How to correctly measure an unknown length with a clock.
Ka-In Yen
by Ka-In Yen,
Chungli city, Taiwan
yen...@yahoo.com.tw
1. Example 1: Tom sits in a train which moves at a constant
velocity. Tom need to measure the distance from city A to
city B. Obviously, He can not use a ruler to do this. Fortunately,
Tom has a clock, and he cleverly figures out a method which
allows him to measure the distance with a clock. Tom has no idea
about the speed of the train, but he knows that a railroad bridge's
length is L. When the train passes the bridge, Tom records the time
difference, t0, of two ends of the bridge; Next, he records the
time difference, t1, between city A and city B. Finally, Tom does
his calculation.
distance AB = L * t1 / t0.
Surprisingly, Tom finds the negative of the length contraction.
| Tom, clock
| Train
| -->
| ---- --------------------
| bridge(L) city A city B
+----------------------------------------
Frame S(ground)
Fig. 1
2. Discussion: The most primitive way to measure a length is
a ruler. But in many situation, a ruler is fail to measure;
for example, a tall tree, or a long distance. A lot of alternate
methods are invented for measuring length, and most of them need a
known length as reference. In example 1, a measuring method is
proposed: a clock can be used to correctly measure an unknown length
without contraction.
3. Conclusion: Example 1 shows: to an intelligent life form, the
length contraction is a result of wrong measuring method.
Shambolic
> How to correctly measure an unknown length with a clock.
>
> by Ka-In Yen,
> Chungli city, Taiwan
> yen...@yahoo.com.tw
>
>
> 1. Example 1: Tom sits in a train which moves at a constant
> velocity. Tom need to measure the distance from city A to
> city B. Obviously, He can not use a ruler to do this. Fortunately,
> Tom has a clock, and he cleverly figures out a method which
> allows him to measure the distance with a clock. Tom has no idea
> about the speed of the train, but he knows that a railroad bridge's
> length is L. When the train passes the bridge, Tom records the time
> difference, t0, of two ends of the bridge; Next, he records the
> time difference, t1, between city A and city B. Finally, Tom does
> his calculation.
>
> distance AB = L * t1 / t0.
>
Your problem is that your value of L is measured in the rest frame of
the bridge, so 'Tom' cannot use it to compare to intervals measured in
his moving frame. The time Tom takes to traverse the bridge will be
t'=L'/v, where L' is the length of the bridge after Lorentz
contraction.
(By the way, a 'ruler' doesn't have any theoretical limits...it
doesn't have to be a real ruler, it is just a crutch to help people
picture what's happening, so it is ALWAYS valid to measure with)
Joakim
To: Ka-In Yen
I agree with your statement.
Length contraction in SR is a result of not seeing the front and the
end of a rod simultaneously. SR is a correct theory that allows us to
correct a wrong measuring.
The Length contraction in SR is NOT physical.
Example 1 is not SR problem:
1-Tom knows the "physical length" of the bridge.
2-Tom records the time difference between beginning and end of the
bridge with his "clock rate"
3-With the same "clock rate" he measures the city distances, the real
distance.
No matter the time dilation or length contraction, as long as he uses
the same clock rate for the two measurements.
To:Shambonic
There is no length contraction as Tom records the time at the
beginning of the bridge with the clock near the beginning (fixed
point) and after a while he records the end of the bridge, with the
clock near the end (fixed point). There is no problem of simultaneity.
The clock of Tom has maybe a time dilation wrt the rest frame, but it
doesn't matter as he uses the same clock in both measurements.
Best regards
Joakim
Dirk Van de moortel
"Joakim" <fa56...@skynet.be> wrote in message news:c4463f11.0306...@posting.google.com...
[snip]
> To: Ka-In Yen
> I agree with your statement.
> Length contraction in SR is a result of not seeing the front and the
> end of a rod simultaneously. SR is a correct theory that allows us to
> correct a wrong measuring.
> The Length contraction in SR is NOT physical.
>
> Example 1 is not SR problem:
> 1-Tom knows the "physical length" of the bridge.
