Forces in GTR

[Norm Dresner]

I can't quite explain the thought process because I was half asleep,
meditating on nothing to try to suppress some neurogenic pain when I started
musing about time travel and tried to "picture" what might be involved when
the notion of a time-like "force" occurred to me. Okay, let's ignore that
for the short term because I have a more fundamental problem: I can't ever
remember seeing any treatment of "forces" in the dynamics of GTR in any of
the books I've read.

a) Have I missed something obvious?

b) Can someone give me a reference or two to a treatment of this subject?

c) (Extra Credit) What would a time-like force be?

TIA
Norm

[tessel@um.bot]

On Tue, 27 Sep 2005, Norm Dresner wrote:

> I have a more fundamental problem: I can't ever remember seeing any
> treatment of "forces" in the dynamics of GTR in any of the books I've
> read.
>
> a) Have I missed something obvious?

Not sure. If you mean that you don't know how gtr handles things like
(nongravitational) "body forces", (gravitational) tidal stresses on
extended objects, or pressure in a fluid, etc., then that is easily
explained: in both str and gtr, the acceleration of a bit of matter with
world line given by a parameterized timelike curve X is given by the
acceleration vector D_X X (i.e. the covariant derivative of X, taken along
X).

> b) Can someone give me a reference or two to a treatment of this subject?

Carroll, Spacetime and Gravitation, offers a nice appendix on geodesic
congruences (Raychaudhuri equation and all that). At a higher level,
try MTW, Wald, Hawking & Ellis, etc. HE to treat general congruences
(you need the general Raychaudhuri equation for perfect fluids, since
the world line of a bit of fluid, in a fluid with nonzero pressure, is
not a geodesic curve).

If I guessed wrong and you are asking about "gravitational force" as in
the Newtonian limit, these books discuss that too, if only briefly. But
in this case you might prefer Ohanian & Ruffini.

> c) (Extra Credit) What would a time-like force be?

Well, if X is a unit timelike vector field, D_X X is orthogonal to X,
hence a spacelike vector field. So any physical force exerted on
anything with a timelike world line will be represented by a spacelike
vector. At least, according to gtr.

"T. Essel" (hiding somewhere in cyberspace)

[tessel@um.bot]

On Tue, 27 Sep 2005, Norm Dresner wrote:

> I have a more fundamental problem: I can't ever remember seeing any
> treatment of "forces" in the dynamics of GTR in any of the books I've
> read.
>
> a) Have I missed something obvious?

Not sure. If you mean that you don't know how gtr handles things like
(nongravitational) "body forces", (gravitational) tidal stresses on
extended objects, or pressure in a fluid, etc., then that is easily
explained: in both str and gtr, the acceleration of a bit of matter with
world line given by a parameterized timelike curve X is given by the
acceleration vector D_X X (i.e. the covariant derivative of X, taken along
X).

> b) Can someone give me a reference or two to a treatment of this subject?

Carroll, Spacetime and Gravitation, offers a nice appendix on geodesic
congruences (Raychaudhuri equation and all that). At a higher level,
try MTW, Wald, Hawking & Ellis, etc. HE to treat general congruences
(you need the general Raychaudhuri equation for perfect fluids, since
the world line of a bit of fluid, in a fluid with nonzero pressure, is
not a geodesic curve).

If I guessed wrong and you are asking about "gravitational force" as in
the Newtonian limit, these books discuss that too, if only briefly. But
in this case you might prefer Ohanian & Ruffini.

> c) (Extra Credit) What would a time-like force be?

Well, if X is a unit timelike vector field, D_X X is orthogonal to X,
hence a spacelike vector field. So any physical force exerted on
anything with a timelike world line will be represented by a spacelike
vector. At least, according to gtr.

"T. Essel" (hiding somewhere in cyberspace)

[tessel@um.bot]

On Tue, 27 Sep 2005, Norm Dresner wrote:

> I have a more fundamental problem: I can't ever remember seeing any
> treatment of "forces" in the dynamics of GTR in any of the books I've
> read.
>
> a) Have I missed something obvious?

Not sure. If you mean that you don't know how gtr handles things like
(nongravitational) "body forces", (gravitational) tidal stresses on
extended objects, or pressure in a fluid, etc., then that is easily
explained: in both str and gtr, the acceleration of a bit of matter with
world line given by a parameterized timelike curve X is given by the
acceleration vector D_X X (i.e. the covariant derivative of X, taken along
X).

