Principle of Equivalence

[Alan Grayson]

How, exactly, is the Principle of Equivalence used by Einstein to develop GR? TIA, AG

[Alan Grayson]

On Wednesday, July 1, 2020 at 12:18:43 AM UTC-6, Alan Grayson wrote:

How, exactly, is the Principle of Equivalence used by Einstein to develop GR? TIA, AG

Is it because a description of gravity can be achieved by locally substituting accelerating frames for gravity? Does it imply that paths in space-time must be curved? It's not clear to me exactly how the EP is applied. TIA, AG

[Alan Grayson]

Supposedly, the EP gave Einstein his key insight for GR, but his November 1915 doesn't reference it, not once! AG

[John Clark]

On Fri, Jul 3, 2020 at 8:41 PM Alan Grayson <agrays...@gmail.com> wrote:

> Supposedly, the EP gave Einstein his key insight for GR, but his November 1915 doesn't reference it, not once! AG

Einstein didn't need to spell it out because he found a tensor to describe how things move through spacetime, and tensors by their very mathematical nature are frame indifferent, if a tensor works in one reference frame it will work in any reference frame. And in scientific papers it's not customary to give a history of the evolution of your thought process or anecdotes about how you happen to come up with your idea, you just state your idea and then make suggestions about how it could be tested.

 John K Clark

[Alan Grayson]

I generally agree with your comment about the style of scientific papers even though motivating comments for specific theories are not unheard of. However, tensors are inherently independent of coordinate systems, and any theory of gravity, indeed any theory of nature, must be written in tensor form to preserve this independence. What has this to do with the Equivalence Principle?  TIA, AG

[John Clark]

On Sat, Jul 4, 2020 at 10:55 AM Alan Grayson <agrays...@gmail.com> wrote:

> tensors are inherently independent of coordinate systems

Yes exactly, but it's not easy to find a tensor that correctly describes how objects move through spacetime, and its far from obvious that such a tensor even exists, but it does and Einstein managed to find it. And that's why he's so famous.

> What has this to do with the Equivalence Principle?

Alan.... you just said "tensors are inherently independent of coordinate systems".... what is it that you think "The Equivalence Principle" means?

 John K Clark

[Alan Grayson]

I stated it earlier. The EP means gravity is locally indistinguishable from acceleration. How does one get from this insight, to "indistinguishable from coordinate system"? The latter is always true, must be true, if laws of physics are to exist. AG 

[Alan Grayson]

Do you see my point? For laws of physics to exist, they must be independent of coordinate system. I don't see what the EP has to do with this, or how Einstein used it to formulate GR. AG 

[John Clark]

On Mon, Jul 6, 2020 at 2:36 AM Alan Grayson <agrays...@gmail.com> wrote:

> For laws of physics to exist, they must be independent of coordinate system.

That statement IS the Equivalence Principle, it's just using different language, and Einstein passionately thought it was true, but there were some instances where it didn't seem to be. For example, if there was no limit on how fast you could move and the speed of causality was infinite then you could move at the speed of light alongside a light beam and if you looked at the light beam you would see that it consisted of a unmoving standing wave of electric and magnetic fields; but that's NOT what Maxwell's equations says it should ever look like. So Maxwell's equation, a very important law of physics, would NOT be independent of the coordinate system.

Einstein was just about the only one who was bothered by this and so he worked on the problem and in 1905 he found the solution, at least for Maxwell's equations, he found a way to make them true regardless of the coordinate system. But doing the same thing for gravity was far far more difficult, he concentrated on the problem for 10 years after that so hard he got sick, lost 60 pounds and nearly died, but eventually he found a tensor to describe how objects move through space-time and a tensor to describe how mass curved space-time. And so with those tensors gravity became independent of the coordinate system too

> I don't see what the EP has to do with this, 

I do.

 John K Clark

[Alan Grayson]

On Monday, July 6, 2020 at 5:29:51 AM UTC-6, John Clark wrote:

On Mon, Jul 6, 2020 at 2:36 AM Alan Grayson <agrays...@gmail.com> wrote:

> For laws of physics to exist, they must be independent of coordinate system.

That statement IS the Equivalence Principle,

In every text that I've seen the EP is specifically related to gravity, and for good reason; namely, it is conditioned by "locally". In a gravitational field, two bodies allowed to fall free, do NOT take parallel paths. Each falls to the center of mass of the gravitating body. My statement above is NOT the EP.  It's a general statement of the requirements of a law of physics. AG 

 

it's just using different language, and Einstein passionately thought it was true, but there were some instances where it didn't seem to be. For example, if there was no limit on how fast you could move and the speed of causality was infinite then you could move at the speed of light alongside a light beam and if you looked at the light beam you would see that it consisted of a unmoving standing wave of electric and magnetic fields; but that's NOT what Maxwell's equations says it should ever look like. So Maxwell's equation, a very important law of physics, would NOT be independent of the coordinate system.

Before Einstein's 1905 paper, it was known that ME's are invariant under the LT. They predicted c for the SoL, but didn't specifically indicate in which coordinate system this would be true. They suggested it would be true in ANY coordinate system, and gave Einstein a clue about the invariance of the SoL for SR. AG

Einstein was just about the only one who was bothered by this and so he worked on the problem and in 1905 he found the solution, at least for Maxwell's equations, he found a way to make them true regardless of the coordinate system.

As previously stated, before 1905 it was known that ME's are invariant under the LT. In his 1905 paper, Einstein didn't modify ME's; he just modified Newtonian mechanics to make mechanics invariant under the LT. AG 

[Bruce Kellett]

On Wed, Jul 1, 2020 at 4:18 PM Alan Grayson <agrays...@gmail.com> wrote:

How, exactly, is the Principle of Equivalence used by Einstein to develop GR? TIA, AG

This lecture by Sean Carroll should answer all your questions:

URL: https://wp.me/p2WMeM-3vl

Bruce

[Alan Grayson]

I'll watch it tonight, but I think I've figured it out; specifically, the EP implies space-time is curved by the presence of mass/energy (and this is independent of the need to express the laws of physics in a coordinate independent way via tensors). AG

[Alan Grayson]

Here's my reasoning regarding the EP; if an observer is in a box subject to uniform acceleration, a beam of light starting on the extreme left side (moving transverse or perpendicular to the acceleration vector), will hit a lower point on the right side, showing that uniform acceleration results in curved paths in space-time. But if this result is identical to gravity, locally, it means that curved paths in space-time are produced by, or are equivalent to gravity. BUT gravity is only observed in the presence of mass/energy. ERGO, the EP implies mass/energy curves space-time. AG 

[Alan Grayson]

For Bruce; so far I've gotten about two-thirds through Carroll's video. Will complete it this weekend. I sense a flaw in GR, suggested by the inclusion of G, the gravitational constant. How can a constant inferred from an approximate theory of gravity, Newton's Theory of Gravitation, be included in a presumed perfect theory of gravity, General Relativity? Don't you think something very subtle is awry here? AG

[John Clark]

On Sat, Jul 11, 2020 at 3:54 AM Alan Grayson <agrays...@gmail.com> wrote:

> I sense a flaw in GR

I'll inform the Nobel Prize committee. Your gold medal should be arriving by UPS any day now.

