Questions about the Equivalence Principle (EP) and GR

[agrays...@gmail.com]

1) Using the EP and the example of an accelerating elevator, it follows that light takes a curved path in space (not space-time).  Wasn't this known by virtue of Newtonian gravity?

2) Assuming a geodesic is the shortest distance between two *spatial* points on a curved surface, does it follow from the EP that free falling bodies move on geodesics, and if if so how? 

3) Concerning the above questions, how does "space-time" enter the picture since it seems the questions can be asked without referencing space-time. 

TIA, AG

[Lawrence Crowell]

On Saturday, February 16, 2019 at 6:06:58 PM UTC-6, agrays...@gmail.com wrote:

1) Using the EP and the example of an accelerating elevator, it follows that light takes a curved path in space (not space-time).  Wasn't this known by virtue of Newtonian gravity?

Newton computes half the correct value by general relativity.

 

2) Assuming a geodesic is the shortest distance between two *spatial* points on a curved surface, does it follow from the EP that free falling bodies move on geodesics, and if if so how? 

It is an extremal distance, and because of the Lorentzian metric is is the maximal distance. This extremal principle derives the geodesic equation. This is a standard exercise in introductory courses on general relativity.

 

3) Concerning the above questions, how does "space-time" enter the picture since it seems the questions can be asked without referencing space-time. 

It is because the global or flat theory is special relativity that pertains to local inertial frames.

LC

 

TIA, AG

[agrays...@gmail.com]

On Sunday, February 17, 2019 at 6:34:24 AM UTC-7, Lawrence Crowell wrote:

On Saturday, February 16, 2019 at 6:06:58 PM UTC-6, agrays...@gmail.com wrote:

1) Using the EP and the example of an accelerating elevator, it follows that light takes a curved path in space (not space-time).  Wasn't this known by virtue of Newtonian gravity?

Newton computes half the correct value by general relativity.

I know, but the question is what principle in Newtonian gravity allows us to infer that? AG 

[John Clark]

On Sat, Feb 16, 2019 at 7:07 PM <agrays...@gmail.com> wrote:

1) Using the EP and the example of an accelerating elevator, it follows that light takes a curved path in space (not space-time). 

No, it's spacetime. If a photon of light has moved from one side of an elevator to the other then it has moved in BOTH space and time because, although it's the fastest thing there is, light does not move at infinite speed. Light, just like everything else, always needs time to move through space. You can't change your position in space without changing your position in time.

> Wasn't this known by virtue of Newtonian gravity?

That depends on if light had mass or not; if it didn't, and there was no experimental evidence to indicate that it does, then Newton would say light wouldn't curve at all near the sun, if light does have a rest mass but was just too small to be detected then Newton would say light would curve but only half as much as Einstein said it would. But to Einstein it doesn't make any difference if it has a rest mass or not light must must curve in a gravitational field. So no curvature or slight curvature of light by the sun would be consistent with Newton but only large curvature was consistent with Einstein. And large curvature was exactly what was found in the eclipse of 1918. So Einstein won and Newton lost.

> 2) Assuming a geodesic is the shortest distance between two *spatial* points on a curved surface, does it follow from the EP that free falling bodies move on geodesics, and if if so how? 

Yes Einstein says everything is always following a geodesic path through spacetime unless it is acted on by a force, and to Einstein gravity is not considered a force. So if you jumped out the window you'd follow a geodesic path through spacetime but just standing on the floor you are not because the floor is exerting a upward force on your feet. If spacetime were flat that force would let you to float off the ground but at the surface of the Earth Spacetime is curved so you can't, and we call that spacetime curvature "gravity".

It takes light 1/19,184,132 of a second to move 60 feet 6 inches from pitcher's mound to home plate on a baseball field, Earth's gravity is 32 feet per second per second so in that time something near the Earth surface would drop by D=1/2 *AT^2 =16*(1/19,184,132)^2= 2.7*10^-15 inches, that is the amount the spacetime curvature  a baseball field deviates from perfect flatness,  it's about the same amount of curvature as a sphere with a radius of one light year would have. That's pretty flat but if it were absolutely flat baseball would be a VERY different game.  

3) Concerning the above questions, how does "space-time" enter the picture since it seems the questions can be asked without referencing space-time. 

As Einstein's teacher Hermann Minkowski said about his former student's theory:

"Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."

John K Clark

 

[agrays...@gmail.com]

On Sunday, February 17, 2019 at 6:34:24 AM UTC-7, Lawrence Crowell wrote:

On Saturday, February 16, 2019 at 6:06:58 PM UTC-6, agrays...@gmail.com wrote:

1) Using the EP and the example of an accelerating elevator, it follows that light takes a curved path in space (not space-time).  Wasn't this known by virtue of Newtonian gravity?

Newton computes half the correct value by general relativity.

 

2) Assuming a geodesic is the shortest distance between two *spatial* points on a curved surface, does it follow from the EP that free falling bodies move on geodesics, and if if so how? 

It is an extremal distance, and because of the Lorentzian metric is is the maximal distance. This extremal principle derives the geodesic equation. This is a standard exercise in introductory courses on general relativity.

Is it correct to say that in 3-space with the Euclidian metric the geodesic is the path determined by minimal distance between two points, whereas in 4-space with the Lorentzian metric it's the maximal distance? TIA, AG

[agrays...@gmail.com]

On Sunday, February 17, 2019 at 2:26:12 PM UTC-7, John Clark wrote:

On Sat, Feb 16, 2019 at 7:07 PM <agrays...@gmail.com> wrote:

1) Using the EP and the example of an accelerating elevator, it follows that light takes a curved path in space (not space-time). 

No, it's spacetime. If a photon of light has moved from one side of an elevator to the other then it has moved in BOTH space and time because, although it's the fastest thing there is, light does not move at infinite speed. Light, just like everything else, always needs time to move through space. You can't change your position in space without changing your position in time.

Sure, but why does this obvious fact force us to merge space and time in one concept, aka a manifold? Also, why is it that Newton's law of gravity is not Lorentz invariant, yet it seems to work in all inertial frames? TIA, AG 

> Wasn't this known by virtue of Newtonian gravity?

That depends on if light had mass or not; if it didn't, and there was no experimental evidence to indicate that it does, then Newton would say light wouldn't curve at all near the sun, if light does have a rest mass but was just too small to be detected then Newton would say light would curve but only half as much as Einstein said it would. But to Einstein it doesn't make any difference if it has a rest mass or not light must must curve in a gravitational field. So no curvature or slight curvature of light by the sun would be consistent with Newton but only large curvature was consistent with Einstein. And large curvature was exactly what was found in the eclipse of 1918. So Einstein won and Newton lost.

> 2) Assuming a geodesic is the shortest distance between two *spatial* points on a curved surface, does it follow from the EP that free falling bodies move on geodesics, and if if so how? 

Yes Einstein says everything is always following a geodesic path through spacetime unless it is acted on by a force, and to Einstein gravity is not considered a force.

So how does GR explain motion? That is, how does curvature of space-time result in motion? AG

 

So if you jumped out the window you'd follow a geodesic path through spacetime but just standing on the floor you are not because the floor is exerting a upward force on your feet. If spacetime were flat that force would let you to float off the ground but at the surface of the Earth Spacetime is curved so you can't, and we call that spacetime curvature "gravity".

It takes light 1/19,184,132 of a second to move 60 feet 6 inches from pitcher's mound to home plate on a baseball field, Earth's gravity is 32 feet per second per second so in that time something near the Earth surface would drop by D=1/2 *AT^2 =16*(1/19,184,132)^2= 2.7*10^-15 inches, that is the amount the spacetime curvature  a baseball field deviates from perfect flatness,  it's about the same amount of curvature as a sphere with a radius of one light year would have. That's pretty flat but if it were absolutely flat baseball would be a VERY different game.  

What would baseball look like without that tiny curvature? AG 

[Brent Meeker]

On 2/18/2019 2:05 PM, agrays...@gmail.com wrote:

Is it correct to say that in 3-space with the Euclidian metric the geodesic is the path determined by minimal distance between two points, whereas in 4-space with the Lorentzian metric it's the maximal distance? TIA, AG

That's right as far as it goes.  "Geodesic" is a general term in geometry, applying to curved spaces as well as flat and it refers to paths that are extremal.  So in general relativity there can be different geodesics between the same two events, each of which is a local extremal.

Brent

[agrays...@gmail.com]

Do you mean the metric tensor differs, depending on the coordinate system? TIA, AG 

Brent

[agrays...@gmail.com]

I don't understand your comment. Curvature of space-time should be independent of coordinate systems, so how can there be different extremals for two fixed events in the manifold?  AG

Brent

[John Clark]

On Mon, Feb 18, 2019 at 5:30 PM <agrays...@gmail.com> wrote:

> Sure, but why does this obvious fact force us to merge space and time in one concept, aka a manifold?

If you want to meet me in Manhattan you're going to have to give me 4 numbers (aka dimensions); 2 of them will give me the street corner, another one will tell me what floor to get off the elevator,  and the fourth will give me the time of the meeting.

 

> Also, why is it that Newton's law of gravity is not Lorentz invariant, yet it seems to work in all inertial frames? TIA, AG 

Newton's law of gravity only approximately works, although the approximation is quite good provided the speeds involved are not too large and the spacetime curvature (aka gravity) is not too great.  Newton's world was not Lorentz invariant because there was no limit on how fast you could go, so the laws of physics would look different depending on how fast you were going; if you could move at the speed of light in a closed elevator you could tell you were moving because a  beam of light would look frozen in violation of Maxwell's Equations which says light always moves at the same speed. Therefore if things are Lorentz invariant you can't move at the speed of light in a closed elevator.

By the way, when Maxwell came up with his theory some thought the one flaw in the idea was that the speed of light that the theory produced with did not say the speed relative to what. But Einstein realized that Maxwell's greatest flaw was really his greatest triumph. 

> So how does GR explain motion? That is, how does curvature of space-time result in motion? AG

Motion is how a change in time relates to a change in space,  if spacetime is flat a given instance in time corresponds to a particular point in space,  if spacetime is curved that same instance in time would correspond to a different point in space.

> What would baseball look like without that tiny curvature? AG 

Imagine a baseball game played on the International Space Station.

John K Clark

[agrays...@gmail.com]

On Tuesday, February 19, 2019 at 6:41:52 AM UTC-7, John Clark wrote:

On Mon, Feb 18, 2019 at 5:30 PM <agrays...@gmail.com> wrote:

> Sure, but why does this obvious fact force us to merge space and time in one concept, aka a manifold?

If you want to meet me in Manhattan you're going to have to give me 4 numbers (aka dimensions); 2 of them will give me the street corner, another one will tell me what floor to get off the elevator,  and the fourth will give me the time of the meeting.

You seem to have a firm grasp of the obvious. Perhaps the reason space and time must be merged is for a much deeper reason; namely, only by merging them can we get a curvature of the result. AG  

 

> Also, why is it that Newton's law of gravity is not Lorentz invariant, yet it seems to work in all inertial frames? TIA, AG 

Newton's law of gravity only approximately works, although the approximation is quite good provided the speeds involved are not too large and the spacetime curvature (aka gravity) is not too great.  Newton's world was not Lorentz invariant because there was no limit on how fast you could go, so the laws of physics would look different depending on how fast you were going; if you could move at the speed of light in a closed elevator you could tell you were moving because a  beam of light would look frozen in violation of Maxwell's Equations which says light always moves at the same speed. Therefore if things are Lorentz invariant you can't move at the speed of light in a closed elevator.

