[Eternal Student]

Hi.

   Halc, you've given a good reply but you might want to check your last paragraph (of a post one before your very last one).  I believe the composition of two Lorentz transformations would itself be a suitable Lorentz transformation.   So, if you could get a disk to a grain of rice and then use another transformation to get that rice to a sphere then you can find a single transformation to get a disk straight to a sphere.

Back to the original question:
    In a very round-about way I think I can see what @Dimensional  was trying to ask or discuss:
They have probably read that "the laws of physics are the same in all inertial reference frames", which is often considered as the "strong equivalence principle" for relativity.
   Their problem is trying to determine exactly what "the laws of physics" are supposed to be.   Specifically, is it a law of physics that large astronomical bodies tend to be spheres?
 
   Well, obviously not - since they don't look like spheres to observers that are racing past them.

    The first thing I would say is that "the laws of physics" are quite difficult to define.   The main alternative is just that something is a only a general observation or a rule of thumb that seems to hold from our situation (e.g. from here on Earth).
 
    Now the density arguments that have already been presented are extremely complicated to categorise but they are much more like a fundamental law of physics.  They can be formulated as "laws of physics" but you just have to be very careful handling a parameter like density.  The main problem with relativity is that due to length contraction occurring only along the direction of travel, density stops being an isotropic property of a fluid.   Fluids have a linear density along the direction of travel that is much higher than the linear density in the other two orthogonal directions.   So, in this respect, the principle about density and things arranging themselves so that you get the most energetcally favourable shape remains valid,  it's just unfortunate that density is now a little harder to work with.  A shape can spread out more along a direction with a low linear density but in a direction where the linear density is high the best way to keep as much mass as possible near the centre is to stay narrow in that direction.

   Anyway...   We can turn this around to present an argument: 
 

You are not answering the question.  Why can't, say, the Earth exist as a disc in its rest frame, when it can exist as a disc for a muon?

   The same "laws of physics" do indeed apply in the rest frame of the earth, so it certainly could exist as something more like a thin disk instead of a sphere - but that will only happen when the linear density is  anisotropic (not isotropic).  It just is quite isotropic in the rest frame of the earth, while it isn't in the rest frame of the muon speeding past planet earth.

   I didn't say the wording would be good or easy to follow:   The gist of it is as follows:
Why can't Earth exist as a disc in it's rest frame?   Because in that frame the density has properties that favour spheres not disk-like shapes.

Best Wishes.

[Halc]

Hi.

   Halc, you've given a good reply but you might want to check your last paragraph (of a post one before your very last one).  I believe the composition of two Lorentz transformations would itself be a suitable Lorentz transformation.   So, if you could get a disk to a grain of rice and then use another transformation to get that rice to a sphere then you can find a single transformation to get a disk straight to a sphere.

Love to see you do that: Find a frame in which a star is a rice grain shape instead of a disk.

They have probably read that "the laws of physics are the same in all inertial reference frames", which is often considered as the "strong equivalence principle" for relativity.

Well, that principle works only locally for GR.

Their problem is trying to determine exactly what "the laws of physics" are supposed to be.   Specifically, is it a law of physics that large astronomical bodies tend to be spheres?

Not a law, but composite objects often tend to achieve an equilibrium in a low energy state, and a round proper shape is the lowest energy. A shape that is round only in some high speed frame is not in such equilibrium and is unstable. This is like saying that the large long skinny object tends to compress to a proper sphere under its own weight. This is true regardless of linear motion, so I'd say the 'law' holds in any frame.
Likewise with my garden hose example, a pressurized garden hose (completely flexible but not stretchable) will always form a circle only in its proper frame (a cross section perpendicular to its length) and not in any other cross section.

Fluids have a linear density along the direction of travel that is much higher than the linear density in the other two orthogonal directions.   So, in this respect, the principle about density and things arranging themselves so that you get the most energetcally favourable shape remains valid

This sound a lot like the argument that a fast moving star should get dense enough to form a black hole, but it doesn't. Density is probably best described with a tensor which can be rotated to any frame in question without change of objective properties. The tensor says the star is insufficiently dense to form a black hole, and abstract computations of vastly higher density relative to exotic frames (like the muon frame) doesn't change that.

