spacetime

Is it possible that a sufficiently strong
magnetic field will distort spacetime?
(acting the same way as an extremely massive object)

"Zdenek Jizba" wrote in message news:9aUsf.48$MV3.35@trnddc05...
Is it possible that a sufficiently strong
magnetic field will distort spacetime?
(acting the same way as an extremely massive object)

The magnetic field has energy, and energy affects
space just as mass does (E = mc^2).

Zdenek Jizba wrote in news:9aUsf.48$MV3.35@trnddc05:

Is it possible that a sufficiently strong
magnetic field will distort spacetime?
(acting the same way as an extremely massive object)

Energy in any form distorts spacetime. G = T, where T is the stress-energy
tensor . T even includes pressure, which has a big effect for objects with
extremely high pressure such as a neutron star.

Klazmon.

What was the evidence which implied that all energy,
not just mass, warps spacetime (causes gravity)?

-- Jeff, in Minneapolis

"Jeff Root" wrote in message
oups.com...

What was the evidence which implied that all energy,
not just mass, warps spacetime (causes gravity)?

-- Jeff, in Minneapolis


One such is the difference in mass between the
initial components and final products in fusion
reactions, demonstrating that nuclear binding
energy gravitates. The same thing can be
measured with chemical binding energy (which is
electromagnetic in origin).

In fact, there are strong empirical limits for
electrostatic and magnetostatic energy, strong
interaction energy, and gravitational binding
energy. Even for kinetic energy and the energy
associated with the parity-conserving part of the
weak interactions, it's been experimentally ruled
out that they don't gravitate. [I'm paraphrasing
here from an old post of Steve Carlip's on
sci.physics that I recall. A google search would
probably turn up the thread].

"Jeff Root" bravely wrote to "All" (29 Dec 05 22:17:57)
--- on the heady topic of " spacetime"

JR From: "Jeff Root"
JR Xref: core-easynews sci.astro:454670


JR What was the evidence which implied that all energy,
JR not just mass, warps spacetime (causes gravity)?
JR
JR -- Jeff, in Minneapolis

PHYSICS NEWS UPDATE
A digest of physics news items prepared by Phillip F. Schewe, AIP
Public Information
Number 147 October 13, 1993

THE PHYSICS NOBEL PRIZE GOES TO JOSEPH TAYLOR AND RUSSELL HULSE, both
of Princeton University, for their discovery of the first binary
pulsar and for subsequent studies leading to a verification of the
theory of general relativity for a system outside our solar system.
Using the 300m Arecibo radio telescope in Puerto Rico, Taylor and
Hulse in 1974 monitored the beacon-like emissions of the pulsar PSR
1913+16 and inferred that the pulsar -- believed to be a rapidly
spinning neutron star -- was accompanied by a nearby comparably-
massive (1.5 solar masses) and compact (20-km diameter) companion
object. A great deal has been learned from the pulsar's radio bursts,
which arrive at Earth about 17 times a second with a regularity that
rivals that of the best atomic clocks. For example, a Doppler effect
evident in the pulse sequence provides the information needed to work
out the orbit parameters for the system. Furthermore, by recording
the pulses over a multi-year period, general-relativistic properties
of the binary system could be extracted. In particular, a very slight
inward spiralling of the two partners causes their mutual orbit to
speed up and close in. According to Taylor, this phenomenon, which
shows up as a decrease in the orbital period of about 75 msec per
year, comes about because the system is losing energy (about 10**32
ergs/sec) via the emission of gravitational waves. (Equivalently, the
advance of the system's periastron is 4.2 degrees per year; by
contrast the advance of the periastron for the planet Mercury is only
43 arc-sec per century.) Because the observed decrease in the period
so closely matches the value predicted by Einstein's theory of general
relativity, many astronomers regard these observations as being
important (albeit indirect) evidence for the existence of
gravitational waves. (Taylor, 609-452-4368; Hulse, 609-243-2418. See
also the October 1981 issue of Scientific American.)

Jeff Root wrote:

What was the evidence which implied that all energy,
not just mass, warps spacetime (causes gravity)?

This is really a three-part question, because there are
three different kinds of "mass" involved. In Newtonian
language, we can write

F = m_1 a
F = Gm_2 M/r^2

m_1 is "inertial mass," m_2 is "passive gravitational
mass" (which describes the response of an object to a
gravitational field); and M is "active gravitational
mass."

The contribution of energy to inertial mass is very well-
tested, in many different ways. The most recent result
was announced in the December 22 issue of Nature (Nature
438, 1096-1097 (22 December 2005)). It involved a very
accurate measurement of atomic mass differences, using
a Penning trap, and gamma ray energies, for isotopes of
silicon and sulfur, and confirmed the contribution E/c^2
of binding energy to inertial mass to about 4 parts in
10^7.

