I was contemplating how to visualize the universe expanding when it
struck me that instead of thinking of the universe as expanding, you
could think of matter as shrinking. Then, after reading the Einstein
Hoax (I hate to mention it because the author is regarded as such a
crank, but to give credit where it is due), I realized that, for
general relativity, instead of viewing space-time as curved you could
view it as flat, but with objects that shrink or expand. For example,
instead of viewing space as expanding as your rocket ship nears a
black hole, you could imagine your rocket ship shrinking in a fixed
space.

Since having this insight I discovered that the mathematician Cartan
worked out an equivalent of general relativity for flat space-time and
that Sir Arthur Eddington also proposed this same idea of shrinking
atoms, etc. Also, I found a very brief reference to this alternative
paradigm in a book by Kip Thorne "Black Holes & Time Warps".

This brings me to an overwhelming question. Since almost anyone can
imagine easily objects shrinking or expanding and since almost no one
understands what curved space-time means when they first encounter it,
why has the physics profession opted for explaining everything with
the curved space-time paradigm? Is this just traditional because
Hilbert and Einstein first derived the field equations for general
relativity? The idea of shrinking objects and changes in the rates at
which physical processes occur seems so much simpler from a
pedagogical point of view. At least, it was so for me.

Philosophically, it is difficult to see which paradigm is superior.
Why prefer fixed objects and a changing space-time to a fixed
space-time and changing objects?

Theoretically, there seems to be a slight advantage to the flat
space-time paradigm. To get an identical theory out of the curved
space-time paradigm you have to add the qualification that the
space-time manifold has a Euclidean chart. That eliminates the
possibility of worm-holes, which, in view of the fact that there are
no known worm-holes, is a point in favor of flat space-time. That is,
the flat space-time theory implicitly makes the prediction "there are
no worm holes" and, in fact, that prediction has so far been
confirmed.

Why was the idea of flat space-time, the traditional view in 1909 when
Harry Bateman solved the problem of transforming the electrodynamical
equations for the general case, thrown out by 1915 when Hilbert and
Einstein added in gravity with the aid of the equivalence principle?

Also, why is there almost no reference ever to the alternative
paradigm in physics texts? I found much to my surprise that many
physicists are entirely unacquainted with it, but found it interesting
and illuminating when they were told about it.

Heimdall

Heimdall wrote:
I was contemplating how to visualize the universe expanding when it
struck me that instead of thinking of the universe as expanding, you
could think of matter as shrinking.

That works for a scale-independent theory like Newtonian mechanics,
classical electrodynamics, or GR. But we know that we live in a quantum
world, and quantum phenomena have an inherent scale. So you cannot do
this and remain consistent with what we already know and observe about
the world.


Then, after reading the Einstein
Hoax (I hate to mention it because the author is regarded as such a
crank, but to give credit where it is due), I realized that, for
general relativity, instead of viewing space-time as curved you could
view it as flat, but with objects that shrink or expand.

This doesn't work, either. See above.

[I ignore the fool who calls himself the Einstein hoax,
because he spams identical material repeatedly to the
newsgroups, and never answers his critics. I don't
bother responding to robots. And he has no valid evidence
of any "hoax", either (except the hoax he perpetuates
on his readers).]


Since having this insight I discovered that the mathematician Cartan
worked out an equivalent of general relativity for flat space-time and
that Sir Arthur Eddington also proposed this same idea of shrinking
atoms, etc. Also, I found a very brief reference to this alternative
paradigm in a book by Kip Thorne "Black Holes & Time Warps".

What Cartan did is not what you claim above.

But there is a theoretical model that is locally equivalent to GR that
postulates gravitational interactions on a flat spacetime. See, e.g.
Weinberg. It's much more recent than Cartan, AFAIK.

And while "shrinking matter" was indeed considered by famous physicists
for a while, today it is a non-starter; see above.


This brings me to an overwhelming question. Since almost anyone can
imagine easily objects shrinking or expanding and since almost no one
understands what curved space-time means when they first encounter it,
why has the physics profession opted for explaining everything with
the curved space-time paradigm?

Because it is consistent with what we know and observe about the world.


Philosophically, it is difficult to see which paradigm is superior.

It is TRIVIAL: one works, the other doesn't.


Why prefer fixed objects and a changing space-time to a fixed
space-time and changing objects?

Because one works, the other doesn't.


[... more of the same]


Tom Roberts

Heimdall:
I was contemplating how to visualize the universe expanding when it
struck me that instead of thinking of the universe as expanding, you
could think of matter as shrinking. Then, after reading the Einstein
Hoax (I hate to mention it because the author is regarded as such a
crank, but to give credit where it is due),

The only credit due einsteinhoax is credit for being a
crackpot who spams the newsgroups with his crackpottery.

I realized that, for
general relativity, instead of viewing space-time as curved you could
view it as flat, but with objects that shrink or expand. For example,
instead of viewing space as expanding as your rocket ship nears a
black hole, you could imagine your rocket ship shrinking in a fixed
space.

