This puzzle was written by someone who doesn't believe in the theory of
special relativity. I was hoping someone more knowledgeable than myself
on usenet could try to refute the argument of the author of the puzzle,
if possible.
Thank you,
Craig
"Belief" isn't necessary. All they need to do is show where it
fails.
> I was hoping someone more knowledgeable than
> myself on usenet could try to refute the argument
> of the author of the puzzle, if possible.
Seen so many times...
<QUOTE>
Assume that both the spaceship A and the buoy B carry on board
identical and accurate stop watches. Assume that some suitable
mechanism (which can easily be devised) causes both the stop
watches to measure the time interval taken for the spaceship A to
pass the buoy B.
<END QUOTE>
Can't be done, since the clock in ship A isn't located
*everywhere* in A. Instantaneous signalling is required. This
Universe is limited to lightspeed signalling.
"If only I could have this fictitious thing, I could prove
Reality false".
David A. Smith
I can't imagine anyone with the slightest of insights into the world
of SR could be considering this a paradox. In fact, this is the most
straight forward SR problem I've ever seen. Much more the type of
thing that a student would get as homework after the first SR lecture
than something that someone could actually get stuck on. Anyways, I
will do your homework...
First of all, the readouts are different.
As seen from B, the space ship approaches at 0.8660254038. The length
of the buoy is 1 meter. Therefore the time required for passage is
1/(0.8660254038*299792458) = 1.926 ns
As seen from A, the buoy approaches at 0.8660254038. The length of the
buoy is .5 m (length contraction). The total time required to pass
the buoy is
0.5/(0.8660254038*299792458) = 3.852 ns
If two buoys would pass each other and both would measure the time it
took them to pass the other buoy, then they would measure the same
time. In the scenario given, both measure the time it takes to pass
something that moves with one of the frames, of course they see it
differently that's the whole point of SR.
Ok, I believe I've done your homework now. Hope this was helpful. :-)
Cheers
Fredrik
Suppose
- we call both objects a ship,
- A uses primed coordinates x' and t',
- B uses unprimed coordinates x and t,
- A moves with velocity v w.r.t. B along their common x and x' axes,
- the clocks are set to zero when front of A passes the rear of B,
- A has proper length P,
- B has proper length p
Then
- in units where c = 1, the transformation equations
between A and B are
/ x' = g (x - v t)
\ t' = g (t - v x)
/ x = g (x' + v t')
\ t = g (t' + v x')
where g = 1/sqrt(1-v^2)
- the world line of the rear end of A is in A's system:
x' = -P
- the world line of the front end of B is in B's system:
x = p
- A and B stop passing each other at the event where
the rear end of A passes the front end of B.
So, to find the times it takes the ships to pass each other,
you solve the system of equations for t and t'
/ t' = g (t - v x)
/ t = g (t' + v x')
\ x' = -P
\ x = p
and you get
/ t = ( P/g + p ) / v
\ t' = ( p/g + P ) / v
With the numeric values from the example you get
/ t = 0.499654 s
\ t' = 0.999308 s
These numbers are sent to Earth.
Now mr. Metha can make the exercise of deciding "which
ship is really moving" ;-)
Dirk Vdm
Notes:
- Fredrik made a little mistake and swapped the answers of the calculations.
- David pointed out that the time measurement with B's stopwatch "can't be
done": it's not a pure time measurement but a "measurement" at a distance.
And the "simple challenge" is simple indeed: it's similar to muons arriving
at the earth, which is taken as evidence in favour of SRT.
> If two buoys would pass each other and both would measure the time it
> took them to pass the other buoy, then they would measure the same
> time. In the scenario given, both measure the time it takes to pass
> something that moves with one of the frames, of course they see it
> differently that's the whole point of SR.
Good remark.
> Ok, I believe I've done your homework now. Hope this was helpful. :-)
>
> Cheers
> Fredrik
Cheers,
Harald
You have a rather different interpretation of the setup.
It seems you are working with a zero-length spaceship A.
He specified a proper length of 259627884 meters.