By the way, when Maxwell came up with his theory some thought the one flaw in the idea was that the speed of light that the theory produced with did not say the speed relative to what. But Einstein realized that Maxwell's greatest flaw was really his greatest triumph. 

Can you cite any statement by Einstein to this effect? AG 

> So how does GR explain motion? That is, how does curvature of space-time result in motion? AG

Motion is how a change in time relates to a change in space,  if spacetime is flat a given instance in time corresponds to a particular point in space,  if spacetime is curved that same instance in time would correspond to a different point in space.

Please elaborate. I don't understand how curvature in itself produces accelerated motion. AG 

> What would baseball look like without that tiny curvature? AG 

Imagine a baseball game played on the International Space Station.

It's strange that such a small change in curvature, produces such a hugely different result. AG 

John K Clark

[Brent Meeker]

No.  A tensor, like a vector, is a geometric object.  It has different representations depending on the coordinate system, but those representations transform like a real object that is independent of the coordinate system.

Brent

[Brent Meeker]

On 2/19/2019 3:41 AM, agrays...@gmail.com wrote:

I don't understand your comment. Curvature of space-time should be independent of coordinate systems, so how can there be different extremals for two fixed events in the manifold?  AG

There can be a "hill" between the two events so that there are extremal paths around it, one on each side.  This how a galactic mass produces Einstein's ring.  A common test question is: There is a clock in low Earth orbit.  Another clock is launched straight up (assume non-rotating Earth) so that it just passes the orbiting clock on the way up and then it falls back such that it just passes the orbiting clock, one orbit later, on it's way down.  Between the two coincident events the clocks are in free fall, following geodesics.   Which one registers the longer interval between the coincident events?

Brent

[John Clark]

On Tue, Feb 19, 2019 at 1:28 PM <agrays...@gmail.com> wrote:

>> If you want to meet me in Manhattan you're going to have to give me 4 numbers (aka dimensions); 2 of them will give me the street corner, another one will tell me what floor to get off the elevator,  and the fourth will give me the time of the meeting.

> You seem to have a firm grasp of the obvious.

Is there any particular reason you always feel the need to be a dick even to one who is trying his best to answer your questions?

 

> Perhaps the reason space and time must be merged is for a much deeper reason; namely, only by merging them can we get a curvature of the result. AG  

Talk about a firm grasp of the obvious!  You can't have a curve without at least 2 dimensions.

 

>> Also, why is it that Newton's law of gravity is not Lorentz invariant, yet it seems to work in all inertial frames? TIA, AG 

Newton's law of gravity only approximately works, although the approximation is quite good provided the speeds involved are not too large and the spacetime curvature (aka gravity) is not too great.  Newton's world was not Lorentz invariant because there was no limit on how fast you could go, so the laws of physics would look different depending on how fast you were going; if you could move at the speed of light in a closed elevator you could tell you were moving because a  beam of light would look frozen in violation of Maxwell's Equations which says light always moves at the same speed. Therefore if things are Lorentz invariant you can't move at the speed of light in a closed elevator.

By the way, when Maxwell came up with his theory some thought the one flaw in the idea was that the speed of light that the theory produced with did not say the speed relative to what. But Einstein realized that Maxwell's greatest flaw was really his greatest triumph. 

> Can you cite any statement by Einstein to this effect? AG 

I could, but it would be obvious.

 

>>Motion is how a change in time relates to a change in space,  if spacetime is flat a given instance in time corresponds to a particular point in space,  if spacetime is curved that same instance in time would correspond to a different point in space.

> Please elaborate.

No, why should I?

 

> I don't understand

I'm not surprised.

John K Clark

[agrays...@gmail.com]

On Tuesday, February 19, 2019 at 2:50:42 PM UTC-7, John Clark wrote:

On Tue, Feb 19, 2019 at 1:28 PM <agrays...@gmail.com> wrote:

>> If you want to meet me in Manhattan you're going to have to give me 4 numbers (aka dimensions); 2 of them will give me the street corner, another one will tell me what floor to get off the elevator,  and the fourth will give me the time of the meeting.

> You seem to have a firm grasp of the obvious.

Is there any particular reason you always feel the need to be a dick even to one who is trying his best to answer your questions?

I apologize. I really do. But seriously, your explanation for merging space and time is hugely simplistic, and in fact not right. They have to be merged in order to create curvature in 4 dimensions. Otherwise, if only space is involved, we can't even define a Lorentzian metric. AG 

 

> Perhaps the reason space and time must be merged is for a much deeper reason; namely, only by merging them can we get a curvature of the result. AG  

Talk about a firm grasp of the obvious!  You can't have a curve without at least 2 dimensions.

I explained at least one of the requirements for going to 4 dimensions. AG 

 

>> Also, why is it that Newton's law of gravity is not Lorentz invariant, yet it seems to work in all inertial frames? TIA, AG 

Newton's law of gravity only approximately works, although the approximation is quite good provided the speeds involved are not too large and the spacetime curvature (aka gravity) is not too great.  Newton's world was not Lorentz invariant because there was no limit on how fast you could go, so the laws of physics would look different depending on how fast you were going; if you could move at the speed of light in a closed elevator you could tell you were moving because a  beam of light would look frozen in violation of Maxwell's Equations which says light always moves at the same speed. Therefore if things are Lorentz invariant you can't move at the speed of light in a closed elevator.

By the way, when Maxwell came up with his theory some thought the one flaw in the idea was that the speed of light that the theory produced with did not say the speed relative to what. But Einstein realized that Maxwell's greatest flaw was really his greatest triumph. 

> Can you cite any statement by Einstein to this effect? AG 

I could, but it would be obvious.

 

>>Motion is how a change in time relates to a change in space,  if spacetime is flat a given instance in time corresponds to a particular point in space,  if spacetime is curved that same instance in time would correspond to a different point in space.

> Please elaborate.

No, why should I?

 

> I don't understand

I'm not surprised.

What you wrote makes no sense. It fails to explain why motion occurs in the absence of force. AG 

John K Clark

[Brent Meeker]

On 2/19/2019 5:10 PM, agrays...@gmail.com wrote:

What you wrote makes no sense. It fails to explain why motion occurs in the absence of force. AG 

So did Newton: "A body in motion will remain in motion."

Brent

[Brent Meeker]

On 2/19/2019 5:10 PM, agrays...@gmail.com wrote:

I apologize. I really do. But seriously, your explanation for merging space and time is hugely simplistic, and in fact not right. They have to be merged in order to create curvature in 4 dimensions. Otherwise, if only space is involved, we can't even define a Lorentzian metric. AG 

A Lorentz boost mixes space and time in a way that Newtonian/Galilean transforms do not.
Here's a man who has a bullet fired at him from about 12ft away.  He has light which illuminates the bullet so he sees the bullet 20 nanosec after it was fired



If we look at it from the bullet's frame of reference using a Galilean transformation the events of the origination of the photons the man sees, their reflection off the bullet and their arrival at the man's eye are arranged like this. 



But this implies that in the bullets reference frame the light was moving faster as it approached the bullet and slower as it was reflected back toward the man.  This was in conflict the experimental evidence that light had the same speed no matter which reference frame you used to measure it, and with Maxwell's equations which also made no reference to a special frame.  So Einstein hypothesized that Galileo's transform was wrong and that transforming to a moving frame had to keep the speed of light the same:



The Lorentz transform does this, but such that the space axes have a time component, thus mixing space and time.  It is not just to accommodate curvature.

Brent

[agrays...@gmail.com]

Right, but Newton "explained" why a body at "rest" can start moving, via the application of "force".  What does "rest" mean in GR and what causes "motion" from that pov? Incidentally, when I posed the question of why space and time must be fused in relativity. I didn't know the answer. I came to a partial explanation by posing the question. AG

Brent

[Philip Thrift]

Physics doesn't really explain anything. It only creates expressions in different mathematical dialects that we interpret.

https://www.newyorker.com/science/elements/a-different-kind-of-theory-of-everything 

In 1964, during a lecture at Cornell University, the physicist Richard Feynman articulated a profound mystery about the physical world. He told his listeners to imagine two objects, each gravitationally attracted to the other. How, he asked, should we predict their movements? Feynman identified three approaches, each invoking a different belief about the world. The first approach used Newton’s law of gravity, according to which the objects exert a pull on each other. The second imagined a gravitational field extending through space, which the objects distort. The third applied the principle of least action, which holds that each object moves by following the path that takes the least energy in the least time. All three approaches produced the same, correct prediction. They were three equally useful descriptions of how gravity works.

“One of the amazing characteristics of nature is this variety of interpretational schemes,” Feynman said. ... “If you modify the laws much, you find you can only write them in fewer ways,” Feynman said. “I always found that mysterious, and I do not know the reason why it is that the correct laws of physics are expressible in such a tremendous variety of ways. They seem to be able to get through several wickets at the same time.”

...

- pt

[agrays...@gmail.com]

On Wednesday, February 20, 2019 at 12:30:01 AM UTC-7, Philip Thrift wrote:

On Wednesday, February 20, 2019 at 1:06:25 AM UTC-6, agrays...@gmail.com wrote:

On Tuesday, February 19, 2019 at 8:16:51 PM UTC-7, Brent wrote:

On 2/19/2019 5:10 PM, agrays...@gmail.com wrote:

What you wrote makes no sense. It fails to explain why motion occurs in the absence of force. AG 

So did Newton: "A body in motion will remain in motion."

Right, but Newton "explained" why a body at "rest" can start moving, via the application of "force".  What does "rest" mean in GR and what causes "motion" from that pov? Incidentally, when I posed the question of why space and time must be fused in relativity. I didn't know the answer. I came to a partial explanation by posing the question. AG

Physics doesn't really explain anything. It only creates expressions in different mathematical dialects that we interpret.

Right. That's why I put the quotes around *explained*. AG 

https://www.newyorker.com/science/elements/a-different-kind-of-theory-of-everything 

In 1964, during a lecture at Cornell University, the physicist Richard Feynman articulated a profound mystery about the physical world. He told his listeners to imagine two objects, each gravitationally attracted to the other. How, he asked, should we predict their movements? Feynman identified three approaches, each invoking a different belief about the world. The first approach used Newton’s law of gravity, according to which the objects exert a pull on each other. The second imagined a gravitational field extending through space, which the objects distort. The third applied the principle of least action, which holds that each object moves by following the path that takes the least energy in the least time. All three approaches produced the same, correct prediction. They were three equally useful descriptions of how gravity works.

Except that it's wrong to put Newton's gravity theory on the same level as Einstein's. Also, I think we can dispense with the Principle of Least Action and just use the geodesic hypothesis as a postulate of GR.  We could say that God preferred a unique path, the extremal, rather than having to choose among an uncountable set of paths for each path between distinct events in the manifold. AG

[John Clark]

> Newton "explained"

Why did you put explained in quotation marks? If you can predict what something is going to do then you've explained it, the better the prediction the better the explanation. I don't know what else the word could possibly mean. And in science no explanation is perfect, but some are less wrong than others.

> why a body at "rest" can start moving, via the application of "force"

And Einstein explained that a body moving in a geodesic through 4D spacetime will take a path that is not a geodesic if a force is applied. The Earth is moving in a straight line (aka a geodesic) through curved spacetime; the reason Earth's orbit looks elliptical to us is due to map distortion, the same reason that in a flat map of the curved surface of the Earth Greenland looks larger than South America and is almost as large as Africa. Except that it's even worse, in one we're projecting the 2 D curved surface of the Earth into the flat 2D surface of the map, but with Einstein we're projecting a curved 4D volume into a flat 3D volume.

