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The Equivalence Principle
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par...@yahoo.com
Nov 21, 2015, 1:21:35 PM11/21/15
to
Consider two observers inhabit a spacetime with a mass m at its origin of coordinates (usual Schw. coordinates used). Each is at a constant r coordinate (implying her spaceship's engine keeps working). They can verify that they hold a constant distance by exchanging light pulses. And they can also measure the Doppler shift of these pulses.
Now consider two observers in a flat spacetime, each accelerating at the same acceleration a. Also assume they hold a constant distance between them. Again, they can verify that by exchanging light pulses, and again they can measure their Doppler shift. But the shift is different from the example above (i.e. its dependence on their mutual distance is different).
Thus, by comparing their distance to the Doppler shift, they can determine whether they're accelerating or subject to gravity, apparently violating the Equivalence Principle. The measurement could be local, as these two observers can be arbitrarily close.
How about it?
Now consider two observers in a flat spacetime, each accelerating at the same acceleration a. Also assume they hold a constant distance between them. Again, they can verify that by exchanging light pulses, and again they can measure their Doppler shift. But the shift is different from the example above (i.e. its dependence on their mutual distance is different).
Thus, by comparing their distance to the Doppler shift, they can determine whether they're accelerating or subject to gravity, apparently violating the Equivalence Principle. The measurement could be local, as these two observers can be arbitrarily close.
How about it?
Alan Folmsbee
Nov 21, 2015, 5:29:53 PM11/21/15
to
On Saturday, November 21, 2015 at 8:21:35 AM UTC-10, par...@yahoo.com wrote:
" Consider two observers inhabit a spacetime with a mass m at its origin of coordinates (usual Schw. coordinates used). Each is at a constant r coordinate (implying her spaceship's engine keeps working). " For example, Bob is on Earth and Alice is hovering 1000 km above Bob, overhead.
"They can verify that they hold a constant distance by exchanging light pulses."
So the light has a gravitational red shift. one way, blue shift, the other way.
" And they can also measure the Doppler shift of these pulses."
But their relative velocity is zero so no doppler shift.
"Now consider two observers in a flat spacetime, each accelerating at the same acceleration a. Also assume they hold a constant distance between them. "
They are 1000km apart going the same direction, accelerating at the same rate.
"Again, they can verify that by exchanging light pulses, and again they can measure their Doppler shift. " Zero shift from Doppler, because they have the same velocity.
But the shift is different from the example above (i.e. its dependence on their mutual distance is different).
>
> Thus, by comparing their distance to the Doppler shift, they can determine whether they're accelerating or subject to gravity, apparently violating the Equivalence Principle. The measurement could be local, as these two observers can be arbitrarily close.
>
> How about it?
What Doppler shift? They are going the same speed.
" Consider two observers inhabit a spacetime with a mass m at its origin of coordinates (usual Schw. coordinates used). Each is at a constant r coordinate (implying her spaceship's engine keeps working). " For example, Bob is on Earth and Alice is hovering 1000 km above Bob, overhead.
"They can verify that they hold a constant distance by exchanging light pulses."
" And they can also measure the Doppler shift of these pulses."
"Now consider two observers in a flat spacetime, each accelerating at the same acceleration a. Also assume they hold a constant distance between them. "
"Again, they can verify that by exchanging light pulses, and again they can measure their Doppler shift. " Zero shift from Doppler, because they have the same velocity.
But the shift is different from the example above (i.e. its dependence on their mutual distance is different).
>
> Thus, by comparing their distance to the Doppler shift, they can determine whether they're accelerating or subject to gravity, apparently violating the Equivalence Principle. The measurement could be local, as these two observers can be arbitrarily close.
>
> How about it?
kefischer
Nov 21, 2015, 9:50:55 PM11/21/15
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On Sat, 21 Nov 2015 14:29:38 -0800 (PST), Alan Folmsbee
<omni...@gmail.com> wrote:
>On Saturday, November 21, 2015 at 8:21:35 AM UTC-10, par...@yahoo.com wrote:
>
>" Consider two observers inhabit a spacetime with a mass m at its origin of coordinates (usual Schw. coordinates used). Each is at a constant r coordinate (implying her spaceship's engine keeps working). " For example, Bob is on Earth and Alice is hovering 1000 km above Bob, overhead.
>
>"They can verify that they hold a constant distance by exchanging light pulses."
>So the light has a gravitational red shift. one way, blue shift, the other way.
>
>" And they can also measure the Doppler shift of these pulses."
>But their relative velocity is zero so no doppler shift.
>
>"Now consider two observers in a flat spacetime, each accelerating at the same acceleration a. Also assume they hold a constant distance between them. "
>They are 1000km apart going the same direction, accelerating at the same rate.
>
>"Again, they can verify that by exchanging light pulses, and again they can measure their Doppler shift. " Zero shift from Doppler, because they have the same velocity.
>
>
>But the shift is different from the example above (i.e. its dependence on their mutual distance is different).
The stated conditions are flat spacetime and holding
<omni...@gmail.com> wrote:
>On Saturday, November 21, 2015 at 8:21:35 AM UTC-10, par...@yahoo.com wrote:
>
>" Consider two observers inhabit a spacetime with a mass m at its origin of coordinates (usual Schw. coordinates used). Each is at a constant r coordinate (implying her spaceship's engine keeps working). " For example, Bob is on Earth and Alice is hovering 1000 km above Bob, overhead.
>
>"They can verify that they hold a constant distance by exchanging light pulses."
>So the light has a gravitational red shift. one way, blue shift, the other way.
>
>" And they can also measure the Doppler shift of these pulses."
>But their relative velocity is zero so no doppler shift.
>
>"Now consider two observers in a flat spacetime, each accelerating at the same acceleration a. Also assume they hold a constant distance between them. "
>They are 1000km apart going the same direction, accelerating at the same rate.
>
>"Again, they can verify that by exchanging light pulses, and again they can measure their Doppler shift. " Zero shift from Doppler, because they have the same velocity.
>
>
>But the shift is different from the example above (i.e. its dependence on their mutual distance is different).
constant distance and have same velocity.
That apparently also assumes flat spacetime has
no effect on motion or light, which is not a certainty.
>> Thus, by comparing their distance to the Doppler shift, they can determine whether they're accelerating or subject to gravity,
>>apparently violating the Equivalence Principle. The measurement could be local, as these two observers can be arbitrarily close.
>>
>> How about it?
>
>What Doppler shift? They are going the same speed.
to the equivalence principle or the "Principle of
Equivalence or any of the modern versions of
the Einstein EP.
A problem with the whole premise of being
able to measure acceleration, is that energy is
coordinate dependent, an object in freefall has
energy _relative_ to the surface, in any and all
models of gravitation.
That being said, the only way to measure
"proper" acceleration is with a precision
accelerometer. With adequate precision,
the microgravity on the ISS can be measured
if the device is held rigid some distance from
the center of gravity of the space station.
I don't know if such a device exists.
The original equivalence principle states
that gravitational mass is equivalent to inertial
mass.
The Einstein "Principle of Equivalence"
(as first worded) states that it is not possible
to tell if a person is in a room on Earth, or,
in an elevator in space pulled by a rope.
At some point, the qualifier that "in a small
enough local region, the difference is impossible
to tell".
But now, technology has progressed to
the point, that signals from a device to a
receiver only centimeters or inches away
differ enough to tell the difference.
That is "on the Earth".
What has not been tested, is that in
an accelerating space ship.
John Heath
Nov 22, 2015, 9:36:48 AM11/22/15
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However if we cut Uncle Albert some slack by assuming ideal condition , no cheating , the intent of the equivalence principle can be seen. Say the ship in space is accelerating at 32 feet per second and the ship on earth is in a gravity gradient of 32 feet per second. If you toss a base ball across the ship it will fall down in both the space ship and the earth ship. You can not tell the difference. If this is true then a photon must also fall when moving across the ship. As a photon has no mass therefore zero weight then it must be the shape of space not a force that is causing objects to fall. This is the foundation for general relativity. The rest of the theory writers itself. Mass shapes space and space tells mass how to move. This solves the issue of all objects falling at the same rate. If a force is used for gravity a wooden ball will fall faster than a lead ball. This is true for a Coulomb force as an electron will accelerate faster in a electric field than a muon but they both fall at the same rate in a gravitational field. It is also why most attempts at unification theories of electrodynamics and gravity fail. They are apples and oranges as shown by the equivalence principle.
Poutnik
Nov 22, 2015, 10:02:12 AM11/22/15
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Dne 22/11/2015 v 15:36 John Heath napsal(a):
>
> You are correct. It is understood in the equivalence principle
> that you can look out the window of a spaceship and tell if you
> are accelerating or just setting on earth. You can also measure
> a small difference in gravity up and down within the spaceship
> to tell the difference between gravity and acceleration. Strictly
> speaking the equivalence principle is limited to a spaceship
> of zero dimensions , single point. It is hard to be inside a
> ship that does not have dimensions let alone do experiments inside.
