lorentz always offered a physical explanation for his equations. Objects undergo Lorentz transformations as they move through the ether. What are Einstein's explanations? If his explanations are not physically valid, how do you expect them to replace Lorentz's? Edited April 20 by externo
Mordred Posted April 20 Posted April 20 (edited) great provide his solution to the twin paradox in his mathematical form using LET. I for one have never seen his solution using Lorentz ether for the twin paradox so provide it for reference with the mathematics Edited April 20 by Mordred
externo Posted April 20 Author Posted April 20 22 minutes ago, Mordred said: provide the mathematics for the twin solution using Lorentz ether theory give us a demonstration that you actually understand his theory Lorentz's explanation is that if we assume the Earth is stationary in the ether, the traveling twin ages less than the Earth during the journey there and back. There is no paradox. Time dilation depends on the twin's speed relative to the ether and not relative to Earth. The observational symmetry of time dilation comes from the observational symmetry of the relativistic Doppler effect. The classic Dopple effect is not symmetrical. If the transmitter is at rest and the receiver is moving it will receive a different Doppler effect than if it is the transmitter which is moving and the receiver which is at rest. But when we add the dilation of time it is impossible to make the distinction, we cannot know if it is the transmitter which is moving or the receiver. Einstein's theory amounts to assuming that the observer is always at rest and moving objects are therefore always at the origin of the observed Doppler effect. But this is a completely arbitrary hypothesis and contrary to physics. It is invalidated during acceleration periods : When we accelerate we perceive the Doppler effect immediately, so the twin who turns around will notice a Doppler effect in the signal coming from the Earth immediately upon turning around, and that means that it is him that causes this effect and therefore changes its speed relative to the ether. The Earth, for its part, must wait for the Doppler effect produced by the traveler to propagate towards it at the speed of light. The situation is therefore not symmetrical and we can distinguish who is at the origin of the motion. We deduce that during the entire period of the twin's return to Earth the situation is never symmetrical since the Doppler effect was generated during the acceleration period. So, observationally, in inertials periods, each can say that it is the other who is experiencing time dilation, but physically this is not the case."
Mordred Posted April 20 Posted April 20 I asked you to provide his mathematical solution not an interpretation
swansont Posted April 20 Posted April 20 2 minutes ago, externo said: Lorentz's explanation is that if we assume the Earth is stationary in the ether, the traveling twin ages less than the Earth during the journey there and back. You said the CMB is the rest frame, so we are not at rest wrt the ether. I notice you did not address why the M-M experiment got a null result.
externo Posted April 20 Author Posted April 20 27 minutes ago, Mordred said: great provide his solution to the twin paradox in his mathematical form using LET. I for one have never seen his solution using Lorentz ether for the twin paradox so provide it for reference with the mathematics The mathematics of relativity are those of Lorentz theory. Lorentz uses Galilean kinematics so he has nothing to prove. What matters is whether Einstein's explanations are consistent with the physical world. Einstein only gave an explanation for inertial frames with a non-standard kinematic.
Mordred Posted April 20 Posted April 20 No the mathematics used in LET in his transformations are not the same as those used in SR. Provide the solution using Lorentz ether transformation rules
externo Posted April 20 Author Posted April 20 (edited) 9 minutes ago, Mordred said: I asked you to provide his mathematical solution not an interpretation All mathematical solutions are those of Lorentz theory by default. Einstein only gave a new interpretation, he did not produce any new mathematics. The theory of relativity is the work of Lorentz and Poincaré, Einstein only gave a new physical interpretation of Lorentz transformations. Edited April 20 by externo
Mordred Posted April 20 Posted April 20 no they are not the transformation rules differ between LET and Lorentz as per SR. Show you can actually calculate the age difference
externo Posted April 20 Author Posted April 20 4 minutes ago, Mordred said: No the mathematics used in LET in his transformations are not the same as those used in SR. Provide the solution using Lorentz ether transformation rules They are THE SAME : https://en.wikipedia.org/wiki/Lorentz_ether_theory
Mordred Posted April 20 Posted April 20 (edited) this is the SR Lorentz transformations \[\acute{x}=(x-vt)\] \[\acute{t}=\gamma(t-\frac{vx}{c^2})\] they are not the same as in that link now calculate the age using the link you just provided. You need the math to calculate age so obviously the math is a huge part of the solution to the twin paradox. Yet you choose to ignore the mathematics while claiming Einstein theory is incorrect. Yet in the same breath claim they are the same Edited April 20 by Mordred
externo Posted April 20 Author Posted April 20 (edited) 36 minutes ago, swansont said: You said the CMB is the rest frame, so we are not at rest wrt the ether. I notice you did not address why the M-M experiment got a null result. Yes, we are not at rest. Lorentz explained the null result of the MM experiment by Lorentz's transformations, like Einstein, but while for Lorentz matter contracts and slows down physically as it moves through the ether, Einstein attributes these transformations to changes in physical simultaneities. It is this assumption that implies that the speed of light in one direction is always c. In aether theory the speed of light is measured at c on a round trip due to time dilation and length contraction, but on a one way trip the measurement should give a different result. It is nevertheless impossible to make this measurement because nothing moves faster than light and one must first synchronize two distant clocks using light signals before making the measurement and this synchronization implies in itself that the measurement will give an isotropic result. . ----------------------- 21 minutes ago, Mordred said: this is the SR Lorentz transformations x´=(x−vt) t´=γ(t−vxc2) they are not the same as in that link now calculate the age using the link you just provided. You need the math to calculate age so obviously the math is a huge part of the solution to the twin paradox. Yet you choose to ignore the mathematics while claiming Einstein theory is incorrect. Yet in the same breath claim they are the same Lorentz transformations were established by Lorentz as part of his theory. Minkowski space-time was first described by Poincaré within the framework of this same theory in 1905. Edited April 20 by externo
