Re: On The Subject of The Mosquito And The Ladder

From: Androcles (Androcles_at_)
Date: 02/23/05 

Date: Wed, 23 Feb 2005 03:22:20 GMT

"Daryl McCullough" <stevendaryl3016@yahoo.com> wrote in message
news:cvgjk6016p1@drn.newsguy.com...
> Sue... says...
>
>>Ah yes ... the psychology.
>>In our normal experience light travels "somewhat faster than sound, if
>>not instantaneously". The student scarcely bats an eye as revered
>>professor claims that clocks viewed through a delay become clocks
>>indicating the delay.
>>
>>When an all too familiar blood sucking messenger replaces the light,
>>the students howl at the absurbdity.
>
> Well, the Lorentz transformations work perfectly well with a
> mosquito replacing the speed of light, because the Lorentz
> transformations are just a definition of a coordinate transformation.
> There is no right or for coordinates---you can use whatever
> coordinates
> you like to describe the world. That's the lesson of relativity.
> However,
> the laws of physics are simpler and more intuitive when expressed in
> some coordinate systems than in others. In a rotating coordinate
> system,
> there are strange Coriolis forces and Centrifugal forces at work that
> disappear when you use nonrotating coordinates.
>
> If Sam and Joe are walking along at 3 feet/second, there is nothing
> preventing them from using a "mosquito clock" to measure the passage
> of time.

Dang... Wish I'd seen that before. Nice one, McCullough. I went
straight into MMX.

The mosquito clock is a fine-meshed cage in the shape of a
> cylinder 5 feet long, oriented perpendicular to the direction that
> Sam and Joe are walking. Their unit of time is the time it takes for
> the mosquito to fly from one end of the cage to the other. The
> mosquito has a counter that records the number of times the mosquito
> has made a trip from one end to the other. That's
> a perfectly good way to measure time. Sam and Joe similarly can use
> mosquito-based measurements of distance. If there is an object O
> that is at rest relative to Sam, then Sam can associate with O
> a distance x_O defined as follows:
>
> x_O = 5 feet/second * T_O, where T_O = 1/2 the time it takes for
> a mosquito to fly from Sam to O and back to Sam, where time
> is measured using a mosquito clock
>
> That's a perfectly good way to measure distances.
>
> Sam can also use mosquito-based clock synchronization. To synchronize
> his clock with Joe (who is at rest relative to Sam), Sam does the
> following: He computes the mosquito-based distance x_Joe as described
> above. Then when the counter on Sam's mosquito-clock reads t=0, Sam
> sends a mosquito towards Joe. When the mosquito reaches Joe, Joe
> sets the counter of his mosquito clock to t=x_Joe/5.

The problem, though, is that Joe sets his clock behind that of Sam
by 16 seconds, and Sam sets his clock 4 seconds behind Joe,
and they are in the same frame.
So which way is the correct sync?
Oh, wait.... Each sets their clock 8 seconds behind the other.

>
> So Sam and Joe can use mosquitos to measure distance and time, and to
> synchronize clocks. That gives them a perfectly good coordinate
> system.
> And, if you work out the details, you will find that Sam and Joe's
> coordinate system is related to the coordinate system used by
> "stationary"
> observers through the "Mosquito transformations" (the Lorentz
> transformations
> with mosquito-speed replacing light-speed).
>
> The hard question, though, is what does physics look like in a
> mosquito-based coordinate system? In particular, we would like to
> know the answers to the following questions:
>
> 1. Suppose we have a wind-up clock that is initially at rest in the
> stationary system. It ticks at the rate of one tick per second in
> the stationary frame. Now, we slowly accelerate the clock until it
> is at rest in Sam's frame. What is its tick rate in Sam's
> mosquito-based coordinate system?
>
> Mathematically, let r_stationary be the rate of the clock, as
> measured in the stationary frame, before the clock is accelerated.
> Let r_sam be the rate of the clock, as measured in Sam's coordinate
> system, after the clock has come to rest in Sam's frame. Then the
> question is: how does r_stationary relate to r_sam?
>
> 2. Suppose we have a stick that is initially at rest in the
> stationary
> frame. The stick is exactly one foot long, as measured in the
> stationary frame. (For definiteness, let's assume the stick is
> oriented in the same direction as Joe and Sam are moving.) Now
> we slowly accelerate the stick until it is at rest in Sam's frame.
> What is its length as measured in Sam's mosquito-based coordinate
> system?
>
> Mathematically, let L_stationary be the length of the stick, as
> measured in the stationary frame, before the stick is accelerated.
> Let L_sam be the length of the stick, as measured in Sam's
> coordinate
> system, after the stick has come to rest in Sam's frame. Then the
> question is: how does L_stationary relate to L_sam?
>
> The answer is that r_stationary will not be equal to r_sam,
> and L_stationary will not be equal to L_sam. So the physics
> governing the rates of clocks and the lengths of objects is
> not invariant under Mosquito transformations.
>
> On the other hand, according to all available evidence, the
> laws of physics *are* invariant under the Lorentz transformations
> (using lightspeed instead of mosquito-speed). That is, using
> light-based coordinates, we find that:
>
> 1. If a clock initially at rest in one frame has rate r as
> measured in that frame, and it is gently accelerated until
> it is at rest in a new frame, then it will have rate r as
> measured in the new frame.
>
> 2. If a stick initially at rest in one frame has length L as
> measured in that frame, and it is gently accelerated until
> it is at rest in a new frame, then it will have length L as
> measured in the new frame.
>
> In other words, the laws of physics that govern rates of clocks
> and lengths of sticks are invariant under the Lorentz transformations.
> There is no physical content to the Lorentz transformations until
> you say how the laws of physics transform.
>
I dont think that's the hard question at all. What worries me is when
Sam and Joe accelerate and pass 4.33 fps. The ladder keeps getting
longer, Sam and Joe get further apart, and pretty soon Sam is back
at "Origins" getting another cheeseburger while poor Joe is still
running.
When Joe stops, the ladder instantly shrinks to 32 ft, dragging Sam with
it, still munching. Joe, puffing and out of breath, sees Sam amiably
walking up the last 32 ft, cheeks full of cheeseburger and Joe punches
him in the mouth for not bringing a burger and getting a free ride.
That's a good reason to change the laws of physics, I think.

Androcles

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