Einstein 1918 - The clock paradox and other objections against 1916 GRT
harry
accelerated frames, and according to him, acceleration as well as
gravitational fields are purely "relative".
A number of scientists advanced counter arguments, arguing that acceleration
must be "absolute" and not "relative" - a debate that has never really
ended. In 1918, Einstein published a paper in which he attempted to debunk
such arguments. His 1918 paper is highly interesting for its metaphysical
content; and in contrast to most textbooks, he did not duck the issues. It
is also interesting that he explicitly disagreed with claims that GRT did
away with all ether concepts.
I will start by simply linking to an unoffical English translation of his
1918 paper:
http://en.wikisource.org/wiki/Dialog_about_objections_against_the_theory_of_relativity
Einstein's 1918 paper provides so much food for thought, that on purpose I
postpone a discussion of the arguments to a later posting which will include
more counter arguments that were presented by others and, surprisingly, even
by Einstein himself.
Enjoy!
Harald
harry
In 1916 Einstein proposed to extend the principle of relativity to
accelerated frames, and according to him, acceleration as well as
gravitational fields are purely "relative".
A number of scientists advanced counter arguments, arguing that acceleration
must be "absolute" and not "relative" - a debate that has never really
ended. In 1918, Einstein published a paper in which he attempted to debunk
such arguments. His 1918 paper is highly interesting for its metaphysical
content; and in contrast to most textbooks, he did not duck the issues.
It is also interesting that he explicitly disagreed with claims that GRT did
away with all ether concepts.
I will start by simply linking to an unoffical English translation of his
1918 paper:
http://en.wikisource.org/wiki/Dialog_about_objections_against_the_theory_of_relativity
As Einstein remarked himself in that paper through the mouth of a critic, he
planted the seeds of the controversy when he, in his 1905 paper, at first
suggested that only relative motion between objects should matter, but next
went on to predict asymmetrical aging of relatively moving clocks.
In this context it is also worth mentioning that in 1911, Langevin published
a paper on relativity in which he elaborated on Einstein's prediction with
an example of two space travellers, in order to argue that just as in
classical mechanics, with (special) relativity acceleration is "absolute" in
the sense of being absolute relative to (neo-)Newtonian space. Consequently,
the same old absolutist concepts can be used, but corrections must be made
for relativistic effects which he explained as due to motion relative to
"space".
Thus it must have come as a surprise when in 1916 Einstein again argued that
all motion (incl. acceleration) is only "relative". It must be noted that
the terms "absolute" and "relative" are often used with different meanings;
however, in this case there is a clear disagreement nevertheless. This led
to the "twin" or "clock" paradox.
Now, in his 1918 paper, Einstein claimed that from the perspective of a
co-moving frame, a "homogenous gravitational field comes into being" when
the rocket motors are started, under influence of which the stay-at-home
clock speeds up. He recognized the fact that to many people, his "induced
gravitational fields" are pure fiction, and it may be worth to discuss his
arguments for the physical reality of those fields (as for me, I don't buy
it!).
According to Einstein, "the calculation shows that this speeding up
constitutes exactly twice as much as the lagging behind during the partial
processes 2 and 4." Indeed, later authors such as Moller and also Builder
(1957, "The resolution of the clock paradox", Aus J. P. and 1958(?) Am.J.P.)
confirmed that calculation. However, Builder stressed that this was to be
expected: the imagined gravitational field was *designed* to have that
effect (based on the equivalence principle); so that he argued that the use
of GRT only makes for a circular argument that "can contribute nothing of
physical significance".
Builder made another remark that is pertinent IMO: according to him, "the
specified field would have to be created simultaneously at all points in S'
and be destroyed simultaneously at all points in S0."
Obviously that would be in contradiction with GRT, according to which fields
propagate at a speed equal to c (locally). If anyone thinks that he can show
that this issue isn't lethal for Einstein's 1918 view (Ken?) then I'm very
much interested to see it!
If I understand it correctly, also Einstein himself changed his opinion on
this issue. Although he claimed in 1918 that:
"a complete clarification of the questions you have raised can only be
attained if one envisions for the geometric-mechanical constitution of the
Universe a representation that complies with the theory. I have attempted to
do so last year, and I have reached a conception that - to my mind - is
completely satisfactory";
I am not aware of him having published such a representation. Instead, two
years afterwards (1920), he stated in his Leyden inauguration speech:
"the mechanical behaviour of a corporeal system hovering freely in empty
space depends not only on relative positions (distances) and relative
velocities, but also on its state of rotation, which physically may be taken
as a characteristic not appertaining to the system in itself. [...] what is
essential is merely that besides observable objects, another thing, which is
not perceptible, must be looked upon as real, to enable acceleration or
rotation to be looked upon as something real.
It is true that Mach tried to avoid having to accept as real something which
is not observable by endeavouring to substitute in mechanics a mean
acceleration with reference to the totality of the masses in the universe in
place of an acceleration with reference to absolute space. But inertial
resistance opposed to relative acceleration of distant masses presupposes
action at a distance; and as the modern physicist does not believe that he
may accept this action at a distance, he comes back once more, if he follows
Mach, to the ether, which has to serve as medium for the effects of
inertia."
- http://www.tu-harburg.de/rzt/rzt/it/Ether.html
I now interpret the above as indicative of a change of mind about his own
(strong) general relativity principle that he defended two years earlier.
The equivalence principle and the GRT-based theory of gravitation remained,
but apparently he had abandoned his true relativity of acceleration and its
"induced gravitational fields" at a distance that it requires. If my
interpretation is correct, then Einstein himself realised the abovementioned
problems as early as 1920.
Regards,
Harald
Ken S. Tucker
thank you for your refs to the 1918 article.
On Apr 20, 6:26 am, "harry" <harald.vanlintelButNotT...@epfl.ch>
wrote:
...
> I now interpret the above as indicative of a change of mind about his own
> (strong) general relativity principle that he defended two years earlier.
> The equivalence principle and the GRT-based theory of gravitation remained,
> but apparently he had abandoned his true relativity of acceleration and its
> "induced gravitational fields" at a distance that it requires. If my
> interpretation is correct, then Einstein himself realised the abovementioned
> problems as early as 1920.
> Regards,
> Harald
The most modern interpretation I know of the
General Principle of Relativity (GPoR), is in the
so-called Principle of General Covariance (GC),
in which any CS (Coordinate System, aka a FoR)
is valid, provided measurements made in any of
those CS's can be related to an inertial frame,
mathematically by a "proper transformation".
(FoR = Frame of Reference).
You can reverse that meaning: wherever the Laws
of Physics are valid (for any FoR subject to the Laws
of nature), GC applies.
In turn that means acceleration is subject to GC
and is therefore relative. IOW's if you get on a roller-
coaster you are subject to the laws of nature,
therefore you have a valid FoR and you can consider
yourself at "rest", in fact you must, since you are at
rest relatively to yourself, it's rather quite simple.
Rhetorically, how can "absolute motion" of any kind
exist, if you can find a FoR wherein you are at rest
relatively to yourself? IOW's you can always find an
FoR where "absolute motion" is zero.
Due to GC, relative acceleration is true throughout
the universe, since absolute acceleration vanishes
wherever the laws of nature apply.
Regards
Ken S. Tucker
eugene_st...@usa.net
> The most modern interpretation I know of the
> General Principle of Relativity (GPoR), is in the
> so-called Principle of General Covariance (GC),
> in which any CS (Coordinate System, aka a FoR)
> is valid, provided measurements made in any of
> those CS's can be related to an inertial frame,
> mathematically by a "proper transformation".
> (FoR = Frame of Reference).
The Principle of General Covariance relies on the the "principle of
equivalence", which is an assumptions that in the gravitational field
all bodies move with exactly the same acceleration. This acceleration
is supposed to be independent on
1. the composition of the system
2. the mass of the system
3. system's initial velocity.
As far as I know, points 1. and 2. have been verified by experiment
rather accurately. What about point 3? Are there experiments which
demonstrate the independence of the acceleration on the velocity. I
mean velocities comparable with the speed of light c?
Thanks.
Eugene.
Ken S. Tucker
On Apr 20, 2:36 pm, eugene_stefanov...@usa.net wrote:
> On Apr 20, 1:46 pm, "Ken S. Tucker" <dynam...@vianet.on.ca> wrote:
>
> > The most modern interpretation I know of the
> > General Principle of Relativity (GPoR), is in the
> > so-called Principle of General Covariance (GC),
> > in which any CS (Coordinate System, aka a FoR)
> > is valid, provided measurements made in any of
> > those CS's can be related to an inertial frame,
> > mathematically by a "proper transformation".
> > (FoR = Frame of Reference).
>
> The Principle of General Covariance relies on the the "principle of
> equivalence",
As I defined, my understanding of GC, there is
no need to rely on the Principle of Equivalence,
(PoE), b/c PoE results from GC.
which is an assumptions that in the gravitational field
> all bodies move with exactly the same acceleration. This acceleration
> is supposed to be independent on
>
> 1. the composition of the system
> 2. the mass of the system
> 3. system's initial velocity.
>
> As far as I know, points 1. and 2. have been verified by experiment
> rather accurately. What about point 3? Are there experiments which
> demonstrate the independence of the acceleration on the velocity. I
> mean velocities comparable with the speed of light c?
It becomes more difficult to add energy in a
particle accelerator as the particle approaches "c",
(I think you and the fella's who post to our group
know more that than I do)
Is your point (3) going to become a discussion?
> Thanks.
> Eugene.
Your Welcome, and thank you.
GC is exceptionally foundational, it's one of the
few things in theoretics I hold dear.
Best
Ken
eugene_st...@usa.net
> > ... the "principle of
> > equivalence" is an assumptions that in the gravitational field
> > all bodies move with exactly the same acceleration. This acceleration
> > is supposed to be independent on
> > .......
> > 3. system's initial velocity.
> Is your point (3) going to become a discussion?
Yes, I would like to discuss this. How well this assumption is
established in experiments? I understand, this is not directly related
to the initial posting. Perhaps I should open another thread about it?
> GC is exceptionally foundational, it's one of the
> few things in theoretics I hold dear.
General covariance is a very nice idea, which allows us to reduce
gravitational physics to an exercise in differential geometry.
However, what if acceleration does depend on velocity? Then the
principle of equivalence does not hold. And general covariance is not
valid as well.
I have my doubts about general covariance (in particular, about the
idea of equivalence between time and space coordinates) primarily
because of its apparent inconsistency with quantum mechanics.
I suggested an alternative quantum theory of gravity
http://www.arxiv.org/physics/0612019 in which the principle of
equivalence is violated (the gravitational acceleration depends on the
velocity at high values of v) but all experimental manifestations of
GR are reproduced. If someone knows an experiment that clearly
establishes the velocity-independence of the gravitational
acceleration, then I should probably withdraw my paper.
Eugene.
Oh No
>Hi Eugene and all.
>
>On Apr 20, 2:36 pm, eugene_stefanov...@usa.net wrote:
>> On Apr 20, 1:46 pm, "Ken S. Tucker" <dynam...@vianet.on.ca> wrote:
>>
>> > The most modern interpretation I know of the
>> > General Principle of Relativity (GPoR), is in the
>> > so-called Principle of General Covariance (GC),
I would prefer to call the principle of general covariance an
application of the general principle of relativity. The gpor is
essentially physical, whereas the pgc is essentially mathematical. I
would prefer to talk of the physical as being an interpretation of the
mathematical, not the other way about. In practice, the principle of
general covariance is the expression of the general principle of
relativity as used in the classical theory of general relativity, but
they are not equivalent. The general principle of relativity is more
general than general covariance, since it assumes that vector and tensor
quantities are always defined independent of measurement. I would not
expect that assumption to hold in a quantum theory, and I have relaxed
it for relational quantum gravity, such that gpor is retained while gc
is not.
>> > in which any CS (Coordinate System, aka a FoR)
Distinguish a coordinate system - i.e. a mathematical representation in
terms of R^n, from a frame of reference, the physical matter used to
determine coordinates through measurement.
>> > is valid, provided measurements made in any of
>> > those CS's can be related to an inertial frame,
>> > mathematically by a "proper transformation".
>> > (FoR = Frame of Reference).
>>
>> The Principle of General Covariance relies on the the "principle of
>> equivalence",
>
>As I defined, my understanding of GC, there is
>no need to rely on the Principle of Equivalence,
>(PoE), b/c PoE results from GC.
Indeed. The principle of equivalence may be used to define what we mean
by the "force" of gravity.
>
>which is an assumptions that in the gravitational field
>> all bodies move with exactly the same acceleration. This acceleration
>> is supposed to be independent on
>>
>> 1. the composition of the system
>> 2. the mass of the system
>> 3. system's initial velocity.
>>
>> As far as I know, points 1. and 2. have been verified by experiment
>> rather accurately. What about point 3? Are there experiments which
>> demonstrate the independence of the acceleration on the velocity. I
>> mean velocities comparable with the speed of light c?
>
If you dispense with the PoE you would also be dispensing with the
general principle of relativity. One is then getting into the area of
theories without experimental support. I would question whether that is
physics.
Regards
--
Charles Francis
moderator sci.physics.foundations.
substitute charles for NotI to email
eugene_st...@usa.net
> >> Are there experiments which
> >> demonstrate the independence of the acceleration on the velocity. I
> >> mean velocities comparable with the speed of light c?
>
> If you dispense with the PoE you would also be dispensing with the
> general principle of relativity. One is then getting into the area of
> theories without experimental support. I would question whether that is
> physics.
I don't think that "general principle of relativity" was ever directly
checked by experiment. There are experimental verifications of the
P(rinciple)o(f)E(quivalence), but it seems that all of them involve
slowly moving bodies. We cannot be sure that this principle remain
valid at high velocities. There are not so many firmly established
experimental facts in relativistic gravitational physics:
1. Mercury's perihelion precession
2. Light bending by Sun's gravity
3. Shapiro time delay
4. Gravitational time dilation
5. Gravitational red shift.
.....
If a theory can explain these 5 facts, then it has a chance to compete
with G(eneral)R(elativity).
The theory I proposed does explain these facts. As a bonus, this
theory is fully consistent with quantum mechanics.
Eugene.
Oh No
If you dispense with the idea that the laws of physics are everywhere
the same then you may as well say anything you like and propose it as
physical law. I am not interested in such theories. There is no
experiment which shows magic is not possible. You may as well explain
your five fact by magic. That is essentially what you are doing when you
deny the idea that there is an underling reality beyond experiment. I
don't think this is physics.
Oh No
>http://en.wikisource.org/wiki/Dialog_about_objections_against_the_theor
>y_of_relativity
>
>Einstein's 1918 paper provides so much food for thought, that on
>purpose I postpone a discussion of the arguments to a later posting
>which will include more counter arguments that were presented by others
>and, surprisingly, even by Einstein himself.
>
form, forces an ether concept. I don't think this represents the full
depth of his thinking in the matter. In fact I think he saw this as a
problem with general relativity, both in the years prior to publication,
and subsequently. There is some discussion of his difficulties prior to
finalising the theory here
http://plato.stanford.edu/entries/spacetime-holearg/
In my view this boils down to a problem with the affine connection.
According to the notion of an affine connection, spacetime is defined
such that an origin of coordinates can be defined anywhere in a
continuous manifold. This has lead to a view that a substantivalist
manifold is required, which I think is broadly equivalent to Einstein's
ether concept expressed in the paper you cite. But this is clearly a
non-empirical assumption and it is one which runs against the
philosophies which Einstein used to develop special relativity. Einstein
continued to have problems with it and later developed the idea of a
remote, or teleparallel, connection
http://www.lrz-muenchen.de/~aunzicker/ae1930.html
Einstein did not make much headway with teleparallelism, but I think
this is in large part because he could not get quantum theory on board.
One man can only do so much. I actually came to a similar idea
independently. I had serious problems with the affine connection when I
was learning general relativity because I could not see its empirical
basis. I came to the notion of a teleconnection by studying the
philosophical foundations of quantum theory and attempting to build a
model according to foundational considerations and applying as much
rigour as I felt able. It is natural then to consider what happens when
initial and final quantum states are determined in different reference
frames. This lead to a different application of teleparallelism from
that of Einstein, and I think it resolves the problems.
eugene_st...@usa.net
> If you dispense with the idea that the laws of physics are everywhere
> the same then you may as well say anything you like and propose it as
> physical law.
On the contrary, I accept the idea that the laws of physics are the
same everywhere. This is called "translational invariance", and it is
a part of the Poincare group - based approach, which I am trying to
promote.
> I am not interested in such theories. There is no
> experiment which shows magic is not possible. You may as well explain
> your five fact by magic. That is essentially what you are doing when you
> deny the idea that there is an underling reality beyond experiment. I
> don't think this is physics.
I don't deny the idea of "underlying reality". I rather remain
agnostic about it. It is difficult enough to formulate a self-
consistent mathematical theory that explains all facts in "observable
reality" (which is, by the way, physics, in my understanding). So, the
"underlying reality" can wait.
