I'm reposting this at a higher level, because it seems to be a common
theme in many threads, not just the one from which this message was in
context. Nor am I beating up on Bill Hobba -- similar comments have
been made by many. Finally, forgive the preamble -- it's not a
flagrant top-posting ettiquette violation.

PD
=======================================

"Bill Hobba" wrote in message ...
"Paul Bramscher" wrote in message
...
I've got a question regarding relativity: is there any way to state SR,
GR, or QM fully without mathematics?
I ask because of the curious problem I've encountered with Karl Popper
and the claim that a scientific statement is one which is falsifiable.
But the problem with any mathematical tautology is that it is *not*
falsifiable, not due to empirical/experimental evidence to the contrary,
but because math can be proven to be inherently correct beyond the realm
of the empirical.

You have hit upon a very interesting point. A number of supposed laws of
physics such as Ohms law are in fact tautologies. Even Newton's first law
is a tautology - ie a particle moves at constant velocity unless acted on by
a force. But this is only a special case of Newton's second law which is
really a definition of force anyway. The way out of the impasse is to
understand what they are saying. What the first law is really saying is
that frames exist (without going into the detail of what a frame is) such
that Newton's first law holds - these are called inertial frames. Newton's
second law is really half a law as is discussed in the Feynamn Lectures of
Physics - Chapter 12 Volume 1 - The Chacteristics of Force. The bottom line
is while they may seem to be a tautology deeper digging shows what its
physical content is eg for ohms law the physical content is objects called
resistors that obey ohms law to good accuracy exist. This is discussed in
further detail here
http://www.colorado.edu/philosophy/v...r/nothing.html.


I find this distasteful. Moreover, it leads to these really awful
discussions about tautologies and circular logic that have plagued
these n.g.s perpetually.

First off, let's deal with SR directly. SR makes two completely
unfounded assumptions: 1) that the speed of light is independent of
inertial reference frame, and 2) that the laws of physics have the
same form in every inertial reference frame. What one does then is to
work out the implications of those assumptions and see if they all
agree with experiment. If they do, then one may assume there is
nothing wrong with those assumptions. What many, if not most, critics
of SR then say is, "But don't you have to now go back and defend the
basis behind your assumptions? Don't you have to validate them with
some intuitive concept?" The answer to that question is, simply and
finally, NO. In fact, if you *do* attempt to go back and defend your
assumptions with rationales other than "it works", then indeed you are
engaging in circular logic. But the point is, you never do have to go
back and defend the assumptions. There is nothing circular or
self-referential or "tautological" (sic) about SR at all. SR does
*not* have as a conclusion that the speed of light is c in every
inertial frame. It *assumes* that the speed of light is c in every
inertial frame. At no point and at no time does one have to verify
that the speed of light is in fact c. This is a CRUCIAL point. The
test of SR is not whether the speed of light is c. The test of SR is
whether everything *else* that SR predicts (in terms of *measurable*
quantities) is correct. The value of invariant mass of a system,
independent of inertial reference frame, is a good example. Now, of
course, if someone would measure that the speed of light was NOT c in
every inertial frame, this would immediately dismantle SR, but the
onus is NOT on SR to validate that it is.

But back to Ohm's Law. Is there physics content in Ohm's Law? You
betcha. What it says is that there is a proportionality between
voltage applied across the object and current through an object, in a
broad class of objects, and that proportionality constant depends only
on the physical properties of the object (usually, what the "stuff" is
and the dimensions of the object. Does V=IR define what R is? Sure, if
you want to define R operationally -- that is, by only knowing V and
I. That does NOT make the operational definition of R the sole content
of the law. If it did, then even diodes and transistors would have R
defined as V/I, even though that number would depend strongly on what
V and I are. And that's the point! For resistors, and chunks of wire,
and airplane wing coatings, the ratio of V/I is *independent* of the
values of V and I. There's your physics content.

Let me give you another example. If I asked you how much a cable on
the Golden Gate bridge stretched under load, you'd say, "It depends."
And I'd say, "It depends on what?" And you might say, "Well, it
depends on the length of the cable, L," (and I might say, how?
linearly? like L^2?) and then "and on the area of the cable, A" (and I
might say, are you sure it's not the circumference like the miniscus
in a capillary tube?) and then "and how much load F is on it" and then
"and what the cable is made of." And I would congratulate and tell you
you've just done physics, deriving a simple law with some non-obvious
parts: delL = (1/Y)*L*F/A, where Y is the constant that depends on
what the cable is made of. Other folks look at that and say its the
*definition* of stress and strain: stress = Y * strain. Well, yeah,
maybe, but there's lots of physics content in there. And yes, it only
applies in the elastic regime for the cable. Universality in this case
is not claimed, either.

The same goes for Newton's law of gravitation. The fact that F is
proportional to the product of the two attracting masses is consistent
with Newton's own 2nd and 3rd laws, but the r^2 term is certainly NOT
obvious -- in fact, it's still the subject of much discussion and
experimental data fitting. The constant of proportionality G that
converts kg^2/m^2 to N even has physics content! Because, unlike Y in
the case above, G does not depend on what any "stuff" is or what any
conditions are -- its universality is a big, big claim.

The same even goes for Newton's 1st Law. Yes, in retrospect, it is
simply a special case of the 2nd Law. But consider what preceded it --
the Aristotelean notion that if you didn't keep pushing on an object,
it would stop. It was a big deal for Newton to say, "Not so!" Yes, it
*benchmarks* what an inertial frame is, in the sense that if the 1st
law doesn't hold in some frame, then it's not an inertial frame. But
that doesn't mean that the 1st law is devoid of content or that the
principle of relativity is self-referential in that benchmark. The
principle of relativity says that not only is the 1st law valid in any
inertial frame, but also the 2nd law, and also the 3rd law, and also
Maxwell's equations, etc. -- that certainly doesn't follow from the
benchmark using the 1st law.

