What is the Expert Opinion on Special Relativity Trivialities?
Perfectly Innocent
relativity theory exists.
http://www.everythingimportant.org/viewtopic.php?t=605
It seems to me that if two theories agree locally and disagree
globally, then you have two different theories.
What do the experts say?
Eugene Shubert
http://www.everythingimportant.org/viewtopic.php?t=605
PS. The local equivalence of the two theories may be inferred with
this observation from Tom Roberts:
Tom Roberts <tjro...@Lucent.com> wrote in message news:<3F44D70C...@Lucent.com>...
> Several people around here have advocated the transforms
>
> x' = g(x - v t)
> y' = y
> z' = z
> t' = t / g
> g = 1/sqrt(1 - v^2/c^2)
>
> ... The unprimed frame is unique, and the one-way
> speed of light is not isotropic in any primed frame (assuming it is
> isotropic in the aether frame). On the other hand, the round-trip speed
> of light is indeed isotropically c in every frame, and the theory using
> these transforms is experimentally indistinguishable from SR.
>
> Tom Roberts tjro...@lucent.com
Bill Hobba
'Let an observer in the circle universe be at rest in her own "inertial
frame of reference." Let her pick a positive and negative direction. Suppose
she has a nice watch on her wrist to note the time. Other than just looking
nice and being able to see how old she's getting, let her do experiments.
Let t1 be the time she measures for a photon to circumnavigate the universe
in the positive direction. Let t2 be the time she measures for a photon to
circumnavigate the universe in the negative direction.'
I fired a torch off yesterday. I am still waiting for it to return to me.
I seem to recall firing a torch off 40 years ago and no one has ever
reported it returning. Exactly how long it this experiment of yours
supposed to take? The lifetime of the universe? God give me strength.
Thanks
Bill
Tom Roberts
> I think it's obvious that a viable alternative to Einstein's special
> relativity theory exists.
> http://www.everythingimportant.org/viewtopic.php?t=605
SR is generally accepted to be the application of GR to a flat
Lorentzian manifold with topology R^4.
A direct consequence of that definition is the fact that one
can find a single set of Riemann normal coordinates that
covers the manifold. This is not true in your theory, for
the same reason one cannot find a single coordinate that
covers the circle -- there is always either an overlap or
a gap.
This is directly related to, but different from, the fact that in some
sense SR is the local limit of GR (one must restrict the region of
interest based on one's measurement accuracy and the local curvature).
Your theory differs from SR in its topology, so it isn't an
"alternative" to SR, it is just plain different from SR.
Yes, locally they are indistinguishable.
> It seems to me that if two theories agree locally and disagree
> globally, then you have two different theories.
Yes and no. If the theory is independent of topology, like GR[#], then
the difference you point out is irrelevant, and you do not really have
two different theories. If the theory is intrinsically dependent on
topology, like SR, then you do have two different theories. Nobody would
dispute the applicability of GR to your manifold; nobody would expect SR
to apply.
BTW there are an infinite number of topologies suitable for
flat Lorentzian manifolds. Most are uninteresting; your
manifold is SxR^3 and is among the interesting ones. T^2xR^2
is also interesting, and T^2xT^2 is outrageous (closed
timelike loops!). This surely does not exhaust the list....
"uninteresting" topologies in this context differ from
others merely in the deletion of points or regions, or
other local operations. They are "uninteresting" because
there's no reason to suppose the real world has such
deletions....
[#] GR is inherently a local theory (i.e. it can be expressed
in terms of differential equations).
Tom Roberts tjro...@lucent.com
Perfectly Innocent
> Perfectly Innocent wrote:
> > I think it's obvious that a viable alternative to Einstein's special
> > relativity theory exists.
> > http://www.everythingimportant.org/viewtopic.php?t=605
>
> SR is generally accepted to be the application of GR to a flat
> Lorentzian manifold with topology R^4.
>
> A direct consequence of that definition is the fact that one
> can find a single set of Riemann normal coordinates that
> covers the manifold. This is not true in your theory, for
> the same reason one cannot find a single coordinate that
> covers the circle -- there is always either an overlap or
> a gap.
>
different.
>
> This is directly related to, but different from, the fact that in some
> sense SR is the local limit of GR (one must restrict the region of
> interest based on one's measurement accuracy and the local curvature).
>
> Your theory differs from SR in its topology, so it isn't an
> "alternative" to SR, it is just plain different from SR.
>
absolute time order, no absolute frame of reference and that motion
faster than light is impossible.
The essential feature of my theory is the existence of an absolute
past, present and future. There is also a physically distinguished,
absolute frame of reference. In SR, motion faster than light results
in some observer interpreting the motion as time-travel into the past.
This contradiction doesn't exist in my theory.
The difference in topology is a feature of least importance. Of
greatest importance is that my theory be defined as I have defined it,
not as a general relativist would prefer to reinterpret it.
http://www.everythingimportant.org/viewtopic.php?t=605
> Yes, locally they are indistinguishable.
>
> > It seems to me that if two theories agree locally and disagree
> > globally, then you have two different theories.
>
> Yes and no. If the theory is independent of topology, like GR[#], then
> the difference you point out is irrelevant, and you do not really have
> two different theories.
My theory presupposes the (S^3)xR topology as an axiom.
> If the theory is intrinsically dependent on
> topology, like SR, then you do have two different theories.
It's settled then. My theory is clearly different from SR yet is
experimentally indistinguishable from SR, according to you. As a
corollary therefore, I have proven that all the SR hype about no
absolute time order, no absolute frame of reference and no
superluminal velocities is just unessential and unsubstantiated
hoopla.
> Nobody would dispute the applicability of GR to your manifold;
> nobody would expect SR to apply.
GR and SxR may share the same manifold; I'm just waiting for general
relativists to catch up with my conclusions in the static case.
http://www.everythingimportant.org/viewtopic.php?t=533
>
> BTW there are an infinite number of topologies suitable for
> flat Lorentzian manifolds.
Actually, there are only 18.
http://qcd.th.u-psud.fr/page_perso/Uzan/fileps/art_2002_ullp_ejp23.pdf
> Most are uninteresting; your
> manifold is SxR^3 and is among the interesting ones.
No. My manifold is (S^3)xR. (That's if you call spacetime, spacetime).
If you call spacetime, time-space then it's RxS^3.
> T^2xR^2
> is also interesting, and T^2xT^2 is outrageous (closed
> timelike loops!). This surely does not exhaust the list....
>
> "uninteresting" topologies in this context differ from
> others merely in the deletion of points or regions, or
> other local operations. They are "uninteresting" because
> there's no reason to suppose the real world has such
> deletions....
>
> [#] GR is inherently a local theory (i.e. it can be expressed
> in terms of differential equations).
>
> Tom Roberts tjro...@lucent.com
Eugene Shubert
http://www.everythingimportant.org/relativity/simultaneity.htm
Tom Roberts
> Tom Roberts <tjro...@lucent.com> wrote in message news:<bj69ed$n...@netnews.proxy.lucent.com>...
>>"alternative" to SR, it is just plain different from SR.
>
> It is defended as an essential consequence of SR that there is no
> absolute time order, no absolute frame of reference and that motion
> faster than light is impossible.
Yes, those are all consequences of the structure of SR. Well, the last
is not strictly impossible (c.f. tachyons).
> The essential feature of my theory is the existence of an absolute
> past, present and future.
I don't see that. There is a distinguished frame of reference, but in
the locally-inertial coordinates of different observers,
spacelike-separated events can still have different time orders to those
two observers. You can DEFINE the "absolute time order" to be that of
the distinguished frame, but that is merely defining words, and does not
affect how observers in your theory observe the temporal order of such
events.
> There is also a physically distinguished,
> absolute frame of reference.
Yes. But beware of which aspects of "absolute" apply and which don't. In
particular, there is no local experiment that can discover the
distinguished frame.
> In SR, motion faster than light results
> in some observer interpreting the motion as time-travel into the past.
> This contradiction doesn't exist in my theory.
Sure this happens in your theory. It's not a "contradiction" though,
just as it isn't one in SR.
> The difference in topology is a feature of least importance. Of
> greatest importance is that my theory be defined as I have defined it,
> not as a general relativist would prefer to reinterpret it.
Hmmm. To me it seems to be the only distinguishing characteristic of
your theory.
> My theory presupposes the (S^3)xR topology as an axiom.
Oops! I read your intro and assumed you meant SxR^3. S^3xR is
inconsistent with a flat metric. Aparently you have fooled yourself with
your 1 dimensional analogy. That 1-d model does NOT generalize to 3
spatial dimensions as you suppose.
>>If the theory is intrinsically dependent on
>>topology, like SR, then you do have two different theories.
> It's settled then. My theory is clearly different from SR yet is
> experimentally indistinguishable from SR, according to you.
Well, you need to fix the incompatibility of your postulated topology
with a flat metric. Good luck (:-)).
> As a
> corollary therefore, I have proven that all the SR hype about no
> absolute time order, no absolute frame of reference and no
> superluminal velocities is just unessential and unsubstantiated
> hoopla.
No, you haven't. See above.
In addition, you have unacknowledged puns in your usage of "absolute"
that destroy your argument. "Absolute time order" in the sense of
related to the distinguished frame is OK, "absolute time order" in the
sense that all observers agree on the time ordering of all events is not
(when they use their locally-inertial coordinates).
>> BTW there are an infinite number of topologies suitable for
>> flat Lorentzian manifolds.
>
> Actually, there are only 18.
> http://qcd.th.u-psud.fr/page_perso/Uzan/fileps/art_2002_ullp_ejp23.pdf
I have not looked at that, but here is a countably-infinite enumeration
of topologies consistent with a flat Lorentzian manifold. Start with
Minkowski spacetime, then:
1) delete one point
2) delete another point distinct from all previous ones
... iterate (2) as often as desired
These are all "uninteresting" in the sense I described.
>> Most are uninteresting; your
>> manifold is SxR^3 and is among the interesting ones.
> No. My manifold is (S^3)xR.
Sorry. I did not examine your entire webpage carefully enough.
S^3xR is inconsistent with a flat metric. Back to the drawing board....
Tom Roberts tjro...@lucent.com
Perfectly Innocent
> On 9/4/2003 9:43 AM, Perfectly Innocent wrote:
> > Tom Roberts <tjro...@lucent.com> wrote in message news:<bj69ed$n...@netnews.proxy.lucent.com>...
> >>Your theory differs from SR in its topology, so it isn't an
> >>"alternative" to SR, it is just plain different from SR.
> >
> > It is defended as an essential consequence of SR that there is no
> > absolute time order, no absolute frame of reference and that motion
> > faster than light is impossible.
>
> Yes, those are all consequences of the structure of SR. Well, the last
> is not strictly impossible (c.f. tachyons).
I am only speaking in terms of the conventional interpretation of SR.
For example, it is the opinion of the relativity expert Wolfgang
Rindler that tachyons are strictly impossible. However, instead of
arguing whose view is the most conventional I am very willing to
rephrase my point. SR exhibits causality violations for superluminal
motion whereas SxR doesn't.
> > The essential feature of my theory is the existence of an absolute
> > past, present and future.
>
> I don't see that.
My result isn't obvious. You need to go through my derivation.
http://www.everythingimportant.org/relativity/simultaneity.htm
> There is a distinguished frame of reference, but in
> the locally-inertial coordinates of different observers,
> spacelike-separated events can still have different time orders to those
> two observers.
