Grand secret between Einsteinians
Pentcho Valev
"A curvature of rays of light can only take place when the velocity of
propagation of light VARIES with position."
So, according to Einstein, an observer positioned in a gravitational
field will measure a VARIABLE, not constant velocity of light. The
observer can measure, for instance, the frequency shift and, if
Einstein is right, a non-zero frequency shift corresponding to the
changing velocity of light will be detected.
Einsteinians never discuss this problem voluntarily but, when pressed,
they produce a combination of words more or less like this: The
velocity of light is constant only locally, non-locally it is variable.
The meaning of this combination of words, especially when applied to
Einstein's assertion, is a grand secret between Einsteinians.
Pentcho Valev
JanPB
>
> Einsteinians never discuss this problem voluntarily
Patent nonsense. It's in every GR textbook. But if all you read is pop
science books then of course you wouldn't know that.
--
Jan Bielawski
Androcles
"JanPB" <fil...@gmail.com> wrote in message
news:1125558444.7...@z14g2000cwz.googlegroups.com...
[snip crap]
Empirical idiot.
Androcles
Dr Photon
>"A curvature of rays of light can only take place when the velocity of
>propagation of light VARIES with position."
even I've heard of the Shapiro delay, and I've never even done any GR.
It's also been measured to quite a few decimal place, see
http://relativity.livingreviews.org/Articles/lrr-2001-4/node10.html
section 3.4.2 for example.
br
Sam Wormley
Valev confuses *velocity* of light with *speed* of light!
Mark Martin
This is all quite well known, has been for decades, and is no dirty
little secret. (If it were proprietary, then why did you find it in a
book written by Einstein targeted at the general public?)
Even in special relativity it's necessary for the speed of light to
vary between frames of reference having a relative velocity. The speed
of light is invariant locally. WITHIN any INERTIAL reference frame, c
will always measure out to 3.0 x 10^8 m/s.
-Mark Martin
Dr Photon
>Valev confuses *velocity* of light with *speed* of light!
Indeed!
Since Einstein died in 1955, and the Shapiro delay was only predicted
in 1964, then he couldn't have been referring to that.
br
Tom Roberts
> Since Einstein died in 1955, and the Shapiro delay was only predicted
> in 1964, then he couldn't have been referring to that.
Sure he could -- Einstein was extremely well-versed in the basis of GR,
and he most definitely knew that the speed of light can vary when
measured over non-local paths. Shapiro's contribution was to realize
that this esoteric aspect of GR could actually be measured, and he went
on to measure it.
Tom Roberts tjro...@lucent.com
Tom Roberts
> A. Einstein, "Relativity", Chapter 22:
> "A curvature of rays of light can only take place when the velocity of
> propagation of light VARIES with position."
>
> So, according to Einstein, an observer positioned in a gravitational
> field will measure a VARIABLE, not constant velocity of light.
No, he did NOT say that. He said what he said. <shrug>
But indeed, when an observer measures (say) the deflection of stars'
images during an eclipse, that observer can conclude that the presence
of the sun's gravitation did affect the propagation of light from those
stars, and that means a position-dependent variation in speed
(necessarily over the different non-local paths from star to observer).
> The
> observer can measure, for instance, the frequency shift and, if
> Einstein is right, a non-zero frequency shift corresponding to the
> changing velocity of light will be detected.
Hmmm. For the case of observing stars' images before, during, and after
an eclipse, the change in frequency is higher order in (extremely) small
quantities than the deflection. I'm pretty sure it is well below
realistic experimental resolutions.
> Einsteinians never discuss this problem voluntarily
This is not a "problem", it is merely your personal misconceptions and
errors.
Sam Wormley wrote:
> Valev confuses *velocity* of light with *speed* of light!
AFAIK Einstein basically thought in German, which does not have
different words for "speed" and "velocity" ("die Geschwindigkeit" is
used for both). Certainly his "velocity of propagation" could be phrased
as "speed of propagation" without changing the underlying physics. While
Valev is indeed confused, I don't think this is relevant.
Tom Roberts tjro...@lucent.com
sal
> Pentcho Valev wrote:
[ some of Pentcho's garbage snipped, along with Tom's reasonable
responses ]
>> The observer can measure, for instance, the frequency shift and, if
>> Einstein is right, a non-zero frequency shift corresponding to the
>> changing velocity of light will be detected.
>
> Hmmm. For the case of observing stars' images before, during, and
> after an eclipse, the change in frequency is higher order in
> (extremely) small quantities than the deflection. I'm pretty sure it
> is well below realistic experimental resolutions.
If the Sun is stationary relative to us (bad assumption but let's make
it anyway) then shouldn't there be _no_ frequency shift induced in the
light as a result of its passing near the Sun? (Assume the Moon is
massless or else so light we can ignore it -- "Styrofoam Moon".)
After all, a particular number of wave crests went into the Sun's gravity
well, the same number came out, and whether the light went near the Sun or
not makes no difference to how many seconds of time our clocks tick off.
So, there can't be any redshift/blueshift from that cause, _if_ the Sun
is stationary relative to us. (I stated that rather loosely; I hope it's
clear what I meant.)
On the other hand, if the Sun is moving transverse to our line of
sight, then ... uh ... wouldn't the light "steal" a little energy from
the Sun if it passes by the backside, and wouldn't it "give up" a
little energy if it passes by the front side, with the Sun being slowed
or accelerated slightly as a result? That would imply that stars on the
edge of the sun which is "in front of" our orbital path around the Sun
should be slightly blueshifted, and light which is "in back of" our
orbital path should be slightly redshifted, as a result of its trek close
to the Sun.
Right...?
Viewed differently, on the backside, the 3-d path is "getting shorter" as
the Sun moves out of the way, so the number of wavecrests "in transit"
must be decreasing, which implies there's a blueshift. On the front side,
the path is "getting longer" as the Sun moves into our line of sight, so
the number of wavecrests "in transit" along that line is increasing, and
there must be redshift. Rather pleasingly, both these rather fuzzy mental
models arrive at the same conclusion -- maybe it's even correct...
--
Nospam becomes physicsinsights to fix the email
Tom Roberts
> On Thu, 01 Sep 2005 11:41:07 -0500, Tom Roberts wrote:
>>For the case of observing stars' images before, during, and
>>after an eclipse, the change in frequency is higher order in
>>(extremely) small quantities than the deflection. I'm pretty sure it
>>is well below realistic experimental resolutions.
>
> If the Sun is stationary relative to us (bad assumption but let's make
> it anyway) then shouldn't there be _no_ frequency shift induced in the
> light as a result of its passing near the Sun? (Assume the Moon is
> massless or else so light we can ignore it -- "Styrofoam Moon".)
Well, earth is not at infinite radius from the sun, so there is some
solar blueshift for light emitted at essentially infinite radius.
But that's not the situation I was discussing. Watching the sun
"traverse" in front of a distant star, the star's light will be
redshifted as the sun approaches its line-of-sight, corresponding to an
increasing Shapiro time delay (in addition to the star's image being
deflected - see below); this redshift and delay will be undone as the
sun receeds from that line-of-sight (as will the deflection).
This redshift is incredibly small, corresponding to several
tens of microseconds delay over several hours, which is just
a few parts per billion.
> After all, a particular number of wave crests went into the Sun's gravity
> well, the same number came out, and whether the light went near the Sun or
> not makes no difference to how many seconds of time our clocks tick off.
> So, there can't be any redshift/blueshift from that cause, _if_ the Sun
> is stationary relative to us. (I stated that rather loosely; I hope it's
> clear what I meant.)
Sure. Except for the residual blueshift due to earth's finite distance
from the sun.
> On the other hand, if the Sun is moving transverse to our line of
> sight, then ... uh ... wouldn't the light "steal" a little energy from
> the Sun if it passes by the backside, and wouldn't it "give up" a
> little energy if it passes by the front side, with the Sun being slowed
> or accelerated slightly as a result?
No. See above. I suppose there is an outrageously miniscule
Lense-Thirring effect due to the rotation of the sun. But your notion of
"stealing" energy does not make sense (your geometrical argument later,
however, does).
> That would imply that stars on the
> edge of the sun which is "in front of" our orbital path around the Sun
> should be slightly blueshifted, and light which is "in back of" our
> orbital path should be slightly redshifted, as a result of its trek close
> to the Sun.
No. See above.
> Viewed differently, on the backside, the 3-d path is "getting shorter" as
> the Sun moves out of the way, so the number of wavecrests "in transit"
> must be decreasing, which implies there's a blueshift. On the front side,
> the path is "getting longer" as the Sun moves into our line of sight, so
> the number of wavecrests "in transit" along that line is increasing, and
> there must be redshift.
Let's estimate this: The maximum deflection is 1.75 arc-seconds (8.48E-6
radians) and the earth-sun distance is 1.5E13 cm, so the height of the
obvious triangle is 1.27E8 cm, and the hypoteneuse minus base is 5.4E2
cm, corresponnding to a delay of about 18 ns. By contrast, the Shapiro
time delay can be several tens of microseconds, so this merely modulates
that slightly. When the line-of-sight is far from the sun, all the
effects must cancel out, of course.
Tom Roberts tjro...@lucent.com
sal
Two things.
First, if the light is redshifted while the sun is approaching its path,
it lost energy. Where'd the energy go?
Second, more to the point: If the Sun is moving to the _right_, light
passing to the right of it will be deflected to the _left_.
That means the momentum of the photons increased along a 3-vector pointing
to the _left_.
Therefore, if momentum is to be conserved, the Sun's momentum
must have increased along a 3-vector pointing to the _right_.
So, since the Sun is moving to the right, it actually gained kinetic
energy (in our FoR).
The reverse must be true as well for light passing to the left of the sun
in this case.
Same effect as slingshotting a spacecraft around Jupiter -- only the scale
is different :-)
>
>>
>> That would imply that stars on the edge of the sun which is "in
>> front of" our orbital path around the Sun should be slightly
>> blueshifted, and light which is "in back of" our orbital path
>> should be slightly redshifted, as a result of its trek close to the
>> Sun.
>
> No. See above.
But the effect is, at least, in the right direction. Perhaps my
terminology is confusing to the point of murk -- "in back of" our
orbital path, the Sun will appear to be approaching the stars, and as
you agreed the light should be redshifted. "In front of" our orbital
path the Sun will be moving away and there will be blueshift.
>
>
>> Viewed differently, on the backside, the 3-d path is "getting
>> shorter" as the Sun moves out of the way, so the number of
>> wavecrests "in transit" must be decreasing, which implies there's a
>> blueshift. On the front side, the path is "getting longer" as the
>> Sun moves into our line of sight, so the number of wavecrests "in
>> transit" along that line is increasing, and there must be redshift.
>
> Let's estimate this: The maximum deflection is 1.75 arc-seconds
> (8.48E-6 radians) and the earth-sun distance is 1.5E13 cm, so the
> height of the obvious triangle is 1.27E8 cm, and the hypoteneuse
> minus base is 5.4E2 cm, corresponnding to a delay of about 18 ns. By
> contrast, the Shapiro time delay can be several tens of
> microseconds, so this merely modulates that slightly.
Cool. Presumably it's the modulation that causes the red/blue shift.
> When the line-of-sight is far from the sun, all the effects must
> cancel out, of course.
>
>
> Tom Roberts tjro...@lucent.com
--
Tom Roberts
> On Fri, 02 Sep 2005 02:35:34 +0000, Tom Roberts wrote:
>>But your
>>notion of "stealing" energy does not make sense (your geometrical
>>argument later, however, does).
>
> it lost energy. Where'd the energy go?
Nowhere, or anywhere. Energy need not be conserved for this non-local
situation. I don't think it is possible to trace it in detail, given the
approximation used, because it is so very tiny.
> Second, more to the point: If the Sun is moving to the _right_, light
> passing to the right of it will be deflected to the _left_.
> That means the momentum of the photons increased along a 3-vector pointing
> to the _left_.
> Therefore, if momentum is to be conserved, the Sun's momentum
> must have increased along a 3-vector pointing to the _right_.
> So, since the Sun is moving to the right, it actually gained kinetic
> energy (in our FoR).
> The reverse must be true as well for light passing to the left of the sun
> in this case.
> Same effect as slingshotting a spacecraft around Jupiter -- only the scale
> is different :-)
OK. Now that makes sense. Except that the approximation used treats the
sun as motionless (and therefore an infinite sink for momentum). This,
too, is related to the approximation used.
> Perhaps my
> terminology is confusing to the point of murk -- "in back of" our
> orbital path, the Sun will appear to be approaching the stars, and as
> you agreed the light should be redshifted. "In front of" our orbital
> path the Sun will be moving away and there will be blueshift.
I think of it as we observe it -- the sun traverses in front of the
stars. That's how I described it.
>>>Viewed differently, on the backside, the 3-d path is "getting
>>>shorter" as the Sun moves out of the way, so the number of
>>>wavecrests "in transit" must be decreasing, which implies there's a
>>>blueshift. On the front side, the path is "getting longer" as the
>>>Sun moves into our line of sight, so the number of wavecrests "in
>>>transit" along that line is increasing, and there must be redshift.
>>
>>Let's estimate this: The maximum deflection is 1.75 arc-seconds
>>(8.48E-6 radians) and the earth-sun distance is 1.5E13 cm, so the
>>height of the obvious triangle is 1.27E8 cm, and the hypoteneuse
>>minus base is 5.4E2 cm, corresponnding to a delay of about 18 ns. By
>>contrast, the Shapiro time delay can be several tens of
>>microseconds, so this merely modulates that slightly.
>
> Cool. Presumably it's the modulation that causes the red/blue shift.
