NEWTON CHALLENGES EINSTEIN

A javelin graduated in centimeters is thrown downwards from the top of
a tower of height h. Initially the centimeter marks pass an observer
at the top of the tower with frequency f, speed s and "wavelength" L
(1cm):

f = s/L

What are the frequency f', speed s' and "wavelength" L' as measured by
an observer on the ground? Newton gives a straightforward answer (it
is assumed that s's'-s):

f' = f(1+gh/s^2) = (s+v)/L
s' = s(1+gh/s^2) = s+v
L' = L

where v=s'-s is the increase in speed.

Then the observer at the top of the tower emits light towards the
ground. Relative to this observer, the light has frequency f, speed c
and wavelength L:

f = c/L

What are the frequency f', speed c' and wavelength L' as measured by
an observer on the ground? Newton's emission theory of light gives a
straightforward answer again:

f' = f(1+gh/c^2) = (c+v)/L
c' = c(1+gh/c^2) = c+v
L' = L

where v=c'-c is the increase in speed.

The answer given by Einstein's relativity is by no means
straightforward:

f' = f(1+gh/c^2) = ...
c' = ... = ...
L' = ...

In 1911 Einstein explicitly recognized the equation c'=c(1+gh/c^2) but
simultaneously contested it by introducing gravitational time
dilation:

http://www.conspiracyoflight.com/Lig...onal_Field.pdf
"In 1911 Einstein published the paper "On the Influence of Gravitation
on the Propagation of Light." (...) Light is blue-shifted (has a
higher frequency) as it approaches a massive body... (...) Similarly,
light red-shifts and goes to a lower frequency as it escapes a massive
body... (...) To counter the absurdity that more or less periods per
second can be received than were emitted, Einstein argues that this is
because the time is dilated near a massive body... (...) When the
velocity of light c is measured at S1 and S2 with identical clocks in
local time, the speed of light is always the same. When clocks
corrected for gravitational time dilation are used instead, (count in
common or absolute time) the light at S2 is travelling faster than the
light at S1. The speed of light c is no longer constant, but increases
with increasing phi. c=co(1+phi/c^2). where co is the speed of light
when phi=0."

In 1915 Einstein replaced c'=c(1+gh/c^2) with c'=c(1+2gh/c^2):

http://www.mathpages.com/rr/s6-01/6-01.htm
"In geometrical units we define c_0 = 1, so Einstein's 1911 formula
can be written simply as c=1+phi. However, this formula for the speed
of light (not to mention this whole approach to gravity) turned out to
be incorrect, as Einstein realized during the years leading up to 1915
and the completion of the general theory. In fact, the general theory
of relativity doesn't give any equation for the speed of light at a
particular location, because the effect of gravity cannot be
represented by a simple scalar field of c values. Instead, the "speed
of light" at a each point depends on the direction of the light ray
through that point, as well as on the choice of coordinate systems, so
we can't generally talk about the value of c at a given point in a non-
vanishing gravitational field. However, if we consider just radial
light rays near a spherically symmetrical (and non- rotating) mass,
and if we agree to use a specific set of coordinates, namely those in
which the metric coefficients are independent of t, then we can read a
formula analogous to Einstein's 1911 formula directly from the
Schwarzschild metric. (...) In the Newtonian limit the classical
gravitational potential at a distance r from mass m is phi=-m/r, so if
we let c_r = dr/dt denote the radial speed of light in Schwarzschild
coordinates, we have c_r =1+2phi, which corresponds to Einstein's 1911
equation, except that we have a factor of 2 instead of 1 on the
potential term."

http://www.speed-light.info/speed_of_light_variable.htm
"Einstein wrote this paper in 1911 in German (download from:
http://www.physik.uni-augsburg.de/an...35_898-908.pdf
). It predated the full formal development of general relativity by
about four years. You can find an English translation of this paper in
the Dover book 'The Principle of Relativity' beginning on page 99; you
will find in section 3 of that paper Einstein's derivation of the
variable speed of light in a gravitational potential, eqn (3). The
result is: c'=c0(1+phi/c^2) where phi is the gravitational potential
relative to the point where the speed of light co is measured......You
can find a more sophisticated derivation later by Einstein (1955) from
the full theory of general relativity in the weak field
approximation....For the 1955 results but not in coordinates see page
93, eqn (6.28): c(r)=[1+2phi(r)/c^2]c. Namely the 1955 approximation
shows a variation in km/sec twice as much as first predicted in 1911."