> What does "rest" mean in GR

In General Relativity moving in a geodesic is as close as you can get to the traditional idea of rest, but as long as time passes you're going to be moving through 4D spacetime.

>  what causes "motion" from that pov?

Force, same as with Newton.

John K Clark

[agrays...@gmail.com]

On Wednesday, February 20, 2019 at 7:09:10 AM UTC-7, John Clark wrote:

> Newton "explained"

Why did you put explained in quotation marks? If you can predict what something is going to do then you've explained it, the better the prediction the better the explanation. I don't know what else the word could possibly mean. And in science no explanation is perfect, but some are less wrong than others.

QM better illustrates the justification for quotes. Many interpretations that make the same predictions. AG 

> why a body at "rest" can start moving, via the application of "force"

And Einstein explained that a body moving in a geodesic through 4D spacetime will take a path that is not a geodesic if a force is applied. The Earth is moving in a straight line (aka a geodesic) through curved spacetime; the reason Earth's orbit looks elliptical to us is due to map distortion, the same reason that in a flat map of the curved surface of the Earth Greenland looks larger than South America and is almost as large as Africa. Except that it's even worse, in one we're projecting the 2 D curved surface of the Earth into the flat 2D surface of the map, but with Einstein we're projecting a curved 4D volume into a flat 3D volume.

> What does "rest" mean in GR

In General Relativity moving in a geodesic is as close as you can get to the traditional idea of rest, but as long as time passes you're going to be moving through 4D spacetime.

If you're at spatial rest in spacetime in the presence of a gravitational source, how does GR explain the subsequent spatial motion? AG 

[John Clark]

On Wed, Feb 20, 2019 at 11:42 AM <agrays...@gmail.com> wrote:

> QM better illustrates the justification for quotes. Many interpretations that make the same predictions. AG 

Yes, many interpretations of Quantum Mechanics make the same predictions, so at least for now which interpretation (explanation) you use is a matter of taste. I hope someday we will know enough to be able to decide among them. I like Many Worlds but that's just me

> If you're at spatial rest in spacetime

Then you're still moving through 4D spacetime

> in the presence of a gravitational source,

If I'm at spatial rest in the presence of a gravitational source then I'm not on a geodesic path; I could be hovering 500 feet off the ground in a rocket pushing me upward, and then the rocket stops and, since a force is no longer operating, I'm back on a geodesic path until I reach the ground and then the force of the ground provides a upward force again and I'm back on a non geodesic path through spacetime, or at least the broken parts of my body are.

 

> how does GR explain the subsequent spatial motion? AG 

I don't understand the question, if I'm at spatial rest how can I be at spatial motion?

John K Clark

 

[Brent Meeker]

On 2/19/2019 11:06 PM, agrays...@gmail.com wrote:

On Tuesday, February 19, 2019 at 8:16:51 PM UTC-7, Brent wrote:

On 2/19/2019 5:10 PM, agrays...@gmail.com wrote:

What you wrote makes no sense. It fails to explain why motion occurs in the absence of force. AG 

So did Newton: "A body in motion will remain in motion."

Right, but Newton "explained" why a body at "rest" can start moving, via the application of "force".  What does "rest" mean in GR and what causes "motion" from that pov?

Same thing.   Any body that have no forces on it is "at rest" in it's own frame, just like in Newtonian physics...except that gravity is no longer a force.   So free falling bodies are "at rest".

Brent

Incidentally, when I posed the question of why space and time must be fused in relativity. I didn't know the answer. I came to a partial explanation by posing the question. AG

Brent

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[Brent Meeker]

When you were at "spatial rest" you had a force applied to you.  Removing it allowed you to follow a geodesics path through spacetime....also known as "falling".

Brent

>  what causes "motion" from that pov?

Force, same as with Newton.

John K Clark

--

[agrays...@gmail.com]

On Wednesday, February 20, 2019 at 12:16:31 PM UTC-7, Brent wrote:

On 2/20/2019 8:42 AM, agrays...@gmail.com wrote:

On Wednesday, February 20, 2019 at 7:09:10 AM UTC-7, John Clark wrote:

> Newton "explained"

Why did you put explained in quotation marks? If you can predict what something is going to do then you've explained it, the better the prediction the better the explanation. I don't know what else the word could possibly mean. And in science no explanation is perfect, but some are less wrong than others.

QM better illustrates the justification for quotes. Many interpretations that make the same predictions. AG 

> why a body at "rest" can start moving, via the application of "force"

And Einstein explained that a body moving in a geodesic through 4D spacetime will take a path that is not a geodesic if a force is applied. The Earth is moving in a straight line (aka a geodesic) through curved spacetime; the reason Earth's orbit looks elliptical to us is due to map distortion, the same reason that in a flat map of the curved surface of the Earth Greenland looks larger than South America and is almost as large as Africa. Except that it's even worse, in one we're projecting the 2 D curved surface of the Earth into the flat 2D surface of the map, but with Einstein we're projecting a curved 4D volume into a flat 3D volume.

> What does "rest" mean in GR

In General Relativity moving in a geodesic is as close as you can get to the traditional idea of rest, but as long as time passes you're going to be moving through 4D spacetime.

If you're at spatial rest in spacetime in the presence of a gravitational source, how does GR explain the subsequent spatial motion? AG

When you were at "spatial rest" you had a force applied to you.  Removing it allowed you to follow a geodesics path through spacetime....also known as "falling".

Brent

So it seems that GR doesn't explain motion; rather, it assumes motion is a natural state of things. AG 

[Brent Meeker]

On 2/20/2019 1:23 PM, agrays...@gmail.com wrote:

On Wednesday, February 20, 2019 at 12:16:31 PM UTC-7, Brent wrote:

On 2/20/2019 8:42 AM, agrays...@gmail.com wrote:

On Wednesday, February 20, 2019 at 7:09:10 AM UTC-7, John Clark wrote:

> Newton "explained"

Why did you put explained in quotation marks? If you can predict what something is going to do then you've explained it, the better the prediction the better the explanation. I don't know what else the word could possibly mean. And in science no explanation is perfect, but some are less wrong than others.

QM better illustrates the justification for quotes. Many interpretations that make the same predictions. AG 

> why a body at "rest" can start moving, via the application of "force"

And Einstein explained that a body moving in a geodesic through 4D spacetime will take a path that is not a geodesic if a force is applied. The Earth is moving in a straight line (aka a geodesic) through curved spacetime; the reason Earth's orbit looks elliptical to us is due to map distortion, the same reason that in a flat map of the curved surface of the Earth Greenland looks larger than South America and is almost as large as Africa. Except that it's even worse, in one we're projecting the 2 D curved surface of the Earth into the flat 2D surface of the map, but with Einstein we're projecting a curved 4D volume into a flat 3D volume.

> What does "rest" mean in GR

In General Relativity moving in a geodesic is as close as you can get to the traditional idea of rest, but as long as time passes you're going to be moving through 4D spacetime.

If you're at spatial rest in spacetime in the presence of a gravitational source, how does GR explain the subsequent spatial motion? AG

When you were at "spatial rest" you had a force applied to you.  Removing it allowed you to follow a geodesics path through spacetime....also known as "falling".

Brent

So it seems that GR doesn't explain motion; rather, it assumes motion is a natural state of things. AG

So called "standing still" is just motion in the time direction only...in Newtonian and special relativity as well. Just as there is no absolute motion, there's no absolution motionless either...it's called "relativity" for a reason.

Brent

[agrays...@gmail.com]

On Wednesday, February 20, 2019 at 7:50:51 PM UTC-7, Brent wrote:

On 2/20/2019 1:23 PM, agrays...@gmail.com wrote:

On Wednesday, February 20, 2019 at 12:16:31 PM UTC-7, Brent wrote:

On 2/20/2019 8:42 AM, agrays...@gmail.com wrote:

On Wednesday, February 20, 2019 at 7:09:10 AM UTC-7, John Clark wrote:

> Newton "explained"

Why did you put explained in quotation marks? If you can predict what something is going to do then you've explained it, the better the prediction the better the explanation. I don't know what else the word could possibly mean. And in science no explanation is perfect, but some are less wrong than others.

QM better illustrates the justification for quotes. Many interpretations that make the same predictions. AG 

> why a body at "rest" can start moving, via the application of "force"

And Einstein explained that a body moving in a geodesic through 4D spacetime will take a path that is not a geodesic if a force is applied. The Earth is moving in a straight line (aka a geodesic) through curved spacetime; the reason Earth's orbit looks elliptical to us is due to map distortion, the same reason that in a flat map of the curved surface of the Earth Greenland looks larger than South America and is almost as large as Africa. Except that it's even worse, in one we're projecting the 2 D curved surface of the Earth into the flat 2D surface of the map, but with Einstein we're projecting a curved 4D volume into a flat 3D volume.

> What does "rest" mean in GR

In General Relativity moving in a geodesic is as close as you can get to the traditional idea of rest, but as long as time passes you're going to be moving through 4D spacetime.

If you're at spatial rest in spacetime in the presence of a gravitational source, how does GR explain the subsequent spatial motion? AG

When you were at "spatial rest" you had a force applied to you.  Removing it allowed you to follow a geodesics path through spacetime....also known as "falling".

Brent

So it seems that GR doesn't explain motion; rather, it assumes motion is a natural state of things. AG

So called "standing still" is just motion in the time direction only...in Newtonian and special relativity as well. Just as there is no absolute motion, there's no absolution motionless either...it's called "relativity" for a reason.

Brent

Other than gravity, the remaining known forces are moderated, or shall we say "caused by" particles. Doesn't GR remain an exception; that is, wouldn't it preclude the existence of a graviton? TIA, AG 

[Philip Thrift]

On Thursday, February 21, 2019 at 7:27:27 AM UTC-6, agrays...@gmail.com wrote:

Other than gravity, the remaining known forces are moderated, or shall we say "caused by" particles. Doesn't GR remain an exception; that is, wouldn't it preclude the existence of a graviton? TIA, AG

Just my opinion: There are at least two possibilities for gravity people are considering.

1. Gravity is "mediated" by particles: gravitons.  Here, all particles (including gravitons) "move" in a conventional spacetime background.

2. Space (or spacetime) itself is composed in some way as a collection of "particles" ("cells", "tiles", ...). This is the approach of LQG and CDT. There is no background "space" that things move in anymore in the conventional sense: just a bunch of spacicles and particles interacting.

There could be others of course (e.g. HOPE - Histories of Phenomenally Everything, ...).

- pt

[Brent Meeker]

On 2/21/2019 5:27 AM, agrays...@gmail.com wrote:

On Wednesday, February 20, 2019 at 7:50:51 PM UTC-7, Brent wrote:

On 2/20/2019 1:23 PM, agrays...@gmail.com wrote:

On Wednesday, February 20, 2019 at 12:16:31 PM UTC-7, Brent wrote:

On 2/20/2019 8:42 AM, agrays...@gmail.com wrote:

On Wednesday, February 20, 2019 at 7:09:10 AM UTC-7, John Clark wrote:

> Newton "explained"

Why did you put explained in quotation marks? If you can predict what something is going to do then you've explained it, the better the prediction the better the explanation. I don't know what else the word could possibly mean. And in science no explanation is perfect, but some are less wrong than others.

