Re: [Phys-L] special relativity: observers, or not

[John Denker <jsd@av8n.com>]

On 3/25/19 4:49 AM, Antti Savinainen via Phys-l wrote:

> How should one think about "observer" in QM and relativity? 

Good question.  The short answer is, replace the "observer"
with something else, something that has the desired properties
but is simpler and easier to understand and free of undesired
properties.

> The term is widely used

Yes, alas.

> Or perhaps Mermin's lecture will clear it up.

Nope.

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

As for special relativity:  Short answer:  replace the "observer"
with a /reference frame/.  The recipe couldn't be simpler:  Every
time you read (or are tempted to make) a statement of the form
"according to a lab-frame observer" substitute a simpler statement
"relative to the lab frame".

Rationale:  A reference frame does not move.  This is important.
In contrast, an anthropomorphic "observer" /moves/ through
spacetime.  An observer at rest in the lab reference frame has
a spacetime velocity of:
	u_obs := [dt/dτ, dx/dτ, dy/dτ, dz/dτ]@lab
	       = [1, 0, 0, 0]@lab

where the timelike component is not zero and must not be zero.
A friend of mine likes to say she is:
  Proceeding toward the future at a rate of 60 minutes per hour.

   Notation: as usual, τ is the frame-independent proper time,
   whereas t is the timelike component of velocity in some
   specified frame.

The same goes for an inanimate object, such as a brick.  It is
proceeding toward the future at a rate of 60 minutes per hour:
	u_brick := [dt/dτ, dx/dτ, dy/dτ, dz/dτ]@lab
	         = [1, 0, 0, 0]@lab

Now if somebody asks what is the velocity of the brick relative
to the "observer", the answer is that they are moving together.
There is a temptation to subtract velocity vectors, as one would
do in Galilean relativity:
	Δu = u_brick - u_obs
	   = [0, 0, 0, 0]@lab

which cannot be considered the spacetime velocity of anything.
In particular, this weird Δu has the property
	Δu ⋅ Δu = 0
which is a frame-independent Lorentz-invariant scalar but is
weird because the actual spacetime velocity of anything has
the property
	u_anything ⋅ u_anything = -1
(also a frame-independent Lorentz-invariant scalar).

Bottom line:  Everything in special relativity is relative to
some reference frame that does *not* move.  (In contrast, any
"observer" moves, which creates conceptual difficulties.)

Similarly, an /event/ in spacetime does not move.  An event
happens at a particular place and time.  Time moves on, but
the event does not.

For the next level of detail:
  https://www.av8n.com/physics/spacetime-welcome.htm