Finally, Einsteinians replaced c'=c(1+2gh/c^2) with c'=c:

http://www.amazon.com/Brief-History-.../dp/0553380168
Stephen Hawking, "A Brief History of Time", Chapter 6:
"Under the theory that light is made up of waves, it was not clear how
it would respond to gravity. But if light is composed of particles,
one might expect them to be affected by gravity in the same way that
cannonballs, rockets, and planets are.....In fact, it is not really
consistent to treat light like cannonballs in Newton's theory of
gravity because the speed of light is fixed. (A cannonball fired
upward from the earth will be slowed down by gravity and will
eventually stop and fall back; a photon, however, must continue upward
at a constant speed...)"

http://helios.gsfc.nasa.gov/qa_sp_gr.html
"Is light affected by gravity? If so, how can the speed of light be
constant? Wouldn't the light coming off of the Sun be slower than the
light we make here? If not, why doesn't light escape a black hole?
Yes, light is affected by gravity, but not in its speed. General
Relativity (our best guess as to how the Universe works) gives two
effects of gravity on light. It can bend light (which includes effects
such as gravitational lensing), and it can change the energy of light.
But it changes the energy by shifting the frequency of the light
(gravitational redshift) not by changing light speed. Gravity bends
light by warping space so that what the light beam sees as "straight"
is not straight to an outside observer. The speed of light is still
constant." Dr. Eric Christian

http://math.ucr.edu/home/baez/physic..._of_light.html
Steve Carlip: "Einstein went on to discover a more general theory of
relativity which explained gravity in terms of curved spacetime, and
he talked about the speed of light changing in this new theory. In the
1920 book "Relativity: the special and general theory" he wrote:
". . . according to the general theory of relativity, the law of the
constancy of the velocity of light in vacuo, which constitutes one of
the two fundamental assumptions in the special theory of relativity
[. . .] cannot claim any unlimited validity. A curvature of rays of
light can only take place when the velocity of propagation of light
varies with position." Since Einstein talks of velocity (a vector
quantity: speed with direction) rather than speed alone, it is not
clear that he meant the speed will change, but the reference to
special relativity suggests that he did mean so. THIS INTERPRETATION
IS PERFECTLY VALID AND MAKES GOOD PHYSICAL SENSE, BUT A MORE MODERN
INTERPRETATION IS THAT THE SPEED OF LIGHT IS CONSTANT in general
relativity."

Pentcho Valev

On Sat, 11 Sep 2010 21:55:26 -0700 (PDT), Pentcho Valev
wrote:

A javelin graduated in centimeters is thrown downwards from the top of
a tower of height h. Initially the centimeter marks pass an observer
at the top of the tower with frequency f, speed s and "wavelength" L
(1cm):

f = s/L

What are the frequency f', speed s' and "wavelength" L' as measured by
an observer on the ground? Newton gives a straightforward answer (it
is assumed that s's'-s):

f' = f(1+gh/s^2) = (s+v)/L
s' = s(1+gh/s^2) = s+v
L' = L

where v=s'-s is the increase in speed.

Then the observer at the top of the tower emits light towards the
ground. Relative to this observer, the light has frequency f, speed c
and wavelength L:

f = c/L

What are the frequency f', speed c' and wavelength L' as measured by
an observer on the ground? Newton's emission theory of light gives a
straightforward answer again:

f' = f(1+gh/c^2) = (c+v)/L
c' = c(1+gh/c^2) = c+v
L' = L

where v=c'-c is the increase in speed.

The answer given by Einstein's relativity is by no means
straightforward:

f' = f(1+gh/c^2) = ...
c' = ... = ...
L' = ...

