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General Relativity Explained

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On 1/24/2020 at 3:33 PM, swansont said:

Starlight on a particular path — that which ended up at the telescope — followed that path. Light heading to Jupiter would not have traveled a shorter path by passing near the sun.

But the question here is : shorter than what? There's only one path to get from point A to point B that follows the laws of nature.

It sounds like you are trying to apply the principle of least time (Fermat's principle). That the path taken by light will be the one that has the smallest travel time, but that's not physically the shortest path in situations like materials with different indices of refraction. 

 

On 1/24/2020 at 3:42 PM, Mordred said:

I would suggest you look into the principle of least action and how it applies to the geodesics equation. I would also suggest you look at the Principle of equivalence.

mi=mg  

 

If two photons are traveling from A to B, one photon's path is uninterrupted whilst the other follows a curved path around a massive object the straight line photon will arrive at B first as it travels the shorter distance. The curved line photon will have traveled farther but will experience time dilation due the the gravitational effects of the massive object so will both photons have the same proper time even though one arrives after the other?

Something doesn't quite seem right with that???

 

For anyone who says 'do the math(s)' I am trying to spend 20 mins per day learning, I have finished multiplying pairs of brackets and am now on factorising. Gives you some idea where I'm at.

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9 minutes ago, between3and26characterslon said:

 

 

If two photons are traveling from A to B, one photon's path is uninterrupted whilst the other follows a curved path around a massive object the straight line photon will arrive at B first as it travels the shorter distance. The curved line photon will have traveled farther but will experience time dilation due the the gravitational effects of the massive object so will both photons have the same proper time even though one arrives after the other?

That's a separate question from the one I was answering, but the path around the massive object will also be length contracted. Locally, an observer anywhere on that path will measure the light to be going at c.

 

I am not addressing the problem of having two paths that fit your criteria, which seems unphysical.

 

 

 

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7 minutes ago, swansont said:

That's a separate question from the one I was answering, but the path around the massive object will also be length contracted. Locally, an observer anywhere on that path will measure the light to be going at c.

 

 

 

So what I was thinking about is the question that came up earlier: if a photon traveling from one medium to another is refracted such that it follows the path of shortest duration between A and B (A is in one medium and B in the other) then if it was going through many layers of progressively increasing then decreasing refractive index would the path it follows be analogous to a photon traveling past a massive object?

I think that's the question you answered in the last two lines of your comment, I'm just not sure I understood your answer. That led me on to another question which is the one I asked.

In that question, yes "Locally, an observer anywhere on that path will measure the light to be going at c", I understand that. The question is, from B's POV one photon will arrive after the other because it has traveled farther, but from the photon's POV do they both consider they have traveled the same distance in the same time but one still arrives after the other? Being that they were both emitted together.

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38 minutes ago, between3and26characterslon said:

So what I was thinking about is the question that came up earlier: if a photon traveling from one medium to another is refracted such that it follows the path of shortest duration between A and B (A is in one medium and B in the other) then if it was going through many layers of progressively increasing then decreasing refractive index would the path it follows be analogous to a photon traveling past a massive object?

I think that's the question you answered in the last two lines of your comment, I'm just not sure I understood your answer. That led me on to another question which is the one I asked.

My previous answer was to the claim that it is always advantageous to travel near a massive object, which is patently false. As I had said, a photon going to a distant planet in the opposite direction doesn't gain an advantage by detouring around the sun.

 

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In that question, yes "Locally, an observer anywhere on that path will measure the light to be going at c", I understand that. The question is, from B's POV one photon will arrive after the other because it has traveled farther, but from the photon's POV do they both consider they have traveled the same distance in the same time but one still arrives after the other? Being that they were both emitted together.

The only way for that scenario to happen with simultaneously-emitted photons is if one goes through some medium to slow it down, or you bounce it off a mirror, but the photons will be taking different paths. So then you aren't comparing apples to apples. 

You could do it with and without the massive object at two different times, but they still won't travel the same path.

If the photons don't travel the same path, why is there an expectation that the travel time would be the same?

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33 minutes ago, swansont said:

My previous answer was to the claim that it is always advantageous to travel near a massive object, which is patently false. As I had said, a photon going to a distant planet in the opposite direction doesn't gain an advantage by detouring around the sun.

