Begin forwarded message:
From: Paul Zielinski <
Date: January 3, 2011 12:50:30 PM PST
To: JACK SARFATTI <
Subject: Re: Fwd: Fock's position is simply silly in my opinion
On 12/31/2010 8:52 PM, JACK SARFATTI wrote:
Subject: Fock
Sure no problem with that.
General covariance is T4 ---> T4(x)
Of course one can have LNIFs even when the curvature is zero.
OK.
This is mere quibbling about definitions.
There is no necessary link between "relativity" and "uniformity".
There is a link between "relativity" and the uniformity of Minkowski spacetime wrt
the Lorentz group.
Obviously in the case of zero curvature globally.
The principle of relativity as stated by Einstein in his 1905 paper requires that the phenomena
*directly observed* by an observer in inertial motion be exactly the same for every inertial frame.
It *also* requires that the mathematical description of such phenomena be identical in every
inertial frame (Einstein wearing his Machian-empiricist "hat" expresses this as "the physical laws
are the same in every inertial frame of reference").
Sure, so what? The same thing is true in 1916 GR PROVIDED THAT Alice and Bob are LOCALLY COINCIDENT.
Now local coincidence is a restriction, but there is also a new freedom. Alice and Bob need not be inertial, though they can be.
This is a consequence of local gauge invariance.
In SR this in turn requires the objective uniformity of Minkowski spacetime, as Fock defines it in
his "Three Lectures".
Yes, in SR which is the global Poincare symmetry prior to at least localizing T4 ---> T4(x) introducing "nonuniformity" in the four translations.
Going further localizing SO1,3 ---> SO1,3(x) gives anisotropy in the 6 spacetime rotations. We can also have nonuniform dilations (Weyl 1918) as well as inhomogenous special conformal acceleration boosts to Rindler observers. Finally we need to use the de Sitter group localized to a /\(x) that can be both positive and negative on different scales. So really we need x and a new scale parameter related to the hologram horizon getting us to the entropic emergent gravity perhaps.
Covariance is trivial once the physical laws are put in tensor form.
Well known.
Uniformity of spacetime is not trivial.
That's the meaning of local gauge invariance applied to the universal spacetime symmetries of the global dynamical actions of all interaction non-gravity matter fields. Gravity is the local gauging of all universal spacetime symmetries. EEP is a consequence of local gauging.
Both the geometric uniformity of globally flat space and the geometric non-uniformity of
a general Riemannian space can be expressed covariantly using the Riemann metric. The two
issues -- covariance and uniformity -- are conceptually "orthogonal".
Glad you finally got that. ;-)
What you are talking about here from the mathematical standpoint is covariance of tensor
quantities and tensor equations, with coordinates adapted to and interpreted as representing
observer reference frames. But theories (such as Newton's , as shown by Elie Cartan) that are
not considered "relativistic" can also be formulated in a generally covariant manner.
No, you still don't understand that local gauging is Fock's "nonuniformity." The global actions of the original matter fields now supplemented with the induced GeoMetroDynamical (GMD) connections are invariant under the larger group G ---> G(x). Global G is a subgroup of G(x).
Tensors and spinors are simply multilinear maps relative to the group G (covariance). The PHYSICS is the choice of which G and which subgroup of G to localize (nonuniformity).
So this is not really the issue, is it? And that is Fock's point.
Why wouldn't your definition of "relativity" apply to Cartan's generally covariant formulation of
Newtonian theory?
The principle of relativity has two parts covariance and nonuniformity.
Newton's PHYSICS is that of GLOBAL Galilean group G with absolute time.
Localize Galilean group and indeed you have Einstein's GR in the weak curvature and non-relativistic limit v/c << 1 for test particles.
I'm not sure if you can do black hole and cosmological horizons there because static LNIF accelerations are infinite at the horizons.
e.g. outside a black hole of mass M
g(r) = (GM/r^2)(1 - 2GM/c^2r)^-1/2 ---> infinity as r ---> 2GM/c^2 +
The hot Unruh temperature at the horizon generates a relativistic plasma for the hovering static LNIF observer Bob - not directly seen by the LOCALLY COINCIDENT LIF observer Alice - unless Alice gets too close and catches fire as Bob burns up. Now this horizon complementarity is very weird.
Sure spacetime is uniform in 1905 SR, i.e. curvature field vanishes globally.