> b) Can someone give me a reference or two to a treatment of this subject?

Carroll, Spacetime and Gravitation, offers a nice appendix on geodesic
congruences (Raychaudhuri equation and all that). At a higher level,
try MTW, Wald, Hawking & Ellis, etc. HE to treat general congruences
(you need the general Raychaudhuri equation for perfect fluids, since
the world line of a bit of fluid, in a fluid with nonzero pressure, is
not a geodesic curve).

If I guessed wrong and you are asking about "gravitational force" as in
the Newtonian limit, these books discuss that too, if only briefly. But
in this case you might prefer Ohanian & Ruffini.

> c) (Extra Credit) What would a time-like force be?

Well, if X is a unit timelike vector field, D_X X is orthogonal to X,
hence a spacelike vector field. So any physical force exerted on
anything with a timelike world line will be represented by a spacelike
vector. At least, according to gtr.

"T. Essel" (hiding somewhere in cyberspace)

[tessel@um.bot]

On Tue, 27 Sep 2005, Norm Dresner wrote:

> I have a more fundamental problem: I can't ever remember seeing any
> treatment of "forces" in the dynamics of GTR in any of the books I've
> read.
>
> a) Have I missed something obvious?

Not sure. If you mean that you don't know how gtr handles things like
(nongravitational) "body forces", (gravitational) tidal stresses on
extended objects, or pressure in a fluid, etc., then that is easily
explained: in both str and gtr, the acceleration of a bit of matter with
world line given by a parameterized timelike curve X is given by the
acceleration vector D_X X (i.e. the covariant derivative of X, taken along
X).

> b) Can someone give me a reference or two to a treatment of this subject?

Carroll, Spacetime and Gravitation, offers a nice appendix on geodesic
congruences (Raychaudhuri equation and all that). At a higher level,
try MTW, Wald, Hawking & Ellis, etc. HE to treat general congruences
(you need the general Raychaudhuri equation for perfect fluids, since
the world line of a bit of fluid, in a fluid with nonzero pressure, is
not a geodesic curve).

If I guessed wrong and you are asking about "gravitational force" as in
the Newtonian limit, these books discuss that too, if only briefly. But
in this case you might prefer Ohanian & Ruffini.

> c) (Extra Credit) What would a time-like force be?

Well, if X is a unit timelike vector field, D_X X is orthogonal to X,
hence a spacelike vector field. So any physical force exerted on
anything with a timelike world line will be represented by a spacelike
vector. At least, according to gtr.

"T. Essel" (hiding somewhere in cyberspace)

[tessel@um.bot]

On Tue, 27 Sep 2005, Norm Dresner wrote:

> I have a more fundamental problem: I can't ever remember seeing any
> treatment of "forces" in the dynamics of GTR in any of the books I've
> read.
>
> a) Have I missed something obvious?

Not sure. If you mean that you don't know how gtr handles things like
(nongravitational) "body forces", (gravitational) tidal stresses on
extended objects, or pressure in a fluid, etc., then that is easily
explained: in both str and gtr, the acceleration of a bit of matter with
world line given by a parameterized timelike curve X is given by the
acceleration vector D_X X (i.e. the covariant derivative of X, taken along
X).

> b) Can someone give me a reference or two to a treatment of this subject?

Carroll, Spacetime and Gravitation, offers a nice appendix on geodesic
congruences (Raychaudhuri equation and all that). At a higher level,
try MTW, Wald, Hawking & Ellis, etc. HE to treat general congruences
(you need the general Raychaudhuri equation for perfect fluids, since
the world line of a bit of fluid, in a fluid with nonzero pressure, is
not a geodesic curve).

If I guessed wrong and you are asking about "gravitational force" as in
the Newtonian limit, these books discuss that too, if only briefly. But
in this case you might prefer Ohanian & Ruffini.

> c) (Extra Credit) What would a time-like force be?

Well, if X is a unit timelike vector field, D_X X is orthogonal to X,
hence a spacelike vector field. So any physical force exerted on
anything with a timelike world line will be represented by a spacelike
vector. At least, according to gtr.

"T. Essel" (hiding somewhere in cyberspace)

[tessel@um.bot]

On Tue, 27 Sep 2005, Norm Dresner wrote:

> I have a more fundamental problem: I can't ever remember seeing any
> treatment of "forces" in the dynamics of GTR in any of the books I've
> read.
>
> a) Have I missed something obvious?