 

The only way for that scenario to happen with simultaneously-emitted photons is if one goes through some medium to slow it down, or you bounce it off a mirror, but the photons will be taking different paths. So then you aren't comparing apples to apples. 

You could do it with and without the massive object at two different times, but they still won't travel the same path.

If the photons don't travel the same path, why is there an expectation that the travel time would be the same?

There is no expectation, there is a question. Your reply is one of pedantry and evasiveness! No offense, it may suggest I'm asking an invalid question! I'll try this.

If you had a glass sphere where the refractive index was greatest at the center and got progressively less as you moved out from the center following a 1/r^2 rule would the light follow a path similar to if it were passing a massive object through its gravitational field?

Is it a meaningless comparison, is it a reasonable visualisation like a heavy ball on a rubber sheet or can you consider the progressively changing refractive index in the same way you consider the progressively changing time dilation in a gravitational field?

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42 minutes ago, between3and26characterslon said:

There is no expectation, there is a question. Your reply is one of pedantry and evasiveness! No offense, it may suggest I'm asking an invalid question! I'll try this.

Part of that is that you shouldn't be asking me independent questions. That's thread hijacking. That's why I was tying my answer to the discussion with scuddyx. My "evasiveness" is an attempt to be within the spirit of the rules.

 

42 minutes ago, between3and26characterslon said:

If you had a glass sphere where the refractive index was greatest at the center and got progressively less as you moved out from the center following a 1/r^2 rule would the light follow a path similar to if it were passing a massive object through its gravitational field?

I think you could set that up in a way that was like passing near a massive object. (It would have to be very massive, though, and/or the index very close to 1) What you describe is called a GRIN (gradient index) lens, where the light continually refracts, rather than just doing it at the surface as in a traditional lens.

 

42 minutes ago, between3and26characterslon said:

Is it a meaningless comparison, is it a reasonable visualisation like a heavy ball on a rubber sheet or can you consider the progressively changing refractive index in the same way you consider the progressively changing time dilation in a gravitational field?

Gravitational lensing is a real effect, so I'd say it's not meaningless. But it depends on what you're trying to demonstrate. Further discussion should be in a new thread.

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On 1/18/2020 at 7:56 PM, swansont said:

No, probably not. You would be using an effect of GR to explain GR. Not to mention implying a causal connection that doesn’t exist.

What one uses as an effect and what as an explanation depends on the choices of axioms. 

It is quite usual to define theories postulating a Lagrangian.  Proper time defines a nice Lagrangian for the movement of test particles on a fixed GR background.  That means, if you define the maximum principle that \(\tau= \int \sqrt{g_{\mu\nu}(x,t)\dot{\gamma}^\mu\dot{\gamma}^\nu}dt\) has to be maximal, you can derive the geodetic equation for the test particle.  

The usual visualizations of curvature using curved surfaces in a higher dimensional flat space has, indeed, the disadvantage of suggesting the existence of such a higher dimensional space. 

Test particles seek the path where time runs the fastest way.  So, in the twin experiment, the twin which simply follows his own geodesic trajectory - the one who remains at home - is the older one.  Similarly, if you travel from point A to B which is opposite of the Sun, going the direct way would leave you most of the time in a region where time runs slower.  So, it is better to stay away from these inner regions.  But going too far away too fast is not a good idea too, because fast motion slows time too.  So, it appears optimal to move around the Sun following a Keplerian orbit (almost). This approach is valid. 

Ther other question is how to visualize curvature without external dimensions.  There are nice ways to do this. One can measure distances with usual metallic rulers, which expand with temperature.  Then, if you have homogeneous temperature in flat Eucliean space, you will not see anything strange, Euclidean geometry works fine, no curvature.  But if the temperature is inhomogeneous, the metric defined by the measurements with temperature-dependent rulers will give a metric with non-trivial curvature.  Say, if the center of a circle is hotter, the radius measurement will be distorted distorted because the  ruler expands. Measuring u and r will be influenced by this effect differently, and you will measure \(u>2\pi r\).  