This doesn't quite work. The quantity \hbar, for example,
fixes a scale, which may defined to be 1 and then expansion
or contraction becomes relative to that scale. If you allow
for the scaling to scale, so-to-speak, then you've removed
all of the physics without gaining anything.

[...]
This brings me to an overwhelming question. Since almost anyone can
imagine easily objects shrinking or expanding and since almost no one
understands what curved space-time means when they first encounter it,
why has the physics profession opted for explaining everything with
the curved space-time paradigm?

Because gravity is not a force in the same sense as the other known
forces. The basic premise behind general relativity is not curved
spacetime, but the equivalence principle. Curved spacetime follows
naturally from the assumption that gravitational mass is equivalent
to inertial mass, which then provides a description gravitiy in which
gravity is not a force, but simply a description of inertial motion.

Is this just traditional because
Hilbert and Einstein first derived the field equations for general
relativity? The idea of shrinking objects and changes in the rates at
which physical processes occur seems so much simpler from a
pedagogical point of view. At least, it was so for me.

I have a hard time seeing how that would pedagogically simpler.

Philosophically, it is difficult to see which paradigm is superior.

I would think that superior ``philosophical paridigm'' would be
the one in which we take our measurements to be reality rather
than first having to invoke some philosophical paridigm to translate
measurements into some reality we don't measure nor could ever
demonstrate had anything to do with any reality.

Why prefer fixed objects and a changing space-time to a fixed
space-time and changing objects?

We don't measure objects changing nor do we measure spacetime.
We measure objects and relationships between objects using
instruments that don't give numbers that would indicate objects
are changing. Why would anyone prefer a ``paridigm'' in which
reality is hidden from measurements by the very nature of the
``paridigm''? What could possibly be philosophically satisfying
about some ad hoc assumption that what we measure is not reality,
but reality is something we can't measure?

Theoretically, there seems to be a slight advantage to the flat
space-time paradigm. To get an identical theory out of the curved
space-time paradigm you have to add the qualification that the
space-time manifold has a Euclidean chart.

Why is that? We don't want a theory which is equivalent to flat
spacetime, since the point is that spacetime isn't flat. However, the real
issue is not whether spacetime is flat or curved but why it should be
anything other than what it is. ``Flat'' is just curved spacetime in which
a particular value for the curvature has been given special status. A
physicist would then pose the question, why should this value be special?
So, in a sense, that would require some additional explanation, since
it would have been necessary for nature to make that choice and we
expect the choices nature makes to be due to physics not a concious
descision on nature's part.

That eliminates the
possibility of worm-holes, which, in view of the fact that there are
no known worm-holes, is a point in favor of flat space-time. That is,
the flat space-time theory implicitly makes the prediction "there are
no worm holes" and, in fact, that prediction has so far been
confirmed.

Why was the idea of flat space-time, the traditional view in 1909 when
Harry Bateman solved the problem of transforming the electrodynamical
equations for the general case, thrown out by 1915 when Hilbert and
Einstein added in gravity with the aid of the equivalence principle?

Also, why is there almost no reference ever to the alternative
paradigm in physics texts? I found much to my surprise that many
physicists are entirely unacquainted with it, but found it interesting
and illuminating when they were told about it.

Physics is not about ``philosophical pardigms''. It's about measuring
things and explaining the measurements. Any ``philosophical paridigm''
that develops does so as a result of attempts to understand the common
threads which link those theories together. Also, any such ``paridigm''
would instantly be abandoned for another which is more successful in
acheiving that goal. I'm also unaware of any actual ``philosophical
paridigm'' being advanced by physicists. Physicists exploit explanations
which seem to work, have broad application and minimize the requirements
for fine tuning lots of magic numbers. Most of the people who try to
pidgeon-hole physics into paridigms are those who have some pet theory
which doesn't work, but explains some small set of isolated phenomena
in a way they find philosophically satisfying (and even that satisfaction
is probably unique to them). In other words, crackpots with a personal
agenda (who usually don't even agree with other crackpots about anything
other than ``overthrowing modern physics'').

The physics taught to students is the physics that works. In all
the time I spent in school studying physics, I don't recall a single
instance where any philosophical viewpoint was pushed or even mentioned.
Most everyone was too busy trying to understand the physics well enough
to work problems and ask intelligent questions to worry about any esoteric
``philosophical paridigm.''

(Bilge) wrote in message ...
Heimdall:
I realized that, for
general relativity, instead of viewing space-time as curved you could
view it as flat, but with objects that shrink or expand. For example,
instead of viewing space as expanding as your rocket ship nears a
black hole, you could imagine your rocket ship shrinking in a fixed
space.

This doesn't quite work. The quantity \hbar, for example,
fixes a scale, which may defined to be 1 and then expansion
or contraction becomes relative to that scale. If you allow
for the scaling to scale, so-to-speak, then you've removed
all of the physics without gaining anything.