It's true that we are free to reset clocks in any spacetime in all
frames of reference. And that changes the simple coordinate definition
of time order. However, the mathematical and physical constraints of
my theory single out a unique law of light propagation. Consequently,
light speed is a function of an observer's motion with respect to the
absolute frame of reference.
C(v) is the velocity of light in the direction of motion.
->
C(v) is the velocity of light opposite the direction of motion.
<-
C(v)= (Y(v)^2)(c-v)
->
C(v)= (Y(v)^2)(c+v)
<-
The same the mathematical and physical constraints determine the
transformation equations to be:
x'=Y(v)(x-vt)
t'=t/Y(v)
Y(v)=1/sqrt(1-v^2/c^2)
Consequently, the spacetime SxR has an absolute time order.
> You can DEFINE the "absolute time order" to be that of
> the distinguished frame,
You're just imagining arbitrariness in my derivation. The truth is
that my derivation is based entirely on mathematical and physical
constraints.
> but that is merely defining words, and does not
> affect how observers in your theory observe the temporal order of such
> events.
My law of light propagation is required due mainly to the topology of
S^3.
>
> > There is also a physically distinguished,
> > absolute frame of reference.
>
> Yes. But beware of which aspects of "absolute" apply and which don't.
Which aspects of "absolute" don't apply?
> In particular, there is no local experiment that
> can discover the distinguished frame.
That's a desired property not a flaw.
> > In SR, motion faster than light results
> > in some observer interpreting the motion as time-travel into the past.
> > This contradiction doesn't exist in my theory.
>
> Sure this happens in your theory.
Obviously not! Where's your proof?
> It's not a "contradiction" though,
> just as it isn't one in SR.
It's clear that, in SxR, if a trajectory moves forward in time in one
frame of reference, then it does so in all frames of reference.
> > The difference in topology is a feature of least importance. Of
> > greatest importance is that my theory be defined as I have defined it,
> > not as a general relativist would prefer to reinterpret it.
>
> Hmmm. To me it seems to be the only distinguishing characteristic of
> your theory.
I expect all relativists to say that initially due to their acquired
programming.
> > My theory presupposes the (S^3)xR topology as an axiom.
>
> Oops! I read your intro and assumed you meant SxR^3. S^3xR is
> inconsistent with a flat metric.
I just finished saying that I presuppose the (S^3)xR topology as an
axiom. I never presupposed any property requiring flatness or a
metric.
> Aparently you have fooled yourself with
> your 1 dimensional analogy.
Since I never presupposed any property requiring a metric, S^3xR
couldn't possibly be inconsistent.
> That 1-d model does NOT generalize to 3
> spatial dimensions as you suppose.
Let's avoid your obfuscation for the moment and try to resolve our
differences in 1 spatial dimension before we continue on to (S^2)xR
and (S^3)xR.
> >>If the theory is intrinsically dependent on
> >>topology, like SR, then you do have two different theories.
>
> > It's settled then. My theory is clearly different from SR yet is
> > experimentally indistinguishable from SR, according to you.
>
> Well, you need to fix the incompatibility of your postulated topology
> with a flat metric. Good luck (:-)).
>
Since my axiom set says nothing about metrics or flatness, there is
nothing to repair.
http://www.everythingimportant.org/viewtopic.php?t=605
>
> > As a
> > corollary therefore, I have proven that all the SR hype about no
> > absolute time order, no absolute frame of reference and no
> > superluminal velocities is just unessential and unsubstantiated
> > hoopla.
>
> No, you haven't. See above.
Sure I have. See below.
http://www.everythingimportant.org/viewtopic.php?t=605
>
> In addition, you have unacknowledged puns in your usage of "absolute"
> that destroy your argument.
Where is your argument that my argument is faulty?
> "Absolute time order" in the sense of
> related to the distinguished frame is OK, "absolute time order" in the
> sense that all observers agree on the time ordering of all events is not
> (when they use their locally-inertial coordinates).
According to their coordinates:
x'=Y(v)(x-vt)
t'=t/Y(v)
Y(v)=1/sqrt(1-v^2/c^2)
So, if events E1 (x1, t1) and E2 (x2, t2) are simultaneous in 1
inertial frame, then t1=t2 and the events are simultaneous in all
inertial frames. If event E1 precedes event E2 in 1 inertial frame,
then t1<t2 and event E1 precedes event E2 in all inertial frames.
Consequently, the spacetime SxR has an absolute time order.
> >> BTW there are an infinite number of topologies suitable for
> >> flat Lorentzian manifolds.
> >
> > Actually, there are only 18.
> > http://qcd.th.u-psud.fr/page_perso/Uzan/fileps/art_2002_ullp_ejp23.pdf
>
> I have not looked at that, but here is a countably-infinite enumeration
> of topologies consistent with a flat Lorentzian manifold. Start with
> Minkowski spacetime, then:
> 1) delete one point
> 2) delete another point distinct from all previous ones
> ... iterate (2) as often as desired
>
> These are all "uninteresting" in the sense I described.
"Suitable" spacetimes should be geodesically complete.
>
> >> Most are uninteresting; your
> >> manifold is SxR^3 and is among the interesting ones.
> > No. My manifold is (S^3)xR.
>
> Sorry. I did not examine your entire webpage carefully enough.
>
> S^3xR is inconsistent with a flat metric. Back to the drawing board....
Where in the world did you ever get the idea that I require or
presuppose a flat metric?
Titan Point
I would suggest you implore god give you longevity. Lots of longevity. ;-)
Bilge
>news:<bj69ed$n...@netnews.proxy.lucent.com>...
>
>> topology, like SR, then you do have two different theories.
>
>It's settled then. My theory is clearly different from SR yet is
>experimentally indistinguishable from SR, according to you. As a
>corollary therefore, I have proven that all the SR hype about no
>absolute time order, no absolute frame of reference and no
>superluminal velocities is just unessential and unsubstantiated
>hoopla.
transform preserves inertial frame. Your "theory" doesn't:
x' = x cosh(A) - t sinh(A)
t' = t/cosh(A)
=> \Delta x'^2 = (cosh(A)\Delta x)^2 + (sinh(A)\Delta t)^2
- 2 \Delta x\Delta t sinh(A) cosh(A)
\Delta t = (\Delta t)/cosh(A))^2 = (sech(A)\Delta t)^2
(\Delta t')^2 - (\Delta x') = (sech(A)^2 - sinh(A)^2)\Delta t)^2
- (cosh(A)\Delta x)^2
- 2 \Delta x\Delta t sinh(A) cosh(A)
Are you going to try and tell me that the lhs is equal to rhs?
Perfectly Innocent
> Perfectly Innocent:
> >Tom Roberts <tjro...@lucent.com> wrote in message
> >news:<bj69ed$n...@netnews.proxy.lucent.com>...
> >
> >> If the theory is intrinsically dependent on
> >> topology, like SR, then you do have two different theories.
> >
> >It's settled then. My theory is clearly different from SR yet is
> >experimentally indistinguishable from SR, according to you. As a
> >corollary therefore, I have proven that all the SR hype about no
> >absolute time order, no absolute frame of reference and no
> >superluminal velocities is just unessential and unsubstantiated
> >hoopla.
>
> I don't think it's indistinguishable, locally or otherwise. The lorentz
Bilge,
There are plenty of mathematical differences between SR and SxR. The
fact that both theories use different coordinate systems and that
these coordinate systems have different mathematical properties is
irrelevant. Dissimilarity in formalism doesn't necessarily mean that
the two theories predict different outcomes for physical experiments.
Do you agree that, in SxR, the average back-and-forth speed of light
is c in every moving frame of reference?
Do you agree that, in SxR, if you carry out the stunning thought
experiment cited in
http://www.everythingimportant.org/viewtopic.php?t=605
and measure the one-way speed of light in any moving frame of
reference (in the exact manner prescribed), then you will get the
value c ?
If you need help with these mathematical exercises, Tom Roberts and I
will be happy to assist.
If you agree that SxR passes these tests and wish to propose other
tests, then I'm willing to consider a true, physically meaningful
gedanken experiment.
You realize, of course, that Tom Roberts and I agree on the point of
physical indistinguishability of the two theories in terms of local
experiments.
Eugene Shubert
http://www.everythingimportant.org/relativity/simultaneity.htm
Bilge
>There are plenty of mathematical differences between SR and SxR. The
>fact that both theories use different coordinate systems and that
>these coordinate systems have different mathematical properties is
>irrelevant. Dissimilarity in formalism doesn't necessarily mean that
>the two theories predict different outcomes for physical experiments.
Answer the question I posted regarding your equations. Do you think
your transforms preserve inertial frames?
>Do you agree that, in SxR, the average back-and-forth speed of light
>is c in every moving frame of reference?
No, because different observers won't agree on what `c' is. That
is apparent from the question you didn't answer.
>Do you agree that, in SxR, if you carry out the stunning thought
>experiment cited in
>http://www.everythingimportant.org/viewtopic.php?t=605
>and measure the one-way speed of light in any moving frame of
>reference (in the exact manner prescribed), then you will get the
>value c ?
"Stunning thought experiment"? Hardly. It's a tautology. Your
"stunning thought experiment" consists of measuring the speed
of light in the same frame at points that differ by a translation.
So what? The relative velocity between the clocks is zero and any
transformation f(v) which is unity for f(0) gives the same result.
Galilean transforms, for instance.
>If you need help with these mathematical exercises, Tom Roberts and I
>will be happy to assist.
Since you didn't answer my question, it is apparently you who needs
help and you are attempting to disguise that through bullshit and
posturing.
>If you agree that SxR passes these tests and wish to propose other
>tests, then I'm willing to consider a true, physically meaningful
>gedanken experiment.
I don't really give a damn whether or not you say you are willing
to consider anything. You aren't and only say so to appear something
other than the egomaniacal jerk you are.
>You realize, of course, that Tom Roberts and I agree on the point of
>physical indistinguishability of the two theories in terms of local
>experiments.
And? Tom's opinion was the only reason I looked again at what you
posted. I disagree with him. Why is it that you can never answer
questions?
Tom Roberts
> Perfectly Innocent:
> >physical indistinguishability of the two theories in terms of local
> >experiments.
>
> And? Tom's opinion was the only reason I looked again at what you
> posted. I disagree with him.
The transform equations he uses are a member of the equivalence class of
theories that are experimentally indistinguishable from SR. Refer to my
1999 set of posts on "Theories Equivalent to SR", in which I believe
they are mentioned explicitly.
[I just noticed that those transform equations are NOT valid
"all the way around"; no single set of coordinates can cover
the manifold. So be careful comparing my old posts with SxR;
locally all conclusions follow, but not necessarily globally.]
From that immediately follow several conclusions:
1. The coordinates used in his SxR differ from the coordinates
used in SR _ONLY_ in the way clocks are synchronized.
Locally. Remember, please, that clock synchronization is an
arbitrary human choice, and cannot affect any physical
phenomena.
2. The round-trip speed of light is isotropically c in every
frame; the one-way speed of light is isotropically c only
in the physically-distinguished frame. Locally.
In my old posts, all theories were in essence applied to a manifold with
topology R^4, and there is no way to discover the "ether frame". But in
SxR there is a way to discover the physically distinguished frame
(measure OWLS all the way around, in all directions).
Tom Roberts tjro...@lucent.com
Perfectly Innocent
> Perfectly Innocent:
>
> >There are plenty of mathematical differences between SR and SxR. The
> >fact that both theories use different coordinate systems and that
> >these coordinate systems have different mathematical properties is
> >irrelevant. Dissimilarity in formalism doesn't necessarily mean that
> >the two theories predict different outcomes for physical experiments.
