Re http://hermes.physics.adelaide.edu.a.../velocity.html

Suppose an object A is moving with a velocity v relative to an object
B and B is moving with a velocity u (in the same direction) relative
to an object C. What is the velocity of A relative to C?

v
u ------- A
------- B
C w
-----------------

Could someone please attempt to explain the reason for the reference
frame changing such as in the above? Why not stick to one reference
frame, such as C, and get both the speed/velocity of B and A relative
to it?
I also have an issue about "time", perhaps also about reference frames
and "observers", but for later.
Peter Kinanehttp://www.effectuationism.com/

Peter Kinane wrote:

Re

http://hermes.physics.adelaide.edu.a.../velocity.html

Suppose an object A is moving with a velocity v relative to an object
B and B is moving with a velocity u (in the same direction) relative
to an object C. What is the velocity of A relative to C?

v
u ------- A
------- B
C w
-----------------

Could someone please attempt to explain the reason for the reference
frame changing such as in the above? Why not stick to one reference
frame, such as C, and get both the speed/velocity of B and A relative
to it?
I also have an issue about "time", perhaps also about reference frames
and "observers", but for later.
Peter Kinanehttp://www.effectuationism.com/

Multiple refrence frames are something I do everyday. Consider the real life
problem of trying to get, say, a rover to Mars. Look at what gets involved.
The co-ordinate system of the launch vehicle, the co-ordinate system of the
landing vehicle, a coordinate system attached to the earth (earth centered
earth fixed), a coordinate system centered on the sun, a coordinate system
centered on mars. So why do things in all theses systems when we know at
least one mission failed due to one transformation not being done
correctlY? Only because it is easier. If your problem can be easily solved
by choosing one coordinate system and sticking to it, do so. If C is
inertial and the desired final references are relative to C, make it
stationary and go from there. BTW, in your example, there is an unshown
system D that has a velocity of 0. Thus C is moving at velocity w relative
to D, B is moving at velocity u relative to D, A is moving at velocity A
relative to D.
In the end, I would say don't do any coordinate transformations you don't
have to, but be sure to do all you need to.
--
Russ Lyttle

"Peter Kinane" wrote in message
om...
Re
http://hermes.physics.adelaide.edu.a.../velocity.html

Suppose an object A is moving with a velocity v relative to an object
B and B is moving with a velocity u (in the same direction) relative
to an object C. What is the velocity of A relative to C?

v
u ------- A
------- B
C w
-----------------

Could someone please attempt to explain the reason for the reference
frame changing such as in the above? Why not stick to one reference
frame, such as C, and get both the speed/velocity of B and A relative
to it?

Any one frame of reference (FOR) is just as good as any other. The laws of
nature are the same as measured in FOR-A as in FOR-B or FOR-C. The *exact
values* measured for *relative phenomena such as velocity will change
dependent on the FOR.

For the following, we can establish that there are no accelerations going
on, so that all motions are inertial.

In FOR-A, for example, the velocity of A is zero, but the velocity of B
is -v, while in FOR-B, the velocity of B is zero and the velocity of A is +v
(assuming that they both follow the same sign convention with velocities to
the right being positive).

Both of them will measure the speed of light in a vacuum to be c. When we
consider FOR-C, however, thing get a little confusing. The velocity of B
relative to FOR-C (and of C relative to FOR-B) acts just like the velocity
of A relative to FOR-B and of B relative to FOR-A.

Where gets confusing (read "counterintuitive"), however is when we realize
that all 3 FORs must get the same value for the speed of light in a vacuum.
That means that if we get 3 identical experimental set-ups going, one in
each frame of reference, that will measure the speed of light in a vacuum,
then observers in EACH frame of reference will see the identical result in
ALL THREE experimental set-ups: the setups in A and B (both of which are
moving relative to FOR-C) will both produce exactly the same result as the
setup at C that is *not* moving in FOR-C.

The math gets a little Byzantine for people used to Euclidean geometry and
simple addition, but the conclusion is that velocities (which have physical
dimension) do not add like abstract numbers.

IOW, w does NOT equal u + v.

Because the measurement of the speed of light in a vacuum involves measuring
both distance AND time, it turns out that the only way that all three
observers can get the same number from all three experimental set-ups
independently is if the apparent flow of time and static distances in each
FOR is distorted as observed in any other FOR such that

w = (u + v)/(1 + u*v/c^2)

HTH


Tom Davidson
Richmond, VA

"Peter Kinane" wrote in message
om...
Re
http://hermes.physics.adelaide.edu.a.../velocity.html

Suppose an object A is moving with a velocity v relative to an object
B and B is moving with a velocity u (in the same direction) relative
to an object C. What is the velocity of A relative to C?

v
u ------- A
------- B
C w
-----------------

Could someone please attempt to explain the reason for the reference
frame changing such as in the above?

