Re: Hobba's misconceptions


<surrealistic-dream@xxxxxxxxxxx> wrote in message
news:1134824360.649234.293270@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
>
> Bill Hobba wrote:
>> <surrealistic-dream@xxxxxxxxxxx> wrote in message
>> news:1134687363.369440.117520@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
>> > Bill Hobba wrote:
>> >> <surrealistic-dream@xxxxxxxxxxx> wrote in message
>> >> news:1134484250.900232.79440@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
>> >> > Bill Hobba wrote:
>> >> >> <surrealistic-dream@xxxxxxxxxxx> wrote in message
>> >> > ...
>> >> >> >>
>> >> >> >> > If all of matter in the universe were evacuated,
>> >> >> >> > leaving only a rocket ship, and if that rocket blasts its
>> >> >> >> > rockets,
>> >> >> >> > the
>> >> >> >> > objects interior of the rocket will feel the acceleration
>> >> >> >> > according
>> >> >> >> > to
>> >> >> >> > Newton's theory because acceleration is with respect to
>> >> >> >> > "absolute
>> >> >> >> > space." But that acceleration is the same for every inertial
>> >> >> >> > observer,
>> >> >> >> > so I see no violation of the PoR,
>> >> >> >>
>> >> >> >> You are very confused. The POR says all inertial frames are
>> >> >> >> equivalent.
>> >> >
>> >> > The literature gives different versions of what is meant by the PoR.
>> >>
>> >> Not the ones I read. Reference please.
>> >
>> > <BEGIN QUOTE>
>> > In order to account, also, for the equivalence of all inertial systems
>> > with regard to the phenomena of nature, it is necessary to postulate
>> > invariance of all systems of physical equations which express general
>> > laws with respect to Lorentz transformations. The elaboration of this
>> > requirement forms the content of the special theory of relativity.
>> > <END QUOTE>
>> >
>> > --- Physics and reality, Ideas and Opinions, p. 308.
>> >
>> > That's just covariance, pure and simple.
>>
>> The above states that for the equivalence of inertial frames we need to
>> have
>> the principle of invariance
>
> No. Form invariance is covariance, to put it very tersely. What
> Einstein actually claimed one needed to postulate for use in a theory
> was: "invariance of all systems of physical equations....[under]
> Lorentz transformations." That's covariance.

Invariance is not covariance. Look up the reference I gave. Invariance
implies things not implied by covariance ie a statement about absolute and
dynamical terms.

> You didn't read far enough. We all know that Einstein postulated the
> Principle of
> Relativity in 1905. At the very least, Einstein is saying something
> confusing in the quote above.

The only confusion I can see is you not understanding the terms.

>
>>- and is true. That is not a statement about
>> the POR - the principle of invariance is different from the principle of
>> covariance and does have physical content - the principle of covariance
>> does
>> not. The principle of invariance, while strongly implied by the POR, is
>> not
>> the same as the POR. I stated: 'It is well known the principle of
>> general
>> covariance has no physical statement. That was pointed out by Kretchmann
>> to
>> Einstein. No current book on physics claims it does. It is replaced by
>> the
>> principle of general invariance which contains physics.'. One must be
>> exact
>> in the use of technical terms in physics. So lets get our terms
>> straight:
>>
>> POR - The laws of physics are the same in all inertial reference frames.
>> The principle of covariance - the laws of physics should be put in
>> covariant
>> form.
>
> And "covariant form" means?

>From page 371 Gravitation and Space-Time - Ruffini: 'An equation is said to
be covariant under general coordinate transformations if the form of the
equations is left unchanged by the transformations'

>
> I disagree on your definiton of the PoR.
>

Are you claiming it is not the one used in physics? You claimed 'The
literature gives different versions of what is meant by the PoR.'. I
challenged you to back it up. So far you have failed. The POR is stated in
Ruffini in a different way. Why it may be preferred for more advanced work
to the definition I gave (which is basically the way Einstein defined it)
could form the basis of an interesting discussion. But I will not mention
it here. Get the book (or similar), digest it, then we can have a
meaningful discussion.

> LET has the same laws as SR,

Wrong. LET says rod shortening for example is caused by motion though the
aether. SR says it is caused by space-time goemetrtry.