>
> Answer the question I posted regarding your equations. Do you think
> your transforms preserve inertial frames?
>
For questions to have answers, they have to make sense. From my point
of view, spacetime of elementary SR type is merely a complete set of
"inertial frames of reference" and a set of transformation equations
between frames. The only requirement of the transformation equations
is that the coordinates of events in one frame are expressible in
terms of the coordinates of any other frame.
I don't require any group property. So what does it mean for the
transforms to preserve inertial frames?
Nothing!
Eugene Shubert
http://www.everythingimportant.org/viewtopic.php?t=605
Bilge
>> Perfectly Innocent:
>> >You realize, of course, that Tom Roberts and I agree on the point of
>> >physical indistinguishability of the two theories in terms of local
>> >experiments.
>>
>> And? Tom's opinion was the only reason I looked again at what you
>> posted. I disagree with him.
>
>The transform equations he uses are a member of the equivalence class of
>theories that are experimentally indistinguishable from SR. Refer to my
>1999 set of posts on "Theories Equivalent to SR", in which I believe
>they are mentioned explicitly.
give:
x' = cosh(A)[ x - ct tanh(A)]
ct' = cosh(A)[ct - x tanh(A)] + q cosh(A)[ct tanh(A) - x]
ct' = cosh(A)[ct - x tanh(A)] - qx'
(which differs from what you have by an irrelevant sign). So, those
are equivalent to the lorentz transforms for q = 0 or x' = 0. I
don't see the point.
> [I just noticed that those transform equations are NOT valid
> "all the way around"; no single set of coordinates can cover
> the manifold. So be careful comparing my old posts with SxR;
> locally all conclusions follow, but not necessarily globally.]
His transforms are not SxR. SxR is a cylinder.
> From that immediately follow several conclusions:
> 1. The coordinates used in his SxR differ from the coordinates
> used in SR _ONLY_ in the way clocks are synchronized.
> Locally. Remember, please, that clock synchronization is an
> arbitrary human choice, and cannot affect any physical
> phenomena.
I'm sorry, but I don't agree. Perhaps agreeing that the big hand and
little hand on a pair of wall clocks go around at the same rate is an
arbitrary human choice, but there exist clocks in nature. I can't see that
a constant offset means anything more than relabeling the clock face,
which is irrelevant. Sure, you can define anything you wish for a set of
coordinates, but without a physical marker you can interpret, the
coordinates are meaningless. Can you show that his coordinate
transforms conserve energy, momentum and angular momentum?
> 2. The round-trip speed of light is isotropically c in every
> frame; the one-way speed of light is isotropically c only
> in the physically-distinguished frame. Locally.
>
>In my old posts, all theories were in essence applied to a manifold with
>topology R^4, and there is no way to discover the "ether frame". But in
>SxR there is a way to discover the physically distinguished frame
>(measure OWLS all the way around, in all directions).
The only reason that there is "no way to discover the ether frame",
is because ether theories make no predictions based upon any ether.
That makes those ether theories trivially equivalent, in the sense,
that the word "ether" could be replaced by "used cars" or "brothels"
without having any affect whatsoever.
You can't really say that LET is equivalent by design, either, because
LET was proposed before the discovery of the weak or strong interaction.
Since maxwell's equations were the justification for LET and I can
write sets of maxwell equations for the strong and weak interactions,
the justification for defining c through the electromagnetic maxwell
equations evaporates. [I've done this for the strong interaction,
which I've posted before, but I'd rather not expend the effort to
do this for the weak interaction at the moment].
I'm not sure how one would go about defining those equations using LET.
LET takes `c' as 1/sqrt(\mu\epsilon). The equivalent \epsilon for the
strong interaction is negative. I'm not really sure how one would define
\mu and \epsilon for the weak interaction. Anyone who wishes to give
me numbers for \mu and \epsilon as they relate to the weak and strong
interaction, feel free to do so.
So, I think that ether theories do result in different predictions if
you force them to be ether theories rather empty semantics. However,
before I would agree that ether theories make the same predictions
as special relativity, I would have to see the ether theory make some
predictions using the weak and strong "permittivities" and "permeabilities".
Bilge
>> Perfectly Innocent:
>>
>> >There are plenty of mathematical differences between SR and SxR. The
>> >fact that both theories use different coordinate systems and that
>> >these coordinate systems have different mathematical properties is
>> >irrelevant. Dissimilarity in formalism doesn't necessarily mean that
>> >the two theories predict different outcomes for physical experiments.
>>
>> Answer the question I posted regarding your equations. Do you think
>> your transforms preserve inertial frames?
>>
>> Why is it that you can never answer questions?
>
>For questions to have answers, they have to make sense.
Just answer the question.
>From my point of view, spacetime of elementary SR type is merely a
>complete set of "inertial frames of reference" and a set of
What's an inertial frame according to you?
>transformation equations between frames.
If that's so, then why can you not show that the transform
preserves inertial frames?
>The only requirement of the transformation equations
>is that the coordinates of events in one frame are expressible in
>terms of the coordinates of any other frame.
In other words, choosing any coordinate transformation on a
whim is equivalent to special relativity and regardless of
what the transformation is, one simply defines those frames
as inertial? Does that about sum it up?
>I don't require any group property.
Or any corrsepondence to physics. Show that your transforms
lead to conserved energy, momentum andd angular momentum.
> So what does it mean for the
>transforms to preserve inertial frames?
If you don't know, why are you arguing?
>Nothing!
Same as your coordinates.
Perfectly Innocent
> Tom Roberts:
> > the manifold. So be careful comparing my old posts with SxR;
> > locally all conclusions follow, but not necessarily globally.]
>
> His transforms are not SxR. SxR is a cylinder.
Tom Roberts understands that I call my theory SxR.
By SxR, I mean the SeXieR and more modern version of SR. The X stands
for Modern as in OSX or Windows XP. Obviously, SxR also represents a
cylinder, which again, represents my theory:
http://www.everythingimportant.org/relativity/simultaneity.htm
Sincerely not X (eXperimental)
Eugene Shubert
Tom Roberts
> Tom Roberts:
> >Bilge wrote:
> >> Perfectly Innocent:
> >> >You realize, of course, that Tom Roberts and I agree on the point of
> >> >physical indistinguishability of the two theories in terms of local
> >> >experiments.
> >>
> >> And? Tom's opinion was the only reason I looked again at what you
> >> posted. I disagree with him.
> >
> >The transform equations he uses are a member of the equivalence class of
> >theories that are experimentally indistinguishable from SR. Refer to my
> >1999 set of posts on "Theories Equivalent to SR", in which I believe
> >they are mentioned explicitly.
>
> The equations you have written in those posts can be re-arranged to
> give:
> x' = cosh(A)[ x - ct tanh(A)]
> ct' = cosh(A)[ct - x tanh(A)] + q cosh(A)[ct tanh(A) - x]
> ct' = cosh(A)[ct - x tanh(A)] - qx'
> (which differs from what you have by an irrelevant sign). So, those
> are equivalent to the lorentz transforms for q = 0 or x' = 0. I
> don't see the point.
I have not checked your rearrangement in detail, but it looks reasonable
superfically. The point is q=0 yields the Lorentz transform, and for q
nonzero the ONLY difference is in how clocks are synchronized in the
moving frame (to each clock with spatial coordinates x',y',z' is added a
CONSTANT offset -qx').
[I used the symbol q' rather than your q, to indicate that the
value of this parameter is associated with the moving frame,
not the "fixed/ether" frame.]
> > [I just noticed that those transform equations are NOT valid
> > "all the way around"; no single set of coordinates can cover
> > the manifold. So be careful comparing my old posts with SxR;
> > locally all conclusions follow, but not necessarily globally.]
> His transforms are not SxR. SxR is a cylinder.
Actually, his transforms are local, and do not affect or reflect the
topology of this theory, which is S^3xR (loosely, a more complicated
cylinder). My comment applied to Prefectly Innocent's theory, not my old
posts.
> > From that immediately follow several conclusions:
> > 1. The coordinates used in his SxR differ from the coordinates
> > used in SR _ONLY_ in the way clocks are synchronized.
> > Locally. Remember, please, that clock synchronization is an
> > arbitrary human choice, and cannot affect any physical
> > phenomena.
>
> I'm sorry, but I don't agree. Perhaps agreeing that the big hand and
> little hand on a pair of wall clocks go around at the same rate is an
> arbitrary human choice, but there exist clocks in nature.
For the above transforms, the hands of a coordinate clock in a given
frame move at the same rate as a collocated SR coordinate clock (i.e.
the clocks tick at the same rate).
> I can't see that
> a constant offset means anything more than relabeling the clock face,
> which is irrelevant.
RIGHT!!! That's my point. In a given frame, each coordinate clock in the
above transforms differs by a CONSTANT offset from a collocated SR
coordinate clock. As I said, this CANNOT affect any physical processes
(only the way the clocks are used to describe phenomena).
> Sure, you can define anything you wish for a set of
> coordinates, but without a physical marker you can interpret, the
> coordinates are meaningless. Can you show that his coordinate
> transforms conserve energy, momentum and angular momentum?
All the conservation laws of SR can be expressed in tensor form, and are
thus independent of coordinates. So all LOCAL conservation laws remain
valid. Global laws have to be examined individually.
And the inconsistency of S^3xR with a flat metric will
cause havoc in that.... [I'm preparing a post on that]
>>In my old posts, all theories were in essence applied to a manifold with
>>topology R^4, and there is no way to discover the "ether frame".
>
> The only reason that there is "no way to discover the ether frame",
> is because ether theories make no predictions based upon any ether.
Hmmm. The underlying derivation and description depend on an ether. But
it drops out -- that is not obvious up front (c.f. greywolf42's
confusions on this for LET). Since it drops out of all predictions,
there is no way to discover it.
> That makes those ether theories trivially equivalent, in the sense,
> that the word "ether" could be replaced by "used cars" or "brothels"
> without having any affect whatsoever.
Well, they do have a supposedly-distinguished ether frame. It's just
that it drops out of all predictions of the theory. So while these
theories LOOK quite different from SR, they are physically
indistinguishable from it. The supposedly-fundamental ether and its
frame become empty labels of no consequence, as you say.
> So, I think that ether theories do result in different predictions if
> you force them to be ether theories rather empty semantics.
But if they do that, then they must "live in the error bars" of existing
experiments. That's EXCEEDINGLY difficult, and to my knowledge nobody
has succeeded in constructing such an ether theory. I doubt anyone ever
will.
Tom Roberts tjro...@lucent.com
Bilge
>Bilge wrote:
>> > [I just noticed that those transform equations are NOT valid
>> > "all the way around"; no single set of coordinates can cover
>> > the manifold. So be careful comparing my old posts with SxR;
>> > locally all conclusions follow, but not necessarily globally.]
>> His transforms are not SxR. SxR is a cylinder.
>
>Actually, his transforms are local, and do not affect or reflect the
>topology of this theory, which is S^3xR (loosely, a more complicated
>cylinder). My comment applied to Prefectly Innocent's theory, not my old
>posts.
His transforms cannot be local. If the transform is local, then the
transform is completely defined by an infinitessimal displacement.
>
>
>> > From that immediately follow several conclusions:
>> > 1. The coordinates used in his SxR differ from the coordinates
>> > used in SR _ONLY_ in the way clocks are synchronized.
>> > Locally. Remember, please, that clock synchronization is an
>> > arbitrary human choice, and cannot affect any physical
>> > phenomena.
>>
>> I'm sorry, but I don't agree. Perhaps agreeing that the big hand and
>> little hand on a pair of wall clocks go around at the same rate is an
>> arbitrary human choice, but there exist clocks in nature.