Eugene.
Oh No
>On Apr 21, 1:19 am, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
>
>> If you dispense with the idea that the laws of physics are everywhere
>> the same then you may as well say anything you like and propose it as
>> physical law.
>
>On the contrary, I accept the idea that the laws of physics are the
>same everywhere. This is called "translational invariance", and it is a
>part of the Poincare group - based approach, which I am trying to
>promote.
It is difficult to understand the meaning of the Poincare group in a
curved space-time.
harald.v...@epfl.ch
Hi Ken, as I stated, I regard Builder's argument againt Einstein's
dynamic "gravitational fields" as pertinent and lethal to that idea.
It was natural for Builder to discover this, as he first made a full
calculation in SRT that included Doppler shifts. As far as I can see
he was roughly correct with his calculation, but actually
underestimated the problem.
For if I'm not mistaken, when taking a very large distance between the
two clocks, even with a (forbidden!) instantaneously propagating
gravitational (pseudo-) field, radio waves that are emitted from the
stay-at-home cannot correctly Doppler shift at the traveller,
immediately after he activates his rockets. Thus, not only is
relativity of gravitational fields conceptually flawed due to a
complete neglect of causality, but even mathematically it only works
at a very superficial level.
I also brought this problem up a few years ago in the relativity
group, see
http://tinyurl.com/2mu4jv
At that time you also participated in that thread, but just ashere,
you did not respond to the main issue (unlike Tom Roberts). If it is
not clear what I'm talking about, I can expand on it with a sketch.
Regards,
Harald
Oh No
>Hi Ken, as I stated, I regard Builder's argument againt Einstein's
>dynamic "gravitational fields" as pertinent and lethal to that idea.
>It was natural for Builder to discover this, as he first made a full
>calculation in SRT that included Doppler shifts. As far as I can see
>he was roughly correct with his calculation, but actually
>underestimated the problem.
>For if I'm not mistaken, when taking a very large distance between the
>two clocks, even with a (forbidden!) instantaneously propagating
>gravitational (pseudo-) field, radio waves that are emitted from the
>stay-at-home cannot correctly Doppler shift at the traveller,
>immediately after he activates his rockets. Thus, not only is
>relativity of gravitational fields conceptually flawed due to a
>complete neglect of causality, but even mathematically it only works
>at a very superficial level.
>
I am not clear what the problem is. General relativity is a local
theory. The principle of equivalence describes gravity locally as an
inertial force. I don't understand what you mean by relativity of
gravitational fields. I don't even know that it is meaningful to talk of
a gravitational field, except within a locally defined reference frame.
Ken S. Tucker
> On Apr 20, 5:17 pm, "Ken S. Tucker" <dynam...@vianet.on.ca> wrote:
>
> > > ... the "principle of
> > > equivalence" is an assumptions that in the gravitational field
> > > all bodies move with exactly the same acceleration. This acceleration
> > > is supposed to be independent on
> > > .......
> > > 3. system's initial velocity.
> > Is your point (3) going to become a discussion?
>
> Yes, I would like to discuss this. How well this assumption is
> established in experiments? I understand, this is not directly related
> to the initial posting. Perhaps I should open another thread about it?
"another thread", that's up to you, the OP and the
moderators.
The perihelion shift depends on *orbital velocity* so
your (Eugene's) point (3) is true. I can provide details,
most good GR books will provide that dependence.
This is topical since the GP-b team announced the
confirmation of that as the so-called "geodetic effect",
where the force used for the calculation is a slight
modification to the Newtonian Force "F" to get,
f = F*(1 - V(orbital)^2 / c^2) = true force.
> > GC is exceptionally foundational, it's one of the
> > few things in theoretics I hold dear.
>
> General covariance is a very nice idea, which allows us to reduce
> gravitational physics to an exercise in differential geometry.
AE's GR1916 assumed a continuum, but
his Eq.(65..66) set Lorentz force to zero,
which IMV sets-up the Quantum Theory.
> However, what if acceleration does depend on velocity? Then the
> principle of equivalence does not hold. And general covariance is not
> valid as well.
I think we need a mathematical thread.
I'll snip the rest agreeably...
Regards
Ken
Ken S. Tucker
>
> >Hi Eugene and all.
>
> >On Apr 20, 2:36 pm, eugene_stefanov...@usa.net wrote:
> >> On Apr 20, 1:46 pm, "Ken S. Tucker" <dynam...@vianet.on.ca> wrote:
>
> >> > The most modern interpretation I know of the
> >> > General Principle of Relativity (GPoR), is in the
> >> > so-called Principle of General Covariance (GC),
>
> I would prefer to call the principle of general covariance an
> application of the general principle of relativity. The gpor is
> essentially physical, whereas the pgc is essentially mathematical. I
> would prefer to talk of the physical as being an interpretation of the
> mathematical, not the other way about. In practice, the principle of
> general covariance is the expression of the general principle of
> relativity as used in the classical theory of general relativity, but
> they are not equivalent. The general principle of relativity is more
> general than general covariance, since it assumes that vector and tensor
> quantities are always defined independent of measurement. I would not
> expect that assumption to hold in a quantum theory, and I have relaxed
> it for relational quantum gravity, such that gpor is retained while gc
> is not.
Understood, to disect that issue I'll use a scalpel.
The Absolute Derivative of the metric tensor,
D g_uv = 0.
((IOW,s g_uv;w dx^w =0)).
IMHO that equation is under-respected,
let me explain why.
If one can transform a set of measurements from
an accelerating FoR to an inertial FoR, then we'll
find D g_uv =0 in the free-falling "inertial FoR".
( That's the basic PoE too).
(the ordinary differentials like dg_uv vary by using
different FoR's and CS's.)
So I suppose I should ask my fellow collegues,
(Especially Charles and Eugene)
does D g_uv =0 hold in your theories?
Best regards...
Ken
PS: I'm setting a trap.
eugene_st...@usa.net
> This is topical since the GP-b team announced the
> confirmation of that as the so-called "geodetic effect",
> where the force used for the calculation is a slight
> modification to the Newtonian Force "F" to get,
>
> f = F*(1 - V(orbital)^2 / c^2) = true force.
This sounds troubling to me. When I ride in an accelerating elevator,
all objects around me have the same acceleration independent on their
velocity. According to the principle of equivalence we should expect
the same for objects moving under the force of gravity: their
acceleration should not depend on their velocity. Am I missing
something?
Eugene.
eugene_st...@usa.net
> >On the contrary, I accept the idea that the laws of physics are the
> >same everywhere. This is called "translational invariance", and it is a
> >part of the Poincare group - based approach, which I am trying to
> >promote.
>
> It is difficult to understand the meaning of the Poincare group in a
> curved space-time.
Poincare transformations are applied to the system as a whole (e.g.,
the Solar system). Whatever is the mechanism of interaction within the
system (space-time curvature or anything else) this interaction must
remain the same independent on the system's position in space,
orientation, time, and total velocity. So, the Poincare group remains
a valid concept even within Einsteinian theory of gravity.
Eugene.
eugene_st...@usa.net
> So I suppose I should ask my fellow collegues,
> (Especially Charles and Eugene)
> does D g_uv =0 hold in your theories?
I don't use 4D tensor notation (metric tensor, etc.) at all, because I
do not believe in the Einstein-Minkowski "symmetry" between space and
time coordinates. In quantum mechanics, position is a quantum-
mechanical operator while time is an external parameter. Boost
transformations of particle's position have simple Lorentz-like form
only if the particle does not interact with anything. For interacting
systems, Lorentz transformations are valid only approximately. So, the
idea of 4D Minkowski space-time is just an approximation.
Eugene.
Oh No
whatsoever.
Oh No
I think you are missing that this acceleration is not defined in a
sufficiently local reference frame. That is true for the inverse square
law anyway, where F depends on position.
Oh No
>On Apr 20, 11:58 pm, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
>
>The Absolute Derivative of the metric tensor,
>
>D g_uv = 0.
>
>((IOW,s g_uv;w dx^w =0)).
>
>IMHO that equation is under-respected,
>let me explain why.
I think the reason is that it is not true. At any rate, allowing for
ASCII, I cannot think of a true equation which looks a bit like this.
>
>If one can transform a set of measurements from
>an accelerating FoR to an inertial FoR, then we'll
>find D g_uv =0 in the free-falling "inertial FoR".
>( That's the basic PoE too).
>
>(the ordinary differentials like dg_uv vary by using
>different FoR's and CS's.)
>
>So I suppose I should ask my fellow collegues,
>(Especially Charles and Eugene)
>does D g_uv =0 hold in your theories?
Exactly the same formulae hold in the teleconnection theory as in
classical gtr, up to the connection itself.
>
>Best regards...
>Ken
>PS: I'm setting a trap.
>
Ken S. Tucker
> Thus spake Ken S. Tucker <dynam...@vianet.on.ca>
>
> >On Apr 20, 11:58 pm, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
>
> >The Absolute Derivative of the metric tensor,
>
> >D g_uv = 0.
>
> >((IOW,s g_uv;w dx^w =0)).
>
> >IMHO that equation is under-respected,
> >let me explain why.
>
> I think the reason is that it is not true. At any rate, allowing for
> ASCII, I cannot think of a true equation which looks a bit like this.
Yeah ASCII is a problem, see the "vanishing of the
covariant derivative of the metric" here.
http://en.wikipedia.org/wiki/Christoffel_symbol#Definition
I should have written it as g_uv;w = 0.
> >If one can transform a set of measurements from
> >an accelerating FoR to an inertial FoR, then we'll
> >find D g_uv =0 in the free-falling "inertial FoR".
> >( That's the basic PoE too).
>
> >(the ordinary differentials like dg_uv vary by using
> >different FoR's and CS's.)
>
> >So I suppose I should ask my fellow collegues,
> >(Especially Charles and Eugene)
> >does D g_uv =0 hold in your theories?
>
> Exactly the same formulae hold in the teleconnection theory as in
> classical gtr, up to the connection itself.
Good, if g_uv;w =/=0 math get's complicated.
Thanks Charles
Sorry for the bad notation.
Ken
Oh No
I should have recognised it, but sometimes things just don't fall into
place.
harald.v...@epfl.ch
> Thus spake harald.vanlin...@epfl.ch
Einstein's relativity of gravitational fields is directly related to
his relativity of acceleration, as he explained rather well in his
1918 article that this thread discusses. Note: I could copy-paste his
article in this thread (and I originally had in mind to do so!), but
instead, I count on everyone who participates here to have clicked on
the link I provided and studied Einstein's solution of the clock
paradox before reading my comments on that. Here it is again:
http://en.wikisource.org/wiki/Dialog_about_objections_against_the_theory_of_relativity
Einstein's solution from the traveller's perspective was far from
"local": instead, it consisted of homogeneous "induced gravitational
fields" that are supposed to act over astronomical distances. Here
below I wil paste back the comments that I wrote in this thread as
well as some of the comments by myself and Tom Roberts to which I
referred, and I'll add a few more clarifications and a sketch for more
clarity.
In his 1918 paper, Einstein claimed that from the perspective of a co-
moving frame, a "homogenous gravitational field comes into being" when
the rocket motors are started, under influence of which the stay-at-
home clock speeds up.
IMO, relativity of acceleration as based on relativity of
gravitational fields is conceptually flawed due to a complete neglect
of causality. But I think that we even don't need to discuss that,
because also mathematically the paradox messes up with Einstein's 1916
point of view.
According to Einstein, "the calculation shows that this speeding up
constitutes exactly twice as much as the lagging behind during the
partial processes 2 and 4."
Indeed, later authors such as Moller and also Builder (1957, "The
resolution of the clock paradox", Aus J.P. and 1959, Am.J.P.)
confirmed that calculation, and many people stop thinking at that
point.
However, Builder made another remark that is pertinent IMO. According
to him, "the specified field would have to be created simultaneously
at all points in S' and be destroyed simultaneously at all points in
S0."
Obviously that would be in contradiction with GRT, according to which
fields propagate at a speed equal to c (locally).
As I stated, I regard Builder's argument againt Einstein's dynamic
"gravitational fields" (from the perspective of the traveller) as
pertinent and lethal to Einstein's idea. It was natural for Builder to
discover this, as he first made a full calculation in SRT that
included Doppler shifts. As far as I can see he was roughly correct
with his calculation, but actually underestimated the problem.
If I'm not mistaken, when taking a very large distance between the two
clocks, even with a (forbidden!) instantaneously propagating
gravitational (pseudo-) field that originates from C2, radio pulses
that are emitted from C1 (the stay-at-home) cannot correctly Doppler
shift at C2 (the traveller), immediately after its rockets are fired.
Looking at the problem in 2D instead of in 1D, we obtain the following
picture with another clock C12 aligned at a far distance to the side
of C1, "when" the rockets of C2 fire for the turn-around and with
signals sent from the stay-at-home clocks towards the traveller:
C1 C12 [higher "gravitational potential"]
Ś /
Ś /
Ś / [distance of for example 1 light day]
Ś /
Ś/
C2 [firing its rockets]
Here clock C12 must accelerate synchronously with clock C1, and radio
pulses that are emitted from C1 as well as C12 must immediately
Doppler shift at C2 when the rockets of C2 fire. Obviously that cannot
work.
Thus, even mathematically Einstein's solution only works at a very
superficial level. As soon as one looks at it in more detail, it turns
out to be unworkable.
I also brought this problem up a few years ago in the relativity
group, see http://tinyurl.com/2mu4jv .
There, Tom Roberts was more outspoken than me, calling Einstein's
solution of the clock paradox "Mathematical magic":
"This is magic invoked by Stella to "explain" how she can remain
motionless in spite of turning on her thrusters. It is no real
"gravitational force", it is mathematical magic invented by Stella --
analogous to "centrifugal force" in Newtonian mechanics: when one
starts
rotating, the "centrifugal force" must turn on INSTANTLY throughout
the
universe; it, too, is mathematical magic invented by the rotating
observer to maintain the fiction that in the rotating coordinates
Newton's laws remain valid."
I fully agree with that, and thus I also support the following
clarification by Baez in the FAQ:
" So modern usage demotes the uniform "gravitational" field back to
its old status as a pseudo-field, with all the pejorative connotations
of the prefix "pseudo". "
- http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/SR/TwinParadox/twin_gr.html
Of course, as I said before, if anyone thinks that he can show that
this issue isn't lethal for Einstein's 1918 view about relativity of
acceleration and gravitational fields, then I'm very much interested
to see it!
Best regards,
Harald
Oh No
>
>In his 1918 paper, Einstein claimed that from the perspective of a co-
>moving frame, a "homogenous gravitational field comes into being" when
>the rocket motors are started, under influence of which the stay-at-
>home clock speeds up.
>
>IMO, relativity of acceleration as based on relativity of
>gravitational fields is conceptually flawed due to a complete neglect
>of causality.
I don't think causality has anything to do with it. This is an illusory
field brought about by a coordinate choice, not a physical field. The
point of the equivalence principle is that any gravitational field is
likewise illusory in the sense of it being a force field.
>
>According to Einstein, "the calculation shows that this speeding up
>constitutes exactly twice as much as the lagging behind during the
>partial processes 2 and 4."
>Indeed, later authors such as Moller and also Builder (1957, "The
>resolution of the clock paradox", Aus J.P. and 1959, Am.J.P.)
>confirmed that calculation, and many people stop thinking at that
>point.
>
>However, Builder made another remark that is pertinent IMO. According
>to him, "the specified field would have to be created simultaneously
>at all points in S' and be destroyed simultaneously at all points in
>S0."
As I have said, that is the choice of coordinates too. If one defines
coordinates from the radar method then the field does not appear
simultaneously, but forward and back along the light cone from the point
of accelerations.
>Obviously that would be in contradiction with GRT, according to which
>fields propagate at a speed equal to c (locally).
Possibly Builder's analysis may actually be wrong. I don't know if he
has used a physically defined set of coordinates, as given by radar. Of
course you can choose coordinates in which light speed is not c in gtr,
so this isn't necessarily a contradiction with gtr.
>As I stated, I regard Builder's argument againt Einstein's dynamic
>"gravitational fields" (from the perspective of the traveller) as
>pertinent and lethal to Einstein's idea. It was natural for Builder to
>discover this, as he first made a full calculation in SRT that
>included Doppler shifts. As far as I can see he was roughly correct
>with his calculation, but actually underestimated the problem.
I think the problem is in thinking that gravity is an active force. It
isn't.
>
>
>Thus, even mathematically Einstein's solution only works at a very
>superficial level. As soon as one looks at it in more detail, it turns
>out to be unworkable.
I don't agree that it is unworkable, but it is superficial in the sense
that gravitational fields are not real force fields.
>
>I also brought this problem up a few years ago in the relativity
>group, see http://tinyurl.com/2mu4jv .
>There, Tom Roberts was more outspoken than me, calling Einstein's
>solution of the clock paradox "Mathematical magic":
That is a good description.
