The disk is allowed to free fall down the length of the shaft. Since the
spinning disk constitutes a clock, then wrt an observer at rest wrt the
top of the shaft, the gravitational time dilation should cause the
angular velocity of the disk to decrease wrt him. If the shaft does not
incur a change in angular velocity then it follows necessarily that the
disk/clock does not in fact slow down. If OTOH the disk 'does lose
angular velocity, then it must necessarily exert a torque on the shaft
in order to do so. Moreover the torque will be in a direction such that
the shaft loses rotational energy, and thus the disk must gain
rotational energy. Both the torque and energy increase can only be
accomplished with a 'gravitational induced' mass increase of the disk,
i.e. the reduced displacement between the disk and the Earth must result
in an increase in the inertial mass of the disk. This mass increase
cannot be ascribed to the velocity of the disk along the shaft, since
the disk can be lowered along the shaft at any arbitrary rate, i.e. it
must exist even when the disk is at rest wrt the shaft, though at a
lower altitude than the top of the shaft. However if the mass of the
disk increases, and this is the cause of the torque on the shaft, and if
this torque is the reason that the angular velocity of the assembly
decreases, then this has nothing whatsoever to do with time dilation,
but rather it is a direct physical consequence of gravitational mass
increase. Which is to say, as Spaceman so cleverly puts it, 'The clock
goofed'.
--
Richard Perry
http://www.cswnet.com/~rper
There are two ways of looking at time dilation.
1) time dilation.
2) physical quantities appear changed in such a way as to conspire to
make clocks run slower.
It may be that increased apparent mass is one of several changes which
conspire to make clocks run slower. Its just two equivalent ways of
looking at the same thing.
--
Be a counter terrorist perpetrate random senseless acts of kindness
Rave: Immanentization of the Eschaton in a Temporary Autonomous Zone.
"Anyone who trades liberty for security deserves neither liberty nor security"
-Benjamin Franklin
Lawrence Foard wrote:
"increased apparent mass" is nothing else than an
increase of inertia. Induced by surrounding gravitating
masses, or by traveling through the field generated by
these masses.
Hayek.
--
The small particles wave at
the big stars and get noticed.
:-)
Two sensible replies in a row, egads!;-)
Since the above observation is argued to be supported by direct
experiment, (albeit it is classically interpreted incorrectly) then a
few testable predictions can be asserted:
1) Given a system of discrete masses in uniform motion through an
isolated region of space, as the system cools and condenses it's
inertial mass must increase, per above. Hence conservation of momentum
requires that the velocity of the c.g. of the system be reduced wrt all
inertial frames, i.e.:
"An actively condensing closed system in uniform motion along a strait
line will not remain in that motion, even if no outside force acts on
it. It's velocity will decrease over time".
The _ _ _? Law of Thermodynamics.
2) Conservation of energy requires that:
"The angular velocity, if any, of a closed system be reduced during
condensation.
The _ _ _? +2 Law of Thermodynamics.
3) The converse of the above two must also hold, i.e.
"An actively expanding system in uniform motion along a strait line will
not remain in that motion, even if no outside force acts on it. It's
velocity will increase over time"
The _ _ _ ? +1 Law of Thermodynamics.
4) Conservation of energy requires that:
"The angular velocity, if any, of a closed system be increased during
expansion.
The _ _ _ ? +3 Law of Thermodynamics.
Now certainly there will be two obvious objections registered, which I
will address beforehand to stave off needless debate.
1) The term closed system above should be interpreted to mean a "closed
system of matter", i.e. as a "discrete object". If it seems preferable,
then simply replace the term with "isolated set of material particles".
2) The phrases "It's velocity will increase/decrease over time" begs of
a wholly unintended master frame. However the phrases are intended to
mean "It's velocity will become more positive/negative wrt the
coordinate system of the frame of reference. Simply note that if a
velocity becomes more positive wrt a frame, then its velocity is
increased in the positive direction of the axis, or equivalently its
velocity is decreased in the negative direction of the axis. In this way
the expression obtains an invariance wrt frames whose axes are aligned
in the positive and negative directions, and which are not rotating wrt
each other.
3) Certainly it should be quite obvious that the angular velocity of a
collapsing system will increase, which was perhaps one of the first
physical laws documented, so then the expressions above that seem to
state the opposite were not intended to state that the opposite were
true, but rather that the angular velocities will not change as much as
predicted by Newton when constant mass is assumed. That is they should
probably have been expressed as:
The angular velocity of an expanding system will 'increase over the
value expected by Newton when assuming constant mass'. Similarly for the
collapsing system.
These laws were not intended to 'supersede' the Newtonian laws, in fact
the Newtonian laws are in fact taken as premises when modified to refer
to the instantaneous force on an instantaneous mass. The fact that mass
is not constant is taken in conjunction with the Newtonian laws to
produce the above laws as corollaries. Instantaneous force should be
taken to mean
"instantaneous average force"-- This latter expression introduces as
new concept (that should be readily understood) but was long overdue in
that it quickly resolves the issue of
dp/dt = ma, rendering the terms on each side of the equation precisely
equivalent to one another.
