Consider a distant observer traveling at .867 c relative to the solar system along the line that is co-linear with the sun's axis of rotation. In this situation the Lorentz transforms inform us that gamma = 2. So in accordance with SR, and after takingthe relativistic doppler into account, from the observer's point of view it takes the earth twice as long--730.5 days--to complete one revolution around the sun.
The observer measures the major and minor axes of the earth's orbit around the sun to be identical to its major and minor axes in the solar system's rest frame, where the orbital period is only 365.25 days.first postulate of special relativity.
We therefore conclude that Kepler's 3rd law of planetary motion is ONLY valid in the rest frame of the solar system. This famous law of physics has a preferred FoR in which it applies and is false in all other frames. This is a blatant violation of the
Note: Newtonian gravity is not assumed in this paradox. InvariantLet us see if we can fix Kepler 3 to make it relativity-proof. It takes a genius to try this--and to know when to cry "uncle"
spacetime curvature is assumed to be the cause of the earth's orbit
around the sun.
Consider a distant observer traveling at .867 c ( 𝛾=2 ) relative to the solar system...
In his inertial frame of reference the earth's orbital velocity is only half the velocity
necessary to keep the earth in stable orbit...
Invariant spacetime curvature...
Will the earth spiral into the sun?
Ridiculous! See Einstein's First vs. Kepler's Third, ibid.
Consider a distant observer traveling at .867 c relative to the solar system along the line that is co-linear with the sun's axis of rotation. In this situation the Lorentz transforms inform us that gamma = 2. So in accordance with SR, and after takingthe relativistic doppler into account, from the observer's point of view it takes the earth twice as long--730.5 days--to complete one revolution around the sun.
The observer measures the major and minor axes of the earth's orbit around the sun to be identical to its major and minor axes in the solar system's rest frame, where the orbital period is only 365.25 days.first postulate of special relativity.
We therefore conclude that Kepler's 3rd law of planetary motion is ONLY valid in the rest frame of the solar system. This famous law of physics has a preferred FoR in which it applies and is false in all other frames. This is a blatant violation of the
Note: Newtonian gravity is not assumed in this paradox. Invariant
spacetime curvature is assumed to be the cause of the earth's orbit
around the sun.
On Sunday, September 3, 2023 at 1:24:13 PM UTC-7, patdolan wrote:invariant, which may be surprising to you if you aren't taking the time component of the trajectory into account.
Consider a distant observer traveling at .867 c ( 𝛾=2 ) relative to the solar system...
In his inertial frame of reference the earth's orbital velocity is only half the velocity
necessary to keep the earth in stable orbit...
Not true, the earth follows a helical geodesic trajectory through spacetime, and this helical geodesic is not intrinsically altered by being described in terms of a different system of coordinates. Also, the *extrinsic* curvature of the trajectory is
high speed object is at rest, superimposed on the mildly curved spacetime surrounding the sun), but the components of the *intrinsic* curvature tensor of spacetime are not invariant under coordinate transformations, they change along with the componentsInvariant spacetime curvature...
Be careful... the *extrinsic* curvature of the trajectory is invariant under Lorentz transformation (which is essentially what you are applying to the Schwarzschild coordinates by switching to the background inertial coordinates in which the distant
trajectory of a putt going into the hole in terms of one coordinate system, it will also go into the hole in terms of the other coordinate system. Yes, the ball has different coordinates at the end, but the cup also has different coordinates, so the ballWill the earth spiral into the sun?
No, describing the phenomena in terms of a different system of coordinates doesn't change the intrinsic phenomena, and doesn't alter any of the invariant intervals. For example, if you draw two chalk grids on a putting green, and describe the
and I assume that by "Kepler's Third" you mean Kepler's proposition that the squares of the angular orbital periods of the planets are directly proportional to the cubes of the semi-major axes of their orbits. There's no conflict between either of theseRidiculous! See Einstein's First vs. Kepler's Third, ibid.
I assume by "Einstein's First" you mean the principle of relativity, i.e., that the laws by which the states of physical systems undergo change take the same simple homogeneous and isotropic form in terms of any standard system of inertial coordinates,
What may be confusing you is that you may be thinking of Newton's elaboration and refinement of Kepler's propositions based on his concepts of instantaneous gravity and mass and force, combined with the assumption that inertial coordinate systems arerelated by Galilean transformations, and the lack of accounting for the inertia of energy. There is indeed a conflict between those Newtonian concepts applied to relativistic velocities versus the relativistic account.
