Hello,
after having done a bit of exercices on Taylor & Wheeler ( just for self-study ), I felt
the need to go on a bit differently, i.e. trying to solve qualitative problems instead of
quantitative ones, i.e. using a bit of diagrams ( all in all, as Susskind always suggest
"when you face a SR problem, plot a diagram first ).
That said, I was trying to solve this Trekker oriented problem:
http://www.phys.vt.edu/~takeuchi/rel...problem07.html
The overall diagram is quite clear to me, since I was able to answer to all
questions "almost" without problems. But then I thought "wait a minute: it's easy looking
at a already well cooked diagram...let's try to do it by myself from scratch, now!!!"
( Incidentally this is needed, for example, if you wanna to solve the T & W 3.7 exercice,
called Space War, which is exactly this problem without Kirk & friends ).
But here start having problem, highligthing probably my real doubts on it.
So I started to draw a simple x/t diagram, i.e. the enterprise frame, adding a
light beam from origin heading to the right ( x > 0 ).
The I plotted the klingon's primed frame, obviously making it a simmetric around
the light beam, with a certain rapidity angle with x/t axes.
So far, so good. Now I decided to add the Enterprise at rest in its frame ( the unprimed ).
This actually leads to 2 vertical lines ( parallel to t time axis ). This also result in deciding
where to put the event of klingon front reaching the enterprise rear.
Looking at the original plot, the author decided to put it onto the light beam line, i.e.
C point. It's not really clear from this diagram, but if you look at its book ( I own it ), you
can see the enterprise rear wordline intersects the lightbeam EXACTLY in C point.
So my point is: is this a licky strike, or a specific design? Why choosing the C event
to be light-like?
From C, you can draw a line parallel to t', which intersect the enterprise x axis in point
V ( let's imagine to call the intersection of x axis on the right of the O origin respectively
V, W and Z ).
So the distance OV is actually the contracted distance of the klingon ship as the enterprise sees it ( this is because the V point is got as intersection between the front klingon wordline with the
enterprise x axis ).
So, the way contraction is actually a f() in which you choose the C point.
This puzzles me a bit: imagine to keep the enterprise with the same lenght at rest, i.e. WZ length
as constant. Now we decide to move the W point shifting on its right. This shifts the Z point as well, leading to a new C point with the beam : this result in a klingon ship contracted a bit wider than before.
So the point is: how the contraction, which a f() of just the relative beta ( v/c ), may vary
changing the point in which we choose to draw the enterprise ship? ( i.e. V point )
2) I cannot figure how to relate the VW distance with the OV one. From the picture it seems
exactly the same distance. I mean, I'm able to derive the contracted X from the uncontracted
one ( at t=0, for instance ), but I'd like to desume it from the plot, not with formulas...
This is also because let's imagine to keep the W point as costant, i.e. getting a given OV contracted klingon ship. where is the constrain for the W point, i.e. for the enterprise front point?
I'm asking this, because if we'll be able to move this W on its left without constrains, i.e. to change the enterprise size, we could lead to a situation in which the enterprise front it's on the left of firing E points, leading to a hit, instead of a miss.
This doesn't make sense, of course. So my reasonign is wrong in somewhere.
Let me know where you find my error, please, eventually.
Regards
Ricky
after having done a bit of exercices on Taylor & Wheeler ( just for self-study ), I felt
the need to go on a bit differently, i.e. trying to solve qualitative problems instead of
quantitative ones, i.e. using a bit of diagrams ( all in all, as Susskind always suggest
"when you face a SR problem, plot a diagram first ).
That said, I was trying to solve this Trekker oriented problem:
http://www.phys.vt.edu/~takeuchi/rel...problem07.html
The overall diagram is quite clear to me, since I was able to answer to all
questions "almost" without problems. But then I thought "wait a minute: it's easy looking
at a already well cooked diagram...let's try to do it by myself from scratch, now!!!"
( Incidentally this is needed, for example, if you wanna to solve the T & W 3.7 exercice,
called Space War, which is exactly this problem without Kirk & friends ).
But here start having problem, highligthing probably my real doubts on it.
So I started to draw a simple x/t diagram, i.e. the enterprise frame, adding a
light beam from origin heading to the right ( x > 0 ).
The I plotted the klingon's primed frame, obviously making it a simmetric around
the light beam, with a certain rapidity angle with x/t axes.
So far, so good. Now I decided to add the Enterprise at rest in its frame ( the unprimed ).
This actually leads to 2 vertical lines ( parallel to t time axis ). This also result in deciding
where to put the event of klingon front reaching the enterprise rear.
Looking at the original plot, the author decided to put it onto the light beam line, i.e.
C point. It's not really clear from this diagram, but if you look at its book ( I own it ), you
can see the enterprise rear wordline intersects the lightbeam EXACTLY in C point.
So my point is: is this a licky strike, or a specific design? Why choosing the C event
to be light-like?
From C, you can draw a line parallel to t', which intersect the enterprise x axis in point
V ( let's imagine to call the intersection of x axis on the right of the O origin respectively
V, W and Z ).
So the distance OV is actually the contracted distance of the klingon ship as the enterprise sees it ( this is because the V point is got as intersection between the front klingon wordline with the
enterprise x axis ).
So, the way contraction is actually a f() in which you choose the C point.
This puzzles me a bit: imagine to keep the enterprise with the same lenght at rest, i.e. WZ length
as constant. Now we decide to move the W point shifting on its right. This shifts the Z point as well, leading to a new C point with the beam : this result in a klingon ship contracted a bit wider than before.
So the point is: how the contraction, which a f() of just the relative beta ( v/c ), may vary
changing the point in which we choose to draw the enterprise ship? ( i.e. V point )
2) I cannot figure how to relate the VW distance with the OV one. From the picture it seems
exactly the same distance. I mean, I'm able to derive the contracted X from the uncontracted
one ( at t=0, for instance ), but I'd like to desume it from the plot, not with formulas...
This is also because let's imagine to keep the W point as costant, i.e. getting a given OV contracted klingon ship. where is the constrain for the W point, i.e. for the enterprise front point?
I'm asking this, because if we'll be able to move this W on its left without constrains, i.e. to change the enterprise size, we could lead to a situation in which the enterprise front it's on the left of firing E points, leading to a hit, instead of a miss.
This doesn't make sense, of course. So my reasonign is wrong in somewhere.
Let me know where you find my error, please, eventually.
Regards
Ricky
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