Yes, I'll explain. It won't help much, but there is a reason.
A is moving at velocity w with respect to c.
A is moving at v with respect to B
B is moving at u with respect to C
Now we define some function, call it f, and state
w = f(u,v)
u = f(w,-v)
v = f(w,-u)
At first glance, it would seem that f(u,v) = u+v.

Then you are asked if there is some other function g, g =/= f, such that
w = g(u,v)
u = g(w,-v)
v = g(w,-u)

so that
c v -c
Q----- u ------- A ----P
------- B
C w
-----------------
all three, A, B and C, observe the same velocities c and -c from P and Q.

Why not stick to one reference
frame, such as C, and get both the speed/velocity of B and A relative
to it?
Because that would be no fun!

I also have an issue about "time", perhaps also about reference frames
and "observers", but for later.
Peter Kinanehttp://www.effectuationism.com/
Any 'time' will do

Androcles

"tadchem" wrote in message ...
"Peter Kinane" wrote in message
om...
Re
http://hermes.physics.adelaide.edu.a.../velocity.html

Suppose an object A is moving with a velocity v relative to an object
B and B is moving with a velocity u (in the same direction) relative
to an object C. What is the velocity of A relative to C?

v
u ------- A
------- B
C w
-----------------

Could someone please attempt to explain the reason for the reference
frame changing such as in the above? Why not stick to one reference
frame, such as C, and get both the speed/velocity of B and A relative
to it?

Any one frame of reference (FOR) is just as good as any other. The laws of
nature are the same as measured in FOR-A as in FOR-B or FOR-C. The *exact
values* measured for *relative phenomena such as velocity will change
dependent on the FOR.


"Absolute time, in astronomy, is distinguished from relative, by the
equation or correlation of the vulgar time. For the natural days are
truly unequal, though they are commonly considered as equal and used
for a measure of time; astronomers correct this inequality for their
more accurate deducing of the celestial motions. It may be, that there
is no such thing as an equable motion, whereby time may be accurately
measured." Principia

Tommy boy,Newton when he defines and distinguishes absolute time from
relative time by means of the Equation of Time the basis for this is
axial rotation of the Earth in 24 hours through 360 degrees,you have
no choice in the matter.

Relativist shifted the 'frame of reference' for axial rotation through
360 degrees to 23 hours 56 min 04 sec and for the first time in
history of astronomy,idiots determined that there is equable motion
through 360 degrees by means of stellar circumpolar motion.


As the basis for the equable 24 hour day is within the grasp of anyone
who studies the development of clocks,it is amazing that the geometric
and astronomical principles which Newton accurately reflects are
left in the hands of Albert and his cult followers who,in dealing with
Newton's definitions and distinctions, seem to be devoid of the
slightest trace of recognition of the original purpose and intent of
the text of the Principia and the accurate description of the EoT in
terms of the axial rotation of the Earth.

The history of man has produced men with the most absurd outlook but
relativity takes some beating.The counterintuitive part is that most
people know what the rotation of the Earth is and how clocks and
geometry mesh in terms of the 24 hour/360 degree equivalency but
relativists decide that it is the stellar circumpolar value of 23 hrs
56 min 04 sec.

Want to see 'warped space' ?, here it is -

http://home.t-online.de/home/sjkowollik/polaris.jpg



If your opponents ever get around to clarifying Newton's definition of
the equable 24 hour day from the natural unequal day via the
astronomical Equation of Time computation ,they may join in the fun
of seeing how your 'frames of reference' look plain silly,seeing that
you picked the wrong one for the axial rotation of the Earth.

"Androcles" wrote in message
...

"Peter Kinane" wrote in message
om...
Re
http://hermes.physics.adelaide.edu.a.../velocity.html

Suppose an object A is moving with a velocity v relative to an object
B and B is moving with a velocity u (in the same direction) relative
to an object C. What is the velocity of A relative to C?

Yes, I'll explain. It won't help much, but there is a reason.

Androcles is one of the regular crackpots on this group.