 John K Clark 

[Alan Grayson]

We know it's not a perfect theory. No theory is. Do you know how G got included, or as a Trumper do you prefer to BS? AG 

[Brent Meeker]

On 7/11/2020 12:54 AM, Alan Grayson wrote:

On Tuesday, July 7, 2020 at 10:06:44 PM UTC-6, Alan Grayson wrote:

On Tuesday, July 7, 2020 at 8:50:50 PM UTC-6, Alan Grayson wrote:

On Tuesday, July 7, 2020 at 8:05:28 PM UTC-6, Bruce wrote:

On Wed, Jul 1, 2020 at 4:18 PM Alan Grayson <agrays...@gmail.com> wrote:

How, exactly, is the Principle of Equivalence used by Einstein to develop GR? TIA, AG

This lecture by Sean Carroll should answer all your questions:

URL: https://wp.me/p2WMeM-3vl

Bruce

I'll watch it tonight, but I think I've figured it out; specifically, the EP implies space-time is curved by the presence of mass/energy (and this is independent of the need to express the laws of physics in a coordinate independent way via tensors). AG

Here's my reasoning regarding the EP; if an observer is in a box subject to uniform acceleration, a beam of light starting on the extreme left side (moving transverse or perpendicular to the acceleration vector), will hit a lower point on the right side, showing that uniform acceleration results in curved paths in space-time. But if this result is identical to gravity, locally, it means that curved paths in space-time are produced by, or are equivalent to gravity.

That makes no sense.  You're saying that because curved paths can be produced two different ways then they must always be produced the second way.

BUT gravity is only observed in the presence of mass/energy. ERGO, the EP implies mass/energy curves space-time. AG

And that's not even true.  Gravitational waves can propagate thru the vacuum.  The Schwarzschild solution is for empty space.  De Sitter space is an empty cosmos.

Brent

For Bruce; so far I've gotten about two-thirds through Carroll's video. Will complete it this weekend. I sense a flaw in GR, suggested by the inclusion of G, the gravitational constant. How can a constant inferred from an approximate theory of gravity, Newton's Theory of Gravitation, be included in a presumed perfect theory of gravity, General Relativity? Don't you think something very subtle is awry here? AG

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[Alan Grayson]

On Saturday, July 11, 2020 at 5:05:02 PM UTC-6, Brent wrote:

On 7/11/2020 12:54 AM, Alan Grayson wrote:

On Tuesday, July 7, 2020 at 10:06:44 PM UTC-6, Alan Grayson wrote:

On Tuesday, July 7, 2020 at 8:50:50 PM UTC-6, Alan Grayson wrote:

On Tuesday, July 7, 2020 at 8:05:28 PM UTC-6, Bruce wrote:

On Wed, Jul 1, 2020 at 4:18 PM Alan Grayson <agrays...@gmail.com> wrote:

How, exactly, is the Principle of Equivalence used by Einstein to develop GR? TIA, AG

This lecture by Sean Carroll should answer all your questions:

URL: https://wp.me/p2WMeM-3vl

Bruce

I'll watch it tonight, but I think I've figured it out; specifically, the EP implies space-time is curved by the presence of mass/energy (and this is independent of the need to express the laws of physics in a coordinate independent way via tensors). AG

Here's my reasoning regarding the EP; if an observer is in a box subject to uniform acceleration, a beam of light starting on the extreme left side (moving transverse or perpendicular to the acceleration vector), will hit a lower point on the right side, showing that uniform acceleration results in curved paths in space-time. But if this result is identical to gravity, locally, it means that curved paths in space-time are produced by, or are equivalent to gravity.

That makes no sense.  You're saying that because curved paths can be produced two different ways then they must always be produced the second way.

BUT gravity is only observed in the presence of mass/energy. ERGO, the EP implies mass/energy curves space-time. AG

And that's not even true.  Gravitational waves can propagate thru the vacuum.  The Schwarzschild solution is for empty space.  De Sitter space is an empty cosmos.

Light can propagate through empty space, but it can't arise from nothing. Same presumably for gravitational waves. AG 

Brent

For Bruce; so far I've gotten about two-thirds through Carroll's video. Will complete it this weekend. I sense a flaw in GR, suggested by the inclusion of G, the gravitational constant. How can a constant inferred from an approximate theory of gravity, Newton's Theory of Gravitation, be included in a presumed perfect theory of gravity, General Relativity? Don't you think something very subtle is awry here? AG

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[Alan Grayson]

On Saturday, July 11, 2020 at 5:29:03 PM UTC-6, Alan Grayson wrote:

On Saturday, July 11, 2020 at 5:05:02 PM UTC-6, Brent wrote:

On 7/11/2020 12:54 AM, Alan Grayson wrote:

On Tuesday, July 7, 2020 at 10:06:44 PM UTC-6, Alan Grayson wrote:

On Tuesday, July 7, 2020 at 8:50:50 PM UTC-6, Alan Grayson wrote:

On Tuesday, July 7, 2020 at 8:05:28 PM UTC-6, Bruce wrote:

On Wed, Jul 1, 2020 at 4:18 PM Alan Grayson <agrays...@gmail.com> wrote:

How, exactly, is the Principle of Equivalence used by Einstein to develop GR? TIA, AG

This lecture by Sean Carroll should answer all your questions:

URL: https://wp.me/p2WMeM-3vl

Bruce

I'll watch it tonight, but I think I've figured it out; specifically, the EP implies space-time is curved by the presence of mass/energy (and this is independent of the need to express the laws of physics in a coordinate independent way via tensors). AG

Here's my reasoning regarding the EP; if an observer is in a box subject to uniform acceleration, a beam of light starting on the extreme left side (moving transverse or perpendicular to the acceleration vector), will hit a lower point on the right side, showing that uniform acceleration results in curved paths in space-time. But if this result is identical to gravity, locally, it means that curved paths in space-time are produced by, or are equivalent to gravity.

That makes no sense.  You're saying that because curved paths can be produced two different ways then they must always be produced the second way.

BUT gravity is only observed in the presence of mass/energy. ERGO, the EP implies mass/energy curves space-time. AG

And that's not even true.  Gravitational waves can propagate thru the vacuum.  The Schwarzschild solution is for empty space.  De Sitter space is an empty cosmos.

Light can propagate through empty space, but it can't arise from nothing. Same presumably for gravitational waves. AG 

In a universe with no matter or energy, aren't we back to SR where there's no curvature and light travels in a straight line? So the gravitational waves you refer to don't take curved paths. AG

[Brent Meeker]

On 7/11/2020 4:29 PM, Alan Grayson wrote:

On Saturday, July 11, 2020 at 5:05:02 PM UTC-6, Brent wrote:

On 7/11/2020 12:54 AM, Alan Grayson wrote:

On Tuesday, July 7, 2020 at 10:06:44 PM UTC-6, Alan Grayson wrote:

On Tuesday, July 7, 2020 at 8:50:50 PM UTC-6, Alan Grayson wrote:

On Tuesday, July 7, 2020 at 8:05:28 PM UTC-6, Bruce wrote:

On Wed, Jul 1, 2020 at 4:18 PM Alan Grayson <agrays...@gmail.com> wrote:

How, exactly, is the Principle of Equivalence used by Einstein to develop GR? TIA, AG

This lecture by Sean Carroll should answer all your questions:

URL: https://wp.me/p2WMeM-3vl

Bruce

I'll watch it tonight, but I think I've figured it out; specifically, the EP implies space-time is curved by the presence of mass/energy (and this is independent of the need to express the laws of physics in a coordinate independent way via tensors). AG

Here's my reasoning regarding the EP; if an observer is in a box subject to uniform acceleration, a beam of light starting on the extreme left side (moving transverse or perpendicular to the acceleration vector), will hit a lower point on the right side, showing that uniform acceleration results in curved paths in space-time. But if this result is identical to gravity, locally, it means that curved paths in space-time are produced by, or are equivalent to gravity.