There are important 2 words: locally and homogenous.
By physical means, for homogenous gravity
you would not be able to tell the difference by measurement.
Limiting it to a point would mean devices have infinite accuracy,
what is not achievable.
Therefore it is limited to a restricted region of space,
where you measure constant gravity.
Similarly as a locally inertial frame in GR
is considered in a restricted region of space,
where you measure no deviation from inertiality.
--
Poutnik ( the Czech word for a wanderer )
Knowledge makes great men humble, but small men arrogant.
>
> You are correct. It is understood in the equivalence principle
> that you can look out the window of a spaceship and tell if you
> are accelerating or just setting on earth. You can also measure
> a small difference in gravity up and down within the spaceship
> to tell the difference between gravity and acceleration. Strictly
> speaking the equivalence principle is limited to a spaceship
> of zero dimensions , single point. It is hard to be inside a
> ship that does not have dimensions let alone do experiments inside.
By physical means, for homogenous gravity
you would not be able to tell the difference by measurement.
Limiting it to a point would mean devices have infinite accuracy,
what is not achievable.
Therefore it is limited to a restricted region of space,
where you measure constant gravity.
Similarly as a locally inertial frame in GR
is considered in a restricted region of space,
where you measure no deviation from inertiality.
--
Poutnik ( the Czech word for a wanderer )
Knowledge makes great men humble, but small men arrogant.
Alan Folmsbee
Nov 22, 2015, 11:13:44 AM11/22/15
to
On Sunday, November 22, 2015 at 4:36:48 AM UTC-10, John Heath wrote:
"As a photon has no mass therefore zero weight then it must be the shape of space not a force that is causing objects to fall. ...the equivalence principle." John 11:21
Good description, John. Consider that mass is not equivalent for gravity and for inertia, as follows:
"A mass has no volume, only area, therefore zero causation of gravity. It must be the derivative motion of space, not a mass area, that is causing gravity to attract. ...the non-equivalence principle. Matter causes gravity, mass is affected by gravity, but cannot cause it. Mass causes inertia." Alan 11:22
Get your new units of measure here:
http://fcgravity.blogspot.com/p/first-law-of-difffusion-of-herenowium.html
"As a photon has no mass therefore zero weight then it must be the shape of space not a force that is causing objects to fall. ...the equivalence principle." John 11:21
Good description, John. Consider that mass is not equivalent for gravity and for inertia, as follows:
"A mass has no volume, only area, therefore zero causation of gravity. It must be the derivative motion of space, not a mass area, that is causing gravity to attract. ...the non-equivalence principle. Matter causes gravity, mass is affected by gravity, but cannot cause it. Mass causes inertia." Alan 11:22
Get your new units of measure here:
http://fcgravity.blogspot.com/p/first-law-of-difffusion-of-herenowium.html
Tom Roberts
Nov 22, 2015, 1:51:53 PM11/22/15
to
On 11/21/15 11/21/15 12:21 PM, par...@yahoo.com wrote:
> Consider two observers inhabit a spacetime with a mass m at its origin of
> coordinates (usual Schw. coordinates used). Each is at a constant r
> coordinate (implying her spaceship's engine keeps working). They can verify
> that they hold a constant distance by exchanging light pulses. And they can
> also measure the Doppler shift of these pulses.
For comparison to the next paragraph, let me assume they are located on a single
> Consider two observers inhabit a spacetime with a mass m at its origin of
> coordinates (usual Schw. coordinates used). Each is at a constant r
> coordinate (implying her spaceship's engine keeps working). They can verify
> that they hold a constant distance by exchanging light pulses. And they can
> also measure the Doppler shift of these pulses.
radial ray -- i.e. have the same values of theta and phi but different values of r.
> Now consider two observers in a flat spacetime, each accelerating at the same
> acceleration a. Also assume they hold a constant distance between them.
> Again, they can verify that by exchanging light pulses, and again they can
> measure their Doppler shift. But the shift is different from the example
> above (i.e. its dependence on their mutual distance is different).
shift still depends on the distance from the mass (i.e. on r).
> Thus, by comparing their distance to the Doppler shift, they can determine
> whether they're accelerating or subject to gravity, apparently violating the
> Equivalence Principle.
says, or when it does not apply.
There are several different types of EP, with different statements of them, such
as "the gravitational and inertial masses of a given body are equal", or "the
acceleration imparted to a body by a gravitational field is independent of the
nature of the body", or "the outcome of any local non-gravitational experiment
in a freely falling laboratory is independent of the velocity of the laboratory
and its location in spacetime". There are others -- Google is your friend.
You seem to think that the EP implies that acceleration in flat spacetime is
"equivalent" to being at rest in a gravitational field. That is valid ONLY in a
sufficiently small region of spacetime, with the size of the region depending on
both the local curvature of spacetime (how "strong" is gravity) and on one's
measurement accuracy (better accuracy => smaller volume). For instance, Einstein
often discussed the EP in the context of an elevator that is either at rest on
the earth's surface or being accelerated (upward) far from any massive object.
The key point is that the elevator is small -- your spaceships won't fit into an
elevator.
It should be obvious that the size of the elevator depends on
measurement accuracy, because when on earth's surface, g is
smaller near its ceiling than near its floor, and objects
dropped with horizontal separation will approach each other
(they fall radially toward the center of the earth). Neither
of these applies to an elevator accelerated far from any
massive object, so if those small effects can be measured the
elevator is too large.
> The measurement could be local, as these two observers
> can be arbitrarily close.
to distinguish the two situations; but then the volume in which the EP applies
will be smaller. Indeed, if you can distinguish the two situations, then for the
measurement accuracy you have, the volume in which the EP is valid does not
include both spaceships.
This is not a problem with the EP or with GR. But you do need to understand what
the EP actually says.
Tom Roberts
Walter Ilinois
Nov 22, 2015, 2:37:28 PM11/22/15
to
Tom Roberts wrote:
> There are several different types of EP, with different statements of
> them, such as "the gravitational and inertial masses of a given body are
> equal", or "the acceleration imparted to a body by a gravitational field
> is independent of the nature of the body", or "the outcome of any local
> non-gravitational experiment in a freely falling laboratory is
> independent of the velocity of the laboratory and its location in
> spacetime". There are others -- Google is your friend.
This is deeper than you think it is. The fundamental question is, would be
> There are several different types of EP, with different statements of
> them, such as "the gravitational and inertial masses of a given body are
> equal", or "the acceleration imparted to a body by a gravitational field
> is independent of the nature of the body", or "the outcome of any local
> non-gravitational experiment in a freely falling laboratory is
> independent of the velocity of the laboratory and its location in
> spacetime". There are others -- Google is your friend.
possible in this Universe, or in other particular Universes if you insist,
that the characteristics of Space, Spacetime and Time to be different?
The quick answer would be that NO, no other characteristics can be
possible. Which drives us back to the origins, the this configuration is
an UNIQUE solution to the Logic concern. Aka, not other solution are
available. This is really deep.
Tom Roberts
Nov 22, 2015, 10:50:16 PM11/22/15
to
On 11/22/15 11/22/15 1:37 PM, Walter Ilinois wrote:
> Tom Roberts wrote:
>> There are several different types of EP, [...]
> Tom Roberts wrote:
>
> This is deeper than you think it is.
I don't think so -- you have NO IDEA how "deep" I think it is. And your word
> This is deeper than you think it is.
salad doesn't change that.
> The fundamental question is, would be
> possible in this Universe, or in other particular Universes if you insist,
> that the characteristics of Space, Spacetime and Time to be different?
can be "different" at either different places in the world we inhabit, or in
different "universes" (manifolds).
> The quick answer would be that NO, no other characteristics can be
> possible.
> Which drives us back to the origins, the this configuration is
> an UNIQUE solution to the Logic concern. Aka, not other solution are
> available. This is really deep.
Tom Roberts
John Heath
Nov 22, 2015, 11:20:44 PM11/22/15
to
>Therefore it is limited to a restricted region of space,
where you measure constant gravity.
Possibly I misunderstood to meaning.
Poutnik
Nov 23, 2015, 2:43:06 AM11/23/15
to
Dne 23/11/2015 v 05:20 John Heath napsal(a):
It can.
E.g. comparing experiments done on the Earth,
( but omitting the rotation ) versus experiments
in the spaceship accelerating by equivalent acceleration.
But the gravity gradient is exactly the thing,
those tests cannot be based on,
as by definition it must not be measurable
or at least must be negligible in context of experiments.
It is like as if gravity is a curve
and the acceleration is a tangent line
and you approximate the curve by the tangent.
You can do so locally when approximation error
is not determinable
or at least negligible for given purpose.
You attempt to insist on approximation
where the error is relevant.
In such case approximation fails.
Not to fail, you would have to replace the tangenta by another curve.
You would need an elastic spaceship
where acceleration in each its point
would follow the gravity gradient.
E.g. comparing experiments done on the Earth,
( but omitting the rotation ) versus experiments
in the spaceship accelerating by equivalent acceleration.