QM better illustrates the justification for quotes. Many interpretations that make the same predictions. AG 

> why a body at "rest" can start moving, via the application of "force"

And Einstein explained that a body moving in a geodesic through 4D spacetime will take a path that is not a geodesic if a force is applied. The Earth is moving in a straight line (aka a geodesic) through curved spacetime; the reason Earth's orbit looks elliptical to us is due to map distortion, the same reason that in a flat map of the curved surface of the Earth Greenland looks larger than South America and is almost as large as Africa. Except that it's even worse, in one we're projecting the 2 D curved surface of the Earth into the flat 2D surface of the map, but with Einstein we're projecting a curved 4D volume into a flat 3D volume.

> What does "rest" mean in GR

In General Relativity moving in a geodesic is as close as you can get to the traditional idea of rest, but as long as time passes you're going to be moving through 4D spacetime.

If you're at spatial rest in spacetime in the presence of a gravitational source, how does GR explain the subsequent spatial motion? AG

When you were at "spatial rest" you had a force applied to you.  Removing it allowed you to follow a geodesics path through spacetime....also known as "falling".

Brent

So it seems that GR doesn't explain motion; rather, it assumes motion is a natural state of things. AG

So called "standing still" is just motion in the time direction only...in Newtonian and special relativity as well. Just as there is no absolute motion, there's no absolution motionless either...it's called "relativity" for a reason.

Brent

Other than gravity, the remaining known forces are moderated, or shall we say "caused by" particles. Doesn't GR remain an exception; that is, wouldn't it preclude the existence of a graviton? TIA, AG

Gravitons, the weak-field limit quanta of the gravitational field, aren't precluded.  They are implicit in string-theory; which is why string theory is a candidate for the quantum theory of gravity.  The problem is there's no mathematically consistent way to extend the graviton, weak field, picture to the strong field limit and predict what happens in a black hole where GR predicts a singularity.

Brent

[John Clark]

On Thu, Feb 21, 2019 at 8:27 AM <agrays...@gmail.com> wrote:

> Other than gravity, the remaining known forces are moderated, or shall we say "caused by" particles. Doesn't GR remain an exception; that is, wouldn't it preclude the existence of a graviton? TIA, AG 

3 of the 4 fundamental forces of nature are explained by Quantum Mechanics and all 3 are moderated by particles; General Relativity alone deals with gravity, so far at least Quantum Mechanics  has proved itself useless there and we can't even get these 2 very successful theories to talk to each other much less merge. If space and time are quantized then the graviton could exist but due to its elusive nature even if it does exist it is quite likely nobody will ever be able to detect a graviton. 

As far as I know the first person to point this out was Freeman Dyson in  a brilliant  talk he gave in 2014 (on his 90th birthday!!) and shows that something like LIGO could never detect one and other methods have little chance either:

Freeman Dyson: Is a Graviton Detectable?

In rebuttal to Dyson some say graviton might be datatable in theory but not in practice:

Can Gravitons Be Detected?

John K Clark

[agrays...@gmail.com]

On Thursday, February 21, 2019 at 1:35:17 PM UTC-7, Brent wrote:

On 2/21/2019 5:27 AM, agrays...@gmail.com wrote:

On Wednesday, February 20, 2019 at 7:50:51 PM UTC-7, Brent wrote:

On 2/20/2019 1:23 PM, agrays...@gmail.com wrote:

On Wednesday, February 20, 2019 at 12:16:31 PM UTC-7, Brent wrote:

On 2/20/2019 8:42 AM, agrays...@gmail.com wrote:

On Wednesday, February 20, 2019 at 7:09:10 AM UTC-7, John Clark wrote:

> Newton "explained"

Why did you put explained in quotation marks? If you can predict what something is going to do then you've explained it, the better the prediction the better the explanation. I don't know what else the word could possibly mean. And in science no explanation is perfect, but some are less wrong than others.

QM better illustrates the justification for quotes. Many interpretations that make the same predictions. AG 

> why a body at "rest" can start moving, via the application of "force"

And Einstein explained that a body moving in a geodesic through 4D spacetime will take a path that is not a geodesic if a force is applied. The Earth is moving in a straight line (aka a geodesic) through curved spacetime; the reason Earth's orbit looks elliptical to us is due to map distortion, the same reason that in a flat map of the curved surface of the Earth Greenland looks larger than South America and is almost as large as Africa. Except that it's even worse, in one we're projecting the 2 D curved surface of the Earth into the flat 2D surface of the map, but with Einstein we're projecting a curved 4D volume into a flat 3D volume.

> What does "rest" mean in GR

In General Relativity moving in a geodesic is as close as you can get to the traditional idea of rest, but as long as time passes you're going to be moving through 4D spacetime.

If you're at spatial rest in spacetime in the presence of a gravitational source, how does GR explain the subsequent spatial motion? AG

When you were at "spatial rest" you had a force applied to you.  Removing it allowed you to follow a geodesics path through spacetime....also known as "falling".

Brent

So it seems that GR doesn't explain motion; rather, it assumes motion is a natural state of things. AG

So called "standing still" is just motion in the time direction only...in Newtonian and special relativity as well. Just as there is no absolute motion, there's no absolution motionless either...it's called "relativity" for a reason.

Brent

Other than gravity, the remaining known forces are moderated, or shall we say "caused by" particles. Doesn't GR remain an exception; that is, wouldn't it preclude the existence of a graviton? TIA, AG

Gravitons, the weak-field limit quanta of the gravitational field, aren't precluded.  They are implicit in string-theory; which is why string theory is a candidate for the quantum theory of gravity.  The problem is there's no mathematically consistent way to extend the graviton, weak field, picture to the strong field limit and predict what happens in a black hole where GR predicts a singularity.

Brent

ISTM that gravitons would be inconsistent with GR, which derives gravitating motion from geometry, not mediating particles.  AG

[Brent Meeker]

It is conceptually inconsistent, just as GR is conceptually inconsistent with Newtonian gravity.  But that doesn't mean the theories make detectably different predictions in the domain where we can test them.  Notice how difficult it was to test GR vs Newton.

Brent

[agrays...@gmail.com]

Even if gravitons are detected, and they account for "force" consistent with the other three forces, wouldn't there remain the task of changing the form of gravity to make it covariant? Would that require tensors? AG

[Brent Meeker]

Gravitons, as quanta of the metric field, are already relativistic particles and covariant.

Would that require tensors? AG

Dunno.  But it would have to reduce to GR in the weak field statmech limit, so it would have something that reduced to tensors in that limit.

Brent

[agrays...@gmail.com]

Even if gravitons are detected, and they account for "force" consistent with the other three forces, wouldn't there remain the task of changing the form of gravity to make it covariant? AG

Gravitons, as quanta of the metric field, are already relativistic particles and covariant.

I thought it's the equations of motion for the particular force, not the mediating particles, that must be covariant. On a related topic for this thread, where does GR depart from Mach's principle? That is, what did Einstein implicitly (or explicitly) deny about Mach's principle? TIA, AG 

[Brent Meeker]

On 2/22/2019 2:40 PM, agrays...@gmail.com wrote:

Gravitons, as quanta of the metric field, are already relativistic particles and covariant.

I thought it's the equations of motion for the particular force, not the mediating particles, that must be covariant. On a related topic for this thread, where does GR depart from Mach's principle? That is, what did Einstein implicitly (or explicitly) deny about Mach's principle? TIA, AG 

Einstein thought he would develop a theory that satisfied Mach's principle, but as it turned out GR doesn't. For example the metric of spacetime is a dynamic field and transmit momentum and energy, as shown by LIGO.  Mach's idea of spacetime as purely a relation between material events couldn't do that.

Brent

[agrays...@gmail.com]

Were you inferring covariance simply because the mediating particle for gravity, the graviton, travels at the SoL? I thought it's the equations of motion for the particular force, not the mediating particles, that must be covariant.  Do we have equations of motions for strong and weak forces, which are covariant? AG

[Brent Meeker]

On 2/22/2019 6:04 PM, agrays...@gmail.com wrote:

On Friday, February 22, 2019 at 4:55:41 PM UTC-7, Brent wrote:

On 2/22/2019 2:40 PM, agrays...@gmail.com wrote:

Gravitons, as quanta of the metric field, are already relativistic particles and covariant.

I thought it's the equations of motion for the particular force, not the mediating particles, that must be covariant. On a related topic for this thread, where does GR depart from Mach's principle? That is, what did Einstein implicitly (or explicitly) deny about Mach's principle? TIA, AG 

Einstein thought he would develop a theory that satisfied Mach's principle, but as it turned out GR doesn't. For example the metric of spacetime is a dynamic field and transmit momentum and energy, as shown by LIGO.  Mach's idea of spacetime as purely a relation between material events couldn't do that.

Brent

Were you inferring covariance simply because the mediating particle for gravity, the graviton, travels at the SoL?

GR is a covariant theory.  So it's quanta, gravitons, are covariant.

I thought it's the equations of motion for the particular force, not the mediating particles, that must be covariant.  Do we have equations of motions for strong and weak forces, which are covariant? AG

Forces are mediated by exchange of bosons.  Those bosons appear in the Standard Model Lagrangian, from which equations of motion can be derived.

https://en.wikipedia.org/wiki/Mathematical_formulation_of_the_Standard_Model

Brent

[agrays...@gmail.com]

On Friday, February 22, 2019 at 8:13:21 PM UTC-7, Brent wrote:

On 2/22/2019 6:04 PM, agrays...@gmail.com wrote:

On Friday, February 22, 2019 at 4:55:41 PM UTC-7, Brent wrote:

On 2/22/2019 2:40 PM, agrays...@gmail.com wrote:

Gravitons, as quanta of the metric field, are already relativistic particles and covariant.

I thought it's the equations of motion for the particular force, not the mediating particles, that must be covariant. On a related topic for this thread, where does GR depart from Mach's principle? That is, what did Einstein implicitly (or explicitly) deny about Mach's principle? TIA, AG 

Einstein thought he would develop a theory that satisfied Mach's principle, but as it turned out GR doesn't. For example the metric of spacetime is a dynamic field and transmit momentum and energy, as shown by LIGO.  Mach's idea of spacetime as purely a relation between material events couldn't do that.

Brent

Were you inferring covariance simply because the mediating particle for gravity, the graviton, travels at the SoL?

GR is a covariant theory.  So it's quanta, gravitons, are covariant.

I could be mistaken, but I see gravitons as being part of a distinct theory of gravity, which might give the same results as GR. In GR, the paths are determined by geometry in the absence of forces, not by mediating particles. AG 

[Bruce Kellett]

On Sat, Feb 23, 2019 at 3:08 PM <agrays...@gmail.com> wrote:

On Friday, February 22, 2019 at 8:13:21 PM UTC-7, Brent wrote:

On 2/22/2019 6:04 PM, agrays...@gmail.com wrote:

On Friday, February 22, 2019 at 4:55:41 PM UTC-7, Brent wrote:

On 2/22/2019 2:40 PM, agrays...@gmail.com wrote:

Gravitons, as quanta of the metric field, are already relativistic particles and covariant.

I thought it's the equations of motion for the particular force, not the mediating particles, that must be covariant. On a related topic for this thread, where does GR depart from Mach's principle? That is, what did Einstein implicitly (or explicitly) deny about Mach's principle? TIA, AG 

Einstein thought he would develop a theory that satisfied Mach's principle, but as it turned out GR doesn't. For example the metric of spacetime is a dynamic field and transmit momentum and energy, as shown by LIGO.  Mach's idea of spacetime as purely a relation between material events couldn't do that.