That makes no sense.  You're saying that because curved paths can be produced two different ways then they must always be produced the second way.

BUT gravity is only observed in the presence of mass/energy. ERGO, the EP implies mass/energy curves space-time. AG

And that's not even true.  Gravitational waves can propagate thru the vacuum.  The Schwarzschild solution is for empty space.  De Sitter space is an empty cosmos.

Light can propagate through empty space, but it can't arise from nothing. Same presumably for gravitational waves. AG

Are you going to say the same thing about matter?  electric charge?

Brent

[Alan Grayson]

I'm not sure what your point is. All I was saying above is that mass/energy causes curvature of space-time as per the EP. A gravitational wave moving through empty space seems no different in principle than light moving through empty space. In both cases there is a mathematical solution for the wave motion, with the source of the wave left undefined. But every wave motion must has a source. AG

[Brent Meeker]

And every source must have an origin?  There is nothing in the equations that says there must be a source.

Brent

[Alan Grayson]

Can EM waves exist if there are no charges and currents? If you affirm, has this ever been observed? This result, if it is a result, is likely an artifact of the mathematics which has no basis in physical reality. Anyway, are you claiming that spacetime curvature can exist in the absence of matter/energy? Is this what the EP says? AG 

[Brent Meeker]

It's what the equations say.  So if waves only exist due to matter sources that's a separate fact, not part of the theory.  It seems just as plausible to me that fields existed first and "stuff" appeared as quantized waves in the fields. 

Brent

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[Alan Grayson]

What do you find erroneous in my interpretation of the EP? I never heard it interpreted to mean that curvature of space-time is NOT caused by gravity. AG 

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[Alan Grayson]

Are you claiming that because there are gravitational wave solutions to GR in the absence of matter/energy, curvature of space-time isn't caused by, or is equivalent to gravity? But how can there be curvature of space-time in the absence of matter/energy since, in this case, we're dealing with SR, wherein space-time has no curvature? AG 

[Brent Meeker]

There can be because it's consistent with the equations.  A black hole doesn't include any matter.  General relativity is non-linear, that's why there can be non-flat cosmologies that contain no matter.  Of course there may be some different, better theory in which spacetime can't be curved without matter...but it seems unlikely since we have good evidence that gravitational waves exist.

Brent

since, in this case, we're dealing with SR, wherein space-time has no curvature? AG 

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[Lawrence Crowell]

On Saturday, July 11, 2020 at 11:00:18 PM UTC-5, Alan Grayson wrote:

Can EM waves exist if there are no charges and currents? If you affirm, has this ever been observed? This result, if it is a result, is likely an artifact of the mathematics which has no basis in physical reality. Anyway, are you claiming that spacetime curvature can exist in the absence of matter/energy? Is this what the EP says? AG 

Yes they do. A plane or spherical EM wave in a region of space without charges is an elementary solution to Maxwell's equations.

LC 

[Lawrence Crowell]

I have not followed this thread much. I get the impression there is a lot of confusion. 

The equivalence principle states there is no distinguishing difference between a frame far away in flat spacetime and one in a region of spacetime that is curved so long as the frame is small in extent. In other words, it there is a curvature R and the dimensions of the frame are d then d << √R. This will mean that any test masses in this small frame will be on co-parallel geodesics and the local physics is no different than if you are on a frame in very distant flat spacetime. The converse of this then is that being on an accelerated frame is indistiguishable from being held fixed in a gravitational field. The surface of the Earth does that for us. Then comparing gravity with acceleration this way the implication is that inertial mass is equal to gravitational mass. The previous case indicates a way forwards to general relativity with local frames or patches that are meshed together in a coordinate atlas and transition function that define connection coefficients and curvature.

Is there a better way to do this, Yes! this is what I have been working on. Instead of a single small inertial frame consider two frames and in each there is one of each EPR pair, The easy part is to show that the entanglement is constant so long as the two frames are on geodesic motion. This is a sort of extended EP which is potentially useful for quantum gravitation. This is in particular if spacetime is built up from quantum entangled states. Things becomes much more difficult when black hole horizons enter the picture. 

The standard EP is not that hard to understand, and in weak gravitation the obvious example of this are weightless objects and astronauts in spacecraft and the ISS. In effect this is moving horizontally fast enough to keep missing the Earth and it just keeps falling. This is a visual example of the EP.

LC

[Alan Grayson]

I don't believe EM waves can exist without charges and/or currents being the source of the waves. Has anyone done an experiment to prove this is possible? Same with gravitational waves existing without the physical presence of mass/energy.  IMO, in both cases, the results of the equations are being misinterpreted. AG

[Alan Grayson]

What those solutions tell us is that EM waves can travel in regions of space without charges and/or currents. They don't tell us that EM waves can arise, come into existence, in the absence of charges and/or currents.  AG

[Alan Grayson]

On Sunday, July 12, 2020 at 4:37:15 PM UTC-6, Lawrence Crowell wrote:

I have not followed this thread much. I get the impression there is a lot of confusion. 

The equivalence principle states there is no distinguishing difference between a frame far away in flat spacetime and one in a region of spacetime that is curved so long as the frame is small in extent. In other words, it there is a curvature R and the dimensions of the frame are d then d << √R. This will mean that any test masses in this small frame will be on co-parallel geodesics and the local physics is no different than if you are on a frame in very distant flat spacetime. The converse of this then is that being on an accelerated frame is indistiguishable from being held fixed in a gravitational field. The surface of the Earth does that for us. Then comparing gravity with acceleration this way the implication is that inertial mass is equal to gravitational mass. The previous case indicates a way forwards to general relativity with local frames or patches that are meshed together in a coordinate atlas and transition function that define connection coefficients and curvature.

What you write above is not substantially different from my description of the EP. AG

[Alan Grayson]

Yes, good evidence that gravitational waves exist, but as far I know they're always associated with material interactions such as collisions of black holes. In the case of EM waves, I'd be more receptive of your claim that they can exist independent of charges and/or currents, but as far as I know there's no evidence of that. AG 

since, in this case, we're dealing with SR, wherein space-time has no curvature? AG 

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[Brent Meeker]

On 7/12/2020 11:50 PM, Alan Grayson wrote:

There can be because it's consistent with the equations.  A black hole doesn't include any matter.  General relativity is non-linear, that's why there can be non-flat cosmologies that contain no matter.  Of course there may be some different, better theory in which spacetime can't be curved without matter...but it seems unlikely since we have good evidence that gravitational waves exist.