>
>For the above transforms, the hands of a coordinate clock in a given
>frame move at the same rate as a collocated SR coordinate clock (i.e.
>the clocks tick at the same rate).
The interval, ds^2 is not invariant.
The inverse of his transforms is:
x = x'/cosh(A) - ct sinh(A)
t = t' cosh(A)
What does he define a ruler as in order to obtain agreement with
special relativity?
>> I can't see that
>> a constant offset means anything more than relabeling the clock face,
>> which is irrelevant.
>
>RIGHT!!! That's my point. In a given frame, each coordinate clock in the
>above transforms differs by a CONSTANT offset from a collocated SR
>coordinate clock. As I said, this CANNOT affect any physical processes
>(only the way the clocks are used to describe phenomena).
>
>
>> Sure, you can define anything you wish for a set of
>> coordinates, but without a physical marker you can interpret, the
>> coordinates are meaningless. Can you show that his coordinate
>> transforms conserve energy, momentum and angular momentum?
>
>All the conservation laws of SR can be expressed in tensor form, and are
>thus independent of coordinates. So all LOCAL conservation laws remain
>valid. Global laws have to be examined individually.
I'm sorry, but I disagree with that statement as it pertains to
interpreting physical quantities. Sure, you can say that the tensors are
coordinate independent, but when you choose to relate those tensors to
_physical_ quantities, you have to specify what you call invariants and
covariants. I can always change coordinates and reedefine the invariants
and covariants. However, he did not do that.
In addition, coordinates are not entirely man-made. Your assertion that
the tensor equations are invariant is slightly deceptive. If I choose to
define mass and charge as invariants, then I'm stuck with the coordinates
in which those are invariants. Electromagnetism, written as dF = j, means
two different things, if I define charge to be invariant in a galilean
system than if I define charge to be an invariant in minkowski space. What
you aren't stating are the assumptions implicit in the definitions of your
tensors.
If I simply write the equation dX = j and call that the tensor that
represents the theory of everything and say because it's a tensor, it
doesn't matter what it is, how many indicies it has, how the coordinates
are defined or what the physical quantities are, do I get a nobel prize?
Writing quantities using coordinate free form is all well and good,
but if you didn't define the quantites in some coordinate system in the
first place, the tensors would be meaningless.
What perfectly innocent does is to confuse mathematics with physics,
as it doesn't appear that he has checked to see if he can measure
things like distance using rulers.
> And the inconsistency of S^3xR with a flat metric will
> cause havoc in that.... [I'm preparing a post on that]
>> is because ether theories make no predictions based upon any ether.
>
>Hmmm. The underlying derivation and description depend on an ether. But
>it drops out -- that is not obvious up front (c.f. greywolf42's
>confusions on this for LET). Since it drops out of all predictions,
>there is no way to discover it.
But it doesn't drop out. It is simply never used for anything. That
doesn't count. Ether waves described in terms of vector wave equation
are not automatically transverse. How is it that light in an ether
theory appears transverse to every observer, i.e., no longitudinal
polarizations? Sound propagates at a (nominally) constant velocity,
yet, does not exhibit transverse modes.
>> That makes those ether theories trivially equivalent, in the sense,
>> that the word "ether" could be replaced by "used cars" or "brothels"
>> without having any affect whatsoever.
>
>Well, they do have a supposedly-distinguished ether frame. It's just
>that it drops out of all predictions of the theory. So while these
>theories LOOK quite different from SR, they are physically
>indistinguishable from it. The supposedly-fundamental ether and its
>frame become empty labels of no consequence, as you say.
>
>
>> So, I think that ether theories do result in different predictions if
>> you force them to be ether theories rather empty semantics.
>
>But if they do that, then they must "live in the error bars" of existing
>experiments. That's EXCEEDINGLY difficult, and to my knowledge nobody
>has succeeded in constructing such an ether theory. I doubt anyone ever
>will.
Of that, I'm sure. However, I still think it's erroneous to say that
ether theories are indistinguishable from special relativity, because
ether theories do not make the same predictions, i.e., special relativity
can be used to make many more predictions than ether theories do. Unless,
of course, those theories simply abandon the ether concept and use special
relativity without acknowledging that fact. Since gluons are massless and
propagate at `c', an ether theory should be able to derive the strong
interaction from a wave equation and a negative perittivity (along with
enough observations to write down the equivalent maxwell equations. Where
would they get the equivalent of lenz's law for a strong charge?
Tom Roberts
> Tom Roberts:
> >topology of this theory, which is S^3xR
> transform is completely defined by an infinitessimal displacement.
Pun on "local" -- I meant it in the sense of a small but finite region,
and you interpreted it as an infinitesimal region around a given point
(or similar).
His transforms are valid in any region of the manifold that need not be
small, it merely must not extend "all the way around" (i.e. they're
valid in any open set). IOW: the transforms themselves are independent
of the topology, their domains of validity are not. Perfectly Innocent
has not considered the domains of his transforms -- that's why he thinks
he can use an S^3 spatial submanifold, when in fact that is inconsistent....
> >For the above transforms, the hands of a coordinate clock in a given
> >frame move at the same rate as a collocated SR coordinate clock (i.e.
> >the clocks tick at the same rate).
>
> The interval, ds^2 is not invariant.
As perfectly Innocent said (my paraphrase): "so what?". But see below
about puns on the word "invariant".
> What does he define a ruler as in order to obtain agreement with
> special relativity?
AFAIK he has never done so.... But presumably he expects his coordinates
to be measured by clocks and rulers at rest in the moving frame....
> coordinates are not entirely man-made.
Sure they are.
> If I choose to
> define mass and charge as invariants, then I'm stuck with the coordinates
> in which those are invariants.
You cannot "choose" arbitrarily. Quantities either are or are not
invariant over coordinate transforms. BUT IT DEPENDS ON WHAT YOU MEAN:
One can, if one likes, specify a quantity "A" in some specified
coordinates {x^i}, and DEFINE it to be invariant over coordinate
transforms. That just means that for any coordinate transform {x^i} ->
{x^i'} one substitutes the inverse transform (i.e. x^i(x^i')) into the
original definition[#]. Of course in general the equations for A in
terms of the {x^i'} will be very different from the equations defining A
in terms of the {x^i}.
[#] Geometrically, this is known as a "pull-back" by the inverse
transform; functions are intrinsically contravariant.
That is a DIFFERENT meaning of "invariant" than is normally used in
physics, where we say a quantity is invariant over coordinate transforms
if the EQUATIONS DEFINING IT are invariant over such transforms -- the
equations defining A in terms of the {x^i'} are the same as those
defining A in terms of the {x^i}. As usual, physicists are rather
cavalier about precise wording and definitions....
For instance, the underlying reason why Lorentz transforms are so
important in SR is that they are the isometry group of the manifold --
the equations defining the metric are invariant over Lorentz transforms.
> Electromagnetism, written as dF = j, means
> two different things, if I define charge to be invariant in a galilean
> system than if I define charge to be an invariant in minkowski space. What
> you aren't stating are the assumptions implicit in the definitions of your
> tensors.
See above for the pun on "invariant" implicit in your discussion. This
extends to a pun on "tensor" (tensors are merely a specific class of
invariants).
Mathematicians cringe when physicists talk about "tensors" in SR --
mathematically tensors are geometrical, and coordinates are simply
irrelevant (implying that tensors are invariant over coordinate
transforms [up to isomorphism, and admitting that this phrase bends the
terminology a bit]). But in SR the "tensors" discussed are only
invariant over Lorentz transforms, not general coodinate transforms. You
are doing this, and even extending it to Galilean transforms....
> >Hmmm. The underlying derivation and description depend on an ether. But
> >it drops out -- that is not obvious up front (c.f. greywolf42's
> >confusions on this for LET). Since it drops out of all predictions,
> >there is no way to discover it.
>
> But it doesn't drop out. It is simply never used for anything.
Sure it is. In LET the only transform defined is (ether frame)->(moving
frame). To relate two moving frames A and B, one must transform
A->ether->B. Remarkably, the ether frame does drop out. But it's not
obvious until one analyzes it in detail.
Yes, with knowledge of the Poincare' group one can simplify
the equations of LET and formulate A->B without reference
to the ether frame. I suppose that's what you mean.
> However, I still think it's erroneous to say that
> ether theories are indistinguishable from special relativity, because
> ether theories do not make the same predictions, i.e., special relativity
> can be used to make many more predictions than ether theories do.
But it's only reasonable to consider a given theory within its domain of
applicability. Within their common domains of applicability, every one
of those ether theories is indistinguishable from SR. Yes, SR has wider
applicability.... That's one reason why those ether frames are dead as a
doornail (except around here).
Tom Roberts tjro...@lucent.com
Tom Roberts
points are essentially linguistic, related to what "absolute time order"
means.]
Perfectly Innocent wrote:
> Tom Roberts <tjro...@Lucent.com> wrote in message news:<3F577165...@Lucent.com>...
>>>The difference in topology is a feature of least importance. Of
>>>greatest importance is that my theory be defined as I have defined it,
>>>not as a general relativist would prefer to reinterpret it.
>>
>>Hmmm. To me it seems to be the only distinguishing characteristic of
>>your theory.
>
> I expect all relativists to say that initially due to their acquired
> programming.
Except for topology, your theory is identical to that proposed by Ives,
Tanghileri, Selleri, et al (i.e. the transform equations are the same).
These are CERTAINLY not included in "acquired programming"....
>>>My theory presupposes the (S^3)xR topology as an axiom.
>>Oops! I read your intro and assumed you meant SxR^3. S^3xR is
>>inconsistent with a flat metric.
>
> I just finished saying that I presuppose the (S^3)xR topology as an
> axiom. I never presupposed any property requiring flatness or a
> metric.
OK. I was thinking of a 4-metric. I agree you don't need one, and can
formulate your theory without a 4-metric.
But you DO need a 3-metric (if you want to relate your theory to the
real world), as we observe space to be metrical (i.e. we can measure
distances unequivocally). S^3 is inconsistent with a flat 3-metric. This
means EITHER:
1) your theory is self inconsistent.
OR
2) your theory is distinguishable from SR (just measure the
spatial 3-curvature).
OR
3) your theory is incommensurate with the world we observe.
Given your statements around here, I believe (1) is it, which makes the
others irrelevant.
>>Aparently you have fooled yourself with
>>your 1 dimensional analogy.
> Since I never presupposed any property requiring a metric, S^3xR
> couldn't possibly be inconsistent.
I implicitly assumed you want to compare your theory to the real world.
If you don't want to do that, don't expect anyone to take you seriously.
If you do that, you'll have to face up to the incompatibility of S^3 and
a flat 3-metric.
> Let's avoid your obfuscation for the moment and try to resolve our
> differences in 1 spatial dimension before we continue on to (S^2)xR
> and (S^3)xR.
This is not "obfuscation", this is an inconsistency that does not appear
in 1 spatial dimension -- "flat" does not really apply, as the curvature
tensors are not defined on a 1-d manifold.
>>here is a countably-infinite enumeration
>>of topologies consistent with a flat Lorentzian manifold. Start with
>>Minkowski spacetime, then:
>> 1) delete one point
>> 2) delete another point distinct from all previous ones
>> ... iterate (2) as often as desired
>>These are all "uninteresting" in the sense I described.
>
> "Suitable" spacetimes should be geodesically complete.
Your "suitable" is used to mean the same as my "uninteresting".