Not sure. If you mean that you don't know how gtr handles things like
(nongravitational) "body forces", (gravitational) tidal stresses on
extended objects, or pressure in a fluid, etc., then that is easily
explained: in both str and gtr, the acceleration of a bit of matter with
world line given by a parameterized timelike curve X is given by the
acceleration vector D_X X (i.e. the covariant derivative of X, taken along
X).

> b) Can someone give me a reference or two to a treatment of this subject?

Carroll, Spacetime and Gravitation, offers a nice appendix on geodesic
congruences (Raychaudhuri equation and all that). At a higher level,
try MTW, Wald, Hawking & Ellis, etc. HE to treat general congruences
(you need the general Raychaudhuri equation for perfect fluids, since
the world line of a bit of fluid, in a fluid with nonzero pressure, is
not a geodesic curve).

If I guessed wrong and you are asking about "gravitational force" as in
the Newtonian limit, these books discuss that too, if only briefly. But
in this case you might prefer Ohanian & Ruffini.

> c) (Extra Credit) What would a time-like force be?

Well, if X is a unit timelike vector field, D_X X is orthogonal to X,
hence a spacelike vector field. So any physical force exerted on
anything with a timelike world line will be represented by a spacelike
vector. At least, according to gtr.

"T. Essel" (hiding somewhere in cyberspace)

[Marcel LeBel]

Norm Dresner wrote:
> I can't quite explain the thought process because I was half asleep,
> meditating on nothing to try to suppress some neurogenic pain when I
> started musing about time travel and tried to "picture" what might be
> involved when the notion of a time-like "force" occurred to me. Okay,
> let's ignore that for the short term because I have a more fundamental
> problem: I can't ever remember seeing any treatment of "forces" in the
> dynamics of GTR in any of the books I've read.
>
> a) Have I missed something obvious?
>
> b) Can someone give me a reference or two to a treatment of this subject?
>
> c) (Extra Credit) What would a time-like force be?
>
> TIA
> Norm
>
Norm,

I will go straight to c) for extra credits. We know that the rate of
passage of time is slower in a gravitational field and that this field's
intensity weakens as we move away from Earth. We may therefore infer a
gradient in the rate of passage of time above Earth; time runs faster at
our head than at our feet(very small differential). The things is that
an object "exist more" where it stays longer. Consequently, the
probability of existence of anything that exists is greater in the
direction where time runs slower. ( in a gradient it always runs slower
in one point relative to above that point). The object in such a
gradient will spontaneously fall/move. (To the gradient in the rate of
passage of time corresponds a gradient in the probability of existence).
Iff you stop its fall by catching it, the FORCE you will feel in your
hand is the weight of this higher probability your are holding back.
----This is your time-like force.--- It is a force, if you hold it back.

It is interesting to consider that this higher probability of existence
in one direction affects Equally everything that exists; all objects
fall with the same acceleration. On the other hand, if you hold back
this spontaneous motion, then/then the force felt IS proportional to the
amount of mass... Why? (This is extra-extra credits item d) )

Marcel,

[Marcel LeBel]

Norm Dresner wrote:
> I can't quite explain the thought process because I was half asleep,
> meditating on nothing to try to suppress some neurogenic pain when I
> started musing about time travel and tried to "picture" what might be
> involved when the notion of a time-like "force" occurred to me. Okay,
> let's ignore that for the short term because I have a more fundamental
> problem: I can't ever remember seeing any treatment of "forces" in the
> dynamics of GTR in any of the books I've read.
>
> a) Have I missed something obvious?
>
> b) Can someone give me a reference or two to a treatment of this subject?
>
> c) (Extra Credit) What would a time-like force be?
>
> TIA
> Norm
>
Norm,

I will go straight to c) for extra credits. We know that the rate of
passage of time is slower in a gravitational field and that this field's
intensity weakens as we move away from Earth. We may therefore infer a
gradient in the rate of passage of time above Earth; time runs faster at
our head than at our feet(very small differential). The things is that
an object "exist more" where it stays longer. Consequently, the
probability of existence of anything that exists is greater in the
direction where time runs slower. ( in a gradient it always runs slower
in one point relative to above that point). The object in such a
gradient will spontaneously fall/move. (To the gradient in the rate of
passage of time corresponds a gradient in the probability of existence).
Iff you stop its fall by catching it, the FORCE you will feel in your
hand is the weight of this higher probability your are holding back.
----This is your time-like force.--- It is a force, if you hold it back.

