OT: speeds (physical, not computing) [was Re: 1-0.95]

Steven D'Aprano steve at pearwood.info
Thu Jul 3 11:15:59 CEST 2014

On Wed, 02 Jul 2014 21:06:52 -0700, Rustom Mody wrote:

> On Thursday, July 3, 2014 7:49:30 AM UTC+5:30, Steven D'Aprano wrote:
>> On Wed, 02 Jul 2014 23:00:15 +0300, Marko Rauhamaa wrote:
>> > On the other hand, floating-point numbers are perfect whenever you
>> > deal with science and measurement.
>> /head-desk
> <wink>
> Just as there are even some esteemed members of this list who think that
> c - a is a meaningful operation
>   where
>     c is speed of light
>     a is speed of an automobile
> </wink>

You seem to be having some sort of nervous tic.

Subtracting two numbers a and c *is* a meaningful operation, even if they 
are speeds, and even in special relativity.

Consider an observer O in an inertial frame of reference. A car x is 
driving towards the observer at v metres per second, while a photon p 
travels away from the observer at c m/s:

x --> v          O         p ----------> c

According to the observer, the difference in speeds between x and p is 
just (c - v), the same as in classic mechanics. The technical term for it 
is "closing speed" (or "opening speed" as the case may be) as seen by O.

Note that this is *not* the difference in speeds as observed by x, but I 
never said it was.

You don't have to believe me. You can believe the Physics FAQs, 
maintained by John Baez:


The important part is the paragraph titled "How can that be right?" and 
ending "In this sense velocities add according to ordinary vector 

As I wanted to confirm my understanding of the situation:



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