Another nice analogy are crystal deformations. If the lattice is regular but deformed by external pressure, you can describe this by a tensor field with described the deformation.  It is a symmetric tensor, in fact simply the difference between the original Euclidean metric and the deformed metric. As long as the original regular lattice remains valid, the curvature of this metric is zero.  But there may be defects in the lattice. For a lattice with such defects, there is already no way to deform it into a stress-free state.  And this can be computed by computing the curvature tensor of the deformed metric. 

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5 hours ago, Schmelzer said:

What one uses as an effect and what as an explanation depends on the choices of axioms. 

It is quite usual to define theories postulating a Lagrangian.  Proper time defines a nice Lagrangian for the movement of test particles on a fixed GR background.  That means, if you define the maximum principle that τ=gμν(x,t)γ˙μγ˙νdt has to be maximal, you can derive the geodetic equation for the test particle.  

1. Did the OP do that?

2. Where do guv and gamma-dot come from?

 

5 hours ago, Schmelzer said:

The usual visualizations of curvature using curved surfaces in a higher dimensional flat space has, indeed, the disadvantage of suggesting the existence of such a higher dimensional space. 

Test particles seek the path where time runs the fastest way. 

Explain why time runs at a different rate - without invoking relativity.

 

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3 hours ago, swansont said:

1. Did the OP do that?

2. Where do guv and gamma-dot come from?

Explain why time runs at a different rate - without invoking relativity.

(1) no, but he suggested something very close, namely "Would a better explanation for the novice be to say things fall because they are seeking out the place where time runs the slowest?".

That's the wrong sign, but the idea is a quite reasonable one, so I tell him that this can, indeed, be done, the equations for the test particle can be derived from such a maximum principle. 

(2) \(g_{\mu\nu}\) is the gravitational field, and \(\dot{\gamma}\) is the velocity of the clock.  

(3) Incorrect question.  Explanation always requires a base, some more fundamental things which do not require further explanation. Some more fundamental theory which explains GR would be speculation, thus, forbidden here. (BTW, relativity also does not explain why time runs at a different rate.)

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48 minutes ago, Schmelzer said:

(1) no, but he suggested something very close, namely "Would a better explanation for the novice be to say things fall because they are seeking out the place where time runs the slowest?".

That's the wrong sign, but the idea is a quite reasonable one, so I tell him that this can, indeed, be done, the equations for the test particle can be derived from such a maximum principle. 

(2) gμν is the gravitational field, and γ˙ is the velocity of the clock.  

The gravitational field? From...GR?

 

48 minutes ago, Schmelzer said:

(3) Incorrect question.  Explanation always requires a base, some more fundamental things which do not require further explanation. Some more fundamental theory which explains GR would be speculation, thus, forbidden here.

More of this alleged "forbidden here" nonsense? You're smart. You can read the rules and understand them, so you can see that this is BS. Being willfully ignorant (or appearing to be) of the rules and whining about this is probably not garnering the sympathy you might think it is. What's "forbidden" is bringing up your own pet theory to answer a mainstream issue. 

For your position to be true, it would have to mean there is no mainstream physics upon which you could base an explanation, in which case, time would have to be a foreign concept, and clearly it is not. Time is included in Newtonian physics.

 

48 minutes ago, Schmelzer said:

(BTW, relativity also does not explain why time runs at a different rate.)

Really? Special relativity isn't based on c being invariant, and relative time being a consequence of that? 

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22 minutes ago, swansont said:

The gravitational field? From...GR?

Or from other metric theories of gravity.  

Quote

More of this alleged "forbidden here" nonsense? You're smart. You can read the rules and understand them, so you can see that this is BS.

I have had enough negative experience showing me that relying on rules in forums gives nothing. Last but not least, rules are necessarily vague, and have to be interpreted, and if an admin interprets them differently than I do, I'm the loser. But, ok, in future I will write, instead of "forbidden here" something like "I'm afraid it may be forbidden here".  

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For your position to be true, it would have to mean there is no mainstream physics upon which you could base an explanation, in which case, time would have to be a foreign concept, and clearly it is not. Time is included in Newtonian physics.

