Re: Simple four velocity question


"Jonathan Doolin" <good4usoul@xxxxxxxxx> wrote in message
news:a7d35254-67a1-4dfc-b17e-ad27dbd33573@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
On Mar 14, 1:28 am, "Androcles" <Headmas...@xxxxxxxxxxxxxxxx> wrote:
"Jonathan Doolin" <good4us...@xxxxxxxxx> wrote in message

news:bf6f4bd6-4d61-43ab-aec5-aa57c5d6952a@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
On Mar 13, 12:59 pm, "Ken S. Tucker" <dynam...@xxxxxxxxxxxx> wrote:





On Mar 12, 4:18 pm, Jonathan Doolin <good4us...@xxxxxxxxx> wrote:

On Mar 11, 9:20 pm, "Ken S. Tucker" <dynam...@xxxxxxxxxxxx> wrote:
On Mar 11, 4:26 pm, "Ken S. Tucker" <dynam...@xxxxxxxxxxxx> wrote:
On Mar 11, 7:27 am, Jonathan Doolin <good4us...@xxxxxxxxx> wrote:
On Mar 10, 9:48 am, Tom Roberts <tjroberts...@xxxxxxxxxxxxx>
wrote:

Jonathan Doolin wrote:
Does it seem awkward to anybody else to take the the
derivative of the
"four-position" with respect to tau instead of with respect
to
t?

No. This is the general geometric way to form the tangent
vector
to a
path (where tau is an affine parameter of the path).

This pretty much assures that for all objects, you'll get
the
same
first coordinate (c*gamma*t)/d(tau) = d(c*tau)/d(tau) = c,

Not true. It is the norm of 4-velocity that is c, not the
"first
coordinate" (by which I assume you mean the time component).

For an object moving with speed v along the x axis of the
inertial frame used for the components of 4-velocity, those
components are (c*gamma,gamma*v,0,0), gamma=1/sqrt(1-v^2/c^2).

and as Mr.
Green said, you don't have a well-defined four-velocity for
light.

Yes (more on this soon...). But the tangent vector to the path
is well
defined for light, as is the 4-momentum, and they are equally
useful.

Is the wikipedia article error?

It looked OK to me. But it did not imply your claim above.

Tom Roberts

Just to be sure, though, look carefully where the article
states:
=======================
"Components of the four-velocity"
The relationship between the time t and the coordinate time x0
is
given by
x0 = c*t = c*gamma*tau
=======================
But you appear to have said x0=c*gamma

Are these definitions agreeable,

http://farside.ph.utexas.edu/teaching/jk1/lectures/node15.html

Ken

IMO, Ken, that link entails an ambiguity as to
what type of derivative is employed in Eq.(115),
to justify defining the L.H.S. of (115) as a
tensor. Would you say it's an absolute derivative?
Apparently this does certainly needs the attention
of expert discussion, especially to evaluate Eq.(118).
Ken S. Tucker
So I guess the question is whether it is physically meaningful to take
the second derivative with respect to tau? (Eq 115.)

This may or may not be a difficulty, but I see that the first
derivative takes into account a reference frame with an origin
(t=0,x=0,y=0,z=0) in the rest frame.

Another way of looking at the problem is this.
In an inertial frame (accelometer reading zero),
at a Point P, (origin) is a lab where Physics
experiments are being conducted.

In SR, a multitude of references may have a uniform
motion (not accelerating) with velocities from v=0
to v<c, and take measurements of the Physics at P,
and all FoR's will agree the Physical Laws are true,
at P.
The Lorentz Transform also allows for the arbitary
observer to be displaced in space from P.

When an acceleration is applied,
the "generalized Lorentz Transform" involves a translation, so the
origin will NOT stay in the same place.

I think "shoe-horning" acceleration into LT was tried
after SR1905, but found unsatisfactory necessitating
the full developement of GR1916.

I'm not sure what you mean by "shoe-horning" and I distrust the word
"unsatisfactory" when used in relation to General and Special
Relativity. If you want something satisfactory, get cake and ice
cream. But a good understanding of the Lorentz Transformations is
rather more like car-sickness or vertigo.

I think this would be okay as long as the accelerating particle is at
the origin.

Yes, that's about my understanding too. I'm not
sure whether it's a physical requirement or a
limitation imposed by using tensor analysis.
In tensors, the transformation between two CS's
is at the same point.

I was speaking of a physical limitation. The Lorentz Transformation

====================================
doesn't exist.

SANITY WARNING (Droolin' Doolin)

Scruffy Rat's postulate: "light is always propagated in empty space with
a definite velocity c which is independent of the state of motion of
the emitting body" bears no resemblance whatsoever to Doolin's:
"Scruffy Rat's 2nd postulate of S.cruffy R.at*** says that the speed
of light is c in every inertial frame."

