Re: That Minkowski time intervals cannot be current in both frames.


"Jonah Thomas" <jethomas5@xxxxxxxxx> wrote in message
news:20090826180810.10007654.jethomas5@xxxxxxxxxxxx
"Androcles" <Headmaster@xxxxxxxxxxxxxxxxxx> wrote:
"Jonah Thomas" <jethomas5@xxxxxxxxx> wrote in message
"Androcles" <Headmaster@xxxxxxxxxxxxxxxxxx> wrote:
"Jonah Thomas" <jethomas5@xxxxxxxxx> wrote in message
"Androcles" <Headmaster@xxxxxxxxxxxxxxxxxx> wrote:
"Jonah Thomas" <jethomas5@xxxxxxxxx> wrote in message
I think of a wave as anything periodic.

Lines on screens or paper are not periodic.

If you look from left to right, yours are.

Ok, my desk is periodic because I looked at it from left to right.
The road outside my window is periodic because I looked at it from
left to right.


If it's periodic in time or
space or any other dimension, then it can be described as the sum
of> > some number of sine waves.

Chasing Fourier? You need to learn the basics first. Let's go with
"a wave is anything periodic". The Moon orbiting the Earth is
periodic. The Moon is a wave?

Its motion can be described as a wave.

So can any periodic motion, including photons, but that doesn't
mean they ARE waves.

What does it take for it to BE a wave? I figure if the math fits, use
it.

You have to look at it from left to right, apparently.


What is a wave to you?

Sound, water crashing on the shore, riding on a rollercoaster,
periodic movement.
Here's some waves:
http://www.androcles01.pwp.blueyonder.co.uk/Wave/waves.htm
The oscillating piston of the steam locomotive is periodic.

I agree with all of those.

The cycloid is a frozen wave in space, the sinusoid is a frozen
wave> in time.
If you travel in time with the cycloid by sitting on this:


http://media-2.web.britannica.com/eb-media/88/6488-004-96D89FFF.jpg
you'll see an up and down motion like the mass on a spring.> >
Sure.

http://www.androcles01.pwp.blueyonder.co.uk/Wave/ripple.gif
That's a model of a real wave.

OK.

http://www.androcles01.pwp.blueyonder.co.uk/Wave/Relative.gif
That's a mathematical model of a real wave, AND a spacetime
model of a red person or point. That's you, moving with the
wave.> >> Note that the lower wavy line doesn't travel across the
screen.> >> It is a sketch of the travelling wave above, but it's
"wavelength"> >> is twice the real wavelength. You didn't measure it
correctly,> >> because you can't be in two places at once. You do
not live in> >> spacetime.

Now... THINK before you answer... what is the frequency of the
travelling wave?

The procedure is to pick an axis where the function is periodic,
and> > watch the value rise and fall along that axis, and the number
of> > cycles per unit is the frequency.

This is a moving graph, and so we can measure the frequency along
the x axis at one time, or along the t axis at one x-value, or
some> > combination. Since it is periodic along both dimensions I
think the> > combination would be best, but I don't know how to do
that by eye.> >
it's something like:

(at,bx,sine(ax+bt),0)

I haven't thought about it carefully enough yet, but it looks
like> > the wavelength along the ax+bt axis would be something like
2pi(ax+bt). I'm not clear what to count as frequency,

Ok, let's pause there, that's what I wanted to clarify. Unless you
separate the t-axis from the x-axis in your mind you'll remain
unclear.

No, when it changes along both you'll get a misleading picture if
you describe it only along one.

No, you are not clear what to count as frequency.
No, unless you separate the t-axis from the x-axis in your mind you'll
remain
unclear.
No.
No.
No. :-)

There are lots of circumstances where it's appropriate to make your axis
be a linear combination of fundamental axes. Why isn't this one of them?

Frequency is DEFINED as follows.
http://www.merriam-webster.com/dictionary/frequency
1 : the fact or condition of occurring frequently
2 a : the number of times that a periodic function repeats the same sequence
of values during a unit variation of the independent variable b : the
number, proportion, or percentage of items in a particular category in a set
of data
3 : the number of repetitions of a periodic process in a unit of time: as a
: the number of complete alternations per second of an alternating current b
: the number of complete oscillations per second of energy (as sound or
electromagnetic radiation) in the form of waves

Nowhere does it say the number of complete wiggles per mile.

The number of wiggles per inch depends on the length of each wiggle,
the number of wiggles per second depends on the duration of each wiggle.
Inches per second is speed, if you confuse wiggles per inch with wiggles
per second then speed will be unclear and you will not be clear what to
count as frequency.






