Re: Thruster's => time dilation, (kst).

On Nov 9, 9:59 am, stevendaryl3...@xxxxxxxxx (Daryl McCullough) wrote:
Ken S. Tucker says...

Daryl you snipped part of my post,
"If you care to dismiss GR1916 that's
fine

I think you misunderstood that paper.

You claim to know GR yet you haven't even
studied the originating paper!

Einstein was definitely not saying that
4-acceleration is always zero. He was
saying that for a *geodesic* it is zero.
An accelerated rocket is *not* following
a geodesic.

Myself and Jay Yablon discussed that at
length and I helped with a paper for ArXiv, see
http://arxiv.org/ftp/gr-qc/papers/0511/0511050.pdf

Note I'm acknowledged. See the analysis
just past Eq.(2.39), where Mr. Yablon
analyses the kappa_nu = 0.

then we can discuss the new GR
you are using, but I think you'll find
you're taking a great leap backward
into Newton's classical mind-set, by
going back to an absolute acceleration,
as your components predict.

I didn't say anything about acceleration
being absolute. It's a 4-vector. Its components
have different values in different coordinate
systems.

That's nit-picking words.
IF the A^u =0 is one system, it's zero in
all.

http://www.damtp.cam.ac.uk/user/examples/D22Lb.pdf

Section 10.2:

"...the 4-momentum is defined by A^a = DU^a/Dtau..." (equation 190)

Later, in section 10.2.2:

"For a paticle of charge e moving in an electromagnetic field we
have the Lorentz equation m DU^a/Dlambda = e F^a_b U^b"

In section 10.2.3 "Example: Relativistic Rockets...DmU^a/Dtau = J^a
where J^a is the rate of emission of 4-momenta of the ejecta
[what I'm calling thrust]"

Clearly, this reference agrees with me that the 4-acceleration
is *not* zero, and that it is equal to the 4-force (divided by
the mass).

Another reference:

http://www.ucl.ac.uk/~ucahmab/Relativity/genrel.pdf

Equation 6.63: "f^a = m(DU/dtau)^a ... if f^a = 0 an object
follows a geodesic"

Section 6.6 "The Twin Paradox": Equation 6.70:
(for a ship accelerating at rate g)

"F^a = m (DU/Dtau)^a = mg"

None of the above has anything to do
with GR. IMO it's garbage. Can we go
back to the original Einstein GR1916
article and discuss REAL GR.

Science is not a matter of consulting holy scripture.

Holy *** :-), Mr. McCullough is equating
an analysis of AE's GR1916 as religious.

If you understand the material, you can explain it
yourself. In my opinion,

How can you have an opinion on something
you haven't studied?

you've completely misunderstood
the relationship between Einstein's physics and Newton's.
Einstein's physics is a *generalization* of Newton's, but
it reduces to Newton's physics in the following limit:

When spacetime is approximately flat, when all objects
are travelling slowly compared with the speed of light,
when inertial Cartesian coordinates are used.

In this limit, Einstein's physics recover Newton's physics.

Why do word salad, let's stay with the
problem you and I are discussing.

Let me ask a leading question for your approach, Ken. You
claim that 4-acceleration is always zero. But I assume that
you agree that where a rocket ends up will depend on how
that rocket aims its thrusters, and how strong those thrusters
are. So what is the equation of motion relating the path of
the rocket to the thrust supplied?

The rocket is at rest, there are exhaust
gases moving from the rocket engine,
propelled electromagnetically.

I asked for an equation governing the trajectory
of the rocket. Suppose you want to send a rocket to
Mars. What equations do you use to figure out what
thrust is needed?

I gave you the correct answer:

F^u = m [dU^u/dtau + Gamma^u_vw U^v U^w]

That's correct if m=1 and F^u=0 in GR.

You use this equation to solve for the 4-velocity U^u
in terms of the applied force F^u. Integrate the 4-velocity
to get the position x^u. That's how you compute the trajectory
of a rocket.

That's the Newtonian method.

What do think was accelerated, the rocket
or the exhaust gases?

They both are. The exhaust is accelerated in one direction,
while the rocket is accelerated in the opposite direction.

Bingo! You Daryl have adopted the Center
of Mass (CoM) of the system and made that
a preferred FoR.

Do you have an answer?

I think so :-)

Then write it down. What is the trajectory of the rocket
as a function of the applied thrust?

When we resolve A^u=0, we'll can proceed.

I certainly do:

d/ds U^u + Gamma^u_vw U^v U^w = F^u/m

where F^u is the 4-force applied, and U^u is the 4-velocity
and Gamma^u_vw is the connection coefficients. What is your
answer? How do you compute the trajectory of a rocket given
a particular applied thrust?

Einstein and I are in agreement that your
"F^u" vanishes, IOW's it does not exist,

Einstein never said such a thing.

Open a book, I provided REAL ref's.
Myself, Mr.Yablon and Einstein agree
on what I've stated.
Are you trolling me?
Regards
Ken S. Tucker


Once again, how
do you think one would send a rocket to Mars? You
don't think thrust is involved? Of course it is.
If you don't apply any thrust, the rocket will never
leave the Earth, and will never get to Mars.
So what is the relationship between the thrust applied
and the resulting motion? How much thrust does it take
to leave the Earth and get to Mars?

We can make the problem even simpler. Suppose
you are floating in space in a capsule
far from any planet. Through a telescope,
you can see the mothership, also floating, no
rockets firing. You compute the distance to
the mothership to L by radar ranging (you
send a radar signal to the ship, and time
how long it takes for the signal to return
to you).

Daryl if you intend to debunk the
Foundation of AE's GR that's fine,

I am not arguing with Einstein, I'm arguing with
*you*. I think you have misinterpreted Einstein.

if you have good reason.
You can do Newtonian physics in terms
of tensors, but that's all you doing.

More correctly, I'm doing Special Relativity
in curved spacetime using curvilinear coordinates.
And that's all you need to be able to solve problems
involving the motions of rockets and test particles
in a fixed curved spacetime. Full General Relativity
is only needed if you are taking into account how
matter curves spacetime. When we are talking about
rockets and so forth, full General Relativity is
overkill, since a rocket has a negligible effect
on the spacetime curvature.

If you are talking about accelerated rockets in
*flat* spacetime, then all you need is Special
Relativity. You *don't* need General Relativity.

--
Daryl McCullough
Ithaca, NY


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