Martin Hogbin

"Russ Lyttle" wrote in message hlink.net...
Peter Kinane wrote:

Re

http://hermes.physics.adelaide.edu.a.../velocity.html

Suppose an object A is moving with a velocity v relative to an object
B and B is moving with a velocity u (in the same direction) relative
to an object C. What is the velocity of A relative to C?

v
u ------- A
------- B
C w
-----------------

Could someone please attempt to explain the reason for the reference
frame changing such as in the above? Why not stick to one reference
frame, such as C, and get both the speed/velocity of B and A relative
to it?
I also have an issue about "time", perhaps also about reference frames
and "observers", but for later.
Peter Kinanehttp://www.effectuationism.com/

Multiple refrence frames are something I do everyday. Consider the real life
problem of trying to get, say, a rover to Mars. Look at what gets involved.
The co-ordinate system of the launch vehicle, the co-ordinate system of the
landing vehicle, a coordinate system attached to the earth (earth centered
earth fixed), a coordinate system centered on the sun, a coordinate system
centered on mars. So why do things in all theses systems when we know at
least one mission failed due to one transformation not being done
correctlY? Only because it is easier. If your problem can be easily solved
by choosing one coordinate system and sticking to it, do so. If C is
inertial and the desired final references are relative to C, make it
stationary and go from there. BTW, in your example, there is an unshown
system D that has a velocity of 0. Thus C is moving at velocity w relative
to D, B is moving at velocity u relative to D, A is moving at velocity A
relative to D.
In the end, I would say don't do any coordinate transformations you don't
have to, but be sure to do all you need to.
--
Russ Lyttle



Thank you; that is quite helpful- -reassuring.

In the case of "the rover" it seems to make sense to progress to new
FOR at different stages of the exercise.

"If C is inertial and the desired final references are relative to C,
make it stationary and go from there.": Good.

"BTW, in your example, there is an unshown system D that has a
velocity of 0.": I was somewhat overlooking that. So, that would seem
to imply that C is not the (essential) FOR, or that there is rather
hectic FOR jumping - which makes it a somewhat better example, given
the topic?

Re "Thus C is moving at velocity w relative to D, B is moving at
velocity u relative to D": Would that imply that "B is moving at
velocity u relative to D" and, as stated, "B is moving with a velocity
u (in the same direction) relative to an object C", even though "C is
moving at velocity w relative to D"? Or is there some confusion in
saying "B is moving at velocity u relative to D"?

"In the end, I would say don't do any coordinate transformations you
don't have to, but be sure to do all you need to.": Indeed; I'm just
taking a look, with your kind help, at the efficiency of the general
discipline.


--
Peter Kinane
http://www.effectuationism.com/

"tadchem" wrote in message ...

"Peter Kinane" wrote in message
om...
Re
http://hermes.physics.adelaide.edu.a.../velocity.html

Suppose an object A is moving with a velocity v relative to an object
B and B is moving with a velocity u (in the same direction) relative
to an object C. What is the velocity of A relative to C?

v
u ------- A
------- B
C w
-----------------

Could someone please attempt to explain the reason for the reference
frame changing such as in the above? Why not stick to one reference
frame, such as C, and get both the speed/velocity of B and A relative
to it?

Any one frame of reference (FOR) is just as good as any other. The laws of
nature are the same as measured in FOR-A as in FOR-B or FOR-C. The *exact
values* measured for *relative phenomena such as velocity will change
dependent on the FOR.

For the following, we can establish that there are no accelerations going
on, so that all motions are inertial.

In FOR-A, for example, the velocity of A is zero, but the velocity of B
is -v, while in FOR-B, the velocity of B is zero and the velocity of A is +v
(assuming that they both follow the same sign convention with velocities to
the right being positive).

While I'm not sure I wish to address the 'conventional conventions'
about light at this stage, could you please say a little about why
'approaching' velocities are stated as -v while 'departing' velocity
is +v? I mean, for example, if "the velocity of A is zero", why should
the velocity of B be in part determined by whether it is 'approaching'
or 'departing'? (I'm presuming that there is a difference in velocity
between -v and +v and that it is due to the 'approach' versus 'depart'
distinction).


Both of them will measure the speed of light in a vacuum to be c. When we
consider FOR-C, however, thing get a little confusing. The velocity of B
relative to FOR-C (and of C relative to FOR-B) acts just like the velocity
of A relative to FOR-B and of B relative to FOR-A.

Where gets confusing (read "counterintuitive"), however is when we realize
that all 3 FORs must get the same value for the speed of light in a vacuum.
That means that if we get 3 identical experimental set-ups going, one in
each frame of reference, that will measure the speed of light in a vacuum,
then observers in EACH frame of reference will see the identical result in
ALL THREE experimental set-ups: the setups in A and B (both of which are
moving relative to FOR-C) will both produce exactly the same result as the
setup at C that is *not* moving in FOR-C.

