Time Dilation Scenario: Einstein's Skaters on a Moving Conveyor Belt

[zarmewa]

Let Einstein and his army stand still on their roller skates all the way on a conveyor belt of many light years in length between two planets. Each skater has mini model light clock on his head. Also granting toe and heel of two consecutive skaters touches each other on this conveyor belt which is moving say at 0.95c. Although Einstein and all his followers seems stand-still but the belt enables their wheels to roll along on its smooth surface.

Questions:

Since there is a coetaneous contact between skaters and moving belt therefore would skaters be contracted in length along with aforementioned belt?

If they don’t abridge then would some of Einstein’s followers be levitated due to foreshortened of the belt?:[/I]devil:

 

[ghwellsjr]

No and no.

 

[harrylin]

This doesn't sound like a serious question in order to understand how SR works, so I'll be brief: free moving things are Lorentz contracted while constrained things can be under stress as discussed here:
http://en.wikipedia.org/wiki/Bell's_spaceship_paradox

 

[zarmewa]

Since both the skaters and moving belt have coetaneous contact with each other therefore can I ask reason WHY?

 

[ghwellsjr]

You didn't say anything was moving except the rolling wheels and the belt with a length fixed by two planets so I don't know why you think the skaters would be contracted or levitated.

 

[zarmewa]

Sorry about the confusion.

I edited my question too many times but couldn't pay attention to the tailored one

A conveyor belt [with on skaters] connected the aforementioned two planets should be considered at rest before it get close to the speed of light –

Let AB is the distance between two planets

AT REST

Skaters are stand-still on their roller skates all the way on this belt such that toe of one skater touches the heel of other

NOW let a belt starts moving.

All skaters seem stand-still but the belt enables their wheels to roll along on its smooth surface.

Since belt contracted when its speed reaches close to the speed of light therefore would some of the end skaters be levitated if they didn’t contract in length?

Similarly,

Why the moving clock of belt and stationary clock of each skater are in disagreement when the rolling wheels and belt have equal amount of contact though skaters didn’t move forward?

 

[ghwellsjr]

The belt is going to have to be made out of a compliant material that can stretch, otherwise it will break, unless you're thinking that it's going to pull the planets together. Nothing else will be out of the ordinary. I have no idea why you think any levitation will be happening.

 

[zarmewa]

I think it’s presumable that the belt is made of ideal/ compliant material. At rest, the length of the conveyer belt [like a treadmill belt] with on skaters’ is also AB. First planet touches “A” point of belt while second planet touches the “B” point of belt.

 

[bahamagreen]

Simplify...

Conveyor between two planets (or just between to locations, does not matter whether planets or just locations - all that is specified is a distance agreed on by the army and the conveyor at rest)

Army of clock wearing roller skaters (does not have to be roller skates, probably better to just assume the army is floating in formation arbitrarily close to the conveyor, the conveyor has a length and the army has a length, both the same)

The conveyor begins to move, the army stays in place...

The conveyor movement approaches c... this is the first tricky part concerning Frames of reference:

FOR Army
FOR Upper belt of conveyor
FOR Lower belt of conveyor
FOR Planet Left
FOR Planet Right

Army folks see the upper and lower belts become length contracted. The question about "levitation" is just an awkward word - it means will the army continue to fit on the the upper belt or be crowed off of it? Army folks will see the lower belt contract same amount as the upper belt. Army will observe that the belt no longer extends all the way to either planet.

Upper and lower belts will see the army contract... and each belt will see the other belt contract even more than the army contraction, and each belt will see the planets contracting.

Each of the planets will see both upper and lower belts contracting.

The question is about how to reconcile the various length distortions. When an observer at rest is observing a fast mover, the usual way to "measure" is to use the transforms to convert the observed distortions to local values for the resting observer, but in this case it is as if the resting observer has an indefinitely long measuring rod that extends to the place of the fast mover - and the rest observer is measuring by this long rod as an extension of his FOR... I think this is the problem with the problem.

This problem is similar to the "Lightspeed Submarine Paradox" where a submerged sub is approaching lightspeed. The FOR from the sub sees the water rushing past gaining mass and conclude the sub should become more buoyant and surface. Observers on the coast see the sub as gaining mass and should dive. Something has to happen...?

But maybe "something happening" is always local? Maybe the resolution to both is that relativistic effects require distance... measurements of events (distant FOR) made from a distance (local FOR). Local measurements will always be non-relativistic and relativistic measures from a distance will have no bearing on the local mechanics of what is happening?

In which case, the army of skaters will have plenty of room on the conveyor, and I guess the sub will surface...?