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Re: [Phys-L] More on Gravity Waves



1) John wrote (at the end of this post) that "The radiative field is purely transverse." What does he mean by this?

2) Common waves are usually characterized as longitudinal or transverse. I say that gravitational waves are longitudinal.

3) How do I justify this? Suppose the spheres are treated as point particles, and that the line between them (the direction of wave propagation) is our x axis.

Then we can say that directions of gravitational force field vectors F coincide with the direction of propagation.

4) If the M (the source of the field) is forced to oscillate along the x axis then the m (the detector) will also be oscillating along this axis.

Ludwik
===================================

On Apr 25, 2016, at 3:19 PM, John Denker wrote:

On 04/25/2016 10:48 AM, Ludwik Kowalski wrote:
Suppose two balls (Masses M and m) are suspended vertically at the
same elevation.

Suppose this happens in a room without air, in a stable and rigid
building, and that M>>m.

Suppose the ball M is pushed suddenly toward the ball m (along the
line connecting the two centers of mass).

OK.

I predict that m will also be disturbed, practically at the same time
and along the same direction.

Cavendish, who measured the gravitational constant G, would probably
agree with my prediction.

The effect is real, and examples have been known for a long
time, even before Cavendish came along. Newton calculated
the size of the effect. It's called the /tide/. (Actually
it's the /tidal stress/ which is not quite the same as the
observed tide, but let's not worry about that just yet.)
The tide is easy to observe if you spend a few hours at the
beach.

1) What is wrong with saying that propagations of disturbances of
this kind are examples of gravitational waves?

Yes, I know that the term "gravitational wave" is already used for
something completely different

Technically, that's the correct answer.
a) The aforementioned /disturbance/ is one thing, and
b) the actual /waves/ are something else.

The physical significance of the answer is as follows:
a) The aforementioned /disturbance/ is significant only in
the near field. This is the /reactive/ field.
b) In contrast, in the far field, it is negligible compared
to the actual /waves/. This is the /radiative/ field.

Here "reactive" is an electrical engineering term, in the sense
that inductors and capacitors are reactive while resistors are
dissipative. (It is not "reactive" in the sense of chemical
reactivity.) The reactive field can store energy, but it
cannot run away with it.

That's because:
a) The amplitude of the reactive field falls off like (λ/r)^3.
The power per unit area goes like the square of that.
b) The amplitude of the radiative field falls of like (λ/r).
The power per unit area goes like the square of that.

Let's plug in some numbers. Suppose you wiggle the transmitter
mass (M) at a rate of 1 kHz. That corresponds to a wavelength
of 300 km. If you observe from a point 3000 km away, the
reactive field is smaller than the radiative field by a factor
of 10,000 in terms of received power per unit area.

If you observe from a point that is far away on a cosmic length
scale, the reactive effect is smaller than the radiative effect
by 20 or 30 orders of magnitude. That's a lot.

Detecting the waves is already mind-bogglingly hard. If you
were to overestimate the difficulty by many orders of magnitude,
you would make wrong policy decisions about whether or not to
attempt it.

As an additional minor consideration, there are differences in
polarization:
a) The reactive field has a longitudinal component.
b) The radiative field is purely transverse.

===================

These are not new or subtle ideas. The same ides apply to
other kinds of waves, including electromagnetism. There is
all kinds of stuff that goes on in the near field zone that
does not extend into the radiation zone. This has practical
applications, including NSOM.
http://www.olympusmicro.com/primer/techniques/nearfield/nearfieldintro.html

Bottom line: The reactive field is perfectly real. It's just
not the same as the radiative field. It doesn't extend into
the far field. It's not what we call waves.
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