I meant there is an overall delay of a few 10s of microseconds,
"modulated" by an additional ~18 ns as the sun gets closer to the
line-of-sight, and later reduced by ~18 ns as the sun receeds. These
should be taken as only order-of-magnitude estimates, as their
dependencies on time will be different; those values are the total delay
at the sun's outer radius relative to the sun being far from the
line-of-sight. The Shapiro delay goes from ~zero to maximum over several
weeks, but the deflection goes from ~zero to maximum over a few hours or
days (IIRC).
Tom Roberts tjro...@lucent.com
Dr Photon
>sal wrote:
>> it lost energy. Where'd the energy go?
>Nowhere, or anywhere. Energy need not be conserved for this non-local
>situation. I don't think it is possible to trace it in detail, given the
>approximation used, because it is so very tiny.
Do you mean that energy is not conserved due to approximations in the
modelling, or really that energy may not be conserved?
(must get ready to patent my perpetual motion machine... bet I'll make
mine before Bearden makes his MEG)
I've heard rumours that conservation of energy is a murky subject in
GR, are you implying this simple situation is an example?
br
Dr Photon
>Dr Photon wrote:
>> Since Einstein died in 1955, and the Shapiro delay was only predicted
>> in 1964, then he couldn't have been referring to that.
>Sure he could -- Einstein was extremely well-versed in the basis of GR,
hehe!
>and he most definitely knew that the speed of light can vary when
>measured over non-local paths.
smart guy that Einstein
>Shapiro's contribution was to realize
>that this esoteric aspect of GR could actually be measured, and he went
>on to measure it.
I presume Einstein would have appreciated it could be measured had he
given it a thought (and maybe he did), but actually figuring out a
practical way to do it and then measuring it is a good contribution. It
still intrigues me how some effects get to be named after people and
some don't, even though the effect was known before. Seems pretty
random some times, but that's history for you.
br
Tom Roberts
> Tom Roberts wrote:
>>Energy need not be conserved for this non-local
>>situation. I don't think it is possible to trace it in detail, given the
>>approximation used, because it is so very tiny.
>
> Do you mean that energy is not conserved due to approximations in the
> modelling, or really that energy may not be conserved?
Either or both. I'm not sure.
> I've heard rumours that conservation of energy is a murky subject in
> GR, are you implying this simple situation is an example?
Conservation of energy is indeed a "murky subject" when one considers
non-local measurements. Locally there's no doubt that energy is
conserved. This is a non-local example.
By "locally" I mean over a region of spacetime small enough
so that variations in the metric and curvature tensors can be
neglected compared to the measurement resolution.
For example, a high-energy interaction at Fermilab in the D0
detector is clearly a local measurement; throwing a baseball
is not. The former covers a region of ~20 meters in spacetime,
the latter covers ~10^9 meters (~3 light-seconds) in spacetime.
Tom Roberts tjro...@lucent.com
Dr Photon
>Conservation of energy is indeed a "murky subject" when one considers
>non-local measurements. Locally there's no doubt that energy is
>conserved. This is a non-local example.
> By "locally" I mean over a region of spacetime small enough
> so that variations in the metric and curvature tensors can be
> neglected compared to the measurement resolution.
> For example, a high-energy interaction at Fermilab in the D0
> detector is clearly a local measurement; throwing a baseball
> is not. The former covers a region of ~20 meters in spacetime,
> the latter covers ~10^9 meters (~3 light-seconds) in spacetime.
I guess there will always be a problem with comparing what's "over
here" with what's "over there", but what about the following:
If there is a way that conservation of energy is not conserved
non-locally, is there any way to get at it? So if I threw a baseball at
an electric generator (via all sorts of weird spacetime curvatures, if
necessary), that then powered a light bulb, which directed its light
back to me, is it possible I could get back more than I spent? Even in
this "closed-loop" situation, by the time the light-energy returns to
me, I am in a different point in space-time, so even the closed-loop is
a non-local situation? Or is it that so long as the metric and
curvature tensors haven't changed where I am, then I cannot avail of
any strange results "over there"?
What about Noether's theorem - if the laws of physics stay constant in
time, then energy is conserved? This only applies "over here"?
br
Tom Roberts
> I guess there will always be a problem with comparing what's "over
> here" with what's "over there"
Yes, and that implies a similar problem summing up what's "over there"
with what's "over here"....
The basic problem with non-local "conservation of energy" is the
difficulty or impossibility of integration in curved manifolds.
> If there is a way that conservation of energy is not conserved
> non-locally, is there any way to get at it?
No. Thermodynamically this is not free energy.
> What about Noether's theorem - if the laws of physics stay constant in
> time, then energy is conserved? This only applies "over here"?
It's not the "laws of physics" that must stay constant in time, it is
the Lagrangian of the system in question. Geometrically, this means that
the manifold in question must have a timelike Killing vector; such
manifolds are quite rare, and certainly the universe we inhabit cannot
be modeled by any of them. In essence, the presence of a timelike
Killing vector implies that no gravitational radiation is emitted, and
that's what screws up energy conservation in finite regions. Of course
nothing "moves" in a manifold with a timelike Killing vector, so such
manifolds can model only a VERY restricted set of physical systems....
Tom Roberts tjro...@lucent.com
Bill Hobba
"Dr Photon" <brendan....@nmrc.ie> wrote in message
news:1125670196.2...@g43g2000cwa.googlegroups.com...
> Tom Roberts wrote:
>
>>Conservation of energy is indeed a "murky subject" when one considers
>>non-local measurements. Locally there's no doubt that energy is
>>conserved. This is a non-local example.
>
>> By "locally" I mean over a region of spacetime small enough
>> so that variations in the metric and curvature tensors can be
>> neglected compared to the measurement resolution.
>
>
>> For example, a high-energy interaction at Fermilab in the D0
>> detector is clearly a local measurement; throwing a baseball
>> is not. The former covers a region of ~20 meters in spacetime,
>> the latter covers ~10^9 meters (~3 light-seconds) in spacetime.
>
> I guess there will always be a problem with comparing what's "over
> here" with what's "over there", but what about the following:
>
> If there is a way that conservation of energy is not conserved
> non-locally, is there any way to get at it?
Well that depends on what you mean by get at it. The energy of a closed
system is always conserved even when using GR in the unversed at large so
there is no real way to get a free lunch. Unless you consider the unversed
itself as the ultimate free lunch - it total energy is - you guessed it is
zero (see the paper I give later for the details). This means if you get
energy from somewhere it must come from somewhere else.
> So if I threw a baseball at
> an electric generator (via all sorts of weird spacetime curvatures, if
> necessary), that then powered a light bulb, which directed its light
> back to me, is it possible I could get back more than I spent? Even in
> this "closed-loop" situation, by the time the light-energy returns to
> me, I am in a different point in space-time, so even the closed-loop is
> a non-local situation? Or is it that so long as the metric and
> curvature tensors haven't changed where I am, then I cannot avail of
> any strange results "over there"?
>
> What about Noether's theorem - if the laws of physics stay constant in
> time, then energy is conserved? This only applies "over here"?
Noethers theorem is the exact cause of the problem. Energy conservation is
the conserved charge related to time symmetry which in general only occurs
if a timelike killing vector exists, which if memory serves me correctly, is
the same as the gravitational field being stationary. It really is only a
problem for the unverse at large from which the most interesting question I
suppose is what happens to the energy of the CBMR photons as they are red
shifted - it goes into the gravitational field. I found the following paper
helped me understand what is happening -
http://arxiv.org/PS_cache/gr-qc/pdf/9701/9701028.pdf
Thanks
Bill
>
> br
>
Mike
Tom Roberts wrote:
> Dr Photon wrote:
> > Tom Roberts wrote:
> >>Energy need not be conserved for this non-local
> >>situation. I don't think it is possible to trace it in detail, given the
> >>approximation used, because it is so very tiny.
> >
> > Do you mean that energy is not conserved due to approximations in the
> > modelling, or really that energy may not be conserved?
>
> Either or both. I'm not sure.
>
>
> > I've heard rumours that conservation of energy is a murky subject in
> > GR, are you implying this simple situation is an example?
>
> Conservation of energy is indeed a "murky subject" when one considers
> non-local measurements. Locally there's no doubt that energy is
> conserved. This is a non-local example.
I suppose you understand the ramifications of your statements on the
nature of physical reality. If you do not, I suggest you refrain from
such absurd statements. If you do understand what non-local
non-conservation of energy implies, why do you still deal with GR and
not going back to your drawing board for a better theory?
Just for the purpose or being a little more explicit without crashing
the ongoing party, do you believe Dr. Roberts there is some process
that non-locally pumps or drains energy so that the world is
maintained?
I have tried to explain to you numerous time not to use heterological
assertions. Take a non-local region. Divide it into N local regions. In
each local region energy is conserved. But that may not be the case in
the union of these non-local regions according to your heterology.
This is strange in indeed. I do not see anything that happens according
to GR in between these local regions that can result in a non-local
non-conservation of energy. Hmmmmm....
Mike
ytyour...@p.zapto.org
Pentcho Valev wrote:
> A. Einstein, "Relativity", Chapter 22:
>
> "A curvature of rays of light can only take place when the velocity of
> propagation of light VARIES with position."
>
This is called "quoting out of context". The sentence that you pose
there appears originally in this context:
[quote]
In the second place our result shows that, according to the general
theory of relativity, the law of the constancy of the velocity of light
in vacuo, which constitutes one of the two fundamental assumptions in
the special theory of relativity and to which we have already
frequently referred, cannot claim any unlimited validity. A curvature
of rays of light can only take place when the velocity of propagation
of light varies with position. Now we might think that as a consequence
of this, the special theory of relativity and with it the whole theory
of relativity would be laid in the dust. But in reality this is not the
case. We can only conclude that the special theory of relativity cannot
claim an unlimited domain of validity; its result hold only so long as
we are able to disregard the influences of gravitational fields on the
phenomena (e.g. of light).
Since it has often been contended by opponents of the theory of
relativity that the special theory of relativity is overthrown by the
general theory of relativity is overthrown by the general theory of
relativity, it is perhaps advisable to make the facts of the case
clearer by means of an appropriate comparison. Before the development
of electrodynamics the laws of electrostatics and the laws of
electricity were regarded indiscriminately. At the present time we know
that electric fields can be derived correctly from electrostatic
considerations only for the case, which is never strictly realised, in
which the electrical masses are quite at rest relatively to each other,
and to the co-ordinate system. Should we be justified in saying that
for this reason electrostatics is overthrown by the field-equations of
Maxwell in electrodynamics? Not in the least. Electrostatics is
contained in electrodynamics as a limiting case; the laws of the latter
lead directly to those of the former for the case in which the fields
are invariable with regard to time. No fairer destiny could be allotted
to any physical theory, than that it should of itself point out theway
to the introduction of a more comprehensive theory, in which it lives
on as a limiting case.
[end quote]
So in 1922, Mr Einstein already knew what the brainless were going to
say in 2005 in response to the one sentence that you ripped out of
context above there and already presented the case why it is invalid.
You have been preempted by a guy who's been dead for 50 years.
That's pretty pathetic.
>
> Einsteinians never discuss this problem voluntarily but,
>
1) There is no "problem" here anywhere
2) thus there's nothing to "discuss" here
3) There's no such things as an "Einsteinian"
cordially
Y.T.
--
Remove YourClothes before you email me.
Tom Roberts
> Tom Roberts wrote:
>>Conservation of energy is indeed a "murky subject" when one considers
>>non-local measurements. Locally there's no doubt that energy is
>>conserved. This is a non-local example.
>
> I suppose you understand the ramifications of your statements on the
> nature of physical reality.
Somehow I don't think my statements are going to affect nature or how
she operates the universe. (:-))
> If you do understand what non-local
> non-conservation of energy implies, why do you still deal with GR and
> not going back to your drawing board for a better theory?
Because GR _IS_ the best theory we have right now for such phenomena. By
a considerable margin. Non-local non-conservation of energy is not a
problem, and GR itself agrees with all experiments within its domain of
applicability[#]. Experiment is the touchstone for physics, not the
nebulous ideas you seem to think imply there is a "better theory" out
there....
[#] But there are some tantalizing intimations of new
phenomena and/or possible violations of GR: dark matter
and energy, and the anomalous accelerations of Pioneer
and other spacecraft.
> Just for the purpose or being a little more explicit without crashing
> the ongoing party, do you believe Dr. Roberts there is some process
> that non-locally pumps or drains energy so that the world is
> maintained?
Huh? There is no "pump or drain" involved in the non-local
non-conservation of energy, it's just that in general there is no
self-consistent definition of "energy" over a finite region, and if
there is no well-defined notion of "energy", how could it possibly be
"conserved"?
> Take a non-local region. Divide it into N local regions. In
> each local region energy is conserved.
No. In GR energy is conserved only approximately in any finite region;
it is exactly conserved only in the limit as the 4-volume of the region
goes to zero. That is, conservation of energy is expressed as a
differential equation, and in general it is not integrable.
> But that may not be the case in
> the union of these non-local regions according to your heterology.
I have no "heterology", I merely point out that you cannot generalize
this property that holds only in the limit as 4-volume => 0 to a finite
region. <shrug>
> I do not see anything that happens according
> to GR in between these local regions that can result in a non-local
> non-conservation of energy.
Clearly you do not understand the issues involved. There are thorns when
attempting to union an infinite number of infinitesimal regions into a
finite-sized region. This is called "integration" and for the integrals
we are concerned with, the general integrability condition is that the
Riemann curvature tensor be zero (i.e. the manifold be flat throughout
the region of interest). That is sufficient but not necessary, and there
are some special cases for which Riemann is nonzero but a meaningful
global definition of energy can be made.
Tom Roberts tjro...@lucent.com
Mike
Tom Roberts wrote:
> Mike wrote:
> > Tom Roberts wrote:
> >>Conservation of energy is indeed a "murky subject" when one considers
> >>non-local measurements. Locally there's no doubt that energy is
> >>conserved. This is a non-local example.