Brent

Were you inferring covariance simply because the mediating particle for gravity, the graviton, travels at the SoL?

GR is a covariant theory.  So it's quanta, gravitons, are covariant.

I could be mistaken, but I see gravitons as being part of a distinct theory of gravity, which might give the same results as GR. In GR, the paths are determined by geometry in the absence of forces, not by mediating particles. AG 

GR, as a theory, implies the existence of gravity waves. Wave, when quantised, give particles: these are the gravitons of the theory. Exchange of such gravitons does not necessarily have anything to do with the forces in the theory, or the formation of geodesics.

Bruce 

[agrays...@gmail.com]

Very clarifying. Then, since gravitational waves have been detected, it must be that gravitons exist, but too low in energy to be detected. AG 

[Philip Thrift]

That is news for sure!

- pt 

[John Clark]

On Fri, Feb 22, 2019 at 11:08 PM <agrays...@gmail.com> wrote:

> In GR, the paths are determined by geometry in the absence of forces, not by mediating particles.

Yes, that's because General Relativity is a classical theory that is not quantized, it has so far passed every experimental test posed to it with flying colors but we know it can't be entirely correct because when we ask it what happens when things become very small and very massive, such as in the center of Black Holes, it gives the absurd answer of infinity. Neither Quantum Mechanics or General Relativity works when things get massive and small, perhaps quantizing General Relativity will fix this or maybe there is some other way to do so. Nobody knows.

 > I could be mistaken, but I see gravitons as being part of a distinct theory of gravity, which might give the same results as GR,

 

Nobody has ever experimentally detected a graviton and it's extremely unlikely anybody ever will, so if they make the same predictions as standard General Relativity there would be no point in introducing the idea. 

 John K Clark

[Philip Thrift]

If all experiments proposed to determine if gravity is quantized fail

 Such measurements, they say, could enable them to uncover the quantum nature of gravity and determine whether or not gravity is quantized.

https://physics.aps.org/synopsis-for/10.1103/PhysRevLett.122.071101

that is: the search for a quantized gravity is a wild goose chase

what do theorists do then?

(I asked Hossenfelder. No answer.)

- pt 

[agrays...@gmail.com]

The article you cite indicates increasing hypothetical sensitivity for measuring gravity for tiny effects. If gravity can be quantized, what exactly would be quantized? Bruce says that gravity waves would involve gravitons under a quantized theory. Is that all? AG 

[Lawrence Crowell]

On Friday, February 22, 2019 at 4:40:31 PM UTC-6, agrays...@gmail.com wrote:

On Friday, February 22, 2019 at 1:34:31 PM UTC-7, Brent wrote:

On 2/21/2019 10:47 PM, agrays...@gmail.com wrote:

Even if gravitons are detected, and they account for "force" consistent with the other three forces, wouldn't there remain the task of changing the form of gravity to make it covariant? AG

Gravitons, as quanta of the metric field, are already relativistic particles and covariant.

I thought it's the equations of motion for the particular force, not the mediating particles, that must be covariant. On a related topic for this thread, where does GR depart from Mach's principle? That is, what did Einstein implicitly (or explicitly) deny about Mach's principle? TIA, AG 

Would that require tensors? AG

General relativity is covariant, and curvature is expressed according to Riemann tensors. 

LC

[Philip Thrift]

I suppose it needs to defined what an experiment would be that would determine that gravity is quantized in a measurable way.

Theories disconnected from experiments are mere math games.

- pt

[agrays...@gmail.com]

Thanks, but I think you missed the thrust of my question; namely, if a theory using gravitons is independent of GR, since it would have to be covariant, could that be done without tenors, or are tensors nevertheless necessary.  AG

[Lawrence Crowell]

Tensors transform homogeneously with the Lorentz group and are thus covariant. Yep you need tensors. 

LC 

[agrays...@gmail.com]

A good theory gives pointers on what to measure and how. AG 

- pt

[agrays...@gmail.com]

Are you assuming uniqueness to tensors; that only tensors can produce covariance in 4-space? Is that established or a mathematical speculation? TIA, AG 

[Brent Meeker]

On 2/27/2019 4:58 PM, agrays...@gmail.com wrote:

Are you assuming uniqueness to tensors; that only tensors can produce covariance in 4-space? Is that established or a mathematical speculation? TIA, AG 

That's looking at it the wrong way around.  Anything that transforms as an object in space, must be representable by tensors. The informal definition of a tensor is something that transforms like an object, i.e. in three space it's something that has a location and an orientation and three extensions.  Something that doesn't transform as a tensor under coordinate system changes is something that depends on the arbitrary choice of coordinate system and so cannot be a fundamental physical object.

Brent

[agrays...@gmail.com]

1) Is it correct to say that tensors in E's field equations can be represented as 4x4 matrices which have different representations depending on the coordinate system being used, but represent the same object? 

2) In SR we use the LT to transform from one non-accelerating frame to another. In GR, what is the transformation for going from one accelerating frame to another? 

AG

[Brent Meeker]

On 2/28/2019 4:07 AM, agrays...@gmail.com wrote:

On Wednesday, February 27, 2019 at 8:10:16 PM UTC-7, Brent wrote:

On 2/27/2019 4:58 PM, agrays...@gmail.com wrote:

Are you assuming uniqueness to tensors; that only tensors can produce covariance in 4-space? Is that established or a mathematical speculation? TIA, AG 

That's looking at it the wrong way around.  Anything that transforms as an object in space, must be representable by tensors. The informal definition of a tensor is something that transforms like an object, i.e. in three space it's something that has a location and an orientation and three extensions.  Something that doesn't transform as a tensor under coordinate system changes is something that depends on the arbitrary choice of coordinate system and so cannot be a fundamental physical object.

Brent

1) Is it correct to say that tensors in E's field equations can be represented as 4x4 matrices which have different representations depending on the coordinate system being used, but represent the same object?

That's right as far as it goes.   Tensors can be of any order.  The curvature tensor is 4x4x4x4.

2) In SR we use the LT to transform from one non-accelerating frame to another. In GR, what is the transformation for going from one accelerating frame to another?

The Lorentz transform, but only in a local patch.

Brent

[agrays...@gmail.com]

That's what I thought you would say. But how does this advance Einstein's presumed project of finding how the laws of physics are invariant for accelerating frames? How did it morph into a theory of gravity? TIA, AG 

Brent

[agrays...@gmail.com]

Or suppose, using GR, that two frames are NOT within the same local patch.  If we can't use the LT, how can we transform from one frame to the other? TIA, AG 

Or suppose we have two arbitrary accelerating frames, again NOT within the same local patch, is it true that Maxwell's Equations are covariant under some transformation, and what is that transformation? TIA, AG

Brent

[agrays...@gmail.com]

I think I can simplify my issue here, if indeed there is an issue: did Einstein, or anyone, ever prove what I will call the General Principle of Relativity, namely that the laws of physics are invariant for accelerating frames? If the answer is affirmative, is there a transformation equation for Maxwell's Equations which leaves them unchanged for arbitrary accelerating frames? TIA, AG 

Brent

[Brent Meeker]

Your question isn't clear.  If you're simply asking about the equations describing physics as expressed in an accelerating (e.g. rotating) reference frame, that's pretty trivial.  You write the equations in whatever reference frame is convenient (usually an inertial one) and then transform the coordinates to the accelerated frame coordinates.   But if you're asking about what equations describe some physical system while it is being accelerated as compared to it not being accelerated, that's more complicated.  Maxwell's equations apply to the description of the EM field of an accelerating charged particle and show that the particle loses energy to an EM wave, but how the particle interacts with it's own field when accelerated produces unrealistic results which were superceded by quantum field theory.  Bill Unruh showed that the accelerated system interacts with the vacuum as though the vacuum is hot. 

Brent

[agrays...@gmail.com]

On Wednesday, March 6, 2019 at 1:03:16 AM UTC-7, Brent wrote:

On 3/5/2019 10:02 PM, agrays...@gmail.com wrote:

On Saturday, March 2, 2019 at 2:29:50 AM UTC-7, agrays...@gmail.com wrote:

On Friday, March 1, 2019 at 10:14:02 PM UTC-7, agrays..@gmail.com wrote:

On Thursday, February 28, 2019 at 12:09:27 PM UTC-7, Brent wrote:

On 2/28/2019 4:07 AM, agrays...@gmail.com wrote:

On Wednesday, February 27, 2019 at 8:10:16 PM UTC-7, Brent wrote:

On 2/27/2019 4:58 PM, agrays...@gmail.com wrote:

Are you assuming uniqueness to tensors; that only tensors can produce covariance in 4-space? Is that established or a mathematical speculation? TIA, AG 

That's looking at it the wrong way around.  Anything that transforms as an object in space, must be representable by tensors. The informal definition of a tensor is something that transforms like an object, i.e. in three space it's something that has a location and an orientation and three extensions.  Something that doesn't transform as a tensor under coordinate system changes is something that depends on the arbitrary choice of coordinate system and so cannot be a fundamental physical object.

Brent

1) Is it correct to say that tensors in E's field equations can be represented as 4x4 matrices which have different representations depending on the coordinate system being used, but represent the same object?

That's right as far as it goes.   Tensors can be of any order.  The curvature tensor is 4x4x4x4.

2) In SR we use the LT to transform from one non-accelerating frame to another. In GR, what is the transformation for going from one accelerating frame to another?

The Lorentz transform, but only in a local patch.

That's what I thought you would say. But how does this advance Einstein's presumed project of finding how the laws of physics are invariant for accelerating frames? How did it morph into a theory of gravity? TIA, AG 

Or suppose, using GR, that two frames are NOT within the same local patch.  If we can't use the LT, how can we transform from one frame to the other? TIA, AG 

Or suppose we have two arbitrary accelerating frames, again NOT within the same local patch, is it true that Maxwell's Equations are covariant under some transformation, and what is that transformation? TIA, AG

I think I can simplify my issue here, if indeed there is an issue: did Einstein, or anyone, ever prove what I will call the General Principle of Relativity, namely that the laws of physics are invariant for accelerating frames? If the answer is affirmative, is there a transformation equation for Maxwell's Equations which leaves them unchanged for arbitrary accelerating frames? TIA, AG

Your question isn't clear.  If you're simply asking about the equations describing physics as expressed in an accelerating (e.g. rotating) reference frame, that's pretty trivial.  You write the equations in whatever reference frame is convenient (usually an inertial one) and then transform the coordinates to the accelerated frame coordinates.   But if you're asking about what equations describe some physical system while it is being accelerated as compared to it not being accelerated, that's more complicated. 

Thanks, but I wasn't referring to either of those cases; rather, the case of transforming from one accelerating frame to another accelerating frame, and whether the laws of physics are invariant. Here the "laws" could be ME or Mechanics. It seem as if GR is a special case for gravity, but I was asking whether invariance, or covariance, has been generally established. Also, if the LT works locally in GR, how do we transform between non-local frames? TIA, AG

[John Clark]

On Wed, Mar 6, 2019 at 1:02 AM <agrays...@gmail.com> wrote:

> did Einstein, or anyone, ever prove what I will call the General Principle of Relativity, namely that the laws of physics are invariant for accelerating frames? If the answer is affirmative, is there a transformation equation for Maxwell's Equations which leaves them unchanged for arbitrary accelerating frames? 