Note that ALL useful and interesting manifolds in GR are
not geodesically complete (with the exception of Minkowski
spacetime). In particular, the FRW manifolds, the
Schwarzschild manifold, the Kerr manifold, etc.... Look
in Hawking and Ellis for the singularity theorems....
But the _arbitrary_ deletion of points is uninteresting.
>>S^3xR is inconsistent with a flat metric. Back to the drawing board....
> Where in the world did you ever get the idea that I require or
> presuppose a flat metric?
Because we observe space to be metrical, and (at least approximately)
flat. You claimed your theory was in principle indistinguishable from SR
via local experiments; that implies I can assume infinite measurement
accuracy, which means the spatial metric of your theory must be flat if
it is to be indistinguishable from SR.
Tom Roberts tjro...@lucent.com
Perfectly Innocent
> [I'm only responding to issues related to metric and topology. Other
> points are essentially linguistic, related to what "absolute time order"
> means.]
I accept your wonderful admission and feel vindicated by its
extraordinary transparence. It's so obvious that SxR has an "absolute
time order" that you have no mathematical argument to prove that it
isn't so.
> Perfectly Innocent wrote:
> >>>The difference in topology is a feature of least importance. Of
> >>>greatest importance is that my theory be defined as I have defined it,
> >>>not as a general relativist would prefer to reinterpret it.
> >>
> >>Hmmm. To me it seems to be the only distinguishing characteristic of
> >>your theory.
> >
> > I expect all relativists to say that initially due to their acquired
> > programming.
>
> Except for topology, your theory is identical to that proposed by Ives,
> Tanghileri, Selleri, et al (i.e. the transform equations are the same).
> These are CERTAINLY not included in "acquired programming"....
The axiom of (S^3)xR topology has staggering consequences. It compels
the appearance of an absolute frame of reference and establishes an
absolute time order. ** AN ABSOLUTE TIME ORDER PRECLUDES ANYTHING
FALLING INTO A BLACK HOLE. ** I believe that elevates my insights
( http://www.everythingimportant.org/relativity/simultaneity.htm ) to
a category C scientific theory. See J. L. Synge, Relativity: The
Special Theory, 2nd ed., North-Holland Publishing Company, 1965, p. 1;
Subsection 1: "fruitful excursions;" subsection 2: "critical
scrutiny."
"A scientific theory may be divided into three parts: (a) foundations,
(b) accepted dogma, (c) excursions. The foundations are axioms,
principles or laws (e.g. Newton's laws of motion or the first and
second laws of thermodynamics). The accepted dogma consists of
deductions from the foundations confirmed by observation and
experiment, linking reason with nature in a satisfying way (e.g.
Newtonian mechanics as it stood before relativity was thought of). The
excursions wander out of the domain of accepted dogma, sometimes
arousing in cautious minds a feeling that they have more imagination
than solid fact in them (e.g. Maxwell's electromagnetic theory of
light at the time when he put it forward --- all excursions are not so
successful!). A scientific theory is a living thing which grows and
changes; fruitful excursions extend the body of accepted dogma and
critical scrutiny of the foundations clarifies and sometimes modifies
them." Quoted by Patrick Reany (re...@asu.edu) in the thread: "On
scientific theories, by J. L. Synge."
The theory at http://www.everythingimportant.org/relativity/simultaneity.htm
is most certainly not identical to that proposed by Ives, Tanghileri,
Selleri, et al. The transform equations are not the same. Apparently
you have fooled yourself with my two-dimensional analogy.
Have Ives, Tanghileri, Selleri, et al ever argued that an absolute
time order precludes anything falling into a black hole? I'd be
absolutely astonished if they did!
> >>S^3xR is inconsistent with a flat metric. Back to the drawing board....
>
> > Where in the world did you ever get the idea that I require or
> > presuppose a flat metric?
>
> Because we observe space to be metrical, and (at least approximately)
> flat. You claimed your theory was in principle indistinguishable from SR
> via local experiments; that implies I can assume infinite measurement
> accuracy, which means the spatial metric of your theory must be flat if
> it is to be indistinguishable from SR.
>
> Tom Roberts tjro...@lucent.com
I didn't say "in principle indistinguishable" from SR. I have clearly
written that superluminal motion is possible in SxR
( http://www.everythingimportant.org/relativity/simultaneity.htm ).
If, for example, quantum mechanical tunneling can be measured to be
faster than light, then SxR distinguishes itself from SR in a local
experiment and proves my theory right, invalidating SR.
Hopefully, history will forgive my stressing the great similarity
between SxR and SR in a newsgroup full of hysterically reverent SR and
Einstein devotees. To all persons mislead by my imprecise language: I
repent. I hereby amend all my previous writings (where necessary) and
choose that option that makes my theory stronger, not weaker. I now
say, for the record, that "in principle" real experiments do indeed
exist that make SxR distinguishable from SR. Am I forgiven? Are you
all happy now?
Eugene Shubert
http://www.everythingimportant.org/relativity/simultaneity.htm
Perfectly Innocent
> Bilge wrote:
> > What does he define a ruler as in order to obtain agreement with
> > special relativity?
>
> AFAIK he has never done so.... But presumably he expects his coordinates
> to be measured by clocks and rulers at rest in the moving frame....
I define a ruler to be a ruler. But since the physical substance of a
ruler is immaterial, I take a limit and imagine a material number line
or an infinitesimally thin, notched rod with numbers attached.
I define an inertial frame of reference to be a gliding, non-rotating
ruler that moves under its own inertia with a clock attached to each
point. All clocks are genuine Shubertian clocks.
http://www.everythingimportant.org/relativity
Eugene Shubert
Tom Roberts
> Tom Roberts <tjro...@lucent.com> wrote in message news:<bjgbft$j...@netnews.proxy.lucent.com>...
>>[I'm only responding to issues related to metric and topology. Other
>>points are essentially linguistic, related to what "absolute time order"
>>means.]
>
> I accept your wonderful admission and feel vindicated by its
> extraordinary transparence. It's so obvious that SxR has an "absolute
> time order" that you have no mathematical argument to prove that it
> isn't so.
As always, absence of reply does NOT imply agreement.
[There is a specific meaning of "absolute time order" that
applies to SxR, and there are other connotations of that
phrase that do not apply; IMHO those other connotations
are more important than the aspects that do apply. But
it's not worth the effort to argue....]
> The axiom of (S^3)xR topology has staggering consequences. It compels
> the appearance of an absolute frame of reference and establishes an
> absolute time order. ** AN ABSOLUTE TIME ORDER PRECLUDES ANYTHING
> FALLING INTO A BLACK HOLE. **
There _IS_ no black hole in SxR. You're merely fantasizing....
And when you say "absolute frame of reference" you did not mention that
only some of the connotations of that phrase apply. Remember, for
instance, that Schwarzschild spacetime has an "absolute frame of
reference" in the same sense, as do the FRW manifolds, etc....
Tom Roberts tjro...@lucent.com
Perfectly Innocent
I have one more definition.
Suppose an event happens at the point x on ruler E. Then the clock at
point x, motionless on ruler E, reads some time t when the event at x
occurs. If another ruler E' is moving with respect to ruler E, sliding
along the same line, then the event recorded as (x,t) in E is recorded
as (x', t') in E'. x' is the location on the ruler E' marking the
location of the event and t' is the time on the clock at x'.
Note: In my formulation of relativity, I abandon completely the notion
of simultaneity. I presuppose that all physics is local and then
arrive at a notion of simultaneity but only if my derived spacetime
model exhibits the properties of simultaneity.
http://www.everythingimportant.org/relativity
Eugene Shubert
Perfectly Innocent
> On 9/8/2003 12:49 AM, Perfectly Innocent wrote:
> > Tom Roberts <tjro...@lucent.com> wrote in message news:<bjgbft$j...@netnews.proxy.lucent.com>...
> >>[I'm only responding to issues related to metric and topology. Other
> >>points are essentially linguistic, related to what "absolute time order"
> >>means.]
> >
> > I accept your wonderful admission and feel vindicated by its
> > extraordinary transparence. It's so obvious that SxR has an "absolute
> > time order" that you have no mathematical argument to prove that it
> > isn't so.
>
> As always, absence of reply does NOT imply agreement.
Likewise for the claim of no absolute time order, no absolute frame
of reference, and no possibility of motion faster than light:
The evidence of absence is not the absence of evidence.
http://www.everythingimportant.org/viewtopic.php?t=605
> [There is a specific meaning of "absolute time order" that
> applies to SxR, and there are other connotations of that
> phrase that do not apply; IMHO those other connotations
> are more important than the aspects that do apply. But
> it's not worth the effort to argue....]
I hereby happily accept winning this debate by the clear and forceful
arguments already presented by me, and by default, because my opposers
are speechless.
Somebody call Stephen Hawking and ask if he's willing to answer my
challenge with enlightening statements.
> > The axiom of (S^3)xR topology has staggering consequences. It compels
> > the appearance of an absolute frame of reference and establishes an
> > absolute time order. ** AN ABSOLUTE TIME ORDER PRECLUDES ANYTHING
> > FALLING INTO A BLACK HOLE. **
>
> There _IS_ no black hole in SxR. You're merely fantasizing....
I was referring to the next level of SxR generalization:
The consequences of an absolute time order on FRW manifolds and the
complete death of black hole fantasy.
http://www.everythingimportant.org/viewtopic.php?t=533
> And when you say "absolute frame of reference" you did not mention that
> only some of the connotations of that phrase apply. Remember, for
> instance, that Schwarzschild spacetime has an "absolute frame of
> reference" in the same sense, as do the FRW manifolds, etc....
>
> Tom Roberts tjro...@lucent.com
An absolute frame of reference is nothing. An absolute time order is
everything.
http://www.everythingimportant.org/relativity/simultaneity.htm
Eugene Shubert
Bill Hobba
> > Perfectly Innocent write in his paper:
> >
> > 'Let an observer in the circle universe be at rest in her own "inertial
> > frame of reference." Let her pick a positive and negative direction.
Suppose
> > she has a nice watch on her wrist to note the time. Other than just
looking
> > nice and being able to see how old she's getting, let her do
experiments.
> > Let t1 be the time she measures for a photon to circumnavigate the
universe
> > in the positive direction. Let t2 be the time she measures for a photon
to
> > circumnavigate the universe in the negative direction.'
> >
> > I fired a torch off yesterday. I am still waiting for it to return to
me.
> > I seem to recall firing a torch off 40 years ago and no one has ever
> > reported it returning. Exactly how long it this experiment of yours
> > supposed to take? The lifetime of the universe? God give me strength.
Titan Point replied
> I would suggest you implore god give you longevity. Lots of longevity. ;-)
I have been reading with great interest Tom's and Bilge's discussion on this
matter which is about the only good thing to come out of it. Tom also
mentioned he was going to post some further stuff which I also look forward
to.
I suspect Tom is correct (although Bilge also has compelling points) when he
says it is locally indistinguishable from SR. But the point is globally it
is distinguishable. His equations do not obey the symmetry properties of an
inertial reference frame (they demand that the equations be linear) and his
circular universe (cylinder or whatever) definitely is not Euclidian which
is one of the assumed properties of an inertial frame. But I also think Tom
has a point when he says that a lot of the problems are really a
redefinition of clock syncing and other such. I eagerly await further
posts.
Thanks
Bill
Tom Roberts
> I hereby happily accept winning this debate
I am interested in physics, not debates. Goodbye.
Tom Roberts tjro...@lucent.com
Perfectly Innocent
If you were interested in communicating physics, you would explain the
expert opinion or the mathematical proof of why the spacetime SxR
doesn't really have an absolute time order when all obvious
appearances indicates that it does.
