Natural Science Forum / Physics / Research / January 2008

..

I think that the Strong Equivalence Principle simply can't be accepted
in the form generally given (as in Wikipedia below):

http://en.wikipedia.org/wiki/Equivalence_principle#The_strong_equivalence_principle

The strong equivalence principle
The strong equivalence principle suggests the laws of gravitation are
independent of velocity and location. In particular, The gravitational
motion of a small test body depends only on its initial position in
spacetime and velocity, and not on its constitution. and The outcome of
any local experiment, whether gravitational or not, in a laboratory
moving in an inertial frame of reference is independent of the velocity
of the laboratory, or its location in spacetime.
endquote

Note the contrast with The Einstein equivalence principle:
quoted:
The Einstein equivalence principle states that the weak equivalence
principle holds, and that The outcome of any local non-gravitational
experiment in a laboratory moving in an inertial frame of reference is
independent of the velocity of the laboratory, or its location in
spacetime.
..
The Einstein equivalence principle has been criticized as imprecise,
because there is no universally accepted way to distinguish
gravitational from non-gravitational experiments (see for instance ...
end quote

I've usually heard just between strong and weak, and it's odd to see the
phrase "non-gravitational experiment."  Just what is that supposed to
mean, as noted.  Is how things fall, a "gravitational experiment"
because it's about non-contact forces on neutral matter, so only EM etc.
is equivalent? That sounds silly, since the whole motivation was about
how things fall, wasn't it?

In any case, the very existence of "gravitomagnetism" means the EP is
wrong. (I mean gravitational *analog* of magnetism, not the perhaps
outré idea that EM effects can produce gravity effects over and above
standard GR concepts like from mass-energy of the fields, etc.)  Let's
say you're standing on a floor on the Earth etc, with a stream of matter
flowing rapidly below you. So, you've got the basic gravity field, tidal
fields and all, but also the g-M field from the flow.  That means, the
force, acceleration on a particle zipping by you is not the same as for
one you drop straight down.  OK, we understand why that is so.  But for
rapidly moving bodies to accelerate differently than straight-falling
ones at a given point (for any reason related to gravitational issues)
is a local distinction (since it can't be transformed away by
acceleration), not a distinction about large regions (like tidal fields,
etc.)

Gravitomagnetism apparently isn't the only example of unequal
acceleration applying to bodies at different velocities transiting a
small region.  As I asked about as OP of "How unlike real elevator
(Rindler field) is field from planar mass?", Greg Egan on a thread at
Cosmic Variance assures me of the following surprising distinction: The
metrics of the Rindler Field and of the basically parallel and uniform
field around an extended planar mass not the same, and not just
regarding the extended field structure (like the hyperbolic g  = -c^2/Z
relation), but it also matters for *local* experiments.  He says, the
lab-frame acceleration of a body in rapid transverse motion in a PF is:
g(moving) = g(1 + v^2/c^2).  I thought, WTF?!  But he seems to know what
he's talking about, and said:

Greg Egan:  "In the Rindler "elevator", transverse motion is just an
extra degree of freedom that has no effect whatsoever in the Z
direction. In the curved space-time near a planar mass, the geometry is
sliced differently by world lines with different transverse velocities."

That just seems weird to me, but if it is, it is. G-m and presumably
Greg's distinction have been known for a fairly long time, so somehow
folks just didn't appreciate the implications. But they mean you can't
just transform every gravitational field using acceleration, even in a
tiny region (since accelerations are formally defined at points in time
and space.)  Tell me if I didn't get the fine points of defining the EP,
but I swear I've heard that definition a lot.

Hello Juan:

Since this is a poll, I guess I should stick to the structure
provided.

Spacetime is 3D+time, since time does not behave like space.  There is
no 5th, 6th, 7th, 8th, 9th, 10th and/or 11th dimension, regardless of
funding.

Spacetime is a continuum, and events in spacetime are discrete and
countable (spacetime is not countable, ever).

Spacetime needs events, events need spacetime.

Global Lorentz symmetry is an approximation to local Lorentz symmetry,
because all important laws are local.

The question confuses me.

If true, it would be hard to sell because everything would have to be
utterly perfect and pristine (from a clod with experience).

