"Jesse Mazer" wrote in message
...
Androcles wrote:
"Jesse Mazer" wrote in message
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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).
For some duration of time.
For another duration of time the rate is v+c.
These durations are not equal.
Time is not a vector, it has no additive inverse.
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.
I don't believe in magic. If c = c+v and c = c-v, then v = 0.
Nowhere has anyone said that c = c-v.
Really? Tell all those that claim c is invariant that they are not to
say it,
then.
Rather, the idea here is that if
you measure the speed that the distance between k and the light ray is
growing using K's rulers and clocks, it is growing at the rate (c-v);
but if you measure the speed that the distance between k and the light
ray is growing using k's rulers and clocks, it is growing at the rate
c.
Yeah. I know. Stupidity is rife around here.
Since K and k use different rulers and clocks, then *if* you believe
that rulers shrink and clocks dilate, it shouldn't be so surprising
that
K's rulers and clocks will give a different answer than k's rulers and
clocks.
As I said, I don't believe in magic.
I know you don't actually believe that, but the point is that
advocates of relativity do, so clearly they are not saying anything so
silly as c = c-v, rather they are saying:
speed measured by K's rulers and clocks = c-v
speed measured by k's rulers and clocks = c
Show me the evidence.
If V = (c+v)/(1+v/c) then use that to derive the LTs.
If the system of equations is linear as Einstein claims, it shoud be
no trouble.
Where are you getting V = (c+v)/(1+v/c)? That's not an equation I can
remember seeing.
§ 5. The Composition of Velocities
http://www.fourmilab.ch/etexts/einstein/specrel/www/
You don't know very much about relativity, do you?
Why are you talking to me as if you did?
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".
Bull****.
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.
Go on then, explain circularity .... err .... Lorentz invariance to
me.
Well, first I'll describe Galilei invariance since it's mathematically
a
bit simpler, then I'll explain Lorentz invariance. Here are the
Galilei
transformations for transforming between inertial reference frames in
Newtonian physics:
x'=x - vt
y'=y
z'=z
t'=t
x=x' + vt'
y=y'
z=z'
t=t'
To say a certain physical equation is "Galilei-invariant" just means
the
form of the equation is unchanged if you make these substitutions. For
example, suppose at time t you have a mass m1 at position (x1, y1, z1)
and another mass m2 at position (x2, y2, z2) in your reference frame.
Then the Newtonian equation for the gravitational force between them
would be:
F = Gm1m2/[(x1 - x2)^2 + (y1 - y2)^2 + (z1 - z2)^2]
Now, suppose we want to transform into a new coordinate system moving
at
velocity v with respect to the first one. In this coordinate system,
at
time t' the mass m1 has coordinates (x1', y1', z1') and the mass m2
has
coordinates (x2', y2', z2'). Using the Galilei transformations, we can
figure how the force would look in this new coordinate system, by
substituting in x1 = x1' + vt', x2 = x2' + vt', y1 = y1', y2 = y2',
and
so forth. With these substitutions, the above equation becomes:
F = Gm1m2/[(x1' + vt' - (x2' + vt'))^2 + (y1' - y2')^2 + (z1' -
z2')^2]
and you can see that this simplifies to:
F = Gm1m2/[(x1' - x2')^2 + (y1' - y2')^2 + (z1' - z2')^2]
In other words, the equation has exactly the same form in both
coordinate systems. This is what it means to be "Galilei invariant".
More generally, if you have *any* physical equation which computes
some
quantity (say, force) as a function of various space and time
coordinates, like f(x,y,z,t) [of course it may have more than one of
each coordinate, like the x1 and x2 above, and it may be a function of
additional variables as well, like m1 and m2 above] then for this
equation to be "Galilei invariant", it must satisfy:
f(x'+vt,y',z',t') = f(x',y',z',t')
Oh, that's an easy one.
v = 0.
From this, it's pretty simple to see what it must mean for a given
physical equation to be "Lorentz invariant" as well. Here are the
Lorentz transformation equations:
x'=gamma(x - vt)
Don't you mean xi = gamma.x' ?
Einstein uses x' = x-vt. See, you've called the Galilean Transform
x' = x-vt, which is correct. The Lorentz is the Galilean * gamma.
y'=y
z'=z
t'=gamma(t - vx/c^2)
Oops. You did it again. be careful with those primes.
*tau* =gamma(t - vx/c^2)
Another easy one.
v = x/t, by definition, so
tau = (t- vt * v /c^2) * gamma.
tau = t (1-v^2/c^2) * gamma.
= t * sqrt(1-v^2/c^2)
So the simpler form is
xi = x' * gamma
tau = t / gamma.
The speed of the "stationary" frame as measured from the "moving" frame
is then
upsilon = xi/tau
Prove |upsilon| = |v| (to preseve symmetry).
x=gamma(x' + vt')
y=y'
z=z'
t=gamma(t' + vx'/c^2)
where gamma = 1/squareroot(1-v^2/c^2)
So, if you have some physical equation f(x,y,z,t), then for it to be
"Lorentz-invariant" it just must have the following property:
f(gamma(x'+vt'),y',z',gamma(t'+vx'/c^2)) = f(x',y',z',t')
This is just a mathematical property of a given equation or set of
equations, it is just a matter of calculation to check if the equation
satisfies it (the equation for Newtonian gravity would not have this
property, so it would not be Lorentz-invariant).