>
>"This is magic invoked by Stella to "explain" how she can remain
>motionless in spite of turning on her thrusters. It is no real
>"gravitational force", it is mathematical magic invented by Stella --
>analogous to "centrifugal force" in Newtonian mechanics: when one
>starts
>rotating, the "centrifugal force" must turn on INSTANTLY throughout
>the
>universe; it, too, is mathematical magic invented by the rotating
>observer to maintain the fiction that in the rotating coordinates
>Newton's laws remain valid."
>
>I fully agree with that, and thus I also support the following
>clarification by Baez in the FAQ:
>
>" So modern usage demotes the uniform "gravitational" field back to
>its old status as a pseudo-field, with all the pejorative connotations
>of the prefix "pseudo". "
>- http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/SR/TwinParad
>ox/twin_gr.html
>
>Of course, as I said before, if anyone thinks that he can show that
>this issue isn't lethal for Einstein's 1918 view about relativity of
>acceleration and gravitational fields, then I'm very much interested
>to see it!
I am less interested in Einstein's view at a particular time than in the
physics. I would not want to say what his view really was if I could not
get inside his head.
Andrea Croci
"Oh No" <No...@charlesfrancis.wanadoo.co.uk> wrote in message
news:3YO3F7DN...@charlesfrancis.wanadoo.co.uk...
If I'm not mistaken, in a certain reference frame, the coordinate
acceleration (a=d^2x/dt^2) should go to zero as time goes by, otherwise the
object would surpass the velocity of light sooner or later. That means that
the acceleration actually does depend on the (coordinate) velocity, right?
(This "coordinate" characterization is obviously essential here, since we
are dealing with "relative" concepts, so one must always specify: velocity
and acceleration with respect to whom.)
Regards, Andrea.
CarlBrannen
I think you are right about Poincare invariance applying as a global
transformation to any set of charts, (uh providing that the charts
are flat at infinity as would be appropriate in things smaller than
cosmology). The Poincare transformation on the flat space
can be continued on to all the other charts (where it has
no effect under the usual assumptions of GR of course).
And you are right about QM treating time different
from space and this being a strong clue incompatible
with GR.
As far as showing that GR is incompatible with QM, the best
things I've seen recently are the evidence for black holes having
a violation of the spin statistics theorem for spin-0 and spin-2
(Higgs and graviton) Hawking radiation. See
http://www.arxiv.org/abs/gr-qc/0212096 for the "tripled Pauli
statistics". A discussion is here:
http://www.physicsforums.com/showthread.php?t=164471
The spin statistics theorem is amazingly complicated. It
is a "theorem" only in the sense that a mathematics theorem
depends on its assumptions. Since humanity has access to
absolutely no measurements that are exact, extended over
all space, have duration equal to the age of the universe,
or probe distances infinitely small, there are no experimental
observations that have been proven exact.
Furthermore, it is widely accepted that QM and GR do not
marry up very well. In such a circumstance, that is where
the postulates contradict one another, one expects that as
a matter of probability, blatant errors will show up in sufficiently
complicated "theorems", while sufficiently simple "theorems"
will be fully consistent with observations.
If one wishes to avoid the very large number of assumptions
built into the spin statistics theorem (for a list, read the
book "Spin, Statistics, and all that"), one can simply suppose
that all normal matter is composite and built from spin-1/2
objects that have Fermi statistics. Spin - statistics then
follows.
This is far simpler than the route physics has taken, and it
is also compatible with the above GR evidence that there exist
spin-0 and spin-2 objects that have Fermi statistics.
The other half to this is recent evidence that dark matter and
dark energy do not obey the virial theorem, but have the same
factor of 3 error. See http://arxiv.org/abs/astro-ph/0703462
for the paper. I had difficulty explaining why this comes about
and had to write a long discussion of it in Matt's blog here
(which you are of course welcome to join):
http://matpitka.blogspot.com/2007/04/new-strange-finding-about-dark-matter.html
Also, I love your dressed particle approach. I'm working on a
non perturbational version of this. The usual perturbation
theory ignores very complicated Feynman diagrams because
the simple ones dominate. With a bound state, one cannot
ignore very complicated Feynman diagrams and so the usual
perturbation theory does not work.
However, one can solve a sort of dual problem, where one
ignores the very simple Feynman diagrams and pays
attention only to the very complicated ones. The method
for this is given in section 5 page 24 of this unfinished paper:
http://www.brannenworks.com/dmfound.pdf
The method amounts to looking at the bound state with
long time delays (and therefore complicated Feynman
diagrams only), and where one assumes that all the
important Feynman diagrams are "composite", that is,
can be written as the time ordered product of simpler
Feynman diagrams. Thus one ignores the "prime"
diagrams that figure so importantly in the usual perturbation
theory.
Keep up the posting, not everyone who reads your stuff
disagrees with you.
Carl Brannen
harry
"Ken S. Tucker" <dyna...@vianet.on.ca> wrote in message
news:1177097853.9...@l77g2000hsb.googlegroups.com...
> Hi Harald, and all
> thank you for your refs to the 1918 article.
>
> On Apr 20, 6:26 am, "harry" <harald.vanlintelButNotT...@epfl.ch>
> wrote:
> ...
>> I now interpret the above as indicative of a change of mind about his own
>> (strong) general relativity principle that he defended two years earlier.
>> The equivalence principle and the GRT-based theory of gravitation
>> remained,
>> but apparently he had abandoned his true relativity of acceleration and
>> its
>> "induced gravitational fields" at a distance that it requires. If my
>> interpretation is correct, then Einstein himself realised the
>> abovementioned
>> problems as early as 1920.
>> Regards,
>> Harald
>
> General Principle of Relativity (GPoR), is in the
> so-called Principle of General Covariance (GC),
> is valid, provided measurements made in any of
> those CS's can be related to an inertial frame,
> mathematically by a "proper transformation".
> (FoR = Frame of Reference).
>
> You can reverse that meaning: wherever the Laws
> of Physics are valid (for any FoR subject to the Laws
> of nature), GC applies.
Hi Ken, the point was that the laws of physics are broken in Einstein's
example, see below.
> In turn that means acceleration is subject to GC
> and is therefore relative. IOW's if you get on a roller-
> coaster you are subject to the laws of nature,
> therefore you have a valid FoR and you can consider
> yourself at "rest", in fact you must, since you are at
> rest relatively to yourself, it's rather quite simple.
As Tom Roberts pointed out so correctly, one must call on magic in order for
the laws of physics to be retained in such a frame; and as I cited, even
Einstein abandoned that idea.
> Rhetorically, how can "absolute motion" of any kind
> exist, if you can find a FoR wherein you are at rest
> relatively to yourself? IOW's you can always find an
> FoR where "absolute motion" is zero.
>
> Due to GC, relative acceleration is true throughout
> the universe, since absolute acceleration vanishes
> wherever the laws of nature apply.
> Regards
> Ken S. Tucker
I don't think so; can you show that that view can correctly handle the
Doppler test for the clock paradox, as I described more specifically in a
parallel sub-thread?
Regards,
Harald
harry
> Thus spake harald.v...@epfl.ch
>>
>>In his 1918 paper, Einstein claimed that from the perspective of a co-
>>moving frame, a "homogenous gravitational field comes into being" when
>>the rocket motors are started, under influence of which the stay-at-
>>home clock speeds up.
>>
>>IMO, relativity of acceleration as based on relativity of
>>gravitational fields is conceptually flawed due to a complete neglect
>>of causality.
>
> I don't think causality has anything to do with it. This is an illusory
> field brought about by a coordinate choice, not a physical field. The
> point of the equivalence principle is that any gravitational field is
> likewise illusory in the sense of it being a force field.
I don't understand how you can claim that fields are "illusory" according to
Einstein, just after reading how he argued for the *reality* of such
fields - he was forced to do so, because of his strong desire to keep up the
relativity of physical acceleration.
>>According to Einstein, "the calculation shows that this speeding up
>>constitutes exactly twice as much as the lagging behind during the
>>partial processes 2 and 4."
>>Indeed, later authors such as Moller and also Builder (1957, "The
>>resolution of the clock paradox", Aus J.P. and 1959, Am.J.P.)
>>confirmed that calculation, and many people stop thinking at that
>>point.
>>
>>However, Builder made another remark that is pertinent IMO. According
>>to him, "the specified field would have to be created simultaneously
>>at all points in S' and be destroyed simultaneously at all points in
>>S0."
>
> As I have said, that is the choice of coordinates too. If one defines
> coordinates from the radar method then the field does not appear
> simultaneously, but forward and back along the light cone from the point
> of accelerations.
If you mean that according to GRT, gravitational fields must propagate at
speed c: that's exactly the point. Just keep in mind that the discussion is
not about coordinate acceleration but about physical effects (acceleration
vs gravitational fields) from physical causes (the firing of rockets).
>>Obviously that would be in contradiction with GRT, according to which
>>fields propagate at a speed equal to c (locally).
>
> Possibly Builder's analysis may actually be wrong. I don't know if he
> has used a physically defined set of coordinates, as given by radar. Of
> course you can choose coordinates in which light speed is not c in gtr,
> so this isn't necessarily a contradiction with gtr.
Hmm... that's besides the point. The discussion was about physical fields in
physics, when using valid coordinate systems.
>>As I stated, I regard Builder's argument againt Einstein's dynamic
>>"gravitational fields" (from the perspective of the traveller) as
>>pertinent and lethal to Einstein's idea. It was natural for Builder to
>>discover this, as he first made a full calculation in SRT that
>>included Doppler shifts. As far as I can see he was roughly correct
>>with his calculation, but actually underestimated the problem.
>
> I think the problem is in thinking that gravity is an active force. It
> isn't.
According to Einstein 1918, the stay-at-home is accelerated by the induced
gravitational field. Is that what you mean with "active force"?
>>Thus, even mathematically Einstein's solution only works at a very
>>superficial level. As soon as one looks at it in more detail, it turns
>>out to be unworkable.
>
> I don't agree that it is unworkable, but it is superficial in the sense
> that gravitational fields are not real force fields.
If you think that "induced" but "real" gravitational fields produce a
workable solution (that is, respecting the laws of physics), please do show
how the Doppler shifts in the sketched signals from the stay-at-home can be
observed by the traveller when he fires his rockets (you snipped it!). And
note that Einstein needed those fields for his defence of relativity of
acceleration.
>>I also brought this problem up a few years ago in the relativity
>>group, see http://tinyurl.com/2mu4jv .
>>There, Tom Roberts was more outspoken than me, calling Einstein's
>>solution of the clock paradox "Mathematical magic":
>
> That is a good description.
Good - we agree on the essentials!
>>"This is magic invoked by Stella to "explain" how she can remain
>>motionless in spite of turning on her thrusters. It is no real
>>"gravitational force", it is mathematical magic invented by Stella --
>>analogous to "centrifugal force" in Newtonian mechanics: when one
>>starts
>>rotating, the "centrifugal force" must turn on INSTANTLY throughout
>>the
>>universe; it, too, is mathematical magic invented by the rotating
>>observer to maintain the fiction that in the rotating coordinates
>>Newton's laws remain valid."
>>
>>I fully agree with that, and thus I also support the following
>>clarification by Baez in the FAQ:
>>
>>" So modern usage demotes the uniform "gravitational" field back to
>>its old status as a pseudo-field, with all the pejorative connotations
>>of the prefix "pseudo". "
>>- http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/SR/TwinParad
>>ox/twin_gr.html
>>
>>Of course, as I said before, if anyone thinks that he can show that
>>this issue isn't lethal for Einstein's 1918 view about relativity of
>>acceleration and gravitational fields, then I'm very much interested
>>to see it!
>
> I am less interested in Einstein's view at a particular time than in the
> physics. I would not want to say what his view really was if I could not
> get inside his head.
There's certainly no need to get into someone's head after he explained his
view and elaborated on it in very clear terms; and it happens that the cited
view was Einstein's General Relativity Theory of 1916-1918. I brought this
up because that view is still held to be correct by a number of people,
probably because for some reason the issue was swept under the carpet and
modern GRT is presented as a theory of gravitation (frame acceleration was
transferred to SRT, just as Builder suggested).
This failure of the original theory to be truly "relative" provides us with
a standard test for alternative theories: any new theory must correctly
handle the twin paradox, instead of handling it with "distorted nothingness"
(as Heaviside put it harshly).
Regards,
Harald
Oh No
>
>"Oh No" <No...@charlesfrancis.wanadoo.co.uk> wrote in message
>news:KUb4WySZ...@charlesfrancis.wanadoo.co.uk...
>> Thus spake harald.v...@epfl.ch
>>>
>>>In his 1918 paper, Einstein claimed that from the perspective of a co-
>>>moving frame, a "homogenous gravitational field comes into being" when
>>>the rocket motors are started, under influence of which the stay-at-
>>>home clock speeds up.
>>>
>>>IMO, relativity of acceleration as based on relativity of
>>>gravitational fields is conceptually flawed due to a complete neglect
>>>of causality.
>>
>> I don't think causality has anything to do with it. This is an illusory
>> field brought about by a coordinate choice, not a physical field. The
>> point of the equivalence principle is that any gravitational field is
>> likewise illusory in the sense of it being a force field.
>
>I don't understand how you can claim that fields are "illusory" according to
>Einstein, just after reading how he argued for the *reality* of such
>fields - he was forced to do so, because of his strong desire to keep up the
>relativity of physical acceleration.
>
helpful". I go along with that, in the sense that, relative to a non-
inertial frame, the field exists in a mathematical sense, in the same
way that the coriolis and centrifugal forces exist relative to a
rotating reference frame. If one doubts that these are real forces, get
on a childs roundabout. You can feel them, so they are real in that
sense. At the same time, they are inertial, i.e. not transmitted by
interactions between matter, and a product of motion relative to a
particular frame.
>>>According to Einstein, "the calculation shows that this speeding up
>>>constitutes exactly twice as much as the lagging behind during the
>>>partial processes 2 and 4."
>>>Indeed, later authors such as Moller and also Builder (1957, "The
>>>resolution of the clock paradox", Aus J.P. and 1959, Am.J.P.)
>>>confirmed that calculation, and many people stop thinking at that
>>>point.
>>>
>>>However, Builder made another remark that is pertinent IMO. According
>>>to him, "the specified field would have to be created simultaneously
>>>at all points in S' and be destroyed simultaneously at all points in
>>>S0."
>>
>> As I have said, that is the choice of coordinates too. If one defines
>> coordinates from the radar method then the field does not appear
>> simultaneously, but forward and back along the light cone from the point
>> of accelerations.
>
>If you mean that according to GRT, gravitational fields must propagate at
>speed c: that's exactly the point.
in grt gravitational fields propagate at the speed of light - this is a
speed depending on the coordinate system, and is c in a local Minkowski
frame.
> Just keep in mind that the discussion is
>not about coordinate acceleration but about physical effects (acceleration
>vs gravitational fields) from physical causes (the firing of rockets).
I don't agree. The gravitational field depends on the coordinate system.
In this case the firing of rockets means the coordinate system is not
defined in an inertial frame, hence the field.
>
>>>Obviously that would be in contradiction with GRT, according to which
>>>fields propagate at a speed equal to c (locally).
>>
>> Possibly Builder's analysis may actually be wrong. I don't know if he
>> has used a physically defined set of coordinates, as given by radar. Of
>> course you can choose coordinates in which light speed is not c in gtr,
>> so this isn't necessarily a contradiction with gtr.
>
>Hmm... that's besides the point. The discussion was about physical fields in
>physics, when using valid coordinate systems.
in gtr loads of coordinate systems are valid. If you choose a non-
inertial frame, you find non-inertial forces. Just like the coriolis and
centrifugal forces in classical mechanics, but now gravity also appears
as a non-inertial force.
>>>As I stated, I regard Builder's argument againt Einstein's dynamic
>>>"gravitational fields" (from the perspective of the traveller) as
>>>pertinent and lethal to Einstein's idea. It was natural for Builder to
>>>discover this, as he first made a full calculation in SRT that
>>>included Doppler shifts. As far as I can see he was roughly correct
>>>with his calculation, but actually underestimated the problem.
>>
>> I think the problem is in thinking that gravity is an active force. It
>> isn't.
>
>According to Einstein 1918, the stay-at-home is accelerated by the induced
>gravitational field. Is that what you mean with "active force"?
The opposite. That is what I mean by an inertial force.
>>>Thus, even mathematically Einstein's solution only works at a very
>>>superficial level. As soon as one looks at it in more detail, it turns
>>>out to be unworkable.
>>
>> I don't agree that it is unworkable, but it is superficial in the sense
>> that gravitational fields are not real force fields.
>
>If you think that "induced" but "real" gravitational fields produce a
>workable solution (that is, respecting the laws of physics), please do show
>how the Doppler shifts in the sketched signals from the stay-at-home can be
>observed by the traveller when he fires his rockets (you snipped it!). And
>note that Einstein needed those fields for his defence of relativity of
>acceleration.
