Shubee
http://www.everythingimportant.org/relativity/special.pdf
http://en.wikipedia.org/wiki/Lorentz_force#Lorentz_force_and_Faraday.27s_law_of_induction
Sue...
>
> Shubee
Do we have to search this for the answer, Suzy? SNO-O-O-O-RE .....
I don't think you'll find the answer there - it concerns the Lorentz
force - not the Lorentz transformation. The answer to the OP is that
the Lorentz transformation is enough if both systems are inertial (no
accelerations or strong gravity fields).
It is no more than knowing the rules of chess before
offering comment on some particular strategy.
http://farside.ph.utexas.edu/teaching/em/lectures/lectures.html
http://web.mit.edu/8.02t/www/802TEAL3D/visualizations/light/index.htm
Sue...
Well, that lets me out. I'm just a draughts champion! :-)
>
> http://farside.ph.utexas.edu/teaching/em/lectures/lectures.htmlhttp://web.mit.edu/8.02t/www/802TEAL3D/visualizations/light/index.htm
>
> Sue...
This wording ("time dilation *for* a clock-carrying traveler?")
reveals a definitely sad amount of ignorance.
>
> Shubee
> http://www.everythingimportant.org/relativity/special.pdf
Relevant equation:
Dt' = gamma ( Dt - v Dx )
Assumption:
A clock is at rest in the unprimed frame, i.o.w.
Dx = 0
Result:
Dt' = gamma Dt
whence
Dt' > Dt
meaning that in the unprimed frame the time between two ticks of
the (moving) clock is dilated with respect to the time between those
ticks as measured in the rest frame of the clock.
General conclusion:
Physics is not "merely an application of algebra".
Dirk Vdm
Deletion must be added, time dilation doesn't happen.
Why did Einstein 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?
"Easy: he did NOT say that." - cretin harald.vanlin...@epfl.ch
According to moron van lintel, Einstein did not write the equation he wrote.
According to xxein:
It is an artefactual/superficially imposed yin-yang of sorts.
According to Lamenting Shubert:
Why do you want to know?
" 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."
-- cretin Jimmy Black fml...@organization.edu.
According to the imbecile Jimmy Black, Einstein did not write the equation
he wrote.
If there is no force in either system then there is nothing
to affect a clock.
<<...it is impossible to perform a physical
experiment which differentiates in any fundamental sense
between different inertial frames. By definition, Newton's
laws of motion take the same form in all inertial frames.
Einstein generalized this result in his special theory of
relativity by asserting that all laws of physics take
the same form in all inertial frames. >>
http://farside.ph.utexas.edu/teaching/em/lectures/node108.html
Sue...
I noticed that you repeated the same definitely sad amount of
ignorance below.
> > Shubee
> > http://www.everythingimportant.org/relativity/special.pdf
>
> Relevant equation:
> Dt' = gamma ( Dt - v Dx )
>
> Assumption:
> A clock is at rest in the unprimed frame, i.o.w.
> Dx = 0
>
> Result:
> Dt' = gamma Dt
> whence
> Dt' > Dt
> meaning that in the unprimed frame the time between two ticks of
> the (moving) clock is dilated with respect to the time between those
> ticks as measured in the rest frame of the clock.
>
> General conclusion:
> Physics is not "merely an application of algebra".
Correct, which means that we should ignore your ignorant application
of algebra and complete misunderstanding of what the Lorentz
transformation implies.
Shubee
http://www.everythingimportant.org/relativity/special.pdf
This is what you get for trying to teach Shitbert :-)
> If there is no force in either system then there is nothing
> to affect a clock.
>
> <<...it is impossible to perform a physical
> experiment which differentiates in any fundamental sense
> between different inertial frames. By definition, Newton's
> laws of motion take the same form in all inertial frames.
> Einstein generalized this result in his special theory of
> relativity by asserting that all laws of physics take
> the same form in all inertial frames. >>http://farside.ph.utexas.edu/teaching/em/lectures/node108.html
You are assuming that the Lorentz transformation implies the principle
of relativity, which is a false assumption.
Shubee
So how would you prove that the Lorentz transformation implies time
dilation without presupposing more than just the Lorentz
transformation?
Shubee
Dirk Vdm
HUH.
Teach Shitbert?
Utterly impossible.
Dirk Vdm
You absolutely need to add this "pearl", Juanshito "correcting" Eric:
http://groups.google.com/group/sci.physics.relativity/msg/5cd8b0421f4f2b4a
Pay attention to:
"The third mistake being his confusion between the Lagrangian and the
energy in special relativity. Note that Eric *multiplies* by the
factor
(1 - (v^2/ c^2))
instead DIVIDING by it."
The "master" at his best :-)
The word "Lorentz" is not even on the page.
<<A Lorentz transformation or any other coordinate
transformation will convert electric or magnetic
fields into mixtures of electric and magnetic fields,
but no transformation mixes them with the
gravitational [inertial by equivalence] field. >>
http://www.aip.org/pt/vol-58/iss-11/p31.html
http://scitation.aip.org/journals/doc/PHTOAD-ft/vol_58/iss_11/31_1.shtml
Sue...
>
> Shubee
Yes, I had seen this, but alas, it is insufficiently self-explaining to
serve as an entry.
And besides, he should have multiplied with the square root
of that factor :-)
Dirk Vdm
Edward Green said it best: None
Ben Green (no relation)
OK U Ben,
Please answer the same question I asked Edward Green:
So how would you prove that the Lorentz transformation implies time
dilation without presupposing more than just the Lorentz
transformation?
Shubee
http://www.everythingimportant.org/relativity/special.pdf
Calculate how fast a clock ticks using the Lorentz transformation.
Why is this a mystery?
>
> Shubeehttp://www.everythingimportant.org/relativity/special.pdf
It is not a mystery at all,
http://www.hyperdeath.co.uk/spaceman/message.html
:)
--
James M Driscoll Jr
Spaceman
Sometimes one wonders whether he is just pretending to be
such an infinite dope - just to discredit the other dopes
around here.
Amazing.
Dirk Vdm
He likes to be reminded on a daily basis :-)
OK Shitbert,
This has been going on too long.
There is no time dilation for the clock carrying traveller.
So you are asking a stupid question that reflects your level of (mis)
understanding of SR.
There is time dilation for any DIFFERENT observer IN MOTIOn wrt the
traveller that is carrying the clock.
As you have been told by several others, the time dilation can be
calculated directly by the sole application of the Lorentz tranforms:
t=gamma(\tau-\zeta*v/c^2)
t=coordinate time
\tau=proper time (on the traveller clock)
\zeta=proper distance
So:
For \dzeta=0
dt=gamma*d(\tau)
dt=\
> Sometimes one wonders whether he is just pretending to be
> such an infinite dope - just to discredit the other dopes
> around here.
> Amazing.
>
> Dirk Vdm
For my next trivial yet impossible to believe theorem at
http://www.everythingimportant.org/relativity/special.pdf I shall
start with the Lorentz transformation and the clock synchronization
scheme it implies and then reset all clocks in all but one inertial
frames of reference. From there I shall change the definition of
distance in all but that one special inertial frame by a suitable
scaling factor. I shall also fiddle with clock rates by applying a
similar suitable change of time scale and thus finally arrive at the
traditional and easy to understand Galilean group of transformations.
This will prove that the Lorentz transformation alone doesn't imply
time dilation.
Shubee
Doesn't anyone remember me calling this result the most entertaining
exploit in the history of physics?
