On Saturday, June 11, 2022 at 12:47:46 AM UTC-4, Stan Fultoni wrote:
> On Friday, June 10, 2022 at 8:46:36 PM UTC-7, tgca...@gmail.com wrote:
> > Do you disagree that measurement is about the distance between endpoints,
> > regardless of coordinate system orientation?
> A measurement of Q "is about" a measurement of Q. Duh. For example, a measurement of a spatial distance between two entities in terms of a given system of coordinates x,t is about the spatial distance (i.e., difference in the space coordinates) between those two entities at the same time (i.e., equal time coordinates).
>
> > What happens to the meter stick when it is moving?
>
> Again, you need to make the crucial distinction between passive and active transformations, and when you use the phrase "what happens to" you need to grasp the distinction between the concepts of (1) acceleration and (2) changing coordinate systems, as opposed to simply being in some state of uniform motion. We covered all this this before. Remember Maxwell's equations?
>
> > The displacement is the cosine projection of distance...
>
> What displacement, and what distance, and what projection? You're just mindlessly stringing words together, with no rational content.
> > the cosine projection of the distance is just the dot product of the path with
> > the displacement vector.
> What distance, and what displacement vector, and what projection? Again, you're just mindlessly stringing words together.
>
> > Forget everything else I wrote, except this. The correct relativistic protocol for
> > measurement is the Euclidean dot product.
> Look, physical phenomena can be described in terms of any system of coordinates we like, and it so happens that there is a special class of coordinate systems -- the inertia-based systems -- in terms of which the equations of physical laws take a uniquely simple homogeneous and isotropic form. Those are operationally established by constructing an orthogonal grid of standard rulers with clocks at each node, all at rest and inertially synchronized. Now, it can be shown that if every quantity of energy E has inertia E/c^2, then any two inertia-based coordinate systems are related by a Lorentz transformation, and this entails all the well-known relativistic effects. Is there something you think is wrong or unclear about this?
>
> > ...measurement only accounts for the real component, the part we can observe and
> > measure. There is more that we cannot see (but the co-moving observer can).
> No, relativity is not a subjectivist theory... there are not different realities for different observers, there are merely different descriptions in terms of different systems of coordinates. And the energy of inertia implies that the laws of physics are locally Lorentz invariant. That is all.
> > Einstein agreed with the measurements predicted by Lorentz Aether theory, but
> > he did not support the aether.
> It is well known that there is a Lorentzian interpretation of special relativity. It is not a different theory, it is just a different vocabulary for describing the same theory.
> > They predict identical results, for completely different reasons.
> Not true, they are entirely equivalent in every way except for descriptive vocabulary.
> > Show me how using the Euclidean dot product as a measurement standard leads to
> > a contradiction, and quit playing semantic games.
> You have not explained what you mean by "using a dot product as a measurement standard". A spatio-temporal measurement standard is ordinarily understood to be a coordinate system, and it makes no sense to say a dot product is a coordinate system. They are different categories of things. If you are trying to say that the manifold of spatio-temporal relations has a Euclidean metric, then that is easily shown to be wrong. Is that what you are trying to claim?
> > I thought Minkowski believed in 4 spacetime dimensions and it was Galileo and
> > Newton who believed in the 3+1 model.
> Nope, everyone from pre-historic times until today has recognized that there are three spatial dimensions and one time dimension. The difference between Newtonian space-time and the space-time of special relativity is just due to the fact that we now know that energy E has inertia E/c^2, so the manifold of spatio-temporal relations has a Minkowski pseudo-metric, represented by what you could call the "dot product", i.e., the invariant line element is given by the Lorentzian inner product.
> > I think the case is strong for each dimension to have a complex scalar coordinate.
> Nope, all evidence indicates conclusively that the coordinates are real-valued.

I see. You disagree about something fundamental. I say measurements are only possible for real-valued coordinates, but measurement procedures that are correct at lower speeds no longer represent the magnitude of the total at higher speeds, because there are imaginary components present. But we know exactly how much of the total it represents, because we have the Lorentz factor, which depends only on the magnitude of the relative velocity. Is it active or passive if we plot the Lorentz factor vs relative velocity? But I see you like to imagine what I meant and then argue your point. That isn't productive. Regurgitated dogma is of no value in this argument, because it is circular logic. Even if special relativity had no defects, you could not prove that by circular logic.
Thank you for your participation and bye.

On Friday, June 10, 2022 at 10:31:08 PM UTC-7, tgca...@gmail.com wrote:
> I see.

You do not appear to see. You have ignored everything that's been explained to you, and disregarded the exposure of all your fallacies and misconceptions.

> You disagree about something fundamental.

I'm just explaining things to you, and you are responding with incoherent verbiage.

> I say measurements are only possible for real-valued coordinates...

Nope, you said that coordinates are complex-valued. Now, as usual, you contradict yourself.

> Measurement procedures that are correct at lower speeds no longer
> represent the magnitude of the total at higher speeds, because there are
> imaginary components present.

Nope, inertia-based coordinate systems give perfectly valid systems of measurement for entities at all speeds. This has been empirically established countless times.

> We know exactly how much of the total it represents, because we have the Lorentz factor

No, that's gibberish... including the neologism of "Lorentz factor". Again, inertia-based coordinate systems are related by Lorentz transformations (not by a "Lorentz factor"... sheesh), and this fact entails all the relativistic effects. Do you dispute this?

> Is it active or passive if we plot the Lorentz factor vs relative velocity?

Neither. The descriptors "active" and "passive" apply to transformations, not to plots of functions. Duh.

> I see you like to imagine what I meant and then argue your point.

To be fair, you are so profoundly inarticulate that, in order to engage with you at all, it's necessary for a rational person to charitably infer what you might plausibly be trying to convey.

> Regurgitated dogma is of no value....

Agreed, so I wish you would stop regurgitating your own fantasized dogma and start listening to the actual grown-up explanations. You could understand this subject if you really wanted to.

> Even if special relativity had no defects, you could not prove that by circular logic.

As always, your attempted reasoning is fallacious. If you know of a defect (logical inconsistency) in special relativity, go ahead and point it out. [crickets]

> Thank you for your participation and bye.

As always, after just a few rounds of being confronted with reality, yet another anti-relativity person runs away.

On Saturday, June 11, 2022 at 12:47:33 AM UTC-4, Thomas Heger wrote:
> Am 10.06.2022 um 07:38 schrieb Maciej Wozniak:
> > On Friday, 10 June 2022 at 07:28:18 UTC+2, Thomas Heger wrote:
> >
> >> Appartently the universe 'speaks' in a mathematical language, which is
> >> also known as 'geometric algebra'.
> >
> > The universe is silent, like it always was. If you're
> > applying some mathematical language to it - that's
> > because you're trained to try.
> >
> >
> No, the universe is not silent.
>
> We see things all around us, which are somehow produced by the universe.
>
> Now we could think, the universe itself would operate on a mathematical
> foundation and acts like a large analoge computer.
>
> This was more or less my own assumption, which I have used in my 'book'
> about 'structured spacetime':
>
> https://docs.google.com/presentation/d/1Ur3_giuk2l439fxUa8QHX4wTDxBEaM6lOlgVUa0cFU4/edit?usp=sharing
>
>
>
> This concept works quite well and was based on the assumption, that the
> universe itself uses a certain kind of math, by which pointlike elements
> of spacetime are interconnected.
>
> This would create certain patterns, which we call 'matter' in case of
> they are timelike stable.
>
>
> It is actually a relatively simple concept, streight forward and based
> on a small set of plausible assumptions.
>
> The only problem is, that these assumptions are not very intuitive and
> difficult to understand.
>
>
>
> TH

In my own musings, I have considered a similar system. I noticed that through several isomorphisms of spacetime coordinates (I say isomorphisms because there is no combination of Lorentz transforms that can map one to another) the invariant s² and the rapidity w were the same in all of the isomorphisms. I realized it was because s is the hyperbolic magnitude and rapidity is the hyperbolic rotation angle. They are the coordinates of a point in a Cartesian orthogonal coordinate system. Since this grid is orthogonal, the two coordinates are independent, resulting in what we call invariance. In other words, after passing local coordinates through the transform that maps hyperbolic coordinates to another frame, the relationship that restores the hyperbolic magnitude associated with any point in hyperbolic spacetime is just the inverse of the coordinate transform that created the map. Despite the fact that the axes are no longer orthogonal, the inverse transform reconstructs the hyperbolic magnitude. The property of invariance implies an isomorphism to hyperbolic trigonometry, in which hyperbolic magnitude and rotation angle are orthogonal. This seems to imply that the universe prefers hyperbolic coordinate systems. In the hyperbolic coordinate system, the Lorentz transform takes on an especially simple form. If the hyperbolic rotation angle is w, then w1 is initial angle, w2 is the angle associated with a Lorentz boost and w3 is the result. Then, (s,w3) = (0,w2) + (s,w1). In the Minkowski isomorphism, the first and last points are replaced by column vectors, and the boost is a 2x2 matrix. In the Euclidean isomorphism, the 2x2 matrix is diagonal, because the axes are the real eigenvectors of the Lorentz matrix. The elements of the diagonal matrix are the two real eigenvalues of the Lorentz matrix, while in the Minkowski isomorphism, the elements are hyperbolic functions of the rotation angle, the magnitude of which is the natural log of the eigenvalue. The interesting thing about the eigenvector isomorphism is that it cannot be reached by any combination of Lorentz boosts. A single Lorentz boost can take a point that is stationary and boost it to any finite velocity, less than c. For the eigenvector frame to be unreachable by any combination of Lorentz boosts implies that it, like the eigenvectors which are the worldlines of photons, is the frame of lightspeed. How many questions have gone unanswered because we can't transform to the light frame? But this frame maps to both the hyperbolic grid and Minkowski spacetime. As isomorphisms, any disturbance in any one of them produces ripples in all of them. Not necessarily similar, though.

What caught my attention was the idea of a set of points being in a fixed geometric pattern. Magnitudes in hyperbolic coordinates are unaffected by relative velocity. So a set of points in a line represents a set of magnitudes that all share the same velocity, and are invariant as a set over all rapidities. These could be structures like atoms or molecules. Does any of this sync with what you're doing?