It is interesting to consider that this higher probability of existence
in one direction affects Equally everything that exists; all objects
fall with the same acceleration. On the other hand, if you hold back
this spontaneous motion, then/then the force felt IS proportional to the
amount of mass... Why? (This is extra-extra credits item d) )

Marcel,

[Marcel LeBel]

Norm Dresner wrote:
> I can't quite explain the thought process because I was half asleep,
> meditating on nothing to try to suppress some neurogenic pain when I
> started musing about time travel and tried to "picture" what might be
> involved when the notion of a time-like "force" occurred to me. Okay,
> let's ignore that for the short term because I have a more fundamental
> problem: I can't ever remember seeing any treatment of "forces" in the
> dynamics of GTR in any of the books I've read.
>
> a) Have I missed something obvious?
>
> b) Can someone give me a reference or two to a treatment of this subject?
>
> c) (Extra Credit) What would a time-like force be?
>
> TIA
> Norm
>
Norm,

I will go straight to c) for extra credits. We know that the rate of
passage of time is slower in a gravitational field and that this field's
intensity weakens as we move away from Earth. We may therefore infer a
gradient in the rate of passage of time above Earth; time runs faster at
our head than at our feet(very small differential). The things is that
an object "exist more" where it stays longer. Consequently, the
probability of existence of anything that exists is greater in the
direction where time runs slower. ( in a gradient it always runs slower
in one point relative to above that point). The object in such a
gradient will spontaneously fall/move. (To the gradient in the rate of
passage of time corresponds a gradient in the probability of existence).
Iff you stop its fall by catching it, the FORCE you will feel in your
hand is the weight of this higher probability your are holding back.
----This is your time-like force.--- It is a force, if you hold it back.

It is interesting to consider that this higher probability of existence
in one direction affects Equally everything that exists; all objects
fall with the same acceleration. On the other hand, if you hold back
this spontaneous motion, then/then the force felt IS proportional to the
amount of mass... Why? (This is extra-extra credits item d) )

Marcel,

[Marcel LeBel]

Norm Dresner wrote:
> I can't quite explain the thought process because I was half asleep,
> meditating on nothing to try to suppress some neurogenic pain when I
> started musing about time travel and tried to "picture" what might be
> involved when the notion of a time-like "force" occurred to me. Okay,
> let's ignore that for the short term because I have a more fundamental
> problem: I can't ever remember seeing any treatment of "forces" in the
> dynamics of GTR in any of the books I've read.
>
> a) Have I missed something obvious?
>
> b) Can someone give me a reference or two to a treatment of this subject?
>
> c) (Extra Credit) What would a time-like force be?
>
> TIA
> Norm
>
Norm,

I will go straight to c) for extra credits. We know that the rate of
passage of time is slower in a gravitational field and that this field's
intensity weakens as we move away from Earth. We may therefore infer a
gradient in the rate of passage of time above Earth; time runs faster at
our head than at our feet(very small differential). The things is that
an object "exist more" where it stays longer. Consequently, the
probability of existence of anything that exists is greater in the
direction where time runs slower. ( in a gradient it always runs slower
in one point relative to above that point). The object in such a
gradient will spontaneously fall/move. (To the gradient in the rate of
passage of time corresponds a gradient in the probability of existence).
Iff you stop its fall by catching it, the FORCE you will feel in your
hand is the weight of this higher probability your are holding back.
----This is your time-like force.--- It is a force, if you hold it back.

It is interesting to consider that this higher probability of existence
in one direction affects Equally everything that exists; all objects
fall with the same acceleration. On the other hand, if you hold back
this spontaneous motion, then/then the force felt IS proportional to the
amount of mass... Why? (This is extra-extra credits item d) )

Marcel,

[Marcel LeBel]

Norm Dresner wrote:
> I can't quite explain the thought process because I was half asleep,
> meditating on nothing to try to suppress some neurogenic pain when I
> started musing about time travel and tried to "picture" what might be
> involved when the notion of a time-like "force" occurred to me. Okay,
> let's ignore that for the short term because I have a more fundamental
> problem: I can't ever remember seeing any treatment of "forces" in the
> dynamics of GTR in any of the books I've read.
>
> a) Have I missed something obvious?
>
> b) Can someone give me a reference or two to a treatment of this subject?
>
> c) (Extra Credit) What would a time-like force be?
>
> TIA
> Norm
>
Norm,

