Eugene Wigner's Greatest Blunder?

**Jack Sarfatti**

On Feb 6, 2005, at 4:16 PM, wrote:

Jack Sarfatti wrote:

bcc
On Feb 6, 2005, at 3:01 PM, wrote:

But I think you are missing my point, which is that the only reason we
impose Lorentz invariance on all
laws of physics as a fundamental kinematical condition is the *guarantee
of universality* of length
contraction (and time dilatation) phenomena that is squarely based on
the Einstein relativity hypothesis.

This is trivial.

It's very basic and very important.

Yes, it's basic and important, but still trivial. You are quibbling. In
GR, Lorentz invariance is a local symmetry. In SR it is a global
symmetry. The point is that these symmetries are left intact at the
dynamical level. The kind of "preferred frame" Cahill reports is merely
a vacuum property that does not affect the dynamics. The principle of
relativity and covariance refer to the structure of the dynamical action
and its Euler-Lagrange equations not to the vacuum solutions!

I am talking about much more than that.

Without strict relativity, there is no basis for assuming universality
of length contraction; with no basis for
assuming universality of contraction; there is no known reason to
*assume* that the fundamental laws are Lorentz
covariant.

That is not to say that they cannot be.

All the experimental evidence requires Lorentz covariance (subject to GR
corrections) in the dynamics. There is no evidence to the contrary.
Cahill's allegations show spontaneous broken vacuum symmetry - that's all!

Also, do you not yet understand that Cahill's results, if corroborated,
DO NOT VIOLATE LORENTZ INVARIANCE at all where it matters, i.e. in the
DYNAMICS? You don't seem to get that? Also I am talking about ALL groups
in ALL physical situations not only the Lorentz group O(1,3).

Cahill's argument does not violate Lorentz covariance. It only violates
the *relativity hypothesis* and thus
undermines the *Einstein model for the Lorentz transformations*, which
is different.

Clearly, without Einstein relativity there is no need to build the
Lorentz transformations into the kinematics.
They can be treated as a dynamical effect, as in the classic Lorentzian
model.

This is too vague. Show the alleged distinction as a mathematical
difference.

The kinematics is there when you perform a O(1,3) transformation on a
physical quantity like the local Lagrangian density, or the local
Euler-Lagrange equations of motion. Or, if GR is not important, when you
perform a GLOBAL O(1,3) transformation on the entire global classical
action. Similarly working with states in qubit Hilbert space using
unitary representations of O(1,3). So, frankly, Paul your words above
are meaningless until you show examples.

Once we go to a Lorentzian model, then this guarantee no longer holds,
and we are deprived of a theoretical
basis for imposing Lorentz covariance *a priori* on the fundamental
physical laws; and so we then need only
recover length contraction as an *emergent dynamical effect*, which
could be based on underlying *Galilean*
laws.

No you have this all wrong. The dynamical laws (the structure of the
action) remain Lorentz covariant even when there is a preferred Lorentz
frame

Sure. I'm not disputing that.

Then you have no point. Where's the beef? Anything beyond that is of no
interest. It's meta-theoretic.

- it's exactly like broken gauge symmetry in a superconductor when the
U(1) phases all line up, e.g. see pictures in Frank Wilzcek's Jan 20,
2005 Nature paper. Instead of U(1) ~ O(2) think of O(1,1) in the
simplest case.

That's a model for the vacuum in which there are preferred frames, which
is OK.

What Cahill is seeing is what P.W. Anderson calls "generalized phase
rigidity" a long range coherence selecting out a preferred Lorentz
inertial frame in a limited space-time region where we can ignore GR
effects - another story.

OK, I have no problem with this as a tentative model for a physical
vacuum with a locally detectable preferred frame.

Well that is what the problem is. I mean that's the only part of the
problem that is important. What are you worrying about beyond that? BTW
I suspect that Cahill does not know about the above way of looking at
what he is allegedly seeing. People are still looking for dynamical
violations i.e. putting terms into the action that violate O(1,3)
covariance like in the magnetic Zeeman effect for O(3) violation. This
is a very wrong way to go.