On Saturday, June 11, 2022 at 1:56:06 AM UTC-4, Stan Fultoni wrote:
> On Friday, June 10, 2022 at 10:31:08 PM UTC-7, tgca...@gmail.com wrote:
> > I see.
>
> You do not appear to see. You have ignored everything that's been explained to you, and disregarded the exposure of all your fallacies and misconceptions.
> > You disagree about something fundamental.
> I'm just explaining things to you, and you are responding with incoherent verbiage.
>
> > I say measurements are only possible for real-valued coordinates...
>
> Nope, you said that coordinates are complex-valued. Now, as usual, you contradict yourself.
>
> > Measurement procedures that are correct at lower speeds no longer
> > represent the magnitude of the total at higher speeds, because there are
> > imaginary components present.
> Nope, inertia-based coordinate systems give perfectly valid systems of measurement for entities at all speeds. This has been empirically established countless times.
>
> > We know exactly how much of the total it represents, because we have the Lorentz factor
>
> No, that's gibberish... including the neologism of "Lorentz factor". Again, inertia-based coordinate systems are related by Lorentz transformations (not by a "Lorentz factor"... sheesh), and this fact entails all the relativistic effects. Do you dispute this?
> > Is it active or passive if we plot the Lorentz factor vs relative velocity?
> Neither. The descriptors "active" and "passive" apply to transformations, not to plots of functions. Duh.
> > I see you like to imagine what I meant and then argue your point.
> To be fair, you are so profoundly inarticulate that, in order to engage with you at all, it's necessary for a rational person to charitably infer what you might plausibly be trying to convey.
>
> > Regurgitated dogma is of no value....
>
> Agreed, so I wish you would stop regurgitating your own fantasized dogma and start listening to the actual grown-up explanations. You could understand this subject if you really wanted to.
> > Even if special relativity had no defects, you could not prove that by circular logic.
> As always, your attempted reasoning is fallacious. If you know of a defect (logical inconsistency) in special relativity, go ahead and point it out. [crickets]
> > Thank you for your participation and bye.
> As always, after just a few rounds of being confronted with reality, yet another anti-relativity person runs away.

And yet you responded. I am not running away from a troll. I have more useful things to do with other readers. It's a waste of time responding when you block out details so you can lie about my not answering your arguments. I haven't heard a peep about the dot product leading to a contradiction. I already pointed out that Einstein used a Newtonian approximation of the dot product to build special relativity that describes events well outside the validity of a Newtonian approximation. And this has nothing to do with the actual theory. This biases it before it begins. But, of course, you disagree. Relativity cultists always make excuses for Einstein.

On Friday, June 10, 2022 at 11:46:09 PM UTC-7, tgca...@gmail.com wrote:
> > > Even if special relativity had no defects, you could not prove that by circular logic.
> >
> > As always, your attempted reasoning is fallacious. If you know of a defect (logical inconsistency) in special relativity, go ahead and point it out. [crickets]
> >
> > > Thank you for your participation and bye.
> >
> > As always, after just a few rounds of being confronted with reality, yet another anti-relativity person runs away.
>
> And yet you responded.

Of course. I'm not the one who announced he would no longer be responding... that was you, remember? And yet you responded. And then you launch the zinger "And yet you responded". Hilarious.

> The displacement is the cosine projection of distance...

What displacement, and what distance, and what projection? You're just mindlessly stringing words together, with no rational content.

> the cosine projection of the distance is just the dot product of the path with
> the displacement vector.

What distance, and what displacement vector, and what projection? Again, you're just mindlessly stringing words together.

> It's a waste of time responding when you block out details so you can lie
> about my not answering your arguments.

I have merely asked you to explain what on earth you are talking about... and you refuse to answer.

> I haven't heard a peep about the dot product leading to a contradiction.

That is a bald-faced lie. You declared that a dot product is a measurement procedure, and I pointed out that that's a senseless statement because a dot product is not a measurement procedure at all, nor a coordinate system; those are different categories of things, so your words make no sense at all. And I've explained that you really need to talk about the inner product that gives the relevant metrical line element... if you had any clue what you were talking about.

> I already pointed out that Einstein used a Newtonian approximation of the
> dot product to build special relativity...

And I explained why you are mistaken, and your claim makes absolutely no rational sense at all. Remember? Again, inertia-based coordinate systems manifestly represent a perfectly objective operational system of measure that applies to the quantification of the spatio-temporal relations for all events throughout space and time. It is infantile gibberish for you to string together the words "Einstein used a Newtonian approximation of the dot product to build special relativity". When Einstein referred to systems of coordinates in which the equations of Newtonian mechanics hold good, and the footnote was added to say "i.e., to the first approximation", it means "in the low speed limit", i.e., the homogeneity and isotropy for Newton's laws quasi-statically suffices to establish inertia-based coordinates. This does *not* mean that those coordinate systems apply only to quasi-static objects. Duh.

If you have something sane and rational to say, go ahead and say it. Do you dispute the ability to construct inertia-based coordinate systems? Do you dispute that they are related by Lorentz transformations? Do you dispute that this entails all the well-known relativistic effects? If you don't dispute any of this, then you are espousing special relativity. And if you do dispute any of it, your beliefs are abundantly falsified empirically.

On Saturday, June 11, 2022 at 3:36:29 AM UTC-4, Stan Fultoni wrote:
> On Friday, June 10, 2022 at 11:46:09 PM UTC-7, tgca...@gmail.com wrote:
> > > > Even if special relativity had no defects, you could not prove that by circular logic.
> > >
> > > As always, your attempted reasoning is fallacious. If you know of a defect (logical inconsistency) in special relativity, go ahead and point it out. [crickets]
> > >
> > > > Thank you for your participation and bye.
> > >
> > > As always, after just a few rounds of being confronted with reality, yet another anti-relativity person runs away.
> >
> > And yet you responded.
> Of course. I'm not the one who announced he would no longer be responding... that was you, remember? And yet you responded. And then you launch the zinger "And yet you responded". Hilarious.
> > The displacement is the cosine projection of distance...
>
> What displacement, and what distance, and what projection? You're just mindlessly stringing words together, with no rational content.
>
> > the cosine projection of the distance is just the dot product of the path with
> > the displacement vector.
>
> What distance, and what displacement vector, and what projection? Again, you're just mindlessly stringing words together.
> > It's a waste of time responding when you block out details so you can lie
> > about my not answering your arguments.
> I have merely asked you to explain what on earth you are talking about... and you refuse to answer.
> > I haven't heard a peep about the dot product leading to a contradiction..
> That is a bald-faced lie. You declared that a dot product is a measurement procedure, and I pointed out that that's a senseless statement because a dot product is not a measurement procedure at all, nor a coordinate system; those are different categories of things, so your words make no sense at all. And I've explained that you really need to talk about the inner product that gives the relevant metrical line element... if you had any clue what you were talking about.
> > I already pointed out that Einstein used a Newtonian approximation of the
> > dot product to build special relativity...
>
> And I explained why you are mistaken, and your claim makes absolutely no rational sense at all. Remember? Again, inertia-based coordinate systems manifestly represent a perfectly objective operational system of measure that applies to the quantification of the spatio-temporal relations for all events throughout space and time. It is infantile gibberish for you to string together the words "Einstein used a Newtonian approximation of the dot product to build special relativity". When Einstein referred to systems of coordinates in which the equations of Newtonian mechanics hold good, and the footnote was added to say "i.e., to the first approximation", it means "in the low speed limit", i.e., the homogeneity and isotropy for Newton's laws quasi-statically suffices to establish inertia-based coordinates. This does *not* mean that those coordinate systems apply only to quasi-static objects. Duh.
>
> If you have something sane and rational to say, go ahead and say it. Do you dispute the ability to construct inertia-based coordinate systems? Do you dispute that they are related by Lorentz transformations? Do you dispute that this entails all the well-known relativistic effects? If you don't dispute any of this, then you are espousing special relativity. And if you do dispute any of it, your beliefs are abundantly falsified empirically.
You act as if your pronouncements are gospel. If I take the time and effort to elaborate, you will repeat some bs from a corrupt theory. One last try. Consider the following experiment. You know what. Nevermind. You will just trot out the noise about active and passive transformations. The active transformation is just me observing you change location in my coordinate system, where the passive transformation is just you observing my coordinate system changing under you. According to the principle of relativity, both views are equivalent, as they both describe the same event.

On Saturday, June 11, 2022 at 3:36:29 AM UTC-4, Stan Fultoni wrote:
> On Friday, June 10, 2022 at 11:46:09 PM UTC-7, tgca...@gmail.com wrote:
> > > > Even if special relativity had no defects, you could not prove that by circular logic.
> > >
> > > As always, your attempted reasoning is fallacious. If you know of a defect (logical inconsistency) in special relativity, go ahead and point it out. [crickets]
> > >
> > > > Thank you for your participation and bye.
> > >
> > > As always, after just a few rounds of being confronted with reality, yet another anti-relativity person runs away.
> >
> > And yet you responded.
> Of course. I'm not the one who announced he would no longer be responding... that was you, remember? And yet you responded. And then you launch the zinger "And yet you responded". Hilarious.
> > The displacement is the cosine projection of distance...
>
> What displacement, and what distance, and what projection? You're just mindlessly stringing words together, with no rational content.
>
> > the cosine projection of the distance is just the dot product of the path with
> > the displacement vector.
>
> What distance, and what displacement vector, and what projection? Again, you're just mindlessly stringing words together.
> > It's a waste of time responding when you block out details so you can lie
> > about my not answering your arguments.
> I have merely asked you to explain what on earth you are talking about... and you refuse to answer.
> > I haven't heard a peep about the dot product leading to a contradiction..
> That is a bald-faced lie. You declared that a dot product is a measurement procedure, and I pointed out that that's a senseless statement because a dot product is not a measurement procedure at all, nor a coordinate system; those are different categories of things, so your words make no sense at all. And I've explained that you really need to talk about the inner product that gives the relevant metrical line element... if you had any clue what you were talking about.
> > I already pointed out that Einstein used a Newtonian approximation of the
> > dot product to build special relativity...
>
> And I explained why you are mistaken, and your claim makes absolutely no rational sense at all. Remember? Again, inertia-based coordinate systems manifestly represent a perfectly objective operational system of measure that applies to the quantification of the spatio-temporal relations for all events throughout space and time. It is infantile gibberish for you to string together the words "Einstein used a Newtonian approximation of the dot product to build special relativity". When Einstein referred to systems of coordinates in which the equations of Newtonian mechanics hold good, and the footnote was added to say "i.e., to the first approximation", it means "in the low speed limit", i.e., the homogeneity and isotropy for Newton's laws quasi-statically suffices to establish inertia-based coordinates. This does *not* mean that those coordinate systems apply only to quasi-static objects. Duh.
>
> If you have something sane and rational to say, go ahead and say it. Do you dispute the ability to construct inertia-based coordinate systems? Do you dispute that they are related by Lorentz transformations? Do you dispute that this entails all the well-known relativistic effects? If you don't dispute any of this, then you are espousing special relativity. And if you do dispute any of it, your beliefs are abundantly falsified empirically.

"This does *not* mean that those coordinate systems apply only to quasi-static objects. Duh. " Says who?
And yet those coordinate systems do not apply at relativistic velocities. Maybe you should elaborate on what you claim "to the first approximation" means.

On Saturday, June 11, 2022 at 6:47:44 AM UTC-7, tgca...@gmail.com wrote:
> The active transformation is just me observing you change location in my coordinate system,

No. Cretin.

On Saturday, June 11, 2022 at 6:55:54 AM UTC-7, tgca...@gmail.com wrote:
> > It is infantile gibberish for you to string together the words "Einstein used a
> > Newtonian approximation of the dot product to build special relativity".. When
> > Einstein referred to systems of coordinates in which the equations of Newtonian
> > mechanics hold good, and the footnote was added to say "i.e., to the first
> > approximation", it means "in the low speed limit", i.e., the homogeneity and isotropy
> > for Newton's laws quasi-statically suffices to establish inertia-based coordinates.
>
> Maybe you should elaborate on what you claim "to the first approximation" means.