I have a diagram of this somewhere in my files I think, but it is too
complicated for ASCII. The Doppler shift is not much of a problem. That
changes from red to blue at the point when the rocket is fired. Showing
the time expansion/contractions in the non-inertial frame is a little
more subtle, but quite doable. The real point is that it is an artefact
of coordinates though.
harry
> Thus spake harry <harald.vanlin...@epfl.ch>
>>http://en.wikisource.org/wiki/Dialog_about_objections_against_the_theor
>>y_of_relativity
>>
>>Einstein's 1918 paper provides so much food for thought, that on
>>purpose I postpone a discussion of the arguments to a later posting
>>which will include more counter arguments that were presented by others
>>and, surprisingly, even by Einstein himself.
>>
> I agree that Einstein did think that general relativity, in its present
> form, forces an ether concept. I don't think this represents the full
> depth of his thinking in the matter. In fact I think he saw this as a
> problem with general relativity, both in the years prior to publication,
> and subsequently. There is some discussion of his difficulties prior to
> finalising the theory here
>
> http://plato.stanford.edu/entries/spacetime-holearg/
Nice one! Thanks for the link, I had never heard of the hole argument! Only
a strange thing: to my knowledge (and in any case in 1918 and 1920),
Einstein discussed the substance of space and not of space-time which avoids
much of the problems. If anyone has his paper, I'm interested to read it (or
even just a precise reference may do)!
> In my view this boils down to a problem with the affine connection.
> According to the notion of an affine connection, spacetime is defined
> such that an origin of coordinates can be defined anywhere in a
> continuous manifold. This has lead to a view that a substantivalist
> manifold is required, which I think is broadly equivalent to Einstein's
> ether concept expressed in the paper you cite.
That paper is in the first place about the clock (or twin) paradox. But
indeed, he does mention his ether concept, and the issues are related - one
tries to come up with both a conceptual model for the physics (=metaphysics)
and a mathematical description.
> But this is clearly a
> non-empirical assumption and it is one which runs against the
> philosophies which Einstein used to develop special relativity. Einstein
> continued to have problems with it and later developed the idea of a
> remote, or teleparallel, connection
>
> http://www.lrz-muenchen.de/~aunzicker/ae1930.html
Thanks, that's an interesting approach. However, at first sight it's about
his efforts to combine EM with gravitation, and not so much about the
realtivity of motion. Which of the cited articles do you recommend for
reading, in the context of this thread?
> Einstein did not make much headway with teleparallelism, but I think
> this is in large part because he could not get quantum theory on board.
> One man can only do so much. I actually came to a similar idea
> independently. I had serious problems with the affine connection when I
> was learning general relativity because I could not see its empirical
> basis. I came to the notion of a teleconnection by studying the
> philosophical foundations of quantum theory and attempting to build a
> model according to foundational considerations and applying as much
> rigour as I felt able. It is natural then to consider what happens when
> initial and final quantum states are determined in different reference
> frames. This lead to a different application of teleparallelism from
> that of Einstein, and I think it resolves the problems.
I'm curious to see if it really works, and if so, what it means for physics.
Regards,
Harald
Oh No
>> But this is clearly a
>> non-empirical assumption and it is one which runs against the
>> philosophies which Einstein used to develop special relativity. Einstein
>> continued to have problems with it and later developed the idea of a
>> remote, or teleparallel, connection
>>
>> http://www.lrz-muenchen.de/~aunzicker/ae1930.html
>
>Thanks, that's an interesting approach. However, at first sight it's
>about his efforts to combine EM with gravitation, and not so much about
>the realtivity of motion. Which of the cited articles do you recommend
>for reading, in the context of this thread?
This is the problem. The papers are concerned with unifying EM with
gravitation. They don't go into the philosophical ideas which he may
have had. My take on that has to do with my own approach to problems
which I know he considered and ultimately did not solve. One may
summarise the problem in a similar way to his original sr paper, which
asks how to assign space and time coordinates to a point remote from a
clock. In general relativity one is concerned not just with the
coordinates, but one has to ask what is the relationship between a
coordinate system with an origin at one point and one with an origin at
a remote point. In differential geometry that relationship is called a
connection. An affine connection defines the relationship between
coordinates in the limit when the distance between origins goes to zero.
In a continuous manifold one can then slide a coordinate system from one
point to another along a path, and thus find a more distant
relationship. But, following Einsteins sr ideas this never seemed right
to me. If we want to compare a coordinate system on earth to one in
space we do so by looking at the light which passes from one to the
other. It seems to me that this physical process must be used to define
the connection.
>
>> Einstein did not make much headway with teleparallelism, but I think
>> this is in large part because he could not get quantum theory on board.
>> One man can only do so much. I actually came to a similar idea
>> independently. I had serious problems with the affine connection when I
>> was learning general relativity because I could not see its empirical
>> basis. I came to the notion of a teleconnection by studying the
>> philosophical foundations of quantum theory and attempting to build a
>> model according to foundational considerations and applying as much
>> rigour as I felt able. It is natural then to consider what happens when
>> initial and final quantum states are determined in different reference
>> frames. This lead to a different application of teleparallelism from
>> that of Einstein, and I think it resolves the problems.
>
>I'm curious to see if it really works, and if so, what it means for
>physics.
Obviously I think it works, but no math should be taken as error free
without independent checking from another qualified mathematician. That
is difficult to get. Hopefully my paper on stellar motions will be
accepted and that will get people's interest going.
What it means for physics is that local physics remains unchanged,
according to the general principle of relativity which is preserved. It
does mean that gtr and qt are unified and explains gravity as an
adjustment to qed. What it means for cosmology is more important. It
implies we are in an "Einstein preferred" closed finite universe, and no
need for exotic cold dark matter or cosmological constant, and resolves
a number of problems which have been described as a "crisis in
cosmology".
harry
Such fields only exist in mathematical sense if the related physics is
valid; however, such is not the case, except for a very limited set of
problems.
> If one doubts that these are real forces, get
> on a childs roundabout. You can feel them, so they are real in that
> sense. At the same time, they are inertial, i.e. not transmitted by
> interactions between matter, and a product of motion relative to a
> particular frame.
Sorry but that argument is based on a confusion, the force you feel in a
merry-go-round is definitely a contact force! One way to clear up the
confusion is to refer to Newton who discussed centrifugal force, while at
the same time rejecting the use of fictitious forces. This is rather well
explained in Wikipedia:
http://en.wikipedia.org/wiki/Centrifugal_force
>>>>According to Einstein, "the calculation shows that this speeding up
>>>>constitutes exactly twice as much as the lagging behind during the
>>>>partial processes 2 and 4."
>>>>Indeed, later authors such as Moller and also Builder (1957, "The
>>>>resolution of the clock paradox", Aus J.P. and 1959, Am.J.P.)
>>>>confirmed that calculation, and many people stop thinking at that
>>>>point.
>>>>
>>>>However, Builder made another remark that is pertinent IMO. According
>>>>to him, "the specified field would have to be created simultaneously
>>>>at all points in S' and be destroyed simultaneously at all points in
>>>>S0."
>>>
>>> As I have said, that is the choice of coordinates too. If one defines
>>> coordinates from the radar method then the field does not appear
>>> simultaneously, but forward and back along the light cone from the point
>>> of accelerations.
>>
>>If you mean that according to GRT, gravitational fields must propagate at
>>speed c: that's exactly the point.
>
> in grt gravitational fields propagate at the speed of light - this is a
> speed depending on the coordinate system, and is c in a local Minkowski
> frame.
Exactly. That was neglected in Einstein's discussion of the paradox.
>> Just keep in mind that the discussion is
>>not about coordinate acceleration but about physical effects (acceleration
>>vs gravitational fields) from physical causes (the firing of rockets).
>
> I don't agree. The gravitational field depends on the coordinate system.
> In this case the firing of rockets means the coordinate system is not
> defined in an inertial frame, hence the field.
Perhaps here we disagree on words...
>>>>Obviously that would be in contradiction with GRT, according to which
>>>>fields propagate at a speed equal to c (locally).
>>>
>>> Possibly Builder's analysis may actually be wrong. I don't know if he
>>> has used a physically defined set of coordinates, as given by radar. Of
>>> course you can choose coordinates in which light speed is not c in gtr,
>>> so this isn't necessarily a contradiction with gtr.
>>
>>Hmm... that's besides the point. The discussion was about physical fields
>>in
>>physics, when using valid coordinate systems.
>
> in gtr loads of coordinate systems are valid. If you choose a non-
> inertial frame, you find non-inertial forces. Just like the coriolis and
> centrifugal forces in classical mechanics, but now gravity also appears
> as a non-inertial force.
Newtonian mechanics does not permit fictitious forces. And in both cases,
whoever introduces them will have to face the consequences. Einstein fought
bravely. :-)
>>>>As I stated, I regard Builder's argument againt Einstein's dynamic
>>>>"gravitational fields" (from the perspective of the traveller) as
>>>>pertinent and lethal to Einstein's idea. It was natural for Builder to
>>>>discover this, as he first made a full calculation in SRT that
>>>>included Doppler shifts. As far as I can see he was roughly correct
>>>>with his calculation, but actually underestimated the problem.
>>>
>>> I think the problem is in thinking that gravity is an active force. It
>>> isn't.
>>
>>According to Einstein 1918, the stay-at-home is accelerated by the induced
>>gravitational field. Is that what you mean with "active force"?
>
> The opposite. That is what I mean by an inertial force.
Then that's not the problem.
>>>>Thus, even mathematically Einstein's solution only works at a very
>>>>superficial level. As soon as one looks at it in more detail, it turns
>>>>out to be unworkable.
>>>
>>> I don't agree that it is unworkable, but it is superficial in the sense
>>> that gravitational fields are not real force fields.
>>
>>If you think that "induced" but "real" gravitational fields produce a
>>workable solution (that is, respecting the laws of physics), please do
>>show
>>how the Doppler shifts in the sketched signals from the stay-at-home can
>>be
>>observed by the traveller when he fires his rockets (you snipped it!). And
>>note that Einstein needed those fields for his defence of relativity of
>>acceleration.
>
> I have a diagram of this somewhere in my files I think, but it is too
> complicated for ASCII. The Doppler shift is not much of a problem. That
> changes from red to blue at the point when the rocket is fired. Showing
> the time expansion/contractions in the non-inertial frame is a little
> more subtle, but quite doable. The real point is that it is an artefact
> of coordinates though.
According to Einstein-1918 it's not an artefact but as "real" as any other
field in physics - for if it were an artefact, it could not be physical and
acceleration would be "absolute", as he denied then but admitted in 1920.
Again, the situation of Einstein's 1918 theory is the following: the
traveller fires his rockets, thus inducing a homogeneous gravitational field
that upon reaching the very distant stay-at-home, causes the stay-at home
(as well as other clocks at a far distance next to it) to accelerate towards
the traveller. Signals that are consecutively sent from the stay-at-home (as
well as from other clocks) will be Doppler-shifted when these reach the
traveller, and we can estimate how long after firing the rockets this
Doppler shifted signal will arrive at the traveller, from the traveller's
point of view. However, we know that all the received signals will be
Doppler shifted immediately after the traveller fires his rockets.
Note that for v<0.1c, the shift is roughly equal to the classical Doppler
shift; in fact, the error is most obvious for even lower speeds while
maintaining large distances as then the signal propagation time is the most
important factor to take into account.
Regards,
Harald
Oh No
>
>"Oh No" <No...@charlesfrancis.wanadoo.co.uk> wrote in message
>news:asDG$OMU2K...@charlesfrancis.wanadoo.co.uk...
>> Thus spake harry <harald.vanlin...@epfl.ch>
>>>
>> helpful". I go along with that, in the sense that, relative to a non-
>> inertial frame, the field exists in a mathematical sense, in the same
>> way that the coriolis and centrifugal forces exist relative to a
>> rotating reference frame.
>
>Such fields only exist in mathematical sense if the related physics is
>valid; however, such is not the case, except for a very limited set of
>problems.
A field exists in a mathematical sense if it is defined as a function on
R^n. That says nothing of physical existence.
>
>> If one doubts that these are real forces, get
>> on a childs roundabout. You can feel them, so they are real in that
>> sense. At the same time, they are inertial, i.e. not transmitted by
>> interactions between matter, and a product of motion relative to a
>> particular frame.
>
>Sorry but that argument is based on a confusion, the force you feel in a
>merry-go-round is definitely a contact force!
Depends on how you think of it. If you move you will feel a sideways
force. That is not a contact force.
>One way to clear up the
>confusion is to refer to Newton who discussed centrifugal force, while at
>the same time rejecting the use of fictitious forces.
Fictitious forces were invented by Huygens I believe. There is nothing
wrong with them. They are defined by mass x acceleration relative to a
given coordinate system. It is important to understand them in order to
understand gravity.
>> in gtr loads of coordinate systems are valid. If you choose a non-
>> inertial frame, you find non-inertial forces. Just like the coriolis and
>> centrifugal forces in classical mechanics, but now gravity also appears
>> as a non-inertial force.
>
>Newtonian mechanics does not permit fictitious forces.
It certainly does, according to the definition
F = ma
They are forces relativity to a coordinate system.
>And in both cases,
>whoever introduces them will have to face the consequences. Einstein fought
>bravely. :-)
I think I disagree about the message of the equivalence principle.
Einstein showed gravity as a fictitious force, i.e. a force relative to
a coordinate system. His language was different though. If force is
defined as F = ma, then a "fictitious" force is "real". But like he
said, this language is unhelpful.
>
>
>>>>>Thus, even mathematically Einstein's solution only works at a very
>>>>>superficial level. As soon as one looks at it in more detail, it turns
>>>>>out to be unworkable.
>>>>
>>>> I don't agree that it is unworkable, but it is superficial in the sense
>>>> that gravitational fields are not real force fields.
>>>
>>>If you think that "induced" but "real" gravitational fields produce a
>>>workable solution (that is, respecting the laws of physics), please do
>>>show
>>>how the Doppler shifts in the sketched signals from the stay-at-home can
>>>be
>>>observed by the traveller when he fires his rockets (you snipped it!). And
>>>note that Einstein needed those fields for his defence of relativity of
>>>acceleration.
>>
>> I have a diagram of this somewhere in my files I think, but it is too
>> complicated for ASCII. The Doppler shift is not much of a problem. That
>> changes from red to blue at the point when the rocket is fired. Showing
>> the time expansion/contractions in the non-inertial frame is a little
>> more subtle, but quite doable. The real point is that it is an artefact
>> of coordinates though.
>
>According to Einstein-1918 it's not an artefact but as "real" as any other
>field in physics
I think that is probably because he was using the mathematical notion of
"real", i.e. the equations are satisfied, not that there is something
ontologically there. As he said, discussion of "reality" in that sense
is unhelpful.
Ken S. Tucker
Harald, you've stated above two contradictory statements.
1) You do not understand tensor notation.
2) You find GR mathematics superficial.
The legalese of GR is written in tensor analysis.
The analogies, like the elevator experiment, are
indeed superficial extentions of the mathematical
theory of GR, (GToR), but to turn around and use
those to disect GToR or it's Principles is trouble.
I got "whomped" for over-use of analogies in HS,
in explaining GR. Looking back it was a good thing,
because I went on to learn Vector Analysis and it's
Calculus then Curvilinear CS's and Tensor Analysis.
If the moderators will permit, I'd be happy to use
some analogies to support my point of view, that's
fine with me.
Regards
Ken
On Apr 23, 6:19 am, "harry" <harald.vanlintelButNotT...@epfl.ch>
wrote:
> "Ken S. Tucker" <dynam...@vianet.on.ca> wrote in messagenews:1177097853.9...@l77g2000hsb.googlegroups.com...
======================================= MODERATOR'S COMMENT:
Top posting is ok, leaving so much unsnipped is not. Go ahead with the analogies.
harald.v...@epfl.ch
> Thus spake harry <harald.vanlintelButNotT...@epfl.ch>
>
>
>
> >"Oh No" <N...@charlesfrancis.wanadoo.co.uk> wrote in message
> >news:asDG$OMU2K...@charlesfrancis.wanadoo.co.uk...
> >> Thus spake harry <harald.vanlintelButNotT...@epfl.ch>
>
> >> Actually, what he said was that "the distinction real-unreal is hardly
> >> helpful". I go along with that, in the sense that, relative to a non-
> >> inertial frame, the field exists in a mathematical sense, in the same
> >> way that the coriolis and centrifugal forces exist relative to a
> >> rotating reference frame.
>
> >Such fields only exist in mathematical sense if the related physics is
> >valid; however, such is not the case, except for a very limited set of
> >problems.
>
> A field exists in a mathematical sense if it is defined as a function on
> R^n. That says nothing of physical existence.
Physical existence or non-existence is hard to show and debatable, but
mathematical non-existence as part of a theory is easier to show. If
it conflicts with the theory, it can't mathematically exist as part of
it.
