I don't think I have a problem thinking in terms of proper mass, proper
length, proper time being invariant and that we could just drop the
"proper" and call them mass, length, time. I don't have a problem with
the notion of projections and appearances. I think the problem I have
is knowing what to call "real."
Let me give some examples.
A colleague begins in my frame and we discuss some measurements we would
like to make. My colleague then accelerates to a different frame and
observes the same events I do. We both record our measurements in our
lab notebooks. She will record different data in her lab notebook than
what I record... and this includes different lengths, different masses,
and different times for objects and events that we can agree were the
same objects and events.
I don't have a problem realizing that upon getting together later we
notice our lab notebooks really do have different data recorded in them
even though we were observing the same objects and events. Indeed, I
could have predicted, based upon my measurements and my knowledge of our
relative velocity, what her lab notebook would say before I actually
looked at it. But that doesn't change the fact that when we get
together to compare our notebooks that they really are different. Thus,
as a result of my colleague having left my frame, having made some of
the same measurements I made, then having returned to my frame, there is
a lasting difference... the data recorded in our notebooks.
Neither notebook is wrong. Neither notebook is better than the other.
I would be inclined to say they both represent reality even though they
differ. But I think that bugs people. How can two notebooks describing
the same events both be "the real data" if they don't agree with each
other? The common perception of "real" would require us to declare one
notebook as "the real one." I think the fact we can't do that requires
a broader definition of "real" than some people want to accept.
The example just given just describes what is written in notebooks. The
second example describes how we build an instrument. When we build an
accelerator, the portions of the accelerator that handle the
higher-speed particles need relativistic corrections. For a linear
accelerator we either have to build the drift chambers longer than we
would calculate classically, or we need to slow down the oscillator as a
burst of particles travels through the classically calculated chambers.
For a cyclotron we likewise have to slow down the oscillator or we have
to increase the magnetic field at larger radii. For both machines it is
common to keep the oscillator constant. Therefore the later drift
chambers in a linear accelerator are indeed designed longer than a
classical calculation would dictate, and the magnet on a sector-focused
cyclotron has the outer high-field regions expanding in size beyond an
ordinary pie-shape.
It is common to refer to this requirement as an adjustment for the
increased mass of the particles as they reach higher and higher speeds.
It's okay with me if we want to say mass is invariant and that our
measurements of the masses of high-speed particles are different than
the proper mass because they are in a different frame from us. But we
still have sitting in front of us the cyclotron with sectors made
broader to accommodate "the increasing mass." The cyclotron is real,
the widening sectors are real, it works when designed that way, it
doesn't work if not designed that way. Thus, it seems to me the
increased mass is just as real as is the notion that mass is invariant.
Again, two real descriptions of the same objects even though the
descriptions differ.
Finally, the "twin paradox." My twin takes a long high-speed trip. We
know she took the trip (and I did not)because she changed frames three
times... (1) my frame to an outbound frame, (2) the outbound frame to an
inbound frame, (3) the inbound frame back to my frame. Upon her return
here we sit with the lasting difference that she is younger than I am.
It's okay with me if we want to say her clock did not run slow because
her clock was her proper time. However, in the end we have the lasting
difference that she is now physically younger than I am. I like John
D's description of this that we started at the same place, ended up at
the same place, but she took a different space-time path to get here
than I took. As a result of the different paths we arrived here at
different times in our lives.
These three examples are a kind of progression. The numbers recorded in
the notebook are just measurements, and you might describe the
differences as being different projections of a single reality. The
particle accelerator seems to require thinking of the difference as more
than just a projection, although I suppose you could still define
projection to include this. That is, the different projection involves
more than human perception; it forces a tangible design change in an
instrument. My twin being younger really seems to stretch the
projection idea. I repeat...as a result of the different spacetime
paths we arrived here at different times in our lives. How does
projection fit into this? Is she not younger but just looks younger?
In the end I have difficulty with reality and projections and
appearances. If we describe relativistic differences as different
projections yielding different appearances that seems to connote they
are not real. Yet here we sit with notebooks having different numbers
recorded in them (and both are correct)... with accelerators that only
work when tangible changes are made in their construction to accommodate
"the appearance of increasing mass"... and here I sit with my twin
sister whose hair is not as gray as mine.
Are these differences in appearance? Differences in reality? Both?.
Does relativity ultimately mean we have to accept multiple descriptions
of reality? Phrased differently... do we have to say that the lack of
an absolute reference frame also implies an inability to have a single
description of reality?
Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu
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