> 2-Tom records the time difference between beginning and end of the
> bridge with his "clock rate"
> 3-With the same "clock rate" he measures the city distances, the real
> distance.
>
> No matter the time dilation or length contraction, as long as he uses
> the same clock rate for the two measurements.
>
> To:Shambonic
>
> There is no length contraction as Tom records the time at the
> beginning of the bridge with the clock near the beginning (fixed
> point) and after a while he records the end of the bridge, with the
> clock near the end (fixed point). There is no problem of simultaneity.
> The clock of Tom has maybe a time dilation wrt the rest frame, but it
> doesn't matter as he uses the same clock in both measurements.
>
>
> Best regards
>
> Joakim
You don't really listen to people, do you?
http://groups.google.com/groups?&threadm=vLpHa.55808$1u5....@afrodite.telenet-ops.be
Dirk Vdm
Shambolic
> r.da...@ugrad.unimelb.edu.au (Shambolic) wrote in message news:<e37c3dcf.03061...@posting.google.com>...
> > yen...@yahoo.com.tw (Ka-In Yen) wrote in message news:<9f181401.03061...@posting.google.com>...
> To:Shambonic
>
> There is no length contraction as Tom records the time at the
> beginning of the bridge with the clock near the beginning (fixed
> point) and after a while he records the end of the bridge, with the
> clock near the end (fixed point). There is no problem of simultaneity.
> The clock of Tom has maybe a time dilation wrt the rest frame, but it
> doesn't matter as he uses the same clock in both measurements.
>
>
> Best regards
>
> Joakim
You're absolutely correct. Tom will be able to accurately measure the
'true' distance between the cities. This doesn't mean that length
contraction is 'a result of the wrong measuring method' though. Using
proportionality arguments, you can't find the distance between the
cities in the moving frame by using the length of the bridge in the
rest frame. These two quantities are not in the same proportion as the
two time intervals.
(All the suggested method does is provide one trivial extra piece of
information to avoid having to apply the Lorentz transforms, which
would give the correct distance anyway)
Ka-In Yen
> > How to correctly measure an unknown length with a clock.
> >
> >
> [snip]
>
> Your problem is that your value of L is measured in the rest frame of
> the bridge,
Of course, my dear friend.
> so 'Tom' cannot use it to compare to intervals measured in
> his moving frame. The time Tom takes to traverse the bridge will be
> t'=L'/v, where L' is the length of the bridge after Lorentz
But, how do you get the value of velocity v?
> contraction.
>
Below I quote from Einstein's book "Relativity:The Special
and General Theory" which can be found on
http://www.marxists.org/reference/archive/einstein/works/1910s/relative/ch12.htm
"But the metre-rod is moving with the velocity v relative
to K. It therefore follows that the length of a rigid
metre-rod moving in the direction of its length with a
velocity v is of a metre."
-- The Behaviour of Measuring-Rods and Clocks in Motion
It seems that the velocity v is pre-known, but how does Einstein
measure the velocity?
In sci-fi, Einstein can get a velocity without reason; in physics,
he has to explain his method of measuring velocity.
Shambolic
Relative velocity could be measured unambiguously by the Doppler
effect.
My last post was a little vague, sorry.We can assume Tom has never
(EVER) been at rest w.r.t. the bridge, but wants to measure its
length. In this case, there is no way around the length contraction,
clock or no clock.
Your idea is good, but the Lorentz contraction remains untouched, I'm
afraid.
Joakim
To Shambolic
1- In the first problem (by Ka-In Yen) the length of the bridge " L"
in rest frame was given. If so, Tom doesn't need SR to know the "real
distance" between cities in the rest frame, using his clock.
2- If "L" is not given but "v" the speed is given, Tom can measure the
length of the bridge "L-contracted" in his moving frame. Using SR
(Lorentz transformation )he can figure out what the real length "L"
is. He can calculate the real distance between cities in the rest
frame, using is clock.
3- If Tom doesn't know "L" or "v" than he needs at least something
like a mirror fixed in the rest frame to measure his speed by the
Doppler effect.