Right.
And introducing LNIFs into uniform spacetime gives us curvilinear metrics guv(x)
with connection fields of zero curl.
I assume by "curvilinear metrics" you mean curvilinear coordinate representations of
the Minkowski metric (g_uv = n_uv in rectilinear coordinates, g'_u'v' =/= n_uv in curved
coordinates).
Yes, physically those are the metrics for accelerated observers not on geodesics.
The new physical difference between 1905 SR and 1916 GR is the non-vanishing curl of the LC connection - the curvature.
The relativity is still there.
Depending on what you mean by "relativity". EInstein thought it meant coordinate covariance. Fock,
like Kretschmann before him, rejected that view.
No, Einstein always meant by relativity exactly what I mean.
Einstein said exactly what he meant in 1905: the laws describing the physics observed in different inertial frames are "the same".
Of course, and in 1916 the laws in different COINCIDENT local frames are also the same whether or not each frame is inertial - it does not matter.
In a LIF: GIJ + kTIJ = 0 Einstein's T4(x) gravity field equation.
In a COINCIDENT LNIF: Guv + kTuv = 0
Guv(LNIF) = eu^Iev^JGIJ(LIF)
eu^I = &u^I + Au^I
Au^I = T4(x) induced compensating spin 1 gravity tetrad field.
This is the analog of the electromagnetic U1(x) vector potential Au(LNIF) = eu^IAI(LIF).
||&u^I|| = 4x4 identity matrix (Kronecker delta)
But there is a subtlety here. Einstein's 1905 concept of a "physical law" was heavily influence by Mach. It was an empiricist definition:
if the phenomena directly observed by a moving observer are the same, then the physical laws are the same, since physical laws
are nothing more than mathematical descriptions of what is directly observed.
No one in foundations of physics or philosophy of science thinks this way any more. Physical laws are not simply mathematical descriptions
of what is empirically observed.
So Einstein was not talking about tensor covariance in 1905. He was talking about something quite different.
Einstein did not learn tensors from Marcel Grossman until after 1905 as I recall. So what?
Alice and Bob each measure the same events. They compute the invariants from their measurements of those events. If their invariants are aways the same numbers then
1) the theory is good
2) their measurements are good
So why doesn't this also apply to Cartan-Newton? Are you saying that Cartan-Newton is not generally covariant? Or are you saying
that Cartan-Newton is "relativistic"?
You are hung up on a very trivial semantic point. Of course C-N is generally covariant. Its physics is that of the localized Galilean group which is the limit of the localized Poincare group as c ---> infinity.
One can define a spacetime manifold, coordinate frames, frame fields, and so on in generally covariant Newtonian theory.
Michael Friedman is good on all that:
1905 special relativity is that Alice and Bob are each on geodesics.
No there are no "geodesics" in 1905 Einstein relativity. There is no Minkowski spacetime in 1905 Einstein relativity.
You are quibbling and being over pedantic. I don't mean how Einstein thought about it back in 1905. Who cares? I mean how his ideas have been further developed now in 2011. Of course he did not have the mathematical tools in 1905 and he never apparently understood Cartan's exterior calculus and tetrads. He died in 1955.
Now if you treat Minkowski spacetime as a globally flat Riemann manifold, then yes Alice and Bob are moving along
geodesics -- the geodesics of the generally covariant "Minkowski" metric, [g_uv] = [n_uv] (in inertial coordinates).
Since there is no curvature they need not be close together when they measure the same events e.g. the redshifts from a group of Type1a super novae far from either of them.
OK.
In 1916 GR Alice and Bob must be close together when they measure the same Type 1a supernovae but they can be each in any motion they like geodesic or non-geodesic.
But the theory allows us to correct non-local measurements for gravitational effects. Are you saying that we can only
make *local* objective measurements in GR?
What are "non-local measurements"? You mean light from a distant source on the past light cone of the detector?
If so this would appear to be a strong argument against curved spacetimes, and in favor of a Minkowski background.
1916 GR is the local T4(x) version of 1905 SR.
Only by correspondence.
Quibble - I ALWAYS mean by correspondence.
In 1905 SR we only look at maps between Global Inertial Frames (GIFs) that we can extend to LNIFs
i.e. accelerating and rotating detectors e.g. Sagnac effect.
http://en.wikipedia.org/wiki/Sagnac_effect
Special relativity means invariants for GIF's --> GIF's
Global invariants.