Hopefully everyone can extrapolate that the issue of accelerated
expansion of the Universe is a natural consequence of these new laws.
The particles of the system may experience a decrease in speed
relative to each other (vs. Newtonian predictions) due to time dilation.
>"An actively condensing closed system in uniform motion along a strait
>line will not remain in that motion, even if no outside force acts on
>it. It's velocity will decrease over time".
The system as a whole will not change speed unless its ejected material or
light from itself in an uneven manner. Only interacting particles can change
speed. The particles within the system can slow relative to each other
because they are interacting via gravity, but the system as a whole cannot
change speed relative to an external observer.
You are discounting the empirical evidence to the contrary. The speed of
systems in our universe are indeed increasing relative to all observers.
Consider this: The reduction in angular velocity of a rotating object
descending into a gravitational well is accompanied by, and produced by,
an increase in the inertial mass of that object. Since empirically this
reduction in angular velocity occurs wrt all frames, then the inertial
mass must also increase wrt all frames. The inertia of a moving
expanding or collapsing system is therefore necessarily alter wrt 'all'
frames. Again I cite the empirical cosmological evidence of this effect.
A mass descending into a potential well is interacting with another object,
the mass which creates the potential well. Newton predicts "for every action
there will be an equal and opposite reaction", an action being a given
change in momentum. Within a system of interacting particles any particle
can change velocity, angular momentum, etc. without violating this, because
another particle will be doing the opposite. But a system moving (or not
moving its all relative) through space by itselfm can't speed up or
slow down. Without interacting with other matter or ejecting matter like
a rocket engine does.
But the Earth's mass must also increase, it has fallen into the objects
gravity well. Both masses increase, and do so wrt all frames. The
empirical evidence has been established.
Energy and momentum are conserved in all frames during this event. There
is no contradiction within either the logical system, or with the
empirical evidence, which mind you 'verifies' the effect.
>
> --
> Be a counter terrorist perpetrate random senseless acts of kindness
> Rave: Immanentization of the Eschaton in a Temporary Autonomous Zone.
> "Anyone who trades liberty for security deserves neither liberty nor security"
> -Benjamin Franklin
"Hayek" <hay...@nospam.xs4all.nl> wrote in message
news:3E947343...@nospam.xs4all.nl...
Tom M-G wrote:
> I read in Einstein's Sidelights on Relativity (Methuen, 1922), which
> expounds a 1920 lecture, 'Relativity teaches that the inertia increases with
> proximity of the ponderable masses'.
Not only in proximity.
I point at *all* the masses surrounding us.
As Uncle All pointed out recently :
A point source -> 1/r^2
A line source -> 1/r
plane soure -> constant
surrounding sphere source -> density ?
But this is contrary to empirical
> evidence, which finds a self-energy that causes masses to be greater on
> account of distance from one another.
> The gedanken experiment of Richard Perry's is in essence the same as my
> idea of a cogwheel train - you take the train Einstein used for constructing
> SR and suppose that its wheels are cogs and the track has corresponding
> teeth. The train cannot contract in length without fracturing the teeth, but
> this violates the First Law of Thermodynamics. Frthermore, the wheels can
> run clocks, by belt drive, and also can drive counters that ascribe
> distances to revolutions of the wheels. There will be no divergence between
> reference frames: the distance and time relationships will not only be
> immediately observable (eg. through the train's windows by looking at/
> potographing the counters and dials), but also recorded unit for unit for
> comparison in (eg.) a different reference frame altogether.
> SR has been struck in the heart.
Remember that a wheel has zero velocity wrt the road/rail.
Constant potential (well possibly not exactly because gravity isn't exactly
a 1/r^2 field). This to me seems like a good Newtonian approximation of
Mach's principle. A constant potential which determines absolute rotation.
"Einstein used a train for constructing SR"
Good one :-)
> and suppose that its wheels are cogs and the track has corresponding
> teeth. The train cannot contract in length without fracturing the teeth, but
> this violates the First Law of Thermodynamics. Frthermore, the wheels can
> run clocks, by belt drive, and also can drive counters that ascribe
> distances to revolutions of the wheels. There will be no divergence between
> reference frames: the distance and time relationships will not only be
> immediately observable (eg. through the train's windows by looking at/
> potographing the counters and dials), but also recorded unit for unit for
> comparison in (eg.) a different reference frame altogether.
Do you know some basic classical dynamics?
Did it ever occur to you that the translational forward velocity
of the lowermost point of the rolling wheel has velocity *zero*?
> SR has been struck in the heart.
That is a truly remarkable achievement for someone who
does not even seem to understand the concept of a coordinate
transformation ;-)
SR struck in the heart by the First Law of Thermodynamics...
<LOL>
Dirk Vdm
Conceptually, he did.