Shubee
http://www.everythingimportant.org/relativity/special.pdf
> This will prove that the Lorentz transformation alone
> doesn't imply time dilation.
Shitbert, in your case it only implies that you are a Shithead.
Stop spamming sci.math, you have nothing to contribute.
Sorry Shooby, modern special relativity is not defined by either the
Lorentz transformation or clock synchronization. In fact, no mention
of light is made at all.
You know this of course, but that prevents you from playing semantic
games that purposefully confuse the issue.
>> Relevant equation:
>> Dt' = gamma ( Dt - v Dx )
>>
>> Assumption:
>> A clock is at rest in the unprimed frame, i.o.w.
>> Dx = 0
>>
>> Result:
>> Dt' = gamma Dt
>> whence
>> Dt' > Dt
>> meaning that in the unprimed frame the time between two ticks of
>> the (moving) clock is dilated with respect to the time between those
>> ticks as measured in the rest frame of the clock.
>>
>> General conclusion:
>> Physics is not "merely an application of algebra".
>
> Correct, which means that we should ignore your ignorant application
> of algebra and complete misunderstanding of what the Lorentz
> transformation implies.
Shubee, did you try it derive it yourself? I usually need to
start with a specific example, and work toward something more
general.
Start with two coordinate systems in standard configuration.
In the one defined as at rest, put a clock at x=0. Each tick
of the clock marks a second in the rest frame, and the Lorentz
transform will map the tick events to a time (and place, but
that's not the question here) in the moving frame, which
tells us how fast the clock is running in the moving frame.
Dirk Vdm's solution is more general. Note that his first
equation is simply the derivative of Lorentz transform
equation for t'.
http://en.wikipedia.org/wiki/Lorentz_transformation
--
--Bryan
Yes, but is it allowed to do all this fiddling?
(Written after posting a worked example.)
Uncle Ben
Bryan,
I have derived the Lorentz transformation from the weakest axiom set
possible. Trust me, I know that the Lorentz transformation says almost
nothing by itself.
See http://www.everythingimportant.org/relativity/special.pdf
Shubee
UB,
My derivation of the Lorentz transformation is from the weakest axiom
set possible. For example, my approach doesn't presuppose any
significant conditions on the comparative distance and time scales for
different frames of reference. So why can't I invoke an arbitrary
change of scale afterwards?
http://www.everythingimportant.org/relativity/special.pdf
Shubee
... part of your inferior brain?
Yes, we know.
Dirk Vdm
Let's not go there. You'll just start calling people STC's,
and the derivation you asked about here is different.
How far did you get on this one? What's the first step that
isn't clear?
> Trust me, I know that the Lorentz transformation says almost
> nothing by itself.
Why did you ask the question if you did not want the answer?
--
--Bryan
Just do an example:
Suppose a traveler is in a spaceship moving at 0.1c w.r.t. a space
platform. Let the traveler start smoking a cigarette at t=0. Let's
suppose he is at the origin x=0 with respect to his own frame of
reference. Suppose he takes 100 seconds to smoke the cigarette, w.r.t.
his own frame of reference.
With respect to the space platform, the traveler is moving at 0.1 c,
so their description of his smoking will be a bit different. W.r.t.
the platform, the traveler's clock runs slow, so his 100 seconds
should be more w.r.t. the space platform's faster clock. Let's see
how much more:
Let the traveler's frame be S and the space platforms frame be S'. By
the Lorentz transformation,
t' = gamma(t-xv/c*c)
t=100, x=0, v=-0.1c, c=1
t' = 1.01 * 100
t' = 101.
W.r.t. the space platform, he takes 101 seconds to smoke his
cigarette. His clock counts only 100 seconds, so his clocks must run
slower than the space platform's clock.
Uncle Ben
Why don't you ask a mathematician? You might get an answer, and if you
do you will automatically assume it is correct.
PD
Should be 100.5 seconds. Forgot the sq. root.
Then why do arbitrary hyperbolic rotations preserve a particular
speed?
This depends upon what assumptions accompany the Lorentz transform. If
one merely assumes the usual schoolbook equations, then one must add a
large number of assumptions/definitions relating to what the symbols
mean and how they are applied.
Once one has sufficient structure to establish that the LT relates
Minkowski coordinates between two inertial frames, and how the symbols
in the LT map to properties of those frames, then the only assumptions
required are related to the specific physical situation you have in
mind, and to what you mean by "time dilation for a clock-carrying traveler".
The usual meaning of "time dilation" is the difference in
measured rates among clocks at rest in different inertial
frames. But your "carried by a traveler" suggests you
probably have something else in mind, such as a twin
scenario. Note that the twin scenario does NOT display
"time dilation", it displays a difference in elapsed
proper times for clocks that travel on different paths.
This is analogous to the distinction between the slope of
a line and its path length -- quite different concepts.
But still for a twin scenario, to compute the difference in elapsed
proper times with the above structure it only requires assumptions
related to the specific physical situation you have in mind.
Oh yes, to compute anything one must also assume that the analyst
understands how to apply the Lorentz transform. Unfortunately, around
here that can be a rather shaky assumption.
Tom Roberts
PD,
I already know the answer. Here is a second unanswerable question.
Isn't it amusing that physicists are able to pontificate eloquently
about the specific nature of physical reality and believe that they
are about to figure out how the universe exploded into existence out
of nothingness but they are totally confused about fundamental
questions in special relativity?
Shubee
Igor,
Why is my arbitrarily elementary result too unfathomable for you? Are
you a physicist?
Shubee
http://www.everythingimportant.org/relativity/special.pdf
I take it the first one was an unanswerable question, and yet you know
the answer to it.
Did a mathematician give you an answer yet?
>
> Isn't it amusing that physicists are able to pontificate eloquently
> about the specific nature of physical reality and believe that they
> are about to figure out how the universe exploded into existence out
> of nothingness but they are totally confused about fundamental
> questions in special relativity?
You're right. That's unanswerable. So I don't know why you'd ask it.
Did a mathematician answer this one for you, too?
>
> Shubee
You must have forgotten. I've explained it to you before.
I simply enjoy using all the weapons in my arsenal "for pulling down
strongholds, casting down arguments and every high thing that exalts
itself against the knowledge of God" (2 Corinthians 10:4-5). NKJV.
Shubee
Shooby's arsenal contains but one weapon - the weapon of choice of
just about every SPR crackpot - delusion.
Normal people use their weapons on their adversaries, Shooby, not on
themselves. Don't stop though, we really like watching you punish the
establishment by banging yourself over the head.
Yes, I know. You feel it is critical that physicists be taken down a
peg, because they are usurping that which belongs to God. You do this
by attempting your own physical theory.
But on this theme, has it not crossed your mind that God may be
delighted in our discovering the elegance and beauty of his design,
and that he left it precisely so that we might be able to gradually
uncover it?
How internally conflicted ARE you, Shubee?
PD
Yes, and that physicists should stop debasing themselves.
http://www.bnl.gov/community/Tours/TYSaDTW.asp
http://www.bnl.gov/community/Tours/EinsteinPics/Einsteine.jpg
http://www.physicstoday.org/vol-58/iss-7/images/devine_einstein.mp3
> You do this by attempting your own physical theory.
I merely enjoy removing from special relativity everything that is
confused, unnecessary and not amenable to experimental verification.
http://www.everythingimportant.org/relativity/special.pdf
> But on this theme, has it not crossed your mind that God may be
> delighted in our discovering the elegance and beauty of his design,
You believe that physicists have discovered beautiful physical law. I
assert that physicists are in love with the Frankenstein corpse.