Maybe you should learn to read. See above. If there is something you don't understand there, just ask.

> And yet those coordinate systems do not apply at relativistic velocities.

Of course they do. Your weird notion that an operationally-specified system of coordinates that manifestly provides a one-to-one mapping between coordinates and times-places somehow fails to "apply" to objects moving at some speeds, such as light pulses moving at c, is just self-indulgent silliness.. My goodness, coordinate systems are routinely established *using* entities moving at the speed c. A system of coordinates is nothing but an assignment of numerical labels to events. An entity moving from x1,t1 to x2,t2 has the velocity (x2-x1)/(t2-t1). This applies to any timelike trajectories.. That is all. There is simply no rational basis for your silly claim that this -- or any other -- coordinate system stops "applying" for entities at certain speeds.

> Consider the following experiment. You know what. Nevermind.

You see, that's the problem, right there. You simply refuse to give any coherent statement that specifies what you are really trying to say. You seem to be afraid to do so, because you sense that your cherished verbiage, if exposed to the light of day, would be instantly demolished by grown-up rational explanation ... so you just run away.

> The active transformation is just me observing you change location in my
> coordinate system, where the passive transformation is just you observing
> my coordinate system changing under you.

Nope, you have failed to grasp the distinction... which is strange because I've explained it to you several times. Again (try to concentrate), to describe an object that is in a given state of motion (unaccelerated) in terms of two different systems of coordinates is a passive transformation, because nothing physically is being done to the object, i.e., no forces applied. It is purely mathematical, changing the terms of description, and we can choose any systems of coordinates like.

In contrast, if we stick to a single system of coordinates, but we subject the object to forces, causing it to accelerate and change its state of motion, we can describe the object before and after the acceleration, both in terms of that single system of coordinates. In this case we are not changing the terms of description, we are physically changing the object's state of motion by the application of forces. This is an active transformation, and it is not purely mathematical, it depends on the laws of physics.

> According to the principle of relativity, both views are equivalent, as they both describe the same event.

Well, to be more accurate, once we determine how active transformations behave, we can adopt passive transformations that match those active transformations, so that we can exploit the relativistic symmetry in our descriptions of phenomena. That's why we often describe things in terms of coordinate systems related by Lorentz transformations, because all the laws of physics have been found to be Lorentz invariant, meaning they take exactly the same form when expressed in terms of a particular class of coordinate systems that are related by Lorentz transformations.

Now do you understand?

On Saturday, 11 June 2022 at 06:47:46 UTC+2, Stan Fultoni wrote:

Look, physical phenomena can be described in terms of any system of coordinates we like, and it so happens that there is a special class of coordinate systems -- the inertia-based systems -- in terms of which the equations of physical laws take a uniquely simple homogeneous and isotropic form.

No, poor idiot, there are no such systems. You've only
gedanken them.

On Saturday, June 11, 2022 at 10:32:16 AM UTC-4, Stan Fultoni wrote:
> On Saturday, June 11, 2022 at 6:55:54 AM UTC-7, tgca...@gmail.com wrote:
> > > It is infantile gibberish for you to string together the words "Einstein used a
> > > Newtonian approximation of the dot product to build special relativity". When
> > > Einstein referred to systems of coordinates in which the equations of Newtonian
> > > mechanics hold good, and the footnote was added to say "i.e., to the first
> > > approximation", it means "in the low speed limit", i.e., the homogeneity and isotropy
> > > for Newton's laws quasi-statically suffices to establish inertia-based coordinates.
> >
> > Maybe you should elaborate on what you claim "to the first approximation" means.
> Maybe you should learn to read. See above. If there is something you don't understand there, just ask.
> > And yet those coordinate systems do not apply at relativistic velocities.
> Of course they do. Your weird notion that an operationally-specified system of coordinates that manifestly provides a one-to-one mapping between coordinates and times-places somehow fails to "apply" to objects moving at some speeds, such as light pulses moving at c, is just self-indulgent silliness. My goodness, coordinate systems are routinely established *using* entities moving at the speed c. A system of coordinates is nothing but an assignment of numerical labels to events. An entity moving from x1,t1 to x2,t2 has the velocity (x2-x1)/(t2-t1). This applies to any timelike trajectories. That is all. There is simply no rational basis for your silly claim that this -- or any other -- coordinate system stops "applying" for entities at certain speeds.
> > Consider the following experiment. You know what. Nevermind.
> You see, that's the problem, right there. You simply refuse to give any coherent statement that specifies what you are really trying to say. You seem to be afraid to do so, because you sense that your cherished verbiage, if exposed to the light of day, would be instantly demolished by grown-up rational explanation ... so you just run away.
> > The active transformation is just me observing you change location in my
> > coordinate system, where the passive transformation is just you observing
> > my coordinate system changing under you.
> Nope, you have failed to grasp the distinction... which is strange because I've explained it to you several times. Again (try to concentrate), to describe an object that is in a given state of motion (unaccelerated) in terms of two different systems of coordinates is a passive transformation, because nothing physically is being done to the object, i.e., no forces applied.. It is purely mathematical, changing the terms of description, and we can choose any systems of coordinates like.
>
> In contrast, if we stick to a single system of coordinates, but we subject the object to forces, causing it to accelerate and change its state of motion, we can describe the object before and after the acceleration, both in terms of that single system of coordinates. In this case we are not changing the terms of description, we are physically changing the object's state of motion by the application of forces. This is an active transformation, and it is not purely mathematical, it depends on the laws of physics.
> > According to the principle of relativity, both views are equivalent, as they both describe the same event.
> Well, to be more accurate, once we determine how active transformations behave, we can adopt passive transformations that match those active transformations, so that we can exploit the relativistic symmetry in our descriptions of phenomena. That's why we often describe things in terms of coordinate systems related by Lorentz transformations, because all the laws of physics have been found to be Lorentz invariant, meaning they take exactly the same form when expressed in terms of a particular class of coordinate systems that are related by Lorentz transformations.
>
> Now do you understand?

I understand you want to rewrite everything I say so you can create strawmen to argue against and pretend you are refuting me. For example, you wrote, "You declared that a dot product is a measurement procedure, and I pointed out that that's a senseless statement because a dot product is not a measurement procedure at all, nor a coordinate system;" What I wrote was not the same, " The correct relativistic protocol for measurement is the Euclidean dot product. Show me how that leads to a contradiction." Rather than show how the dot product model leads to a contradiction, you simply deny the model. What I haven't heard a peep about is that contradiction. Just because you think that your narrow definitions are the only ones possible doesn't make it so. The dot product is commonly used to determine the parallelness of two arbitrary vectors. Is it so difficult to understand that if one of the arbitrary vectors is a unit reference, then the result of the dot product is the part of the other vector that is parallel to the reference unit? This is exactly what we get when we try to measure an arbitrary vector in a relatively moving frame, because ct = γct' is the same equation as ct' = ct cos(tilt), which is the result of the dot product of an arbitrary vector with a unit reference. cos(tilt) = 1/γ. The axes of the reference frame and the moving frame are typically parallel, spatially, but the angle between the axes is set by relative velocity, and this angle is not included in the setup of the inertial frames. And just stop with the bs about active and passive. Those are your assertions. It is dishonest to claim that a passive transformation is just mathematics, but an active transformation is physics. I can apply any Lorentz transformation that I choose to an inertial frame, without using any force to actually change anything. I can find the result of any virtual acceleration without actually changing the velocity. According to you, accelerating a frame in one set of coordinates makes it an active transformation. I contend that this transformation is just mathematical, despite the fact that it is an example of an active transformation. Your distinction is meaningless. And if an observer moves from the reference frame to the moving frame, then uses a passive transformation to find the new coordinate system, is that not physical? There has been no acceleration of the moving coordinate system, but all the coordinates have changed. Pure mathematics?

You said, " Maybe you should learn to read. See above. If there is something you don't understand there, just ask." Well I did ask what you claim "to a first approximation" means. You alleged that it means low speed approximation, but also assert that a low speed approximation is valid at relativistic speeds. You just redirected me to your first statement. And you continue to claim that the same coordinate system applies at high velocity when the axes are no longer orthogonal, and the size of the units is no longer the same. You call that the same coordinate system? You simply ignore the Einstein assertion that an indirect measurement is valid if it yields the same result as a direct measurement when confronted with relativistic measurements that are dilated and contracted. They hardly agree with a static measurement.

Here's another gem, "> I say measurements are only possible for real-valued coordinates...
Nope, you said that coordinates are complex-valued. Now, as usual, you contradict yourself." More of your double-talk. You are the one claiming a contradiction where there isn't one. Coordinates are complex valued. Complex coordinates have two parts, a real part and an imaginary part. I merely pointed out that you can only measure the real part of a complex coordinate. After all, the imaginary part is not visible, and even if it were, it is perpendicular to the real part, and its magnitude cannot contribute to the real magnitude.

If you were a world-renowned scientist, I would still argue the claims you've made. But you aren't, so I have even less reason to take you seriously. People say, "Let the asshole have the last word." Have at it.

On Saturday, June 11, 2022 at 3:42:28 PM UTC-7, tgca...@gmail.com wrote:
> The correct relativistic protocol for measurement is the Euclidean dot product.

Again, that is utterly senseless statement because a dot product is not a measurement procedure (or protocol) at all, nor is it a coordinate system. Those are completely different categories of things.

> Rather than show how the dot product model leads to a contradiction, you
> simply deny the model.

No, I deny that your string of word *is* a model at all. It is nothing but an utterly senseless string of words. A dot product is not a measurement protocol. A dot product is a dot product. If you want to describe a "measurement protocol" that involves the concept of a dot product, then please do so.

> The dot product is commonly used to determine the parallelness of two arbitrary vectors.

Well, a grown-up would say that, in a 3D Euclidean space, the dot product of two vectors (x1,y1,z1) and (x2,y2,z2) is simply the scalar x1x2+y1y2+z1z2, which equals |L1||L1|cos(q) where |L1|and |L2| are the magnitudes of the vectors and q is the angle between them. Two vectors are perpendicular if and only if their dot product vanishes. And so on. This is elementary grade school geometry, and it does not constitute a measurement protocol. Obviously the coordinates of a point are the dot products of the displacement vector with the unit vectors on the coordinate axes. And so on. This, again, is just grade school geometry.

> If one of the arbitrary vectors is a unit reference, then the result of the dot
> product is the part of the other vector that is parallel to the reference unit?

It is the projection of the vector onto the axis of the unit vector. Again, this is grade school geometry.

> This is exactly what we get when we try to measure an arbitrary vector in a
> relatively moving frame, because ct = γct' is the same equation as ct' = ct cos(tilt),
> which is the result of the dot product of an arbitrary vector with a unit reference. cos(tilt) = 1/γ.