> >> If one doubts that these are real forces, get
> >> on a childs roundabout. You can feel them, so they are real in that
> >> sense. At the same time, they are inertial, i.e. not transmitted by
> >> interactions between matter, and a product of motion relative to a
> >> particular frame.
>
> >Sorry but that argument is based on a confusion, the force you feel in a
> >merry-go-round is definitely a contact force!
>
> Depends on how you think of it. If you move you will feel a sideways
> force. That is not a contact force.
Please indicate where you snipped some of my text... by chance(?),
here you snipped my explanation with the link that explains what is
erroneous about that statement...
> >One way to clear up the
> >confusion is to refer to Newton who discussed centrifugal force, while at
> >the same time rejecting the use of fictitious forces.
>
> Fictitious forces were invented by Huygens I believe. There is nothing
> wrong with them. They are defined by mass x acceleration relative to a
> given coordinate system. It is important to understand them in order to
> understand gravity.
Hmm... I have no use for fiction or magic!
> >> in gtr loads of coordinate systems are valid. If you choose a non-
> >> inertial frame, you find non-inertial forces. Just like the coriolis and
> >> centrifugal forces in classical mechanics, but now gravity also appears
> >> as a non-inertial force.
>
> >Newtonian mechanics does not permit fictitious forces.
>
> It certainly does, according to the definition
>
> F = ma
Actually, it's F = d(mv)/dt and it describes the force of inertia. Of
course, if according to your definition, Newton's postulated physical
space is fiction, then inertia may be fiction too and the force you
feel is just fantasy. However, the force you feel is a contact force
that can be measured using Hooke's law. :-)
> They are forces relativity to a coordinate system.
>
> >And in both cases,
> >whoever introduces them will have to face the consequences. Einstein fought
> >bravely. :-)
>
> I think I disagree about the message of the equivalence principle.
> Einstein showed gravity as a fictitious force, i.e. a force relative to
> a coordinate system. His language was different though. If force is
> defined as F = ma, then a "fictitious" force is "real". But like he
> said, this language is unhelpful.
>
Indeed, metaphysical language is tricky. Therefore, instead I
approached the problem from another angle by showing that Einstein's
1918 solution even fails mathematically, as soon as one digs a little
deeper.
[...]
Cheers,
Harald
harald.v...@epfl.ch
> Hi Harald and all, permit me a top post.
> Harald, you've stated above two contradictory statements.
> 1) You do not understand tensor notation.
> 2) You find GR mathematics superficial.
Hi Ken,
In fact I must disagree with your top posting, for it leads to errors:
I certainly didn't state that I find GR mathematics superficial!
Instead I pointed out - as also acknowledged by Tom Roberts - that
Einstein used mathematical magic in his claimed solution of the clock
paradox (and I equally doubt that he finds GR mathematics
superficial).
What I did show, elaborating on Builder's rejection, is that such
magic has its limits so that when one examines it more closely, it
doesn't really work at all - as was confirmed to me in the relativity
group three years ago. And below once more I kindly invited you to
show, if you disagree, how it does work:
> > I don't think so; can you show that that view can correctly handle the
> > Doppler test for the clock paradox, as I described more specifically in a
> > parallel sub-thread?
Here it's not about comparisons but about a straightforward
calculation of signal propagation time. Probably you agree with Moller
and Builder that rather simple equations suffice for describing these
events (certainly for v<<c)? If so, then this is really not a
complicated matter.
Best regards,
Harald
Ken S. Tucker
> On Apr 23, 9:52 pm, "Ken S. Tucker" <dynam...@vianet.on.ca> wrote:
>
> > Hi Harald and all, permit me a top post.
> > Harald, you've stated above two contradictory statements.
> > 1) You do not understand tensor notation.
> > 2) You find GR mathematics superficial.
>
> Hi Ken,
>
> In fact I must disagree with your top posting, for it leads to errors:
> I certainly didn't state that I find GR mathematics superficial!
Sorry I have misunderstood what you wrote Apr.22, 11:22am, quote,
"Thus, even mathematically Einstein's solution only works at a very
superficial level. As soon as one looks at it in more detail, it turns
out to be unworkable."
> Instead I pointed out - as also acknowledged by Tom Roberts - that
> Einstein used mathematical magic in his claimed solution of the clock
> paradox (and I equally doubt that he finds GR mathematics
> superficial).
"Einstein used mathematical magic"
What does that mean?
> What I did show, elaborating on Builder's rejection, is that such
> magic has its limits so that when one examines it more closely, it
> doesn't really work at all - as was confirmed to me in the relativity
> group three years ago. And below once more I kindly invited you to
> show, if you disagree, how it does work:
> > > I don't think so; can you show that that view can correctly handle the
> > > Doppler test for the clock paradox, as I described more specifically in a
> > > parallel sub-thread?
>
> Here it's not about comparisons but about a straightforward
> calculation of signal propagation time. Probably you agree with Moller
> and Builder that rather simple equations suffice for describing these
> events (certainly for v<<c)? If so, then this is really not a
> complicated matter.
>
> Best regards,
> Harald
GR is basically fairly simple. It subtlely varies
measurements, from those of Newtons theory,
because light is form of energy (E=mc2) and is
subject to gravitation.
Regards
Ken
PS: my email is dynamics (at) uniserve.com
perhaps we should discuss some of that privately.
harry
> On Apr 23, 5:27 pm, harald.vanlin...@epfl.ch wrote:
>> On Apr 23, 9:52 pm, "Ken S. Tucker" <dynam...@vianet.on.ca> wrote:
>>
>> > Hi Harald and all, permit me a top post.
>> > Harald, you've stated above two contradictory statements.
>> > 1) You do not understand tensor notation.
>> > 2) You find GR mathematics superficial.
>>
>> Hi Ken,
>>
>> In fact I must disagree with your top posting, for it leads to errors:
>> I certainly didn't state that I find GR mathematics superficial!
>
> Sorry I have misunderstood what you wrote Apr.22, 11:22am, quote,
> "Thus, even mathematically Einstein's solution only works at a very
> superficial level. As soon as one looks at it in more detail, it turns
> out to be unworkable."
>
>> Instead I pointed out - as also acknowledged by Tom Roberts - that
>> Einstein used mathematical magic in his claimed solution of the clock
>> paradox (and I equally doubt that he finds GR mathematics
>> superficial).
>
> "Einstein used mathematical magic"
>
> What does that mean?
See the linked discussion (here once more: http://tinyurl.com/2mu4jv ).
>> What I did show, elaborating on Builder's rejection, is that such
>> magic has its limits so that when one examines it more closely, it
>> doesn't really work at all - as was confirmed to me in the relativity
>> group three years ago. And below once more I kindly invited you to
>> show, if you disagree, how it does work:
>
>> > > I don't think so; can you show that that view can correctly handle
>> > > the
>> > > Doppler test for the clock paradox, as I described more specifically
>> > > in a
>> > > parallel sub-thread?
>>
>> Here it's not about comparisons but about a straightforward
>> calculation of signal propagation time. Probably you agree with Moller
>> and Builder that rather simple equations suffice for describing these
>> events (certainly for v<<c)? If so, then this is really not a
>> complicated matter.
>>
>> Best regards,
>> Harald
>
> GR is basically fairly simple. It subtlely varies
> measurements, from those of Newtons theory,
> because light is form of energy (E=mc2) and is
> subject to gravitation.
Indeed. However, Einstein wanted to do more with it, he wanted to obtain
that all motion is purely "relative". And I have put your attention that his
solution of the twin paradox messes up when when goes over it again with a
finer brush, as most easily seen at low speeds and large distances.
> Regards
> Ken
> PS: my email is dynamics (at) uniserve.com
> perhaps we should discuss some of that privately.
Yes we could and we may do so later; but it's important for further
discussions in this group to make clear for all that this is not just a
matter of opinion - it should not be ducked.
Regards,
Harald
Oh No
>On Apr 23, 8:30 pm, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
>> Thus spake harry <harald.vanlintelButNotT...@epfl.ch>
>>
>>
>
>mathematical non-existence as part of a theory is easier to show. If
>it conflicts with the theory, it can't mathematically exist as part of
>it.
Indeed. That is why Einstein describes valid mathematical relationships
as though they are "real". As he also says, there are semantic
difficulties which make it best to avoid this kind of terminology.
>
>> >> If one doubts that these are real forces, get
>> >> on a childs roundabout. You can feel them, so they are real in that
>> >> sense. At the same time, they are inertial, i.e. not transmitted by
>> >> interactions between matter, and a product of motion relative to a
>> >> particular frame.
>>
>> >Sorry but that argument is based on a confusion, the force you feel in a
>> >merry-go-round is definitely a contact force!
>>
>> Depends on how you think of it. If you move you will feel a sideways
>> force. That is not a contact force.
>
>Please indicate where you snipped some of my text... by chance(?),
>here you snipped my explanation with the link that explains what is
>erroneous about that statement...
I looked at the explanation. I saw no indication in it that anything I
have said is erroneous. It is better to think of the physics than third
party explanations, however. To discuss inertial forces such as gravity
one must be very clear about definitions, and about the distinction
between active and inertial forces.
>
>> >One way to clear up the
>> >confusion is to refer to Newton who discussed centrifugal force, while at
>> >the same time rejecting the use of fictitious forces.
>>
>> Fictitious forces were invented by Huygens I believe. There is nothing
>> wrong with them. They are defined by mass x acceleration relative to a
>> given coordinate system. It is important to understand them in order to
>> understand gravity.
>
>Hmm... I have no use for fiction or magic!
"fiction" is just a word, meaning that the forces are not-active, or
inertial. Magic is just a word for something which is true but one does
not understand.
>
>> >> in gtr loads of coordinate systems are valid. If you choose a non-
>> >> inertial frame, you find non-inertial forces. Just like the coriolis and
>> >> centrifugal forces in classical mechanics, but now gravity also appears
>> >> as a non-inertial force.
>>
>> >Newtonian mechanics does not permit fictitious forces.
>>
>> It certainly does, according to the definition
>>
>> F = ma
>
>Actually, it's F = d(mv)/dt
Makes no difference. Matter does not change mass.
>and it describes the force of inertia.
Force of inertia??? That is almost an oxymoron. Inertia means not-
active. F = ma describes both inertial and non-inertial forces relative
to a coordinate system. That is the definition which is extended to
include gravity in gtr.
> Of
>course, if according to your definition, Newton's postulated physical
>space is fiction, then inertia may be fiction too
Perfect inertia implies perfect isolation. That may be a fiction, but
the concept that actions on a body are negligible is still valid, so it
is not reasonable to call inertia a fiction, particularly in classical
mechanics.
> and the force you
>feel is just fantasy.
The force is not a fantasy. It is a mass acceleration relative to a
given coordinate system. That is a real mathematical relationship. I
think your confusion comes from thinking that a real mathematical
relationship means a real underlying physical process. It doesn't.
> However, the force you feel is a contact force
>that can be measured using Hooke's law. :-)
I think you should try the test. What you feel is something which causes
you to accelerate relative to your coordinate system. That is the
definition of force.
>
>> They are forces relativity to a coordinate system.
>>
>> >And in both cases,
>> >whoever introduces them will have to face the consequences. Einstein fought
>> >bravely. :-)
>>
>> I think I disagree about the message of the equivalence principle.
>> Einstein showed gravity as a fictitious force, i.e. a force relative to
>> a coordinate system. His language was different though. If force is
>> defined as F = ma, then a "fictitious" force is "real". But like he
>> said, this language is unhelpful.
>>
>
>Indeed, metaphysical language is tricky. Therefore, instead I
>approached the problem from another angle by showing that Einstein's
>1918 solution even fails mathematically, as soon as one digs a little
>deeper.
Except that it doesn't fail mathematically, until such point as you
recognise that real forces of gravity are caused by space-time geometry
and may be distinguished from g-forces on that ground. The only thing
that fails is the idea that a field necessarily has an ontological
analogue, and Einstein attempts to distance himself from that idea.
harry
According to physics theory, what you feel is the inertial force that your
body exerts against the merry-go-round in reaction to the centripetal
acceleration of the merry-go-round. If one knows the elasticity modulus of
the skin on your arm that squizes against the side of the merry-go-round,
the value of that contact force can be determined by means of a ruler and
Hooke's law.
>>> >One way to clear up the
>>> >confusion is to refer to Newton who discussed centrifugal force, while
>>> >at
>>> >the same time rejecting the use of fictitious forces.
>>>
>>> Fictitious forces were invented by Huygens I believe. There is nothing
>>> wrong with them. They are defined by mass x acceleration relative to a
>>> given coordinate system. It is important to understand them in order to
>>> understand gravity.
>>
>>Hmm... I have no use for fiction or magic!
>
> "fiction" is just a word, meaning that the forces are not-active, or
> inertial. Magic is just a word for something which is true but one does
> not understand.
Magic is Harry Potter on his magic broom. To put it in other words: we have
no use of replacing understanding by distorted nonsense.
>>> >> in gtr loads of coordinate systems are valid. If you choose a non-
>>> >> inertial frame, you find non-inertial forces. Just like the coriolis
>>> >> and
>>> >> centrifugal forces in classical mechanics, but now gravity also
>>> >> appears
>>> >> as a non-inertial force.
>>>
>>> >Newtonian mechanics does not permit fictitious forces.
>>>
>>> It certainly does, according to the definition
>>>
>>> F = ma
>>
>>Actually, it's F = d(mv)/dt
>
> Makes no difference. Matter does not change mass.
>
>>and it describes the force of inertia.
>
> Force of inertia??? That is almost an oxymoron. Inertia means not-
> active. F = ma describes both inertial and non-inertial forces relative
> to a coordinate system. That is the definition which is extended to
> include gravity in gtr.
No inertia, no force against acceleration. For that reason, m is even
sometimes called "inertial mass".
>> Of
>>course, if according to your definition, Newton's postulated physical
>>space is fiction, then inertia may be fiction too
>
> Perfect inertia implies perfect isolation. That may be a fiction, but
> the concept that actions on a body are negligible is still valid, so it
> is not reasonable to call inertia a fiction, particularly in classical
> mechanics.
>
>> and the force you
>>feel is just fantasy.
>
> The force is not a fantasy.
At least we agree on that.
> It is a mass acceleration relative to a
> given coordinate system.
But here the disagreement could not be greater. Coordinate systems are our
free choice, they cannot affect our measurements.
> That is a real mathematical relationship. I
> think your confusion comes from thinking that a real mathematical
> relationship means a real underlying physical process. It doesn't.
No, but I'm glad to see that you acknowledge that. However, forces are
defined by means of real physical processes. My physics textbooks were not
perfect (especially their history was crappy), but at least the authors did
very well in avoiding any use of fictitious forces when explaining and
deriving relative rotational motion. I am still thankful to them for that,
and I can understand why some teachers even want to put a ban on the term
"centrifugal force" (some went as far as putting up angry web pages about
it). However, there is nothing wrong with the way that term was used by
Newton.
>> However, the force you feel is a contact force
>>that can be measured using Hooke's law. :-)
>
> I think you should try the test. What you feel is something which causes
> you to accelerate relative to your coordinate system. That is the
> definition of force.
That's not physics. I can make you accelerate at will relative to any
coordinate system that I set up. You won't feel anything!
>>> They are forces relativity to a coordinate system.
>>>
>>> >And in both cases,
>>> >whoever introduces them will have to face the consequences. Einstein
>>> >fought
>>> >bravely. :-)
>>>
>>> I think I disagree about the message of the equivalence principle.
>>> Einstein showed gravity as a fictitious force, i.e. a force relative to
>>> a coordinate system. His language was different though. If force is
>>> defined as F = ma, then a "fictitious" force is "real". But like he
>>> said, this language is unhelpful.
>>>
>>
>>Indeed, metaphysical language is tricky. Therefore, instead I
>>approached the problem from another angle by showing that Einstein's
>>1918 solution even fails mathematically, as soon as one digs a little
>>deeper.
>
> Except that it doesn't fail mathematically, until such point as you
> recognise that real forces of gravity are caused by space-time geometry
> and may be distinguished from g-forces on that ground. The only thing
> that fails is the idea that a field necessarily has an ontological
> analogue, and Einstein attempts to distance himself from that idea.
This has nothing to do with my views. The published explanation of how
Einstein's solution fails is rather short; therefore I have elaborated on
it. I also invited you to show the contrary, i.e. that it doesn't fail and
that instead I made a calculation error (as well as Builder and his
referees). Perhaps I should have given an example with numbers? Indeed, the
difference between delta_t = 0 and delta_t = <a large number> can be more
striking. In any case, I'm of course willing to discuss alternative
calculations. I'm afraid that this is as far as a discussion can go.
Regards,
Harald
Oh No
Then you agree with me. Good.
>
>>>> >One way to clear up the
>>>> >confusion is to refer to Newton who discussed centrifugal force, while
>>>> >at
>>>> >the same time rejecting the use of fictitious forces.