I agree, there is no dark matter in the Universe, but there are
velocity profiles and distributions that need some new math badly!

My bet is against this one, but I will not put in all the chips (I
would on 7).

Time cannot have an arrow because it is a scalar, but spacetime can
have a handedness. When Lorentz symmetry goes local, irreversibility
is a handjob.

True because it is the stuff outside the past and future lightcone
that rolls the quantum dice.

The question is poorly formed, since time must be part of spacetime.

Disagree.  There are fields with really fun and confusing math
properties.

General relativity has been and will remain a great theory, but there
is a better one to get along with EM and the standard model.

I would NEVER write it this way, since we observe E, we observe p, and
we calculate m.  In curved spacetime, the value of any 4-vector
contraction will change in ways we understand.  {mc^2}^2 = E^2 -
{pc}^2 in flat spacetime.

Disagree.

No opinion.

No, don't buy strings.

The equivalence principle is too simple to arise from something else.
I believe the active, passive and inertial masses are all equivalent.

Yes.  New math will be fun.

We have one life, and one Universe, even if we don't have a good
understanding of either.

3D+time is sexier than people give it credit for.

doug

Hello Juan:

I mean something else.  It is an accounting issue.  The mathematician
Giuseppe Peano was able to build up the various number sets (from the
natural numbers to rationals, irrationals, reals, ...) starting from 0
and the successor of zero (1).  I view the vacuum of spacetime as
zero, and an event as the successor of the vacuum.

I view FTG as what I define "an area of study" which has yet to reach
the rare plateau of a hypothesis, something that can be tested.  When
there is a test that can distinguish the proposal from general
relativity, I will read up on it.  The same applies to the vast body
of work with strings, which saves me a lot of time!  The Rosen metric,
which looks prettier than the Schwarzschild metric because it is all
exponentials on the diagonal, is a hypothesis that could be tested
because it predicts 12% more bending of light around the Sun when we
go to the next level of measurement.  We know that Rosen's bi-metric
theory is wrong because it would allow dipole gravity waves.

If a question is not asked correctly, all replies will not make
sense.  The question "What does 2 + equal?" is poorly formed: good
English, flawed logic.  Since the logic of my view of the Universe
sets 0 to be the vacuum, and 1 to be an event in spacetime, it makes
no logical sense to discuss time in isolation of spacetime.  That is
not a popular way to go :-)

I have no doubt you can find this in the literature.  Just to prove I
am irritatingly consistent, I think it is poorly formed to ever
discuss energy without 3-momentum, just as bad as time without space.
Bad accounting...

OK

If the strong equivalence principle means that gravitational fields
gravitate, then my opinion is that the weak equivalence principle is
correct, and the strong equivalence principle is false.

You are entitled to hold this popular opinion.  Respectably, I don't
think Nature allows the simplest and weakest of her forces to interact
with itself, so this argument will remain missing.

doug
sweetser@alum.mit.edu

On Nov 21, 8:37 am, Doug Sweetser <dougsweet...@gmail.com> wrote:

Events are not synonymous with 'points in spacetime'.  Events
represent something happening - a change in the world at a point in
time somewhere in space, like the change in direction of an electron
because of an interaction or the 'creation' of an electron-positron
pair at a point.  Obviously, all such events occur at SOME spacetime
points but very few 'points in the manifold' of spacetime are the
location of physical events.  Physicists must keep reminding
themselves they are studying the real world - not mathematics.

Hello Maxwell:

The misses is not a physicist or mathematician.  She does post-award
grant accounting for a college.  She does not read any general physics
books for 'fun'.  I am able to take expressions, make animations, and
put them up on YouTube or Picasa (gif87a, retro tech).  I can tell her
that the group U(1) which looks like an ellipse in three complex
planes and is a straight line animation is related to light.  The
animation for SU(2) is odd but fun to look at.  That animation was the
reason I bought an iPod.  A search for 'group U(1)' or 'group SU(2)'
should turn in up on YouTube.

I have no idea why that animation as a representation of the group
SU(2) is connected to the weak force.  This is the fun of exploring.
The group U(1) makes a bit more sense since that is what a transverse
wave should look like.

doug

I see spacetime as a concept used to model 3 dimensions of space and
one of time.

I don't know of any experiment that illustrates non-continuity of
space or time.