Enough with this balderdash about tautologies and circular reasoning
and self-reference in SR. Enough, I say!

PD

"Paul Draper" wrote in message
om...
I'm reposting this at a higher level, because it seems to be a common
theme in many threads, not just the one from which this message was in
context. Nor am I beating up on Bill Hobba -- similar comments have
been made by many. Finally, forgive the preamble -- it's not a
flagrant top-posting ettiquette violation.

PD
=======================================

"Bill Hobba" wrote in message
...
"Paul Bramscher" wrote in message
...
I've got a question regarding relativity: is there any way to state
SR,
GR, or QM fully without mathematics?
I ask because of the curious problem I've encountered with Karl Popper
and the claim that a scientific statement is one which is falsifiable.
But the problem with any mathematical tautology is that it is *not*
falsifiable, not due to empirical/experimental evidence to the
contrary,
but because math can be proven to be inherently correct beyond the
realm
of the empirical.

You have hit upon a very interesting point. A number of supposed laws
of
physics such as Ohms law are in fact tautologies. Even Newton's first
law
is a tautology - ie a particle moves at constant velocity unless acted
on by
a force. But this is only a special case of Newton's second law which
is
really a definition of force anyway. The way out of the impasse is to
understand what they are saying. What the first law is really saying is
that frames exist (without going into the detail of what a frame is)
such
that Newton's first law holds - these are called inertial frames.
Newton's
second law is really half a law as is discussed in the Feynamn Lectures
of
Physics - Chapter 12 Volume 1 - The Chacteristics of Force. The bottom
line
is while they may seem to be a tautology deeper digging shows what its
physical content is eg for ohms law the physical content is objects
called
resistors that obey ohms law to good accuracy exist. This is discussed
in
further detail here
http://www.colorado.edu/philosophy/v...r/nothing.html.


I find this distasteful. Moreover, it leads to these really awful
discussions about tautologies and circular logic that have plagued
these n.g.s perpetually.

First off, let's deal with SR directly. SR makes two completely
unfounded assumptions: 1) that the speed of light is independent of
inertial reference frame, and 2) that the laws of physics have the
same form in every inertial reference frame.

For some reason you find what I wrote distasteful. You know what I find
distasteful? People who make unfounded statements when a little research
will show they are way off target. For example 'SR makes two completely
unfounded assumptions' is, too put it bluntly, without any foundation at
all. Physics is an experimental science. Both the assumptions of SR are
based on experiment as you would have discovered if you had decided to a
little research and found the UseNet FAQ questions on physics:
http://math.ucr.edu/home/baez/physics/. Specifically see 'What is the
experimental basis of Special Relativity?'
http://math.ucr.edu/home/baez/physic...periments.html

What one does then is to
work out the implications of those assumptions and see if they all
agree with experiment.

Yes one does do that - but that is not to say the assumptions are themselves
not without direct experimental support.

If they do, then one may assume there is
nothing wrong with those assumptions. What many, if not most, critics
of SR then say is, "But don't you have to now go back and defend the
basis behind your assumptions? Don't you have to validate them with
some intuitive concept?" The answer to that question is, simply and
finally, NO.

The answer is that being an experimental science physics does experiments,
not only to test the assumptions, but to test the implications of the
assumptions.

In fact, if you *do* attempt to go back and defend your
assumptions with rationales other than "it works", then indeed you are
engaging in circular logic.

No circular logic is involved.

But the point is, you never do have to go
back and defend the assumptions.

That is simply not true as a perusal of the experimental basis will show.

There is nothing circular or
self-referential or "tautological" (sic) about SR at all. SR does
*not* have as a conclusion that the speed of light is c in every
inertial frame.

Yes and no. To see what is really happening see a proper derivation eg
http://arxiv.org/abs/physics/0110076 and note, from the POR alone:

'We have found the form of transformation functions between two frames in
the standard configuration. The only remaining unknown is the value of the
universal
constant u. From the transformation functions we can make a number of
conclusions, for example about possibility of time dilation. Then we could
use time
dilation experiments (involving decay of stationery and moving mesons) to
measure the value of u. Another (but not the only) way to find a value of u
is by
deriving velocity addition formula and observing that if u = -c2 and an
object moves with speed c in one inertial frame, then it moves with the same
speed in all
others. This would enable us to identify c as the speed of light in vacuum.
But I stress once again that other experiments could be used to find the
value of the
constant.'

It *assumes* that the speed of light is c in every
inertial frame. At no point and at no time does one have to verify
that the speed of light is in fact c.

It is an assumption with direct experimental and theoretical evidence.

This is a CRUCIAL point. The
test of SR is not whether the speed of light is c. The test of SR is
whether everything *else* that SR predicts (in terms of *measurable*
quantities) is correct. The value of invariant mass of a system,
independent of inertial reference frame, is a good example. Now, of
course, if someone would measure that the speed of light was NOT c in
every inertial frame, this would immediately dismantle SR, but the
onus is NOT on SR to validate that it is.

But back to Ohm's Law. Is there physics content in Ohm's Law? You
betcha. What it says is that there is a proportionality between
voltage applied across the object and current through an object, in a
broad class of objects, and that proportionality constant depends only
on the physical properties of the object (usually, what the "stuff" is
and the dimensions of the object. Does V=IR define what R is? Sure, if
you want to define R operationally -- that is, by only knowing V and
I. That does NOT make the operational definition of R the sole content
of the law. If it did, then even diodes and transistors would have R
defined as V/I, even though that number would depend strongly on what
V and I are. And that's the point! For resistors, and chunks of wire,
and airplane wing coatings, the ratio of V/I is *independent* of the
values of V and I. There's your physics content.

