Re: What would the end velocity be if...?

finite guy wrote:
> On Feb 22, 11:42 am, Erik Max Francis <m...@[EMAIL PROTECTED]
> wrote:
>> finite guy wrote:
>>> On Feb 22, 10:11 am, Erik Max Francis <m...@[EMAIL PROTECTED]
> wrote:
>>>> finite guy wrote:
>>>>> On Feb 22, 9:26 am, Erik Max Francis <m...@[EMAIL PROTECTED]
> wrote:
>>>>>> finite guy wrote:
>>>>>>> Where is the 'boundary' between Newton and Einstein?
>>>>>>> What percentage of light 'speed'?
>>>>>> It depends on what accuracy level you're going for.  A good rule of
>>>>>> thumb is that 10% c is the point at which relativistic effects
start to
>>>>>> creep into the third significant figure.
>>>>> There are too many 'rules of thumb' used for such precise
>>>>> calculations...
>>>> As I said, it depends on what level of accuracy you're going for.  If
>>>> you want a more precise figure, you can solve for beta(gamma)
yourself.
>>>>   It comes out to roughly 10% c for third-significant-figure effects,
>>>> 30% for second, and 70% for first.
>>> Do you mean that the 'boundary' is subject to my decision...?
>> There is no boundary, just a continuous transition.  So when you ask
>> what "the 'boundary'" is, the answer depends on what _you_ mean by the
>> boundary.  To answer that, you have to specify quantitatively where you
>> think that relativistic effects become significant, and you haven't
done
>> that.
>>
>> However, even without that information I've given about the most
>> complete answer possible, so I don't see what your point is.  Did you
>> want your question answered, or did you want to try to argue?
>>
>>> Roughly, is that a base-10 'third-significant-figure' or something
>>> more precise?   :-)
>> It is the standard meaning.  I'm suspecting you're just trying to be
>> difficult at this point.
> 
> Sorry, I'm not trying to be difficult.
> 
> I am alluding to the question: "What makes it so-called
> significant...?"

If you're asking what significant figures are, they're a way of 
measuring accuracy, and yes, they're base 10.  Something accurate to 
three significant figures would be 1.64 -- it's not 1.63, and it's not 
1.65.  The more significant figures, the more accurate it is.

At speeds of about 10% c, relativistic effects will tend to start 
creeping into that third significant figure, so they could change a 1.63 
to a 1.64 or a 1.65.

-- 
Erik Max Francis && max@[EMAIL PROTECTED]
 && http://www.alcyone.com/max/
  San Jose, CA, USA && 37 18 N 121 57 W && AIM, Y!M erikmaxfrancis
   There is no easy way from the Earth to the stars.
    -- Seneca, ca. 1st C.