Equivalence paper
Graham Rounce
I believe this is starting to sound interesting.
(Of course, it should be even more interesting once the "gravitation" paper
comes out).
".........The key insight is that the asymmetry in an accelerating reference
frame in flat spacetime is identical to that in a stationary reference frame
(one that is not falling) in curved spacetime. Therefore the same Rindler
flux that creates inertial reaction forces also creates weight.........."
The paper's at:
http://xxx.lanl.gov/abs/gr-qc/0106075
Any comments?
Graham Rounce
Mark William Hopkins
<gra...@rounce.freeserve.co.uk> writes:
>http://xxx.lanl.gov/abs/gr-qc/0106075
>Any comments?
That maybe the online archives DO need to be peer-reviewed; and
that they sound like they're grasping at straws to desperately
try and keep the funding spigot running.
A theory of inertia is NOT going to come out of some superficial
analysis of the Unruh-Davies effect and semi-classical notions
of quantum vacuums.
At the very least, a theory of inertia will have to explain why
the mass spectrum is what it is, and (almost in the same ballpark)
the issue of why the Mass Operator M does NOT commute with the
SU(2) generating operators T1, T2, T3; but instead appears to
form a rather elaborate Lie algebra of (I think) 60 dimensions.
This (combined with the rest of SU(3)xU(1)) is the algebra which
actually holds the vast representation spaces which underlies
the generational structure of the fermion spectrum and whose
structure coefficients are directly responsible for the
mass mixing parameters. If all you looked at was the
SU(3) x SU(2) x U(1) part of the total algebra, the
generational part would look like an unnecessary duplication
and you'd probably exclaim something like 'Who ordered ThAT?!"
and the mass degeneracy wouldn't be totally out of the blue.
What is this Lie algebra?
zirkus
> Here is an extract from the Abstract of a recent paper by Haisch and Rueda.
> http://xxx.lanl.gov/abs/gr-qc/0106075
I don't know anything about this particular paper, but I already have
2 comments:
1) The abstract mentions the "EM quantum vacuum" which, at least in
this case, is another term for the zero-point field. I once read a
quick calculation on the web by some physics prof in Hawaii that even
if these kinds of ideas about exploiting zero-point energy could be
theoretically meaningful it could still take 100 years operating at
full capacity to obtain any significant amount of energy which means
that this type of approach does not seem very practical.
2) Regardless of the practicality issue, NASA has a special program
which has funded/sponsored work by Haisch and other "interesting"
proposals:
http://www.grc.nasa.gov/WWW/bpp
(Btw, my friend used to have a landlord who was also the first guy to
receive a U.S. patent for a nuclear powered spaceship. NASA said they
liked his idea but that it would have cost them about 1 billion
dollars to just test the idea - and that was back in the 70s when he
got the patent).
[Moderator's note: The best short article I know about the amount
of energy in the vacuum is one that my co-moderator John Baez wrote:
http://math.ucr.edu/home/baez/vacuum.html -MM]
Aaron J. Bergman
zir...@my-deja.com (zirkus) wrote:
> 2) Regardless of the practicality issue, NASA has a special program
> which has funded/sponsored work by Haisch and other "interesting"
> proposals:
The BPP has funded a number of very wacky ideas (not that this is a bad
thing.)
As far as I know, they haven't given a penny to Haisch and Rueda.
Aaron
--
Aaron Bergman
<http://www.princeton.edu/~abergman/>
Graham Rounce
on this ( http://xxx.lanl.gov/abs/gr-qc/0106075 ).
> I don't know anything about this particular paper, but I already have 2
comments
>.....I once read a quick calculation on the web by some physics prof in
Hawaii that
....I'm pretty sure that Haisch et al are not crackpots (though their ideas
have certainly been latched on to by many who are), and understand the
objections as well as anyone. Maybe I am being gullible here, which is why
I posted in the first place, but it seems that once you accept
(provisionally, for the sake of argument) that there is a real zero-point
field which doesn't for some reason wrap the universe up to the size of a
proton, some interesting results can follow.
I'm definitely not enough of an expert to take on the job of defense
counsel, and would have liked some more balanced replies from people who
have at least read the arguments being put forward.
Here is the main site address: http://www.calphysics.org/index.html . It's
interesting reading - your eyes will probably not roll upwards out of your
head.
Thanks,
Graham Rounce
zirkus
says...
>The BPP has funded a number of very wacky ideas (not that this is a bad
>thing.)
>
>As far as I know, they haven't given a penny to Haisch and Rueda.
According to the website below, Haisch has had NASA funding but I don't know
if the funding involved BPP or what part of NASA. Btw, I didn't mean to
imply that Haisch and the other theorists on the BPP website are cranks
because I personally cannot show that any of their ideas are wrong. I
only meant to emphasize that some of the ideas might be unorthodox (which
doesn't bother me).
http://www.calphysics.org/inertia.html
Charles Francis
nce.freeserve.co.uk> writes:
>Here is an extract from the Abstract of a recent paper by Haisch and Rueda.
>".........The key insight is that the asymmetry in an accelerating reference
>frame in flat spacetime is identical to that in a stationary reference frame
>(one that is not falling) in curved spacetime.
This is a key insight, but a key insight into what?
>Therefore the same Rindler
>flux that creates inertial reaction forces also creates weight.........."
Certainly not that, I would suggest. If we are to understand any of this
then we must start with inertial coordinates on which, by definition,
there is no action. Then we can understand accelerated coordinates on
the basis of what is being done to accelerate the physical coordinate
axes. Nothing is being done to the vacuum, and inertial forces are not
created by Rindler flux. These forces are called inertial, and sometimes
fictional, precisely because they are not an action; they are created by
action on the physical co-ordinate axis, not by any other process.
Weight is merely the mass of an inertial body multiplied by the
acceleration of the coordinate axes due to impressed force on the
physical matter representing the axes.
Inertial forces were introduced by Huygens precisely for the purpose of
treating non-inertial coordinate axes, and putting them down to a
Rindler flux (I neither know nor care what that is) is either a
misrepresentation of the credit due to Huygens, or a fictional process
to explain a fictional force.
Regards
--
Charles Francis
[Moderator's note: presumably "Rindler flux" refers to the
thermal radiation seen by an accelerating observer, as predicted
by quantum field theory. This effect is too tiny to have been
seen in experiments yet, and as Francis notes, it could not
plausibly serve as the primary explanation of inertia. - jb]
Charles Francis
<cha...@clef.demon.co.uk> writes
>[Moderator's note: presumably "Rindler flux" refers to the
>thermal radiation seen by an accelerating observer, as predicted
>by quantum field theory. This effect is too tiny to have been
>seen in experiments yet, and as Francis notes, it could not
>plausibly serve as the primary explanation of inertia. - jb]
That sounds rather like Unruh radiation. What is the precise
distinction? Is Unruh radiation matter and antimatter, whereas and
Rindler is photonic?
Many people seem to be quite hung up on these effects and have important
and difficult implications for the unification of field theory and gtr,
but I just think they illustrate the fundamental importance of using
inertial reference frames. From the point of view of an inertial
observer there is no mystery. Suppose an accelerated observer goes past,
producing Unruh radiation and Rindler radiation, apparently
spontaneously out of the vacuum. Clearly the radiation is real, so the
inertial observer sees it. But it does not appear spontaneously out of
the vacuum. It is a simple side effect of the forces being applied to
accelerate the other observer.