Shubee
> Start with two coordinate systems in standard configuration.
> In the one defined as at rest, put a clock at x=0. Each tick
> of the clock marks a second in the rest frame, and the Lorentz
> transform will map the tick events to a time (and place, but
> that's not the question here) in the moving frame, which
> tells us how fast the clock is running in the moving frame.
Obviously not. The first tick of the clock in the "rest frame" is
labeled as an event in a moving frame by the point x1' and by a clock
at x1' that notes the time of that event as t1'. The second tick of
the clock in the "rest frame" is labeled by the event at a different
point x2' in the moving frame and the time of that event is recorded
by the clock at the point x2'.
Your whole argument is based on the concept of the simultaneity of
spatially separated clocks, which is fallacious reasoning.
Shubee
Of course the Lorentz transformation can be used (and is used) for other
purposes than what the symbols stand for. However, the t and t' stand for
clock time in two Newtonian coordinate systems that move relative to each
other with the X axes coinciding. It is standard for basic physics textbooks
to show that for dx' = 0, dt = gamma*dt', and that this is called "time
dilation".
Cheers,
Harald
Bravo Honest Roberts! If you continue to develop this verbiage, soon
Einstein zombie world will start singing "Divine Roberts":
No-one’s as dee-vine as Thomas Roberts
Not Maxwell, Curie, or Bohr!...etc:
http://www.bnl.gov/community/Tours/EinsteinPics/Einsteine.jpg
http://www.haverford.edu/physics-astro/songs/divine.htm
http://www.physicstoday.org/vol-58/iss-7/images/devine_einstein.mp3
However, Honest Roberts, there is a grand secret betwen hypnotists in
Einstein criminal cult: in 1918 Divine Albert wrote a paper about the
twin paradox which was so silly that Einsteinians, both silly and
clever, are forbidden to refer to it. Yet analyses of Divine Albert's
1918 very silly paper do exist:
http://www.ias.ac.in/currsci/dec252005/2009.pdf
"On Einstein’s resolution of the twin clock paradox" by C. S.
Unnikrishnan
I think Honest Roberts it is time for you to demonstrate the power of
your verbiage: you just analyse Divine Albert's 1918 very silly paper,
prove it is in fact very clever and then the world, both relativists
and anti-relativists, immediately starts singing "Divine Roberts". I
will be singing too Honest Roberts:
Pentcho Valev (after Honest Roberts has proved that Divine Albert's
1918 very silly paper is very clever): "No-one’s as dee-vine as Thomas
Roberts not Maxwell, Curie, or Bohr!..."
Pentcho Valev
pva...@yahoo.com
> > So how would you prove that the Lorentz transformation implies time
> > dilation without presupposing more than just the Lorentz
> > transformation?
>
> Of course the Lorentz transformation can be used (and is used) for other
> purposes than what the symbols stand for. However, the t and t' stand for
> clock time in two Newtonian coordinate systems that move relative to each
> other with the X axes coinciding. It is standard for basic physics textbooks
> to show that for dx' = 0, dt = gamma*dt', and that this is called "time
> dilation".
Harald,
What I'm getting at is a trivial yet impossible to believe theorem
that I wish to include in my paper on special relativity. I shall
start with the Lorentz transformation and the clock synchronization
scheme it implies and then reset all clocks in all but one inertial
frames of reference. From there I shall change the definition of
distance in all but that one special inertial frame by a suitable
scaling factor. I shall also fiddle with clock rates by applying a
similar suitable change of time scale and thus finally arrive at the
traditional and easy to understand Galilean group of transformations.
This will prove that the Lorentz transformation alone doesn't imply
time dilation.
Shubee
http://www.everythingimportant.org/relativity/special.pdf
Pentcho,
I freely admit that Einstein's resolution of the twin paradox was
silly and incompetent.
Shubee
http://www.everythingimportant.org/relativity/special.pdf
Forget it.
You don't know what the variables mean in that transformation.
> and the clock synchronization
> scheme it implies and then reset all clocks in all but one inertial
> frames of reference.
See?
No, of course you don't see ;-)
My point entirely.
Dirk Vdm
If only Poncho would engage in a conversation with you.
*That* would be interesting.
Come on Pispo, go for it!
Dirk Vdm
> Pentcho Valev
> pva...@yahoo.com
>
http://bip.cnrs-mrs.fr/bip10/valevfaq.htm
--
kd
I go to great lengths to explain what the variables mean in
http://www.everythingimportant.org/relativity/special.pdf
You obviously can't defend your incompetence,
http://www.everythingimportant.org/relativity/moortel.fumble.htm
so you throw shit to hide your ignorance.
You are a smelly, shit-throwing chimpanzee.
Shubee
>
>http://www.ias.ac.in/currsci/dec252005/2009.pdf
>"On Einstein’s resolution of the twin clock paradox" by C. S.
>Unnikrishnan
>
From there:
Planck’s assertion2 that there is no physical method
of measurement of the velocity of motion through space
is made void by the various markers available in cosmology,
especially the dipole anisotropy of the CMBR.
end cit.
When did Planck live?
When was CMBR measured?
How good are those measurements?
How do we calibrate our speedometers then?
Interstellar matter does have -what- influence or none?
Where are the "various markers available"?
What are our coordinates in the Universe?
Where is the Universe Point Zero ?
Where can I buy a "Universe Positioning System"?
Please Pentcho, ask Unnikrishnan.
w.
I will wait to read your work [#], but my current understanding is that
is not true.
ds = ds'
or, dividing by c,
d\tau = d\tau'
((\sqrt (1 - (v^2/c^2))) * dt) = ((\sqrt (1 - (v'^2/c^2))) * dt')
If (v' = 0) then
((\sqrt (1 - (v^2/c^2))) * dt) = dt'
This formula for time dilation is subjected to the validity of the LT,
which is not universal.
[#] Is your work somewhat related to some kind of difficulty when passing
from spacetime (x,t) to clock paths (x(t),t)?
--
Center for CANONICAL |SCIENCE)
http://canonicalscience.org
I don't care about Unnikrishnan. Unnikrishnan is innocent. He did not
destroy rationality in science. Einstein did (rather, finished what
Clausius had already started):
http://www.nature.com/nature/journal/v433/n7023/full/433218a.html
John Barrow in the journal Nature: "Einstein restored faith in the
unintelligibility of science. Everyone knew that Einstein had done
something important in 1905 (and again in 1915) but almost nobody
could tell you exactly what it was. When Einstein was interviewed for
a Dutch newspaper in 1921, he attributed his mass appeal to the
mystery of his work for the ordinary person: "Does it make a silly
impression on me, here and yonder, about my theories of which they
cannot understand a word? I think it is funny and also interesting to
observe. I am sure that it is the mystery of non-understanding that
appeals to them...it impresses them, it has the colour and the appeal
of the mysterious."
http://www.aapps.org/archive/bulletin/vol15/15-5/15_5_p2p3%7F.pdf
Pentcho Valev
pva...@yahoo.com
> Dono <sa...@comcast.net> wrote in message
> 2c6f483d-0f41-4bb0...@34g2000hsf.googlegroups.com
>>
>> You absolutely need to add this "pearl", Juanshito "correcting" Eric:
>>
>> http://groups.google.com/group/sci.physics.relativity/
msg/5cd8b0421f4f2b4a
>>
>> Pay attention to:
>>
>> "The third mistake being his confusion between the Lagrangian and the
>> energy in special relativity. Note that Eric *multiplies* by the factor
>>
>> (1 - (v^2/ c^2))
>>
>> instead DIVIDING by it."
