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Science Forum Index » Physics - Relativity Forum » Do light have velocity dependent trajectories?
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| Guest |
Posted: Thu Feb 22, 2007 7:33 am |
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Given a X,Y,Z cordinate system with "earth in origo" a spaceship "A"
travels along X axis in a
velocity close to c.
Assuming the side of spaceship is along the Y
axis and a pulsecanon is aligned along Y(side of ship) it fire a
pulse
of one Plank length in a straight line along Y.
1. What will the actual trajectory of the pulse be?
(will it not at all be affected by the ships trajectory and travel in
a straight line along Y, i have a hard time to imagine it travelling
in a straight line parallell with ship c along the X axis but maybe
it
will?) or maybe it will take have a trajectory like a ball thrown
from
a car left side but that would be a velocity dependent trajectory
dependent on ~c and c?
2. Maybe a very stupid question, is it possible for the pulse(given a
light pulse) to expand not only in a positive direction from the
pulse
canon?
Maybe it is not quite clear what i mean, must the pulse always travel
positive from the emitter given a light or radio pulse, even if the
emitter is an object moving at ~c.
Could anyone be so kind make plot the trajectorie for me assuming
planet earth at rest in origo and ship travel positive along x-axis.
The ship passing origo "earth frame t0 sec" firing pulse postive in y-
axis
could anyone plot out for me "ship" and "pulse front" respective
origo
"earth frame t1 sec".
Where is lightpulse with respect to origo "earth" anyone?
The ship travels very close to ~c let us say indistinguasable.
I would also like to know how the trajectory would look in 0.9 0.8
0.7
0.6 c ...... and so on if someone got the time.
Best regards JT |
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Posted: Thu Feb 22, 2007 7:48 am |
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On 22 Feb, 12:33, j...@tele2.se wrote:
Quote: Given a X,Y,Z cordinate system with "earth in origo" a spaceship "A"
travels along X axis in a
velocity close to c.
Assuming the side of spaceship is along the Y
axis and a pulsecanon is aligned along Y(side of ship) it fire a
pulse
of one Plank length in a straight line along Y.
1. What will the actual trajectory of the pulse be?
(will it not at all be affected by the ships trajectory and travel in
a straight line along Y, i have a hard time to imagine it travelling
in a straight line parallell with ship c along the X axis but maybe
it
will?) or maybe it will take have a trajectory like a ball thrown
from
a car left side but that would be a velocity dependent trajectory
dependent on ~c and c?
2. Maybe a very stupid question, is it possible for the pulse(given a
light pulse) to expand not only in a positive direction from the
pulse
canon?
Maybe it is not quite clear what i mean, must the pulse always travel
positive from the emitter given a light or radio pulse, even if the
emitter is an object moving at ~c.
Could anyone be so kind make plot the trajectorie for me assuming
planet earth at rest in origo and ship travel positive along x-axis.
The ship passing origo "earth frame t0 sec" firing pulse postive in y-
axis
could anyone plot out for me "ship" and "pulse front" respective
origo
"earth frame t1 sec".
Where is lightpulse with respect to origo "earth" anyone?
The ship travels very close to ~c let us say indistinguasable.
I would also like to know how the trajectory would look in 0.9 0.8
0.7
0.6 c ...... and so on if someone got the time.
Best regards JT
Aetherians, SRians or anyone?
Maybe it is just a dumb question but i really do now know the answer,
is it clear that it only will travel positive along the y-axis, no
deformation of the trajectory due to velocity in positive x-axis
direction?
JT |
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| Sue... |
Posted: Thu Feb 22, 2007 8:02 am |
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Guest
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On Feb 22, 6:33 am, j...@tele2.se wrote:
Quote: Given a X,Y,Z cordinate system with "earth in origo" a spaceship "A"
travels along X axis in a
velocity close to c.
Assuming the side of spaceship is along the Y
axis and a pulsecanon is aligned along Y(side of ship) it fire a
pulse
of one Plank length in a straight line along Y.
1. What will the actual trajectory of the pulse be?
(will it not at all be affected by the ships trajectory and travel in
a straight line along Y, i have a hard time to imagine it travelling
in a straight line parallell with ship c along the X axis but maybe
it
will?) or maybe it will take have a trajectory like a ball thrown
from
a car left side but that would be a velocity dependent trajectory
dependent on ~c and c?
