New Improved Twin Paradox Explanation
Jonathan Doolin
Some time ago I made a rather stuttering attempt at this explanation
on YouTube, (math free version)
http://www.youtube.com/watch?v=nmAVkj9fTnU
http://www.youtube.com/watch?v=76BB-qZXEho
http://www.youtube.com/watch?v=eT-3R8ju9V0
but I did not feel like doing the mathematics at that time.
This morning, I'd like to try to put a FEW equations down. Don't
expect here any profound discovery. Typically an explanation has a
quality in inverse proportion of the explainer's pride. I'm pretty
proud of this explanation, so that's probably not a good sign. :)
This morning I wanted to describe in my own words and at least give
what little bit of the math that I know how to do. I apologize in
advance for the math and grammatical errors you'll probably find.
In any case, let us consider two parties, A and B, A stays at home,
while B moves away into the distance to point C, 1 "light" unit away
and then returns home.
The speed of light in this model is 1 and the distance is 1 and the
velocity which B chooses to travel is v. (where, of course, v=1
represents the speed of light)
----------------
Part 1, What do things look like from the Home Twin, A?
So A watches B travel toward point C at velocity v. How long does
this take? B arrives at C at time t = distance/velocity = 1/v.
However when B arrives at C, there will be a time delay before A sees
the event of arrival because of the time the light takes to return
from that point. So A observes B's arrival at C at time t = 1+1/v
An interesting thing to consider here is that the observed velocity is
explicitly calculable from the two observed events (departure
observation and arrival observation). A will have observed B's
journey at a constant speed. Observed Velocity of Outward trip =
distance/time = 1/(1+1/v) = v/(1+v)
A similar consideration of the inbound trip yields an Observed Time of
the inbound trip of (1/v)-1, and observed velocity v/(1-v)
Thus if v=.5, then the observed velocity outbound =.5/1.5 = .3333c,
and the obseved velocity inbound = .5/.5 = 1c.
If v=.9 then the observed velocity outbound = .9/1.9 = 0.47c and the
observed velocity inbound = .9/.1 = 9c.
So the maximum observable outbound velocity is .5c but there is NO
maximum observable inbound velocity.
---------
Part 2. What do things look like from the perspective of the
traveling twin, B?
http://www.youtube.com/watch?v=eT-3R8ju9V0
From B's perspective there must be some things which are the same, and
some things that are different. If all of the same physics apply,
then we must assume that the same chemical, nuclear, or matter/anti-
matter reactions that produced the velocity v (Between A and B) for
observer A must also have produced the same velocity v (Between A and
B) for observer B.
The real velocities are the same. If the real velocities are the same
then should the observed outbound velocity v/(1+v) and observed
inbound velocity v/(1-v) be the same? Yes, these calculations are
general. The observed inbound and observed outbound velocities are
based ONLY on the actual velocity, and nothing else. Though I did the
calculation based on a specific pair of events, departure and arrival
of observer B, any two events could be used, and they cancel out of
the final calculation.)
A thing that will be different for the two observers, though is the
apparent time that it takes B to travel from A to C and back. Whereas
A observed the return trip to happen much faster than outbound trip, B
will observe the outbound trip and inbound trip to take the same
amount of time. (Other famous gedanken experiments determine that
this time would be (1/v)*(1/sqrt(1-v^2)) whereas 1/v would be the
expected time it takes to travel distance 1, and the other factor is
the time dilation factor)
The Observed velocities are the same, but the amount of time traveled
at those velocities is different. This means that the observed
distance traveled by B is different for B than it is for A.
(Technically, B remains stationary relative to observer B, just to be
troublesome.)
But the greatest point of interest is what happens to the Observed
distance to A from the perspective of B during the turn-around. The
apparent relative velocity of A on the way out was v/(1+v). The
apparent relative velocity of A on the way in will be v/(1-v).
If the time is the same, but the apparent velocity is different, then
there is only one possibility. The distance CHANGED. You cannot move
away from an object at one apparent velocity and then return at a
faster apparent velocity for the same period of time unless that
object has moved away from you.
In effect, the traveling twin at his point of turning-around is
transitioning himself into a new reference frame where his home-world
is much further away than it was before. Also as his home goes from
slow-motion [v/(1+v)< .5] to fast forward [v/(1-v) = unlimited.] For
the moving twin it may be a surprise that the earth lurches away from
him at the point of turnaround, but he will be able to watch the rise
and fall of civilizations in fast-forward on his return trip. It
won't be a surprise to him when he gets home and everyone he knew is
dead unless he has no windows on his space-ship.
harry
"Jonathan Doolin" <good4...@gmail.com> wrote in message
news:7f867f03-0b1e-4c11...@s24g2000vbp.googlegroups.com...
> Good morning.
>
> Some time ago I made a rather stuttering attempt at this explanation
> on YouTube, (math free version)
>
> http://www.youtube.com/watch?v=nmAVkj9fTnU
> http://www.youtube.com/watch?v=76BB-qZXEho
> http://www.youtube.com/watch?v=eT-3R8ju9V0
>
> but I did not feel like doing the mathematics at that time.
>
> This morning, I'd like to try to put a FEW equations down. Don't
> expect here any profound discovery. Typically an explanation has a
> quality in inverse proportion of the explainer's pride. I'm pretty
> proud of this explanation, so that's probably not a good sign. :)
First off all, what did you set out to explain? There are different versions
of the Twin / Clock paradox. For example, the popular textbook version
merely explains how special relativity works while the original one
concerned general relativity.
Sorry I didn't check the math and only quickly skipped over your story (itat
first glance you tried to account for the Doppler effect without mentioning
it and without distinguishing between that and time dilation); but I
expected to see an attempt to explain something. I saw you give some
descriptions of observations, including a rather unphysical ("surprise")
lurching away of the earth, but what did you set out to explain?
Regards,
Harald
Strich.9
> "Jonathan Doolin" <good4us...@gmail.com> wrote in message
>
> - Show quoted text -
I think he does not have the full handle yet, but he is seeing the
light. More than I can say for relativists...
rotchm
<SNIP>
> This morning I wanted to describe in my own words and at least give
> what little bit of the math that I know how to do. I apologize in
> advance for the math and grammatical errors you'll probably find.
>
> In any case, let us consider two parties, A and B, A stays at home,
> while B moves away into the distance to point C, 1 "light" unit away
> and then returns home.
>
> The speed of light in this model is 1 and the distance is 1 and the
> velocity which B chooses to travel is v. (where, of course, v=1
> represents the speed of light)
>
> ----------------
> Part 1, What do things look like from the Home Twin, A?
First, good for you to reason out the problem on your own.
However, reading your post, there are many things you have
"ignored". First, do indicate which version of the TP you
are referring to. Secondly, you are convoluting the words used;
Already SR uses common words but with different meanings and you
mix up the baggage moreso...
> So A watches B travel toward point C at velocity v.
IN the SR jargon, this means that A observes B's speed to
be v. More precisely it meant that A measures B's speed to be v.
>How long does
> this take? B arrives at C at time t = distance/velocity = 1/v.
> However when B arrives at C, there will be a time delay before A sees
> the event of arrival because of the time the light takes to return
> from that point.
To "see" is quite irrelevant and many SR books which use it do not
mean to
actually "see" with our eyes ( nor with any detecting instrument which
A possesses)
>So A observes B's arrival at C at time t = 1+1/v
The common SR jargon is "A observes B's arrival at C at time t=1/v".
What you are referring to is the time at which A receives the image of
B's arrival at C. Your word of 'observed" is out of context and
induces
misinterpretations. This happens all along your post. You should work
on that,
and to do so, read many...many books on SR to get to know its
language.
Jonathan Doolin
> "Jonathan Doolin" <good4us...@gmail.com> wrote in message
>
> - Show quoted text -
Hi Harald. I am dealing with Special Relativity and ignoring any
gravitational effects, and I am not dealing with the Doppler effect
since I am ignoring frequencies and wavelenths.
Are these other valid explanations that you are familiar with, or just
your favorite straw-men?
Dono
>
>
> Are these other valid explanations that you are familiar with, or just
> your favorite straw-men?
Your "calculations" are all wrong. So, your explanation is neithe
"new" , nor "improved", it is just plain wrong. You could buy a
book.Much better use of your time.
Jonathan Doolin
> On Jan 7, 10:24 am, Jonathan Doolin <good4us...@gmail.com> wrote:
> <SNIP>
>
> > This morning I wanted to describe in my own words and at least give
> > what little bit of the math that I know how to do. I apologize in
> > advance for the math and grammatical errors you'll probably find.
>
> > In any case, let us consider two parties, A and B, A stays at home,
> > while B moves away into the distance to point C, 1 "light" unit away
> > and then returns home.
>
> > The speed of light in this model is 1 and the distance is 1 and the
> > velocity which B chooses to travel is v. (where, of course, v=1
> > represents the speed of light)
>
> > ----------------
> > Part 1, What do things look like from the Home Twin, A?
>
> First, good for you to reason out the problem on your own.
> However, reading your post, there are many things you have
> "ignored". First, do indicate which version of the TP you
> are referring to. Secondly, you are convoluting the words used;
> Already SR uses common words but with different meanings and you
> mix up the baggage moreso...
>
I'm sorry, I've been away from the group for a long time. I am not
familiar with the abbreviation TP.
> > So A watches B travel toward point C at velocity v.
>
> IN the SR jargon, this means that A observes B's speed to
> be v. More precisely it meant that A measures B's speed to be v.
>
> >How long does
> > this take? B arrives at C at time t = distance/velocity = 1/v.
> > However when B arrives at C, there will be a time delay before A sees
> > the event of arrival because of the time the light takes to return
> > from that point.
>
> To "see" is quite irrelevant and many SR books which use it do not
> mean to
> actually "see" with our eyes ( nor with any detecting instrument which
> A possesses)
>
Ah. Therein lies a great problem. One should admit that we should be
concerned primarily with what is "actually" going on, but in order to
know what is actually going on, there must also be what is "actually"
seen. Admittedly, there are many effects which would warp the scene--
especially the effect that oncoming objects appear to be moving faster
than the speed of light, while receding objects appear to be moving
slower than they actually are. If SR (Special Relativity) books
ignore this phenomenon, and this separation of "what is actual" and
"what is seen", it is not exactly an error, but it is an unfortunate
pedagogical dogma which creates confusion and should be remedied.
> >So A observes B's arrival at C at time t = 1+1/v
>
> The common SR jargon is "A observes B's arrival at C at time t=1/v".
> What you are referring to is the time at which A receives the image of
> B's arrival at C. Your word of 'observed" is out of context and
> induces
> misinterpretations. This happens all along your post. You should work
> on that,
> and to do so, read many...many books on SR to get to know its
> language.
As you already mentioned, most SR books specifically DO NOT address
the issue of when something is "observed" so it would be very
difficult to cling to the terminology of SR books while discussing
this. The fact that you know what I am talking about means that it is
not "out of context" and "subject to misinterpretation."
If you want to make it not subject to misinterpretation, then the best
thing to do is not read "many many books" on SR, because how do you
know any of them have any idea what they are talking about? The best
thing is to use the Lorentz Transformation equations to verify the
relationships between the three events (departure, turn-around, and
arrival) in the three reference frames (home, outbound, inbound) and
verify the space-time coordinates of those three events. Then you
will know whether you have interpreted correctly.
harry
> On Jan 7, 10:00 am, "harry" <harald.NOTTHISvanlin...@epfl.ch> wrote:
>> "Jonathan Doolin" <good4us...@gmail.com> wrote in message
>>
>> news:7f867f03-0b1e-4c11...@s24g2000vbp.googlegroups.com...
>>
>>> Good morning.
>>
>> First off all, what did you set out to explain? There are different
>> versions of the Twin / Clock paradox. For example, the popular
>> textbook version merely explains how special relativity works while
>> the original one concerned general relativity.
[..]
>>
>> Sorry I didn't check the math and only quickly skipped over your
>> story (itat first glance you tried to account for the Doppler effect
>> without mentioning it and without distinguishing between that and
>> time dilation); but I expected to see an attempt to explain
>> something. I saw you give some descriptions of observations,
>> including a rather unphysical ("surprise") lurching away of the
>> earth, but what did you set out to explain?
>>
>> Regards,
>> Harald- Hide quoted text -
>>
>> - Show quoted text -
>
> Hi Harald. I am dealing with Special Relativity and ignoring any
> gravitational effects, and I am not dealing with the Doppler effect
> since I am ignoring frequencies and wavelenths.
I see. But even when you ignore frequencies, it is important to distinguish
between the different effects and one of the effects you describe is related
to Doppler. For example, also in classical descriptions one receives a
faster image of the earth during and after turnaround and that has nothing
to do with clock rate.
> Are these other valid explanations that you are familiar with, or just
> your favorite straw-men?
You forgot to answer my main question: what do you try to explain, or in
other words, what is it that you think needs to be explained?
The standard textbook explanations don't explain any deep questions.
Effectively, they just give it as exercise to show that the Lorentz
transformations are self consistent. For me the best explanation (of why it
physically works) was given by Langevin in 1911, well before it became a
paradox(!).
And I dislike straw-men, I like to shoot them. :-)
Cheers,
Harald
Androcles
"Jonathan Doolin" <good4...@gmail.com> wrote in message
news:7f867f03-0b1e-4c11...@s24g2000vbp.googlegroups.com...
> Good morning.
>
> Some time ago I made a rather stuttering attempt at this explanation
> on YouTube, (math free version)
>
> http://www.youtube.com/watch?v=nmAVkj9fTnU
> http://www.youtube.com/watch?v=76BB-qZXEho
> http://www.youtube.com/watch?v=eT-3R8ju9V0
>
> but I did not feel like doing the mathematics at that time.
>
> This morning, I'd like to try to put a FEW equations down. Don't
> expect here any profound discovery. Typically an explanation has a
> quality in inverse proportion of the explainer's pride. I'm pretty
> proud of this explanation, so that's probably not a good sign. :)
Hey Droolin' Doolin!
Ref:
http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img22.gif
What kind of lunacy prompted Einstein to say
the speed of light from A to B is c-v,
the speed of light from B to A is c+v,
the "time" each way is the same?
[rest of crap snipped]
dlzc
On Jan 7, 10:05 am, Jonathan Doolin <good4us...@gmail.com> wrote:
> On Jan 7, 10:25 am, rotchm <rot...@gmail.com> wrote:
...
> > > ----------------
> > > Part 1, What do things look like from the Home
> > > Twin, A?
>
> > First, good for you to reason out the problem on
> > your own. However, reading your post, there are
> > many things you have "ignored". First, do
> > indicate which version of the TP you are referring
> > to. Secondly, you are convoluting the words used;
> > Already SR uses common words but with different
> > meanings and you mix up the baggage moreso...
>
> I'm sorry, I've been away from the group for a long
> time. I am not familiar with the abbreviation TP.
From your thread title: "Twin Paradox".
David A. Smith
Uncle Al
[snip]
> This morning, I'd like to try to put a FEW equations down.
[snip rest]
http://www.hawaii.edu/suremath/SRtwinParadox.html
<http://physics.syr.edu/courses/modules/LIGHTCONE/twins.html>
http://sheol.org/throopw/sr-twin-01.html
Twin Paradox
[In the Newtonian approximation to GR, the line element for "Newtonian
coordinates" is to excellent approximation:
ds^2 = -(1 - 2\phi) dt^2 + dx^2 + dy^2 + dz^2
where \phi is the Newtonian gravitational potential, c=1
The only deviation from Minkowski spacetime is in the time coordinate
- using these coordinates the 3-space corresponding to a given value
of t is Euclidean flat.]
Twin Paradox: One twin travels relativistically, one twin stays
home. They reunite. The traveling twin aged much less. The twin who
travels through more space accumulates less time; also true for an
orbit. Interval sqrt(t^2 - x^2 - y^2 - z^2) between the two events,
expressed in inertial coordinate system (t,x,y,z), is conserved.
Given the invariant interval, the larger sqrt(x^2 + y^2 + z^2)is the
smaller sqrt(t^2) must be.
The ratio by which the two aged when they are again local is identical
in all reference frames: ratio = sqrt(t^2 - x^2 - y^2 - z^2)/t (units
of c=1).
Acceleration is irrelevant, demonstrated by Triplets.
Three identical clocks as kits and not constructed until the
experiment is running. Each clock has a short toggle switch.
Individual spaceships carry a kit each. Set up the experiment.
CLOCK 1: Our clock sits stationary in our inertial reference frame
with its toggle sticking out. Touch the toggle and "off" state goes
"on" or "on" state goes "off." Build it from parts just before
needed, in the "off" state, zeroed.
CLOCK 2: In a spaceship traveling at 0.999c relative to our inertial
frame and positioned far to our left. Clock 2 was built after all
acceleration ceased during setup, set to zero, "off" state. It skims
past Clock 1 (our clock) in vacuum free fall, toggles touch, both
Clocks 1 and 2 are "on" and locally synchronized by touching. Elapsed
time accumulates in each clock.
CLOCK 3: In a spaceship traveling at 0.999c relative to our inertial
frame of reference, but 180 degrees counter in direction to Clock 2,
far far to our right. It was built after all acceleration ceased
during setup, set to zero, "off" state.
An arbitrary time after Clocks 1 and 2 synchronize and turn "on" by
touching, Clocks 2 and 3 brush past each other, both in vacuum free
fall, touching toggles. Clock 2 is now "off," Clock 3 is now "on."
Write down the elapsed time in "off" Clock 2. The spaceship with
Clock 3 returns over the path taken by the spaceship with Clock 2.
CLOCK 1: Our clock. It sits stationary in our inertial reference
frame with a little toggle sticking out. Clock 3 vacuum free falls
past, toggles touch. Clocks 3 and 1 are off. Write down elapsed
times. No clock accelerated while "on" or while existing.
BOTTOM LINE: Send results by radio. Numbers on paper don't change.
Throughout the entire run three clocks were passive observers in
vacuum free fall with zero acceleration.
Compare elapsed times. Elapsed times #2+#3 does not equal #1, the
local stationary reference frame summation. The sum of #2+#3 elapsed
time is about 4.5% that than of #1's accumulated elapsed time. The
Twin (Triplets) Paradox obtains without any clock having been
accelerated.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2
Strich.9
> Twin paradox
What is the sci.physics.relativity charter? Right here:
Notice that this group was formed with the intent to contain the
spread of correct information regarding the fallacy of relativity in
this nice small crucible. Note that in the charter it specifically
discourages cross posting in other categories, especially where the
twin paradox is concerned.
What does this mean? All posters going against relativity are subject
to four layers of defense from the establishment.
FIRST LAYER: so called academics (Tom Roberts, PD, etc), who will try
to argue with what is in the textbook. these so caled academics have
weak credentials, similar to the paid professionals you see on TV
endorsing various types of snakeoil.