On Sunday, September 3, 2023 at 1:24:13 PM UTC-7, patdolan wrote:taking the relativistic doppler into account, from the observer's point of view it takes the earth twice as long--730.5 days--to complete one revolution around the sun.
Consider a distant observer traveling at .867 c relative to the solar system along the line that is co-linear with the sun's axis of rotation. In this situation the Lorentz transforms inform us that gamma = 2. So in accordance with SR, and after
the first postulate of special relativity.The observer measures the major and minor axes of the earth's orbit around the sun to be identical to its major and minor axes in the solar system's rest frame, where the orbital period is only 365.25 days.
We therefore conclude that Kepler's 3rd law of planetary motion is ONLY valid in the rest frame of the solar system. This famous law of physics has a preferred FoR in which it applies and is false in all other frames. This is a blatant violation of
Jan, do you find my supposed error concealed in Lunatic Legion's word-wall? Or do you have something else in mind?Note: Newtonian gravity is not assumed in this paradox. Invariant spacetime curvature is assumed to be the cause of the earth's orbitExercise: find the error in the above reasoning.
around the sun.
--
Jan
taking the relativistic doppler into account, from the observer's point of view it takes the earth twice as long--730.5 days--to complete one revolution around the sun.Consider a distant observer traveling at .867 c relative to the solar system along the line that is co-linear with the sun's axis of rotation. In this situation the Lorentz transforms inform us that gamma = 2. So in accordance with SR, and after
the first postulate of special relativity.The observer measures the major and minor axes of the earth's orbit around the sun to be identical to its major and minor axes in the solar system's rest frame, where the orbital period is only 365.25 days.
We therefore conclude that Kepler's 3rd law of planetary motion is ONLY valid in the rest frame of the solar system. This famous law of physics has a preferred FoR in which it applies and is false in all other frames. This is a blatant violation of
Note: Newtonian gravity is not assumed in this paradox. Invariant spacetime curvature is assumed to be the cause of the earth's orbitExercise: find the error in the above reasoning.
around the sun.
On Sunday, September 3, 2023 at 2:17:41 PM UTC-7, JanPB wrote:taking the relativistic doppler into account, from the observer's point of view it takes the earth twice as long--730.5 days--to complete one revolution around the sun.
Consider a distant observer traveling at .867 c relative to the solar system along the line that is co-linear with the sun's axis of rotation. In this situation the Lorentz transforms inform us that gamma = 2. So in accordance with SR, and after
the first postulate of special relativity.The observer measures the major and minor axes of the earth's orbit around the sun to be identical to its major and minor axes in the solar system's rest frame, where the orbital period is only 365.25 days.
We therefore conclude that Kepler's 3rd law of planetary motion is ONLY valid in the rest frame of the solar system. This famous law of physics has a preferred FoR in which it applies and is false in all other frames. This is a blatant violation of
overall solar system behaves the same way *intrinsically*, regardless of the rest frame of the center of mass of the solar system, but it does not say that the description of a physical system in a certain state of motion is the same in terms of everyThat's sort of a trick question, because there are actually about a dozen errors underlying the above. Just to take one at random...Note: Newtonian gravity is not assumed in this paradox. Invariant spacetime curvature is assumed to be the cause of the earth's orbit around the sun.Exercise: find the error in the above reasoning.