>>
>> The "master" at his best :-)
>
> Yes, I had seen this, but alas, it is insufficiently self-explaining to
> serve as an entry.
Hum!
> And besides, he should have multiplied with the square root of that
> factor :-)
One of problems is that Dono likes to truncate the message. The last part
is
(\blockquote
instead dividing by it. According to *Eric* when a particle travel to
energies close to c its energies vanishes...
)
It is obvious, that I am referring to division by the factor of velocity
(with the square root of course) in the expression of the *Energy*.
you know
E(Eric) = -mc^2 * [1 - v^2/ c^2 ]
is wrong and, of course, Eric latter
E(Eric) = - mc^2 [1 - v^2 / c^2 ]^1/2
containing the square root continues being wrong, because the velocity
factor may be dividing *not* multiplying.
The other problem is that only Dono and Eric wrote next Lagrangian even
if Dono tries to lie about that.
http://sci.tech-archive.net/Archive/sci.physics.relativity/2008-07/
msg00824.html
In that text you go to great lengths to demonstrate what an
infinite imbecile you are :-)
Dirk Vdm
He also likes to remind us to remind him on a daily basis ;-)
Dirk Vdm
You are lying, Shito :-)
You are so comical when you try to weasel out of your blunders :-)
Thank you Juan. Your skepticism encourages me to write out the
details.
> [#] Is your work somewhat related to some kind of difficulty when passing
> from spacetime (x,t) to clock paths (x(t),t)?
Nope. My paper is devoted to removing from special relativity
everything that is confused, unnecessary and not amenable to
experimental verification.
Shubee
http://www.everythingimportant.org/relativity/special.pdf
Please don't engage the chimpanzees on your topic in my thread. You
have your own thread for that.
Shubee
Should not have used the -v switch on that grep.
Everything you wrote is confused, unnecessary, and not amenable to
When did I ever say it was the energy?
>> It is obvious, that I am referring to division by the factor of
>> velocity (with the square root of course) in the expression of the
>> *Energy*.
>>
>> you know
>>
>> E(Eric) = -mc^2 * [1 - v^2/ c^2 ]
>>
>> is wrong and, of course, Eric latter
>>
>> E(Eric) = - mc^2 [1 - v^2 / c^2 ]^1/2
>>
>> containing the square root continues being wrong, because the velocity
>> factor may be dividing *not* multiplying.
>>
>>
>
(...)
I already explained to you that the velocity factor may be *dividing* in
the energy (*not* multiplying as you claim) because otherwise
E(v=c) = 0
which is the nonsense you and Eric continue to promote.
I already corrected this specific mistake from you in
http://groups.google.com/group/sci.physics.relativity/msg/d952ddaeb7f35777
where I wrote
(\blockquote
[...] for obtaining the energy Dono "MULTIPLIES" by sqrt(1-(v/c)^2)
and finally give a total "negative" sign Ha ha ha ha ha ha ha.
)
Dono, you may continue to confuse the energy and the Hamiltonian with the
Lagrangian just as you did before
http://sci.tech-archive.net/Archive/sci.physics.relativity/2008-07/
msg00824.html
I will say again, you are wrong "H is not L" and "E is not L".
>> It is obvious, that I am referring to division by the factor of
>> velocity (with the square root of course) in the expression of the
>> *Energy*.
>>
>> you know
>>
>> E(Eric) = -mc^2 * [1 - v^2/ c^2 ]
>>
>> is wrong and, of course, Eric latter
>>
>> E(Eric) = - mc^2 [1 - v^2 / c^2 ]^1/2
>>
>> containing the square root continues being wrong, because the velocity
>> factor may be dividing *not* multiplying.
>
> When did I ever say it was the energy?
Are lying again crackpot?
You wrote
(\blockquote
> But expressing a Hamiltonian as a function of velocity was only one of
> Eric mistakes.
I didn't bother writing the Hamiltonian in the correct set of
generalized coordinates, instead I left it be because IT IS SO FUCKING
OBVIOUS and it was irrelevant to my point.
But since you are pitching a shitfit over it, here: v = p/m --> H = -
mc^2 [1 - p^2 / (mc)^2 ]^1/2
)
and also
(\blockquote
> *They* sure us that Hamiltonian is negative
> H(Eric) = -mc^2 * [1 - v^2/ c^2 ].
With a ^1/2...
)
http://groups.google.com/group/sci.physics.relativity/msg/d8b3c42f450091d8
I.e. *you* wrote the next NONSENSE
E = - mc^2 [1 - v^2 / c^2 ]^1/2
> I freely admit that Einstein's resolution of the twin paradox was
> silly and incompetent.
>
> Shubee
[snip more crap]
1) Fucking imbecile
2) Experimental constraints on Special Relativity
<http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html>
3) Fucking imbecile
4) Google
"twin paradox" 93,800 hits
5) Fucking imbecile
6) You are an ignorant perseverative ass,
The ratio by which the twins have aged at the end when they are back
together again is the same in all reference frames:
ratio = sqrt(t^2 - x^2 - y^2 - z^2)/t (with units of c=1)
Inertial frames with relative *velocities* pursue different paths
through spacetime. No clock anomaly is apparent in any of them until
clocks are compared (by all being local when you do it, initial
calibration then experiment). The situation is NOT symmetric.
Past acceleration is irrelevant to the running of present clocks but
not to the mixture of space and time in the reference frame that said
clocks measure. You cannot synchronize clocks except by having them
local. If they are local at the start, you can tell who was naughty
thereafter without measuring acceleration.
Given three identical clocks that are off (a state of not running, or
of not even having been fabricated) and zeroed. Each clock has/will
have a very short toggle jiggger switch sticking out. We load them (or
their parts, or ore and a smelter and a machine shop) in individual
spaceships and set up the experiment.
CLOCK 1: That's our clock. It sits stationary in our inertial
reference frame with a little jigger sticking out. Touch the jigger
and the "off" state becomes "on" or the "on" state becomes "off."
Clock 1 is "off." Or we can build it from parts just before we need
it, and in the "off" state, zeroed.
CLOCK 2: In a spaceship traveling at 0.999c relative to our inertial
frame of reference. Clock 2 is "off." It was built after all
acceleration ceased, and set to zero. It skims past Clock 1 (our
clock), the jiggers touch, both Clocks 1 and 2 are now "on" and
locally synchronized by touching. Elapsed time accumulates in each
one. The situation is NOT symmetric!
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.
Clock 3 is zeroed and "off." It was built after all acceleration
ceased, and set to zero.
Some arbitrary time after Clocks 1 and 2 synchronize and turn "on" by
touching, Clocks 2 and 3 brush past each other, touching jiggers.
Clock 2 is now "off," Clock 3 is now "on." Write down the elapsed time
in now "off" Clock 2, then smash the clock with a sledgehammer. Or
melt it down, or toss it over the side. The spaceship with Clock 3 is
returning back over the path taken by the spaceship with Clock 2.
CLOCK 1: That's our clock. It sits stationary in our inertial
reference frame with a little jigger sticking out. Clock 3 rushes
past, jiggers touch. Clocks 3 and 1 are now off. All clocks are off.
