On Apr 19, 2013, at 4:39 PM, JACK SARFATTI <
My reply to Z's comments below.
Special relativity is 10-parameter Poincare group P10 covariance of local field equations (invariant action S) + Global Inertial Frame (GIF) invariance of physical speed of light in vacuum.
P10 = T4 * SO1,3
* = semi-direct product
General relativity is 6- parameter Lorentz subgroup SO1,3 of Poincare group covariance of local field equations (invariant action S) + Local Inertial Frame (LIF) invariance of physical speed of light in vacuum.
The latter is the Einstein Equivalence Principle (EEP) in a formal form.
In addition, there is a new group of local general coordinate transformations that is the global translation group T4 locally gauged to T4(x) with the new gravity field as a local gauge field.
ds^2 is still locally invariant under both groups T4(x) & SO1,3
For the most general Local Non-Inertial Frame (LNIF)
ds^2 = g00c^2dt^2 + g0icdtdx^i + gijdx^idx^j
Now in the special case of light rays - classical null geodesics, no quantum theory yet
ds^2 = 0
Therefore,
0 = g00c^2dt^2 + g0icdtdx^i + gijdx^idx^j
0 = 1 + g0icdtdx^i/ g00c^2dt^2 + gijdx^idx^j/g00c^2dt^2
0 = 1 + g0idx^i/ g00cdt+ gijdx^/dtidx^j/dt/g00c^2
define V^i = dx^i/dt = coordinate speed component of light ray in the LNIF
define Ray Chiao's gravi-magnetic 3-vector field
Bi = g0i
0 = 1 + B.V/cg00 + V^2/c^2g00
V = 3-vector coordinate velocity of light measured in the LNIF
The physical velocity 3-vector of light in the LNIF is
c' = V/g00^1/2
So when either B = 0 or B.V = 0, the physical speed of light in the LNIF is the same as in the coincident LIF (vacuum case only)
In general this simple quadratic equation has two roots c'+ & c'-, which in the special case of a rotating Sagnac interferometer gives the fringe shift
The Sagnac effect (also called Sagnac interference), named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is elicited by rotation. The Sagnac effect manifests itself in a setup called a ring interferometer. A beam of light is split and the two beams are made to follow the same path but in opposite directions. To act as a ring the trajectory must enclose an area. On return to the point of entry the two light beams are allowed to exit the ring and undergo interference. The relative phases of the two exiting beams, and thus the position of the interference fringes, are shifted according to the angular velocity of the apparatus. This arrangement is also called a Sagnac interferometer http://en.wikipedia.org/wiki/Sagnac_effect
0 = 1 + B.c'/cg00^1/2 + c'^2/c^2
define x = |c'/c|
Therefore
x^2 + Bcos@x/g00^1/2 + 1 = 0
<3ca857f705daba6b9e6e6d3ccad7990f.png>
2x+,- = (-Bcos@x/2g00^1/2 +,- [B^2cos^2@/g00 - 4]^1/2)
Note, the very bizarre behavior at a horizon g00 --> 0, where the constant "4" term is ignorable
one root for the physical speed of light converges to zero, but the other diverges to infinity (classical limit) when cos@ =/= 0
On Apr 18, 2013, at 7:57 PM, Paul Zielinski <
If the physical speed of light propagating through the vacuum depends on acceleration or rotation of the observer's reference frame, then it follows that in the absence of a light medium, the relativity principle of 1905 SR doesn't generalize to accelerating frames.
If the physical speed of light depends on physical acceleration or rotation of the source, then the light principle of 1905 SR doesn't generalize to non-inertial motion.
Either way, if you're right, the Sagnac experiment would appear to block generalization of Einstein's two principles as stated in his 1905 relativity paper. Which means that the ability to generalize application of these two principles does not discriminate between the Einstein and Poincare versions of "special" relativity.
