The Lorentz trasformation expresses time as a function of speed of
moving
frame and light speed. After that, people apply Lorentz trasformation
to derive several govermenning equations related to special
relativity.
So many different versions of derivation for Lorentz transformation
can be seen presently.These used a lot of different constraint
equations to link
time, velocity and velocity of light, merely wanted to successfully
derive Lorntz Transformation, and were based on comparing speed of a
moving frame and light travelling.
Could someone tell me how to write the relativity equations if light
never exists in our universe?

chenmou:
The Lorentz trasformation expresses time as a function of speed of
moving
frame and light speed. After that, people apply Lorentz trasformation
to derive several govermenning equations related to special
relativity.
So many different versions of derivation for Lorentz transformation
can be seen presently.These used a lot of different constraint
equations to link
time, velocity and velocity of light, merely wanted to successfully
derive Lorntz Transformation, and were based on comparing speed of a
moving frame and light travelling.
Could someone tell me how to write the relativity equations if light
never exists in our universe?

Assume that time and space are on equal footing as "spacetime" so
that you recoginze that `c' is nothing but a conversion constant
that converts seconds to meters. Assume there exists a transformation
A, for the vector x = (ct, r) in frame S to a frame S', so that the
vector x transforms as:

[ct'] [a b] [ct]
x' = Ax = [ ] = [ ] [ ]
[ x'] [d e] [ x]

giving you two equations in 4 unknowns:

ct' = act + bx
x' dct + ex

Require (ct)^2 - x^2 = (ct')^2 - x'^2, so that you have:


(ct)^2 - x^2 = (act + bx)^2 - (dct + ex)^2

= (a^2 - d^2)(ct)^2 + (b^2 - e^2)x^2 + 2ctx(ab - de)

which requires

a^2 - d^2 = 1
b^2 - e^2 = -1

ab - de = 0


Those will be true if a = e = cosh(K) and b = d = -sinh(K), where
cosh(K) and sinh(K) are hyperbolic rotations for some angle K, (usually
called the rapidity). That gives you the lorentz transforms in hyperbolic
form:

ct' = ct cosh(K) - x sinh(K)
x' = x cosh(K) - ct sinh(K)

The relationship between the hyperbolic functions and the velocity may
be deduced by noting that a velocity is the slope of a line in the
x-t plane so that the slope is:

v = c tanh(K) or \beta = (v/c) = tanh(K)

From cosh(K)^2 - sinh(K)^2 = 1 you get

1 - tanh(K)^2 = 1/cosh(K)^2

cosh(K) = 1/sqrt(1 - tanh(K)^2) = 1/sqrt(1 - (v/c)^2)

so that cosh(K) = \gamma and sinh(K) = \gamma\beta

Bilge wrote:

The relationship between the hyperbolic functions and the velocity may
be deduced by noting that a velocity is the slope of a line in the
x-t plane so that the slope is:

v = c tanh(K) or \beta = (v/c) = tanh(K)

From cosh(K)^2 - sinh(K)^2 = 1 you get

1 - tanh(K)^2 = 1/cosh(K)^2

cosh(K) = 1/sqrt(1 - tanh(K)^2) = 1/sqrt(1 - (v/c)^2)

so that cosh(K) = \gamma and sinh(K) = \gamma\beta

Slicker than Harvard Beets on sliced white. I am familiar with this
derivation, but I love to see it, each and every time. It is really to
bad that the so-called Lorentz Contraction is not called the Lorentz
Projection, which would unconfuse many folks.

The "contraction" of length under a rotation is no more mysterious than
looking at a yardstick from a 45 degree angle. The "contraction" is
purely an artifact of projection and nothing more. Turning a yard stick
does not stress its material longitudinally.

Bob Kolker

(chenmou) wrote in message . com...

Derive Lorentz Transformation for a universe in which 'Light' never exists...

Here's a derivation of the Lorentz Transformation without any reference to light:

http://www.everythingimportant.org/relativity

Eugene Shubert

Subject: Derive Lorentz Transformation for a universe in which 'Light'
never exists...
From: (Perfectly Innocent)
Date: 11/25/03 8:26 AM US Mountain Standard Time
Message-id:

(chenmou) wrote in message
.com...

Derive Lorentz Transformation for a universe in which 'Light' never
exists...

Here's a derivation of the Lorentz Transformation without any reference to
light:

http://www.everythingimportant.org/relativity

Eugene Shubert

As you've been told before that is not a derivation.