I'm not sure I've correctly understood you, but, if I have, then the
physics is in the scaling of processes (objects undergoing change)
rather than in the scaling of space-time. I don't see why you prefer
to scale space-time, so to speak, but I may by the time I get to the
end of your letter.

This brings me to an overwhelming question. Since almost anyone can
imagine easily objects shrinking or expanding and since almost no one
understands what curved space-time means when they first encounter it,
why has the physics profession opted for explaining everything with
the curved space-time paradigm?

Because gravity is not a force in the same sense as the other known
forces. The basic premise behind general relativity is not curved
spacetime, but the equivalence principle. Curved spacetime follows
naturally from the assumption that gravitational mass is equivalent
to inertial mass, which then provides a description gravitiy in which
gravity is not a force, but simply a description of inertial motion.

Would you view the detection of gravitons as disproving the notion
that gravity is not a force? If not, why not?

What about Kaluza-Klein five-dimensional unification of GR with
electromagnetism? Does that demonstrate that electromagnetic forces
don't exist either? If so, what's the exchange of photons for?

How does curved space-time follow naturally from the equivalence of
gravitational and inertial mass?

Is this just traditional because
Hilbert and Einstein first derived the field equations for general
relativity? The idea of shrinking objects and changes in the rates at
which physical processes occur seems so much simpler from a
pedagogical point of view. At least, it was so for me.

I have a hard time seeing how that would pedagogically simpler.

Let me give you an example. Imagine watching a spherical object
(rigid enough so we don't have to worry about tidal forces) through a
telescope approaching a black hole. It will look like its shrinking.
If you're instructing newbies to physics wouldn't it be more readily
accepted to say "See, the object is shrinking as it approaches the
black hole", than to say "Actually, the object is not shrinking, but
space is expanding as the black hole is neared."


Philosophically, it is difficult to see which paradigm is superior.

I would think that superior ``philosophical paridigm'' would be
the one in which we take our measurements to be reality rather
than first having to invoke some philosophical paridigm to translate
measurements into some reality we don't measure nor could ever
demonstrate had anything to do with any reality.

I am not sure what you mean here. Let me try an example. I'm in my
lab on earth. Someone in a lab near a black hole sends me a blip when
he begins and a bleep when he ends an experiment. He then tells me he
measured the experiment as lasting 10 seconds. I respond that I
measured it as lasting 11 seconds. Under the standard interpretation
(a better word than "paradigm", which I picked up from the Thorne
book), he then says "Oh yeah, time runs slower over here". Under the
alternative interpretation, he then says "Oh yeah, processes run
slower over here". I don't see a big difference, except the concept
of slower processes is immediately familiar to anyone who's ever
watched a movie in slow motion.

Why prefer fixed objects and a changing space-time to a fixed
space-time and changing objects?

We don't measure objects changing nor do we measure spacetime.
We measure objects and relationships between objects using
instruments that don't give numbers that would indicate objects
are changing. Why would anyone prefer a ``paridigm'' in which
reality is hidden from measurements by the very nature of the
``paridigm''? What could possibly be philosophically satisfying
about some ad hoc assumption that what we measure is not reality,
but reality is something we can't measure?

Here, too, I don't understand what you mean.

Under either interpretation, objects in the lab aren't changing as we
measure them.

Where there is a difference is in the "measurement" of objects at a
distance - like the sphere approaching the black hole. Under the
standard interpretation, you measure the image and say "after
correcting for the expansion of space in the vicinity of the black
hole, we see that the sphere is so rigid, it's shape has not been
affected by tidal forces". Under the alternative interpretation, you
measure the image and say "the shrinkage is exactly explained by our
GR-equivalent theory. The shape has not been affected by tidal
forces." Again, I don't see a problem here.

I think what you're saying is the standard interpretation is reality
and therefore measurements under an alternative interpetation are not
of reality. That's not a valid argument in favor of the standard
interpretation.

What I'm saying is there are two ways of looking at reality. In both
we are measuring reality.

Theoretically, there seems to be a slight advantage to the flat
space-time paradigm. To get an identical theory out of the curved
space-time paradigm you have to add the qualification that the
space-time manifold has a Euclidean chart.

Why is that? We don't want a theory which is equivalent to flat
spacetime, since the point is that spacetime isn't flat. However, the real
issue is not whether spacetime is flat or curved but why it should be
anything other than what it is. ``Flat'' is just curved spacetime in which
a particular value for the curvature has been given special status. A
physicist would then pose the question, why should this value be special?
So, in a sense, that would require some additional explanation, since
it would have been necessary for nature to make that choice and we
expect the choices nature makes to be due to physics not a concious
descision on nature's part.

There is the same problem here as above. Under the assumption that
the standard intepretation is "real", then other interpretations
aren't measuring "reality".
Here the problem manifests itself as this "since the standard
interpretation says space-time is curved, space-time is curved, and,
therefore, the alternative interpretation that says space-time is flat
is wrong.