And as far as any causality problem is concerned, as to whether the
radiation is produced "before" it takes energy from the accelerating
force, that is just causality as it appears in quantum field theory
anyway. So there really is nothing special about these forms of
radiation, and no particular insight to be had from thinking about them,
beyond the insight that in gr we can do everything we need to by
studying the laws of physics in inertial frames
Regards
--
Charles Francis
John Baez
Charles Francis <cha...@clef.demon.co.uk> wrote:
>In article <s714aKBH...@clef.demon.co.uk>, Charles Francis
><cha...@clef.demon.co.uk> writes
>>[Moderator's note: presumably "Rindler flux" refers to the
>>thermal radiation seen by an accelerating observer, as predicted
>>by quantum field theory. This effect is too tiny to have been
>>seen in experiments yet, and as Francis notes, it could not
>>plausibly serve as the primary explanation of inertia. - jb]
>That sounds rather like Unruh radiation.
Exactly! - I was guessing that "Rindler flux" was none other
than Unruh radiation.
I've never heard anyone talk about a "Rindler flux" before...
but when people study Unruh radiation they usually use Rindler
coordinates, and everything else about that guy's description
of "Rindler flux" sounded exactly like Unruh radiation... so
I was using my moderator's note to suggest that maybe that guy
was talking about Unruh radiation - that is, the thermal radiation
seen by an accelerating observer.
>Is Unruh radiation matter and antimatter, whereas
>Rindler is photonic?
Let's forget this "Rindler flux" business....
Unruh radiation is perfectly thermalized: it contains a bit
of everything, but in perfect thermal equilibrium for whatever
temperature it's at. This implies that it consists mainly of
massless particles (e.g. photons) at low temperatures, and
contains significant quantities of mass m particles only when
kT gets to be about mc^2 or higher.
Graham Rounce
news:9nroiv$ggi$1...@glue.ucr.edu...
> Exactly! - I was guessing that "Rindler flux" was none other
> than Unruh radiation.
> I've never heard anyone talk about a "Rindler flux" before...
> but when people study Unruh radiation they usually use Rindler
> coordinates, and everything else about that guy's description
> of "Rindler flux" sounded exactly like Unruh radiation... so
> I was using my moderator's note to suggest that maybe that guy
> was talking about Unruh radiation - that is, the thermal radiation
> seen by an accelerating observer.
>
> Let's forget this "Rindler flux" business....
As I've said before, I'm surprised at the amount of comment based on
guessing what the paper could be about, when with a couple of clicks you
could actually read it, and know what it's about. Had H & R been talking
about about Unruh radiation, they would have said so. In fact, they
specifically say otherwise (page 4). I asked (and still ask) for "Any
comments?" - but not ANY comments. Please read the paper, and then deride
it if you wish.
Graham Rounce
John Baez
Graham Rounce <gra...@rounce.freeserve.co.uk> wrote:
>"John Baez" <ba...@galaxy.ucr.edu> wrote in message
>news:9nroiv$ggi$1...@glue.ucr.edu...
>As I've said before, I'm surprised at the amount of comment based on
>guessing what the paper could be about, when with a couple of clicks you
>could actually read it, and know what it's about.
Oh, you mean actual work - as opposed to chatting with people
on sci.physics.research? Hmm. A novel concept! How much will you pay me?
>Had H & R been talking about about Unruh radiation, they would have said
>so. In fact, they specifically say otherwise (page 4). I asked (and
>still ask) for "Any comments?" - but not ANY comments. Please read
>the paper, and then deride it if you wish.
Okay - I'll even do it for free, just this once. :-)
On page 4 of the paper you cite:
Bernard Haisch, Alfonso Rueda
Geometrodynamics, Inertia and the Quantum Vacuum
http://xxx.lanl.gov/abs/gr-qc/0106075
the authors say that the usual description of Unruh radiation as
purely thermal comes from a calculation involving spin-0 fields.
They say that when one more correctly treats the electromagnetic
field as a spin-1 field, "there appear additional terms beyond the
quasi-thermal Unruh-Davies component". They give a formula for
these and add: "While these additional acceleration-dependent terms
do not show any spatial asymmetry in the expression for the spectral
energy density, certain asymmetries do appear when the momentum
flux of this radiation is calculated, resulting in a non-zero Rindler
flux".
Then they take a giant leap into the blue and say "This asymmetry
appears to be the process underlying inertial and gravitational force."
At this point the needle on my skeptometer shoots way into the red
zone....
But forget that: what about their perfectly testable mathematical
claim that when we repeat the usual Unruh calculation for spin-1
fields we get a nonzero momentum flux - their so-called "Rindler
flux"?
For this they give two references to previous papers of theirs:
Contribution to inertial mass by reaction of the vacuum to accelerated
motion
http://xxx.lanl.gov/abs/physics/9802030
and
Inertia as reaction of the vacuum to accelerated motion
http://xxx.lanl.gov/abs/physics/9802031
To get anywhere I need to read these. (See, this is actual work!)
Looking at the first paper I instantly see the phrases "Mach's
principle", "zero-point-field", and "a reaction force heretofore
attributed solely to the existence of an unexplained property called
inertia". All of this makes the needle on my skeptometer edge upward.
Normally I would stop reading right here, but I'll be nice and see if
I can find the darn calculation for spin-1 fields. Hmm....
The real meat appears to be in Appendix A, which starts on page 20
of this 40-page paper. "Appendix A: ZPF-averaged products for the
ZPF Poynting Vector."
Hmm... I see pages and pages of calculations, but I don't yet see
the actual formula for the expectation value of the Poynting vector,
which is what I really want: that's the vector describing their
"Rindler flux".
Well, this is getting to be real work! I like to tackle these
things efficiently, so what I'll do now is email Bill Unruh and
ask him if a calculation with spin-1 fields gives a nonzero expectation
value for the Poynting vector. He's the real expert on this stuff.
Of course, even experts can be wrong, but his opinion on this is worth
100 times mine.
John Baez
>Hmm... I see pages and pages of calculations, but I don't yet see
>the actual formula for the expectation value of the Poynting vector,
>which is what I really want: that's the vector describing their
>"Rindler flux".
>
>Well, this is getting to be real work! I like to tackle these
>things efficiently, so what I'll do now is email Bill Unruh and
>ask him if a calculation with spin-1 fields gives a nonzero expectation
>value for the Poynting vector.
Unruh says that Haisch and Rueda's calculations are wrong, and
that a correct calculation shows a uniformly accelerating observer
zipping through the vacuum state of a quantized electromagnetic
field on Minkowski spacetime sees a *perfectly thermalized* bath
of photons.
In particular, this means such an observer will see no "Rindler flux" -
i.e., the expectation value of the Poynting vector is zero. Or in
less fancy language: there will be, on average, no net flux of momentum
in the photons seen by the accelerating observer.
He gives a very simple argument showing that the expectation value
of the Poynting vector *must* be zero: the whole situation is
time-symmetric, and time reversal flips the direction of the
Poynting vector!
He also says that Haisch and Rueda don't do a straightforward
calculation; rather, they use the "Boyer stochastic field technique,
together with assumptions I have never been able to figure out."
