Re: Feeling Acceleration

[John Mallinckrodt <ajmallinckro@CSUPomona.Edu>]

On Mon, 7 Apr 1997, A. R. Marlow wrote:

> Am I the only one who finds a problem with the term "feeling acceleration"
> that has been so freely used recently on this list?  I cannot believe that
> I have any sense mechanisms for accelerations, whether in my glutei maximi
> or my inner ears  --  if I did have such mechanisms, they would 
> continually be triggered by all the accelerations I am continually
> subjected to.  Acceleration is a purely kinematical notion, and is totally
> meaningless until you specify a particular reference frame.  I am always
> accelerating relative to someone's reference frame  --  why do I not feel
> that if I have sensors for accelerations?  

I don't have too much trouble with the above; I think most respondents
here have meant to say something like, "We sense internal forces or
pressures that are generated in response to the forces that cause us to
accelerate."  This is why I prefer to say simply, "We experience
acceleration."

On the other hand, acceleration is not quite as arbitrary as you imply. 
The principle of equivalence teaches us that there are preferred reference
frames--those in which there are no local gravitational fields.  We
experience acceleration whenever we are not in one of those reference
frames. 

> The fact is we ONLY have
> sensors for the dynamical quantity pressure = force/area, and such sensors
> are distributed throughout our bodies.  As discovered by Newton and 
> confirmed by Einstein, ONLY relative to inertial frames of reference do
> accelerations have any correspondence with the forces we feel.

Well...  Newton's inertial reference frames were "global" (i.e., they
could be extended to fill all of space) and were based upon the motion of
ideal, "force-free" objects in the deep voids of space.  Thus, for Newton,
to the extent that we can ignore rotation and revolution of the earth, we
are in an inertial frame when we stand upon its surface.  For Newton,
local gravity is a real force.  Unfortunately, the correspondence between
acceleration with respect to a Newtonian inertial frame and our sensations
is very peculiar.  For instance, the sensations we experience when
accelerating upward at 2 m/s^2 with respect to the earth's surface are far
from double what we experience when we accelerate at 1 m/s^2.  The ratio
is more like (9.8+2)/(9.8+1) = 1.093.

On the other hand, in accord with the principle of equivalence, Einstein's
inertial frames are always free of local gravitational effects; they are
based on the motion of "freely falling" objects.  Because of the
gravitational effect of matter, which causes freely falling frames in one
location to accelerate with respect to freely falling frames in a
different location (the "tidal effect"), Einstein's inertial frames are
necessarily "local" (i.e., they are limited to a region small enough that
the tidal effect is negligible.)  Strictly speaking they have no extent
whatsoever.  For Einstein, local gravity is always the result of
acceleration with respect to local inertial frames.  Now the
correspondence between acceleration with respect to inertial frames and
our sensations is simple; when our acceleration is twice as great we
"experience" twice the sensation.

> Why should
> we say we feel accelerations when it is actually only forces that we feel?
> I can hardly think of a more misleading or confusing practice.  We seem
> to be mesmerized by the misnomer "accelerometer" for an instrument that
> registers zero unless it is acted upon by a force!  It is high time we
> cleared up such silly confusions.

Accelerometers are nonsensical devices indeed within the framework of
Newtonian gravitation.  But they are simple to understand and very useful
within the framework of a theory of gravitation based upon the principle
of equivalence like GR. 

John
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