The difference between Poincaré and Einstein with regard to the ether was not a dispute about whether redundant elements should be eliminated from physical theories; it was a dispute about whether a light medium was truly redundant. Poincaré, the conventionalist, stated quite clearly well before 1905 that once it was determined that the "hypothesis" of an ether was no longer useful to physics, it should be abandoned. His position in 1905 however was that it was still theoretically useful, and not "superfluous" as Einstein argued.
The existence of a light medium in the context of the wave theory of light not only ensures automatic satisfaction of the relativity principle, but also *explains* why the speed of light is independent of the speed of the source. For Einstein this was simply a postulate, assumed as a premise with no physical justification. This alone suggests that Poincaré was right not to regard the idea of a light medium as "superfluous".
Also, the Poincaré-Lorentz ether was not a material ether. The only essential properties attributed to it were (1) it serves as a physical medium for light propagation; and (2) it defines a preferred inertial frame wrt which inertial clock retardation is an objective physical phenomenon, as opposed to being an observer-dependent kinematical artifact according to Einstein 1905.
Point (1) alone shows that notwithstanding Einstein's clever "Machian" 1905 argument for the relativity of simultaneity, Poincaré's ether was not at all "superfluous" once the comparative explanatory powers of the theories are taken into account.
Thus it is no mystery as to why Einstein later changed his position on the ether to the point where it became almost indistinguishablefrom Poincaré's, once he had discarded his Machian blinders.
I think it's interesting that Smolin, who wrote a book titled "The Trouble With Physics", is to all appearances unaware of this reality.
On 4/18/2013 5:39 AM, Jackpacbell wrote:
The physical speed of light depends on g0idx^i/cg00dt
There are two roots for c solving a quadratic equation for ds^2 = 0
Sent from my iPhone
On Apr 18, 2013, at 7:11 AM, Paul Zelinsky f <
In any case, doesn't the Sagnac effect invalidate the light principle, which says that the speed of light is independent of the state of motion of the emitter?
On 4/17/2013 11:07 PM, Paul Zielinski wrote:
Do you distinguish between geometric g_0i =/= 0 and coordinate g_0i =/= 0?
On 4/17/2013 10:35 PM, Jackpacbell wrote:
Speed of light depends on g0i
In Sagnac effect
Sent from my iPhone
On Apr 18, 2013, at 4:19 AM, Paul Zielinski <
Jack, if the theory is generally covariant then the physics can't depend on rotation of the reference frame. The Sagnac effect can only be due to *physical* rotation of the sources wrt the vacuum, caused by geometric g_0i =/= 0. So this doesn't have any impact on my argument below.
On 4/17/2013 5:01 PM, Jackpacbell wrote:
What Z says is wrong because of the Sagnac effect
Speed of light can depend on the acceleration of the frame from g0i terms
In GR the *coordinate* speed of light is not necessarily the same as the actual physical speed of light. Only the coordinate speed depends on frame acceleration.
For example, the Rindler horizon is a coordinate singularity, not a geometric inflection boundary. It is a coordinate artifact in globally flat Minkowski spacetime.
Wrong - the Rindler horizon is physical for the LNIF Rindler observer, who sees Hawking black body radiation from it. Of course it's not there for the coincident LIF geodesic observer. Basically this is group theory The field equations must be covariant under different groups & for SO1,3 c is invariant in vacuum
The GR field equations and the spacetime metric are generally covariant. Which means the objective physics does not depend on the choice of coordinates. Neither does it depend on the choice of Galilean vs. Lorentzian coordinate frame transformations.
In GR the objective physics is determined entirely by the locally Lorentzian property of the metric.
Isn't that obvious?
It's more complicated for propagation of light in media c/n
Of course interacting fields matter + light is Lorentz covariant but not if you integrate out matter This breaks Lorentz symmetry in the partial description of light alone
You are not making the necessary distinctions between geometric Lorentz symmetry and Lorentzian coordinate invariance.
The physics is determined by the Lorentzian property of the metric, not by coordinate invariance. This should be obvious given the general covariance of the theory.