> >
> > I suppose you understand the ramifications of your statements on the
> > nature of physical reality.
>
> Somehow I don't think my statements are going to affect nature or how
> she operates the universe. (:-))
Of course not, but again of course they imply something along those
lines.
>
>
> > If you do understand what non-local
> > non-conservation of energy implies, why do you still deal with GR and
> > not going back to your drawing board for a better theory?
>
> Because GR _IS_ the best theory we have right now for such phenomena. By
> a considerable margin. Non-local non-conservation of energy is not a
> problem, and GR itself agrees with all experiments within its domain of
> applicability[#]. Experiment is the touchstone for physics, not the
> nebulous ideas you seem to think imply there is a "better theory" out
> there....
>
> [#] But there are some tantalizing intimations of new
> phenomena and/or possible violations of GR: dark matter
> and energy, and the anomalous accelerations of Pioneer
> and other spacecraft.
>
Violation of GR, is a term used in place of falsification of GR.
>
> > Just for the purpose or being a little more explicit without crashing
> > the ongoing party, do you believe Dr. Roberts there is some process
> > that non-locally pumps or drains energy so that the world is
> > maintained?
>
> Huh? There is no "pump or drain" involved in the non-local
> non-conservation of energy, it's just that in general there is no
> self-consistent definition of "energy" over a finite region, and if
> there is no well-defined notion of "energy", how could it possibly be
> "conserved"?
Why are you playing with words? Are you affirming the consequent maybe?
of course you are.
>
>
> > Take a non-local region. Divide it into N local regions. In
> > each local region energy is conserved.
>
> No. In GR energy is conserved only approximately in any finite region;
> it is exactly conserved only in the limit as the 4-volume of the region
> goes to zero. That is, conservation of energy is expressed as a
> differential equation, and in general it is not integrable.
>
But this is what you said in this topic that local means:
" By "locally" I mean over a region of spacetime small enough
so that variations in the metric and curvature tensors can be
neglected compared to the measurement resolution.
Now, you are talking about something diffwerent. Please not that
the3-body problem equations are not integrable, but still 3 or more
bodies out there in the planetary system do pretty well.
>
> > But that may not be the case in
> > the union of these non-local regions according to your heterology.
>
> I have no "heterology", I merely point out that you cannot generalize
> this property that holds only in the limit as 4-volume => 0 to a finite
> region. <shrug>
You do have heterology in your argument. Because, eventually, whether
the equations are not integrabl;e or not, a non-local region is a
continuum at each point of which you can have a limit that defines a
non-local region. Unless, it is not a continuum. and unless you believe
motion is not continuous.
>
>
> > I do not see anything that happens according
> > to GR in between these local regions that can result in a non-local
> > non-conservation of energy.
>
> Clearly you do not understand the issues involved. There are thorns when
> attempting to union an infinite number of infinitesimal regions into a
> finite-sized region.
Clearly you do not understand something very simple. (great minds often
have this problem). Ther are 'thorns" with the math, yes. But,
continuity implies that eventually, whether you can integrate or not,
the Infinite Sume Principle must apply (look it up). otherwise, you are
subject to Zeno's paradoxes or plurality.
> This is called "integration" and for the integrals
> we are concerned with, the general integrability condition is that the
> Riemann curvature tensor be zero (i.e. the manifold be flat throughout
> the region of interest). That is sufficient but not necessary, and there
> are some special cases for which Riemann is nonzero but a meaningful
> global definition of energy can be made.
>
You are mixing math and physics in an very clumsy way. The Axiom of
Energy Conservation is a principle of physics and it precludes
perpetual machines of the second kind. Mathematics are still inedequate
to provide close form solutions even to the simplest phenomena, such as
for instance the 3-body problem. When math because the platform on
which physics is build, the game is lost. And you seem to have lost the
game.
It is sommon sense that any theory that does not conserve energy
non-locally to be abandoned. Instead, you cry non-integrable. Yak...
Mike
>
> Tom Roberts tjro...@lucent.com
Bill Hobba
"Mike" <ele...@yahoo.gr> wrote in message
news:1125783870.6...@g49g2000cwa.googlegroups.com...
Mike what Tom is saying is perfetly logical. If enrgy can not be defined
how can it be conserved? For the universe at large however it is possible
to define energy - and quite interestingly it turns out ot be zero. So
overall enrgy is conserved
Mike please acquaint yourself with modern treatments of energy as sorted out
by Noether in her famous theorem. Energy conservation is not a principle of
physics - it is simply a tautological statement about the symmetries of a
systems lagrangian. And in situations where energy can not be readily
defined how would you know if it is conserved or not?
> Mathematics are still inedequate
> to provide close form solutions even to the simplest phenomena, such as
> for instance the 3-body problem. When math because the platform on
> which physics is build, the game is lost. And you seem to have lost the
> game.
Then build it on another foundation - just make sure it can make peditions
as well as current theries and is equally in accord with expriemnt.
Bill
Mike
Mixing models and laws Bill?
Any model that fails to adequatly describe energy is flawed. I have
explained many times to you and Roberts why non-local conservation is a
logical impossibility and thus any model subject to it contains
contradictions. But Roberts switches between infinitesimals and limits
depending on the argument.
Case (1): local is defined in terms of limits
Then, the equivalence principle cannot be tested experimentally since
in practice there can be no such region. Therefore, EP cannot be
falsified. But since EP has been confirmed to about 1 part in a
trillion for non-local regions, then local EP holding in theory leads
to non-local EP holding in practice. Hence, non-local entails local in
that theory.
case (2): local is defined in terms of infinitesimals
In this case, by using non-standard analysis, since conservations
applies to every infinitesimal region, it must apply to every region,
whether infinitesimal or not. This case better explains the physical
situation while case (1) is only used in arguments in favor of the
non-conservation of energy/momentum in GR.
case (3): local is defined in terms of X
Just to be fair, there is a possibility that the failure of
energy/momentum conservation non-locally in GR is due to the wrong
application of the concept of local. This leads to interesting
possibilities having to do with discrete space-time and a GR like
theory that is inherently quantized while it conforms to non-local
conservation.
Neverteless, it is not very scientific to use terms, such as local,
with different definitions just to justify different situations of the
same theory.
Mike
John C. Polasek
wrote:
All of this debate is due to the fact that relativity has no strong
model. It's all done with Schwarzschild and it contains errors. I can
see that nearly everyone believes gravity reduces the frequency of
light. And that clocks run slow in gravity. And that, generally
speaking the velocity of light is constant. Er, except for Shapiro.
Lots of debate about how energy can't be conserved.
Dual Space theory has it right: a clock in gravity will run slower and
its emitted frequency will be lower than out of gravity. But, energy E
= hf never changes after that. Likewise the speed of light is reduced
at the origin in gravity. Therefore right at the source (with the
clock in gravity) the clock is X% low, its emitted frequency is X%
low, and the WL is normal = 1.
But on rising out of the gravity field, the energy hf remains the
same, but c increases by X% so the WL stretches by X%. That's the red
shift-increase in wavelength. The frequency remains as manufactured
and with its original energy never more or less.
But in relativity, the Pound and Rebka ("Possible Weight of Photons")
experiment talks as if the frequency is reduced on the way out of a
gravity well due to energy loss % = gh/c^2. So if it loses X% in
frequency on the way out, and is now measured for frequency by a clock
outside that is thereby running X% faster, the difference in frequency
will be 2X% double the ideal value.
The cause for the Shapiro effect should be derivable from the
Schwarzschild metric but I haven't seen it done.
In Dual Space, c reduces X% with gravity (in place of "time dilation")
and also the underlying space cells dilate by X%, because gravity is a
sign of a weakened underlying Espace. With DS you can get all of
relativity in a Cartesian model, besides which DS can explain the
Pioneer anomaly. I am finishing up a paper on it for the arxiv's.
John Polasek
http://www.dualspace.net
Tom Roberts
> Tom Roberts wrote:
>>>Take a non-local region. Divide it into N local regions. In
>>>each local region energy is conserved.
>>
>>No. In GR energy is conserved only approximately in any finite region;
>>it is exactly conserved only in the limit as the 4-volume of the region
>>goes to zero. That is, conservation of energy is expressed as a
>>differential equation, and in general it is not integrable.
>
> But this is what you said in this topic that local means:
> " By "locally" I mean over a region of spacetime small enough
> so that variations in the metric and curvature tensors can be
> neglected compared to the measurement resolution.
> Now, you are talking about something diffwerent.
Not really. When one NEGLECTS something, that does not mean it is zero,
it means (in this case) that is is smaller than the measurement
resolution, and thus cannot significantly affect the measurement. Math
is not physics -- in physics we ALWAYS make approximations (at a minimum
our apparatus does so for us), and it is important to understand the
validity of those approximations. <shrug>
> Please not that
> the3-body problem equations are not integrable, but still 3 or more
> bodies out there in the planetary system do pretty well.
That is not non-integrable -- the 3-body problem (in Newtonian
mechanics) has no closed-form solution, but it definitely has a well
defined mathematical solution (available via numerical integration) --
the equations of motion are definitely integrable. But in GR the "total
energy" in a finite region of a curved manifold in general has no
solution; at base this is due to the fact that such integrals are path
dependent, and if you attempt to sum up a region the answer you get
depends on the order and method you use to sum up the (infinitesimal)
parts, so the integral is not well defined.
Simple analogy: in the Euclidean plane with Cartesion
coordinates x and y, \integral f(x,y) dx dy is equal to
\integral f(x,y) dy dx. But in a curved manifold, the
analogous integrals do not necessarily equal each other,
which means that the quantity represented by such an
integral is not well defined.
Note: this is a simple analogy, not a rigorous argument. For that you'll
need to consult a textbook on differential geometry.
> a non-local region is a
> continuum at each point of which you can have a limit that defines a
> non-local region. Unless, it is not a continuum. and unless you believe
> motion is not continuous.
You are thinking of FINITE sets and/or sums. An infinite sum of
infinitesimals does not necessarily behave the same as a finite sum of
finite regions.
> continuity implies that eventually, whether you can integrate or not,
> the Infinite Sume Principle must apply (look it up).
Not in curved manifolds. <shrug>
> The Axiom of
> Energy Conservation is a principle of physics
No, it is not. In the (very) old days is was perhaps thought of that
way, but now we know that energy conservation is merely a consequence of
a specific symmetry of the Lagrangian of the system, and is by itself of
no deep significance at all. The fundamental thing is the Lagrangian
itself, and conservation of energy is a consequence of that (Newtonian
mechanics).
> and it precludes
> perpetual machines of the second kind.
Such are not possible in GR, even though global energy conservation is
not well defined. NOTE: I am NOT saying "energy is not conserved", I'm
saying that "energy" itself is not well defined so "conservation" cannot
be determined.
> Mathematics are still inedequate
> to provide close form solutions even to the simplest phenomena, such as
> for instance the 3-body problem.
Math has given us solutions for any 3-body system of interest, via
numerical integration. You are confusing simplicity with capability. <shrug>
> When math because the platform on
> which physics is build, the game is lost.
Nonsense. Without math there is no ability to compare theory with
experiment, which is the FOUNDATION of physics.
> And you seem to have lost the
> game.
You don't even know what the game is. This issupposed to be _science_,
not whatever it is you are trying to do.
> It is sommon sense that any theory that does not conserve energy
> non-locally to be abandoned.
Common sense has proven to be COMPLETELY AND UTTERLY UNRELIABLE in
regimes far removed from our everyday lives where that common sense was
developed. This ought to be obvious (the universe does not revolve
around humans). <shrug>
Tom Roberts tjro...@lucent.com
Bilge
>
>>Conservation of energy is indeed a "murky subject" when one considers
>>non-local measurements. Locally there's no doubt that energy is
>>conserved. This is a non-local example.
>
>> By "locally" I mean over a region of spacetime small enough
>> so that variations in the metric and curvature tensors can be
>> neglected compared to the measurement resolution.
>
>
>> For example, a high-energy interaction at Fermilab in the D0
>> detector is clearly a local measurement; throwing a baseball
>> is not. The former covers a region of ~20 meters in spacetime,
>> the latter covers ~10^9 meters (~3 light-seconds) in spacetime.
>
>I guess there will always be a problem with comparing what's "over
>here" with what's "over there", but what about the following:
>
>If there is a way that conservation of energy is not conserved
>non-locally, is there any way to get at it? So if I threw a baseball at
>an electric generator (via all sorts of weird spacetime curvatures, if
>necessary), that then powered a light bulb, which directed its light
addresses your question regarding noether's theorem, too. Energy is
defined as the conserved quantity associated with invariance under
time translations. That comes straight from noether's theorem.
The metric has 16 components, 10 of which are independent, so
the metric has 10 degrees of freedom. You will be able to define
a conserved energy if you can make the metric time independent.
You are free to make a change of coordinates to do that, but a
coordinate transformation only has 4 degrees of freedom. In general,
that is not sufficient to remove the time dependence. That means you
cannot define a quantity called the energy such that it is conserved.
Dr Photon
>Dr Photon wrote:
>> I guess there will always be a problem with comparing what's "over
>> here" with what's "over there"
>Yes, and that implies a similar problem summing up what's "over there"
>with what's "over here"....
>The basic problem with non-local "conservation of energy" is the
>difficulty or impossibility of integration in curved manifolds.
so what exactly does the paper Bill Hobba referenced imply?
http://arxiv.org/PS_cache/gr-qc/pdf/9701/9701028.pdf
This seems to be basically saying that whether or not we can define the
energy of a region (at least it is not defined absolutely), we still
know that it is not arbitrarily increasing or decreasing. But does it
also give a measure of the energy of a region?
>> If there is a way that conservation of energy is not conserved
>> non-locally, is there any way to get at it?