I think you have misread or misinterpreted what I said - on the surface it
is a tautology because Ohms law applies to resistors and a resistor is
defined as something to which ohms law is applicable to. If you doubt this
then I suggest you read different physics books than me and I would like to
see a reference that claims otherwise. What I then said is that one must
dig a little deeper than the surface to see what the physical content really
is - I did not say that such digging was hard or not realty oblivious. It
is obvious the physical content of Ohms law is that, as you say, a broad
class of objects exist that obey it to a reasonable accuracy. Nor do I
claim that physics textbooks do not go to pains to ensure this point is
understood eg see page 270 - Griffith - Introduction to Electrodynamics
where he is careful to point out the real physics behind ohms law is that
for most substances experiment shows the current density is proportional to
the force per unit charge. Thus he carefully points out it is not a law in
the usual sense and only applies to most substances.


Let me give you another example. If I asked you how much a cable on
the Golden Gate bridge stretched under load, you'd say, "It depends."
And I'd say, "It depends on what?" And you might say, "Well, it
depends on the length of the cable, L," (and I might say, how?
linearly? like L^2?) and then "and on the area of the cable, A" (and I
might say, are you sure it's not the circumference like the miniscus
in a capillary tube?) and then "and how much load F is on it" and then
"and what the cable is made of." And I would congratulate and tell you
you've just done physics, deriving a simple law with some non-obvious
parts: delL = (1/Y)*L*F/A, where Y is the constant that depends on
what the cable is made of. Other folks look at that and say its the
*definition* of stress and strain: stress = Y * strain. Well, yeah,
maybe, but there's lots of physics content in there. And yes, it only
applies in the elastic regime for the cable. Universality in this case
is not claimed, either.

The same goes for Newton's law of gravitation. The fact that F is
proportional to the product of the two attracting masses is consistent
with Newton's own 2nd and 3rd laws, but the r^2 term is certainly NOT
obvious -- in fact, it's still the subject of much discussion and
experimental data fitting. The constant of proportionality G that
converts kg^2/m^2 to N even has physics content! Because, unlike Y in
the case above, G does not depend on what any "stuff" is or what any
conditions are -- its universality is a big, big claim.

The same even goes for Newton's 1st Law. Yes, in retrospect, it is
simply a special case of the 2nd Law. But consider what preceded it --
the Aristotelean notion that if you didn't keep pushing on an object,
it would stop. It was a big deal for Newton to say, "Not so!" Yes, it
*benchmarks* what an inertial frame is, in the sense that if the 1st
law doesn't hold in some frame, then it's not an inertial frame. But
that doesn't mean that the 1st law is devoid of content or that the
principle of relativity is self-referential in that benchmark. The
principle of relativity says that not only is the 1st law valid in any
inertial frame, but also the 2nd law, and also the 3rd law, and also
Maxwell's equations, etc. -- that certainly doesn't follow from the
benchmark using the 1st law.

Enough with this balderdash about tautologies and circular reasoning
and self-reference in SR. Enough, I say!

Again I think you have misread or misinterpreted what I said - I claimed
that on the surface these things looked like tautologies but in fact they
have real physical content when you dig a little deeper. It may be that some
dude like yourself says - hey I saw they were not really tautologies from
the start. When the greats like Feynman discusses such in his classic
Feynman Lectures on Physics you pat yourself on the back and say - hey I
will never fall into that trap. Great. Good on you. But not everyone is
that smart. The respected physicist and philopher Victor Stenger says:
(from the link I gave):

'Of course, the laws of physics must agree with observations. But, beyond
that, they are formulated in such a way as to assure, as best as possible,
that they do not depend on any particular point of view. Otherwise they
cannot be expected to faithfully describe an objective reality. When these
requirements are met, the laws, as we know them, appear as virtual
tautologies. Furthermore, the forces that account for the interactions
between bodies are seen to be fictions that are introduced in the theory to
preserve that theory's independence of point of view.'

I suppose when he writes 'When these requirements are met, the laws, as we
know them, appear as virtual tautologies.' it is something he pulled out of
thin air - no one would ever fall into the trap of thinking they are
tautologies.

Thanks
Bill


PD

"Paul Draper" wrote in message
om...
I'm reposting this at a higher level, because it seems to be a common
theme in many threads, not just the one from which this message was in
context. Nor am I beating up on Bill Hobba -- similar comments have
been made by many. Finally, forgive the preamble -- it's not a
flagrant top-posting ettiquette violation.

PD
=======================================

"Bill Hobba" wrote in message
...
"Paul Bramscher" wrote in message
...
I've got a question regarding relativity: is there any way to state SR,
GR, or QM fully without mathematics?
I ask because of the curious problem I've encountered with Karl Popper
and the claim that a scientific statement is one which is falsifiable.
But the problem with any mathematical tautology is that it is *not*
falsifiable, not due to empirical/experimental evidence to the
contrary,
but because math can be proven to be inherently correct beyond the
realm
of the empirical.

You have hit upon a very interesting point. A number of supposed laws of
physics such as Ohms law are in fact tautologies. Even Newton's first
law
is a tautology - ie a particle moves at constant velocity unless acted on
by
a force. But this is only a special case of Newton's second law which is
really a definition of force anyway. The way out of the impasse is to
understand what they are saying. What the first law is really saying is
that frames exist (without going into the detail of what a frame is) such
that Newton's first law holds - these are called inertial frames.
Newton's
second law is really half a law as is discussed in the Feynamn Lectures
of
Physics - Chapter 12 Volume 1 - The Chacteristics of Force. The bottom
line
is while they may seem to be a tautology deeper digging shows what its
physical content is eg for ohms law the physical content is objects
called
resistors that obey ohms law to good accuracy exist. This is discussed
in
further detail here
http://www.colorado.edu/philosophy/v...r/nothing.html.


I find this distasteful.

Relativity, like bad fish, leaves a bad taste in a lot of people's mouths
once they realize what they are eating is rotten.


Moreover, it leads to these really awful
discussions about tautologies and circular logic that have plagued
these n.g.s perpetually.