[Bored chemist]

So why are there only spheres?

Do you read what people post?

The reason we do not see the moon or any other celestial body as a disk is simply because the velocity of earth compared to other bodies is very very slow when compared to c. 

Anything that is close enough for us to judge what shape it is will be travelling sufficiently slowly that relativistic effects will be small.

Only if the relative velocities involved are high.

Why can't, say, the Earth exist as a disc in its rest frame,

Because it would collapse under gravity.

[Dimensional (OP)]

Hi.

   Halc, you've given a good reply but you might want to check your last paragraph (of a post one before your very last one).  I believe the composition of two Lorentz transformations would itself be a suitable Lorentz transformation.   So, if you could get a disk to a grain of rice and then use another transformation to get that rice to a sphere then you can find a single transformation to get a disk straight to a sphere.

Back to the original question:
    In a very round-about way I think I can see what @Dimensional  was trying to ask or discuss:
They have probably read that "the laws of physics are the same in all inertial reference frames", which is often considered as the "strong equivalence principle" for relativity.
   Their problem is trying to determine exactly what "the laws of physics" are supposed to be.   Specifically, is it a law of physics that large astronomical bodies tend to be spheres?
 
   Well, obviously not - since they don't look like spheres to observers that are racing past them.

    The first thing I would say is that "the laws of physics" are quite difficult to define.   The main alternative is just that something is a only a general observation or a rule of thumb that seems to hold from our situation (e.g. from here on Earth).
 
    Now the density arguments that have already been presented are extremely complicated to categorise but they are much more like a fundamental law of physics.  They can be formulated as "laws of physics" but you just have to be very careful handling a parameter like density.  The main problem with relativity is that due to length contraction occurring only along the direction of travel, density stops being an isotropic property of a fluid.   Fluids have a linear density along the direction of travel that is much higher than the linear density in the other two orthogonal directions.   So, in this respect, the principle about density and things arranging themselves so that you get the most energetcally favourable shape remains valid,  it's just unfortunate that density is now a little harder to work with.  A shape can spread out more along a direction with a low linear density but in a direction where the linear density is high the best way to keep as much mass as possible near the centre is to stay narrow in that direction.

   Anyway...   We can turn this around to present an argument: 
 

You are not answering the question.  Why can't, say, the Earth exist as a disc in its rest frame, when it can exist as a disc for a muon?

   The same "laws of physics" do indeed apply in the rest frame of the earth, so it certainly could exist as something more like a thin disk instead of a sphere - but that will only happen when the linear density is  anisotropic (not isotropic).  It just is quite isotropic in the rest frame of the earth, while it isn't in the rest frame of the muon speeding past planet earth.

   I didn't say the wording would be good or easy to follow:   The gist of it is as follows:
Why can't Earth exist as a disc in it's rest frame?   Because in that frame the density has properties that favour spheres not disk-like shapes.

Best Wishes.

Ok thanks, that is what I thought in that the proper shape is not conceivable as a whole, at least not for the human, as far as I know. 

So getting back to my concern in the OP, it would seem to me that there shouldn't be a preferred shape.  Shouldn't the initial development of the body be more or less random and exist just as easily as a disk than as a sphere?

[Dimensional (OP)]

Because it would collapse under gravity.

Then why doesn't it collapse under gravity something travels fast enough to make it a disk?

[Bored chemist]

Because it would collapse under gravity.

Then why doesn't it collapse under gravity something travels fast enough to make it a disk?

What are you talking about?

[Eternal Student]

Hi.

   It's quiet again.  So I'll challenge Halc's point (because he/she should already know that they are an expert and so they aren't going to mind too much). 

Love to see you do that: Find a frame in which a star is a rice grain shape instead of a disk.

