Jump to content

qchiang2

Members
  • Posts

    2
  • Joined

  • Last visited

Retained

  • Suspended

qchiang2's Achievements

Lepton

Lepton (1/13)

10

Reputation

  1. I am not trying to prove Einstein wrong. I simply think certain logic can be improved with the same philosophy that Einstein followed. The outcome is a more general 4+1 spacetime which covers rather than contradicts Lorentz spacetime. The positive thing with this improvement is a promising gravitation theory, which may answer some of the most mysterious problems in gravitation. Qchiang
  2. The assumptions discussed here are: 1. Assumption of inertial frames in special relativity (SR), and 2. Assumption of consistent proper time in general relativity (GR), which are both logically imperfect and can be improved to possibly solve most of the mysterious riddles in gravitation and particle physics. At the time when special relativity was developed, there was no better logical definition of inertial frames than an abrupt assumption. Both particle physics and gravitation are based on the Lorentz spacetime defined based on this assumption. But 20th century physics had progressed faster than this assumption and this spacetime definition can keep pace with and numerous mysteries (e.g. quantum gravity, dark matter, gravitational waves, Higgs particle, parity violation, etc.) linger. The good news is that 20th century physics also provides a logical definition of inertial frames unavailable previously, which enlarges rather than contradicts this assumption, as to be shown next. The greatness of Einstein lies in his teaching that spacetime be defined by (relevant) physical phenomenon. Unfortunately, absoluteness is reclaimed again for Lorentz spacetime. Throughout 20th century, particle and gravitation physics are developed on a “subjective” Lorentz spacetime in the same way electromagnetism was on Newtonian space and time previously. This prohibited a more suitable spacetime for gravitation and massive particles from being defined directly by gravitation and massive particles in the way Lorentz spacetime was defined by electromagnetism. In what follows, I will present the logical definition, then show how it can help to solve some of the mysteries in gravitation. The Assumption of Inertial Frames in Special Relativity Lorentz spacetime is defined for uniformly moving frames to measure light at the same speed, regardless of the frame velocity. The problem is that “uniformly moving” frames are pre-selected before Lorentz spacetime scales are defined to justify its uniformity. Likewise, light and faster-than-light (FTL) mono matter waves also cannot be distinguished until Lorentz spacetime scales are defined. The remedy: the strict spacetime definition without presumption would be based on the principle that all light and FTL (according to Lorentz scales) mono waves be measured at the same speed, and include both inertial and non-inertial frames, with “uniformly” moving frames defined “as measured by the spacetime scales being defined”. Not being pre-occupied with Lorentz spacetime, just imagine what would be the spacetime definition which accommodates “all” mono matter waves most elegantly. It is a 4+1 spacetime, as mono waves have but one more degree of freedom, its speed. Adding one extra dimension to accommodate this degree of freedom naturally levels all mono waves to the same (light) speed. The 4+1 spacetime is the “inevitable” conclusion of special relativity if the definition of Lorentz spacetime is executed rigorously. The 4+1 spacetime is the most natural and symmetric spacetime for both massive and massless particles as all of their associated waves share the same massless wave equation in the 4+1 spacetime [ (∂0)^2 - (∂1)^2 - (∂2)^2 - (∂3)^2 - (∂m)^2 ] φ = 0 (1) But when observed from the Lorentz subspace, the same waves appear as [ (∂L0)^2 - (∂L1)^2 - (∂L2)^2 - (∂L3)^2 – m^2 ] φL = 0 (2) where mass is gained automatically due to change of scales. (Subscript L means under Lorentz measurements, while no subscript is for the 4+1 scales). Superscript m is for the extra dimension, xm. The transformation between them, for “each” mono wave, is dxL1 = dx1 (3a) dxL2 = dx2 (3b) dxL3 = dx3 (3c) dxL0 = dx0 • [(p1)^2 + (p2)^2 + (p3)^2 ]^½ / [(p1)^2 + (p2)^2 + (p3)^2 + m^2]^½ ≤ dx0 (3d) dxLm = 0 (3e) Since Lorentz time scale is shorter than the 4+1 time scale, eq. (3.d), it measures “the same” mono wave as FTL. Just like SR uniting the absolute Newtonian time and space to form a 3+1 space-time continuum, the 4+1 spacetime unites mass with Lorentz spacetime to form a 4+1 space-time-mass continuum, as demonstrated in eq. (1). Eq. (1) is also more beautiful than (2) as xm is treated on the same footing as all other dimensions. The 4+1 spacetime doesn’t contradict the verified Lorentz spacetime, but only augments it. It makes no sense to rule out the FTL mono waves at the beginning as they are “not” faster than light in the more natural 4+1 spacetime. Instead, what should be ruled out is actually the assumption of inertial frames. (Note: since in the real world we feel only one time flow, the various Lorentz times for different waves are synchronized and spatial dimensions are expanded.) This immediately leads to a 4+1 universe (like the spatial dimensions, the extra dimension, xm, is also external) with the universe we see being a curved 3+1 manifold (most likely the curved 3-surface of a 4-sphere) in the flat 4+1 spacetime. If this were true, the same quasars (or whatever objects sitting at the other end of the spherical universe) would likely be observed from both opposite directions in each of the 3 dimensions of the universe (just like two persons traveling from north pole in opposite directions at equal speeds will eventually meet at south pole.) Actually, the numerous double quasars may already serve as partial evidence, where the whole spherical universe serves as the lens. The scarcity of galaxies immediately before the quasar region might also reveal the fact that the 3-volume near the quasar region is actually quite small, as conjectured by this model. The philosophy behind: SR and GR have reached the deepest quest for the nature of mass. We have to define inertial mass, gravitational mass and the equivalence between them through the definition of space and time. Correct understanding will only emerge with correct definition, which usually is the one which renders physics in the simplest and most elegant form. Before all these quantities are defined, we should just let physics define them without imposing any assumptions. However, presuming knowledge of uniform frame velocity, we inadvertently closed the door of finding the real nature of mass (thus “forced” mass to be “intrinsic”). Put differently, based on the energy-momentum-mass relation of SR, (E)2 – (p1)2 - (p2)2 - (p3)2 - m2 = 0, space (inverse of energy), time (inverse of momentum) and mass can be defined. But there are 5, not 4, quantities to be defined. All the 5 should be defined simultaneously, none should take precedence over the other. But Lorentz spacetime is defined prior to mass by electromagnetism. Even though GR attempted to incorporate gravity later, it is still based on Lorentz spacetime, and the real nature of mass (i.e. nature of inertia and gravity) cannot be revealed. To have mass involved in equal status, both light and FTL (massive) waves must be used in its definition, as suggested by Lorentz and agreed by Weyl. This leads unambiguously to the elegant 4+1 space-time-mass continuum, which has built-in equivalence of inertial and gravitational mass (i.e. the real essence of gravitation), and, if interpreted appropriately, the simplest and most elegant gravitation theory should come out of it. Obviously, this is a profound change not easy to adjust over night. Point is there are in fact logically imperfect assumptions in SR and GR (to be discussed next) which can be improved and I didn’t impose anything of my own, I just carried out Einstein’s teaching one more step and replaced assumptions by logical definitions whenever possible. This is the only logical conclusion which yields just perfect answer to quantum gravity and unification with quantum mechanics as to be shown next. The Assumption Of Consistent Proper Time In General Relativity; Gravity From The 4+1 Spacetime And Unification With Quantum Mechanics The GR theory constructed on the