Hello,

A couple questions:

1.

Let's say I'm doing an experiment, measuring the length of a rod. I can
use special relativity to predict the effects of length contraction on
that measurement given the initial conditions of the experiment (length
of rod, relative velocities, ect). Correct?

2.

Not necessarily related to my next question but just for kicks can some
show me how the mathematical model of SR is used to solve a problem
like this?

3.

If I calculate my prediction for the measurement of the length
contracted rod, and then decide that another observer should take part
in the experiment, with a different relative velocity to myself and the
rod. In this case, I'm going to need to predictions, what I measure and
what the other observer measures. Can I derive those predictions with a
single set of initial conditions for the mathematical model of SR, or
do I crunch two separate problems?

Thanks!

Yes, yes, yes.
Go to library or buy a book.
http://www.amazon.com
SearchSpecial Relativity.

PD

"MobyDikc" wrote in message oups.com...
Hello,

A couple questions:

1.

Let's say I'm doing an experiment, measuring the length of a rod. I can
use special relativity to predict the effects of length contraction on
that measurement given the initial conditions of the experiment (length
of rod, relative velocities, ect). Correct?

yes


2.

Not necessarily related to my next question but just for kicks can some
show me how the mathematical model of SR is used to solve a problem
like this?

It is not really a problem, just a little application.

The mathematics would go somewhat like this.

Suppose that the rod is at rest in a frame S where coordinates
x and t are used. Suppose that the rod has length L in that frame.
L is the what is called the "proper length" of the rod.
Suppose you are at rest in a frame S' where coordinates x' and t'
are used.
Suppose that you move with velocity v with respect to the rod
and that the direction of motion is in the direction of the rod.
Suppose that the clocks are set to zero when and where the
origins of the frame coincide.
This fixes the coincidence event O of the origins of the frames S
and S' to be given by
O: (x,t) = (x',t') = (0,0).
This also fixes the transformation of the coordinates to be given by
x' = g ( x - v t )
t' = g ( t - v x /c^2 )
where
g = 1/sqrt(1-v^2/c^2)
or equivalently by
x = g ( x' + v t' )
t = g ( t' + v x' /c^2 )
The first two equations give the (x',t') coordinates of an event of
which the (x,t) coordinates are known. The last two equations do
the opposite.

Now, the rod.
If you want to measure the length of it, you must measure the
distance of the two end points at the same time according to you.
That is crucial. So you need the distance between the end points
at two events
E1: (x',t') = (x1',T')
E2: (x',t') = (x2',T')
where T' is some arbitrary time on your clock.
The the length that you will measure will be
L' = x2' - x1'

Now you must pick one of the equations that gives a relation
between the coordinates x and x', but where you also use the
known time t'=T'.
There is one candidate for this:
x = g ( x' + v t' )
You fill in the coordinates for the first event:
x1 = g ( x1' + v T' )
and for the second event:
x2 = g ( x2' + v T' )
Since we have used the same time t'=T', this can be easily
eliminated by subtracting the equations:
x2 - x1 = g ( x2' - x1' )
from which you find
L' = x2'-x1' = 1/g ( x2 - x1 ) = 1/g L

So you see that the measured length L' is shorter than the proper
length L.

3.

If I calculate my prediction for the measurement of the length
contracted rod, and then decide that another observer should take part
in the experiment, with a different relative velocity to myself and the
rod. In this case, I'm going to need to predictions, what I measure and
what the other observer measures. Can I derive those predictions with a
single set of initial conditions for the mathematical model of SR, or
do I crunch two separate problems?

The contraction factor 1/g depends on the velocity:
1/g = sqrt(1-v^2/c^2)

Dirk Vdm

Dirk Van de moortel wrote:
"MobyDikc" wrote in message oups.com...
Hello,

A couple questions:

1.

Let's say I'm doing an experiment, measuring the length of a rod. I can
use special relativity to predict the effects of length contraction on
that measurement given the initial conditions of the experiment (length
of rod, relative velocities, ect). Correct?

yes


2.

Not necessarily related to my next question but just for kicks can some
show me how the mathematical model of SR is used to solve a problem
like this?