So, it seems pretty obvious that an accelerating observer in a
quantized electromagnetic field will not see the "Rindler flux"
predicted by Haisch and Rueda. Less obvious, but also reassuring
to my intuition, is that the observer will simply see isotropic
blackbody radiation!
Charles Francis
>In article <9nsg08$aoq$1...@newsg1.svr.pol.co.uk>,
>Graham Rounce <gra...@rounce.freeserve.co.uk> wrote:
>>"John Baez" <ba...@galaxy.ucr.edu> wrote in message
>>news:9nroiv$ggi$1...@glue.ucr.edu...
>
>>As I've said before, I'm surprised at the amount of comment based on
>>guessing what the paper could be about, when with a couple of clicks you
>>could actually read it, and know what it's about.
I could have done, but my internet connection doesn't work every day.
And it didn't that day.
>>Had H & R been talking about about Unruh radiation, they would have said
>>so. In fact, they specifically say otherwise (page 4). I asked (and
>>still ask) for "Any comments?" - but not ANY comments. Please read
>>the paper, and then deride it if you wish.
But anyway there was quite enough in the abstract to show that the
authors were working on some bizarre explanation for a perfectly mundane
effect to do with accelerating reference frames. I rather felt that was
as much comment as the paper needed. There is not much point in further
comment when one has already ascertained that the authors are not making
sense. In other words, and in spite of your previous assertion, at least
as far as this is concerned, they are crackpots. Don't hold that against
them. Its the human condition and we all suffer from it, the worst
afflicted being those who do not recognise it in themselves.
>Okay - I'll even do it for free, just this once. :-)
My, John, you are being generous today. We just don't deserve you.
<snip>
>the authors say that the usual description of Unruh radiation as
>purely thermal comes from a calculation involving spin-0 fields.
>They say that when one more correctly treats the electromagnetic
>field as a spin-1 field, "there appear additional terms beyond the
>quasi-thermal Unruh-Davies component".
Ah, so Rindler flux is a proposed correction to Unruh radiation. Well
that's nice. But as I said earlier not terribly important, even if its
true.
>Then they take a giant leap into the blue and say "This asymmetry
>appears to be the process underlying inertial and gravitational force."
And at this point it is certainly not true.
<snip>
>To get anywhere I need to read these. (See, this is actual work!)
Goodness, what dedication.
>Normally I would stop reading right here, but I'll be nice and see if
>I can find the darn calculation for spin-1 fields. Hmm....
You're a glutton for punishment.
>Hmm... I see pages and pages of calculations,
That in itself is a warning sign. Well, I've no idea whether the
calculations are correct, but for the sake of a gamble I'll give odds of
two to one on all virtual bets that they aren't.
>Well, this is getting to be real work! I like to tackle these
>things efficiently, so what I'll do now is email Bill Unruh
I expect he won't mind.
>and
>ask him if a calculation with spin-1 fields gives a nonzero expectation
>value for the Poynting vector. He's the real expert on this stuff.
Like a true gambler, I'm looking forward to spending my virtual winnings
already.
Regards
--
Charles Francis
Graham Rounce
> Oh, you mean actual work - as opposed to chatting with people on
> sci.physics.research? Hmm. A novel concept!
Work?? No - fun, interest, enjoyment!
> How much will you pay me?
Wrong time of the month, I'm afraid.... any other time I'd have been happy
to .... :-)
> ... what about their perfectly testable mathematical claim that when we
> repeat the usual Unruh calculation for spin-1 fields we get a nonzero
> momentum flux - their so-called "Rindler flux"?
Yes...
> For this they give two references to previous papers of theirs:
> Contribution to inertial mass by reaction of the vacuum to accelerated
> motion http://xxx.lanl.gov/abs/physics/9802030
> and Inertia as reaction of the vacuum to accelerated motion
> http://xxx.lanl.gov/abs/physics/9802031
> To get anywhere I need to read these. (See, this is actual work!)
I thought this kind of thing would have been delivered to your breakfast
table on a tray by a liveried flunky ages ago?? At least, that's how I
Thought it worked!
> ... what I'll do now is email Bill Unruh and ask him if a
> calculation with spin-1 fields gives a nonzero expectation value for the
> Poynting vector. He's the real expert on this stuff. Of course, even
> experts can be wrong, but his opinion on this is worth 100 times mine.
OK, thanks for your trouble.
Graham Rounce
Graham Rounce
> In article <9nue1m$c9n$1...@glue.ucr.edu>, John Baez <ba...@galaxy.ucr.edu>
> wrote:
> Unruh says that Haisch and Rueda's calculations are wrong, and that a
correct calculation shows a uniformly accelerating observer zipping through
the vacuum state of a quantized electromagnetic field on Minkowski spacetime
sees a *perfectly thermalized* bath of photons.
Oh.
Well, it does make it very confusing for laymen like myself when the
professionals make wrong calculations. Un-disprovable speculation I can
understand, but the sums should be right, because I for one sure wouldn't
know if they weren't! Maybe someone should tell them....
> In particular, this means such an observer will see no "Rindler flux" -
> i.e., the expectation value of the Poynting vector is zero. Or in less
> fancy language: there will be, on average, no net flux of momentum in the
> photons seen by the accelerating observer.
> He gives a very simple argument showing that the expectation value of the
> Poynting vector *must* be zero: the whole situation is time-symmetric, and
> time reversal flips the direction of the Poynting vector!
I don't really understand this. Does it mean that if "the expectation
value of the Poynting vector" wasn't zero, in a time-reversed situation
objects would just zoom off by themselves?
> He also says that Haisch and Rueda don't do a straightforward
> calculation; rather, they use the "Boyer stochastic field technique,
> together with assumptions I have never been able to figure out."
> So, it seems pretty obvious that an accelerating observer in a quantized
> electromagnetic field will not see the "Rindler flux" predicted by Haisch
> and Rueda. Less obvious, but also reassuring to my intuition, is that the
> observer will simply see isotropic blackbody radiation!
Fair enough. But the approach did seem to get them quite a long way.
F = ma, relativistic effects, stability of the hydrogen atom, etc etc.
Thanks again for your trouble, and pls thank Unruh for me, too.
What IS the mechanism of inertia, in "standard physics"?
Graham Rounce
John Baez
Graham Rounce <gra...@rounce.freeserve.co.uk> wrote:
>"John Baez" <ba...@galaxy.ucr.edu> wrote in message
>news:9nuuis$h4j$1...@glue.ucr.edu...
>>Unruh says that Haisch and Rueda's calculations are wrong, and that a
>>correct calculation shows a uniformly accelerating observer zipping through
>>the vacuum state of a quantized electromagnetic field on Minkowski spacetime
>>sees a *perfectly thermalized* bath of photons.
>Oh.
>
>Well, it does make it very confusing for laymen like myself when the
>professionals make wrong calculations.
Yes. Of course, that's life. You can't tell when the experts
are wrong unless you yourself are an expert... and even then,
sometimes you're wrong!
>Un-disprovable speculation I can
>understand, but the sums should be right, because I for one sure wouldn't
>know if they weren't! Maybe someone should tell them....
They have! If you look at gr-qc for the list of papers by Haisch
and Rueda, you'll see one called
The Case for Inertia as a Vacuum Effect: A Reply to Woodward and Mahood
http://xxx.lanl.gov/abs/gr-qc/0002069
The title makes it clear that the authors are arguing against
criticism of their results. Whenever you see something like this,
it's a good hint that you should be careful and read both sides
of the argument before making up your mind.
