Reality knows of no frames, frames are human constructs and not physical at all.Cleonis said:So let's examine the perspective of a frame that at the beginning has such a velocity relative to the spaceships that it's co-moving with the tether at the point in time that it breaks. In that frame the tether length is initially length contracted. As its velocity relative to the chosen frame decreases its length contraction decreases. As mapped in the chosen frame the two spaceships do not start accelerating simultaneously. Does the length contraction decrease fast enough to make up for the non-simultaneous start of acceleration? No it doesn't, the tether breaks.
Depending on what inertial frame of reference is chosen the narrative comes out differently, in how length contraction and shift of simultaneity proceed over time.
My underlying assumption is that SR is by nature a causal theory; a theory in which there is a one-on-one relation between cause and effect.
You got it exactly backwards. The creation of frames creates the false contradictions the reality is simple and unambiguous.Cleonis said:Having multiple narratives means a deeper interpretation must exist, of a more abstract nature.
Passionflower said:You got it exactly backwards.
The words I quoted are yours aren't they?Cleonis said:Your disagreement is not with me. You are attributing a point of view to me that isn't mine.
starthaus said:Once you start accelerating the rods around the perimeter they expand since they are not Born rigid, so you could not fit in more than 2*r rods. This is not a valid thought experiment for demonstrating length contraction. The above is a variant of the Ehrenfest paradox and the resolution is the same. Direct experimental verification of length contraction (as opposed to the direct experimental verification of time dilation) is not possible with today's technology. Indirect verification , including the calculation for the length of particle beams and the explanation of the Michelson Morley experiment as viewed from a frame external to the moving Earth (like the Sun) are the only things we have available today.
This is just nonsense. The rods do not expand because they are not linked to each other. In the Ehrenfest paradox the train carriages are more rigid than the elastic links between the carriages and so the links have to expand to take up the extra space between the carriages at higher velocities. In the rod thought experiment, it is the gaps between the rods that expands as the rods contract and so you can fit additional rods in the gaps. I don't think Born rigidity is even relevant here. Born rigidity is a method of acceleration, rather than a property of a material. It does not matter how the rods are accelerated as long as they get to a final velocity and are allowed to stabilize to their length contracted length. It is only when we are considering methods of spinning up solid discs to relativistic speeds that applying Born rigid acceleration becomes a problem. For rods that are not connected to each other, it is not a problem.starthaus said:Once you start accelerating the rods around the perimeter they expand since they are not Born rigid, so you could not fit in more than 2*r rods. This is not a valid thought experiment for demonstrating length contraction. The above is a variant of the Ehrenfest paradox and the resolution is the same.
You are correct. Linear acceleration can be done without material strain (Born rigid), but there is no way to have angular acceleration without mechanical strain. Something must stretch.Passionflower said:how can a rod remain Born rigid if it rotates? I thought only rods that accelerate in one direction can remain Born rigid? It seems to me that because the rod is spatially separated there will be some form of Thomas precession which will make Born rigidity impossible.
Am I wrong?
William Nelso said:Length contraction is real. You can compute the length of a moving ruler using E&M and Quantum Mechanics, without ever using Relativity or the Lorentz Transformation. Relativity comes from the physics, not the other way around.
Passionflower said:I think this topic is not the place to discuss the Erhenfest paradox, ...
yuiop said:This is just nonsense. The rods do not expand because they are not linked to each other.
In the Ehrenfest paradox the train carriages are more rigid than the elastic links between the carriages and so the links have to expand to take up the extra space between the carriages at higher velocities.
In the rod thought experiment, it is the gaps between the rods that expands as the rods contract and so you can fit additional rods in the gaps.
I don't think Born rigidity is even relevant here.
I came across this thread late in the game.jeebs said:Hi,
I am aware that time dilation has been observed experimentally with atomic clocks on satellites etc. but after a few google searches I have not found anything about experimental confirmation of length contraction. Has this been observed at all? If so, how was it tested?
thanks.
Meir Achuz said:I came across this thread late in the game.
The quick answer is that length contraction has NOT "been observed at all".
Some of the controversy in this thread might be resolved by reading the first section of <http://arxiv.org/abs/0906.1919>.[/QUOTE]
I believe there are some misleading statements in that paper. One is their claim that Lorentz contraction would predict a positive result for the MM experiment. The other is this statement:
It should also be pointed out that another classically reasonable method of
measuring the length is to take a photograph of a moving object and compare
it with a photograph of the same object at rest. As Terrell[3] showed some time
ago, the photograph would show an object that is somewhat rotated, but of
the same shape and dimensions as it had at rest. Indeed, the photograph of a
moving sphere would show a sphere of the same size.
Although they mention a sphere at the end, they neglect to mention that the claim "the photograph would show an object that is somewhat rotated, but of the same shape and dimensions as it had at rest." is true if and only if the moving object is a sphere. It is not true for a rod for example and this shows the biased view of the authors.
There is another way to "photograph" length contraction. Set up an array of inject jet nozzles on one side of a narrow passage. Have the moving object pass through the passage and set off the ink jets nozzles simultaneously and briefly. The silhouette of the object left on the opposite side of the passage will be length contracted.
As for ... length contraction has NOT "been observed at all"... an example was given earlier in this thread of the observed length contraction in bunches of particles moving around a particle accelerator ring. Do you disagree with that?