On 11/8/19 9:35 AM, Nicolaas Vroom wrote:
> Consider a rod with 8 clocks, equally spaced, a distance l apart.
> The rod is considered at rest. This implies that the speed of light c
> in all directions is the same. We call this rule 1.
> The clocks are numbered from #1 to #8.
> The strategy is to perform a certain number of experiments.
Let me call this initial inertial frame K.
> The first experiment is called clock synchronisation.
> Halfway in between clock #4 and #5, there is a light source which emits a
> reset signal. The setup is such that the length lightpath to each clock is
> the same.
As you subsequently explained, there are additional components involved
to make the light paths equal.
It is important to describe the physical situation completely.
> Using rule 1 the light signal will reach all the clocks simultaneous.
> This is important because all the clocks at any moment will all show the same
> count.
By "any moment" you mean "observed simultaneously in K, by observers
co-located with each clock".
It is important to describe things precisely.
> The second experiment starts with making an exact copy of rod #1.
Presumably all of its clocks are synchronized in K, and with all the
clocks of the original rod.
It is important to describe things completely.
> Also
> attached to each clock there is an engine which can be fired with a standard
> burst in either the forward or backward direction. Each clock also has
> an observer.
> The second experiment consists that each observer on rod #2 fires his engine
> with a standard burst in the same direction when his clock is reset.
This "when" is ambiguous. I presume the observers are not clairvoyant,
so each one actually fires their engine a negligibly short time after
their clock receives the reset signal. So they all fire simultaneously in K.
> This burst will give the rod a certain speed v.
Let me call this second inertial frame K', and we agree not to discuss
it before or during the firing of the engines.
> The now moving observers will perform the next tasks when they reach the next
> clock at rest: They will write down the reading of the clock at rest and
> the reading of their own moving clock.
OK. Of course the leading clock at rest in K' never meets a clock at
rest in K, so ignore it.
> This is the result:
> They are the same for all observers. The number of counts of the moving
> clocks is less than the number of counts of the clocks at rest.
Yes. The clocks at rest in K' are all synchronized in K -- NOT K'. Seven
of them meet the next clock at rest in K at the same time in K, and the
same time displayed on their own clocks (which is different from the
time indicated by the clocks at rest in K).
Note that an observer at rest in K' would describe the clocks at rest in
K as closer together than the clocks at rest in K', and none of the
clocks are synchronized in K'. In terms of the coordinates of K', the
clocks successively meet in pairs, but when each clock from K' meets the
clock in K, all clocks in K indicate the same time, and all clocks in K'
indicate the same time (that is different from those in K).
> This is not so strange because it means that the physical forces which
> influence the behaviour of each clock are identical.
None of these forces influence the behavior of any clock in any way.
I assume the engines are not so powerful that they
damage the clocks of the second rod.
> Specific what this
> means is that all the moving clocks stay synchronised. This is rule 2.
> You can repeat this experiment, but still, rule 2 applies.
Your "rule 2" is VERY LIMITED, and applies to this physical situation only.
> Experiment 3 is almost identical to experiment 2. That means all
> the engines are fired after the reset signal is received.
Oh. Then you assumed that the observers were indeed clairvoyant in
experiment 2. So take my discussion above and apply it here.
> This defines the starting condition of experiment 3. The starting
> condition of experiment 3 is a moving rod with the speed v.
This last sentence is different from what you said before, and
inconsistent with the engines being fired AFTER the reset signal is
received. One paragraph earlier the starting condition of experiment 3
was the same as experiment 2: both rods at rest in K.
It is important to describe things consistently.
> Experiment 3 involves that a certain moment the light signal between
> clock #4 and #5 of the moving rod issues a reset signal.
> Like before the moving observers write down the results when they reach
> the next clock at rest. This is the result:
> All the observers write down the same number of counts for the clocks
> at rest. For the moving clocks, the results are different. The clock
> in front will have the lowest count. The clock at the back the highest
> count. Physical the clock in the back is reset the first.
This is wrong. See above.
> [... too complicated to bother with.]
You MUST describe the physical situation completely AND PRECISELY AND
CONSISTENTLY. Details matter, because relativity is both complicated and
subtle. Whenever you say "synchronized" you must also state in which
frame it applies. Whenever you say "when", you must reword to state
"simultaneously in frame ...". Do not ever say "at any moment", but
rather specify which frame you are using and specify values of its time
coordinate. And don't assume observers are clairvoyant.
Tom Roberts