In Newtonian physics time runs at a constant rate, in quantum theory there is not even a time measurement operator, and the time parameter is absolute, so based on Newtonian physics I cannot explain it.  Relativity you have excluded explicitly.  I don't know any more fundamental theory than GR which is not speculation, and even if you would accept string theory or LQG as such theories, I would certainly not use them, given my own opinion about their scientific value. The "speculation" which I would agree to use would be based on my own pet theory.  So, your request remains problematic.  

But, ok, one thing I can try.  I take the SM of particle physics.  I ignore relativity, as required.  The SM consists of field equations, they make sense without relativity too. Last but not least, the Maxwell equations have made sense long before 1905 too. Then, I know that if you have a wave equation, you can construct for each solution also a Doppler-shifted solution.  This construction uses simply the Lorentz transformation with the speed of that particular wave equation.  It works for sound waves too, if you use the speed of sound in the Lorentz transformation, it gives you the Doppler-shifted sound waves. So, I can use Lorentz transformations without invoking relativity simply because I have some wave equations. Now, take a solution of the SM which describes a material clock at rest which measures 1 second.  All the SM equations are wave equations with the same c, so this trick can be applied to construct a Doppler-shifted solution.  This gives a solution for a material clock of the same construction moving with some velocity and measuring the same 1 second. Looking now what is measured in terms of absolute time, one can easily see that it is a different amount of absolute time which is measured by the two clocks as 1 second. 

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Really? Special relativity isn't based on c being invariant, and relative time being a consequence of that? 

Really.  In the Lorentz ether interpretation of special relativity time is absolute, only clock time is relative.  It is the Minkowski spacetime interpretation where time itself becomes relative. The thing named proper time (badly translated "Eigenzeit") is relative in both interpretations, but this is only clock time, apparent time, not absolute time. "Time is what the clock shows" is already interpretation, not physics. 

 

 

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21 minutes ago, Schmelzer said:

I have had enough negative experience showing me that relying on rules in forums gives nothing. Last but not least, rules are necessarily vague, and have to be interpreted, and if an admin interprets them differently than I do, I'm the loser. But, ok, in future I will write, instead of "forbidden here" something like "I'm afraid it may be forbidden here".  

I seriously suggest you study (your) split thread in

 

 

22 minutes ago, Schmelzer said:

Really.  In the Lorentz ether interpretation of special relativity time is absolute, only clock time is relative.  It is the Minkowski spacetime interpretation where time itself becomes relative. The thing named proper time (badly translated "Eigenzeit") is relative in both interpretations, but this is only clock time, apparent time, not absolute time. "Time is what the clock shows" is already interpretation, not physics. 

Moderators can we please have a split thread to discuss the nature of time?

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43 minutes ago, Schmelzer said:

Or from other metric theories of gravity.  

I have had enough negative experience showing me that relying on rules in forums gives nothing. Last but not least, rules are necessarily vague, and have to be interpreted, and if an admin interprets them differently than I do, I'm the loser. But, ok, in future I will write, instead of "forbidden here" something like "I'm afraid it may be forbidden here".  

I'm afraid you miss the point, but studiot has posted a link to where this can be discussed.

43 minutes ago, Schmelzer said:

In Newtonian physics time runs at a constant rate, in quantum theory there is not even a time measurement operator, and the time parameter is absolute, so based on Newtonian physics I cannot explain it. 

Was SR developed with no basis in Newtonian physics? I don't think so. You're being absurd.

 

43 minutes ago, Schmelzer said:

Relativity you have excluded explicitly.

I have only excluded a self-reference to it, because that's a circular argument — the two concepts need to be established independently. Unless there is a (mainstream) explanation of time dilation that does not use relativity, you can't use time dilation to explain relativity, because it's part of relativity.

 

43 minutes ago, Schmelzer said:

  I don't know any more fundamental theory than GR which is not speculation, and even if you would accept string theory or LQG as such theories, I would certainly not use them, given my own opinion about their scientific value. The "speculation" which I would agree to use would be based on my own pet theory.  So, your request remains problematic.

Einstein was able to develop SR and then GR. You aren't Einstein and there's no shame in that, but that's the standard.

