Page 3 of 3 FirstFirst 123
Results 21 to 26 of 26
Like Tree1Likes

Thread: Photons slowed to less than 'c' in vacuum by reconfiguring spatial orientatation

  1. #21
    Senior Member
    Join Date
    Jun 2012
    Location
    Santa Barbara, CA
    Posts
    2,766

    Default Mass interpretation of the "time dilation" equation

    The "time dilation" equation can be interpreted as a "mass creation" equation, where c is the rate of "rest" mass creation, t is the time of "rest" mass creation, and the "rest" mass is given by:

    m0 = ct, where t is a specific time needed to create a fundamental rest mass. If this is the minimum mass in the universe (think Higgs boson), then all other bosons can be created by specifying a "perturbation" v (a different mass creation rate) and a different time t' (a different mass creation time), which taken with m0 allow one to "create" the "rest" masses of all the other particles:

    m' = m0

    (this equation can be related to space-time by interpreting as a light density that defines each boson independently, but based on the funamenal particle m0

    One can, of course, take ct' to be a new fundamental rest particle, and define further bosons from that, which amounts to either specifying a different value of m0 to begin with, or defining different "fundamental" particles, all defined by the same mass creation rate, in which the transition from ct -> ct' does not explicitly include v.

    By deconstruction v/c this relation () can be preserved, provided that either the space "ruler" or the "time" clock is taken to be equal in the primed and unprimed frames, in which case can be taken as a density that depends on the free variable (and is thus "co-variant").
    Last edited by BuleriaChk; 05-05-2016 at 11:39 AM.
    _______________________________________
    "Flamenco Chuck" Keyser
    The Relativistic Unit Circle 03/28/2017 07:40 AM PST
    Proof of Fermat's Last Theorem Updates 03/19/2017 8:23 PM PST
    Ignore List -The Peanut Gallery.

  2. #22
    Senior Member
    Join Date
    Jun 2012
    Location
    Santa Barbara, CA
    Posts
    2,766

    Default Polarization, spin, and Fermions

    But what of the "(vt)" term in the "Lorentz/Fitzgerald" contraction?

    If this equation is no longer Galilean, but the above term is in the "()" "dimension", it can be interpreted as "polarization" of a photon, or "spin" of an electron. This means that photons can interact via their polarizations; like polarizations repel, unlike polarizations attract.

    So we have ((ct'),(VT),}), where ct' is the new "rest mass" for the boson defined by c,v, and VT is the spin perturbation that accounts for the fermion.. The resultant "spin mass" can be thought of as the cross product between the radius ct' and the tangent to the radius at the circumference, which corresponds to the "v x B" term in the Lorentz Force equation....

    , where the first term correpnds to inline force (between charges "permittivity") and the second corresponds to "spin") So, (very) roughly speaking, the quantity dependent on E corresponds to the "boson" part of the characterization, and the quantity depending on B corresponds to the "fermion" part of the equation.

    m0 = 1 and v=0 gives the classical expression.

    Note that V can be either positive or negative, corresponding to two "directions" of spin. For V = 0, the boson equation obtains. Also, permittivity and permittivity have not been explicitly included -see Coulomb's and Gauss's law for reference).

    (It is interesting that the trace of the four dimensional EM field tensor is 0, subject to symmetry conditions on A . If anyone is at all interested, I'll attempt to clarify)

    (Note: this equation requires a bit more discussion (in particular, one has to get much more persnickety about signs, and Dirac applies both positive and negative values to m0, etc.), but shows the relation of spin to mass in the Lorentz force equation in relation to the vector potential. Also, F is a vector sum. I'll write more on it later on.)

    Dividing the r.h.s. by m gives the vector (the vector potential) as the Lorentz force per unit "rest" mass (EM. STR) (ct), which now includes "spin" Note that this is also subject to a "perturbation", which requires further modification of the equation (which can be interpreted as "gravity" (inertial) perturbation/interaction in GTR).

    (In classical atomic (spin-orbit) quantum mechanics, one ignores the 0 component in favor of the magnetic moment (0) , and considers the and vectors. Modifying these to include relativity results in the hyperfine structures of energy levels of the atom...)