See landau & lifshitz electrodynamics of continuous media.
e.g., in a Bose Einstein condensate u can make c/n -> 0
But this is all premised on Einstein kinematics. I'm talking about a very different model with Galilean kinematics, and objective clock retardation accounted for by the locally Lorentzian character of the metric. That this works is guaranteed by the general
covariance of the theory and the tensor character of the Riemann metric.
That won't work.
Sent from my iPhone
On Apr 18, 2013, at 12:37 AM, Tam Hunt <
Paul, that's my feeling too, as should be clear from my interview questions and my articles that I link to in the interview.
That said, I think Smolin is being smart in how he approaches this needed paradigm shift - pushing a bit but not too hard to alienate people. Time will tell if his approach is right.
I'm curious, Paul, if you have a list of attempts to generalize Lorentzian or Poincarean relativity? I know only of Reg Cahill's process physics as a generalization of Lorentzian relativity (neo-Lorentzian), but I'm sure there are others.
Tam Hunt, J.D.
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On Wed, Apr 17, 2013 at 4:01 PM, Paul Zelinsky <
In case there is any doubt that this myth is still alive an well, here's Smolin:
"The relativity of simultaneity is a consequence of the two postulates that Einstein proposed and so it is deduced from the postulates. The postulates and their consequences are then checked experimentally and, so far, they hold remarkably well."
Smolin clearly states that the the Lorentz coordinate frame transformations and thus the relativity of simultaneity of 1905 Einstein SR are a logical consequence of Einstein's two postulates, the light principle and the inertial relativity principle. He also indicates that the relativity of simultaneity is somehow confirmed by empirical observations.
These are both red herrings.
The light principle is a natural feature of any wave theory of light propagating in a physical medium. It is Einstein who had to pull the light principle out of thin air as a postulate, not the ether theorists. In contrast, the light principle has no natural explanation in Einstein's 1905 version of "special" relativity.
The relativity principle is automatically satisfied by any wave theory of light propagating through a medium, since the speed of propagation relative to the medium is automatically invariant under changes in any observer's frame of reference, whether inertial or non-inertial. And even if the state of inertial motion of the medium itself changes, this will not affect the speed of propagation of light with respect to the medium.
Finally, a theory of relativity such as Poincare's, which assumes a preferred inertial frame and absolute kinematical simultaneity, can also be formulated in a Minkowski spacetime with Lorentzian metric using Galilean coordinate frames, and yields exactly the same empirical predictions as Einstein's 1905 theory.
So from my POV Smolin, while he is quite critical of the current state of theoretical physics, doesn't go nearly far enough.
On 4/17/2013 11:46 AM, Paul Zielinski wrote:
I found Smolin's responses on SR and the invariance of the speed of light to be somewhat disappointing. I think
they understate the case.
According to Einstein's 1905 relativity paper the basis for the invariance of the speed of light was supposed to be
(1) The independence of the speed of light from the speed of the emitter;
(2) The relativity principle, which as stated by Einstein requires that the laws of electrodynamics be invariant under
changes in the observer's inertial frame of reference.
Few realize that both conditions (1) and (2) are automatically satisfied in a wave theory of light propagating through
a medium (since the pertinent laws are formulated with reference to the speed of propagation wrt the medium). Not
only that, but the light principle (1) is a natural feature of that model, whereas in Einstein's theory it comes out of
nowhere and is simply presented as a postulate.
In other words, one has to *assume* that there is no light medium in order for (1) and (2) to present a problem to
begin with. Einstein tacitly assumes that there is no light medium, resolves the resulting apparent inconsistency of (1)
and (2) by abandoning objective kinematical simultaneity in favor of Lorentzian kinematical transformations, and then
declares that there is thus *no need* for any reference to a light medium in his theory (which is correct).
Of course an unreconstructed Machian would immediately conclude based on this "redundancy" that the hypothesis of
a light medium is *ips