This is why Cahill's speed is not the same as the motion of Earth
relative to GR Hubble flow as seen in CMB anisotropy. Two different groups.

OK.

Cahill's effect is O(1,3) broken vacuum symmetry,

Well, obviously a preferred inertial frame will violate this symmetry,
since it establishes a preferred direction in Minkowski spacetime.

Yes, that's what I am saying. However, I am not aware of anyone else
saying this?

and the Hubble flow is broken T4 vacuum symmetry!

OK.

Of course there can be more than one physically preferred frame of
reference, which can show up in different kinds of measurements.

Yes, I have said that.

Now if I can also relate the Pioneer anomaly to O(1,3)/O(3) ~ S2? as a
hedgehog defect in the "multi-layered multi-colored" (Wilzcek) vacuum
order parameter cosmic superconducting field - that would clinch it. I
have not shown that yet mathematically, but I smell it's true. I could
be wrong - or not even wrong. I think it's actually an easy elementary
problem.

So you seem to be confusing Cahill's acceptance of the Lorentz
transformation formulas as empirically valid
with an Einsteinian insistence on imposing Lorentz covariance *a priori*
on *all* physical laws, as a
kinematical condition -- which I think is a serious misreading of
Cahill's position.

No Paul. You obviously do not understand the actual math. I don't care
about Cahill's theory position.

OK.

I don't think he understands what he is seeing BTW. I am only interested
in his empirics, not his interpretation of them.

OK. So you have your own theory to account for the appearance of these
residual shifts and their evident connection with the earth's motion
through space.

Right - all based on only two battle-tested ideas

1. Local gauging of symmetry groups (both internal and space-time)

2. Spontaneous breaking of selected symmetry groups in the vacuum
(ground state) is essentially the DEFINITION of what the term "preferred
frame" means as "generalized phase rigidity" (PW Anderson).

Example 1: ferromagnetism is a preferred spatial orientation over a
finite domain in the ground state even though the dynamics is still
rotationally invariant the ground state is not.

Example 2: alleged Cahill effect is a preferred space-time orientation,
i.e. a definite hyperbolic "rapidity" (rather than Euclidean "angle of
orientation") is selected out in a finite space-time domain over which
the vacuum coherence condensate has a coherent phase rigidity in the
appropriate internal order parameter space. I will explain that in more
detail later. This is a global topology effect.

He is backed up by the Catanians though they get a different number
using He-Ne lasers rather than interferometers. I think they claim
Cahill made a minor error?

The dust hasn't had time to settle yet.

The point is that the dynamical equations remain, for example, Lorentz
form-invariant (at least locally when GR is important).

Certainly the phenomenological equations do. I wasn't suggesting otherwise.

OK. I don't know then what you were suggesting.

The observed fringe shifts are vacuum effects - a kind of Higgs field
effect!

Yes, they are vacuum effects, even while you need a propagation medium
in the MM light path to detect them.

Maxwell waves propagate in classically empty space. So what's your
point? Quantum mechanically the vacuum is primarily (at low energy) a
"normal fluid" micro-quantum random plasma of ionized unbound virtual
electron-positron pairs and virtual photons. I have added in the NEW
macro-quantum "superfluid" vacuum condensate of bound virtual
electron-positron pairs out of which Einstein's 1916 GR local field
equation emerge via

Bu = (Goldstone Phase of Virtual Electron-Positron Vacuum Condensate),u
from spontaneous breaking of EM U(1) in the physical vacuum out of which
the geometrodynamic fabric of warped space-time emerges "More is
different" (PW Anderson)

Bu = Bu^aPa/h = compensating gauge potential connection field from
locally gauging T4

Bu^a = non-trivial part of Cartan tetrad eu^a = (Kronecker Delta)u^a + Bu^a

{Pa} = Lie algebra of T4 subgroup of the Conformal Group.