> > and suppose that its wheels are cogs and the track has corresponding
> > teeth. The train cannot contract in length without fracturing the teeth,
but
> > this violates the First Law of Thermodynamics. Frthermore, the wheels
can
> > run clocks, by belt drive, and also can drive counters that ascribe
> > distances to revolutions of the wheels. There will be no divergence
between
> > reference frames: the distance and time relationships will not only be
> > immediately observable (eg. through the train's windows by looking at/
> > potographing the counters and dials), but also recorded unit for unit
for
> > comparison in (eg.) a different reference frame altogether.
>
> Do you know some basic classical dynamics?
> Did it ever occur to you that the translational forward velocity
> of the lowermost point of the rolling wheel has velocity *zero*?
This is totally irrelevant. If the axles of the train are at velocity, they
must according to SR contract in the axis of motion, so something must
break. In any case, it is for precisely one instant that the lowermost point
is at zero velocity - an instant being infinitely short.
>
> > SR has been struck in the heart.
>
> That is a truly remarkable achievement for someone who
> does not even seem to understand the concept of a coordinate
> transformation ;-)
> SR struck in the heart by the First Law of Thermodynamics...
And exactly what form of conceptual understanding is necessitated in working
through a set of mathematical equations? Just the blind assumption that they
are unquestionably correct...?
If your next post is as shallow as all your others have been, I shan't
waste my time with it.
Why go to all the trouble of imagining teeth and cogs and such? After all,
if the train is moving at more than c/2, the top of any train wheel must be
moving faster than c, right? And that disproves SR, right? Oh wait, maybe
the wheel isn't round any more from the tracks perspective. Oh yeah, and
maybe from the trains perspective, the ratio of the circumference to the
radius of the wheel isn't 2 * pi anymore. Oh yeah, and maybe you just
hadn't thought this thing through to good yet...
<snip>
Alfred
Again you have *no clue* about how silly your cog wheel
is, have you?
Dirk Vdm
What's your point? There's a whole range of things that would prove to be
the downfall of Einstein's thought experiment, but if you prove, whether by
logic or by experiment, that c can be surpassed, I'll bet you anything that
relativists will say just that SR needs a bit of amendment.
One thing that comes to mind is that the machinery in the train is made up
of parts that are all moving at different speeds, and by SR they will be
length-contracted accordingly, it's not difficult to see how the parts will
no longer intermesh and the train will end up as scrap metal.
My point is that you make statements like this:
<snip>
> One thing that comes to mind is that the machinery in the train is made up
> of parts that are all moving at different speeds, and by SR they will be
> length-contracted accordingly, it's not difficult to see how the parts
will
> no longer intermesh and the train will end up as scrap metal.
as if they are given without providing even rudimentry evidence to (a)
support your conclusion and (b) that you even understand SR.
Alfred
Definitely a keeper!
"The mechanical downfall of special relativity"
http://users.pandora.be/vdmoortel/dirk/Physics/ImmortalFumbles.html#MechSR
Welcome to immortality :-)
Dirk Vdm
What a way to start a weekend! "The mechanical downfall of
special relativity" is a perfect name.
"... the parts will no longer intermesh and the train
will end up as scrap metal."
Immortality, indeed.
This sort of humor puts me in just the right mood for the Adam
Sandler and Jack Nicholson film I plan to see this afternoon.
--
Stephen
s...@speicher.com
Ignorance is just a placeholder for knowledge.
Printed using 100% recycled electrons.
-----------------------------------------------------------
Control Anger, Before It Controls You :-)
Enjoy and let us know how it was.
Dirk Vdm
A disappointment. If you have seen the movie trailer then you
have seen most of the funniest parts.
I couldn't resist seeing the movie because of that incredibly
unique combination of Nicholson and Sandler. Their acting was
just fine, but the story, and, some of the humor, was a bit flat.
"Stephen Speicher" <s...@speicher.com> wrote in message
news:Pine.LNX.4.33.03041...@localhost.localdomain...
> On Sat, 12 Apr 2003, Dirk Van de moortel wrote:
> >
> > "Stephen Speicher" <s...@speicher.com> wrote in message
news:Pine.LNX.4.33.03041...@localhost.localdomain...
> > >
> > > This sort of humor puts me in just the right mood for the Adam
> > > Sandler and Jack Nicholson film I plan to see this afternoon.
> >
> > Control Anger, Before It Controls You :-)
> > Enjoy and let us know how it was.
> >
>
> A disappointment. If you have seen the movie trailer then you
> have seen most of the funniest parts.
>
> I couldn't resist seeing the movie because of that incredibly
> unique combination of Nicholson and Sandler. Their acting was
> just fine, but the story, and, some of the humor, was a bit flat.
Unless the viewer has had psychotherapy, I don't think a lot of the
references make sense. Fine for the Hollywood crowd, considering the
nature of their job. The editing was pretty choppy too.
But, "I feel pretty..."
David A. Smith
I agree. The "I feel pretty ..." scene on the bridge was probably
the funniest scene in the movie.
Thanks for saving me 6 euros :-)
Dirk Vdm