    (if the Lorentz forces are equal and opposite, the parts of the equation are squared independently, similar to the "time dilation" equation to derive the energy)

    The term then adds mass to the "time dilation" equation via the prescription [tex]\pm[/tex(VT), where V and T are now different from the v,t of , and define an added energy to that given by the rest mass definition. These are not subtracted, since the energy equation is ultimately squared, but rather contributes to the two particles split by the B field in the Stern-Garlach experiment; if there is no B field, the particles do not interact - Physics interprets this as the particles having an intrinsic spin, so that fermions are defined differently from bosons. (If the positive mass is equal to the negative mass, the VT term disappears, but because of the squaring, the "rest" mass ct' changes (increases) yet again i.e., the pair has recombined to add vectorially to the "bare" mass ct' i.e., the spins are equal and opposite).

    ("spin/polarization mass" is actually a cross product between a change in radius and circumference)..

    The Pauli equation only interprets the VT term, where as the Dirac equation interprets the whole equation, which includes the (vt',ct) - defined "rest" mass as well as spin/ploarization.

    (Actually there is a direct "head-on" interaction in addition to the tilted "spin" interaction, but this would correspond to a "red shift" - much harder to detect. - For gravity B probe, the spin would correspond to the "geodetic" effect, and the "head-on" effect would correspond to "frame-dragging". Frame- dragging is much more difficult to detect, since it lies along the geodesic, rather than being the "shear" effect of the geodetic..)

    There is much more to be said about this, but the bottom line is that polarization converts the boson model of photons to fermions, and allows interaction (Note that Newton's law of gravity does not include spin, and I think the was Einstein's motivation for interpreting the non-linear (coordinate dependent) version of such an interaction as gravity. Since such a transformation depends on BOTH space and time, the transformation is contra-variant, and thus changes the effective speed of light in space-time (actually momentum/energy) diagram)...

    So the photons do interact, and are slowed down in one direction by the "headwind" created by the other since they interact like fermions via polarization; the angular conic section is necessary so that plane waves are not involved (which would have no interaction).... and if there is no "headwind", the photons travel at c, since they are now non-interacting bosons...

    (One can also say the "headwind" is an increased "density" in the vacuum created by the opposing beam. This will, of course, change the E and B fields to effective E' and B' fields - i.e. D and H fields - within the beam path)

    Well, that's quite exhausting for me this morning, but is my basic interpretation of what is going on (IMO, at least for the next three minutes) - the angle produces the interacting local E,B that allows the photons to interact, which slows them down compared to the case where only one "lens" is used....

    Cosmologically, this "headwind" is responsible for red shift (photons toward a distance source - e.g. "from behind" us, interacting with incoming photons from the source, lowering their energy, and thus the locally observed red shift, interpreted relative to a local blackbody)

    Photon "spin" interactions are responsible for "Einstein" rings.... (For Einstein, this is independent of photon spin (an EM effect), but comes from a "curvature" due to an un-specified mass - unspecified because it would involve action at a distance, which Einstein is desperate to avoid...)
    Last edited by BuleriaChk; 05-10-2016 at 01:43 PM.
    _______________________________________
    "Flamenco Chuck" Keyser
    The Relativistic Unit Circle 03/28/2017 07:40 AM PST
    Proof of Fermat's Last Theorem Updates 03/19/2017 8:23 PM PST
    Ignore List -The Peanut Gallery.

  3. #23
    Senior Member
    Join Date
    Jun 2012
    Location
    Santa Barbara, CA
    Posts
    2,766

    Default Relativistic effect on path lengths

    Note: I edited the expression for the Lorentz force in the previous post by replacing q with which makes relativity consistent with Maxwel's equations. Replacing q with solves the issue. One can just as well apply to E and B instead, leaving invariant.
    ==========================================

    The above post was to show how spin increases the mass of the total system from the "bare" mass (m'=ct'), where m' is the mass of the system in terms of some even more fundamental mass ct, defined by relativistic perturbation v via .


    The "time-like" expression of this bare mass is given by t' = t.

    However, the "space-like" expression of this bare mass is given by

    (covariant transform w.r.t. space, preserving inertial frames and v/c) - i.e., here represents a light density depending on v/c. So an increase in implies an increase in the mass x'.

    With one of the lenses "masked", the "head-on" change would be described by v = 0 the boson, so that x' = x.