No, that is utterly senseless. Using units so c=1, it is an empirical fact -- with which you have agreed repeatedly -- that the invariant inner product in flat 3+1 dimensional space and time of two vectors t1,x1,y1,z1 and t2,x2,y2,z2 is given by t1t2 - x1x2 - y1y2 - z1z2. Hence the inner product of a vector with itself is it's squared absolute magnitude, and two vectors are perpendicular if their inner product vanishes, and so on, analogous to the dot product in Euclidean geometry. As a result, the relationship between coordinates t,x,y,z of a given event in terms of S and the corresponding coordinates t',x',y',z' of that event in terms of S' (aligned and moving at speed v in the positive x direction) is t'=(t-vx)g, x'=(x-vt)g, y'=y, z'=z where g=1/sqrt(1-v^2).
Remember?

> I can apply any Lorentz transformation that I choose to an inertial frame....

You sure can, and the result is as noted above. What part of this do you dispute?

> I did ask what you claim "to a first approximation" means. You alleged that it means
> low speed approximation, but also assert that a low speed approximation is valid at
> relativistic speeds.

No, please try to concentrate: An inertia-based coordinate system is defined as one in which the equations of Newtonian mechanics hold good in the low speed limit. For example, we can inertially synchronize clocks by shooting identical bullets from identical guns *at rest* (low speed limit) at the mid point between the clocks. But once we have established our coordinate system and inertially synchronized our clocks, those coordinates cover every time and place, and they are perfectly valid to describe the trajectories of objects moving at arbitrary speeds, including the speed of light. Duh..

> You simply ignore the Einstein assertion that an indirect measurement is
> valid if it yields the same result as a direct measurement when confronted with
> relativistic measurements that are dilated and contracted.

Oh my goodness, you are totally confused. What Einstein was describing in that little popular booklet was the meaning of space and time coordinates, and saying that a direct measurement would be by an grid of rulers (and later, synchronized clocks) covering all of space and time, but in practice we obviously don't construct infinite grids like this, we make indirect measurements (such as by remote optical means), but those indirect measurements must be made to yield what we would get by direct measurements with an complete grid of rulers and clocks at rest in some specified frame. So, for example, the spatial length of a given object in terms of S is the same, regardless of whether we use direct or indirect measurement. The mistake you are making is to think that he is saying we get the same spatial length in terms of S' as we get in terms of S. That is obviously not what he is saying. In fact, he explained to the contrary the effects of length contraction, etc.

> Here's another gem, "> I say measurements are only possible for real-valued coordinates... "
> [and] Coordinates are complex valued.

You contradict yourself.

> ...the imaginary part is not visible, and even if it were, it is perpendicular to the real part,
> and its magnitude cannot contribute to the real magnitude.

Then it is not a scientific concept. Science is concerned only with things that are, at least in principle, observable. Science does not concern invisible pink elephants. Look, if you want to understand special relativity, then you have to set aside your silly verbiage and actually learn about special relativity. See above.

Am 11.06.2022 um 08:34 schrieb Tom Capizzi:
> On Saturday, June 11, 2022 at 12:47:33 AM UTC-4, Thomas Heger wrote:
>> Am 10.06.2022 um 07:38 schrieb Maciej Wozniak:
>>> On Friday, 10 June 2022 at 07:28:18 UTC+2, Thomas Heger wrote:
>>>
>>>> Appartently the universe 'speaks' in a mathematical language, which is
>>>> also known as 'geometric algebra'.
>>>
>>> The universe is silent, like it always was. If you're
>>> applying some mathematical language to it - that's
>>> because you're trained to try.
>>>
>>>
>> No, the universe is not silent.
>>
>> We see things all around us, which are somehow produced by the universe.
>>
>> Now we could think, the universe itself would operate on a mathematical
>> foundation and acts like a large analoge computer.
>>
>> This was more or less my own assumption, which I have used in my 'book'
>> about 'structured spacetime':
>>
>> https://docs.google.com/presentation/d/1Ur3_giuk2l439fxUa8QHX4wTDxBEaM6lOlgVUa0cFU4/edit?usp=sharing
>>
>>
>>
>> This concept works quite well and was based on the assumption, that the
>> universe itself uses a certain kind of math, by which pointlike elements
>> of spacetime are interconnected.
>>
>> This would create certain patterns, which we call 'matter' in case of
>> they are timelike stable.
>>
>>
>> It is actually a relatively simple concept, streight forward and based
>> on a small set of plausible assumptions.
>>
>> The only problem is, that these assumptions are not very intuitive and
>> difficult to understand.
>>
>>
>>
>> TH
>
> In my own musings, I have considered a similar system. I noticed that through several isomorphisms of spacetime coordinates (I say isomorphisms because there is no combination of Lorentz transforms that can map one to another) the invariant s² and the rapidity w were the same in all of the isomorphisms. I realized it was because s is the hyperbolic magnitude and rapidity is the hyperbolic rotation angle. They are the coordinates of a point in a Cartesian orthogonal coordinate system. Since this grid is orthogonal, the two coordinates are independent, resulting in what we call invariance. In other words, after passing local coordinates through the transform that maps hyperbolic coordinates to another frame, the relationship that restores the hyperbolic magnitude associated with any point in hyperbolic spacetime is just the inverse of the coordinate transform that created the map. Despite the fact that the axes are no longer orthogonal, the inverse transform reconstructs the hyperb
olic magnitude. The property of invariance implies an isomorphism to hyperbolic trigonometry, in which hyperbolic magnitude and rotation angle are orthogonal. This seems to imply that the universe prefers hyperbolic coordinate systems. In the hyperbolic coordinate system, the Lorentz transform takes on an especially simple form. If the hyperbolic rotation angle is w, then w1 is initial angle, w2 is the angle associated with a Lorentz boost and w3 is the result. Then, (s,w3) = (0,w2) + (s,w1). In the Minkowski isomorphism, the first and last points are replaced by column vectors, and the boost is a 2x2 matrix. In the Euclidean isomorphism, the 2x2 matrix is diagonal, because the axes are the real eigenvectors of the Lorentz matrix. The elements of the diagonal matrix are the two real eigenvalues of the Lorentz matrix, while in the Minkowski isomorphism, the elements are hyperbolic functions of the rotation angle, the magnitude of which is the natural log of the eigenvalue. The interes
ting thing about the eigenvector isomorphism is that it cannot be reached by any combination of Lorentz boosts. A single Lorentz boost can take a point that is stationary and boost it to any finite velocity, less than c. For the eigenvector frame to be unreachable by any combination of Lorentz boosts implies that it, like the eigenvectors which are the worldlines of photons, is the frame of lightspeed. How many questions have gone unanswered because we can't transform to the light frame? But this frame maps to both the hyperbolic grid and Minkowski spacetime. As isomorphisms, any disturbance in any one of them produces ripples in all of them. Not necessarily similar, though.
>
> What caught my attention was the idea of a set of points being in a fixed geometric pattern. Magnitudes in hyperbolic coordinates are unaffected by relative velocity. So a set of points in a line represents a set of magnitudes that all share the same velocity, and are invariant as a set over all rapidities. These could be structures like atoms or molecules. Does any of this sync with what you're doing?

First:

you should add some white space into your text, what would make it much
more readable.

Second:

yes actually, but I had a different approach.

I wanted to find use for a certain quaternion equation, because I wanted
to take spacetime as real physical entity and model it as quaternion
field. These 'elements of spacetime' are assumed to interact with their
direct neighbors in a certain way, which generates certain patterns.
These patterns are, what we regard as the real world, while they are in
fact internal structure of spacetime.

TH

On Sunday, 12 June 2022 at 01:56:07 UTC+2, Stan Fultoni wrote:

> Then it is not a scientific concept. Science is concerned only with things that are, at least in principle, observable.

Bullshit. Your moronic physics, for instance, is only concerned with
its moronic gedanken scenarios.

On Saturday, June 11, 2022 at 3:42:28 PM UTC-7, tgca...@gmail.com wrote:
> The correct relativistic protocol for measurement is the Euclidean dot product.

Again, that's a senseless string of words because a dot product is not a measurement procedure or protocol at all, nor is it a coordinate system. Those are completely different categories of things.

> Rather than show how the dot product model leads to a contradiction, you
> simply deny the model.

No, I deny that your string of words *is* a model at all. It is nothing but an utterly senseless string of words. A dot product is not a measurement protocol. A dot product is a dot product. If you want to describe a "measurement protocol" that involves the concept of a dot product, then please do so.

> The dot product is commonly used to determine the parallelness of two arbitrary vectors.

Well, a grown-up person would say that, in a 3D Euclidean space, the dot product of two vectors (x1,y1,z1) and (x2,y2,z2) is simply the scalar x1x2+y1y2+z1z2, which equals |L1||L2|cos(q) where |L1|and |L2| are the magnitudes of the vectors and q is the angle between them. Two vectors are perpendicular if and only if their dot product vanishes. And so on. This is elementary grade school geometry, and it does not constitute a measurement protocol. Obviously the coordinates of a point are the dot products of the displacement vector with the unit vectors on the coordinate axes. And so on. This, again, is just grade school geometry.

> If one of the arbitrary vectors is a unit reference, then the result of the dot
> product is the part of the other vector that is parallel to the reference unit?

It's the projection of the vector onto the axis of the unit vector. Again, this is grade school geometry.

> This is exactly what we get when we try to measure an arbitrary vector in a
> relatively moving frame, because ct = γct' is the same equation as ct' = ct cos(tilt),
> which is the result of the dot product of an arbitrary vector with a unit reference. cos(tilt) = 1/γ.

No, that's utterly senseless. Using units so c=1, it is an empirical fact -- with which you have agreed repeatedly -- that the invariant inner product in flat 3+1 dimensional space and time of two vectors t1,x1,y1,z1 and t2,x2,y2,z2 is given by t1t2 - x1x2 - y1y2 - z1z2. Hence the inner product of a vector with itself is it's squared absolute magnitude, and two vectors are perpendicular if their inner product vanishes, and so on, analogous to the dot product in Euclidean geometry. As a result, the relationship between coordinates t,x,y,z of a given event in terms of S and the corresponding coordinates t',x',y',z' of that event in terms of S' (aligned and moving at speed v in the positive x direction) is t'=(t-vx)g, x'=(x-vt)g, y'=y, z'=z where g=1/sqrt(1-v^2). Remember?

> I can apply any Lorentz transformation that I choose to an inertial frame....

Sure you can, and the result is as noted above. What part of this do you dispute?

> I did ask what you claim "to a first approximation" means. You alleged that it means
> low speed approximation, but also assert that a low speed approximation is valid at
> relativistic speeds.

No, please try to concentrate: An inertia-based coordinate system is defined as one in which the equations of Newtonian mechanics hold good in the low speed limit. For example, we can inertially synchronize clocks by shooting identical bullets from identical guns *at rest* (low speed limit) at the mid point between the clocks. But once we've established our coordinate system and inertially synchronized our clocks, those coordinates cover every time and place, and they are perfectly valid to describe the trajectories of objects moving at arbitrary speeds, including the speed of light. Duh.

> You simply ignore the Einstein assertion that an indirect measurement is
> valid if it yields the same result as a direct measurement when confronted with
> relativistic measurements that are dilated and contracted.