4- If Tom doesn't have an information from the rest frame he will
never know the distance between the 2 cities.
You can measure "Length contraction" but it is not a "real physical
contraction". It occurs only because you can not see simultaneously
the front and the end of a rod in the moving frame.
I don't deny the 奏ime dilation' and 鼠ength contraction".
To Ka-In Yen:
Example 1 does not show that the length contraction is a result of a
wrong measuring method. You have only to know "what" you are measuring
and how to deal with the result.
Best regards
Joakim
Ka-In Yen
> To Ka-In Yen:
> Example 1 does not show that the length contraction is a result of a
> wrong measuring method. You have only to know "what" you are measuring
> and how to deal with the result.
Hello Joakim,
I found an example from "Fundamentals of physics extended", 1997, fifth
edition, by Halliday, Resnick, and Walker. In section 38-6, The relativity
of length, a paragraph is titled "Proof of Eq. 38-9". Shortly described
as below:
The proper length(L0) L0=v*t
The contracted length(L) L=v*t0
After carefully analyzing the above example, I found that the length
contraction is a result of measuring length with three clocks. In
the above example, totally three clocks are used; two synchronized
clocks in rest frame, and one clock in moving frame. The length
contraction is a result of the discrepancy of clocks.
There are many known or unknown reasons causing clock slow or fast, eg
temperature, pressure, magnetic field, mechanical friction etc. To
eliminate the discepancy of clocks, single clock method is a better
method to measure length.
Best regards,
Ka-In Yen
yen...@yahoo.com.tw
Ka-In Yen
> > > > yen...@yahoo.com.tw (Ka-In Yen) wrote in message news:<9f181401.03061...@posting.google.com>...
> > > > > How to correctly measure an unknown length with a clock.
> Example 1 does not show that the length contraction is a result of a
> wrong measuring method. You have only to know "what" you are measuring
> and how to deal with the result.
>
Recently, I had an idea to use two synchronized clocks for length
measurement. I found that Kevin C Davis has proposed his idea in 1995.
Reference:
1) "Length contraction in special relativity (SR)", by Kevin C Davis,
http://groups.google.com/groups?selm=3kd80l%24pce%40mcd1.fm.intel.com
2) "The Length of a Moving Rod", by Demetrios Kalamidas,
http://groups.google.com/groups?selm=20020428234945.29171.00005559%40mb-mu.aol.com
Ka-In Yen
> 1) "Length contraction in special relativity (SR)", by Kevin C Davis,
> http://groups.google.com/groups?selm=3kd80l%24pce%40mcd1.fm.intel.com
> 2) "The Length of a Moving Rod", by Demetrios Kalamidas,
> http://groups.google.com/groups?selm=20020428234945.29171.00005559%40mb-mu.aol.com
Now, we have one-clock method, two-clocks method, and three-clocks method
for length measurement. Which method will you choose for length measurement?
Human being will face the following scenario soon. A group of astronauts
travel in deep space, far away from earth. How will they measure their
traveling distance? Will NASA develop a three-clocks measuring system
for length measurement? I do'nt think so.
Surprisingly, physicists still believe that the three-clocks method
is a proof of length contraction. It is not a proof of length contraction,
it is a mathematic magic; by using three clocks, the discrepancy of clocks
is transformed to length contraction.
Physicists are hypnotized by the education system. There is a punishing
system in the school. Any student can not proof the length contraction
by three-clocks method, he or she will gain a zero point of score. In
the past hundred years, millions of physicists are hypnotized by this
punishing system; now, we need another one hundred years effort to
anti-hypnotize our education system.
Ka-In Yen
yen...@yahoo.com.tw
Ka-In Yen
is a proof of length contraction? If you do believe in it,
could you explain more detail. Or, it is a responsibility of
SR society to announce that the three-clock method is not a
proof of length contraction before the new semester. It is
not proper to teach student with wrong material.
Ka-In Yen
yen...@yahoo.com.tw
yen...@yahoo.com.tw (Ka-In Yen) wrote in message news:<9f181401.0307...@posting.google.com>...