Dear All ~

(1) A coordinate system is merely a reference system. It contains no physics. It allows us to record the results of measurements such as times, distances and speeds, to describe the interrelationships of those measurements and make predictions.

(2) A recorded measurement of a time or a distance or a speed is dependent on the experimental method employed in the measurement process. I take that to be self-evident.

(3) A physically valid statement about an observed and measured phenomenon is a statement that is independent of the choice of coordinate system. That is, it must be expressed in terms of invariants.

(3) The “proper time” calculated from the observed trajectory of any moving point in a material physical system is an invariant. “Coordinate times” are not. Nor are coordinate-based “distances” and “speeds”. All we need to know about "time dilation" is contained in an appreciation of the meaning of "proper time" and the method of calculating it.

(4) Special Relativity purports to provide a formulation of physical laws for phenomena in which gravitational effects are absent. Its propositions can be expressed in a coordinate-independent way as follows:

(a) According to SR physical phenomena are contained in a four-dimensional geometrical continuum, “Minkowskian spacetime”.

(b) Minkowskian spacetime is flat; that is, the Riemann tensor is zero everywhere. That is a coordinate-independent statement.

(c) The trajectory of any material point on which no forces act is a geodesic.

(d) The trajectory of a “light ray” is a null geodesic.

(5) Proposition (c) is essentially Newton’s first law expressed in a coordinate-independent way and it can reasonably be argued that (d) is a consequence of Maxwell’s electrodynamics.

(6) Because the geometry of Minkowski’s spacetime is “flat”, it is expedient to employ a particular kind of coordinate system when analysing a physical system mathematically. Such a coordinate system is an “ineritial frame”. Inertial frames are the reference systems appropriate to observers on which no forces act (by Newton's first law, unaccelerated observers). They are related to each other by Lorentz transformations. As Ed Gerck has explained, there is nothing sacrosanct about “inertial frames”. They offer the simplest way of formulating physical laws and describing physical phenomena, that’s all!

(7) Proposion (5d) is equivalent to: "Relative to any inertial frame light travels in a straight line with constant velocity c".

(8) It is often of interest to describe things from the point of view of a non-inertial observer; that is, an observer subject to forces and therefore accelerating. An appropriate reference system for such an observer is a curvilinear coordinate system. But that does not mean that spacetime for that observer is not Minkowskian! Changing the coordinate system does not change the geometry of spacetime! For example, there is an extensive literature on “rotating discs” in SR. The coordinates introduced in those discussions may feature three-dimensional spaces that are not flat (giving rise, for example, to the apparent “paradox” that the circumference of a rotationg disc is “Lorentz contracted” but its “radius” is not! But the 4-dimensional space in these situations is flat − changeing coordinates cannot change the geometry of the problem!

In summary: “inertial frames” are employed in Special Relativity for convenience − for simplification of the mathematics. Special Relativity, properly understood, is not in conflict with the concept of “acceleration”.

In Special Relativity space-time has Minkowsky metric.

One could rewrite the metric in any coordinate system.

I.e. non-inertial frames are just curvilinear coordinate systems.

The Lorentz transformation are selected because L.transformation conserve the standard form of Minkowsky metric.

P.S. To relate non-inertial frame with curvilinear coordinate system one have to consider the measurement process for time and coordinates. I.e. in some cases one have to consider elasticity properties of reference body.

Take a look at sagnac effect and the Ehrenfest paradox

I agree, the phenomena have to be present, but it is not easy to have an accurate and reliable measurement.

relativistic electro-dynamics should apply to arbitrary motion. If SR is a reliable model of relativistic-electrodynamics it certainly should.

I agree, since basically the Classical Physics is not solely based on the Galilean Transformations, conservation laws and symmetries are the foundations.

This "vice" of use transformations is inherited from Minkowski.

Hello Andre and all: In both cases, geometry in spacetime is non-Euclidean for rotating observers. There are no paradoxes.

That is another reason to abandon Lorentz transformations as the basis of special relativity. The basis of special relativity was changed to spacetime, more than 100 years ago, and Einstein was part of this change. This is the realization that we live in at least 4D, that space can transform into time and vice-versa.