2. Maybe a very stupid question, is it possible for the pulse(given a
light pulse) to expand not only in a positive direction from the
pulse
canon?
Maybe it is not quite clear what i mean, must the pulse always travel
positive from the emitter given a light or radio pulse, even if the
emitter is an object moving at ~c.
Could anyone be so kind make plot the trajectorie for me assuming
planet earth at rest in origo and ship travel positive along x-axis.
The ship passing origo "earth frame t0 sec" firing pulse postive in y-
axis
could anyone plot out for me "ship" and "pulse front" respective
origo
"earth frame t1 sec".
Where is lightpulse with respect to origo "earth" anyone?
The ship travels very close to ~c let us say indistinguasable.
I would also like to know how the trajectory would look in 0.9 0.8
0.7
0.6 c ...... and so on if someone got the time.
Best regards JT
A light path is determined by the matter in the region.
Usually classified as a conductor or a dielectric.
Propagation in a dielectric medium
http://farside.ph.utexas.edu/teaching/em/lectures/node98.html
http://en.wikipedia.org/wiki/Wave_impedance
http://en.wikipedia.org/wiki/Free_space
http://www-ssg.sr.unh.edu/ism/what.html
<<Now, does not the prize to Einstein imply
that the Academy recognised the particle
nature of light? The Nobel Committee says
that Einstein had found that the energy exchange
between matter and ether occurs by atoms emitting
or absorbing a quantum of energy,hv .
As a consequence of the new concept of light quanta
(in modern terminology photons) Einstein proposed the
law that an electron emitted from a substance by
monochromatic light with the frequency has to have
a maximum energy of E=hv-p, where p is the energy needed to
remove the electron from the substance. Robert Andrews
Millikan carried out a series of measurements over a
period of 10 years, finally confirming the validity of this
law in 1916 with great accuracy. Millikan had, however,
found the idea of light quanta to be unfamiliar and strange.
The Nobel Committee avoids committing itself to the
particle concept. Light-quanta or with modern terminology,
photons, were explicitly mentioned in the reports on
which the prize decision rested only in connection with
emission and absorption processes. The Committee says
that the most important application of Einstein's photoelectric
law and also its most convincing confirmation has come from
the use Bohr made of it in his theory of atoms, which explains
a vast amount of spectroscopic data. >>
http://nobelprize.org/physics/articles/ekspong/index.html
Sue... |
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Posted: Thu Feb 22, 2007 8:24 am |
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On 22 Feb, 13:02, "Sue..." <suzysewns...@yahoo.com.au> wrote:
Quote: On Feb 22, 6:33 am, j...@tele2.se wrote:
Given a X,Y,Z cordinate system with "earth in origo" a spaceship "A"
travels along X axis in a
velocity close to c.
Assuming the side of spaceship is along the Y
axis and a pulsecanon is aligned along Y(side of ship) it fire a
pulse
of one Plank length in a straight line along Y.
1. What will the actual trajectory of the pulse be?
(will it not at all be affected by the ships trajectory and travel in
a straight line along Y, i have a hard time to imagine it travelling
in a straight line parallell with ship c along the X axis but maybe
it
will?) or maybe it will take have a trajectory like a ball thrown
from
a car left side but that would be a velocity dependent trajectory
dependent on ~c and c?
2. Maybe a very stupid question, is it possible for the pulse(given a
light pulse) to expand not only in a positive direction from the
pulse
canon?
Maybe it is not quite clear what i mean, must the pulse always travel
positive from the emitter given a light or radio pulse, even if the
emitter is an object moving at ~c.
Could anyone be so kind make plot the trajectorie for me assuming
planet earth at rest in origo and ship travel positive along x-axis.
The ship passing origo "earth frame t0 sec" firing pulse postive in y-
axis
could anyone plot out for me "ship" and "pulse front" respective
origo
"earth frame t1 sec".
Where is lightpulse with respect to origo "earth" anyone?
The ship travels very close to ~c let us say indistinguasable.
I would also like to know how the trajectory would look in 0.9 0.8
0.7
0.6 c ...... and so on if someone got the time.
Best regards JT
A light path is determined by the matter in the region.
Usually classified as a conductor or a dielectric.
