Re: How do you know that acceleration is absolute? <eom>


"Jack Martinelli" <jack@xxxxxxxxxxxxxx> wrote in message news:DICde.3630$HL2.2173@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
>
> "Dirk Van de moortel" <dirkvandemoortel@xxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote
> in message news:AXlde.4786$W16.4542@xxxxxxxxxxxxxxxxxxx
> >
> > "Jack Martinelli" <jack@xxxxxxxxxxxxxx> wrote in message
> > news:Wzdde.3722$GQ5.2825@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> >>
> >> "Dirk Van de moortel" <dirkvandemoortel@xxxxxxxxxxxxxxxxxxxxxxxxxxx>
> >> wrote
> >> in message news:Na4de.78443$Gx2.5104773@xxxxxxxxxxxxxxxxxxxxxxxx
> >> >
> >> > "Jack Martinelli" <jack@xxxxxxxxxxxxxx> wrote in message
> >> > news:7CZce.2510$HL2.42@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> >> >>
> >> >> "Dirk Van de moortel" <dirkvandemoortel@xxxxxxxxxxxxxxxxxxxxxxxxxxx>
> >> >> wrote
> >> >> in message news:7DHce.77345$oT7.5041223@xxxxxxxxxxxxxxxxxxxxxxxx
> >> >> >
> >> >> > "Jack Martinelli" <jack@xxxxxxxxxxxxxx> wrote in message
> >> >> > news:Yqyce.1925$HL2.245@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> >> >> >>
> >> >> >
> >> >> > Let's work in one dimension only.
> >> >> >
> >> >> > Suppose a particle is described in one inertial frame S as
> >> >> > a function x(t) and in another frame S' as a function x'(t).
> >> >> > Suppose frame S' is moving with a constant relative
> >> >> > velocity u w.r.t. frame S.
> >> >> > In Galilean Relativity you have the relation between the
> >> >> > distance coordinates given by
> >> >> > x' = x - u t
> >> >> >
> >> >> > The velocity v of the particle in the two frames is then given by
> >> >> > in S: v = dx/dt
> >> >> > in S': v' = dx'/dt = d(x- u t)/dt = dx/dt - u = v - u
> >> >> > So you see that velocity of the particle depends on the frame:
> >> >> > v' = v - u
> >> >> > i.o.w. velocity is "relative".
> >> >> >
> >> >> > The accerelation however:
> >> >> > in S: a = dv/dt
> >> >> > in S': a' = dv'/dt = d(v- u)/dt = dv/dt = a
> >> >> > So you see that acceleration of the particle does not depend
> >> >> > on the frame:
> >> >> > a' = a
> >> >> > i.o.w. acceleration is "absolute".
> >>
> >> And last night I realized that you can also write:
> >>
> >> v' = v - bt // where b is the acceleration of the primed frame (S')
> >> with
> >> respect to a "stationary frame".
> >>
> >> Then you can write:
> >>
> >> in: S: a = dv/dt
> >> in S': a' = dv'/dt = d(v - bt)/dt = a - b
> >>
> >> Which means acceleration _might_ be relative -- at least in
> >> the Galilean sense.
> >
> > Sure, but then S' would not be an inertial frame anymore.
> > Of course, you can transform the acceleration of the particle
> > to any value you want, and like I showed, even to zero, in
> > the extreme case of "riding with it". But in each case you
> > would "feel" (-see below-) your own acceleration and be
> > forced to take that into account when contemplating the
> > "absoluteness" of the particle's acceleration that you are
> > measuring.
>
> If you _feel_ the acceleration how do you know that its the acceleration
> that you're feeling & not your own inertia? If we're talking acceleration,
> do we really need to bring mass into the picture?
>
> >
> >> >> >
> >> >> > In special relativity it is a bit more complicated since S
> >> >> > describes the particle as x(t) and S' describes it as x'(t').
> >> >> > Each frame uses its own 'time'.
> >> >> > Supposing a relative velocity u between the frames again,
> >> >> > the coordinate transformation is now given by the equations
> >> >> > x' = g (x - u t)
> >> >> > t' = g (t - u x/c^2)
> >> >> > where
> >> >> > g = 1 /sqrt(1-u^2/c^2)
> >> >> >
> >> >> > A similar but bit more complicated exercise as before gives
> >> >> > the result for velocity of the particle:
> >> >> > v' = (v - u)/(1 - u v/c^2)
> >> >> > and for the acceleration:
> >> >> > a' = a / ( g (1- u v/c^2) )^3
> >> >> >
> >> >> > The difference with Galilean relativity is of course that it is
> >> >> > not true that
> >> >> > a' = a
> >> >> > but you can still say that the accelaration is absolute in the
> >> >> > sense that if it is non-zero in one frame, it is also nonzero
> >> >> > in every other frame, i.o.w. you cannot transform it away
> >> >> > by choosing another inertial frame.
> >> >>
> >> >> Why another inertial frame? Why not another accelerating frame?
> >> >
> >> > Inertial frames are easier to make the calculations and
> >> > show a point.
> >>
> >> agreed
> >>
> >> > That's why I used two of them, and a
> >> > particle in one dimensional motion along the line of
> >> > relative motion of the frames.
> >> > But sure, take the most extreme case where you would
> >> > sit on the accelerated particle itself. You will find that its
> >> > coordinates are pretty constant, so as seen in your own
> >> > frame, it would have no acceleration.
> >>
> >> And that makes sense.
> >>
> >> > But then *you*
> >> > would fee the proper acceleration yourself (like we
> >> > say, as measured in the momentarily comoving inertial
> >> > frame at each point of your worldline), and again be
> >> > forced to conclude that the particle is 'absolutely'
> >> > accelerated together with yourself.
> >>
> >> But aren't you assuming that riding an electron is just like riding a
> >> rocket. And besides what _I_ feel & and and an electron _feels_ and what
> >> coordinates are... well, I'm not sure how feeling and coordinates are
> >> related. Wouldn't you prefer to stick to clocks and rulers?
> >
> > With "feeling" I refer to "measuring your proper acceleration",
> > where proper acceleration is the second derivative of
> > coordinate distance in the momentarily comoving inertial
> > frame w.r.t. proper time. Conceptually this can be measured
> > with clocks and rulers, or much simpler, with radar, and
> > practically it can be measured with masses and springs or
> > with a set of gyroscopes. Since you can "feel" it, I call it
> > absolute.
>
> Labels are useful, but doesn't the word "absolute" need some kind of
> prototype. IOW, without a "gold standard" for the word "absolute" how would
> you know what "absolute" really means? OTOH, if you make "feeling" a part
> of the criteria, aren't you making the word subjective?

