"Paul Cardinale" wrote in message
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(Randy Poe) wrote in message
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(Roshard Davis) wrote in message
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Greetings everyone. I have a question concerning Albert Einstein's
Theory of Relativity. I heard that the theory is split up into 2
sections call Special Relativity and General Relativity and I was
wondering, what is difference between these two and what compelled
Einstein to create to different sections on this Theory of
Relativity?Thanks.

Special Relativity came first (in 1905). Einstein worked out
what happens when two things are moving at some velocity
relative to each other, but it doesn't handle acceleration.
It is limited to what are called "inertial frames".

That is not correct. It handles acceleration just fine.

That's incorrect by definition - Special relativity is *defined* to be
"physics in an inertial frame of referance". And you can't really say what
physics is like in an accelerating frame unless you do what Einstien did -
assert the equivalence principle

Pmb wrote:
Special relativity is *defined* to be
"physics in an inertial frame of referance".

Hmmm. Say rather that SR is physics in Minkowski spacetime (i.e. the
flat 4-d Lorentzian manifold with topology R^4). Your "definition" is
too restrictive.

While traditionally SR used inertial corodinates, there's no physical
reason to restrict it to such coordinates. This has been discussed
around here several times over the past few years, and the consensus
among knowledgeable people is that the definition I gave above more
acurately characterizes SR than what you say.


And you can't really say what
physics is like in an accelerating frame unless you do what Einstien did -
assert the equivalence principle

The equivalence principle relates gravitation to acceleration, but no
gravitation is involved here. SR is adequate -- simply use calculus to
relate what happens wrt an inertial frame to the accelerated frame. One
does not need the equivalence principle for this, one merely needs to
assume that in a generally-accelerated frame both clocks and rulers
behave at each instant as if they were at rest in their
instantaneously-comoving local inertial frame. This is a DIFFERENT
assumption from the equivalence principle, and is essentially Einstein's
"hidden" hypothesis that clocks and rulers have no memory.

For clocks there is ample experimental evidence that this is valid (it's
called the "clock hypothesis"; see the FAQ for references to several
experiments that validate it up to accelerations of ~10^18 g). For
rulers, a little thought indicates it had better be valid, as
inter-atomic bonds must behave to make it so (but AFAIK there are no
direct measurmeents, due to the difficulty of doing so -- we can measure
time intervals vastly better than distances; there are no direct
measurements of basic length contraction for inertial motion, either).


Tom Roberts

"Tom Roberts" wrote in message
...
Pmb wrote:
Special relativity is *defined* to be
"physics in an inertial frame of referance".

Hmmm. Say rather that SR is physics in Minkowski spacetime (i.e. the
flat 4-d Lorentzian manifold with topology R^4). Your "definition" is
too restrictive.

Tell me something tom. Why do you keep refering to these definitions as
"yours" refering to me? It is *the* definition. I was defined by Einstein
and used throughout most of relativity as are many other definitions you've
refered to as mine

While traditionally SR used inertial corodinates, there's no physical
reason to restrict it to such coordinates.

Not really - You keep thinking of "special" as refering to flat spacetime.
And it seems that's all you think about when it comes to this term. SR is
defined according to inertial frames since the postulates of SR refer only
to inertial frames. GR is what states that the laws of physics are the same
in all coordinate systems - nor SR.


This has been discussed
around here several times over the past few years, and the consensus
among knowledgeable people is that the definition I gave above more
acurately characterizes SR than what you say.

That's also incorrect. One simply has to look the term up.


And you can't really say what
physics is like in an accelerating frame unless you do what Einstien
did -
assert the equivalence principle

The equivalence principle relates gravitation to acceleration, but no
gravitation is involved here.

Again you're arguing about definitions again - you forget that Einstein
defined "gravitational field" differently then you use the term . And nobody
has proved Einstein wrong. At best some just choose to define things
differently - but I haven't see that in almost all the literature I've seen
on this.

Look it up = Browse a representative collection

Pmb


Pmb

Pmb wrote:
"Tom Roberts" wrote in message
...
Pmb wrote:
Special relativity is *defined* to be
"physics in an inertial frame of referance".

Hmmm. Say rather that SR is physics in Minkowski spacetime (i.e. the
flat 4-d Lorentzian manifold with topology R^4). Your "definition" is
too restrictive.
Tell me something tom. Why do you keep refering to these definitions as
"yours" refering to me?

Because you are the one writing. While other people have made such
definitions LONG AGO, today they are outmoded, except to you -- those
other people are not writing TODAY; you are.


It is *the* definition.

No, it is not. Not as we use the term "SR" today. Accelerated motion was
analyzed in SR many decades ago, including accelerated coordinates.


While traditionally SR used inertial corodinates, there's no physical
reason to restrict it to such coordinates.
Not really - You keep thinking of "special" as refering to flat spacetime.
And it seems that's all you think about when it comes to this term. SR is
defined according to inertial frames since the postulates of SR refer only
to inertial frames.

Yes, the postulates of SR refer only to inertial frames. That does not
ipso facto limit the theory to such frames. SR is a PHYSICAL theory, and
as such physicists consider mathematics to be "free", in the sense that
applying mathematics to the postulates of the theory does not yield a
new theory[#]. As I said before, one can simply apply calculus to
inertial frames and determine anything of interest using accelerated
coordinates. As no additional postulates are needed to do that, this
remains within the bounds of SR.

[#} Think about that, as without mathematics there would
be no physical theories....


GR is what states that the laws of physics are the same
in all coordinate systems - nor SR.

Right. Apply SR in non-inertial coordinates and the "laws of physics"
are QUITE different than they are in inertial coordinates. That's
because in SR we drop the "complicated" terms related to the connection....