There is no matter in the region it is empty except for the planet in
origo.
possible to plot the trajectories within the defined cordinate system.
But i understand maybe there is no way to plot the trajectories if you
say so i take your word for it.
Quote: Now, does not the prize to Einstein imply
that the Academy recognised the particle
nature of light? The Nobel Committee says
that Einstein had found that the energy exchange
between matter and ether occurs by atoms emitting
or absorbing a quantum of energy,hv .
I do not see the relevance.
Quote: As a consequence of the new concept of light quanta
(in modern terminology photons) Einstein proposed the
law that an electron emitted from a substance by
monochromatic light with the frequency has to have
a maximum energy of E=hv-p, where p is the energy needed to
remove the electron from the substance. Robert Andrews
Millikan carried out a series of measurements over a
period of 10 years, finally confirming the validity of this
law in 1916 with great accuracy. Millikan had, however,
found the idea of light quanta to be unfamiliar and strange.
Maybe i am just stupid i do not see the relevance to my question.
Quote: The Nobel Committee avoids committing itself to the
particle concept. Light-quanta or with modern terminology,
photons, were explicitly mentioned in the reports on
which the prize decision rested only in connection with
emission and absorption processes. The Committee says
that the most important application of Einstein's photoelectric
law and also its most convincing confirmation has come from
the use Bohr made of it in his theory of atoms, which explains
a vast amount of spectroscopic data. >>http://nobelprize.org/physics/articles/ekspong/index.html
Ok i determine that you either not got time to plot it out, are
unable, can but refuse or think i should do it myself but since i am
not psycic i do not really now.
If you try to say that there is no easy answer say so.
If you try to say that answer the question put you in trouble say so.
If you just like me do not know the answer to the question, it is just
ok probably someone else got the answer.
Suppose an empty space without matter or magnetic fields surrounding
origo. Just the ship A origo planet B (very small just a pebble) to
define rest space.
Is this really such a tricky question? I just want to see if light
have velocity dependent trajectory?
Best regards Jonas T
Quote: Sue...- Dölj citerad text -
- Visa citerad text - |
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Posted: Thu Feb 22, 2007 8:32 am |
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On 22 Feb, 13:51, "Dirk Van de moortel" <dirkvandemoor...@ThankS-NO-
SperM.hotmail.com> wrote:
Quote: j...@tele2.se> wrote in messagenews:1172143993.831564.238420@j27g2000cwj.googlegroups.com...
Given a X,Y,Z cordinate system with "earth in origo" a spaceship "A"
travels along X axis in a
velocity close to c.
Assuming the side of spaceship is along the Y
axis and a pulsecanon is aligned along Y(side of ship) it fire a
pulse
of one Plank length in a straight line along Y.
1. What will the actual trajectory of the pulse be?
In the ship's frame the pulse has trajectory
x' = 0
y' = c t'
so in the earth's frame it has trajectory
g ( x - v t ) = 0
y = c g ( t - v/c^2 x )
giving
x = v t
y = c/g t = sqrt(c^2-v^2) t
or, eliminating t:
y = sqrt( c^2/v^2 - 1 ) x
which is a straight line in the Earth's frame.
(will it not at all be affected by the ships trajectory and travel in
a straight line along Y, i have a hard time to imagine it travelling
in a straight line parallell with ship c along the X axis but maybe
it
will?) or maybe it will take have a trajectory like a ball thrown
from
a car left side but that would be a velocity dependent trajectory
dependent on ~c and c?
It has a straigth line with equation
y = sqrt( c^2/v^2 - 1 ) x
2. Maybe a very stupid question, is it possible for the pulse(given a
light pulse) to expand not only in a positive direction from the
pulse
canon?
Maybe it is not quite clear what i mean, must the pulse always travel
positive from the emitter given a light or radio pulse, even if the
emitter is an object moving at ~c.
Since it has a straigth line with equation
y = sqrt( c^2/v^2 - 1 ) x ,
the slope of which is always positive.
Could anyone be so kind make plot the trajectorie for me assuming
planet earth at rest in origo and ship travel positive along x-axis.
The ship passing origo "earth frame t0 sec" firing pulse postive in y-
axis
could anyone plot out for me "ship" and "pulse front" respective
origo
"earth frame t1 sec".