 

43 minutes ago, Schmelzer said:

But, ok, one thing I can try.  I take the SM of particle physics.  I ignore relativity, as required.  The SM consists of field equations, they make sense without relativity too. Last but not least, the Maxwell equations have made sense long before 1905 too. Then, I know that if you have a wave equation, you can construct for each solution also a Doppler-shifted solution.  This construction uses simply the Lorentz transformation with the speed of that particular wave equation.  It works for sound waves too, if you use the speed of sound in the Lorentz transformation, it gives you the Doppler-shifted sound waves. So, I can use Lorentz transformations without invoking relativity simply because I have some wave equations. Now, take a solution of the SM which describes a material clock at rest which measures 1 second.  All the SM equations are wave equations with the same c, so this trick can be applied to construct a Doppler-shifted solution.  This gives a solution for a material clock of the same construction moving with some velocity and measuring the same 1 second. Looking now what is measured in terms of absolute time, one can easily see that it is a different amount of absolute time which is measured by the two clocks as 1 second. 

If two clocks make different measurements, how is that absolute time?

And how does your description differ from SR? Where does the non-ad hoc Lorentz transformation come from, if not SR?

 

43 minutes ago, Schmelzer said:

Really.  In the Lorentz ether interpretation of special relativity time is absolute, only clock time is relative.  It is the Minkowski spacetime interpretation where time itself becomes relative. The thing named proper time (badly translated "Eigenzeit") is relative in both interpretations, but this is only clock time, apparent time, not absolute time. "Time is what the clock shows" is already interpretation, not physics. 

There is no aether in special relativity, so there can be no aether interpretation that one can count as being part of special relativity.

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57 minutes ago, Schmelzer said:

The SM consists of field equations, they make sense without relativity too.

The Standard Model is a QFT on a Minkowski spacetime background. I don’t see how it could be constructed without relativity.

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17 hours ago, Schmelzer said:

But, ok, in future I will write, instead of "forbidden here" something like "I'm afraid it may be forbidden here".  

!

Moderator Note

Maybe not say anything about it.

 

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10 hours ago, swansont said:

Was SR developed with no basis in Newtonian physics? I don't think so.

????? Of course, the development of new theories is based on what has been reached by old theories. But they necessarily contain essentially new elements.  One cannot derive them based on old theories, they contradict them in some essential points. 

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Unless there is a (mainstream) explanation of time dilation that does not use relativity, you can't use time dilation to explain relativity, because it's part of relativity.

I disagree.  If you present a new theory, you have to start with some axioms.  These axioms cannot be derived from old theories, at least some of them are in conflict with the old theories, contradict them.  What you use as axioms, is a free choice.  But the axioms of a theory may be, at best, plausible from the point of view of the old theories.  It is quite common in classical physics to define new theories by postulating a Lagrangian.  For a test particle on a fixed background of a metric theory of gravity, proper time can be used as the Lagrangian. Once one has defined that theory in this way, everything else can be derived from this.  So, the , and geodetic equations will be derived as Euler-Lagrange equations.  And a derivation is certainly also an explanation. 

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Einstein was able to develop SR and then GR. You aren't Einstein and there's no shame in that, but that's the standard.

What's the point of this remark?  I was also able to develop new theories and to publish them.  They have big enough advantages compared with existing competitors, their only problem is that they are completely ignored by the mainstream.  Ignorance is not an argument, so I have no reason at all for shame even in comparison with Einstein. 

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If two clocks make different measurements, how is that absolute time?

It is not, because, following Newton's definition, time measured with clocks is not absolute time, but apparent time. He writes in Principia Mathematica (1687)

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And thence arise certain prejudices, for the removing of which, it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common.

2. Absolute, true, and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration: [Absolute time is to be contrasted with] relative, apparent, and common time, [which] is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.

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And how does your description differ from SR? Where does the non-ad hoc Lorentz transformation come from, if not SR?

Nobody cares about where things come from.  Kepler's laws came from astrological considerations, this does not diminish their scientific value.  Mathematical methods can be used freely, without any copyright.  So, if you want to compute Doppler-shifted sound waves, you are free to use the Lorentz transformations with the speed of sound instead of c. 

Moreover, if we look at the history, we find that the Lorentz transformations go back to Lorentz 1895, thus, was developed before Einstein's 1905 paper, and therefore independently of SR. 