But the gravity gradient is exactly the thing,
those tests cannot be based on,
as by definition it must not be measurable
or at least must be negligible in context of experiments.
It is like as if gravity is a curve
and the acceleration is a tangent line
and you approximate the curve by the tangent.
You can do so locally when approximation error
is not determinable
or at least negligible for given purpose.
You attempt to insist on approximation
where the error is relevant.
In such case approximation fails.
Not to fail, you would have to replace the tangenta by another curve.
You would need an elastic spaceship
where acceleration in each its point
would follow the gravity gradient.
John Heath
Nov 23, 2015, 8:14:52 AM11/23/15
to
A] On earth pear shaped
B] In space not accelerating round
C] In space accelerating pear shaped
As we are using ship A and ship C to test the equivalence principle both will be pear shaped. How would the pare shape effect the test?? That would depend on the vacuum being pear shaped , ship being pear shaped or both the ship and the vacuum being pare shaped. If it is both the ship and the vacuum then no difference. But it can not be said for sure it is the vacuum and the ship. It could be just the ship. The vacuum has an elasticity of 8.8 p Farad , epsilon , making it 1000s of times harder than a diamond. From this I will venture a guess that the ship is pear shaped but not the vacuum. This will complicate the equivalence test so I see your point. I am not sure how much of an effect this will have on a equivalence test. Inertia is relative to the vacuum that is not pear shaped however the spaceship is pear shaped so it will have some effect. The question is how much. Then again both the earth ship and the accelerating ship are pear shaped so maybe it all cancels out?
Poutnik
Nov 23, 2015, 10:51:34 AM11/23/15
to
On 11/23/2015 02:14 PM, John Heath wrote:
>
> I see. Hmmm. Let us use a rubbery spaceship and see what happens.
> the spaceship will be a balloon full of water. It will be round
> in a inertia frame but sitting on earth with a gravity gradient
> of 32 feet per second it will look like a pear fatter at the
> bottom and shorter in height. The spaceship in space accelerated
> to 32 feet per second will change from round to pear shaped fatter
> at the bottom and shorter in length. This assumes a
> rear thrust engine. So we have three ships.
You may confuse gravity and gravity gradient.
>
> I see. Hmmm. Let us use a rubbery spaceship and see what happens.
> the spaceship will be a balloon full of water. It will be round
> in a inertia frame but sitting on earth with a gravity gradient
> of 32 feet per second it will look like a pear fatter at the
> bottom and shorter in height. The spaceship in space accelerated
> to 32 feet per second will change from round to pear shaped fatter
> at the bottom and shorter in length. This assumes a
> rear thrust engine. So we have three ships.
surface gravity g = G.M/R^2 = about 9.806 kg/m/m
gravity gradient is dg/dr = - 2.G.M / R^3
>
> A] On earth pear shaped
> B] In space not accelerating round
> C] In space accelerating pear shaped
equivalent to gravity gradient for ship A ?
>
> As we are using ship A and ship C to test the equivalence principle
> both will be pear shaped. How would the pare shape effect the
> test?? That would depend on the vacuum being pear shaped , ship
> being pear shaped or both the ship and the vacuum being pare
> shaped. If it is both the ship and the vacuum then no difference.
--
Poutnik ( the Czech word for a wanderer )
Eventual Wikipedia articles are provided with intention
of a convenient reference, not as an evidence, argument,
and usually not as a primary source of my knowledge.
par...@yahoo.com
Nov 23, 2015, 2:33:06 PM11/23/15
to
בתאריך יום ראשון, 22 בנובמבר 2015 בשעה 20:51:53 UTC+2, מאת tjrob137:
> > Now consider two observers in a flat spacetime, each accelerating at the same
> > acceleration a. Also assume they hold a constant distance between them.
>
> And are moving in the same direction along a straight line.
>
> > Again, they can verify that by exchanging light pulses, and again they can
> > measure their Doppler shift. But the shift is different from the example
> > above (i.e. its dependence on their mutual distance is different).
>
I made a mistake here. In case of equal proper accelerations, their mutual distance (as measured by the accelerating observers) will not be fixed. What I meant is two observers with different proper accelerations, as follows. Suppose you take an inertial frame, and draw two hyperbolas, both confocal at the origin. Observers following these two hyperbolic worldlines, respectively, will experience constant proper acceleration, different for each. The confocality assures that their lines of simultaeity coincide, and the mutual distance remain constant. So that's the scheme I speak of.
It's interesting that no one has pointed out my mistake. Apparently no one has bothered to check my math....
I'll state my understanding of the EP. I think it's equivalent to yours - please correct me if I'm wrong.
Gravity and acceleration are alike in that the worldlines of freefalling objects do not follow the coordinates axes. One could argue that gravity and acceleration are two different cases, because in the case of acceleration the worldlines are straight, while the coordinates are curved (the t axis is curved in the case of the elevator) while in gravity it's the other way - the coordinates are straight while the geodesics are curved. However the EP states that these two situations are equal, since in either case all you can say is that the axes are curved in respect to the geodesics and vice versa. There's no (measurable) "absolute" spacetime relative to which we can determine which is curved and which isn't. Needless to say, this understanding of the EP implies locality. Do we concur?
My point was that if you emit a light pulse, tracing its path can't differ gravity from acceleration, since all you can say is that the geodesic deviates from your notion of "straight" (defined by the coordinates you chose to use). However another measurement does. If you measure the Doppler change along the ray, even if this measurement is local (in the infinitesimal sense - the same sense we use to define the deviation of the geodesics from the coordinates, locally), you'll find a difference between gravity and acceleration. The dependence of the Doppler on the radial distance is different in each case.
I usually get messed with many unnecessary words when I try to explain things that look simple to me. I apologize, and hope I was clear nevertheless.
>
> > The measurement could be local, as these two observers
> > can be arbitrarily close.
>
> Hmmmm. The closer they are, the better measurement accuracy you need to be able
> to distinguish the two situations; but then the volume in which the EP applies
> will be smaller. Indeed, if you can distinguish the two situations, then for the
> measurement accuracy you have, the volume in which the EP is valid does not
> include both spaceships.
>
What you say is, that with sufficient inaccuracy, every two measurements are equal.... the masses of the sun and earth are euqal. If you measure any difference, it means you're too close to the masses for the instrument you use... get away from the sun and earth, or use a less accurate measurement device, and you won't be able to differ the masses. So you say that we can't differ grav from accel provided that we measure inaccurately enough. I don't think that's what you meant to say.
I think the EP is a mathematical principle, having nothing to do with actual physical measurements (and the implied inaccuracies). If you calculate the geodesic path in a given point (of a curved space) and follow your calculations for some distance, you'll soon find yourself away from the actual geodesic, since its directions has to be calculated again in each and every point. That's the meaning of "locality" the EP uses, and it's purely mathematical.
> On 11/21/15 11/21/15 12:21 PM, par...@yahoo.com wrote:
> > Consider two observers inhabit a spacetime with a mass m at its origin of
> > coordinates (usual Schw. coordinates used). Each is at a constant r
> > coordinate (implying her spaceship's engine keeps working). They can verify
> > that they hold a constant distance by exchanging light pulses. And they can
> > also measure the Doppler shift of these pulses.
>
> For comparison to the next paragraph, let me assume they are located on a single
> radial ray -- i.e. have the same values of theta and phi but different values of r.
>
>
Of course. I forgot to mention it.
> > Consider two observers inhabit a spacetime with a mass m at its origin of
> > coordinates (usual Schw. coordinates used). Each is at a constant r
> > coordinate (implying her spaceship's engine keeps working). They can verify
> > that they hold a constant distance by exchanging light pulses. And they can
> > also measure the Doppler shift of these pulses.
>
> For comparison to the next paragraph, let me assume they are located on a single
> radial ray -- i.e. have the same values of theta and phi but different values of r.
>
>
> > Now consider two observers in a flat spacetime, each accelerating at the same
> > acceleration a. Also assume they hold a constant distance between them.
>
> And are moving in the same direction along a straight line.
>
> > Again, they can verify that by exchanging light pulses, and again they can
> > measure their Doppler shift. But the shift is different from the example
> > above (i.e. its dependence on their mutual distance is different).
>
It's interesting that no one has pointed out my mistake. Apparently no one has bothered to check my math....
Gravity and acceleration are alike in that the worldlines of freefalling objects do not follow the coordinates axes. One could argue that gravity and acceleration are two different cases, because in the case of acceleration the worldlines are straight, while the coordinates are curved (the t axis is curved in the case of the elevator) while in gravity it's the other way - the coordinates are straight while the geodesics are curved. However the EP states that these two situations are equal, since in either case all you can say is that the axes are curved in respect to the geodesics and vice versa. There's no (measurable) "absolute" spacetime relative to which we can determine which is curved and which isn't. Needless to say, this understanding of the EP implies locality. Do we concur?
