[Phys-L] Re: "moving clock runs slower" (yes)

[John Denker <jsd@AV8N.COM>]

Antti Savinainen wrote:

> | Now John D. suggests a new way of interpreting length
> | contraction and time dilation. If I have understood his point
> | correctly, John's interpretation puts mass, length, and time
> | in the same footing. The concept of mass has already been
> | reinterpreted, perhaps the same could happen also for length
> | and time in relativity?

Rauber, Joel responded:

> I'd be careful, depending on what you mean by "the same footing".
>
> In some sense, he is being very careful to put them on different
> footings.
>
> Mass is an invariant quantity, intrinsic to the object.
>
> Length and time are projections, not intrinsic to the object but rather
> related, in part, to the geometry of the reference frame used to make
> those measurements.

Actually, Professor Savinainen expressed quite nicely the physical
idea I am suggesting.  (However, I'm not convinced there's anything
new about it.)

1) In the bad old days, the word "mass" was used to refer to something
that was, in general, frame dependent;  now most folks use "mass" to
refer to an invariant quantity.  This is simpler and more useful.

2) In exactly the same spirit, I recognize that in the bad old days,
the word "length" was used to refer to something that was, in general
frame-dependent.  But there is no reason for it.  A ruler certainly
has a property called "invariant length".  I suggest that should be
considered "THE length" ... so that "invariant length" becomes just
as redundant as "invariant mass".  This is simpler and more useful.

3) Ditto for the "invariant interval" between clock-ticks, which is
just the "proper time".  Simpler and more useful.

=====================

As the saying goes, learning proceeds from the known to the unknown.

When it comes to learning or teaching relativity, we need to ask,
what is the most natural way to extend and generalize pre-existing
notions of mass, length, and time.  It seems to me that far and
away most natural and most useful mapping is this:

       Galilean  -->  Relativistic
      ----------      ------------
         mass    -->    mass  (by which I mean invariant mass)
        length   -->   length (by which I mean invariant length)
         time    -->    time  (by which I mean invariant time)

Using mass, length, and time in the way I recommend does not cause
a problem.  If you want to express the bad old projected length
or projected time, there are lots of ways of saying it.

  -- You can talk about "projected time" or "projected length",
   in precise analogy to the way projections work in Euclidean
   space.

  -- You can talk about finding the components (using Joe's basis)
   of the vector that represents Moe's 4-velocity.  This is how
   I was taught to do calculations.  It just works.  No muss,
   no fuss, lots of analogous concepts, no paradoxical concepts.

====================

It would never have occurred to me to publish on this subject.
I still judge it to be unlikely that I have said anything new
or original.  I can't off the top of my head point to any
references that say in so many words "length means invariant
length" or "time means invariant time" but there are some
homework problems in MTW that almost require you to think
that way.
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