>> In particular, this means such an observer will see no "Rindler flux" -
>> i.e., the expectation value of the Poynting vector is zero. Or in less
>> fancy language: there will be, on average, no net flux of momentum in the
>> photons seen by the accelerating observer.
>> He gives a very simple argument showing that the expectation value of the
>> Poynting vector *must* be zero: the whole situation is time-symmetric, and
>> time reversal flips the direction of the Poynting vector!
>I don't really understand this. Does it mean that if "the expectation
>value of the Poynting vector" wasn't zero, in a time-reversed situation
>objects would just zoom off by themselves?
No. The Poynting vector - the vector describing the flow of
momentum - gets a minus sign in front of it when you switch
from any situation to the time-reversed version of this situation.
However, the situation we're talking about here - a uniformly
accelerating particle - doesn't change when you switch to the
time-reversed version. It's time-symmetric! So the Poynting vector
must stay the same when you stick a minus sign in front of it.
So it must be zero.... contrary to Haisch and Rueda's claim.
>But the approach did seem to get them quite a long way.
>F = ma, relativistic effects, stability of the hydrogen atom, etc etc.
Since all that stuff is already fairly well understood, it's not
clear how helpful it is to have a new, erroneous explanation.
>What IS the mechanism of inertia, in "standard physics"?
I'm sorry, now you're almost asking for a physics course - starting
with Newtonian physics, then special relativity, then general relativity,
and finally some quantum mechanics to get another angle on this
question.
Hopefully someone is brave enough to tackle this, but not me!
Norbert Dragon
>* Graham Rounce <gra...@rounce.freeserve.co.uk> wrote:
>> What IS the mechanism of inertia, in "standard physics"?
> Hopefully someone is brave enough to tackle this, but not me!
Physics has no picture with toothed wheels to explain inertia.
but offers the following explanation:
Whenever a quantum field theory contains interacting spin 2 particles
then for consistency (absence of negative probabilities) there can
be only one kind of particles, gravitons. Their coupling is highly
restricted: they can couple only to the energy-momentum tensor T^mn
and the energy-momentum tensor is necessarily conserved
D_m T^mn = 0.
For n=1,2,3 this equation states the conservation of momentum:
The momentum of a particle can be changed only if momentum
is transfered to it. If the particle is isolated such that
no momentum can be transfered then it follows a straight line
in spacetime. Moreover the form of the energy-momentum tensor
of a test particle is comletely fixed up to a constant M
T_mn(x) = M u_m u_n delta^3(x - X(t)) sqrt(1-v^2)/sqrt(g)
In simpler words: the dependence of momentum on the velocity
of the particle is completely fixed, we only lack an explanation
of the M values for elementary particles. The mass M of a
macroscopic body is nearly continuous.
--
Norbert Dragon
http://www.itp.uni-hannover.de/~dragon
Matt McIrvin
> [Graham Rounce asked:]
> >What IS the mechanism of inertia, in "standard physics"?
> I'm sorry, now you're almost asking for a physics course - starting
> with Newtonian physics, then special relativity, then general relativity,
> and finally some quantum mechanics to get another angle on this
> question.
>
> Hopefully someone is brave enough to tackle this, but not me!
I would say that there *is no* known mechanism of inertia.
It always seems to be something built in from the start of any viable
physical theory. The closest thing to a derivation I know is the
Feynman path integral-- but even there, we haven't explained why the
Lagrangian is what it is, and that's crucial to getting out inertia as
we know it.
The way inertia behaves in our world is implied by the set of
space-time symmetries: if an object at rest tends to remain at rest,
that implies through a symmetry (Galileo or Lorentz invariance,
depending on how accurate you want to get) that an object in motion
tends to remain in motion. But this is about the best that I can do.
--
Matt McIrvin
AG
> In article <9o4kmh$vu4$1...@newsg4.svr.pol.co.uk>,
> Graham Rounce <gra...@rounce.freeserve.co.uk> wrote:
> >"John Baez" <ba...@galaxy.ucr.edu> wrote in message
> >news:9nuuis$h4j$1...@glue.ucr.edu...
> >What IS the mechanism of inertia, in "standard physics"?
> I'm sorry, now you're almost asking for a physics course - starting
> with Newtonian physics, then special relativity, then general relativity,
> and finally some quantum mechanics to get another angle on this
> question.
But if this is true we must be really far off from an ultimate theory of
absolute everything. Because just to be able to define one
word, “inertia,” we need to invoke 4 different theories.
There was a time when inertia meant the motion of a projectile when the
projector ceased to act.
Newton stole Descartes’ concept of the rectilinear inertia and stated
as his Axiom II according to which an object moved indefinitely on a
straight line when no force was acting on it, in analogy to the
sling motion. This terrestrial observation cannot be carried over
to space since sling does not work in space and this rectilinear
inertial motion has never been observed.
Another problem regarding the observation of such a motion is the scale of
the curvature. For instance, the distance that the earth moves on its orbit
in one second can be considered a straight line for any practical purposes,
but the earth actually describes a closed curve, so it has curvature. It
would be hard to differentiate such curved motion from straight line motion.
Galileo, in some of his writings suggested that he may have believed in
circular inertia. But in fact Galileo was considering a “neutral” motion
which was neither “natural” nor “forced.” He also said that
on a horizontal surface the smallest “force” would move the
greatest “mass.”
Why wouldn’t that motion have acceleration? By definition the projector
changes the speed of the projectile. After the projector ceases to act, the
projectile will either keep increasing or decreasing its speed but its speed
will never stay the same.
Furthermore, everything is already moving. If something has uniform motion
it’ll keep moving, but if it doesn’t, then, it could never made to move
inertially (without force) uniformly on a straight line. But in any case,
after the force ceases to act the resulting motion must have acceleration,
its speed must change.
Einstein also worried about this concept. But he was, as common with
physicists, enamored with the latest mathematical fad of his era and thought
that new mathematics (i.e. new notation) would help him understand
fundamental relationships that he was trying to understand. But this only
took him away from his goal. Which means I don’t know what Einstein
understood by inertia.
It seems that there are several working definitions of inertia depending on
the specific models one is considering. Unless we can say
“inertia is ...” we might as well say that we don’t know what
it is.
Charles Francis
unce.freeserve.co.uk> writes
>Well, it does make it very confusing for laymen like myself when the
>professionals make wrong calculations.
It is quite impossible for anyone, layman or professional to keep up
with everything anyone says and every calculation everyone does. It is
important therefore to develop guiding philosophical principles which
will tell you what is worth paying attention to, before entering into
the lanl archive. The question of inertia is a fundamental one, and it
was clear in the abstract that Haisch and Rueda had not grasped it.
>What IS the mechanism of inertia, in "standard physics"?
Since inertia just means "no action" or "not acting" in latin, by
definition there is no mechanism. It is difficult to know exactly what
you mean by this, so I will answer three times, for inertial motion,
inertial force and inertial mass.
Inertial motion is just the motion of a body when no external agency
acts upon it. The definition of inertial motion is that there is no
mechanism.