It is not really a problem, just a little application.

The mathematics would go somewhat like this.

Suppose that the rod is at rest in a frame S where coordinates
x and t are used. Suppose that the rod has length L in that frame.
L is the what is called the "proper length" of the rod.
Suppose you are at rest in a frame S' where coordinates x' and t'
are used.
Suppose that you move with velocity v with respect to the rod
and that the direction of motion is in the direction of the rod.
Suppose that the clocks are set to zero when and where the
origins of the frame coincide.
This fixes the coincidence event O of the origins of the frames S
and S' to be given by
O: (x,t) = (x',t') = (0,0).
This also fixes the transformation of the coordinates to be given by
x' = g ( x - v t )
t' = g ( t - v x /c^2 )
where
g = 1/sqrt(1-v^2/c^2)
or equivalently by
x = g ( x' + v t' )
t = g ( t' + v x' /c^2 )
The first two equations give the (x',t') coordinates of an event of
which the (x,t) coordinates are known. The last two equations do
the opposite.

Now, the rod.
If you want to measure the length of it, you must measure the
distance of the two end points at the same time according to you.
That is crucial. So you need the distance between the end points
at two events
E1: (x',t') = (x1',T')
E2: (x',t') = (x2',T')
where T' is some arbitrary time on your clock.
The the length that you will measure will be
L' = x2' - x1'

Now you must pick one of the equations that gives a relation
between the coordinates x and x', but where you also use the
known time t'=T'.
There is one candidate for this:
x = g ( x' + v t' )
You fill in the coordinates for the first event:
x1 = g ( x1' + v T' )
and for the second event:
x2 = g ( x2' + v T' )
Since we have used the same time t'=T', this can be easily
eliminated by subtracting the equations:
x2 - x1 = g ( x2' - x1' )
from which you find
L' = x2'-x1' = 1/g ( x2 - x1 ) = 1/g L

So you see that the measured length L' is shorter than the proper
length L.

Wow, thanks, Dirk. I'm going on a train ride tonight (26 hours long) so
I'm going to print this out and see what I can make of it.

As I said, my next question is the main inquirey I have right now, but
I really appreciate your response to this one.


3.

If I calculate my prediction for the measurement of the length
contracted rod, and then decide that another observer should take part
in the experiment, with a different relative velocity to myself and the
rod. In this case, I'm going to need to predictions, what I measure and
what the other observer measures. Can I derive those predictions with a
single set of initial conditions for the mathematical model of SR, or
do I crunch two separate problems?

The contraction factor 1/g depends on the velocity:
1/g = sqrt(1-v^2/c^2)

So, to make sure I understand fully: an experiment with two observers
requires two predictions, so the mathematical model of SR must be
applied twice, to two sets of intial conditions.

Correct?

"MobyDikc" wrote in message oups.com...
Dirk Van de moortel wrote:
"MobyDikc" wrote in message oups.com...
Hello,

A couple questions:

[snip]


3.

If I calculate my prediction for the measurement of the length
contracted rod, and then decide that another observer should take part
in the experiment, with a different relative velocity to myself and the
rod. In this case, I'm going to need to predictions, what I measure and
what the other observer measures. Can I derive those predictions with a
single set of initial conditions for the mathematical model of SR, or
do I crunch two separate problems?

The contraction factor 1/g depends on the velocity:
1/g = sqrt(1-v^2/c^2)

So, to make sure I understand fully: an experiment with two observers
requires two predictions, so the mathematical model of SR must be
applied twice, to two sets of intial conditions.

Correct?

I don't really understand that question.

In this particular example, you are the observer corresponding
to frame S'. I can imagine another observer being at home in
some frame we could call S", and that has a velocity u w.r.t.
frame S, such that the transformation is given by
x" = gu ( x - u t )
t" = gu ( t - u x /c^2 )
where
gu = 1/sqrt(1-u^2/c^2)
or equivalently by
x = gu ( x" + u t" )
t = gu ( t" + u x" /c^2 )
Okay.
Now, in order for me to understand the question, what exactly
do you mean with
"predictions",
"inititial conditions"
"sets of initial conditions"
in the setup of this particular example.

