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

[John Denker <jsd@AV8N.COM>]

Edmiston, Mike wrote:

> As John said, projections and/or appearances become important in the
> twin situation only if one wants a blow-by-blow account of what each
> twin is thinking during the trip, but not necessary in the final
> analysis when the two twins are standing side by side in the same
> reference frame.  Yes... I agree with that.

:-)

>  But I thought all or part
> of the original question was trying to get an answer to the question of
> whether the twin who travelled truly ends up being younger.  The answer
> to that question is yes.

Indubitably.

> The next question then becomes, does that mean
> the travelling twin's biological clock really slowed down.  I think I
> would answer that question as no.  I continue to like John's description
> that in the end the twins arrived at the same place by different
> spacetime paths.  That seems less problematic than saying the biological
> clock slowed down.

:-)

> So what does that say about the idea of relativistic
> time dilation?  If it means the clock slows down, maybe it's not good
> wording to use.  If it means the travelling twin ends up younger, then
> maybe it's okay wording to use.  If we decide "time dilation" is not
> good wording, what concise wording would we want to use to describe the
> fact that the travelled twin ends up younger?  Do we just leave it as,
> "Oh, the travelling twin ended up younger because she took a different
> spacetime path than her brother."  I'm okay with that, and probably like
> that, but we do need to change a lot of textbooks that use "time
> dilation" wording.

I agree with that in spirit, and agree with most of the details.

1) Yes, at the end of the trip, Moe is younger, i.e. he aged less than
  Joe did.
2a) It is traditional in some quarters to explain this by saying something
   funny happened to Moe's clocks (biological and otherwise).  This however
   is *not* the only way or even the best way of explaining point (1).
2b) The simplest and IMHO most satisfactory explanation is that elapsed
   time is path-dependent for the same reason that path-length is
   path-dependent.  Clocks are like odometers.

I'm not ready to agree that (2a) versus (2b) is "just" a matter of wording.
Feynman in volume II chapter 42 devotes 4+ pages (including 14 priceless
diagrams) to making the point that you cannot really tell whether (a) your
ruler changes its length from place to place, or (b) your space is curved.
These are two alternative ways of thinking about the physics;  they are not
just different terminology.

[I would add that the same goes for special relativity:  you cannot
really tell whether (a) your ruler changes its length from place to
place, or (b) your ruler keeps its length but appears foreshortened
because of the geometry of the situation.]

So I don't think it is a question of right versus wrong, or real
versus unreal.  Indeed, if you have truly mastered the physics you
should be able to able to see things both ways, switching from one
model to the other.

I agree that if we must choose between one model and the other, we
should choose on the basis of considerations such as simplicity
and usefulness.  I might add that _consistency_ is also a factor.
The primary virtue of model (b) compared to (a) is that it is
more consistent with the way we think about length as being
invariant with respect to Euclidean rotations, and consistent with
the modern notion that mass is invariant w.r.t boosts.

    [I don't mean inconsistent in the sense of logically inconsistent
     i.e. self-contradictory;  I just mean dissimilar, i.e. passing  up
     the opportunity to make a useful analogy.]

> John D., in response to my post, said that the question of what is real
> is less important than it might appear.  That may or may not be true,
> but isn't it the question that started this discussion?  Do clocks
> really slow down?

I'm not sure what the original issue was ... and I don't much care.
We should focus on the important issues, not necessarily the original
issues.

> Likewise, I agree with John that the two lab notebooks look the same in
> the end after each person has done the proper analysis of the data.  My
> point is that the raw data are different.  In one sense this is no
> different than non-relativistic differences in raw data when two people
> make observations from different frames for which the relative velocity
> between the frames is zero or not very fast.

:-)

> In another sense this is
> different because the non-relavistic reckoning between the notebooks can
> use a Galilean transformation and the relativisitic reckoning requires a
> Lorentz transformation.  If time dilation, relativistic mass versus rest
> mass, and length contraction are/were terms that described the various
> aspects of the necessary relativistic transformations needed to make the
> notebooks become reconciled (i.e. to come to the same laws of physics),
> then time dilation, relativistic mass versus rest mass, and length
> contraction serve some sort of usefull purpose.

I still think viewpoint (b) is more simple, more useful, more pictorial,
more rich in analogies, more easily learned, and more easily taught ...
but viewpoint (a) is not wrong and not useless.  If for some reason a
student can't cope with viewpoint (b), viewpoint (a) can be used to get
the job done.  At the end of the day, if you get all the details right,
the physically-observable predictions are the same either way.

I might also mention that in my experience, viewpoint (b) is easier
to remember correctly.  In particular, the boost matrix in the form
       [ cosh   sinh ]
       [             ]
       [ sinh   cosh ]
is correct, complete, and well-nigh unforgettable, because of the analogy
to the Euclidean rotation matrix.  In contrast, just saying clocks slow
down and rulers shrink is *not* a complete description of SR;  it addresses
only two of the four elements in the matrix.  This is an exceeeeedingly
common source of confusion for students.  (It is also food for trolls who
like to allege "errors" in SR.)

> If we decide to abandon
> those words it is okay with me, but we still need to recognize that
> until the relativistic adjustments/corrections/analysis are performed,
> the lab notebooks look different just like the slower-relative-motion
> observers have different notebooks until the Galilean transformation
> reconciles the notebooks with each other.

OK.

   (But still I think it is more than just a matter of "words".  It's a
   whole package, including a way of looking at things, a way of drawing
   diagrams, and a strategy for setting up calculations.)

> Another example I always have thought intriging is that for two
> observers having large relative velocity between them there is a sizable
> portion of their space-time graphs for which they will disagree on the
> ordering of events.  One observer will record event A happened before
> event B.  The other will record event B happened before event A.  Both
> lab notebooks are correct, and they do disagree... until the
> relativisitic analysis ie performed.  You have to do the analysis before
> they agree.
>
> John ought to respond to this, "Of course.  That's no different than
> reconciling different raw data taken from different but non-relativistic
> frames."

Exactly.  For example, two people reading a dial-type gauge will disagree
on the reading unless/until they correct for parallax error.  This is due
to the plain old Euclidean geometry of the situation.

> I agree, except the reconciliation for the relativistic case
> is a different level of complexity, especially for students not used to
> thinking that way.  The need to make and how to make those
> transformations is what teaching relativity involves.

Yes.

> It's not difficult to convince students the picture of Saturn is real
> and that Saturn's rings are really nearly circular even though they
> appear elliptical in the picture.  Students are used to that reckoning.
> Convincing them of the need and process for relativistic reckoning is
> much more difficult.

I find that using lots of diagrams makes it somewhat less difficult.
Exploiting the analogy between rotations and boosts makes it somewhat
less difficult, somewhat less spooky.
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