Brent

Yes, good evidence that gravitational waves exist, but as far I know they're always associated with material interactions such as collisions of black holes. In the case of EM waves, I'd be more receptive of your claim that they can exist independent of charges and/or currents, but as far as I know there's no evidence of that. AG 

But a collision of black holes does NOT involve matter.  Black holes (as far as the theory goes) are purely geometric things, i.e. made of empty space.

Brent

[Alan Grayson]

How then does the BH at the center of our galaxy weigh in at 4 million solar masses? AG 

[Alan Grayson]

It's measured by observing the rotation rates of stars near the galactic core, and not so small by comparison with other BH's at the center of galaxies, called Super Massive BH's. AG 

[Alan Grayson]

If you assume zero mass solutions in GR, or no charges or currents in EM, the solutions you get are expected; namely, that in regions of space or space-time which are vacuums, waves can propagate.  AG

[Lawrence Crowell]

It is unfortunately apparent that you are pretty highly confused by some of this. You need to sit down and read a comprehensive book or text on GR and related subjects. It is not going to be possible to clear this up with dozens of email posts.

LC 

[Alan Grayson]

Correction; I meant that our BH is small by comparison to Super Massive BH's, which are orders of magnitude larger than 4 million solar masses. AG 

[Alan Grayson]

About the EP; I merely stated that it demonstrates that acceleration is locally indistinguishable from gravity, and then I stated what "locally" means. This is what Wiki and other sources say.  Yet you say I am confused. How so? About masses of BH's, I watch documentaries which feature astrophysicists offering their opinions, and they uniformly claim that BH's have mass. How could it be otherwise if they're remnants of massive collapsed stars? Not one makes Brent's claim, that they're just geometric manifestations.  AG

[Alan Grayson]

About the EP, I was careful to state that uniform acceleration is locally equivalent to gravity. I suggest you edit the Wiki article if you think it's "confused" and then post it here. I did state that the existence of gravity implies matter/energy, and you might object to that. But, IMO, you're misinterpreting what the GR field equations (and ME's) imply about the viability of wave motion in a vacuum. I see no reason to assume no source disturbance for the wave. AG

[Alan Grayson]

In reviewing Wiki's article on the Equivalence Principle, I see the details there are not exactly what I stated. But it doesn't really matter, except possibly for a purist, in the sense that I was trying to see how Einstein could have inferred curvature of space-time from the EP, using the enclosed elevator example subject to uniform acceleration. What I wrote seems sufficient to my objective. I am not confused. AG

[Lawrence Crowell]

Black hole mass is a pure spacetime physics. There is no material stuff anyone can get their hands on. With the tortoise coordinate the distant observer might say the matter-fields that made of a black hole exist, but if one tried to reach them they always recede away. Black holes do not have mass in a standard sense, though they have an ADM mass defined by the curvature of spacetime.

LC 

[Alan Grayson]

Generally, what resides inside a BH interacts gravitationally with what's exterior and is the remnant of a Type 1A supernova. It's unreachable, but has some correspondence with normal mass, which is why its mass can be estimated by its exterior effects, say for the one residing at the core of the Milky Way. I don't know how their masses are estimated when they are cores of distant galaxies. AG 

LC 

[Lawrence Crowell]

The interior does not interact with the exterior. The event horizon prevents that. From the perspective of anyone in the exterior the interior of a black hole is nothing more than a theoretical abstraction. It only exists as a counter factual situation, where instead of remaining outside an observer enters the BH/ 

LC

[Brent Meeker]

On 7/14/2020 3:34 AM, Lawrence Crowell wrote:

On Monday, July 13, 2020 at 6:30:46 PM UTC-5, Alan Grayson wrote:

On Monday, July 13, 2020 at 5:19:30 PM UTC-6, Lawrence Crowell wrote:

On Monday, July 13, 2020 at 4:42:24 PM UTC-5, Alan Grayson wrote:

On Monday, July 13, 2020 at 1:42:49 PM UTC-6, Alan Grayson wrote:

On Monday, July 13, 2020 at 11:57:50 AM UTC-6, Brent wrote:

On 7/12/2020 11:50 PM, Alan Grayson wrote:

There can be because it's consistent with the equations.  A black hole doesn't include any matter.  General relativity is non-linear, that's why there can be non-flat cosmologies that contain no matter.  Of course there may be some different, better theory in which spacetime can't be curved without matter...but it seems unlikely since we have good evidence that gravitational waves exist.

Brent

Yes, good evidence that gravitational waves exist, but as far I know they're always associated with material interactions such as collisions of black holes. In the case of EM waves, I'd be more receptive of your claim that they can exist independent of charges and/or currents, but as far as I know there's no evidence of that. AG 

But a collision of black holes does NOT involve matter.  Black holes (as far as the theory goes) are purely geometric things, i.e. made of empty space.

Brent

How then does the BH at the center of our galaxy weigh in at 4 million solar masses? AG 

It's measured by observing the rotation rates of stars near the galactic core, and not so small by comparison with other BH's at the center of galaxies, called Super Massive BH's. AG 

It is unfortunately apparent that you are pretty highly confused by some of this. You need to sit down and read a comprehensive book or text on GR and related subjects. It is not going to be possible to clear this up with dozens of email posts.

LC 

About the EP; I merely stated that it demonstrates that acceleration is locally indistinguishable from gravity, and then I stated what "locally" means. This is what Wiki and other sources say.  Yet you say I am confused. How so? About masses of BH's, I watch documentaries which feature astrophysicists offering their opinions, and they uniformly claim that BH's have mass. How could it be otherwise if they're remnants of massive collapsed stars? Not one makes Brent's claim, that they're just geometric manifestations.  AG

I didn't say they lacked mass.  I said they lacked matter.  Thus countering your assumption that gravity requires matter.

Brent

Black hole mass is a pure spacetime physics. There is no material stuff anyone can get their hands on. With the tortoise coordinate the distant observer might say the matter-fields that made of a black hole exist, but if one tried to reach them they always recede away. Black holes do not have mass in a standard sense, though they have an ADM mass defined by the curvature of spacetime.

LC 

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[Alan Grayson]

On Tuesday, July 14, 2020 at 11:31:42 AM UTC-6, Brent wrote:

On 7/14/2020 3:34 AM, Lawrence Crowell wrote:

On Monday, July 13, 2020 at 6:30:46 PM UTC-5, Alan Grayson wrote:

On Monday, July 13, 2020 at 5:19:30 PM UTC-6, Lawrence Crowell wrote:

On Monday, July 13, 2020 at 4:42:24 PM UTC-5, Alan Grayson wrote:

On Monday, July 13, 2020 at 1:42:49 PM UTC-6, Alan Grayson wrote:

On Monday, July 13, 2020 at 11:57:50 AM UTC-6, Brent wrote:

On 7/12/2020 11:50 PM, Alan Grayson wrote:

There can be because it's consistent with the equations.  A black hole doesn't include any matter.  General relativity is non-linear, that's why there can be non-flat cosmologies that contain no matter.  Of course there may be some different, better theory in which spacetime can't be curved without matter...but it seems unlikely since we have good evidence that gravitational waves exist.