Dirk Vdm

Dirk Van de moortel wrote:
"MobyDikc" wrote in message oups.com...
Dirk Van de moortel wrote:
"MobyDikc" wrote in message oups.com...
Hello,

A couple questions:

[snip]


3.

If I calculate my prediction for the measurement of the length
contracted rod, and then decide that another observer should take part
in the experiment, with a different relative velocity to myself and the
rod. In this case, I'm going to need to predictions, what I measure and
what the other observer measures. Can I derive those predictions with a
single set of initial conditions for the mathematical model of SR, or
do I crunch two separate problems?

The contraction factor 1/g depends on the velocity:
1/g = sqrt(1-v^2/c^2)

So, to make sure I understand fully: an experiment with two observers
requires two predictions, so the mathematical model of SR must be
applied twice, to two sets of intial conditions.

Correct?

I don't really understand that question.

In this particular example, you are the observer corresponding
to frame S'. I can imagine another observer being at home in
some frame we could call S", and that has a velocity u w.r.t.
frame S, such that the transformation is given by
x" = gu ( x - u t )
t" = gu ( t - u x /c^2 )
where
gu = 1/sqrt(1-u^2/c^2)
or equivalently by
x = gu ( x" + u t" )
t = gu ( t" + u x" /c^2 )
Okay.
Now, in order for me to understand the question, what exactly
do you mean with
"predictions",
"inititial conditions"
"sets of initial conditions"
in the setup of this particular example.

Previouslly you showed me (though I may be wrong) how to find the
measured length of a rod given its proper length and the relative
velocity of the measurer.

The prediction is the measured length. The initial conditions are the
relative velocity of the observer and the proper length.

What I'm wondering is, can the mathematical model of special relativity
be applied to a single set of initial conditions and still describe the
universe for multiple observers, or is a new set of initial conditions
always required for every new observer taken into consideration?

"MobyDikc" wrote in message ups.com...
Dirk Van de moortel wrote:
"MobyDikc" wrote in message oups.com...
Dirk Van de moortel wrote:
"MobyDikc" wrote in message oups.com...
Hello,

A couple questions:

[snip]


3.

If I calculate my prediction for the measurement of the length
contracted rod, and then decide that another observer should take part
in the experiment, with a different relative velocity to myself and the
rod. In this case, I'm going to need to predictions, what I measure and
what the other observer measures. Can I derive those predictions with a
single set of initial conditions for the mathematical model of SR, or
do I crunch two separate problems?

The contraction factor 1/g depends on the velocity:
1/g = sqrt(1-v^2/c^2)

So, to make sure I understand fully: an experiment with two observers
requires two predictions, so the mathematical model of SR must be
applied twice, to two sets of intial conditions.

Correct?

I don't really understand that question.

In this particular example, you are the observer corresponding
to frame S'. I can imagine another observer being at home in
some frame we could call S", and that has a velocity u w.r.t.
frame S, such that the transformation is given by
x" = gu ( x - u t )
t" = gu ( t - u x /c^2 )
where
gu = 1/sqrt(1-u^2/c^2)
or equivalently by
x = gu ( x" + u t" )
t = gu ( t" + u x" /c^2 )
Okay.
Now, in order for me to understand the question, what exactly
do you mean with
"predictions",
"inititial conditions"
"sets of initial conditions"
in the setup of this particular example.

Previouslly you showed me (though I may be wrong) how to find the
measured length of a rod given its proper length and the relative
velocity of the measurer.

The prediction is the measured length. The initial conditions are the
relative velocity of the observer and the proper length.

What I'm wondering is, can the mathematical model of special relativity
be applied to a single set of initial conditions and still describe the
universe for multiple observers, or is a new set of initial conditions
always required for every new observer taken into consideration?

I think "initial conditions" is not a good choice as a name
for the pair (relative velocity of the observer / proper
length of the rod).
Reason: one element of the set depends on the observer
and the other element does not.
And of course the term "initial conditions" is already used
in the technical context of differential equations.