Actually not, because we apply SR in spherical coordinates,
for which the connection is nonzero. Note that accelerated
coordinates are in principle no different from spherical
coordinates in this....

If you prohibit accelerated coordinates, then how can you admit
spherical coordinates?

Useful exercise: write down the Lorentz transform in terms
of spherical coordinates. Hint: this should take no more than
2 minutes. Second hint: this is not a test, and you get no
credit for lengthy algebra.

Useful exercise: describe the range of validity of the
transforms of the previous exercise. Why don't they
cover the manifold?

[Accelerated coordinates (aka Rindler coords.) do not
cover the manifold, which is why I present this second
exercise.]


This has been discussed
around here several times over the past few years, and the consensus
among knowledgeable people is that the definition I gave above more
acurately characterizes SR than what you say.
That's also incorrect. One simply has to look the term up.

It is certainly correct that this has been discussed around here, and
the consensus AMONG KNOWLEDGEABLE PEOPLE was as I said.

Be careful where you "look it up", as elementary books tend to take the
simplistic way out....

Look at MTW section 6, and its relationship to the introduction
of both SR and GR. Why do you think they titled part 2 "Physics
in Flat Spacetime" rather than "SR"?

[my answer: because they did not want to get embroiled in the
dead horse you are flogging.]


And you can't really say what
physics is like in an accelerating frame unless you do what Einstien
did - assert the equivalence principle

The equivalence principle relates gravitation to acceleration, but no
gravitation is involved here.

Again you're arguing about definitions again - you forget that Einstein
defined "gravitational field" differently then you use the term .

Not really. But that's irrelvant -- in the Minkowski spacetime of SR
there is no "gravitation" of any sort. So the equivalence principle is
not needed, as I said.

You do need the "hidden" postulate that clocks and rulers have no
memory, as I said.

Useful exercise: How does GR avoid that "hidden" postulate?


Of course the precise "location" of the boundary between SR and GR is
not of major importance -- GR is the real theory and SR is merely a
local approximation to it. So don't expect me to keep beating this....


Tom Roberts

Tom Roberts wrote in message ...
Pmb wrote:
"Tom Roberts" wrote in message
...
Pmb wrote:
Special relativity is *defined* to be
"physics in an inertial frame of referance".

Hmmm. Say rather that SR is physics in Minkowski spacetime (i.e. the
flat 4-d Lorentzian manifold with topology R^4). Your "definition" is
too restrictive.
Tell me something tom. Why do you keep refering to these definitions as
"yours" refering to me?

Because you are the one writing.

So if I use the term "general relativity" it's supposed to mean that
it's mine?

While other people have made such
definitions LONG AGO, today they are outmoded, except to you -- those
other people are not writing TODAY; you are.

That's totally wrong. Just look in most texts today and you'll see.

We've been through all of this before already so I'm not going to
repeat myself again.

[snipped same old comments from these past years]

Pmb

(Gauge) wrote in message . com...
Tom Roberts wrote in message ...
Pmb wrote:
"Tom Roberts" wrote in message
...
Pmb wrote:
Special relativity is *defined* to be
"physics in an inertial frame of referance".

Hmmm. Say rather that SR is physics in Minkowski spacetime (i.e. the
flat 4-d Lorentzian manifold with topology R^4). Your "definition" is
too restrictive.
Tell me something tom. Why do you keep refering to these definitions as
"yours" refering to me?

Because you are the one writing.

So if I use the term "general relativity" it's supposed to mean that
it's mine?

While other people have made such
definitions LONG AGO, today they are outmoded, except to you -- those
other people are not writing TODAY; you are.

That's totally wrong. Just look in most texts today and you'll see.

We've been through all of this before already so I'm not going to
repeat myself again.

[snipped same old comments from these past years]


You can easily be shown to be wrong.
IF SR couldn't handle acceleration,
then it should be easy for you to come up with a problem involving
acceleration that can't be solved using SR.
You won't be able to do that.

Paul Cardinale

(Paul Cardinale) wrote in message . com...
(Gauge) wrote in message . com...
Tom Roberts wrote in message ...
Pmb wrote:
"Tom Roberts" wrote in message
...
Pmb wrote:
Special relativity is *defined* to be
"physics in an inertial frame of referance".

Hmmm. Say rather that SR is physics in Minkowski spacetime (i.e. the
flat 4-d Lorentzian manifold with topology R^4). Your "definition" is
too restrictive.
Tell me something tom. Why do you keep refering to these definitions as
"yours" refering to me?

Because you are the one writing.

So if I use the term "general relativity" it's supposed to mean that
it's mine?

While other people have made such
definitions LONG AGO, today they are outmoded, except to you -- those
other people are not writing TODAY; you are.

That's totally wrong. Just look in most texts today and you'll see.

We've been through all of this before already so I'm not going to
repeat myself again.

[snipped same old comments from these past years]


You can easily be shown to be wrong.

Nope. That is incorrect.

IF SR couldn't handle acceleration, ...

And there's your misunderstanding right here. You're trying to use the
term to define it instead of the correct sequence wher you define it
and then show what it implies.

Do you think Einstein was so stupid as to not undersand what he was
implying when he defined these terms? Of course not.

Pmb

Tom Roberts wrote:
Be careful where you "look it up", as elementary books tend to take the
simplistic way out....


Aren't that the truth. On page 5 of Introduction to Special Relativity
Rindler defines SR as:

'special relativity is the theory of an ideal physics refereed to an ideal
set of infinitely extended gravity-free inertial reference frames'

Now of course Rindler is a genuine expert so all you can conclude is that
what Tom said is true.

BTW he also used rigid scales in his definition of an inertial reference
frame. Rigid in SR?

Thanks
Bill