No clock has accelerated while "on" or even while existing. Write down
elapsed times, smash each clock with a sledgehammer. Or melt them
down, or toss them.
BOTTOM LINE: Get all three slips of paper together... Accelerate as
you need. Or send all the results to all three folks by radio and
never decelerate. All clocks have been smashed, melted, tossed. Their
elapsed times were written down. The numbers on the papers won't
change when you accelerate or broadcast the data.
Finally.... compare elapsed times. Elapsed time #2+#3 does not equal
#1, the local stationary reference frame summation. The sum of #2+#3
elasped time is only about 4.5% that than of #1's accumulated elapsed
time. You have the Twin Paradox (Triplets) without any running clock
having been accelerated - or having even existed during acceleration
up or down.
7) Fucking imbecile
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2
>
> CLOCK 2: In a spaceship traveling at 0.999c relative to our inertial
> frame of reference. Clock 2 is "off." It was built after all
> acceleration ceased, and set to zero. It skims past Clock 1 (our
> clock), the jiggers touch, both Clocks 1 and 2 are now "on" and
> locally synchronized by touching. Elapsed time accumulates in each
> one. The situation is NOT symmetric!
<< Note that $K$ at $P$ is also independent of the
choice of standard coordinates in $S$ and $S'$.
Since the frames are Euclidian, the values of
$dx^2 + dy^2 +dz^2$ and $dx'^2+dy'^2 + dz'^2$
relevant to $P$ and $Q$ are independent of the
choice of axes. Furthermore, the values of
$dt^2$ and $dt'^2$ are independent of the choice
of the origins of time. Thus, without affecting
the value of $K$ at $P$, we can choose coordinates
such that $P=(0,0,0,0)$ in both $S$ and $S'$.
Since the orientations of the axes in $S$ and $S'$
are, at present, arbitrary, and since inertial
frames are isotropic, the relation of $S$ and $S'$
relative to each other, to the event $P$, and to
the locus of possible events $Q$, is now
completely symmetric. >>
http://farside.ph.utexas.edu/teaching/em/lectures/node109.html
Sue...
And what does your signature and Einstein's incompetence have to with
experimental constraints on special relativity?
> 3) Fucking imbecile
> 4) Google
> "twin paradox" 93,800 hits
> 5) Fucking imbecile
Likewise, what does your signature and Einstein's incompetence have to
with google hit results?
> 6) You are an ignorant perseverative ass,
This is the first time in my life that I mentioned Einstein's
inability to resolve the twin paradox. If not believing in your god
makes me an ignorant ass, so be it.
http://www.bnl.gov/community/Tours/TYSaDTW.asp
http://www.bnl.gov/community/Tours/EinsteinPics/Einsteine.jpg
http://www.physicstoday.org/vol-58/iss-7/images/devine_einstein.mp3
Shubee
> 1) Fucking imbecile
> 2) Experimental constraints on Special Relativity
>
> <http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments....>
Each of these tests covers a small piece of SR. <shrug> Not a single
one of these tests addresses the issue that is the twin’s paradox.
> 3) Fucking imbecile
> 4) Google
> "twin paradox" 93,800 hits
Google “god”. 667,000,000 hits. <shrug>
> 5) Fucking imbecile
> 6) You are an ignorant perseverative ass,
<shrug>
> The ratio by which the twins have aged at the end when they are back
> together again is the same in all reference frames:
>
> ratio = sqrt(t^2 - x^2 - y^2 - z^2)/t (with units of c=1)
So, the ratio is sqrt(1 – v^2 / c^2). There is nothing significant.
<shrug>
> Inertial frames with relative *velocities* pursue different paths
> through spacetime. No clock anomaly is apparent in any of them until
> clocks are compared (by all being local when you do it, initial
> calibration then experiment). The situation is NOT symmetric.
The Lorentz transform is always symmetric even if v is not constant.
<shrug>
> Past acceleration is irrelevant to the running of present clocks but
> not to the mixture of space and time in the reference frame that said
> clocks measure. You cannot synchronize clocks except by having them
> local. If they are local at the start, you can tell who was naughty
> thereafter without measuring acceleration.
The observed time dilation of the other is mutually identical. As
long as all the moving parties never meet again, relative simultaneity
holds. However, when they meet again at anyone particular frame of
reference, sh*t is going to hit the fan.
Nice scenario you have come up with. Let’s see if your conclusion
abides by the Lorentz transform.
> Finally.... compare elapsed times. Elapsed time #2+#3 does not equal
> #1, the local stationary reference frame summation. The sum of #2+#3
> elasped time is only about 4.5% that than of #1's accumulated elapsed
> time.
To discuss this issue thoroughly. Allow me to define the following.
** T1 = Total elapsed time of clock 1
** T2 = Total elapsed time of clock 2
** T3 = Total elapsed time of clock 3
** T0 = Elapsed time of clock 1 when 2 and 3 connects
** B2 c = Speed of 2 as observed by 1
** B3 c = Speed of 3 as observed by 1
Thus, we have
T1 – T0 = Elapsed time of clock 1 from T0
when 3 and 1 connects
Writing down the equations, from 1’s point of view, we have
** T = T2 / sqrt(1 – B2^2)
** T1 – T = T3 / sqrt(1 – B3^2)
From 2’s point of view, we have
** T2 = T / sqrt(1 – B2^2)
From 3’s point of view, we have
** T3 = (T1 – T) / sqrt(1 – B3^2)
The only circumstance that these equations can coexist is when
** T1 = T2 = T3 = T = 0
This is obviously impossible in real life.
Or when
** B2 = B3 = 0
This means 2 and 3 can never move away
from 1. This is also absurd.
Thus, your conclusion is faulty. Under the Lorentz transform, you
cannot even begin to equate/synchronize the clocks. This is the
meaning of relative simultaneity. That is why the twin’s paradox can
never have any resolution. That is why the Lorentz transform is
wrong. That is why you are 1). After all these years without
understanding the Lorentz transform, that is why you are still 7).
<shrug>
> You have the Twin Paradox (Triplets) without any running clock
> having been accelerated - or having even existed during acceleration
> up or down.
>
> 7) Fucking imbecile
Shubert is correct in stating Einstein’s attempt to use acceleration
to resolve the twin’s paradox is absurd. It does not work. All you
have to do is to send both 2 and 3 away with identical acceleration
profiles starting at rest with 1. At maximum speeds, leave a time
period where 2 and 3 are coasting without any acceleration. Then,
bring 2 and 3 home also with the same acceleration profile in which 2
and 3 have already agreed before hand to execute on cue. According to
the Lorentz transform, it is impossible to compare the clocks of all
three. Thus, Einstein was a nitwit, a plagiarist, and a lair. The
Lorentz transform is kaput. You are merely priests to continue the
religion of SR based on the stupidity of the Lorentz transform with
Einstein the nitwit, the plagiarist, and the liar being the messiah.
<shrug>
Viva the Orwellian education:
** MYSTICISM IS WISDOM
** PLAGIARISM IS CREATIVITY
** CONJECTURE IS REALITY
** FAITH IS THEORY
** LYING IS TEACHING
** BELIEVING IS LEARNING
** IGNORANCE IS TRUTH
** STUPIDITY IS INTELLECT
> Shubert is correct in stating Einstein's attempt to use
> acceleration to resolve the twin's paradox is absurd.
The reason Einstein's approach demonstrates incompetence is that
accelerating from one inertial frame to another can be thought of as
an instantaneous process or something that only takes a negligible
amount of time when compared to the entire trip.