The OP imagines that it's a violation of relativity for the orbit of an object to take a particularly simple form in terms of the rest frame of the central gravitating body. That, of course, is false. The principle of relativity signifies that the
The OP doesn't seem to have noticed that, for example, Kepler's FIRST proposition that planets move in closed ellipses in space is obviously only true (approximately) in terms of inertial coordinates in which the sun is more or less at rest. In termsof other coordinate systems, the planets move in spatial helical or spiraling paths. And this is true in Newtonian physics as well, and yet the OP doesn't imagine that it contradicts Newtonian gravity. His brain just doesn't (can't?) grasp the
overall solar system behaves the same way *intrinsically*, regardless of the rest frame of the center of mass of the solar system, but it does not say that the description of a physical system in a certain state of motion is the same in terms of everyThe OP imagines that it's a violation of relativity for the orbit of an object to take a particularly simple form in terms of the rest frame of the central gravitating body. That, of course, is false. The principle of relativity signifies that the
of other coordinate systems, the planets move in spatial helical or spiraling paths. And this is true in Newtonian physics as well, and yet the OP doesn't imagine that it contradicts Newtonian gravity. His brain just doesn't (can't?) grasp theThe OP doesn't seem to have noticed that, for example, Kepler's FIRST proposition that planets move in closed ellipses in space is obviously only true (approximately) in terms of inertial coordinates in which the sun is more or less at rest. In terms
Kepler's coordinates were earth-centered.
Consider a distant observer traveling at .867 c ( 𝛾=2 ) relative to the solar system...
In his inertial frame of reference the earth's orbital velocity is only half the velocity
necessary to keep the earth in stable orbit...
Will the earth spiral into the sun?
On Sunday, September 3, 2023 at 5:09:09 PM UTC-7, patdolan wrote:
Kepler's coordinates were earth-centered.
What is wrong with you? How could the trajectory of the earth be an ellipse in terms of earth-centered coordinates? Did you get kicked in the head by a mule or something?
On Sunday, September 3, 2023 at 6:58:14 PM UTC-7, Bill wrote:Muttonchops, have you come down with Legionnaire's disease too? Kep worked out his laws of planetary motion on the other planets. I merely applied those laws to the earth in my earth-sun scenario. Lunatic Legion has gone mad with the overload of
On Sunday, September 3, 2023 at 5:09:09 PM UTC-7, patdolan wrote:
Kepler's coordinates were earth-centered.
What is wrong with you? How could the trajectory of the earth be an ellipse in terms of earth-centered coordinates? Did you get kicked in the head by a mule or something?I think you are on to something here, Bill... kicked in the head by a mule would explain a LOT about Dolan...
We therefore conclude that Kepler's 3rd law of planetary motion is
ONLY valid in the rest frame of the solar system. This famous law of
physics has a preferred FoR in which it applies and is false in all
other frames. This is a blatant violation of the first postulate of
special relativity.
On 04-Sept-23 6:24 am, patdolan wrote:
We therefore conclude that Kepler's 3rd law of planetary motion isIf your analysis is correct, which I haven't checked, all this means is
ONLY valid in the rest frame of the solar system. This famous law of physics has a preferred FoR in which it applies and is false in all
other frames. This is a blatant violation of the first postulate of
special relativity.
that Kepler's law is not covariant, which in turn tells us that it
cannot be a correct law of nature.
On 04-Sept-23 6:24 am, patdolan wrote:
We therefore conclude that Kepler's 3rd law of planetary motion is
ONLY valid in the rest frame of the solar system. This famous law of physics has a preferred FoR in which it applies and is false in all
other frames. This is a blatant violation of the first postulate of
special relativity.
If your analysis is correct, which I haven't checked, all this means is
that Kepler's law is not covariant, which in turn tells us that it
cannot be a correct law of nature. This is a problem for Kepler's law,
not for special relativity.
Sylvia.
since length and time have the same natural dimension.
Yes, it is that simple,
Jan
Consider a distant observer traveling at .867 c ( 𝛾=2 ) relative to the solar system...
In his inertial frame of reference the earth's orbital velocity is only half the velocity
necessary to keep the earth in stable orbit...
Invariant spacetime curvature...
Will the earth spiral into the sun?
Ridiculous! See Einstein's First vs. Kepler's Third, ibid.
Kepler's coordinates were earth-centered.
On 04-Sept-23 6:24 am, patdolan wrote:Sylvia, this answer of yours is exactly the same answer, given by the top relativity guru on physics.stackexchange. The guru's answer garnered the most points as the best answer to the Einstein Kepler Paradox. Below I print my response to the guru's
We therefore conclude that Kepler's 3rd law of planetary motion isIf your analysis is correct, which I haven't checked, all this means is
ONLY valid in the rest frame of the solar system. This famous law of physics has a preferred FoR in which it applies and is false in all
other frames. This is a blatant violation of the first postulate of special relativity.
that Kepler's law is not covariant, which in turn tells us that it
cannot be a correct law of nature. This is a problem for Kepler's law,
not for special relativity.