Re "then observers in EACH frame of reference": In my opening: "I also
have an issue [] perhaps also about reference frames and
"observers"[]". Are you saying- -implying, for example, that A moving
in FOR C is an observer (of the speed of light in a vacuum)? I mean,
it would appear to me that either A is an FOR, in which case C's view
of A is irrelevant, or A is not an FOR - and so not an observer.


The math gets a little Byzantine for people used to Euclidean geometry and
simple addition, but the conclusion is that velocities (which have physical
dimension) do not add like abstract numbers.

IOW, w does NOT equal u + v.

Because the measurement of the speed of light in a vacuum involves measuring
both distance AND time, it turns out that the only way that all three
observers can get the same number from all three experimental set-ups
independently is if the apparent flow of time and static distances in each
FOR is distorted as observed in any other FOR such that

w = (u + v)/(1 + u*v/c^2)

Re "involves measuring both distance AND time": Well, I'll leave
"time" wait a bit, if I may.


HTH



--
Peter Kinane
http://www.effectuationism.com/

"Androcles" wrote in message ...

"Peter Kinane" wrote in message
om...
Re
http://hermes.physics.adelaide.edu.a.../velocity.html

Suppose an object A is moving with a velocity v relative to an object
B and B is moving with a velocity u (in the same direction) relative
to an object C. What is the velocity of A relative to C?

v
u ------- A
------- B
C w
-----------------

Could someone please attempt to explain the reason for the reference
frame changing such as in the above?

Yes, I'll explain. It won't help much, but there is a reason.
A is moving at velocity w with respect to c.

Sorry I'm not able to get further into your reply, at this point. I'm
not readily quite clear and comfortable about the premises to, or
connotations of "A is moving at velocity w with respect to c". Perhaps
better luck further into the thread.

A is moving at v with respect to B
B is moving at u with respect to C
Now we define some function, call it f, and state
w = f(u,v)
u = f(w,-v)
v = f(w,-u)
At first glance, it would seem that f(u,v) = u+v.

Then you are asked if there is some other function g, g =/= f, such that
w = g(u,v)
u = g(w,-v)
v = g(w,-u)

so that
c v -c
Q----- u ------- A ----P
------- B
C w
-----------------
all three, A, B and C, observe the same velocities c and -c from P and Q.

Why not stick to one reference
frame, such as C, and get both the speed/velocity of B and A relative
to it?
Because that would be no fun!

I also have an issue about "time", perhaps also about reference frames
and "observers", but for later.
Peter Kinanehttp://www.effectuationism.com/
Any 'time' will do


--
Peter Kinane
http://www.effectuationism.com/

Peter Kinane wrote:
Re http://hermes.physics.adelaide.edu.a.../velocity.html

Suppose an object A is moving with a velocity v relative to an object
B and B is moving with a velocity u (in the same direction) relative
to an object C. What is the velocity of A relative to C?

v
u ------- A
------- B
C w
-----------------

Could someone please attempt to explain the reason for the reference
frame changing such as in the above? Why not stick to one reference
frame, such as C, and get both the speed/velocity of B and A relative
to it?

The answer is that you solve the problem in whichever frame
is easiest and then transform to the frame where you need to
know the result. Generally speaking, you always *can* solve
any problem in a single, arbitrary frame, but it often gets
ridiculously complicated.

Taking an example from real life, when a muon decays
at rest, we know what energy distribution of the resulting electron
looks like. Now what about a muon decaying in flight? Do I have
to do the calculation all over again? No; I take the electron
distribution for the muon at rest (call if frame "B" above), and
tranform it into the frame where my detector is (say, frame "C").
This is very straightforward and turn-key.

Now, yes, I could have re-calculated everything starting with
a muon in flight, but that would have been ridiculously hard.

This is not just true of special relativity. As an exercise,
start from first principles and try to calculate simple,
non-relativistic, elastic scattering for two bodies colliding
with arbitrary velocity vectors. You'll find that pretty soon
you have several pages of algebra, and unless you spot some
clever tricks, you'll be hopelessly
bogged. In fact, it's very messy even in one dimension.
Now do the same problem by transforming to the center of mass
frame, and then transforming back, and you'll find it's trivial.

We can see another good example of the importance of
reference frames on the news today. Imagine if you had to
calculate orbital insertion for Mars working in the
frame of the Earth!!! It absolutely *could* be done,
but I'd sure as hell hate to be the one to do it.

-E


I also have an issue about "time", perhaps also about reference frames
and "observers", but for later.
Peter Kinanehttp://www.effectuationism.com/