In 1911 Einstein explicitly recognized the equation c'=c(1+gh/c^2) but
simultaneously contested it by introducing gravitational time
dilation:

http://www.conspiracyoflight.com/Lig...onal_Field.pdf
"In 1911 Einstein published the paper "On the Influence of Gravitation
on the Propagation of Light." (...) Light is blue-shifted (has a
higher frequency) as it approaches a massive body... (...) Similarly,
light red-shifts and goes to a lower frequency as it escapes a massive
body... (...) To counter the absurdity that more or less periods per
second can be received than were emitted, Einstein argues that this is
because the time is dilated near a massive body... (...) When the
velocity of light c is measured at S1 and S2 with identical clocks in
local time, the speed of light is always the same. When clocks
corrected for gravitational time dilation are used instead, (count in
common or absolute time) the light at S2 is travelling faster than the
light at S1. The speed of light c is no longer constant, but increases
with increasing phi. c=co(1+phi/c^2). where co is the speed of light
when phi=0."

In 1915 Einstein replaced c'=c(1+gh/c^2) with c'=c(1+2gh/c^2):

http://www.mathpages.com/rr/s6-01/6-01.htm
"In geometrical units we define c_0 = 1, so Einstein's 1911 formula
can be written simply as c=1+phi. However, this formula for the speed
of light (not to mention this whole approach to gravity) turned out to
be incorrect, as Einstein realized during the years leading up to 1915
and the completion of the general theory. In fact, the general theory
of relativity doesn't give any equation for the speed of light at a
particular location, because the effect of gravity cannot be
represented by a simple scalar field of c values. Instead, the "speed
of light" at a each point depends on the direction of the light ray
through that point, as well as on the choice of coordinate systems, so
we can't generally talk about the value of c at a given point in a non-
vanishing gravitational field. However, if we consider just radial
light rays near a spherically symmetrical (and non- rotating) mass,
and if we agree to use a specific set of coordinates, namely those in
which the metric coefficients are independent of t, then we can read a
formula analogous to Einstein's 1911 formula directly from the
Schwarzschild metric. (...) In the Newtonian limit the classical
gravitational potential at a distance r from mass m is phi=-m/r, so if
we let c_r = dr/dt denote the radial speed of light in Schwarzschild
coordinates, we have c_r =1+2phi, which corresponds to Einstein's 1911
equation, except that we have a factor of 2 instead of 1 on the
potential term."

http://www.speed-light.info/speed_of_light_variable.htm
"Einstein wrote this paper in 1911 in German (download from:
http://www.physik.uni-augsburg.de/an...35_898-908.pdf
). It predated the full formal development of general relativity by
about four years. You can find an English translation of this paper in
the Dover book 'The Principle of Relativity' beginning on page 99; you
will find in section 3 of that paper Einstein's derivation of the
variable speed of light in a gravitational potential, eqn (3). The
result is: c'=c0(1+phi/c^2) where phi is the gravitational potential
relative to the point where the speed of light co is measured......You
can find a more sophisticated derivation later by Einstein (1955) from
the full theory of general relativity in the weak field
approximation....For the 1955 results but not in coordinates see page
93, eqn (6.28): c(r)=[1+2phi(r)/c^2]c. Namely the 1955 approximation
shows a variation in km/sec twice as much as first predicted in 1911."

Finally, Einsteinians replaced c'=c(1+2gh/c^2) with c'=c:

http://www.amazon.com/Brief-History-.../dp/0553380168
Stephen Hawking, "A Brief History of Time", Chapter 6:
"Under the theory that light is made up of waves, it was not clear how
it would respond to gravity. But if light is composed of particles,
one might expect them to be affected by gravity in the same way that
cannonballs, rockets, and planets are.....In fact, it is not really
consistent to treat light like cannonballs in Newton's theory of
gravity because the speed of light is fixed. (A cannonball fired
upward from the earth will be slowed down by gravity and will
eventually stop and fall back; a photon, however, must continue upward
at a constant speed...)"