My point was that if you emit a light pulse, tracing its path can't differ gravity from acceleration, since all you can say is that the geodesic deviates from your notion of "straight" (defined by the coordinates you chose to use). However another measurement does. If you measure the Doppler change along the ray, even if this measurement is local (in the infinitesimal sense - the same sense we use to define the deviation of the geodesics from the coordinates, locally), you'll find a difference between gravity and acceleration. The dependence of the Doppler on the radial distance is different in each case.
I usually get messed with many unnecessary words when I try to explain things that look simple to me. I apologize, and hope I was clear nevertheless.
>
> > The measurement could be local, as these two observers
> > can be arbitrarily close.
>
> Hmmmm. The closer they are, the better measurement accuracy you need to be able
> to distinguish the two situations; but then the volume in which the EP applies
> will be smaller. Indeed, if you can distinguish the two situations, then for the
> measurement accuracy you have, the volume in which the EP is valid does not
> include both spaceships.
>
I think the EP is a mathematical principle, having nothing to do with actual physical measurements (and the implied inaccuracies). If you calculate the geodesic path in a given point (of a curved space) and follow your calculations for some distance, you'll soon find yourself away from the actual geodesic, since its directions has to be calculated again in each and every point. That's the meaning of "locality" the EP uses, and it's purely mathematical.
John Heath
Nov 24, 2015, 3:35:44 AM11/24/15
to
On Monday, November 23, 2015 at 10:51:34 AM UTC-5, Poutnik wrote:
> On 11/23/2015 02:14 PM, John Heath wrote:
>
> >
> > I see. Hmmm. Let us use a rubbery spaceship and see what happens.
> > the spaceship will be a balloon full of water. It will be round
> > in a inertia frame but sitting on earth with a gravity gradient
> > of 32 feet per second it will look like a pear fatter at the
> > bottom and shorter in height. The spaceship in space accelerated
> > to 32 feet per second will change from round to pear shaped fatter
> > at the bottom and shorter in length. This assumes a
> > rear thrust engine. So we have three ships.
>
> You may confuse gravity and gravity gradient.
> surface gravity g = G.M/R^2 = about 9.806 kg/m/m
> gravity gradient is dg/dr = - 2.G.M / R^3
>
If we assume the equivalence principle is correct than there is not a difference between accelerating at 32 feet per second and sitting on earth with a gravity acceleration of 32 feet per second. There are different combinations of gravity density and gradients that will arrive at the same gravitational acceleration of 32 feet per second . you may have denser gravity but less of a gradient and have 32 feet per second. you can have less dense gravity with a greater gradient and have 32 feet per second . That has relevant to gravity time dilation but not to the equivalence principle.
> On 11/23/2015 02:14 PM, John Heath wrote:
>
> >
> > I see. Hmmm. Let us use a rubbery spaceship and see what happens.
> > the spaceship will be a balloon full of water. It will be round
> > in a inertia frame but sitting on earth with a gravity gradient
> > of 32 feet per second it will look like a pear fatter at the
> > bottom and shorter in height. The spaceship in space accelerated
> > to 32 feet per second will change from round to pear shaped fatter
> > at the bottom and shorter in length. This assumes a
> > rear thrust engine. So we have three ships.
>
> You may confuse gravity and gravity gradient.
> surface gravity g = G.M/R^2 = about 9.806 kg/m/m
> gravity gradient is dg/dr = - 2.G.M / R^3
>
>
> >
> > A] On earth pear shaped
> > B] In space not accelerating round
> > C] In space accelerating pear shaped
>
> How did you managed acceleration gradient for the ship C,
> equivalent to gravity gradient for ship A ?
>
> >
> > As we are using ship A and ship C to test the equivalence principle
> > both will be pear shaped. How would the pare shape effect the
> > test?? That would depend on the vacuum being pear shaped , ship
> > being pear shaped or both the ship and the vacuum being pare
> > shaped. If it is both the ship and the vacuum then no difference.
>
> Also, you cannot test EP when ship is once in air and once in vacuum.
>
If you feel it is necessary then subtract 2 pound per cubic meter of air. I am joking of course . Assume it is ideal conditions of a vacuum.
I would add that Wikipedia is your friend. It is by far the best source of fast physics facts that can be found on the net. And if there are any mistakes it is quickly remedied as there are many of eyes watching for such mistakes to maintain its high quality of a information. Why would you think otherwise?
mlwo...@wp.pl
Nov 24, 2015, 4:08:43 AM11/24/15
to
W dniu wtorek, 24 listopada 2015 09:35:44 UTC+1 użytkownik John Heath napisał:
> If we assume the equivalence principle is correct than there is not a difference between accelerating at 32 feet per second and sitting on earth with a gravity acceleration of 32 feet per second.
Yeah, IF we assume, THEN there is no difference.
> If we assume the equivalence principle is correct than there is not a difference between accelerating at 32 feet per second and sitting on earth with a gravity acceleration of 32 feet per second.
And if we assume you're a camel, there is
no difference between your feet and a hoof.
Poutnik
Nov 24, 2015, 7:31:42 AM11/24/15
to
On 11/24/2015 09:35 AM, John Heath wrote:
> On Monday, November 23, 2015 at 10:51:34 AM UTC-5, Poutnik wrote:
>>
>> You may confuse gravity and gravity gradient.
>> surface gravity g = G.M/R^2 = about 9.806 kg/m/m
>> gravity gradient is dg/dr = - 2.G.M / R^3
>>
>
> If we assume the equivalence principle is correct than there
> is not a difference between accelerating at 32 feet per second
> and sitting on earth with a gravity acceleration of 32 feet per
> second.
Yes, if other conditions are the same,
> On Monday, November 23, 2015 at 10:51:34 AM UTC-5, Poutnik wrote:
>>
>> You may confuse gravity and gravity gradient.
>> surface gravity g = G.M/R^2 = about 9.806 kg/m/m
>> gravity gradient is dg/dr = - 2.G.M / R^3
>>
>
> If we assume the equivalence principle is correct than there
> is not a difference between accelerating at 32 feet per second
> and sitting on earth with a gravity acceleration of 32 feet per
> second.
what is not trivial to manage.
> ..........There are different combinations of gravity density and
> gradients that will arrive at the same gravitational acceleration
> of 32 feet per second . You may have denser gravity but less
> of a gradient and have 32 feet per second. you can have less
> dense gravity with a greater gradient and have 32 feet per second
> . That has relevant to gravity time dilation but not
> to the equivalence principle.
What exactly do you mean
> dense gravity with a greater gradient and have 32 feet per second
> . That has relevant to gravity time dilation but not
> to the equivalence principle.
by different gravity density at the same gravitional acceleration ?
( different gravity gradient at the same gr. acceleration is clear).
Value of the gr. gradient wrt gr acceleration is essential,
as it limits the space region where you can evaluate the EP.
>>
>>>
>>> A] On earth pear shaped
>>> B] In space not accelerating round
>>> C] In space accelerating pear shaped
>>
>> How did you managed acceleration gradient for the ship C,
>> equivalent to gravity gradient for ship A ?
>
> C spaceship is in space with thrusters accelerating it at 32 feet per second
>>
>> Also, you cannot test EP when ship is once in air and once in vacuum.
>>
>
> It is a given in a physics debate that idea conditions are assumed.
> If you feel it is necessary then subtract 2 pound per cubic meter of air. I am joking of course . Assume it is ideal conditions of a vacuum.
I had in mind the basic principle if you test one parameter, you keep
>> Also, you cannot test EP when ship is once in air and once in vacuum.
>>
>
> It is a given in a physics debate that idea conditions are assumed.
> If you feel it is necessary then subtract 2 pound per cubic meter of air. I am joking of course . Assume it is ideal conditions of a vacuum.
all other constant. In our case, if you compare acceleration and
gravity, and have different conditions for each of them,
how would you know what would cause the difference of the result ?
>
> I would add that Wikipedia is your friend. It is by far the best
> source of fast physics facts that can be found on the net. And
> if there are any mistakes it is quickly remedied as there are
> many of eyes watching for such mistakes to maintain its high
> quality of a information. Why would you think otherwise?
Why would you think I thing otherwise otherwise?
> I would add that Wikipedia is your friend. It is by far the best
> source of fast physics facts that can be found on the net. And
> if there are any mistakes it is quickly remedied as there are
> many of eyes watching for such mistakes to maintain its high
> quality of a information. Why would you think otherwise?
But Wikipedia definitely is not the best source of physics knowledge,
just one of the best first references and summaries of other sources.
But reliability of W. data is variable.
John Heath
Nov 24, 2015, 5:32:23 PM11/24/15
to
On Tuesday, November 24, 2015 at 7:31:42 AM UTC-5, Poutnik wrote:
> On 11/24/2015 09:35 AM, John Heath wrote:
> > On Monday, November 23, 2015 at 10:51:34 AM UTC-5, Poutnik wrote:
>
> >>
> >> You may confuse gravity and gravity gradient.