SECOND LAYER: if you are smart enough to argue and stump the first
layer (which most people here are), you meet the second layer, the
hecklers (Dono, Doug, etc). obviously if you are smart enough not to
line up behind relativity, then your character must be dirtied so no
one will believe you.
THIRD LAYER: if the second layer is unsuccessful in destroying your
credibility, then the third layer, usually with non-descript names of
a fly-by-night nature, start posting inanities, irrelevancies, and
flame posts to confuse, muddle, and cover the main issue. note that
if there is a strong post against the Muon experiment for example,
then a lot of different postings in different topics will draw the
attention of any prospective reader from the relevant topic.
Why all these layers? Simple. It is hard to hide the truth...
PD
> On Jan 7, 12:05 pm, Jonathan Doolin <good4us...@gmail.com> wrote:
>
> > Twin paradox
>
> What is the sci.physics.relativity charter? Right here:
>
>
> Notice that this group was formed with the intent to contain the
> spread of correct information regarding the fallacy of relativity in
> this nice small crucible. Note that in the charter it specifically
> discourages cross posting in other categories, especially where the
> twin paradox is concerned.
>
> What does this mean? All posters going against relativity are subject
> to four layers of defense from the establishment.
Notice that the count below comes up to three. Strich9 apparently has
problems counting to four.
>
> FIRST LAYER: so called academics (Tom Roberts, PD, etc), who will try
> to argue with what is in the textbook.
This is an interesting statement. What textbook are you referring to,
and what statement in said textbook do you think I'm arguing with?
> these so caled academics have
> weak credentials, similar to the paid professionals you see on TV
> endorsing various types of snakeoil.
>
> SECOND LAYER: if you are smart enough to argue and stump the first
> layer (which most people here are), you meet the second layer, the
> hecklers (Dono, Doug, etc). obviously if you are smart enough not to
> line up behind relativity, then your character must be dirtied so no
> one will believe you.
Oh, you do a fine job of dirtying yourself without any help from
anybody.
>
> THIRD LAYER: if the second layer is unsuccessful in destroying your
> credibility, then the third layer, usually with non-descript names of
> a fly-by-night nature, start posting inanities, irrelevancies, and
> flame posts to confuse, muddle, and cover the main issue. note that
> if there is a strong post against the Muon experiment for example,
Which strong post was that? Your post wasn't at all strong, as was
pointed out. Now, you may have been under the impression that it was
strong before you actually posted it. It's nice to see that you are so
ineducable that your position on such matters is immovable.
> then a lot of different postings in different topics will draw the
> attention of any prospective reader from the relevant topic.
>
> Why all these layers? Simple. It is hard to hide the truth...
Such is the self-rationalization of the cranks.
"If I were wrong, they would say nothing. Since they take the trouble
to object to what I'm saying, this obviously means I'm right, and
they're covering up the truth."
I realize that getting ANY attention is a novelty for you and so it's
easy to misconstrue. Just recognize how desperate you appear in so
doing.
PD
Strich.9
> On Jan 7, 1:45 pm, "Strich.9" <strich.9...@gmail.com> wrote:
>
> > On Jan 7, 12:05 pm, Jonathan Doolin <good4us...@gmail.com> wrote:
>
> > > Twin paradox
>
> > What is the sci.physics.relativity charter? Right here:
> >http://groups.google.com/group/sci.answers/browse_frm/thread/e1f2e072...
>
> > Notice that this group was formed with the intent to contain the
> > spread of correct information regarding the fallacy of relativity in
> > this nice small crucible. Note that in the charter it specifically
> > discourages cross posting in other categories, especially where the
> > twin paradox is concerned.
>
> > What does this mean? All posters going against relativity are subject
> > to four layers of defense from the establishment.
>
> Notice that the count below comes up to three. Strich9 apparently has
> problems counting to four.
>
Just waiting for you to ask :-)
FOURTH LAYER. These consist of the double-agents. They pretend to be
'mainsteam' anti-relativists, and then go on to post and behave as
cranks. This discredits the anti-relativist movement in the eyes of
the public. A newbie gets an impression that all anti-relativists are
similarly crank in nature. A prominent example is Spaceman.
Androcles
"dlzc" <dl...@cox.net> wrote in message
news:8b26fb23-c9e4-422b...@d42g2000prb.googlegroups.com...
Dear Jonathan Doolin:
David A. Smith
==================================
Really? I thought it meant "Thick Prat" or possibly "Totally Psychotic".
Jonathan Doolin
> (Toxic URL! Unsafe for children and most mammals)http://www.mazepath.com/uncleal/lajos.htm#a2
Hi uncle Al. The scenario I was developing was equivalent to yours
except that you added extra mechanism. So, we could have my traveler
"B" jump from clock 2 to clock 3 as they pass each other at point C,
and then it would be the same scenario. But your contribution is
correct in that it doesn't matter how suddenly the change in reference
frames occurs. You are pointing out that an acceleration is
"irrelevant" since no physical object is required to change speed, but
in the simplest construction of the twin paradox, one of the parties
does change speed. In that case, it is the changing of velocity which
is important. (It is also the changing from the velocity of the
outbound clock to the velocity of the inbound clock teshat is
important in your construction.)
I would take issue with your statement, though, that "the object that
travels through less space ages less" In the twin paradox, both twins
measure themselves to travel through no space at all. Though one of
the twins accelerates, three times through the trip, at all other
times, he is stationary and the other twin is moving away or toward
him.
PD
Ah. So there is a conspiracy of *fake* cranks that have been planted
to make the real cranks look bad.
Strich9, you have a regular springtime blossoming in your delusion
greenhouse going on. So many vibrant colors, too!
PD
doug
By strich's own logic, he must be one of those fake cranks put in to
discredit antirelativists. He has made them look pretty stupid and
has helped to discredit them quite a bit. He let his secret out.
Also by strich's criteria that he does not belive work by people he
does not consider famous enough, we cannot believe anything strich
says since he is a nobody with no education.
Koobee Wublee
> [Snipped garbage references]
>
> In the Newtonian approximation to GR, the line element for "Newtonian
> coordinates" is to excellent approximation:
>
> ds^2 = -(1 - 2\phi) dt^2 + dx^2 + dy^2 + dz^2
> where \phi is the Newtonian gravitational potential, c=1
Since nothing can travel beyond the speed of light, c, you are wrong
with the signature. The above equation should be written as follows.
dTau^2 = c^2 (1 – 2 U) dt^2 - ds^2 ... (1)
Where
** U = G M / c^2 / r
** ds^2 = dx^2 + dy^2 + dz^2
> The only deviation from Minkowski spacetime is in the time coordinate
> - using these coordinates the 3-space corresponding to a given value
> of t is Euclidean flat.]
Yes, for (U = 0). <shrug>
> Twin Paradox: One twin travels relativistically, one twin stays
> home. They reunite. The traveling twin aged much less. The twin who
> travels through more space accumulates less time; also true for an
> orbit. Interval sqrt(t^2 - x^2 - y^2 - z^2) between the two events,
> expressed in inertial coordinate system (t,x,y,z), is conserved.
> Given the invariant interval, the larger sqrt(x^2 + y^2 + z^2)is the
> smaller sqrt(t^2) must be.
Nonsense. You have to understand what Lorentz transform means. The
more specific way of writing equation (1) with (U = 0) according to
the Lorentz transform is as follows.
c^2 dt’^2 – ds’^2 = c^2 dt^2 - ds^2 ... (2)
The observers are the primed and the unprimed frames. The observed is
observed to have a coordinate (t’, s’) according to the primed frame
and (t, s) according to the unprimed frame. The speed relative to
each these two frames is v which cancels out if all the equations of
the Lorentz transform are condensed into just one as described above.
Since the Lorentz transform is a tale of three parties with two
observers and one observed, there is a need to merge an observer and
the observed together where this observer would observe himself.
Let’s say the unprimed is the same as the observed. Then, equation
(2) simplifies into the following.
** c^2 dt’^2 – ds’^2 = c^2 dt^2
Or
** dt’^2 (1 – v^2 / c^2) = dt^2
Where
** ds^2 = 0
** (ds’/dt’)^2 = v^2
This means 1 second as observed by the unprimed is observed to be sqrt
(1 – v / c^2) seconds by the primed. Thus, the time of the unprimed
slows down relative the primed.
On the other hand, let’s say the primed is the same as the observed.
Then, equation (2) simplifies into the following.
** c^2 dt’^2 = c^2 dt^2 – ds^2
Or
** dt’^2 = dt^2 (1 – v^2 / c^2)
Where
** ds’^2 = 0
** (ds/dt)^2 = v^2
This means 1 second as observed by the primed is observed to be sqrt(1
– v / c^2) seconds by the unprimed. Thus, the time of the primed
slows down relative the unprimed.
This is the paradox. To resolve the paradox, either time dilation or
the principle of relativity has to be shown false, and there is no
other way. <shrug>
> Acceleration is irrelevant, demonstrated by Triplets. [...]
This is correct. Acceleration was suggested to resolve the paradox by
Einstein the nitwit, the plagiarist, and the liar. That suggestion is
utterly groundless. <shrug>
rotchm
> As you already mentioned, most SR books specifically DO NOT address
> the issue of when something is "observed"
True. The "observed" usually means the calculated value for the
clock "over there", and not what is "seen".
>so it would be very
> difficult to cling to the terminology of SR books while discussing
> this. The fact that you know what I am talking about means that it is
> not "out of context" and "subject to misinterpretation."
Your words are out of context in the sense that your words differ in
meaning
from SR's words.
>
> If you want to make it not subject to misinterpretation, then the best
> thing to do is not read "many many books" on SR, because how do you
> know any of them have any idea what they are talking about?
Exactly... reading many many books will enable your to figure out what
author
means what in which context.
>The best
> thing is to use the Lorentz Transformation equations to verify the
> relationships between the three events (departure, turn-around, and
> arrival) in the three reference frames (home, outbound, inbound) and
> verify the space-time coordinates of those three events.
Correct. The issue as to "when" these observations have been made is
of no concern
since "observation" implies that these concerns have already been
dealt with.
Jonathan Doolin
Well, if you noticed nothing new in my explanation then you're fine.
It's the people who don't realize that to the traveling twin Earth
would appear to "lurch" away then approach superluminally. To call
this the Doppler effect, even preceding it with "relativistic Doppler"
is waving a profoundly surprising phenomenon away as if it were
nothing.
I am not trying to add so much to the explanation, but to build on the
self-consistency.
>
> The standard textbook explanations don't explain any deep questions.
> Effectively, they just give it as exercise to show that the Lorentz
> transformations are self consistent. For me the best explanation (of why it
> physically works) was given by Langevin in 1911, well before it became a
> paradox(!).
>
I think I haven't read that particular explanation.
> And I dislike straw-men, I like to shoot them. :-)
>
Me too! When I can identify them for what they are! Usually when
people bring up the Doppler effect it is to accuse me of talking about
it, and then try to explain to me that the Doppler effect is not
sufficient to do what I am talking about, which of course, I know
already. So that is why I thought you were trying to do a straw-man.
In any case, I like to keep it simple. We really just have three
events, departure, turn-around, and arrival, and while discussion of
the Doppler effect is possible, it is not necessary.
> Cheers,
harry
OK- so you are not really trying to come up with a metaphysical model that
can explain the phenomena.
>> The standard textbook explanations don't explain any deep questions.
>> Effectively, they just give it as exercise to show that the Lorentz
>> transformations are self consistent. For me the best explanation (of
>> why it physically works) was given by Langevin in 1911, well before
>> it became a paradox(!).
>>
>
> I think I haven't read that particular explanation.
He used the illustration of two space travellers to argue that motion is
physically absolute, although the measurements are relative - basically it's
Newton's explanation with some enhancements, and he showed with the "twin"
example that SRT strengthens the evidence for Newton's concept of the
relativity principle.
>> And I dislike straw-men, I like to shoot them. :-)
>>
>
> Me too! When I can identify them for what they are! Usually when
> people bring up the Doppler effect it is to accuse me of talking about
> it, and then try to explain to me that the Doppler effect is not
> sufficient to do what I am talking about, which of course, I know
> already. So that is why I thought you were trying to do a straw-man.
> In any case, I like to keep it simple. We really just have three
> events, departure, turn-around, and arrival, and while discussion of
> the Doppler effect is possible, it is not necessary.
In real life we have as many events as we want to measure, and everything
must work out correctly. But as far as I can see, that is not a problem for
SRT.
Regards,
Harald
Androcles
"harry" <harald.NOTT...@epfl.ch> wrote in message
news:1231404...@sicinfo3.epfl.ch...
The cretin van lentil has rose tinted glasses where his precious religion is
concerned, the guy is a vegetable.
Strich.9
If Doug posted more ideas instead of mere trolling, he'd be helping
out the anti-relativisits. Too bad he has not posted any content :-)
Strich.9
Of course. But you will merely deny it. That is your main
argumentative tool these days, denial. Which is an improvement from
your previous ones of running away, hiding, or whining.
PD
Heck, no. I'm going to just let your statement stand there all by
itself, in flagrant glory.
Ooooh. Aaaaah.
Strich.9
>
> - Show quoted text -- Hide quoted text -
>
> - Show quoted text -
At least you agreed on one point. Well, you also seem to be agreeing
on the one-truth-many-interpretation principle. You're on the right
path...
PD
What point do you think I agreed with?
As I've tried to indicate to you, not attempting to stomp on a
statement that you make is not an indicator of assent.
If you claim to be Madonna, I'm certainly not going to try to prove to
you or anyone else that you are not Madonna. In fact, I'm very likely
to let your claim that you are Madonna just sit there on display, for
all to admire.
PD
Strich.9
PD uses the demented approach. You forgot again?
>
> As I've tried to indicate to you, not attempting to stomp on a
> statement that you make is not an indicator of assent.
PD uses his brand of falso logic. He pretends to ignore my
statements, but is still compelled to give a whiny reply.
>
> If you claim to be Madonna...
PD tries his hand again on false reasoning by analogy... He has a
natural predilection for reasoning by analogy... Thus his stupidity.
Jonathan Doolin
Right.
> >> The standard textbook explanations don't explain any deep questions.
> >> Effectively, they just give it as exercise to show that the Lorentz
> >> transformations are self consistent. For me the best explanation (of
> >> why it physically works) was given by Langevin in 1911, well before
> >> it became a paradox(!).
>
> > I think I haven't read that particular explanation.
>
> He used the illustration of two space travellers to argue that motion is
> physically absolute, although the measurements are relative - basically it's
> Newton's explanation with some enhancements, and he showed with the "twin"
> example that SRT strengthens the evidence for Newton's concept of the
> relativity principle.
>
It's hard for me to imagine how my explanation could lead anyone to
say Special Relativity is "Newton's concept with enhancements" but
maybe there is work Newton did that I am not aware of. In that the
Lorentz Transformations make Newton's Laws of motion (which are frame
independent) consistent with Maxwell's Laws (which are frame
dependent). Newton's laws can be fixed to become frame dependent by
applying the Lorentz Factor to the momentum. If I were to say "motion
is physically absolute" I would be concerned that people would believe
I meant that physics was frame dependent.
Then you have Newton's explanation with enhancements--an enhancement
to make it frame dependent. That is necessary but not sufficient to
have relativity (i.e. frame independence.) For that, you need to
apply the Lorentz Transformation based on the events based on the
velocity of the observer.
Realize that I am trying to put together Langevin's argument from
several easily misinterpreted phrases: "motion is physically
absolute" and "Newton's explanation with some enhancements" but it
sounds like an argument for absolute motion.
It seems like it would be easy to misinterpret--any explanation that
conludes its argument with the phrase "motion is physically absolute"
could be construed as a negation of the Special Theory of relativity
rather than an explanation for it.
Basically what I'm trying to say is... I might be wrong, but it sounds
like another strawman. Langevin wrote a book to explain Special
Relativity and concluded that motion was physically absolute. So...
FIX. What in the world could Langevin have possibly meant by "motion
is physically absolute" in an explanation FOR relativity?
> >> And I dislike straw-men, I like to shoot them. :-)
>
> > Me too! When I can identify them for what they are! Usually when
> > people bring up the Doppler effect it is to accuse me of talking about
> > it, and then try to explain to me that the Doppler effect is not
> > sufficient to do what I am talking about, which of course, I know
> > already. So that is why I thought you were trying to do a straw-man.
> > In any case, I like to keep it simple. We really just have three
> > events, departure, turn-around, and arrival, and while discussion of
> > the Doppler effect is possible, it is not necessary.
>
> In real life we have as many events as we want to measure, and everything
> must work out correctly. But as far as I can see, that is not a problem for
> SRT.
>
> Regards,
Jonathan Doolin
> "Jonathan Doolin" <good4us...@gmail.com> wrote in message
Wow, Androcles. You crushed another strawman. Right in front of me!
Good job. Hey, maybe you can call me another mean name now! That
would really hurt my feelings! Awesome! You're the MASTER!
Androcles
===================================================
I know I am.
Now, how about learning something and answering the fucking question,
or are you a straw chicken?
Your answer goes here:
________________________________________________________
Other answers have been:
According to Cretin harald.vanlin...@epfl.ch
Easy: he did NOT say that.
According to cretin van lintel, Einstein did not write the equation he
wrote.
________________________________________________________
According to the illiterate crank "Peter Webb"
<webbf...@DIESPAMDIEoptusnet.com.au>
Its two equations.
________________________________________________________
According to the novice mitch sper...@gmail.com (or mitchs perkins)
because +v / -v cancel out?
________________________________________________________
According to the Pillock Shawn Pollock (aka mathkills):
Mikelzon Morrly, whatever.
What Einstein does is basically modify Galilean relativity as follows
X'=A(X-vt)
yes you [Androcles] are an ass (presumably because I asked the question)
________________________________________________________
According to glird the tord:
Both x and x' are in the domain of the function x |-> x' such that x' =
x-vt
________________________________________________________
According to Idiot Ian Parker:
We are not talking about the speed of light here we are talking
classical stability theory.
________________________________________________________
According to xxein (not a true dingleberry):
It is an artefactual/superficially imposed yin-yang of sorts.
________________________________________________________
According to Lamenting Shubert:
Why do you want to know?
________________________________________________________
According to Imbecile Jimmy Black:
" In neither system (meaning frame of reference in modern-day terminology)
is the speed of light c-v or c+v. In both systems the speed of light is c."
According to Imbecile Jimmy Black, Einstein did not write the equation he
wrote.
________________________________________________________
According to Cretin Dork Bruere
I don't give a damn what Einstein wrote.
________________________________________________________
According to Lying Little Shit Matthew Johnson
And even the question is wrong! For he never said any such thing.
This should be painfully obvious from what he _did_ say,
namely, that the vacuum speed of light is a constant of nature,
invariant under all admissable [sic] transformations between
inertial reference frames.
Apparently LLS Matthew Johnson has rewritten Einstein's paper.