Mathematicians prove things Physicists don't, they find theories that are less wrong than previous ideas, but Maxwell's original equations already did what you ask for, they enabled you to calculate the speed of light and they indicated the speed was the same for any reference frame.  In fact this was the reason Einstein suspected Newtonian physics didn't tell the entire story and is why he started working on Relativity in the first place. Maxwell needs modification to be consistent with Quantum Mechanics but with Special or General Relativity no change is required.

 John K Clark

[agrays...@gmail.com]

On Wednesday, March 6, 2019 at 7:18:04 AM UTC-7, John Clark wrote:

On Wed, Mar 6, 2019 at 1:02 AM <agrays...@gmail.com> wrote:

> did Einstein, or anyone, ever prove what I will call the General Principle of Relativity, namely that the laws of physics are invariant for accelerating frames? If the answer is affirmative, is there a transformation equation for Maxwell's Equations which leaves them unchanged for arbitrary accelerating frames? 

Mathematicians prove things Physicists don't, they find theories that are less wrong than previous ideas, but Maxwell's original equations already did what you ask for,

I don't think so. ME's are invariant under the LT. AFAIK, this applies to inertial frames, not accelerating frames, which is what I was asking about. AG

[John Clark]

On Wed, Mar 6, 2019 at 11:21 AM <agrays...@gmail.com> wrote:

 >>Maxwell's original equations already did what you ask for,

>I don't think so. ME's are invariant under the LT. AFAIK, this applies to inertial frames, not accelerating frames, which is what I was asking about. AG

If you are accelerating (or equivalently standing in a gravitational field)  and you measure the speed of light produced by the Laser pointer in your hand you will find it is exactly what Maxwell said it would be. And. although it could look different for other observers the frequency and wavelength of the light you measure is the same as when you measured it when you were not accelerating or in a gravitational field. 

John K Clark

 

[Brent Meeker]

On 3/6/2019 1:27 AM, agrays...@gmail.com wrote:

On Wednesday, March 6, 2019 at 1:03:16 AM UTC-7, Brent wrote:

On 3/5/2019 10:02 PM, agrays...@gmail.com wrote:

On Saturday, March 2, 2019 at 2:29:50 AM UTC-7, agrays...@gmail.com wrote:

On Friday, March 1, 2019 at 10:14:02 PM UTC-7, agrays..@gmail.com wrote:

On Thursday, February 28, 2019 at 12:09:27 PM UTC-7, Brent wrote:

On 2/28/2019 4:07 AM, agrays...@gmail.com wrote:

On Wednesday, February 27, 2019 at 8:10:16 PM UTC-7, Brent wrote:

On 2/27/2019 4:58 PM, agrays...@gmail.com wrote:

Are you assuming uniqueness to tensors; that only tensors can produce covariance in 4-space? Is that established or a mathematical speculation? TIA, AG 

That's looking at it the wrong way around.  Anything that transforms as an object in space, must be representable by tensors. The informal definition of a tensor is something that transforms like an object, i.e. in three space it's something that has a location and an orientation and three extensions.  Something that doesn't transform as a tensor under coordinate system changes is something that depends on the arbitrary choice of coordinate system and so cannot be a fundamental physical object.

Brent

1) Is it correct to say that tensors in E's field equations can be represented as 4x4 matrices which have different representations depending on the coordinate system being used, but represent the same object?

That's right as far as it goes.   Tensors can be of any order.  The curvature tensor is 4x4x4x4.

2) In SR we use the LT to transform from one non-accelerating frame to another. In GR, what is the transformation for going from one accelerating frame to another?

The Lorentz transform, but only in a local patch.

That's what I thought you would say. But how does this advance Einstein's presumed project of finding how the laws of physics are invariant for accelerating frames? How did it morph into a theory of gravity? TIA, AG 

Or suppose, using GR, that two frames are NOT within the same local patch.  If we can't use the LT, how can we transform from one frame to the other? TIA, AG 

Or suppose we have two arbitrary accelerating frames, again NOT within the same local patch, is it true that Maxwell's Equations are covariant under some transformation, and what is that transformation? TIA, AG

I think I can simplify my issue here, if indeed there is an issue: did Einstein, or anyone, ever prove what I will call the General Principle of Relativity, namely that the laws of physics are invariant for accelerating frames? If the answer is affirmative, is there a transformation equation for Maxwell's Equations which leaves them unchanged for arbitrary accelerating frames? TIA, AG

Your question isn't clear.  If you're simply asking about the equations describing physics as expressed in an accelerating (e.g. rotating) reference frame, that's pretty trivial.  You write the equations in whatever reference frame is convenient (usually an inertial one) and then transform the coordinates to the accelerated frame coordinates.   But if you're asking about what equations describe some physical system while it is being accelerated as compared to it not being accelerated, that's more complicated. 

Thanks, but I wasn't referring to either of those cases; rather, the case of transforming from one accelerating frame to another accelerating frame, and whether the laws of physics are invariant.

For simplicity consider just flat Minkowski space time.  If you know the motion of a particle in reference frame, whether the reference frame is accelerated or not, you can determine its motion in any other reference frame.  As for the particle path through spacetime, that's just some geometric path and you're changing from describing it in one coordinate system to describing it in another system...no physics is changing, just the description.  If the reference frames are accelerated you get extra terms in this description, like "centrifugal acceleration" which are just artifacts of the frame choice. This is the same as in Newtonian mechanics. 

But if the particle is actually accelerated, then there may be more to the problem than just it's world line through spacetime.  For example, if the particle has an electric charge, then it will radiate when accelerated and there will be a back reaction.

Here the "laws" could be ME or Mechanics. It seem as if GR is a special case for gravity, but I was asking whether invariance, or covariance, has been generally established.

Einstein's equations are written in a covariant form, so they look the same for all (smooth) coordinate systems.  But the problem arises on the right hand side, the stress-energy tensor.  If you are considering the motion of a charged particle then the stress-energy tensor has to include the EM field of the particle and the interaction of the particle with that field.  This requires a global spacetime solution since, due to the curvature of spacetime, the particle can emit EM radiation at one event and then run into that same radiation at a later event.  The solution may even include singularities; which we know are unphysical.  So there is no simple transformation between frames like the Lorentz transform between inertial frames in flat spacetime.  The classical theory is probably not even self-consistent when applied globally. Here's a paper that addresses a simple form of the problem:

https://arxiv.org/pdf/1509.08757.pdf

Also, if the LT works locally in GR, how do we transform between non-local frames?

There can be no general answer to that.  In curved spacetime, you would have to solve the problem in a global frame to determine the relation between two local frames.  The LT can only be relied on within a local patch where spacetime is approximately Minkowski.

Brent

TIA, AG

 

Maxwell's equations apply to the description of the EM field of an accelerating charged particle and show that the particle loses energy to an EM wave, but how the particle interacts with it's own field when accelerated produces unrealistic results which were superceded by quantum field theory.  Bill Unruh showed that the accelerated system interacts with the vacuum as though the vacuum is hot. 

Brent

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[agrays...@gmail.com]

I know this is pretty basic, but with ME's we can apply the LT and find that the equations are invariant, or covariant (which I think means the same as invariant). But in GR, there's no general transformation from one accelerating frame to another accelerating frame to verify that the field equations are covariant, yet you say they are. Could you elaborate a bit on this? AG

[agrays...@gmail.com]

Does GR require or imply that the laws of gravity are invariant, or covariant, for all accelerating frames? If so, how can that be the case if there's no general transformation from one accelerating frame to any other? Recall, that the independence of coordinate systems doesn't imply that invariance, or covariance, among accelerating frames AFAICT. TIA, AG 

[agrays...@gmail.com]

I suppose the foregoing is another dumb question. I think the answer has something to do with how tensors transform. Further, I suppose Einstein started with the motivation of finding a general transformation from one accelerating frame to another, and later gave up on this project and settled for a theory of gravity. Is this true? TIA, AG

[John Clark]

On Tue, Mar 19, 2019 at 4:50 AM <agrays...@gmail.com> wrote:

 > I suppose Einstein started with the motivation of finding a general transformation from one accelerating frame to another, and later gave up on this project and settled for a theory of gravity. Is this true? TIA, AG

Einstein's breakthrough, what he called "the happiest thought of my life" was when he realized a man in a falling elevator will not feel gravity but a man in a accelerating elevator will. In other words an accelerating frame and gravity are the same thing, that's why it's called the Equivalence Principle.

John K Clark

[agrays...@gmail.com]

I think your claim, in response to my question, is that if you have a theory of gravity, then via the EP you also have a general theory of how to transform from one accelerating frame to another which obeys the Principle of Relativity. I tend not to believe this since gravity is only locally equivalent to acceleration. AG 

[Brent Meeker]

I wonder if Einstein ever considered whether a charged particle in the falling radiate would radiate?

Brent

[agrays...@gmail.com]

Because of your typos, at first I thought you were joking. Well, maybe it was a joke, but for me it sounds like a damned good question. I surmise that a charged particle accelerating due to gravity does NOT radiate energy, but why? AG 

[John Clark]

On Wed, Mar 20, 2019 at 6:07 AM <agrays...@gmail.com> wrote:

 

> I surmise that a charged particle accelerating due to gravity does NOT radiate energy, but why? AG 

If you were in a elevator with a charged particle accelerating due to gravity or due to a rocket in deep space you would not observe any electromagnetic radiation, although if the elevator were made of glass an outside observer who was not accelerating would.  If the elevator were sitting on the surface of the Earth you would not notice any light from the particle because it would be accelerating but you would not be.

John K Clark 

[John Clark]

On Tue, Mar 19, 2019 at 7:54 PM <agrays...@gmail.com> wrote:

>> Einstein's breakthrough, what he called "the happiest thought of my life" was when he realized a man in a falling elevator will not feel gravity but a man in a accelerating elevator will. In other words an accelerating frame and gravity are the same thing, that's why it's called the Equivalence Principle.

> I think your claim, in response to my question, is that if you have a theory of gravity, then via the EP you also have a general theory of how to transform from one accelerating frame to another which obeys the Principle of Relativity. I tend not to believe this since gravity is only locally equivalent to acceleration. AG 

Einstein was certainly aware  that the EP was only true for regions that were very small compared to the curvature of the gravitational field, in fact working out the consequences of tidal effects was one of the reasons it took him nearly a full decade of grueling work to go from "the happiest thought of my life" to a fully developed theory of General Relativity. Einstein had to master how 4D Tensors work in Non-Euclidean space and was so obsessed and worked so hard it nearly killed him. When he finished he lost nearly 50 pounds felt weak and expected to die soon, but fortunately didn't.

John K Clark

[agrays...@gmail.com]

But getting back to my original question a few messages ago; if there is no general transformation from one accelerating frame to another (except locally), how does GR establish the Principle of Relativity (for accelerating frames)? AG 

[John Clark]

On Wed, Mar 20, 2019 at 9:16 AM <agrays...@gmail.com> wrote:

> how does GR establish the Principle of Relativity (for accelerating frames)? AG 

It doesn't, Einstein never said everything is relative. Unlike velocity there is such a thing as absolute acceleration, if that were not true the Twin Paradox could not be resolved.

John K Clark

[Brent Meeker]

On 3/20/2019 3:07 AM, agrays...@gmail.com wrote:

On Tuesday, March 19, 2019 at 7:23:29 PM UTC-6, Brent wrote:

On 3/19/2019 9:32 AM, John Clark wrote:

On Tue, Mar 19, 2019 at 4:50 AM <agrays...@gmail.com> wrote:

 > I suppose Einstein started with the motivation of finding a general transformation from one accelerating frame to another, and later gave up on this project and settled for a theory of gravity. Is this true? TIA, AG

Einstein's breakthrough, what he called "the happiest thought of my life" was when he realized a man in a falling elevator will not feel gravity but a man in a accelerating elevator will. In other words an accelerating frame and gravity are the same thing, that's why it's called the Equivalence Principle.