> >> surface gravity g = G.M/R^2 = about 9.806 kg/m/m
> >> gravity gradient is dg/dr = - 2.G.M / R^3
> >>
> >
> > If we assume the equivalence principle is correct than there
> > is not a difference between accelerating at 32 feet per second
> > and sitting on earth with a gravity acceleration of 32 feet per
> > second.
>
> Yes, if other conditions are the same,
> what is not trivial to manage.
>
> > ..........There are different combinations of gravity density and
> > gradients that will arrive at the same gravitational acceleration
> > of 32 feet per second . You may have denser gravity but less
> > of a gradient and have 32 feet per second. you can have less
> > dense gravity with a greater gradient and have 32 feet per second
> > . That has relevant to gravity time dilation but not
> > to the equivalence principle.
>
> What exactly do you mean
> by different gravity density at the same gravitional acceleration ?
> ( different gravity gradient at the same gr. acceleration is clear).
>
> Value of the gr. gradient wrt gr acceleration is essential,
> as it limits the space region where you can evaluate the EP.
>
I will define
> On 11/24/2015 09:35 AM, John Heath wrote:
> > On Monday, November 23, 2015 at 10:51:34 AM UTC-5, Poutnik wrote:
>
> >>
> >> You may confuse gravity and gravity gradient.
> >> surface gravity g = G.M/R^2 = about 9.806 kg/m/m
> >> gravity gradient is dg/dr = - 2.G.M / R^3
> >>
> >
> > If we assume the equivalence principle is correct than there
> > is not a difference between accelerating at 32 feet per second
> > and sitting on earth with a gravity acceleration of 32 feet per
> > second.
>
> Yes, if other conditions are the same,
> what is not trivial to manage.
>
> > ..........There are different combinations of gravity density and
> > gradients that will arrive at the same gravitational acceleration
> > of 32 feet per second . You may have denser gravity but less
> > of a gradient and have 32 feet per second. you can have less
> > dense gravity with a greater gradient and have 32 feet per second
> > . That has relevant to gravity time dilation but not
> > to the equivalence principle.
>
> What exactly do you mean
> by different gravity density at the same gravitional acceleration ?
> ( different gravity gradient at the same gr. acceleration is clear).
>
> Value of the gr. gradient wrt gr acceleration is essential,
> as it limits the space region where you can evaluate the EP.
>
A] gravity density , the degree that space is expanding caused by mass also equal to gravitational time dilation.
B] gradient of gravity , the degree that the density of gravity has changed within one meter. The gradient has 3 dimensions of x , y and z so there are 3. We are only interested in y gradient for EP.
C] gravitational acceleration , 32 feet per second. this is a combination of density and gradient. You may have high density and low gradient for 32 feet per second or low density and high gradient for the same 32 feet per second of acceleration. An example of high density and low gradient is on earth where we are being pulled sideways as well as down for 32 feet per second. An example low density high gradient is a fair distance from a black hole where most of the force is in the y dimension only for 32 feet per second.
D] Acceleration of ?? feet per second equals how much you weigh on a weight scale.
As the EP deals mainly with acceleration then weight on a weight scale measured is the bottom line for The bottom line for a comparison between a accelerating spaceship and a spaceship on earth at rest. This ends up being 32 feet per second.
This would be my take on it.
>
> >>
> >>>
> >>> A] On earth pear shaped
> >>> B] In space not accelerating round
> >>> C] In space accelerating pear shaped
> >>
> >> How did you managed acceleration gradient for the ship C,
> >> equivalent to gravity gradient for ship A ?
> >
> > C spaceship is in space with thrusters accelerating it at 32 feet per second
>
> that is management of acceleration, not of acceleration *gradient* .
> >>
> >> Also, you cannot test EP when ship is once in air and once in vacuum.
> >>
> >
> > It is a given in a physics debate that idea conditions are assumed.
> > If you feel it is necessary then subtract 2 pound per cubic meter of air. I am joking of course . Assume it is ideal conditions of a vacuum.
>
> I had in mind the basic principle if you test one parameter, you keep
> all other constant. In our case, if you compare acceleration and
> gravity, and have different conditions for each of them,
> how would you know what would cause the difference of the result ?
> >
> > I would add that Wikipedia is your friend. It is by far the best
> > source of fast physics facts that can be found on the net. And
> > if there are any mistakes it is quickly remedied as there are
> > many of eyes watching for such mistakes to maintain its high
> > quality of a information. Why would you think otherwise?
>
> Why would you think I thing otherwise otherwise?
> But Wikipedia definitely is not the best source of physics knowledge,
> just one of the best first references and summaries of other sources.
> But reliability of W. data is variable.
mlwo...@wp.pl
Nov 25, 2015, 2:05:46 AM11/25/15
to
W dniu wtorek, 24 listopada 2015 23:32:23 UTC+1 użytkownik John Heath napisał:
>
> I will define
John, you can define all you want the way you want,
but it doesn't have to be wise. And nobody have to
buy it.
Making a good set of terms is - difficult. Mathematics
didn't tell you, how to do it, but it's not because
it's easy or not important; it's because mathematics
doesn't have the slightest idea.
>
> I will define
John, you can define all you want the way you want,
but it doesn't have to be wise. And nobody have to
buy it.
Making a good set of terms is - difficult. Mathematics
didn't tell you, how to do it, but it's not because
it's easy or not important; it's because mathematics
doesn't have the slightest idea.
Poutnik
Nov 25, 2015, 3:11:49 AM11/25/15
to
Dne 24/11/2015 v 23:32 John Heath napsal(a):
as density is generally local intensive parameter,
while this is integral parameter across the space.
Also I doubt if if it is related to local space expansion.
If anything, that local gravity acceleration and it derivatives, not
integral.
Anyway, this your term gravity density (GD) is proportional
to path integral of gravitational acceleration to infinity
and therefore is mutually exclusive with EP testing,
EP applies to locally homogeneous gravity,
that is in no way homogenous in GD integration interval.
Definition of rest of terms is clear, with 2 objections.
1/ acceleration has dimension m/s/s, resp feet/s/s there not feet per
second. I am sure you are aware of that.
2/ I have thought even scientists in imperial unit regions use SI units
in scientific context, while imperial units are used rather in citizen
and technology area,
--
Poutnik ( the Czech word for a wanderer )
> On Tuesday, November 24, 2015 at 7:31:42 AM UTC-5, Poutnik wrote:
>> On 11/24/2015 09:35 AM, John Heath wrote:
>>
>> What exactly do you mean
>> by different gravity density at the same gravitional acceleration ?
>> ( different gravity gradient at the same gr. acceleration is clear).
>>
>> Value of the gr. gradient wrt gr acceleration is essential,
>> as it limits the space region where you can evaluate the EP.
>>
>
> I will define
>
> A] gravity density , the degree that space is expanding caused by mass also equal to gravitational time dilation.
I am not sure if GR uses term gravity density for this parameter,
>> On 11/24/2015 09:35 AM, John Heath wrote:
>>
>> What exactly do you mean
>> by different gravity density at the same gravitional acceleration ?
>> ( different gravity gradient at the same gr. acceleration is clear).
>>
>> Value of the gr. gradient wrt gr acceleration is essential,
>> as it limits the space region where you can evaluate the EP.
>>
>
> I will define
>
> A] gravity density , the degree that space is expanding caused by mass also equal to gravitational time dilation.
as density is generally local intensive parameter,
while this is integral parameter across the space.
Also I doubt if if it is related to local space expansion.
If anything, that local gravity acceleration and it derivatives, not
integral.
Anyway, this your term gravity density (GD) is proportional
to path integral of gravitational acceleration to infinity
and therefore is mutually exclusive with EP testing,
EP applies to locally homogeneous gravity,
that is in no way homogenous in GD integration interval.
Definition of rest of terms is clear, with 2 objections.
1/ acceleration has dimension m/s/s, resp feet/s/s there not feet per
second. I am sure you are aware of that.
2/ I have thought even scientists in imperial unit regions use SI units
in scientific context, while imperial units are used rather in citizen
and technology area,
--
Poutnik ( the Czech word for a wanderer )
Poutnik
Nov 25, 2015, 3:28:43 AM11/25/15
to
Dne 25/11/2015 v 09:11 Poutnik napsal(a):
> Anyway, this your term gravity density (GD) is proportional
> to path integral of gravitational acceleration to infinity
> and therefore is mutually exclusive with EP testing,
> EP applies to locally homogeneous gravity,
> that is in no way homogenous in GD integration interval.
>
Better than exclusive may be
its value as being a large scale parameter is irrelevant for EP test,
if local gravity homogenity requirement is maintained.
BTW the GD is called in Newton gravity
and in flat spacetime limit case of GR
the gravitational potential.
AS Gr. time dilation if proportional to that.
> Anyway, this your term gravity density (GD) is proportional
> to path integral of gravitational acceleration to infinity
> and therefore is mutually exclusive with EP testing,
> EP applies to locally homogeneous gravity,
> that is in no way homogenous in GD integration interval.
>
its value as being a large scale parameter is irrelevant for EP test,
if local gravity homogenity requirement is maintained.