The contribution of energy to passive gravitational mass
is tested by comparing the responses of different materials
to a fixed gravitational field. Suppose, for example, that
nuclear binding energy contributed to inertial mass (as we
observe), but not to passive gravitational mass. Since
acceleration due to gravity is proportional to m_2/m_1,
this would means that materials with a higher proportion of
nuclear binding energy would experience less acceleration
than materials with a lower proportion of nuclear binding
energy. Such differences in acceleration can be measured
very accurately, with free fall experiments and with torsion
pendulum experiments. The experimental conclusion is that
a great many different kinds of energy -- electrostatic,
nuclear binding, magnetostatic, weak, gravitational, and
kinetic) contribute E/c^2 to passive gravitational mass,
typically to accuracies of a part in a million or better.
You can find a nice summary in section 2.4 of Will's book
_Theory and experiment in gravitational physics_.

Active gravitational mass is much harder top measure, mainly
because gravity is such a weak interaction. The best direct
lab experiment is due to Kreuzer, Phys. Rev. 169 (1968) 1007.
This experiment compared active gravitational mass to passive
gravitational mass for bromine and fluorine, and showed that
the ratio M/m_2 was equal for the two elements, to a few parts
in 10^5. This is good enough to show that electrostatic and
nuclear binding energy contribute E/c^2 to active gravitational
mass to an accuracy of a percent or so.

A much stronger, but slightly less direct, limit comes from
Lunar laser ranging -- see Bartlett and Van Buren, Phys. Rev.
Lett. 57, 21 (1986). The basic idea is that if the ratio
M/m_2 differs for two materials, a system made up of the two
materials will experience a net self-acceleration. (As an
extreme example, imagine attaching two rocks to the ends of
a pole, and suppose that rock 1 has equal active and passive
gravitational mass, while rock 2 has passive gravitational
mass but zero active gravitational mass. Then rock 2 will
be attracted toward rock 1, but rock 1 will not be attracted
toward rock 2, so the whole system will accelerate.) There
is good evidence that the Moon's iron-rich mantle and its
aluminum-rich crust have slightly different centers of mass;
the observed lack of self-acceleration of the Moon then implies
that the ratios of active to passive mass for Fe and Al are
the same to a precision of 4 parts in 10^12. Since Fe and Al
have different proportional contributions of various types of
energies to their passive gravitational masses, this is enough
to push down the limits from the Kreuzer experiment by six
orders of magnitude.

(I expect that this is enough to observationally demonstrate --
in answer to the original question -- that the magnetostatic
energies of iron and aluminum gravitate. I'm not sure, though;
while the contribution of magnetostatic binding energy has been
computed for aluminum, I don't know of a computation for iron.
One would have to repeat the computations of Haugan and Will,
Phys. Rev. D15 (1977) 2711, section 3, for iron.)

Steve Carlip

wrote in message
...
Jeff Root wrote:

What was the evidence which implied that all energy,
not just mass, warps spacetime (causes gravity)?

This is really a three-part question, because there are
three different kinds of "mass" involved. In Newtonian
language, we can write

F = m_1 a
F = Gm_2 M/r^2

m_1 is "inertial mass," m_2 is "passive gravitational
mass" (which describes the response of an object to a
gravitational field); and M is "active gravitational
mass."

The contribution of energy to inertial mass is very well-
tested, in many different ways. The most recent result
was announced in the December 22 issue of Nature (Nature
438, 1096-1097 (22 December 2005)). It involved a very
accurate measurement of atomic mass differences, using
a Penning trap, and gamma ray energies, for isotopes of
silicon and sulfur, and confirmed the contribution E/c^2
of binding energy to inertial mass to about 4 parts in
10^7.

The contribution of energy to passive gravitational mass
is tested by comparing the responses of different materials
to a fixed gravitational field. Suppose, for example, that
nuclear binding energy contributed to inertial mass (as we
observe), but not to passive gravitational mass. Since
acceleration due to gravity is proportional to m_2/m_1,
this would means that materials with a higher proportion of
nuclear binding energy would experience less acceleration
than materials with a lower proportion of nuclear binding
energy. Such differences in acceleration can be measured
very accurately, with free fall experiments and with torsion
pendulum experiments. The experimental conclusion is that
a great many different kinds of energy -- electrostatic,
nuclear binding, magnetostatic, weak, gravitational, and
kinetic) contribute E/c^2 to passive gravitational mass,
typically to accuracies of a part in a million or better.
You can find a nice summary in section 2.4 of Will's book
_Theory and experiment in gravitational physics_.

Active gravitational mass is much harder top measure, mainly
because gravity is such a weak interaction. The best direct
lab experiment is due to Kreuzer, Phys. Rev. 169 (1968) 1007.
This experiment compared active gravitational mass to passive
gravitational mass for bromine and fluorine, and showed that
the ratio M/m_2 was equal for the two elements, to a few parts
in 10^5. This is good enough to show that electrostatic and
nuclear binding energy contribute E/c^2 to active gravitational
mass to an accuracy of a percent or so.