On 11/25/2003 7:07 AM, Robert J. Kolker wrote:
[...] It is really to
bad that the so-called Lorentz Contraction is not called the Lorentz
Projection, which would unconfuse many folks.

Thanks! That's a great idea!


The "contraction" of length under a rotation is no more mysterious than
looking at a yardstick from a 45 degree angle. The "contraction" is
purely an artifact of projection and nothing more. Turning a yard stick
does not stress its material longitudinally.

Yes.


Tom Roberts

(WaiteDavid137) wrote in message ...

Perfectly Innocent:
Here's a derivation of the Lorentz Transformation without any reference to
light:

http://www.everythingimportant.org/relativity

Eugene Shubert

As you've been told before that is not a derivation.

David,

You've fallen into a closed temporal loop. Perhaps you can find a way
out if you can answer my last rebuttal:

http://www.everythingimportant.org/v...hp?p=2229#2229

Eugene Shubert

"Perfectly Innocent" wrote in message
om...
(WaiteDavid137) wrote in message
...

Perfectly Innocent:
Here's a derivation of the Lorentz Transformation without any
reference to
light:

http://www.everythingimportant.org/relativity

Eugene Shubert

As you've been told before that is not a derivation.

David,

You've fallen into a closed temporal loop. Perhaps you can find a way
out if you can answer my last rebuttal:

http://www.everythingimportant.org/v...hp?p=2229#2229

Eugene Shubert

Forget it Eugene. Once he starts with the "you've been told" then he's in
parrot mode and is unable to stop and think.

"Robert J. Kolker" wrote in message ...

The "contraction" of length under a rotation is no more mysterious than
looking at a yardstick from a 45 degree angle. The "contraction" is
purely an artifact of projection and nothing more. Turning a yard stick
does not stress its material longitudinally.

Bob Kolker

On the contrary, the Lorentz circumferential contraction of a rotating
elastic isotropic disc give rise to a negative spatial curvature :
C = 2piR/(1-v^2/c^2)^(1/2) where R is the radius of the rotating disc
and C its relative circumference, (see Landau and Lifschitz, Tome 2,
§89 the rotation, Mir edition, 4th edition).

This Lorentz circumferential contraction give rise to a slight
stress-strain field (actually, a very slight perturbation of the
classical stress-strain field of a real rotating elastic isotropic
disc).

When performing the calculations of the stress-stain field stemming
from the Lorentz Circumferential contraction of the rotating disc, one
finds traction stresses and traction strains in the circumferential
direction and compression in the radial one.

Radial stress (at radius r)
s_r = 3E (e_0(r)-e_0(R))/8

Circumferential stress (at radius r)
s_thêta = 3E (3e_0(r)-e_0(R))/8

Radial strain (at radius r)
e_r = (s_r – nu s_thêta )/E = 3[(1–3nu) e_0(r) –(1–nu) e_0(R)]/8

Circumferential strain (at radius r)
e_thêta = (s_thêta – nu s_r)/E = 3[(3–nu) e_0(r) –(1–nu) e_0(R)]/8

Where
* R is the radius of the rotating disc
* r and thêta are the polar coordinates of a rotating observer
* E is the Young elastic modulus of the disc
* nu is the Poisson coefficient of the disc
* e_0(r)= 1/(1-v^2/c^2)^(1/2)-1 is the "initial" strain stemming
from the Lorentz circumferential contraction effect, with v = omega r
and omega = angular speed of the rotating disc

Bernard Chaverondier
http://perso.wanadoo.fr/lebigbang

PS : in a "possible" flat but finite and static spacetime like a T^3
static spacetime for instance (the 3D hypertorus), neither the Lorentz
time dilatation of the moving Langevin twin, nor the Lorentz
contraction of evenly moving bodies are artifacts (Though I consider
this example to be only a mathematical one. I don't believe the
spatial part of our universe to have not simply connected geodesics).

"Robert J. Kolker" wrote in message
...

The "contraction" of length under a rotation is no more mysterious than
looking at a yardstick from a 45 degree angle. The "contraction" is
purely an artifact of projection and nothing more. Turning a yard stick
does not stress its material longitudinally.

Bob Kolker


Are you saying that a change in spatial velocity is merely a change in
direction within space-time and any measured length contraction is just a
result of the altered perspective?