Brent

Yes, good evidence that gravitational waves exist, but as far I know they're always associated with material interactions such as collisions of black holes. In the case of EM waves, I'd be more receptive of your claim that they can exist independent of charges and/or currents, but as far as I know there's no evidence of that. AG 

But a collision of black holes does NOT involve matter.  Black holes (as far as the theory goes) are purely geometric things, i.e. made of empty space.

Brent

How then does the BH at the center of our galaxy weigh in at 4 million solar masses? AG 

It's measured by observing the rotation rates of stars near the galactic core, and not so small by comparison with other BH's at the center of galaxies, called Super Massive BH's. AG 

It is unfortunately apparent that you are pretty highly confused by some of this. You need to sit down and read a comprehensive book or text on GR and related subjects. It is not going to be possible to clear this up with dozens of email posts.

LC 

About the EP; I merely stated that it demonstrates that acceleration is locally indistinguishable from gravity, and then I stated what "locally" means. This is what Wiki and other sources say.  Yet you say I am confused. How so? About masses of BH's, I watch documentaries which feature astrophysicists offering their opinions, and they uniformly claim that BH's have mass. How could it be otherwise if they're remnants of massive collapsed stars? Not one makes Brent's claim, that they're just geometric manifestations.  AG

I didn't say they lacked mass.  I said they lacked matter.  Thus countering your assumption that gravity requires matter.

Brent

I could have said that gravity requires mass/energy. What's the distinction between matter and mass? TIA, AG 

Black hole mass is a pure spacetime physics. There is no material stuff anyone can get their hands on. With the tortoise coordinate the distant observer might say the matter-fields that made of a black hole exist, but if one tried to reach them they always recede away. Black holes do not have mass in a standard sense, though they have an ADM mass defined by the curvature of spacetime.

LC 

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[Alan Grayson]

Then how can a BH interact gravitationally with objects external to the event horizon, or do you deny that? AG

[Brent Meeker]

On 7/14/2020 12:22 PM, Alan Grayson wrote:

On Tuesday, July 14, 2020 at 11:31:42 AM UTC-6, Brent wrote:

On 7/14/2020 3:34 AM, Lawrence Crowell wrote:

On Monday, July 13, 2020 at 6:30:46 PM UTC-5, Alan Grayson wrote:

On Monday, July 13, 2020 at 5:19:30 PM UTC-6, Lawrence Crowell wrote:

On Monday, July 13, 2020 at 4:42:24 PM UTC-5, Alan Grayson wrote:

On Monday, July 13, 2020 at 1:42:49 PM UTC-6, Alan Grayson wrote:

On Monday, July 13, 2020 at 11:57:50 AM UTC-6, Brent wrote:

On 7/12/2020 11:50 PM, Alan Grayson wrote:

There can be because it's consistent with the equations.  A black hole doesn't include any matter.  General relativity is non-linear, that's why there can be non-flat cosmologies that contain no matter.  Of course there may be some different, better theory in which spacetime can't be curved without matter...but it seems unlikely since we have good evidence that gravitational waves exist.

Brent

Yes, good evidence that gravitational waves exist, but as far I know they're always associated with material interactions such as collisions of black holes. In the case of EM waves, I'd be more receptive of your claim that they can exist independent of charges and/or currents, but as far as I know there's no evidence of that. AG 

But a collision of black holes does NOT involve matter.  Black holes (as far as the theory goes) are purely geometric things, i.e. made of empty space.

Brent

How then does the BH at the center of our galaxy weigh in at 4 million solar masses? AG 

It's measured by observing the rotation rates of stars near the galactic core, and not so small by comparison with other BH's at the center of galaxies, called Super Massive BH's. AG 

It is unfortunately apparent that you are pretty highly confused by some of this. You need to sit down and read a comprehensive book or text on GR and related subjects. It is not going to be possible to clear this up with dozens of email posts.

LC 

About the EP; I merely stated that it demonstrates that acceleration is locally indistinguishable from gravity, and then I stated what "locally" means. This is what Wiki and other sources say.  Yet you say I am confused. How so? About masses of BH's, I watch documentaries which feature astrophysicists offering their opinions, and they uniformly claim that BH's have mass. How could it be otherwise if they're remnants of massive collapsed stars? Not one makes Brent's claim, that they're just geometric manifestations.  AG

I didn't say they lacked mass.  I said they lacked matter.  Thus countering your assumption that gravity requires matter.

Brent

I could have said that gravity requires mass/energy. What's the distinction between matter and mass? TIA, AG

Some things, e.g. black holes, have mass without matter (at least as far as GR goes).

Brent

[Alan Grayson]

What's the distinction between matter and mass? AG 

[Brent Meeker]

What's your problem.  Do  you just want to argument semantics.  I don't care if you want to call a black hole "matter", but nobody else does.  Everybody else means localized packets of mass-energy in the form of fermions.

Brent

[Lawrence Crowell]

The black hole does not interact with material outside, the material outside interacts with the black hole. A black hole is a causality sink; causal propagation is into the black hole. Only stochastic quantum events propagate out. 

LC

[Alan Grayson]

Do I just want to argue semantics? No, of course not, But you seem to want that. Otherwise, instead of trying to put me down, you could have just assumed I meant MASS!  IIRC, at some point above I did refer to E=mc^2, which equates MASS with energy. AG 

[Alan Grayson]

But if I wanted to argue semantics, I could win!  Can't fermions be considered "matter"? AG

[Alan Grayson]

I am not sure I understand or agree. Space-time is strongly curved near a BH. Are you claiming this curvature is not caused by the BH? In any event, doesn't this put a nail in the coffin of quantum gravity? IIUC, the force carrying particle in a quantum gravity theory is the graviton. If nothing can get out of a BH, this would apply to the graviton. Seems like a problem for any quantum gravity theory. AG 

[Philip Thrift]

> Can't fermions be considered "matter"? AG

"Thus, matter can be defined as everything composed of elementary fermions."
https://en.wikipedia.org/wiki/Matter

@philipthrift

[Alan Grayson]

Let me put the question another way; if gravitons exist, could they escape a BH? If not, does this adversely effect the existence of a quantum theory of gravity? TIA, AG 

[Lawrence Crowell]

Gravitons do not escape from a BH, any more than can light. However, from the perspective of an outside observer all matter than went into a BH is on the surface above the event horizon, called the stretched horizon. 

LC

[Brent Meeker]

I wonder about the use of cicumlocutions like "from the perspective of an outside observer".  In special relativity it it is often said that a moving object will looked shortened along the direction of motion.  But as Terrell pointed out that's not at all how they look.  It is more accurate to say that measuring a moving a object will show that it is shortened along the direction of motion; the difference being that the measurement corrects for the fact that you want the difference in arrival time of photons that left the ends of the object at the same time (an ill defined concept), instead of the image formed by photons that arrived at the same time.  But then I think, why not correct for the Lorentz contraction too in the measurement and arrive at what we might call "the proper length".  That's just as "measured" as either of the other two.

By the same reasoning, you're really saying the visual impression of a distant observer is that infalling stuff appears to be on the surface of the event horizon. Which is because it takes forever for photons to reach him.  But why should he be so naive.  He knows what he's seeing is arbitrarily far in his past; so what he should be said to "measure" or "calculate" is that the stuff has already been annihilated at the "singularity" in his reference frame.