As for special status, you have to give processes (a better word than
"objects") a special status as not changing or space-time a special
status as flat. Why is one special status inferior to the other?

That eliminates the
possibility of worm-holes, which, in view of the fact that there are
no known worm-holes, is a point in favor of flat space-time. That is,
the flat space-time theory implicitly makes the prediction "there are
no worm holes" and, in fact, that prediction has so far been
confirmed.

Why was the idea of flat space-time, the traditional view in 1909 when
Harry Bateman solved the problem of transforming the electrodynamical
equations for the general case, thrown out by 1915 when Hilbert and
Einstein added in gravity with the aid of the equivalence principle?

Also, why is there almost no reference ever to the alternative
paradigm in physics texts? I found much to my surprise that many
physicists are entirely unacquainted with it, but found it interesting
and illuminating when they were told about it.

Physics is not about ``philosophical pardigms''. It's about measuring
things and explaining the measurements. Any ``philosophical paridigm''
that develops does so as a result of attempts to understand the common
threads which link those theories together. Also, any such ``paridigm''
would instantly be abandoned for another which is more successful in
acheiving that goal. I'm also unaware of any actual ``philosophical
paridigm'' being advanced by physicists. Physicists exploit explanations
which seem to work, have broad application and minimize the requirements
for fine tuning lots of magic numbers. Most of the people who try to
pidgeon-hole physics into paridigms are those who have some pet theory
which doesn't work, but explains some small set of isolated phenomena
in a way they find philosophically satisfying (and even that satisfaction
is probably unique to them). In other words, crackpots with a personal
agenda (who usually don't even agree with other crackpots about anything
other than ``overthrowing modern physics'').

You didn't really address the worm-hole question. If someone had
convincing evidence for a worm-hole, I would admit the inadequacy of
the flat space-time interpretation. I would admit its inadequacy if
there were convincing evidence that space-time doesn't have a
Euclidean chart. As it is, to make GR as strong a theory, you would
have to augment it to be "GR is true and space-time has a Euclidean
chart". That sounds clunky, not that that's very important.

The physics taught to students is the physics that works. In all
the time I spent in school studying physics, I don't recall a single
instance where any philosophical viewpoint was pushed or even mentioned.
Most everyone was too busy trying to understand the physics well enough
to work problems and ask intelligent questions to worry about any esoteric
``philosophical paridigm.''

There is always a philosophical point of view present when you have
two mathematically equivalent interpretations for a theory. I think
another example is the equivalence between Schroedinger's wave
mechanics and Heisenberg's matrix mechanics. It took some while to
demonstrate that these were identical, but having two interpretations
is a help, not a hindrance, in understanding the underlying physical
reality.

Perhaps a better example is Einstein's special relativity and
Lorentzian relativity as formulated by Poincare. They are
mathematically equivalent. Special relativity has become the
standard, but this hasn't stopped physicists from using the older
descriptions of objects contracting and clocks slowing as the speed of
light is approached and they speak of modeling particles accelerated
to a high speed by accelerators as "disks" due to the Lorentz
contraction.

Heimdall

Heimdall:
(Bilge) wrote:
in message ...
Heimdall:
I realized that, for
general relativity, instead of viewing space-time as curved you could
view it as flat, but with objects that shrink or expand. For example,
instead of viewing space as expanding as your rocket ship nears a
black hole, you could imagine your rocket ship shrinking in a fixed
space.

This doesn't quite work. The quantity \hbar, for example,
fixes a scale, which may defined to be 1 and then expansion
or contraction becomes relative to that scale. If you allow
for the scaling to scale, so-to-speak, then you've removed
all of the physics without gaining anything.

I'm not sure I've correctly understood you, but, if I have, then the
physics is in the scaling of processes (objects undergoing change)
rather than in the scaling of space-time. I don't see why you prefer
to scale space-time, so to speak, but I may by the time I get to the
end of your letter.

You missed my point. If you are free to choose a reference point,
then what you described would work just fine. However, you aren't
free to do that. Quantum processes fix a scale and you are stuck
with that. Trying to scale that as well, doesn't buy you anything.

Because gravity is not a force in the same sense as the other known
forces. The basic premise behind general relativity is not curved
spacetime, but the equivalence principle. Curved spacetime follows
naturally from the assumption that gravitational mass is equivalent
to inertial mass, which then provides a description gravitiy in which
gravity is not a force, but simply a description of inertial motion.

Would you view the detection of gravitons as disproving the notion
that gravity is not a force? If not, why not?

What about Kaluza-Klein five-dimensional unification of GR with
electromagnetism? Does that demonstrate that electromagnetic forces
don't exist either?

I'll try to answer both of those together as simply as I can. Whether
to interpret interactions as forces or as some aspect of spacetime is
probably more of a personal preference than anything else, since it
appears the descriptions are interchangeble, provided one has no
objection to adding additional dimensions. So, I think gravity could be
interpreted either way. In other words, spacetime is our perception of
the gravitational field, so it's convenient for us to describe it
geometrically. It might be more convenient to describe it some other
way in a quantum theory of gravity and think of the geometric picture
as a low energy limit.