In Newtonian mechanics we may distinguish between inertial force and
impressed force. A force is anything which causes an acceleration
according to the second law; an impressed force implies the action of
one body on another. An inertial force is caused not by the action of
one body on another but by the choice of reference frame, like the
coriolis and centrifugal forces in rotating frames, and g-forces in
accelerated frames. So again, the mechanism of an inertial force is that
there is no mechanism. Inertial force is an illusiary action produced by
the motion of one's reference frame, while the motion of the reference
frame is simply the product of ordinary impressed forces on ones
environment.
Inertial mass is described as the resistance to acceleration per amount
of impressed force. There is again no mechanism for it in standard
physics, because it is a fundamental notion on which other ideas our
based. The effect of inertia is summarised in the law of conservation of
momentum. The origin of conservation of momentum is that the laws of
physics are everywhere the same. Conservation of momentum is a principle
which makes this possible as mass moves from A to B, or interacts at C.
I could tell you that if particle interactions are discrete inertial
mass is a measure of the time between interactions. If, for example, the
interactions of a muon are identical to, but much less frequent than,
the interactions of an electron then we would expect to observe a
proportionately smaller change in motion from the same stimulus. But I
must emphasise that is not standard physics.
Regards
--
Charles Francis
Squark
>Graham Rounce <gra...@rounce.freeserve.co.uk> wrote:
>>What IS the mechanism of inertia, in "standard physics"?
When I hear the word "mechanism", I think of a an explanation for a specific
phenomenon in the framework of an established model, or at least meta-model of
some sort. The concept of "inertia" hardly falls into these bounds, at least
without further specification - for instance, what model (approximation) do you
want to consider here? Newtonian physics? Special/General relativity? Quantum
mechanics?
Best regards,
Squark.
-------------------------------------------------------------------------------
Write to me at:
[Note: the fourth letter of the English alphabet is used in the following
exclusively as anti-spam]
dSdqudarkd_...@excite.com
John Baez
Matt McIrvin <mmci...@world.std.com> wrote:
>In article <9oge45$1r2$1...@glue.ucr.edu>, ba...@galaxy.ucr.edu (John Baez)
> [Graham Rounce asked:]
>> >What IS the mechanism of inertia, in "standard physics"?
>> I'm sorry, now you're almost asking for a physics course - starting
>> with Newtonian physics, then special relativity, then general relativity,
>> and finally some quantum mechanics to get another angle on this
>> question.
>>
>> Hopefully someone is brave enough to tackle this, but not me!
>I would say that there *is no* known mechanism of inertia.
>It always seems to be something built in from the start of any viable
>physical theory.
As Norbert Dragon so eloquently put it, current physics has no
mechanism with toothed wheels to explain inertia. It's built
in from the start, in somewhat different ways for the various
theories I listed.
I guess the physics course Graham Rounce was secretly asking for
would have to include a history of the notion of "mechanism",
including how this notion fell into disrepute with the failure
of the "mechanical models" for electromagnetism due to Kelvin,
the early Maxwell, and others. This would make it clear why
current theories *avoid* seeking a "mechanism" for inertia
of the sort Haisch and Rueda seem to want.
For a nice description of the *rise* of the notion of mechanism,
this book is really good:
E. J. Dijksterhuis, The Mechanization of the World Picture:
Pythagoras to Newton, Princeton U. Press, 1986.
Unfortunately I know of no comparable book that treats the
*fall* of the notion of mechanism!
Daryl McCullough
>Whenever a quantum field theory contains interacting spin 2 particles
>then for consistency (absence of negative probabilities) there can
>be only one kind of particles, gravitons. Their coupling is highly
>restricted: they can couple only to the energy-momentum tensor T^mn
>and the energy-momentum tensor is necessarily conserved
>
>D_m T^mn = 0
Do you know of a reference for that proof? I've seen a sketch of a
similar argument (quoted in Misner, Thorne and Wheeler's _Gravitation_)
with the conclusion that any consistent spin-two field that couples to the
energy momentum tensor must obey Einstein's field equations. But I
didn't realize that this was the only possible consistent spin-two
theory---that is, it doesn't seem obvious that there couldn't be some
other type of coupling.
--
Daryl McCullough
CoGenTex, Inc.
Ithaca, NY
G Rounce
news:ds%q7.786$ev2....@www.newsranger.com...
> >Graham Rounce <gra...@rounce.freeserve.co.uk> wrote:
> >>What IS the mechanism of inertia, in "standard physics"?
<snip> what model (approximation) do you want to consider here? Newtonian
physics? Special/General relativity? Quantum mechanics?
All of them. And any others that have anything to say on the subject.
G Rounce
news:6SXtw2A8...@clef.demon.co.uk...
> In article <9o4kmh$vu4$1...@newsg4.svr.pol.co.uk
> Graham Rounce <gra...@rounce.freeserve.co.uk> writes
> >What IS the mechanism of inertia, in "standard physics"?
> Since inertia just means "no action" or "not acting" in latin, by
definition there is no mechanism. It is difficult to know exactly what you
mean by this
I mean, why does it take more energy to accelerate a lead ball than a wooden
one? Or any energy? Of course, if it didn't, the slightest touch would
cause an object to go zooming off at the speed of light. Would there then
be no such thing as relative motion? I don't know what principles dictated
the kind of universe that got created, but I'd bet that consistency was one
of them (perhaps the main, or even the only one). Maybe making a consistent
universe in which everything moved at c was just too difficult... (or maybe
too trivial, not giving rise to intelligent beings?)
> so I will answer three times, for inertial motion, inertial force and
inertial mass.
>
> Inertial motion is just the motion of a body when no external agency acts
upon it. The definition of inertial motion is that there is no mechanism.
I'm fine with that
> In Newtonian mechanics we may distinguish between inertial force and
impressed force. A force is anything which causes an acceleration according
to the second law; an impressed force implies the action of one body on
another. An inertial force is caused not by the action of one body on
another but by the choice of reference frame, like the coriolis and
centrifugal forces in rotating frames, and g-forces in accelerated frames.
So again, the mechanism of an inertial force is that there is no mechanism.
Inertial force is an illusiary action produced by the motion of one's
reference frame, while the motion of the reference frame is simply the
product of ordinary impressed forces on ones environment.
Ok, that too.
> Inertial mass is described as the resistance to acceleration per amount
of impressed force. There is again no mechanism for it in standard physics,
because it is a fundamental notion on which other ideas our based.
Does that mean we don't know, or we don't ask?
> The effect of inertia is summarised in the law of conservation of
momentum. The origin of conservation of momentum is that the laws of physics
are everywhere the same. Conservation of momentum is a principle which makes
this possible as mass moves from A to B, or interacts at C.
This sounds to me like arguing backwards - like saying there is a law that
says we must drive on one side of the road because, if we didn't, vehicles
would crash into each other. In spite of what I said earlier, in
investigatory practice I think we can treat Nature as if it didn't
anticipate problems and define laws on that basis. Instead of saying "if
there wasn't inertia, conservation of momentum wouldn't work", one should
say, "there is inertia, which makes conservation of momentum work, but where
does inertia come from?"
I'm probably wrong, but I can't help feeling that there must be a fairly
simple explanation based on SR... (excuse the loose terminology in the
following musings):
1) To speak of the inertia of a relatively stationary object is meaningless.
2) Practically speaking, the inertia of an object increases with its
relative speed.
3) The energy-equivalent of the so-called "mass increase" of an accelerated
massive object (even at everyday speeds) is its kinetic energy.