This discovery was not an invention, it was there billions of years ago, as we can measure with today's time machines, also called telescopes. On Earth's academic culture this dates back to more than 100 years, undergraduate college education needs to change, popular accounts need to change.

There is no Ehrenfest paradox, Sagnac problem, or faster than light paths measured on star trajectories.

Hello Mikhail G. Ivanov and all: Agreed, but in your PS please note that this need disappears when each part is considered in its own local non-inertial frame.

Hello Stefano Quattrini and all: Thank you. I note that the term "relativistic electro-dynamics" should be avoided as it points to the misconception that there might be an electro-dynamics that is not relativistic. This does not exist in nature, although it exists in some books.

I do not understand your last sentence -- This "vice" of use transformations is inherited from Minkowski. Please explain.

Hello Ed,

We do not need to abandon Lorentz transformations. We just need to consider local Lorentz transformations such that boosts and rotations depends on space and time, instead of global Lorentz transformations for which boosts and rotations are just constants.

Hello Andre Gontijo Campos and all: The Lorentz transformation, though, is a second fiddle in the spacetime treatment, not the basis.

Quite a different position than initially proposed by Einstein a few years earlier, but the change to spacetime as the basis was accepted by Einstein, and so used in his general relativity to model gravity, as creating a curvature of the same spacetime.

Note also what I wrote in the preamble, motivating this discussion:

"The expectation has been realized by placing a spacetime description, e.g. Minkowsky, not the Lorentz transformation, as the basis of special relativity."

and

"The discussion suggests that the Lorentz transformation alone should have a less central role in higher education of special relativity, ..."

And, as Mikhail G. Ivanov said in the first answer above, "The Lorentz transformation are selected because L.transformation conserve the standard form of Minkowsky metric."

So, we do need to abandon the Lorentz transformations as the basis of special relativity.

It is finally time everyone does that. For more than one century, the Lorentz transformation is NOT an axiom, NOR the basis of special relativity, NOR "abandoned", though, but used as a CONSEQUENT of the spacetime approach, and so validated. This was said and done long ago, it is not a mater of research anymore, nor questions in RG, not even in history.

Without spacetime, there is no general relativity, and no special relativity as we know it. With it, one can calculate ARBITRARY accelerated motion, motion in curves, and do it without the Ehrenfest "paradox", for example.

If "each part is considered in its own local non-inertial frame"

1) it fix the unique coordinate system, but this coordinate system is not global.

2) You still need some measurement theory to interpret your results.

Hello Mikhail and all: Good, that is how the Ehrenfest "paradox" is solved, the coordinate system is not global, each part is considered in its own local non-inertial frame, and global quantities can be derived by integrating local contributions.

The global geometry is non-Euclidean, so pi may not apply for all the global circumferences calculated at all points. The geodesic takes the role of a straight line, extending the concept of a "straight line" that is followed under no external force.

The geometry in the neighborhood of each point is approximately given by the Langevin-Landau-Lifschitz metric.

Hello all, A review of the most important points in the discussion was added, in NOTES, in the main text of the discussion itself. Some points were omitted, for brevity, but are represented in the replies above.

Hello all: The original reference by Minkowski on spacetime, began with, "Henceforth, space for itself, and time for itself shall completely reduce to a mere shadow, and only some sort of union of the two shall preserve independence." [1], 120 years ago.

Cheers, Ed Gerck

[1] http://rgs.vniims.ru/books/spacetime.pdf

the assumed constancy of the speed of light in every IRF which is one of the main postulates at the base of the LT, is the actual reason of the Space-time.

The space-time is born with the LT although it was named as such later on by Minkowski.

Hello Stefano Quattrini: We should follow what is correct, historically and in physics, not the false controversy that you present. Mathematically, these were not the words of Minkowski [1], and not the difficulty Einstein [1] momentarily had with them.

The difficulty was that the Lorentz transformation became second-fiddle, introduced to keep the Minkowski metric valid, not the other way around, as you wrote, "The space-time is born with the LT". These false controversies need to stop at RG, and stop being used to create traffic.