Perhaps answering your question about kaluza-klein theories will
help clarify this. In a simple kaluza-klein model, (without gravity
since I want to solve a simple equation here), the metric may be
written:

ds^2 = dt^2 -dx^2 - dy^2 - dz^2 - (RdA)^2

where the fifth dimension, in the A direction is intrinsically
circular with a radius R. I claim the following:

(1) using the quantum substitutions for energy and momentum,
I get a five-dimensional wave equation analogous to the
wave equation I get in four dimensions,

(2) the solution may be written \Psi = C\exp(ik.r - iwt), with
k.r = (k_x)x + (k_y) + (k_z)z + (Rk_A) A, which I'll
write as simple k.x + R(k_A)A, so that the wavefunction
is,

\Psi = C\exp(ik.x - iwt + i(Rk_A)A)

= C\exp(ik.x - iwt)\exp((iRk_A) A)

= C\Phi(x,y,z,t)\exp(iS)

where \Phi(x,y,z,t) = C\exp(ik.x - iwt)

and S = R(k_A) A


(3) this is precisely the same wave equation I get when solving the
wave equation in _four_ dimensions and incliding a phase,
\exp(-iS) to obtain the photon via local gauge invariance.


[I can do this in more detail, if necessary]

So, essentially one ends up with the same equations regardless of
whether treat E&M as force or treat it as fifth dimension. By the way,
kaluza-klein theories were the forerunner of modern string theory.

The third (and currently preferred by many) equivalent way to write this
is to use the language of fiber bundles and differential forms, in which
case, the interpretation doesn't so much favor one picture over the other.

If so, what's the exchange of photons for?

At the risk of giving too casual a description, photons are the
means by which electrons (for example), are electrons independent
of what electrons elsewhere in the universe are doing.

How does curved space-time follow naturally from the equivalence of
gravitational and inertial mass?

If gravity isn't a force, then inertial motion is the motion of an
object which is freely falling in a gravitational field. In other words,
in general relativity, one takes seriously, the idea that astronauts
experiencing weightlessness _really_ have no force acting on them. The
astronauts are falling freely in the earth's gravitational field and since
no experiment has yet shown that _any_ objects fall differently than any
other, there is nothing which could demonstrate that gravity is no less a
fictional force than centrifugal force. By fictional, I mean that it's
possible to define coordinates such that the force vanishes. A force that
depends only upon a choice of coordinates cannot be a real force. I can't
define (4-dimensional) coordinates which make the force between two charges
disappear, for example.

I have a hard time seeing how that would pedagogically simpler.

Let me give you an example. Imagine watching a spherical object
(rigid enough so we don't have to worry about tidal forces) through a
telescope approaching a black hole. It will look like its shrinking.

I wasn't aware that was the case, but for the sake of argument, I'll
assume that's correct.

If you're instructing newbies to physics wouldn't it be more readily
accepted to say "See, the object is shrinking as it approaches the
black hole", than to say "Actually, the object is not shrinking, but
space is expanding as the black hole is neared."

Actually, I wouldn't think that describing the object as shrinking is
``better'', even if I accept the possibility that it would be better
received by students. The reason is that the ``shrinking'' description is
inconsistent with the basic principle of relativity, which is that objects
are what they are, independent of coordinates. In other words, if I'm an
observer _on_ that spherical object, then what I observe about what's
happening to me, doesn't depend upon what it might appear to you looking
through a telescope. So, the proper description is the one in which _I_
observe what's happening to _me_ and the transformation between the
coordinates I use to describe me and the ones you use to describe me is
the proper way to account for what you observe about me.

Philosophically, it is difficult to see which paradigm is superior.

I would think that superior ``philosophical paridigm'' would be
the one in which we take our measurements to be reality rather
than first having to invoke some philosophical paridigm to translate
measurements into some reality we don't measure nor could ever
demonstrate had anything to do with any reality.

I am not sure what you mean here. Let me try an example. I'm in my
lab on earth. Someone in a lab near a black hole sends me a blip when
he begins and a bleep when he ends an experiment. He then tells me he
measured the experiment as lasting 10 seconds. I respond that I
measured it as lasting 11 seconds. Under the standard interpretation
(a better word than "paradigm", which I picked up from the Thorne
book), he then says "Oh yeah, time runs slower over here". Under the
alternative interpretation, he then says "Oh yeah, processes run
slower over here". I don't see a big difference, except the concept
of slower processes is immediately familiar to anyone who's ever
watched a movie in slow motion.