>No. Thermodynamically this is not free energy.
well I expected that of course, but it's fun to try!
br
Dr Photon
> Here's the basic problem with defining a conserved energy, which
>addresses your question regarding noether's theorem, too. Energy is
>defined as the conserved quantity associated with invariance under
>time translations. That comes straight from noether's theorem.
according to such *definitions*, then energy can never be created or
destroyed. It intrigued me in the paper Bill Hobba referenced, that the
author seemed to be *looking* for a conserved quantity (ok, not that I
followed all the tensors...). But still it seems to make sense that in
some (currently unknown) circumstance that energy *could* be created?
Otherwise we are saying it is an impossibility by definition.
>The metric has 16 components, 10 of which are independent, so
>the metric has 10 degrees of freedom. You will be able to define
>a conserved energy if you can make the metric time independent.
>You are free to make a change of coordinates to do that, but a
>coordinate transformation only has 4 degrees of freedom. In general,
>that is not sufficient to remove the time dependence. That means you
>cannot define a quantity called the energy such that it is conserved.
which taken by itself seems to imply that energy *could* increase. I
appreciate Tom's point that if something is undefined, then you can't
talk about it increasing or decreasing. Bill pointed out that if the
metric is static then energy will not increase, and went on to imply
that if the metric does change and the local energy increases, then
that energy must have come from somewhere else. (for example, moving
masses around may change the metric and increase the potential where I
am, but it must have taken energy to move the masses around).
However, I am still a little concerned about defining energy as "that
which does not increase in time". As far as Noether and Lagragians go,
I guess that is saying that if the Lagrangian needed to describe a
system changed with time, then energy *could* increase, but that would
require changing the laws of motion. Ok, this has never been observed,
but is it a-priori impossible?
br
Tom Roberts
> The metric has 16 components, 10 of which are independent, so
> the metric has 10 degrees of freedom. You will be able to define
> a conserved energy if you can make the metric time independent.
> You are free to make a change of coordinates to do that, but a
> coordinate transformation only has 4 degrees of freedom. In general,
> that is not sufficient to remove the time dependence. That means you
> cannot define a quantity called the energy such that it is conserved.
The usual way of stating this requirement is that the manifold must have
a timelike Killing vector (that guarantees the 4-fold freedom of a
coordinate transfom is indeed sufficient to remove the time dependence
from all metric components; it of course does this by limiting the
permitted form of those components). This GREATLY limits the set of
manifolds with this property. In such a manifold, using the timelike
Killing vector as the time coordinate, nothing moves, so it's not useful
as a model of the real world.
BTW the metric components have 10 ALGEBRAICALLY-independent
degrees of freedom, but they are not completely independent.
In fact, the Einstein field equation and the Bianchi identities
are sufficient to determine them all (given suitable boundary
conditions, as these are differential equations, not algebraic
ones).
Tom Roberts tjro...@lucent.com
John C. Polasek
Schoenfeld
Bilge wrote:
>
> Here's the basic problem with defining a conserved energy, which
> addresses your question regarding noether's theorem, too. Energy is
> defined as the conserved quantity associated with invariance under
> time translations. That comes straight from noether's theorem.
Energy conservation of some system may be _equivalent_ to the time
translation symmetry of the systems Lagrangian but it is not
necessarily DEFINED that way. The difference is important because lack
of said symmetry does not imply energy conservation violation. Energy
is DEFINED as an abstract quantity remaining constant throughout a
closed systems time-evolution. If such quantity changes, then it is not
energy. Lack of time-translation symmetry reveals more on the character
of GR/Noether's thereom than it does on energy conservation.
Tom Roberts
> Energy conservation of some system may be _equivalent_ to the time
> translation symmetry of the systems Lagrangian but it is not
> necessarily DEFINED that way.
Sure it is. This is 2005, not ~1900.
> The difference is important because lack
> of said symmetry does not imply energy conservation violation.
Actually it does (insofar as "energy" can be defined at all in such
systems). That's why the definition changed once Noether's theorem
explained the inconsistencies. Of course in classical mechanics the
Lagrangian is time invariant, so the question never came up. <shrug>
Noether's theorem says that for every continuous symmetry of
the Lagrangian there is a corresponding conserved quantity,
and for every conserved quantity there is a corresponding
symmetry. It also specifies how either can be determined from
the other.
> Energy
> is DEFINED as an abstract quantity remaining constant throughout a
> closed systems time-evolution.
Not true. See above -- what you claim simply is not possible. If your
"abstract quantity" is conserved, there is a symmetry of the Lagrangian
corresponding to it, and if that symmetry is not time translation
invariance, then your "abstract quantity" is not energy. <shrug>
In modern physics, energy is specifically defined as the conserved
Noether current related to time translation invariance of the system's
Lagrangian. This is not "abstract" at all. <shrug>
> If such quantity changes, then it is not
> energy.
If there is no time translation invariance of the Lagrangian, then there
is no useful definition of "energy".
> Lack of time-translation symmetry reveals more on the character
> of GR/Noether's thereom than it does on energy conservation.
Your statements reveal more about your lack of knowledge about modern
physics, than about energy conservation.
I know of no simple examples of systems with a time dependent
Lagrangian. But an advanced example is any system in GR that emits or
absorbs gravitational radiation. In some sense, gravitational radiation
can carry "the ability of the system to do work" into or out of an
ostensibly closed system. It can, in general, zoom out to or come in
from spatial infinity, so there is no possibility of "closing the system".
The Lagrangian for GR includes the term \integral R dV, where R is the
Ricci scalar and dV is the invariant volume element; the integral
extends over the entire manifold. A sufficient condition for this term
to be time-translation invariant is the existence of a timelike Killing
vector (and its use as the time coordinate); necessary conditions are
more complicated....
Tom Roberts tjro...@lucent.com
Tom Roberts
> All of this debate is due to the fact that relativity has no strong
> model. It's all done with Schwarzschild and it contains errors.
That is simply not true. The Schwarzschild solution is ONE solution to
the equations of GR. By no means is "all done with Schwarzschild".
What "errors" do you think there are? The odds are very high that the
"errors" you mean are your own, and not in GR itself.
> I can
> see that nearly everyone believes gravity reduces the frequency of
> light. And that clocks run slow in gravity. And that, generally
> speaking the velocity of light is constant. Er, except for Shapiro.
> Lots of debate about how energy can't be conserved.
The "debate" comes from people who don't understand GR. The issues
themselves are not debatable. GR is what it is. <shrug>
> The cause for the Shapiro effect should be derivable from the
> Schwarzschild metric but I haven't seen it done.
Then you haven't looked. That's how Shapiro himself derived it. Of
course he may well have used an approximation....
Tom Roberts tjro...@lucent.com
Schoenfeld
Tom Roberts wrote:
> Schoenfeld wrote:
> > Energy conservation of some system may be _equivalent_ to the time
> > translation symmetry of the systems Lagrangian but it is not
> > necessarily DEFINED that way.
>
> Sure it is. This is 2005, not ~1900.
There is no reason to define energy in that way.
hint: The work exchanged in an adiabatic process depends only on the
initial and the final state and not on the details of the process.
>
> > The difference is important because lack
> > of said symmetry does not imply energy conservation violation.
>
> Actually it does (insofar as "energy" can be defined at all in such
> systems). That's why the definition changed once Noether's theorem
> explained the inconsistencies. Of course in classical mechanics the
> Lagrangian is time invariant, so the question never came up. <shrug>
That is a school-boy reasoning error. "If today is tuesday implies Tom
has to go to school" does NOT mean that "if today is not tuesday then
Tom does not have to go to school". There is a fundamental difference
between an equivalency and a definition, a difference which you should
learn.
> Noether's theorem says that for every continuous symmetry of
> the Lagrangian there is a corresponding conserved quantity,
> and for every conserved quantity there is a corresponding
> symmetry. It also specifies how either can be determined from
> the other.
More accurately, it says that certain symmetries imply certain
conserved quantities. The difference is important.
>If your
> "abstract quantity" is conserved, there is a symmetry of the Lagrangian
> corresponding to it,
That's not necessarily true. Noether's thereom applies only to theories
describable by a Lagrangian (or a Hamiltonian). In other cases, there
is no bijection between the set of symmetries and the set of conserved
quantities. For this reason there is NO reason to define energy in
general terms, as the time-translation symmetry of the Lagrangian.
> and if that symmetry is not time translation
> invariance, then your "abstract quantity" is not energy. <shrug>
Again NOT generally true.
> In modern physics, energy is specifically defined as the conserved
> Noether current related to time translation invariance of the system's
> Lagrangian. This is not "abstract" at all. <shrug>
That's false again. Some theories don't carry Lagrangian of Hamiltonian
formalisms, so you can't express energy with the definition you gave.
>
> > If such quantity changes, then it is not
> > energy.
>
> If there is no time translation invariance of the Lagrangian, then there
> is no useful definition of "energy".
Profoundly wrong.
Dr Photon
[snip]
>Tom Roberts wrote:
>> In modern physics, energy is specifically defined as the conserved
>> Noether current related to time translation invariance of the system's
>> Lagrangian. This is not "abstract" at all. <shrug>
>That's false again. Some theories don't carry Lagrangian of Hamiltonian
>formalisms, so you can't express energy with the definition you gave.
QM uses Hamiltonians, and GR uses Lagrangians (and I'm sure the
equations could be rearranged if needs be). They describe everything we
know so far, what theories do you refer to that *can't* be expressed
these ways?
br
Dr Photon
>Schoenfeld wrote:
>> Energy conservation of some system may be _equivalent_ to the time
>> translation symmetry of the systems Lagrangian but it is not
>> necessarily DEFINED that way.
>Sure it is. This is 2005, not ~1900.
My complaint is that we know QM and GR have to be modified, so there is
a small window for the possibility for the creation of energy. Say
under an extremely high E-field (a single electron orbiting a Z=200
nucleus, for example), what if the vacuum really becomes unstable and
has a small runaway effect which spits out a million particles for no
currently known reason? (ok I'm making this up, but for the sake of
argument...). Can we say that energy wasn't created, *by definition*?
Seems a bit over the top.
What if such a runaway condition accidentally happened in the centre of
the Sun, which turned into a gamma-ray burster and fried Earth?
Of course I'm not arguing that we can actually create energy, or the
above situations will happen, but I must admit discomfort in going from
"this is the way the universe seems to work" to saying "this is the way
the universe *does* work, *by definition*".
It reminds of the case of *defining* the speed of light as constant.
Sure it's consistent with everything we currently know, but I don't get
the point of *defining* it that way rather than saying that's just the
way it happens to be (as far as we know).
br
Bilge
>> The metric has 16 components, 10 of which are independent, so
>> the metric has 10 degrees of freedom. You will be able to define
>> a conserved energy if you can make the metric time independent.
>> You are free to make a change of coordinates to do that, but a
>> coordinate transformation only has 4 degrees of freedom. In general,
>> that is not sufficient to remove the time dependence. That means you
>> cannot define a quantity called the energy such that it is conserved.
>
>The usual way of stating this requirement is that the manifold must have
>a timelike Killing vector (that guarantees the 4-fold freedom of a
>coordinate transfom is indeed sufficient to remove the time dependence
or persons to whom you are stating it.
>from all metric components;
If that were the case, every metric would be invariant under a
time translation.
>it of course does this by limiting the
>permitted form of those components). This GREATLY limits the set of
>manifolds with this property. In such a manifold, using the timelike
>Killing vector as the time coordinate, nothing moves, so it's not useful
>as a model of the real world.
>
> BTW the metric components have 10 ALGEBRAICALLY-independent
> degrees of freedom, but they are not completely independent.
I have no idea what you mean by that. My best guess is that you are
trying to say that because several degrees of freedom are coupled,
the number of degrees of freedom is reduced, which simply isn't
true. The number of independent degrees of freedom is not a function
a function of whether or not those degrees of freedom are separable.
> In fact, the Einstein field equation and the Bianchi identities
> are sufficient to determine them all (given suitable boundary
> conditions, as these are differential equations, not algebraic
> ones).
Huh? Who said anything about not being able to determine any
metric components? Quie honestly, I havent the slightest idea how
any of this is connected to anything I wrote.
Bilge
>Bilge wrote:
>>
>> Here's the basic problem with defining a conserved energy, which
>> addresses your question regarding noether's theorem, too. Energy is
>> defined as the conserved quantity associated with invariance under
>> time translations. That comes straight from noether's theorem.
>
>Energy conservation of some system may be _equivalent_ to the time
>translation symmetry of the systems Lagrangian but it is not
>necessarily DEFINED that way.
Find another hobby. This one isn't working for you.
Bilge
>Tom Roberts wrote:
>> Schoenfeld wrote:
>> > Energy conservation of some system may be _equivalent_ to the time
>> > translation symmetry of the systems Lagrangian but it is not
>> > necessarily DEFINED that way.
>>
>> Sure it is. This is 2005, not ~1900.
>
>There is no reason to define energy in that way.
definition.
John C. Polasek
wrote:
>John C. Polasek wrote:
Well with your improvident editing you omitted a specific example of
GR self-contradiction that I mentioned, namely Pound-Rebka.
They (and apparently most everybody) thinks the "photon" loses energy
and frequency hf climbing up in a gravity well, and likewise think
that energy gravitates. It is agreed a clock out of gravity runs
faster. So when it comes time to test hf (-X%) out of the well against
a clock there, (+X%), the result is twice the book value -2X%. The
frequency loss is spuriously doubled. That's self-contradiction that's
been there forever, and should be examined, explained and then
disposed of.
OTOH if E = hf at time of emission and we deny any mechanism that
could cause a gain or loss in energy, then when it comes out with 0%
change in f, the +X% clock will indicate a loss of X% which is just
whatt we want. You might say it proves that energy does not gravitate.