   Technically you (Halc) were supposed to find the two transformations.  I only offered to multiply the two matrices together. 
   However, If I had to do your job for you then I would have thought you can get a transformation from sphere to rice grain by trying a boost, followed by a rotation to turn the squashed axis through 90 degrees and then apply another boost.   
    This wouldn't be expressable as a single boost, so there's no direction of movement that will do the job in one go but a combination of boosts and spatial rotations is still acceptable.  Lorentz transformations aren't just boosts.  So I reckon you can identify a frame of reference where the original spherical shape now has characteristics of a grain of rice but the axis might be a little un-physical.  Or to say that another way, the things you are considering as lengths and spatial directions might seem like un-natural combinations of what a human being would normally consider to be space and time - but that's just a human problem.  A computer has no problem using those defintions of lengths and times and the spacetime interval that they will construct from them does indeed remain as an invariant, i.e. completely consistent with a spacetime interval determined in any other ordinary frame of reference.  So the computer can calculate and determine things like the "proper length" of a rod that is moving (or stationary) relative to their reference frame just as easily as anyone else can and their answers will agree.
      Anyway, having re-read what Halc originally stated, you were probably talking only about boosts.  Re-reading my own post, you might notice that I was talking about Lorentz transformations.   This discussion is also probably getting a bit abstract and not all that helpful for @Dimensional .      I will concede the point that there isn't going to be a boost that will transform a (whatever it was, star?) into a (whatever it was, rice grain?) but there could be a Lorentz transformation that will do the job.

Late editing:
    I've cut the rest of this discussion.  It's not useful for the OP.
I can see that @Dimensional has been busy posting while I was writing this.   

Best Wishes.

[Dimensional (OP)]

Because it would collapse under gravity.

Then why doesn't it collapse under gravity something travels fast enough to make it a disk?

What are you talking about?

Why doesn't earth collapse under gravity when it becomes a disk from a different frame of reference?

[Origin]

Why doesn't earth collapse under gravity when it becomes a disk from a different frame of reference?

I'm beginning to think you are a troll.
Lets imagine a space ship flies past Earth at 0.9c, we would see that ship as 'flattened' in his direction of travel and he would see the earth as flattened.  We would not see the earth as a disk and we would not see each other as flattened.  So your question about the world collapsing into a sphere from a disk makes no sense.

[Bored chemist]

Why doesn't earth collapse under gravity when it becomes a disk from a different frame of reference?

Because it's not in that frame of reference.

[Dimensional (OP)]

Why doesn't earth collapse under gravity when it becomes a disk from a different frame of reference?

I'm beginning to think you are a troll.
Lets imagine a space ship flies past Earth at 0.9c, we would see that ship as 'flattened' in his direction of travel and he would see the earth as flattened.  We would not see the earth as a disk and we would not see each other as flattened.  So your question about the world collapsing into a sphere from a disk makes no sense.

But the people on the ship that do not understand general relativity would wonder why the flattened Earth would not collapse, right?  But never mind, I just realized the answer to my OP.

[Bored chemist]

But the people on the ship that do not understand general relativity would wonder why the flattened Earth would not collapse, right?

Only if they were too dim to notice that they got accelerated up to nearly the speed of light.

[Dimensional (OP)]

But the people on the ship that do not understand general relativity would wonder why the flattened Earth would not collapse, right?

Only if they were too dim to notice that they got accelerated up to nearly the speed of light.

That doesn't matter.  The Earth is actual flat in their frame. 

[Kryptid]

But the people on the ship that do not understand general relativity would wonder why the flattened Earth would not collapse, right?

Then they could fix that problem by learning relativity.

[Colin2B]

But the people on the ship that do not understand general relativity would wonder why the flattened Earth would not collapse, right? 

If they don’t understand relativity they won’t wonder anything, because they will see the earth as a sphere, but slightly (depending on their speed) rotated.
They would need to understand relatively to distinguish between measurement (Lorentz transforms) and visual appearance (time for light to travel from the object their eyes).

Even if they worked it out the earth would not collapse for reasons given by the other posters.
I like the hosepipe analogy halc.

[Dimensional (OP)]

Even if they worked it out the earth would not collapse for reasons given by the other posters.
I like the hosepipe analogy halc.

I know that the Earth would not collapse.  My question is why there aren't other large compact objects like Earth that exist in the form of a disk.

[Origin]

My question is why there aren't other large compact objects like Earth that exist in the form of a disk.

That was answered in post #2 and post #5.

[Kryptid]

My question is why there aren't other large compact objects like Earth that exist in the form of a disk.

As Origin has pointed out, this question has been answered multiple times in this thread (and even more times than he pointed out). You can't expect the answer to change just because you keep asking the same question over and over.