The transformation equations of special relativity state very
explicitly that the value physicist A assigns to any physical variable
differs from that assigned by physicist B (in motion relative to A).
All experiments on record support such statements. But there are two
ways one can interpret them:

(1) The physical entity the variable defines is really observer
dependent;

(2) The physical entity is one that exists whether is it is observed
or not; only the units used in defining it differ from one observer to
another.

The momentum of a particle or set of particles and all associated
velocities clearly belong in category (1). But texts on special
relativity almost invariably assume that this is true for all
measurable physical variables (the "interval" is not one that can be
measured), that the only invariants are such constants as the charge
and rest mass of a particle or set of particles. I have yet to find
one that discusses option (2) at all.

To take a specific case, "Is the total energy of the universe really
observer dependent or not? Or is it just the units physicists use
that vary? Does matter and energy exist when no one is looking? Does
the universe exist?"

The realist answer is surely that they do exist, that only the
physical units people use in measuring them vary from frame to frame.
It must surely follow that an observer independent description is
possible, one that can be transformed into one that is specific to any
arbitrary frame. For this observer independent description we need a
preferred frame, presumably the frame in which the equations that
describe the universe take their simplest form.

Phil Gardner

Dear Phil Gardner:

"Phil Gardner" wrote in message
om...
The transformation equations of special relativity state very
explicitly that the value physicist A assigns to any physical variable
differs from that assigned by physicist B (in motion relative to A).
All experiments on record support such statements.

This is not strictly true. Length contraction is limited to the single
axis of motion. "Width" and "depth" would be agreed on by A and B.

But there are two
ways one can interpret them:

(1) The physical entity the variable defines is really observer
dependent;

(2) The physical entity is one that exists whether is it is observed
or not; only the units used in defining it differ from one observer to
another.

Mox nix.

The momentum of a particle or set of particles and all associated
velocities clearly belong in category (1).

Not "clearly", since definition 1 says that the "observed" changes, and by
inference so would an observer. This leads to 2).

But texts on special
relativity almost invariably assume that this is true for all
measurable physical variables (the "interval" is not one that can be
measured), that the only invariants are such constants as the charge
and rest mass of a particle or set of particles. I have yet to find
one that discusses option (2) at all.

I think you need to be a little more clear in your definition, unless I
have misunderstood you. Remember that an observer and his instruments is
made out of the same type stuff as the object of his study.

To take a specific case, "Is the total energy of the universe really
observer dependent or not?

Yes.

Or is it just the units physicists use
that vary?

Yes, since they are based on comparisons to objects in his frame.
(Calibration masses and c and a time standard.)

Does matter and energy exist when no one is looking?

You cannot prove that it does, but we get energy from matter that is only
300 ky younger than the Universe, and there was "no one looking" then.

Does
the universe exist?"

Philosophy 101.

David A. Smith

On 12/4/2003 5:30 AM, Phil Gardner wrote:
The transformation equations of special relativity state very
explicitly that the value physicist A assigns to any physical variable
differs from that assigned by physicist B (in motion relative to A).
All experiments on record support such statements. But there are two
ways one can interpret them:
(1) The physical entity the variable defines is really observer
dependent;
(2) The physical entity is one that exists whether is it is observed
or not; only the units used in defining it differ from one observer to
another.

Your attempt to argue by exhaustive enumeration fails, because you did
not include all possibilities. In particular, you forgot:

(3) the measurement is not of any physical quantity, but rather
is a measurement of the PROJECTION of a physical quantity onto
the measuring apparatus.

This is how this is described in SR/GR, for lengths and time intervals.

This is also how we measure the length of a rod in Euclidean 3-space.

If you think about how clocks and rulers work, it should be clear that
they can ONLY measure the appropriate projections....


(the "interval" is not one that can be
measured),

Hmmm. It cannot be measured in the same sense that the length of a rod
cannot be measured -- all one can measure is the PROJECTION of the rod's
length onto a ruler. But people don't normally claim the length of a rod
cannot be measured, because we can align the ruler to be parallel to the
rod, so the projection onto the ruler is the full length of the rod (and
we typically ignore such a trivial projection). Similarly for any
interval, one can (in principle) arrange so the PROJECTION onto the
measuring apparatus is the full interval (clock or ruler, depending on
whether the interval is timelike or spacelike).

This is in SR; GR has more difficulties....

Exercise for the reader: What important interval did I omit
above. Why? How can this be corrected?


Tom Roberts

Phil Gardner:
The transformation equations of special relativity state very
explicitly that the value physicist A assigns to any physical variable
differs from that assigned by physicist B (in motion relative to A).
All experiments on record support such statements. But there are two
ways one can interpret them:

I smell another attempt to reinvent special relativity fashioned
after the old notion, that if you can't make someone go along with
your alternative as a valid alternative, try to recast their argument
as identical to your own, except in disguise.


(1) The physical entity the variable defines is really observer
dependent;

That isn't true. The theoretical "variables" which are intrinsic
to relativity are the invariants in the theory, so the real physics
is contained only in the quantities which are observer _independent_.


(2) The physical entity is one that exists whether is it is observed
or not; only the units used in defining it differ from one observer to
another.

Special relativity is not a theory about observers in relative motion.
It's a theory of invariance and it doesn't matter whether the universe
is filled with observers or if there is but a single observer.

The momentum of a particle or set of particles and all associated
velocities clearly belong in category (1). But texts on special
relativity almost invariably assume that this is true for all
measurable physical variables (the "interval" is not one that can be
measured), that the only invariants are such constants as the charge
and rest mass of a particle or set of particles.

If the charge is an invariant, the so is the speed of light.
Therefore, you have a natural ruler which all observers agree upon.

To take a specific case, "Is the total energy of the universe really
observer dependent or not? Or is it just the units physicists use
that vary?

That is straight forward to address in relativity. If you have
invariance under time translations, you have conservation of
energy, through noether's theorem.

Does matter and energy exist when no one is looking? Does
the universe exist?"

The realist answer is surely that they do exist, that only the
physical units people use in measuring them vary from frame to frame.
It must surely follow that an observer independent description is
possible, one that can be transformed into one that is specific to any
arbitrary frame. For this observer independent description we need a
preferred frame, presumably the frame in which the equations that
describe the universe take their simplest form.

What could be simpler than equations which are the simplest in
_every_ inertial frame precisely because of the invariance?

On 4 DEC (Phil Gardner) wrote:

It must surely follow that an observer independent description is
possible, one that can be transformed into one that is specific to any
arbitrary frame. For this observer independent description we need a
preferred frame, presumably the frame in which the equations that
describe the universe take their simplest form.
Phil Gardner

Wrong, it seems Newtonian coordinates are preferred (mostly
because they simplify certain specific problems), but the least
complicated _general_ solution does not use Newtonian coordinates,
but does need the tools to translate to and from Newtonian coordinates
and concepts.

Joe Fischer

On 4 DEC (Phil Gardner) wrote:
It must surely follow that an observer independent description is
possible, one that can be transformed into one that is specific to any
arbitrary frame.

Yes, certainly. That is what tensor equations do, which is why modern
theories of physics are expressed in tensor equations.


For this observer independent description we need a
preferred frame, presumably the frame in which the equations that
describe the universe take their simplest form.

No, not at all. What one needs are tensor equations, as in GR.


Tom Roberts