Note I use both local gauging of T4 and spontaneous symmetry breaking of
U(1) in the vacuum i.e. low energy part of Frank Wilczek's
"multi-layered multi-colored" cosmic field of superconductivity. I use
BOTH 1 & 2 for different groups.

guv(LNIF) = eu^aev^b(Minkowski)ab is EEP

guv(LNIF) = (Minkowski)uv + Lp^2[Bu,v + Bv,u]

Lp^2 = hG/c^3

Gauge transformations of Bu --- Diff(4) GCT

You do not understand the different between what's happening in the laws
of nature and what's happening in the vacuum!

I am simply pointing out that the fundamental theory of the vacuum
doesn't *have* to be kinematically Lorentz covariant in order to recover
Lorentz contractions at the phenomenological level -- although it could be.

That seems to be a very vague way of saying what I have been saying
without any of the all-important details. God is in the details. I never
heard you once use "spontaneous symmetry breaking" in this context - a
battle-tested idea with a large literature since at least 1967.

You do not at all AS YET understand what I mean in

There are only two important ideas in theoretical physics.

1. Locally gauging a symmetry group G (either external or internal).

2. Spontaneously breaking the vacuum (or ground state for real
quanta) to make a "preferred frame" relative to the group G.

This is just flying right by you under your radar.

Of course I understand that you can recover a certain symmetry by
locally gauging the relevant symmetry group
and then adding back the resulting gauge field.

That's 1. What about 2.?

I also understand in a quantum theory how you could lower the symmetry
of the physical vacuum by spontaneous
symmetry breaking.

I am simply pointing out the the physical meaning of Lorentz covariance
shifts dramatically when you have locally
detectable preferred frames.

Too vague to be useful. I am being very specific here.

Until you read P.W. Anderson you will not grok it. It's sort of subtle.
Even Eugene Wigner had trouble with this and P.W. Anderson recounts.
They were both at Princeton of course.

Yes. I'll have to look at all that.

It's important not to confuse the dynamical Lagrange-Euler equations for
stationary action with their lowest energy solutions in a given
well-posed problem.

OK. Of course I understand that the solutions of a set of dynamical
equations can and typically do have lower
symmetry than the equations themselves.

What is important is that it is the lowest energy state that has a lower
symmetry. That the excited states have lower symmetry is not the point.
Apparently up until 1967 no one understood that! It was Eugene Wigner's
greatest blunder! (As I read PW Anderson). I think everyone assumed that
the lowest energy state had to have ALL the symmetries of the dynamics!
This led to false super-selection rules like the one on total electric
charge that is violated in a superconductor. There was a lot of
confusion on this in the 1960's.

Z.

Jack Sarfatti wrote:

bcc

Tom Phipps was completely wrong in "Heretical Varieties".

BTW Paul, this shows in a concrete example why covariance is important
and why you too abstract comment - that any theory can be made covariant
misses the key idea, which is what group of frame transformation we are
talking about and in what kind of representation.

For example, the unitary group representations of the rotation group on
electron qubit spinors in the field of complex numbers describe
Stern-Gerlach reference frames, i.e. orientations of magnets with
inhomogeneous magnetic fields.

In contrast, the orthogonal group representations of the Lorentz group
in the real number flat space-time continuum include boosts connecting
global inertial frames in uniform relative motion. This is broken down
to local symmetry between coincident LIFs in GR (something Puthoff does
not understand in his PV theory).

The unitary representations of the Poincare group describe possible
elementary particles in flat quantum field theory (Wigner, Bargmann) and
so on.

Besides the elegance, there is real physical content in the requirement
that the dynamical laws of nature are covariant i.e. form-invariant
under different groups acting on different kinds of reference frames.
The same group can act on different kinds of reference frames in
different spaces. For example, the Poincare group acting on physical
frames in space-time in one situation and then acting on qubit
information (Hilbert spaces) in another situation describing how
different observers in the first situation compare their micro-quantum
statistical data on equivalent ensembles.

That is, vague lofty Scholastic generalizations should be avoided. God
is in the details. :-)

On Feb 6, 2005, at 2:19 PM, Jack Sarfatti wrote:

In order to calibrate what Cahill and the Catanians are claiming, let's
review the "mainstream position" circa 1955 in the text book "Classical
Electricity and Magnetism" by Panofsky & Phillips Ch 15 "The
Experimental Basis of the Theory of Special Relativity".