However since quantum particles follow paths that are not
differentiable, it might be reasonable to assume that spacetime is
continuous but not differentiable at the quantum scale.

The following paper shows how such an assumption allows derivation of
the Schrödinger equation.

Scale calculus and the Schrödinger equation
Jacky Cresson
J. Math. Phys. -- November 2003 -- Volume 44, Issue 11, pp. 4907-4938
Preprint
http://arxiv.org/abs/math/0211071

The following experiment found that free falling neutrons exhibit
quantum states. I guess that could imply that the neutrons were
following geodesics that were non-differentiable as well as curved,
rather than merely curved as described by GR.

A quantum mechanical description of the experiment on the observation
of gravitationally bound states
http://arxiv.org/abs/hep-ph/0602093

Regards.
Surfer

Hello Gary:

I liked your verbal description of the group U(1).  It does have more
content than my brief collection of words.  My goal was not to come up
with a story of math, but pictures of math.

It was not clear to me if you had viewed the animations.  The reason
that matters is that animations are processed in a different part of
the brain than the verbal descriptions.  Visual analysis happens in
the back of the skull.  Some people estimate that some 40% of the
processing in the brain is devoted to visual information.  Tapping
this source is a great advantage.

I have animated real numbers, and the animation is scary.  The reason
is that a pattern of real numbers blinks at the origin, never moving a
pixel left or right.  Ever.  The reason that frightens me is that we
have such a huge investment in real numbers, and real numbers are dead
dull.

I have animated addition.  It is fascinating.  This most simple act,
addition, generates an inertial observer.

Light is difficult to understand.  I accept any handle I can get on
what it is about.  One of the ideas I was taught, but was not happy
about internally, was that light is a transverse wave.  The animations
make me more comfortable with that.  I did not claim that my lady can
say anything about the phase differences versus phases.  It is not a
goal of mine to hear her master those words.  We can chat about what
we see in the U(1) animation, and that is related to part of our
understanding of light.

Pontificate on the groups SU(2), U(1)xSU(2), SU(3) and Diff(M).  Or
look at a gallery of images I have produced.  The visual part of my
brain is happy with the partial story.

http://picasaweb.google.com/dougsweetser/AnalyticAnimationsStandardModelGroups

Please refrain from referring to images that involve more than 30,000
points as mere "pretty pictures".  As Maxwell (the poster here)
pointed out, mostly spacetime is empty.  It takes a clear vision to
place that many events in a ten second animation with a specific
purpose.  That purpose is to give a visual handle on hard ideas that
appear from the simplest tools in Nature.

doug

On Dec 10, 8:57 pm, Doug Sweetser <dougsweet...@gmail.com> wrote:

More to this point: though QED is founded on a classical abelian gauge
theory, electromagnetism is NOT part of a classical abelian gauge
theory. It's part of a classical NON-abelian gauge theory. In
particular, the right-hand sides of the "homogeneous" Maxwell
equations are of the form:
  del B = B.A - A.B
  del x E + dB/dt = -(A x E + E x A + B phi - phi B),
with a non-zero magnetic current arising from the non-Abelian nature
of the U(2) gauge field
  A = (A^a) Y_a, phi = (phi^a) Y_a (summed over a = 0,1,2,3)
which electromagnetism is a part of.

For the electromagnetic component of this field, the contributions to
the non-linear terms on the right come from the field components
associated with the W particle and W anti-particle.

So, here'a case in point about making a distinction between a
mathematical model (i.e., QED) and the real world (i.e.,
electromagnetism). QED is not electromagnetism.

Hello Rock:

This sounds like you are describing the road to electroweak symmetry,
or U(1)xSU(2).  Skimming the web, I see someone claims U(2) =
U(1)xSU(2).  If that is the case, the symmetry of U(1) is a subgroup
of a bigger symmetry.

Because U(1) is a subgroup of U(2), I will disagree with you on this
point.  Electromagnetism, and its model of the gauge symmetry, U(1),
are a subgroup of a bigger group, electroweak symmetry, U(2) =
U(1)xSU(2).  That group is then a subgroup of the standard model,
U(1)xSU(2)xSU(3).  The standard model is a subgroup of a yet to be
defined group that includes gravity.  I hope you clicked over and
looked at the electroweak symmetry group.  And SU(3).  And maybe
Diff(M).  If you chose not to look, then there is no hope for your
visual processor to get what I am driving at.  No collection of word
reach the back of your brain.  Ever.