But wait, there really is no loss of X% in frequency out of the well,
merely a resistance to thinking twice. No, as I show in Dual Space
theory, the velocity of light increases by X% on its way out of
gravity, so the wavelength stretches X%. This would become evident if
it could be tested with a prism, or has everyone forgotten that
that's what redshift is, an increase in wavelength?
It seems the practice in casual GR is to find some minute fraction eg
gh/c^2 and then apply it where it will do the most good, in this case
to debit frequency. This is not trivial because without reading all
the haranguing. the debate in this thread seems to center on whether
energy is conserved or not. It is conserved and light does not
gravitate and all the GR explication is really of no tutorial value.
John Polasek
http://www.dualspace.net
mme...@cars3.uchicago.edu
>Tom Roberts wrote:
>
>>Schoenfeld wrote:
>>> Energy conservation of some system may be _equivalent_ to the time
>>> translation symmetry of the systems Lagrangian but it is not
>>> necessarily DEFINED that way.
>
>
>>Sure it is. This is 2005, not ~1900.
>
>a small window for the possibility for the creation of energy. Say
>under an extremely high E-field (a single electron orbiting a Z=200
>nucleus, for example), what if the vacuum really becomes unstable and
>has a small runaway effect which spits out a million particles for no
>currently known reason? (ok I'm making this up, but for the sake of
>argument...). Can we say that energy wasn't created, *by definition*?
>Seems a bit over the top.
>
have to say on a situation which may arise if our science is quite
wrong?" The answer, obviously, is "nothing".
>What if such a runaway condition accidentally happened in the centre of
>the Sun, which turned into a gamma-ray burster and fried Earth?
>
>Of course I'm not arguing that we can actually create energy, or the
>above situations will happen, but I must admit discomfort in going from
>"this is the way the universe seems to work" to saying "this is the way
>the universe *does* work, *by definition*".
If semantics bothers you, make it "this is the way the universe does
work, to our knowledge".
>
>It reminds of the case of *defining* the speed of light as constant.
>Sure it's consistent with everything we currently know, but I don't get
>the point of *defining* it that way rather than saying that's just the
>way it happens to be (as far as we know).
>
Why do you think this is different from defining the length of
standard meter as constant?
Mati Meron | "When you argue with a fool,
me...@cars.uchicago.edu | chances are he is doing just the same"
Dr Photon
>Dr Photon wrote:
>>My complaint is that we know QM and GR have to be modified, so there is
>>a small window for the possibility for the creation of energy. Say
>>under an extremely high E-field (a single electron orbiting a Z=200
>>nucleus, for example), what if the vacuum really becomes unstable and
>>has a small runaway effect which spits out a million particles for no
>>currently known reason? (ok I'm making this up, but for the sake of
>>argument...). Can we say that energy wasn't created, *by definition*?
>>Seems a bit over the top.
>Well, what you're asking here, in effect, is "What does our science
>have to say on a situation which may arise if our science is quite
>wrong?" The answer, obviously, is "nothing".
Not quite. Highly charged ions are a subject of much attention right
now, and are promising new tests of QED. By being tests of QED, it
implies that QED could be measurably inaccurate in such cases. Of
course, people are not discussing creation of energy in such cases, but
whether a decimal place goes astray at some stage. I just point out
that if something *really* strange could happen, we wouldn't be
*allowed* to call it creation of energy, by definition.
>>Of course I'm not arguing that we can actually create energy, or the
>>above situations will happen, but I must admit discomfort in going from
>>"this is the way the universe seems to work" to saying "this is the way
>>the universe *does* work, *by definition*".
>If semantics bothers you, make it "this is the way the universe does
>work, to our knowledge".
by making energy a conserved quantity by definition, there is no
possibility for an alternative way the universe works, so the implied
uncertainty in such a statement is redundant.
>>It reminds of the case of *defining* the speed of light as constant.
>>Sure it's consistent with everything we currently know, but I don't get
>>the point of *defining* it that way rather than saying that's just the
>>way it happens to be (as far as we know).
>Why do you think this is different from defining the length of
>standard meter as constant?
that question did indeed occur to me. I guess it's permissible to make
as many definitions as you like so long as no contradictions arise.
Possibly you *should* define as much as possible, just to get a grip on
things, and which things are taken as constant is decided by
convention. Such questions as "were the fundamental universal
'constants' different in the past?" would be reduced to "we have
defined some values as being the same in the past, but seeing as not
all of them can be defined as constant (without contradiction
somewhere), were the remaining 'constants' that *could* have been
different, different?". So if we define the speed of light as being
always constant, then if there was a period of inflation in the early
universe it must have been due to distance expanding, rather than the
speed of light slowing. Makes sense, so long as we remember it is a
*convention*.
In the high E-field case I suggested, even if new matter was pulled out
of the vacuum, I guess you could say it just came from a reservoir
somewhere (other dimension? ;)) which previously hadn't been included
in the calculation.
br
Tom Roberts
> Tom Roberts wrote:
>>Schoenfeld wrote:
>>>Energy conservation of some system may be _equivalent_ to the time
>>>translation symmetry of the systems Lagrangian but it is not
>>>necessarily DEFINED that way.
>>Sure it is. This is 2005, not ~1900.
>
> There is no reason to define energy in that way.
Sure there is -- it is the only definition that holds in ALL modern
theories of physics, and is a straightforward generalization of the
definition in Newtonian mechanics.
Besides, this _IS_ how the word is used, _TODAY_.
> hint: The work exchanged in an adiabatic process depends only on the
> initial and the final state and not on the details of the process.
Sure. So what? "Adiabatic" is a thermodynamic term, not an aspect of any
fundamental theory of physics (thermodynamics is an approximation,
albeit a very good one) -- the actual transfer of work/energy does VERY
MUCH depend on the details of the process, it's just that thermodynamics
ignores that and approximates it statistically.
>>>The difference is important because lack
>>>of said symmetry does not imply energy conservation violation.
>>Actually it does (insofar as "energy" can be defined at all in such
>>systems). That's why the definition changed once Noether's theorem
>>explained the inconsistencies. Of course in classical mechanics the
>>Lagrangian is time invariant, so the question never came up. <shrug>
>
> That is a school-boy reasoning error. [...]
You are wrong, and apparently did not read what I wrote. Noether's
theorem goes BOTH WAYS -- symmetry implies conservation _AND_
conservation implies symmetry. So if there is a conserved quantity, then
there is a corresponding symmetry of the Lagrangian, and lack of such a
symmetry does indeed imply lack of such a conserved quantity (== "energy
conservation violation" in your words).
Need I mention that here we are still discussing Lagrangian
based theories?
>> Noether's theorem says that for every continuous symmetry of
>> the Lagrangian there is a corresponding conserved quantity,
>> and for every conserved quantity there is a corresponding
>> symmetry. It also specifies how either can be determined from
>> the other.
>
> More accurately, it says that certain symmetries imply certain
> conserved quantities. The difference is important.
You mentioned only half of the theorem, and your statement of that half
is actually less accurate and complete than mine. Yes, the difference is
important, and you should learn it.
>>If your
>>"abstract quantity" is conserved, there is a symmetry of the Lagrangian
>>corresponding to it,
>
> That's not necessarily true. Noether's thereom applies only to theories
> describable by a Lagrangian (or a Hamiltonian).
Technically, yes. But all current fundamental theories of physics are
derived from a Lagrangian.
Feel free to construct your own theory that is not based on a
Lagrangian. But don't attempt to foist definitions appropriate to such a
theory on everybody else until and unless you can show that this theory
is better than the current ones. Right now, the definitions appropriate
to the CURRENT theories of physics are appropriate.
> there is NO reason to define energy in
> general terms, as the time-translation symmetry of the Lagrangian.
Once again: SURE THERE IS! Because all current fundamental theories of
physics make it appropriate. We cannot formulate definitions based on
unknown, future theories (such re-definitions naturally occur when
formulating new theories, of course).
>>In modern physics, energy is specifically defined as the conserved
>>Noether current related to time translation invariance of the system's
>>Lagrangian. This is not "abstract" at all. <shrug>
>
> That's false again. Some theories don't carry Lagrangian of Hamiltonian
> formalisms, so you can't express energy with the definition you gave.
Name them. While in principle there can be such theories, TODAY there
are none left standing. I am discussing modern physics TODAY, not some
hypothetical future of your imagination.
>>If there is no time translation invariance of the Lagrangian, then there
>>is no useful definition of "energy".
>
> Profoundly wrong.
Actually, in today's theories that is a profound truth. Of course the
only current theory in which this applies is GR (all others have
Lagrangians that are explicitly time-translation invariant).
Tom Roberts tjro...@lucent.com
mme...@cars3.uchicago.edu
>mme...@cars3.uchicago.edu wrote:
>>Dr Photon wrote:
>>>a small window for the possibility for the creation of energy. Say
>>>under an extremely high E-field (a single electron orbiting a Z=200
>>>nucleus, for example), what if the vacuum really becomes unstable and
>>>has a small runaway effect which spits out a million particles for no
>>>currently known reason? (ok I'm making this up, but for the sake of
>>>argument...). Can we say that energy wasn't created, *by definition*?
>>>Seems a bit over the top.
>
>
>>Well, what you're asking here, in effect, is "What does our science
>>have to say on a situation which may arise if our science is quite
>>wrong?" The answer, obviously, is "nothing".
>
Oh, quite.
> Highly charged ions are a subject of much attention right
>now, and are promising new tests of QED. By being tests of QED, it
>implies that QED could be measurably inaccurate in such cases. Of
>course, people are not discussing creation of energy in such cases, but
>whether a decimal place goes astray at some stage. I just point out
>that if something *really* strange could happen, we wouldn't be
>*allowed* to call it creation of energy, by definition.
>
Only if your definition of energy is "anything strange that
happens":-) Seriously now, if said "something really strange" is
wholly inconsistent with known science, then you cannot ask what known
science has to say about. And if it is consistent, then energy is
conserved.
>>>Of course I'm not arguing that we can actually create energy, or the
>>>above situations will happen, but I must admit discomfort in going from
>>>"this is the way the universe seems to work" to saying "this is the way
>>>the universe *does* work, *by definition*".
>
>
>>If semantics bothers you, make it "this is the way the universe does
>>work, to our knowledge".
>
>by making energy a conserved quantity by definition, there is no
>possibility for an alternative way the universe works, so the implied
>uncertainty in such a statement is redundant.
>
Oh, please, this is silly. Energy is a *defined quantity*, as are
length, time span, velocity and a host of other things. If I define a
physical quantity called "quenkenplotz" as the mass of an object,
multiplied by the cube of its velocity relative to the CM of the
Lesser Magellanic Cloud, multiplied by the square root of the
temperature in downtown Kiev at noon of the preceding day, then this
is how quenkenplotz is defined. And if somebody will say that "yes,
that's how you define quenkenplotz, but how do you know what it
*really* is", then it'll just be plain silly. It is what it is
defined. Whether the definition is of any use, that's another
question, but quite separate.
You've to realize that physics, schematically, consists of two parts.
One part is a set of mathematical entities which are either defined
(yes, defined) or derived from defined entities, olus mathematical
rules specifying interactions between said entities. And, if that
would have been all physics is then it would've been just a
mathematical theory, detached from the real world. But, there is also
a second part and this one consists of mappings between the
mathematical entities described above and *measurable entities* in the
observable world. This is "wherre the rubber hits the road". This
part, of mappings, is what makes physics useful, and this is also the
part where the uncertainties creep in, *as they should*. It is useful
since it gives you the ability to make actual predictions about
results of measurements. And it is uncertain because you've no way to
make absolutely sure that your mappings are "true". So, it is
possible that your theory is mathematically fully consistent, yet the
results of the measurements disagree with the predictions. That's how
theories are being falsified.
To give couple examples of the distinction between definitions and
mappings, consider first something as mundane as a sphere. A sphere
(spherical surface, to be exact) is *defined* as the set of all points
equidistant from a given point. Thus, the question "how can be really
sure that all the points on the surface of a sphere are equidistant
from the center" is nonsensical. There is nothing to make sure of,
the sphere is defined this way. On the other hand, the question of
"how can we make sure that an observable object being modeled as a
sphere is really so" does make sense and is subject to observation.
Said observation may falsify the model, it may also confirm that the
model is valid *to a given accuracy*, but never quite prove it.
As a second example, lets take the first of Maxwell's equations, the
one about div E being proportional to charge density. As a
mathematical statement it follows from defining (or postulating, if
you prefer) the electric field of a point charge as being proportional
to charge and inversely proportional to distance squared. And for
this field the result is rigorously true. As for the real, physical
field, the result is only true to the extent that the Q/r^2 model is a
truthful model of the real field. And this is something that can
never be proven rigorously true and that is open to observation.
So, coming back to your statement about energy, certainly there is
possibility for alternative ways for the universe to work. If you get
discrepancies between results based on the definition and results
obtaied from measurements, this may indicate that your definition does
not map properly into the observable world. In this case, you'll have
to change your definitions.
>>>It reminds of the case of *defining* the speed of light as constant.
>>>Sure it's consistent with everything we currently know, but I don't get
>>>the point of *defining* it that way rather than saying that's just the
>>>way it happens to be (as far as we know).
>
>
>>Why do you think this is different from defining the length of
>>standard meter as constant?
>
>that question did indeed occur to me. I guess it's permissible to make
>as many definitions as you like so long as no contradictions arise.
Yes.
>Possibly you *should* define as much as possible,
Well, the "as much as possible" is just limited by the requirement of
no contradictions, as you said above.
> just to get a grip on
>things, and which things are taken as constant is decided by
>convention. Such questions as "were the fundamental universal
>'constants' different in the past?" would be reduced to "we have
>defined some values as being the same in the past, but seeing as not
>all of them can be defined as constant (without contradiction
>somewhere), were the remaining 'constants' that *could* have been
>different, different?". So if we define the speed of light as being
>always constant, then if there was a period of inflation in the early
>universe it must have been due to distance expanding, rather than the
>speed of light slowing. Makes sense, so long as we remember it is a
>*convention*.
>
Yes.
>In the high E-field case I suggested, even if new matter was pulled out
>of the vacuum, I guess you could say it just came from a reservoir
>somewhere (other dimension? ;)) which previously hadn't been included
>in the calculation.
>
There is no problem, within current physics, of new matter being
pulled out of the vacuum, as long as the total energy and moemntum are
conserved. If the aren't, then yes, you may try to postulate
additional physical entities which account for the discrepancy. But,
if with every new measurement you're forced to add yet another fudge
factor to get the accounting work out, then you start suspecting that
your model as a whole is off (the classic "epicycles" situation). If,
on the other hand, the addition of each new factor into the
description accounts correctly (within measurement accuracy, of
course) not just for the specific instance for which it was introduced
but for a whole set of other instances, then you've a reason to
believe that the model is pretty good (and that's the most you've a
right to believe in).
Tom Roberts
> by making energy a conserved quantity by definition, there is no
> possibility for an alternative way the universe works,
But that's the point: energy is NOT defined that way, it is defined as
the conserved current corresponding to time translation invariance of
the Lagrangian. If in the future we find that the universe does not
really work that way, it will be reflected in either a theory with a
non-time-translation-invariant Lagrangian, or a non-Lagrangian theory.
Of course in some sense we have already learned the universe
does not work that way -- the GR Lagrangian for the universe
we inhabit is quite clearly not time translation invariant.
This is rather different from your examples, however.
> Possibly you *should* define as much as possible, just to get a grip on
> things,
MTW has a great quote from Poincare', saying something like: in physics
we do not define our terms and then make theories corresponding to those
definitions; instead the theories themselves implicitly define their own
terms. That is happening here, but all too many contributors don't know
enough about GR and modern physics.
Tom Roberts tjro...@lucent.com
bz
news:ra6rh1h1on6ift15b...@4ax.com:
> But wait, there really is no loss of X% in frequency out of the well,
> merely a resistance to thinking twice. No, as I show in Dual Space
> theory, the velocity of light increases by X% on its way out of
> gravity, so the wavelength stretches X%. This would become evident if
> it could be tested with a prism, or has everyone forgotten that
> that's what redshift is, an increase in wavelength?
>
>
Better test with a grating as diffraction by a grating depends only on
wavelength[and grating spacing].
n lamda = d sin(theta)
or theta= arcsin(n lamda/d) where d is distance between the elements of the
grating and n is the order of the spectra.
http://www.physics.smu.edu/~scalise/emmanual/diffraction/lab.html
In other words the angle of diffraction is independent of the waves
velocity and frequency.
The Hubble Space Telescope should have, by now, provided thousands of such
tests.
I have seen nothing about HST discovering that light travels at a different
velocity in orbit.
This would tend to falsify your theory.
--
bz
please pardon my infinite ignorance, the set-of-things-I-do-not-know is an
infinite set.
bz...@ch100-5.chem.lsu.edu remove ch100-5 to avoid spam trap
John C. Polasek
<bz...@ch100-5.chem.lsu.edu> wrote:
>John C. Polasek <jpol...@cfl.rr.com> wrote in
>news:ra6rh1h1on6ift15b...@4ax.com:
>
>> But wait, there really is no loss of X% in frequency out of the well,
>> merely a resistance to thinking twice. No, as I show in Dual Space
>> theory, the velocity of light increases by X% on its way out of
>> gravity, so the wavelength stretches X%. This would become evident if
>> it could be tested with a prism, or has everyone forgotten that
>> that's what redshift is, an increase in wavelength?
>>
>>
>
>Better test with a grating as diffraction by a grating depends only on
>wavelength[and grating spacing].
>
>n lamda = d sin(theta)
>or theta= arcsin(n lamda/d) where d is distance between the elements of the
>grating and n is the order of the spectra.
>
>http://www.physics.smu.edu/~scalise/emmanual/diffraction/lab.html
>
>In other words the angle of diffraction is independent of the waves
>velocity and frequency.
You're right and I am very aware of diffraction mathematics. But in
the Pound Rebka experiment they used Mossbauer resonance with a sharp
Mossbauer window that they oscillated on a speaker cone with
amplitudes on the order of the Bohr radius, thus getting a null when
the the filter had just the velocity change that the light did. In
22.5m dc/c = dL/L = 2.4e-15 for a velocity of 7e-7m/s in dc. Their
10hz speaker cone would have had to move by 1.8e-9m: w*x=7e-7m/s.
That amplitude is 35 Bohr radii. In short, they couldn't use a
diffraction filter could they?
But they did unwittingly test the velocity difference and called it
frequency difference.
Similarly Brault used oscilling detectors to find the velocity shift
at the Sun which is 635m/s by DS or relativity and he bracketed maybe
520 to 750 m/s, there's that much noise. He actually denominated his
results in meters/second. Both are described in MTW Gravitation and of
course the results are way too fine-grain to use diffraction gratings.
>The Hubble Space Telescope should have, by now, provided thousands of
such
>tests.
>
>I have seen nothing about HST discovering that light travels at a different
>velocity in orbit.
HST has no way of making that test (that I know of).
The ONLY way c changes is in a gravitational field, increasing toward
its nominal value as g gets weaker. The original frequency is set by
the clock and its place in a gravity field. It too is lower in the
field. Once it emits a wave that wave never changes frequency
thereafter. It only stretches by virtue of increase in c.
My formula for this is dc/dr = MG/r^2c =g/c = 3.2e-8(m/s)/meter
In 22.5m c changed by 7.4e-7 m/s or 2.4e-15 fractionally just as I
said above.
Bear in mind that the redshift in these tests is magnitudes lower than
are obtained with galaxies and Doppler shift, where z > .01 for
example and in Pound it's 2.4x10^-15!
>This would tend to falsify your theory.
Read it again and pardon my verbosity.
John Polasek
http://www.dualspace.net
Dr Photon
>Dr Photon wrote:
>> by making energy a conserved quantity by definition, there is no
>> possibility for an alternative way the universe works,
>But that's the point: energy is NOT defined that way, it is defined as
>the conserved current corresponding to time translation invariance of
>the Lagrangian. If in the future we find that the universe does not
>really work that way, it will be reflected in either a theory with a
>non-time-translation-invariant Lagrangian, or a non-Lagrangian theory.
Sorry to be boring (I'm nearly finished with this thread, but maybe one
more post), but doesn't "<energy> is defined as the conserved current
corresponding to time translation invariance of the Lagrangian" imply
that energy is a conserved quantity by definition?
Before this thread, I was of the opinion that E=T+V, which as far as
equations of motion go is equivalent to L=T-V. Do we agree that there
is a difference in saying that dE/dt=0 (which could happen
accidentally, due to the equations of motion being the way they are)
and *defining* E as the quantity such that dE/dt=0 (which is still how
I interpret what you wrote). If for some unknown reason both T and V
increased, in the first defintion (E=T+V) energy would be well defined
and would have increased, in the second definition (dE/dt=0) there
would be no "conserved current corresponding to time translation
invariance of the Lagrangian" and so no definition of energy (?). In
the first definition, we would have to change the laws of motion, but
in the second definition we would have to change both the laws of
motion *and* the definition of energy. So while I fully accept that no
case of d(T+V)/dt>0 has been found, it sort of seems a step beckwards
to define it such that it could never happen (which we don't fully
know), and leave ourselves stumped in a situation if it did happen.
So that's IMO, (which I realise isn't going to impress many...).
Also, what about the wikipedia entry on energy?
http://en.wikipedia.org/wiki/Energy
"Energy is defined as the amount of work required to change the state
of a physical system."
and
"Noether's theorem relates the conservation of energy to the time
invariance of physical laws"
note use of "relates" which implies equivalence but not definition (it
could be an accidental relation rather than "is by definition").
Do you mind that the definition is this way around and is equivalent in
any case to your definition, or would you say this definition has it
backwards? (ie the first line should read "Energy is defined via
Noether's theorem..." and only later write "which happens to be the
amount of work required to change the state of a system")
regards,
br
p.s. thanks for patience ;)
mme...@cars3.uchicago.edu
>Tom Roberts wrote:
>
>>> by making energy a conserved quantity by definition, there is no
>>> possibility for an alternative way the universe works,
>
>
>>But that's the point: energy is NOT defined that way, it is defined as
>>the conserved current corresponding to time translation invariance of
>>the Lagrangian. If in the future we find that the universe does not
>>really work that way, it will be reflected in either a theory with a
>>non-time-translation-invariant Lagrangian, or a non-Lagrangian theory.
>
>more post), but doesn't "<energy> is defined as the conserved current
>corresponding to time translation invariance of the Lagrangian" imply
>that energy is a conserved quantity by definition?
>
bz
> On Wed, 7 Sep 2005 05:58:30 +0000 (UTC), bz
> <bz...@ch100-5.chem.lsu.edu> wrote:
>
>>John C. Polasek <jpol...@cfl.rr.com> wrote in
>>news:ra6rh1h1on6ift15b...@4ax.com:
>>
>>> But wait, there really is no loss of X% in frequency out of the well,
>>> merely a resistance to thinking twice. No, as I show in Dual Space
>>> theory, the velocity of light increases by X% on its way out of
>>> gravity, so the wavelength stretches X%. This would become evident if
>>> it could be tested with a prism, or has everyone forgotten that
>>> that's what redshift is, an increase in wavelength?
>>>
>>>
>>
>>Better test with a grating as diffraction by a grating depends only on
>>wavelength[and grating spacing].
>>
>>n lamda = d sin(theta)
>>or theta= arcsin(n lamda/d) where d is distance between the elements of
>>the grating and n is the order of the spectra.
>>
>>http://www.physics.smu.edu/~scalise/emmanual/diffraction/lab.html
>>
>>In other words the angle of diffraction is independent of the waves
>>velocity and frequency.
> You're right and I am very aware of diffraction mathematics. But in
> the Pound Rebka experiment they used Mossbauer resonance with a sharp
> Mossbauer window that they oscillated on a speaker cone with
> amplitudes on the order of the Bohr radius, thus getting a null when
> the the filter had just the velocity change that the light did.
Pound Rebka has been looked at as doppler shift due to gravity and,
alternately, as clocks running faster as g field decreases.
The results are indisputable. The reasons is still under dispute.
> In
> 22.5m dc/c = dL/L = 2.4e-15 for a velocity of 7e-7m/s in dc.
Amazingly, using the Schwartzchild Metric, I compute 2.4e-15 difference in
time due to GR for 22.5 m +r_e vs r_e, where r_e is 6.3781e6 m. So it can be
looked at as gravitational red shift or gravitational time dilation.
> Their
> 10hz speaker cone would have had to move by 1.8e-9m: w*x=7e-7m/s.
> That amplitude is 35 Bohr radii. In short, they couldn't use a
> diffraction filter could they?
Well, their Mossbauer effect used the gamma transition of iron 57. Hard to
construct a grating for that wavelength.
Since the recoil energy of the iron nuclii is 5 orders of magnitude larger
than the natural line width of the transition, you have to either nail down
the nuclii in a crystal lattice or move the target at the right speed so that
the doppler shifted target matches the energy of the source.
http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/mossfe.html
> But they did unwittingly test the velocity difference and called it
> frequency difference.
It wasn't exactly unwitting.
> Similarly Brault used oscilling detectors to find the velocity shift
> at the Sun which is 635m/s by DS or relativity and he bracketed maybe
> 520 to 750 m/s, there's that much noise. He actually denominated his
> results in meters/second. Both are described in MTW Gravitation and of
> course the results are way too fine-grain to use diffraction gratings.
>>The Hubble Space Telescope should have, by now, provided thousands of
> such
>>tests.
>>
>>I have seen nothing about HST discovering that light travels at a
>>different velocity in orbit.
> HST has no way of making that test (that I know of).
If light traveled at a different velocity there, giving a different wave
length, their spectroscopes should show a shift in calibration.
All spectra should be shifted if c were constant, but different from c on
earth, and for c'=c+/-v folks, there should be some very strange stellar
spectra collectect.
> The ONLY way c changes is in a gravitational field, increasing toward
> its nominal value as g gets weaker. The original frequency is set by
> the clock and its place in a gravity field. It too is lower in the
> field. Once it emits a wave that wave never changes frequency
> thereafter. It only stretches by virtue of increase in c.
So, you change c instead of time, whereas GR changes time instead of c.
> My formula for this is dc/dr = MG/r^2c =g/c = 3.2e-8(m/s)/meter
> In 22.5m c changed by 7.4e-7 m/s or 2.4e-15 fractionally just as I
> said above.
I agree to the amplitude of the change, but see it as a change in t rather
than c.
> Bear in mind that the redshift in these tests is magnitudes lower than
> are obtained with galaxies and Doppler shift, where z > .01 for
> example and in Pound it's 2.4x10^-15!
>>This would tend to falsify your theory.
> Read it again and pardon my verbosity.
No problem.
Ilja Schmelzer
"Tom Roberts" <tjro...@lucent.com> schrieb
> Mike wrote:
> > Tom Roberts wrote:
> > the3-body problem equations are not integrable, but still 3 or more
> > bodies out there in the planetary system do pretty well.
>
> That is not non-integrable -- the 3-body problem (in Newtonian
> mechanics) has no closed-form solution, but it definitely has a well
> defined mathematical solution (available via numerical integration) --
> the equations of motion are definitely integrable.
Just for fun: There are solutions of the Newtonian four-body problem
where the trajectories reach infinity in finite time (of course highly
artificial, and only for ideal point particles so that you can extract as
much energy as you like by placing two point particles very close to each
other).
> But in GR the "total
> energy" in a finite region of a curved manifold in general has no
> solution; at base this is due to the fact that such integrals are path
> dependent, and if you attempt to sum up a region the answer you get
> depends on the order and method you use to sum up the (infinitesimal)
> parts, so the integral is not well defined.
The point is not that GR is a metric theory of gravity. There are
metric theories of gravity with well-defined local and global energy and
momentum conservation laws.
> > The Axiom of
> > Energy Conservation is a principle of physics
>
> No, it is not. In the (very) old days is was perhaps thought of that
> way, but now we know that energy conservation is merely a consequence of
> a specific symmetry of the Lagrangian of the system, and is by itself of
> no deep significance at all. The fundamental thing is the Lagrangian
> itself, and conservation of energy is a consequence of that (Newtonian
> mechanics).
I would say the final decision about this question is unknown. In QM, we
have the Schrödinger equation, H is a fundamental operator, and exact
conservation of energy follows. If this survives the unification of QM and
GR is yet unknown.
> > It is sommon sense that any theory that does not conserve energy
> > non-locally to be abandoned.
>
> Common sense has proven to be COMPLETELY AND UTTERLY UNRELIABLE in
> regimes far removed from our everyday lives where that common sense was
> developed. This ought to be obvious (the universe does not revolve
> around humans). <shrug>
"Common sense" is too uncertain to combine it with statements like "proven"
in one sentence.
Note that there are common sense principles which we use as the foundation
of the scientific method.
Ilja
Ilja Schmelzer
"Bilge" <dub...@radioactivex.lebesque-al.net> schrieb
> Here's the basic problem with defining a conserved energy, which
> addresses your question regarding noether's theorem, too. Energy is
> defined as the conserved quantity associated with invariance under
> time translations. That comes straight from noether's theorem.
>
> the metric has 10 degrees of freedom. You will be able to define
> a conserved energy if you can make the metric time independent.
> You are free to make a change of coordinates to do that, but a
> coordinate transformation only has 4 degrees of freedom. In general,
> that is not sufficient to remove the time dependence. That means you
> cannot define a quantity called the energy such that it is conserved.
What about the Landau pseudo-tensor?
What about the energy conservation in other metric theories of
gravity (like GLET)?
Ilja
Dr Photon
>>Tom Roberts wrote:
>>>Dr Photon wrote:
>>>> by making energy a conserved quantity by definition, there is no
>>>> possibility for an alternative way the universe works,
>>>But that's the point: energy is NOT defined that way, it is defined as
>>>the conserved current corresponding to time translation invariance of
>>>the Lagrangian. If in the future we find that the universe does not
>>>really work that way, it will be reflected in either a theory with a
>>>non-time-translation-invariant Lagrangian, or a non-Lagrangian theory.
>>Sorry to be boring (I'm nearly finished with this thread, but maybe one
>>more post), but doesn't "<energy> is defined as the conserved current
>>corresponding to time translation invariance of the Lagrangian" imply
>>that energy is a conserved quantity by definition?
>Only if the Lagrangian is, indeed, invariant under time translation.
So this definition is not complete, as it doesn't define energy for
non-invariant under time translation circumstances (where it surely
should still have *some* definition).
Taking "conserved" and "invariant" out of the defintion would give
"Energy is defined as the current corresponding to time translation of
the Lagrangian"
is that ok, or is it too vague to be useful?
Checking Wikipedia again (not an ultimate authority, I know, but it's a
start), about 2/3 the way down
http://en.wikipedia.org/wiki/Noether%27s_theorem
we have a section titled "An example" (directly after the "A more
general and elegant proof" section)
"You might recognize the right hand side as the energy and Noether's
theorem states that jdot=0 (i.e. the conservation of energy is a
consequence of invariance under time translations)."
This implies to me that this current may be non-zero, and if a system
has invariance under time translation, then this quantity will be
conserved. I think I'm happy with this definition.
However, that is different than saying energy is the quantity such that
jdot=0 (I may be arguing with myself at this point, but it seems to be
getting clearer to me).
br
mme...@cars3.uchicago.edu
>Mati Meron wrote:
>
>>>Tom Roberts wrote:
>
>>>>Dr Photon wrote:
>>>>> by making energy a conserved quantity by definition, there is no
>>>>> possibility for an alternative way the universe works,
>
>
>>>>But that's the point: energy is NOT defined that way, it is defined as
>>>>the conserved current corresponding to time translation invariance of
>>>>the Lagrangian. If in the future we find that the universe does not
>>>>really work that way, it will be reflected in either a theory with a
>
>
>>>Sorry to be boring (I'm nearly finished with this thread, but maybe one
>>>more post), but doesn't "<energy> is defined as the conserved current
>>>corresponding to time translation invariance of the Lagrangian" imply
>>>that energy is a conserved quantity by definition?
>
>
>
>>Only if the Lagrangian is, indeed, invariant under time translation.
>
>non-invariant under time translation circumstances (where it surely
>should still have *some* definition).
>
A polite person (or a person with some humility left, i.e. not a
product of the modern educational establishment) asks, at this point,
"so how do you define energy in the case where the Lagrangian is not
invariant under time tranlation?". That's a legitimate question.
A usenet crank, on the other hand, proclaims gleefully "so your
defintion is not complete..."
What does it make you?
Now, did I (or anybody else, for that matter) said that the definition
only exists for time invariant Lagrangians?
Anyway, for the sake of the few readers who may deserve a response,
here it is.
You take the action, which is the integral of the Lagrangian along a
physically allowed trajectory (i.e. a trajectory along which the
action is stationary).
You find the variation of the action resulting from an infinitsmal
change of some parameter.
Said variation is, in general, the difference between the values of
said quantity at the beginning and the end of the trajectory
(multiplied by the differential of the parameter being varied). If
the variation ends up being zero then said physical quantity doesn't
change along the trajectory. But said quantity is still defined (by
the end point variation) whether the action changes or not.
Thus, the end point variation of the action under infinitsimal time
translation is the energy.
The end point variation of the action under infinitsimal spatial
translation is the momentum.
The end point variation of the action under infinitsimal rotation
is the angular momentum.
Conversely, if a system is invariant under time translation, energy
(defined by the end point variation) is conserved. If the system is
invariant under spatial tranlation, momentum is conserved. And, if
the system is invariant under rotation, angular moemntum is conserved.
But all these quantities are defined by the end point variation,
*regardkless* of whether they're conserved of not.
That's all there is to it. And, don't bother to apologize. Frakly, I
don't give a damn.
Dr Photon
>And here is where you, as others of your kind, get offensive.
eh?
>A polite person (or a person with some humility left, i.e. not a
>product of the modern educational establishment) asks, at this point,
>"so how do you define energy in the case where the Lagrangian is not
>invariant under time tranlation?". That's a legitimate question.
they could indeed ask it that way
>A usenet crank, on the other hand, proclaims gleefully "so your
>defintion is not complete..."
>What does it make you?
you're projecting glee onto me, which is inappropriate
>Now, did I (or anybody else, for that matter) said that the definition
>only exists for time invariant Lagrangians?
I was going on what Tom Roberts wrote:
"energy is NOT defined that way, it is defined as the conserved current
corresponding to time translation invariance of the Lagrangian"
the follow up sentences, while considering the possibilities of
non-time-translation-invariant Langrangians, which don't have such
*conserved* currents, didn't include a generalised definition of energy
"If in the future we find that the universe does not
really work that way, it will be reflected in either a theory with a
non-time-translation-invariant Lagrangian, or a non-Lagrangian theory."
leaving the possibility that the definition in such cases has not yet
been formalised.
[snip]
>But all these quantities are defined by the end point variation,
>*regardkless* of whether they're conserved of not.
which (AFAICT) seems to agree with the second half of my previous post
(which you snipped).
br
donsto...@hotmail.com
digging holes and filling them back in, also known as "debating" each
other on sci.physics?"
"Oh, I dont know, Lilttle Wilfredina, maybe they're college student
forlorn over the fact that their lives have no meaning now and will
have even less meaning after they get out and go to work for some
useless hi-tech company?"
"But why do they ruin it for the rest of us, us who would easily solve
all questions within physics and all other disciplines if only they
would go volunteer to clean up New Orleans and get out of the way of
people who have a useful use for Usenet?"
"I dont know, my little darling, I guess it's just human Nature that if
your family suppressed foul language in your home that you would come
to sci.physic and spew it out at everyone. The anonymity of usenet
also brings out the very worst in people, human slime that they are."
"Mommy, is there any hope for the Earth with such human slime crawling
the Earth as these filthy-mouthed sci.physics creatures/semi-humans???"
"And then the cooking-monk tipped over the urn with his toe, and became
head of the monistery."
sal
>
> "Tom Roberts" <tjro...@lucent.com> schrieb
>> Mike wrote:
>> > Tom Roberts wrote:
>> > Please not that the3-body problem equations are not integrable,
>> > but still 3 or more bodies out there in the planetary system do
>> > pretty well.
>>
>>
>> That is not non-integrable -- the 3-body problem (in Newtonian
>> mechanics) has no closed-form solution, but it definitely has a
>> well defined mathematical solution (available via numerical
>> integration) -- the equations of motion are definitely integrable.
>
> Just for fun: There are solutions of the Newtonian four-body problem
> where the trajectories reach infinity in finite time (of course
> highly artificial, and only for ideal point particles so that you
> can extract as much energy as you like by placing two point
> particles very close to each other).
Whoa! Are you making this up just to bug Tom, or is this for real?
If all four particles have mass then you need infinite energy for
that, and in classical Newtonian mechanics with gravitating particles,
you don't end up with more than you started with ... or so I certainly
thought. "very close" => distance is still nonzero => energy is still
finite => you won't get infinite velocity that way, or so I should
think, and an arbitrarily high but finite velocity still won't carry
your trajectory to infinity in finite time. So what's the scoop?
Could you post a reference or, if the situation is simple enough, an
explanation?
Tx.
--
Nospam becomes physicsinsights to fix the email
sal
IOW if the trajectory of some particle P reaches infinity by positive time
T, take the closed interval [0,T]. That's compact and it follows that, if
the velocity of P is finite at all points in [0,T], then we can bound it
above with a finite value V. And the farthest the particle could have
gone would therefore have been VT which is finite. Ergo, the particle's
velocity must actually be infinite at some point in [0,T]. At that moment
the particle's kinetic energy is also infinite, so you must have extracted
an infinite amount of energy from something to get it going that fast.
The only way to do that is let two particles actually fuse; as long as
their separation is positive the kinetic energy of the system remains
finite. This violates the implication of your statement that they can
be "very close" ... as a rule "very close" doesn't imply zero separation.
But even assuming two or more particles actually "touch", I still don't
see how to pump up the velocity of anything in the system to infinity,
unless we care to take advantage of the fact that any real computer doing
such an integration will suffer from overflow and give a garbage result :-)
> So what's the scoop?
Indeed -- love to see a reference or explanation!
Daryl McCullough
>So this definition is not complete, as it doesn't define energy for
>non-invariant under time translation circumstances (where it surely
>should still have *some* definition).
You can define a quantity that you could call the energy, but
if the Lagrangian isn't invariant under time translations, then
this quantity isn't conserved.
--
Daryl McCullough
Ithaca, NY
jmfb...@aol.com
'ey, Mati. Do you wanna borrow my box of Kleenix?
Well, I do give a damn. Due to my lack of experience, I know
I can't fully appreciate what you just wrote. I have no idea
how you use this stuff in the lab.
[emoticon struggles to think of a question to ask]
Are those quantities you mention data that you collect?
Note that a suggestion that I need to take two more years
of classes is an acceptable answer.
/BAH
Daryl McCullough
>> If all four particles have mass then you need infinite energy for that,
>> and in classical Newtonian mechanics with gravitating particles, you don't
>> end up with more than you started with ... or so I certainly thought.
Here are some references:
http://plus.maths.org/issue31/outerspace/
http://www.expmath.org/expmath/volumes/12/12.2/pp187_198.pdf
The point about requiring infinite energy is conceptually easy
to understand with point masses attracting gravitationally: you
compensate having infinite positive kinetic energy with an
infinite negative gravitational energy.
Dr Photon
>You can define a quantity that you could call the energy, but
>if the Lagrangian isn't invariant under time translations, then
>this quantity isn't conserved.
which connects back to the Noether current under time translation:
http://en.wikipedia.org/wiki/Noether%27s_theorem
section "Proof"
"You might immediately recognize this as the continuity equation for
the current
Jmu= dL/ddphi Q - fmu
which is called the Noether current associated with the symmetry."
which gets referred to later in section "An example"
"More generally, if the Lagrangian does not depend explicitly on time,
the quantity (called the energy)
sum(d/dxdot L)xdot - L
is conserved"
however, if L is function of t then so is E.
Sorted.
You won't find that on
http://en.wikipedia.org/wiki/Energy
www.thefreedictionary.com/energy
www.wordreference.com/definition/energy
physics.about.com/cs/ thermodynamics/g/thermodynamics.htm
though.
br
sal
> sal says...
>
>>>
>>> If all four particles have mass then you need infinite energy for
>>> that, and in classical Newtonian mechanics with gravitating
>>> particles, you don't end up with more than you started with ... or
>>> so I certainly thought.
>
> Here are some references:
Thanks!
> http://plus.maths.org/issue31/outerspace/
The description on this web page is too incomplete to be very helpful.
He doesn't give any of the math, and the behavior as described doesn't
obviously conserve energy.
But this next one, on the other hand:
> http://www.expmath.org/expmath/volumes/12/12.2/pp187_198.pdf
Seriously cool!
I looked at the beginning and the end and at least I got a general
idea of what's going on. At the singularity the distance between two
particles is zero, but it's not exactly a collision because that's the
moment of the singularity, everything breaks down at that moment, and
the "close encounter" takes place at infinity.