Thank goodness for that. You are mixing greek notation with prime
notation,
that can only confuse you (and me). Be consistent. I have no idea what
you
mean by vt', or x'.
And it is a fact that
Maxwell's laws do have this property of Lorentz-invariance, as do all
the most fundamental laws currently known (such as the laws of quantum
field theory).
Maxwell's equations are based on aether. There is no aether.
I'll accept Einstein's opener.
"It is known that Maxwell's electrodynamics--as usually understood
at the present time--when applied to moving bodies, leads to asymmetries
which do not appear to be inherent in the phenomena. "
Nice "facts" you present.
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--
It seemeth impossible for it to be, for if I walk away from a candle
set
by the wall and you walk toward the same candle, we then have some
motion between us. If we then divide that motion equally between us,
and
impart it to the candle such that it appeareth to be at rest upon the
floor upon which we walk, how then doth the light divide it's motion
between us, that we may both observe it to be the same?
Because you and I use different rulers and clocks to measure this
motion.
I've only got one ruler and one clock, there are two light sources, one
I walk toward and the other I walk away from.
Even if we lived in a Newtonian universe where rulers and
clocks
wouldn't *naturally* appear to shrink and slow down, suppose I bought
you some phony gag rulers and clocks from the novelty shop, with the
markings on the rulers too short by a factor of squareroot(1-v^2/c^2),
and each tick of the clock longer then it should be by a factor of
1/squareroot(1-v^2/c^2). Suppose I also made different clocks of yours
be out-of-sync, by using the (false, in a Newtonian universe)
assumption
that a beam of light emitted from the midpoint of two clocks (by a
source at rest relative to me, if you believe light's velocity depends
on the source velocity, although in classical E&M it should actually
depend on the rest frame of the aether) should strike both clocks at
the
same time, even if one clock is moving towards the point the light was
emitted and one is moving away from it.
If you are moving away from me at velocity v, and you are using these
gag rulers and clocks (which have been synchronized using this
incorrect
procedure, in the Newtonian universe we're living in) to measure
things,
do you agree that *as measured by your incorrect rulers and clocks*,
then if I measure the light to be moving at c, you will also measure
it
to be moving at c? Do you agree that if I want to find some equations
to
transform between my correct measurements and your incorrect
measurements, the correct equations will be the Lorentz transformation
equations?
I don't use gag rules and clocks, I have only one rule and one clock.
I approach one source of light as I recede from the other.
You are not involved.
S1-----------------------------me-----------S2
|------------------L1---------------L2-----|
I walk toward S1. I walk away from S2.
Prove that my watch runs at a different rate for S1 than for S2 so that
I get one speed of light from both sources. I love magic, show me some.
But always remember, I know it is magic. All I have to do is figure out
how the trick is done.
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.
I do not see any justification for magic or incorrect assumption.
This is not an assumption, it's just a logical consequence of the idea
that all the fundamental equations of physics exhibit the mathematical
property of "Lorentz invariance" which I described above. You may not
believe that in our final Theory of Everything, the fundamental laws
really *will* all be Lorentz-invariant ones, but do you agree that
*if*
all the fundamental laws were Lorentz-invariant, then if different
observers all used the same procedure to measure distance and time
(excluding procedures that rely on external reference points--imagine
each observer must construct his measuring system in a windowless box,
with no knowledge of how fast the box is moving in relation to the
rest
of the universe), that necessarily implies that the correct way to
transform between different observers' coordinate systems will be the
Lorentz transformation?
Get to the math, start proving. All your words are meaningless attempts
at persuasion, as were Einstein's. You are wasting your time using them
on me. I'm not giving up the PoR in favour of Lorentz invariance.
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...
Quite so, the Lorentz Transforms do not exist.
They are just equations for transforming one set of coordinates to
another, so I don't see how they could fail to "exist".
Because time is not a vector.
When you can rotate an apple into an orange or travel back in time,
Harry Potter will have a unicorn hair core to his magic wand.
Harry Potter's wand exists as fiction only, as do the Lorentz
Transforms.
Fiction can be written in mathematics just as in literature, and you are
discussing fiction.
The empirical
question is whether they would correctly transform between different
observers' measurements on rulers and clocks, but even in a Newtonian
universe where they wouldn't do so if each observer designs his
network
of rulers and clocks in a "natural" way, it would still be possible to
artificially create distorted rulers and clocks such that they would
correctly transform between the normal set and the distorted one, as I
described above in my "novelty shop scenario".
Get to the math, start proving. All your words are meaningless attempts
at persuasion, as were Einstein's. You are wasting your time using them
on me. I'm not giving up the PoR in favour of Lorentz invariance.
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?
If you can use
1/2[tau(0,0,0,t)+tau(0,0,0,t+x'/V+x'/V)] = tau(x',0,0,t+x'/V)
since "the velocity of light c cannot be altered by composition with
a
velocity less than that of light. For this case we obtain V =
(c+w)/(1+w/c) = c."
to derive the Lorentz Transforms, I'll take another look.
Go ahead. I'm amenable to reason.
Explain to me how the two velocities of light, c-v and c+v, measured
over a single distance, are really only one, c.
Is this equation from section 3 of that Einstein paper? I didn't see
it
there, and I need to know the context before I can answer this
question.
No, section 5. Come back when you've read all of it.
[remainder snipped, too many errors already].
Androcles.