No, what Einstein was describing in that little booklet was the meaning of space and time coordinates, saying that a direct measurement would be by an grid of rulers (and later, synchronized clocks) covering all of space and time, but in practice we obviously don't construct grids like this, we make indirect measurements (such as by remote optical means), but those indirect measurements must be made to yield what we would get by direct measurements with an complete grid of rulers and clocks at rest in some specified frame. So, for example, the spatial length of a given object in terms of S is the same, regardless of whether we use direct or indirect measurement. The mistake you are making is to think we get the same spatial length in terms of S' as we get in terms of S. That is obviously not what he is saying. In fact, he explained to the contrary the effects of length contraction, etc.

> ...the imaginary part is not visible, and even if it were, it is perpendicular to the real part,
> and its magnitude cannot contribute to the real magnitude.

Then it's not a scientific concept. Science is concerned only with things that are, at least in principle, observable. Science is not concerned with invisible pink elephants. Look, if you want to understand special relativity, you have to set aside your silly verbiage and actually learn about special relativity like a grown-up. See above. If you have any remaining questions, just ask.

On Sunday, 12 June 2022 at 08:43:36 UTC+2, Stan Fultoni wrote:

No, please try to concentrate: An inertia-based coordinate system is defined as one in which the equations of Newtonian mechanics hold good in the low speed limit.

It's not any definition.

> or example, we can inertially synchronize clocks by shooting identical bullets from identical guns *at rest* (low speed limit) at the mid point between the clocks. But once we've established our coordinate system and inertially synchronized our clocks, those coordinates cover every time and place, and they are perfectly valid to describe the trajectories of objects moving at arbitrary speeds, including the speed of light.

In the meantime in the real world, however, forbidden by your
insane religion GPS and TAI keep measuring t'=t, just like
all serious clocks always did.

> No, what Einstein was describing in that little booklet was the meaning of space and time coordinates, saying that a direct measurement would be by an grid of rulers

And what is the longest ruler you've seen, poor halfbrain?

> we obviously don't construct grids like this, we make indirect measurements (such as by remote optical means), but those indirect measurements must be made to yield what we would get by direct measurements with an complete grid of rulers and clocks at rest in some specified frame.

If a fanatic idiot is asserting - it must be true.

On Sunday, June 12, 2022 at 1:26:12 AM UTC-4, Thomas Heger wrote:
> Am 11.06.2022 um 08:34 schrieb Tom Capizzi:
> > On Saturday, June 11, 2022 at 12:47:33 AM UTC-4, Thomas Heger wrote:
> >> Am 10.06.2022 um 07:38 schrieb Maciej Wozniak:
> >>> On Friday, 10 June 2022 at 07:28:18 UTC+2, Thomas Heger wrote:
> >>>
> >>>> Appartently the universe 'speaks' in a mathematical language, which is
> >>>> also known as 'geometric algebra'.
> >>>
> >>> The universe is silent, like it always was. If you're
> >>> applying some mathematical language to it - that's
> >>> because you're trained to try.
> >>>
> >>>
> >> No, the universe is not silent.
> >>
> >> We see things all around us, which are somehow produced by the universe.
> >>
> >> Now we could think, the universe itself would operate on a mathematical
> >> foundation and acts like a large analoge computer.
> >>
> >> This was more or less my own assumption, which I have used in my 'book'
> >> about 'structured spacetime':
> >>
> >> https://docs.google.com/presentation/d/1Ur3_giuk2l439fxUa8QHX4wTDxBEaM6lOlgVUa0cFU4/edit?usp=sharing
> >>
> >>
> >>
> >> This concept works quite well and was based on the assumption, that the
> >> universe itself uses a certain kind of math, by which pointlike elements
> >> of spacetime are interconnected.
> >>
> >> This would create certain patterns, which we call 'matter' in case of
> >> they are timelike stable.
> >>
> >>
> >> It is actually a relatively simple concept, streight forward and based
> >> on a small set of plausible assumptions.
> >>
> >> The only problem is, that these assumptions are not very intuitive and
> >> difficult to understand.
> >>
> >>
> >>
> >> TH
> >
> > In my own musings, I have considered a similar system. I noticed that through several isomorphisms of spacetime coordinates (I say isomorphisms because there is no combination of Lorentz transforms that can map one to another) the invariant s² and the rapidity w were the same in all of the isomorphisms. I realized it was because s is the hyperbolic magnitude and rapidity is the hyperbolic rotation angle. They are the coordinates of a point in a Cartesian orthogonal coordinate system. Since this grid is orthogonal, the two coordinates are independent, resulting in what we call invariance. In other words, after passing local coordinates through the transform that maps hyperbolic coordinates to another frame, the relationship that restores the hyperbolic magnitude associated with any point in hyperbolic spacetime is just the inverse of the coordinate transform that created the map. Despite the fact that the axes are no longer orthogonal, the inverse transform reconstructs the hyperb
> olic magnitude. The property of invariance implies an isomorphism to hyperbolic trigonometry, in which hyperbolic magnitude and rotation angle are orthogonal. This seems to imply that the universe prefers hyperbolic coordinate systems. In the hyperbolic coordinate system, the Lorentz transform takes on an especially simple form. If the hyperbolic rotation angle is w, then w1 is initial angle, w2 is the angle associated with a Lorentz boost and w3 is the result. Then, (s,w3) = (0,w2) + (s,w1). In the Minkowski isomorphism, the first and last points are replaced by column vectors, and the boost is a 2x2 matrix. In the Euclidean isomorphism, the 2x2 matrix is diagonal, because the axes are the real eigenvectors of the Lorentz matrix. The elements of the diagonal matrix are the two real eigenvalues of the Lorentz matrix, while in the Minkowski isomorphism, the elements are hyperbolic functions of the rotation angle, the magnitude of which is the natural log of the eigenvalue. The interes
> ting thing about the eigenvector isomorphism is that it cannot be reached by any combination of Lorentz boosts. A single Lorentz boost can take a point that is stationary and boost it to any finite velocity, less than c. For the eigenvector frame to be unreachable by any combination of Lorentz boosts implies that it, like the eigenvectors which are the worldlines of photons, is the frame of lightspeed. How many questions have gone unanswered because we can't transform to the light frame? But this frame maps to both the hyperbolic grid and Minkowski spacetime. As isomorphisms, any disturbance in any one of them produces ripples in all of them. Not necessarily similar, though.
> >
> > What caught my attention was the idea of a set of points being in a fixed geometric pattern. Magnitudes in hyperbolic coordinates are unaffected by relative velocity. So a set of points in a line represents a set of magnitudes that all share the same velocity, and are invariant as a set over all rapidities. These could be structures like atoms or molecules. Does any of this sync with what you're doing?
> First:
>
> you should add some white space into your text, what would make it much
> more readable.
>
> Second:
>
> yes actually, but I had a different approach.
>
> I wanted to find use for a certain quaternion equation, because I wanted
> to take spacetime as real physical entity and model it as quaternion
> field. These 'elements of spacetime' are assumed to interact with their
> direct neighbors in a certain way, which generates certain patterns.
> These patterns are, what we regard as the real world, while they are in
> fact internal structure of spacetime.
>
>
> TH

I have also looked into quaternions. But my model of the universe requires more than 4 dimensions. One of the options is to extend the quaternions to 8 dimensions. There are two popular choices, the biquaternions and the octonions. At the beginning of relativity, it was actually modeled with biquaternions (in addition to quaternions). Much more recently, octonions have been demonstrated to exhibit the properties of subatomic particles. Although the octonion multiplication is commonly represented by the Fano plane (a triangle) or cube, they actually employ the same 8x8 checkerboard Cayley table as the biquaternions, and both are the same underlying table as the Walsh sequency multiplication table. The only difference is the pattern of minus signs in front of the product units, and the patterns of the minus signs are themselves Walsh sequencies. The Walsh table has no minus signs at all, and sequency multiplication is both commutative and associative, unlike the other two. The hypercomplex sets are both isomorphisms of the Walsh sequencies. It turns out that all of them are intimately related to the Klein 4-group, and the Sierpinski triangle and tetrahedron.

The Sierpinski figures can be generated by a number of different algorithms, but the one I prefer is Gray code, which is the XOR of a number with half of itself. For numbers represented in binary, like the ones and zeroes of the Sierpinski figures, that is essentially the XOR of adjacent bits, since half a binary number is just a right shift of 1 bit location. The XOR is also the operation that defines the Cayley table for Walsh sequencies, so it is also intimately associated with the hypercomplex algebras associated with relativity and quantum mechanics. I would say looking into interactions of direct neighbors is a productive line of research.

On Sunday, June 12, 2022 at 2:43:36 AM UTC-4, Stan Fultoni wrote:
> On Saturday, June 11, 2022 at 3:42:28 PM UTC-7, tgca...@gmail.com wrote:
> > The correct relativistic protocol for measurement is the Euclidean dot product.
> Again, that's a senseless string of words because a dot product is not a measurement procedure or protocol at all, nor is it a coordinate system. Those are completely different categories of things.
> > Rather than show how the dot product model leads to a contradiction, you
> > simply deny the model.
> No, I deny that your string of words *is* a model at all. It is nothing but an utterly senseless string of words. A dot product is not a measurement protocol. A dot product is a dot product. If you want to describe a "measurement protocol" that involves the concept of a dot product, then please do so.
> > The dot product is commonly used to determine the parallelness of two arbitrary vectors.
> Well, a grown-up person would say that, in a 3D Euclidean space, the dot product of two vectors (x1,y1,z1) and (x2,y2,z2) is simply the scalar x1x2+y1y2+z1z2, which equals |L1||L2|cos(q) where |L1|and |L2| are the magnitudes of the vectors and q is the angle between them. Two vectors are perpendicular if and only if their dot product vanishes. And so on. This is elementary grade school geometry, and it does not constitute a measurement protocol.. Obviously the coordinates of a point are the dot products of the displacement vector with the unit vectors on the coordinate axes. And so on. This, again, is just grade school geometry.
>
> > If one of the arbitrary vectors is a unit reference, then the result of the dot
> > product is the part of the other vector that is parallel to the reference unit?
> It's the projection of the vector onto the axis of the unit vector. Again, this is grade school geometry.
> > This is exactly what we get when we try to measure an arbitrary vector in a
> > relatively moving frame, because ct = γct' is the same equation as ct' = ct cos(tilt),
> > which is the result of the dot product of an arbitrary vector with a unit reference. cos(tilt) = 1/γ.
> No, that's utterly senseless. Using units so c=1, it is an empirical fact -- with which you have agreed repeatedly -- that the invariant inner product in flat 3+1 dimensional space and time of two vectors t1,x1,y1,z1 and t2,x2,y2,z2 is given by t1t2 - x1x2 - y1y2 - z1z2. Hence the inner product of a vector with itself is it's squared absolute magnitude, and two vectors are perpendicular if their inner product vanishes, and so on, analogous to the dot product in Euclidean geometry. As a result, the relationship between coordinates t,x,y,z of a given event in terms of S and the corresponding coordinates t',x',y',z' of that event in terms of S' (aligned and moving at speed v in the positive x direction) is t'=(t-vx)g, x'=(x-vt)g, y'=y, z'=z where g=1/sqrt(1-v^2). Remember?
>
> > I can apply any Lorentz transformation that I choose to an inertial frame...
>
> Sure you can, and the result is as noted above. What part of this do you dispute?
> > I did ask what you claim "to a first approximation" means. You alleged that it means
> > low speed approximation, but also assert that a low speed approximation is valid at
> > relativistic speeds.
> No, please try to concentrate: An inertia-based coordinate system is defined as one in which the equations of Newtonian mechanics hold good in the low speed limit. For example, we can inertially synchronize clocks by shooting identical bullets from identical guns *at rest* (low speed limit) at the mid point between the clocks. But once we've established our coordinate system and inertially synchronized our clocks, those coordinates cover every time and place, and they are perfectly valid to describe the trajectories of objects moving at arbitrary speeds, including the speed of light. Duh.
> > You simply ignore the Einstein assertion that an indirect measurement is
> > valid if it yields the same result as a direct measurement when confronted with
> > relativistic measurements that are dilated and contracted.
> No, what Einstein was describing in that little booklet was the meaning of space and time coordinates, saying that a direct measurement would be by an grid of rulers (and later, synchronized clocks) covering all of space and time, but in practice we obviously don't construct grids like this, we make indirect measurements (such as by remote optical means), but those indirect measurements must be made to yield what we would get by direct measurements with an complete grid of rulers and clocks at rest in some specified frame. So, for example, the spatial length of a given object in terms of S is the same, regardless of whether we use direct or indirect measurement. The mistake you are making is to think we get the same spatial length in terms of S' as we get in terms of S. That is obviously not what he is saying. In fact, he explained to the contrary the effects of length contraction, etc..
>
> > ...the imaginary part is not visible, and even if it were, it is perpendicular to the real part,
> > and its magnitude cannot contribute to the real magnitude.
> Then it's not a scientific concept. Science is concerned only with things that are, at least in principle, observable. Science is not concerned with invisible pink elephants. Look, if you want to understand special relativity, you have to set aside your silly verbiage and actually learn about special relativity like a grown-up. See above. If you have any remaining questions, just ask.