    However, when the lens is unmasked, so that opposing streams of photons are in play, the addition to the system is described by v = c

    This might appear to be a problem for the denominator of the space transform (and I think is the mistake made by GTR in hypothesizing singularities)*, but it assumes that v and c are in the same dimension (i.e., the Galilean description of space - "inline"). Relativistically, however, what has actually happened is that one has added an additional photon to the system. What was described as (ct',v'') (in terms spin perturbation to the bare mass) is now described by two particles (ct',ct') - that is, (m',m'), and n terms of relatistic momentum, (m'c, m'c) so the total momentum is 2(m'c), with the changed momentum appearing as m'c = k' in the wave equation :



    (That is, = 2 for vt' = ct).

    (For the fundamental particle, kx=Et, so = 1, identically, since kxc = (m0c)xc = (m0c)(ctc) = m0c2tc = Etc )

    Then (ignoring the physical shape of the lens, and assuming the distance is defined by the tips of the cones), the "off axis" momentum of the photon will have an additional momentum described by the longer momentum "path" through the additional density characterized by the spin interaction:

    (), so the effective momentum will have changed relative to the "head-on" path as a function of due to the spin/polarization of photon-photon interaction.


    This will be true for every wave in the packet, but the path lengths will be different, depending on , so will change the "spectrum" of the packet compared to the "head-on" packet, where the latter is changed from only one "light on" for a single photon.


    (If there is no photon, the physical distance can still be measured in Galilean coordinates as x = ct.)


    For this reason, I usually use caps for CT as mass, and lower case for ct as distance - they are related by the spatial description of STR above by deconstructing v/c and setting t' = tc

    *For GTR one approach is to change v to Vgravity and t' to T'gravity in its interaction description with the "fundamental particle" m0=ct (Higgs Boson). The scale differences will be astounding, but there it is....
    VT' going to infinity implies that total mass CT' goes to infinity, but the "rest" mass becomes insignificant (goes to zero).....

    This assumes that c is constant throughout the Universe, rather than just being measured within our solar system, in terms of EM defined by the BB temperature on the surface of the earth - that is, the sun..

    Not only that, but every material body (e.g. planets) will have different masses, so there is no such thing as a "conserved" gravitational mass, which is why Einstein avoids mentioning them...

    But then, that may be just me, as a believer in "emergence" rather as opposed to "reductionist" philosophy in physics... not to mention quantum triviality...

    But then, as a relativistic solipsist, I don't believe in coordinate systems anyway....
    Last edited by BuleriaChk; 05-10-2016 at 01:14 PM.
    _______________________________________
    "Flamenco Chuck" Keyser
    The Relativistic Unit Circle 03/28/2017 07:40 AM PST
    Proof of Fermat's Last Theorem Updates 03/19/2017 8:23 PM PST
    Ignore List -The Peanut Gallery.

  4. #24
    Senior Member
    Join Date
    Jun 2012
    Location
    Santa Barbara, CA
    Posts
    2,766

    Default Re: Relativistic effect on path lengths

    Edit/Update -------------------------
    Replacing q with solves the issue. One can just as well apply to E and B instead, leaving [tex]q_0[\tex] unchanged.

    == so this is incorrect ===============
    Now that I think of it, I think one can also postulate the v = V provided that two dimensions (c,v) = (C,V) for inertial frames obtains, provided one makes the distinction between "time-like" transform (xc = xv) and "space-like" transform (tc=tv) (but not both; otherwise one is only describing rest mass with no perturbation) provided that v/c is deconstructed into its space-time components, so that c is still preserved in the characterizations. Then in the Lorentz force equation, v=V=0 implies = 1 and there is no contribution from the B field (i.e., the field is static, only the E field contributes).

    (Not sure abut this, though-- stay tuned..*

    =============================================

    Note that c=0 implies that the mass of light =0 means that there is no other contribution to the mass in the Lorentz force; (which is why the trace = 0 in both the EM Field tensor and the Pauli matrix (1,-1) which characterizes only the spin of an electron, whereas the Dirac equation(s) characterizes the rest mass as well, (as well as including three dimensions of space, where the results of a single experimental event can be observed and characterized via Feynman path integrals)

    That said, "three dimensions of space" can be thought of as Cartesian coordinates, but the total momentum/energy of the (linear, "gauge invariant", inertial) system is characterized by where r=m'=m0 and

    In any case, the vector potential A is the electro-magnetic force per unit mass. Now consider the result of setting A = m' = 1... in the wave equation

    *This characterization of the relation between the Lorentz force and STR assumes that both (v,c) and (E,B) are orthogonal, in which only inertial "frames" are considered. For classical physics, set m = 1, for relativity set m'=m0, so that if Maxwell's Coulomb/Gauss and Ampere's laws are correct, c is a constant (a 1/r^2 law implies symmetry). Einstein's GTR perspective is that E and B might not be orthogonal, and then there must be a fourth dimension which sets (gravitational) mass independent of c, say C". One could then describe a linear form of this by simply setting C" = v' in a new "Time Dilation" equation (with a separate scaling factor t"). Locally, this would be a force that changes direction of an incoming photon due to its interaction with a medium, but this is already modeled in classical/STR....