A team of scientists working under the direction of researchers from the
University of Sussex have recently discovered that Einstein did not say
"inertial".
According to LLS Matthew Johnson, Einstein did not write the equation he
wrote.
________________________________________________________
According to Chief Wanker Uncle Stooopid Schwartz:
"c+v appears nowhere in the paper, nor could it. [sic]
According to Chief Wanker Uncle Stooopid, Einstein did not write the
equation he wrote.
________________________________________________________
According to Dolt "Spirit of Truth"
that math is correct but WRONG
________________________________________________________
Note: some names may be the aliases of a crank or cranks unknown.
http://www.androcles01.pwp.blueyonder.co.uk/Smart/tAB=tBA.gif
"I know that in the past Androcles has used tAB=tBA to
claim Einstein thinks tau_AB = tau_BA (the travel
times in the frame in which the clocks at A and B are
moving)." -- Blind "I'm not a troll" Poe.
http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img21.gif
"Neither [frame] is stationary, which is your problem." -- Blind
"I'm not a troll" Poe.
Ref: news:1189468758....@r29g2000hsg.googlegroups.com
'we establish by definition that the "time" required by
light to travel from A to B doesn't equal the "time" it requires
to travel from B to A in the stationary system, obviously.' --
Heretic Jan Bielawski, assistant light-bulb changer.
Ref: news:1188363019....@k79g2000hse.googlegroups.com
(How many Polacks does it take to change a light bulb?)
"SR is GR with G=0." -- Uncle Stooopid.
The Uncle Stooopid doctrine:
http://sound.westhost.com/counterfeit.jpg
"What can be asserted without evidence can also be dismissed without
evidence." -- Uncle Stooopid.
"Counterfactual assumptions yield nonsense.
If such a thing were actually observed, reliably and reproducibly, then
relativity would immediately need a major overhaul if not a complete
replacement." -- Humpty Roberts.
Rabbi Albert Einstein in 1895 failed an examination that would
have allowed him to study for a diploma as an electrical engineer
at the Eidgenössische Technische Hochschule in Zurich
(couldn't even pass the SATs).
According to Phuckwit Duck it was geography and history that Einstein
failed on, as if Eidgenössische Technische Hochschule would give a
damn. That tells you the lengths these lying bastards will go to to
protect their tin god, but its always a laugh when they slip up.
Trolls, the lot of them.
"This is PHYSICS, not math or logic, and "proof" is completely
irrelevant." -- Humpty Roberts.
harry
That greatly simplifies the discussion - in my language you are not really
trying to explain the twin paradox. Different people mean different things
with the word "explain"!
>>>> The standard textbook explanations don't explain any deep
>>>> questions. Effectively, they just give it as exercise to show that
>>>> the Lorentz transformations are self consistent. For me the best
>>>> explanation (of why it physically works) was given by Langevin in
>>>> 1911, well before it became a paradox(!).
>>
>>> I think I haven't read that particular explanation.
>>
>> He used the illustration of two space travellers to argue that
>> motion is physically absolute, although the measurements are
>> relative - basically it's Newton's explanation with some
>> enhancements, and he showed with the "twin" example that SRT
>> strengthens the evidence for Newton's concept of the relativity
>> principle.
>
> It's hard for me to imagine how my explanation could lead anyone to
> say Special Relativity is "Newton's concept with enhancements"
No, I gave you a nutshell summary of Langevin's explanation in my own words.
In 1911, Langevin was certainly not aware of your explanation attempts!
> but maybe there is work Newton did that I am not aware of. In that the
> Lorentz Transformations make Newton's Laws of motion (which are frame
> independent) consistent with Maxwell's Laws (which are frame
> dependent). Newton's laws can be fixed to become frame dependent by
> applying the Lorentz Factor to the momentum. If I were to say "motion
> is physically absolute" I would be concerned that people would believe
> I meant that physics was frame dependent.
That is not at all what Newton meant. He gave very elaborate and interesting
definitions to remove any ambiguity, see the "Scholium" in his
"Definitions":
http://members.tripod.com/~gravitee/definitions.htm (just press "cancel").
> Then you have Newton's explanation with enhancements--an enhancement
> to make it frame dependent.
Certainly not, see the definitions. And note that I stressed that Newton
held to the relativity principle (for what Einstein called "Newtonian
coordinate systems", as these are also used for special relativity).
> That is necessary but not sufficient to
> have relativity (i.e. frame independence.) For that, you need to
> apply the Lorentz Transformation based on the events based on the
> velocity of the observer.
>
> Realize that I am trying to put together Langevin's argument from
> several easily misinterpreted phrases: "motion is physically
> absolute" and "Newton's explanation with some enhancements" but it
> sounds like an argument for absolute motion.
Indeed that was what Newton stood for, as explained rather well in his
definitions (that should keep you occupied for some time - have fun reading
it this weekend). :-).
> It seems like it would be easy to misinterpret--any explanation that
> conludes its argument with the phrase "motion is physically absolute"
> could be construed as a negation of the Special Theory of relativity
> rather than an explanation for it.
Not for anyone who knows Newton's theory and definitions. But I now checked
Langevin's paper, and I see that he avoided any possible misunderstanding
from different definitions. He simply stressedby means of his "twin" example
that *acceleration* is absolute: a change in speed has measurable physical
effects on the object that changed speed. Note that a few years later
Einstein claimed that acceleration is *relative*, which unavoidably resulted
in the "twin" or "clock" paradox.
> Basically what I'm trying to say is... I might be wrong, but it sounds
> like another strawman. Langevin wrote a book to explain Special
> Relativity and concluded that motion was physically absolute.
His paper is meant to illustrate how special relativity affected our
concepts of "space" and "time". In that paper he provides additional support
for Newton's concepts of motion which you now can read for yourself. But
note that if indeed you don't intend to explain or understand the cause of
the phenomena, this may not be interesting for you!
> So...
> FIX. What in the world could Langevin have possibly meant by "motion
> is physically absolute" in an explanation FOR relativity?
Those were my words, Langevin didn't formulate it as such but expanded on
Newton's and Maxwell's concepts. Newton explained the differences between
"true" or "absolute" motion, and a measurement of such motion. After
catching up with the basics of Newtonian mechanics, you should be able to
understand that. The same happened to me a few years ago (I thought that I
knew Newton's theory as I studied physics - but most textbooks don't really
teach it and don't tell the students!).
Oh and if by any chance you can read French, here is Langevin's paper on
"The evolution of space and time":
http://diglib.cib.unibo.it/diglib.php?inv=7&int_ptnum=10&term_ptnum=39&format=jpg
Cheers,
Harald
Jonathan Doolin
straw-man. He's creepy. He doesn't have any structure--just an
equation without any variables properly defined, and no context.
Jonathan Doolin
I meant to explain WHAT happens in the twin paradox. In so doing I
was also explaining WHY it is not really a paradox.
> "Definitions":http://members.tripod.com/~gravitee/definitions.htm(just press "cancel").
Okay, that fixes it.
> Oh and if by any chance you can read French, here is Langevin's paper on
> "The evolution of space and time":http://diglib.cib.unibo.it/diglib.php?inv=7&int_ptnum=10&term_ptnum=3...
>
> Cheers,
> Harald- Hide quoted text -
>
> - Show quoted text -- Hide quoted text -
Koobee Wublee
> On Jan 8, 12:41 pm, "harry" wrote:
> > That greatly simplifies the discussion - in my language you are not really
> > trying to explain the twin paradox. Different people mean different things
> > with the word "explain"!
>
> I meant to explain WHAT happens in the twin paradox.
You actually do not know jack-sh*t. In doing so, you do not know that
you do not know jack sh*t. <shrug>
> In so doing I
> was also explaining WHY it is not really a paradox.
No, in doing so, you resort to faith to resolve the twin’s paradox.
It is lame, stupid, and unproductive on your part. <shrug>
> > Those were my words, Langevin didn't formulate it as such but expanded on
> > Newton's and Maxwell's concepts. Newton explained the differences between
> > "true" or "absolute" motion, and a measurement of such motion. After
> > catching up with the basics of Newtonian mechanics, you should be able to
> > understand that. The same happened to me a few years ago (I thought that I
> > knew Newton's theory as I studied physics - but most textbooks don't really
> > teach it and don't tell the students!).
>
> Okay, that fixes it.
The twin’s paradox was already considered by Voigt in 1887. That is a
little more than a generation before Langevin also realized the
problem in the Lorentz transform. Unlike Voigt who immediately saw
through the nonsense in the Lorentz transform, Langevin came up with
scriptures to explain the nonsense. <shrug>
> > Oh and if by any chance you can read French, here is Langevin's paper on
> > "The evolution of space and time":
> > http://diglib.cib.unibo.it/diglib.php?inv=7&int_ptnum=10&term_ptnum=3...
My post that plugs up Uncle Al’s rectum sums it all up.
http://groups.google.com/group/sci.physics.relativity/msg/98566e34bf7c74ee?hl=en
So, run, Einstein Dingleberries. Run with your tails between your
legs.
Jonathan Doolin
Hi Kooblee. I noticed that Uncle Al gave an equation of how to
calculate a space-time interval for a particle moving along a curved
path in an inertial reference frame. It was irrelevant to the issue
at hand since all that was important was the initial and final
reference frame and the point in time and space at which the switch of
reference frame happens.
In general a switch in reference frames is caused by an observer
changing velocity. If that change in velocity happens over a period
of time, then it is called an acceleration. Uncle Al points out that
if that change in velocity happens instantaneously, the twin paradox
still works.
Uncle Al chooses to say this means that acceleration is irrelevant.
But the point remains that the change in reference frame happens at a
single point in time and space (Where Clock 2 and Clock 3 meet--the
party of interest changes from the outbound Clock 2 to the inbound
Clock 3)
Whether any material actually changes speed, the "point-of-view" does
change speed, and it is this change of speed, i.e. change of reference
frame that resolves the paradox.
It is also the nature of the Lorentz Transformation Equations that it
takes place around a fulcrum. Now, I would call the fulcrum of the
LT's an "event of acceleration" because it is the point in space-time
where the acceleration of the observer takes place. Now since the
"observer" is just the point in space from which all of the distances
are measured, it does not require the acceleration of a mass. But it
requires the change in velocity of the observer (since at one time the
observer is watching the clock on the outbound trip, and at one time
the observer is watching the clock on the return trip.)
Another reason you might say acceleration is irrelevant... Performing
the Lorentz Transformation at the beginning, middle, end of the trip
gives the same result except for an offset in time and space. Though
the Transform always takes place around a fulcrum (t,x,y,z) =
(0,0,0,0)--the origin--which remains stationary.
But a reason to say that acceleration RESOLVES the paradox is to
realize that the traveling twin applies three Lorentz Transformations
around what seem to him to be three different origins.
Neither Uncle Al, nor Einstein is a liar, but they appear to have a
different idea of the meaning of either "irrelevant" or "acceleration"
Jonathan Doolin
> On Jan 8, 7:18 pm, Jonathan Doolin wrote:
>
> > On Jan 8, 12:41 pm, "harry" wrote:
> > > That greatly simplifies the discussion - in my language you are not really
> > > trying to explain the twin paradox. Different people mean different things
> > > with the word "explain"!
>
> > I meant to explain WHAT happens in the twin paradox.
>
> You actually do not know jack-sh*t. In doing so, you do not know that
> you do not know jack sh*t. <shrug>
>
Kooblee, don't try to emulate Androcles, he is a fake crank trying to
make the real cranks look bad. For instance, instead of criticizing
me, you might actually address my explanation and attempt to find
flaws, or tell me of this jack sh*t that you have been studying.
> > In so doing I
> > was also explaining WHY it is not really a paradox.
>
> No, in doing so, you resort to faith to resolve the twin’s paradox.
> It is lame, stupid, and unproductive on your part. <shrug>
>
> > > Those were my words, Langevin didn't formulate it as such but expanded on
> > > Newton's and Maxwell's concepts. Newton explained the differences between
> > > "true" or "absolute" motion, and a measurement of such motion. After
> > > catching up with the basics of Newtonian mechanics, you should be able to
> > > understand that. The same happened to me a few years ago (I thought that I
> > > knew Newton's theory as I studied physics - but most textbooks don't really
> > > teach it and don't tell the students!).
>
> > Okay, that fixes it.
>
> The twin’s paradox was already considered by Voigt in 1887. That is a
> little more than a generation before Langevin also realized the
> problem in the Lorentz transform. Unlike Voigt who immediately saw
> through the nonsense in the Lorentz transform, Langevin came up with
> scriptures to explain the nonsense. <shrug>
>
Is Voigt the jack sh*t you are studying?
> > > Oh and if by any chance you can read French, here is Langevin's paper on
> > > "The evolution of space and time":
> > >http://diglib.cib.unibo.it/diglib.php?inv=7&int_ptnum=10&term_ptnum=3...
>
> My post that plugs up Uncle Al’s rectum sums it all up.
>
> http://groups.google.com/group/sci.physics.relativity/msg/98566e34bf7...
Matthew Lybanon
<720bed03-c7b4-437d...@r41g2000prr.googlegroups.com>,
Jonathan Doolin <good4...@gmail.com> wrote:
You can remove acceleration entirely from the twin paradox by changing
it to the triplet paradox. One triplet is on the Earth, the second is
already traveling at a constant high speed (relative to the one on the
Earth) in one direction, and the third is already traveling at the same
high speed (relative to the Earth) in the opposite direction. They just
happen to pass one another at the necessary places and times (hey, this
is a thought experiment). No acceleration involved, same conclusion.
And it is a paradox: a statement or proposition that appears to involve
a contradiction even though it is the result of sound reasoning from
acceptable premises.
Androcles
> No, Androcles. You're a meanie, and I'm not going anywhere near your
> straw-man. He's creepy. He doesn't have any structure--just an
> equation without any variables properly defined, and no context.
No, droolin' Doolin.
I own to being a meanie, droolin' Doolin, and you are a fucking gutless
straw chicken without any ability to understand where the "Lorentz"
malformations without any variables properly defined and no context
come from.
New Improved Twin Paradox Explanation = straw chicken without any variables
Androcles
On Jan 9, 2:27 am, Koobee Wublee <koobee.wub...@gmail.com> wrote:
> On Jan 8, 7:18 pm, Jonathan Doolin wrote:
>
> > On Jan 8, 12:41 pm, "harry" wrote:
> > > That greatly simplifies the discussion - in my language you are not
> > > really
> > > trying to explain the twin paradox. Different people mean different
> > > things
> > > with the word "explain"!
>
> > I meant to explain WHAT happens in the twin paradox.
>
> You actually do not know jack-sh*t. In doing so, you do not know that
> you do not know jack sh*t. <shrug>
>
Kooblee, don't try to emulate Androcles, he is a fake crank trying to
make the real cranks look bad. For instance, instead of criticizing
me, you might actually address my explanation and attempt to find
flaws, or tell me of this jack sh*t that you have been studying.
================================================
That's easy, straw chicken. The "Lorentz" malformations upon which
the TP is based was pulled out of a fucking hat, and you are a real crank
who looks and smells bad. As you correctly say, I only fake it.
Koobee the crank aetherialist is right about you not knowing jack shit.
Androcles
Yellow bellied STRAW CHICKEN!
Uncle Al
[snip]
> My post that plugs up Uncle Al’s rectum sums it all up.
>
> http://groups.google.com/group/sci.physics.relativity/msg/98566e34bf7c74ee?hl=en
Another triumph of the Federal Witless Protection program (and its
motto, "uachdar muc garadh").
http://www.hawaii.edu/suremath/SRtwinParadox.html
http://sheol.org/throopw/sr-twin-01.html
<http://physics.syr.edu/courses/modules/LIGHTCONE/twins.html>
<http://fourmilab.to/etexts/einstein/specrel/specrel.pdf>
<http://www.geocities.com/physics_world/sr/ae_1905_error.htm>
[In the Newtonian approximation to GR, the line element for "Newtonian
coordinates" is to excellent approximation:
ds^2 = -(1 - 2\phi) dt^2 + dx^2 + dy^2 + dz^2
where \phi is the Newtonian gravitational potential, c=1
The only deviation from Minkowski spacetime is in the time coordinate
- using these coordinates the 3-space corresponding to a given value
of t is Euclidean flat.]
Twin Paradox: One twin travels relativistically, one twin stays
home. They reunite. The traveling twin aged much less. The twin who
travels through more space accumulates less time; also true for an
orbit. Interval sqrt(t^2 - x^2 - y^2 - z^2) between the two events,
expressed in inertial coordinate system (t,x,y,z), is conserved.
Given the invariant interval, the larger sqrt(x^2 + y^2 + z^2)is the
smaller sqrt(t^2) must be.
The ratio by which the two aged when they are again local is identical
in all reference frames: ratio = sqrt(t^2 - x^2 - y^2 - z^2)/t (units
of c=1).
Acceleration is irrelevant, demonstrated by Triplets.
Three identical clocks as kits and not constructed until the
experiment is running. Each clock has a short toggle switch.
Individual spaceships carry a kit each. Set up the experiment.
CLOCK 1: Our clock sits stationary in our inertial reference frame
with its toggle sticking out. Touch the toggle and "off" state goes
"on" or "on" state goes "off." Build it from parts just before
needed, in the "off" state, zeroed.
CLOCK 2: In a spaceship traveling at 0.999c relative to our inertial
frame and positioned far to our left. Clock 2 was built after all
acceleration ceased during setup, set to zero, "off" state. It skims
past Clock 1 (our clock) in vacuum free fall, toggles touch, both
Clocks 1 and 2 are "on" and locally synchronized by touching. Elapsed
time accumulates in each clock.
CLOCK 3: In a spaceship traveling at 0.999c relative to our inertial
frame of reference, but 180 degrees counter in direction to Clock 2,
far far to our right. It was built after all acceleration ceased
during setup, set to zero, "off" state.
An arbitrary time after Clocks 1 and 2 synchronize and turn "on" by
touching, Clocks 2 and 3 brush past each other, both in vacuum free
fall, touching toggles. Clock 2 is now "off," Clock 3 is now "on."
Write down the elapsed time in "off" Clock 2. The spaceship with
Clock 3 returns over the path taken by the spaceship with Clock 2.
CLOCK 1: Our clock. It sits stationary in our inertial reference
frame with a little toggle sticking out. Clock 3 vacuum free falls
past, toggles touch. Clocks 3 and 1 are off. Write down elapsed
times. No clock accelerated while "on" or while existing.
BOTTOM LINE: Send results by radio. Numbers on paper don't change.
Throughout the entire run three clocks were passive observers in
vacuum free fall with zero acceleration.