http://helios.gsfc.nasa.gov/qa_sp_gr.html
"Is light affected by gravity? If so, how can the speed of light be
constant? Wouldn't the light coming off of the Sun be slower than the
light we make here? If not, why doesn't light escape a black hole?
Yes, light is affected by gravity, but not in its speed. General
Relativity (our best guess as to how the Universe works) gives two
effects of gravity on light. It can bend light (which includes effects
such as gravitational lensing), and it can change the energy of light.
But it changes the energy by shifting the frequency of the light
(gravitational redshift) not by changing light speed. Gravity bends
light by warping space so that what the light beam sees as "straight"
is not straight to an outside observer. The speed of light is still
constant." Dr. Eric Christian

http://math.ucr.edu/home/baez/physic..._of_light.html
Steve Carlip: "Einstein went on to discover a more general theory of
relativity which explained gravity in terms of curved spacetime, and
he talked about the speed of light changing in this new theory. In the
1920 book "Relativity: the special and general theory" he wrote:
". . . according to the general theory of relativity, the law of the
constancy of the velocity of light in vacuo, which constitutes one of
the two fundamental assumptions in the special theory of relativity
[. . .] cannot claim any unlimited validity. A curvature of rays of
light can only take place when the velocity of propagation of light
varies with position." Since Einstein talks of velocity (a vector
quantity: speed with direction) rather than speed alone, it is not
clear that he meant the speed will change, but the reference to
special relativity suggests that he did mean so. THIS INTERPRETATION
IS PERFECTLY VALID AND MAKES GOOD PHYSICAL SENSE, BUT A MORE MODERN
INTERPRETATION IS THAT THE SPEED OF LIGHT IS CONSTANT in general
relativity."

Pentcho Valev




You must be at least 110 years old, Pentcho,
you missed all newer research.

w.

"Pentcho Valev" wrote in message
...
|A javelin graduated in centimeters is thrown downwards from the top of
| a tower of height h. Initially the centimeter marks pass an observer
| at the top of the tower with frequency f, speed s and "wavelength" L
| (1cm):
|
| f = s/L
|
| What are the frequency f', speed s' and "wavelength" L' as measured by
| an observer on the ground? Newton gives a straightforward answer (it
| is assumed that s's'-s):
|
| f' = f(1+gh/s^2) = (s+v)/L
| s' = s(1+gh/s^2) = s+v
| L' = L
|
| where v=s'-s is the increase in speed.
|
| Then the observer at the top of the tower emits light towards the
| ground. Relative to this observer, the light has frequency f, speed c
| and wavelength L:
|
| f = c/L
|
| What are the frequency f', speed c' and wavelength L' as measured by
| an observer on the ground? Newton's emission theory of light gives a
| straightforward answer again:
|
| f' = f(1+gh/c^2) = (c+v)/L
| c' = c(1+gh/c^2) = c+v
| L' = L
|
| where v=c'-c is the increase in speed.
|
| The answer given by Einstein's relativity is by no means
| straightforward:
|
| f' = f(1+gh/c^2) = ...
| c' = ... = ...
| L' = ...
|
An undefined but large number of cars are queued at a toll booth,
bumper-to-bumper. It takes one full minute to pay. As each driver
pays the toll he accelerates from zero to 100 kph (the speed limit),
taking one minute to do so. Cars then remain the same distance
apart for an undefined but large distance, all travelling at 100 kph,
until they arrive at the next toll booth when they slow to zero and
are once again bumper-to-bumper. The process is repeated for
the next stretch of highway.
1) How far apart are the cars that are travelling at 100 kph?
2) At what frequency do cars pass under a bridge midway between
the toll booths?
3) If each car carries a javelin graduated in cm, does this change
the frequency?
4) If each car is attached to the car in front by a rubber band
(also graduated in cm when relaxed) that stretches as the car in
front accelerates, does this change the frequency?

"Androcles" wrote in message
...