First off, let's deal with SR directly. SR makes two completely
unfounded assumptions: 1) that the speed of light is independent of
inertial reference frame, and 2) that the laws of physics have the
same form in every inertial reference frame. What one does then is to
work out the implications of those assumptions and see if they all
agree with experiment. If they do, then one may assume there is
nothing wrong with those assumptions. What many, if not most, critics
of SR then say is, "But don't you have to now go back and defend the
basis behind your assumptions? Don't you have to validate them with
some intuitive concept?" The answer to that question is, simply and
finally, NO. In fact, if you *do* attempt to go back and defend your
assumptions with rationales other than "it works", then indeed you are
engaging in circular logic. But the point is, you never do have to go
back and defend the assumptions. There is nothing circular or
self-referential or "tautological" (sic) about SR at all.

I find this distasteful. SR is worse than self-referential, it denies its
own posulate and is therefore self-contradictory.

You have claimed:
1) the speed of light is independent of inertial reference frame.

That is not what SR claims.

2) that the laws of physics have the same form in every inertial reference
frame.

That is not what SR claims.

You will not find the word "inertial" anywhere in "On the Electrodynamics of
Moving Bodies" by Albert Einstein, which is the definitive paper for SR.

The first postulate of SR (item 2) is NOT stated directly at all. Instead,
examples are given which relate to the concept of Galilean relativity, which
can be summarized as the vector sum of velocities, V = u+v. When two
vehicles travel along a road side by side, One with velocity u and the other
with velocity v, the relative velocity between them is u-v.
How do we know this is what is being referred to?
Because Einstein states: "We will raise this conjecture (the purport of
which will hereafter be called the "Principle of Relativity'') to the status
of a postulate, and also introduce another postulate, which is only
apparently irreconcilable with the former, namely, that light is always
propagated in empty space with a definite velocity c which is independent of
the state of motion of the emitting body. "
Why on earth would anyone find "laws of physics have the same form" to be
irreconcilable with "speed of light is independent" ?
Note that Einstein finds a replacement for V= u+v in the form
V = (u+v)/(1+uv/c^2) to bring about the conciliation between his two
postulates. However, he does not USE his new found postulate consistently
in his derivation.
Einstein states:
"But the ray moves relatively to the initial point of k, when measured in
the stationary system, with the velocity c-v"
he does NOT state:
"But the ray moves relatively to the initial point of k, when measured in
the stationary system, with the velocity (c-v)/(1-v/c)".
This is a CRUCIAL point.

SR does
*not* have as a conclusion that the speed of light is c in every
inertial frame.

Yes it does.


It *assumes* that the speed of light is c in every
inertial frame.

Not at all, that is YOUR conclusion. Einstein did not mention inertial
frames.



At no point and at no time does one have to verify
that the speed of light is in fact c.

At no time does one have to verify that the speed of sound is c either,
since c is merely a symbol representing a particular dx/dt, 300,000km/sec.


This is a CRUCIAL point. The
test of SR is not whether the speed of light is c. The test of SR is
whether everything *else* that SR predicts (in terms of *measurable*
quantities) is correct.

SR fails the test in terms of measurable quantities. A clock at the pole
does not run slower than a clock at the equator, as predicted by SR.


The value of invariant mass of a system,
independent of inertial reference frame, is a good example. Now, of
course, if someone would measure that the speed of light was NOT c in
every inertial frame, this would immediately dismantle SR, but the
onus is NOT on SR to validate that it is.

The burden of proof has ALWAYS been on the claimant.



But back to Ohm's Law. Is there physics content in Ohm's Law? You
betcha. What it says is that there is a proportionality between
voltage applied across the object and current through an object, in a
broad class of objects, and that proportionality constant depends only
on the physical properties of the object (usually, what the "stuff" is
and the dimensions of the object. Does V=IR define what R is? Sure, if
you want to define R operationally -- that is, by only knowing V and
I. That does NOT make the operational definition of R the sole content
of the law. If it did, then even diodes and transistors would have R
defined as V/I, even though that number would depend strongly on what
V and I are. And that's the point! For resistors, and chunks of wire,
and airplane wing coatings, the ratio of V/I is *independent* of the
values of V and I. There's your physics content.

Let me give you another example. If I asked you how much a cable on
the Golden Gate bridge stretched under load, you'd say, "It depends."
And I'd say, "It depends on what?" And you might say, "Well, it
depends on the length of the cable, L," (and I might say, how?
linearly? like L^2?) and then "and on the area of the cable, A" (and I
might say, are you sure it's not the circumference like the miniscus
in a capillary tube?) and then "and how much load F is on it" and then
"and what the cable is made of." And I would congratulate and tell you
you've just done physics, deriving a simple law with some non-obvious
parts: delL = (1/Y)*L*F/A, where Y is the constant that depends on
what the cable is made of. Other folks look at that and say its the
*definition* of stress and strain: stress = Y * strain. Well, yeah,
maybe, but there's lots of physics content in there. And yes, it only
applies in the elastic regime for the cable. Universality in this case
is not claimed, either.

The same goes for Newton's law of gravitation. The fact that F is
proportional to the product of the two attracting masses is consistent
with Newton's own 2nd and 3rd laws, but the r^2 term is certainly NOT
obvious -- in fact, it's still the subject of much discussion and
experimental data fitting. The constant of proportionality G that
converts kg^2/m^2 to N even has physics content! Because, unlike Y in
the case above, G does not depend on what any "stuff" is or what any
conditions are -- its universality is a big, big claim.

The same even goes for Newton's 1st Law. Yes, in retrospect, it is
simply a special case of the 2nd Law. But consider what preceded it --
the Aristotelean notion that if you didn't keep pushing on an object,
it would stop. It was a big deal for Newton to say, "Not so!" Yes, it
*benchmarks* what an inertial frame is, in the sense that if the 1st
law doesn't hold in some frame, then it's not an inertial frame. But
that doesn't mean that the 1st law is devoid of content or that the
principle of relativity is self-referential in that benchmark. The
principle of relativity says that not only is the 1st law valid in any
inertial frame, but also the 2nd law, and also the 3rd law, and also
Maxwell's equations, etc. -- that certainly doesn't follow from the
benchmark using the 1st law.