Scruffy Rat himself says "But the ray moves relatively to the initial
point of k, when measured in the stationary system, with the
velocity c-v, so that t = x'/(c-v).

Doolin makes no apology for misrepresenting Scruffy Rat by echoing
the popular prayer, instead he chants the mantra spoken unto him by
the insane Bonehead Green. Chanting mantras is like saying prayers, a
form of witchcraft known as uttering spells.

Doolin cannot distinguish c-v in the stationary frame from c in the
moving frame.

This form of insanity is known professionally among scientists
as bigotry and lying. Guilty by reason of insanity is still guilty.
The asylum inmates assert that it is the doctors treating them that
are lying, even those untrained in psychiatry.

"Physician, heal thyself." - Jesus H. Christ, self-proclaimed son
of Gawd, superman and god-on-a-stick, professional holy man and sky
pilot, Captain of the starship "Cloud", litterbug of the Holy Grail
(now lost) and diner of Last Suppers.

Other characteristics - walked on water, turned water into whine,
preferred the male company of twelve rent boys and advocated "love"
to them all and their neighbours. Was not popular among the
establishment, having upset their banco and causing widespread
economic disruption. (Banco is an Italian word for bench from
which the English word "Bank" is derived. He upset the money
benches or tables outside the temple to Gawd.)

Favourite quote: "Eloi, eloi, lama sabathani."
(Translation: "Oh, *** it! I screwed up. You were supposed to help
but thanks anyway, I will still kiss your arse, Your Hole-iness!)

Doolin wants to play hardball
http://tinyurl.com/bw55m7- Hide quoted text -

- Show quoted text -

John Parker is inhabited by a demon called Androcles. I pray for John
Parker, that he might be forgiven, so that he could return to his
childhood innocence and desire eternal life. I can only say to John
Parker, that you must *want* to be healed. Then your own faith can
heal you.

John Parker, come out and see the light. I forgive you but I don't
believe that God forgives the demons that live inside you. If you
cling to Androcles and The Big Bad Wolf, where are they going to take
you? I say let go of these dead hopes, and live.
=================================================
You are in the wrong newsgroup. I write about science and mathematics;
if you wish to write about me then try any of alt.social.interaction,
sci.diplomacy, junk.religion, alt.flame, alt.local.village.idiot, a
finishing school for debutantes who are coming out, "People" magazine
or other group that doesn't subscribe to math or science, although
why you would want to is a mystery only you can answer.
If you wish to say that I am wrong on some point of math or science
then point it out and we'll discuss it, but if you merely wish to say
I am wrong according to your pathetic philosophy of everybody has to
agree with you and be polite, regardless of logic, then again you are
in the wrong group.
I am not that interesting, but there is no accounting for taste.
It is after all your choice. You are certainly of zero interest to me,
fuckin' opinionated prima donnas like you never are.
Perhaps you just like bitching about off-topic subjects and ignoring
the newsgroup charter, you rude, hypocritical ***. I suggest you
look to your own hypocrisy and *** off, taking your spam with you.

SANITY WARNING (Droolin' Doolin)

Scruffy Rat's postulate: "light is always propagated in empty space with
a definite velocity c which is independent of the state of motion of
the emitting body" bears no resemblance whatsoever to Doolin's:
"Scruffy Rat's 2nd postulate of S.cruffy R.at*** says that the speed
of light is c in every inertial frame."

Scruffy Rat himself says "But the ray moves relatively to the initial
point of k, when measured in the stationary system, with the
velocity c-v, so that t = x'/(c-v).

Doolin makes no apology for misrepresenting Scruffy Rat by echoing
the popular prayer, instead he chants the mantra spoken unto him by
the insane Bonehead Green. Chanting mantras is like saying prayers, a
form of witchcraft known as uttering spells.

Doolin cannot distinguish c-v in the stationary frame from c in the
moving frame.

This form of insanity is known professionally among scientists
as bigotry and lying. Guilty by reason of insanity is still guilty.
The asylum inmates assert that it is the doctors treating them that
are lying, even those untrained in psychiatry.

"Physician, heal thyself." - Jesus H. Christ, self-proclaimed son
of Gawd, superman and god-on-a-stick, professional holy man and sky
pilot, Captain of the starship "Cloud", litterbug of the Holy Grail
(now lost) and diner of Last Suppers.

Other characteristics - walked on water, turned water into whine,
preferred the male company of twelve rent boys and advocated "love"
to them all and their neighbours. Was not popular among the
establishment, having upset their banco and causing widespread
economic disruption. (Banco is an Italian word for bench from
which the English word "Bank" is derived. He upset the money
benches or tables outside the temple to Gawd.)

Favourite quote: "Eloi, eloi, lama sabathani."
(Translation: "Oh, *** it! I screwed up. You were supposed to help
but thanks anyway, I will still kiss your arse, Your Hole-iness!)

Doolin wants to play hardball
http://tinyurl.com/bw55m7





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