Regarding the science of time order: please note that you cowardly
bowed out of answering the question BEFORE I claimed to have won a
debate.
Perfectly Innocent
> On 9/8/2003 12:49 AM, Perfectly Innocent wrote:
> > Tom Roberts <tjro...@lucent.com> wrote in message news:<bjgbft$j...@netnews.proxy.lucent.com>...
> >>[I'm only responding to issues related to metric and topology. Other
> >>points are essentially linguistic, related to what "absolute time order"
> >>means.]
> >
> > I accept your wonderful admission and feel vindicated by its
> > extraordinary transparence. It's so obvious that SxR has an "absolute
> > time order" that you have no mathematical argument to prove that it
> > isn't so.
>
> applies to SxR, and there are other connotations of that
SxR has an "absolute time order" or it doesn't. Common sense, an
understanding of the physics and your public equivocation proves that
an absolute time order exists.
> > The axiom of (S^3)xR topology has staggering consequences. It compels
> > the appearance of an absolute frame of reference and establishes an
> > absolute time order.
> And when you say "absolute frame of reference" you did not mention that
> only some of the connotations of that phrase apply.
Equivocation is mostly linguistic. You're speaking nonsense.
100% of the meaning of "an absolute frame of reference" applies to
SxR. A frame is an absolute frame of reference if it is physically
distinguished from all other frames and if it is totally independent
of the distribution of matter/energy in the universe.
http://www.everythingimportant.org/viewtopic.php?t=533
Eugene Shubert
dlzc@aol.com (formerly)
"Perfectly Innocent" <perfectl...@as-if.com> wrote in message
news:c45b45b3.03090...@posting.google.com...
...
> SxR has an "absolute time order" or it doesn't. Common sense, an
> understanding of the physics and your public equivocation proves that
> an absolute time order exists.
There is irrefutable logic for you! Mr. Wittke would be proud of you.
If two events occur at two different locations, is there an "absolute time
order" as to which happened first? For many setups, frames could be found
that would have different "time orders". What do you mean by your babble?
David A. Smith
Perfectly Innocent
> Dear Perfectly Innocent:
>
> "Perfectly Innocent" wrote in message
> news:c45b45b3.03090...@posting.google.com...
> ...
> > SxR has an "absolute time order" or it doesn't. Common sense, an
> > understanding of the physics and your public equivocation proves that
> > an absolute time order exists.
>
> There is irrefutable logic for you!
>
> order" as to which happened first? For many setups, frames could be found
> that would have different "time orders". What do you mean by your babble?
>
> David A. Smith
Time order is inextricably tied to the globally valid frame dependent
speed of light in SxR, which is inextricably tied to an absolute frame
of reference. No one has contested my global law of light propagation
for SxR. Do you wish to do that now?
http://www.everythingimportant.org/viewtopic.php?t=605
If you have the might, try to apply Einstein's criterion for absolute
time order from Einstein's famous train and embankment gedanken
experiment to SxR. Do you realize that trying to repeat Einstein's
demonstration of relative simultaneity derails itself immediately in
SxR?
If you mean by your babbling that clocks could by reset to foil or
obfuscate the obvious physically based, reality grounded, global
synchronization of events in SxR, I say, that's a wonderful deception.
I use the same trick and make it appear that I can derive the Lorentz
transformation from the Galilean transformation. The problem is any
mathematically literate person can see that my math-based magic is
superior to your feeble attempts at trickery.
http://www.everythingimportant.org/viewtopic.php?t=451
Eugene Shubert
Perfectly Innocent
> [I'm only responding to issues related to metric and topology. Other
> points are essentially linguistic, related to what "absolute time order"
> means.]
If you believe that an absolute time order is essentially semantics
and not physics or mathematics, then please explain all the hoopla and
religious fervor about the non-science of relative simultaneity in a
universe with a presumed (S^3)xR topology?
http://www.everythingimportant.org/viewtopic.php?t=605
Eugene Shubert
Perfectly Innocent
I've updated http://www.everythingimportant.org/viewtopic.php?t=605
today with the distilled essence of the debate representing many
points of view and several independent threads.
I thank you for your interest.
Eugene Shubert
http://www.everythingimportant.org/viewtopic.php?t=605
Bilge
>Bilge wrote:
>> The interval, ds^2 is not invariant.
>
>As perfectly Innocent said (my paraphrase): "so what?". But see below
>about puns on the word "invariant".
He hasnt defined _any_ physical quantities that give meaning to
his transforms. He cannot possibly give x and t the same meaning
as distance and time measured by rulers and clocks.
>> What does he define a ruler as in order to obtain agreement with
>> special relativity?
>
>AFAIK he has never done so.... But presumably he expects his coordinates
>to be measured by clocks and rulers at rest in the moving frame....
He may presume that, but his rulers and clocks cannot possibly be the
same rulers and clocks as everyone else thinks of them if he expects his
transforms to be equivalent to lorentz transforms.
>> coordinates are not entirely man-made.
>
>Sure they are.
I'm not sure how you think of coordinates, but it wouldn't be possible
to compare theory to experiment unless one chose coordinates to represent
physical quantities. For example, is the speed of light a constant?
It's pretty darn close, but the physics is quite different depending
upon whether it is or isn't. if it isn't, maxwell's equations are
no longer valid tensor equations. The only way to determine whether charge
is conserved is to measure something.
>> If I choose to define mass and charge as invariants, then I'm stuck
>> with the coordinates in which those are invariants.
>
>You cannot "choose" arbitrarily. Quantities either are or are not
>invariant over coordinate transforms. BUT IT DEPENDS ON WHAT YOU MEAN:
Precisely, that is my point above. You just said it in a rather odd
way.
>One can, if one likes, specify a quantity "A" in some specified
>coordinates {x^i}, and DEFINE it to be invariant over coordinate
>transforms. That just means that for any coordinate transform {x^i} ->
>{x^i'} one substitutes the inverse transform (i.e. x^i(x^i')) into the
>original definition[#]. Of course in general the equations for A in
>terms of the {x^i'} will be very different from the equations defining A
>in terms of the {x^i}.
Sure. And my point is, that given the same invariants, the transforms
given by perfectly innocent are not equivalent to lorentz transforms.
>
> [#] Geometrically, this is known as a "pull-back" by the inverse
> transform; functions are intrinsically contravariant.
>
>That is a DIFFERENT meaning of "invariant" than is normally used in
>physics, where we say a quantity is invariant over coordinate transforms
>if the EQUATIONS DEFINING IT are invariant over such transforms -- the
>equations defining A in terms of the {x^i'} are the same as those
>defining A in terms of the {x^i}. As usual, physicists are rather
>cavalier about precise wording and definitions....
I don't think that statement regarding physicists is accurate. First of
all, the definition you just gave is what most physicists would define as
a covariant (which is in keeping with the mathematical definition, at
least insofar as my text, "Classical Invariant Theory", Olver, Peter, J.,
is concerned). Second, Physicists and mathematicians may use the same
mathematics, but in physics, the objective is different. The math has to
relate to physical quantities. It isn't very useful to say that F is a
tensor if you can't point to a physical quantity that it represents and
have some way of determining if you chose the object correctly.
>For instance, the underlying reason why Lorentz transforms are so
>important in SR is that they are the isometry group of the manifold --
>the equations defining the metric are invariant over Lorentz transforms.
This is getting away from the issue at hand and I think you're missing
the point. Perfectly innocent's transforms do not even define a group,
let alone are they equivalent to the lorentz group.
What you are saying is all well and good as far as it goes, but a
manifold is just a collection of points. Those points mean nothing
and a metric means nothing without a physical marker for it. Given
the minkowski metric, it makes a difference whether the speed of
light is 1 or the speed of light is represented by some other physical
quantity. The tensors may all be the same, but they represent different
things.
>> Electromagnetism, written as dF = j, means
>> two different things, if I define charge to be invariant in a galilean
>> system than if I define charge to be an invariant in minkowski space. What
>> you aren't stating are the assumptions implicit in the definitions of your
>> tensors.
>
>See above for the pun on "invariant" implicit in your discussion. This
>extends to a pun on "tensor" (tensors are merely a specific class of
>invariants).
>
>Mathematicians cringe when physicists talk about "tensors" in SR --
>mathematically tensors are geometrical, and coordinates are simply
>irrelevant (implying that tensors are invariant over coordinate
>transforms [up to isomorphism, and admitting that this phrase bends the
>terminology a bit]).
Mathematicians can cringe all they want. They don't have to relate
tensors to physical objects and determine if they've done so correctly.
> But in SR the "tensors" discussed are only invariant over Lorentz
>transforms, not general coodinate transforms. You are doing this,
>and even extending it to Galilean transforms....
Huh? I'm not sure what "this" means, but for the point I'm making, it
really doesn''t matter whether you consider only lorentz transforms or you
extend it to include general coordinate transforms. My point is that one
chooses a coordinate system based upon what one believes it represents
physically.
>> >Hmmm. The underlying derivation and description depend on an ether. But
>> >it drops out -- that is not obvious up front (c.f. greywolf42's
>> >confusions on this for LET). Since it drops out of all predictions,
>> >there is no way to discover it.
>>
>> But it doesn't drop out. It is simply never used for anything.
>
>Sure it is. In LET the only transform defined is (ether frame)->(moving
>frame). To relate two moving frames A and B, one must transform
>A->ether->B. Remarkably, the ether frame does drop out. But it's not
>obvious until one analyzes it in detail.
OK. Analyze this in detail. From experimental observations, deduce
the maxwell equations for the strong interactions. If you wish, I'll
write them down and allow you to insert the \mu and \epsilon that
correspond to the mechanical properties of the ether and then explain
why and how they should relate to the \mu and \epsilon of E&M.
> Yes, with knowledge of the Poincare' group one can simplify
> the equations of LET and formulate A->B without reference
> to the ether frame. I suppose that's what you mean.
No, what I mean is that if that you assert the ether is unobservable
(or not) and formulate all of your physics without ever incorporating
the ether in the explanation, you aren't talking about an ether theory.
You're talking about relativity. For example, assume I grant you that
the relation E^2 = p^2 + m^2 in both theories without disputing any
of the metaphysical aspects of how one arrives at it. Now, I assume
you know how to obtain the dirac lagrangian from this, so further
assume that I grant you the dirac lagrangian as obtainable from ether
relativity or an ether theory (even though, the latter about which I
am dubious):
_
L = e(p/ - m)e
Now, relativity is a theory of invariance so requiring lorentz invariance
under a change of phase is rather natural and in less than a half-dozen
lines of some algebra, I have the qed lagrangian. Obtain the qed
lagrangian using the semantics of LET, i.e., relate all of the quantities
to the ether and show that the ether disappears.
> > However, I still think it's erroneous to say that
>> ether theories are indistinguishable from special relativity, because
>> ether theories do not make the same predictions, i.e., special relativity
>> can be used to make many more predictions than ether theories do.
>
>But it's only reasonable to consider a given theory within its domain of
>applicability. Within their common domains of applicability, every one
>of those ether theories is indistinguishable from SR. Yes, SR has wider
>applicability.... That's one reason why those ether frames are dead as a
>doornail (except around here).
Thats my point. The domain of applicability for ether theories was
exceeded shortly after the turn of the century, but the only valid
way to compare the two is according to what they can explain _today_.
Perfectly Innocent
>
> What's an inertial frame according to you?
My definition is presented here:
http://www.everythingimportant.org/viewtopic.php?t=648
Eugene Shubert
Bilge
well, inertia. Now, do you have a definition that doesn't use
the term you are are defining to define itself?