The correct interpretation is _neither_ of those. The correct number to
use is the proper time, d\tau, which for one observer is,

d\tau^2 = dt^2 - dx^2 - dy^2 - dz^2

and for the other is,

d\tau^2 = dt'^2 - dx'^2 - dy'^2 - dz'^2

Since the proper time is an invariant, those two expressions must
be equal and both observers must agree on the that quantity. The
coordinates used are just coordinates, so the correct explanation
is that what the observers measure and describe in terms of coordinates
is coordinate dependent, but they both must agree on the length of
the interval measured. For an observer performing an experiment in
his own restrame, the time he measures is also the proper time.

[...]

As for special status, you have to give processes (a better word than
"objects") a special status as not changing or space-time a special
status as flat. Why is one special status inferior to the other?

I give ``special status'' to those things which don't require
constructing some hypothetical reality to convert numbers I measure
into ``the real measurements''. I don't observe time to slow down
or rulers to shrink regardless of what I do, so I assume that rulers
don't shrink and time doesn't slow down until such time that someone
demonstrates that the shrinking of rulers and slowing of clocks in
my own frame means something more than metaphysical knuckleraps.

[...]

You didn't really address the worm-hole question. If someone had
convincing evidence for a worm-hole, I would admit the inadequacy of
the flat space-time interpretation.

I see no reason to address any interpretation based upon speculation
of wormholes one-way or another. The existence or non-existence of
wormholes can't be determined and since general relativity without
wormholes does not equal special relativity, there's no reason to
even consider wormholes as anything more than something which is
compatible with general relativity as far as anyone knows at the
moment.

The physics taught to students is the physics that works. In all
the time I spent in school studying physics, I don't recall a single
instance where any philosophical viewpoint was pushed or even mentioned.
Most everyone was too busy trying to understand the physics well enough
to work problems and ask intelligent questions to worry about any esoteric
``philosophical paridigm.''

There is always a philosophical point of view present when you have
two mathematically equivalent interpretations for a theory.

Special relativity and general relativity are _not_ mathematically
equivalent. If they were, either both would be compatible with wormholes
or neither would.

I think another example is the equivalence between Schroedinger's wave
mechanics and Heisenberg's matrix mechanics. It took some while to
demonstrate that these were identical, but having two interpretations
is a help, not a hindrance, in understanding the underlying physical
reality.

But, those _really_ are equivalent. No transformation of coordinates
will chage special relativity into general relativity.

Perhaps a better example is Einstein's special relativity and
Lorentzian relativity as formulated by Poincare. They are
mathematically equivalent. Special relativity has become the
standard, but this hasn't stopped physicists from using the older
descriptions of objects contracting and clocks slowing as the speed of
light is approached and they speak of modeling particles accelerated
to a high speed by accelerators as "disks" due to the Lorentz
contraction.

I'm not sure what you mean by ``Lorentzian relativity as formulated by
Poincare'', but if that means an ether theory, I don't agree that those
are equivalent except in a very superficial sense. The reason that
special relativity prevailed is that what is important to physicists
is the very non-superficial way those two theories differ.

"Bilge" wrote in message
...
Heimdall:
(Bilge) wrote:
in message
...
Heimdall:
I realized that, for
general relativity, instead of viewing space-time as curved you
could
view it as flat, but with objects that shrink or expand. For
example,
instead of viewing space as expanding as your rocket ship nears a
black hole, you could imagine your rocket ship shrinking in a fixed
space.

This doesn't quite work. The quantity \hbar, for example,
fixes a scale, which may defined to be 1 and then expansion
or contraction becomes relative to that scale. If you allow
for the scaling to scale, so-to-speak, then you've removed
all of the physics without gaining anything.

I'm not sure I've correctly understood you, but, if I have, then the
physics is in the scaling of processes (objects undergoing change)
rather than in the scaling of space-time. I don't see why you prefer
to scale space-time, so to speak, but I may by the time I get to the
end of your letter.

You missed my point. If you are free to choose a reference point,
then what you described would work just fine. However, you aren't
free to do that. Quantum processes fix a scale and you are stuck
with that. Trying to scale that as well, doesn't buy you anything.

Because gravity is not a force in the same sense as the other known
forces. The basic premise behind general relativity is not curved
spacetime, but the equivalence principle. Curved spacetime follows
naturally from the assumption that gravitational mass is equivalent
to inertial mass, which then provides a description gravitiy in which
gravity is not a force, but simply a description of inertial motion.

Would you view the detection of gravitons as disproving the notion
that gravity is not a force? If not, why not?

What about Kaluza-Klein five-dimensional unification of GR with
electromagnetism? Does that demonstrate that electromagnetic forces
don't exist either?

I'll try to answer both of those together as simply as I can. Whether
to interpret interactions as forces or as some aspect of spacetime is
probably more of a personal preference than anything else, since it
appears the descriptions are interchangeble, provided one has no
objection to adding additional dimensions. So, I think gravity could be
interpreted either way. In other words, spacetime is our perception of
the gravitational field, so it's convenient for us to describe it
geometrically. It might be more convenient to describe it some other
way in a quantum theory of gravity and think of the geometric picture
as a low energy limit.