"Pentcho Valev" wrote in message
...
|A javelin graduated in centimeters is thrown downwards from the top of
| a tower of height h. Initially the centimeter marks pass an observer
| at the top of the tower with frequency f, speed s and "wavelength" L
| (1cm):
|
| f = s/L
|
| What are the frequency f', speed s' and "wavelength" L' as measured by
| an observer on the ground? Newton gives a straightforward answer (it
| is assumed that s's'-s):
|
| f' = f(1+gh/s^2) = (s+v)/L
| s' = s(1+gh/s^2) = s+v
| L' = L
|
| where v=s'-s is the increase in speed.
|
| Then the observer at the top of the tower emits light towards the
| ground. Relative to this observer, the light has frequency f, speed c
| and wavelength L:
|
| f = c/L
|
| What are the frequency f', speed c' and wavelength L' as measured by
| an observer on the ground? Newton's emission theory of light gives a
| straightforward answer again:
|
| f' = f(1+gh/c^2) = (c+v)/L
| c' = c(1+gh/c^2) = c+v
| L' = L
|
| where v=c'-c is the increase in speed.
|
| The answer given by Einstein's relativity is by no means
| straightforward:
|
| f' = f(1+gh/c^2) = ...
| c' = ... = ...
| L' = ...
|
An undefined but large number of cars are queued at a toll booth,
bumper-to-bumper. It takes one full minute to pay. As each driver
pays the toll he accelerates from zero to 100 kph (the speed limit),
taking one minute to do so. Cars then remain the same distance
apart for an undefined but large distance, all travelling at 100 kph,
until they arrive at the next toll booth when they slow to zero and
are once again bumper-to-bumper. The process is repeated for
the next stretch of highway.
1) How far apart are the cars that are travelling at 100 kph?

1 minute * 100 kph = 1.6 kms

2) At what frequency do cars pass under a bridge midway between
the toll booths?

one per minute, or 1/60th of a Hz.

3) If each car carries a javelin graduated in cm, does this change
the frequency?

No

4) If each car is attached to the car in front by a rubber band
(also graduated in cm when relaxed) that stretches as the car in
front accelerates, does this change the frequency?


No

"Peter Webb" wrote in message
...
|
| "Androcles" wrote in message
| ...
|
| "Pentcho Valev" wrote in message
|
...
| |A javelin graduated in centimeters is thrown downwards from the top of
| | a tower of height h. Initially the centimeter marks pass an observer
| | at the top of the tower with frequency f, speed s and "wavelength" L
| | (1cm):
| |
| | f = s/L
| |
| | What are the frequency f', speed s' and "wavelength" L' as measured by
| | an observer on the ground? Newton gives a straightforward answer (it
| | is assumed that s's'-s):
| |
| | f' = f(1+gh/s^2) = (s+v)/L
| | s' = s(1+gh/s^2) = s+v
| | L' = L
| |
| | where v=s'-s is the increase in speed.
| |
| | Then the observer at the top of the tower emits light towards the
| | ground. Relative to this observer, the light has frequency f, speed c
| | and wavelength L:
| |
| | f = c/L
| |
| | What are the frequency f', speed c' and wavelength L' as measured by
| | an observer on the ground? Newton's emission theory of light gives a
| | straightforward answer again:
| |
| | f' = f(1+gh/c^2) = (c+v)/L
| | c' = c(1+gh/c^2) = c+v
| | L' = L
| |
| | where v=c'-c is the increase in speed.
| |
| | The answer given by Einstein's relativity is by no means
| | straightforward:
| |
| | f' = f(1+gh/c^2) = ...
| | c' = ... = ...
| | L' = ...
| |
| An undefined but large number of cars are queued at a toll booth,
| bumper-to-bumper. It takes one full minute to pay. As each driver
| pays the toll he accelerates from zero to 100 kph (the speed limit),
| taking one minute to do so. Cars then remain the same distance
| apart for an undefined but large distance, all travelling at 100 kph,
| until they arrive at the next toll booth when they slow to zero and
| are once again bumper-to-bumper. The process is repeated for
| the next stretch of highway.
| 1) How far apart are the cars that are travelling at 100 kph?
|
| 1 minute * 100 kph = 1.6 kms

1) How FAR APART are the cars that are travelling at 100 kph?

|
| 2) At what frequency do cars pass under a bridge midway between
| the toll booths?
|
| one per minute, or 1/60th of a Hz.

Correct, the frequency doesn't change. It was one a minute
at the toll booth and is still one a minute at the bridge.

|
| 3) If each car carries a javelin graduated in cm, does this change
| the frequency?
|
| No

Correct.

|
| 4) If each car is attached to the car in front by a rubber band
| (also graduated in cm when relaxed) that stretches as the car in
| front accelerates, does this change the frequency?
|
|
| No
|
Correct. So changing the speed changes the "wavelength", not the
frequency.
Now we introduce two police patrol cars, one travelling at 50 kph
and the other at -50 kph.
How often does a car pass a patrol car (two answers needed, one
for each car) ?

