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



Michael Edmiston wrote:
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.

That's all good :-)

I think the problem I have is knowing what to call "real."

I think that question is less important than it might appear. Consider
the example of the picture of Saturn.
-- The picture is real, in the sense that it is really a picture of
Saturn. It is not an artist's conception. It is not a fake.
-- The image of the rings is really elliptical. Indeed it is
really, really elliptical. You can easily measure the eccentricity.
++ However the rings (the real rings) are not really elliptical to
any significant degree.

From this I conclude that the same thing can be real, not real, or
both ... depending on what you're trying to say about it.

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 see how that can be. Suppose the task is to measure the
mass of the proton. If her value is significantly different from
your value, somebody has made a mistake. I thought we agreed a
moment ago that "mass" meant "invariant mass" ... so the mass
numbers in the notedbooks really ought to agree. If you measure
something that is not invariant, it isn't the mass.

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.

I can understand that _some_ of the data is different. But the
differences are trivial.
*) Maybe she chooses to find the mass of 10,000 protons and then
divide by 10,000. All her data will differ from yours, right
until the very last step. But at the last step, the quantity
of interest -- the mass of the proton -- will be the same.
*) For all I care, she can use Roman numerals if she wants.
The numerals in her notebook will differ from yours, but the
corresponding _numbers_ will be the same. "Seven" means the
same thing as "VII".
*) If you are measuring the length of a vector in the Euclidean
plane, you might record different values for the _components_
of the vector, depending on your choice of basis, but at the
last step where you calculate the quantity of interest -- the
invariant length -- the numbers will be the same.

.... 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.

To my mind, special relativity is the geometry of spacetime. Saying
we need "relativistic corrections" is just a fancy way of saying we
need to account for the geometry of the situation. Big deal! We
always need to account for the geometry of the situation. If I need
to carry a table through a doorway, I need to account for the geometry
of the situation. I find that I can get through the doorway if I
rotate the table, and not otherwise. But rotation of the table is
an isometry; it does not change the intrinsic properties of the
table. It just changes the projection of the table relative to
the axes of the door.

For a linear
accelerator we either have to build the drift chambers longer than we
would calculate classically,

That's because the classical calculation is wrong. That's not
exactly headline news. Lots of things that are true in the
classical limit are not true in general.

It is common

How 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."

I understand that phraseology was common in the past, but is it
still common? Capacitors used to be called condensers, and CH3COOH
used to be called Spiritus Veneris ... but things have changed.

1) We agree that there is really and truly a factor of gamma that shows
up in the design of the accelerator.

2) I'm not trying to be difficult here, but I really and truly do not
attribute this to any sort of "increasing mass". In my book, there
is a factor of gamma that shows up in the relationship between the
4-velocity (d X / d tau) and the 3-velocity (d x / d t) ... for
reasons having nothing to do with mass.

I repeat: (d t / d tau) has to do with the geometry of spacetime.
It has nothing to do with mass. Mass is invariant. (d t / d tau)
suffices to explain the observed structure and function of the
accelerator.

The term "Spiritus Veneris" died out long ago. The term "condenser"
died out quite recently; when I first started teaching, I felt
obliged to teach "condenser" as an alternative term, but I don't
anymore. I don't know anybody who speaks in terms of non-invariant
"relativistic" mass. I'm sure such exist, but I reckon they are
the last of the Mohicans.

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.

OK!


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?

The travelling twin is *really* younger after the trip, by any
reasonable definition of younger. This statement can be made
without invoking any notion of projection, because the two twins
are side-by-side after the trip, and no projection is necessary.

The idea of projection may be useful if someone requests a
blow-by-blow accounting for what each twin thinks the other
twin's clock is doing _during_ the trip.

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.

The photograph of Saturn is a real photograph. The image of the
rings is really elliptical. But the real rings are not elliptical.

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?

There's nothing special about relativity. It is just the geometry of
spacetime. For hundreds of years, Cartesian geometry has afforded us
multiple ways of describing the same events, because we get to choose
what basis to use. My basis may be rotated relative to yours.

A boosted basis is not conceptually much different from a rotated basis.
The invariant scalars will be the same in all bases. The vectors, in
the abstract sense, will be the same, although their components will
be written differently in the different bases. Anything of observable
physical significance will depend on the abstract vectors, not on the
choice of basis.
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