The Dogschool of Mathematics presents

7.  A Visit With the Perplexed

Below is an actual post to the usnet newsgroup.
I will intersperse my commentary in bold font. -- Arf!

(The names have been changed to protect the ignorant)

>> Taking into account all of the earth's motions eg. polar, orbital,
>> galactic etc, how fast are we travelling?
>> Dan

Dan is asking for the absolute motion of the earth.
"How fast is the earth traveling relative to . . . nothing."
In Newtonian physics this was unfindable.
In Maxwellian physics this was findable but the experiments
came up, strangely, to detect no motion.
In Einsteinian physics the question is meaningless.
Now comes comments by someone else who does not understand
the most basic ideas of SR: -- Arf!
>This worries me, too. Let me pose a couple of spaceship questions,
>that might add to the dilemna.

>1. Imagine yourself sitting in a sealed space capsule totally unaware
>of the outside world. You know the mass of your capsule, which is
>fitted with a rocket engine.
>You fire the engine and measure, (with a spring balance) your
>acceleration, which turns out to be, say, 3x10^6 metres per sec^2.
>After 200 seconds, you calculate that your velocity is 6x 10^8 m/s^2
>or double the speed of light.

Velocity relative to what? He doesn't say but from the context
we'll assume he means relative to the inertial frame he was in before
he fired the engines.

He also used the Galilean/Newtonian formula for calculating his final
velocity as measured in that inertial frame from the acceleration.
What he has calculated will NOT be what is measured by the folks
he left behind in the original frame.
They will measure him as going less than the speed of light in their
(and his original) frame.

>Now, before the SR experts jump up and down with explanations about
>mass increases, etc., consider question 2.

>2. When I fired my rocket, did I accelerate or did I decelerate? What
>was my spatial reference? Had I already been travelling with constant
>velocity in the direction of the rocket jet?

Acceleration as opposed to deceleration refer to whether the speed
is increasing or decreasing. This depends upon the frame of reference.
When the car steps on the brakes the people sitting by the road
observe the car slowing down. The people in the car in the next
lane (going the same direction) notice the formerly "stationary" car
speed up in the "backwards" direction. It all depends on the frame
of reference. This, by the way, is all old Galilean/Newtonian
physics and needs none of the subtleties of relativity.
His question as to what he had been doing before he fired the
jets also sounds like he was asking for his absolute state of
motion -- a direct contradiction of postulate 1) -- Arf!
>Now back to the relativists. They say that while I was accelerating,
>my mass was increasing and therefore my estimate of acceleration was
>I retaliate by arguing that, whether I was speeding up or slowing
>down, the mass on my spring balance was changing proportionally, as
>was the rocket exhaust.
Again he brings up the acceleration/deceleration question without a frame.
Also the "mass increase" is frame dependent. The mass of an object
measured in different frames will, according to SR, give different
results. The different frames are neither mentioned or implied. -- Arf!
>Ah! but unknown to me, my time scale had dilated and my length scale
>had changed!, say the relativists. If I had performed an MMX while I
>was accelerating then I would have deduced, from the null result, that
>my length had certainly changed. (they could not say whether it had
>increased or decreased or whether it had actually done both, depending
"MMX" refers to the Michaelson-Morely experiment. It was a famous
experiment done in the 1890's which detected no motion through
the "ether."

Again the time and length changes are differences in measurements made
in different frames. In his frame nothing has changed. In his original
frame (with respect to which he is now moving) his ship is shorter and
his clocks are running slower.) In some other frame his ship is
thinner. -- Arf!

>on the spatial references I used)
>And the rocket exhaust had not experienced the same mass increase
>because it was firing the opposite way. So my calculations were all up
>the creek.
In the frame of the ship now, the rocket exhaust is travelling faster
than the ship (in fact, in the frame of the ship the ship is, by definition,
at rest) and therefore the exhaust experienced the "mass increase"
He is not specifying which frame(s) he is talking about. -- Arf!
>OK, that being so, I became an instant SR convert and tried to
>calculate the changes in my M,L and T using the Lorentz equations.
>Surprise, surprise, I could not determine what value I should use for
>my velocity. I had no reason to assume that it was initially zero and
>if I used any arbitrary value for Vo then I could produce an infinite
>number of solutions.
He wants his ABSOLUTE velocity to put into the equations when the 'v'
in the equations stands for the velocity relative to the frame in which
the measurements are being made.

The Lorentz transform equations are a way to calculate length, time, etc.
as measured in a frame that is moving at velocity v RELATIVE TO YOU from
the measurements made in that frame. Thus if I make a bunch of
measurements in my frame and I am moving at velocity v RELATIVE TO YOU
then you can filter my measurements through the Lorentz transform
equations and get the results of measurements in YOUR frame. The poster
is attempting to apply the Lorentz Transforms to ONE FRAME ALONE. This
makes no sense. -- Arf!

>From this apparent paradox and using all my brainpower, I was able to
>deduce that, if there were to be a unique set of solutions to the
>relativistic equations, then there had also to be a unique absolute
>reference point in space, from which all velocities and positions
>could be absolutely measured.
Right! The equations are nothing more than formulas to calculate
measurements in one frame from measurements in another. There
must be two frames in order for the formulas to have meaning. Choose
different frames and you'll get different answers. He wants THE
ANSWER. It's like asking if Columbus, Ohio is to the north or not
without giving any leeway to where the asker might be located. He wants
the absolute true answer: is Columbus, Ohio to the north or not? -- Arf!
>However, since SR says that no such entity exists, I am now totally
>confused! SR appears to contradict itself!


Hott2Trott's version of SR certainly is contradictory. However, it
bears little resemblance to Einstein's version.
Maybe he should be surfing this website. -- Arf!

Next: The Twin Paradox

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