Take a piece of paper and use the equations
x = v t
y = c/g t = sqrt(c^2-v^2) t
At time t the ship is a point
(x,y) = ( v t , 0 )
and the pulse front is at point
(x,y) = ( v t , sqrt(c^2-v^2) t )
Where is lightpulse with respect to origo "earth" anyone?
The ship travels very close to ~c let us say indistinguasable.
I would also like to know how the trajectory would look in 0.9 0.8
0.7
0.6 c ...... and so on if someone got the time.
Just take a piece of paper and draw some lines with equations
y = sqrt( c^2/v^2 - 1 ) x
for various values of v
Dirk Vdm
Ok i am lazy is there a simple freeware graph program someware.
Thank you JT |
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| Sue... |
Posted: Thu Feb 22, 2007 8:45 am |
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Guest
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On Feb 22, 7:24 am, j...@tele2.se wrote:
Quote: On 22 Feb, 13:02, "Sue..." <suzysewns...@yahoo.com.au> wrote:
On Feb 22, 6:33 am, j...@tele2.se wrote:
Given a X,Y,Z cordinate system with "earth in origo" a spaceship "A"
travels along X axis in a
velocity close to c.
Assuming the side of spaceship is along the Y
axis and a pulsecanon is aligned along Y(side of ship) it fire a
pulse
of one Plank length in a straight line along Y.
1. What will the actual trajectory of the pulse be?
(will it not at all be affected by the ships trajectory and travel in
a straight line along Y, i have a hard time to imagine it travelling
in a straight line parallell with ship c along the X axis but maybe
it
will?) or maybe it will take have a trajectory like a ball thrown
from
a car left side but that would be a velocity dependent trajectory
dependent on ~c and c?
2. Maybe a very stupid question, is it possible for the pulse(given a
light pulse) to expand not only in a positive direction from the
pulse
canon?
Maybe it is not quite clear what i mean, must the pulse always travel
positive from the emitter given a light or radio pulse, even if the
emitter is an object moving at ~c.
Could anyone be so kind make plot the trajectorie for me assuming
planet earth at rest in origo and ship travel positive along x-axis.
The ship passing origo "earth frame t0 sec" firing pulse postive in y-
axis
could anyone plot out for me "ship" and "pulse front" respective
origo
"earth frame t1 sec".
Where is lightpulse with respect to origo "earth" anyone?
The ship travels very close to ~c let us say indistinguasable.
I would also like to know how the trajectory would look in 0.9 0.8
0.7
0.6 c ...... and so on if someone got the time.
Best regards JT
A light path is determined by the matter in the region.
Usually classified as a conductor or a dielectric.
There is no matter in the region it is empty except for the planet in
origo.
There is no no such space in this universe.
The term *trajectory* is normally reserved for a particle with mass.
Light, (wiggling electrons and protons) propagtes over a path
and it may do so bidirectionally.
In optics, there are special cases where a ray or particle model
is used for simplicity. But that doesn't alter the electromagnetic
models that provide more complete description.
Quote:
Now, does not the prize to Einstein imply
that the Academy recognised the particle
nature of light? The Nobel Committee says
that Einstein had found that the energy exchange
between matter and ether occurs by atoms emitting
or absorbing a quantum of energy,hv .
I do not see the relevance.
As a consequence of the new concept of light quanta
(in modern terminology photons) Einstein proposed the
law that an electron emitted from a substance by
monochromatic light with the frequency has to have
a maximum energy of E=hv-p, where p is the energy needed to
remove the electron from the substance. Robert Andrews
Millikan carried out a series of measurements over a
period of 10 years, finally confirming the validity of this
law in 1916 with great accuracy. Millikan had, however,
found the idea of light quanta to be unfamiliar and strange.
Maybe i am just stupid i do not see the relevance to my question.
The Nobel Committee avoids committing itself to the
particle concept. Light-quanta or with modern terminology,
photons, were explicitly mentioned in the reports on
which the prize decision rested only in connection with
emission and absorption processes. The Committee says
that the most important application of Einstein's photoelectric
law and also its most convincing confirmation has come from
the use Bohr made of it in his theory of atoms, which explains
a vast amount of spectroscopic data. >>http://nobelprize.org/physics/articles/ekspong/index.html
Ok i determine that you either not got time to plot it out, are
unable, can but refuse or think i should do it myself but since i am
not psycic i do not really now.