Compare elapsed times. Elapsed times #2+#3 does not equal #1, the
local stationary reference frame summation. The sum of #2+#3 elapsed
time is about 4.5% that than of #1's accumulated elapsed time. The
Twin (Triplets) Paradox obtains without any clock having been
accelerated.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2
Strich.9
>
> Cheers,
> Harald- Hide quoted text -
>
>
> - Show quoted text -
Here is the simple twin paradox question:
Stay at home twin has:
1) relative velocity
2) gamma
3) time dilation
And what happened to #3? Exempt. Exempt from the laws of physics.
That is the answer to the twin paradox. One twin is exempted from the
laws of physics. [Or simply, the laws of physics referring to time
dilation are just false]
Strich.9
> "Lorentz" malformations without any variables properly defined and no context
> come from.
Androcles, you should be a poet. I like your choice of words...
Strich.9
> Koobee Wublee wrote:
>
> [snip]
>
> > My post that plugs up Uncle Al’s rectum sums it all up.
>
>
Must be a SUBSTANTIAL post
Jonathan Doolin
>
> - Show quoted text -
Oh! I'm crying. Seriously. You've hurt my feelings. You're really
good at this Androcles. I just can't compete!
Koobee Wublee
> Koobee Wublee wrote:
> > My post that plugs up Uncle Al’s rectum sums it all up.
>
> >http://groups.google.com/group/sci.physics.relativity/msg/98566e34bf7...
>
> Another triumph of the Federal Witless Protection program (and its
> motto, "uachdar muc garadh").
>
> [Toxic waste cleansed]
Uncle Al’s droppings appear to be extraordinarily toxic. It seems not
to be able to be contained by any scholarly reasoning. <shrug>
Koobee Wublee
> On Jan 7, 8:05 pm, Koobee Wublee wrote:
> > Since nothing can travel beyond the speed of light, c, you are wrong
> > with the signature. The above equation should be written as follows.
>
> > dTau^2 = c^2 (1 – 2 U) dt^2 - ds^2 ... (1)
>
> > Where
>
> > ** U = G M / c^2 / r
> > ** ds^2 = dx^2 + dy^2 + dz^2
>
> > Acceleration was suggested to resolve the paradox by
> > Einstein the nitwit, the plagiarist, and the liar. That suggestion is
> > utterly groundless. <shrug>
>
> Hi Kooblee. I noticed that Uncle Al gave an equation of how to
> calculate a space-time interval for a particle moving along a curved
> path in an inertial reference frame. It was irrelevant to the issue
> at hand since all that was important was the initial and final
> reference frame and the point in time and space at which the switch of
> reference frame happens.
It does not matter what equations Uncle Al try to pull out of his
*ss. He has to understand what the Lorenz transform really mean and
how to properly apply them. Relative simultaneity is a property of
the Lorentz transform. It comes about through the very combination of
the principle of relativity and time dilation. To resolve the twin’s
paradox, you must either show the invalidity in the principle of
relativity or time dilation. Either way, it would prove the Lorentz
transform garbage. <shrug>
> [...]
>
> Uncle Al chooses to say this means that acceleration is irrelevant.
> But the point remains that the change in reference frame happens at a
> single point in time and space (Where Clock 2 and Clock 3 meet--the
> party of interest changes from the outbound Clock 2 to the inbound
> Clock 3)
As equation (2) in my last post is derived from the Lorentz transform,
there is no justification to support acceleration breaking the
symmetry also known as the principle of relativity.
The irrelevance of acceleration in the problem of the twin’s paradox
can be justified through the though experiment where both twins
** Start out at rest,
** Travel away with identical acceleration profile,
** Coast away with no acceleration, and
** Return back at rest with same acceleration profile.
Since both experience the same acceleration profile, acceleration
cannot be hand-waved to resolve the paradox as suggested by Einstein
the nitwit, the plagiarist, and the liar. Since there is a period
where both coast away with no acceleration, according to the Lorentz
transform, the time dilation build-up must not be ignored. Thus, the
twin’s paradox still haunts the Lorentz transform. That means special
relativity and LET where both are mere different interpretations to
the same nonsense called the Lorentz transform. <shrug>
Jonathan Doolin
> In article
> <720bed03-c7b4-437d-a61b-c064f8173...@r41g2000prr.googlegroups.com>,
Hey, cool. Uncle Al was just telling me that. And then Kooblee
started arguing with Uncle Al, and agreeing that acceleration wasn't
important, but then I said, actually acceleration is important, but
then you came in and said, no acceleration isn't important.
To clarify, both the twin paradox and the triplet paradox have three
events, and three reference frames. The important thing to each is
the relationship (both in space and time) between those three events
within those three reference frames. The three events in the two
versions can share the exact same coordinates, especially if the twin
is hitch-hiking with the triplets.
> And it is a paradox: a statement or proposition that appears to involve
> a contradiction even though it is the result of sound reasoning from
> acceptable premises.- Hide quoted text -
>
> - Show quoted text -
But, yes, under your definition, the Twin Paradox appears to be a
contradiction but is not, so is a paradox.
(I had another definition of paradox floating around in my head which
was a statement or proposition that actually WAS a contradiction
though it sounded like a simple statement. For instance "This
statement is false," is a very simple paradox.)
Strich.9
>
> - Show quoted text -
JD, you suck up to AL-zheimer so much, all you can see are his
innards.
eric gisse
You have never once offered a scholarly reference.
Androcles
On Jan 9, 9:32 am, "Androcles" <Headmas...@Hogwarts.physics> wrote:
> "Jonathan Doolin" <good4us...@gmail.com> wrote in message
>
> Yellow bellied STRAW CHICKEN!- Hide quoted text -
>
> - Show quoted text -
Oh! I'm crying. Seriously. You've hurt my feelings. You're really
good at this Androcles. I just can't compete!
===================================
So you put up a straw chicken, set about explaining it, and now
you think it is a competition at which you are unsuccessful?
Why don't you do something useful like explaining to everyone
which hat the "Lorentz" malformations were pulled from...
or better yet, simply fuck off like a good little moron?
Jonathan Doolin
> "Jonathan Doolin" <good4us...@gmail.com> wrote in message
>
> news:96c6b0a8-b26d-4576...@d42g2000prb.googlegroups.com...
> On Jan 9, 9:32 am, "Androcles" <Headmas...@Hogwarts.physics> wrote:
>
> > "Jonathan Doolin" <good4us...@gmail.com> wrote in message
> > I meant to explain WHAT happens in the twin paradox.
>
> > Yellow bellied STRAW CHICKEN!- Hide quoted text -
>
> > - Show quoted text -
>
> Oh! I'm crying. Seriously. You've hurt my feelings. You're really
> good at this Androcles. I just can't compete!
>
> ===================================
> So you put up a straw chicken, set about explaining it, and now
> you think it is a competition at which you are unsuccessful?
>
> Why don't you do something useful like explaining to everyone
> which hat the "Lorentz" malformations were pulled from...
> or better yet, simply fuck off like a good little moron?
No, Androcles. There's nothing in that argument I can defend at all!
You are the master at building strawmen. There is no way I can
compete with you. I don't know what a straw chicken is! I don't know
what a Lorentz malformation is!
It's like you've created a whole universe of strawmen who exist only
so that you can throw them into the firy furnace of hell while you
laugh gleefully. No, Androcles. How could I match this limitless
power? You are not bound by politeness, not bound by truth, not bound
by any comprehensible theory, not bound by evidence, and not bound by
the scientific method. You are drunk on this power of creating straw-
men from nothing, and I cannot stop you.
Sometimes, I have no idea what you're talking about at all, yet I'm
sure all those poor straw men you've created are doomed to eternal
damnation... and that too, makes me sad. How could a creator be so
cruel to his creations? I feel bad for not being able to defend them,
but they really don't deserve to be saved.
Androcles
On Jan 9, 3:59 pm, "Androcles" <Headmas...@Hogwarts.physics> wrote:
> "Jonathan Doolin" <good4us...@gmail.com> wrote in message
>
> news:96c6b0a8-b26d-4576...@d42g2000prb.googlegroups.com...
> On Jan 9, 9:32 am, "Androcles" <Headmas...@Hogwarts.physics> wrote:
>
> > "Jonathan Doolin" <good4us...@gmail.com> wrote in message
> > I meant to explain WHAT happens in the twin paradox.
>
> > Yellow bellied STRAW CHICKEN!- Hide quoted text -
>
> > - Show quoted text -
>
> Oh! I'm crying. Seriously. You've hurt my feelings. You're really
> good at this Androcles. I just can't compete!
>
> ===================================
> So you put up a straw chicken, set about explaining it, and now
> you think it is a competition at which you are unsuccessful?
>
> Why don't you do something useful like explaining to everyone
> which hat the "Lorentz" malformations were pulled from...
> or better yet, simply fuck off like a good little moron?
No, Androcles. There's nothing in that argument I can defend at all!
You are the master at building strawmen.
===============================================
Do you even know what a "strawman" is, dork?
You set one up with the TP so that you could knock it down.
Einstein set one up with his so called "Lorentz Transformations",
droolin' Doolin.
-------------------------------------------------------------------------------------
There is no way I can
compete with you. I don't know what a straw chicken is! I don't know
what a Lorentz malformation is!
------------------------------------------------------------------------------------
Big surprise... but then, you don't know anything as Wubbly Jubbly
pointed out. Jack shit, he said.
-------------------------------------------------------------------------------------
It's like you've created a whole universe of strawmen who exist only
so that you can throw them into the firy furnace of hell while you
laugh gleefully. No, Androcles. How could I match this limitless
power? You are not bound by politeness, not bound by truth, not bound
by any comprehensible theory, not bound by evidence, and not bound by
the scientific method.
================================================
But you are wrong, droolin' Doolin. I AM bound by evidence and the
scientific method. It is you that ignore the evidence.
Politeness? Truth? Theory? No, they are not science, I'm not bound
by those.
==================================================
You are drunk on this power of creating straw-
men from nothing, and I cannot stop you.
=====================================
What strawman have I created, you lying little shit?
It's your straw "Lorentz Transform" and your straw new improved TP
you want to explain, you straw fuckwit.
Sometimes, I have no idea what you're talking about at all,
==========================================
Of course.. you are totally thick.
yet I'm
sure all those poor straw men you've created are doomed to eternal
damnation... and that too, makes me sad.
============================================
You poor sick psychotic bastard. Name one strawman I've set up,
you lying pile of shit.
How could a creator be so
cruel to his creations? I feel bad for not being able to defend them,
but they really don't deserve to be saved.
===============================================
What "creator", cretin?
Koobee Wublee
> Koobee Wublee wrote:
> >Uncle Al’s droppings appear to be extraordinarily toxic. It seems not
> >to be able to be contained by any scholarly reasoning. <shrug>
>
> You have never once offered a scholarly reference.
The college drop is having a fit again today. <shrug>
In the meantime, what are the differences between claiming to have a
resolution to the twin’s paradox and a perpetual motion machine?
None!
<shrug>
Jonathan Doolin
>
> There is no way I can
> compete with you. I don't know what a straw chicken is! I don't know
> what a Lorentz malformation is!
> Big surprise... but then, you don't know anything as Wubbly Jubbly
> pointed out. Jack shit, he said.
>
> - Show quoted text -
All hail Androcles. The creator God of the Straw-People! Watch out
straw-men. For Androcles is an angry God.
One question though, Androcles, did you create straw-people in your
own image?
Jonathan Doolin
> But you are wrong, droolin' Doolin. I AM bound by evidence and the
> scientific method. It is you that ignore the evidence.
> Politeness? Truth? Theory? No, they are not science, I'm not bound
> by those.
> ==================================================
>
You see, most of us here ARE bound by a concept that truth IS part of
science. This is what distinguishes you as a fake crank from the real
cranks.
eric gisse
<koobee...@gmail.com> wrote:
>On Jan 9, 12:05 pm, eric gisse wrote:
>> Koobee Wublee wrote:
>
>> >Uncle Al’s droppings appear to be extraordinarily toxic. It seems not
>> >to be able to be contained by any scholarly reasoning. <shrug>
>>
>> You have never once offered a scholarly reference.
>
>The college drop is having a fit again today. <shrug>
I'm not a dropout, moron.
Every few months you start lying about something new and
uninteresting. Says a lot about your character that you are so
pathetic that you have to lie about my education almost every time you
respond to me.
>
>In the meantime, what are the differences between claiming to have a
>resolution to the twin’s paradox and a perpetual motion machine?
>
>None!
>
><shrug>
>
What's the difference between you and a crank? None.
No literature references, no coherent arguments. Just insults and
repeated assertions.
Cue followup with insults and repeated assertions.
Jonathan Doolin
> "Jonathan Doolin" <good4us...@gmail.com> wrote in message
>
>
> > Good morning.
>
> > Some time ago I made a rather stuttering attempt at this explanation
> > on YouTube, (math free version)
>
> >http://www.youtube.com/watch?v=nmAVkj9fTnU
> >http://www.youtube.com/watch?v=76BB-qZXEho
> >http://www.youtube.com/watch?v=eT-3R8ju9V0
>
> > but I did not feel like doing the mathematics at that time.
>
> > This morning, I'd like to try to put a FEW equations down. Don't
> > expect here any profound discovery. Typically an explanation has a
> > quality in inverse proportion of the explainer's pride. I'm pretty
> > proud of this explanation, so that's probably not a good sign. :)
>
> First off all, what did you set out to explain? There are different versions
> of the Twin / Clock paradox. For example, the popular textbook version
> merely explains how special relativity works while the original one
> concerned general relativity.
>
>
>
>
>
> > what little bit of the math that I know how to do. I apologize in
> > advance for the math and grammatical errors you'll probably find.
>
> > In any case, let us consider two parties, A and B, A stays at home,
> > while B moves away into the distance to point C, 1 "light" unit away
> > and then returns home.
>
> > The speed of light in this model is 1 and the distance is 1 and the
> > velocity which B chooses to travel is v. (where, of course, v=1
> > represents the speed of light)
>
> > ----------------
> > Part 1, What do things look like from the Home Twin, A?
>
> > So A watches B travel toward point C at velocity v. How long does
> > this take? B arrives at C at time t = distance/velocity = 1/v.
> > However when B arrives at C, there will be a time delay before A sees
> > the event of arrival because of the time the light takes to return
> > from that point. So A observes B's arrival at C at time t = 1+1/v
>
> > An interesting thing to consider here is that the observed velocity is
> > explicitly calculable from the two observed events (departure
> > observation and arrival observation). A will have observed B's
> > journey at a constant speed. Observed Velocity of Outward trip =
> > distance/time = 1/(1+1/v) = v/(1+v)
>
> > A similar consideration of the inbound trip yields an Observed Time of
> > the inbound trip of (1/v)-1, and observed velocity v/(1-v)
>
> > Thus if v=.5, then the observed velocity outbound =.5/1.5 = .3333c,
> > and the obseved velocity inbound = .5/.5 = 1c.
>
> > If v=.9 then the observed velocity outbound = .9/1.9 = 0.47c and the
> > observed velocity inbound = .9/.1 = 9c.
>
> > So the maximum observable outbound velocity is .5c but there is NO
> > maximum observable inbound velocity.
>
> > ---------
> > Part 2. What do things look like from the perspective of the
> > traveling twin, B?
>
> >http://www.youtube.com/watch?v=eT-3R8ju9V0
>
> > From B's perspective there must be some things which are the same, and
> > some things that are different. If all of the same physics apply,
> > then we must assume that the same chemical, nuclear, or matter/anti-
> > matter reactions that produced the velocity v (Between A and B) for
> > observer A must also have produced the same velocity v (Between A and
> > B) for observer B.
>
> > The real velocities are the same. If the real velocities are the same
> > then should the observed outbound velocity v/(1+v) and observed
> > inbound velocity v/(1-v) be the same? Yes, these calculations are
> > general. The observed inbound and observed outbound velocities are
> > based ONLY on the actual velocity, and nothing else. Though I did the
> > calculation based on a specific pair of events, departure and arrival
> > of observer B, any two events could be used, and they cancel out of
> > the final calculation.)
>
> > A thing that will be different for the two observers, though is the
> > apparent time that it takes B to travel from A to C and back. Whereas
> > A observed the return trip to happen much faster than outbound trip, B
> > will observe the outbound trip and inbound trip to take the same
> > amount of time. (Other famous gedanken experiments determine that
> > this time would be (1/v)*(1/sqrt(1-v^2)) whereas 1/v would be the
> > expected time it takes to travel distance 1, and the other factor is
> > the time dilation factor)
>
> > The Observed velocities are the same, but the amount of time traveled
> > at those velocities is different. This means that the observed
> > distance traveled by B is different for B than it is for A.
> > (Technically, B remains stationary relative to observer B, just to be
> > troublesome.)
>
> > But the greatest point of interest is what happens to the Observed
> > distance to A from the perspective of B during the turn-around. The
> > apparent relative velocity of A on the way out was v/(1+v). The
> > apparent relative velocity of A on the way in will be v/(1-v).
>
> > If the time is the same, but the apparent velocity is different, then
> > there is only one possibility. The distance CHANGED. You cannot move
> > away from an object at one apparent velocity and then return at a
> > faster apparent velocity for the same period of time unless that
> > object has moved away from you.
>
> > In effect, the traveling twin at his point of turning-around is
> > transitioning himself into a new reference frame where his home-world
> > is much further away than it was before. Also as his home goes from
> > slow-motion [v/(1+v)< .5] to fast forward [v/(1-v) = unlimited.] For
> > the moving twin it may be a surprise that the earth lurches away from
> > him at the point of turnaround, but he will be able to watch the rise
> > and fall of civilizations in fast-forward on his return trip. It
> > won't be a surprise to him when he gets home and everyone he knew is
> > dead unless he has no windows on his space-ship.
>
> Sorry I didn't check the math and only quickly skipped over your story (itat
> first glance you tried to account for the Doppler effect without mentioning
> it and without distinguishing between that and time dilation); but I
> expected to see an attempt to explain something. I saw you give some
> descriptions of observations, including a rather unphysical ("surprise")
> lurching away of the earth, but what did you set out to explain?
>
> Regards,
>
> - Show quoted text -
Okay, I did a little more math and wanted to justify the "surprise"
lurching away of the earth. Let us specify more clearly what we mean
by physical or unphysical. You distinguish "observed" from "observed
the image of" This is an important distinction, because the location
of distant objects are not where the image is observed, because of the
light delay.
However, what is physical, and what is unphysical? Is "physical" the
object which is approaching you but has not reached you, nor has it's
light reached you, or is "physical" the image of the object which is
currently interacting with you by penetrating your eye and registering
in your brain? In any case, whatever your definition of which is
physical, what the eye would see is the earth lurching away,
unsettlingly into the distance.
Let's take our twin going out 1 light year, and returning 1 light year
at a velocity of .999c.
We will take the location of the turn-around event at (t,x) = (0,0) in
all three reference frames.
(That makes the earth located at -1 in its own reference frame)
So the events, according to Earth are:
(where g is 1/sqrt(1-v^2) and v is in light-years/year.)