Dirk Vdm
Why, don't you like straightforward logic that disagrees with your religion?
http://www.androcles01.pwp.blueyonder.co.uk/Smart/Smart.htm
http://www.androcles01.pwp.blueyonder.co.uk/Synchronize/Synchronize.htm
http://www.androcles01.pwp.blueyonder.co.uk/Doppler/Doppler.htm
Androcles
Moronic local village psychopath,
x' = x-vt, so x' is the length of the ship.
http://www.fourmilab.ch/etexts/einstein/specrel/www/
Androcles
Straightfoward logic ? When you will understand why such basic logic
statements as "False => True" (resp. 0 => 1) is True (resp. 1) you
will be allowed to talk about logic (what will never happen).
Thank you all for your answers.
Craig
Yes, straightforward logic.
You wouldn't know what that was and I wasn't addressing you, so fuck off.
http://www.androcles01.pwp.blueyonder.co.uk/Dork/zeroone.htm
http://www.androcles01.pwp.blueyonder.co.uk/Dork/falsetrue.htm
Androcles.
Androcles.
Straigtforward indeed :-)
http://users.telenet.be/vdmoortel/dirk/Physics/Fumbles/Gibberish.html
http://users.telenet.be/vdmoortel/dirk/Physics/Fumbles/XOROnceMore.html
http://users.telenet.be/vdmoortel/dirk/Physics/Fumbles/XORrevisited.html
http://users.telenet.be/vdmoortel/dirk/Physics/Fumbles/LooksBoolean.html
Dirk Vdm
And do you agree with any of them?
Martin Hogbin
http://mathworld.wolfram.com/Implies.html
> In classical logic, A=>B is an abbreviation for ŹA v B, where ŹA
> denotes NOT and v denoted OR.
What is ((not False) OR True) dumby ?
http://www.rwc.uc.edu/koehler/comath/21.html
> p q p -> q
> T T T
> T F F
> F T T
> F F T
What could you read on the "F T" line dumby ?
http://www.mapfree.com/sbf/tips/logic.html
Here is a truth table that defined "C IMPLIES P".
> C P C IMPLIES P
> true true true
> true false false
> false true true
> false false true
What could you read on the "false true" line dumby ?
http://www.everything2.com/index.pl?node_id=450472
> The following is a truth table for two boolean arguments. Any larger truth tables would be quite difficult to node
>
> A B |1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
> _____|_____________________________________________________
> T T |T T T T T T T T F F F F F F F F
> T F |T T T T F F F F T T T T F F F F
> F T |T T F F *T* T F F T T F F T T F F
> F F |T F T F T F T F T F T F T F T F
>
> legend:
> 1. true
> 2. or ( V )
> 3. consequence ( <= )
> 5. implication ( => )
what could you read on the third line of the fifth column dumby ?
Androcles
You can't read, Trough. He said he was HOPING someone MORE
knowledgeable that himself could TRY to refute the argument,
you've never read http://www.fourmilab.ch/etexts/einstein/specrel/www/
and wouldn't understand it if you did.
http://www.androcles01.pwp.blueyonder.co.uk/Pigbin/cantread.htm
Here's some pictures to explain it to you:
http://www.androcles01.pwp.blueyonder.co.uk/Smart/Smart.htm
(with a train so that a knowledgeable person can measure it's speed).
Androcles.
A = "Androcles was not addressing Your Basic Moron."
B = "Fuck off."
A implies B.
A is true.
B is also true.
So fuck off.
Androcles.
If you want a real entertaining 'solution' of the challenge,
look here:
http://homepage.mac.com/ardeshir/SingleBestArgumentAgainstSR.pdf
Have fun! :-)
More fun here:
http://homepage.mac.com/ardeshir/Relativity.html
Paul
[snip]
> So, to find the times it takes the ships to pass each other,
> you solve the system of equations for t and t'
> / t' = g (t - v x)
> / t = g (t' + v x')
> \ x' = -P
> \ x = p
> and you get
> / t = ( P/g + p ) / v
> \ t' = ( p/g + P ) / v
>
> With the numeric values from the example you get
> / t = 0.499654 s
> \ t' = 0.999308 s
Ha. I used c = 3 10^8 m/s here.
With the exact value 299792458 we get
/ t = 0.5 s
\ t' = 1 s
Paul, thanks for pointing to
http://homepage.mac.com/ardeshir/SingleBestArgumentAgainstSR.pdf
;-)
Dirk Vdm
> And do you agree with any of them?
> Martin Hogbin
The last time I formally studied relativity was in high school a long
time ago. My head is spinning from thinking about it now just as it did
then. The website http://www.mathpages.com/home/kmath024/kmath024.htm
convinced me that the main argument of the first website that I posted
is probably invalid.