Shubee
http://www.everythingimportant.org/relativity/special.pdf
> Nope. My paper is devoted to removing from special relativity
> Shubeehttp://www.everythingimportant.org/relativity/special.pdf
thus:
the obvious problem with the "rubber snake wave power" would
be the one that all sea-going ships face, even
in the wet-dock.
--Welome to the Cheenysphere --
your 24/7/51 channel for everyhting that can be known, and
lots of speculation, about Trickier Dick
form the Nixon Admin. ..."You mean,
Dick was doing his magic, then, two?"
yeah, but *what* he & Rumfseld were doing,
seems to be a national security matter.
http://larouchepub.com
> frames. But your "carried by a traveler" suggests you
> probably have something else in mind, such as a twin
> scenario. Note that the twin scenario does NOT display
> "time dilation", it displays a difference in elapsed
> proper times for clocks that travel on different paths.
> But still for a twin scenario, to compute the difference in elapsed
> proper times with the above structure it only requires assumptions
> related to the specific physical situation you have in mind.
thus:
I don't get it; I finally unscrolled the end of your paper,
to find the usual 1D Lorentz thingy, applicable
to dilation of relative time, mass etc.; so, What?
> Shubeehttp://www.everythingimportant.org/relativity/special.pdf
So what were you expecting? If you're looking for salvation, try
reading the Bible.
Shubee
the idea of "instantaneous acceleration" is absurd, and
also a big waste of energy, a total conversion of mass,
the big crime of the wouldbejihadi -- all 98# of him or her (also
known
as "quantun teleportation to Paradise" .-)
> >>http://www.ias.ac.in/currsci/dec252005/2009.pdf
> >> "On Einstein’s resolution of the twin clock paradox" by C.S.Lewis & H.R.Pufnstuf.
> > I freely admit that Einstein's resolution of the twin paradox was
thus:
horse****; one twin accelerates, presumably
so as to experience the "slowing of his clock,"
relative to the twin, who stayed at the F-type planet, or
"time dilation;" you are being supercilious!
> frames. But your "carried by a traveler" suggests you
> probably have something else in mind, such as a twin
> scenario. Note that the twin scenario does NOT display
> "time dilation", it displays a difference in elapsed
> proper times for clocks that travel on different paths.
thus:
I don't get it; I finally unscrolled the end of your paper,
to find the usual 1D Lorentz thingy, applicable
to dilation of relative time, mass etc.; so, What?
> Shubeehttp://www.everythingimportant.org/relativity/special.pdf
I know you didn't understand my question. So I'm just going to walk
away and let you jibber and jabber about absolutely nothing.
..and how is accelerated motion treated in Shitbertian relativity?
Nonsense. Einstein's original article pointed explicitly to the case
where the acceleration of one of the clocks is *throughout* the entire
trip. The GPS satellites are a fine example of the twin puzzle.
Idiot.
Correction: uninformed idiot.
Correction: fastidiously perpetually uninformed idiot.
>
> Shubeehttp://www.everythingimportant.org/relativity/special.pdf
Do you also know that the invariance of the speed of light has nothing
to do with the Lorentz transformation being consistent with an
absolute frame of reference?
> So I'm just going to walk away and let you jibber and jabber
> about absolutely nothing.
Isn't it amusing that physicists are able to pontificate eloquently
about the specific nature of physical reality and believe that they
are about to figure out how the universe exploded into existence out
of nothingness but they are totally confused about fundamental
questions in special relativity?
Shubee
http://www.everythingimportant.org/relativity/special.pdf
To make the first step easy, might as will make the first tick
at t=t'=0.
> and by a clock
> at x1' that notes the time of that event as t1'.
I suggest keeping this as simple as possible to start. No need for a
second clock.
> The second tick of
> the clock in the "rest frame" is labeled by the event at a different
> point x2' in the moving frame and the time of that event is recorded
> by the clock at the point x2'.
You're just confusing yourself by adding complexity.
> Your whole argument is based on the concept of the simultaneity of
> spatially separated clocks, which is fallacious reasoning.
Instead of making up your own multi-clock example that doesn't help you
to understand, try looking at the simple example. A clock marks time in
the rest frame; the Lorentz transform maps its ticks to times (and
places) in the moving frame.
Later might look at how the Lorentz transform implies the relativity of
simultaneity, but I recommend looking at one issue at a time for now.
--
--Bryan
And that doesn't answer the twin paradox, and physicists know that,
which is why Einstein's embarrassing paper is never parroted as an
authoritative answer to silence critics.
> The GPS satellites are a fine example of the twin puzzle.
The subject is the twin paradox in special relativity. There is only
one question. How brainless do physicists have to be to not realize
that the acceleration and deceleration of a traveling twin only
requires a negligible amount of time?
I think it's amazing that anyone who ridicules your god is labeled an
idiot, an uninformed idiot and a fastidiously perpetually uninformed
idiot.
http://www.ias.ac.in/currsci/dec252005/2009.pdf
Shubee
It doesn't need to be parroted and there are no credible critics to
silence, though there are a number of incredible critics to mock.
>
> > The GPS satellites are a fine example of the twin puzzle.
>
> The subject is the twin paradox in special relativity. There is only
> one question. How brainless do physicists have to be to not realize
> that the acceleration and deceleration of a traveling twin only
> requires a negligible amount of time?
Rhetorical question. The amount of time spent in the acceleration and
deceleration is *completely* irrelevant to the teaching puzzle. The
fact that the world line is not straight is what matters. It doesn't
matter whether it's two straight legs with a rather abrupt kink or
whether it's a gradual arc.
That would be the reason for mentioning both GPS and the example that
Einstein actually cited in his original paper, both of which feature
gradual arcs in the world lines.
There is only one question for you: Why is it that you consistently
think that completely irrelevant details should suddenly become the
focus of attention for physicists, just because you've managed to
latch onto irrelevancies?
>
> I think it's amazing that anyone who ridicules your god is labeled an
> idiot, an uninformed idiot and a fastidiously perpetually uninformed
> idiot.
No, I don't do that for anyone, regardless whether they ridicule my
god or Einstein or both. Only you, because YOU are an idiot, an
uninformed idiot, and a fastidiously perpetually uninformed idiot. You
know that phrase: Don't take it personally? That comment you should
take personally.
>
> http://www.ias.ac.in/currsci/dec252005/2009.pdf
>
> Shubee
> > And that doesn't answer the twin paradox, and physicists know that,
> > which is why Einstein's embarrassing paper is never parroted as an
> > authoritative answer to silence critics.
>
> It doesn't need to be parroted and there are no credible critics to
> silence, though there are a number of incredible critics to mock.
It is absolutely unbelievable that a stupid comment like the above
would come from a professor of physics. Oh, well. Pathetic life
marches on.
> > The subject is the twin paradox in special relativity. There is only
> > one question. How brainless do physicists have to be to not realize
> > that the acceleration and deceleration of a traveling twin only
> > requires a negligible amount of time?
>
> Rhetorical question. The amount of time spent in the acceleration and
> deceleration is *completely* irrelevant to the teaching puzzle. The
> fact that the world line is not straight is what matters. It doesn't
> matter whether it's two straight legs with a rather abrupt kink or
> whether it's a gradual arc.
Hmmm... It actually does matter how much time is spent on
acceleration or coasting. If claimed otherwise by you, please show
the math from both twins’ points of view. If not, then please shut
the f*ck up.