Brent

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[Alan Grayson]

On Thursday, July 16, 2020 at 5:08:57 PM UTC-6, Lawrence Crowell wrote:

Gravitons do not escape from a BH, any more than can light. However, from the perspective of an outside observer all matter than went into a BH is on the surface above the event horizon, called the stretched horizon. 

LC

Gravitons might not exist (and hence quantum gravity can't exist)  But whatever the case, how can BH's interact gravitationally with objects beyond its event horizon? You say this doesn't happen. I don't understand your argument. AG 

[Alan Grayson]

On Thursday, July 16, 2020 at 7:50:07 PM UTC-6, Alan Grayson wrote:

On Thursday, July 16, 2020 at 5:08:57 PM UTC-6, Lawrence Crowell wrote:

Gravitons do not escape from a BH, any more than can light. However, from the perspective of an outside observer all matter than went into a BH is on the surface above the event horizon, called the stretched horizon. 

LC

Gravitons might not exist (and hence quantum gravity can't exist)  But whatever the case, how can BH's interact gravitationally with objects beyond its event horizon? You say this doesn't happen. I don't understand your argument. AG 

I may have identified the thousand pound gorilla in the room; the hypothetical force carrying particle of the quantum gravitating field, the graviton, which for BH's doesn't exert any force! AG 

[Lawrence Crowell]

On Friday, July 17, 2020 at 5:01:41 AM UTC-5 agrays...@gmail.com wrote:

On Thursday, July 16, 2020 at 7:50:07 PM UTC-6, Alan Grayson wrote:

On Thursday, July 16, 2020 at 5:08:57 PM UTC-6, Lawrence Crowell wrote:

Gravitons do not escape from a BH, any more than can light. However, from the perspective of an outside observer all matter than went into a BH is on the surface above the event horizon, called the stretched horizon. 

LC

Gravitons might not exist (and hence quantum gravity can't exist)  But whatever the case, how can BH's interact gravitationally with objects beyond its event horizon? You say this doesn't happen. I don't understand your argument. AG 

That you are saying this illustrates you do not understand general relativity.

 

I may have identified the thousand pound gorilla in the room; the hypothetical force carrying particle of the quantum gravitating field, the graviton, which for BH's doesn't exert any force! AG 

I have no idea why you are saying this. Gravitation is not a force in the usual sense and so the graviton does not produce a force in the standard meaning. For the weak field limit the nonlinear terms are negligable and a gravitational wave is linear. This is easily quantized. In fact it is similar to the Hanbury-Brown and Twiss theory of the diphoton. It is when the field becomes strong that general relativity becomes nonlinear and runs into trouble with quantum mechanics.

LC

[Alan Grayson]

I assumed a quantum field theory of gravity must have a particle associated with it, and that this particle is called the graviton. Gravity is a fictitious force. So what would the role of the graviton be, if not to produce some force? If you detect gravitational waves, don't they consist of gravitons if a quantum theory of gravity exists, analogous to photons in EM waves? AG

[Alan Grayson]

Before you can present yourself as deeply knowledgeable of GR, you should be able to give a coherent account how presumably isolated bodies such as BH's, can gravitationally interact with what's exterior to them. If gravitons can't do that in the context of a quantum theory of gravity, what can?  AG

[Lawrence Crowell]

It is the delay or tortoise coordinate basis for an external observer.

LC 

[Alan Grayson]

This is a tough subject to wrap one's head around. Wiki has a decent article on it. There's an objective gravitational effect of a BH beyond its event horizon. Are you claiming that the effect is only supported by theory by a particular choice of coordinate system for an external observer? AG 

LC 

[Lawrence Crowell]

The tortoise coordinates is found from the Schwarzschild metric

ds^2 = (1 - 2m/r)dt^2 -  (1 - 2m/r)^{-1}dr^2 - r^2dΩ^2   

where for a signal leaving a point near the black hole with ds = 0 (null path) and propagating radially out, dΩ = 0, we have dt = dr/(1 - 2m/r) which then leads to

T = t - t0 - 2m ln|r - 2m|.

That is the tortoise coordinate. Please look this up to read further. I can't spend beaucoup time going over this for weeks to come.

LC

[Alan Grayson]

On Saturday, July 18, 2020 at 6:18:28 AM UTC-6, Lawrence Crowell wrote:

The tortoise coordinates is found from the Schwarzschild metric

ds^2 = (1 - 2m/r)dt^2 -  (1 - 2m/r)^{-1}dr^2 - r^2dΩ^2   

where for a signal leaving a point near the black hole with ds = 0 (null path) and propagating radially out, dΩ = 0, we have dt = dr/(1 - 2m/r) which then leads to

T = t - t0 - 2m ln|r - 2m|.

That is the tortoise coordinate. Please look this up to read further. I can't spend beaucoup time going over this for weeks to come.

LC

You don't have to. We're done.  But you should IMO address Brent's objection, maybe on another thread. AG

[Alan Grayson]

On Saturday, July 18, 2020 at 6:31:23 AM UTC-6, Alan Grayson wrote:

On Saturday, July 18, 2020 at 6:18:28 AM UTC-6, Lawrence Crowell wrote:

The tortoise coordinates is found from the Schwarzschild metric

ds^2 = (1 - 2m/r)dt^2 -  (1 - 2m/r)^{-1}dr^2 - r^2dΩ^2   

where for a signal leaving a point near the black hole with ds = 0 (null path) and propagating radially out, dΩ = 0, we have dt = dr/(1 - 2m/r) which then leads to

T = t - t0 - 2m ln|r - 2m|.

That is the tortoise coordinate. Please look this up to read further. I can't spend beaucoup time going over this for weeks to come.

LC

You don't have to. We're done.  But you should IMO address Brent's objection, maybe on another thread. AG

When it comes to GR, you're a genius; no question about it. I wouldn't want to waste your valuable time. But consider this; the Schwartzschild metric applies to NON-ROTATING masses. Do you really think a massive contracting star which forms a BH will be non-rotating? Obviously, it will be RAPIDLY rotating, like an ice skater who contracts her arms. Brent also had some substantive questions about your model. But I see you prefer your illusions than to address his objections. AG

[Lawrence Crowell]

On Thursday, July 23, 2020 at 5:56:32 AM UTC-5 agrays...@gmail.com wrote:

On Saturday, July 18, 2020 at 6:31:23 AM UTC-6, Alan Grayson wrote:

On Saturday, July 18, 2020 at 6:18:28 AM UTC-6, Lawrence Crowell wrote:

The tortoise coordinates is found from the Schwarzschild metric

ds^2 = (1 - 2m/r)dt^2 -  (1 - 2m/r)^{-1}dr^2 - r^2dΩ^2   

where for a signal leaving a point near the black hole with ds = 0 (null path) and propagating radially out, dΩ = 0, we have dt = dr/(1 - 2m/r) which then leads to

T = t - t0 - 2m ln|r - 2m|.

That is the tortoise coordinate. Please look this up to read further. I can't spend beaucoup time going over this for weeks to come.