The take-off: (t,x) = (-1/v,-1) = (-1.001, -1) (at the earth, about 1
year before the meeting point, 1 light year from the meeting point)
The turnaround (t,x) = (0,0)
The landing: (t,x)=(+1/v,1)=(1.001,-1) (at the earth, about 1 year
after the meeting point, 1 light year from the meeting point)
The events in the outbound frame are
The take-off:(t,x) = (g(-1/v+v)),0) = (-.0448,0) = 16 days ago, at the
location of the outbound twin.
The turn-around:(t,x) = (0,0) = at the meeting point, or accleration
point of the traveling twin
The landing: (t,x)=(g(-1/v+v),-44.777) = (44.733,-44.777) = 44.733
years after meeting, 44.777 light years behind the outbound triplet.
The events in the inbound frame are
The take-off:(t,x) = (-44.733,-44.777)= 44.733 years before meeting,
44.777 light years in front of the inbound triplet.
the meeting: (t,x) = (0,0) = at the meeting point, the location of the
traveling twin, the inbound triplet, and the outbound triplet
the landing: (t,x)= (g(1/v-v), 0) = (.0448,0) = 16 days after meeting,
at the location of the traveling twin, and the inbound triplet, and
the earth.
Phew!
So the point is that as the twin travels out with the outbound
triplet, the event of his take-off actually is located where he is.
(Outbound frame; take-off event, x=0, see above) The take-off
happened, and the earth began to move away from him. But the event of
the take-off remains mapped at his location.
But After his acceleration, and he is traveling with the inbound
triplet, he's changed to the reference frame of the inbound triplet,
and the event of his take-off lies behind the oncoming earth. That
event now lies not just 1 light year away, like one might expect, but
instead almost 45 light years away. Along with the event that has
lurched away, so has the image of the earth moved almost 45 light
years away, and it will appear to move superluminally toward him over
those 45 light years in the following 16 days until he lands.
Thank you for the comments that inspired me to overcome my laziness
and work this problem out. And actually, that triplet concept is very
helpful to describe the take-off from the inbound reference frame, and
the landing from the out-bound reference frame. The triplets give
actual observers at the origins, for those events. But realizing that
the triplet observers would have to be set up 90 years before and
after the events to actually observe them! (Of course if I had chosen
light-seconds, instead of light years, it would only be 90 seconds.)
Koobee Wublee
> Koobee Wublee wrote:
> >The college drop is having a fit again today. <shrug>
>
> I'm not a dropout, moron.
As usual, when I have pointed out exactly what you are, you always
come back with insults. <shrug>
> Every few months you start lying about something new and
> uninteresting. Says a lot about your character that you are so
> pathetic that you have to lie about my education almost every time you
> respond to me.
As I have identified, you are throwing one of your fits today as
usual. <shrug>
> >In the meantime, what are the differences between claiming to have a
> >resolution to the twin’s paradox and a perpetual motion machine?
>
> >None!
So, no argument from a college dropout and the rest of Einstein
Dingleberries. <shrug>
It is time to wake up to associate stupid claims of resolution of the
twin’s paradox with proposals of perpetual motion machines.
Ahahaha...
> What's the difference between you and a crank? None.
Is that supposed to be a joke?
> No literature references, no coherent arguments. Just insults and
> repeated assertions.
Still whining about the toxic sh*t you have inhaled. Ahahaha...
> Cue followup with insults and repeated assertions.
<shrug>
Sam Wormley
>
> In the meantime, what are the differences between claiming to have a
> resolution to the twin’s paradox and a perpetual motion machine?
>
> None!
>
The "The Twin Paradox" is not a paradox at all.
Physics FAQ: The Twin Paradox
http://hermes.physics.adelaide.edu.au/~dkoks/Faq/Relativity/SR/TwinParadox/twin_paradox.html
And "perpetual motion machine"--The term perpetual motion,
taken literally, refers to movement that goes on forever.
However, the term more generally refers to any closed system
that produces more energy than it consumes.
Suggest Koobee do a bit of self education concerning the laws
of thermodynamics and the Law of conservation of Energy.
Perhaps, then Koobee, might start to see that the "The Twin Paradox"
and "perpetual motion machines" have little to do with each other.
Androcles
=================================================
Do you still beat your mother, you poor sick psychotic bastard?
Androcles
This pencil is broken, I can see it is, but you will ignore the evidence:
http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/optpic/brokpen.jpg
The truth is: the evidence shows the pencil is broken.
Define "truth", real crank.
If you were anything of a scientist, real crank, you would not be setting
up new improved straw chickens to theoretically explain.
New improved Algol explanation:
http://www.androcles01.pwp.blueyonder.co.uk/Algol/Algol.htm
New improved Mira explanation:
http://www.androcles01.pwp.blueyonder.co.uk/Orbit/Orbit.htm
I work with real data, not Einstein's snivelling drivel, real crank.
Go on, wanker, put up another straw chicken to explain and tell
us how new and improved it is.
Koobee Wublee
> Koobee Wublee wrote:
> > In the meantime, what are the differences between claiming to have a
> > resolution to the twin’s paradox and a perpetual motion machine?
>
> > None!
> >
>
> The "The Twin Paradox" is not a paradox at all.
The statement is utterly ridiculous. It reflects the author’s
ignorance in understanding the Lorentz transform. The paradox is
created when the following are present in a mathematical model.
** Principle of Relativity
** Time dilation
> Physics FAQ: The Twin Paradox
>
> http://hermes.physics.adelaide.edu.au/~dkoks/Faq/Relativity/SR/TwinPa...
Another nitwit trying to sell his perpetual motion machine. <shrug>
> And "perpetual motion machine"--The term perpetual motion,
> taken literally, refers to movement that goes on forever.
> However, the term more generally refers to any closed system
> that produces more energy than it consumes.
That is almost correct. <shrug>
> Suggest Koobee do a bit of self education concerning the laws
> of thermodynamics and the Law of conservation of Energy.
Done!
> Perhaps, then Koobee, might start to see that the "The Twin Paradox"
> and "perpetual motion machines" have little to do with each other.
Koobee Wublee sees still the claims to the resolution of the twin’s
paradox and building perpetual motion machines as utter nonsense.
Both are inborn on arrival. <shrug>
jem
The differential aging in SR's Twin Paradox is not attributable to a
difference in the twin's accelerations, simply because the twin's can
undergo identical accelerations and reunite at different ages or
undergo different accelerations and reunite at the same age.
Jonathan Doolin
> "Jonathan Doolin" <good4us...@gmail.com> wrote in message
>
> news:db74de85-cb16-4114...@f40g2000pri.googlegroups.com...
>
> > On Jan 9, 6:19 pm, "Androcles" <Headmas...@Hogwarts.physics> wrote:
> >> ================================================
> >> But you are wrong, droolin' Doolin. I AM bound by evidence and the
> >> scientific method. It is you that ignore the evidence.
> >> Politeness? Truth? Theory? No, they are not science, I'm not bound
> >> by those.
> >> ==================================================
>
> > You see, most of us here ARE bound by a concept that truth IS part of
> > science. This is what distinguishes you as a fake crank from the real
> > cranks.
>
> This pencil is broken, I can see it is, but you will ignore the evidence:
> http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/optpic/brokpen.jpg
> The truth is: the evidence shows the pencil is broken.
> Define "truth", real crank.
>
For one, the pursuit of truth does not begin with a claim that an
unbroken pencil is broken. However, you do make a valid point
elsewhere that there are such things as optical illusions. In the
case of the pencil in the glass of water, of course. There are
different ways of describing the "truth." One is to develop equations
that successfully predict the position of the image, based on the
refractive index of air, water, and glass. Another would be to note
that the speed that electromagnetic waves is slowed down in the
substances.
http://en.wikipedia.org/wiki/Refractive_index
Still another would be to consider how each individual water molecule
and glass crystal respond to the electromagnetic fields passing
through... Whether each photon/molecule interaction counts as an event
and how momenta are exchanged in the process. As far as I know, this
level of "truth" has never been attempted.
On the other hand, the claim that "the pencil broke" is false
regarless of what level of "truth" you are seeking. (Unless the
person taking the photo deliberately broke the pencil, then tried to
make it look as though it were entirely a trick of diffraction... A
trick surely not above you.)
> If you were anything of a scientist, real crank, you would not be setting
> up new improved straw chickens to theoretically explain.
>
> New improved Algol explanation:
> http://www.androcles01.pwp.blueyonder.co.uk/Algol/Algol.htm
> New improved Mira explanation:
> http://www.androcles01.pwp.blueyonder.co.uk/Orbit/Orbit.htm
First of all, you present two cases for the speed of light being added
to the speed of the source. I want to credit you, now with at least a
self-consistent model. When you are arguing FOR something, it is not
a strawman. It is when you define other people's arguments
incorrectly that you are building a strawman.
However, the most immediately obvious question from your model is why
does it produce blurring in the Mira example, and no blurring in the
Algol example? According to your explanation, we see the image of
Mira approaching and receding at the same time, but also according to
your explanation, we see the image of Algol receding, then
approaching.
Secondly, if your explanation for blurring in Mira is accurate then
why don't we see it everywhere? There are a lot of binary systems
lying very far away. Certainly far enough away that the faster light
should overtake the slower light. If your explanation were true, then
we should see this phenomenon in EVERY binary system--not just in
Mira.
On the other hand, your Goodricke strawman was very good. The part
where you say "Here is what Goodricke imagined" and then present the
stupidest possible configuration of the three star system, and
gradually work your way down to what appears to be a fairly accurate
representation. If you want to make Goodricke cry, maybe you should
call him a lot of mean names while you misrepresent his explanation.
I tell you, it works on me.
>
> I work with real data, not Einstein's snivelling drivel, real crank.
> Go on, wanker, put up another straw chicken to explain and tell
> us how new and improved it is.
Oh no, now you've called me a wanker! I'm crying. My feelings hurt.
I'm SO sad.
Androcles
http://en.wikipedia.org/wiki/Refractive_index
=============================================
For a third, that would require a real pencil and a real glass of real
water.
Not too difficult, I can manage that.
Where are your real twins, one staying home and one going on a real
journey?
Oh wait, you have straw twins and straw clocks - presumably you wish
to explain straw truth.
==============================================
On the other hand, the claim that "the pencil broke" is false
regarless of what level of "truth" you are seeking. (Unless the
person taking the photo deliberately broke the pencil, then tried to
make it look as though it were entirely a trick of diffraction... A
trick surely not above you.)
==============================================
I do not neet to fake real data, droolin' Doolin. That's for you with
your new improved straw data and new improved straw truth.
> If you were anything of a scientist, real crank, you would not be setting
> up new improved straw chickens to theoretically explain.
>
> New improved Algol explanation:
> http://www.androcles01.pwp.blueyonder.co.uk/Algol/Algol.htm
> New improved Mira explanation:
> http://www.androcles01.pwp.blueyonder.co.uk/Orbit/Orbit.htm
First of all, you present two cases for the speed of light being added
to the speed of the source. I want to credit you, now with at least a
self-consistent model. When you are arguing FOR something, it is not
a strawman. It is when you define other people's arguments
incorrectly that you are building a strawman.
===============================================
Second of all your new improved explanation of a straw chicken doesn't
include where the equation without any variables properly defined and
no context comes from. I refer, of course, to the so-called "Lorentz"
malformations Einstein created and upon which your straw chicken
relies. I want to discredit you with an entirely inconsistent straw chicken.
===============================================
However, the most immediately obvious question from your model is why
does it produce blurring in the Mira example, and no blurring in the
Algol example?
=================================================
Algol IS blurred. Why do you assume it isn't? The next generation of
super telescopes hasn't been built yet or you'd see it plainly.
EVERY star appears as a point without sufficient magnification (Sol
excepted because of its proximity). That include Proxima Centauri,
a mere four light years distant. Mira is both huge and 400 light years
distant.
==============================================
According to your explanation, we see the image of
Mira approaching and receding at the same time,
==============================================
Not so. We see the predicted multiple image only as the star approaches
and turns the corner. That's the image that everyone said we NEVER see,
BTW. But before Hubble (and without it) Mira is a point of light,
unresolved.
==============================================
but also according to
your explanation, we see the image of Algol receding, then
approaching.
================================================
Not so. We see the predicted multiple image only as the star approaches
and turns the corner. The prediction as made in 1987, BTW.
================================================
Secondly, if your explanation for blurring in Mira is accurate then
why don't we see it everywhere?
================================================
Your telescope isn't powerful enough. CCD arrays have improved
tremendously since Hubble was launched in 1990, 19 years ago, and
nowadays have multi-megapixel arrays.
================================================
There are a lot of binary systems
lying very far away.
===========================================
Not as many as you believe. Most binaries have long periods like
Sirius, 50 years, and is only 8 light year away.
There are no binaries with a period of mere days, they'd break up from
tidal effects. See Roche.
===========================================
Certainly far enough away that the faster light
should overtake the slower light.
===========================================
It does. Do the arithmetic as I have.
http://www.androcles01.pwp.blueyonder.co.uk/Copernicus/LCV.htm
Real data:
http://www.androcles01.pwp.blueyonder.co.uk/Copernicus/image021.jpg
============================================
If your explanation were true, then
we should see this phenomenon in EVERY binary system--not just in
Mira.
============================================
If your explanation of refractive index were true, then EVERY pencil
should appear broken. - Does that ring true? Of course it does for as
long as you have your head up your arse.
============================================
On the other hand, your Goodricke strawman was very good. The part
where you say "Here is what Goodricke imagined" and then present the
stupidest possible configuration of the three star system, and
gradually work your way down to what appears to be a fairly accurate
representation. If you want to make Goodricke cry, maybe you should
call him a lot of mean names while you misrepresent his explanation.
I tell you, it works on me.
============================================
Sagnac would him cry. Sagnac's strawman is now in use every day.
http://material-handling.globalspec.com/Industrial-Directory/ring-laser_gyroscope_(RLG)
How it works:
http://www.androcles01.pwp.blueyonder.co.uk/Sagnac/Sagnac.htm
============================================
> I work with real data, not Einstein's snivelling drivel, real crank.
> Go on, wanker, put up another straw chicken to explain and tell
> us how new and improved it is.
Oh no, now you've called me a wanker! I'm crying. My feelings hurt.
I'm SO sad.
============================================
For one, the pursuit of truth does not begin with a claim that a
star with a planet is a double star. That's what a wanker would call
a strawman. It doesn't work on me and my emotional response is
not of importance to anyone. It sure produces your knee jerk reactions,
though.
glird
- Does that ring true? Of course it does for as
I looked. It ends thus: "This page is subject to further
modification."
> For one, the pursuit of truth does not begin with a claim that a
statement made to there is subject to later modification!
> It doesn't work on me and my emotional response is
> not of importance to anyone.
We agree, at last!!
Uncle Al
[snip crap]
Hopeless idiot. Too stupid to use a card index.
> Still another would be to consider how each individual water molecule
> and glass crystal respond to the electromagnetic fields passing
> through...
[snip 120 lines of crap crap]
Fucking imbecile,
J. Am. Chem. Soc 127(5) 1368 (2005)
Chem. Phys. 117 581 (2002)
<http://www.chem.buffalo.edu/autschbach_research.php>
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2
Jonathan Doolin
> ================================================
>
> why don't we see it everywhere?
> ================================================
> Your telescope isn't powerful enough. CCD arrays have improved
> tremendously since Hubble was launched in 1990, 19 years ago, and
> nowadays have multi-megapixel arrays.
> ================================================
>
> There are a lot of binary systems
> lying very far away.
> ===========================================
> Not as many as you believe. Most binaries have long periods like
> Sirius, 50 years, and is only 8 light year away.
>
> There are no binaries with a period of mere days, they'd break up from
> tidal effects. See Roche.
> ===========================================
> Certainly far enough away that the faster light
> should overtake the slower light.
> ===========================================
> It does. Do the arithmetic as I have.
> http://www.androcles01.pwp.blueyonder.co.uk/Copernicus/LCV.htm
>
> Real data:
> http://www.androcles01.pwp.blueyonder.co.uk/Copernicus/image021.jpg
>
> ============================================
>
Actually, you have the arithmetic there for the intensity, not the
blurring. You should be able to predict the arclength of the blurred
image as a function of radius, period, and distance.
eric gisse
<koobee...@gmail.com> wrote:
[snip]
>> Cue followup with insults and repeated assertions.
>
><shrug>
>
What a good little puppet! Always dancing on cue...
Androcles
Intensity is what novae are all about. Blurring requires positional
displacement
and all stars are points of light, the actual blurring is mostly one image
behind
the other when seen along the line of sight.
> You should be able to predict the arclength of the blurred
> image as a function of radius, period, and distance.
Hmm... very perceptive of you. There may be hope for you yet.
But... a project for you, then. You can start by first learning how to
calculate
a Keplerian orbit.
http://www.androcles01.pwp.blueyonder.co.uk/Orbit/Orbit.xls
It's a whole lot more interesting than the aetherial ghost of a new
improved
straw chicken - it's real science, not crank theory. All you need do is
actually
understand the PoR, the ignorant dork Einstein got it right when he said:
"But the ray moves relatively to the initial point of k, when measured in
the stationary system, with the velocity c-v"
Ref: http://www.fourmilab.ch/etexts/einstein/specrel/www/
A real scientist would have followed up on that instead a fooling around
with H.G. Wells' straw sci-fi.
'Really, this is what is meant by the Fourth Dimension, though some people
who talk about the Fourth Dimension do not know they mean it. It is only
another way of looking at Time. There is no difference between Time and any
of the three dimensions of Space except that our consciousness moves along
with it.' -- Herbert George Wells - "The Time Machine" - 1895.
How old was Einstein in 1895? 16 ?
"The secret to creativity is knowing how to hide your sources." --Einstein
Oh wait... c-v does have any variables properly defined and no context.
Right, son?
Jonathan Doolin
> Androcles wrote:
>
> [snip crap]
>
> Hopeless idiot. Too stupid to use a card index.
>
> > Still another would be to consider how each individual water molecule
> > and glass crystal respond to the electromagnetic fields passing
> > through...
>
> [snip 120 lines of crap crap]
>
> Fucking imbecile,
>
> J. Am. Chem. Soc 127(5) 1368 (2005)
> Chem. Phys. 117 581 (2002)
> <http://www.chem.buffalo.edu/autschbach_research.php>
>
> --
> (Toxic URL! Unsafe for children and most mammals)http://www.mazepath.com/uncleal/lajos.htm#a2
Actually, that was my error. Sorry about that.
Androcles
===================================
Take no notice of fucking cretin Uncle Stooopid and NEVER apologise
to the bastard, he keeps his head firmly up his arse.
The Uncle Stooopid doctrine:
http://sound.westhost.com/counterfeit.jpg
' "c+v appears nowhere in the paper, nor could it. (including the unpaired
double apostrophe)' -- Uncle Stooopid.