Perhaps answering your question about kaluza-klein theories will
help clarify this. In a simple kaluza-klein model, (without gravity
since I want to solve a simple equation here), the metric may be
written:

ds^2 = dt^2 -dx^2 - dy^2 - dz^2 - (RdA)^2

Just something I want to add for the original posters benefit. When authors
in popularizations claim unification in Kaluza-Klein theories they are
leaving something very important out, something that becomes glaringly
obvious when you examine the mathematics. You see GR works because the
equations of gravity take the same form is all coordinate systems (this is
called covariance) But to get Kaluza-Klein to work only certain coordinate
transformation are allowed - those transformations that leaves the form of
the Kaluza-Klein metric invariant (Bilges equation above) - this condition
being called the cylinder condition. Mathematically it means no physical
quantities depend on the 5th coordinate - eg the R above does not depend on
the 5th dimension. It is only by imposing this condition it works. So
basically what it means is the equations of EM are a left over remnants of
full covariance. The physical reason why nature should impose such a
condition is a bit of a mystery in the theory - Klein later gave an
explanation based on the 5th dimension being curled up into a small circle
which when you work out the math (and use a bit of QM) is the same as the
cylinder condition. See http://xxx.lanl.gov/abs/gr-qc/9805018. This link
also explains modern Kaluza-Klein theory where the cylinder condition is not
to imposed to see what happens. In this approach (called Space Time Matter
by its prominent supporter Wesson) the cylinder condition is only one of the
possible conditions for 'matter' that is formed from 'aspects' of a 5th
dimension that appears in our world - other conditions lead to other types
of matter. The article makes interesting reading. If it appeals then you
might consider getting Wesson's Book Space, Time Matter - highly
recommended. An interesting thing that I can not resist mentioning here is
that Wesson shows that general types of matter - matter sufficient to
explain the gross features of the world we see around us - result if we
consider the 5th dimension to be flat and devoid on any matter at all. This
is a realization of Einstein's dream of the wood of matter from the marble
of geometry.

Thanks
Bill


where the fifth dimension, in the A direction is intrinsically
circular with a radius R. I claim the following:

(1) using the quantum substitutions for energy and momentum,
I get a five-dimensional wave equation analogous to the
wave equation I get in four dimensions,

(2) the solution may be written \Psi = C\exp(ik.r - iwt), with
k.r = (k_x)x + (k_y) + (k_z)z + (Rk_A) A, which I'll
write as simple k.x + R(k_A)A, so that the wavefunction
is,

\Psi = C\exp(ik.x - iwt + i(Rk_A)A)

= C\exp(ik.x - iwt)\exp((iRk_A) A)

= C\Phi(x,y,z,t)\exp(iS)

where \Phi(x,y,z,t) = C\exp(ik.x - iwt)

and S = R(k_A) A


(3) this is precisely the same wave equation I get when solving the
wave equation in _four_ dimensions and incliding a phase,
\exp(-iS) to obtain the photon via local gauge invariance.


[I can do this in more detail, if necessary]

So, essentially one ends up with the same equations regardless of
whether treat E&M as force or treat it as fifth dimension. By the way,
kaluza-klein theories were the forerunner of modern string theory.

The third (and currently preferred by many) equivalent way to write this
is to use the language of fiber bundles and differential forms, in which
case, the interpretation doesn't so much favor one picture over the other.

If so, what's the exchange of photons for?

At the risk of giving too casual a description, photons are the
means by which electrons (for example), are electrons independent
of what electrons elsewhere in the universe are doing.

How does curved space-time follow naturally from the equivalence of
gravitational and inertial mass?

If gravity isn't a force, then inertial motion is the motion of an
object which is freely falling in a gravitational field. In other words,
in general relativity, one takes seriously, the idea that astronauts
experiencing weightlessness _really_ have no force acting on them. The
astronauts are falling freely in the earth's gravitational field and since
no experiment has yet shown that _any_ objects fall differently than any
other, there is nothing which could demonstrate that gravity is no less a
fictional force than centrifugal force. By fictional, I mean that it's
possible to define coordinates such that the force vanishes. A force that
depends only upon a choice of coordinates cannot be a real force. I can't
define (4-dimensional) coordinates which make the force between two
charges
disappear, for example.

I have a hard time seeing how that would pedagogically simpler.

Let me give you an example. Imagine watching a spherical object
(rigid enough so we don't have to worry about tidal forces) through a
telescope approaching a black hole. It will look like its shrinking.

I wasn't aware that was the case, but for the sake of argument, I'll
assume that's correct.

If you're instructing newbies to physics wouldn't it be more readily
accepted to say "See, the object is shrinking as it approaches the
black hole", than to say "Actually, the object is not shrinking, but
space is expanding as the black hole is neared."