spacetime scale definition based on the “assumption of consistent proper time” is self-consistent and hard-to-disprove. While a definition cannot be judged right or wrong, the assumption should be subject to a simplicity test, that is, whether the definition renders physics in the simplest and obvious form (on top of experimental verifications). That is how Lorentz spacetime replaced Newtonian space and time in special relativity. Unfortunately, no further test has been carried out since gravitation, strong and weak interactions are invoked. This is why Lorentz spacetime provides only elegant electromagnetism, but not simple and obvious gravitation and particle physics. (Though Einstein Equation is considered to be elegant, the complexity and persistent failure of quantum gravity and numerous mysteries. e.g. unfound graviton, dark matter, flat universe, etc., are sufficient grounds to doubt if the assumption is appropriate and if GR is the right expression for gravity). A higher perspective is needed for a clue. While Lorentz spacetime is perfect for electromagnetism, it is not as beautiful as the 4+1 spacetime for massive particles due to the mass term. (Even though GR tried to amend it, the best elegance has already been lost. In other words, SR and GR should be done in one shot). In what follows, I will show the problems with this assumption and that proper time should logically be proportional to the mass which generates the local curvature. (Consistent proper time is a concept belonging to special relativity only). Quantum gravity, unification with quantum mechanics and other mysteries should readily be answered. In defining spacetime scales over a curved manifold, general relativity lets proper time act as the standard yardstick and assumes it be consistent throughout the universe. The problem can be seen as follows. Einstein equation is written as G = 8πGT (4) Consider the curvature generated by the stress-energy of a single type of particles with uniform mass m and uniform momentum p (and E = (p2 + m2 )½ ). As stress-energy tensor of such a curvature can be decomposed as a product of two 3+1 vectors, T(E,p^) = (E,p^)×(E,p^)/[V(E^2 – p^2 )½ ] (5) Einstein curvature tensor can also be decomposed in the same way, G(T,X^) = (T,X^)×(T,X^)/[V (T^2 – X^2 )^½ ] (6) Hence Einstein equation can be written as (T,X^)×(T,X^)/[V(T^2 – X^2 )^½ ] = 8πG (E,p^)×8πG(E,p^)/[V 8πG (E^2 – p^2 )^½ ] (7) Thus we obtain a 3+1 “vector” equation, (T,X^) = 8πG (E,p^) (8) • There are complicated mathematics with some parameters to be set between the metric gμν (distance and time units) and the vector (T,X). It is reasonable to assume these parameters should be set to make local time unit dξ0 and distance unit dξ be proportional to nothing but T and X of the vector (T, X). Let’s call this the “Assumption of Local Space and Time Units”. Let dξ0 = kT (9a) dξ^ = kX^ (9b) Hence, (dξ0 , dξ^ ) = (kT,kX^) = 8πkG (E,p^) (10) On the other hand, this assumption, eq. (9), is also supported by quantum mechanics. Consider these particles as waves of energy E and momentum p, the natural space and time units should be related to nothing but the wave length and frequency of the waves, as there exists nothing else. This is a pre-requisite for unification of gravitation with quantum mechanics. From (10), the local proper time unit can be derived as dτ = [(dξ0)^2 - |dξ|^2 ] ½ = k [T^2 – X^2 ]^½ = 8πkG [E^2 – p^2 ]^ ½ = 8πkG m (11) which clearly depends on the mass behind local stress-energy. In other words, Einstein equation itself dictates proper time variation according to underlying masses (at least in this case). If a neighboring curvature is generated by a uniform-mass-uniform-momentum stress-energy of mass twice as big, then its proper time unit should also be twice as big. Assuming the same proper time units would inadvertently reduce all 4-vector and mass values by half for the neighboring locality. Thus, Einstein equation is self-contradictory. This is why 4-vectors and masses cannot remain constant after parallel transport. Even if the “Assumption of Local Space and Time Units”, eq.