The original reference by Minkowski on spacetime, began with, "Henceforth, space for itself, and time for itself shall completely reduce to a mere shadow, and only some sort of union of the two shall preserve independence." [1], 120 years ago.

The transformations of special relativity may be defined as those which do not change the Minkowski metric, since all such observers will agree on physical distances and so also agree on physical laws that are expressed in terms of them. And, as Mikhail G. Ivanov said in the first answer, "The Lorentz transformation are selected because L.transformation conserve the standard form of Minkowsky metric."

So, we do need to abandon the Lorentz transformations as the basis of special relativity. It is finally time everyone does that. For more than one century, the Lorentz transformation is NOT an axiom, NOR the basis of special relativity, NOR "abandoned", though, but used as a CONSEQUENT of the spacetime approach, and so validated. This was said and done long ago, it is not a matter of research anymore, nor questions in RG, not even in history.

Cheers, Ed Gerck

[1] http://rgs.vniims.ru/books/spacetime.pdf

Hello all: This thread arrived, in the past, at a conclusion, which is stated in the NOTES and the body of the initial text. There is no room to refuse to notice an obvious thing, or to re-explain here, the reasoning and references are available above, to anyone.

We are now ready to move to non-mathematical and non-physical aspects. We are talking about the historical and intersubjective aspects, which are important to us qua humans. Finding a humanly acceptable answer is difficult in physics or maths today, and, pretty soon, in all natural sciences. Therefore, this very thread is important.

We suggest, as in physics, that facts are what you were willing to believe. A bias, preventing a more complete vision. That is another motivation here, to abandon bias. It has no place going forward, and may prevent us from seeing what is plain to see.

In this and different tnreads, a question about inconsistencies in physics seem to bother some people. But physics does not have a target to be consistent, surprising as it may sound.

Any such question, including about consitency versus completness, can be clarified by consulting Gödel. It turns out that one cannot have both, in a system more complex than simple arithmetic. Therefore, unless one prefers to be "blind as a bat," to ignore what is out there but one cannot "see" yet, one must prefer completness also in the personal sphere, not just in natural sciences, like physics. The two are linked, because the same brain and mind are used.

I am adding part 1 of 4, of a tutorial on arbitrary motion in special relativity, in draft form for discussion. It is available at

Preprint On Special Relativity Applied to Accelerated Motion, 1 (tutorial)

I am adding parts 2 and 3 of 4, of a tutorial on arbitrary motion in special relativity, in draft form for discussion. They are available at

Preprint On Special Relativity Applied to Accelerated Motion, II (tutorial)

Preprint Special Relativity Applied to Accelerated Motion, III (tutorial)

I am adding part 4 of 4, of a tutorial on arbitrary motion in special relativity, in draft form for discussion. It is available at

Preprint Special Relativity Applied to Arbitrary Motion

Dear All ~

(1) A coordinate system is merely a reference system. It contains no physics. It allows us to record the results of measurements such as times, distances and speeds, to describe the interrelationships of those measurements and make predictions.

(2) A recorded measurement of a time or a distance or a speed is dependent on the experimental method employed in the measurement process. I take that to be self-evident.

(3) A physically valid statement about an observed and measured phenomenon is a statement that is independent of the choice of coordinate system. That is, it must be expressed in terms of invariants.

(3) The “proper time” calculated from the observed trajectory of any moving point in a material physical system is an invariant. “Coordinate times” are not. Nor are coordinate-based “distances” and “speeds”. All we need to know about "time dilation" is contained in an appreciation of the meaning of "proper time" and the method of calculating it.

(4) Special Relativity purports to provide a formulation of physical laws for phenomena in which gravitational effects are absent. Its propositions can be expressed in a coordinate-independent way as follows:

(a) According to SR physical phenomena are contained in a four-dimensional geometrical continuum, “Minkowskian spacetime”.

(b) Minkowskian spacetime is flat; that is, the Riemann tensor is zero everywhere. That is a coordinate-independent statement.

(c) The trajectory of any material point on which no forces act is a geodesic.

(d) The trajectory of a “light ray” is a null geodesic.

(5) Proposition (c) is essentially Newton’s first law expressed in a coordinate-independent way and it can reasonably be argued that (d) is a consequence of Maxwell’s electrodynamics.