LC

You don't have to. We're done.  But you should IMO address Brent's objection, maybe on another thread. AG

When it comes to GR, you're a genius; no question about it. I wouldn't want to waste your valuable time. But consider this; the Schwartzschild metric applies to NON-ROTATING masses. Do you really think a massive contracting star which forms a BH will be non-rotating? Obviously, it will be RAPIDLY rotating, like an ice skater who contracts her arms. Brent also had some substantive questions about your model. But I see you prefer your illusions than to address his objections. AG

The result is similar, but more complex. The same calculation can be done for the Kerr solution. It is just a lot more complicated mathematically.

LC

 

[Alan Grayson]

If you say so. In any event, the idea that an objectively existing gravitational field outside a BH should depend on the choice of a particular coordinate system, seems a non-starter. AG 

 

[Lawrence Crowell]

Coordinates are not the basis of physics. Curvatures are covariant, while connections and coordinates are not. These can be imposed in many ways, similar to a gauge choice. 

LC

[Alan Grayson]

On Thursday, July 23, 2020 at 8:27:52 AM UTC-6, Lawrence Crowell wrote:

Coordinates are not the basis of physics. Curvatures are covariant, while connections and coordinates are not. These can be imposed in many ways, similar to a gauge choice. 

LC

That right; coordinates are not the basis of physics. That's why Einstein had to cast his GR equation in tensor form, so the laws of physics would be independent of coordinate systems. But you're asserting, or so it seems, that there is a unique coordinate system wherein the external gravitational effect of a BH can be calculated. This is what I object to. AG

[Brent Meeker]

On 7/23/2020 4:41 AM, Lawrence Crowell wrote:

On Thursday, July 23, 2020 at 5:56:32 AM UTC-5 agrays...@gmail.com wrote:

On Saturday, July 18, 2020 at 6:31:23 AM UTC-6, Alan Grayson wrote:

On Saturday, July 18, 2020 at 6:18:28 AM UTC-6, Lawrence Crowell wrote:

The tortoise coordinates is found from the Schwarzschild metric

ds^2 = (1 - 2m/r)dt^2 -  (1 - 2m/r)^{-1}dr^2 - r^2dΩ^2   

where for a signal leaving a point near the black hole with ds = 0 (null path) and propagating radially out, dΩ = 0, we have dt = dr/(1 - 2m/r) which then leads to

T = t - t0 - 2m ln|r - 2m|.

That is the tortoise coordinate. Please look this up to read further. I can't spend beaucoup time going over this for weeks to come.

LC

You don't have to. We're done.  But you should IMO address Brent's objection, maybe on another thread. AG

I don't know what objection you're referring to.  LC is just showing why it takes a distant observer forever to see an infalling object reach the event horizon of a black hole.

Brent

When it comes to GR, you're a genius; no question about it. I wouldn't want to waste your valuable time. But consider this; the Schwartzschild metric applies to NON-ROTATING masses. Do you really think a massive contracting star which forms a BH will be non-rotating? Obviously, it will be RAPIDLY rotating, like an ice skater who contracts her arms. Brent also had some substantive questions about your model. But I see you prefer your illusions than to address his objections. AG

The result is similar, but more complex. The same calculation can be done for the Kerr solution. It is just a lot more complicated mathematically.

LC

 

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[Brent Meeker]

On 7/23/2020 7:33 AM, Alan Grayson wrote:

On Thursday, July 23, 2020 at 8:27:52 AM UTC-6, Lawrence Crowell wrote:

Coordinates are not the basis of physics. Curvatures are covariant, while connections and coordinates are not. These can be imposed in many ways, similar to a gauge choice. 

LC

That right; coordinates are not the basis of physics. That's why Einstein had to cast his GR equation in tensor form, so the laws of physics would be independent of coordinate systems. But you're asserting, or so it seems, that there is a unique coordinate system wherein the external gravitational effect of a BH can be calculated. This is what I object to. AG

Calculations are always done in some coordinate system.   The method is to calculate something, like the curvature tensor or a proper time, that doesn't depend on which coordinate system you used.

Brent

On Thursday, July 23, 2020 at 6:49:44 AM UTC-5 agrays...@gmail.com wrote:

On Thursday, July 23, 2020 at 5:41:42 AM UTC-6, Lawrence Crowell wrote:

On Thursday, July 23, 2020 at 5:56:32 AM UTC-5 agrays...@gmail.com wrote:

On Saturday, July 18, 2020 at 6:31:23 AM UTC-6, Alan Grayson wrote:

On Saturday, July 18, 2020 at 6:18:28 AM UTC-6, Lawrence Crowell wrote:

The tortoise coordinates is found from the Schwarzschild metric

ds^2 = (1 - 2m/r)dt^2 -  (1 - 2m/r)^{-1}dr^2 - r^2dΩ^2   

where for a signal leaving a point near the black hole with ds = 0 (null path) and propagating radially out, dΩ = 0, we have dt = dr/(1 - 2m/r) which then leads to

T = t - t0 - 2m ln|r - 2m|.

That is the tortoise coordinate. Please look this up to read further. I can't spend beaucoup time going over this for weeks to come.

LC

You don't have to. We're done.  But you should IMO address Brent's objection, maybe on another thread. AG

When it comes to GR, you're a genius; no question about it. I wouldn't want to waste your valuable time. But consider this; the Schwartzschild metric applies to NON-ROTATING masses. Do you really think a massive contracting star which forms a BH will be non-rotating? Obviously, it will be RAPIDLY rotating, like an ice skater who contracts her arms. Brent also had some substantive questions about your model. But I see you prefer your illusions than to address his objections. AG

The result is similar, but more complex. The same calculation can be done for the Kerr solution. It is just a lot more complicated mathematically.

LC

If you say so. In any event, the idea that an objectively existing gravitational field outside a BH should depend on the choice of a particular coordinate system, seems a non-starter. AG 

 

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[Alan Grayson]

On Thursday, July 23, 2020 at 11:59:59 AM UTC-6, Brent wrote:

On 7/23/2020 4:41 AM, Lawrence Crowell wrote:

On Thursday, July 23, 2020 at 5:56:32 AM UTC-5 agrays...@gmail.com wrote:

On Saturday, July 18, 2020 at 6:31:23 AM UTC-6, Alan Grayson wrote:

On Saturday, July 18, 2020 at 6:18:28 AM UTC-6, Lawrence Crowell wrote:

The tortoise coordinates is found from the Schwarzschild metric

ds^2 = (1 - 2m/r)dt^2 -  (1 - 2m/r)^{-1}dr^2 - r^2dΩ^2   

where for a signal leaving a point near the black hole with ds = 0 (null path) and propagating radially out, dΩ = 0, we have dt = dr/(1 - 2m/r) which then leads to

T = t - t0 - 2m ln|r - 2m|.

That is the tortoise coordinate. Please look this up to read further. I can't spend beaucoup time going over this for weeks to come.

LC

You don't have to. We're done.  But you should IMO address Brent's objection, maybe on another thread. AG

I don't know what objection you're referring to.  LC is just showing why it takes a distant observer forever to see an infalling object reach the event horizon of a black hole.