4) If there were no requirement by SR for the mass-(or inertia-, or
momenergy-)increase, we would see no inertia.
5) The effects described by SR are basically a set of perspective
effects....
6) These perspective effects originate in the shape of spacetime....
.... Anyone like to wrap it all up?
> I could tell you that if particle interactions are discrete inertial mass
is a measure of the time between interactions. If, for example, the
interactions of a muon are identical to, but much less frequent than, the
interactions of an electron then we would expect to observe a
proportionately smaller change in motion from the same stimulus. But I must
emphasise that is not standard
physics.
but it does sounds a little like Haisch & Rueda's!
Thanks,
Graham Rounce
G Rounce
toothed wheels don't necessarily come into it! It's just that I've learned
that asking questions using "how?" or "why?" provokes no end of semantic
discussions before getting to the meat...
Yes, it is a pity there's no companion book to the one you mention - because
I find it very hard to accept that descriptive equations really count as
"explanations" - which I take it is what you are saying? Sorry, but I want
to take it all the way back, and to understand it all the way, too!
"John Baez" <ba...@galaxy.ucr.edu> wrote in message
news:9oqm27$8kv$1...@glue.ucr.edu...
> >I would say that there *is no* known mechanism of inertia. It always
seems to be something built in from the start of any viable physical theory.
>
> As Norbert Dragon so eloquently put it
memorably, anyway :-)
> , current physics has no mechanism with toothed wheels to explain inertia.
It's built in from the start, in somewhat different ways for the various
theories I listed.
> I guess the physics course Graham Rounce was secretly asking for would
have to include a history of the notion of "mechanism", including how this
notion fell into disrepute with the failure of the "mechanical models" for
electromagnetism due to Kelvin, the early Maxwell, and others.
Secretly??
> This would make it clear why current theories *avoid* seeking a
"mechanism" for inertia
In the absence of such a course - Why Do they? They don't seem to baulk at
anything else, including the creation of the universe - why is inertia
different? More interestingly, for what other features are searches for
"mechanisms" avoided?
Thanks again,
Graham Rounce
j...@itasoftware.com
> I mean, why does it take more energy to accelerate a lead ball than
> a wooden one? Or any energy? Of course, if it didn't, the
> slightest touch would cause an object to go zooming off at the speed
> of light. Would there then be no such thing as relative motion? I
> don't know what principles dictated the kind of universe that got
> created, but I'd bet that consistency was one of them (perhaps the
> main, or even the only one). Maybe making a consistent universe in
> which everything moved at c was just too difficult... (or maybe too
> trivial, not giving rise to intelligent beings?)
You're on the right track.
If you start with the assumption that the laws of physics don't depend
on where you are, you can show (with a bunch of variational calculus)
that momentum must be conserved. Or in other words, the principle of
conservation of momentum and the principle of translational invariance
(laws of physics not depending on location) turn out to be the exact
same thing.
If you start with the assumption that the laws of physics don't depend
on *when* you perform an experiment, you can show (more variational
calculus) that *energy* must be conserved.
If momentum and energy are conserved, then the amount of force
accelerate an object is going to depend on its momentum.
Now we have two more questions: Why does lead have more momentum than
wood? If you believe in atoms, electrons, protons, and neutrons, then
you might argue that there is simply more of them to move given
equivalent volumes of lead and wood. This is the easy question.
The hard question is why does *anything* have momentum? (i.e. is
there some reason that momentum is not exactly zero for some
things?) I don't think anyone knows this.
> I'm probably wrong, but I can't help feeling that there must be a fairly
> simple explanation based on SR... (excuse the loose terminology in the
> following musings):
>
> 1) To speak of the inertia of a relatively stationary object is meaningless.
No, it is meaningful. Some things are harder to get moving than
others, and this is the origin of the idea of inertia.
Remember that `stationary' describes the relationship between an
object and a frame of reference. Your stationary object may be moving
quite fast in my reference frame.
> 2) Practically speaking, the inertia of an object increases with its
> relative speed.
No, inertia seems to be an intrinsic property of an object. I think
you want the word `momentum'.
> 3) The energy-equivalent of the so-called "mass increase" of an
> accelerated massive object (even at everyday speeds) is its
> kinetic energy.
Not exactly. The kinetic energy of an object is proportional to its
mass and its velocity. At everyday speeds, adding kinetic energy to
an object will increase its velocity. But when the speed approaches
C, adding kinetic energy has little effect on velocity, but it has a
huge effect on the mass.
> 4) If there were no requirement by SR for the mass-(or inertia-, or
> momenergy-)increase, we would see no inertia.
Well, a theory (such as SR) could require anything, but that doesn't
mean we would see it! Inertia is a phenomenon.
> 5) The effects described by SR are basically a set of perspective
> effects....
No (at least not in the sense that they are simply `optical
illusions'). The effects are very real and measurable! SR tells us
what to expect when we try to measure things in moving frames of
reference. (Actually, so does gallilean relativity, but SR does a
better job at high speed)
> 6) These perspective effects originate in the shape of spacetime....
Not really. SR is to some extent a fix-up of Newton's laws. Newton's
laws as originally stated aren't invariant under co-ordinate
transformation. What this implies is that Newton's laws of physics
would yield the correct answers only if experiments were performed in
a particular non-moving reference frame. But you and I could be
moving relative to each other, perform the same experiment and get the
same result.
If we start with the assumption that the laws of physics are
independent of relative motion, then with a bit of math we find that
Newton's laws are off by a little when the relative motion is fast
(and that Galilean relativity isn't quite correct either).
John Baez
G Rounce <joann...@gallatinriver.net> wrote:
>What I really mean by "mechanism" is the tracing back of cause and effect -
>toothed wheels don't necessarily come into it! It's just that I've learned
>that asking questions using "how?" or "why?" provokes no end of semantic
>discussions before getting to the meat...
The word "mechanism" does this too, as you now know.
Given that inertia is already thoroughly integrated into our existing
theories, you'll likely make more regress than progress by trying to
find a "mechanism" for it. For example, in their attempts to explain
inertia, Haisch and Rueda constructed what amounts to a high-tech
quantum-field-theoretic Rube Goldberg machine full of toothed wheels.
And it doesn't even work!
It's papers like that which led to item 16 on the crackpot index:
http://math.ucr.edu/home/baez/crackpot.html
Ralph E. Frost
> In article <9oqtl...@enews2.newsguy.com>,
> G Rounce <joann...@gallatinriver.net> wrote:
>
> >What I really mean by "mechanism" is the tracing back of cause and
effect -
> >toothed wheels don't necessarily come into it! It's just that I've
learned
> >that asking questions using "how?" or "why?" provokes no end of semantic
> >discussions before getting to the meat...
>
> The word "mechanism" does this too, as you now know.
>
> Given that inertia is already thoroughly integrated into our existing
> theories,
Just curious. Which version of the Standard Model are you referring to?
--
======================================================================
Kevin Scaldeferri Calif. Institute of Technology
The INTJ's Prayer:
Lord keep me open to others' ideas, WRONG though they may be.
Kevin A. Scaldeferri
difficulties with software that doesn't actually work as documented.
Please bear with me.