BTW the GD is called in Newton gravity
and in flat spacetime limit case of GR
the gravitational potential.
AS Gr. time dilation if proportional to that.
Tom Roberts
Nov 25, 2015, 10:42:36 AM11/25/15
to
On 11/23/15 11/23/15 - 1:33 PM, par...@yahoo.com wrote:
> בתאריך יום ראשון, 22 בנובמבר 2015 בשעה 20:51:53 UTC+2, מאת tjrob137:
>> On 11/21/15 11/21/15 12:21 PM, par...@yahoo.com wrote:
>>> Consider two observers inhabit a spacetime with a mass m at its origin
>>> of coordinates (usual Schw. coordinates used). Each is at a constant r
>>> coordinate (implying her spaceship's engine keeps working). They can
>>> verify that they hold a constant distance by exchanging light pulses. And
>>> they can also measure the Doppler shift of these pulses.
>>
>> For comparison to the next paragraph, let me assume they are located on a
>> single radial ray -- i.e. have the same values of theta and phi but
>> different values of r.
>>
>>
> Of course. I forgot to mention it.
>
>>> Now consider two observers in a flat spacetime, each accelerating at the
>>> same acceleration a. Also assume they hold a constant distance between
>>> them.
>>
>> And are moving in the same direction along a straight line.
>>
>>> Again, they can verify that by exchanging light pulses, and again they
>>> can measure their Doppler shift. But the shift is different from the
>>> example above (i.e. its dependence on their mutual distance is
>>> different).
>>
> I made a mistake here. In case of equal proper accelerations, their mutual
> distance (as measured by the accelerating observers) will not be fixed.
Yes. But you said they "hold a constant distance [apart]". So that's not really
> בתאריך יום ראשון, 22 בנובמבר 2015 בשעה 20:51:53 UTC+2, מאת tjrob137:
>> On 11/21/15 11/21/15 12:21 PM, par...@yahoo.com wrote:
>>> Consider two observers inhabit a spacetime with a mass m at its origin
>>> of coordinates (usual Schw. coordinates used). Each is at a constant r
>>> coordinate (implying her spaceship's engine keeps working). They can
>>> verify that they hold a constant distance by exchanging light pulses. And
>>> they can also measure the Doppler shift of these pulses.
>>
>> For comparison to the next paragraph, let me assume they are located on a
>> single radial ray -- i.e. have the same values of theta and phi but
>> different values of r.
>>
>>
> Of course. I forgot to mention it.
>
>>> Now consider two observers in a flat spacetime, each accelerating at the
>>> same acceleration a. Also assume they hold a constant distance between
>>> them.
>>
>> And are moving in the same direction along a straight line.
>>
>>> Again, they can verify that by exchanging light pulses, and again they
>>> can measure their Doppler shift. But the shift is different from the
>>> example above (i.e. its dependence on their mutual distance is
>>> different).
>>
> I made a mistake here. In case of equal proper accelerations, their mutual
> distance (as measured by the accelerating observers) will not be fixed.
a mistake, they just don't have equal proper accelerations. In either case.
>>> Thus, by comparing their distance to the Doppler shift, they can
>>> determine whether they're accelerating or subject to gravity, apparently
>>> violating the Equivalence Principle.
>>
>> No. You apparently do not know what the equivalence principle (EP)
>> actually says, or when it does not apply.
> I'll state my understanding of the EP. I think it's equivalent to yours -
> please correct me if I'm wrong.
>
> Gravity and acceleration are alike in that the worldlines of freefalling
> objects do not follow the coordinates axes. One could argue that gravity and
> acceleration are two different cases, because in the case of acceleration the
> worldlines are straight, while the coordinates are curved (the t axis is
> curved in the case of the elevator) while in gravity it's the other way - the
> coordinates are straight while the geodesics are curved. However the EP
> states that these two situations are equal, since in either case all you can
> say is that the axes are curved in respect to the geodesics and vice versa.
> There's no (measurable) "absolute" spacetime relative to which we can
> determine which is curved and which isn't. Needless to say, this
> understanding of the EP implies locality. Do we concur?
No. Your description omits the important restriction to a small 4-volume. Within
> please correct me if I'm wrong.
>
> Gravity and acceleration are alike in that the worldlines of freefalling
> objects do not follow the coordinates axes. One could argue that gravity and
> acceleration are two different cases, because in the case of acceleration the
> worldlines are straight, while the coordinates are curved (the t axis is
> curved in the case of the elevator) while in gravity it's the other way - the
> coordinates are straight while the geodesics are curved. However the EP
> states that these two situations are equal, since in either case all you can
> say is that the axes are curved in respect to the geodesics and vice versa.
> There's no (measurable) "absolute" spacetime relative to which we can
> determine which is curved and which isn't. Needless to say, this
> understanding of the EP implies locality. Do we concur?
such a local region all free-falling worldlines are indistinguishable from
straight lines, regardless of whether gravity is present. THAT is the key aspect
of the EP: the size of the local region depends on measurement accuracy (i.e. it
must be small enough so any deviations from straight lines are too small to be
measured).
> My point was that if you emit a light pulse, tracing its path can't differ
> gravity from acceleration, since all you can say is that the geodesic
> deviates from your notion of "straight" (defined by the coordinates you chose
> to use). However another measurement does. If you measure the Doppler change
> along the ray, even if this measurement is local (in the infinitesimal sense
> - the same sense we use to define the deviation of the geodesics from the
> coordinates, locally), you'll find a difference between gravity and
> acceleration. The dependence of the Doppler on the radial distance is
> different in each case.
small enough so any deviations from straight lines are too small to be measured
> What you say is, that with sufficient inaccuracy, every two measurements are
> equal.... the masses of the sun and earth are euqal. If you measure any
> difference, it means you're too close to the masses for the instrument you
> use... get away from the sun and earth, or use a less accurate measurement
> device, and you won't be able to differ the masses. So you say that we can't
> differ grav from accel provided that we measure inaccurately enough. I don't
> think that's what you meant to say.
of free-falling objects.
Consider a horizontal light ray in an elevator 3 meters
on a side. On earth it will deviate from a straight line
by ~ 10^-16 meters. That is ~ a million times smaller
than the best technology today can measure.
> I think the EP is a mathematical principle, having nothing to do with actual
> physical measurements (and the implied inaccuracies).
measured. To date, every one of the dozens of experimental tests of the EP has
confirmed it.
If experiments can test it, it MUST have physical implications.
Tom Roberts
Maciej Woźniak
Nov 25, 2015, 11:54:48 AM11/25/15
to
Użytkownik "Tom Roberts" napisał w wiadomości grup
dyskusyjnych:SKKdnSCEILR1S8jL...@giganews.com...
|No. The EP has direct physical implications on what can be, and what is,
|measured. To date, every one of the dozens of experimental tests of the EP
has
|confirmed it.
CONFIRM!!!!!!!"
Sort of the same thing.
par...@yahoo.com
Nov 26, 2015, 5:21:14 AM11/26/15
to
בתאריך יום רביעי, 25 בנובמבר 2015 בשעה 17:42:36 UTC+2, מאת tjrob137:
>
> >>> Thus, by comparing their distance to the Doppler shift, they can
> >>> determine whether they're accelerating or subject to gravity, apparently
> >>> violating the Equivalence Principle.
> >>
> >> No. You apparently do not know what the equivalence principle (EP)
> >> actually says, or when it does not apply.
> >>[...]
> > I'll state my understanding of the EP. I think it's equivalent to yours -
> > please correct me if I'm wrong.
> >
> > Gravity and acceleration are alike in that the worldlines of freefalling
> > objects do not follow the coordinates axes. One could argue that gravity and
> > acceleration are two different cases, because in the case of acceleration the
> > worldlines are straight, while the coordinates are curved (the t axis is
> > curved in the case of the elevator) while in gravity it's the other way - the
> > coordinates are straight while the geodesics are curved. However the EP
> > states that these two situations are equal, since in either case all you can
> > say is that the axes are curved in respect to the geodesics and vice versa.
> > There's no (measurable) "absolute" spacetime relative to which we can
> > determine which is curved and which isn't. Needless to say, this
> > understanding of the EP implies locality. Do we concur?
>
> No. Your description omits the important restriction to a small 4-volume.
I did mention (in the last sentence) that my statement of the EP implies locality. I elaborated on that in the last paragraph of my last post.
Within
> such a local region all free-falling worldlines are indistinguishable from
> straight lines, regardless of whether gravity is present.
What you actually say is, that withing a sufficiently small 4D region, gravity is undetectable, since worldlines are straight. It's like saying that within a small enough 4d region, nonlinear effects don't exist, as each and every function is linear to a first approximation.... I don't think that's what the EP says. It's not a physical principle concerning measurements accuracies, telling you that deviation from straight lines are undetectable in a small enought region, but rather a philosophical principle, stating that two (apparently different) physical phenomena are the same. More exactly, their mathematical description (within the theory) is essentially the same (provided we're confines to a local region. But this confinement isn't a necessity of measurment's accuracy, but rather a necessity of infinitesimal calculus, stating that the derivatives of a function may be different at each point, so that calculations made at a specific point may be useless in other points. Since the theory uses calculus, all the mathematical restrictions of calculus apply). Hope I'm clearer now.