Enough with this balderdash about tautologies and circular reasoning
and self-reference in SR. Enough, I say!

Enough of the relativity inconsistent balderdash, I say!

Androcles


PD

The first postulate of Special Relativity says that the laws of
electromagnetism and optics are valid in the same frames of reference
where the laws of mechanics are valid.
Maybe Einstein did not spell it out for Androcles, but physicists know
that the laws of mechanics, as expressed by Newton's laws, are valid
in inertial frames of reference.

The second postulate says that the speed of light in empty space does
not depend on the state of motion of the source.
This is based on experimental results (in the same way as, for
example, Coulomb's law was based on experiments).

Complaints by crackpots notwithstanding, the first postulate is quite
reasonable.
The second postulate can be challenged only by proper experiments.

By the way, I do not agree with Bill Hobba's interpretation of
Newton's laws.
The first law introduces the concept of inertia, and allows to identfy
in principle inertial frames of references.
The second links force to acceleration, via a quantification of
inertia (mass).
These two laws require that frames of references and kinematics
(velocity, acceleration) are already defined (this the easy part), and
need force also to be already defined (which is the most questionable
part).

OC

"Bill Hobba" wrote in message ...
Sorry guys - I accidentally sent this before I finished replying.

"Bill Hobba" wrote in message
...

"shevek" wrote in message
om...
"Bill Hobba" wrote in message
...
"Bilge" wrote in message
...
Paul Draper:
[...]
First off, let's deal with SR directly. SR makes two completely
unfounded assumptions: 1) that the speed of light is independent
of
inertial reference frame, and 2) that the laws of physics have the
same form in every inertial reference frame.

The physical content of relativity is in what you've written as
number (2), which is a perfectly reasonable assumption. The
postulate
regarding the speed of light is also rather reasonable, as it
appears
to be experimentally valid. However, it is not necessary and really
belongs in a theory of electromagnetic interactions.


Thanks for your comments Bilge.
I'm not sure how you can claim the postulate 1) is not necessary..
after looking up "meter" in a dictionary. Maybe you are referring to
an ether theory or something?

This is standard stuff - that a speed exists that is the same in all
inertial frames comes from a standard argument eg
http://arxiv.org/abs/physics/0110076 see the section


Thanks Bill.. that's a good paper, but doesn't really change my
understanding much. For example, he begins with assuming the usual
isotropy and "standards of length and time measurement".. in other
words if that is a derivation than rfc
793 derives the tcp/ip protocol.


This constant mu turns out to be -c2 from experiment. But the point being
though that its existence is determined from the POR alone - it is
experiment that fixes its value - see also
http://www.courses.fas.harvard.edu/~...tbook/ch10.pdf and the
section
relativity without c.


Thanks, I liked that one. "To create your own universe, you must only
say 'let there be light'". It is interesting to say "what if we
defined distance with another fundamental speed other than light"..
he goes through the math there.





[...]


Well I think I see where you are heading, but the wording is
confusing. You say the speed of light is not relevant to SR, but
electric charge conservation is. However, the speed of light appears
all throughout Einstein's papers, but electric charge rarely appears.

Einstein is not the last word on relativity . Things have moved on
considerably since Einstein's time.


Agreed.. sorry I should have put my later comments earlier..


However, I think you are basically right; these days SR is taught (at
graduate level at least) in a E&M course.. One way to describe it
might be: "use of electromagnetic oscillations to define metric".

I have no idea what you mean by this - what Bilge is getting at is that
Gauge invariance is the symmetry related to charge invariance but gauge
invariance is really what determines Maxwell's equations - eg see


Which part don't you understand? Probably not the SR is taught (and
tested) in the context of E&M.. you'll find phd qualifying exam
questions in relativity in the section titled "electromagnetism".
Basically SR is about being very careful what you mean by time and
distance, as real readings of clocks and meter sticks, as defined by
electromagnetic forces. Right?



http://www.upscale.utoronto.ca/Gener...F13/Lect13.htm.

Thanks, that's a good one too.. charge conservation from symmetryies
of Scrhoedinger's equation.. These things constrain our choices of
coordinates, metric, etc.. if you propose to use a coordinate system
in which charge is not conserved, you are making life more difficult
for yourself, kind of like if you choose a coordinate system where the
sun goes around the earth.










OK Bilge, tell us which symmetry of the Lagrangian implies charge
conservation, and don't just say "gauge".

Well that is the answer - gauge invariance - specifically that the
lagrangian is invariant to Au + part deriv u F for any arbitrary F. That
this is equivalent to charge conservation can be found from many sources eg
the link I gave above or for example - Schwiinger - Classical
Electrodynamics page 107 under the heading of Gauge Invariance and Local
Conservation Laws. But the issue becomes even clearer in QM - see the link
I gave above.

OK, well I'm familiar with guage invariance in terms of freedom of
magnetic vector potential and electric potential (A_mu for you
4-vector fanatics) but I was looking for something more fundamental,
like what really -is- the magnetic vector potential? Weyl's idea was
that it corresponded to a fundamental freedom in choice of metric or
coordinate system, but Einstein thought that would cause problems
elsewhere.. anyway, just fishing for ideas, sorry if I'm being
unclear.



And when you're finished
with that, how about lepton number conservation?

What has that got to with EM charge conservation?


Perhaps not much, perhaps quite a lot! Hard telling not knowing.

Thanks for you posts once again - regards -

"shevek" wrote in message
m...
"Bill Hobba" wrote in message
...
Sorry guys - I accidentally sent this before I finished replying.

"Bill Hobba" wrote in message
...