(9), were wrong, it wouldn’t help; it only hides the problem, as 4-vectors and masses still cannot remain constant after parallel transport. The “Assumption of Local Space and Time Units” only manifests the hidden problem. This also hints at the cause of the dark matter and flat universe mysteries. The correct parameterization would be obtained by admitting dependence of local proper time on underlying masses and adjusting equation (7) according to eq. (11), [(T,X^)×(T,X^)/(dτ)^2 ] / [V(T^2 – X^2 )^½ /(dτ)] =[8πG(E,p^)×8πG(E,p^)/(8πkGm)^2] /[V8πG(E2–p^2)^½/(8πkGm)] (12) No more mass and 4-vector distortion under parallel transport. Without the adjustment, (7) is applicable only locally, which is the only situation GR can be proved correct (as was done in the solar system). For a swarm of particles, each term must be adjusted separately before summed up, ∫dX^ \sum T\ [(T,X^)×(T,X^)/(dτ)^2 ] /[V(T^2 – X^2 )^½ /(dτ)] = ∫dp^ \sum E\ [8πG(E,p^)×8πG(E,p^) /(8πkGm)^2]/[V8πG(E^2–p^2)^½/(8πkGm)] (13) Notice that the summation over mass is now shifted to that over energy. Because mass is not an independent variable of Einstein tensor, thus must be consistent, otherwise both energy, momentum and mass become independent variables, which are more than actually exist. On the other hand, Einstein equation without adjustments, ∫dX^ \sum dτ\ (T,X^)×(T,X^)/[V(T^2 – X^2 )^½ ] = ∫dp^ \sum m\ 8πG(E,p^)×(E,p^) /[V(E^2 – p^2 )^½ ] (14) is a summation of oranges and apples, i.e. over terms of different masses and space/time scales (i.e. proper times, dτ’s), which is a real mess. One can see the problem in Einstein tensor is real serious, not only between localities, but also is a mess within itself at one locality. Claiming Einstein tensor being non-linear and non-decomposable, or claiming the “Assumption of Local Space and Time Units”, eq.(9), being wrong cannot be an excuse and is irresponsible, as these claims are independent of the mess in Einstein tensor and an arbitrary Einstein tensor is still not based on a consistent proper time (or mass) no matter what, and mass and 4-vectors still distorts after parallel transport. They only hide the problem, which eventually shows up in the persistent failure of quantum gravity, unfound graviton, gravitational waves and dark matter, etc. It is highly doubtful that gravity will be quantized under string theory, as the theory misses the point. It is said Einstein equation is beautiful. But what good does it do if mass and 4-vectors don’t even conserve after parallel transport? Even though the adjusted equation (13) solved the problem of scale distortion, it still suffers from the problem of nonlinearity. Since none of the experimental tests of general relativity verifies that gravitation must be nonlinear and since the verification of GR in the solar system is not super accurate (like QED), we are tempted to cautiously replace it with a fairly close linear equation. It is Einstein’s highly intellectual insight to envision curvature in gravitation, but it should probably be expressed in the language of 3+1 curvature embedded in a “flat” 4+1 spacetime, rather than in terms of Riemann geometry. It is believed the following linear theory from the 4+1 spacetime will produce the same, if not better, result in the solar system, but produce a different and much better result at large scales, like in galaxies and clusters of galaxies, thus solving the dark matter and flat universe problems (in addition to quantum gravity and unification with quantum mechanics). Instead of eq. (13), we adopt the closest linear approach to it, i.e. its basic ingredient, the vector equation (T,X^) = 8πG (E,p^) (15) Since inertia is manifested in each mono wave by the amount it’s faster than light, gravity should also be manifested in each mono wave. Parallel to the superpositioning concept of quantum mechanics, each mono wave in the 4+1 theory also contributes its part to the spacetime definition of the manifold. Thus, corresponding to a wave packet Ψ = ∫dp^ \sum E\ f(E,p^) exp[-iπ(x0p0-x^∙p^)] (16) there is the superpositioned “total curvature vector” (as opposed to curvature tensor) related to the total energy-momentum ∫dX^ \sum T\ f(E,p^)(T,X^)/(dτ) = ∫dp^ \sum E\ 8πGf(E,p^)(E,p^)/(8πkGm) (17) Notice that left and right sides have their