I wonder if Einstein ever considered whether a charged particle in the falling radiate would radiate?

Brent

Because of your typos, at first I thought you were joking. Well, maybe it was a joke, but for me it sounds like a damned good question. I surmise that a charged particle accelerating due to gravity does NOT radiate energy, but why? AG

Sorry about the typos.   Yes, it does seem paradoxical.  Here's a paper that purports to solve the problem.

The radiation of a uniformly accelerated charge is beyond the horizon: a simple derivation

Camila de Almeida, Alberto Saa

(Submitted on 6 Jun 2005 (v1), last revised 2 Dec 2005 (this version, v5))

We show, by exploring some elementary consequences of the covariance of Maxwell's equations under general coordinate transformations, that, despite inertial observers can indeed detect electromagnetic radiation emitted from a uniformly accelerated charge, comoving observers will see only a static electric field. This simple analysis can help understanding one of the most celebrated paradoxes of last century.

Comments:	Revtex, 6 pages, 2 figures. v2: Some small corrections. v3: Citation of a earlier paper included. v4: Some stylistic changes. v5: Final version to appear in AJP
Subjects:	Classical Physics (physics.class-ph); General Relativity and Quantum Cosmology (gr-qc)
Journal reference:	Am.J.Phys. 74 (2006) 154-158
DOI:	10.1119/1.2162548
Cite as:	arXiv:physics/0506049 [physics.class-ph]
	(or arXiv:physics/0506049v5 [physics.class-ph] for this version)

And another paper that looks at possible experimental evidence.

Electrical charges in gravitational fields, and Einstein's equivalence principle

Gerold Gründler

(Submitted on 14 Sep 2015 (v1), last revised 12 Oct 2015 (this version, v3))

According to Larmor's formula, accelerated electric charges radiate electromagnetic waves. Hence charges should radiate, if they are in free fall in gravitational fields, and they should not radiate if they are supported at rest in gravitational fields. But according to Einstein's equivalence principle, charges in free fall should not radiate, while charges supported at rest in gravitational fields should radiate. In this article we point out indirect experimental evidence, indicating that the equivalence principle is correct, while the traditional interpretation of Larmor's formula must be amended.

Subjects:	General Physics (physics.gen-ph)
Cite as:	arXiv:1509.08757 [physics.gen-ph]
	(or arXiv:1509.08757v3 [physics.gen-ph] for this version)

However, I don't find them entirely convincing.  We know that double stars, which are orbiting one another in free-fall, radiate gravitational waves.  Are we to suppose that if one or both of them had an electrical charge that there would be no EM radiation?

Brent

[Brent Meeker]

On 3/20/2019 5:41 AM, John Clark wrote:

On Wed, Mar 20, 2019 at 6:07 AM <agrays...@gmail.com> wrote:

 

> I surmise that a charged particle accelerating due to gravity does NOT radiate energy, but why? AG 

If you were in a elevator with a charged particle accelerating due to gravity

You mean the elevator is stationary relative to the Earth and the charged particle is accelerating, i.e. falling, due to gravity?  Or do you mean both the elevator, you, and the particle are in free fall?

or due to a rocket in deep space you would not observe any electromagnetic radiation, although if the elevator were made of glass an outside observer who was not accelerating would. 

But in that case the observer in the elevator would see the particle mysteriously lose energy without radiating.

Brent

If the elevator were sitting on the surface of the Earth you would not notice any light from the particle because it would be accelerating but you would not be.

John K Clark 

[John Clark]

On Wed, Mar 20, 2019 at 3:06 PM 'Brent Meeker'  t <everyth...@googlegroups.com> wrote:

>> If you were in a elevator with a charged particle accelerating due to gravity

> You mean the elevator is stationary relative to the Earth and the charged particle is accelerating, i.e. falling, due to gravity?  Or do you mean both the elevator, you, and the particle are in free fall?

If the elevation is stationary sitting on the surface of the Earth then it is not accelerating, nor is it in a inertial frame because a force from the ground is being applied.  

 

>> or due to a rocket in deep space you would not observe any electromagnetic radiation, although if the elevator were made of glass an outside observer who was not accelerating would. 

> But in that case the observer in the elevator would see the particle mysteriously lose energy without radiating.

I'm not sure I know what you mean. If you're accelerating side by side with a electron by exactly the same amount how could you observe the electron lose energy? How would that loss of energy manifest itself to you?   It's true that depending on the reference frame a electric field can look like a magnetic field and vice versa, but it makes no difference if the acceleration is caused by a rocket or a gravitational field, you can't use that effect to tell the 2 situations apart.

John K Clark  

[Brent Meeker]

On 3/20/2019 1:59 PM, John Clark wrote:

On Wed, Mar 20, 2019 at 3:06 PM 'Brent Meeker'  t <everyth...@googlegroups.com> wrote:

>> If you were in a elevator with a charged particle accelerating due to gravity

> You mean the elevator is stationary relative to the Earth and the charged particle is accelerating, i.e. falling, due to gravity?  Or do you mean both the elevator, you, and the particle are in free fall?

If the elevation is stationary sitting on the surface of the Earth then it is not accelerating, nor is it in a inertial frame because a force from the ground is being applied. 

OK.  But that doesn't clarify what you meant by, "you were in a elevator with a charged particle accelerating due to gravity."

The "paradox" is that if the elevator is sitting still on the surface of the Earth and you, in the elevator, drop a charged particle, then, as it falls, standard electrodynamics says it will radiate and you can detect the radiation (does it fall slower or faster because it radiates?).  But the EP says this should be the same being in the elevator accelerated by a rocket; in which case when you release the particle you and the elevator continue to accelerate and the particle doesn't, so there should be no radiation observed.

 

>> or due to a rocket in deep space you would not observe any electromagnetic radiation, although if the elevator were made of glass an outside observer who was not accelerating would. 

> But in that case the observer in the elevator would see the particle mysteriously lose energy without radiating.

I'm not sure I know what you mean. If you're accelerating side by side with a electron by exactly the same amount how could you observe the electron lose energy?

A good question, but if the outside observer (who is either inertial or stationary, I'm not sure which) sees radiation then the energy must come from the gravitational potential of the falling (and accelerating) charged particle.

How would that loss of energy manifest itself to you?   It's true that depending on the reference frame a electric field can look like a magnetic field and vice versa,

That's true even for uniform motion in SR.  No acceleration required.

but it makes no difference if the acceleration is caused by a rocket or a gravitational field, you can't use that effect to tell the 2 situations apart.

John K Clark 

This paper concludes that a charged particle which is uniformly accelerated in gravitational field does radiate, but this radiation cannot be detected by an observer who is moving with the particle because the radiation will be beyond an event horizon relative to the observer.

The radiation of a uniformly accelerated charge is beyond the horizon: A simple
derivation
Camila de Almeida & Alberto Saa

By exploring some elementary consequences of the covariance of Maxwell’s equations under general
coordinate transformations, we show that even though inertial observers can detect electromagnetic

radiation emitted from a uniformly accelerated charge, comoving observers will see only a static

electric field. This analysis can add insight into one of the most celebrated paradoxes of the last
century.
arXiv:physics/0506049v5

So if a charged particle is stationary in a gravitational field, as on the surface of the Earth, it is accelerated in spacetime (non-geodesic motion) and radiates, but this is not observable by someone at rest relative to it because of the Rindler horizon.

This paper discusses the result, the impossibility of empirical tests, and compares the question of radiation by EM accelerated particles.
arXiv:1509.08757v3

Both of those papers consider uniform gravity fields and uniform accelerations.  They reference this paper, which considers general motions.
arXiv:physics/9710036v1

Brent

[agrays...@gmail.com]

But in GR don't the field equations take the same form in all frames, including accelerating frames, which if I understand correctly, IS the Principle of Relativity? TIA, AG

[agrays...@gmail.com]

If we go back to classical E&M, where does the EM radiation come from which is emitted for accelerating particles? It can't come from the self field of, say, an electron, since that would imply loss of mass or charge of the electron, which is never claimed. So it must come from the EM field causing the acceleration. Now if we go to the case of gravity without any EM source fields, and we still get EM radiation due to the acceleration, where does it come from? AG 

[Brent Meeker]

No, it comes from the energy source that is providing the acceleration.  In the LHC protons are accelerated by EM fields which are powered by big generators. So that's the source of the energy they radiate.  It's interesting that Grundler claims they radiate because the EM fields act on the charge of the proton but NOT on the field of the proton.  I'm not sure I buy that, though it may be a heuristic way to look at the problem.

which is never claimed. So it must come from the EM field causing the acceleration. Now if we go to the case of gravity without any EM source fields, and we still get EM radiation due to the acceleration, where does it come from? AG

It's unclear what case you're asking about.  Free falling is not accelerating in GR.  Sitting still on the Earth is accelerating in spacetime.  So you need to say whether the charge you're considering is on a geodesic or not AND whether the observer is on a geodesic or is stationary relative to the charge or is on some non-geodesic different from the charge.

Brent

[smitra]

On 21-03-2019 06:21, agrays...@gmail.com wrote:
> On Wednesday, March 20, 2019 at 12:51:18 PM UTC-6, Brent wrote:
>
>> On 3/20/2019 3:07 AM, agrays...@gmail.com wrote:
>>
>> On Tuesday, March 19, 2019 at 7:23:29 PM UTC-6, Brent wrote:
>>
>> On 3/19/2019 9:32 AM, John Clark wrote:
>>
>> On Tue, Mar 19, 2019 at 4:50 AM <agrays...@gmail.com> wrote:
>>

>>> I SUPPOSE EINSTEIN STARTED WITH THE MOTIVATION OF FINDING A
>> GENERAL TRANSFORMATION FROM ONE ACCELERATING FRAME TO ANOTHER, AND
>> LATER GAVE UP ON THIS PROJECT AND SETTLED FOR A THEORY OF GRAVITY.
>> IS THIS TRUE? TIA, AG

>>
>> Einstein's breakthrough, what he called "the happiest thought of my
>> life" was when he realized a man in a falling elevator will not feel
>> gravity but a man in a accelerating elevator will. In other words an
>> accelerating frame and gravity are the same thing, that's why it's
>> called the Equivalence Principle.
>
> I wonder if Einstein ever considered whether a charged particle in
> the falling radiate would radiate?
>
> Brent
>
> Because of your typos, at first I thought you were joking. Well, maybe
> it was a joke, but for me it sounds like a damned good question. I
> surmise that a charged particle accelerating due to gravity does NOT
> radiate energy, but why? AG
>
> Sorry about the typos. Yes, it does seem paradoxical. Here's a
> paper that purports to solve the problem.
>

> THE RADIATION OF A UNIFORMLY ACCELERATED CHARGE IS BEYOND THE HORIZON:
> A SIMPLE DERIVATION
>
> Camila de Almeida [1], Alberto Saa [2]
> (Submitted on 6 Jun 2005 (v1 [3]), last revised 2 Dec 2005 (this