I will go straight to c) for extra credits. We know that the rate of
passage of time is slower in a gravitational field and that this field's
intensity weakens as we move away from Earth. We may therefore infer a
gradient in the rate of passage of time above Earth; time runs faster at
our head than at our feet(very small differential). The things is that
an object "exist more" where it stays longer. Consequently, the
probability of existence of anything that exists is greater in the
direction where time runs slower. ( in a gradient it always runs slower
in one point relative to above that point). The object in such a
gradient will spontaneously fall/move. (To the gradient in the rate of
passage of time corresponds a gradient in the probability of existence).
Iff you stop its fall by catching it, the FORCE you will feel in your
hand is the weight of this higher probability your are holding back.
----This is your time-like force.--- It is a force, if you hold it back.

It is interesting to consider that this higher probability of existence
in one direction affects Equally everything that exists; all objects
fall with the same acceleration. On the other hand, if you hold back
this spontaneous motion, then/then the force felt IS proportional to the
amount of mass... Why? (This is extra-extra credits item d) )

Marcel,

[Marcel LeBel]

Norm Dresner wrote:
> I can't quite explain the thought process because I was half asleep,
> meditating on nothing to try to suppress some neurogenic pain when I
> started musing about time travel and tried to "picture" what might be
> involved when the notion of a time-like "force" occurred to me. Okay,
> let's ignore that for the short term because I have a more fundamental
> problem: I can't ever remember seeing any treatment of "forces" in the
> dynamics of GTR in any of the books I've read.
>
> a) Have I missed something obvious?
>
> b) Can someone give me a reference or two to a treatment of this subject?
>
> c) (Extra Credit) What would a time-like force be?
>
> TIA
> Norm
>
Norm,

I will go straight to c) for extra credits. We know that the rate of
passage of time is slower in a gravitational field and that this field's
intensity weakens as we move away from Earth. We may therefore infer a
gradient in the rate of passage of time above Earth; time runs faster at
our head than at our feet(very small differential). The things is that
an object "exist more" where it stays longer. Consequently, the
probability of existence of anything that exists is greater in the
direction where time runs slower. ( in a gradient it always runs slower
in one point relative to above that point). The object in such a
gradient will spontaneously fall/move. (To the gradient in the rate of
passage of time corresponds a gradient in the probability of existence).
Iff you stop its fall by catching it, the FORCE you will feel in your
hand is the weight of this higher probability your are holding back.
----This is your time-like force.--- It is a force, if you hold it back.

It is interesting to consider that this higher probability of existence
in one direction affects Equally everything that exists; all objects
fall with the same acceleration. On the other hand, if you hold back
this spontaneous motion, then/then the force felt IS proportional to the
amount of mass... Why? (This is extra-extra credits item d) )

Marcel,

[Marcel LeBel]

Norm Dresner wrote:
> I can't quite explain the thought process because I was half asleep,
> meditating on nothing to try to suppress some neurogenic pain when I
> started musing about time travel and tried to "picture" what might be
> involved when the notion of a time-like "force" occurred to me. Okay,
> let's ignore that for the short term because I have a more fundamental
> problem: I can't ever remember seeing any treatment of "forces" in the
> dynamics of GTR in any of the books I've read.
>
> a) Have I missed something obvious?
>
> b) Can someone give me a reference or two to a treatment of this subject?
>
> c) (Extra Credit) What would a time-like force be?
>
> TIA
> Norm
>
Norm,

I will go straight to c) for extra credits. We know that the rate of
passage of time is slower in a gravitational field and that this field's
intensity weakens as we move away from Earth. We may therefore infer a
gradient in the rate of passage of time above Earth; time runs faster at
our head than at our feet(very small differential). The things is that
an object "exist more" where it stays longer. Consequently, the
probability of existence of anything that exists is greater in the
direction where time runs slower. ( in a gradient it always runs slower
in one point relative to above that point). The object in such a
gradient will spontaneously fall/move. (To the gradient in the rate of
passage of time corresponds a gradient in the probability of existence).
Iff you stop its fall by catching it, the FORCE you will feel in your
hand is the weight of this higher probability your are holding back.
----This is your time-like force.--- It is a force, if you hold it back.

It is interesting to consider that this higher probability of existence
in one direction affects Equally everything that exists; all objects
fall with the same acceleration. On the other hand, if you hold back
this spontaneous motion, then/then the force felt IS proportional to the
amount of mass... Why? (This is extra-extra credits item d) )

Marcel,