Frequency is how often a repetition occurs, but if you travel with
the> travelling wave then you change the *place* where the repetition
occurs.

Yes, exactly.
No.
No, exactly.
No. :-)

http://www.androcles01.pwp.blueyonder.co.uk/AC/doppler.gif
The magenta ball "sees" no repetition.
The gold ball "sees" a doubling of the transmitter frequency.
The only frequency that remains constant and makes any sense is
the transmission frequency. Ok, the red/blue antennae see the same
frequency as the transmitter, but only because they don't move
relative to the transmitter.

Yes, but your wave is moving in space and time both, and you want to
measure the movement in time only.

The wheel that produces the cycloid is moving in space and time both.
The cycloid doesn't move at all, not in space and not in time.
A boat on water moves up and down as the wave passes beneath it.

You can describe the cycloid with a movement in space. Look at its graph
from left to right. Agreed on the boat.

You can move back and forth in space, overlaying one wiggle with another,
you can't do that in time. No amount of looking from left to right can tell
you how many wiggles were drawn backwards, but on the time axis only
forward wiggles are allowed and none can be overlaid.
http://www.drillspot.com/pimages/8/841_300.jpg
This is called a chart recorder.
http://www.drillspot.com/pimages/8/841_300.jpg
The pen wiggles in space and the paper goes forward in time.
Running the paper backwards does reverse time, it fucks up the chart.
Do not confuse the time axis with the x-axis and read the chart recorder
top to bottom.




Now here's a quirky thing. If the speed of the travelling wave
is given by c = wavelength * frequency, and you measure
the frequency at the orange ball, then you get
speed = (wavelength/2) * (frequency *2) and the speed doesn't
change. That's obviously nonsense.

Let's call it frequency*2, never mind if the picture gets out of
phase. Now how do you get wavelength/2?

That's a good question.
"The speed is always c, not counting dielectric effects. The
wavelength
is short while you're approaching, and it lengthens as you leave." --
Jonah
Thomas.
How did you get a speed of c?

It's inconvenient to have the speed of light vary.

Well, tough ***. Nature doesn't care about your convenience.


The way people have
dealt with that inconvenience left them with lots of other
inconveniences, things which a lot of physics students take a long time
to learn to deal with. I'm learning how the system works and looking for
a better way at the same time.

You'd better learn it works first and find a better way second.
It's inconvenient if pencils bend in water.
http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/optpic/brokpen.jpg
It's much more convenient if the light bends.
How long it takes you to deal with that depends on your intelligence.





If there was a clear reason to have a preferred absolute rest frame,
then I'd gladly accept the inconvenience of using it. The claim that all
physical laws work the same at all velocities would be wrong, and we'd
all just have to get used to that. It would be a new and exciting time.
But that has not happened. Physicists prefer to believe that no velocity
is better than any other velocity, or even different in any fundamental
way. As a consequence they get lots of results that are
counterintuitive, and nobody goes into physics unless they can believe
these counterintuitive ideas. After they accept these, they have no
resistance to accepting other counterintuitive ideas. We wind up having
only physicists who don't care whether physics makes any sense. They do
get some results this way. I think we might get better results if we
carefully looked for ways to make sense -- we can't demand that the
world fit our preconceptions but we should get clear conceptions that
fit the world. That won't happen while it is not a priority for physics.
So anyway, here we are. People accept that if you measure the speed of
light it will give the same result no matter what your speed is.

Those are called "fools".

You can
accept that or reject it. If you accept it, that doesn't make a virtual
pin crossing a 2D picture of a 3D wave have the same speed no matter
what, nor does it make the speed of the picture of the wave have the
same speed.

Very good. Let's move on and reject it, or we'll be forever philosophizing
about fools and people instead of getting on with understanding the real
world.



It looks to me like newspeed = frequency*2 * wavelength = speed*2.
Which is what it ought to be.

Very good. But the frequency it leaves the transmitter doesn't change
(and is the same at all the red balls) and two crests pass the orange
ball in the same TIME it takes one crest to pass a red ball, c is the
same for all so the wavelength must be halved. Which is what it ought
to be because it is blueshifted.

EVERYBODY KNOWS (haha) "The wavelength is short while you're
approaching, and it lengthens as you leave." -- Jonah Thomas.
EVERYBODY KNOWS (haha) "that light is always propagated in empty
space with a definite velocity c which is independent of the state of
motion of the emitting body." -- Albert Einstein.
After all, if Einstein said it, it MUST be true. He's god, He who
must be believed.
I'm just a dumb crank that refuses to believe a word the arsehole
said.