If you try to say that there is no easy answer say so.
If you try to say that answer the question put you in trouble say so.
If you just like me do not know the answer to the question, it is just
ok probably someone else got the answer.
Suppose an empty space without matter or magnetic fields surrounding
origo. Just the ship A origo planet B (very small just a pebble) to
define rest space.
Again... there is no such place. You need to ask Alice or
the Red Queen.
Quote:
Is this really such a tricky question? I just want to see if light
have velocity dependent trajectory?
The velocity depends on the eps and mu of the dielectric.
The light in your Television cable is moving at about
0.9 percent the speed of light in the air.
http://farside.ph.utexas.edu/teaching/em/lectures/node99.html
Sue...
Quote:
Best regards Jonas T
Sue...- Dölj citerad text -
- Visa citerad text -- Hide quoted text -
- Show quoted text -- Hide quoted text -
- Show quoted text - |
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| Dirk Van de moortel |
Posted: Thu Feb 22, 2007 8:51 am |
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<jt64@tele2.se> wrote in message news:1172143993.831564.238420@j27g2000cwj.googlegroups.com...
Quote: Given a X,Y,Z cordinate system with "earth in origo" a spaceship "A"
travels along X axis in a
velocity close to c.
Assuming the side of spaceship is along the Y
axis and a pulsecanon is aligned along Y(side of ship) it fire a
pulse
of one Plank length in a straight line along Y.
1. What will the actual trajectory of the pulse be?
In the ship's frame the pulse has trajectory
x' = 0
y' = c t'
so in the earth's frame it has trajectory
g ( x - v t ) = 0
y = c g ( t - v/c^2 x )
giving
x = v t
y = c/g t = sqrt(c^2-v^2) t
or, eliminating t:
y = sqrt( c^2/v^2 - 1 ) x
which is a straight line in the Earth's frame.
Quote: (will it not at all be affected by the ships trajectory and travel in
a straight line along Y, i have a hard time to imagine it travelling
in a straight line parallell with ship c along the X axis but maybe
it
will?) or maybe it will take have a trajectory like a ball thrown
from
a car left side but that would be a velocity dependent trajectory
dependent on ~c and c?
It has a straigth line with equation
y = sqrt( c^2/v^2 - 1 ) x
Quote:
2. Maybe a very stupid question, is it possible for the pulse(given a
light pulse) to expand not only in a positive direction from the
pulse
canon?
Maybe it is not quite clear what i mean, must the pulse always travel
positive from the emitter given a light or radio pulse, even if the
emitter is an object moving at ~c.
Since it has a straigth line with equation
y = sqrt( c^2/v^2 - 1 ) x ,
the slope of which is always positive.
Quote:
Could anyone be so kind make plot the trajectorie for me assuming
planet earth at rest in origo and ship travel positive along x-axis.
The ship passing origo "earth frame t0 sec" firing pulse postive in y-
axis
could anyone plot out for me "ship" and "pulse front" respective
origo
"earth frame t1 sec".
Take a piece of paper and use the equations
x = v t
y = c/g t = sqrt(c^2-v^2) t
At time t the ship is a point
(x,y) = ( v t , 0 )
and the pulse front is at point
(x,y) = ( v t , sqrt(c^2-v^2) t )
Quote:
Where is lightpulse with respect to origo "earth" anyone?
The ship travels very close to ~c let us say indistinguasable.
I would also like to know how the trajectory would look in 0.9 0.8
0.7
0.6 c ...... and so on if someone got the time.
Just take a piece of paper and draw some lines with equations
y = sqrt( c^2/v^2 - 1 ) x
for various values of v
Dirk Vdm |
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| Sue... |
Posted: Thu Feb 22, 2007 8:54 am |
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On Feb 22, 7:45 am, "Sue..." <suzysewns...@yahoo.com.au> miswrote:
The velocity depends on the eps and mu of the dielectric.
The light in your Television cable is moving at about
90 percent the speed of light in the air.
http://www.picwire.com/technical/paper2.html
Sue... |
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| Dirk Van de moortel |
Posted: Thu Feb 22, 2007 9:25 am |
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| Guest |
Posted: Thu Feb 22, 2007 9:56 am |
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On 22 Feb, 14:25, "Dirk Van de moortel" <dirkvandemoor...@ThankS-NO-
SperM.hotmail.com> wrote:
Hello Dirk if i understand correct (plotted correct) the ligh pulse
will travel straight along the y-axis without deformation, regardless
of speed.