15-1 presents the equations of the linear Galilean boosts along the
x-axis between inertial frames

x' = x - vt
y' = y
z' = z
t' = t i.e. absolute Newtonian time

The Newtonian point particle mechanical laws are form-invariant
("covariant") under this transformation boost connecting two global
inertial frames. This is a group unto itself if we do not change
direction of the boost. So are the Lorentz boost transformations in a
fixed direction in space, but if we change the direction of the boost,
if I recall correctly, we need the spatial rotations to keep the group
property - that is we need the full O(1,3) in that case? The Lorentz
boosts alone in all directions are not a group. The space rotations of
the Lorentz group O(1,3) are a subgroup O(3), but not the boosts unto
themselves? I need to check that. I mean is O(3) a normal subgroup of
O(1,3) so that the quotient of cosets of O(3) in O(1,3) is a quotient
group O(1,3)/O(3)?

Back to P&P:

"unless all sources of force are known, an inertial frame is not
strictly definable" in Galilean relativity p. 273

The Maxwell free wave equation is not form-invariant under linear the
Galilean relativity boosts.

Therefore, if Galilean relativity were true we would need a preferred
frame of absolute rest in which Maxwell's wave equation has its
canonical form e.g. in 1 space-dimension for simplicity

A,ct,ct - A,x,x = 0

A is the Maxwell vector potential (piece of U(1) internal local gauge
compensation connection field in modern parlance)

Note that

x' = x - vt

1 = x,x' - vt,x'

A,x' = (A,x)(x,x') + (A,t)(t,x')

(t,x') = v^-1(x,x' - 1)

as v - 0, x,x' - 1 i.e. 0/0 indeterminate that we consistently
define as 0 since v - 0 is the identity map.

A,x' = (A,x)(x,x') + (A,t)v^-1(x,x' - 1)

Note that since the transformation is linear x,x',x' = 0 etc.

A,x',x' = (A,x,x)(x,x')^2 + (A,t,t)v^-2(x,x' - 1)^2

At't' = At,t

If we say the primed frame is the absolute rest "ether frame" with the
canonical form for the wave equation, then

c^-2A,t',t' - A,x',x' -- c^-2A,t,t - (A,x,x)(x,x')^2 +
(A,t,t)v^-2(x,x' - 1)^2

which is not form-invariant under these Galilean transformations.

That is, Maxwell's free radiation EM theory is not covariant
(form-invariant) under the Galilean boost group in one fixed space
direction.

Note, that this kind of Galilean ether frame of absolute rest is not at
all what Cahill and the Catanians are talking about! They use the
Lorentz group O(1,3) from the beginning. Their claim has nothing at all
to do with 15.1 & 15.2 in P&P! It's important not to get confused about
that!

The O(1,3) rest frame is a spontaneous broken vacuum symmetry in which
the field equations remain O(1,3) covariant! The broken symmetry is in
the solution not in the dynamics!

When P&P write, on the basis of the Galilean transformations in eqs.
(15-6) to (15-10), not the Lorentz transformations that Cahill uses,
for an individual run, rotating the Michelson interferometer by 90
degrees then and there, not averaging over an ensemble of such runs
when Earth is in widely different parts of its elliptical orbit round
the Sun: "On rotating the apparatus through 90 degrees, we should
expect the interference pattern to shift by N fringes where

N ~ [(L1 + L2)/(wavelength)](v/c)^2 (15-10) p. 276

where v is the absolute speed of the interferometer here with respect
to the above hypothetical Galilean ether.

P&P's (15-10) is not same as Cahill's (2) on p.4 derived using the
Lorentz group and assuming gas index of refraction of light along the
paths n =/= 1 i.e. Cahill's n(n^2 - 1) factor not at all in P&P's
analysis. Therefore, P&P's Table 15-1 "Trials of the Michelson-Morley
Experiment" and P&P's rejection of Miller's claims have no direct
bearing on what Cahill is claiming! It's Apples and Oranges.

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