Well, maybe you can find a better way. If the complaints people had
about galilean relativity were valid, you'd need something better than
galilean relativity. If the complaints they had about classical physics
were valid, you'd need something better than classical physics.

Were those complaints valid, or were there mistakes in them? Note that
the complaints could be valid without validating their solution.

Here's a nice complaint.
http://en.wikipedia.org/wiki/Emission_theory
The simplest form of emission theory says that radiating objects throw off
light with a speed of "c" relative to their own state of motion, and (unless
we have reason to believe that the light changes speed in flight), we then
expect light to be moving towards us with a speed that is offset by the
speed of the distant emitter (c ± v) ).
1.. If a radiant star moves across our field of vision, light given off by
differently-moving atoms in its atmosphere should take different amounts of
time to reach us. Since the retreating atoms would have a "red" Doppler
shift, and the approaching ones a "blue" Doppler shift, the passing star
might be expected to appear as a "rainbow streak".

Is it valid? The star is moving ACROSS our field of vision, which
cannot then be toward us or away, and is supposed to produce a doppler-
shift rainbow streak. No quantification given.

I have a coin, but it has worn down after being in circulation. It
therefore contains less metal than it should and I can't spend it,
it doesn't have full value.
Of course that is nonsense, as is any argument without quantification.
Here's the rainbow streak of the radiant star.
http://www.androcles01.pwp.blueyonder.co.uk/Orbit/Orbit.htm





but if |ax+bt| is the unit of
distance on that axis, then the frequency ought to be 1/2pi per
unit.

Or if the unit is (ax+bt)/|ax+bt| then the frequency might be
1/(2pi|ax+bt|)

Was that right?

You can't mix the x-axis and the t-axis.

If the motion is along both of them, how do you separate them?

You draw a cycloid for one and a sinusoid for the other.
You don't need a time axis for a cycloid, you can rotate the wheel
backwards and forwards and still hit the cycloid curve. It's
a little harder with the piston of a steam engine.
http://www.androcles01.pwp.blueyonder.co.uk/Tornado.gif
That's why a draw animations. They take care of the time axis.
You can't go back in time, but you can go back in space.
Time is not a vector.
http://www.androcles01.pwp.blueyonder.co.uk/Vector/Vector.htm

For purposes of analysis you can go back and recalculate from any time
or place you want. If it isn't too late to collect data you can check
your estimates. I prefer physics where the future doesn't reach back and
communicate with the past. If you create a photon that doesn't interact
with anything at all until it touches an atom in a star 1000 light years
from here, I don't want the atom 1000 years from now to reach back and
tell the photon's source what happened. If that turns out to be a
particularly good way to describe what happens then I'll accept it, but
I'll have to look it over carefully first.

Well, you could choose one for an independent variable if the other
is a dependent variable. But depending, it might make more sense to
have both of them as dependent variables and have the independent
variable be a rotation term.

Makes more sense if you learn that mathematics is a shorthand language
to be used by those that understand it.

Sure. And you can use it wherever it fits.

And you can tell lies with it or write nonsense with it.

1/2 [ tau(0,0,0,t) + tau(0,0,0,t+x'/(c+v)+x'/(c-v))] =
tau(x',0,0, t+ x'/(c-v))



It's very easy to write F =dp/dt, or at a freshman level F= ma,
but Newton said

LAW II.
The alteration of motion is ever proportional to the motive force
impressed; and is made in the direction of the right line in which
that force is impressed.

If any force generates a motion, a double force will generate double
the motion, a triple force triple the motion, whether that force be
impressed altogether and at once, or gradually and successively. And
this motion(being always directed the same way with the generating
force), if the body moved before, is added to or subtracted from the
former motion, according as they directly conspire with or are
directly contrary to each other; or obliquely joined, when they are
oblique, so as to produce a new motion compounded from the
determination of both.


It means the same. F = dp/dt is merely shorthand.
You have to know that p=ma, that p is momentum, that Newton called it
"motion".

When you read mathematics, read it as the shorthand it is. That means
take your time, there is a lot more in it than you realise. I hope
I've shown you that.

I'm slow picking up math that describes physics. I'm not trying to be
slow, it just works out that way.

You and many others. Many haven't learnt to read algebra beyond
the "See Spot Run" level. Trying to make sense of the Declaration
of Independence won't happen without a better vocabulary.
The language of physics is mathematics.