    At any rate, I think this issue is the crux of the interpretation of observation of the Universe; Kaluza added this fifth"spatial" dimension so as to include Maxwell's equations in Einstein's original proposal, where m0 = ct is the "fourth" dimension and vt' is the "fifth" dimension. Even so, it doesn't include global curvature (because x,y,z,m0=ct,vt') is still "flat" - one must change c or k=1/r or both, and especially identically (so "god" (acting at a distance) must be involved in ways not characterized by Newton, STR, or Maxwell ....

    Of course, to a real physicist, "god" is simply a name for (dark energy, dark matter) for mystics, there are parallel universes, wormholes, space-time expansion, whatever...

    (Of course, one can retain local physics, simply by imagining that the (E,B) vector is turned in an imaginary coordinate system....
    Last edited by BuleriaChk; 05-10-2016 at 01:11 PM.
    _______________________________________
    "Flamenco Chuck" Keyser
    The Relativistic Unit Circle 03/28/2017 07:40 AM PST
    Proof of Fermat's Last Theorem Updates 03/19/2017 8:23 PM PST
    Ignore List -The Peanut Gallery.

  5. #25
    Senior Member
    Join Date
    Dec 2012
    Location
    Long Beach Ca.
    Posts
    185

    Default Re: Photons slowed to less than 'c' in vacuum by reconfiguring spatial orientatation

    It would seem to me that up until the midway point of the photons travel, these photons are moving toward each other, hence acceleration, and therefore, time speeds up. I think that the equal and opposite effect to that acceleration must be recorded as Space-time. as this would increase the distance.

  6. #26
    Senior Member
    Join Date
    Jun 2012
    Location
    Santa Barbara, CA
    Posts
    2,766

    Default Re: Photons slowed to less than 'c' in vacuum by reconfiguring spatial orientatation

    Quote Originally Posted by David Hawkins View Post
    It would seem to me that up until the midway point of the photons travel, these photons are moving toward each other, hence acceleration, and therefore, time speeds up. I think that the equal and opposite effect to that acceleration must be recorded as Space-time. as this would increase the distance.
    in STR, "time" does NOT refer to travel time, but "mass creation" time; vt' (second beam on) is a perturbing mass that is absorbed into an original mass ct (one beam off) to produce ct' (both beams on).

    (Distance actually decreases because it is the distance a more massive photon would travel in comparison to a "free" photon - the density transformation is contra-variant, rather than co-variant.) So x'/ = x0 ; as gamma (relative density) increases, x' (as mass) increases, where x' = ct'. However, this is related to Galilean space-time contra-variantly for c, v "velocities" where x=ct interpreted as a distance along the x-axis relative to the origin, rather than a space-time diagram.

    For STR, one has to be very careful about what one means by "space-time", because it determines whether one is interpreting it the coordinate "distance" domain (a la empty space between objects, with light traveling as particles in a straight line between source and sensor) or the mass/energy domain (characterized by the Minkowski metric). It is only in the STR case with QM (i.e., QFT - Quantum Field Theory) that the distinction is resolved via Feynman propagators....

    Again, it is CRITICAL to begin with the Lorentz transform (starting with its relation to the MM experiment) which is the foundation of it all - Einstein does not include spin in STR - the only "acceleration" is the creation of the initial particle and the perturbation to change its effective "mass" via the "time dilation" equation - which is actually a "mass creation" equation which describes a final state in terms of an initial state and a perturbation.

    For STR (i.e., light) one simply CANNOT rely on na´ve concepts of "space" and "time"....
    Last edited by BuleriaChk; 05-12-2016 at 06:22 PM.
    _______________________________________
    "Flamenco Chuck" Keyser
    The Relativistic Unit Circle 03/28/2017 07:40 AM PST
    Proof of Fermat's Last Theorem Updates 03/19/2017 8:23 PM PST
    Ignore List -The Peanut Gallery.

Page 3 of 3 FirstFirst 123

Bookmarks

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •