Re: Is the speed of light really constant ?

From: Eric Baird (eric_baird_at_compuserve.com)
Date: 10/15/04 

Date: Fri, 15 Oct 2004 06:48:21 +0000 (UTC)

On Sun, 10 Oct 2004 21:54:38 -0400, "Mich" <mich@efni.com> wrote:

>Good post!
>
>Eric Baird <eric_baird@compuserve.com> wrote in message
>news:f3n6m0t1s243a6f4d8j9dqtfnru1dpl6oq@4ax.com...
>> On Tue, 28 Sep 2004 22:45:44 -0400, "Mich" <mich@efni.com> wrote:
>>
> > >What does relativty say the cause of the doppler shift is?
>>
>> I suppose that depends on which theory we use, and how lightspeeds and
>> distances are defined in that theory.
>
>ok. This is specifically the question that I'm asking for though. At first
>glance, I was thinking that after an observer changes velocity relative to
>the source, a time dilation would occur, leaving the light's speed as being
>c. Now, let f' = blueshifted frequency caused by a c+v velocity relative to
>two frames of references as per classical prediction .Since we assume the
>observer measures the velocity as being c, and not c+v, then; from c+v/x =
>c; x= c+v/c.
>We therefore have ( f = f' c/c+t ) ; but this also cancels out the
>frequency's doppler shift. Now, in order to reclaim the doppler shift,we
>could say the light's wavelength contracted, but then, we no longer have a
>frequency/ wavelength ratio having the value of c.
>So far, I have no clue as to how it works out.

When you change your assumption about the frame in which lightpseed
"really" propagates, you normally change the associated predictions
for the strength of the propagation effects.

The discrepancy between assuming a fixed c "locked" preferentially wrt
the frame of the emitter and wrt the observer, is Lorentz-squared, so
by making its intermediate prediction, and invoking Lorentz effects,
SR makes the discrepancy go away.

A few illustrative examples might give a taste of how this works in
practice:

===========================
==SR WORKED EXAMPLE #1:==
===========================

An object is seen to be receding from you at 0.8c
You declare that the speed of light is "really" fixed in your frame,
so the propagation-based Doppler effect that you are seeing must be
: freq'/freq = c/(c+v) = 1/1.8 = 5/9 = 0.55555'

but special relativity tells you that since the object is moving at
0.8c wrt the chosen "preferred frame", it is also time-dilated, giving
an additional Lorentz redshift effect of
: freq'/freq = SQRT[1 - vv/cc] = SQRT[1- 0.8^2] = SQRT[1 - 0.64] = SQRT[0.36]
: = 0.6 = 3/5

So the total redshift that you see according to SR is then
: freq'/freq = 5/9 * 3/5 = 3/9 = 1/3

The frequency that you are supposed to see according to SR is one
third of the original frequency, rather than five ninths.

 

===========================
==SR WORKED EXAMPLE #2:==
===========================

Alternatively, you might decide to declare that you know that the
speed of light is "really" fixed in the other guy's frame.
Now you get a different physical prediciton for the propagation-based
effect, of
: freq'/freq = (c-v)/c = 0.2 = 1/5

So now we are saying that we expect the object to appear far more
strongly redshifted, and to appear to be ticking at only one fifth of
its official rate.
But SR also then says that since we are now declared to be "moving"
wrt the chosen preferred frame at 0.8c, /we/ are now supposedly
time-dilated, so, since our own clocks are supposed to be running slow
by the Lorentz ratio, we are supposed to see the rest of the universe
to be sped up by the inverse of that ratio. So this is supposed to
superimpose an additional Lorentz /blue/shift onto our observations,
of
: freq'/freq = 1/ SQRT[1 - vv/cc] = 1/SQRT[1- 0.8^2]
: = 1.66666' = 5/3

The total redshift that you see according to SR is then
: freq'/freq = 1/5 * 5/3 = 1/3

... which is exactly the same result as before.
SR says that you should see the object to be ticking at one third its
official rate, regardless of which frame lightspeed is supposed to be
locked to, thanks to the magical Lorentz terms, and all the other
aspects of how the situation looks according to SR are supposed to be
"fixed" regardless of which frame we use for the propagation of light.
One observer might say that a signal passes between two agreed events
because the SoL is fixed in their frame, another might say that the
lightsignal takes a different amount of time to make the trip, but
that c is still constant, and the different description of the signal
flight-time is explained by a disagreement as to the true length of
the path between the two locations.

It's traditional to say that for each observer, lightspeed is "really"
fixed in their own frame, but mathematically, it doesn't really matter
which frame you choose for each observer to do their clacualtions in,
the numbers come out the same.

Einstein presented this second calculation in his 1905 paper, assuming
fixed-c wrt the emitter and then factoring in a blueshift, by asking,
"what does the /emitter/ think that the observer ought to be seeing?"
, and using that as an excuse to choose a frame other than the
observer's for doing the calculations.

===========================
==SR WORKED EXAMPLE #3:==
===========================

OTOH, if we really want to be really flashy, we can calculate the same
SR result by doing away with the Lorentz terms altogether and just
calculating the thing as the result of propagation effects and
velocity-addiiton.

If we take our object receding at 0.8c, we are entitled to do the
calculations by assuming that lightspeed is "really" fixed in an
exactly intermediate frame (perhaps someone in that frame decides that
c is "really" fixed wrt them, and wants to calculate what we see
happening).
So ... both us and the object are receding at a smaller (equal)
velocity "u" from this third frame. You might expect u to be
" 2u = 0.8c , u = 0.4c ", but thanks to the SR/LET velocity addition
law, velocities don't quite combine like that, and the correct
relationship under SR is supposed to be " 0.5c + 0.5c=0.8c ", giving
"u = 0.5c"

So now we have two signal propagation stages to deal with
source-to-medium, and medium-to-observer

The first shift stage assumes a "moving source", so we can write
: f'/f = c/(c+v) = 1/(1+0.5)
: = 1/1.5 = 2/3

, so the signal is presumed to enter this frame with two thirds its
original frequency, due to the way that the moving source inserts its
successive signal pulses into the medium at different positions.

For the next shift stage, there is a redshift due to the observer
running away from the signal stream, of
: f'/f = (c-v)/c = 1- 0.5
: = 0.5 = 1/2

, and since the source and observer are both deemed to be Lorentz
redshifted by precisely the same amount, we can forget about the
Lorentz terms altogether, and just do it as a propagation calculation

The final SR shift that we see after the two stages is then
: f'/f = 2/3 * 1/2 = 1/3

, just as before

------------------------------

So with SR, while it's common to say that we "know" that lightspeed is
really fixed in our frame, we are entitled to say that it's absolutely
fixed in /a/ frame, but we can choose any "legal" frame that we like
for the propagation of light, and the final physcal predictions should
always come out the same (until we start doing more complicated things
with rotating frames, etc. ).

The particular SR/LET choice of shift equations, velocity addition
formulae, etc is derived specifically to get this result -- in order
for a single result to be explainable by saying that objects don't
drag light, lightbeam geoemtry it totally flat, and lightspeed can be
said to be absolutely fixed in any frame, throughout the experimental
region ... in order to be able to explain a single result by saying
that it either shows the "moving observer" or "moving emitter"
propagaiton effects (or any combination of the two) , we need the
particular form of "modified" Doppler equations used by SR/LET, and we
need to bring in that matching velocity-addition formula, and matching
Lorentz modifications of the energy and mometum laws (etc), and we
need those Lorentz terms to map between different descriptions of what
the spatial distances and temporal intervals between two events
"really" are.

So the disadvantage of SR/LET is that you have to make certain
idealisations, and change almost all the basic fundamental
relationships and invent a new Doppler relationship in order to get
the system to work.
The practical advantage is that the system is Euclidean (which keeps
the geometry straightforward), and to operate it you don't need to
deal with the warped lightbeam distances and wacky nonlianear effects
that would show up with a "light-dragging" approach to relativity
theory.
Instead of staying awake at night wondering how the hell to model a
metric that is warped by the relative motion of masses, we declare
that Fizeau-type effects don't really exist, and then construct a nice
Euclidean scaffolding on that assumption.
  

PS: In the third example, you might be tempted to think that the
exercise shows that the SR relationships are inevitable because we
didn't use the usual Lorentz terms to get our SR outcome, but the form
of that particular velocity addition formula is intimately "owned" by
the SR "relativistic Doppler" shift equations, so this was just a way
of sneaking the SR results in by the back door.

===========================
==SR WORKED EXAMPLE #4:==
===========================

Or, if you don't really care about making declarations about how light
propagates, and you just want the SR answers, you can multiply the
fixed-observer and fixed-emitter calcualtions and square root:

: f'/f = SQRT[ (c-v) / (c+v) ]
: = SQRT[ (1-0.8) / (1+0.8) ]
: = SQRT[ 0.2 / 1.8 ] = SQRT[ 1/9 ]
: = 1/3

===========================

>> Under special relativity, the arrival time of the light-pulse at the
>> two destinations is supposed to be wholly unaffected by whether or not
>> the source is "moving", and all observers agree as to which other
>> things happened at those locations at the same local times.
>> Suppose that the two observers A and B synchronise their clocks by
>> bouncing light-signals back and forth between them to get the total
>> round-trip time, and then divide that time by two to calculate their
>> mutual observation delay, and set their own clocks to appear to be
>> ahead of the other by exactly that amount (ie they to exactly
>> compensate for the calculated, equal, observation timelags).
>
>Let us say that observer A sends a light signal to observer B at time 1:00.
>The signal bounce from B and returns to A at 2:00. A concludes a 1/2
>light hour distance between himself and B. B having received A's signal of
>1:00, does the same and starts with a 1:00 light signal .I cannot see how
>the clocks can be synchronized without first choosing one reference frame as
>being a proper or absolute frame.

Yep, you are right!
Under SR, there is no such thing as "absolute" distant
synchronisation, it's kinda arbitrary.

Einstein, "Relativity" chapter 8, "On the Idea of Time in Physics":
:: " ... That light requires the
:: same time to traverse the path A-->M as for the path
:: B-->M is in reality neither a /supposition or a hypothesis/
:: about the physical nature of light, but a /stipulation/
:: which I can make of my own free will in order to arrive
:: at a definition of simultaneity. "

In other words, if you go along with SR and make the "real"
propagation frame of light something that can't ever be pinned down,
then you are kinda stuck when it comes to saying when distant events
"really" happened, and whether they are "simultaneous" or not, because
then you can never tell how long it "really" took their light to reach
you.
So in order to /impose/ a defintion of simultaneity, you can select a
"useful" reference frame (usually your own), declare lightspeed to be
"really" anisotropic wrt that frame, and then start applying nominal
time labels and nominal distance labels to distant events ... but
those labels are going to be more a matter of convenience than
anything else.

The underlying reality that is constant under SR is the spacetime
distance between two events ... if we look at our block of spacetime
from different angles, and impose an arbitrary set of space and time
coordinates, the "tilting" of those imposed coordinates can give
different nominal values for the distance and time between those
agreed events. The tilt corresponds ot the relative velocity between
two reference frames, and the velocity-addition law means that no
matter how many times you tilt the block in a given direction, the
total tilt never /quite/ gets to 90 degrees.
The shadow of the line linking two events never gets smaller than
zero, and never goes negative, there are no velocity horizons, the
entiure block is visisble to all observers, and no observer can ever
go faster than the speed of light for another observer.

This sort of graph-paper perfection, where you have a sort of rigid
crystalline spacetime block, and where inertial physics for two
particles can be read off by drawing two straight lines through the
block and using Pythagoras's theorem to read off the projected
distances, seems to be appealing to a lot of mathematically-inclined
physics people.

The alternative ... agreeing that lightspeed dragging effects are
real, and building the theory around them ... would give a model where
the motion of a real particle through the region leaves distorted
streak through the block, and you couldn't read off parameters so
easily with a spacetime diagram and a ruler. The distortions in the
block woudl then tell you where real particles were and how they were
moving, so in some ways it might be more realistic than SR, but until
SR can be shown to be seriously inaccurate, I think the mainstream
will prefer to use it wherever possible.

Unfortunately, nobody in the mainstream seems to admit to working on a
possible "warped" lightspeed model of inertial physics, so we don't
know for sure what it is that SR ought to be compared against, and
what other potentially better theory(ies) we might be missing out on
-- we just say that agreement with SR is compulsory for any more
advanced model, and leave it at that.
 

> ... Only then, it seems,
>can either A choose to advance his clock 1/2 hour in order to be
>synchronized with B "or" B chooses to synchronize himself with A. If they do
>it both at the same time, they are no longer synchronized...it seems.I
>wonder what would happen if they both choose to advance their clocks [30]
>minutes instead?

Yep, that's how Einstein clock-synch works.
The distant synched clocks in an array are not /seen/ to be in step
(because of the timelag), but they are /deduced/ to be in step for
observers in the same frame as the array, because the clock-keepers
each bounce sisgnals off the reference clock in the array, time the
round-trip, presume that the outward and return journeys are taking
take the same time, and set their clocks off from the time that they
see on the reference clock by half the round-trip time. Once they've
done this, they can bounce signals off each other and find that all
their settings now seem to be in perfect agreement. Perfect
clock-synch has been achieved!

>From then on, instead of observers in that frame having to calculate
the nominal time at which a remote event happened, they can simply
watch the event and note the time shown on the synched clock at the
event's location -- the clocksynch idea adds a sense of "physicality"
to what woudl otherwise seem a rather nebulous mathematical idea.

Logically, Einstein's synch method is really just another way of
saying that we can attempt to assign nominal times to distant events
by making assumptions about how long it takes light from those events
to reach us. But instead of seeing an event happen at a location and
then calculating backwards to see when we think it happened, we
preempt things by placing a clock at that location and deliberately
giving it an offset that corresponds to how much timelag we /think/ is
present in the signals from that region, according to those same
assumptions , and then when the event happens, we already have a
nearby clock that is already set up to timestamp the event locally for
us.

>> Suppose, also, that we somehow deliberately engineer a situation where
>> the light-pulses just happen to arrive at each of those two clocks
>> exactly at the moment when the clock in question strikes midnight
>> (perhaps the signal is a laserbeam that burns a hole straight through
>> the hour, minute and second hand as they all line up, pointing at the
>> "12" on each clock).
>> Under SR, its then easy to say that for these two clocks, the light
>> arrived simultaneously, at "midnight",and th eburnholes will verify
>> this.
>
>In this, I question the definition of simultanity( if that's a proper word
>to use).
>Since there is a 1/2 light hour distance, this need to be taken into
>question.
>Let us say, that, both tried to adjust their clocks in order to be in synch
>with the other,
>it seems that they will be [30] minutes out of synch. Therefore if both
>received the
>signal from the emitter at 12:00, the signals were not simultaneous.

>>
>> Now let's look at the same SR situation from the point of view of the
>> emitter "X" that has relative motion wrt the two clocks. For X to be
>> able to say that lightspeed is fixed in /their/ frame, they have to be
>> able to say that the lightpulses take /different/ amounts of time to
>> reach A and B, and that they should NOT hit their targets
>> simultaneously.
>> How does X reconcile this with the idea that both clocks get "zapped"
>> while their dials show the same time?
>> Well, says X, those clocks were synchronised at the beginning of the
>> experiment using the "bad" assumption that the observation timelag AB
>> is the same as the timelag BA. This, says X, has resulted in the two
>> clocks being "wrongly" synchronised so that there is actually a
>> mismatch in their displayed times that depends partly on the distance
>> between them.
>
>I fully agree..
>
>> Since clock A is now argued to be showing the "wrong" time wrt clock B
>> (according to X), the fact that both clocks were hit while they were
>> /showing/ midnight means that they must have been hit at /different/
>> times!
>
>ok
>
>> This idea of diagreements about perceived distant simultaneity runs
>> through SR ... if you and I are passing each other at the moment that
>> we both see the light from a supernova, we both agree that the light
>> hit us both at a common event, but if we both have different ideas
>> about what the speed of light really is, we can both end up
>> calculating different nominal dates for when the star "really" blew
>> up. So if we both draw up a map in the form of a 4D spacetime block
>> containing all the events that we see in the surrounding universe,
>> both our maps will contain the same events, with the same basic links
>> between them, but if you and I mark sets of events that we believe
>> happened at the same time (plane of simultaneity), the "planes" in
>> your map that are simultaneous are going to be drawn in at an angle
>> compared to the "planes" in mine, and our concepts of the "direction
>> of time" in the block (the directuion perpendicular to the "plane")
>> are going to be similarly skewed and distorted wrt each other.
>
>
>ok
>>
>> So SR ends up saying that all observers agree about the local sequence
>> of events at any point in the map, but the disagreements about
>> supposed lightpeeds give different observers different definitions of
>> the supposed spatial distance and time separation of pairs of
>> events,and causes them to attach different time and place "labels" to
>> the same events.
>> The conditions that all frames are supposed to be equivalent, and that
>> no matter how many observers you have each of whom is moving at 0.5c
>> more then the previous one, the map can never quite turn through 90
>> degrees for any observer ... this pretty much gives us SR's velocity
>> addition formula, and the Minkowski geometry.
>
>I think I understand this, a bit...
>>
>> ----------------------------
>>
>> If we implement the PoR using "historical" emission theory, then the
>> logic is different. we then say that we have two emitters passing each
>> other when they both emit light-pulses, those pulses will arrive at A
>> and B at /genuinely/ different times. if X1'sa signals hit the clocks
>> when they are showing midnight, then light from X2, moving
>> differently, might hit clock A when the hands haven't reached 12, and
>> B when they have already moved on. Each clock gets hit by two
>> successive pulses, rather than one combined pulse.
>>
>> This sort of "old" emission theory is relativistic and "democratic",
>> but its a bit of a mess, we have lightsignals overtaking each other
>> along the same paths, and no conventient underlying light-metric to
>> refer to. Light is emitted at c wrt every object, but the reception
>> speeds are all over the place.
>
>>
>> --------------------------
>>
>> A third description might be to implent a "relativistic"
>> light-dragging model -- to say that light is emitted at c wrt every
>> mass, and received at c wrt every mass, because relatively-moving
>> masses simply "drag lightspeed about" in their immediate vicinities.
>> In this third sort of relativistic model the two clockkeepers believe
>> that the velocity of light between them is being screwed up by the
>> motion of the ermitter's mass between them, and that although the
>> velocity of light AB and BA might well have been the same if the
>> central emitter wasn't there, the presence of the moving emitter
>> produces a localised light-dragging effect that messes up the previous
>> geometry. So the clocks can end up being physcally synchronised
>> synchronised differently depending on whether an intemediate mass is
>> screwing up the light-signals
>>
>>
>> >> It's common to describe this third equation (known as the
>> >> "relativistic Doppler" equation) as being composed of two components,
>> >> that initial c/(c+v) component due to light being assumed to travel
>> >> preferentially in your own frame, and an additional Lorentz redshift
>> >> component that only depends on relative speed, and not direction, of
>> >>
>> >> : freq'/freq = SQRT[ 1- vv/cc ]
>> >
>> >And according to the particle theory the relationship would have been
>> >
>> > freq'/freq = (c-v)/c... wouldn't this be close to gamma? SQRT[ (cc/cc) -
>> >(vv/cc) ]?
>>
>> Under emission theory, the Doppler predictions divided by eq [1] leave
>> a residual Lorentrz-squared effect,
>> : freq'/freq = 1- vv/cc
>> ,so yes, its similar in character ot the SR prediction, but redder
>> than SR by an additional Lorentz factor.
>> So experiments designed to report a Lorentz effect under SR would
>> normally be expected to report a "Lorentz-squared" effect with
>> emission theory.
>
>But isn't the relativistic red shift due to the disagreement in relative
>velocities between two frames , when compared to the emission theory?

Hmmm ...

[Answer #1]:
 ... In the context of SR, it might be more accurate to describe it as
being due to the disagreement between observers as to what the
"proper" propagation-based Doppler shift ought to be for a given
velocity.
It's a redshift compared to the predictions of a stationary absolute
aether, but a blueshift compared to those of emission theory or of an
aether pegged to the emitter's state of motion.

[Answer #2]:
 ... Outside of SR, the existence of a transverse redshift component
/normally/ means that the experiment is demonstrating at least some
degree of source-dependence in the way that the light-signal
propagates: so for instance, if we believed in an absolute undragged
aether, we'd expect to see a transverse redshift somewhere between
"zero" and "Lorentz-squared", depending on whether the absolute frame
was stationary wrt the observer, emitter, or somewhere in between.
For emission theory (complete source-dependence), it's a
"Lorentz-squared" relationship for everyone, and for dragged aether
models I'd again expect it to be somewhere in this range between zero
and Lorentz-squared, with the amount of redshift telling you how
strong the dragging effect is.

[Answer #3]:
 ... In the context of testing SR against emission theory-based
models, yes, individual results that are often look as if they are
unique to SR do also turn up in similar or identical form under NM, if
we set up our experiment using initial agreed, verifiable,
non-negotiable quantities.
Starting from a "velocity" value and then doing cross-theory
comparisons of a physcal experiment is more dangerous, because to
measure a physcal velocity one has either to be in two places, or to
make certain assumptions about distances and times, and whether or not
those quantitiers are affected by a moving mass. It's bringing us back
to the "clock-synch" issue.

So yes, sometimes when a new SR "effect" is attributed to relativistic
time dilation, identical behaviour appears under NM, and the existence
of the effect in SR can be considered (under other NM-based theory) as
being an artifact of SR's downward redefinition of the velocity values
associated with a given energy or momentum.

 
-----------------------
MUONS

I think the classic example is the case of short-lived muons generated
at the edge of the earth's atmosphere, which manage to travel all the
way to the surface detectors before decaying.
Under special relativity, we say that for a given energy and momentum,
the speed of the muon is slower than under NM, and so the muon should
not be able to reach the detector in time ... but then we say that
SR's time-dilation effect makes the muon live longer by the same
Lorentz amount, so that it can reach the detector after all (or we
say, form the muon's point of view, that the distance to the detector
is Lorentz-contracted, so the muon is able to get by crossing a
Lorentz-contracted distance there before it goes "poof".

Some SR people used to be fond of saying that the muon case proved
that SR's length-contraction and/or time dilaiton effects were known
to be genuine, because if they were not, there is no way that the
muons could reach our detectors before they decayed.

But in a cross-theory comparison, the velocity of the muon is
difficult to pin down, becuase the observer is not in two places at
once -- SR can assign a velocity to an arriving particle based on its
energy and mometum, but that velocity value is then going to be
theory-specific.
In the muon case, although its easy to say that the muon with the
assigned SR velocity can never reach the detector under NM, the fact
is that the forward blueshift and mometum of the arriving particle
interreleate in exactly the same way under SR and NM, and although
these yield different nominal velocity values in the two sorts of
theory, the calculated decay position of the muon under thre two
theories using those /different/ velocity values is then precisely the
same under SR as it would have been under NM ...

------------------------
ROCKETS

Space exploration is another example ... you sometimes see people
starting out by assuming that velocity is a fundamental property that
means the same thing under different theories, and saying that SR's
time dilaiton effect makes it possible (in theory) for an astronaut to
visit the stars in a single lifetime. Yaay for SR!
But if our "practical" calculation starts instead from the amount of
energy or momentum put into the astronaut's ship, and their ship's
rest mass, there's no obvious physical difference between the "new" SR
result and what NM predicts for that one-way trip.
.
Under NM, the ship's engines fire until they've used up all their
fuel, the rocket coasts, and it reaches the nearest star after a known
amount of ship-time.
Under SR, if the ship's engines have the same efficiency, and impart
the same amount of energy and mometum to the ship, the velocity is
lower than NM by the Lorentz amount (so you expect the journey to take
correspondingly longer), but then the SR time dilation effect exactly
compensates by saying that the ship's occupants see less time
elapsing, these two Lorentz effects cancel, and the ship chronometer
at arrival shows precisely the same time at the end of the trip,
regardless of whether we used SR or NM.

>And are
>such velocities defined by the shifts themselves?Can we know for certain
>which velocity is the true one? If they are observed through events, then we
>still have the problem of Relativity having length contractions whereas the
>emission would claim a greater velocity... but not in the same magnetude, I
>agree;

In theory we can rule out either the SR or NM velocity-shift
relationships experimentally, by taking multiple readings from
different angles of an object moving at a constant (undefined)
velocity:

With SR, as an emitting object 's speed wrt us approaches lightspeed,
the forward emitted frequencies (are seen by us to) go to infinity and
the rearward-emitted ones (are seen by us) to go to zero.

Under NM, the rearward frequencie again go to zero at v=c, but the
forward frrequencies at that speed are merely doubled.

So if you fire up your spaceship engines and keep accelerating until
the forward stars' blueshift ratio is approaching 2:1, and then look
over your shoulder at the retreating stars behind you, special
relativity will say that the redshifted stars will have frequencies
dropping towards one half of their original values, whereas emission
theory/NM will say that the rearward stars' redshifted frequencies
will be approaching zeroin this situation

So while its often damned difficult to tell the two equations apart
with readings taken at a single angle (without imposing assumptions
about flat spacetime), with combinations of readings you can do it.

 

>> So, for instance, if we aim a narrow viewing tube at 90 degrees to a
>> moving emitter's path, where "90 degrees" is calibrated in our own lab
>> frame, emission theory predicts that we should see a stronger redshift
>> than SR says. Under emission theory, the redshift is explained simply
>> as an aberration artifact, we are intercepting a rearward-aimed beray
>> that reaches us with a recesson redshift component, but the forward
>> tilt fo the ray due to aberratiuo nmeans that it accidentally ends up
>> registering on our "transverse-aimed" detector.
>
> Is not the calculation based on the orbit of the earth relative to the
>sun, at 30,000km/sec, implementing the length of the tube within the
>equation, giving us the light's velocity as being c? My problem concerning
>this would be that relative transverse velocities between the sources(stars)
>and the earth are "not" 30,000 km/sec, and must be different for different
>stars. If I understand properly( but I doubt that I understand this part
>clearly), the abberation constant ought not to be a constant at all, even
>for Relativity.

Emisison theory uses the same aberration formula as SR.

I wasn't making any calculations for the size or dimensions of the
viewing tube, only that it should be arbitrrarily "narrow".
If the viewing tube is aligned to point at "90 degrees" to the
emitter's path (according to angles marked out on the lab floor), and
is narrow enough to only register light coming in at that angle (or
exceedingly close to it), then if we switch to the viewpoint of the
emitter, they should see the tube angled slightly forwards (due to
aberration), and they can argue that tthe light that they are "really"
throwing off at 90 degrees might well be arriving in the lab
unshifted, but it isn't going into the tube ... the "forward" tilt
angle of the tube means that the lab detector is instead only
registering rays that left the emitter aimed with a "rearward" slant,
and the emitter can say, of /course/ the detector is registering a
redshift, the intercepted light entered the lab diagonally, and
contains a recession component.
Calculate which ray the tube is actually receiving, it's original
angle in the emitter frame, and the recessional component associated
with that angle, and the result is a prediction that the detector sees
a Lorentz-squared redshift, purely due to aberration effects.

Under SR we can do precisely the same calculation by assuming that
light "really" travels preferentially in the emitter's frame, and then
turn it back into an SR calculation at the last moment by saying: "...
and then we have to superimpose a Lorentz blueshift, because the lab
is really moving and is time dilated" ... that then reduces the
Lorentz-squared emission theory prediction back down to the single
Lorentz redshift prediction of special relativity.

>Therefore, wouldn't the velocity of light concluded as being
>c only when the light was absorbed and re-emitted within a medium
>stationnary relative to us?...the atmosphere, the lenses?

Er ... possibly.
There were some attempts at constructing dragged light models in the
C19th, but they all probably looked a bit "ornate", and because we
didn't really know as much back then about curved-spacetime arguments,
they tended to include arbitrary-looking terms and "guessed"
quantities, and when SR came along with its minimalist Euclidean
framework, and reduced parameter set, the theories based on lightspeed
dragging got dumped as being overly complicated.

I personally liked the idea of reviving the old dragging idea and
rewriting it in the language of spacetime curvature, so that the
relative motion of the masses involved is "smudged out" into the
region between them, as a field effect associated with
relatively-moving mass-charge, and so that that the light is already
changing speed before it reaches the surface of the detector.

But that's just me.

>> >According to your understanding, what causes the doppler shift? A change
>in
>> >the wavelength? How is this accomplished?
>>
>> In the first two "nonrelativistic" examples, we have a frequenct
>> difference ocurring due to motion effects where the signal is being
>> insetrted in th emetric, and again where the signal is being extracted
>> In a simple absolute ether theory, we have a mixture of the two
>> effects, depending on how fast the medium is supposed to be moving wrt
>> each object ("aether wind")
>
>ok
>
>> In simple emission theory, it's the second explanation, and the same
>> "stationary emitter" Doppler relationships, but it now applies
>> symmetrically for all observers.
>
>ok
>>
>> In SR, it's "either/or/both" ... we can use either the first
>> explanation (supplemented by an additonal Lorentz time dilation
>> redshift), or the second explanation (supplemented by an additonal
>> Lorentz blueshift), and the final total Doppler effect that we see
>> then has the same value either way.
>
>My problem here is that since there is no ether and the light's velocity is
>constant for all observers,
>why is there no problem using either or both?

See the first three examples further up the page ...

IMO, SR is a bit like, if you imagine group of architects with tape
measures standing in an unpainted car park, around a flat cardboard
*** depicting the top view of a parked car, and trying to decide
what the car's "real" dimensions are. The architect standing behind
the cutout says that the car requires a parking space 4m long by 2m
across, and another standing alongside says that no, its 2m long by 4m
across, and a cluster of other colleagues standing between the first
two and looking at if from different angles wave their tape measures
about and start shouting out different length and breadth values.
It's the same piece of cardboard, and all their drawings of a plan
view of the car will be equivalent, except for a coordinate rotation.

The distance between any two features on the cutout is the same for
all the observers (agreed spacetime separation between pairs of
events), but the way that that "diagonal" distance breaks down into
length and breadth components (space and time intervals) depends on
the angle at which we overlay our reference grid.

If all the architects whip ot their digital cameras and photograph the
cutout, when those photos are uploaded into a computer they can be
distorted and rotated to get rid of perspective effects, and will show
the same thing ... all the details visisble to one observer are
visible to anoher, there are no horizons or concealed surfaces.

-----

OTOH, a more "acoustic" metric, or emission theory overlaid on curved
spacetime, seems to be more like the situaiton that you'd get if the
architects were standing around a real car. You get horizon problems,
details visible in one photo simply don't show up in another
observer's piccy, and its a hell of a lot more difficult to work out
how much surface area is involved.
So its easier to deal with the cardboard cutout, and for a lot of
situations (eg planning parking bays in an open-air car park) the flat
cutout is a perfectly adequate representation of a car.

Where I think current theory has a problem is it's insistence that all
full theories have to reduce exactly to SR ... I personally think that
that's like saying that all real cars have to contain the literal
equivalent of that flat cardboard cutout. Taking the cutout and
extruding it does not necessarily give you the true shape of your car,
and some of the distances and relationships in the cutout are going to
be "wrong" on a real car.

>> Or we can pick any other "legal" frame that we like, declare that
>> light "really" travels preferentially in that frame, and calculate
>> /both/ sets of effects, "emitter-to-medium", and "medium-to-observer",
>> and when we've done all this (including all the necessary Lorentz
>> effects and bearing in mind that the SR velocity addition law means
>> that the two smaller velocities won't add up conventionally to give
>> our total velocity), the final observable Doppler shift will again be
>> exactly the same as before.
>> So SR lets us use any arbitrary mix of the two separate effects, as
>> long as we do that associated Lorentz and velocity-addition stuff.
>
>If it's not too complicated, could you write those equations down? Maybe
>this could give me a clue.