(6) Because the geometry of Minkowski’s spacetime is “flat”, it is expedient to employ a particular kind of coordinate system when analysing a physical system mathematically. Such a coordinate system is an “ineritial frame”. Inertial frames are the reference systems appropriate to observers on which no forces act (by Newton's first law, unaccelerated observers). They are related to each other by Lorentz transformations. As Ed Gerck has explained, there is nothing sacrosanct about “inertial frames”. They offer the simplest way of formulating physical laws and describing physical phenomena, that’s all!

(7) Proposion (5d) is equivalent to: "Relative to any inertial frame light travels in a straight line with constant velocity c".

(8) It is often of interest to describe things from the point of view of a non-inertial observer; that is, an observer subject to forces and therefore accelerating. An appropriate reference system for such an observer is a curvilinear coordinate system. But that does not mean that spacetime for that observer is not Minkowskian! Changing the coordinate system does not change the geometry of spacetime! For example, there is an extensive literature on “rotating discs” in SR. The coordinates introduced in those discussions may feature three-dimensional spaces that are not flat (giving rise, for example, to the apparent “paradox” that the circumference of a rotationg disc is “Lorentz contracted” but its “radius” is not! But the 4-dimensional space in these situations is flat − changeing coordinates cannot change the geometry of the problem!

In summary: “inertial frames” are employed in Special Relativity for convenience − for simplification of the mathematics. Special Relativity, properly understood, is not in conflict with the concept of “acceleration”.

My Dear Eric,

it is only pure math missing to support it two fundamental experiments:

a) equally accelerated clocks manifest an offset proportional to their distance and acceleration and the time of acceleration in their initial IRF.

b) equally accelerated bodies exchanging radiation show a frequency shift same as the Doppler Effect in between IRFs.

Most of accelerated config. have been tested in accelerators linear or circular, never in the a) and b).

I certainly believe that b) will be verifed since it is a consequence of energy and momentum conservation of quanta of light in between MCIF.

Thanks for the comments. The discussion head was changed.

SQ, EL, and all: Does anyone really think that SR only works for those who believe on it?

Yes, SR gets potentially more effective for those who know its laws, such as in creating MRI, but objectively acts on all humans and non-humans alike. Even on inert matter, and fields with no matter -- and particles such as a photon, which can have mass in collective effects (two photons or more).

As CB said elsewhere, it is not SR that should be categorized as metaphysics, but the denial of SR.

Dear all, "Minkowski space" does not exist. Why? Because SRT is the observation of an inertial frame by another inertial frame. Who says 'observation' says 'use of light' in the context of SRT.

It means that light that is send by a frame and received at another is found to be deformed by the frames' velocities. It also follows from SRT that every different observer (place, speed) will see the deformation as being different.

We know that SRT doesn't conclude that the intrinsic physical properties inside the frames change with speed, since different observers get different values, hence these values are only subjective observations.

Hence, "Minkowski space" does not exist, because every observer will calculate a different "Minkowski space".

A "Minkowski space" is only the subjective outprint of one observer with respect to the observed universe. So, there exist trillions of it.

This principle can be extended to accelerations as well.

Best regards,

Thierry De Mees

All: As a reminder, it is easy to deal with fantasy and nonsense posters in this thread:

1. They talk against known physics, such as special relativity.

2. They add one or more of their own links, and call it referencing, but trying to get clicks while hiding self or fringe group advertising and false news, and repeat copying their own links under different titles, questions, etc.

3. When asked to stay on topic, they argue, instead of stopping.

4. When asked to correct their wrong citations by the authors themselves, they do not and continue to offend copyright.

5. One recognizes them, also, by talking about other posters, not about the subject (ad hominen attack). Then, they redefine terms in an effort to control the discussion. We do not do that as a recommended practice in science. So, they are already off-topic.

If this happens, you can treat these messages as they are, ads, and skip them, reducing noise with known fantasy or nonsense posters.

True scientists don't let themselves being put under pressure, neither by the mainstream, nor a gang member, nor by the opinion of 10 million people.