Sylvia.
On Sunday, September 3, 2023 at 11:08:43 PM UTC-7, patdolan wrote:invariant, which may be surprising to you if you aren't taking the time component of the trajectory into account. Misner, et al, illustrate this with a baseball and a bullet.
Consider a distant observer traveling at .867 c ( 𝛾=2 ) relative to the solar system...Not true, the earth follows a helical geodesic trajectory through spacetime, and this helical geodesic is not intrinsically altered by being described in terms of a different system of coordinates. Also, the *extrinsic* curvature of the trajectory is
In his inertial frame of reference the earth's orbital velocity is only half the velocity
necessary to keep the earth in stable orbit...
the trajectory is invariant under Lorentz transformation (which is essentially what you are applying to the Schwarzschild coordinates around the sun by switching to the background inertial coordinates in which the distant high speed object is at rest,Invariant spacetime curvature...
No, the components of the spacetime (intrinsic) curvature tensor are not invariant, they are covariant along with the metric tensor, and of course all invariant intervals are preserved under any coordinate transformation. The *extrinsic* curvature of
a putt going into the hole in terms of one coordinate system, it will also go into the hole in terms of the other coordinate system. Yes, the ball has different coordinates at the end, but the cup also has different coordinates, so the ball still goesWill the earth spiral into the sun?No, describing phenomena in terms of a different system of coordinates doesn't change the intrinsic phenomena, and doesn't alter any of the invariant intervals. For example, if you draw two chalk grids on a putting green, and describe the trajectory of
The idea that changing the coordinate system used to describe the phenomena can somehow change the phenomena is wrong... and, no, this does not imply that local Lorentz invariance has no physical dynamical effects. The dynamical equations of physicsare locally Lorentz invariant, which is the physical content of special relativity.
and I assume that by "Kepler's Third" you mean Kepler's proposition that the squares of the angular orbital periods of the planets are directly proportional to the cubes of the semi-major axes of their orbits. There's no conflict between either of theseRidiculous! See Einstein's First vs. Kepler's Third, ibid.
I assume by "Einstein's First" you mean the principle of relativity, i.e., that the laws by which the states of physical systems undergo change take the same simple homogeneous and isotropic form in terms of any standard system of inertial coordinates,
You may be getting confused by thinking of Newton's elaboration and refinement of Kepler's propositions based on his concepts of instantaneous gravity, mass, and force, combined with the assumption that inertial coordinate systems are related byGalilean transformations, and the lack of accounting for the inertia of energy. There is indeed a conflict between those Newtonian concepts applied to relativistic velocities versus the relativistic account, but you assured us that you were not talking
The fact that Galilean invariance differs from Lorentz invariance is not a new realization, so pointing it out is not particularly illuminating or meaningful. Yes, if special relativity were wrong, then special relativity would be wrong, but thisstatement is devoid of significance, i.e., it does not constitute a reason for thinking special relativity is wrong, which was your objective.
of coordinates in which the sun is (more or less) at rest. That was the whole point of the Copernican revolution, i.e., it would have been impossible to discern the simple laws of motion as long as people worked in terms of earth-centered coordinates, inKepler's coordinates were earth-centered.How could the trajectory of the earth be an ellipse (Kepler's first law) in terms of earth-centered coordinates? What is wrong with you? Did you get kicked in the head by a mule or something? Obviously Kepler's three regularities are expressed in terms
Consider a distant observer traveling at .867 c relative to the solar system along the line that is co-linear with the sun's axis of rotation. In this situation the Lorentz transforms inform us that gamma = 2. So in accordance with
SR, and after taking the relativistic doppler into account, from the observer's
point of view it takes the earth twice as long--730.5 days--to complete one revolution around the sun.
The observer measures the major and minor axes of the earth's orbit around the
sun to be identical to its major and minor axes in the solar system's rest frame,
where the orbital period is only 365.25 days.
We therefore conclude that Kepler's 3rd law of planetary motion is ONLY valid in
the rest frame of the solar system. This famous law of physics has a preferred FoR
in which it applies and is false in all other frames. This is a blatant violation
of the first postulate of special relativity.