THAT is the key aspect
> of the EP: the size of the local region depends on measurement accuracy (i.e. it
> must be small enough so any deviations from straight lines are too small to be
> measured).
>
>
> > My point was that if you emit a light pulse, tracing its path can't differ
> > gravity from acceleration, since all you can say is that the geodesic
> > deviates from your notion of "straight" (defined by the coordinates you chose
> > to use). However another measurement does. If you measure the Doppler change
> > along the ray, even if this measurement is local (in the infinitesimal sense
> > - the same sense we use to define the deviation of the geodesics from the
> > coordinates, locally), you'll find a difference between gravity and
> > acceleration. The dependence of the Doppler on the radial distance is
> > different in each case.
>
> Again: the key point is that the local region in which the EP applies must be
> small enough so any deviations from straight lines are too small to be measured
>
>
> > What you say is, that with sufficient inaccuracy, every two measurements are
> > equal.... the masses of the sun and earth are euqal. If you measure any
> > difference, it means you're too close to the masses for the instrument you
> > use... get away from the sun and earth, or use a less accurate measurement
> > device, and you won't be able to differ the masses. So you say that we can't
> > differ grav from accel provided that we measure inaccurately enough. I don't
> > think that's what you meant to say.
>
> It's not masses that are involved, but rather measurements of the trajectories
> of free-falling objects.
>
Masses were only en example. The statement you made (that grav and accel are inditinguishable if the measurement isn't accurate enopugh) is true to any other two measurements. They're identical if the measurements isn't accurate enough. It's not a statement specific to GR or grav & accel.
> Consider a horizontal light ray in an elevator 3 meters
> on a side. On earth it will deviate from a straight line
> by ~ 10^-16 meters. That is ~ a million times smaller
> than the best technology today can measure.
>
>
> > I think the EP is a mathematical principle, having nothing to do with actual
> > physical measurements (and the implied inaccuracies).
>
> No. The EP has direct physical implications on what can be, and what is,
> measured. To date, every one of the dozens of experimental tests of the EP has
> confirmed it.
>
> If experiments can test it, it MUST have physical implications.
>
Of course it has physical implication. That's no t what I meant. I meant its part of the theory - it's a necessary outcome of its mathematical formulation, and not a technical outcome of the fact that every measurement has limited accuracy (a fact common to all theories... or rather, to all measurements aimed at confirming or fasilyng a theory, regardless of the theory involved).
>
> Tom Roberts
> On 11/23/15 11/23/15 - 1:33 PM, par...@yahoo.com wrote:
> > בתאריך יום ראשון, 22 בנובמבר 2015 בשעה 20:51:53 UTC+2, מאת tjrob137:
> >> On 11/21/15 11/21/15 12:21 PM, par...@yahoo.com wrote:
> >>> Consider two observers inhabit a spacetime with a mass m at its origin
> >>> of coordinates (usual Schw. coordinates used). Each is at a constant r
> >>> coordinate (implying her spaceship's engine keeps working). They can
> >>> verify that they hold a constant distance by exchanging light pulses. And
> >>> they can also measure the Doppler shift of these pulses.
> >>
> >> For comparison to the next paragraph, let me assume they are located on a
> >> single radial ray -- i.e. have the same values of theta and phi but
> >> different values of r.
> >>
> >>
> > Of course. I forgot to mention it.
> >
> >>> Now consider two observers in a flat spacetime, each accelerating at the
> >>> same acceleration a. Also assume they hold a constant distance between
> >>> them.
> >>
> >> And are moving in the same direction along a straight line.
> >>
> >>> Again, they can verify that by exchanging light pulses, and again they
> >>> can measure their Doppler shift. But the shift is different from the
> >>> example above (i.e. its dependence on their mutual distance is
> >>> different).
> >>
> > I made a mistake here. In case of equal proper accelerations, their mutual
> > distance (as measured by the accelerating observers) will not be fixed.
>
> Yes. But you said they "hold a constant distance [apart]". So that's not really
> a mistake, they just don't have equal proper accelerations. In either case.
>
You mentioned (in a previous post) that it's easy to differ a constantly-accelerating elevator from an elevator in a gravity field (as earth's), since the gravity at its top is slightly different from the gravity at its buttom. But now, as we speak of two observers with different proper acceleration, it's obvious that there's no differenec at all. In both cases (gravity and accel) you'll measure a difference in gravity/accel between the top and bottom while they hold their constant mutual distance.
> > בתאריך יום ראשון, 22 בנובמבר 2015 בשעה 20:51:53 UTC+2, מאת tjrob137:
> >> On 11/21/15 11/21/15 12:21 PM, par...@yahoo.com wrote:
> >>> Consider two observers inhabit a spacetime with a mass m at its origin
> >>> of coordinates (usual Schw. coordinates used). Each is at a constant r
> >>> coordinate (implying her spaceship's engine keeps working). They can
> >>> verify that they hold a constant distance by exchanging light pulses. And
> >>> they can also measure the Doppler shift of these pulses.
> >>
> >> For comparison to the next paragraph, let me assume they are located on a
> >> single radial ray -- i.e. have the same values of theta and phi but
> >> different values of r.
> >>
> >>
> > Of course. I forgot to mention it.
> >
> >>> Now consider two observers in a flat spacetime, each accelerating at the
> >>> same acceleration a. Also assume they hold a constant distance between
> >>> them.
> >>
> >> And are moving in the same direction along a straight line.
> >>
> >>> Again, they can verify that by exchanging light pulses, and again they
> >>> can measure their Doppler shift. But the shift is different from the
> >>> example above (i.e. its dependence on their mutual distance is
> >>> different).
> >>
> > I made a mistake here. In case of equal proper accelerations, their mutual
> > distance (as measured by the accelerating observers) will not be fixed.
>
> Yes. But you said they "hold a constant distance [apart]". So that's not really
> a mistake, they just don't have equal proper accelerations. In either case.
>
>
> >>> Thus, by comparing their distance to the Doppler shift, they can
> >>> determine whether they're accelerating or subject to gravity, apparently
> >>> violating the Equivalence Principle.
> >>
> >> No. You apparently do not know what the equivalence principle (EP)
> >> actually says, or when it does not apply.
> >>[...]
> > I'll state my understanding of the EP. I think it's equivalent to yours -
> > please correct me if I'm wrong.
> >
> > Gravity and acceleration are alike in that the worldlines of freefalling
> > objects do not follow the coordinates axes. One could argue that gravity and
> > acceleration are two different cases, because in the case of acceleration the
> > worldlines are straight, while the coordinates are curved (the t axis is
> > curved in the case of the elevator) while in gravity it's the other way - the
> > coordinates are straight while the geodesics are curved. However the EP
> > states that these two situations are equal, since in either case all you can
> > say is that the axes are curved in respect to the geodesics and vice versa.
> > There's no (measurable) "absolute" spacetime relative to which we can
> > determine which is curved and which isn't. Needless to say, this
> > understanding of the EP implies locality. Do we concur?
>
> No. Your description omits the important restriction to a small 4-volume.
Within
> such a local region all free-falling worldlines are indistinguishable from
> straight lines, regardless of whether gravity is present.
THAT is the key aspect
> of the EP: the size of the local region depends on measurement accuracy (i.e. it
> must be small enough so any deviations from straight lines are too small to be
> measured).
>
>
> > My point was that if you emit a light pulse, tracing its path can't differ
> > gravity from acceleration, since all you can say is that the geodesic
> > deviates from your notion of "straight" (defined by the coordinates you chose
> > to use). However another measurement does. If you measure the Doppler change
> > along the ray, even if this measurement is local (in the infinitesimal sense
> > - the same sense we use to define the deviation of the geodesics from the
> > coordinates, locally), you'll find a difference between gravity and
> > acceleration. The dependence of the Doppler on the radial distance is
> > different in each case.
>
> Again: the key point is that the local region in which the EP applies must be
> small enough so any deviations from straight lines are too small to be measured
>
>
> > What you say is, that with sufficient inaccuracy, every two measurements are
> > equal.... the masses of the sun and earth are euqal. If you measure any
> > difference, it means you're too close to the masses for the instrument you
> > use... get away from the sun and earth, or use a less accurate measurement
> > device, and you won't be able to differ the masses. So you say that we can't
> > differ grav from accel provided that we measure inaccurately enough. I don't
> > think that's what you meant to say.
>
> It's not masses that are involved, but rather measurements of the trajectories
> of free-falling objects.
>
> Consider a horizontal light ray in an elevator 3 meters
> on a side. On earth it will deviate from a straight line
> by ~ 10^-16 meters. That is ~ a million times smaller
> than the best technology today can measure.
>
>
> > I think the EP is a mathematical principle, having nothing to do with actual
> > physical measurements (and the implied inaccuracies).