According to Chief Wanker Uncle Stooopid, Einstein did not write the
equation he wrote.
"SR is GR with G=0." -- Uncle Stooopid.
"What can be asserted without evidence can also be dismissed without
evidence." -- Uncle Stooopid.
I've dismissed the hypocritical cretin long ago.
Jonathan Doolin
> "Jonathan Doolin" <good4us...@gmail.com> wrote in message
> >> Certainly far enough away that the faster light
> >> should overtake the slower light.
> >> ===========================================
> >> It does. Do the arithmetic as I have.
> >>http://www.androcles01.pwp.blueyonder.co.uk/Copernicus/LCV.htm
>
> >> Real data:
> >>http://www.androcles01.pwp.blueyonder.co.uk/Copernicus/image021.jpg
>
> >> ============================================
>
> > Actually, you have the arithmetic there for the intensity, not the
> > blurring.
>
> Intensity is what novae are all about. Blurring requires positional
> displacement
> and all stars are points of light, the actual blurring is mostly one image
> behind
> the other when seen along the line of sight.
>
> > You should be able to predict the arclength of the blurred
> > image as a function of radius, period, and distance.
>
> Hmm... very perceptive of you. There may be hope for you yet.
> But... a project for you, then. You can start by first learning how to
> calculate
> a Keplerian orbit.
> http://www.androcles01.pwp.blueyonder.co.uk/Orbit/Orbit.xls
I think I have a better idea.
I take as a priori that any single observer can only see any given
event once.
I use the variable t to represent the emission time of any given event
(when it actually happens). And T to represent the observation time
of any given event. Then dT/dt is an important quanitity. If dT/dt
is 1 then you have observation of events occuring at the same speed
that they are emitted. dT/dt >1 represents slow-motion. dT/dt <1
represents fast-motion. and dT/dt = 0 represents blur, as images from
the two events at different emission times t would be observed at the
same observation times T. Finally, dT/dt<0 would be backwards.
I'll use a particle moving in a circle of radius r, with period P,
around a center at distance, d, from the observer.
x=r*Cos[2*Pi*t/P]
y=r*Sin[2*Pi*t/P]
The observer will be located along the y axis a distance d from the
center of the circle.
The distance to the particle (relative to the observer) is d+y = d +
r*Sin[2*Pi*t/P]
the velocity of the particle (relative to the observer) is vy = dy/dt
= (2*Pi*r/P)*Cos[2*Pi*t/P].
In SR, the speed of the light from that particle (relative to the
observer) is c. But in Androcles model (if I understand correctly)
the velocity of the light is c+vy.
Hence, the transmission time from emission to observer in Androcles
model is
(d+y)/(c+vy)
And so the observation time is
T = (d+y)/(c+vy) + t
= ((d + r*Sin[2*Pi*t/P]) / (c + (2*Pi*r/P)*Cos[2*Pi*t/P])) + t
You can check immdiately if r = 0, then T = d/c + t, which is as you
would expect. The time of observation is approximately equal to the
time of emission plus a transmission delay of d/c.
Also, d > |y| because the observer is far away from the orbit. And c
> |vy| in any ordinary scenario. So unless the observer is within the
radius of orbit, in which case the numerater can be negative, or the
velocity of the source is greater than the speed of light, in which
case the denominator will be zero, there can actually be no blurring
in your model.
Which means... if this calculation is correct, source dependent
velocity of light does not predict blurring in low-velocity distant
orbits, after all.
It does, however, predict a different profile for dT/dt.
Instead of T = (d+y)/(c+vy) + t in the source-dependent velocity of
light, we would have:
T= (d+y)/c in the observer-dependent velocity of light.
An important approximation I've made in this calculation is that I did
not account for the motion of the particle in the x direction, but I
think there should be measurable, subtle differences between the dT/dt
predicted by source-dependent, and observer-dependent speed of light
even in orbits of, for instance, the moons of Jupiter.
Androcles
============================================
Good grief... that makes a horse race photo-finish an impossibility.
The event of a horse crossing the line (a single event) can only be seen
by the camera once. Where is the other horse if it can't be seen?
A priori any single observer has two eyes and can see two (or more)
horses simultaneously.
============================================
I use the variable t to represent the emission time of any given event
(when it actually happens). And T to represent the observation time
of any given event. Then dT/dt is an important quanitity. If dT/dt
is 1 then you have observation of events occuring at the same speed
that they are emitted. dT/dt >1 represents slow-motion. dT/dt <1
represents fast-motion. and dT/dt = 0 represents blur, as images from
the two events at different emission times t would be observed at the
same observation times T. Finally, dT/dt<0 would be backwards.
=============================================
Ok...you mean like this:
http://www.androcles01.pwp.blueyonder.co.uk/Doolin'sStar.GIF
=============================================
I'll use a particle moving in a circle of radius r, with period P,
around a center at distance, d, from the observer.
x=r*Cos[2*Pi*t/P]
y=r*Sin[2*Pi*t/P]
=======================================
That won't do at all; real orbits are ellipses, not circles. Also they
are inclined to the line of sight. Henri Wilson made that error when
he tried to simulate the situation. You can't take short cuts.
=======================================
The observer will be located along the y axis a distance d from the
center of the circle.
The distance to the particle (relative to the observer) is d+y = d +
r*Sin[2*Pi*t/P]
=======================================
y = distance Earth to Sun, about 8 light minutes
d = distance Sun to Proxima Centauri, about 4 light years.
y+d = 8 light minutes + 4 light years = absurd pedantry.
=======================================
the velocity of the particle (relative to the observer) is vy = dy/dt
= (2*Pi*r/P)*Cos[2*Pi*t/P].
==========================================
Ok, velocity IS important.
Wrong equation, you left out cos(inclination) where the orbit might
be seen edge-on, face-on or somewhere in between. If the orbit is
seen face-on then the star has no velocity in the direction of the
telescope.
==========================================
In SR, the speed of the light from that particle (relative to the
observer) is c. But in Androcles model (if I understand correctly)
the velocity of the light is c+vy.
===========================================
Correct. And in Goodricke's Algol (long before SR) the speed of
light was not considered at all. Goodricke was not following the
scientific method.
===========================================
Hence, the transmission time from emission to observer in Androcles
model is
(d+y)/(c+vy)
==========================================
d/(c+v) will do, y is insignificant.
And so the observation time is
T = (d+y)/(c+vy) + t
===========================================
Yep.
= ((d + r*Sin[2*Pi*t/P]) / (c + (2*Pi*r/P)*Cos[2*Pi*t/P])) + t
===========================================
Nope. You need an inclined Keplerian orbit, otherwise you'll make
silly statements like "All cepheids should be the same".
You can check immdiately if r = 0, then T = d/c + t, which is as you
would expect. The time of observation is approximately equal to the
time of emission plus a transmission delay of d/c.
============================================
Nope. The time of observation is almost exactly equal to the time of
emission plus a transmission delay of d/(c+v). d is not known to
any great precision anyway.
============================================
Also, d > |y| because the observer is far away from the orbit. And c
> |vy| in any ordinary scenario. So unless the observer is within the
radius of orbit, in which case the numerater can be negative, or the
velocity of the source is greater than the speed of light, in which
case the denominator will be zero, there can actually be no blurring
in your model.
==============================================
Not true. When nearly all the light from a complete orbit arrives
at once, the star is seen throughout its orbit simultaneously.
However, it is then so distant as to appear only as a point of light.
In this ACTUAL DATA,
http://www.androcles01.pwp.blueyonder.co.uk/Copernicus/image021.jpg
(reproduced with the permission of the British Astronomical Association)
The star appears retrograde (DT/dt < 0) between the peaks.
But you can't see it, its too far away.
==============================================
Which means... if this calculation is correct, source dependent
velocity of light does not predict blurring in low-velocity distant
orbits, after all.
It does, however, predict a different profile for dT/dt.
Instead of T = (d+y)/(c+vy) + t in the source-dependent velocity of
light, we would have:
T= (d+y)/c in the observer-dependent velocity of light.
An important approximation I've made in this calculation is that I did
not account for the motion of the particle in the x direction, but I
think there should be measurable, subtle differences between the dT/dt
predicted by source-dependent, and observer-dependent speed of light
even in orbits of, for instance, the moons of Jupiter.
===============================================
Instead of guessing, I modelled it. I adhere to the scientific method
by which I'm bound. You, on the other hand, are guessing.
What's the subtle difference between c = 186,000 miles/sec and
v = 18.6 miles/sec, the speed of the Earth in its orbit?
You think you have a better idea, but you don't want to do the work.
You see, a few of us here ARE bound by a concept that truth IS part
of science. This is what distinguishes you as a fake scientist and true
crank from the real scientists and fake cranks.
But I will say this for you. Your mind is partially open. Now all you
need do is open it all the way. What does it really take to understand
the Principle of Relativity and ignore the pompous halfwit Einstein?
Jonathan Doolin
> I take as a priori that any single observer can only see any given
> event once.
> ============================================
>
> Good grief... that makes a horse race photo-finish an impossibility.
> The event of a horse crossing the line (a single event) can only be seen
> by the camera once. Where is the other horse if it can't be seen?
>
> A priori any single observer has two eyes and can see two (or more)
> horses simultaneously.
> ============================================
>
Instead of looking having an eye out for error, you seek
misinterpretation. This makes you a very poor contributor.
Jonathan Doolin
> around a center at distance, d, from the observer.
>
>
> x=r*Cos[2*Pi*t/P]
> y=r*Sin[2*Pi*t/P]
>
>
> =======================================
> That won't do at all; real orbits are ellipses, not circles. Also they
> are inclined to the line of sight. Henri Wilson made that error when
> he tried to simulate the situation. You can't take short cuts.
> =======================================
Did Henri Wilson came to the same conclusion I did? If not, there
might be an error somewhere else.
Jonathan Doolin
> An important approximation I've made in this calculation is that I did
> not account for the motion of the particle in the x direction, but I
> think there should be measurable, subtle differences between the dT/dt
> predicted by source-dependent, and observer-dependent speed of light
> even in orbits of, for instance, the moons of Jupiter.
> ===============================================
> Instead of guessing, I modelled it. I adhere to the scientific method
> by which I'm bound. You, on the other hand, are guessing.
Instead of just making the claim that you modelled it, why don't you
produce your model? Are you just waiting for someone to come to the
same conclusion independently?
Jonathan Doolin
> would expect. The time of observation is approximately equal to the
> time of emission plus a transmission delay of d/c.
> ============================================
> Nope. The time of observation is almost exactly equal to the time of
> emission plus a transmission delay of d/(c+v). d is not known to
> any great precision anyway.
> ============================================
I meant r to be precisely zero, not approximately zero.
Hence v=0, and d/(c+v) = d/c
Androcles
Henri Wilson is an incompetent programmer who desperately wants
his own theory.
He actually removed inclination from his original program (circa 2001)
so that he could attempt to promote his "unification" nonsense in which
he proposed that the speed of light somehow magically adjusted its
speed over some undefined distance. As a result he made a complete
fool of himself.
There are many errors somewhere else, son, not least of which
is understanding the PoR and Doppler.
Doppler's equation is
c+v
f' = f * --------------
c
if v = c then f' = 2f
if v = -c then f' = 0
as this gif clearly shows.
http://www.androcles01.pwp.blueyonder.co.uk/AC/doppler.gif
The mustard observer sees 2f, the magenta observer sees 0f.
Applying the PoR:
http://www.androcles01.pwp.blueyonder.co.uk/AC/doppler2.gif
The radiation has constant velocity with respect to the SOURCE.
One only gets
c
f' = f * --------------
c+v
if there is a medium involved. There is no aether, Doppler for
sound does not apply to light.
Henri did at least understand that much.
Oh, and his orbit was by extrapolation, not Kepler's equation
(which is a little beyond your present capabilities, but not by much).
http://mathworld.wolfram.com/KeplersEquation.html
Androcles
Trivial. No r, no v, no anything.
Science is the observation, investigation and explanation of natural
phenomena. Here is the data:
http://www.androcles01.pwp.blueyonder.co.uk/Copernicus/image021.jpg
No crank theories allowed, just the Principle of Relativity, an axiom.
Now explain it. It'll be good for your soul.
Hint:
http://www.androcles01.pwp.blueyonder.co.uk/AC/doppler2.gif
C'mon, Doolin, we both know you are intelligent. Now prove it.
Explain that light curve.
Androcles
>
>
>> An important approximation I've made in this calculation is that I did
>> not account for the motion of the particle in the x direction, but I
>> think there should be measurable, subtle differences between the dT/dt
>> predicted by source-dependent, and observer-dependent speed of light
>> even in orbits of, for instance, the moons of Jupiter.
>> ===============================================
>> Instead of guessing, I modelled it. I adhere to the scientific method
>> by which I'm bound. You, on the other hand, are guessing.
>
> Instead of just making the claim that you modelled it, why don't you
> produce your model?
I did and I have. It's been available since 1993.
It actually predicted the nova of 1999 (V 1493 Aql) six years later and
will predict the light curves of novae in the future.
Why don't you read previous posts?
Here it is again.
http://www.androcles01.pwp.blueyonder.co.uk/Copernicus/LCV.htm
Look at the last line on that page.
It was written long before there was any fear of viruses, but I do
understand the recalcitrance many others have. I personally keep an old
computer for downloading suspicious software. Why, you could even
find the source code if you searched sci.physics.relativity for the early
part of this decade.
> Are you just waiting for someone to come to the
> same conclusion independently?
Yes. You see, I don't have any theories or straw chickens, I work entirely
from raw data. All theories and straw chickens are the work of others...
and they make mistakes.
If you can identify my mistakes then I'd welcome it. I might even be
polite.
"You are not bound by politeness, not bound by truth, not bound
by any comprehensible theory, not bound by evidence, and not bound by
the scientific method." - Doolin.
I am bound by (empirical) evidence, I am bound by the scientific method,
Jonathan Doolin. I am not bound by politeness, truth, or theory.
Truth, like beauty, is in the eye of the beholder, and theory is not truth.
Jonathan Doolin
> "Jonathan Doolin" <good4us...@gmail.com> wrote in message
Androcles, it appears that you have been discussing this V 1493 Aql
for quite some time. Is there any place where you present your case
from scratch, whereby someone with little knowledge of the topic might
find out the nature of the controversy? For instance, what is the
emperical phenomenon being observed? What are the explanations that
have been presented by astronomers? What is Henri Wilson's
explanation?
Androcles
===================================================
Ok... from scratch:
1) Our star, Sol, has multiple planets in orbit. There are billions of
stars.
See the internet or a library for confirmation, or just look up.
2) Orbits are elliptical with a wide range of eccentricities.
Refer to the work of Johannes Kepler, confirmed by Sir Isaac Newton.
http://tinyurl.com/8ax8mo
3) There is no aether. See Albert A. Michelson.
http://en.wikipedia.org/wiki/Albert_Abraham_Michelson
4) The Principle of Relativity is sacrosanct, it is an axiom.
http://www.androcles01.pwp.blueyonder.co.uk/PoR/PoR.htm
5) Any star with a planet will "wobble", i.e. have its own orbit about
a common centre of gravity it shares with the planet, know as the
barycentre. The Earth-Moon barycentre lies 1000 miles beneath
your feet, 3000 miles higher then Earth's centre.
http://www.androcles01.pwp.blueyonder.co.uk/Algol/Barycentre.gif
(This is the principle of a lever, where the barycentre is equivalent to
the fulcrum.)
6) Putting the above together and in agreement with Ockham's Razor,
http://en.wikipedia.org/wiki/Occam's_razor
light from a distant star MUST vary in its speed sinusoidally. This
variation will typically be of the order of 1 - 1000 km/sec, a small
fraction of the fundamental speed, 300,000 km/sec.
If the distance is great enough, fast light emitted later will eventually
pass slow light emitted earlier.
http://www.androcles01.pwp.blueyonder.co.uk/Orbit/slowfast.gif
The distance/time graph for this is shown here:
http://www.androcles01.pwp.blueyonder.co.uk/Doolin'sStar.GIF
(On this scale, the distance to Jupiter is a billionth of a pixel.)
7) Where the faster light meets the slower light, we expect to see
the star appear brighter for a small part of its period. Some stars
will be at this distance and appear as recurrent novae, although
it must be remembered that the period may be many decades.
Pluto in our own solar system, for example, has a period of 208
years.
8) Now that the principles involved have been established the next
task is to quantify the effect. (Obtain a light curve.) This best acheived
using a computer. This I did in 1987 using DOS. Some six years later
I wrote a Windows version which is still available today.
http://www.androcles01.pwp.blueyonder.co.uk/Copernicus.exe
===================================================
For instance, what is the
emperical phenomenon being observed?
Variation in brightness.
===================================================
What are the explanations that
have been presented by astronomers?
For a recurrent nova:
The star blows itself up, magically settles down to normal and blows
itself up again, repeatedly. It is probably feeding itself from a dork
companion.
For a cepheid:
The star puffs up and down like a fucking blowfish, by magic.
For an "eclipsing" variable:
The star hides behind a magical dork companion which cannot be seen.
See Goodricke, world famous inventor of (non-existent) double dork
stars.
http://www.androcles01.pwp.blueyonder.co.uk/Algol/Algol.htm
For Mira:
It has a real magic tail, we can see it does.
http://www.androcles01.pwp.blueyonder.co.uk/Orbit/Orbit.htm
For a broken pencil:
The pencil is really broken, we can see it is. Your explanation about
refraction is obviously nonsense, light doesn't bend. The pencil
straightens when you take it out the water by magic.
For politeness:
On Jan 10, 3:16 pm, Uncle Al <Uncle...@hate.spam.net> wrote:
> Androcles wrote:
>
> [snip crap]
>
> Hopeless idiot. Too stupid to use a card index.
For truth:
Seeing is believing. Trust me.
For theory:
Einstein is the Lord. All praise to Einstein the wholey.
For the scientific method:
Throw it in the can, seeing is believing.
My explanation... in the land of the blind the one-eyed man is king.
Einstein had one eye, so he's king.
I have three, two optical and the logical mind's eye.
As much as Einstein wished it otherwise the velocity of light
isn't sacrosanct, but the PoR is. You can forget your New Improved
Twin Paradox Explanation, you are explaining a strawman.
"we establish by definition that the ``time'' required by light to travel
from A to B equals the ``time'' it requires to travel from B to A. "
Might just as well establish by definition that the ``time'' required by a
TURTLE to travel from A to B
equals the ``time'' it requires to travel from B to A ", the math is just
the same.
That's the true nature of the controversy.
I can turn a cepheid into an eclipsing variable just like this:
http://www.androcles01.pwp.blueyonder.co.uk/Copernicus/A2C.gif
When this turns yellow, that's the model for V 1493 Aql.
http://www.androcles01.pwp.blueyonder.co.uk/Copernicus/period.gif
===================================================
What is Henri Wilson's
explanation?
