Androcles wrote:
"Jesse Mazer" wrote in message
...
Androcles wrote:
"Jesse Mazer" wrote in message
...
Androcles wrote:
"Jesse Mazer" wrote in message
...
Androcles wrote:
"Jesse Mazer" wrote in message
...
Androcles wrote:
Do me a favour.
Einstein wrote
"light is always propagated in empty space with a definite
velocity c which is independent of the state of motion of the
emitting body"
Reference :
http://www.fourmilab.ch/etexts/einstein/specrel/www/
Then he wrote:
"But the ray moves relatively to the initial point of k, when
measured in the stationary system, with the velocity c-v, so that
x'/(c-v) = t."
I don't know what the context of this is. I assume he's not talking
about how fast the light is moving in a given frame, but rather how
fast the light is moving away from some other object, as seen not
in the object's own frame but in a frame where the object itself is
moving at velocity v. In this case, although light will still
travel at c in this frame, the distance between the light ray and
the object moving at velocity v will be seen to grow at the rate
(c-v) in this frame. In the object's own frame, though, the
distance between itself and the light ray would grow at the rate c,
as relativity predicts.
You didn't reply to this part of my post--can you provide me with the
context of that statement by Einstein?
I've given you the reference.
Ah, I didn't notice that you were quoting from a website, sorry. But
that's a pretty long article, which section did you get the quote
involving the equation x'/(c-v) = t from?
Section 3. It wouldn't refer to it as an "article" though. It's the
original
paper that Einstein wrote in 1905 creating special relativity.
I see my interpretation was correct, then. He is saying that you have
two reference frames, K and k, and that in K's reference frame, the
distance between the origin of k and a ray of light is growing at the
rate (c-v). This does not mean that the ray of light is moving at
velocity (c-v) in k's reference frame; in both K and k, the light is
moving at velocity c.
You are one of those that starts at the Lorentz
Transforms, proceeds to lecture on what you imagine I'm not aware of,
then conclude you are right.
You didn't really read my post, so how do you know this?
I didn't read it in depth, no. I quickly glanced down and saw some
equations I recognised as wasn't prepared to comment on, since they
cannot be derived in any sensible manner.
They can be derived from the fact that all the fundamental laws of
physics display the property of "Lorentz invariance". This is a
mathematical property which can be verified simply by examining the
equations. Do you understand what it means to say a given equation shows
Lorentz invariance? If not, I can go into more detail.
However, if it is true that all the fundamental laws of nature obey
Lorentz invariance, it must be true that if different observers in
motion with relation to one another all use the same procedure to define
the coordinates of events in their frame--building a network of rulers
and clocks which are at rest with respect to themselves, and
synchronizing the clocks using the assumption that light moves at the
same speed in all directions in their frame--then the Lorentz
transformation equations will indeed be the correct way to transform
measurements made with one set of rulers and clocks into measurements
made with another set. From your comments I gather you probably believe
that existing laws are not really fundamental, and that when we find the
real fundamental laws they will not be Lorentz-invariant...but would you
at least agree that *if* the fundamental laws are Lorentz-invariant,
then the Lorentz transformation will be the correct way to transform
between measurements on different observers' rulers and clocks?
In fact, I didn't assume the Lorentz transformations were correct
without argument, I pointed out that all the current known laws of
physics are Lorentz-invariant,
Sorry, but I do not agree the laws of physics are illogical.
Are you saying there is something inherently illogical about the idea
that I will see rulers shrink as they move faster, and clocks slow down?
Again, you are free to believe there is a true Absolute Space and that
only rulers and clocks at rest in this space measure distance and time
correctly, and rulers and clocks moving in Absolute Space are
"objectively" shorter and slower. Even if you don't believe this is how
things actually work, are you saying it is *logically impossible* that
they could work this way (ie, that this hypothesis involves a logical
contradiction?) Or are you just using "illogical" to mean "implausible"?
The PoR
stood the test of time until Einstein who corrupted it in favour of his
own
insistence concerning the speed of light, which he stated in 1905 was
"only apparently irreconcilable" and in 1920 recognized was
irreconcilable. He
rejected the PoR in favour of c = (c+v)/(1+v/c). Trouble is, he used
c+v to derive the composition of velocities.