Models have limitations.  My understanding of those models, both in
words and animations, are also limited.  A man has to know his
limitations.

doug

Surfer wrote {nfsml3p8dme2kipvegqhjdruf18d8i9lag@4ax.com} on Tue, 11 Dec
2007 06:29:25 +0000:

But you began from "quantum particles follows paths". Standard
interpretation of quantum mechanics says that particles do not follow
paths.

The path integral formalism does not say a particle follow a path (except
in the limit h--> 0 when particle is classical). But reading the preprint
you cited below it seems author think that quantum particles follow paths
when he says:

{BLOCKQUOTE
typical path of quantum-mechanical particle is continuous and
nondifferentiable.
}

Maybe by "typical" he means the more probable path, but the more probable
path is not the path followed by the particle, except on the classical
limit {h --> 0}.

In Feynman path integral formalism one sums over different paths to get
the total amplitude, but none path alone describes the motion of the
particle. Therefore it has no physical sense to speak of the path of the
particle, only the total sum (integration) has sense. Therein its name:
"path integral".

Interesting, but I find very difficult to accept some aspects of that
paper.

i]
For instance when he writtes about "Generic trajectories of Quantum
mechanics" and about "the regularity of quantum-mechanical path".

There is no path (differentiable or not) in quantum mechanics because x
and p (or v) do not conmmute.

ii]
when he interprets the DELTAp DELTAx on Heisemberg relations like the
"precision of the measurement". Those DELTAs are not due to our lack of
precision on measurement but undeterminacies of the own system. Of
course, since that the x and p are not defined at same time, you cannot
measure both at once.

iii]
the definition of wave-function. He call wave-function to one function of
(X,t) with X a position on a non-differentiable space.

However, in QM, the general state is |PSI(t)> and using a position basis
[1], then one gets PSI(x,t). But x in QM is an operator, whereas X in
that paper is a parameter (like in quantum field theory).

He calls his derived equation (50) the Schrödinger equation. But it is
not Schrödinger equation you find in textbooks of QM, because X is not QM
x, PSI is not QM PSI, U is not QM U...

iv]
I find difficulties to giving mathematical rigor to many operations. For
instance, how to interpret

{PARTIAL L / PARTIAL V}

when L is defined to be L ppp L(X(t), V(t), t)?

The definition of partial derivative has mathematical sense when X, V,
and t are independent variables.

v]
proposals of this kind are known for decades, since Bohm. They vary on
details but all of them finish with some claimed 'derivation' of
Schrödinger one-body equation in position basis. But what about N-body
equations?

vi]
As explained by S. Weinberg, Feynman seems at first to have thought of
his path integral approach as a substitute for ordinary QM. But path
formalism alone can give wrong results [2]. I (like Weinberg) prefer
better to derive the path formalism from the Schrodinger equation. Just
the contrary way to present paper.

I do not think so.

[1] Quantum Mechanics; Volume 1. Hermann; 1977. Cohen-Tannoudji; Diu,
Bernard; Lalo Franck.

[2] The Quantum Theory of Fields; Volume 1. Cambridge University Press;
1996. Chapter 9. Weinberg, Steven.

--
I follow http://canonicalscience.com/guidelines.txt

Hello Gerry:

I had a delightful lunch at the Elephant Walk with my actress friend
Genny Allison, who happens to be 88.  There is no way I could explain
to her that "U(1) is simply the set of complex numbers with norm 1",
no matter how correct that description happens to be.

For almost 15 minutes, we looked at the animations of the symmetries
of the standard model on my iPod.  The representation of U(1) in the
iPod is precisely a set of complex numbers with a norm of 1.  In fact,
this particular representation of U(1) does have pairs of points that
move apart quickly initially, then at their farthest separation, slow
down, reverse, and quickly crash.  This representation is faithful to
U(1) if one maps time to the real axis, and space to the imaginary
axis.  Think of sliding a pencil along the circle in the complex
plane, and that is all it is.