Note: Newtonian gravity is not assumed in this paradox. Invariant
spacetime curvature is assumed to be the cause of the earth's orbit
around the sun.
My entirely reasonable answer above was considered just to hot for physics.stackexchange; and so, was summarily taken down from that platform.
If your analysis is correct, which I haven't checked, all this means is that Kepler's law is not covariant...
[Sylvia's] answer tacitly accepts that Kepler's third law of planetary motion
falsifies the principle of relativity...
In the face of this, [Sylvia] reaches the conclusion that [Newton's laws] can't be laws anymore. Instead, they are relegated to the status of non-relativistic
approximations....
of other, as yet undiscovered relativistic laws...
which presumably will not falsify the principle of relativity.
My entirely reasonable answer...
Sylvia wrote:valid on both systems of coordinates for the situation described, so the whole premise of his question is false.
If your analysis is correct, which I haven't checked, all this means is that Kepler's law is not covariant...
He hasn't done any analysis, but it's been explained to him that Kepler's actual third law ("the squares of the angular orbital periods of the planets are directly proportional to the cubes of the semi-major axes of their orbits") is actually just as
It's also been explained to him that he is confusing Kepler's law with the Newtonian propositions such as m = r^3 w^2 that show how Kelper's laws are (approximately) true as a result of the Newtonian laws of mechanics combined with instantaneousgravitational force, which are Galilean invariant, not Lorentz invariant. Now, the issue isn't really covariance, per se, because nearly any physical laws (including Newton's) can be expressed in covariant form, it is simply that Newton's laws (which the
So, the OP's grand announcement is that, at relativistic speeds, Lorentz invariance is significantly inconsistent with Galilean invariance. At this point I would insert a "Duh", except that I don't think Duh adequately expresses the towering idiocy ofthe belief that this is somehow a revelation, let alone that it represents an argument against general relativity.
On Monday, September 4, 2023 at 9:32:56 AM UTC-7, patdolan wrote:not falsify the principle of relativity (which is satisfied by both Newton's laws of general relativity), it falsifies Galilean invariance.
[Sylvia's] answer tacitly accepts that Kepler's third law of planetary motion
falsifies the principle of relativity...
No, the point is that (1) Kepler's law actually IS (approximately) satisfied in both systems, and (2) you are conflating Kepler's law with Newton's laws, which are NOT even approximately valid when relativistic speeds are involved, and (3) this does
, and these are not undiscovered at all. They are quite well known for over a century.In the face of this, [Sylvia] reaches the conclusion that [Newton's laws] can't be laws anymore. Instead, they are relegated to the status of non-relativistic
approximations....
Yes! That is exactly right. Bravo.
of other, as yet undiscovered relativistic laws...
Nope, you went off the rails again. The laws that accurately cover the scenario you described are called general relativity, which of course is locally Lorentz invariant (entailing all the aspects of special relativity that you were hoping to discredit)
you had hoped to discredit.which presumably will not falsify the principle of relativity.Well, general relativity implies that Lorentz invariance is valid locally, and also in the large scale asymptotically falt background, but yes, for purposes of thwarting your hopes and dreams, general relativity is pefectly consistent with everything
Really Legion, you MUST learn how to communicate with less verbiage. Shakespeare said that brevity is the soul of wit. It is also the soul of science. Equations too, should be short and employed very sparingly. This is because mathematics is like anyMy entirely reasonable answer...
LOL.
[Disgracefully disregards the patient and thorough yet optimally succinct answers to his questions, and replies with:]
me;... (more equations...
Equations should be employed very sparingly....
too long, didn't read
On Monday, September 4, 2023 at 10:36:02 AM UTC-7, patdolan wrote:you disregard as being too lengthy for a mentally-impaired individual such as yourself to read. With those two limitations, it's difficult to see how you can ever make any progress.
[Disgracefully disregards the patient and thorough yet optimally succinct answers to his questions, and replies with:]
me;... (more equations...
Equations should be employed very sparingly....
too long, didn't read
We've established that any text less than 250 words you disregard as being not sufficiently explanatory for a novice such as yourself (using advanced words and concepts without including the elementary background), and any text greater than 250 words
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