A much stronger, but slightly less direct, limit comes from
Lunar laser ranging -- see Bartlett and Van Buren, Phys. Rev.
Lett. 57, 21 (1986). The basic idea is that if the ratio
M/m_2 differs for two materials, a system made up of the two
materials will experience a net self-acceleration. (As an
extreme example, imagine attaching two rocks to the ends of
a pole, and suppose that rock 1 has equal active and passive
gravitational mass, while rock 2 has passive gravitational
mass but zero active gravitational mass. Then rock 2 will
be attracted toward rock 1, but rock 1 will not be attracted
toward rock 2, so the whole system will accelerate.) There
is good evidence that the Moon's iron-rich mantle and its
aluminum-rich crust have slightly different centers of mass;
the observed lack of self-acceleration of the Moon then implies
that the ratios of active to passive mass for Fe and Al are
the same to a precision of 4 parts in 10^12. Since Fe and Al
have different proportional contributions of various types of
energies to their passive gravitational masses, this is enough
to push down the limits from the Kreuzer experiment by six
orders of magnitude.

(I expect that this is enough to observationally demonstrate --
in answer to the original question -- that the magnetostatic
energies of iron and aluminum gravitate. I'm not sure, though;
while the contribution of magnetostatic binding energy has been
computed for aluminum, I don't know of a computation for iron.
One would have to repeat the computations of Haugan and Will,
Phys. Rev. D15 (1977) 2711, section 3, for iron.)

Steve, thanks for a very informative reply.

I believe another of the tests that relates to
this is of the Nordtvedt effect. This paper
relates to its effect on the CMBR.

http://www.arxiv.org/abs/astro-ph/0407208

Wikipedia says the most sensitive test of this
is with Lunar ranging:

"J. G. Williams, S. G. Turyshev and D. H. Boggs,
'Progress in lunar laser ranging tests of
relativistic gravity', Phys. Rev. Lett. 93
261101 (2004)."

http://arxiv.org/abs/gr-qc/0411113

Happy New Year

George

George Dishman wrote:

[...]
Steve, thanks for a very informative reply.

You're welcome.

I believe another of the tests that relates to
this is of the Nordtvedt effect. This paper
relates to its effect on the CMBR.

http://www.arxiv.org/abs/astro-ph/0407208

Wikipedia says the most sensitive test of this
is with Lunar ranging:

"J. G. Williams, S. G. Turyshev and D. H. Boggs,
'Progress in lunar laser ranging tests of
relativistic gravity', Phys. Rev. Lett. 93
261101 (2004)."

http://arxiv.org/abs/gr-qc/0411113


Right. The issue here is whether *gravitational* binding
energy contributes to passive gravitational mass. The
Earth has a larger proportion of gravitational binding
energy than the Moon. If this energy did not contribute
equally to inertial and passive gravitational mass, the
acceleration of the Earth toward the Sun would be slightly
different from the acceleration of the Moon toward the Sun.
This would lead to observable anomalies in the Moon's orbit.
These are not observed. In fact, the measurements are so
accurate that we know that gravitational binding energy
contributes equally to inertial and passive gravitational
mass to a precision of a few parts in 10^4.

Note that this implies that gravity behaves nonlinearly --
gravitational energy itself gravitates. This strongly
suggests that no linear theory can replace GR (though it
would be nice to see an analysis of gravitational energy
and active gravitational mass).

Steve Carlip

wrote in message
...
George Dishman wrote:

[...]
Steve, thanks for a very informative reply.

You're welcome.

I believe another of the tests that relates to
this is of the Nordtvedt effect. This paper
relates to its effect on the CMBR.

http://www.arxiv.org/abs/astro-ph/0407208

Wikipedia says the most sensitive test of this
is with Lunar ranging:

"J. G. Williams, S. G. Turyshev and D. H. Boggs,
'Progress in lunar laser ranging tests of
relativistic gravity', Phys. Rev. Lett. 93
261101 (2004)."

http://arxiv.org/abs/gr-qc/0411113


Right. The issue here is whether *gravitational* binding
energy contributes to passive gravitational mass. The
Earth has a larger proportion of gravitational binding
energy than the Moon. If this energy did not contribute
equally to inertial and passive gravitational mass, the
acceleration of the Earth toward the Sun would be slightly
different from the acceleration of the Moon toward the Sun.
This would lead to observable anomalies in the Moon's orbit.
These are not observed. In fact, the measurements are so
accurate that we know that gravitational binding energy
contributes equally to inertial and passive gravitational
mass to a precision of a few parts in 10^4.

Note that this implies that gravity behaves nonlinearly --
gravitational energy itself gravitates. This strongly
suggests that no linear theory can replace GR (though it
would be nice to see an analysis of gravitational energy
and active gravitational mass).

Thanks Steve, that's clearer than other descriptions
I've seen. It does raise one naive thought. Classically
gravitational potential energy is negative but the
gravitational binding energy you mention is positive.

http://en.wikipedia.org/wiki/Gravita...binding_energy

If I allow two object to move slowly together under
gravitational attraction, I can use that to extract
energy, yet what you say implies the system of the
two objects would have increased active gravitational
mass rather than decreased as I would have expected.
Where am I going wrong?

George