>
> No. The EP has direct physical implications on what can be, and what is,
> measured. To date, every one of the dozens of experimental tests of the EP has
> confirmed it.
>
> If experiments can test it, it MUST have physical implications.
>
>
> Tom Roberts
Poutnik
Nov 26, 2015, 10:46:48 AM11/26/15
to
Dne 26/11/2015 v 11:21 par...@yahoo.com napsal(a):
As if you consider 2 observers far enough each other
to need different proper acceleration to simulate gravity,
than the gravity in the region covering both of them
is not homogenous and EP does not apply in such too large region.
It is like an approximation of gravity ( curve ) by a tangent line
( acceleration ). EP is like taking this approximation as equivalence,
if curve-line deviation is small enough not to be detectable,
or in context of scenario negligible.
If you consider 2 observers
with different proper acceleration within EP test,
it is a never achievable requirement of ( A AND NOT A ).
The curve vs line deviation detectable AND not detectable.
Respectively, curve approximation by 2 tangentas with different slopes,
each being equivalent-like approximation in its limited scope,
but not in the whole considered scope of the curve.
> בתאריך יום רביעי, 25 בנובמבר 2015 בשעה 17:42:36 UTC+2, מאת tjrob137:
>>
>>
>> Yes. But you said they "hold a constant distance [apart]". So that's not really
>> a mistake, they just don't have equal proper accelerations. In either case.
>>
> You mentioned (in a previous post) that it's easy to differ a
> constantly-accelerating elevator from an elevator in a gravity
> field (as earth's), since the gravity at its top is slightly
> different from the gravity at its buttom. But now, as we speak
> of two observers with different proper acceleration, it's obvious
> that there's no differenec at all. In both cases (gravity and
> accel) you'll measure a difference in gravity/accel between the
> top and bottom while they hold their constant mutual distance.
-----------------------
>> a mistake, they just don't have equal proper accelerations. In either case.
>>
> You mentioned (in a previous post) that it's easy to differ a
> constantly-accelerating elevator from an elevator in a gravity
> field (as earth's), since the gravity at its top is slightly
> different from the gravity at its buttom. But now, as we speak
> of two observers with different proper acceleration, it's obvious
> that there's no differenec at all. In both cases (gravity and
> accel) you'll measure a difference in gravity/accel between the
> top and bottom while they hold their constant mutual distance.
>> No. Your description omits the important restriction to a small 4-volume.
>
> I did mention (in the last sentence) that my statement of the
> EP implies locality. I elaborated on that in the
> last paragraph of my last post.
Have you considered the gravity homogenity requirement ?
>
> I did mention (in the last sentence) that my statement of the
> EP implies locality. I elaborated on that in the
> last paragraph of my last post.
As if you consider 2 observers far enough each other
to need different proper acceleration to simulate gravity,
than the gravity in the region covering both of them
is not homogenous and EP does not apply in such too large region.
It is like an approximation of gravity ( curve ) by a tangent line
( acceleration ). EP is like taking this approximation as equivalence,
if curve-line deviation is small enough not to be detectable,
or in context of scenario negligible.
If you consider 2 observers
with different proper acceleration within EP test,
it is a never achievable requirement of ( A AND NOT A ).
The curve vs line deviation detectable AND not detectable.
Respectively, curve approximation by 2 tangentas with different slopes,
each being equivalent-like approximation in its limited scope,
but not in the whole considered scope of the curve.
Jack Monaco
Nov 26, 2015, 10:54:32 AM11/26/15
to
Poutnik wrote:
>> I did mention (in the last sentence) that my statement of the EP
>> implies locality. I elaborated on that in the last paragraph of my last
>> post.
>
> Have you considered the gravity homogenity requirement ?
Wtf is that gravity can't be homogeneous, but depended, always.
>> I did mention (in the last sentence) that my statement of the EP
>> implies locality. I elaborated on that in the last paragraph of my last
>> post.
>
> Have you considered the gravity homogenity requirement ?
> As if you consider 2 observers far enough each other to need different
> proper acceleration to simulate gravity,
> than the gravity in the region covering both of them is not homogenous
> and EP does not apply in such too large region.
> It is like an approximation of gravity ( curve ) by a tangent line
> ( acceleration ). EP is like taking this approximation as equivalence,
> if curve-line deviation is small enough not to be detectable,
> or in context of scenario negligible.
> If you consider 2 observers with different proper acceleration within EP
> test, it is a never achievable requirement of ( A AND NOT A ).
> The curve vs line deviation detectable AND not detectable.
whole thing.
> Respectively, curve approximation by 2 tangentas with different slopes,
> each being equivalent-like approximation in its limited scope,
> but not in the whole considered scope of the curve.
Poutnik
Nov 26, 2015, 11:43:11 AM11/26/15
to
Dne 26/11/2015 v 16:54 Jack Monaco napsal(a):
so first try to understand and than start talking.
>
> Wtf are you talking about.
>
You have obviously no idea what I am talking about,
> Wtf are you talking about.
>
so first try to understand and than start talking.
Jack Monaco
Nov 26, 2015, 12:10:49 PM11/26/15
to
Poutnik wrote:
> Dne 26/11/2015 v 16:54 Jack Monaco napsal(a):
>>
>> Wtf are you talking about.
>>
> You have obviously no idea what I am talking about,
> so first try to understand and than start talking.
Of course not, since you have no idea what you are trying to philosophize
> Dne 26/11/2015 v 16:54 Jack Monaco napsal(a):
>>
>> Wtf are you talking about.
>>
> You have obviously no idea what I am talking about,
> so first try to understand and than start talking.
about. Seemingly the term *EQUIVALENCE* tells you exactly nothing, hence
you choose to ignore it. Learn this, both gravity AND the elevator holding
things ARE both same Geometrical Interpretation. No difference.
John Heath
Nov 27, 2015, 8:52:09 AM11/27/15
to
Poutnik
Nov 27, 2015, 11:21:20 AM11/27/15
to
On 11/27/2015 02:52 PM, John Heath wrote:
>
> If I were to say "the relation between the geometry of a four-dimensional, pseudo-Riemannian manifold representing spacetime" it would sound like the pretentious words of someone new to physics. The intuitive understanding is the heart of it. Best to keep it as simple as possible so the subject at hand is not lost in words. In my opinion.
>
Sure.
>
> If I were to say "the relation between the geometry of a four-dimensional, pseudo-Riemannian manifold representing spacetime" it would sound like the pretentious words of someone new to physics. The intuitive understanding is the heart of it. Best to keep it as simple as possible so the subject at hand is not lost in words. In my opinion.
>
Tom Roberts
Nov 27, 2015, 1:17:16 PM11/27/15
to
On 11/26/15 11/26/15 4:21 AM, par...@yahoo.com wrote:
> בתאריך יום רביעי, 25 בנובמבר 2015 בשעה 17:42:36 UTC+2, מאת tjrob137:
>> [...] Within
> בתאריך יום רביעי, 25 בנובמבר 2015 בשעה 17:42:36 UTC+2, מאת tjrob137:
>> such a local region all free-falling worldlines are indistinguishable from
>> straight lines, regardless of whether gravity is present.
>
> What you actually say is, that withing a sufficiently small 4D region,
> gravity is undetectable, since worldlines are straight. It's like saying that
> within a small enough 4d region, nonlinear effects don't exist, as each and
> every function is linear to a first approximation.... I don't think that's
> what the EP says.
Yes, that is not what the EP says.
>> straight lines, regardless of whether gravity is present.
>
> What you actually say is, that withing a sufficiently small 4D region,
> gravity is undetectable, since worldlines are straight. It's like saying that
> within a small enough 4d region, nonlinear effects don't exist, as each and
> every function is linear to a first approximation.... I don't think that's
> what the EP says.
Wikipedia's article on the EP has some rather serious problems, which "just so
happen" to parallel your issues. A better description is:
http://www.npl.washington.edu/eotwash/EquivalencePrinciple
No standard statement of the EP actually discusses the trajectories of freely
falling objects.
> It's not a physical principle concerning measurements
> accuracies, telling you that deviation from straight lines are undetectable
> in a small enought region,
region's size on measurement accuracy is INHERENT.
> but rather a philosophical principle, stating that
> two (apparently different) physical phenomena are the same.
theoretical context, and in GR there are not any "two apparently different
physical phenomena".
> More exactly,
> their mathematical description (within the theory) is essentially the same
> (provided we're confines to a local region. But this confinement isn't a
> necessity of measurment's accuracy, but rather a necessity of infinitesimal
> calculus, stating that the derivatives of a function may be different at each
> point, so that calculations made at a specific point may be useless in other
> points. Since the theory uses calculus, all the mathematical restrictions of
> calculus apply). Hope I'm clearer now.
as the measurement interval goes to zero -- (old style) infinitesimals, as you
say. But to a physicist, with knowledge that infinite measurement precision is
not possible, this becomes a statement about measurements within a region whose
size depends on measurement accuracy.
Tom Roberts
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