But apart from that, having relabelled the gamma's g and gu as
g(v) = 1/sqrt(1-v^2/c^2)
g(u) = 1/sqrt(1-u^2/c^2) ,
observer S' predicts to measure
L' = 1/g(v) L
and observer S" predicts to measure
L" = 1/g(u) L
The left hand sides of these equations show the "predictions"
and the right hand side contain the "initial conditions".

Clearly the same model has been applied to two different
sets of conditions (unless u = v) and "describes the Universe"
for two observers, *and* a new set of initial conditions is used
for each observer taken into consideration.
Perhaps this answers the question?

I would rather attach the label
"describing the Universe"
to the act of
"Calculating the proper length L of the rod from the
measured length L' using the known value v ( and
of course g(v) ) with the equation L = g(v) L' "
in stead of to the act of
"Measuring length L' as the coordinate length of the
rod"

Exercise: why would I prefer the former?

Dirk Vdm

Dirk Van de moortel wrote:

snip
Clearly the same model has been applied to two different
sets of conditions (unless u = v) and "describes the Universe"
for two observers, *and* a new set of initial conditions is used
for each observer taken into consideration.
Perhaps this answers the question?

It does indeed, thanks.

Do you know much about Process physics? I'm trying to get a clear
answer if Process physics "predicts" length contraction differently
insofar as it can allows you to derive the measurements of several
observers based on one mathematical and one set of initial conditions.

Does anyone know if that's correct?

snip

"MobyDikc" wrote in message ups.com...
Dirk Van de moortel wrote:

snip
Clearly the same model has been applied to two different
sets of conditions (unless u = v) and "describes the Universe"
for two observers, *and* a new set of initial conditions is used
for each observer taken into consideration.
Perhaps this answers the question?

It does indeed, thanks.

Do you know much about Process physics?

Frankly, it severely sounds like gibberish:

http://www.scieng.flinders.edu.au/cp...ssphysics.html
| "A new paradigm for the modelling of reality is
| currently being developed called Process Physics.
| In Process Physics we start from the premise that
| the limits to logic, which are implied by Gödel's
| incompleteness theorems, mean that any attempt to
| model reality via a formal system is doomed to failure.
| Instead of formal systems we use a process system,
| which uses the notions of self-referential noise and
| self-organised criticality to create a new type of
| information-theoretic system that is realising both the
| current formal physical modelling of reality but is also
| exhibiting features such as the direction of time, the
| present moment effect and quantum state entanglement
| (including EPR effects, nonlocality and contextuality),
| as well as the more familiar formalisms of Relativity
| and Quantum Mechanics. In particular a theory of
| Quantum Gravity has already emerged.
|
| In short, rather than the static 4-dimensional modelling
| of present day (non-process) physics, Process Physics is
| providing a dynamic model where space and matter are
| seen to emerge from a fundamentally random but self-
| organising system. The key insight is that to adequately
| model reality we must move on from the traditional non-
| process syntactical information modelling to a process
| semantic information modelling; such information is
| `internally meaningful'. "

http://www.scieng.flinders.edu.au/cp...l_r/Steene.pdf
| "Flinders University theoretical physicist Reg Cahill has
| turned the scientific world on its ear by claiming he has
| found science's Holy Grail - the fabled Theory of
| Everything."

I'm trying to get a clear
answer if Process physics "predicts" length contraction differently
insofar as it can allows you to derive the measurements of several
observers based on one mathematical and one set of initial conditions.

Does anyone know if that's correct?

Having seen what is written about process physics, I will
certainly not waste my time with it, so I can't give you an
answer on this.


snip


How come you didn't make the exercise?

Dirk Vdm

"MobyDikc" wrote in message ups.com...
Dirk Van de moortel wrote:

snip
Clearly the same model has been applied to two different
sets of conditions (unless u = v) and "describes the Universe"
for two observers, *and* a new set of initial conditions is used
for each observer taken into consideration.
Perhaps this answers the question?

It does indeed, thanks.

Do you know much about Process physics?

A quick Google search of the subject show it to
be as nutty as a fruitcake.

Martin Hogbin