Wilson has had so many different explanations I've lost count. Why not
ask him?
===================================================
Albertito
And for a pulsar, too.
Jonathan Doolin
>
> - Show quoted text -
Thanks. You wouldn't to know offhand, the parametric equations for
the Kepler orbits, would you?
Jonathan Doolin
> On Jan 12, 9:28 am, "Androcles" <Headmas...@Hogwarts.physics> wrote:
>
>
>
>
>
> > "Jonathan Doolin" <good4us...@gmail.com> wrote in message
>
> >news:2a769985-1e9e-4822...@p2g2000prf.googlegroups.com...
> > On Jan 11, 3:53 pm, "Androcles" <Headmas...@Hogwarts.physics> wrote:
>
> > > "Jonathan Doolin" <good4us...@gmail.com> wrote in message
>
> > >news:a39da7cd-d17b-4c54...@w24g2000prd.googlegroups.com...
>
> > > >> An important approximation I've made in this calculation is that I did
> > > >> not account for the motion of the particle in the x direction, but I
> > > >> think there should be measurable, subtle differences between the dT/dt
> > > >> predicted by source-dependent, and observer-dependent speed of light
> > > >> even in orbits of, for instance, the moons of Jupiter.
I have got some method for the attack of the problem, though I think
the math is pretty ugly to do by hand.
For now, I am still using parametric equations for a circular orbit,
but I think it shouldn't be too difficult to generalize it to an
elliptical orbit.
x = r*Cos[*Pi*t/P]and y = r*Sin[2*Pi*t/P]
Modify these equations by an angle of inclination q (yz direction.)
/ 1 0 0 \ / x \
| 0 Cos[q] -Sin[q] || y |
\ 0 Sin[q] Cos[q] / \ 0 /
(in the Kepler orbit case, we would also need to apply a rotation in
the lateral xy direction.
From the point of view of the observer, you have
x = r*Cos(2*Pi*t/P)
y = r*Sin[2*Pi*t/P]*Cos[q] + d
z = r*Sin[2*Pi*t/P]*Sin[q]
And the transmission distance would be D=Sqrt(x^2+y^2+z^2)
D=r*Sqrt[Cos^2[2*Pi*t/P] + Sin^2[2*Pi*t/P] + (d/r)^2 + (2*d/r)*Sin
[2*Pi*t/P]]
Now Special Relativity would have the transmission time as simply D/c
However, in the source dependent speed of light case, it becomes quite
a bit more difficult, because we must subtract the component of the
speed of the particle parallel to the direction of transmission. I
think, this would be the inner product of (dx/dt, dy/dt, dz/dt) and
(x,y,z)/D.
So T=D/(c+v) where v=(dx/dt * x/D ,dy/dt * y/D,dz/dt*z/D)
where x = r*Cos(2*Pi*t/P), y = r*Sin[2*Pi*t/P]*Cos[q] + d,z = r*Sin
[2*Pi*t/P]*Sin[q]
and D=r*Sqrt[Cos^2[2*Pi*t/P] + Sin^2[2*Pi*t/P] + (d/r)^2 + (2*d/r)*Sin
[2*Pi*t/P]]
This is simplified, and might not be sufficient for your purposes, but
I tend to need easier problems to work my way up to the harder ones.
Of course, if you want to make it perfect, you should also cosider the
relative velocity of the center of orbit from the observer. The orbit
should be made a Kepler orbit, and a lateral rotation matrix (in the
xy plane) should be multiplied.
Having done all this, it would not surprise me at all if you find an
error in my calculations. You get what you pay for.
Androcles
On Jan 12, 7:23 pm, Jonathan Doolin <good4us...@gmail.com> wrote:
> On Jan 12, 9:28 am, "Androcles" <Headmas...@Hogwarts.physics> wrote:
>
>
>
>
>
> > "Jonathan Doolin" <good4us...@gmail.com> wrote in message
>
> >news:2a769985-1e9e-4822...@p2g2000prf.googlegroups.com...
> > On Jan 11, 3:53 pm, "Androcles" <Headmas...@Hogwarts.physics> wrote:
>
> > > "Jonathan Doolin" <good4us...@gmail.com> wrote in message
>
> > >news:a39da7cd-d17b-4c54...@w24g2000prd.googlegroups.com...
>
> > > >> An important approximation I've made in this calculation is that I
> > > >> did
> > > >> not account for the motion of the particle in the x direction, but
> > > >> I
> > > >> think there should be measurable, subtle differences between the
> > > >> dT/dt
> > > >> predicted by source-dependent, and observer-dependent speed of
> > > >> light
> > > >> even in orbits of, for instance, the moons of Jupiter.
I have got some method for the attack of the problem, though I think
the math is pretty ugly to do by hand.
For now, I am still using parametric equations for a circular orbit,
but I think it shouldn't be too difficult to generalize it to an
elliptical orbit.
==================================================
Why not use a quadrilateral orbit with different velocities on each
unequal side and nice sharp corners? It would be just as silly...
You could always model the Eiffel Tower with an Egyptian pyramid...
close enough for government work, I suppose...
==================================================
x = r*Cos[*Pi*t/P]and y = r*Sin[2*Pi*t/P]
Modify these equations by an angle of inclination q (yz direction.)
/ 1 0 0 \ / x \
| 0 Cos[q] -Sin[q] || y |
\ 0 Sin[q] Cos[q] / \ 0 /
(in the Kepler orbit case, we would also need to apply a rotation in
the lateral xy direction.
===============================================
There are three orientation rotations to any object - pitch, roll and yaw.
For the purpose of stargazing roll can be ignored - you can always
stand on your head; depending on where on Earth you live you will
be, relative to another observer. Henri Wilson in Australia can see
the same stars in the ecliptic as I can from Britain but one of us is
upside down. It is of course him, everybody knows North is up
and Australia is down under :-)
The order in which you perform the rotations is important as this
clearly demonstrates.
http://www.androcles01.pwp.blueyonder.co.uk/Vector/RP.gif
http://www.androcles01.pwp.blueyonder.co.uk/Vector/PR.gif
From the identity of the group (red on top) we arrive at
red + magenta * 2 + blue on top in one case and
red + magenta + blue * 2 on top on the other.
This is the same model seen from three different views:
http://www.androcles01.pwp.blueyonder.co.uk/Orbit/a.gif
http://www.androcles01.pwp.blueyonder.co.uk/Orbit/b.gif
http://www.androcles01.pwp.blueyonder.co.uk/Orbit/c.gif
===============================================
From the point of view of the observer, you have
x = r*Cos(2*Pi*t/P)
y = r*Sin[2*Pi*t/P]*Cos[q] + d
z = r*Sin[2*Pi*t/P]*Sin[q]
===============================================
You are killing your computer's speed with all that repeat computation.
# define PI2 6.283185307179586476925286766559
increment = PI2/ [user selected number of points]
for (t =0; t < PI2; t+=increment)
{
Angle = Kepler( &x, &y, t)
and so on...
It's been a while since I did any serious programming.
===============================================
And the transmission distance would be D=Sqrt(x^2+y^2+z^2)
D=r*Sqrt[Cos^2[2*Pi*t/P] + Sin^2[2*Pi*t/P] + (d/r)^2 + (2*d/r)*Sin
[2*Pi*t/P]]
===============================================
Nah.... D = [user defined distance to star]. He punches in 30 parsecs
or something.
The user chooses the orbit parameters and the distance. This is
astronomy, distances are not known to any precision.
===============================================
Now Special Relativity would have the transmission time as simply D/c
===============================================
Correct. However, we are not really interested in the 10 years or 100
years or whatever it takes the light to traverse the distance even with SR.
What we want is dT/dt.
That is, T = (D/c+t) modulo P.
===============================================
However, in the source dependent speed of light case, it becomes quite
a bit more difficult, because we must subtract the component of the
speed of the particle parallel to the direction of transmission. I
think, this would be the inner product of (dx/dt, dy/dt, dz/dt) and
(x,y,z)/D.
So T=D/(c+v) where v=(dx/dt * x/D ,dy/dt * y/D,dz/dt*z/D)
where x = r*Cos(2*Pi*t/P), y = r*Sin[2*Pi*t/P]*Cos[q] + d,z = r*Sin
[2*Pi*t/P]*Sin[q]
and D=r*Sqrt[Cos^2[2*Pi*t/P] + Sin^2[2*Pi*t/P] + (d/r)^2 + (2*d/r)*Sin
[2*Pi*t/P]]
This is simplified, and might not be sufficient for your purposes, but
I tend to need easier problems to work my way up to the harder ones.
==================================================
That's fair enough, you are on the right track. Polya recommends it.
T = (D/(c+v)+t) modulo P.
Now we use T as an index into an array.
We don't want to index outside the bounds of the array, so
Modulo P is important.
My array was 1000 elements (to correspond with 1024 pixels
on a screen with room for a window frame, although today
I have two widescreen monitors). The array also corresponds
(is scaled) to P.
Now increment array[T] to simulate the arrival of a light particle
at time T that left at time t.
If you are using T = (D/(c)+t) modulo P then you have to get
a flat line, so that's a good check to prove the programming
is correct.
If you are using T = D/(c+v) you get a light curve.
NOTE:
Magnitude is logarithmic! For graphs you need to scale accordingly
or your light curve will be spikey.
http://en.wikipedia.org/wiki/Absolute_magnitude
==================================================
Of course, if you want to make it perfect, you should also cosider the
relative velocity of the center of orbit from the observer. The orbit
should be made a Kepler orbit, and a lateral rotation matrix (in the
xy plane) should be multiplied.
==================================================
Overkill. The time for light to get from Saturn to Earth is about 1 hour
20 minutes. We are interested in hundreds or even thousands of years
to allow fast light to catch up with slow light. An hour can be ignored
(and any motion of the observer).
What you might want to consider is the proper motion of the system
when it comes to modelling spectra, you'll be adding a constant.
It won't affect the luminosity curve but will show up in the velocity
curve.
==================================================
Having done all this, it would not surprise me at all if you find an
error in my calculations. You get what you pay for.
==================================================
I would not expect anyone to get it right first time, but if a job
is worth doing then it is worth doing well. You'll know when
you have it right when you can duplicate real data- such as
V 1493 Aql.
Here you have all you need for your Ph.D. thesis; I've seen your
graphics and know what you are capable of. All I ask is that you
acknowledge my input and kick that egotistical bluffing charlatan,
Einstein, into touch.
Nature doesn't give up her secrets easily and it is not given to Man
to invent Nature as he chooses. Truth is what it is really about, son.
You'll get out of it what you put into it. As for me, I'm just a
grumpy old man with a stent in his aorta causing backache and
arthritis in his ankle. I'm not expecting to last much longer and
some people will be glad to see the back of me, but always
remember this:
Science is the observation, investigation and explanation of natural
phenomena, not inventing black holes or time machines and then go
looking for them, hoping they'll fit our wonderfully stupid theories.
There are enough mysteries in the universe to uncover without
creating them.
There are no relativistic computers because computers are logical.
What kind of lunacy prompted Einstein to say
the speed of light from A to B is c-v,
the speed of light from B to A is c+v,
the "time" each way is the same?
Even if you do pay you'll never get time dilation, but you will get
the appearance of dT/dt < 0 and make a fortune out of it. It's all
in the presentation. Hulse and Taylor got a Nobel prize out of it.
http://www.daviddarling.info/encyclopedia/H/HulseTaylor.html
You get what you work for (sometimes).
Albertito
> Good morning.
>
> Some time ago I made a rather stuttering attempt at this explanation
> on YouTube, (math free version)
>
> http://www.youtube.com/watch?v=nmAVkj9fTnUhttp://www.youtube.com/watch?v=76BB-qZXEhohttp://www.youtube.com/watch?v=eT-3R8ju9V0
>
> but I did not feel like doing the mathematics at that time.
>
> This morning, I'd like to try to put a FEW equations down. Don't
> expect here any profound discovery. Typically an explanation has a
> quality in inverse proportion of the explainer's pride. I'm pretty
> proud of this explanation, so that's probably not a good sign. :)
>
> This morning I wanted to describe in my own words and at least give
> what little bit of the math that I know how to do. I apologize in
> advance for the math and grammatical errors you'll probably find.
>
> In any case, let us consider two parties, A and B, A stays at home,
> while B moves away into the distance to point C, 1 "light" unit away
> and then returns home.
>
> The speed of light in this model is 1 and the distance is 1 and the
> velocity which B chooses to travel is v. (where, of course, v=1
> represents the speed of light)
>
> ----------------
> Part 1, What do things look like from the Home Twin, A?
>
> So A watches B travel toward point C at velocity v. How long does
> this take? B arrives at C at time t = distance/velocity = 1/v.
> However when B arrives at C, there will be a time delay before A sees
> the event of arrival because of the time the light takes to return
> from that point. So A observes B's arrival at C at time t = 1+1/v
>
> An interesting thing to consider here is that the observed velocity is
> explicitly calculable from the two observed events (departure
> observation and arrival observation). A will have observed B's
> journey at a constant speed. Observed Velocity of Outward trip =
> distance/time = 1/(1+1/v) = v/(1+v)
>
> A similar consideration of the inbound trip yields an Observed Time of
> the inbound trip of (1/v)-1, and observed velocity v/(1-v)
>
> Thus if v=.5, then the observed velocity outbound =.5/1.5 = .3333c,
> and the obseved velocity inbound = .5/.5 = 1c.
>
> If v=.9 then the observed velocity outbound = .9/1.9 = 0.47c and the
> observed velocity inbound = .9/.1 = 9c.
>
> So the maximum observable outbound velocity is .5c but there is NO
> maximum observable inbound velocity.
>
> ---------
> Part 2. What do things look like from the perspective of the
> traveling twin, B?
>
> http://www.youtube.com/watch?v=eT-3R8ju9V0
>
> From B's perspective there must be some things which are the same, and
> some things that are different. If all of the same physics apply,
> then we must assume that the same chemical, nuclear, or matter/anti-
> matter reactions that produced the velocity v (Between A and B) for
> observer A must also have produced the same velocity v (Between A and
> B) for observer B.
>
> The real velocities are the same. If the real velocities are the same
> then should the observed outbound velocity v/(1+v) and observed
> inbound velocity v/(1-v) be the same? Yes, these calculations are
> general. The observed inbound and observed outbound velocities are
> based ONLY on the actual velocity, and nothing else. Though I did the
> calculation based on a specific pair of events, departure and arrival
> of observer B, any two events could be used, and they cancel out of
> the final calculation.)
>
> A thing that will be different for the two observers, though is the
> apparent time that it takes B to travel from A to C and back. Whereas
> A observed the return trip to happen much faster than outbound trip, B
> will observe the outbound trip and inbound trip to take the same
> amount of time. (Other famous gedanken experiments determine that
> this time would be (1/v)*(1/sqrt(1-v^2)) whereas 1/v would be the
> expected time it takes to travel distance 1, and the other factor is
> the time dilation factor)
>
> The Observed velocities are the same, but the amount of time traveled
> at those velocities is different. This means that the observed
> distance traveled by B is different for B than it is for A.
> (Technically, B remains stationary relative to observer B, just to be
> troublesome.)
>
> But the greatest point of interest is what happens to the Observed
> distance to A from the perspective of B during the turn-around. The
> apparent relative velocity of A on the way out was v/(1+v). The
> apparent relative velocity of A on the way in will be v/(1-v).
>
> If the time is the same, but the apparent velocity is different, then
> there is only one possibility. The distance CHANGED. You cannot move
> away from an object at one apparent velocity and then return at a
> faster apparent velocity for the same period of time unless that
> object has moved away from you.
>
> In effect, the traveling twin at his point of turning-around is
> transitioning himself into a new reference frame where his home-world
> is much further away than it was before. Also as his home goes from
> slow-motion [v/(1+v)< .5] to fast forward [v/(1-v) = unlimited.] For
> the moving twin it may be a surprise that the earth lurches away from
> him at the point of turnaround, but he will be able to watch the rise
> and fall of civilizations in fast-forward on his return trip. It
> won't be a surprise to him when he gets home and everyone he knew is
> dead unless he has no windows on his space-ship.
Invent a stupid theory. Write a textbook about it. At the
end of each chapter, write a set of exercices, and call them
"paradoxes", as if they were not real paradoxes, but miscellaneous
curiosities that arise from the "Great Theory You Have Invented".
Once that's done, any real paradox that anyone managed to point
out would be suitably labeled as "exercice" in the specific
chapter of your textbook, so that's no a real paradox, but a
well-defined feature of the "Great Theory You Have Invented".
Jonathan Doolin
Ok. Which one did you use in your model?
> x = r*Cos[*Pi*t/P]and y = r*Sin[2*Pi*t/P]
> Modify these equations by an angle of inclination q (yz direction.)
>
> / 1 0 0 \ / x \
> | 0 Cos[q] -Sin[q] || y |
> \ 0 Sin[q] Cos[q] / \ 0 /
>
> (in the Kepler orbit case, we would also need to apply a rotation in
> the lateral xy direction.
> ===============================================
> There are three orientation rotations to any object - pitch, roll and yaw.
>
> For the purpose of stargazing roll can be ignored - you can always
> stand on your head; depending on where on Earth you live you will
> be, relative to another observer. Henri Wilson in Australia can see
> the same stars in the ecliptic as I can from Britain but one of us is
> upside down. It is of course him, everybody knows North is up
> and Australia is down under :-)
>
> The order in which you perform the rotations is important as this
> clearly demonstrates.
>
>
> From the identity of the group (red on top) we arrive at
> red + magenta * 2 + blue on top in one case and
> red + magenta + blue * 2 on top on the other.
>
> This is the same model seen from three different views:
> http://www.androcles01.pwp.blueyonder.co.uk/Orbit/a.gif
> http://www.androcles01.pwp.blueyonder.co.uk/Orbit/b.gif
> http://www.androcles01.pwp.blueyonder.co.uk/Orbit/c.gif
> ===============================================
>
> From the point of view of the observer, you have
> x = r*Cos(2*Pi*t/P)
> y = r*Sin[2*Pi*t/P]*Cos[q] + d
> z = r*Sin[2*Pi*t/P]*Sin[q]
>
> ===============================================
>
> You are killing your computer's speed with all that repeat computation.
>
> # define PI2 6.283185307179586476925286766559
>
> increment = PI2/ [user selected number of points]
>
> for (t =0; t < PI2; t+=increment)
> {
> Angle = Kepler( &x, &y, t)
>
> and so on...
> It's been a while since I did any serious programming.
> ===============================================
>
In Wikipedia h all three of x, y, and t are defined as parametric
functions of E, the eccentric anomoly
http://en.wikipedia.org/wiki/Kepler_orbit equations (20, 21, 27)
Is that how you did it?