>>>>
>>>> Fictitious forces were invented by Huygens I believe. There is nothing
>>>> wrong with them. They are defined by mass x acceleration relative to a
>>>> given coordinate system. It is important to understand them in order to
>>>> understand gravity.
>>>
>>>Hmm... I have no use for fiction or magic!
>>
>> "fiction" is just a word, meaning that the forces are not-active, or
>> inertial. Magic is just a word for something which is true but one does
>> not understand.
>
>Magic is Harry Potter on his magic broom. To put it in other words: we have
>no use of replacing understanding by distorted nonsense.
I just call that nonsense. The context we were talking of was
mathemagical magic.
They are fundamental to our measurements. We cannot make measurements
without first setting up a coordinate system.
>> That is a real mathematical relationship. I
>> think your confusion comes from thinking that a real mathematical
>> relationship means a real underlying physical process. It doesn't.
>
>No, but I'm glad to see that you acknowledge that. However, forces are
>defined by means of real physical processes.
That contradicts the notion you described earlier, that of an inertial
force.
> My physics textbooks were not
>perfect (especially their history was crappy), but at least the authors did
>very well in avoiding any use of fictitious forces when explaining and
>deriving relative rotational motion. I am still thankful to them for that,
>and I can understand why some teachers even want to put a ban on the term
>"centrifugal force" (some went as far as putting up angry web pages about
>it). However, there is nothing wrong with the way that term was used by
>Newton.
I agree. The reason to ban inertial forces is because of the confusion
they cause students who misunderstand them, not because they are not a
valid concept.
Probably. I don't see any calculation errors. Only possible semantic
confusions. They are always difficult to resolve.
Peter
I have the impression that a major part of your discussion stems from using
the same words for different contents. Hopefully, my questions below will
help to clarify that :-)
> >> >> If one doubts that these are real forces, get
> >> >> on a childs roundabout. You can feel them, so they are real in that
> >> >> sense. At the same time, they are inertial, i.e. not transmitted by
> >> >> interactions between matter, and a product of motion relative to a
> >> >> particular frame.
One should clearly discriminate cause and effect.
The curvilinear motion is accompagnied by 'inertial forces'.
If a body is bound to another body that is not moving parallel to the first
body on its own, a force between both bodies occurs. In case both bodies are
in contact and the force appears as a pressure one may call it a 'contact
force'.
To agree one with another, you both must have got the same notions and
wordings of the different forces involved. Which exactly are they?
> >> >One way to clear up the
> >> >confusion is to refer to Newton who discussed centrifugal force, while
> at
> >> >the same time rejecting the use of fictitious forces.
> >> Fictitious forces were invented by Huygens I believe. There is nothing
> >> wrong with them. They are defined by mass x acceleration relative to a
> >> given coordinate system.
This corresponds to my understanding. It's a translation of a kinematical
problem (relative motion) to dynamics. This concept seems to be beloved by
practioners like meteorologists. I'm not sure about its usefulness for
axiomatics.
> >> It is important to understand them in order to
> >> understand gravity.
Is gravity a fictitious force?
> ..."fiction" is just a word, meaning that the forces are not-active, or
> inertial.
What means "not-active"?
> Magic is just a word for something which is true but one does
> not understand.
fine definition :-)
> >> >> in gtr loads of coordinate systems are valid. If you choose a non-
> >> >> inertial frame, you find non-inertial forces.
For me, the definitions of inertial frame and non-inertial forces appear like
a circle...
...
> >> >Newtonian mechanics does not permit fictitious forces.
> >> It certainly does, according to the definition
> >>
> >> F = ma
Note that, (i), there are force that cause acceleration and, (ii), that
acceleration causes ('counter') forces.
> >Actually, it's F = d(mv)/dt...
> Makes no difference. Matter does not change mass.
There is a difference, but not for the issue of fictitious forces.
> >...and it describes the force of inertia.
> Force of inertia??? That is almost an oxymoron.
Indeed, such a force appears in the Definitions of 'Principia', Book I, but
not more in the Laws.
> Inertia means not-active.
What exactly means "not-active"? (Sorry when this was explained in aforegoing
postings!)
> F = ma describes both inertial and non-inertial forces relative
> to a coordinate system.
Is this formulation equivalent to my notion above, "...that, (i), there are
force that cause acceleration and, (ii), that acceleration causes ('counter')
forces."?
...
> Perfect inertia implies perfect isolation. That may be a fiction
No, it may not, at least not in the same sense as 'fictive' was used above.
For this, it's more accurate to call it an approximation, as you have in mind
with your explanation
> , but
> the concept that actions on a body are negligible is still valid, so it
> is not reasonable to call inertia a fiction, particularly in classical
> mechanics.
...
What do you think?
Best,
Peter
Oh No
>Hi Frank and Harald,
>> >> >One way to clear up the
>> >> >confusion is to refer to Newton who discussed centrifugal force, while
>> at
>> >> >the same time rejecting the use of fictitious forces.
>
>> >> Fictitious forces were invented by Huygens I believe. There is nothing
>> >> wrong with them. They are defined by mass x acceleration relative to a
>> >> given coordinate system.
>
>This corresponds to my understanding. It's a translation of a kinematical
>problem (relative motion) to dynamics. This concept seems to be beloved by
>practioners like meteorologists. I'm not sure about its usefulness for
>axiomatics.
I don't see how to understand general relativity without them.
>
>> >> It is important to understand them in order to
>> >> understand gravity.
>
>Is gravity a fictitious force?
In a sufficiently local (in time and space) coordinate system, it is. In
this case one can always transform to an inertial coordinate system in
which it is absent. That is the principle of equivalence.
>
>> ..."fiction" is just a word, meaning that the forces are not-active, or
>> inertial.
>
>What means "not-active"?
It is the literal meaning of inert or inertial, from latin which Newton
of course would have spoken.
>
>> >> >> in gtr loads of coordinate systems are valid. If you choose a non-
>> >> >> inertial frame, you find non-inertial forces.
>
>For me, the definitions of inertial frame and non-inertial forces appear like
>a circle...
They are. Ultimately this is tautology. In the absence of a background
like Newtonian absolute space, we can best talk of motions relative to a
frame of reference defined from inertial matter.
>
>> Inertia means not-active.
>
>What exactly means "not-active"? (Sorry when this was explained in aforegoing
>postings!)
As I recall, Newton talks of active forces, meaning forces caused by the
physical action of one body on another. An inertial state is one in
which this is not happening.
>
>> F = ma describes both inertial and non-inertial forces relative
>> to a coordinate system.
>
>Is this formulation equivalent to my notion above, "...that, (i), there are
>force that cause acceleration and, (ii), that acceleration causes ('counter')
>forces."?
I don't think simply to define force by F=ma contains that, although it
is true.
> ...
>> Perfect inertia implies perfect isolation. That may be a fiction
>
>No, it may not, at least not in the same sense as 'fictive' was used above.
>For this, it's more accurate to call it an approximation, as you have in mind
>with your explanation
ok, an approximation.
Peter
> >> >> Fictitious forces were invented by Huygens I believe. There is
> nothing
> >> >> wrong with them. They are defined by mass x acceleration relative to
> a given coordinate system.
> >This corresponds to my understanding. It's a translation of a kinematical
> >problem (relative motion) to dynamics. This concept seems to be beloved by
> >practioners like meteorologists. I'm not sure about its usefulness for
> >axiomatics.
> I don't see how to understand general relativity without them.
I would understand this if knowing your understanding of general relativity,
but there seems to be a pause in your thread ;-)
> >> >> It is important to understand them in order to
> >> >> understand gravity.
> >Is gravity a fictitious force?
> In a sufficiently local (in time and space) coordinate system, it is. In
> this case one can always transform to an inertial coordinate system in
> which it is absent. That is the principle of equivalence.
Unfortunately, I know little about general relativity. With Newton I see
gravity as a direct force between bodies. In contrast, there is no distance-
dependent force law for the Coriolis force.
> >> ..."fiction" is just a word, meaning that the forces are not-active, or
> >> inertial.
> >What means "not-active"?
> It is the literal meaning of inert or inertial, from latin which Newton
> of course would have spoken.
The fact that Newton wrote in the definitions about inertia as internal force
of bodies, bot didn't mention it in the laws, can be seen as indication of
that Newton felt the conceptual difficulties herein.
What speaks again the view that the 'inertial force' is the net result of the
gravitative interaction with all other masses? I find Sciama's (1953)
exposition of it by means of the gravito-electrodynamic equations fascinating
in its simplicity and clarity :-)
> >> >> >> in gtr loads of coordinate systems are valid. If you choose a non-
> >> >> >> inertial frame, you find non-inertial forces.
Consider your (or my) house and that of a neighbour. There is a gravitative
attraction between them, counterbalanced by their bound to the ground. Which
are the fictious and non-fictious forces?
Now, consider two electrically charged body kept at distance by some
isolating bond. Which are here the fictious and non-fictious forces? Vanishes
the electromagnetic force between them when the bond is removed?
Thank you,
Peter
Oh No
>
>> >Is gravity a fictitious force?
>
>> In a sufficiently local (in time and space) coordinate system, it is. In
>> this case one can always transform to an inertial coordinate system in
>> which it is absent. That is the principle of equivalence.
>
>Unfortunately, I know little about general relativity. With Newton I see
>gravity as a direct force between bodies.
Indeed, but it is a force without physical cause. This taxed minds for
two hundred years before gtr gave an explanation.
> In contrast, there is no distance-
>dependent force law for the Coriolis force.
The force law now comes from the geometry of space-time, not from
kinematic behaviour. In other respects it behaves as an inertial force
like coriolis.
>> >> ..."fiction" is just a word, meaning that the forces are not-active, or
>> >> inertial.
>
>> >What means "not-active"?
>
>> It is the literal meaning of inert or inertial, from latin which Newton
>> of course would have spoken.
>
>The fact that Newton wrote in the definitions about inertia as internal force
>of bodies, bot didn't mention it in the laws, can be seen as indication of
>that Newton felt the conceptual difficulties herein.
>
>What speaks again the view that the 'inertial force' is the net result of the
>gravitative interaction with all other masses? I find Sciama's (1953)
>exposition of it by means of the gravito-electrodynamic equations fascinating
>in its simplicity and clarity :-)
I am not familiar with Sciama's account. I find Machian attempts at
explaining inertia in terms of the behaviour of other masses lack
coherence. Locally "straight" is defined by the relative paths of
inertial bodies. There is no other definition which makes sense in my
view.
>
>
>
>> >> >> >> in gtr loads of coordinate systems are valid. If you choose a non-
>> >> >> >> inertial frame, you find non-inertial forces.
>
>Consider your (or my) house and that of a neighbour. There is a gravitative
>attraction between them, counterbalanced by their bound to the ground. Which
>are the fictious and non-fictious forces?
The active forces are the forces of the ground on the houses.
>
>Now, consider two electrically charged body kept at distance by some
>isolating bond. Which are here the fictious and non-fictious forces? Vanishes
>the electromagnetic force between them when the bond is removed?
>
What is the bond if it is not electromagnetic in origin?
harry
On Apr 25, 7:15 pm, Peter <end...@dekasges.de> wrote:
> Hi Frank and Harald,
>
> I have the impression that a major part of your discussion stems from
> using
> the same words for different contents. Hopefully, my questions below will
> help to clarify that :-)
Thanks but in fact, it was just a side issue and we largely came to
agreement about it.
> > >> >> If one doubts that these are real forces, get
> > >> >> on a childs roundabout. You can feel them, so they are real in
> > >> >> that
> > >> >> sense. At the same time, they are inertial, i.e. not transmitted
> > >> >> by
> > >> >> interactions between matter, and a product of motion relative to a
> > >> >> particular frame.
>
> One should clearly discriminate cause and effect.
> The curvilinear motion is accompagnied by 'inertial forces'.
> If a body is bound to another body that is not moving parallel to the
> first
> body on its own, a force between both bodies occurs. In case both bodies
> are
> in contact and the force appears as a pressure one may call it a 'contact
> force'.
Yes indeed, and now it seems we agree on this.
[...]
> Is gravity a fictitious force?
That is a good question; the answer depends in part on definition, and also
in part on theory. Obviously the force that deforms the spring on the
balance scale on which you stand is real by definition, and usually this is
called the force of gravity.
Note that because of such debatable notions, my focus in this thread is much
more down-to-earth, it's about relatively simple calculations. In a nutshell
(in case you missed it):
When accounting for GRT's speed limit of physical information (radiation and
gravitational fields), Einstein's 1918 solution of the clock paradox fails
to correctly predict observed Doppler shifts. Any alternative theory must be
able to deal with that same consistency test.
However, it turns out that neither a single sentence in a publication, nor a
few additional clarifying sentences in a newsgroup suffice to drive that
point down. And of not surprisingly, statements by experts who call it
"magic" or "pseudo" (again without fully explaining why) are similarly
insufficient. Thus it will certainly be useful to publish a full article on
it.
[...]
> For me, the definitions of inertial frame and non-inertial forces appear
> like
> a circle...
Indeed, Newton's postulate has been replaced by a circular definition. This
thread is related to Einstein's 1916 attempt to resolve that problem.
Best regards,
Harald
Oh No
>Note that because of such debatable notions, my focus in this thread is
>much more down-to-earth, it's about relatively simple calculations. In
>a nutshell (in case you missed it): When accounting for GRT's speed
>limit of physical information (radiation and gravitational fields),
>Einstein's 1918 solution of the clock paradox fails to correctly
>predict observed Doppler shifts.
This does not appear to me to be true. If one defines coordinates in
which the non-inertial observer is stationary, such that the speed of
light is constant, the path of the inertial observer consists of three
parts. In the backward light cone from the acceleration the inertial
observer is in uniform motion away, and Doppler shift is as expected.
The same is true for the part of the motion in the forward light cone,
when the inertial observer is approaching. In the intermediate stage,
outside the light cone, the inertial observer's is stationary in this
coordinate system, and his clock is subjected to a gravitational shift
sufficient to resolve the paradox.
harry
Thanks for coming to the point, or, I should say, for attempting to do so.
:-)
For the issue is about Doppler shifts during Einstein's process 3. Please
specify how you calculated the time in K' that the gravitational induction
reaches C1 ("U1" in the article, from the German Uhr instead of the English
clock), and how you calculated the time in K' that emitted radiowaves from
the accelerated C1 and C12 reach C2.
As a reminder, here it is once more:
When taking a very large distance between the two clocks, even with a
(forbidden!) instantaneously propagating gravitational (pseudo-) field that
originates from C2, radio pulses that are emitted from C1 (the stay-at-home)
cannot correctly Doppler shift at C2 (the traveller), immediately after its
rockets are fired.
Looking at the problem in 2D instead of in 1D, we obtain the following
picture with another clock C12 aligned at a far distance to the side of C1,
"when" the rockets of C2 fire for the turn-around and with signals sent
from the stay-at-home clocks towards the traveller:
C1 C12 [higher "gravitational potential"]
Ś /
Ś /
Ś / [distance of for example 1 light day]
Ś /
Ś/
C2 [firing its rockets]
Here clock C12 must accelerate synchronously with clock C1, and radio pulses
that are emitted from C1 as well as C12 must immediately Doppler shift at C2
when the rockets of C2 fire. Obviously that cannot work.
To make it more concrete (I do this fast so I may make an error, but that
can be straightened out later): We can choose for example 100 light seconds
distance between C1 and C2 as well as between C1 and C12, and a rocket that
"induces a uniform gravitational field" of 1000 m/s^2 for 1 second (which is
rather unhealthy but handy). Then the time of rocket firing (process 3) as
well as time dilation and eventual Shapiro time delays can be neglected for
rough calculations of the time for the change in Doppler shift to be
detected at C2.
- I obtain for the induction to reach C1 from C2: 100 seconds (and to reach
C12: 140 seconds). However, for the sake of the argument we here pretend
that both times are 0 (instantaneous field propagation, against GRT).
- It takes for Doppler-shifted waves from the accelerated C1 about 100
seconds to reach C2; it takes about 140 seconds from C12.
- Thus in K', even when assuming instantaneous field propagation, we get for
the time it takes for the newly Doppler shifted signals to reach C2 about
100 seconds from C1, but about 140 seconds from C12. However, that is in
conflict with SRT and our experience.
Regards,
Harald
Oh No
>
>"Oh No" <No...@charlesfrancis.wanadoo.co.uk> wrote in message
>news:GC1k0sDq...@charlesfrancis.wanadoo.co.uk...
>> Thus spake harry <harald.vanlin...@epfl.ch>
>>>Note that because of such debatable notions, my focus in this thread is
>>>much more down-to-earth, it's about relatively simple calculations. In
>>>a nutshell (in case you missed it): When accounting for GRT's speed
>>>limit of physical information (radiation and gravitational fields),
>>>Einstein's 1918 solution of the clock paradox fails to correctly
>>>predict observed Doppler shifts.