My description differs from SR in its Minkowski time interpretation in quite obvious ways, it does not presuppose the existence of any spacetime, but is compatible with classical absolute space and absolute time, following Newton's definition of them.  The Lorentz transformation simply transforms one particular solution of some wave equations into other, Doppler-shifted ones.  This is a useful operation without any theory of relativity behind it. 

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There is no aether in special relativity, so there can be no aether interpretation that one can count as being part of special relativity.

There is no ether in the Minkowski spacetime interpretation of special relativity. The key source for the Minkowski interpretation is "space and time", a talk held 21. Sept. 1908 and published 1909.  The original interpretation goes back to Lorentz and Poincare and is named today "Lorentz ether".    

 

 

11 hours ago, Markus Hanke said:

The Standard Model is a QFT on a Minkowski spacetime background. I don’t see how it could be constructed without relativity.

That it is possible is an obvious consequence of the history:  One of the key parts of the SM, the EM field, has been constructed by Maxwell completely without relativity, based on an ether theory.  Nothing would have changed if, for whatever reason, Minkowski would not have invented his spacetime interpretation, and the Lorentz ether would have remained the standard interpretation of SR.  

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4 hours ago, Schmelzer said:

My description differs from SR in its Minkowski time interpretation in quite obvious ways, it does not presuppose the existence of any spacetime, but is compatible with classical absolute space and absolute time, following Newton's definition of them. 

!

Moderator Note

Stop bringing your pet theory into every discussion. You already have three threads open for this purpose. (And one to complain about the fact.) Please follow the rules. This is not your blog.

 

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On 2/15/2020 at 5:07 PM, Strange said:
!

Moderator Note

Stop bringing your pet theory into every discussion. You already have three threads open for this purpose. (And one to complain about the fact.) Please follow the rules. This is not your blog.

 

The Lorentz-Poincare interpretation of special relativity is not my pet theory, but was the only interpretation of SR from 1905-1909, until Minkowski proposed his spacetime interpretation in 1909 

Before being banned forever for mentioning this triviality again, I would suggest the adminstration of the forum how to handle the original interpretation of SR, as proposed by Lorentz and Poincare, which is usually named "Lorentz ether", and those who follow the recommendations given by Bell in

Bell, J.S. (1976). How to teach special relativity. Progress in Scientific Culture 1(2), reprinted in Speakable and Unspeakable in Quantum Mechanics

where he suggests to teach also this traditional approach to relativity because it gives the people better intuitions.  

Some forums decide to ban discussions of the Lorentz ether as anathema. In this forum, it was suggested that it is possible to discuss it, but in reality I was banned for doing it. I think banning people for doing things not explicitly forbidden is much worse than explicitly forbidding whatever theories of physics the admins don't like.  That's fine with me, I have, of course, my own opinion about the scientific value of such rules, but I accept the right of the administration of the forum to forbid whatever they don't like.  

But not to forbid it in the rules, but then banning people in reality, naming the Lorentz-Poincare interpretation a personal pet theory, ...   

Just to clarify how I see the actual situation:  There are threads for discussing my "pet theories", namely my generalization of the Lorentz ether to gravity and my ether model of the SM. And there is the Lorentz ether, as the classical interpretation of SR, which is not my pet theory.  Therefore I think that I'm allowed to discuss it in every thread about relativity, if it gives some other perspective which may be interesting for some readers.  I do this following the recommendations made Bell, thus, I follow here an established mainstream scientist too, and I do not see any violation of the actually existing rules of the forum.   

So, please clarify the rules of this forum, regarding the discussion of the original interpretation of SR.  Is it anathema or legitimate part of established science?  

Oh, I see the date is Friday. the 13th.  So, the result of this posting is predictable - a ban forever.  So, good buy.  

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3 hours ago, Schmelzer said:

There are threads for discussing my "pet theories", namely my generalization of the Lorentz ether to gravity and my ether model of the SM.

!

Moderator Note

There are. You should restrict your discussions to those threads and not pollute the rest of the forum. Thank you.

 
3 hours ago, Schmelzer said:

but in reality I was banned for doing it.

!

Moderator Note

You have not been banned. You are still here. So stop playing the martyr. Grow up.

 

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