Don't use any terms you can't define non-circularly. For example,
"moving at a constant velocity" is not a definition, unless you
can define "constant velocity" in some way other than "inertial".
Ditto for "straight line" and "non-rotating". Try again.
Tom Roberts
> Tom Roberts:
> >Bilge wrote:
> >> The interval, ds^2 is not invariant.
> >As perfectly Innocent said (my paraphrase): "so what?". But see below
> >about puns on the word "invariant".
>
> He hasnt defined _any_ physical quantities that give meaning to
> his transforms. He cannot possibly give x and t the same meaning
> as distance and time measured by rulers and clocks.
Sure he can. Locally his transforms differ from Lorentz transforms ONLY
in the way clocks are synchronized. This may not be obvious from the
transforms themselves (in the way he presents them)....
> >> coordinates are not entirely man-made.
> >
> >Sure they are.
>
> I'm not sure how you think of coordinates, but it wouldn't be possible
> to compare theory to experiment unless one chose coordinates to represent
> physical quantities. For example, is the speed of light a constant?
This is merely different meanings of words. One most certainly can
select coordinates based on rulers and clocks; but one can also select
coordinates based on an arbitrary assignment of coordinate values to
points/events (subject to various consistency requirements). Of course
if one want to compare to an experiment one must know how to compute
distances from whichever coordinates one is using; for the clock- and
ruler-based coordinates that is trivial, while for the arbitrary
coordinates one must first determine the metric in terms of the coordinates.
No physicist or engineer would do this latter, but it is
possible to do so, and that possibility is the issue at hand.
Is the speed of light constant? -- yes when "speed" is defined as
(distance traveled wrt inertial frame A)/(elapsed time in inertial frame
A). For all coordinates, one must use the metric to determine both
distance and elapsed time (which is trivial for ruler- and clock-based
coords.).
Is the COORDINATE speed of light constant? -- not at all.
> >One can, if one likes, specify a quantity "A" in some specified
> >coordinates {x^i}, and DEFINE it to be invariant over coordinate
> >transforms. That just means that for any coordinate transform {x^i} ->
> >{x^i'} one substitutes the inverse transform (i.e. x^i(x^i')) into the
> >original definition[#]. Of course in general the equations for A in
> >terms of the {x^i'} will be very different from the equations defining A
> >in terms of the {x^i}.
>
> Sure. And my point is, that given the same invariants, the transforms
> given by perfectly innocent are not equivalent to lorentz transforms.
They are not the isometry group of Minkowski spacetime. But so what?
> >That is a DIFFERENT meaning of "invariant" than is normally used in
> >physics, where we say a quantity is invariant over coordinate transforms
> >if the EQUATIONS DEFINING IT are invariant over such transforms -- the
> >equations defining A in terms of the {x^i'} are the same as those
> >defining A in terms of the {x^i}. As usual, physicists are rather
> >cavalier about precise wording and definitions....
>
> I don't think that statement regarding physicists is accurate. First of
> all, the definition you just gave is what most physicists would define as
> a covariant
To me, only a SET of quantities can be "covariant", and then only if
they are the components of some tensor wrt some basis (usually
implicit). This is so because the "co" in "covariant" means "with-"....
> Perfectly innocent's transforms do not even define a group,
> let alone are they equivalent to the lorentz group.
They do form a group. But all frames are not equivalent, and the group
structure is different from the structure of the Lorentz group. For
instance, there is a preferred frame....
> What you are saying is all well and good as far as it goes, but a
> manifold is just a collection of points. Those points mean nothing
> and a metric means nothing without a physical marker for it.
Sure. This is known as applying math to physics.
> >> However, I still think it's erroneous to say that
> >> ether theories are indistinguishable from special relativity, because
> >> ether theories do not make the same predictions, i.e., special relativity
> >> can be used to make many more predictions than ether theories do.
> >
> >But it's only reasonable to consider a given theory within its domain of
> >applicability. Within their common domains of applicability, every one
> >of those ether theories is indistinguishable from SR. Yes, SR has wider
> >applicability.... That's one reason why those ether frames are dead as a
> >doornail (except around here).
>
> Thats my point. The domain of applicability for ether theories was
> exceeded shortly after the turn of the century, but the only valid
> way to compare the two is according to what they can explain _today_.
Yes. In particular, ether theories have great difficulty with quantum
phenomena. Not to mention nuclear interactions....
Tom Roberts tjro...@lucent.com
Perfectly Innocent
> Perfectly Innocent:
> >dub...@radioactivex.lebesque-al.net (Bilge) wrote in message news:<slrnbljb6q....@radioactivex.lebesque-al.net>...
> >>
> >> What's an inertial frame according to you?
> >
> >My definition is presented here:
> >
> >http://www.everythingimportant.org/viewtopic.php?t=648
>
> Congratulations. You managed to define inertial in terms of,
> well, inertia. Now, do you have a definition that doesn't use
> the term you are are defining to define itself?
http://dictionary.reference.com/search?q=inertia
> Don't use any terms you can't define non-circularly. For example,
> "moving at a constant velocity" is not a definition, unless you
> can define "constant velocity" in some way other than "inertial".
> Ditto for "straight line" and "non-rotating". Try again.
We cannot define anything precisely! If we attempt to, we get into
that paralysis of thought that comes to philosophers, who sit opposite
each other, one saying to the other, 'You don't know what you are
talking about!' The second one says 'What do you mean by know? What
do you mean by talking? What do you mean by you?', and so on.
Feynman, The Character of Physical Law
Eugene Shubert
http://www.everythingimportant.org
Bilge
>http://dictionary.reference.com/search?q=inertia
In other words, you can't.
Bill Hobba
> >dub...@radioactivex.lebesque-al.net (Bilge) wrote in message
news:<slrnbljb6q....@radioactivex.lebesque-al.net>...
> >>
> >> What's an inertial frame according to you?
> >
> >My definition is presented here:
> >
> >http://www.everythingimportant.org/viewtopic.php?t=648
>
Bilge correcty replied:
> Congratulations. You managed to define inertial in terms of,
> well, inertia. Now, do you have a definition that doesn't use
> the term you are are defining to define itself?
>
> Don't use any terms you can't define non-circularly. For example,
> "moving at a constant velocity" is not a definition, unless you
> can define "constant velocity" in some way other than "inertial".
> Ditto for "straight line" and "non-rotating". Try again.
In order to save Eugene torturing this group with his further distortions I
humbly ask him to think about this one carefully. The rigorous definition
of an inertial reference frame is no easy undertaking. For example some
people define it as a frame that obeys Newton's first law ie an object stays
at rest or continues to move at constant velocity unless acted on by a
force. But force is defined as F=MA which makes this definition devoid of
content. Such problems can be overcome (for example by careful definition
of what a free particle is or by defining it via the symmetry properties of
such a frame) but that and a myriad of other issues (such as what constant
velocity and straight line is) require careful consideration. Might I
suggest he actually consult a good textbook - that way I suspect it will be
a win win for all concerned.
I have no doubt the above will fall on deaf ears. Ah well I tried.
Bill
---
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Tom Roberts
> Perfectly Innocent:
> >dub...@radioactivex.lebesque-al.net (Bilge) wrote in message news:<slrnbljb6q....@radioactivex.lebesque-al.net>...
> >> What's an inertial frame according to you?
> >My definition is presented here:
> >http://www.everythingimportant.org/viewtopic.php?t=648
>
> Congratulations. You managed to define inertial in terms of,
> well, inertia. Now, do you have a definition that doesn't use
> the term you are are defining to define itself?
That's the crux of why I don't think SR is really a theory of physics
(it is only an approximation to one) -- I know of no way to define
"inertial frame" in SR. In GR it is easy to do so in a local region, and
I consider that to be the justification for using SR.
GR does not suffer from this problem....
Tom Roberts tjro...@lucent.com
FrediFizzx
Except that mass is defined in terms of mass. So far we can only get the
mass of something by comparing to another mass.
FrediFizzx
Bill Hobba
> > Perfectly Innocent:
> > >dub...@radioactivex.lebesque-al.net (Bilge) wrote in message
news:<slrnbljb6q....@radioactivex.lebesque-al.net>...
> > >> What's an inertial frame according to you?
> > >My definition is presented here:
> > >http://www.everythingimportant.org/viewtopic.php?t=648
> >
> > Congratulations. You managed to define inertial in terms of,
> > well, inertia. Now, do you have a definition that doesn't use
> > the term you are are defining to define itself?
>
Tom Roberts wrote:
> That's the crux of why I don't think SR is really a theory of physics
> (it is only an approximation to one) -- I know of no way to define
> "inertial frame" in SR. In GR it is easy to do so in a local region, and
> I consider that to be the justification for using SR.
>
> GR does not suffer from this problem....
I know Tom has gone way deeper into the foundations of SR than me but from
my limited understanding of such issues I suspect he is correct. However if
SR is to be an applicable theory (and the fact it is used in many areas such
as QFT and relativistic fluid dynamics) then the underlying assumptions must
be a reasonable approximation to things we have experience with. In another
part of this thread Tom wrote (referring to what is necessary to make ideas
like Eugene's gel): ' No physicist or engineer would do this latter, but it
is possible to do so, and that possibility is the issue at hand'. But if SR
is to be an applicable theory then while we can't rule out such things on
logical grounds surely we can say they are not a reasonable generalization
of the near inertial reference frames we see around us? By this I mean
since no physicist or engineer would do such a thing then can't we dismiss
them on the grounds of applicability?
Thanks
Bilge
>> Perfectly Innocent:
>> >dub...@radioactivex.lebesque-al.net (Bilge) wrote in message
>> >news:<slrnbljb6q....@radioactivex.lebesque-al.net>...
>> >> What's an inertial frame according to you?
>> >My definition is presented here:
>> >http://www.everythingimportant.org/viewtopic.php?t=648
>>
>> Congratulations. You managed to define inertial in terms of,
>> well, inertia. Now, do you have a definition that doesn't use
>> the term you are are defining to define itself?
>
>That's the crux of why I don't think SR is really a theory of physics
>(it is only an approximation to one) -- I know of no way to define
>"inertial frame" in SR.
intrinsic to special relativity. However, I do think it's possible
to determine which of two frames is more inertial in any given
thought experiment. One way is to use maxwell's equations. Charges
in inertial frames don't radiate, so in principle, the inertial
observer in a twins paradox is the one which doesn't radiate.
Bilge
>> Tom Roberts:
>> >Bilge wrote:
>> >> The interval, ds^2 is not invariant.
>> >As perfectly Innocent said (my paraphrase): "so what?". But see below
>> >about puns on the word "invariant".
>>
>> He hasnt defined _any_ physical quantities that give meaning to
>> his transforms. He cannot possibly give x and t the same meaning
>> as distance and time measured by rulers and clocks.
>
>Sure he can. Locally his transforms differ from Lorentz transforms ONLY
>in the way clocks are synchronized. This may not be obvious from the
>transforms themselves (in the way he presents them)....
>
>
>> >> coordinates are not entirely man-made.
>> >
>> >Sure they are.
>>
>> I'm not sure how you think of coordinates, but it wouldn't be possible
>> to compare theory to experiment unless one chose coordinates to represent
>> physical quantities. For example, is the speed of light a constant?
>
>This is merely different meanings of words.
Huh?
>One most certainly can select coordinates based on rulers and clocks;
>but one can also select coordinates based on an arbitrary assignment
>of coordinate values to points/events (subject to various consistency
>requirements).