"Androcles" wrote in message
...

"Peter Webb" wrote in message
...
|
| "Androcles" wrote in message
| ...
|
| "Pentcho Valev" wrote in message
|
...
| |A javelin graduated in centimeters is thrown downwards from the top
of
| | a tower of height h. Initially the centimeter marks pass an observer
| | at the top of the tower with frequency f, speed s and "wavelength" L
| | (1cm):
| |
| | f = s/L
| |
| | What are the frequency f', speed s' and "wavelength" L' as measured
by
| | an observer on the ground? Newton gives a straightforward answer (it
| | is assumed that s's'-s):
| |
| | f' = f(1+gh/s^2) = (s+v)/L
| | s' = s(1+gh/s^2) = s+v
| | L' = L
| |
| | where v=s'-s is the increase in speed.
| |
| | Then the observer at the top of the tower emits light towards the
| | ground. Relative to this observer, the light has frequency f, speed
c
| | and wavelength L:
| |
| | f = c/L
| |
| | What are the frequency f', speed c' and wavelength L' as measured by
| | an observer on the ground? Newton's emission theory of light gives a
| | straightforward answer again:
| |
| | f' = f(1+gh/c^2) = (c+v)/L
| | c' = c(1+gh/c^2) = c+v
| | L' = L
| |
| | where v=c'-c is the increase in speed.
| |
| | The answer given by Einstein's relativity is by no means
| | straightforward:
| |
| | f' = f(1+gh/c^2) = ...
| | c' = ... = ...
| | L' = ...
| |
| An undefined but large number of cars are queued at a toll booth,
| bumper-to-bumper. It takes one full minute to pay. As each driver
| pays the toll he accelerates from zero to 100 kph (the speed limit),
| taking one minute to do so. Cars then remain the same distance
| apart for an undefined but large distance, all travelling at 100 kph,
| until they arrive at the next toll booth when they slow to zero and
| are once again bumper-to-bumper. The process is repeated for
| the next stretch of highway.
| 1) How far apart are the cars that are travelling at 100 kph?
|
| 1 minute * 100 kph = 1.6 kms

1) How FAR APART are the cars that are travelling at 100 kph?

|
| 2) At what frequency do cars pass under a bridge midway between
| the toll booths?
|
| one per minute, or 1/60th of a Hz.

Correct, the frequency doesn't change. It was one a minute
at the toll booth and is still one a minute at the bridge.

|
| 3) If each car carries a javelin graduated in cm, does this change
| the frequency?
|
| No

Correct.

|
| 4) If each car is attached to the car in front by a rubber band
| (also graduated in cm when relaxed) that stretches as the car in
| front accelerates, does this change the frequency?
|
|
| No
|
Correct. So changing the speed changes the "wavelength", not the
frequency.
Now we introduce two police patrol cars, one travelling at 50 kph
and the other at -50 kph.
How often does a car pass a patrol car (two answers needed, one
for each car) ?


Insufficient information to answer.

Is there a point to all this? I found these questions boring when I was 10
years old, and learning that v=d/t. Almost 50 years later they are even more
boring.