I've done a quick example as "SR worked example #3", above, for the
special case of using a reference frame exactly intermediate between
the observer and emitter's frames. In that example, the Lorentz
effects don't play a part, and SR's modifications all show up in the
actions of its velocity addition formula.

I picked the easiest example I could think of, where all the ratios
were nice easy fractions ... normally you'd never consider doing SR
this way -- splitting a single-stage problem into the problem into two
successive sections and running the velocity-addition formula
backwards isn't usually easy, and for other intermediate frames, your
two velocities would be different, breaking down the vaf woudl be more
difficult, and you'd have two different-sized Lorentz components to
trade off against each other ... eurgh.

I think that its a nice exercise to attempt /once/, as an exercise to
prove to yourself that it really does work, but it normally isn't
sensible to do it this way!

>> In a relativistic light-dragging model the distinction between "moving
>> observer" and "moving emitter" seems to dissolve away -- we have a
>> variation in the effective llight pathlength between source and
>> emitter that varies with velocity, but we no longer have a flat
>> lightbeam geometry to tell us exactly what those changed distances
>> ought to be.
>> When I started looking into this, I initially expected that if we were
>> merging the two descriptions together, the logical result would be
>> special relativity's "merged", "relativistic Doppler" equations,
>> giving the same basic relaitonships as SR but in a curved-spacetime
>> context.
>> But no matter how hard I tried, I couldn't come up with a totally
>> legal way of rederiving SR in curved spacetime, and everything seemed
>> to be pointing me away from the SR amth and back to the
>> emission-theory relationships. These do seem to work suspiciously well
>> in this sort of curved-spacetime context, and do seem to solve all
>> sorts of problems with current theory, and also turn out to be the
>> unique set of energy relaitonships required for p=mv to be correct, so
>> I'm 99% sure that this sort of model can't use the SR math, and maybe
>> 85% sure that it has to use the emission-theory set.
>
>I'm not certain I understood clearly the above, but, I believe to agree with
>you that the particle theory seems to explain many things, and Relativity,
>from the very little I do understand of it, seems still paradoxial...to me.

Well ... IMO emission theory doesn't seem to support local c-constancy
unless its implemented in a metric where relative velocity between
masses warps the geometry ... and that throws up a whole mountain of
other nasty problems (lots of definitional awkwardnesses about
horizons, and gravitational features propagating nonlinearly),
but even though these seem mathematically more scary, in a way I think
they still seem less counterintuitive than SR, because they tend to
relate to the sort of "sophisticated" mathematically-scary effects
that we already get in conventional acoustics.

The only people who find /those/ counterintuitive seem to be the
people who've spent too much time studying SR. :)

>> (I think the first issue is why nobody seems to study this sort of
>> relativity theory, I guess as soon as a mainstream researcher finds
>> that the theory seems incompatible with SR, they are likely to stop
>> investigating.)
>>
>>
>> But I can't provide a nice linear derivation that takes a preexisting
>> lightmetric, draws a path through it and reads offf the distances,
>> becuase in this sort of model, there's no absolute preexisting
>> geometry ... as soon as you hurl a new particle through a region, the
>> shape of the lightmetric changes in sympathy.
>> :(
>
> I'm not certain I have the capacity to be able in understanding the work
>you've been doing in trying to merge the relativistic doppler with S.R. but
>would be very interested in trying to read your material....do you have a
>web site I could go to?

I shut down the websitre a few years ago.
I don't actually do this stuff any more. The problem-solving was
addictive, but there's currently no market for non-SR relativity
theory. I couldn't get any mainstreamers interested, I needed to earn
money for rent and food, I wasn't interested in committing more years
to the project if nobody was going to make use of it, I ended up with
no social life, and it saying that I did this didn't impress women.
:(

I've been trying to go physics "cold turkey" since about 2001. I now
don't watch science programes or read sciencey articles or magazines,
and try not to look at the newsgroups. the only reason I'm here now is
that I accidentally read an article on Hawking's lecture in a
newspaper a few months ago, decided to take a peep here to see what
was happening, and let myself get sucked back into a few threads. :(

(note to self, try to wind up current conversations and delete spr
from newsreader app)

Now, back to the jobhunting ...

=Erk= (Eric Baird)
: " The more bizarre a thing is the less mysterious it proves to be.
: It is your commonplace, featureless crimes which are really puzzling. "
: "The Redheaded League", Arthur Conan Doyle

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