Faster than the speed of light with only a fishing line

[jamesbird]

Can someone easily explain to me what’s wrong with this thought experiment:
I’m in a spaceship traveling at 0.500001 c . I’ve a long fishing line with knots tied every 186k miles along it’s length (told you it was long). Another spaceship traveling at 0.500001 c in the opposite direction passes me, and at that moment I hook the line onto the other ship’s bumper (fender). The line now leaves the reel and as it passes through my fingers (I’m wearing gloves) I time that the knots are passing through my hand at more than 1 per second. Isn’t the line now moving at >c? If it’s not moving at c+ why not. Not bothering with those strange photon things that physicists come up with willy woolly explanations about, I’m using good old fashioned fishing line, something with (excuse the pun) real physical properties, real length etc.
Ha got you there Einstein – get out of that one.
Confused (or possibly just simple) of St Albans

 

[malawi_glenn]

But the addition of velocity will not give a velocity >c, the relative velocity of the two space ships will be less than c and the fishing line will have velocity less than c also. Sorry but you should study special relativity a bit more :-)

 

[neopolitan]

Can someone easily explain to me what’s wrong with this thought experiment:
I’m in a spaceship traveling at 0.500001 c . I’ve a long fishing line with knots tied every 186k miles along it’s length (told you it was long). Another spaceship traveling at 0.500001 c in the opposite direction passes me, and at that moment I hook the line onto the other ship’s bumper (fender). The line now leaves the reel and as it passes through my fingers (I’m wearing gloves) I time that the knots are passing through my hand at more than 1 per second. Isn’t the line now moving at >c? If it’s not moving at c+ why not. Not bothering with those strange photon things that physicists come up with willy woolly explanations about, I’m using good old fashioned fishing line, something with (excuse the pun) real physical properties, real length etc.
Ha got you there Einstein – get out of that one.
Confused (or possibly just simple) of St Albans

With respect to what are you traveling at 0.500001c? Because you picked 0.500001c for both ships, it makes sense to say "with respect to the other ship", in which case you will have the knots passing you at 0.500001c.

But I don't think you mean that. You are implying that you have an absolute speed, but that won't work. If you pick a third observer, with respect to whom you have a velocity of 0.500001c and with respect to whom the other ship has a velocity of -5.00001c, then the relative speed of that other ship with respect to you is:

w = u - v / ( 1 - v/c . u/c)

w = (0.500001c + 0.500001c) / (1 - (0.500001)(-0.500001)) = 0.800001c

The knots will still hurt as they pass through your fingers though.

cheers,

neopolitan