"shevek" wrote in message
om...
"Bill Hobba" wrote in message
...
"Bilge" wrote in message
...
Paul Draper:
[...]
First off, let's deal with SR directly. SR makes two
completely
unfounded assumptions: 1) that the speed of light is
independent
of
inertial reference frame, and 2) that the laws of physics have
the
same form in every inertial reference frame.

The physical content of relativity is in what you've written
as
number (2), which is a perfectly reasonable assumption. The
postulate
regarding the speed of light is also rather reasonable, as it
appears
to be experimentally valid. However, it is not necessary and
really
belongs in a theory of electromagnetic interactions.


Thanks for your comments Bilge.
I'm not sure how you can claim the postulate 1) is not necessary..
after looking up "meter" in a dictionary. Maybe you are referring
to
an ether theory or something?

This is standard stuff - that a speed exists that is the same in all
inertial frames comes from a standard argument eg
http://arxiv.org/abs/physics/0110076 see the section


Thanks Bill.. that's a good paper, but doesn't really change my
understanding much. For example, he begins with assuming the usual
isotropy and "standards of length and time measurement".. in other
words if that is a derivation than rfc
793 derives the tcp/ip protocol.

I still do not understand your point.



This constant mu turns out to be -c2 from experiment. But the point
being
though that its existence is determined from the POR alone - it is
experiment that fixes its value - see also
http://www.courses.fas.harvard.edu/~...tbook/ch10.pdf and the
section
relativity without c.


Thanks, I liked that one. "To create your own universe, you must only
say 'let there be light'". It is interesting to say "what if we
defined distance with another fundamental speed other than light"..
he goes through the math there.





[...]


Well I think I see where you are heading, but the wording is
confusing. You say the speed of light is not relevant to SR, but
electric charge conservation is. However, the speed of light
appears
all throughout Einstein's papers, but electric charge rarely
appears.

Einstein is not the last word on relativity . Things have moved on
considerably since Einstein's time.


Agreed.. sorry I should have put my later comments earlier..


However, I think you are basically right; these days SR is taught
(at
graduate level at least) in a E&M course.. One way to describe it
might be: "use of electromagnetic oscillations to define metric".

I have no idea what you mean by this - what Bilge is getting at is that
Gauge invariance is the symmetry related to charge invariance but gauge
invariance is really what determines Maxwell's equations - eg see


Which part don't you understand?

Use of electromagnetic oscillations to define metric

Probably not the SR is taught (and
tested) in the context of E&M.. you'll find phd qualifying exam
questions in relativity in the section titled "electromagnetism".
Basically SR is about being very careful what you mean by time and
distance, as real readings of clocks and meter sticks, as defined by
electromagnetic forces. Right?

IMHO no. SR is really a theory about symmetry - specifically space-time
symmetry - see an ancient post by Tom Roberts I have given out a lot
recently

http://www.google.com/groups?selm=38...D%40lucent.com.





http://www.upscale.utoronto.ca/Gener...mic/Lectures/L
ectF13/Lect13.htm.

Thanks, that's a good one too.. charge conservation from symmetryies
of Scrhoedinger's equation.. These things constrain our choices of
coordinates, metric, etc.. if you propose to use a coordinate system
in which charge is not conserved, you are making life more difficult
for yourself, kind of like if you choose a coordinate system where the
sun goes around the earth.

I do not know of a coordinate system in which charge is not conserved. What
that link is talking about is gauge invariance. Suppose we associate a real
number q with a quantum particle. Then we see that q is conserved (ie does
not vary with time or position) is mathematically equivalent to the free
particle Schrodenger equation being invariant under e^i theta q where theta
does not depend of position or time - such is called a global gauge
transformation. But what if it does? ie what if theta does depend on x and
t - then the free particle Schrodenger equation is not invariant and we say
it is not invariant to a local gauge transformation. But what if we demand
it? ie what is has local not just global charge conservation - then we find
we must change the Hamiltonian in such as way that, Au the electromagnetic
four vector, appears and has gauge invariance (it is the only real way to
get rid of the nasty extra terms that are partial derivatives in theta). It
is a straight forward matter to derive the Lagrangeian from such a
Hamiltonian and a standard argument that can, for example be found in
Landau - Classical Theory of Fields (actually I do not understand his
derivation - but it is easy to construct your own) we can derive the EM
Lagrangeian and Maxwell's equations.











OK Bilge, tell us which symmetry of the Lagrangian implies charge
conservation, and don't just say "gauge".

Well that is the answer - gauge invariance - specifically that the
lagrangian is invariant to Au + part deriv u F for any arbitrary F.
That
this is equivalent to charge conservation can be found from many sources
eg
the link I gave above or for example - Schwiinger - Classical
Electrodynamics page 107 under the heading of Gauge Invariance and Local
Conservation Laws. But the issue becomes even clearer in QM - see the
link
I gave above.

OK, well I'm familiar with guage invariance in terms of freedom of
magnetic vector potential and electric potential (A_mu for you
4-vector fanatics) but I was looking for something more fundamental,
like what really -is- the magnetic vector potential? Weyl's idea was
that it corresponded to a fundamental freedom in choice of metric or
coordinate system, but Einstein thought that would cause problems
elsewhere.. anyway, just fishing for ideas, sorry if I'm being
unclear.

You may be interested in how it comes out from Kaluza-Klein type theories -
basically it is the left over covariance when one imposes the cylinder
condition in 5d - see http://xxx.lanl.gov/abs/gr-qc/9805018.

Also it is possible to derive EM from coulombs law and SR - see
http://www.cse.secs.oakland.edu/hask...Relativity.htm. Nice
exercise to see what other hidden assumptions are made.




And when you're finished
with that, how about lepton number conservation?

What has that got to with EM charge conservation?


Perhaps not much, perhaps quite a lot! Hard telling not knowing.