proper time and mass synchronized, i.e. summed up on consistent mass and proper time to avoid summation over oranges and apples, with dτ = 8πkG m (18) This gives a genuine unification of gravitation with quantum mechanics. The mathematics in this theory is extremely simple, but, like electromagnetism, that is what the right theory for such a fundamental force should be. 4+1 Quantum Gravity. Gravitational Waves And Gravitons The most fundamental form of gravity, eq. (15), can be combined with (18) (T,X^,dτ/k) = 8πG (E,p^,m) (19) One sees the proper time, dτ/k, in eqs. (18) and (19) are just the component of the extra dimension xm, because (∂ξ0)^2 - (∂ξ1)^2 - (∂ξ2)^2 - (∂ξ3)^2 - (∂ξm)^2 = 0 (20) and dτ ≡ [(dξ0)^2 - |dξ|^2 ] ^½ = (∂ξm) (21) Thus, we have the most elegant vector equation of gravitation in the 4+1 spacetime, (T,X^,dτ/k) = (T,X^,xm) = 8πG (E,p^,m) (22) The linear equation (22) will generate gravitational waves in the 4+1 spacetime Ψ = exp[-iπ(x0p0- x1p1- x2p2- x3p3- xmpm)] (23) which are observed faster-than-light in the Lorentz spacetime as ΨL = exp[-iπ(xL0pL0 - xL1pL1 - xL2pL2 - xL3pL3 )] = exp[-iπ(xL0pL0 - xL^∙pL^)] (24) In other words, gravitational waves are but the FTL mono matter waves being denied all the time, and gravitons are just all elementary particles formed from the mono waves, which are always observed but never recognized as gravitons. It is conjectured that cosmic rays could just be gravitons emitted as gravitation radiations by astronomical bodies. Dark Matter and Flat Universe Unlike in Einstein theory where only local Lorentz scales is available for measurement, the 4+1 theory uses one consistent 4+1 scales throughout the universe. Assuming a spherical 3-d universe, a locally FTL mono wave far away will be measured “even faster” when translated to the “universal” 4+1 scales which has its xm perpendicular to the Lorentz spacetime on earth. This is simply because the far-away Lorentz spacetime is not parallel to the Lorentz spacetime on earth, thus will augment mass, and naturally cause the missing mass problem. In other words, Einstein theory has never realized the fact that distant masses are actually larger than it appears under the one consistent xm on earth, because it uses the non-consistent local Lorentz scales. Similarly for the flat universe mystery. Discussion The moral should be: 1. if there exists no logical theory or definition, an assumption cannot be avoided (e.g. the principle of relativity). But if one exists (e.g. that for the inertial frames), the assumption should give way to the logical assumption. 2. As to solving the gravitation and particle mysteries, it should first be attempted to replace the assumption by the logical definition. Other attempts would not be necessary and is not likely to be fruitful before the logical replacement. It appears that the logical strengthening of SR and the nature of (inertial and gravitational) mass it reveals in the xm dimension can hardly be defied. The perfect fit of the consequential 4+1 gravitation on explaining almost all mysteries (e.g. quantum gravity, unification with quantum mechanics, gravitational waves and gravitons, dark matter and flat universe, etc.) also appears indispensable. The 4+1 spacetime also answers parity violation due to the xm dimension. The only price is abandoning Einstein equation (and replacing it by a fairly close linear vector equation). But, it has failed on many fronts for nearly a century. Are we going to defend it forever like a religion? Question: Is there someone who is in the capacity of organizing a project to verify: 1. Same quasars observed in opposite directions in all 3 dimensions, which will prove immediately that our universe is 4+1 dimensional. 2. The 4+1 gravity may be as accurate as, or even better than, Einstein theory in the solar system. Mysteries in particles cannot be solved by the 4+1 spacetime alone. It also requires the concept of solid angle rotation discussed in a separate topic through the following link: http://groups-beta.google.com/group/sci.physics.relativity/browse_thread/thread/d31950fa77ab3163/f1665120b8a1db4b#f1665120b8a1db4b qchiang
×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.