Brent

Your words: 

I wonder about the use of cicumlocutions like "from the perspective of an outside observer".  In special relativity it it is often said that a moving object will looked shortened along the direction of motion.  But as Terrell pointed out that's not at all how they look.  It is more accurate to say that measuring a moving a object will show that it is shortened along the direction of motion; the difference being that the measurement corrects for the fact that you want the difference in arrival time of photons that left the ends of the object at the same time (an ill defined concept), instead of the image formed by photons that arrived at the same time.  But then I think, why not correct for the Lorentz contraction too in the measurement and arrive at what we might call "the proper length".  That's just as "measured" as either of the other two.

By the same reasoning, you're really saying the visual impression of a distant observer is that infalling stuff appears to be on the surface of the event horizon. Which is because it takes forever for photons to reach him.  But why should he be so naive.  He knows what he's seeing is arbitrarily far in his past; so what he should be said to "measure" or "calculate" is that the stuff has already been annihilated at the "singularity" in his reference frame.

-----------------------------------------------------

I forget why LC brought up this particular coordinate system. He had some point in response to a comment I made. I'll have to review my comments; maybe that the gravitational field due to a BH, external to the event horizon, has an objective reality. AG

 

When it comes to GR, you're a genius; no question about it. I wouldn't want to waste your valuable time. But consider this; the Schwartzschild metric applies to NON-ROTATING masses. Do you really think a massive contracting star which forms a BH will be non-rotating? Obviously, it will be RAPIDLY rotating, like an ice skater who contracts her arms. Brent also had some substantive questions about your model. But I see you prefer your illusions than to address his objections. AG

The result is similar, but more complex. The same calculation can be done for the Kerr solution. It is just a lot more complicated mathematically.

LC

 

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[Alan Grayson]

On Thursday, July 23, 2020 at 8:56:03 PM UTC-6, Alan Grayson wrote:

On Thursday, July 23, 2020 at 11:59:59 AM UTC-6, Brent wrote:

On 7/23/2020 4:41 AM, Lawrence Crowell wrote:

On Thursday, July 23, 2020 at 5:56:32 AM UTC-5 agrays...@gmail.com wrote:

On Saturday, July 18, 2020 at 6:31:23 AM UTC-6, Alan Grayson wrote:

On Saturday, July 18, 2020 at 6:18:28 AM UTC-6, Lawrence Crowell wrote:

The tortoise coordinates is found from the Schwarzschild metric

ds^2 = (1 - 2m/r)dt^2 -  (1 - 2m/r)^{-1}dr^2 - r^2dΩ^2   

where for a signal leaving a point near the black hole with ds = 0 (null path) and propagating radially out, dΩ = 0, we have dt = dr/(1 - 2m/r) which then leads to

T = t - t0 - 2m ln|r - 2m|.

That is the tortoise coordinate. Please look this up to read further. I can't spend beaucoup time going over this for weeks to come.

LC

You don't have to. We're done.  But you should IMO address Brent's objection, maybe on another thread. AG

I don't know what objection you're referring to.  LC is just showing why it takes a distant observer forever to see an infalling object reach the event horizon of a black hole.

Brent

Your words: 

I wonder about the use of cicumlocutions like "from the perspective of an outside observer".  In special relativity it it is often said that a moving object will looked shortened along the direction of motion.  But as Terrell pointed out that's not at all how they look.  It is more accurate to say that measuring a moving a object will show that it is shortened along the direction of motion; the difference being that the measurement corrects for the fact that you want the difference in arrival time of photons that left the ends of the object at the same time (an ill defined concept), instead of the image formed by photons that arrived at the same time.  But then I think, why not correct for the Lorentz contraction too in the measurement and arrive at what we might call "the proper length".  That's just as "measured" as either of the other two.

By the same reasoning, you're really saying the visual impression of a distant observer is that infalling stuff appears to be on the surface of the event horizon. Which is because it takes forever for photons to reach him.  But why should he be so naive.  He knows what he's seeing is arbitrarily far in his past; so what he should be said to "measure" or "calculate" is that the stuff has already been annihilated at the "singularity" in his reference frame.

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I forget why LC brought up this particular coordinate system. He had some point in response to a comment I made. I'll have to review my comments; maybe that the gravitational field due to a BH, external to the event horizon, has an objective reality. AG

I just reviewed LC's comments. He was claiming that tortoise coordinates show the existence of the gravitational field due to a BH, external to it. He wasn't limiting his argument, which you apparently objected to, to how long a distant observer would have to view an infalling mass, to see it disappear. AG 

[Brent Meeker]

On 7/23/2020 7:56 PM, Alan Grayson wrote:

On Thursday, July 23, 2020 at 11:59:59 AM UTC-6, Brent wrote:

On 7/23/2020 4:41 AM, Lawrence Crowell wrote:

On Thursday, July 23, 2020 at 5:56:32 AM UTC-5 agrays...@gmail.com wrote:

On Saturday, July 18, 2020 at 6:31:23 AM UTC-6, Alan Grayson wrote:

On Saturday, July 18, 2020 at 6:18:28 AM UTC-6, Lawrence Crowell wrote:

The tortoise coordinates is found from the Schwarzschild metric

ds^2 = (1 - 2m/r)dt^2 -  (1 - 2m/r)^{-1}dr^2 - r^2dΩ^2   

where for a signal leaving a point near the black hole with ds = 0 (null path) and propagating radially out, dΩ = 0, we have dt = dr/(1 - 2m/r) which then leads to

T = t - t0 - 2m ln|r - 2m|.

That is the tortoise coordinate. Please look this up to read further. I can't spend beaucoup time going over this for weeks to come.

LC

You don't have to. We're done.  But you should IMO address Brent's objection, maybe on another thread. AG

I don't know what objection you're referring to.  LC is just showing why it takes a distant observer forever to see an infalling object reach the event horizon of a black hole.

Brent

Your words: 

I wonder about the use of cicumlocutions like "from the perspective of an outside observer".  In special relativity it it is often said that a moving object will looked shortened along the direction of motion.  But as Terrell pointed out that's not at all how they look.  It is more accurate to say that measuring a moving a object will show that it is shortened along the direction of motion; the difference being that the measurement corrects for the fact that you want the difference in arrival time of photons that left the ends of the object at the same time (an ill defined concept), instead of the image formed by photons that arrived at the same time.  But then I think, why not correct for the Lorentz contraction too in the measurement and arrive at what we might call "the proper length".  That's just as "measured" as either of the other two.

By the same reasoning, you're really saying the visual impression of a distant observer is that infalling stuff appears to be on the surface of the event horizon. Which is because it takes forever for photons to reach him.  But why should he be so naive.  He knows what he's seeing is arbitrarily far in his past; so what he should be said to "measure" or "calculate" is that the stuff has already been annihilated at the "singularity" in his reference frame.

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I forget why LC brought up this particular coordinate system. He had some point in response to a comment I made. I'll have to review my comments; maybe that the gravitational field due to a BH, external to the event horizon, has an objective reality. AG

LC is perfectly aware of what I wrote.  I was just pointing that we have no reason to privilege how things appear to distant observers, yet it's seems to be a sort of convention in talking about relativity.  It's like discussing the refraction of light and saying, "See, the pencil in bent when it's partly submerged."

 Brent

[Lawrence Crowell]

There are lots of other possible frames. They would share this generic feature  of delay. 

LC