That makes me wonder a little, because after t1(earth/planet time 1
sec) the light beam have travelled 300 000 km relative earth.
But for the ship *distance* to pulsefront we would have to use
pythagoras theorem correct?
424 264 km
That would be the distance as measured from earth frame between ship
and pulsefront correct?
Assume velocity ship 0.9999 c we have a dilation factor of 1/70.7 sec
for inertial frame A ship.
1 sec earth frame =0.014144 ship frame
Should i conclude that the distance to pulsefront from within the
shipframe is 0.01414*424 264 ?
And that the distance to earth is 0,01414*300 000?
Is there other distances from within the ship frame to the pulsefront
and planet? "At moment t1"=clock 1 sec passed earth frame.
I know that length contraction occur in the ship frame does this apply
for space and things outside the ship?
Is there such a thing as distance contraction in SR or does it only
refer to the actual things belonging to the moving frame?
In my mind it would be natural to have the distance as a constant
between the frames 300 000/0,01414 and 424 264/0,01414 but that is of
course wrong according to SR.
Is distance really variant between frames in SR?
And what about the hypotenusa argument is that really invoked in SR?
Best regards Jonas Thörnvall |
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| Randy Poe |
Posted: Thu Feb 22, 2007 10:23 am |
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Guest
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On Feb 22, 8:56 am, j...@tele2.se wrote:
Quote: I know that length contraction occur in the ship frame does this apply
for space and things outside the ship?
Is there such a thing as distance contraction in SR or does it only
refer to the actual things belonging to the moving frame?
Yes. Look up "stellar aberration", where the position of stars
in the sky changes depending on earth's movement relative to the
star. The Lorentz contraction was proposed by Lorentz to
explain this effect in terms of contraction of stellar
distances.
Einstein's contribution was to show how the Lorentz
contraction is a consequence of deeper principles.
Quote:
In my mind it would be natural to have the distance as a constant
between the frames 300 000/0,01414 and 424 264/0,01414 but that is of
course wrong according to SR.
Is distance really variant between frames in SR?
Apparently.
Quote: And what about the hypotenusa argument is that really invoked in SR?
I believe that's the essence of the Lorentz theory of stellar
aberration.
- Randy |
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| Guest |
Posted: Thu Feb 22, 2007 11:03 am |
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On 22 Feb, 15:23, "Randy Poe" <poespam-t...@yahoo.com> wrote:
Quote: On Feb 22, 8:56 am, j...@tele2.se wrote:
I know that length contraction occur in the ship frame does this apply
for space and things outside the ship?
Is there such a thing as distance contraction in SR or does it only
refer to the actual things belonging to the moving frame?
Yes. Look up "stellar aberration", where the position of stars
in the sky changes depending on earth's movement relative to the
star. The Lorentz contraction was proposed by Lorentz to
explain this effect in terms of contraction of stellar
distances.
Einstein's contribution was to show how the Lorentz
contraction is a consequence of deeper principles.
In my mind it would be natural to have the distance as a constant
between the frames 300 000/0,01414 and 424 264/0,01414 but that is of
course wrong according to SR.
Is distance really variant between frames in SR?
Apparently.
I now have to ask you if it also is vector dependent, is there
different distances if travel towards or away from object.
Suppose the ship was travelling towards the planet instead and at same
place at moment t1 would the distance be different in SR?
Is it vector dependent to?
Quote: And what about the hypotenusa argument is that really invoked in SR?
I believe that's the essence of the Lorentz theory of stellar
aberration.
To have the distant as a variant make me abit confused about the
arguments in SR. For me it seem impossible for ships travelling
different vectors to have different distances to planet X when passing
a cordinate in space and same for velocities.
I understand that the argument is rather mathematical built on
definitions but invariant distances seem very foreign for me because
it is very hard for me to use my logic exploring the arguments of SR.
I know little/nothing about mathematics but if distances is variant
does it make sense to talk about invariant light paths betwenn frames.
I know you think i am in deep water now, but some features of SR i
have a hard time to analyse by pure logic.
