Circle.

[Dave]

It's one of these definition threads again, isn't it?

 

To an observer, it wouldn't be a circle. In a mathematical context, it would be.

 

Probably.

[ydoaPs]

why wouldn't it be a circle?

[Aeschylus]

By using relativty what you are infact doing is changing the geometry. In Euclidean geomerty the ratio of a circles diameter to it's circumference is a constant.

[ydoaPs]

euclidean geometry has limits (like motion and curves)

 

since the radius are center are not affected, it still obeys the equation. so, as previously stated, pi is not a constant.

[Dave]

I'm not entirely sure you've thought the entire length contraction argument through. Why does the circumference change, yet the radius remain constant?

[ydoaPs]

because the radius has no length in the direction of motion.

[Dave]

I'm not entirely convinced you've got this right. When you're talking about relativistic problems, you need to clearly state what inertial frame you're in and what exactly is going on.

 

Moreover, I'm not even sure you can apply special relativity to this problem, because these laws only apply when you're in a non-accelerating (i.e. inertial) frame of reference. This obviously isn't true for circular motion; you're constantly accelerating towards the centre of the circle.

[ydoaPs]

isn't speacial relativity FOR acceleration?

[Dave]

No, General Relativity covers that. Same kind of math, but much more involved.

[ydoaPs]

but still, it should shrik, because it is moving at a substantial fraction of the speed of light. what isn't thought through?

[Dave]

Well, what frame of reference are we talking about here, for a start?

[ydoaPs]

the reference frame of an outside observer

[Aeschylus]

Speicla relativty can handle accelarted frames, it's a bit of a myth that it can't.

 

Anyway look at this site as it explains why the spatial slice can no longer be Euclidean:

 

http://math.ucr.edu/home/baez/physics/Relativity/SR/rigid_disk.html

[Sayonara]

the reference frame of an outside observer

So when I said "I'm not sure if yourdad meant to say that the circumference was actually affected, or if it just appears that way to someone in a different relatavistic frame" way back in post #20, you ignored it because...?

 

The changing view of the circle to an outside observer is not the same as the circle's geometry actually changing.

[ydoaPs]

so time dialation is only an illusion also?

[Aeschylus]

No Lorentz-Fitzgerald contraction is real by any objective standard, there is no reason to think of the proper diemnsions of the disc as it's actual dimensions.

[Sayonara]

so time dialation is only an illusion also?

The quoted post is a non sequitur and has nothing to do with my question or the point that followed. Try again.

[Aeschylus]

Yourdad. is actually correct, the dimensions of the disc have changed, you can't say that the proper diemnsions of the disc are it's actual dimensions, it is not an illusion.

[Sayonara]

Yourdad. is actually correct, the dimensions of the disc have changed, you can't say that the proper diemnsions of the disc are it's actual dimensions, it is not an illusion.

Well then I guess it's a good job I didn't say that, now isn't it?

[Aeschylus]

What you said is:

 

 

So when I said "I'm not sure if yourdad meant to say that the circumference was actually affected' date=' or if it just appears that way to someone in a different relatavistic frame"[/i'] way back in post #20, you ignored it because...?

 

The changing view of the circle to an outside observer is not the same as the circle's geometry actually changing.

 

This is incorrect, it is exactly the same as the geometry of that circle changing in that frame of reference and I'll say it again :you should not equate the proper dimensions (the dimensionsn of the disc in it's own frame) with the actual dimensions of the disc as they are frame dependent.

[Sayonara]

This is incorrect, it is exactly[/i'] the same as the geometry of that circle changing in that frame of reference and I'll say it again :you should not equate the proper dimensions (the dimensionsn of the disc in it's own frame) with the actual dimensions of the disc as they are frame dependent.

No, it's only the same under those specific circumstances. What I wanted from Yourdad was an explanation of why in terms of relativity (as you just provided), since otherwise there would be no reason why I could not just provide an image of a circle as distorted by a laterally convex mirror and make the same claims.

 

Although I appreciate the response (god knows I can't expect one from yourdad), I don't need you to reinterpret what I said for me.

[ydoaPs]

The quoted post is a non sequitur[/i'] and has nothing to do with my question or the point that followed. Try again.

 

no it is not. it is an inference based on your post. you said the contraction of length is an illusion, so I assumed you also thought time dialation is also an illusion.

[ydoaPs]

I am not sure what sayo is wanting me to explain. it is pretty simple.

[Sayonara]

no it is not. it is an inference based on your post. you said the contraction of length is an illusion, so I assumed you also thought time dialation is also an illusion.

No, I did not say that it was an illusion. The crazy in your head speaks for you, not me.

[ydoaPs]

The changing view of the circle to an outside observer is not the same as the circle's geometry actually changing.

 

yes, you did.