Since I don't want my head to spin any longer and since my opinion on
the matter isn't really that important, I'll choose to believe the
majority opinion that relativity is logically consistent and not think
about it anymore.
Craig
Bruce
Ooops, you're right about that. I'll be more careful next time! Still
no paradox though and still a very simple problem.
/Fredrik
My, my, my. What incredible anger!
>
Indeed, it was written by a complete crackpot.
> Since I don't want my head to spin any longer and since my opinion on
> the matter isn't really that important, I'll choose to believe the
> majority opinion that relativity is logically consistent and not think
> about it anymore.
Smart move.
Martin Hogbin
I used the link:
http://homepage.mac.com/ardeshir/SimpleChallenge-Relativity.html
The problem with this puzzle is that I do not understand it.
The puzzle is not clear.
Specific the following part:
"Assume that some suitable mechanism (which can easily be devised)
causes both the stop watches to measure the time interval taken for
the spaceship A to pass the buoy B."
What easily can be done is an Observer B at rest on buoy B
to measure the time it takes for spaceship A to pass Observer B.
You need one stop watch.
You start the stopwatch when the front is in front of you and you
stop when the stopwatch when the end is in front of you.
You can also do the same for an Observer A at rest on Spaceship A
to measure the time it takes to pass buoy B.
Both times will be different because the length are different.
To measure the time it takes for spaceship A to pass the buoy B
you need two Observers B1 and B2 on buoy B.
The spaceship moves from left to right and B1 is at the left side
Only B1 has a stopwatch.
B1 starts the stop watch when the front of the space ship is in front
of him.
B1 does nothing when the end is in front of him.
B2 sends a lightsignal to B1 when he sees the end in front of him.
B1 stops the stopwatch when he receives the lightsignal from B2.
You can do the same on the spaceship by two observers A1 and A2.
Is this what Ardeshir Mehta has in mind ?
Assume that the buoy has a length l=0
and that the speed of the spaceship is small.
In that case it takes the same time for the spaceship to pass the buoy
(from the buoys point of view) as for buoy to pass the spaceship
(from the spaceship point of view).
The problem is one the buoy you can use one stopwatch to directly
measure this duration.
On the spaceship you need two observers and a lightsignal.
It is this lightsignal that causes that the durations are different.
Nicolaas Vroom
http://users.pandora.be/nicvroom/
Very interesting essay.
> Since I don't want my head to spin any longer and since my opinion on
> the matter isn't really that important, I'll choose to believe the
> majority opinion that relativity is logically consistent and not think
> about it anymore.
Well, that's what most people end up having to do in most subjects, because
life's too short to figure out everything for yourself. Still, it seems kind
of sad to put a lot of effort into it and then give up.
I wonder if it would help, in your case, to try to learn relativity as a
purely mathematical theory, without thinking about its physical significance
at all. Special relativity is very, very close to analytic geometry in a lot
of ways, and probably the best way to get a feel for its internal
consistency is to understand it as a kind of geometry. The essay you
mentioned above talks about that briefly, and here's an article where I
talked about it a bit more:
http://groups.google.com/group/sci.physics.relativity/msg/77a649653249add9
Once you understand it mathematically, hopefully it will be easier to see
how it connects to the real world.
-- Ben
The recently died J.K. Galbraith apperently made the following statement:
(Free translation from Dutch)
It is more profitable to be a member of a team that has it wrong
than to be the sole person who has it right.
I'am not claiming that because the majority believes in SR that they
have it wrong.
What I would like to advice you is to try to understand SR
as much as possible indepent what the majority thinks.
Anyway that is what I (try to) do and that is not that easy.
For a discussion about SR see the following link:
http://www.cord.edu/dept/physics/credo/etrain_credo.html
IMO the whole discussion about simultaneity boils down to the
following two statements:
1. There exists a set of simultaneous events (Each moment)
2. This set is independent of any observer.
In the above link we read:
"The cowboy sees the lightning bolts strike the two ends of the train
simultaneously."
IMO this should have been:
"Two lightning bolts strike the two ends of the train simultaneously".
IMO the cowboy does not see the actual events.
What he sees is written in the next sentence:
"The cowboy sees the two flashes of light meet at the center
of the distance between the two burn marks SIMULTANEOUS"
I have added the word simultaneous.
