Uncle Ben
2009-02-16 14:32:43 UTC
On Feb 13, 2009, 9:51 am (EST), "Androcles"
Albert Einstein, writing in the 20th, can write an equation containing
the factors (c+v) and (c-v) and yet claim that the speed c is a
universal constant. Thus in his delicate and tactful manner,
Androcles suggests that Einstein violates the 2nd Postulate of SR,
when actually Einstein is merely calculating the time of closure
between a light wave with speed c and a target moving at speed v. If
the target is moving away from the oncoming light beam, the distance
betweem them decreases at the rate c-v; if it is moving towards the
oncoming beam, the closing rate is c-v.
Some of us have used the term "closing speed" for the factors quoted
above, and this has mystified Androcles. Closing speed is the rate of
change of the distance between two objects as they both move. Closing
speed is certainly a rate of change of a distance, but in the given
frame of reference, there is no material object nor even a photon that
moves with that speed.
Relative speed, the speed of one object relative to another, is a
different matter. In Galilean physics, there is no difference between
closing speed and relative speed, because distance and time are on the
same scale regardless of motion between the two frames of reference.
Relative speed, in short, is the speed of one object with respect to a
frame of reference in which the other object is at rest.
Gaileo's big year was 1605. Jump forward 300 years to 1905, leaving
Androcles behind, and Einstein is theorizing that distance and time
change their scales with motion so as to preserve the speed of light
between frames. This is where the difference between closing speed
and relative speed arises.
Consider two light beams aimed at each other, each travelling at speed
c. The distance between their light fronts decreases at the rate 2c,
and this is the closing speed.
To compute their relative speed starting with a Lorentz transformation
with frame speed c is complicated by a singularity in the
transformation. But the general result for sub-luminal speeds u and
v
(u+v) / (1 + uv/c^2)
does not have that singularity. The resulting formula for relative
speed in this case is
(c+c)/(1 + c*c/c^2), which simplfies easily to c.
Androcles has recently omitted his signature complaint about
Einstein's calculations. Maybe the penny in the slot has finally
dropped. But don't count on it yet.
Uncle Ben
Snivelling relativistic lying bastard trolls claim that c+v is not the
speed of anything or is a "closing speed", accusing mathematicians
of not being able to distinguish a "closing speed" from a "relative
speed" (which, with all honesty, I readily own that I cannot -'
Poor Androcles, stuck in the 19th century, cannot understand howspeed of anything or is a "closing speed", accusing mathematicians
of not being able to distinguish a "closing speed" from a "relative
speed" (which, with all honesty, I readily own that I cannot -'
Albert Einstein, writing in the 20th, can write an equation containing
the factors (c+v) and (c-v) and yet claim that the speed c is a
universal constant. Thus in his delicate and tactful manner,
Androcles suggests that Einstein violates the 2nd Postulate of SR,
when actually Einstein is merely calculating the time of closure
between a light wave with speed c and a target moving at speed v. If
the target is moving away from the oncoming light beam, the distance
betweem them decreases at the rate c-v; if it is moving towards the
oncoming beam, the closing rate is c-v.
Some of us have used the term "closing speed" for the factors quoted
above, and this has mystified Androcles. Closing speed is the rate of
change of the distance between two objects as they both move. Closing
speed is certainly a rate of change of a distance, but in the given
frame of reference, there is no material object nor even a photon that
moves with that speed.
Relative speed, the speed of one object relative to another, is a
different matter. In Galilean physics, there is no difference between
closing speed and relative speed, because distance and time are on the
same scale regardless of motion between the two frames of reference.
Relative speed, in short, is the speed of one object with respect to a
frame of reference in which the other object is at rest.
Gaileo's big year was 1605. Jump forward 300 years to 1905, leaving
Androcles behind, and Einstein is theorizing that distance and time
change their scales with motion so as to preserve the speed of light
between frames. This is where the difference between closing speed
and relative speed arises.
Consider two light beams aimed at each other, each travelling at speed
c. The distance between their light fronts decreases at the rate 2c,
and this is the closing speed.
To compute their relative speed starting with a Lorentz transformation
with frame speed c is complicated by a singularity in the
transformation. But the general result for sub-luminal speeds u and
v
(u+v) / (1 + uv/c^2)
does not have that singularity. The resulting formula for relative
speed in this case is
(c+c)/(1 + c*c/c^2), which simplfies easily to c.
Androcles has recently omitted his signature complaint about
Einstein's calculations. Maybe the penny in the slot has finally
dropped. But don't count on it yet.
Uncle Ben