G Rounce
> "G Rounce" <joann...@gallatinriver.net> writes:
> > I'm probably wrong, but I can't help feeling that there must be a fairly
> > terminology in the following musings):
> > 1) To speak of the inertia of a relatively stationary object is
> > meaningless.
> No, it is meaningful. Some things are harder to get moving than others,
> and this is the origin of the idea of inertia.
Ok, what I meant was that you can't measure the inertia of something without
moving it, or else changing its velocity..
> > 2) Practically speaking, the inertia of an object increases with its
> > relative speed.
> No, inertia seems to be an intrinsic property of an object. I think you
> want the word `momentum'.
But as you get its speed nearer to c, it takes a hell of a lot more pushing
to increase it further. Isn't that the same as its inertia effectively
increasing?
> > 3) The energy-equivalent of the so-called "mass increase" of an
> > accelerated massive object (even at everyday speeds) is its kinetic energy.
> Not exactly. The kinetic energy of an object is proportional to its mass
> and its velocity. At everyday speeds, adding kinetic energy to an object
> will increase its velocity.
(...and the amount of energy to be added is precisely the energy-equivalent
of the so-called "mass-increase"......)
> But when the speed approaches C, adding kinetic energy has little effect
> on velocity, but it has a huge effect on the mass.
I thought that by definition kinetic energy is the amount of energy you have
to put into something to make it move at a certain speed. At very high
(relative) speeds, this is rather more than 1/2 * mv^2, which imo is a
better way of looking at it than the so-called mass-(or momenergy) increase?
Why does it work like that? I'd like to know! This, for me, is the basic
question - why the kinetic energy of an object has no maximum, but a minumum
of 1/2 * mv^2?
> > 4) If there were no requirement by SR for the mass-(or inertia-, or
> > momenergy-)increase, we would see no inertia.
> Well, a theory (such as SR) could require anything, but that doesn't mean
> we would see it! Inertia is a phenomenon.
Yes, I have difficulty with the phrasing of that.
Maybe: "If there were no observed mass-(or inertia-, or momenergy-)increase,
we would see no inertia."?
> > 5) The effects described by SR are basically a set of perspective
> > effects....
> No (at least not in the sense that they are simply `optical illusions').
> The effects are very real and measurable! <snip>
No, not optical illusions, but certainly distortions. The best judge of
whether anything really changes for an object is the object itself. Nothing
happens to its mass, length,. how far back in one's seat one is pushed by a
certain setting on the throttle, etc etc, in the object's own frame. What
we see might be just as valid as what anyone else sees, but it can't be as
"real", or "true", as the object's own view?
> > 6) These perspective effects originate in the shape of spacetime....
> Not really <snip>
Then how? I need some more time and reading to assimilate another poster's
(Tom Roberts?) explanation about spacetime being hyperbolic, but I thought
that was the source of it all?
Thanks,
Graham Rounce
[Moderator's note: reformatted for legibility. Please keep your line
lengths below 78 characters -- KS]
G Rounce
> It's papers like [Haisch & Rueda's] which led to item 16 on the crackpot
index:
(10 points for arguing that while a current well-established theory predicts
phenomena correctly, it doesn't explain "why" they occur, or fails to
provide a "mechanism"}
And here's me thinking I was safe because I don't use a load of capital
letters! For my peace of mind I won't go back and check the other items,
but that I must admit that that one fits me to a T.
If I asked someone how a car works, would I not be justified in feeling
short-changed if I was given a set of equations relating the acceleration to
the distance of the pedal from the floor, and nothing more?
Graham Rounce
Charles Francis
<joann...@gallatinriver.net> writes:
>"Charles Francis" <cha...@clef.demon.co.uk> wrote in message
>news:6SXtw2A8...@clef.demon.co.uk...
>>Inertial mass is described as the resistance to acceleration per
>>amount of impressed force. There is again no mechanism for it in
>>standard physics, because it is a fundamental notion on which other
>>ideas our based.
>Does that mean we don't know, or we don't ask?
It means we don't know. There are some ideas that a unification theory
might tell us why we observe the particular masses which we observe in
nature, but I think we are a very long way from answering this question,
and I see little point in asking further. I think we will need a
unification theory before we can have any further insight into the
matter.
>>The effect of inertia is summarised in the law of conservation of
>>momentum. The origin of conservation of momentum is that the laws of
>>physics are everywhere the same. Conservation of momentum is a
>>principle which makes this possible as mass moves from A to B, or
>>interacts at C.
>This sounds to me like arguing backwards - like saying there is a law that
>says we must drive on one side of the road because, if we didn't, vehicles
>would crash into each other. In spite of what I said earlier, in
>investigatory practice I think we can treat Nature as if it didn't
>anticipate problems and define laws on that basis. Instead of saying "if
>there wasn't inertia, conservation of momentum wouldn't work", one should
>say, "there is inertia, which makes conservation of momentum work, but where
>does inertia come from?"
No. The way this answer works is that conservation of momentum makes
inertia work, and we know that conservation of momentum comes from the
homogeneity of physical law.
>I'm probably wrong, but I can't help feeling that there must be a fairly
>simple explanation based on SR... (excuse the loose terminology in the
>following musings):
The simplest way to I know to look at it is to look at an interaction
between the wave functions of two particles. For simplicity I will use
momentum states p and q, and I will make the notation look one
dimensional, although it isn't really. This is the essence of the
argument, to do it properly you really have to write it all out, so you
can see that anything I've not mentioned doesn't change the core
argument. And you also have to do it with different numbers of particles
in the initial and final states. The initial wave functions are
e^-ipx and e^-iqx
After interaction the wave functions become
e^-ip'x and e^-iq'x
and you form the inner product between the initial and final states to
find the probability of going from one to the other. This gives you a
factor like
e^ip'x e^iq'x e^-ipx e^-iqx
The homogeneity of space is represented by integrating an interaction
density which is uniform in space. This allows you collect together the
all the exponentials under the integral, and the formula contains the
factor
integral_all_space dx e^ip'x e^iq'x e^-ipx e^-iqx
but this is a delta function equal to
delta (p+q-p'-q')
So for a non zero probability we have
p+q=p'+q'
>1) To speak of the inertia of a relatively stationary object is meaningless.
>2) Practically speaking, the inertia of an object increases with its
>relative speed.
It would be better to use the word momentum for that quantity.
>3) The energy-equivalent of the so-called "mass increase" of an accelerated
>massive object (even at everyday speeds) is its kinetic energy.
>4) If there were no requirement by SR for the mass-(or inertia-, or
>momenergy-)increase, we would see no inertia.
>5) The effects described by SR are basically a set of perspective
>effects....
>6) These perspective effects originate in the shape of spacetime....
The shape of space-time complicates the above argument, because the
integral to get a delta function was taken over flat space.
>> I could tell you that if particle interactions are discrete inertial
>> mass is a measure of the time between interactions. If, for example,
>> the interactions of a muon are identical to, but much less frequent
>> than, the interactions of an electron then we would expect to observe
>> a proportionately smaller change in motion from the same stimulus.
>> But I must emphasise that is not standard physics.
>but it does sounds a little like Haisch & Rueda's!
To me it sounds completely different.
Regards
--
Charles Francis
A.J. Tolland
> dra...@itp.uni-hannover.de (Norbert Dragon) says...
