PDA

View Full Version : Problem understanding length contraction thought experiment

lafinboylafbubba
2006-Apr-05, 09:51 AM
I was given a thought experiment to explain length
contraction. It works fine but I have some issues.

B is 186,000 miles in front of A travelling in the same
direction through space. B wants to accellerate and
wants A to accellerate at the same time so that their
distance remains equal. B has a clock and a flash
light. He flashes the light and waits one second
before accellerating. All is cool. However, A has
moved towards B in that one second and gets the flash
before the second is up and starts accellerating first.
So there has to be a length contraction to compensate
for this impossible situation. All is cool.

Here's where I get confused.

If A has the flashlight B would have moved a bit
further away and so get the flash after a second.
A will start accellerating first.

Does this not mean that there has to be a length
expansion to sort the problem out.

bigsplit
2006-Apr-05, 02:57 PM
I was given a thought experiment to explain length
contraction. It works fine but I have some issues.

B is 186,000 miles in front of A travelling in the same
direction through space. B wants to accellerate and
wants A to accellerate at the same time so that their
distance remains equal. B has a clock and a flash
light. He flashes the light and waits one second
before accellerating. All is cool. However, A has
moved towards B in that one second and gets the flash
before the second is up and starts accellerating first.
So there has to be a length contraction to compensate
for this impossible situation. All is cool.

Here's where I get confused.

If A has the flashlight B would have moved a bit
further away and so get the flash after a second.
A will start accellerating first.

Does this not mean that there has to be a length
expansion to sort the problem out.

There would be no length contraction or expansion as they are moving the same speed. This is because there would be a cancellation of the two effects regardless of the source (A or B) or the light. In such a situation a third point comes into play and that is the point of interception of the light by the recieving craft.

A flashes his light towards B, There is a point in which B will intercept and A is moving in that direction at the same rate B is moving in that direction. The contraction from A will cancel out the expansion of B. Likewise, If B flashes towards the point of interception, there is an expansion, as A intercepts moving towards the flash at an equal speed there is an equal contraction that cancels.

I think.

Ken G
2006-Apr-06, 04:27 AM
Welcome lafin, I don't have time to think it through right now, but I suspect your confusion stems from forgetting that the concept of where A and B are at the same time is different in the two frames, because the concept of simultaneity is different. Thus the stationary observer may think B accelerated sooner than A while A and B think they accelerated at the same time. Indeed, that's just what you need to get the distance between them to contract more and more as they go faster and faster.

Gerald Lukaniuk
2006-Apr-08, 07:17 PM
Think of looking at a small end fish tank straight on with the fish swimming straight back and forth. They start small and get big then get small again. Tilt it to one side a little and pretend you can't see the corner and it's a whole new deal. The noses of the fish would look a little different, a little bigger when they start and end smaller when they start receeding again or it would take them a little longer to hit nearer the corner appearing to be the same size as before,before they shrink. You've constricted length and depth and dilated time. Objects travelling through at different velocities space warp the space dimensions around them but light doesn't but is affected by the warping. If the tank is moving directly away from us in straight line, the images of the fishes noses appear bigger than expected as if a little bit of all the sides we can't ordinarily see are added to it. This always happens with any moving objects but gets more obvious when the speed differences are huge. If we know we are seeing fish noses and our instruments are corrected so we see fish noses its like we had to put them on a diet because it looked like they had gotten fat and lazy and gained mass. That's a crude look at SR. If you think of looking up at an balloon of vs a balloon of water as you lower them on a pane of glass above your head and imagine nothing changed about the shape of the balloon that's GR.

lafinboylafbubba
2006-Apr-08, 08:40 PM
@Gerald Lukaniuk

Hi Gerald, gunna have a good think about that view
Thanks

Could you correct part of a sentence for me

"think of looking up at an balloon of vs a balloon
of water as you lower them"

Couldn't visualise that bit.
cheers.

hhEb09'1
2006-Apr-08, 09:05 PM
Welcome lafin, I don't have time to think it through right now, but I suspect your confusion stems from forgetting that the concept of where A and B are at the same time is different in the two frames, because the concept of simultaneity is different.One of the first BA forum threads (http://www.bautforum.com/showthread.php?t=13) (number 13 if that tag is to be believed, it was a crossover from a previous version of BABB) was about Bell's rockets and ropes "paradox": two rockets attached by a rope accelerate in the same fashion, does the rope break?