"Peter Webb" wrote in message
u...
|
| "Androcles" wrote in message
| ...
|
| "Peter Webb" wrote in message
| ...
| |
| | "Androcles" wrote in message
| | ...
| |
| | "Pentcho Valev" wrote in message
| |
|
...
| | |A javelin graduated in centimeters is thrown downwards from the top
| of
| | | a tower of height h. Initially the centimeter marks pass an
observer
| | | at the top of the tower with frequency f, speed s and "wavelength"
L
| | | (1cm):
| | |
| | | f = s/L
| | |
| | | What are the frequency f', speed s' and "wavelength" L' as
measured
| by
| | | an observer on the ground? Newton gives a straightforward answer
(it
| | | is assumed that s's'-s):
| | |
| | | f' = f(1+gh/s^2) = (s+v)/L
| | | s' = s(1+gh/s^2) = s+v
| | | L' = L
| | |
| | | where v=s'-s is the increase in speed.
| | |
| | | Then the observer at the top of the tower emits light towards the
| | | ground. Relative to this observer, the light has frequency f,
speed
| c
| | | and wavelength L:
| | |
| | | f = c/L
| | |
| | | What are the frequency f', speed c' and wavelength L' as measured
by
| | | an observer on the ground? Newton's emission theory of light gives
a
| | | straightforward answer again:
| | |
| | | f' = f(1+gh/c^2) = (c+v)/L
| | | c' = c(1+gh/c^2) = c+v
| | | L' = L
| | |
| | | where v=c'-c is the increase in speed.
| | |
| | | The answer given by Einstein's relativity is by no means
| | | straightforward:
| | |
| | | f' = f(1+gh/c^2) = ...
| | | c' = ... = ...
| | | L' = ...
| | |
| | An undefined but large number of cars are queued at a toll booth,
| | bumper-to-bumper. It takes one full minute to pay. As each driver
| | pays the toll he accelerates from zero to 100 kph (the speed limit),
| | taking one minute to do so. Cars then remain the same distance
| | apart for an undefined but large distance, all travelling at 100
kph,
| | until they arrive at the next toll booth when they slow to zero and
| | are once again bumper-to-bumper. The process is repeated for
| | the next stretch of highway.
| | 1) How far apart are the cars that are travelling at 100 kph?
| |
| | 1 minute * 100 kph = 1.6 kms
|
| 1) How FAR APART are the cars that are travelling at 100 kph?
|
| |
| | 2) At what frequency do cars pass under a bridge midway between
| | the toll booths?
| |
| | one per minute, or 1/60th of a Hz.
|
| Correct, the frequency doesn't change. It was one a minute
| at the toll booth and is still one a minute at the bridge.
|
| |
| | 3) If each car carries a javelin graduated in cm, does this change
| | the frequency?
| |
| | No
|
| Correct.
|
| |
| | 4) If each car is attached to the car in front by a rubber band
| | (also graduated in cm when relaxed) that stretches as the car in
| | front accelerates, does this change the frequency?
| |
| |
| | No
| |
| Correct. So changing the speed changes the "wavelength", not the
| frequency.
| Now we introduce two police patrol cars, one travelling at 50 kph
| and the other at -50 kph.
| How often does a car pass a patrol car (two answers needed, one
| for each car) ?
|
|
| Insufficient information to answer.
|
Insufficent intelligence to solve a simple problem.


| Is there a point to all this?

Dumb people ask the dumbest questions.



| I found these questions boring when I was 10
| years old, and learning that v=d/t. Almost 50 years later they are even
more
| boring.

Then **** off, nobody is forcing you to understand Doppler,
speed, wavelength and frequency, Webb. It has be voluntary.
Your answer of 1.6 kms was incorrect, it is 1.67 km, there are
no seconds (s) in the answer.



Now we introduce two police patrol cars, one travelling at 50 kph
and the other at -50 kph.
How often does a car pass a patrol car ?

(two answers needed, one for each patrol car)

| An undefined but large number of cars are queued at a toll booth,
| bumper-to-bumper. It takes one full minute to pay. As each driver
| pays the toll he accelerates from zero to 100 kph (the speed limit),
| taking one minute to do so. Cars then remain the same distance
| apart for an undefined but large distance, all travelling at 100 kph,
| until they arrive at the next toll booth when they slow to zero and
| are once again bumper-to-bumper. The process is repeated for
| the next stretch of highway.

Now we introduce two police patrol cars, one travelling at 50 kph
and the other at -50 kph.
How often does a car pass a patrol car (two answers needed, one
for each car) ?

The rate a car pass a patrol car is given by the equation
Rate = 100/abs(100 - v) minutes
where v = velocity of the police patrol car

v = 50 kph; Rate = 100 / (100 - 50) = 2 minutes; i.e. 1 car per 2
minutes
v = -50 kph; Rate = 100 /(100 + 50) = 2/3 minutes; i.e. 1 car per 2/3
minutes or 3 cars per 2 minutes
v = 0 kph; Rate = 100/(100 - 0) = 1 minute; i.e. 1 car per minute
v = 100 kph; Rate = 100/(100 - 100) = oo minutes; No car can passes
the patrol car and vise versa.