All: This not a general discussion, it is a physics topic on the issue of the title, with limits explained in the question above. It is not open to anything else, for the benefit of the question itself. It is also not proper for people to express themselves as they like, but the RG ToS apply here. Please delete any entry otherwise.

All: Preprint 24 Common Misconceptions of Mass and Energy in Special Relativity

End of rational discussions on that, the sooner they are accepted, the better. You should convince yourself that these answers are correct. Why?

Yes, new entries could be added, personal style choices could be different -- but these are just fruitless, pretend facade choices. This is a meta-study of thousands of published results, with many contributors, with 19 informative references, as cited. So, not just the author agrees 100% with them, this is not just a personal opinion.

The list has also benefited from almost 10 years of public discussions, including WP and RG, and it has 24 entries collated in that experience.

All new questions here will be read and answered when possible (we have four readers in the team) -- but, "new" questions, even if repeated, may fit in the list of already given 24 misconceptions, so look there first!

Stop joking, Ed, Wikipedia "public". Com'on ! Like 99.999% of "public" science, it is all controlled by the LameStream scientists.

All: The DESY (Deutsches Elektronen-Synchrotron ) report says:

“A non-covariant (3+1) approach to relativistic particle dynamics has been used in particle tracking calculations for about seventy years"

and points to other persistent errors, in ref. [22] of

https://www.researchgate.net/publication/334960559_24_Common_Misconceptions_of_Mass_and_Energy_in_Special_Relativity

All: Take five, as the famous jazz song says, and see the paragraphs below. First, you may hear "Take five" at https://www.youtube.com/watch?v=uEMzWuvUX44

Yes, responding to many PMs, GR has to change to be compatible to quantum mechanics (QM), which also will change, and maybe that is the expressive reason why Einstein was against QM, which he helped found -- but not alone.

And maybe that is why Einstein pursued "geometrization" in his later years for a unified theory. As if geometry, decided by humans, would rule the universe. The universe is not Euclidean, and is not non-Euclidean either --- this explains the large (96% about ) space in the interstices, which Caltech and Harvard estimate (see my question on the SM).

The faulty reasoning behind "relativity mass" (that mass would change with speed) was exposed recently (although said earlier, +100 years ago) in the DESY report and FERMILAB video (inter alia), and applies to all phenomena, not just to free-electron lasers. See them in the references at:

Preprint 24 Common Misconceptions of Mass and Energy in Special Relativity

Another faulty reasoning (also noted in the preprint linked above), if one follows Einstein SR, is that comoving observers (not necessarily identical, but seeing the same wavefront, or having the same position and velocity), like you and your ruler nearby (quite approximately), would see a length contraction or time dilation. No one does, at any speed, even 0.99999c. Length contraction or time dilation only work for non-comoving observers, and at any speed. There are other cases of faulty reasoning in Einstein SR, many at the preprint, but not all.

So, Einstein SR has been refuted. And Einstein GR is also a "dead man walking", also refuted. See paragraphs above.

But, Einstein was right. Einstein stands to our admiration in SR and GR, QM and thermodynamics, in that "Einstein always appeared to have a clear view of the problems of physics and the determination to solve them. He had a strategy of his own and was able to visualize the main stages on the way to his goal. He regarded his major achievements as mere stepping-stones for the next advance." in https://www.nobelprize.org/prizes/physics/1921/einstein/biographical/

Interesting questions arise when two clocks are separated by a large distance between them in the direction of their moving inertial frame and they each move from one inertial frame to another inertial frame moving in the same direction with a different speed from the first frame. With respect to an observer for which these two inertial frames are in fast motion, the difference between the times of the two clocks depends on the distance between them in the direction of the motion of the two inertial frames and it depends on the speed of the inertial frame which they are both in. This means that the acceleration that moves the two clocks from one inertial frame to the other with different speed has a very large effect on the clock speeds, how fast the times of the clocks are changing with respect to that observer. With respect to the observer, they have to have different changes in how fast their times change since they are separated in distance and the amount they are out of synchronization depends on the speed of the inertial frame they are in. With respect to the observer one of the clock speeds is not effected the same by the acceleration as the other clock's speed. This is more pronounced if the distance between the clocks is greater.