I tried to make a technical visual point about the watch because
pictures, like algebra, can be wrong.  The handedness of the watch
indicates a non-Abelian group.  The watch forms a plane, and that's
were it goes wrong.  We are accustom to saying a calculation is wrong,
but not so for pictures.  In my animation, the points move in one line
and do not define a plane.

Genny and I moved on to the animation for SU(2).  Someone can correct
me if I am wrong, but I told her that we were looking at the only
visualization of this bit of math available on the planet.  She was
happy to hear that, but the animation itself was odd.  I feel that way
too, but too bad, that is the way it is.  We then looked at the
animations of U(1)xSU(2) and SU(3), which also do not have
visualizations that I am aware of.

Your connection to chemistry was quite fun, I will store it away.  It
got me to thinking about why nuclear reactions are quite rare, while
chemistry happens all the time.  I realized that chemistry involves
only EM, the group U(1).  The far less frequent beta decay exploits
SU(2).  Is it correct to say that fission and fusion are all about
SU(3)?

As far as the math versus stuff issue, my sense is that math can give
a glimpse of what is allowed to go on, but all such glimpses are
partial because only Nature knows hows to play all the mathematical
cards at the same time.  The puzzle of Nature remains huge, but I feel
confident the scientific process will continue to add more.
Analytical animations may provide a useful tool for sharing our brief
glimpses of Nature with others like my friend Genny.

doug

My proposal for reconsideration of GR can be found at gr-qc/0205035.

This has to be combined with my "cellular lattice model"
presented at ilja-schmelzer.de/clm.

Indeed, in my model the continuous fields appear as continuous
approximations of lattice fields.

This holds for all particles.

It is derived in my theory.

I have a term causing inflation in the early universe.

Your title is framing the issue with a premise that, itself, needs to be
called into question. One could equally well ask: what changes in
classical and quantum field theory are required and adopt the stance
that the lion's share of changes need to be done on this end.

The most glaring omission in present-day field theory is, in fact, is
also the gap that lies between the mathematician's approach to field
theory and the physicists' approach. The former does not make or need
any 3+1 decomposition, while this is an essential element of the latter.
What's missing is -- the still unresolved gap -- is what generalization
of the Poisson bracket formalism fits covariant field theory.

Some of this and other issues are discussed in the review

Time in Quantum Theory and General Relativity
http://federation.g3z.com/Physics/index.htm#QG2007_1

I edited together excerpts of key relevant sections below:

1. Introduction
All the fundamental interactions fall into the general mould provided
by gauge theory. This includes the following:
* SU(3) Yang-Mills gauge theory: Strong nuclear force and the quark
force it is derived from
* U(2) Yang-Mills-Higgs gauge theory: Electroweak force with a Higgs
symmetry-breaking scalar
* Gravity: which possesses a GA(4) gauge symmetry, as well as a local
diffeomorphism symmetry
(for invariance under coordinate transformations).

For gravity, the GA(4) world symmetry is broken by the fermions. The
fermions impose a field of local inertial frames through a structure
known as a spin bundle. This breaks the global GA(4) symmetry down to a
local Poincaré symmetry. The homogeneous part SO(3,1) is engaged through
what is called the spin connection, and the translation generators of
the inhomogeneous part yield what is known as the frame bundle. The
frame bundle plays the role of Goldstone-Higgs fields with respect to
the quotient group GL(4)/SO(3,1) (or GA(4)/Poincaré) of the broken
symmetry. The 10 dimensions of the quotient group match, in number, the
10 components of a metric.

The transition from Newtonian to Minkowski spacetime (i.e. Special
Relativity) represented the removal of the invariant 3+1 foliation
structure that sits at the foundation of Newtonian spacetime. Another
equivalent way of stating this is that it replaced infinity as an
invariant velocity by a finite invariant velocity. Consequently, the
planes of simultaneity (the locii of motions from an event at infinite
velocity) bifurcated into a pair of light cones.

The further transition to General Relativity removed the light cone
structure from the background and made it part of the dynamics.

Canonical quantization with constraints can be done à la Dirac. However,
this entails a 3+1 split into space and time. The 3+1 split can
seemingly be avoided by adopting the Feynman approach, however it
returns through the backdoor by the necessity of the
Osterwalder-Schroeder Theorem. More to the point: the theorem does not
generalize to curved spacetimes; except for those that have time-like
Killing fields.