This brings up another interesting topic: Speed greater than c !!!

If an object is moving away from an observer at a velocity of v, what
will be the measured speed?
Let both the observer and the object be at x = 0 at t = 0

The object is moving away at a velocity of 0.5c.
v = 0.5c
At t = 0, x = 0
At t = 1 sec, the object is at x = 0.5 c
It takes another 0.5 second for the image of the object to travel back
to the observer.
At t = 1.5 sec, the object is observed to be at x = 0.5c by the
observer.
v(measured) = x / t = 0.5c / 1.5 = 0.3333 c

The equation can be expressed as
v(measured) = 1/ (1/c + 1/v) = c * v/(c + v)

If c v then c ~ c+v and v(measured) = v
If v = 0.5 c then v(measured) = c * 0.5c/(c + 0.5c) = 0.3333 c.
If v = c then v(measured) = c * c/(c + c) = 0.5 c.
If v = 2c then v(measured) = c * 2c/(c + 2c) = 0.6666 c.
if v = oo then v(measured) = 1/(1/c + 0) = c
This is why we cannot have measured star receding velocity greater
than c.

If the measured receding speed of a star is greater than 0.5 c then
its actual speed is greater than c. We have measured stars velocity
greater than 0.5 c !!!

Newton's challenge to Einstein can be imagined as a friendly advice:

"Albert, the wave model presenting light as a continuous field works
fine in many cases but whenever you deal with the variation/constancy
of the speed of light you should apply the PARTICLE model!"

Einstein was tempted to act upon the advice all along but in the end
turned a deaf ear to it and sealed physics' fate:

http://books.google.com/books?id=JokgnS1JtmMC
"Relativity and Its Roots" By Banesh Hoffmann
"Moreover, if light consists of particles, as Einstein had suggested
in his paper submitted just thirteen weeks before this one, the second
principle seems absurd: A stone thrown from a speeding train can do
far more damage than one thrown from a train at rest; the speed of the
particle is not independent of the motion of the object emitting it.
And if we take light to consist of particles and assume that these
particles obey Newton's laws, they will conform to Newtonian
relativity and thus automatically account for the null result of the
Michelson-Morley experiment without recourse to contracting lengths,
local time, or Lorentz transformations. Yet, as we have seen, Einstein
resisted the temptation to account for the null result in terms of
particles of light and simple, familiar Newtonian ideas, and
introduced as his second postulate something that was more or less
obvious when thought of in terms of waves in an ether."

http://en.wikisource.org/wiki/The_De...e_of_Radiation
The Development of Our Views on the Composition and Essence of
Radiation by Albert Einstein, 1909
"A large body of facts shows undeniably that light has certain
fundamental properties that are better explained by Newton's emission
theory of light than by the oscillation theory. For this reason, I
believe that the next phase in the development of theoretical physics
will bring us a theory of light that can be considered a fusion of the
oscillation and emission theories. The purpose of the following
remarks is to justify this belief and to show that a profound change
in our views on the composition and essence of light is
imperative.....Then the electromagnetic fields that make up light no
longer appear as a state of a hypothetical medium, but rather as
independent entities that the light source gives off, just as in
Newton's emission theory of light......Relativity theory has changed
our views on light. Light is conceived not as a manifestation of the
state of some hypothetical medium, but rather as an independent entity
like matter. Moreover, this theory shares with the corpuscular theory
of light the unusual property that light carries inertial mass from
the emitting to the absorbing object."

http://www.perimeterinstitute.ca/pdf...09145525ca.pdf
Albert Einstein 1954: "I consider it entirely possible that physics
cannot be based upon the field concept, that is on continuous
structures. Then nothing will remain of my whole castle in the air,
including the theory of gravitation, but also nothing of the rest of
contemporary physics."

Pentcho Valev

On 13 Sep, 06:00, Pentcho Valev wrote:

You can read some of the background to this particular troll he-


http://www.martin-nicholson.info/troll/trollvalev.htm