On 8/29/15 8/29/15 5:08 AM, Margarita Cibulkova wrote:
> Tom Roberts wrote:
>> If that's what you mean, you are wrong, and the axle can in principle
>> travel with any speed less than c relative to the track.
>
> You are so wrong. Unbelievable.
No. Apparently YOU cannot believe it, but that does not make it wrong, it makes
YOU wrong.
> What would be the speed of the top of the
> say, a one meter radius wheel?
Read on. (Given the way I set up the calculation, the radius does not matter, so
imagine a one meter wheel if you wish.)
>> NOTE: I am ignoring all practical considerations, such as the
> strength
>> of materials. I consider this a pure gedanken.
>
> Does NOT really matter you ignore this or not.
Sure it does! If one does not ignore it, one cannot have such a wheel.
>> You are presumably thinking that if the bottom of the wheel does not
>> slip along the track, and the axle moves with speed 0.5 c, then the top
>> of the wheel moves with speed c relative to the tack, and cannot go any
>> faster. That thought process is WRONG because speeds do NOT add that
>> way.
>
> Does not matter how it adds. The inherent REQUIREMENTS of the wheel
> DEMANDS the top moving faster than the speed of light, which is IMPOSSIBLE.
Not true. As my example showed, with the wheel rotating with a rim speed of 0.99
c in the rest frame of the center/axle, the center/axle moves with speed 0.99 c
relative to the track, and the top of the wheel moves at speed 0.9999495 c
relative to the track.
It DOES matter how speeds add.
The basic property of rotating wheels is that all points on the rim move with
the same speed relative to the frame in which the center/axle is at rest. Given
the speed of the center/axle relative to the track, we do not know the speed of
the top until we COMPUTE it. That's what I did.
> Please remark. This is not about APPEARANCE or Length Contraction and
> such.
I never said it did, and did not use "length contraction" anywhere in my
discussion. Please pay attention to what is ACTUALLY WRITTEN. Don't add
fantasies of your own like this.
> Since a wheel DEMANDS the top of it MOVES FASTER than the wheel
> itself (say its center if your wish, but is about the wheel entirely
> actually)
Yes, the top moves faster than its center/axle: 0.9999495 c > 0.99 c.
And no, it is not about the "wheel entirely", because different points of the
wheel move differently: IT IS ROTATING. So to be accurate I must specify its
center (or axle).
YOU apparently don't care about accuracy. That's a MAJOR part
of your problem. And it seems so pervasive for you that you
don't even realize it....
>> This is easy to see when looked at from the rest frame of the wheel
>> center/axle. In this frame all points of the rim have the same speed,
>> and the wheel can clearly rotate with any speed as long as its rim speed
>> is less than c relative to this frame. Now pick an instant in time and
>> the point on the rim in contact with the track -- at that time that
>> point is at rest in the track frame.
>
> Completely nonsense.
If you cannot see the relevance of that to the problem, then you need to find
another hobby. That is directly relevant and is indeed how wheels behave.
The basic property of rotating wheels is that all points on the rim move with
the same speed relative to the frame in which the center/axle is at rest. Given
the speed of the center/axle relative to the track, we do not know the speed of
the top until we COMPUTE it. That's what I did.
>> Assume the rim moves with speed 0.99 c in the axle frame. Transforming
>> to the track frame, the bottom of the wheel moves with speed 0, the axle
>> moves with speed 0.99 c, and the top of the wheel moves with speed
>> 0.9999495 c. All is well.
>
> NO, since as already said. The wheel DEMANDS the top moving faster than
> that.
No, it doesn't "demand" that. Rather it "demands" that the top of the wheel move
as I said.
> This is not about the addition of SR speeds.
Sure it is.
The basic property of rotating wheels is that all points on the rim move with
the same speed relative to the frame in which the center/axle is at rest. Given
the speed of the center/axle relative to the track, we do not know the speed of
the top until we COMPUTE it. That's what I did, and the answer (of course) is
less than c.
>> So the wheel can move relative to the track with any speed less than c.
>
> No, absolutely.
You are wrong.
[asked to compute the speed of the top]
> No, you do it for me. Assume that axle at 0.9c, just to make sure.
I see. You are unable to do the math. How sad -- it indicates you do not really
know enough about SR to say anything about it (that is also clear from your
writings around here).
It's straightforward, once you know which math to apply (which seems to be your
basic problem): When the axle moves at 0.9 c relative to the track, and the rim
of the wheel does not slip on the track, the top of the wheel moves relative to
the track with speed:
(0.9 c + 0.9 c) / (1 + 0.9 * 0.9) = 0.9945 c
Have you not noticed that I always write A LOT more text than you? A MAJOR part
of your problem is that you do not specify things precisely enough. Relativity
is subtle, and to understand subtle concepts you MUST be precise in thought and
word. Your writing falls far short of what is needed -- you MUST improve your
game in order to understand this stuff.
Tom Roberts