> The point about requiring infinite energy is conceptually easy to
> understand with point masses attracting gravitationally: you
> compensate having infinite positive kinetic energy with an infinite
> negative gravitational energy.
Right, because the distance between two of the particles goes to zero at
the moment when the kinetic energy goes to infinity.
mme...@cars3.uchicago.edu
>Mati Meron wrote:
>
>>And here is where you, as others of your kind, get offensive.
>
>
>>A polite person (or a person with some humility left, i.e. not a
>>product of the modern educational establishment) asks, at this point,
>>"so how do you define energy in the case where the Lagrangian is not
>>invariant under time tranlation?". That's a legitimate question.
>
>
>>defintion is not complete..."
>
>>What does it make you?
>
>
>>only exists for time invariant Lagrangians?
>
>
>
>the follow up sentences, while considering the possibilities of
>non-time-translation-invariant Langrangians, which don't have such
>*conserved* currents, didn't include a generalised definition of energy
>
>really work that way, it will be reflected in either a theory with a
>
>leaving the possibility that the definition in such cases has not yet
>been formalised.
Well, and that's the point where you should've asked whether it has
been formalized, instead of starting with the assumption that it
hasn't been.
>
Non of the quantities I mentioned is *defined* as being conserved
(which is, it seems, the assumption you jumped into). They're defined
through the variations of the system under specified symmetry
operations. Then, if the system is invariant under such symmetry
operation, then the variation must be zero and the conservation
*follows*.
mme...@cars3.uchicago.edu
>In article <PTTTe.13$25....@news.uchicago.edu>,
> mme...@cars3.uchicago.edu wrote:
>
>>
>I can't fully appreciate what you just wrote. I have no idea
>how you use this stuff in the lab.
>
>[emoticon struggles to think of a question to ask]
>Are those quantities you mention data that you collect?
>
measurable, the answer is yes, of course.
John C. Polasek
It has always struck me as strange that energy is not measureable,
that it is always the result of a mathematical operation mostly
involving two measurables and is never a direct measurement. How would
you measure kinetic energy? A watthourmeter comes closest, cleverly
multiplying voltage and current and being integrated over time by the
wheel that turns. (Multiply? Integrate?).
Strictly speaking none of these three quantities can be measured, only
computed. Velocity is only measurable with a charged mass passing
through a coil for example. Measuring delta x over delta time is not
dx/dt, the velocity. Killing the KE in a spring is a kluge also. It is
easy to think of them as measurable but I don't see how they could be.
John Polasek
http://www.dualspace.net
John C. Polasek
<bz...@ch100-5.chem.lsu.edu> wrote:
Define Doppler shift due to gravity: energy falls like a rock?
("Apparent weight of photons").
Falling 22.5m it would gain v = sqrt(2gh) = 21 m/s and that would make
its Doppler z equal to v/c = 7x10^-8, but the redshift is really
2.4x10^-15. (How Doppler is that? :-).
>alternately, as clocks running faster as g field decreases.
>The results are indisputable. The reasons is still under dispute.
>
>> In
>> 22.5m dc/c = dL/L = 2.4e-15 for a velocity of 7e-7m/s in dc.
>
>Amazingly, using the Schwartzchild Metric, I compute 2.4e-15 difference in
>time due to GR for 22.5 m +r_e vs r_e, where r_e is 6.3781e6 m. So it can be
>looked at as gravitational red shift or gravitational time dilation.
>
>> Their
>> 10hz speaker cone would have had to move by 1.8e-9m: w*x=7e-7m/s.
>> That amplitude is 35 Bohr radii. In short, they couldn't use a
>> diffraction filter could they?
>
>Well, their Mossbauer effect used the gamma transition of iron 57. Hard to
>construct a grating for that wavelength.
>
>Since the recoil energy of the iron nuclii is 5 orders of magnitude larger
>than the natural line width of the transition, you have to either nail down
>the nuclii in a crystal lattice or move the target at the right speed so that
>the doppler shifted target matches the energy of the source.
>http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/mossfe.html
>
>> But they did unwittingly test the velocity difference and called it
>> frequency difference.
>
>It wasn't exactly unwitting. 57
Well I can't lay my hands on Pounds original text but the title is
"Apparent weight of photons" which I interpret as (the wrong) belief
that energy responds to gravity like mass. At Pounds' time 1960 (and
in 2005 I believe) nobody was talking any change in c or nulling any
velocity difference (I believe). It's always been time dilation.
They were just trying to Doppler the frequency to a null by pushing
the detector into the incoming wave (on the way up), thus seeming to
restore f to its original higher value, or squash the wavelength into
a semblance of its former shorter length. .
>> Similarly Brault used oscilling detectors to find the velocity shift
>> at the Sun which is 635m/s by DS or relativity and he bracketed maybe
>> 520 to 750 m/s, there's that much noise. He actually denominated his
>> results in meters/second. Both are described in MTW Gravitation and of
>> course the results are way too fine-grain to use diffraction gratings.
>>>The Hubble Space Telescope should have, by now, provided thousands of
>> such
>>>tests.
>>>
>>>I have seen nothing about HST discovering that light travels at a
>>>different velocity in orbit.
>> HST has no way of making that test (that I know of).
>If light traveled at a different velocity there, giving a different wave
>length, their spectroscopes should show a shift in calibration.
There's no "there" there. You need real gravity to deliver detectible
red shift and it's not at HST. Even right on the Sun z = 2x10^-6 and
it's where Brault went to all the trouble to find it.
>All spectra should be shifted if c were constant, but different from c on
>earth, and for c'=c+/-v folks, there should be some very strange stellar
>spectra collectect.
>
>> The ONLY way c changes is in a gravitational field, increasing toward
>> its nominal value as g gets weaker. The original frequency is set by
>> the clock and its place in a gravity field. It too is lower in the
>> field. Once it emits a wave that wave never changes frequency
>> thereafter. It only stretches by virtue of increase in c.
>
>So, you change c instead of time, whereas GR changes time instead of c.
>
>> My formula for this is dc/dr = MG/r^2c =g/c = 3.2e-8(m/s)/meter
>> In 22.5m c changed by 7.4e-7 m/s or 2.4e-15 fractionally just as I
>> said above.
>
>I agree to the amplitude of the change, but see it as a change in t rather
>than c.
But you don't really, really think time can be stretched do you? It
can't. It's what Minkowski put over on AE.
>
>> Bear in mind that the redshift in these tests is magnitudes lower than
>> are obtained with galaxies and Doppler shift, where z > .01 for
>> example and in Pound it's 2.4x10^-15!
>>>This would tend to falsify your theory.
>> Read it again and pardon my verbosity.
>
>No problem.
I hesitate to bring this up, but we have been talking as if all this
could happen in a vacuum, when it can't. It only happens in Espace
where the speed of transmission is c, and stealing material in
creation weakened the environment so the coefficients Y/rho = c^2 are
reduced. Clocks there participate in the same enfeeblement.
John Polasek
http://www.dualspace.net
Tom Roberts
> Well with your improvident editing you omitted a specific example of
> GR self-contradiction that I mentioned, namely Pound-Rebka.
Huh??? The GR prediction for their measurement is within their
measurement accuracy. There's no "contradiction" there.
> They (and apparently most everybody) thinks the "photon" loses energy
> and frequency hf climbing up in a gravity well, and likewise think
> that energy gravitates. It is agreed a clock out of gravity runs
> faster.
You are speaking FAR too loosely to make any sense. Your words and
concepts are simply inadequate to the task of describing GR.
> So when it comes time to test hf (-X%) out of the well against
> a clock there, (+X%), the result is twice the book value -2X%. The
> frequency loss is spuriously doubled.
Nonsense. That happens only for YOU, not for Pound and Rebka, and not
for anyone who understands GR.
It's really rather simple:
Using one set of coordinates, it is natural to describe the transmission
of a light ray between different gravitational potentials as a "loss or
gain of energy"; and using those same coordinates, clocks always tick in
step with the time coordinate (i.e. are unaffected by gravitational
potential).
Using a DIFFERENT set of coordinates, it is natural to describe the
transmission of a light ray between different gravitational potentials
as being unaffected; using those same coordinates, clocks do not tick in
step with the time coordinate, and one would say that a clock's tick
rate depends on the gravitational potential where it is located.
You are intermixing those two coordinate viewpoints and obtaining nonsense.
People knowledgeable about GR know that NEITHER ONE of those is
describing "reality", because coordinates do not affect any natural
phenomena. So the right way to discuss this is to discuss the
MEASUREMENTS, and not ascribe them to either "light losing/gaining
energy" or "clocks ticking differently".
People who insist on using sound bites for physics are doomed to
failure, and perpetual confusion.
Tom Roberts tjro...@lucent.com
John C. Polasek
wrote:
Putting aside for the moment your vague misdirections, I found this
interesting Abstract while looking for a copy of "Apparent Weight of
Photons". It can be found at this URL:
http://prola.aps.org/abstract/PR/v140/i3B/pB788_1
I had said there was every indication that Pound & Rebka would read
double the relativistic gh/c^2 for their experiment. And indeed that's
what the abstract says: they get 2gh/c^2 = 4.9e-15 twice the book
value.
This was a repetition of the original experiment, citing an
improvement in the velocity component of their transducer (meaning
they probably introduced negative feedback).
It is not reasonable to think they performed the experiment twice once
sending up and again sending down to double the result. Simple logic
would negate that. Here's the article available only to subscribers:
Effect of Gravity on Gamma Radiation
R. V. Pound and J. L. Snider
Laboratory of Physics, Harvard University, Cambridge, Massachusetts
Received 26 May 1965
Recoil-free resonant absorption of the 14.4-keV gamma ray in Fe57 has
been employed to measure the effect of gravity over a 75-ft vertical
path in the Jefferson Laboratory, in an improved version of the
experiment of Pound and Rebka. A Co57 source, initially 1.25 Ci,
large-windowed proportional counters, and an enriched absorber foil 15
in. in diameter permitted a much increased counting rate. The
employment of temperature-regulated ovens for source and absorbers and
a redesigned monitor system to detect variations in waveform of the
source velocity effected a reduction in systematic uncertainties. The
result found was (0.9990ą0.0076) times the value 4.905 x 10-15 of 2gh
/ c2 predicted from the principle of equivalence. The range given here
is the statistical standard deviation set by the number of counts
involved. An estimated limit of systematic error is 0.010.
So my surmise seems correct: loss of frequency on the way up to be
compared with a clock higher in gravity will produce twice the desired
gh/c^2 and they claim 2gh/c^2..
I simply cannot find my copy of the P&R paper, which in any case was
the earlier one. You can probably straighten this out.
John Polasek
http://www.dualspace.net
John C. Polasek
BZ was kind enough to email a copy of the P&R 1960 paper and they do
indeed take the difference between up and down and so their expected
result would be 2gh/c^2, so my cavil was unwarranted. They really
needed both trips as the their data is buried in noise.
They conclude that "frequency increases in falling as expected" and in
amount given by GR: gh/c^2. This has to mean that the Mossbauer
mechanisms are unaffected by gravity and experience no time dilation.
But they are atomic clocks and therefore in GR theory, one would
expect a double effect. The reported double effect is due to 2-way
testing. The explanation in the text is not clear, so their logic is
not arguable.
John Polasek
http://www.dualspace.net
Bilge
What about them? I didn't say you couldn't introduce additional
structure that builds in whatever constraints you want to add.
I suppose you could declare that energy is conserved by fiat if
you really wanted to do that, but then, I'm not sure how you
know what it means. You could just as say burfl is conserved,
but without some idea of how burfl relates to the universe,
so what?
Tom Roberts
> BZ was kind enough to email a copy of the P&R 1960 paper and they do
> indeed take the difference between up and down and so their expected
> result would be 2gh/c^2, so my cavil was unwarranted.
Yes.
> This has to mean that the Mossbauer
> mechanisms are unaffected by gravity and experience no time dilation.
> But they are atomic clocks and therefore in GR theory, one would
> expect a double effect.
You are wrong. Go back and read my posts in this thread for an
explanation of why.
Tom Roberts tjro...@lucent.com
John C. Polasek
wrote:
A simple yes or no would do. You are asking me to wade through 73
messages of sophomoric navel-gazing in order to glean some of your
precious insight and then to decide from your scrolls whetgher
Mossbauer filters are a subject for gravitational "pulling"?
Your offerings are a prime example of that part of my motto about
"then write an essay". I don't think you have ever emitted a useful
number.
You might be able to help out by explaining the principle involved in
the P&R experiment. Someone should. The paper absolutely does not
contain any mathematics that would define the principal involved so
that a comparison could be made with theory.
What was the function of the clock and rack and pinion and the pair of
reducing hydraulics along with the totally separate audio oscillators
and phase shifters, ad nauseum?
No equations were given as to whether the received signal was
dopplered to pull the filter to its center to maximize the count rate,
or in any way what was going on, all this was left out. Even in the
nifty presentation (Google Doppler effect) where loudspeakers at 10 hz
are shown, the arithmetic given is a recitation of the theory, and
with no connection to the experimental apparatus.
I can think of a much simpler experiment, and it uses simply the rack
and pinion machinery that appears as an excrescence at the top of
their apparatus.
Simply declare you can prove that the frequency arriving is going to
be low, and so by continuously pushing the receiver downward you will
doppler it back to the center of the filter. The drill would be to try
different constant velocities, settling on the one showing maximum
count. The arithmetic is encouraging when you consider the Doppler
velocity required:
z*c = 2.5e-15 x 3e8 = 7.5e-7 m/s
This works out to 2 meters/month.
That seems to be a far better scheme than all the unexplained
electronics. You could run it a whole day at a time with far better
results, that would also have a clear logic.
John Polasek
http://www.dualspace.net