> That would be the reason for mentioning both GPS and the example that
> Einstein actually cited in his original paper, both of which feature
> gradual arcs in the world lines.
GPS actually disproves SR. On top of that, you still owe me an answer
why the time dilation of GR contributes to red shift in light while
the time dilation of SR manifests red shift instead.
> There is only one question for you: Why is it that you consistently
> think that completely irrelevant details should suddenly become the
> focus of attention for physicists, just because you've managed to
> latch onto irrelevancies?
<shrug> Please answer your own question on yourself first.
> > I think it's amazing that anyone who ridicules your god is labeled an
> > idiot, an uninformed idiot and a fastidiously perpetually uninformed
> > idiot.
>
> No, I don't do that for anyone, regardless whether they ridicule my
> god or Einstein or both. Only you, because YOU are an idiot, an
> uninformed idiot, and a fastidiously perpetually uninformed idiot. You
> know that phrase: Don't take it personally? That comment you should
> take personally.
Right, keep on labeling everyone disagreeing with your pathetic
education as idiots. <shrug> This is not a typical trait of
professors I know. <shrug>
>> Forget it.
>> You don't know what the variables mean in that transformation.
>
> I go to great lengths to explain what the variables mean in
> http://www.everythingimportant.org/relativity/special.pdf
>
> You obviously can't defend your incompetence,
> http://www.everythingimportant.org/relativity/moortel.fumble.htm
> so you throw shit to hide your ignorance.
>
> You are a smelly, shit-throwing chimpanzee.
Shubee, you asked for time dilation computed from the Lorentz Transform,
and Dirk responded with the correct text-book derivation. An appropriate
response would be to thank him and learn from what he showed you.
--
--Bryan
> On Jul 23, 11:41 am, "Juan R." González-Álvarez
> <juanREM...@canonicalscience.com> wrote:
>> Shubee wrote on Wed, 23 Jul 2008 08:59:15 -0700:
>>
>> > Harald,
>>
>> > What I'm getting at is a trivial yet impossible to believe theorem
>> > that I wish to include in my paper on special relativity. I shall
>> > start with the Lorentz transformation and the clock synchronization
>> > scheme it implies and then reset all clocks in all but one inertial
>> > frames of reference. From there I shall change the definition of
>> > distance in all but that one special inertial frame by a suitable
>> > scaling factor. I shall also fiddle with clock rates by applying a
>> > similar suitable change of time scale and thus finally arrive at the
>> > traditional and easy to understand Galilean group of transformations.
>>
>> > This will prove that the Lorentz transformation alone doesn't imply
>> > time dilation.
>>
>> > Shubee
>> > http://www.everythingimportant.org/relativity/special.pdf
>>
>> I will wait to read your work [#], but my current understanding is that
>> is not true.
>
> Thank you Juan. Your skepticism encourages me to write out the details.
Notice also that in other relativistic theories, time dilation is not
obtained from LT but directly as dynamical effect.
E.g. in Stuckelberg Feynman theory, one obtains directly the equation of
motion for clocks (aka bad called 'time') from the covariant equations of
motion
See
http://canonicalscience.blogspot.com/2007/08/relativistic-lagrangian-and-
limitations_20.html
The equation of motion for clocks is that for x^0 using the generalized
Hamiltonian K.
Aspects as synchronization of multiple clocks is better done in this
formalism than in the old special relativity, which don't work for many
body systems.
See also the reference
Classical Relativistic Many-Body Dynamics. Springer; 1999. Trump, Matthew
A; Schieve, William C.
for a better theory than special relativity.
>> [#] Is your work somewhat related to some kind of difficulty when
>> passing from spacetime (x,t) to clock paths (x(t),t)?
>
> Nope. My paper is devoted to removing from special relativity everything
> that is confused, unnecessary and not amenable to experimental
> verification.
>
> Shubee
> http://www.everythingimportant.org/relativity/special.pdf
--
Shubee, basic physics textbooks already show that the Lorentz
transformations imply "time dilation", as defined in such books and as even
written out by others in this thread. Fiddling with things and changing
definitions can of course always yield different results; but such messing
around doesn't change anything about the correctness of those textbook
derivations.
Apart from that, you can of course reverse-engineer the Lorentz
transformations to Galilean transformations + Poincare/Einstein clock
synchronization method + length contraction + time dilation (the historical
Lorentz-Poincare approach). There's nothing special about that, although it
is perhaps not generally known and certainly instructive.
Harald
>What assumptions, if any, must be added to the Lorentz transformation
>in order to compute time dilation for a clock-carrying traveler?
Well, the Lorentz transformation is a relationship between
coordinate systems, so it has no physical content until you say
what is physically significant about the coordinate systems it
relates. Here is a rough description of what I consider the
physical content of Special Relativity.
First, we assume that there exists devices that I'll call
a "standard clock" and a "standard rod". A clock is just
something that provides us with an ever-increasing real
number called the elapsed time. A clock is one
based on some periodic process of known period, such as
the vibration of a spring.
A rod is just a straight stick
that has a fixed length. We pick some particular clock
and rod to serve as a definition of our standards for
length and time.
Now, we define a special kind of coordinate system,
a standard inertial coordinate system. Such a coordinate
system has the following properties:
1. A standard clock at rest relative to that coordinate
system between times t1 and t2 will show elapsed time
t2 - t1 (as measured in that coordinate system),
regardless of the location of the clock.
2. A standard rod at rest relative to that coordinate
system will have length 1 in that coordinate system,
regardless of its location or orientation. Specifically,
if the cooordinates of the rod's endpoints at a given time are
(x1,y1,z1) and (x2,y2,z2), then X^2 + Y^2 + Z^2, where
X = x2 - x1, Y = y2 - y1, Z = z2 - z1.
These two assumptions don't have a *lot* of physical
content, because they are basically true by definition
of "standard coordinate system". However, there is a
hidden assumption that it is possible to construct
a clock whose rate doesn't depend
on its location, and a rod whose length doesn't depend
on its location or orientation.
Another assumption about standard inertial coordinate
systems is that Newton's first law holds:
3. An object that is not under the influence of any
force will have no coordinate acceleration. That is,
if the object has coordinates x,y,z as a function of
time, then (d/dt)^2 x = 0, (d/dt)^2 y = 0, (d/dt)^2 z = 0.
This only has physical content to the extent that we can
actually identify force-free motion. For most of relativity's
thought experiments, we will assume the only forces involved
are contact forces and electromagnetic forces.
Assumptions 1-2 are used to define "standard inertial
coordinate system". Assumption 3 was introduced by Newton.
The next assumption is more recent, dating from the
Michaelson-Morley experiment.
4. There is a constant c such that a light signal always
has speed c as measured in any standard inertial coordinate
system.
With assumptions and definitions 1-4, we are ready finally
to say what the physical meaning of the Lorentz transformations
is:
5. If S is any standard inertial coordinate system, and S'
is a coordinate system related to S through a Lorentz
transformation, or a translation, or a rotation, then
S' is also a standard inertial coordinate system.
I believe that 5 can be derived from the other 4, but I'm
not going to attempt that here.
Now, to get to time dilation, we also need some more assumptions
about the nature of physical objects and standard clocks.
6. Regardless of the motion of a standard clock, its elapsed time
between times t1 and t2 (as measured in a standard inertial coordinate
system) vanishes in the limit as (t2 - t1) goes to zero.
This just means that in computing elapsed time, we can ignore
what happens during any very short period of time (assuming
that it isn't reset, that is...)