Thanks for you posts once again - regards -

Thanks
Bill

(Bilge) wrote in message ...
shevek:
"Bill Hobba" wrote in message news:
"Bilge" wrote in message
...
Paul Draper:
[...]

Well I think I see where you are heading, but the wording is
confusing. You say the speed of light is not relevant to SR, but
electric charge conservation is.

No, I did't say that. What I said is that specal relativity ties
a constant speed of light to charge conservation. That cleanly
separates special relativity as a geometric theory of spacetime
from the theories to which special relativity applies, like E&M.

However, the speed of light appears all throughout Einstein's papers,
but electric charge rarely appears.

That is hardly surprising. The connection was hardly understood if it
even was understood at that time. By the same token, no one understood
any fundamental reason for conservation of momentum, angular momentum
or energy at that time, either. Basically, until the early part of the
20th century, conservation laws were mostly a mystery.


Actually the importance wasn't of charge conservation to SR wasn't
entirely understood by myself either.. thanks for your posts!!


It wasn't until 1918 that noether published her famous papers which
related symmetries of the lagrangian to conserved currents. It took
considerably more time before the theorems nother published were fully
appreciated for their significance. At this point in time, one could
reasonably argue that noether's theorem is the underpinning of practically
all of physics.

However, I think you are basically right; these days SR is taught (at
graduate level at least) in a E&M course..

For the most part, special relativity shows up in undergraduate
courses on E&M and also courses in modern physics. Sometimes it
gets a brief mention in an advanced undergraduate course in mechanics.
In graduate school, it mainly shows up in E&M until one takes a
course in relativistic quantum mechanics or particle physics. Un-
fortunately, until that point, relativity is always derived in the
context of a constant speed of light, which means that most everyone
but physicists who have gone through graduate school end up with the
idea that light is somehow special by virtue of relativity.

However, what you are missing here is not so much _what_ the kooks
can't seem to grasp, but _why_ they can't seem to grasp it. To see why
the kooks believe that the speed of light postulate is an irrefutable
tautology,

All truth is tautology. Am I a kook?

Since we need theories to elucidate any of that truth, the tautologies
to which you refer are irrelevant.


Yes, sorry for waxing metaphysical.. I'll try to stick to actual
problems.


[...]
and justify it by claiming their theory is equivalent to relativity
and at the same time, argue against the reason charge is conserved,
i.e., c == constant.


OK Bilge, tell us which symmetry of the Lagrangian implies charge
conservation, and don't just say "gauge".

Well, ``gauge'' is the proper term, however, if you prefer, you can
use the term, ``phase''. Make the following substitution in the lagrangian
for the fields (or if you wish, wavefunctions):


\Psi - \Psi' = \Psi\exp(-ia(x)) and simillarly for its h.c.

a(x) is an arbitrary function of the spacetime variables.



Ah, thanks.. that helps.



And when you're finished with that, how about lepton number conservation?

Not every conservation law can be derived from a contiuous symmetry.
However, if I happen to come up with the explanation, I'll post it
right after I accept the nobel prize for my explanation, so you might
not want to go too many days without reading the newsgroup. I'll mention
that it was your post that drove me to the discovery when I give my
speech.


I'll stay tuned. What with neutrino oscillations however I'm not sure
how continuous the symmetry will be.

Regards - thanks again - shevek

shevek:
(Bilge) wrote:

Well, ``gauge'' is the proper term, however, if you prefer, you can
use the term, ``phase''. Make the following substitution in the
lagrangian for the fields (or if you wish, wavefunctions):


\Psi - \Psi' = \Psi\exp(-ia(x)) and simillarly for its h.c.

a(x) is an arbitrary function of the spacetime variables.

Ah, thanks.. that helps.

Sure. I can give you a specific example, if you wish. Note that the
function a(x) in the substitution above is only the simplest way to
write the phase and it corresponds to a U(1) symmetry. What it does,
in effect, is tell you that the free particle lagrangian is not going
to be covariant under a (local) change of phase unless you add a field
to the lagrangian and the field itself transforms properly. In the case
of E&M, the function a(x) is what corresponds to the gauge transform,
A'_u = A_u + (1/e) d_u a(x), where e is the electric charge.

What is also interesting, is that you can obtain basically the
same result by taking spacetime to be five dimensional with the
fifth dimension being intrinsically circular. What you then have
is your basic kaluza-klein model.

If you write the argument to the exponent assuming the symmetry is
SU(2) instead of U(1), you end up with the weak interaction. For
the group SU(3), you get the qcd. If you extend the idea of adding
more dimensions to accomodate these interactions, what you have is
called string theory.

[...]

I'll stay tuned. What with neutrino oscillations however I'm not sure
how continuous the symmetry will be.

Neutrino oscillations, in and of themselves, are not so mysterious,
since any time you have a hamiltonian of the form H_0 + V1 + V2,
where the states which diagonalize V1, don't diagonalize V2, the
states for which V1 is diagonal will get mixed by V2 and vice versa.
So, if the weak eigenstates are, \nu_e, \nu_u, \nu_tau, and those
are not the mass eigenstates, the mass eigenstates will be some
linear combination of those three and vice versa. What that means
in the overall cosmological picture us anybody's guess. The same is
true for the kobayashi-moskawa matrix which describes quark mixing.
It obviously occurs, but so far nature has apparently not made the
point of why it occurs, very clear.

shevek:

Basically SR is about being very careful what you mean by time and
distance, as real readings of clocks and meter sticks, as defined by
electromagnetic forces. Right?

Actually, it probably makes more sense and enables you avoid potentially
circular arguments if you say that special relativity defines the rela-
tionship between inertial frames. That requires special relativity to
hold regardless of whether you create a ``clock'' or ``meter stick'' using
electromagnetic, strong or weak interactions. A priori, there is no
reason to expect such a theory is possible, so the fact that we have
such a theory is a pretty good indication that special relativity applies
to all phenomena (excluding gravity which changes the metric itself).