> version, v5))
>
>> We show, by exploring some elementary consequences of the covariance
>> of Maxwell's equations under general coordinate transformations,
>> that, despite inertial observers can indeed detect electromagnetic
>> radiation emitted from a uniformly accelerated charge, comoving
>> observers will see only a static electric field. This simple
>> analysis can help understanding one of the most celebrated paradoxes
>> of last century.
>
> Comments:
> Revtex, 6 pages, 2 figures. v2: Some small corrections. v3:
> Citation of a earlier paper included. v4: Some stylistic changes. v5:
> Final version to appear in AJP
>
> Subjects:
> Classical Physics (physics.class-ph); General Relativity and
> Quantum Cosmology (gr-qc)
>
> Journal reference:
> Am.J.Phys. 74 (2006) 154-158
>
> DOI:

> 10.1119/1.2162548 [4]
>
> Cite as:
> arXiv:physics/0506049 [5] [physics.class-ph]
>
> (or arXiv:physics/0506049v5 [6] [physics.class-ph] for this

> version)
>
> And another paper that looks at possible experimental evidence.
>

> ELECTRICAL CHARGES IN GRAVITATIONAL FIELDS, AND EINSTEIN&#39;S
> EQUIVALENCE PRINCIPLE
>
> Gerold Gründler [7]
> (Submitted on 14 Sep 2015 (v1 [8]), last revised 12 Oct 2015 (this

> version, v3))
>
>> According to Larmor's formula, accelerated electric charges radiate
>> electromagnetic waves. Hence charges should radiate, if they are in
>> free fall in gravitational fields, and they should not radiate if
>> they are supported at rest in gravitational fields. But according to
>> Einstein's equivalence principle, charges in free fall should not
>> radiate, while charges supported at rest in gravitational fields
>> should radiate. In this article we point out indirect experimental
>> evidence, indicating that the equivalence principle is correct,
>> while the traditional interpretation of Larmor's formula must be
>> amended.
>
> Subjects:
> General Physics (physics.gen-ph)
>
> Cite as:

> arXiv:1509.08757 [9] [physics.gen-ph]
>
> (or arXiv:1509.08757v3 [10] [physics.gen-ph] for this version)

>
> However, I don't find them entirely convincing. We know that double
> stars, which are orbiting one another in free-fall, radiate
> gravitational waves. Are we to suppose that if one or both of them
> had an electrical charge that there would be no EM radiation?
>
> Brent
>

> IF WE GO BACK TO CLASSICAL E&M, WHERE DOES THE EM RADIATION COME FROM
> WHICH IS EMITTED FOR ACCELERATING PARTICLES? IT CAN&#39;T COME FROM
> THE SELF FIELD OF, SAY, AN ELECTRON, SINCE THAT WOULD IMPLY LOSS OF
> MASS OR CHARGE OF THE ELECTRON, WHICH IS NEVER CLAIMED. SO IT MUST
> COME FROM THE EM FIELD CAUSING THE ACCELERATION. NOW IF WE GO TO THE
> CASE OF GRAVITY WITHOUT ANY EM SOURCE FIELDS, AND WE STILL GET EM
> RADIATION DUE TO THE ACCELERATION, WHERE DOES IT COME FROM? AG
>
It comes from the self-force, see here:

https://arxiv.org/abs/0905.2391

Saibal

[agrays...@gmail.com]

In the case of GR, assuming no external EM sources, we still get (according to resident experts) radiation emitted for accelerating charges. So the claim of the article must be true; that the energy comes from the field created by the accelerating charge. But wouldn't that imply the charge of said particle must decrease to account for the reduced self-field?  Yet I don't believe that is claimed, so the result of the article is baffling. AG 

[agrays...@gmail.com]

In the TP we're comparing an inertial frame with an accelerating frame; not the general case I was referring to for accelerating frames. But I'm confused, again. Don't Einstein's field equations take the same form in all frames, and isn't this the Principle of Relativity for gravity? AG

[Brent Meeker]

The energy comes from the field that accelerates the charge, i.e. the gravitational potential.  The photons radiated away carry energy, but not charge.

Brent

Yet I don't believe that is claimed, so the result of the article is baffling. AG 

[agrays...@gmail.com]

That makes sense. Then, do you agree the article posted above is incorrect, or am I missing something here? AG 

[agrays...@gmail.com]

Clark, how about an answer? If the GR field equations have the same form in all frames, including accelerating frames, isn't this what we call the Principle of Relativity? AG

[John Clark]

On Tue, Mar 26, 2019 at 4:40 AM <agrays...@gmail.com> wrote:

>>>Einstein never said everything is relative. Unlike velocity there is such a thing as absolute acceleration, if that were not true the Twin Paradox could not be resolved.

>> But in GR don't the field equations take the same form in all frames, including accelerating frames, which if I understand correctly, IS the Principle of Relativity? TIA, AG

> Clark, how about an answer?

Sir yes sir! Saying the field equations are the same form in all reference frames is just another way of saying the fundamental laws of physics are the same everywhere, and if they weren't the same everywhere General Relativity would be a very bad theory. It took Einstein 10 years to find equations that fit these invariant requirements so that in every reference frame the spacetime distance between 2 events is the same, and in every reference frame absolute acceleration exists but absolute motion does not, and every frame is accelerating except for one moving through flat spacetime (aka a zero gravitational field) in a straight path, and for every curved spacetime path there must be a force being applied unless that particular spacetime curve happens to be a geodesic. 

John K Clark

[agrays...@gmail.com]

TY! But what still puzzles me is that, according to Brent, there is no general transformation from one accelerating frame to another accelerating frame (only a local LT). So, although the field equations are claimed to be the same in all frames, accelerating or not, how does one prove that without applying a general (non existent!) transformation? TIA, AG 

[John Clark]

On Tue, Mar 26, 2019 at 9:14 AM <agrays...@gmail.com> wrote:

> although the field equations are claimed to be the same in all frames, accelerating or not, how does one prove that

Mathematicians prove things Physicists don't. Physicists show that some ideas are less wrong than others and they do that by determining how closely the idea conforms with experimental observation. So far at least General Relativity has conformed very very well.

 John K Clark

 

[John Clark]

By the way, just  2 weeks ago the best test ever made of Einstein's Equivalence Principle was performed in a gravitational field one million times greater than Earth's and Einstein passed the test with flying colors.  

Test of the Einstein Equivalence Principle near the Galactic Center Supermassive Black Hole  

John K Clark

[agrays...@gmail.com]

Thanks, but that's very far removed from a viable explanation of covariance as a property of the GR field equations. How do the mathematicians prove it? You know, Einstein worked with the best of them, such as Grossman and Hilbert. They must have been very satisfied that covariance was an established, provable property. Do you have a clue how that might be done -- to establish covariance? AG 

 

[agrays...@gmail.com]

I read an article about that yesterday. AG 

[John Clark]

On Tue, Mar 26, 2019 at 1:14 PM <agrays...@gmail.com> wrote:

> How do the mathematicians prove it?

Mathematicians can't prove that a physical theory is correct, all they can do is show that changing the coordinate system (for example by rotating the X and Y axis) does not result in different physical predictions. Only exparament can tell you if the predictions is right, or at least mostly right.  

John K Clark

[agrays...@gmail.com]

On Tuesday, March 26, 2019 at 11:29:08 AM UTC-6, John Clark wrote:

On Tue, Mar 26, 2019 at 1:14 PM <agrays...@gmail.com> wrote:

> How do the mathematicians prove it?

Mathematicians can't prove that a physical theory is correct, all they can do is show that changing the coordinate system (for example by rotating the X and Y axis) does not result in different physical predictions. Only exparament can tell you if the predictions is right, or at least mostly right.  

John K Clark

I'm not asking if GR is correct; rather, whether it is covariant. Moreover, for SR we can prove covariance, since under the LT, the law of physics don't change and the SoL is c in any inertial frame. ME are also invariant under the LT.  AG

[smitra]

On 26-03-2019 20:29, agrays...@gmail.com wrote:
> On Tuesday, March 26, 2019 at 11:29:08 AM UTC-6, John Clark wrote:
>
>> On Tue, Mar 26, 2019 at 1:14 PM <agrays...@gmail.com> wrote:
>>

>>> _> How do the mathematicians prove it?_

>>
>> Mathematicians can't prove that a physical theory is correct, all
>> they can do is show that changing the coordinate system (for example
>> by rotating the X and Y axis) does not result in different physical
>> predictions. Only exparament can tell you if the predictions is
>> right, or at least mostly right.
>>
>> John K Clark
>
> I'm not asking if GR is correct; rather, whether it is covariant.
> Moreover, for SR we can prove covariance, since under the LT, the law
> of physics don't change and the SoL is c in any inertial frame. ME are
> also invariant under the LT. AG
>

There are many ways one can do this, the most elegant way is to start
with a Lagrangian of a field theory and then demand that it be invariant
under general coordinate transforms, which requires factors of the
square root of the determinant of the metric tensor to be inserted to
compensate for the Jacobian of a coordinate transform. This seemingly
rather trivial insertion, will yield the field equations of GR as far as
the coupling with the fields desribed by the field theory are concerned.

Compare this with the way you can derive the Maxwell equations from
scratch. You start of a scalar field theory, that is invariant under
global gauge transforms phi ---> exp(i alpha) phi. And then you make the
constant alpha an arbitrary function of space-time, which destroys the
invariance due to derivatives generating additional terms. But you can
compensate for these derivatives by including a gauge potential. This
then yields the coupling of the scalar field to a new field that we can
call the electromagnetic field, and this field will have its own gauge
invariant term proportional to the field strength tensor squared.

So, as Paul Davies puts it, in principle mathematically gifted cave men
who had never done any experiments involving electromagnetism and
gravity could have deduced the Maxwell equations and the Einstein
equations of GR from scratch based only on mathematical elegance.

Saibal

[Brent Meeker]

Look at Appendix C of this very nice paper arXiv:physics/9710036v1  It derives the covariant equations for the field of an arbitrarily moving charge.

Brent

[Brent Meeker]

Look at the paper by Gupta and Padmanabhan that I linked to.  The equations are written a manifestly covariant form, so no "proof" is relevant.  But the equations are local, partial differential equations.  So when you want to calculate something that involves radiation (and accelerating a mass produced gravitational radiation), even though the local equations are covariant the solution depends on an integral equation over the past motion of the body.  Since that motion can be, ex hypothesi, arbitrary, there's no general transformation between two reference systems that have gone through arbitrary motions in the past.

Brent

[agrays...@gmail.com]

On Tuesday, March 26, 2019 at 7:58:11 PM UTC-6, Brent wrote:

On 3/26/2019 12:29 PM, agrays...@gmail.com wrote:

On Tuesday, March 26, 2019 at 11:29:08 AM UTC-6, John Clark wrote:

On Tue, Mar 26, 2019 at 1:14 PM <agrays...@gmail.com> wrote:

> How do the mathematicians prove it?

Mathematicians can't prove that a physical theory is correct, all they can do is show that changing the coordinate system (for example by rotating the X and Y axis) does not result in different physical predictions. Only exparament can tell you if the predictions is right, or at least mostly right.  

John K Clark

I'm not asking if GR is correct; rather, whether it is covariant. Moreover, for SR we can prove covariance, since under the LT, the law of physics don't change and the SoL is c in any inertial frame. ME are also invariant under the LT.  AG

Look at the paper by Gupta and Padmanabhan that I linked to. 

I looked through your posts here and do not find these papers. Please post the links. I want to spend more time reading relevant articles, than asking questions. AG

 

The equations are written a manifestly covariant form, so no "proof" is relevant. 

That's what I need to grasp; what is a covariant form and why it's sufficient to establish covariance, or frame independence of the laws of physics. AG