More rubbish. If I have any questions, I use an authoritative source, not your blathering. Your strong point appears to be ad hominem attacks on people you disagree with. That's not logic or science.

On Sunday, June 12, 2022 at 2:43:36 AM UTC-4, Stan Fultoni wrote:
> On Saturday, June 11, 2022 at 3:42:28 PM UTC-7, tgca...@gmail.com wrote:
> > The correct relativistic protocol for measurement is the Euclidean dot product.
> Again, that's a senseless string of words because a dot product is not a measurement procedure or protocol at all, nor is it a coordinate system. Those are completely different categories of things.
> > Rather than show how the dot product model leads to a contradiction, you
> > simply deny the model.
> No, I deny that your string of words *is* a model at all. It is nothing but an utterly senseless string of words. A dot product is not a measurement protocol. A dot product is a dot product. If you want to describe a "measurement protocol" that involves the concept of a dot product, then please do so.
> > The dot product is commonly used to determine the parallelness of two arbitrary vectors.
> Well, a grown-up person would say that, in a 3D Euclidean space, the dot product of two vectors (x1,y1,z1) and (x2,y2,z2) is simply the scalar x1x2+y1y2+z1z2, which equals |L1||L2|cos(q) where |L1|and |L2| are the magnitudes of the vectors and q is the angle between them. Two vectors are perpendicular if and only if their dot product vanishes. And so on. This is elementary grade school geometry, and it does not constitute a measurement protocol.. Obviously the coordinates of a point are the dot products of the displacement vector with the unit vectors on the coordinate axes. And so on. This, again, is just grade school geometry.
>
> > If one of the arbitrary vectors is a unit reference, then the result of the dot
> > product is the part of the other vector that is parallel to the reference unit?
> It's the projection of the vector onto the axis of the unit vector. Again, this is grade school geometry.
> > This is exactly what we get when we try to measure an arbitrary vector in a
> > relatively moving frame, because ct = γct' is the same equation as ct' = ct cos(tilt),
> > which is the result of the dot product of an arbitrary vector with a unit reference. cos(tilt) = 1/γ.
> No, that's utterly senseless. Using units so c=1, it is an empirical fact -- with which you have agreed repeatedly -- that the invariant inner product in flat 3+1 dimensional space and time of two vectors t1,x1,y1,z1 and t2,x2,y2,z2 is given by t1t2 - x1x2 - y1y2 - z1z2. Hence the inner product of a vector with itself is it's squared absolute magnitude, and two vectors are perpendicular if their inner product vanishes, and so on, analogous to the dot product in Euclidean geometry. As a result, the relationship between coordinates t,x,y,z of a given event in terms of S and the corresponding coordinates t',x',y',z' of that event in terms of S' (aligned and moving at speed v in the positive x direction) is t'=(t-vx)g, x'=(x-vt)g, y'=y, z'=z where g=1/sqrt(1-v^2). Remember?
>
> > I can apply any Lorentz transformation that I choose to an inertial frame...
>
> Sure you can, and the result is as noted above. What part of this do you dispute?
> > I did ask what you claim "to a first approximation" means. You alleged that it means
> > low speed approximation, but also assert that a low speed approximation is valid at
> > relativistic speeds.
> No, please try to concentrate: An inertia-based coordinate system is defined as one in which the equations of Newtonian mechanics hold good in the low speed limit. For example, we can inertially synchronize clocks by shooting identical bullets from identical guns *at rest* (low speed limit) at the mid point between the clocks. But once we've established our coordinate system and inertially synchronized our clocks, those coordinates cover every time and place, and they are perfectly valid to describe the trajectories of objects moving at arbitrary speeds, including the speed of light. Duh.
> > You simply ignore the Einstein assertion that an indirect measurement is
> > valid if it yields the same result as a direct measurement when confronted with
> > relativistic measurements that are dilated and contracted.
> No, what Einstein was describing in that little booklet was the meaning of space and time coordinates, saying that a direct measurement would be by an grid of rulers (and later, synchronized clocks) covering all of space and time, but in practice we obviously don't construct grids like this, we make indirect measurements (such as by remote optical means), but those indirect measurements must be made to yield what we would get by direct measurements with an complete grid of rulers and clocks at rest in some specified frame. So, for example, the spatial length of a given object in terms of S is the same, regardless of whether we use direct or indirect measurement. The mistake you are making is to think we get the same spatial length in terms of S' as we get in terms of S. That is obviously not what he is saying. In fact, he explained to the contrary the effects of length contraction, etc..
>
> > ...the imaginary part is not visible, and even if it were, it is perpendicular to the real part,
> > and its magnitude cannot contribute to the real magnitude.
> Then it's not a scientific concept. Science is concerned only with things that are, at least in principle, observable. Science is not concerned with invisible pink elephants. Look, if you want to understand special relativity, you have to set aside your silly verbiage and actually learn about special relativity like a grown-up. See above. If you have any remaining questions, just ask.

More rubbish, from the "expert":
"No, that's utterly senseless. Using units so c=1, it is an empirical fact -- with which you have agreed repeatedly -- that the invariant inner product in flat 3+1 dimensional space and time of two vectors t1,x1,y1,z1 and t2,x2,y2,z2 is given by t1t2 - x1x2 - y1y2 - z1z2. Hence the inner product of a vector with itself is it's squared absolute magnitude, and two vectors are perpendicular if their inner product vanishes, and so on, analogous to the dot product in Euclidean geometry."
In the first place, I have only agreed in your imagination. Second, you have defined the so-called inner product in Minkowski geometry, not Euclidean. Third, the inner product of a vector with itself in Euclidean geometry is positive definite. The dot product is allowed to be positive negative or 0, not the inner product. In any case, this gobbledegook has nothing to do with my statement of fact, "ct = γct' is the same equation as ct' = ct cos(tilt)".

On Sunday, June 12, 2022 at 2:43:36 AM UTC-4, Stan Fultoni wrote:
> On Saturday, June 11, 2022 at 3:42:28 PM UTC-7, tgca...@gmail.com wrote:
> > The correct relativistic protocol for measurement is the Euclidean dot product.
> Again, that's a senseless string of words because a dot product is not a measurement procedure or protocol at all, nor is it a coordinate system. Those are completely different categories of things.
> > Rather than show how the dot product model leads to a contradiction, you
> > simply deny the model.
> No, I deny that your string of words *is* a model at all. It is nothing but an utterly senseless string of words. A dot product is not a measurement protocol. A dot product is a dot product. If you want to describe a "measurement protocol" that involves the concept of a dot product, then please do so.
> > The dot product is commonly used to determine the parallelness of two arbitrary vectors.
> Well, a grown-up person would say that, in a 3D Euclidean space, the dot product of two vectors (x1,y1,z1) and (x2,y2,z2) is simply the scalar x1x2+y1y2+z1z2, which equals |L1||L2|cos(q) where |L1|and |L2| are the magnitudes of the vectors and q is the angle between them. Two vectors are perpendicular if and only if their dot product vanishes. And so on. This is elementary grade school geometry, and it does not constitute a measurement protocol.. Obviously the coordinates of a point are the dot products of the displacement vector with the unit vectors on the coordinate axes. And so on. This, again, is just grade school geometry.
>
> > If one of the arbitrary vectors is a unit reference, then the result of the dot
> > product is the part of the other vector that is parallel to the reference unit?
> It's the projection of the vector onto the axis of the unit vector. Again, this is grade school geometry.
> > This is exactly what we get when we try to measure an arbitrary vector in a
> > relatively moving frame, because ct = γct' is the same equation as ct' = ct cos(tilt),
> > which is the result of the dot product of an arbitrary vector with a unit reference. cos(tilt) = 1/γ.
> No, that's utterly senseless. Using units so c=1, it is an empirical fact -- with which you have agreed repeatedly -- that the invariant inner product in flat 3+1 dimensional space and time of two vectors t1,x1,y1,z1 and t2,x2,y2,z2 is given by t1t2 - x1x2 - y1y2 - z1z2. Hence the inner product of a vector with itself is it's squared absolute magnitude, and two vectors are perpendicular if their inner product vanishes, and so on, analogous to the dot product in Euclidean geometry. As a result, the relationship between coordinates t,x,y,z of a given event in terms of S and the corresponding coordinates t',x',y',z' of that event in terms of S' (aligned and moving at speed v in the positive x direction) is t'=(t-vx)g, x'=(x-vt)g, y'=y, z'=z where g=1/sqrt(1-v^2). Remember?
>
> > I can apply any Lorentz transformation that I choose to an inertial frame...
>
> Sure you can, and the result is as noted above. What part of this do you dispute?
> > I did ask what you claim "to a first approximation" means. You alleged that it means
> > low speed approximation, but also assert that a low speed approximation is valid at
> > relativistic speeds.
> No, please try to concentrate: An inertia-based coordinate system is defined as one in which the equations of Newtonian mechanics hold good in the low speed limit. For example, we can inertially synchronize clocks by shooting identical bullets from identical guns *at rest* (low speed limit) at the mid point between the clocks. But once we've established our coordinate system and inertially synchronized our clocks, those coordinates cover every time and place, and they are perfectly valid to describe the trajectories of objects moving at arbitrary speeds, including the speed of light. Duh.
> > You simply ignore the Einstein assertion that an indirect measurement is
> > valid if it yields the same result as a direct measurement when confronted with
> > relativistic measurements that are dilated and contracted.
> No, what Einstein was describing in that little booklet was the meaning of space and time coordinates, saying that a direct measurement would be by an grid of rulers (and later, synchronized clocks) covering all of space and time, but in practice we obviously don't construct grids like this, we make indirect measurements (such as by remote optical means), but those indirect measurements must be made to yield what we would get by direct measurements with an complete grid of rulers and clocks at rest in some specified frame. So, for example, the spatial length of a given object in terms of S is the same, regardless of whether we use direct or indirect measurement. The mistake you are making is to think we get the same spatial length in terms of S' as we get in terms of S. That is obviously not what he is saying. In fact, he explained to the contrary the effects of length contraction, etc..
>
> > ...the imaginary part is not visible, and even if it were, it is perpendicular to the real part,
> > and its magnitude cannot contribute to the real magnitude.
> Then it's not a scientific concept. Science is concerned only with things that are, at least in principle, observable. Science is not concerned with invisible pink elephants. Look, if you want to understand special relativity, you have to set aside your silly verbiage and actually learn about special relativity like a grown-up. See above. If you have any remaining questions, just ask.
How long has science recognized the existence of atoms? When was the 1st atom actually observed? Your argument is bullshit. For your information, not that it matters, I got an A in my college course on relativity. I think I understand special relativity. Nevertheless, I think it is a false theory based on false assumptions. And if what you claim about science is true, science is incomplete. Quantum mechanics uses imaginary geometry whenever it fits, but claims that the mathematical description of electron spin, for example, is not physical spin. I submit that it is physical spin in imaginary dimensions. Prove otherwise. I assume you would argue, without proof, that it is just a coincidence that the equations of physical spin just happen to agree with the subatomic properties. There are no coincidences.