> thus your (admittedly common) version of the PoR does not distinguish
> them, but it ought to. My definition of the PoR (total physical
> equivalence of all inertial frames for all modeling purposes), does
> distinguish SR from LET. In my version, one is prohibited from claiming
> an absolute velocity space in which one frame has a property not shared
> by all other frames. Not only does my version require that the laws of
> physics be the same for all inertial frames, it also demands that any
> proposition independent of happenstance which is true of one frame must
> be true of all frames (i.e., physical equivalence).
>
> A logician might state the PoR this way: Let S be the set of all
> inertial frames {s_i} (let's ignore for the moment that this set is
> uncountable). Defn: A proposition is said to be "general" if it is
> independent of happenstance (where matter is located). The PoR claims
> that for every general proposition P such that there exist a frame s in
> S such that P(s) is true, then P(s_i) is true for all s_i in S.
>
> I have never seen the principle of covariance stated as an injunction
> (in your version), but that's no problem. The problem is that you
> didn't include in your concept of covariance that the equations have
> the same form under change of space-time coordinates.

I did not define covariance because I thought it was too well known.
Covariance has precisely that property.

>
> Be that as it may, let's look at your two definitions above. Since I am
> only interested in theories that are either Newton's mechanics or some
> generalization of Newon's mechanics (such as LET, SR, or GR), the
> "laws" of physics in such a theory will be covariant because Newton's
> laws are. (Lorentz at first did not realize the covariance of his
> laws.) But there is a semantic problem revealed here. One should not be
> calling a relationship a "law" unless that equation is unchanged in
> form (form invariant) under transformation of coordinates,

Wrong. Coulombs law for example does not meet that requirement yet is a
law. The principle of covariance says we should modify it to put it in
covariant form so that it is the same under space-time transformations. And
that is exactly what Maxwell's equations accomplish. But having said that
one must be careful to ensure one understands what law is - as I have
already pointed out.

> at least
> from the relativistic point of view. Lorentz could afford to have
> "laws" unique to the rest frame of the luminiferous ether, but the
> relativist cannot get away with that. Relativity changes the very
> meaning of "law," especially what Einstein referred to as the "general
> law," when he wanted to very clear about what he meant.

Relativity does not change the meaning of law. Highly knowledgable physicts
like Steve Carlip have carefully elucidated what that is:
http://groups.google.com/group/sci.physics/msg/5cd4e7054e21d50f?as_umsgid=c904ei$dml$1@xxxxxxxxxxxxxxxxxxx
'Physical law: a historical term referring to certain empirical
relationships among physical quantities that were deemed to be particularly
important at the time of their discovery. The term originated from a
religious view of regularities in nature being '`God's laws.'' Almost all
named ``physical laws'' date from the 19th century or earlier. Since the
decision about whether to call an observed correlation a ``law'' was
typically made before the relevant phenomena were well understood, the
patterns now called ``laws'' vary tremendously in significance, from
fundamental statements about the universal behavior of physical systems
(Newton's laws) to accidental consequences of the complicated dynamics of a
particular small set of physical systems (Ohm's law), to patterns that are
now generally believed to be almost purely accidental (the Titius-Bode law).
The term is used by physicists today to refer to historically established
labels. It reflects the history the relevant ideas, and sometimes a homage
to great physicists of the past, rather >than anything more intrinsic.
Thus, for instance, we speak of ``Newton's law of gravity,'' but we call the
more accurate modern description ``the Einstein field equations,'' not
``Einstein's law of gravity.'' We speak of the ``ideal gas laws,'' but do
not use the term ``law'' for our now much better description of the
corresponding behavior of real gases. In the rare instances that the term
``law'' has been applied since the 19th century, it has usually been a sort
of literary device; the ``laws of black hole mechanics,'' for instance, were
named and numbered in order to encourage a direct comparison with the 19th
century ``laws of thermodynamics.''
In the sense used in realtivity law means 'fundamental statements about the
universal behavior of physical systems'.

>
> The principle of covariance is this: The general laws of physics are
> invariant (keep the same form, or "form invariant") under appropriate
> change of (space-time) coordinates.
>

You are confused between the concept of an equations form invariance under
transformations and the concept of invariance which as I have stated is a
statement about dynamical and absolute terms in the equation. The correct
statement can be found on 373 of Ruffini: 'All the laws of physics shall be
stated as equations covariant with respect to general coordinate
transformations.' That is a standard reference - I suggest, like Landau,
you get a copy and study it. In all fairness I must say that physicsits are
sometimes a bit loose in how they use the terms - using them
interchangeably. But in truth invariance and covariance are different. I
remember I did a post about it and Tom Roberts confirmed such can be a
little confusing for the novice. But once you study a book like Ruffini
then there is no problem.

> So, the term "invariance" is used
> in two different, though very similar, ways. The form invariance which
> Einstein used in the quote above is just covariance under Lorentz
> transformation. Thus, Einstein was speaking above of covariance.

You obliviously do not understand the terms you are throwing about. Read
the reference given then repost.

Rest snipped.

Bill


.

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