But I just *explained* how I define "feeling".
It can be objectively measured.

>
> BTW, to assign a magnitude to an acceleration, you can choose an
> "acceleration ruler". I.e., choose a length that is static with respect to
> the acceleration (or any other dimension you like) you want to measure.
> Then the magnitude for the acceleration can be assigned a value. Like so...
>
> a = (target acceleration)/(reference acceleration)
>
> IOW, the magnitude depends on (is relative to) a reference. Of course you
> have to be careful here since changing "acceleration rulers" doesn't change
> the target's acceleration only the resulting number, (really just a label).
> There is a problem though, how do you know that the resulting magnitude is
> not an acceleration density? It does resemble a density an awful lot.

Acceleration is measured as the second derivative of
a distance w.r.t. time. When you have a ruler and a
clock you are in business. Of course the result is
calibrated on the ruler and the clock.

>
> >
> >>
> >> > All this is of course
> >> > in the context of Galilean and special relativity.
> >> > In the context of general relativity gravity is modeled as
> >> > spacetime curvature, and "acceleration due to gravity"
> >> > is taken as the 'natural way'.
> >>
> >> Galacitic recession/acceleration is inertial too. right?
> >
> > If you mean the sun's rotation about the galactic centre,
> > no, that is not inertial, *unless* you consider a small enough
> > scale in space and time, then it is "locally inertial".
>
> I mean that the universe is expanding and that its expansion is accelerating
> with respect to our clocks and rulers. This acceleration couldn't be
> absolute could it? And if not, don't you then have the one example that
> kills the generalization "acceleration is absolute".