>
> >Whenever a quantum field theory contains interacting spin 2 particles
> >then for consistency (absence of negative probabilities) there can
> >be only one kind of particles, gravitons. Their coupling is highly
> >restricted: they can couple only to the energy-momentum tensor T^mn
>
> Do you know of a reference for that proof?
I don't know of any reference, but maybe I can say something
helpful. I'm fairly sure that "spin-2 particles couple consistently only
to gravity" is actually a folk theorem, accepted wisdom as opposed to a
result written up for the Physical Review. Fortunately, we have a
powerful tool at our disposal; there is a folk meta-theorem which states
that "All folk theorems are proved using the Coleman-Mandula theorem".
So let's review: We've got a massless spin-2. This thing carries
two Lorentz indices. We want it to be in an irrep so we had make the
indices symmetric. The basic problem with massless particles is that they
don't have quite enough polarizations--specifically, they lack a
longitudinal polarization--so to preserve local Lorentz invariance, we
need to "hide" this defect by coupling the potentials for these fields to
a conserved current.
We want to contract the Lorentz indices, so we need a tensor
current. It might as well be symmetric, since our irreps have symmetric
Lorentz indices. Now the question is: How many conserved tensor currents
do we know of. Well, there's one obvious one, the energy-momentum tensor.
The fun thing about conserved currents is that you can integrate their
0-th component over a spacelike surface to get a conserved charge. For
symmetric tensors, it's helpful to regard the tensor as a vector of
vectors; this makes it easy to see that the conserved charge built from a
tensor is actually a vector. In this case, it's the energy-momentum
vector P_u.
Now Coleman-Mandula come into play. The theorem states that the
only possible Lie algebra of symmetries of an interacting relativistic QFT
(with certain additional assumptions *) is generated by (a) the generators
of the Poincare group and (b) various internal symmetry generators which
know nothing about momentum or spin. So now if we've got another
conserved tensor current, we can integrate it, and get another vector
which commutes with the Hamiltonian. Now we've run afoul of the
Coleman-Mandula theorem, and we must conclude that our theory is
non-interacting.
* The assumptions (from Weinberg, Vol. III):
1) Any bounded part of the spectrum of the Hamiltonian is finite
2) Any two particle state undergoes reactions at almost all energies
(e.g. no lines of fixed points)
3) two-body scattering amplitudes are almost always analytic
--A.J.
Steve Carlip
>>Whenever a quantum field theory contains interacting spin 2 particles
>>then for consistency (absence of negative probabilities) there can
>>be only one kind of particles, gravitons. Their coupling is highly
>>restricted: they can couple only to the energy-momentum tensor T^mn
>>and the energy-momentum tensor is necessarily conserved
>>D_m T^mn = 0
> Do you know of a reference for that proof?
Boulware and Deser, Ann. Phys. (NY) 89 (1975) 193. This was based
on earlier work by Weinberg, Phys. Rev. 138 (1965) B988 and B1049.
For the classical version, try Deser, Gen. Rel. Grav. 1 (1970) 9 and
Class. Quant. Grav. 4 (1987) L99.
You might also look at Boulanger et al., Nucl.Phys. B597 (2001) 127,
hep-th/0007220, for a very nice (classical) demonstration of the
impossibility of multiple interacting ``gravitons.''
Steve Carlip
j...@itasoftware.com
> <j...@itasoftware.com> wrote in message news:3d58ll...@itasoftware.com...
> > "G Rounce" <joann...@gallatinriver.net> writes:
> > > I'm probably wrong, but I can't help feeling that there must be a fairly
> > > simple explanation [for inertia based on SR... (excuse the loose
> > > terminology in the following musings):
>
> > > 1) To speak of the inertia of a relatively stationary object is
> > > meaningless.
> > No, it is meaningful. Some things are harder to get moving than others,
> > and this is the origin of the idea of inertia.
>
> Ok, what I meant was that you can't measure the inertia of something without
> moving it, or else changing its velocity..
With Newtonian mechanics, this is true, and it is an amazing
coincidence that the inertia of an object is proportional to its
mass. With GR, however, you can measure the inertia of an object by
looking at the curvature of space-time in the vicinity of the object
(measure the gravitational force).
> > > 2) Practically speaking, the inertia of an object increases with its
> > > relative speed.
> > No, inertia seems to be an intrinsic property of an object. I think you
> > want the word `momentum'.
>
> But as you get its speed nearer to c, it takes a hell of a lot more pushing
> to increase it further. Isn't that the same as its inertia effectively
> increasing?
There are all sorts of difficulties with measuring things at a high
relative speed. You will in fact measure an increase in the mass of
the object and therefore its inertia. However, the `rest mass' of an
object appears to be intrinsic to the object, and if you insist on
measuring a moving object, you can apply the appropriate corrections
to discover the rest mass.
> > > 3) The energy-equivalent of the so-called "mass increase" of an
> > > accelerated massive object (even at everyday speeds) is its kinetic energy.
> > Not exactly. The kinetic energy of an object is proportional to its mass
> > and its velocity. At everyday speeds, adding kinetic energy to an object
> > will increase its velocity.
>
> (...and the amount of energy to be added is precisely the energy-equivalent
> of the so-called "mass-increase"......)
Right.
> > But when the speed approaches C, adding kinetic energy has little effect
> > on velocity, but it has a huge effect on the mass.
>
> I thought that by definition kinetic energy is the amount of energy you have
> to put into something to make it move at a certain speed. At very high
> (relative) speeds, this is rather more than 1/2 * mv^2, which imo is a
> better way of looking at it than the so-called mass-(or momenergy)
> increase?
The actual equation is E = m c^2 / sqrt (1 - v^2/c^2), which if you
expand it gives E = mc^2 + 1/2 m v^2 + 3/8 mv^4/c^2 + ...
where the terms beyond the first one are the kinetic energy.
> Why does it work like that?
I guess I'm not sure what you are asking for here. The equation works
that way because it needs to be invariant under Lorentz
transformations. We have to use Lorentz transformations if we want
our theory of physics to be valid in moving reference frames.
> I'd like to know! This, for me, is the basic
> question - why the kinetic energy of an object has no maximum, but a minumum
> of 1/2 * mv^2?
The kinetic energy of an object has a minimum of 0 at v=0.
> > > 4) If there were no requirement by SR for the mass-(or inertia-, or
> > > momenergy-)increase, we would see no inertia.
> > Well, a theory (such as SR) could require anything, but that doesn't mean
> > we would see it! Inertia is a phenomenon.
>
> Yes, I have difficulty with the phrasing of that.
> Maybe: "If there were no observed mass-(or inertia-, or momenergy-)increase,
> we would see no inertia."?
Ok.
> > > 5) The effects described by SR are basically a set of perspective
> > > effects....
> > No (at least not in the sense that they are simply `optical illusions').
> > The effects are very real and measurable! <snip>
>
> No, not optical illusions, but certainly distortions. The best judge of
> whether anything really changes for an object is the object itself. Nothing
> happens to its mass, length,. how far back in one's seat one is pushed by a
> certain setting on the throttle, etc etc, in the object's own frame. What
> we see might be just as valid as what anyone else sees, but it can't be as
> "real", or "true", as the object's own view?
No, that's what relativity refutes! It relates measurements made in
one frame of reference to those made in different frame of reference.
It shows how to correct for the effect of choosing a reference frame.
Thus the reference frame attached to the object itself is no more
valid than one attached to the observer.