Quantum field theory can be done, alternatively, in the "causal"
approach, which had originally emanated from Epstein & Glaser (and
precursors) and was advanced most notably by the Zurich school, headed
by Scharf. This is the approach that others had come to adopt, such as
Wald and Holland in recent times and, notably, Brunetti and Fredenhagen
who succeeded in adapting the approach to curved spacetimes, in the
process one-upping Feynman.

Both approaches, however, require the light cone structure to remain in
the background. Closely related to this is the fact that field
propagators become singular on the light cone, as do the Green's
functions in classical field theory that they are derived from. It is
almost universally surmised that the two problems are not only related
but are essentially identical and that whatever resolution is found for
one will entail a resolution for both. In other words, the ultraviolet
divergence that ultimately arises from the Green's functions' and
propagators' light cone singularity is locked up with a prospective
theory of "Quantum Gravity" in which the light cone shall have been made
a fully dynamic object too.

However, it is not difficult to conceive of solutions to the former
problem: just smear the Green's functions. In contrast, the latter
involves serious conceptual problems that lead one to question whether
there actually is, or ever can be, any such thing as "Quantum Gravity"!
In particular, how does one superpose two quantum states that disagree
on where the light cones lie? When a timelike interval seen in one state
of the superposition is spacelike seen in the other, then what is the
interval in the superposed state? Timelike or spacelike?

The two issues (ultraviolet divergences vs. Quantum Gravity) are
therefore quite different, and their supposed link will probably prove
to be nothing more than a red herring.

3.3. Zeno's Paradox and the Non-Existence of Quantum Gravity The
Hamiltonian constraint generates the equation for "time evolution",
called the Wheeler-deWitt equation. However, this makes no reference to
time, hence one arrives at the modern-day analogue of Zeno's Paradox!
The Schroedinger picture entails no motion or change at all!

Rovelli says this means mechanics must be made timeless. He advocates
(in his 2004 Quantum Gravity book) an "ephemeral time" as one
alternative; or the "thermal time hypothesis" as another. Reference is
also made to Barbour's Machian dynamics (by both Rovelli and Kiefer in
his book), the central feature of which was that a definition for time
is constructed by a gauge condition.

Finally, the author gets to the main issue that was pointed out above at
the outset of this section. A causal background is needed to define the
underlying quantum theory! But the causal structure for General
Relativity is in the foreground. If you put the two together, this
entails that the light cone is smeared in some fashion.

The paradox at this deep level, along with the Zeno paradox of time,
actually throws into light the entire question whether there even is any
such thing as Quantum Gravity, or whether the whole enterprise is simply
a case of barking up the wrong tree.

It is an entirely open issue as to how (and whether) this resolves
itself with the deDonder-Weyl Hamiltonian, or in the larger context of
the covariant polysymplectic approach to field theory. This is,
essentially, the direction Rovelli advocated heading in.

Others have already gone further along this trajectory, notably
including Sardanashvily, et. al.; whose gauge gravitational formalism
has, as one of its central features, the notion that the frame fields
parametrize between different coherent subspaces, as a Goldstone-Higgs
symmetry- breaking field does. They, therefore, comprise essentially
classical modes that superselect between different vacuum phases and are
not to be quantized, except possibly as quasi-particle modes. The
symmetry breaking comes from the GL(4) --> SO(3,1) reduction associated
with the fermion fields, themselves. The 10 dimensions of the quotient
space are the 10 dimensions of the space where the metric (and frame)
lies.

The different vacuum sectors are precisely those identified by which
subbundle of the frame bundle is taken to be the inertial frame bundle.
Seen in this light, it is not too difficult to understand why these
sectors must be mutually incoherent. The inertial frames of one sector
will, from the vantage point of another sector, be seen to be
accelerating. But, as is known in association with the Unruh-Davies
effect, an accelerating frame generates a vacuum state and state space
that lies in a different sector than that produced by the inertial
frames. Applying that argument here, one is forced to conclude that a
fluctuation in the frame field or metric will bring about decoherence
through gravitational superselection.

This is precisely the argument independently made by Penrose, as well,
and is what underlies the proposed FELIX experiment.