You can't describe the "expanding universe" in the context
of galilean or special relativity, so you can't describe it in terms
of locally measured velocities or accelerations.

>
> >>
> >> > In such a natural free-falling
> >> > frame (that used to be considered as being accelerated,
> >> > but that is now considered as an inertial frame, provided
> >> > it is sufficiently small in space and time), you could say
> >> > that a particle falling with you has zero acceleration.
> >>
> >> You say that as if it were wrong.
> >
> > That was certainly not the intention :-)
> > The particle with you has zero acceleration in your frame.
> > Obviously you can imagine frames where it doesn not have
> > zero acceleration - but again, those frames would not be
> > inertial. The absoluteness remains, provided one labels
> > "being in an inertial frame" or more generally "being in a
> > free-fall frame" or "feeling no acceleration" as absolute.
>
> I'm beginning to wonder if it wouldn't be better to say that inertial &
> non-inertial frames are characteristically different and leave it at that?

Why would we leave it at that? We can precisely and
quantitatively measure and express the difference between
being in an inertial and in a non-inertial frame. It is one the
most fundamental things we actually *can* measure. It is
what helped trigger the development of general reltivity.

> And the reason for this is that because of the connotations carried by the
> word "absolute". For me, when I read the word, I'm thinking absolute unit
> of length. I.e., why shouldn't I choose accelerated units as the best
> choice for "true static" units of length? Aside from practical
> considerations & if acceleration is absolute -- why not? We could choose
> the distance between two galaxies as a static unit of length. But then if
> you did that, our material rulers would have to be shrinking wrt this
> standard and our clocks would be slowing wrt to galactic time? But I don't
> think you're heading in that direction. I'm getting the sense that you want
> to attach the word "absolute" to a particular set of observables & not to
> the classical notion of absolute. No?
>
> >
> >>
> >> > But then again you and the particle are following a geodesic
> >> > in a curved spacetime that is shaped by the mass
> >> > distribution, which is, since you obviously can't transform
> >> > a planet away, nicely absolute again :-)
> >>
> >> Sorry to be a pain, but I don't see how the presence of a planet (or
> >> curvature) makes acceleration absolute?
> >
> > We consider as absolute the presence and existence of a planet,
> > so we consider as absolute the curvature of spacetime.
>
> If, in fact, particles are not spatially extended, then this makes sense.
> But do you know, for a fact, that a particle's field is not just the
> spatial extent of the particle? And that there really isn't a special one
> of a kind container existent, - the "space-time" existent?

Sorry, I don't understand this.

>
> It seems to me that particle & field interact but to say that mass &
> space-time interact is metaphysical -- isn't it?

It is precisely and quantitatively expressed in the equations
of general relativity, so I think we can call that physical.

> Or at least provisional --
> I.e., "Lets say this is so until something better comes along."

But of course. That's the whole idea of science.

>
> > And so
> > we consider as absolute the acceleration of a free-falling observer
> > as measured in another non-free falling (non inertial) frame in
> > which the observer "feels an acceration" - or a force exerted
> > by the chair on which he is sitting.
>
> I understand what you're saying. And it sounds like you too understand that
> _you_ are choosing the criteria for "absolute".

Of course. "_We_" and how we measure and define
things, is all we've got - as far as I know.

> And that other phenomena
> which show these same criteria can also be considered absolute, but the
> sense of the word "absolute" as it's used can't be made quantitative, as we
> would expect in a classical context. E.g., as we would in the case of
> Galilean relativity.

Again, I consider the presence of a mass as absolute.
General relativity quantitatively describes how this mass
influences spacetime and the way other masses behave in it
in a way that is independent of any coordinate system. That
is what I call absolute, and it nicely fits together with the
limiting cases of special and galilean relativities in which it can
be mathematically expressed with increasing ease and
transparency.

Dirk Vdm


.

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