One could say that clocks and meter sticks are defined by electro-
magnetic forces, but if you impose the further constraint that the
photon defines a massless particle, you still have a relativistic
theory, although possibly not the correct theory. However, there are
lots of constraints imposed by experiments on the photon mass that
have to be consistent with what the rest of the theories say. Once
your theory is self-consistent, that's all you can say. Then, your
inertial coordinates are whatever your theory says they are. Attempting
to define time and distance beyond any measurement of time and
distance that can be performed using the physics responsible for
the universe we inhabit is mental masturbation. Even worse, it
introduces additional physics which correspond to no phenomena.


OK, well I'm familiar with guage invariance in terms of freedom of
magnetic vector potential and electric potential (A_mu for you
4-vector fanatics) but I was looking for something more fundamental,
like what really -is- the magnetic vector potential? Weyl's idea was
that it corresponded to a fundamental freedom in choice of metric or
coordinate system, but Einstein thought that would cause problems
elsewhere.. anyway, just fishing for ideas, sorry if I'm being
unclear.

Maybe this will help. I have several different angles for you to
try and picture A, which are rather different, but are related in
a rather fundamental way. First of all, just using maxwell's equations,
the vector potential (as well as the scalar potential) are nothing
but some mathematical artifacts of some vector identities applied
to some differential equations. So, we should establish the vector
potential as something other than an artifact directly from an
experiment with electrons which is the equivalent to the double slit
experiment for light using quantum theory. Consider am experiment
in which ne arranges to have a beam of electrons pass on either
side of a solenoid, such that the magnetic field is zero in the
region of interest (one can always make the field small enough
that it clearly cannot be responsble for the effect shown here).
In the ascii art version below, ``O'' is the solenoid, as seen looking
down its axis and the .'s are the electrons going from left to
right.

. . At point P the wavefunction is \Psi(x,t)
P . . P' is split into \Psi_1(x,t) and \Psi_2(x,t),
. O . corresponding to the two possible paths.
. .
. . Even though B is zero iutside the solenoid,
the vector potential os _not_ zero there.

The solution of the schroedinger equation with the vector potential
included is given by the original wavefintion x a phase factor, i.e.,

\Psi(x,t) - \Psi(x,t)\exp(iS)

with S = (e/hbar) \integral A . dx, where dx is taken over the
path of the electron. If the beam is recombined at point point P',
then the wavefunction there will be the sum of the wave functions
taken over the two paths,

\Psi(x,t) = \Psi_1(x,t)\exp(iS_1) + \Psi_2(x,t)\exp(iS_2)

Taking the mod squared, gives a term that is proportional to
\exp(i(S_2 - S_1)), which is just,

S_2 - S1 = (e/hbar) [\integral A.dx_2 - \integral A.dx_1]

= (e/hbar) [\integral A.dx]

Where the last integral is taken over the closed path defined by
the difference between the two paths. The upshot is that, despite
the absence of any electromagnetic forces on the electrons, you
get an interference pattern that shifts as you change the field
inside the solenoid. That establishes the vector potential A as
an electromagnetic effect beyond that which can be described in
terms of E and B and consequently, beyond that which maxwell's
theory can describe.


The relativistic extension is to replace the vector potential, A,
with A^u giving the integral, \integral A^u d_u.

For picture number two, we start by noting that maxwell's equations
may be written in the form of a wave equation as,

box A^u = j^u

and blindly take A^u to be the photon to start. This is just a
compact way of writing the equations for curl B and div E
in terms of vector and scalar potentials as a single equation.

In free space, we don't have any sources, so our wave equation
is box A^u = 0, which has solutions,

A^u = e^u \exp(-ip.x)

Where e^u is the four-vector polarization and p.x mean p^u x_u or what
might be written in more familiar terms, i(k.x - wt). This equation has
four polarization states yet we know the photon is a spin 1, which has
only three possible polarizations and we know that the physical photon has
only two, so what we have for A^u contains two superfluous degrees of
freedom, since the number of real degrees of freedom can't depend upon how
you write an equation. First we note that in writing the equation above,
we assumed that d_u A^u = 0, which is known as the lorentz condition. We
can use that to eliminate one of the four polarization states, e^u. If we
eliminate the time polarization, we are left with the vector potential, A,
i.e., A^u = (0, A^1, A^2, A^3). You can now interpret your vector
potential as the photon. However, we still need to eliminate one of those
degrees of freedom. We do that by noting that the photon is always
polarized transverse to it's momentum, so that if p is along the z
direction so that p = (0, 0, p_z) and the most general polarization is
given by A = (A_x, A_y, A_z), then we can't have a polarization along z.

Note that if we write p = -i\hbar\grad, what that really means is
that A_z can be a constant, since the derivative of a constant is
zero. That is an example of gauge transformation. So long as a change
to A does not intrduce any change which affects any observable result,
the change is simply an artifact of the mathematics. More generally,
we can change A_z by any scalar function d^u\Phi, such that its
derivative, d_u d^u\Phi = 0, i.e., A'^u = A^u + d^u\Phi leaves the
physics unchanged if d_u A'^u = d_u A^u + d_u d^u \Phi.

I can still make a further generalization and deal with virtual
photons, but I'm going to stop here.

(Bilge) wrote in message ...
OC:

By the way, I do not agree with Bill Hobba's interpretation of
Newton's laws.
The first law introduces the concept of inertia, and allows to identfy
in principle inertial frames of references.

In what way does it do that? Newton defines inertial motion as motion
which is force free. Force free means inertial motion. It's a circular
definition.

I did say that "force" needs to defined somehow before Newton's laws.

Once there is a definition for force (which does not require the
concept of inertia), it is possible to introduce inertia as that
property of a physical object such that the state of motion does not
change if there are no (net) forces acting on the object (Newton's
first law).

Once introduced the first law, the frame of references where this law
is valid are "identified" as inertial.

OC