Actually, I wouldn't think that describing the object as shrinking is
``better'', even if I accept the possibility that it would be better
received by students. The reason is that the ``shrinking'' description is
inconsistent with the basic principle of relativity, which is that objects
are what they are, independent of coordinates. In other words, if I'm an
observer _on_ that spherical object, then what I observe about what's
happening to me, doesn't depend upon what it might appear to you looking
through a telescope. So, the proper description is the one in which _I_
observe what's happening to _me_ and the transformation between the
coordinates I use to describe me and the ones you use to describe me is
the proper way to account for what you observe about me.

Philosophically, it is difficult to see which paradigm is superior.

I would think that superior ``philosophical paridigm'' would be
the one in which we take our measurements to be reality rather
than first having to invoke some philosophical paridigm to translate
measurements into some reality we don't measure nor could ever
demonstrate had anything to do with any reality.

I am not sure what you mean here. Let me try an example. I'm in my
lab on earth. Someone in a lab near a black hole sends me a blip when
he begins and a bleep when he ends an experiment. He then tells me he
measured the experiment as lasting 10 seconds. I respond that I
measured it as lasting 11 seconds. Under the standard interpretation
(a better word than "paradigm", which I picked up from the Thorne
book), he then says "Oh yeah, time runs slower over here". Under the
alternative interpretation, he then says "Oh yeah, processes run
slower over here". I don't see a big difference, except the concept
of slower processes is immediately familiar to anyone who's ever
watched a movie in slow motion.

The correct interpretation is _neither_ of those. The correct number to
use is the proper time, d\tau, which for one observer is,

d\tau^2 = dt^2 - dx^2 - dy^2 - dz^2

and for the other is,

d\tau^2 = dt'^2 - dx'^2 - dy'^2 - dz'^2

Since the proper time is an invariant, those two expressions must
be equal and both observers must agree on the that quantity. The
coordinates used are just coordinates, so the correct explanation
is that what the observers measure and describe in terms of coordinates
is coordinate dependent, but they both must agree on the length of
the interval measured. For an observer performing an experiment in
his own restrame, the time he measures is also the proper time.

[...]

As for special status, you have to give processes (a better word than
"objects") a special status as not changing or space-time a special
status as flat. Why is one special status inferior to the other?

I give ``special status'' to those things which don't require
constructing some hypothetical reality to convert numbers I measure
into ``the real measurements''. I don't observe time to slow down
or rulers to shrink regardless of what I do, so I assume that rulers
don't shrink and time doesn't slow down until such time that someone
demonstrates that the shrinking of rulers and slowing of clocks in
my own frame means something more than metaphysical knuckleraps.

[...]

You didn't really address the worm-hole question. If someone had
convincing evidence for a worm-hole, I would admit the inadequacy of
the flat space-time interpretation.

I see no reason to address any interpretation based upon speculation
of wormholes one-way or another. The existence or non-existence of
wormholes can't be determined and since general relativity without
wormholes does not equal special relativity, there's no reason to
even consider wormholes as anything more than something which is
compatible with general relativity as far as anyone knows at the
moment.

The physics taught to students is the physics that works. In all
the time I spent in school studying physics, I don't recall a single
instance where any philosophical viewpoint was pushed or even
mentioned.
Most everyone was too busy trying to understand the physics well
enough
to work problems and ask intelligent questions to worry about any
esoteric
``philosophical paridigm.''

There is always a philosophical point of view present when you have
two mathematically equivalent interpretations for a theory.

Special relativity and general relativity are _not_ mathematically
equivalent. If they were, either both would be compatible with wormholes
or neither would.

I think another example is the equivalence between Schroedinger's wave
mechanics and Heisenberg's matrix mechanics. It took some while to
demonstrate that these were identical, but having two interpretations
is a help, not a hindrance, in understanding the underlying physical
reality.

But, those _really_ are equivalent. No transformation of coordinates
will chage special relativity into general relativity.

Perhaps a better example is Einstein's special relativity and
Lorentzian relativity as formulated by Poincare. They are
mathematically equivalent. Special relativity has become the
standard, but this hasn't stopped physicists from using the older
descriptions of objects contracting and clocks slowing as the speed of
light is approached and they speak of modeling particles accelerated
to a high speed by accelerators as "disks" due to the Lorentz
contraction.

I'm not sure what you mean by ``Lorentzian relativity as formulated by
Poincare'', but if that means an ether theory, I don't agree that those
are equivalent except in a very superficial sense. The reason that
special relativity prevailed is that what is important to physicists
is the very non-superficial way those two theories differ.

"Bill Hobba" wrote in message ...
"Bilge" wrote in message
...
Heimdall:
(Bilge) wrote:
in message
...
Heimdall:

I replied to you in #8 below.

There seems to be a bug in the Google groups software that rejects my
attempts to post followup messages in the right places from time to
time

Heimdall

Oops! That reply is not #8 (the numbers are not Chronological), but it is the
latest top level submission to this newsgroup as of the 452AM on 6/2/04.

Heimdall

Bilge,

I had to submit my response to you as a top level post. See below.

Sorry, I don't know why sometimes I cannot directly submit follow up
posts through Google groups.

Heimdall