In relativity it is true that if I see you moving in one direction with
velocity v, and I see a light beam moving in the opposite direction with
velocity c, then the distance between you will grow at the rate (c+v),
in my reference frame. But this is not a problem, since you will *not*
measure the light beam to be moving at velocity (c+v) relative to yourself.
thus *if* these laws are correct, the laws must remain unchanged under
a Lorentz transformation but not under other types of coordinate
transformations, which shows that the Lorentz transformation is the
most natural type of coordinate transformation to use if these laws
are correct (and any physical rulers and clocks which obey
Lorentz-invariant laws must also show length contraction and time
dilation).
If you are arguing that physicists have got the laws of physics wrong,
that they should actually use modified laws which are
Galilei-invariant rather than Lorentz-invariant, that's fine, but it's
incumbent on you to show some evidence that existing laws are wrong
and these modified laws are correct.
No it isn't. The burden of proof is upon the claimant, and Einstein
failed to prove
his case. All I have to show is the error in his math/logic.
But it is easy to prove that if all the fundamental laws of physics are
Lorentz-invariant, then if observers use rulers and clocks at rest
relative to themselves and synchronize the clocks using Einstein's
procedure, then the Lorentz transformations will give the correct rule
for transforming between different observer's measuring system. It is
also an objective fact that the laws of electromagnetism exhibit
Lorentz-invariance, as do all our current fundamental laws (like quantum
field theory). So unless someone like you can come up with some new
fundamental laws which don't exhibit Lorentz-invariance, this is
sufficient to prove that the Lorentz transformation will give the
correct rule for transforming between the measurements of different
networks of rulers and clocks.
If you think my understanding of his meaning is incorrect, could you
explain why?
I do not know what you understanding is.
I just explained it in the post you responded to--here it is again: "I
assume he's not talking about how fast the light is moving in a given
frame, but rather how fast the light is moving away from some other
object, as seen not in the object's own frame but in a frame where the
object itself is moving at velocity v.
You admit you are making assumption. Im not in the assumption game.
Einstein makes many assumptions, many invalid.
This is the worst one.
½[tau(0,0,0,t)+tau(0,0,0,t+x'/(c-v)+x'/(c+v))] = tau(x',0,0,t+x'/(c-v))
Where does that ½ come from?
Consider McCullough's silly little puzzle, which I'll embellish
slightly.
Sam and Joe are walking along carrying a 32 ft ladder between
them, at 3 fps. A mosquito flies from Sam to Joe and back to
Sam again at 5 fps, ground frame. How long does it take the
mosquito to make the round trip?
x' is the 32 ft ladder, c the speed of the mosquito and v the speed
of Sam and Joe.
Wait, first you said the mosquito flew at 5 fps, then you said at
c...are you assuming the speed of light is 5 fps in this
thought-experiment, or do you no mean c to be the speed of light?
In either case, I'd solve it like this. In the ground frame, the end of
the ladder starts out at position x=32 feet, moving at 3 fps, and the
mosquito starts out at x=0 feet, and moves at 5 fps, so in this frame
you'd calculate the time t for them to meet using the equation:
0 + 5t = 32 + 3t
which gives t=16 seconds, meeting at position x=80. Then the mosquito
flies backwards from that position at velocity -5 fps, and meanwhile the
other end of the ladder starts at x=48 feet and moves forward at 3 fps,
so to find where they meet you could use this equation:
80 - 5t = 48 + 3t
which gives t = 4 seconds. So, the total time is 20 seconds. Notice that
I calculated everything from the ground frame, without ever switching to
the mosquito's frame or the ladder's frame.
Answer. 16 seconds to reach Joe and 4 seconds to return.
So (16+4)/2 = 16 ?
I don't think so. Einstein tries to justify it by saying Sam cannot
know when the mosquito reaches Joe, so he'll simply use the ½.
That is assumption, not mathematics.
What are you talking about? Einstein would agree with my analysis above,
even if the speed of light was 5 feet per second; notice that I always
assumed the mosquito was travelling at 5 fps in the ground frame, I
never switched to a different frame.
So if we look at light from a given star at two points in the earth's
orbit, the first when the earth is moving away from the star and the
second when it's moving towards it, why isn't any difference in the
speed of light measured?
It is. You'll see as doppler-shift.
Androcles.
A doppler-shift is just a change in the wavelength, not in the velocity.
Jesse