>>
>> This does not appear to me to be true. If one defines coordinates in
>> which the non-inertial observer is stationary, such that the speed of
>> light is constant, the path of the inertial observer consists of three
>> parts. In the backward light cone from the acceleration the inertial
>> observer is in uniform motion away, and Doppler shift is as expected.
>> The same is true for the part of the motion in the forward light cone,
>> when the inertial observer is approaching. In the intermediate stage,
>> outside the light cone, the inertial observer's is stationary in this
>> coordinate system, and his clock is subjected to a gravitational shift
>> sufficient to resolve the paradox.
>
>Thanks for coming to the point, or, I should say, for attempting to do so.
>:-)
>For the issue is about Doppler shifts during Einstein's process 3.
I don't find it very meaningful to talk of Doppler shifts here. Doppler
is the shift due to uniform motion in a Lorentz frame, and we don't have
that situation. One doesn't talk of a Doppler shift from a geostationary
satelite, though one may talk of a gravitational shift.
> Please
>specify how you calculated the time in K' that the gravitational induction
>reaches C1 ("U1" in the article, from the German Uhr instead of the English
>clock), and how you calculated the time in K' that emitted radiowaves from
>the accelerated C1 and C12 reach C2.
These coordinates are calculated by the radar method. If a signal leaves
the accelerated observer at t1, and a reflected signal gets back at t2
then the time of the reflection is
t = (t1 + t2)/2
and the distance of the reflection is
d = (t2 - t1)/2
Outside the light cone, t1 is before the acceleration and t2 is after
it. If the situation is symmetrical, d is constant during this time.
>
>As a reminder, here it is once more:
>
>When taking a very large distance between the two clocks, even with a
>(forbidden!) instantaneously propagating gravitational (pseudo-) field that
>originates from C2,
as the field is an artefact of a coordinate system, instantaneous
propagation would not be forbidden.
>radio pulses that are emitted from C1 (the stay-at-home)
>cannot correctly Doppler shift at C2 (the traveller), immediately after its
>rockets are fired.
As I say, it is not a Doppler shift.
harry
[...]
>>For the issue is about Doppler shifts during Einstein's process 3.
>
> I don't find it very meaningful to talk of Doppler shifts here.
[...]
> the time of the reflection
[...]
> as the field is an artefact of a coordinate system
Evidently you are not discussing the same problem! Let me rephrase it in
terms that highlight the differences:
Einstein discusses here his theory according to which a coordinate system in
which the rocket is continuously in rest (K'), is claimed to be a valid
system for describing physical processes according to the laws of nature
which are thus valid in that system - that is, without "artefacts".
I added a radio emitter to clock C1 (assuming, as is common, a fixed
frequency): that enables a Doppler test in K' at the position of C2. For
more realism, I also added another such emitter at rest with C1, at a large
distance from it. Apparently I must emphasize that no signals are
"reflected". Just before the rocket with C2 fires its engines (process 3),
the received signals are Doppler shifted (this is commonly called
"redshift"). When the rocket fires its engines, this "induces" according to
Einstein as measured in K' "a homogeneous gravitational field"; and in turn,
that field accelerates clock C1 (as well as, I note, all other clocks that
are at rest with C1).
We may neglect the duration of firing the rockets if we make the fire time
sufficiently short compared to other durations; and we can use very simple
equations if we use rather low speeds and weak fields. Now, the issue that I
brought up is the following: With this model and in this coordinate system
K', how long after the rockets fire will it take before the "redshifted"
signals become "blueshifted"? I'm convinced that here the magic fails.
Thus I wrote:
"Please
specify how you calculated the time in K' that the gravitational induction
reaches C1 ("U1" in the article, from the German Uhr instead of the English
clock), and how you calculated the time in K' that emitted radiowaves from
the accelerated C1 and C12 reach C2."
Now that the issue is finally clear (I hope!), here I copy-paste once more
my calculation:
Oh No
>
>"Oh No" <No...@charlesfrancis.wanadoo.co.uk> wrote in message
>news:P9jWb5Fx...@charlesfrancis.wanadoo.co.uk...
>[...]
>
>>>For the issue is about Doppler shifts during Einstein's process 3.
>>
>> I don't find it very meaningful to talk of Doppler shifts here.
>
>[...]
>
>> the time of the reflection
>
>[...]
>
>> as the field is an artefact of a coordinate system
>
>Evidently you are not discussing the same problem! Let me rephrase it in
>terms that highlight the differences:
>
>Einstein discusses here his theory according to which a coordinate system in
>which the rocket is continuously in rest (K'), is claimed to be a valid
>system for describing physical processes according to the laws of nature
>which are thus valid in that system - that is, without "artefacts".
This is the cause of the problem. I think it is entirely semantic, and I
don't see any point in looking at an analysis beyond this statement. I
think you are simply misunderstanding what Einstein and the general
theory of relativity actually says. Einstein described the laws of
physics in a system of differential geometry in which the laws of
physics can be equally well described in any coordinate system. The cost
of doing that is to produce artefacts. As stated in the principle of
equivalence, gravity, in a uniform field, is then just as much an
artefact as the centrifugal and coriolis forces.
harry
> Thus spake harry <harald.vanlin...@epfl.ch>
>>
>>"Oh No" <No...@charlesfrancis.wanadoo.co.uk> wrote in message
>>news:P9jWb5Fx...@charlesfrancis.wanadoo.co.uk...
>>[...]
>>
>>>>For the issue is about Doppler shifts during Einstein's process 3.
>>>
>>> I don't find it very meaningful to talk of Doppler shifts here.
>>
>>[...]
>>
>>> the time of the reflection
>>
>>[...]
>>
>>> as the field is an artefact of a coordinate system
>>
>>Evidently you are not discussing the same problem! Let me rephrase it in
>>terms that highlight the differences:
>>
>>Einstein discusses here his theory according to which a coordinate system
>>in
>>which the rocket is continuously in rest (K'), is claimed to be a valid
>>system for describing physical processes according to the laws of nature
>>which are thus valid in that system - that is, without "artefacts".
>
> This is the cause of the problem. I think it is entirely semantic, and I
> don't see any point in looking at an analysis beyond this statement.
Contrary to your suggestion, Einstein did an analysis - and so did Moller
and others after him.
> I
> think you are simply misunderstanding what Einstein and the general
> theory of relativity actually says. Einstein described the laws of
> physics in a system of differential geometry in which the laws of
> physics can be equally well described in any coordinate system. The cost
> of doing that is to produce artefacts. As stated in the principle of
> equivalence, gravity, in a uniform field, is then just as much an
> artefact as the centrifugal and coriolis forces.
All laws of physics could *always* be described in *any* coordinate system
when one allows for artefacts that violate the same laws of physics - your
example of fictitious forces with classical mechanics serves well to
illustrate that point. In that case, Einstein would have been arguing for no
reason.
In contrast, no artefacts are produced in valid coordinate systems, and that
is the point of interest. Einstein argued that with GRT any frame is valid
just as inertial frames are valid frames in SRT. He explained that this
purpose was to get rid of the preferred status of inertial frames; indeed,
they are no good for a relational (truly "relativistic") theory.
Regards,
Harald
Oh No
>
>"Oh No" <No...@charlesfrancis.wanadoo.co.uk> wrote in message
>news:M6XAryJMtbMGFwQ$@charlesfrancis.wanadoo.co.uk...
>> Thus spake harry <harald.vanlin...@epfl.ch>
>>>
>>>
>>>in
>>>which the rocket is continuously in rest (K'), is claimed to be a valid
>>>system for describing physical processes according to the laws of nature
>>>which are thus valid in that system - that is, without "artefacts".
>>
>> This is the cause of the problem. I think it is entirely semantic, and I
>> don't see any point in looking at an analysis beyond this statement.
>
>Contrary to your suggestion, Einstein did an analysis - and so did Moller
>and others after him.
That is not what I meant. I have also done an analysis. I meant that the
problem is not in the analysis of the twin paradox, but in understanding
what gtr is saying.
>> I
>> think you are simply misunderstanding what Einstein and the general
>> theory of relativity actually says. Einstein described the laws of
>> physics in a system of differential geometry in which the laws of
>> physics can be equally well described in any coordinate system. The cost
>> of doing that is to produce artefacts. As stated in the principle of
>> equivalence, gravity, in a uniform field, is then just as much an
>> artefact as the centrifugal and coriolis forces.
>
>All laws of physics could *always* be described in *any* coordinate system
>when one allows for artefacts that violate the same laws of physics - your
>example of fictitious forces with classical mechanics serves well to
>illustrate that point. In that case, Einstein would have been arguing for no
>reason.
Not at all. Newton only expressed mechanics in terms of absolute space.
Huyghens showed how to generalise to rotating coordinate systems. Not
until ~1865 did Riemann produce the mathematics to describe general
coordinate systems, and not until gtr was it effectively applied.
>In contrast, no artefacts are produced in valid coordinate systems, and that
>is the point of interest.
This isn't true. gtr uses any coordinate system, and of course artefacts
are produced. The point is that they are also mananaged correctly in the
maths and gravity is shown as such an artefact.
>Einstein argued that with GRT any frame is valid
>just as inertial frames are valid frames in SRT.
This is true.
>He explained that this
>purpose was to get rid of the preferred status of inertial frames;
I am not sure if this was the purpose or a confusion. In the maths one
gets rid of the preferred status, because the general formalism works to
compare one frame to another, because it enables one to discuss large
scale geometry, and because it enables one to see the geometrical origin
of gravity, but locally Minkowski frames are still physically preferred
because they give simpler expression to physics and preserve straight
line motion which is part of the statement of a geodesic.
>indeed,
>they are no good for a relational (truly "relativistic") theory.
>
There I disagree completely. Apart from anything else the expression of
quantum theory in a non-inertial frame becomes extremely awkward. The
essential problem in general relativity is not how to express physics in
any coordinate system. That is just mathematical trickery and of course
it produces artefacts. The problem is how to compare physics in one
local frame with physics in another local frame. In both local frames
physics is simplest in using locally Minkowski coordinates, and these
are therefore "preferred". However, to compare the two we need to
formulate general coordinate systems, therefore we need a formulation of
physics which is valid in any coordinate system, artefacts and all.
harald.v...@epfl.ch
> Thus spake harry <harald.vanlintelButNotT...@epfl.ch>
>
>
>
>
>
> >news:M6XAryJMtbMGFwQ$@charlesfrancis.wanadoo.co.uk...
> >> Thus spake harry <harald.vanlintelButNotT...@epfl.ch>
>
> >>>Einstein discusses here his theory according to which a coordinate system
> >>>in
> >>>which the rocket is continuously in rest (K'), is claimed to be a valid
> >>>system for describing physical processes according to the laws of nature
> >>>which are thus valid in that system - that is, without "artefacts".
>
> >> This is the cause of the problem. I think it is entirely semantic, and I
> >> don't see any point in looking at an analysis beyond this statement.
>
> >Contrary to your suggestion, Einstein did an analysis - and so did Moller
> >and others after him.
>
> That is not what I meant. I have also done an analysis. I meant that the
> problem is not in the analysis of the twin paradox, but in understanding
> what gtr is saying.
The clock paradox concerned Einstein's claims (version 1916) about
relative motion. It's the topic of this thread. Now we are drifting to
another topic, but just as interesting: the purpose of this group!
> >> I
> >> think you are simply misunderstanding what Einstein and the general
> >> theory of relativity actually says. Einstein described the laws of
> >> physics in a system of differential geometry in which the laws of
> >> physics can be equally well described in any coordinate system. The cost
> >> of doing that is to produce artefacts. As stated in the principle of
> >> equivalence, gravity, in a uniform field, is then just as much an
> >> artefact as the centrifugal and coriolis forces.
>
> >All laws of physics could *always* be described in *any* coordinate system
> >when one allows for artefacts that violate the same laws of physics - your
> >example of fictitious forces with classical mechanics serves well to
> >illustrate that point. In that case, Einstein would have been arguing for no
> >reason.
>
> Not at all. Newton only expressed mechanics in terms of absolute space.
Yes indeed. There are no artefacts with absolute space - nor are there
any with SRT's inertial frames.
> Huyghens showed how to generalise to rotating coordinate systems.
I don't know about that, but I find it interesting. But first of all,
it's ambiguous: that does not tell me if those were systems of the
artefact-producing kind, or of the kind that I had at college and that
are free of artefacts.
> Not
> until ~1865 did Riemann produce the mathematics to describe general
> coordinate systems, and not until gtr was it effectively applied.
>
> >In contrast, no artefacts are produced in valid coordinate systems, and that
> >is the point of interest.
>
> This isn't true. gtr uses any coordinate system, and of course artefacts
> are produced. The point is that they are also mananaged correctly in the
> maths and gravity is shown as such an artefact.
>
> >Einstein argued that with GRT any frame is valid
> >just as inertial frames are valid frames in SRT.
>
> This is true.
If you show such artefacts in SRT, I will take notice of your
argument!
> >He explained that this
> >purpose was to get rid of the preferred status of inertial frames;
>
> I am not sure if this was the purpose or a confusion. In the maths one
> gets rid of the preferred status, because the general formalism works to
> compare one frame to another, because it enables one to discuss large
> scale geometry, and because it enables one to see the geometrical origin
> of gravity, but locally Minkowski frames are still physically preferred
> because they give simpler expression to physics and preserve straight
> line motion which is part of the statement of a geodesic.
>
> >indeed,
> >they are no good for a relational (truly "relativistic") theory.
>
> There I disagree completely. Apart from anything else the expression of
> quantum theory in a non-inertial frame becomes extremely awkward. The
> essential problem in general relativity is not how to express physics in
> any coordinate system. That is just mathematical trickery and of course
> it produces artefacts.
Good! it was the purpose of this thread to stress that fact. :-)
> The problem is how to compare physics in one
> local frame with physics in another local frame. In both local frames
> physics is simplest in using locally Minkowski coordinates, and these
> are therefore "preferred".
For me, the most interesting problem is to explain how nature
functions. Some explanations result in a big mess, which implies that
they are wrong.
> However, to compare the two we need to
> formulate general coordinate systems, therefore we need a formulation of
> physics which is valid in any coordinate system, artefacts and all.
I could not disagree more! I'd say that we need a formulation of
physics that consistently explains all observed phenomena - that is,
without any artefacts.
-> I'm really curious what other participants of this group think!
Regards,
Harald
Oh No
>On Apr 27, 8:02 pm, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
>> Thus spake harry <harald.vanlintelButNotT...@epfl.ch>
>
>> >> think you are simply misunderstanding what Einstein and the general
>> >> theory of relativity actually says. Einstein described the laws of
>> >> physics in a system of differential geometry in which the laws of
>> >> physics can be equally well described in any coordinate system. The cost
>> >> of doing that is to produce artefacts. As stated in the principle of
>> >> equivalence, gravity, in a uniform field, is then just as much an
>> >> artefact as the centrifugal and coriolis forces.
>>
>> >All laws of physics could *always* be described in *any* coordinate system
>> >when one allows for artefacts that violate the same laws of physics - your
>> >example of fictitious forces with classical mechanics serves well to
>> >illustrate that point. In that case, Einstein would have been arguing for no
>> >reason.
>>
>> Not at all. Newton only expressed mechanics in terms of absolute space.
>
>Yes indeed. There are no artefacts with absolute space - nor are there
>any with SRT's inertial frames.
>
>> Huyghens showed how to generalise to rotating coordinate systems.
>
>I don't know about that, but I find it interesting. But first of all,
>it's ambiguous: that does not tell me if those were systems of the
>artefact-producing kind, or of the kind that I had at college and that
>are free of artefacts.
rotating coordinates produce Coriolis and centrifugal forces as
artefacts.
>
>> Not
>> until ~1865 did Riemann produce the mathematics to describe general
>> coordinate systems, and not until gtr was it effectively applied.
>>
>> >In contrast, no artefacts are produced in valid coordinate systems, and that
>> >is the point of interest.
>>
>> This isn't true. gtr uses any coordinate system, and of course artefacts
>> are produced. The point is that they are also mananaged correctly in the
>> maths and gravity is shown as such an artefact.
>>
>> >Einstein argued that with GRT any frame is valid
>> >just as inertial frames are valid frames in SRT.
>>
>> This is true.
>
>If you show such artefacts in SRT, I will take notice of your
>argument!
Just because a coordinate system produces artefacts, does not mean that
it is not mathematically valid.
>
>> >He explained that this
>> >purpose was to get rid of the preferred status of inertial frames;
>>
>> I am not sure if this was the purpose or a confusion. In the maths one
>> gets rid of the preferred status, because the general formalism works to
>> compare one frame to another, because it enables one to discuss large
>> scale geometry, and because it enables one to see the geometrical origin
>> of gravity, but locally Minkowski frames are still physically preferred
>> because they give simpler expression to physics and preserve straight
>> line motion which is part of the statement of a geodesic.