Sure. And the "consistency requirements" are the consequences
associated with doing so.
>Of course
>if one want to compare to an experiment one must know how to compute
>distances from whichever coordinates one is using; for the clock- and
>ruler-based coordinates that is trivial, while for the arbitrary
>coordinates one must first determine the metric in terms of the
>coordinates.
Which implies that you've chosen some physiscal marker to define
your coordinates/metric.
[...]
>They are not the isometry group of Minkowski spacetime. But so what?
He claims to use the same rulers and clocks that one uses in minkowski
space.
>> >That is a DIFFERENT meaning of "invariant" than is normally used in
>> >physics, where we say a quantity is invariant over coordinate transforms
>> >if the EQUATIONS DEFINING IT are invariant over such transforms -- the
>> >equations defining A in terms of the {x^i'} are the same as those
>> >defining A in terms of the {x^i}. As usual, physicists are rather
>> >cavalier about precise wording and definitions....
>>
>> I don't think that statement regarding physicists is accurate. First of
>> all, the definition you just gave is what most physicists would define as
>> a covariant
>
>To me, only a SET of quantities can be "covariant", and then only if
>they are the components of some tensor wrt some basis (usually
>implicit). This is so because the "co" in "covariant" means "with-"....
The definition I have (and with which I agree as well as find
physically useful) is that a covariant is an invariant which depends
upon the coordinates (which I can write out explicitly if you
wish).
>> Perfectly innocent's transforms do not even define a group,
>> let alone are they equivalent to the lorentz group.
>
>They do form a group.
No, they don't. The set of _all_ matrices of the form:
[a 0]
M = [ ]
[b c]
form a group. His transform restricts the set of matrices to
a subset (not subgroup) of those matrices. If they formed a
group, then for his transform:
t' = t sech(A)
x' = x cosh(A) - t sinh(A)
[which he writes as:
x' = Y(v)(x - vt),
t' = t/Y(v),
Y(v) = 1/sqrt(1-(v/c)^2)],
there must be a transform:
t'' = t' sech(B)
x'' = x' cosh(B) - t' sinh(B)
such that t'' = t; x'' = x. For t, I get:
t'' = t sech(A)sech(B)
and, for t = t'', I get:
cosh(A) = 1/cosh(B)
The condition on x is similar:
x' = x cosh(A) - t sinh(A)
x'' = x' cosh(B) - t' sinh(B)
= [x cosh(A) - t sinh(A)] cosh(B) + t sech(A)sinh(B)
= x cosh(A)cosh(B) - t [sinh(A)cosh(B) + sech(A)sinh(B)]
which requires two things. First:
cosh(A) = 1/cosh(B) [the same requirement as in t above]
Since cosh(A) is always greater than or equal to 1, the only solution
is A = B = 1.
The other requirement is:
sinh(A)cosh(B) + sech(A)sinh(B) = 0
tanh(B) = - sinh(A)cosh(A) = sinh(2A)/2
which is irrelevant at this point.
By contrast, for t, the lorentz transforms yield the condition:
cosh(A)cosh(B) + sinh(A)(sinh(B) = 1
cosh(A)sinh(B) + sinh(A)cosh(B) = 0
which is satisfied for A = -B.
Bill Hobba
> >That's the crux of why I don't think SR is really a theory of physics
> >(it is only an approximation to one) -- I know of no way to define
> >"inertial frame" in SR.
>
Bilge replied:
> Right, primarily because mass is not a concept which is really
> intrinsic to special relativity. However, I do think it's possible
> to determine which of two frames is more inertial in any given
> thought experiment. One way is to use maxwell's equations. Charges
> in inertial frames don't radiate, so in principle, the inertial
> observer in a twins paradox is the one which doesn't radiate.
I am not sure what you mean by 'mass is not a concept which is really
intrinsic to special relativity'. In Mechanics Landau derived the existence
of mass from the POR and the principle of least action. Then from the
assumption that in the non relativistic limit particles behave the same as
in classical mechanics, in the Classical Theory of Fields, from very general
considerations of the form of the lagrangian, he derives the relativistic
lagrangian. So I would say the principle of least action and the POR in
both classical and relativistic mechanics lead to the existence of mass - so
it would seem an intrinsic property - or am I missing something (quite
likely).
BTW I agree with Toms original statement - purely on the basis that inertial
reference frames really do not exist - except maybe locally in GR. However
as an abstraction, and based on its utility, it seems an indispensable idea.
And that is one problem I have with the ideas of Eugene (apart from the fact
that to me a lot of his stuff is nonsense - but to be fair that may be a
factor of my limited knowledge) - exactly what is its applicability. I can
see how to apply standard SR to QFT for example. But overall his ideas have
me bamboozled.
Slightly confused
greywolf42
> Bilge wrote:
> > Tom Roberts:
{snip}
> >>In my old posts, all theories were in essence applied to a manifold with
> >>topology R^4, and there is no way to discover the "ether frame".
> >
> > The only reason that there is "no way to discover the ether frame",
> > is because ether theories make no predictions based upon any ether.
>
> Hmmm. The underlying derivation and description depend on an ether. But
> it drops out -- that is not obvious up front (c.f. greywolf42's
> confusions on this for LET). Since it drops out of all predictions,
> there is no way to discover it.
Tom, the aether doesn't "drop out" of all predictions. It's only in
your own, personal, SR-equivalent L*E*T where it drops out.
See Lorentz' 1904 paper, section 11.
> > That makes those ether theories trivially equivalent, in the sense,
> > that the word "ether" could be replaced by "used cars" or "brothels"
> > without having any affect whatsoever.
>
> Well, they do have a supposedly-distinguished ether frame.
Absolutely false. There are no 'frames' -- aether or otherwise in any
aether theory. The "frame" argument is a an SR strawman.
greywolf42
ubi dubium ibi libertas
Bilge
>> >That's the crux of why I don't think SR is really a theory of physics
>> >(it is only an approximation to one) -- I know of no way to define
>> >"inertial frame" in SR.
>>
>
>Bilge replied:
>> Right, primarily because mass is not a concept which is really
>> intrinsic to special relativity. However, I do think it's possible
>> to determine which of two frames is more inertial in any given
>> thought experiment. One way is to use maxwell's equations. Charges
>> in inertial frames don't radiate, so in principle, the inertial
>> observer in a twins paradox is the one which doesn't radiate.
>
>I am not sure what you mean by 'mass is not a concept which is really
>intrinsic to special relativity'.
for the simple reason that the universe has mass in it. The symmetry
is only a local symmetry conditioned upon the assumption the mass
has none of the physical properties a real mass has.
>In Mechanics Landau derived the existence of mass from the POR and
>the principle of least action.
I don't have the text to which you refer, but I suspect that what
landau did was along the lines of showing that there was a conserved
quantity obtained from the lagrangian (the energy-momentum tensor - not
to be confused with the one in general relativity) and pulling
the mass from that. Something like:
Given a lagrangian L(x), and a change in the spacetime variables,
x -> x' = x + a, where a is an infinitessimal displacement, the
change in the lagrangian can be written,
L(x^u') = L(x^u + a^u) = L(x^u) + a^u d_u L
If the lagrangian is not explicitly dependent on the coordinates,
but dependent upon some generalized q(x), and the first derivatives,
d_u q(x), the change can be written:
\delta L = (dL/dq)\delta q + (dL/d(d_u q)) \delta (d_u q)
and then by equating the expressions and using the euler-lagrange
equations, obtain a conserved current, and evaluate the 00-component
of the hamiltonian derived from it and then I guess he assumes
the mass is some energy confined to a fixed volume. If not, I'd
like to hear the handwaving version.
But, that isn't really what I meant. If the lorentz symmetry were
manifest, then it really would be impossible to determine a physical
difference between point A and point B. Consider a sphere for which the
spherical symmetry is exact. If you observe the sphere at two different
times, is it possible to determine if the sphere has been rotated to a
different position? It's not and so it doesn't even really mean anything,
physically to assign coordinates to it, since you have no physical marker
to which the coordinates could be attached. If there is a dot on the
sphere, then the manifestly spherical symmetry is broken by the appearance
of the dot. The dot can be used to identify a special coordinate system of
which the dot is the origin and you can go and mark dots at points on the
sphere and determine a distance between them, etc. The original spherical
symmetry still exists, because you can choose any point on the sphere to
be the origin and the coordinates differ only by a rotation. You can
determine that the symmetry isn't exact, because the dots exist as
physical markers for "preferred" coordinates (or a frame of reference). An
inertial frame in special relativity is a special set of coordinates in
which something is "at rest". If everything propagated at the speed of
light, the symmetry would be exact and every point in spacetime would
literally be indistinguishable from every other.
The fact that mass gravitates means that landau could not have shown
explicitly that mass is a consequence of least action assuming only
special relativity. If he had litterally derived the mass from only
the principle of least action and the principle of relativity, he would
have ended up with general relativity, not special relativity. I imagine
that the "mass" he derived is really a quantity he identified as
mass, but is only equivalent to physical mass under the assumption that
its actual physical properties can be neglected. The fact that he
fixed the geometry by fixing the metric means he was really guaranteed
to get that result, since his mass is really just a marker (like the
dot on the sphere) for a special coordinate system, inertial frames.
[...]
>in classical mechanics, in the Classical Theory of Fields, from very general
>considerations of the form of the lagrangian, he derives the relativistic
>lagrangian. So I would say the principle of least action and the POR in
>both classical and relativistic mechanics lead to the existence of mass - so
>it would seem an intrinsic property - or am I missing something (quite
>likely).
Only the part about fixing the metric in the lagrangian, so that it
too is not subjected to the principle of least action. If he had
allowed the metric to vary as well, he wouldn't have obtained a
result which gives masses in a globally flat spacetime. The masses
act as a quantity that lets you (physically) define reference frames
as inertial one in the limit that the mass itself has no impact on
the physics, and allows you use special relativity to treat accelerations
and forces by being able to say that some frames are more inertial
than others. For example, the twins paradox if constructed under
the assumption that the twins exert a force on each other in order
to boost the twins into different frames, shows that the ratio of
their masses can be used to determine which twin was accelerated the
least and therefore the proper choice to call "inertial".
>BTW I agree with Toms original statement - purely on the basis that inertial
>reference frames really do not exist - except maybe locally in GR. However
>as an abstraction, and based on its utility, it seems an indispensable idea.
>And that is one problem I have with the ideas of Eugene (apart from the fact
>that to me a lot of his stuff is nonsense - but to be fair that may be a
>factor of my limited knowledge) - exactly what is its applicability. I can
>see how to apply standard SR to QFT for example. But overall his ideas have
>me bamboozled.
Eugene confuses math with physics. A mathematician simply assumes
one can attach a set of coordinates to a manifold via the mathematical
formalism and show various properties of the geometry that results.
The mathematician can then say A, B, C,... are invariants and are
tensors. One can call them things like "stress-energy tensor", "mass",
"charge", and so on. On the other hand, physicists already have a
notion of what these things mean. Eugene assumes that a numberline
is a physical ruler, but "equally spaced" points on a number line
don't necessarily correspond to the intervals on what we call a ruler.
Take the definition of a clock. In special relativity, a clock is
essentially a perfect wall clock. You could say that equal intervals
on the numberline correspond to equal intervals on the clock. But,
you could also define equal increments on a clock as the time required
for N particles of a lump of a particluar isotope to decay. The number
line is still a number line and by assuming it to represent the physics,
you would end up with exactly the same lorentz transforms, but the
definition of `t' in the transforms wouldn't correspond to reality.