"Patrick Reany" wrote in message
om...
What makes special relativity 'relativistic'?

Is Maxwell's or Lorentz's ether theories 'relativistic'? Why or why not?

Is Newtonian mechanics 'relativistic'? Explain your answer.

Is covariance of laws alone sufficient to claim the label 'relativistic'?

Take Newtonian mechanics as an example: There is no dynamical observation
that distinguishes one inertial frame of referance from another. This is the
principle of Newtonian Relativity. As such the position and velocity of a
particle are not absolutes. They have meaning only with respect to something
else. I.e. position and velocity are only relative quantities. Newton's laws
of motion have the same form in all inertial frames of referance and remain
invariant under a Galilean transformation (as such inertial frames are
sometimes called "Galilean frames"). Therefore Newtonian mechanics is a
Galilean invariant theory.

So to answer your first question

(1) What makes special relativity 'relativistic'?

Special relativity implies that no experiment can distinguish one inertial
frame of referance from another. As such position and velocity are only
meaningful with respect to something else - i.e. position and velocity are
relative quantities. This is a bit different from Newtonian relativity since
it says nothing about other phenomena other than dynamical such as
electrical phenomena.

(2) Is Maxwell's or Lorentz's ether theories 'relativistic'? Why or why
not?

Maxwell's equations remain invariant under Lorentz transformations from one
inertial frame to another. As such there is no electrical observeration that
allows one to determine their absolute state of motion. Keep in mind that
Maxwell's theory does not say, for example, that there are no quantum
mechanical observations that allow one to determine absolute motion. So
Maxwell's theory is a Lorentz invariant theory.

(3) Is Newtonian mechanics 'relativistic'? Explain your answer.

See above.

(4) Is covariance of laws alone sufficient to claim the label
'relativistic'?

I'd say so. But its covariant with respect to a given phenomena. Einstein
came along and created special relativity. At that point all the laws of
nature was invariant under Lorentz transformations. In that sense special
relativity is a law about laws.


Pmb

PMB wrote regarding the if the principle og gneral covarience makes
something relativistic.
I'd say so. But its covariant with respect to a given phenomena. Einstein
came along and created special relativity. At that point all the laws of
nature was invariant under Lorentz transformations. In that sense special
relativity is a law about laws.

I must disagree here. This principle has applications outside GR (see
Levi-Civita - The Absolute Differential Calculus) thus it alone does not
imply relativity. Also obviously SR is as maximally relativistic as you can
get ie once acceleration is allowed coordinate systems are differentiable so
the the principle of general covariance has no real physical content. What
it is saying is natures laws take on their most transparent form when
expressed that way.

Thanks
Bill

"Bill Hobba" wrote in message
...
PMB wrote regarding the if the principle og gneral covarience makes
something relativistic.
I'd say so. But its covariant with respect to a given phenomena.
Einstein
came along and created special relativity. At that point all the laws of
nature was invariant under Lorentz transformations. In that sense
special
relativity is a law about laws.

I must disagree here. This principle has applications outside GR (see
Levi-Civita - The Absolute Differential Calculus) thus it alone does not
imply relativity.

I don't understand your point. Special Relativity consists of two postulates

(1) The Principle of Relativity - The laws of physics are the same in all
inertial frames of referance

(2) The speed of light in a vacuum is independant of the motion of the
source

Do you think one of these is wrong? Do you think one of these is
inconsistent with something I said?

Pmb

Pmb wrote:
I don't understand your point. Special Relativity consists of two
postulates

(1) The Principle of Relativity - The laws of physics are the same in all
inertial frames of referance

(2) The speed of light in a vacuum is independant of the motion of the
source

Do you think one of these is wrong? Do you think one of these is
inconsistent with something I said?


Of course your axioms are correct (well the second axiom we may have a minor
debate about - but I would be really stretching a point). What the
principle of general covariance says however is that the laws of physics
should be expressed in a form that is invariant between all coordinate
systems inertial and non inertial. Now axiom 1 implies for inertial
coordinate systems the form of the laws of physics are the same (if they
were different you would be able to differentiate between inertial systems
in violation of (1)). However (1) does not apply to general coordinate
systems. The existence of inertial forces breaks Newton's first law in
accelerated coordinate systems. So the principle of general covariance has
no physical basis. In fact any equation can be put in covariant form so it
lacks any kind of physical content at all. So what is its meaning? As you
know from Gravitation and Space-time (a copy of which I know you have; read
Chapter 7 page 370 - 380 where this is discussed in detail) its meaning lies
in imposing restrictions on the terms of an equation in covariant form.
Specifically we divide the terms in covariant equations into two types:
absolute and dynamical terms. Absolute terms are things like the speed of
light in an inertial reference frame, a particles rest mass, Nuv etc. If it
is not an absolute term then it is a dynamical variable. The outcome of
this is when Newton's first law is put in covariant form we see that the
metric guv determines a particles motion. It is obvious that it is not an
absolute term so it must be a dynamical variable. Thus it has its own
lagrangian and the EFE follow. Another way of looking at it is to say if
Guv was an absolute term then that would fix space-times geometry. But
similar to SR saying no velocity is special we believe no geometry is
special and thus believe in 'no fixed geometry' ie the metric is not an
absoluter term it is a dynamical variable.

Thanks
Bill