On Sunday, June 12, 2022 at 2:43:36 AM UTC-4, Stan Fultoni wrote:
> On Saturday, June 11, 2022 at 3:42:28 PM UTC-7, tgca...@gmail.com wrote:
> > The correct relativistic protocol for measurement is the Euclidean dot product.
> Again, that's a senseless string of words because a dot product is not a measurement procedure or protocol at all, nor is it a coordinate system. Those are completely different categories of things.
> > Rather than show how the dot product model leads to a contradiction, you
> > simply deny the model.
> No, I deny that your string of words *is* a model at all. It is nothing but an utterly senseless string of words. A dot product is not a measurement protocol. A dot product is a dot product. If you want to describe a "measurement protocol" that involves the concept of a dot product, then please do so.
> > The dot product is commonly used to determine the parallelness of two arbitrary vectors.
> Well, a grown-up person would say that, in a 3D Euclidean space, the dot product of two vectors (x1,y1,z1) and (x2,y2,z2) is simply the scalar x1x2+y1y2+z1z2, which equals |L1||L2|cos(q) where |L1|and |L2| are the magnitudes of the vectors and q is the angle between them. Two vectors are perpendicular if and only if their dot product vanishes. And so on. This is elementary grade school geometry, and it does not constitute a measurement protocol.. Obviously the coordinates of a point are the dot products of the displacement vector with the unit vectors on the coordinate axes. And so on. This, again, is just grade school geometry.
>
> > If one of the arbitrary vectors is a unit reference, then the result of the dot
> > product is the part of the other vector that is parallel to the reference unit?
> It's the projection of the vector onto the axis of the unit vector. Again, this is grade school geometry.
> > This is exactly what we get when we try to measure an arbitrary vector in a
> > relatively moving frame, because ct = γct' is the same equation as ct' = ct cos(tilt),
> > which is the result of the dot product of an arbitrary vector with a unit reference. cos(tilt) = 1/γ.
> No, that's utterly senseless. Using units so c=1, it is an empirical fact -- with which you have agreed repeatedly -- that the invariant inner product in flat 3+1 dimensional space and time of two vectors t1,x1,y1,z1 and t2,x2,y2,z2 is given by t1t2 - x1x2 - y1y2 - z1z2. Hence the inner product of a vector with itself is it's squared absolute magnitude, and two vectors are perpendicular if their inner product vanishes, and so on, analogous to the dot product in Euclidean geometry. As a result, the relationship between coordinates t,x,y,z of a given event in terms of S and the corresponding coordinates t',x',y',z' of that event in terms of S' (aligned and moving at speed v in the positive x direction) is t'=(t-vx)g, x'=(x-vt)g, y'=y, z'=z where g=1/sqrt(1-v^2). Remember?
>
> > I can apply any Lorentz transformation that I choose to an inertial frame...
>
> Sure you can, and the result is as noted above. What part of this do you dispute?
> > I did ask what you claim "to a first approximation" means. You alleged that it means
> > low speed approximation, but also assert that a low speed approximation is valid at
> > relativistic speeds.
> No, please try to concentrate: An inertia-based coordinate system is defined as one in which the equations of Newtonian mechanics hold good in the low speed limit. For example, we can inertially synchronize clocks by shooting identical bullets from identical guns *at rest* (low speed limit) at the mid point between the clocks. But once we've established our coordinate system and inertially synchronized our clocks, those coordinates cover every time and place, and they are perfectly valid to describe the trajectories of objects moving at arbitrary speeds, including the speed of light. Duh.
> > You simply ignore the Einstein assertion that an indirect measurement is
> > valid if it yields the same result as a direct measurement when confronted with
> > relativistic measurements that are dilated and contracted.
> No, what Einstein was describing in that little booklet was the meaning of space and time coordinates, saying that a direct measurement would be by an grid of rulers (and later, synchronized clocks) covering all of space and time, but in practice we obviously don't construct grids like this, we make indirect measurements (such as by remote optical means), but those indirect measurements must be made to yield what we would get by direct measurements with an complete grid of rulers and clocks at rest in some specified frame. So, for example, the spatial length of a given object in terms of S is the same, regardless of whether we use direct or indirect measurement. The mistake you are making is to think we get the same spatial length in terms of S' as we get in terms of S. That is obviously not what he is saying. In fact, he explained to the contrary the effects of length contraction, etc..
>
> > ...the imaginary part is not visible, and even if it were, it is perpendicular to the real part,
> > and its magnitude cannot contribute to the real magnitude.
> Then it's not a scientific concept. Science is concerned only with things that are, at least in principle, observable. Science is not concerned with invisible pink elephants. Look, if you want to understand special relativity, you have to set aside your silly verbiage and actually learn about special relativity like a grown-up. See above. If you have any remaining questions, just ask.
Here's another gem:
" the spatial length of a given object in terms of S is the same, regardless of whether we use direct or indirect measurement." and
" a direct measurement would be by an grid of rulers (and later, synchronized clocks) covering all of space and time, but in practice we obviously don't construct grids like this, we make indirect measurements "
The corollary is that it is impossible to make a direct measurement of an object in a relatively moving frame. My point is simply that indirect measurements only agree with direct measurements in quasistatic frames. Otherwise, indirect measurement methods that are valid for quasistatic velocities, are not accurate for relativistic velocities. They may represent all that we can see, but we cannot see all that there is to see.

On Sunday, June 12, 2022 at 10:54:12 AM UTC-7, tgca...@gmail.com wrote:
> If I have any questions, I use an authoritative source, not your blathering.

Science isn't about authority, it's about understanding. I've patiently answered each of your questions and provided you with clear and thorough explanations of each of each of the topics you've raised (you're welcome), and your reaction is to cover your ears and run away. Why not actually engage in a substantive discussion, by responding to the careful answers and explanations that are provided to you?

> > No, that's utterly senseless. Using units so c=1, it is an empirical fact -- with which you have
> > agreed repeatedly -- that the invariant inner product in flat 3+1 dimensional space and time
> > of two vectors t1,x1,y1,z1 and t2,x2,y2,z2 is given by t1t2 - x1x2 - y1y2 - z1z2.
>
> I have only agreed in your imagination.

Not true, you've stated repeatedly that you agree with all the empirical predictions of special relativity, among which is the fact stated above, so you have indeed agreed with it. Of course, you also disagree with it... your statements are highly self-contradictory.

> > Hence the inner product of a vector with itself is it's squared absolute magnitude,
> > and two vectors are perpendicular if their inner product vanishes, and so on, analogous
> > to the dot product in Euclidean geometry."
>
> You have defined the so-called inner product in Minkowski geometry, not Euclidean.

Again, the invariant spacetime intervals are among the empirically verified facts with which you have claimed to agree. If you are not saying that you deny the empirical facts, then your beliefs are falsified. Remember, time is not the same as space, and the time dimension is not the same as a space dimension. Yes, 3+1 dimensional manifold is analogous to a purely spatial manifold, but it is not the same, and does not even have a true metrical character, it is a pseudo-metrical manifold. That's why the transformations are hyperbolic rotations rather than Euclidean rotations.

> The inner product of a vector with itself in Euclidean geometry is positive definite.

Right, whereas the inner-product in spacetime is not, which is precisely why it is a pseudo-metric manifold (triangle inequality not satisfied, etc.).

> The dot product is allowed to be positive negative or 0, not the inner product.

Huh? You contradict yourself. As you said above, the dot product in Euclidean space is positive definite.

> This gobbledegook

These are simple statements of fact, none of which you have even attempted to refute, so it is senseless to refer to it as gobbledegook.

> has nothing to do with my statement of fact, "ct = γct' is the same equation as ct' = ct cos(tilt)".

Now *that* is an example of gobbledegook, because the correct relationship between x,t and x',t' as you have agreed repeatedly (see above) is t'=(t-vx)g, x'=(x-vt)g where g=1/sqrt(1-v^2). Naturally we can express this in terms of hyperbolic trig functions as t'=sinh(q)x + cosh(q)t, x'=cosh(q)x - sinh(q)t. Do you understand this?

> I think I understand special relativity.

But we've seen here in this discussion that all your beliefs about special relativity are fundamentally wrong. You totally misunderstand it.

> > a direct measurement would be by an grid of rulers (and later, synchronized clocks)
> > covering all of space and time, but in practice we obviously don't construct grids like
> > this, we make indirect measurements...
>
> The corollary is that it is impossible to make a direct measurement of an object
> in a relatively moving frame.

No, that is incorrect. We can certainly make measurements with a grid of standard rulers and clocks, but in practice we find other ways to make measures that give the same results as measurements with a grid. There is more than one way of measuring things, but the point is that they must accurately measure the thing, and "the thing" is defined as what you would get with a grid of rulers and clocks. This is absolutely fundamental... you simply must try to understand this, since it is the basis for all of science for the past 400 years.

> My point is simply that indirect measurements only agree with direct measurements
> in quasistatic frames.