IMO this can only be the case if the speed of the cowboy
is zero times the speed of light.
From his point of view the passenger on the moving train
can not see the two flashes simultaneous.
But now let us see the point of view of the passenger.
There are two simultaneous events
and she stays at rest in the train.
Why can not she say that her speed is also
zero times the speed of light (in her frame)
and that she sees the two flashes simultaneous
and the cowboy not ?
IMO neither the cowboy nor the passenger is correct
but that is accordingly to SR wrong.
(Except one at a rare occasion)
Nicolaas Vroom
http://users.pandora.be/nicvroom/
Everyone understands it in his/or personal way, although no doubt some
understandings are better than others. As long as you think it's not that
easy, probably you don't really understand it yet (not even your way).
> For a discussion about SR see the following link:
> http://www.cord.edu/dept/physics/credo/etrain_credo.html
> IMO the whole discussion about simultaneity boils down to the
> following two statements:
> 1. There exists a set of simultaneous events (Each moment)
> 2. This set is independent of any observer.
That's erroneous - what is defined as being simultaneous in one system,
isn't generally simultaneous in other systems.
> In the above link we read:
> "The cowboy sees the lightning bolts strike the two ends of the train
> simultaneously."
> IMO this should have been:
> "Two lightning bolts strike the two ends of the train simultaneously".
> IMO the cowboy does not see the actual events.
IMO nobody sees the actual events.
> What he sees is written in the next sentence:
> "The cowboy sees the two flashes of light meet at the center
> of the distance between the two burn marks SIMULTANEOUS"
> I have added the word simultaneous.
It is immaterial how he sees the flashes...
> IMO this can only be the case if the speed of the cowboy
> is zero times the speed of light.
Speed relative to what, and according to which instruments?
> From his point of view the passenger on the moving train
> can not see the two flashes simultaneous.
??
> But now let us see the point of view of the passenger.
> There are two simultaneous events
> and she stays at rest in the train.
> Why can not she say that her speed is also
> zero times the speed of light (in her frame)
> and that she sees the two flashes simultaneous
> and the cowboy not ?
Probably you misunderstood the question...
Harald
I expect you mean observer.
The sets of events seen by one observer (at one instance)
is not the same as the events seen by a different observer.
If you declare the two events simultaneous
than they are simultaneous for the cowboy
and for the passenger.
(The question is who will see the flashes simultaneous)
>> In the above link we read:
>> "The cowboy sees the lightning bolts strike the two ends of the train
>> simultaneously."
>> IMO this should have been:
>> "Two lightning bolts strike the two ends of the train simultaneously".
>> IMO the cowboy does not see the actual events.
>
> IMO nobody sees the actual events.
That means you agree that that sentence is slightly incorrect.
The cowboy (passenger) can see the lightning bolt strike the train
at one end of the train only if he stands there
(but than he will the flash from the other end later
and also the passenger)
>> What he sees is written in the next sentence:
>> "The cowboy sees the two flashes of light meet at the center
>> of the distance between the two burn marks SIMULTANEOUS"
>> I have added the word simultaneous.
>
> It is immaterial how he sees the flashes...
I think that that is the main point of the argument.
He sees them simultaneous
and the passenger not.
>> IMO this can only be the case if the speed of the cowboy
>> is zero times the speed of light.
>
> Speed relative to what, and according to which instruments?
Relative to the speed of light.
How do you define that the passenger has a speed of 0.5 * c ?
>> From his point of view the passenger on the moving train
>> can not see the two flashes simultaneous.
>
> ??
That is what you see in the movie.
>> But now let us see the point of view of the passenger.
>> There are two simultaneous events
>> and she stays at rest in the train.
>> Why can not she say that her speed is also
>> zero times the speed of light (in her frame)
>> and that she sees the two flashes simultaneous
>> and the cowboy not ?
>
> Probably you misunderstood the question...
There is no question.
There is an argumentation.
The argumentation is not clear to me.
I think we all agree that both observers will not see
the two flashes simultaneous in one experiment.
IMO this has nothing to do with SR.
The question is who will see them simultaneous and when.
The sad point with SR is that you can not settle this argument
by performing a real experiment.
(The same with length contraction)
For moving clocks this is a whole different ballgame.
> Harald
>
Nicolaas Vroom
http://users.pandora.be/nicvroom/