Mordred Posted April 20 Posted April 20 (edited) do you agree the mathematics are required to calculate the age in order for the twin paradox to have any meaning Yes or no. The transforms in the Ether Link was prior to the SR version or did you forget Lorentz had to regularly fix his theory ? So what your telling me is that in order to calculate the age difference I would use the SR transforms in the same manner as done in SR and GR and they would be equivalent. However You also claimed that SR and GR cannot resolve the twin paradox yet you cannot calculate the age difference without using SR/GR is that correct ? Edited April 20 by Mordred 1
externo Posted April 20 Author Posted April 20 (edited) 34 minutes ago, Mordred said: do you agree the mathematics are required to calculate the age in order for the twin paradox to have any meaning Yes or no. No, the paradox can be explained without math within the framework of Lorentz theory, because there is no paradox in this theory. Quote In the relativity of Poincaré and Hendrik Lorentz, which assumes an absolute (though experimentally indiscernible) frame of reference, no paradox arises due to the fact that clock slowing (along with length contraction and velocity) is regarded as an actuality, hence the actual time differential between the reunited clocks. https://en.wikipedia.org/wiki/Twin_paradox#No_twin_paradox_in_an_absolute_frame_of_reference The problem with Lorentz transformations is that they are misleading. As they are symmetrical, we have the impression that inertial reference frames are equivalent. For Lorentz, there are immobile objects in the ether which measure things correctly and moving objects which measure them falsely. The Earth being almost immobile in relation to the ether, we can say that it correctly measures the aging of the traveler, but the traveler being at high speed uses false measurement standards and is mistaken when he measures that the time on Earth passes more slowly than his own. Einstein interprets the equations literally, Lorentz seeks a hidden reality behind these equations. 34 minutes ago, Mordred said: So what your telling me is that in order to calculate the age difference I would use the SR transforms in the same manner as done in SR and GR and they would be equivalent. However You also claimed that SR and GR cannot resolve the twin paradox yet you cannot calculate the age difference without using SR/GR is that correct ? I claim that the postulate of invariance of the speed of light of SR is not consistent with physical reality, therefore that the only possible interpretation of the equations is that of Lorentz. Quote That interpretation of relativity, which John A. Wheeler calls "ether theory B (length contraction plus time contraction)", did not gain as much traction as Einstein's, which simply disregarded any deeper reality behind the symmetrical measurements across inertial frames. There is no physical test which distinguishes one interpretation from the other. https://en.wikipedia.org/wiki/Twin_paradox#No_twin_paradox_in_an_absolute_frame_of_reference Edited April 20 by externo
Mordred Posted April 20 Posted April 20 If you placed two regions of a static space described by Eather. Those regions would be symmetric, The Eather treated as a field would be described by scalar functions. So it too is symmetric. The freefall state or more accurately the state which has no force or interaction is symmetric as per SR. The constant velocity conditions. pray tell how is symmetry not applicable to the Eather. If you want I can readily provide the mathematics for a static scalar field. It will be symmetric The Cartesian coordinates used are symmetric. so pray tell why would you believe symmetry doesn't apply to Lorentz eather ? or is it some particular symmetry relation your referring to perhaps
externo Posted April 20 Author Posted April 20 2 minutes ago, Mordred said: If you placed two regions of a static space described by Eather. Those regions would be symmetric, The Eather treated as a field would be described by scalar functions. So it too is symmetric. The freefall state or more accurately the state which has no force or interaction is symmetric as per SR. The constant velocity conditions. pray tell how is symmetry not applicable to the Eather. If you want I can readily provide the mathematics for a static scalar field. It will be symmetric The Cartesian coordinates used are symmetric. so pray tell why would you believe symmetry doesn't apply to Lorentz eather ? or is it some particular symmetry relation your referring to perhaps Quote That interpretation of relativity, which John A. Wheeler calls "ether theory B (length contraction plus time contraction)", did not gain as much traction as Einstein's, which simply disregarded any deeper reality behind the symmetrical measurements across inertial frames. There is no physical test which distinguishes one interpretation from the other. https://en.wikipedia.org/wiki/Twin_paradox#No_twin_paradox_in_an_absolute_frame_of_reference What is not really symmetrical is the reality behind Lorentz transformations, not the ether. I can provide you with a non-symmetrical writing of the Lorentz transformation as an Euclidean rotation in space-time and not a hyperbolic one.
Mordred Posted April 20 Posted April 20 Lets look at the reality of the SR/GR symmetry relations. The reality is that they describe in many cases our conservation laws. For SR this directly relates to measuring physical properties. Properties such as the momentum/velocity accelerations particle spin etc etc etc including temperature Any measurable quantity is physically real. If anything it could be argued that the Eather isn't real as its not measurable.
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