Best regards Jonas Thörnvall
> - Randy |
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| Dirk Van de moortel |
Posted: Thu Feb 22, 2007 11:03 am |
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<jt64@tele2.se> wrote in message news:1172152583.929321.68710@s48g2000cws.googlegroups.com...
No, in the setup you sketched, it will travel straight along the
ship's y'-axis, regardless of speed.
It will not travel straight along the Earth's y-axis, but along a
straight line with equation
y = sqrt( c^2/v^2 - 1 ) x
the slope of which depends on the speed v.
Quote: That makes me wonder a little, because after t1(earth/planet time 1
sec) the light beam have travelled 300 000 km relative earth.
Yes.
If you take the equations
x = v t
y = sqrt(c^2-v^2) t
you see that the velocity components in the x-direction and in the
y-direction are given by
x/t = v
y/t = sqrt(c^2-v^2) ,
so the composed velocity in the light signal's direction is then
sqrt( (x/t)^2 + (y/t)^2 ) = c
as expected.
Quote: But for the ship *distance* to pulsefront we would have to use
pythagoras theorem correct?
424 264 km
That would be the distance as measured from earth frame between ship
and pulsefront correct?
If you make your drawing, you will see that after an Earth-time t the
ship is at point
(x,y) = ( v t , 0 )
and the pulse front is at point
(x,y) = ( v t , sqrt(c^2-v^2) t )
the distance between which is
sqrt(c^2-v^2) t .
On the other hand, going to the frame of the ship again, the
signal's equations are
x' = 0
y' = c t'
and the Earth obeyes the equations
x' = - v t'
y' = 0 .
So you see that after a ship-time t', the signal is at point
(x',y') = ( 0 , c t' )
and the Earth is at point
(x',y') = ( -v t' , 0 )
the distance between which, as you can verify, is
sqrt(c^2+v^2) t'
Does this help?
In the remainder you used numeric values which destroy all
interesting bits about this, so I skipped it.
Dirk Vdm |
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| Guest |
Posted: Thu Feb 22, 2007 11:35 am |
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On 22 Feb, 16:03, j...@tele2.se wrote:
Quote: On 22 Feb, 15:23, "Randy Poe" <poespam-t...@yahoo.com> wrote:
On Feb 22, 8:56 am, j...@tele2.se wrote:
I know that length contraction occur in the ship frame does this apply
for space and things outside the ship?
Is there such a thing as distance contraction in SR or does it only
refer to the actual things belonging to the moving frame?
Yes. Look up "stellar aberration", where the position of stars
in the sky changes depending on earth's movement relative to the
star. The Lorentz contraction was proposed by Lorentz to
explain this effect in terms of contraction of stellar
distances.
Einstein's contribution was to show how the Lorentz
contraction is a consequence of deeper principles.
In my mind it would be natural to have the distance as a constant
between the frames 300 000/0,01414 and 424 264/0,01414 but that is of
course wrong according to SR.
Is distance really variant between frames in SR?
Apparently.
I now have to ask you if it also is vector dependent, is there
different distances if travel towards or away from object.
Suppose the ship was travelling towards the planet instead and at same
place at moment t1 would the distance be different in SR?
Is it vector dependent to?
And what about the hypotenusa argument is that really invoked in SR?
I believe that's the essence of the Lorentz theory of stellar
aberration.
To have the distant as a variant make me abit confused about the
arguments in SR. For me it seem impossible for ships travelling
different vectors to have different distances to planet X when passing
a cordinate in space and same for velocities.
I understand that the argument is rather mathematical built on
definitions but invariant distances seem very foreign for me because
it is very hard for me to use my logic exploring the arguments of SR.
I know little/nothing about mathematics but if distances is variant
does it make sense to talk about invariant light paths betwenn frames.
I know you think i am in deep water now, but some features of SR i
have a hard time to analyse by pure logic.
Best regards Jonas Thörnvall
- Randy- Dölj citerad text -
- Visa citerad text -- Dölj citerad text -
- Visa citerad text -
I understand that the argument is rather mathematical built on
definitions but
TYPO invariant *variant*
distances seem very foreign for me because
it is very hard for me to use my logic exploring the arguments of SR. |
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| shuba |
Posted: Thu Feb 22, 2007 2:20 pm |
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