No, that is utterly wrong -- on multiple levels. Look, to get started thinking rationally, just focus on grids of standard rulers and clocks, all mutually at rest and inertially synchronized. There is no reason in principle why you would ever need to measure things in any other way. The entire subject and the descriptions of all phenomena can be perfectly well expressed in terms of such measurements. The class of other experimental techniques that have been shown to yield identical results can then be the subject of your later studies, but learning about those alternative (cheaper, easier to construct) experimental techniques is not fundamental to understanding the subject.

On Sunday, 12 June 2022 at 20:50:06 UTC+2, Stan Fultoni wrote:

> Again, the invariant spacetime intervals are among the empirically verified facts

gedanken by some insane fanatics.

> No, that is incorrect. We can certainly make measurements with a grid of standard rulers and clocks

And what is the longest ruler you've ever seen,
poor idiot?

On Sunday, June 12, 2022 at 2:50:06 PM UTC-4, Stan Fultoni wrote:
> On Sunday, June 12, 2022 at 10:54:12 AM UTC-7, tgca...@gmail.com wrote:
> > If I have any questions, I use an authoritative source, not your blathering.
> Science isn't about authority, it's about understanding. I've patiently answered each of your questions and provided you with clear and thorough explanations of each of each of the topics you've raised (you're welcome), and your reaction is to cover your ears and run away. Why not actually engage in a substantive discussion, by responding to the careful answers and explanations that are provided to you?
> > > No, that's utterly senseless. Using units so c=1, it is an empirical fact -- with which you have
> > > agreed repeatedly -- that the invariant inner product in flat 3+1 dimensional space and time
> > > of two vectors t1,x1,y1,z1 and t2,x2,y2,z2 is given by t1t2 - x1x2 - y1y2 - z1z2.
> >
> > I have only agreed in your imagination.
> Not true, you've stated repeatedly that you agree with all the empirical predictions of special relativity, among which is the fact stated above, so you have indeed agreed with it. Of course, you also disagree with it... your statements are highly self-contradictory.
> > > Hence the inner product of a vector with itself is it's squared absolute magnitude,
> > > and two vectors are perpendicular if their inner product vanishes, and so on, analogous
> > > to the dot product in Euclidean geometry."
> >
> > You have defined the so-called inner product in Minkowski geometry, not Euclidean.
>
> Again, the invariant spacetime intervals are among the empirically verified facts with which you have claimed to agree. If you are not saying that you deny the empirical facts, then your beliefs are falsified. Remember, time is not the same as space, and the time dimension is not the same as a space dimension. Yes, 3+1 dimensional manifold is analogous to a purely spatial manifold, but it is not the same, and does not even have a true metrical character, it is a pseudo-metrical manifold. That's why the transformations are hyperbolic rotations rather than Euclidean rotations.
>
> > The inner product of a vector with itself in Euclidean geometry is positive definite.
>
> Right, whereas the inner-product in spacetime is not, which is precisely why it is a pseudo-metric manifold (triangle inequality not satisfied, etc.).
> > The dot product is allowed to be positive negative or 0, not the inner product.
> Huh? You contradict yourself. As you said above, the dot product in Euclidean space is positive definite.
>
> > This gobbledegook
>
> These are simple statements of fact, none of which you have even attempted to refute, so it is senseless to refer to it as gobbledegook.
>
> > has nothing to do with my statement of fact, "ct = γct' is the same equation as ct' = ct cos(tilt)".
>
> Now *that* is an example of gobbledegook, because the correct relationship between x,t and x',t' as you have agreed repeatedly (see above) is t'=(t-vx)g, x'=(x-vt)g where g=1/sqrt(1-v^2). Naturally we can express this in terms of hyperbolic trig functions as t'=sinh(q)x + cosh(q)t, x'=cosh(q)x - sinh(q)t. Do you understand this?
> > I think I understand special relativity.
> But we've seen here in this discussion that all your beliefs about special relativity are fundamentally wrong. You totally misunderstand it.
> > > a direct measurement would be by an grid of rulers (and later, synchronized clocks)
> > > covering all of space and time, but in practice we obviously don't construct grids like
> > > this, we make indirect measurements...
> >
> > The corollary is that it is impossible to make a direct measurement of an object
> > in a relatively moving frame.
> No, that is incorrect. We can certainly make measurements with a grid of standard rulers and clocks, but in practice we find other ways to make measures that give the same results as measurements with a grid. There is more than one way of measuring things, but the point is that they must accurately measure the thing, and "the thing" is defined as what you would get with a grid of rulers and clocks. This is absolutely fundamental... you simply must try to understand this, since it is the basis for all of science for the past 400 years.
> > My point is simply that indirect measurements only agree with direct measurements
> > in quasistatic frames.
> No, that is utterly wrong -- on multiple levels. Look, to get started thinking rationally, just focus on grids of standard rulers and clocks, all mutually at rest and inertially synchronized. There is no reason in principle why you would ever need to measure things in any other way. The entire subject and the descriptions of all phenomena can be perfectly well expressed in terms of such measurements. The class of other experimental techniques that have been shown to yield identical results can then be the subject of your later studies, but learning about those alternative (cheaper, easier to construct) experimental techniques is not fundamental to understanding the subject.
I will waste no more of my time. You misrepresent what I say or simply deny it for specious reasons. So much circular logic. I can sum up your position as "It is what it is because that's what it is." Brilliant!

On Sunday, June 12, 2022 at 5:27:38 PM UTC-7, tgca...@gmail.com wrote:
> On Sunday, June 12, 2022 at 2:50:06 PM UTC-4, Stan Fultoni wrote:
> > On Sunday, June 12, 2022 at 10:54:12 AM UTC-7, tgca...@gmail.com wrote:
> > > If I have any questions, I use an authoritative source, not your blathering.
> > Science isn't about authority, it's about understanding. I've patiently answered each of your questions and provided you with clear and thorough explanations of each of each of the topics you've raised (you're welcome), and your reaction is to cover your ears and run away. Why not actually engage in a substantive discussion, by responding to the careful answers and explanations that are provided to you?
> > > > No, that's utterly senseless. Using units so c=1, it is an empirical fact -- with which you have
> > > > agreed repeatedly -- that the invariant inner product in flat 3+1 dimensional space and time
> > > > of two vectors t1,x1,y1,z1 and t2,x2,y2,z2 is given by t1t2 - x1x2 - y1y2 - z1z2.
> > >
> > > I have only agreed in your imagination.
> > Not true, you've stated repeatedly that you agree with all the empirical predictions of special relativity, among which is the fact stated above, so you have indeed agreed with it. Of course, you also disagree with it... your statements are highly self-contradictory.
> > > > Hence the inner product of a vector with itself is it's squared absolute magnitude,
> > > > and two vectors are perpendicular if their inner product vanishes, and so on, analogous
> > > > to the dot product in Euclidean geometry."
> > >
> > > You have defined the so-called inner product in Minkowski geometry, not Euclidean.
> >
> > Again, the invariant spacetime intervals are among the empirically verified facts with which you have claimed to agree. If you are not saying that you deny the empirical facts, then your beliefs are falsified. Remember, time is not the same as space, and the time dimension is not the same as a space dimension. Yes, 3+1 dimensional manifold is analogous to a purely spatial manifold, but it is not the same, and does not even have a true metrical character, it is a pseudo-metrical manifold. That's why the transformations are hyperbolic rotations rather than Euclidean rotations.
> >
> > > The inner product of a vector with itself in Euclidean geometry is positive definite.
> >
> > Right, whereas the inner-product in spacetime is not, which is precisely why it is a pseudo-metric manifold (triangle inequality not satisfied, etc.).
> > > The dot product is allowed to be positive negative or 0, not the inner product.
> > Huh? You contradict yourself. As you said above, the dot product in Euclidean space is positive definite.
> >
> > > This gobbledegook
> >
> > These are simple statements of fact, none of which you have even attempted to refute, so it is senseless to refer to it as gobbledegook.
> >
> > > has nothing to do with my statement of fact, "ct = γct' is the same equation as ct' = ct cos(tilt)".
> >
> > Now *that* is an example of gobbledegook, because the correct relationship between x,t and x',t' as you have agreed repeatedly (see above) is t'=(t-vx)g, x'=(x-vt)g where g=1/sqrt(1-v^2). Naturally we can express this in terms of hyperbolic trig functions as t'=sinh(q)x + cosh(q)t, x'=cosh(q)x - sinh(q)t. Do you understand this?
> > > I think I understand special relativity.
> > But we've seen here in this discussion that all your beliefs about special relativity are fundamentally wrong. You totally misunderstand it.
> > > > a direct measurement would be by an grid of rulers (and later, synchronized clocks)
> > > > covering all of space and time, but in practice we obviously don't construct grids like
> > > > this, we make indirect measurements...
> > >
> > > The corollary is that it is impossible to make a direct measurement of an object
> > > in a relatively moving frame.
> > No, that is incorrect. We can certainly make measurements with a grid of standard rulers and clocks, but in practice we find other ways to make measures that give the same results as measurements with a grid. There is more than one way of measuring things, but the point is that they must accurately measure the thing, and "the thing" is defined as what you would get with a grid of rulers and clocks. This is absolutely fundamental... you simply must try to understand this, since it is the basis for all of science for the past 400 years.
> > > My point is simply that indirect measurements only agree with direct measurements
> > > in quasistatic frames.
> > No, that is utterly wrong -- on multiple levels. Look, to get started thinking rationally, just focus on grids of standard rulers and clocks, all mutually at rest and inertially synchronized. There is no reason in principle why you would ever need to measure things in any other way. The entire subject and the descriptions of all phenomena can be perfectly well expressed in terms of such measurements. The class of other experimental techniques that have been shown to yield identical results can then be the subject of your later studies, but learning about those alternative (cheaper, easier to construct) experimental techniques is not fundamental to understanding the subject.
>
> You misrepresent what I say or simply deny it for specious reasons.

I have not misrepresented anything you have said I have quoted you verbatim, and then I've carefully and patiently explain why what you've said is wrong. (You're welcome.) If you think I have misrepsented something you have said, go ahead and point it out.

> I can sum up your position as "It is what it is because that's what it is.."

What on earth are you talking about? You have not asked me to explain *why* the universe is locally Lorentz invariant, you have simply expressed a load of misconceptions about what local Lorentz invariance means, and I've been explaining what it means. Before you can understand why the world is Lorentz invariant -- or claim that it isn't -- you must first understand what Lorentz invariance means, i.e., the objective empirical facts.

Look, your idiocy boils down to your claim that the expression ct = γct' is the same as the expression ct' = ct cos(tilt)", which just amounts to the claim that sqrt(1-v^2) = cos(tilt), which amounts to the claim that v = sin(tilt), so all you are doing is defining the term "tilt" as invsin(v). The silliness of this is exceed only by its utter pointlessness.. It what not represent any kind of theory, nor even an interpretation. You are just defining a useless symbol in a senseless way.

Meanwhile, the empirical fact is that x,t and x',t' are related by t'=(t-vx)g, x'=(x-vt)g where g=1/sqrt(1-v^2). Naturally we can express this in terms of hyperbolic trig functions as t'=sinh(q)x + cosh(q)t, x'=cosh(q)x - sinh(q)t. This is a hyperbolic rotation. Do you dispute this?