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Lorentz contraction 
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#55
Nov1509, 06:43 PM

P: 687

Yet, the launch frame does not see it this way. It sees the distance as constant. How is this so? 


#56
Nov1509, 06:59 PM

P: 3,967




#57
Nov1509, 07:05 PM

P: 687

Isn't length contraction a phenomena of the "at rest" frame when viewing the moving frame? 


#58
Nov1509, 07:28 PM

P: 3,967

We have four rockets all with identical solid fuel propellants that burn at a fixed rate for a fixed length of time. Rocket A and B are joined by a tough cable of length d and rockets C and D are separated by a distance of d but not physically connected. All 4 rockets launch simultaneously in the launch frame. When they have exhausted their fuel rockets C and D are still a distance d apart, but rockets A and B are less than d apart. Rockets A and B have been physically pulled closer together by the length contraction of the cable. If a fifth rocket and observer was introduced and this time only the fifth observer accelerated, then distances between the unconnected and connected rocket pairs would appear to length contract equally, but the apparent length contraction of the gap between the unconnected rockets is not physical. The changes in the clock rates and ruler lengths of the fifth observer makes the gap appear to contract. 


#59
Nov1509, 07:32 PM

P: 3,967




#60
Nov1509, 07:35 PM

P: 687

The rest frame does not see the gap getting wider. 


#61
Nov1509, 07:38 PM

P: 687

This thought experiment changes the game. It should be solvable in the context we were in. If the string contracts from the rest observer and the distance does not change, does this imply space does not contract but rods do? 


#62
Nov1509, 07:52 PM

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#63
Nov1509, 07:59 PM

P: 687

Assuming your post though, how do you explain this? We have the rest frame not seeing any distance differentials. We have the accelerating frames getting further apart in their context. How do you reconcile this? 


#64
Nov1509, 08:31 PM

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P: 1,843

We know y < z. That is Lorentz contraction. We also know x = y. ("We have the rest frame not seeing any distance differentials. ") Therefore z > x. ("We have the accelerating frames getting further apart in their context.") 


#65
Nov1509, 08:50 PM

P: 687

In order to compare these like this, you must have a uniform space. You are depending on the trichotomy of the real numbers but the spaces are not the same in the frame to frame analysis. Do you compare these another way I am not seeing? 


#66
Nov1609, 02:49 AM

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#67
Nov1609, 04:24 AM

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#69
Nov1609, 07:50 PM

P: 687

1) One solution suggests there exists length contraction for the string. 2) One solution suggests the ships get further apart. 3) The rest frame concludes the distance remains constant between the ships and the v and any time t is the same. Actually, if you look from the rest frame, a reaction may be that as v increases, length contraction for the string should increase. Yet, the SR acceleration equations do not predict this and predict a constant distance between the ships. How is this worked out? 


#70
Nov1609, 07:57 PM

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#71
Nov1609, 08:13 PM

P: 687

So, how would the launch frame conclude the string contracts when the launch frame concludes the distance between the ships does not change? 


#72
Nov1609, 08:16 PM

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