Gerald Lukaniuk
2006-Apr-11, 12:30 AM
@Gerald Lukaniuk

Hi Gerald, gunna have a good think about that view
Thanks

Could you correct part of a sentence for me

"think of looking up at an balloon of vs a balloon
of water as you lower them"

Couldn't visualise that bit.
cheers.
Thanks for taking a look at this explanation and I apologize if it’s a little shaky, I explained Relativity a bit in University lectures I did and I always feel its better to over simplify. It may be a bit inaccurate to get at less a better picture than all that Observer A Observer B gobbly goop my prof said nobody understands anyway .but use to impress other people.
First I have to add to my fish tank view (and of course all this viewing takes really good eyes). I should probably add that this space-time distortion thing gives objects a completely different but equally the same (1) view of each other when they are traveling together in the same direction than when they ain’t going nowhere in particular.(2). The fish in the tank in the sideways rotation would say, “My tank did tilt and there ain’t nothing wrong with my mouth, but your eyeball sure looks weird. This different amount of space warp thing gives him a look at sides of us he would ordinarily expect to see plus the one he would.
He would say speak for yourself, “you’re the one that got fat and lazy”
If one of us decided to go after the other guy while we’re coming at each other warping would go the opposite way It .would be like the space time we are pushing through was getting scrunched up instead of stretching. We’d be seeing less of the big red mouth that we wanted to punch than usual and he’d be seeing a lesser view of our eyeball that he wanted to bite. We would say, “Why have you gotten so skinny and why are you acting so hyper and you looking a little blue around the gills, liver lips”
“I’m hyper….you’re the one that’s hyper. Wait until I get my lips on your eyeball wise guy….won’t that make your brown eyes blue’
(What both of us don’t know is that we should be blaming it on our light rays buddies for taking a short cut and some of them getting lost?) (3)
If one or both of us decided to cool, down and come to a dead stop eye to mouth we’d be surprised to see we both look pretty much normal to each .other (4) We’d be so mad arguing about who was pulling a prank on who we might really end up with a fat lip and a red eye.
That’s when Mr. Einstein comes to the rescue with this E=MC²..(5) Or rather M=E/C² business. and ends our hostilities by putting the figure on those pesky light rays and their pulling a mass out of the hat illusion (6).There had been a few complaints about these guys behavior and someone even accused them of that before , but old Albert really had the goods on them this time.(6)
We thank the good professor and agree to bury the hatchet until we look at our supply of fish food and notice there is more missing than we expected. We are back at it mouth to eyeball. “See you did get fat, you ate too much food. “ “I did not you ate it yourself lard…”
Instead of throwing fist, this is where we throw water balloons instead.(I have to got but will finish shortly)

(1) or should I say “exactly different in the same sort ways” or : ”different sort of ways that are precisely the same., or always exactly different from what they are expecting to see but in the same way or just shut up and let you figure it out.
(2) They like to use impressive words like “sharing the same inertial frame of reference” which really does not mean squat.
(3) This tilting of perspective moving effect seems to be clipping of a little bit off the wavelength the light ray that isn’t missing us all together..(kinda like their coming at us sideways. giving us a broad side body check. sending our helmets flying in the stands)
(4) If we don’t we won’t be around to see what happens .but the survivors will see what happens when totally opposing points of view come together. Some call that quantum particle physics but I prefer to call it a mess (or mesh) . Someday when we have a minute, I will explain what I mean but I think by then you’ll have figured it out better than me or the quantum guys.
(5) The second way is actually a better way to spell it out. Einstein was a fun loving peaceful dude and I always wanted to meet him but I was to young and turned out too stupid for that to happen. Some old guys I knew who met him said it was just a mass thing anyway and he was upset about being blamed for those big bombs it has nothing to do with.