>>
>> >indeed,
>> >they are no good for a relational (truly "relativistic") theory.
>>
>> There I disagree completely. Apart from anything else the expression of
>> quantum theory in a non-inertial frame becomes extremely awkward. The
>> essential problem in general relativity is not how to express physics in
>> any coordinate system. That is just mathematical trickery and of course
>> it produces artefacts.
>
>Good! it was the purpose of this thread to stress that fact. :-)
>
>> The problem is how to compare physics in one
>> local frame with physics in another local frame. In both local frames
>> physics is simplest in using locally Minkowski coordinates, and these
>> are therefore "preferred".
>
>For me, the most interesting problem is to explain how nature
>functions. Some explanations result in a big mess, which implies that
>they are wrong.
gtr is quite tidy really. Something may have a simple underlying
structure, but when its parts are put together it becomes complex.
Mathematics itself is very simple in its underlying structure, but it is
possible to use it to discuss very abstract and difficult ideas.
>
>> However, to compare the two we need to
>> formulate general coordinate systems, therefore we need a formulation of
>> physics which is valid in any coordinate system, artefacts and all.
>
>I could not disagree more!
>I'd say that we need a formulation of
>physics that consistently explains all observed phenomena - that is,
>without any artefacts.
It should be enough to be clear that artefacts of a coordinate system
are artefacts, not physical reality. The statement is true. There is no
way of doing a comparison between a Minkowski frame in one place with a
Minkowski frame in another which does not involve us in going through
the stage of using general coordinate systems. When we do so, we find
that the "force" of gravity is an artefact of the comparison, and that
there is no way of transforming gravity away on the large scale. Since
gravity is observed, "all observed phenomena" necessarily includes
artefacts.
Ken S. Tucker
> On Apr 27, 8:02 pm, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> > However, to compare the two we need to
> > formulate general coordinate systems, therefore we need a formulation of
> > physics which is valid in any coordinate system, artefacts and all.
>
> I could not disagree more! I'd say that we need a formulation of
> physics that consistently explains all observed phenomena - that is,
> without any artefacts.
> -> I'm really curious what other participants of this group think!
Sometimes working with relativity is easier using
Quantum Theory around Planck's constant invariant,
"h", let me do a bit ground work,
Energy (E) = h * f , (frequency).
In old style, frequency = number of cycles / second,
I'll call f = N cycles/ (t=1second) , giving,
E = h*N/t == h/T with T = t/N
where T is the time of 1 cycle expressed as a fraction
of a second, providing us with,
h = E*T = 6.62...x10^-27 Ergs x 1 second,
the RHS being the common value of "h".
Of course, because E=Mc2, fiddle with constants
and make,
h = M*T.
We can think of Mass "M" sitting in CS K lab,
beside a clock ticking every T, as a "lab" standard
of "h". Relatively to a moving (even accelerating) CS K',
those "lab" standards transform as,
h = E*T = E'*T' ,
because "h" is a universal constant invariant.
For example, if K' is moving at 0.8c relative to K
then,
E' = (10/6)*E , T' = (6/10)*T
meaning the Mass standard in K has more energy
(because of the kinetic energy component) relative
to K', and the clock in K ticks slower relative to K'.
Is that an agreeable alternative, perhaps easier way
to study the "twin paradox"?
Regards
Ken S. Tucker
>
> Regards,
> Harald
harry
> Thus spake harald.vanlin...@epfl.ch
[...]
> >> Huyghens showed how to generalise to rotating coordinate systems.
> rotating coordinates produce Coriolis and centrifugal forces as
> artefacts.
Not the rotating systems that most physicists use! My reference is
Alonso&Finn, Fundamental university physics. Which mechanics books are
you referring to?
[...]
> >> we need a formulation of
> >> physics which is valid in any coordinate system, artefacts and all.
>
> >I could not disagree more!
> >I'd say that we need a formulation of
> >physics that consistently explains all observed phenomena - that is,
> >without any artefacts.
I'm STILL interested to know what other participants think that is
needed. Probably this issue is worth starting a new topic on!
> It should be enough to be clear that artefacts of a coordinate system
> are artefacts, not physical reality.
The "mathematical trickery", as you call it, of K' is certainly not
suited for describing physical reality and as I demonstrated, such
coordinate systems are of limited use.
> The statement is true. There is no
> way of doing a comparison between a Minkowski frame in one place with a
> Minkowski frame in another which does not involve us in going through
> the stage of using general coordinate systems.
>
> When we do so, we find
> that the "force" of gravity is an artefact of the comparison, and that
> there is no way of transforming gravity away on the large scale. Since
> gravity is observed, "all observed phenomena" necessarily includes
> artefacts.
Nowadays there is a general acknowledgement that gravitation is a
physical reality that originates from matter instead of from magic.
The fact that we can identify real fields makes it unnecessay to
include such artefacts, which is certainly much more elegant.
Regards,
Harald
Oh No
>On Apr 28, 9:00 am, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
>> Thus spake harald.vanlin...@epfl.ch
>[...]
>
>> >> Huyghens showed how to generalise to rotating coordinate systems.
>
>> rotating coordinates produce Coriolis and centrifugal forces as
>> artefacts.
>
>Not the rotating systems that most physicists use! My reference is
>Alonso&Finn, Fundamental university physics. Which mechanics books are
>you referring to?
I am a Cambridge trained mathematician. I refer only to the axioms of
the subject. I don't use mechanics books, since everything in classical
mechanics follows from Newton's laws and the assumptions of absolute
space and absolute time. Huyghens also was one of the best
mathematicians in history. There is no mistake in the correct use of
rotating coordinates in which centrifugal and Coriolis forces appear,
though pedagogues have found they can cause confusion and therefore seek
to avoid them. As I recall, there was a nice account in Encyclopedia
Brittanica.
>> >> we need a formulation of
>> >> physics which is valid in any coordinate system, artefacts and all.
>>
>> >I could not disagree more!
>> >I'd say that we need a formulation of
>> >physics that consistently explains all observed phenomena - that is,
>> >without any artefacts.
>
>I'm STILL interested to know what other participants think that is
>needed. Probably this issue is worth starting a new topic on!
>
>> It should be enough to be clear that artefacts of a coordinate system
>> are artefacts, not physical reality.
>
>The "mathematical trickery", as you call it, of K' is certainly not
>suited for describing physical reality and as I demonstrated, such
>coordinate systems are of limited use.
Nonetheless they are essential for the full description of gravity. Bear
in mind that general relativity describes space-time as locally
Minkowski everywhere, so you an always describe local processes in
"artefact free" coordinates. In such coordinates, as Einstein showed,
gravity does not appear. That is not sufficient, however, to describe
physical reality, in which we know very well that gravity does appear.
>> The statement is true. There is no
>> way of doing a comparison between a Minkowski frame in one place with a
>> Minkowski frame in another which does not involve us in going through
>> the stage of using general coordinate systems.
>>
>> When we do so, we find
>> that the "force" of gravity is an artefact of the comparison, and that
>> there is no way of transforming gravity away on the large scale. Since
>> gravity is observed, "all observed phenomena" necessarily includes
>> artefacts.
>
>Nowadays there is a general acknowledgement that gravitation is a
>physical reality that originates from matter instead of from magic.
>The fact that we can identify real fields makes it unnecessay to
>include such artefacts, which is certainly much more elegant.
We cannot identify "real fields" in the sense in which I think you have
been using the word, but note that this is a different sense than the
one in which Einstein used it.
harry
> On Apr 27, 3:36 pm, harald.vanlin...@epfl.ch wrote:
>
> > On Apr 27, 8:02 pm, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> ...
> > > However, to compare the two we need to
> > > formulate general coordinate systems, therefore we need a formulation of
> > > physics which is valid in any coordinate system, artefacts and all.
>
> > I could not disagree more! I'd say that we need a formulation of
> > physics that consistently explains all observed phenomena - that is,
> > without any artefacts.
> > -> I'm really curious what other participants of this group think!
>
> Sometimes working with relativity is easier using
> Quantum Theory around Planck's constant invariant,
> "h", let me do a bit ground work,
>
> Energy (E) = h * f , (frequency).
Here you are introducing additional concepts with more issues that are
worth to get into. And it is not really to the point I'm afraid.
> In old style, frequency = number of cycles / second,
> I'll call f = N cycles/ (t=1second) , giving,
>
> E = h*N/t == h/T with T = t/N
>
> where T is the time of 1 cycle expressed as a fraction
> of a second, providing us with,
>
> h = E*T = 6.62...x10^-27 Ergs x 1 second,
What are Ergs?
> the RHS being the common value of "h".
>
> Of course, because E=Mc2, fiddle with constants
> and make,
>
> h = M*T.
Somewhere you must have lost a c^2...
Also, what do you claim that this period T stands for?
> We can think of Mass "M" sitting in CS K lab,
> beside a clock ticking every T, as a "lab" standard
> of "h".
Perhaps you mean, in the sense that the change of both that T and the
one in the equation must be proportional? It is not clear to me how
you intend to measure M and T real-time...
> Relatively to a moving (even accelerating) CS K',
> those "lab" standards transform as,
>
> h = E*T = E'*T' ,
>
> because "h" is a universal constant invariant.
>
> For example, if K' is moving at 0.8c relative to K
> then,
>
> E' = (10/6)*E , T' = (6/10)*T
>
> meaning the Mass standard in K has more energy
> (because of the kinetic energy component) relative
> to K', and the clock in K ticks slower relative to K'.
OK I'm with you again. :-)
Note that this is standard SRT, no need to get it from Planck:
E = gamma * E0 = Ekin + E0.
> Is that an agreeable alternative, perhaps easier way
> to study the "twin paradox"?
Not really: I stressed that the time dilations do work out correctly,
as all textbooks also emphasize - thus I don't see how that can be an
issue.
Regards,
Harald
harry
> Thus spake harry <harald.vanlin...@epfl.ch>
>
> >On Apr 28, 9:00 am, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> >> Thus spake harald.vanlin...@epfl.ch
> >[...]
>
> >> >> Huyghens showed how to generalise to rotating coordinate systems.
>
> >> rotating coordinates produce Coriolis and centrifugal forces as
> >> artefacts.
>
> >Not the rotating systems that most physicists use! My reference is
> >Alonso&Finn, Fundamental university physics. Which mechanics books are
> >you referring to?
>
> I am a Cambridge trained mathematician. I refer only to the axioms of
> the subject. I don't use mechanics books, since everything in classical
> mechanics follows from Newton's laws and the assumptions of absolute
> space and absolute time.
Evidently, the axioms you learned are incompatible with the ones I
learned. "Fundamental" mechanics books include relativity of course
but indeed, modern physics is built "on the shoulders of giants".
> Huyghens also was one of the best
> mathematicians in history.
I'm still interested in reading a text by Huygens that demonstrates
this alleged abuse (in my eyes) of the laws of mechanics. So far I
have the impression that it occurred much more recently.Thus, if you
or some other participant knows where I can obtain such a text, I'll
be glad to hear it.
> There is no mistake in the correct use of
> rotating coordinates in which centrifugal and Coriolis forces appear,
> though pedagogues have found they can cause confusion and therefore seek
> to avoid them. As I recall, there was a nice account in Encyclopedia
> Brittanica.
The account in Wikipedia encyclopedia explains rather clearly that
there is no need for fictitious forces with rotating coordianates.
Confusion only came from introducing fictitious forces and then
calling them by the same names as contact forces (which are as real as
they can get).
[...]
> >The "mathematical trickery", as you call it, of K' is certainly not
> >suited for describing physical reality and as I demonstrated, such
> >coordinate systems are of limited use.
>
> Nonetheless they are essential for the full description of gravity.
I agree with that, in the sense that the equivalence principle showed
the way to predicting effects of gravity that had not been imagined
before Einstein.
[...]
>
> >Nowadays there is a general acknowledgement that gravitation is a
> >physical reality that originates from matter instead of from magic.
> >The fact that we can identify real fields makes it unnecessay to
> >include such artefacts, which is certainly much more elegant.
>
> We cannot identify "real fields" in the sense in which I think you have
> been using the word, but note that this is a different sense than the
> one in which Einstein used it.
"Real" in the sense of plausibly ascribing material causes to them,
and in a way that the laws of nature can be applied to them without
exceptions.
Please take note that I may not comment further in this subthread, as
we have drifted away from the topic. Insofar as worthwhile topics
remain, it may be better to re-start them as new topics.
Regards,
Harald
Oh No
>On Apr 28, 2:18 pm, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
>> Thus spake harry <harald.vanlin...@epfl.ch>
>>
>> >On Apr 28, 9:00 am, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
>> >> Thus spake harald.vanlin...@epfl.ch
>> >[...]
>>
>> >> >> Huyghens showed how to generalise to rotating coordinate systems.
>>
>> >> rotating coordinates produce Coriolis and centrifugal forces as
>> >> artefacts.
>>
>> >Not the rotating systems that most physicists use! My reference is
>> >Alonso&Finn, Fundamental university physics. Which mechanics books are
>> >you referring to?
>>
>> I am a Cambridge trained mathematician. I refer only to the axioms of
>> the subject. I don't use mechanics books, since everything in classical
>> mechanics follows from Newton's laws and the assumptions of absolute
>> space and absolute time.
>
>Evidently, the axioms you learned are incompatible with the ones I
>learned.
Not at all. You were just taught not to use valid mathematical structure
because it has been found that people get confused by it.
> "Fundamental" mechanics books include relativity of course
>but indeed, modern physics is built "on the shoulders of giants".
I was talking of classical mechanics. Of course I learned relativity as
well, though as is my won't I concentrated on building it from first
principles, rather than applying it which is the emphasis of most
courses. Interestingly Einstein's original account is probably the best
I have read. Text books typically make philosophical errors, such as
attributing ontology to space-time.
>
>> Huyghens also was one of the best
>> mathematicians in history.
>
>I'm still interested in reading a text by Huygens that demonstrates
>this alleged abuse (in my eyes) of the laws of mechanics. So far I
>have the impression that it occurred much more recently.Thus, if you
>or some other participant knows where I can obtain such a text, I'll
>be glad to hear it.
Unfortunately I cannot refer you to a text by Huygens. The use of such
forces was attributed to him in Encyclopedia Britannica. I have no
reason to doubt it. I think pedagogues wanted to ban the centrifugal
force much later, C20th I think.
>
>> There is no mistake in the correct use of
>> rotating coordinates in which centrifugal and Coriolis forces appear,
>> though pedagogues have found they can cause confusion and therefore seek
>> to avoid them. As I recall, there was a nice account in Encyclopedia
>> Brittanica.
>
>The account in Wikipedia encyclopedia explains rather clearly that
>there is no need for fictitious forces with rotating coordianates.
Certainly there is no need for them. That does not mean they cannot be
used. If used correctly, they are convenient on occasion.
>Confusion only came from introducing fictitious forces and then
>calling them by the same names as contact forces (which are as real as
>they can get).
Indeed, one should distinguish clearly between these types of force.
>
>> >The "mathematical trickery", as you call it, of K' is certainly not
>> >suited for describing physical reality and as I demonstrated, such
>> >coordinate systems are of limited use.
>>
>> Nonetheless they are essential for the full description of gravity.
>
>I agree with that, in the sense that the equivalence principle showed
>the way to predicting effects of gravity that had not been imagined
>before Einstein.
>
>[...]
>
>>
>> >Nowadays there is a general acknowledgement that gravitation is a
>> >physical reality that originates from matter instead of from magic.
>> >The fact that we can identify real fields makes it unnecessay to
>> >include such artefacts, which is certainly much more elegant.
>>
>> We cannot identify "real fields" in the sense in which I think you have
>> been using the word, but note that this is a different sense than the
>> one in which Einstein used it.
>
>"Real" in the sense of plausibly ascribing material causes to them,
>and in a way that the laws of nature can be applied to them without
>exceptions.
>
Even that is a difficult definition of real. There is a plausible
material cause for a "fictitious" force, namely the acceleration of the
reference matter with respect to which it is defined, e.g. the fact that
a reference frame is rotating, or in the case of gravity, the geometry
of spacetime as described by Einstein's field equation. Differential
geometry does precisely what you say, it enables us to describe the laws
of nature in any coordinate system without exceptions, just as Einstein
decreed. This is why Einstein said that the word "real" should be
avoided.
Ken S. Tucker
> On Apr 28, 1:37 pm, "Ken S. Tucker" <dynam...@vianet.on.ca> wrote:
> > h = E*T = 6.62...x10^-27 Ergs x 1 second,
>
> What are Ergs?
Ergs is an obsure term used by scientists
to quantified energy.
> > Is that an agreeable alternative, perhaps easier way
> > to study the "twin paradox"?
> Not really: I stressed that the time dilations do work out correctly,
> as all textbooks also emphasize - thus I don't see how that can be an
> issue.
I always thought that using various different ways
to solve a problem is good to do.
> Regards,
> Harald
Elvis has left the building.
Ken S. Tucker