General Relativity means invariants for LNIFs---> LNIF's
Local invariants.
with the new requirement of LOCAL COINCIDENCE and the EEP
EEP means TETRAD maps LIF <---> LNIF.
It means that the metric assumes its diagonal normal form [-1, 1, 1, 1] in LIFs.
That's what I said.
That is automatic for any orthonormal vector basis. The vector representation of the metric
takes the normal form.
In the Einstein-Cartan tetrad model this means an orthonormal set {e_a} of non-coordinate
basis vectors (tetrad) at each spacetime point.
In the coordinate frame model it means Riemann normal coordinates.
It's Fock who wrote philofawzical nonsense in my opinion.
Fock was a leading mathematical physicist, not a "cocktail party philosopher".
Yes indeed. He gave lectures at Harvard I think in 1960.
Obviously the Global T4 group of 1905 SR is a SUBGROUP of local T4(x).
Fock's remark that
is what is nonsensical in my opinion.
He's saying that the term "relativity" means one thing in 1905 SR (uniformity of spacetime),
and quite another in 1916 GR (coordinate generality).
Not clear. In any case it's a quibble.
It's not considered to be a "quibble" in the mainstream view Jack. I think you're on your own here. Fock's
views are now quite influential.
Among who? Name names. Also Fock restricts himself to those harmonic coordinates with asymptotic boundary conditions that are too restrictive.
General coordinate covariance as "general relativity" is now considered to be a red herring. Einstein even
admitted he had been confused on this point, and was forced to retreat by Kretschmann and others.
Who cares about these nit-picking distinctions of the philofawzers? - unless it makes a prediction and/or explains anomalies like dark energy etc. If you show me that then I will reconsider.
Fock's complaint was that Einstein did not follow this argument through to its full logical consequences,
and continued to use the language of "general relativity" after it had ceased to have any legitimate
meaning in the context of the 1916 theory.
Actually "relativity" refers to a number of things.
As originally stated by Poincare, the "principle of relativity" simply means that the mathematical
descriptions of physical phenomena ("laws of the phenomena") observed in different inertial frames
of reference are identical.
No, that's part of 1905 special relativity. You also need that speed of light in vacuum is the same for all inertial geodesic observers.
I'm sorry Jack but this was all published by Poincare well before 1905. In particular Poincare published what
*he* called the "principle of relativity" well before 1905. Einstein's version as stated in his 1905 paper was almost
identical.
More quibbling over minor pedantry in my opinion.
However there was a very subtle difference in the two versions, which can be attributed at least in part to Mach's
influence on the young Einstein.
If you want to write a history about Einstein's transient thinking along the way fine - but I am not interested in that - unless it solves the dark energy, the dark matter and the Pioneer Anomaly problems and more.
If you are in any doubt about this I'll give you a bibliography.
Even if you are right, it's not important in my opinion. When you solve a major empirical mystery let me know. I think you are barking up the wrong tree.
In his 1905 paper, Einstein substituted "physical laws" for Poincare's
"laws of the phenomena"; for Einstein, the physical laws were quite literally *the same* for all
inertial frames, as long as the phenomena observed in such frames *look* the same to the inertially
moving observers.
But the use of tensor quantities and tensor equations in physics shows quite clearly that the
phenomena can *look* different to different observers, even while the physical laws (expressed as
tensor equations) are the same.
In the context of 1905 SR, "relativity" also refers to the *relativity of simultaneity*, which in the
modern SR formalism clearly has nothing to do with covariance of the physical equations. There
is no logical connection in SR between the coordinate invariance of the Minkowski interval s, and
the relativity of simultaneity that formed the theoretic foundation of Einstein's 1905 paper.
Obviously,
OK.
however 1916 GR lets the observers be in any motion including non-inertial translational accelerations and rotations about their centers of mass.
Even in a globally flat spacetime.
Agreed that GR in flat spacetime is a generally covariant formulation of Minkowski SR.
Also they must be close together when measuring the same events. Furthermore special relativity works in Local Inertial Frames (LIFs), i.e. EEP
Yes SR works (to a good approximation) in LIFs. LIFs cover finite regions of spacetime, so the agreement is not exact.
Which is fine as a local correspondence principle!
So where's the beef?