(This can be made more mathematically precise by saying that
there is some constant K greater than zero such that
limit as x --> 0 of Tau(t,t+x)/x < K, where Tau(t1,t2) is
the elapsed time on the clock between times t1 and t2.)
7. If a standard clock has nonzero, but very small velocity
between times t1 and t2 (where velocity and times are measured
relative to a single standard inertial coordinate system),
then the elapsed time will be approximately given by t2 - t1.
This means that we can ignore tiny variations in the velocity
of the clock, as long as it is never moving very fast.
(This can be made more mathematically precise by saying that
there is some constant K2 greater than zero such that if a
clock's velocity between times t1 and t2 is always less than
v, then |Tau(t1,t2)/(t2 - t1) - 1| < K2 v^2)
8. For any standard clock, for any standard inertial coordinate
system, for any finite period of time, the clock's position as
a function of time, as measured in that coordinate system, is
continuous, and its velocity is continuous except for possibly
a finite number of discontinuities. We allow for discontinuities
in velocity so that we can idealize rapid accelerations such
as a clock bouncing off a wall or a rocket accelerating from
0 to some speed v in a short amount of time.
Assumptions 1-8 allow us to compute the following formula
for the elapsed time for a standard clock, which holds in
any standard inertial coordinate system S:
Tau(t1,t2) = Integral from t1 to t2 of
square-root(1-(v(t)/c)^2) dt
where v(t) is the magnitude of the clock's velocity
at time t, as measured in S, and times are measured
in S.
To see how to prove this, we break up the interval into
several small segments, such that the clock's velocity is
approximately constant in each segment. To compute the
elapsed time in each segment, we perform a Lorentz
transformation to a coordinate system in which the
clock is approximately at rest in that segment, and
use assumption 7. Then we add up the elapsed times
for all segments.
To see how this works, consider a segment that starts
at time t_j and ends at time t_{j+1}, and the velocity
of the clock during this segment is approximately v
(assume it's in the x-direction, for simplicity).
So we transform to a coordinate system in which
the clock is at rest, where the times are given
by
t_j' = gamma (t_j - v/c^2 x_j)
t_{j+1}' = gamma (t_{j+1} - v/c^2 x_{j+1})
where x_j and x_{j+1} are the locations of the
clock at times t_j and t_{j+1}. Since the clock
is at rest (approximately) in this segment, we
get:
elapsed time for this segment = t_{j+1}' - t_j'
= gamma ((t_{j+1} - t_j) - v/c^2 (x_{j+1} - x_j))
But since the clock has velocity v, we can write:
x_{j+1} - x_j = v (t_{j+1} - t_j). So the elapsed
time is just
gamma (1 - v^2/c^2) (t_{j+1} - t_j)
But since gamma = 1/square-root(1-(v/c)^2), this simplifies
to
elapsed time = square-root(1-v^2/c^2) (t_{j+1} - t_j)
--
Daryl McCullough
Ithaca, NY
But that would be inconsistent with Shubee's *real* and overriding
objective, which is to take physicists down a peg, which in turn
driven by a religiously-motivated disgust for uncovering the secrets
of God's design by lowly mankind.
But keep in mind that Shubee is a conflicted sinner. He couples his
attempt to take physicists down a peg with his attempt to climb a peg
higher himself, by proposing a "cleaner" theory himself and putting on
airs that he considers himself more closely aligned with
mathematicians (a holier and more godlike creature) than with
physicists -- even though he makes essentially no conversations with
mathematicians and is in turn ignored by them.
PD
I certainly invite you to list some names of people you consider to be
credible critics.
>
> > > The subject is the twin paradox in special relativity. There is only
> > > one question. How brainless do physicists have to be to not realize
> > > that the acceleration and deceleration of a traveling twin only
> > > requires a negligible amount of time?
>
> > Rhetorical question. The amount of time spent in the acceleration and
> > deceleration is *completely* irrelevant to the teaching puzzle. The
> > fact that the world line is not straight is what matters. It doesn't
> > matter whether it's two straight legs with a rather abrupt kink or
> > whether it's a gradual arc.
>
> Hmmm... It actually does matter how much time is spent on
> acceleration or coasting. If claimed otherwise by you, please show
> the math from both twins’ points of view. If not, then please shut
> the f*ck up.
Since the math has been rendered several other places already, it is
more efficient for me to direct you to a place where you can look it
the f*ck up yourself, rather than to suffer your demands to be spoon-
fed like a baby bird. Since the discussion surrounding it is also
pertinent and illuminating, I will suggest first the chapter on the
structure of spacetime (it's a little more than halfway in) in Roger
Penrose's book, The Road to Reality. There he does exactly what you
are looking for. Happy self-educating!
>
> > That would be the reason for mentioning both GPS and the example that
> > Einstein actually cited in his original paper, both of which feature
> > gradual arcs in the world lines.
>
> GPS actually disproves SR.
:>)
> On top of that, you still owe me an answer
> why the time dilation of GR contributes to red shift in light while
> the time dilation of SR manifests red shift instead.
>
> > There is only one question for you: Why is it that you consistently
> > think that completely irrelevant details should suddenly become the
> > focus of attention for physicists, just because you've managed to
> > latch onto irrelevancies?
>
> <shrug> Please answer your own question on yourself first.
>
> > > I think it's amazing that anyone who ridicules your god is labeled an
> > > idiot, an uninformed idiot and a fastidiously perpetually uninformed
> > > idiot.
>
> > No, I don't do that for anyone, regardless whether they ridicule my
> > god or Einstein or both. Only you, because YOU are an idiot, an
> > uninformed idiot, and a fastidiously perpetually uninformed idiot. You
> > know that phrase: Don't take it personally? That comment you should
> > take personally.
>
> Right, keep on labeling everyone disagreeing with your pathetic
> education as idiots.
It is not the disagreement with my education that produces the label.
It is the method by which you arrive at the disagreement that is
idiotic:
- your refusal to *study* that which you intend to oppose
- your complete disregard for experimental evidence
- your overriding, emotional desire to overcome your feelings of
inadequacy as an engineer by taking physicists down a peg.
If you managed to reverse these idiotic behaviors and *still*
disagreed with relativity, then you would be doing so from a less
idiotic position.
- Ian Parker
No assumptions need to be added to compute time dilation.
Pete
Einstein didn't base his arguement on any instantaneous proccess. There is
no reason to assume that Einstein was referring to anything other than
continuous velocity and acceleration. In fact its possible to analyize the
so-called "Grandfather Paradox" using anything that is accelerating at all.
And, in general, accelerating from one inertial frame to another cannot be
thought of as an instantaneous process. If you believe otherwise then please
provide a proof. Thank you.
Pete
> Shubee, you asked for time dilation computed from the Lorentz Transform,
I asked, "What assumptions, if any, must be added to the Lorentz
transformation in order to compute time dilation for a clock-carrying
traveler?"
It is nonsense and ignorance of the highest order to believe that the
Lorentz transformation contains more information than the weakest
physical assumptions needed to derive the Lorentz transformation,
which is almost nothing.
Tom Roberts
http://groups.google.com/group/sci.physics.relativity/msg/4707d98cd208ee39
and Daryl McCullough
http://groups.google.com/group/sci.physics.relativity/msg/8d0981dc259d134e
both recognized that "one must add a large number of assumptions/
definitions relating to what the symbols mean and how they are
applied."
Shubee
http://www.everythingimportant.org/relativity/special.pdf