Accelerated Triangle and Length Contraction

[Ibix]

The reason Neil still sees the dots matching the triangle is that the triangle is assumed to undergo the same stretching process that the ground does.

This isn't my understanding of the scenario. I think the triangle template is carried by Neil and is unstressed - it's just a set-square used to draw the dots and is not attached to the planet's surface. The dots, of course are attached to the surface and are stressed. Thus from Neil's perspective the triangle template is as it always was and the triangle of dots is stretched. From Michael's perspective, the triangle template is length contracted, while the triangle of dots is length contracted and stretched in such a way that the measured length equals the rest length.

I'm assuming that the radius of the planet does not change.

 

[PeterDonis]

This isn't my understanding of the scenario

As the scenario is presented in the OP, it is inconsistent. The OP claims that Neil will see the triangle still match the dots, which implies that the triangle must stretch. But it also claims that Michael will see the triangle length contracted, which implies that the triangle does not stretch.

Either choice would be consistent by itself; but only one of the two can be true of a single scenario.

 

[metastable]

Can I say the triangle became stretched due to the normal force when it was rested on the ground? How do we calculate the reduction in normal force on the triangle from centrifugal forces once the planet is up to speed?

 

[PeterDonis]

Can I say the triangle became stretched due to the normal force when it was rested on the ground?

No, because the normal force points in the wrong direction--it points vertically upward, but the stretching is horizontal.

 

[metastable]

No, because the normal force points in the wrong direction--it points vertically upward, but the stretching is horizontal.

Suppose the planet is a prolate spheroid such that when it rotates it becomes a sphere through centrifugal forces... when Neil descends from orbit with a "pristine" isoscelese, he sets it on the surface...

Assuming the planet isn't spinning too quickly, will the corners of the triangle sag slightly or not from the differential applied forces-- the triangle only be supported by a minuscule point in the middle (or from the side if he's holding)?

If so when the points are drawn on the surface, wouldn't they no longer have the same distance between them as the "holes" in the triangle originally had when they were still "pristine" in orbit?

Above a certain angular speed wouldn't centrifugal forces cause Neil to lift off the surface (and possibly bounce) if he wasn't holding something, causing the triangle to stretch in the opposite direction as it would under the normal force if Neil is using any force to hold it to the surface?

 

[PeterDonis]

Suppose the planet is an oblate spheroid such that when it rotates it becomes a sphere through centrifugal forces

An object that is oblate before it starts rotating will get more oblate as it rotates, not less.

More generally, I don't see the point of piling on complications to the scenario, since all they do is distract and obfuscate the primary issues that the OP was raising.

 

[metastable]

Yes, thank you I corrected it to prolate.

 

[Ibix]

As the scenario is presented in the OP, it is inconsistent. The OP claims that Neil will see the triangle still match the dots, which implies that the triangle must stretch. But it also claims that Michael will see the triangle length contracted, which implies that the triangle does not stretch.

Either choice would be consistent by itself; but only one of the two can be true of a single scenario.

The triangle is specified to be loose. So, to my mind, the OP is describing the scenario where the triangle does not stretch and incorrectly describing Neil's observations.

Possible I'm reading more into your writing than you intended, but it seemed to me you were entertaining the possibility that the loose triangle could stretch. I've been answering on the basis that it wouldn't, and still can't see a reason it would. But you've been known to correct my understanding on occasion...

 

[Foppe Hoekstra]

As the scenario is presented in the OP, it is inconsistent. The OP claims that Neil will see the triangle still match the dots, which implies that the triangle must stretch. But it also claims that Michael will see the triangle length contracted, which implies that the triangle does not stretch.

Actually I did not intent to “claim” the matching, but more assumed that it would match. From my previous question (Why is the null-result of M&M experiment considered as proof for RT) I learned (from Nugatory) that “the experiments are at rest relative to the apparatus, so they find no length contraction.”. Hence, I also assumed that the stretching of the dots would not take place in Neil’s perspective.
But as you try to tell me now, I should understand that here an influence of ‘higher’ order is involved.

 

[PeterDonis]

it seemed to me you were entertaining the possibility that the loose triangle could stretch

No, I wasn't. If it is clearly specified that the triangle is loose, then it won't stretch and the description of what Neil will see in the OP is incorrect.

 

[Ibix]

But as you try to tell me now, I should understand that here an influence of ‘higher’ order is involved.

I wouldn't call it an influence of a higher order. It's just that there is an awful lot of mass bound together and undergoing ferocious acceleration, and you can't neglect the effects of that by using an inertial frame (or any other way). In the Michelson-Morley case nothing is accelerating so there are no forces distorting anything.