I would try to put the predictions of SR right next to the predictions
of this, along with the actual data. I am curious though, about your
selection of V 1493 Aql. Shouldn't there be visible differences
between the models for more common objects?
> Nature doesn't give up her secrets easily and it is not given to Man
> to invent Nature as he chooses. Truth is what it is really about, son.
> You'll get out of it what you put into it. As for me, I'm just a
> grumpy old man with a stent in his aorta causing backache and
> arthritis in his ankle. I'm not expecting to last much longer and
> some people will be glad to see the back of me, but always
> remember this:
You often do come across as grumpy. I'm glad I hadn't just imagined
it.
> Science is the observation, investigation and explanation of natural
> phenomena, not inventing black holes or time machines and then go
> looking for them, hoping they'll fit our wonderfully stupid theories.
> There are enough mysteries in the universe to uncover without
> creating them.
>
> There are no relativistic computers because computers are logical.
> What kind of lunacy prompted Einstein to say
> the speed of light from A to B is c-v,
> the speed of light from B to A is c+v,
> the "time" each way is the same?
>
I would compare Einstein to a new poster on sci.physics.relativity who
is just starting to grasp the theory and does not know the
thoroughness to which new contributors to the group are humiliated for
a careless phrase. With a good grasp of the theory, his meaning is
perfectly clear, though he clearly switched reference frames in the
middle.
> Even if you do pay you'll never get time dilation, but you will get
> the appearance of dT/dt < 0 and make a fortune out of it. It's all
> in the presentation. Hulse and Taylor got a Nobel prize out of it.
> http://www.daviddarling.info/encyclopedia/H/HulseTaylor.html
>
Yes, I'm fairly sure I made an error in my original calculation--
either conceptual or mathematical, because I had another look at my
demo from a few years ago and there was evidence that dT/dt < 0 for
the source-dependent speed-of-light. I may have forgotten a
derivative somewhere. I'll look over it again.
> You get what you work for (sometimes).- Hide quoted text -
Jonathan Doolin
Whoah! I totally didn't do that derivative.
> Which means... if this calculation is correct, source dependent
> velocity of light does not predict blurring in low-velocity distant
> orbits, after all.
>
> It does, however, predict a different profile for dT/dt.
>
> Instead of T = (d+y)/(c+vy) + t in the source-dependent velocity of
> light, we would have:
>
> T= (d+y)/c in the observer-dependent velocity of light.
>
> An important approximation I've made in this calculation is that I did
> not account for the motion of the particle in the x direction, but I
> think there should be measurable, subtle differences between the dT/dt
> predicted by source-dependent, and observer-dependent speed of light
> even in orbits of, for instance, the moons of Jupiter.- Hide quoted text -
Androcles
==================================================
I used a Keplerian ellipse because I know circles have no major axis.
===============================================
Wackypedia needs to combine that page with
http://en.wikipedia.org/wiki/Kepler's_Equation
wherein it states
"The problem is to compute the polar coordinates (r,?) of the planet from
the time since perihelion, t."
The diagram is this one:
http://en.wikipedia.org/wiki/File:Anomalies.PNG
but the labelling of x, y and z is (to me) confusing since
they are named points and not cartesian coordinates;
z is periapsis which I'd label as P[0,0] or P_xy.
Creating points around the red auxiliary circle is of course as
easy as pi; you know how to do that, it is simply the angle M
which increments in regular steps.
Kepler's Equation computes the angle E.
Converting from polar coordinates to cartesian you can see
at a glance that P_x = cos(E).
Once you have P_xyz (z =0, of course) you can use your rotation
matrix to cope with
http://en.wikipedia.org/wiki/File:Orbit1.svg
and calculate velocity - which is simply [this x - last x]/dt
==========================================
=================================================
Your equivalent SR prophecy is: The pencil is really broken, light
speed is sacrosanct. If a star is seen to vary in intensity then it really
is varying in intensity. The variation must be an intrinsic property of
the star.
Some stars puff up and down like blowfish, some play peek-a-boo,
some blow themselves to smithereens and then magically repair
themselves, some give off flares brighter than the star itself.
V 1493 Aql is EXACTLY what one would expect from dT/dt < 0,
that is why I place such importance on it.
This is what YOU asked for:
http://www.androcles01.pwp.blueyonder.co.uk/Doolin'sStar.GIF
The SR prophecy is:
"IN FACT", the star explodes itself up twice, "OBVIOUSLY", "OF COURSE"
because we can see it does. Anyone that doesn't understand that must be
either
stupid or blind.
That is blind faith, not science, not truth, and is the kind of rhetoric one
sees
repeatedly by the ignorant bigots that infest usenet.
Yet: the explanation I've given actually accounts for a double explosion
and the curve between them; and I'm neither stupid nor blind. You are not
stupid but you haven't opened your eyes yet.
The Newtonian model is: Light changes speed and direction, not the pencil
and not the energy output of the star.
You can put the predictions of Nostradamus and St John the Divine
alongside that as well for what use they are. Pale horses ridden by Death
and your newspaper horoscope are not science.
I'm not interested in the wild hallucinations of Einstein but you can play
his silly games if you want to and I'll still continue to call you a fucking
idiot and a sucker. I thought you wanted truth.
==============================================
> Nature doesn't give up her secrets easily and it is not given to Man
> to invent Nature as he chooses. Truth is what it is really about, son.
> You'll get out of it what you put into it. As for me, I'm just a
> grumpy old man with a stent in his aorta causing backache and
> arthritis in his ankle. I'm not expecting to last much longer and
> some people will be glad to see the back of me, but always
> remember this:
You often do come across as grumpy. I'm glad I hadn't just imagined
it.
==============================================
That's because I AM grumpy. Years of fruitless debate with cretins
who keep whining about Lorentz transforms as if they knew anything
about Nature is enough to make anyone irritable. The worst are the
silly pompous schoolmarms of academia who parrot the garbage
they've been indoctrinated with and swallow up expensive grants to
continue with their "research" looking for black holes, bright green
flying elephant's eggs, dork matter, standard model hadrons at the
beginning of the Universe or whatever else they've invented.
I don't go begging for money for my research, I've earned it the
hard way. I've discovered planets further than anyone else and I'm
proud of it, but the bottom line is: the only one it really matters to
is me.
==============================================
> Science is the observation, investigation and explanation of natural
> phenomena, not inventing black holes or time machines and then go
> looking for them, hoping they'll fit our wonderfully stupid theories.
> There are enough mysteries in the universe to uncover without
> creating them.
>
> There are no relativistic computers because computers are logical.
> What kind of lunacy prompted Einstein to say
> the speed of light from A to B is c-v,
> the speed of light from B to A is c+v,
> the "time" each way is the same?
>
I would compare Einstein to a new poster on sci.physics.relativity who
is just starting to grasp the theory and does not know the
thoroughness to which new contributors to the group are humiliated for
a careless phrase. With a good grasp of the theory, his meaning is
perfectly clear, though he clearly switched reference frames in the
middle.
==================================================
You didn't answer the question, but go ahead. Tell me why it is
perfectly clear. Explain (using appropriate equations) how to
program a computer so that
A) If you use c+v you can write:
http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img22.gif
(which is nonsense anyway.)
B) From that you can derive the cuckoo malformations:
http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img53.gif
C) From that you arrive at:
http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img76.gif
which says you cannot use c+v.
D) Goto A).
> Even if you do pay you'll never get time dilation, but you will get
> the appearance of dT/dt < 0 and make a fortune out of it. It's all
> in the presentation. Hulse and Taylor got a Nobel prize out of it.
> http://www.daviddarling.info/encyclopedia/H/HulseTaylor.html
>
Yes, I'm fairly sure I made an error in my original calculation--
either conceptual or mathematical, because I had another look at my
demo from a few years ago and there was evidence that dT/dt < 0 for
the source-dependent speed-of-light. I may have forgotten a
derivative somewhere. I'll look over it again.
==================================================
Yes, I'm absolute certain Einstein made an error in his original
calculation--
either conceptual or mathematical, because I had another look at his
paper from a few years ago and there was V 1493 Aql evidence that
dT/dt < 0 for the source-dependent speed-of-light. He may have forgotten
the Principle of Relativity somewhere. He'll never look over it again, the
old fool is dead and his crank theory was stillborn anyway.
Paul B. Andersen
> Invent a stupid theory. Write a textbook about it. At the
> end of each chapter, write a set of exercices, and call them
> "paradoxes", as if they were not real paradoxes, but miscellaneous
> curiosities that arise from the "Great Theory You Have Invented".
> Once that's done, any real paradox that anyone managed to point
> out would be suitably labeled as "exercice" in the specific
> chapter of your textbook, so that's no a real paradox, but a
> well-defined feature of the "Great Theory You Have Invented".
A scientific theory must be:
1. Consistent.
That means that it is one and only one set of predictions
for each experiment or thought experiment.
2. Falsifiable.
That means that it must be possible to do an experiment
which proves it wrong - if it is wrong.
A theory is proven wrong if its predictions for an experiment
are not consistent with the results of the experiment.
A scientific theory is valid if it is tested by several
experiments and isn't falsified by any.
SR and GR are consistent.
It is not possible to make SR or GR produce more than
one set of predictions for any experiment or thought experiment.
SR and GR are falsifiable.
SR and GR would be proven wrong if their predictions are not
consistent with the result of an experiment.
SR and GR are valid theories.
A high number of experiments are done, testing SR and GR,
and the predictions of the theories have in every case
been consistent with the results of the experiments.
No experiment has falsified SR or GR.
Is there anything in the above you think is wrong?
--
Paul
Jonathan Doolin
> > There are no relativistic computers because computers are logical.
> > What kind of lunacy prompted Einstein to say
> > the speed of light from A to B is c-v,
> > the speed of light from B to A is c+v,
> > the "time" each way is the same?
>
> I would compare Einstein to a new poster on sci.physics.relativity who
> is just starting to grasp the theory and does not know the
> thoroughness to which new contributors to the group are humiliated for
> a careless phrase. With a good grasp of the theory, his meaning is
> perfectly clear, though he clearly switched reference frames in the
> middle.
> ==================================================
> You didn't answer the question, but go ahead. Tell me why it is
> perfectly clear. Explain (using appropriate equations) how to
> program a computer so that
> A) If you use c+v you can write:
> http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img22.gif
> (which is nonsense anyway.)
>
A and B are traveling to the right with A behind B. When the light
transmits from A to B, it has to catch up with B so the velocity of B
is subtracted from the velocity of light to find out how much time the
two take to come together. When the light transmits back from B to A,
A is coming headlong into the transmitted light, so the velocity of A
is added to the velocity of light to find out how much time the two
take to come together. Naturally these two times are NOT equal.
However, when you look at things from the perspective of A or B, the
two times must be equal, because the speed of light for them, should
be the same, coming and going.
> B) From that you can derive the cuckoo malformations:
>
> http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img53.gif
>
> C) From that you arrive at:
> http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img76.gif
>
> which says you cannot use c+v.
>
> D) Goto A).
>
> > Even if you do pay you'll never get time dilation, but you will get
> > the appearance of dT/dt < 0 and make a fortune out of it. It's all
> > in the presentation. Hulse and Taylor got a Nobel prize out of it.
> >http://www.daviddarling.info/encyclopedia/H/HulseTaylor.html
>
> Yes, I'm fairly sure I made an error in my original calculation--
> either conceptual or mathematical, because I had another look at my
> demo from a few years ago and there was evidence that dT/dt < 0 for
> the source-dependent speed-of-light. I may have forgotten a
> derivative somewhere. I'll look over it again.
>
> ==================================================
>
> Yes, I'm absolute certain Einstein made an error in his original
> calculation--
> either conceptual or mathematical, because I had another look at his
> paper from a few years ago and there was V 1493 Aql evidence that
> dT/dt < 0 for the source-dependent speed-of-light. He may have forgotten
> the Principle of Relativity somewhere. He'll never look over it again, the
> old fool is dead and his crank theory was stillborn anyway.> You get what you work for (sometimes).
Ah, don't be an atheist, John. You have an eternal life. Your
grandchildren will benefit from seeds you plant that will not come to
fruition during your mortal lifetime, so live your life as though you
were going to live forever with whatever decisions you make.
Whatever mistakes Einsteien made, I think he either came by them
honestly, or he had his reasons. I don't think Einstein will be too
disappointed if someone finds mistake in his work, as long as we are
pursuing what is good and true. And of course, even if we do pursue
the ultimate truth, and the ultimate goodness, we are all blind
beggars. None of us know what we are doing. Did Judas Iscariot
understand with his heart? Did he do what was right, or should he
have defied prophesy?
I'm going to see if I can remember how to write a program, because I
have an idea in mind for a program that would take in all the
parameters of a distant elliptical orbit and present what should be
seen by the viewer, taking into account the light propagation. A full
presentation should present position, intensity, and frequency. That
could take me more than a month of full time effort, but I probably
would just have to work on it piecemeal. It's probably quite
redundant work anyway; I'm sure a PhD with some programming skills and
some classical mechanics background could do it inside of a week.
Jonathan Doolin
>
> Is that how you did it?
> ===============================================
>
> Wackypedia needs to combine that page with
> http://en.wikipedia.org/wiki/Kepler's_Equation
> wherein it states
> "The problem is to compute the polar coordinates (r,?) of the planet from
> the time since perihelion, t."
>
Indeed. And later the same article defines M = (2*Pi*t/P) and states:
"The catch is that Kepler's equation cannot be rearranged to isolate
E. The function E = f(M) is not an elementary formula, but Kepler's
equation is solved either iteratively by a root-finding algorithm or,
as derived in the article on eccentric anomaly, by an infinite
series."
Androcles
==============================================
I agree:
http://www.androcles01.pwp.blueyonder.co.uk/Smart/tAB=tBA.gif
But your precious "Lorentz" transformations are derived from img22.gif
above and depend on Einstein's absurd claim that he can make them
equal.
Which hat will you pull the rabbit from if that one is empty?
==============================================
However, when you look at things from the perspective of A or B, the
two times must be equal, because the speed of light for them, should
be the same, coming and going.
==============================================
That's Irish blarney. If you are at A or B you cannot detect the light
moving away, you have to take "some frame of reference" wherein
you can determine the times of emission, reflection and reception,
external to A or B so that you can determine tau not equal to t and
derive the cuckoo malformations.
Remember, you are studying for a Masters, you should know
what "linear" means.
"In the first place it is clear that the equations must be linear on account
of the properties of homogeneity which we attribute to space and time." --
Einstein.
He's LYING.
http://www.androcles01.pwp.blueyonder.co.uk/Smart/tAB=tBA.gif
tau(A,0) = 0
tau (B,12) = 6 (= 12/2)
tau (A', 16) = 12 ( = (12+4)/2)
That is NOT linear.
> B) From that you can derive the cuckoo malformations:
>
> http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img53.gif
>
> C) From that you arrive at:
> http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img76.gif
>
> which says you cannot use c+v.
>
> D) Goto A).
>
> > Even if you do pay you'll never get time dilation, but you will get
> > the appearance of dT/dt < 0 and make a fortune out of it. It's all
> > in the presentation. Hulse and Taylor got a Nobel prize out of it.
> >http://www.daviddarling.info/encyclopedia/H/HulseTaylor.html
>
> Yes, I'm fairly sure I made an error in my original calculation--
> either conceptual or mathematical, because I had another look at my
> demo from a few years ago and there was evidence that dT/dt < 0 for
> the source-dependent speed-of-light. I may have forgotten a
> derivative somewhere. I'll look over it again.
>
> ==================================================
>
> Yes, I'm absolute certain Einstein made an error in his original
> calculation--
> either conceptual or mathematical, because I had another look at his
> paper from a few years ago and there was V 1493 Aql evidence that
> dT/dt < 0 for the source-dependent speed-of-light. He may have forgotten
> the Principle of Relativity somewhere. He'll never look over it again, the
> old fool is dead and his crank theory was stillborn anyway.
> You get what you work for (sometimes).
Ah, don't be an atheist, John.You have an eternal life. Your
grandchildren will benefit from seeds you plant that will not come to
fruition during your mortal lifetime, so live your life as though you
were going to live forever with whatever decisions you make.
====================================================
What, you want me to a gullible, bullshitting, dishonest fool like you?
Fuck you, Doolin, I'm a realist, a mathematician, a logician and a
scientist. Don't come to me with any emotional appeals, this is
mathematics.
====================================================
Whatever mistakes Einsteien made, I think he either came by them
honestly, or he had his reasons.
==================================================
I don't believe you. Provide some evidence that you think. You
behave like a trained ape; monkey see, monkey do.
==================================================
I don't think
===========
Ah, so I was right. I recommend that you try it, you are quite capable
of thinking. Perhaps you are just lazy. The more you do it the easier it
will get.
==================================================
Einstein will be too
disappointed if someone finds mistake in his work, as long as we are
pursuing what is good and true.
===================================================
As I said... gullible. In the world I live in people go to prison for making
"mistakes", especially hucksters; but only if they get caught.
There is nothing new under the Sun.
"Ptolemy was the most influential of Greek astronomers and geographers of
his time. He propounded the geocentric theory that prevailed for 1400
years."
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Ptolemy.html
Newton minces no words: "Ptolemy is not the greatest astronomer of
antiquity, but he is something still more unusual. He is the most successful
fraud in the history of science."
http://www.time.com/time/magazine/article/0,9171,919182,00.html
What are we going to have, 1400 years of Einstein's idiocy,
the velocity of light plays the part of an infinitely great velocity?
Einstein was a FRAUD and you are a sucker! Wake up.
================================================
And of course, even if we do pursue
the ultimate truth, and the ultimate goodness, we are all blind
beggars. None of us know what we are doing. Did Judas Iscariot
understand with his heart? Did he do what was right, or should he
have defied prophesy?
I'm going to see if I can remember how to write a program, because I
have an idea in mind for a program that would take in all the
parameters of a distant elliptical orbit and present what should be
seen by the viewer, taking into account the light propagation. A full
presentation should present position, intensity, and frequency. That
could take me more than a month of full time effort, but I probably
would just have to work on it piecemeal. It's probably quite
redundant work anyway; I'm sure a PhD with some programming skills and
some classical mechanics background could do it inside of a week.
================================================
It took me more than a week - but I had nobody to advise me.
My nearest equivalent (Vladimir Sekerin) was behind the Iron Curtain
and incommunicado at the time.
http://www.datasync.com/~rsf1/binarie2.htm
It's clear Sekerin came to the same conclusions I did, but via a different
route. When (if) you get out of bed and quite dreaming so will you.
Androcles
=======================================
Yep. Since there is convergence one can choose an epsilon such that
the difference is small enough to quit adding another term in the series.
That's no different to adding terms to find exp(x) or sin(x) from a
Taylor series.
You can never get to an exact value but you can be as close as you
choose.
You can go further into it here if you are curious:
http://mathworld.wolfram.com/KeplersEquation.html