Doppler says
c-v
f' = f -----------
c

That's "See Spot Run" level for light.

Doppler says
c
f' = f ----------------
c-u

That's "See Spot Run" level for sound.

Doppler REALLY says

c-v
f' = f -----------
c-u

where v and u are speeds relative to the AIR.







Look at it this way:
Here's the rifled barrel of a spud gun.
http://www.spudtech.com/images/products/sch80rifled.jpg
The spud pellet will spin in flight.
If I increase the air pressure in the gun
1) the pellet will travel faster.
2) the pellet will spin faster.
3) it will have a longer "wavelength".
The "wavelength" is one full turn of the spud pellet in the barrel
of the gun.
The barrel shown isn't long enough for a full wavelength, it only
has 2/3 of a turn, but obviously I could change that ratio
with different machining. What this means is two spud pellets
can travel at the same speed but with different spin rates.
It also means that I can change the speed of one and not the other
by changing the pressure, and I can run toward the target
which will change the speed at which the pellet hits the target
without changing the muzzle speed.
The time axis is INDEPENDENT of the x-axis.

So with two independent variables you don't have an equation in one
variable unless you can set the other one.

Yes.

Match the caption to the gif:

A) http://tinyurl.com/lv2fl7
B) http://tinyurl.com/njgouh
C) http://tinyurl.com/klkfc9
D) http://tinyurl.com/l6lt4g
1) applies to light (in vacuum) and sound (in air)
2) applies to light but not sound
3) applies to sound but not light
4) applies to neither light nor sound

A1
Correct.

B4
Incorrect.

C3 -- traveling at the speed of sound

Correct.

D4 -- Maybe in a hurricane where the wind is Mach 1?
Correct.

B2 is merely A1 with the principle of relativity applied.
From the starship Enterprise's point of view, the star
is approaching the ship. It cannot change the speed of
the light it approaches.

It looks to me like the star is changing the speed of the light as it
approaches. Not just the light it emits now, but all the light it has
already emitted gets redrawn as if it had started out in the new
location.

A) is the rest frame of the star.
The star is not moving, but it is emitting light at c.
The ship is approaching the star at c, so the light
is received by the ship at 2c.


If there was a clear reason to have a preferred absolute rest frame,
then you'd gladly accept the inconvenience of using it. The claim that all
physical laws work the same at all velocities would be wrong, and we'd
all just have to get used to that. It would be a new and exciting time.
But that has not happened. Physicists prefer to believe that no velocity
is better than any other velocity, or even different in any fundamental
way. As a consequence they get lots of results that are
counterintuitive, and nobody goes into physics unless they can believe
these counterintuitive ideas. After they accept these, they have no
resistance to accepting other counterintuitive ideas.

B) is the rest frame of the ship.
The ship is not moving, but it is receiving light at 2c.
The star is approaching the ship at c, so the light
is received by the ship at 2c.


As for D4, you are correct, there is no way approaching a star
will cause the light it emits to slow down.
BUT...
"It follows from these results that to an observer approaching a
source of light with the velocity c, this source of light must appear
of infinite intensity." -- Albert Einstein.
The star is a source of light. The observer is the starship.
The compressed pattern is that of C3, a sonic boom, you were
correct on that. But there is no equivalent lumic boom without
aether. And the aether went away with Michelson-Morley.
So you've disagreed with Einstein. Never mind, he was an idiot
and you are smarter than you realised.
You scored 75%.

Problem:
A train has a whistle, which emits a 400 Hz sound. You are
stationary
and you hear the whistle, but the pitch is 440 Hz. How fast is train
moving towards or away from you? Solution:
The pitch is higher, so the train is moving towards you.
Its speed relative to you is found from f = f0v/(v-vs).
We have(v-vs) = f0v/f = (400/s)(340 m/s)/(440/s) = 309m/s.
Therefore vs = 340m/s-309m/s = 31m/s = 69mph.

If both source and observer are in motion, then the apparent frequency
of the sound wave reaching the observer is

f = f0(v + vo)/(v - vs)

If observer is in motion and the train stationary, then the apparent
frequency of
the sound wave reaching the observer is

f = f0(v + vo)/v

http://electron9.phys.utk.edu/phys135d/modules/m10/doppler.htm

Yes?

A train has a whistle, which emits a 400 Hz sound. You are
moving and you hear the whistle, but the pitch is 440 Hz.

What is YOUR speed? (assume the train is standing still)


.

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