It occurred to me that my exposition of Euclidean Relativity was unintentionally skewed into Cartesian coordinates. There are circles in Euclidean geometry, and when dealing with radially symmetric properties, polar coordinates are more fitting. Using spherical geometry, a point on a shell can be viewed as the sum of a 0-phase linear radius and the sum of circular arcs embedded in the surface. We will associate circular arcs with relative velocity, an arbitrary quantity. The linear radius will be associated with the Galilean coordinates. This vector is independent of the circular component, so it is invariant in magnitude with respect to the relative velocity. But when we try to measure it, it gives the illusion of being shorter. In this post, I explore the nature of multi-dimensional units and the paradoxical situation of multiple different measurements, and how they coexist with resting measurements.

Working in Euclidean geometry does not mean Cartesian, however. Symmetry, especially cyclic symmetry, is better represented by circles. We normally think of a vector as the displacement between two points. It is literally a function of just the endpoints. But the distance between those two points can be anything greater than or equal to the vector magnitude. It is a function of the path itself. We are interested in a set of paths that have very specific symmetry. What they have in common is the magnitude of the radius to the spherical surface that they intersect. The grid on these shells is formed by latitude and longitude lines, and position is specified by two angles. At angles between the two grid lines, the curves are loxodromes, because all these curves on the surface of the sphere map to Mercator's rectangular grid as straight lines.

For the spirals, arclength from pole to pole depends on the tilt angle of the spiral and the corresponding line to the vertical. At 0 tilt, the arclength is πr. When the tilt angle is not 0, the arclength is increased by the secant of the tilt angle. Arclength, in general, is proportional to the radius for two similar curves. Specifically, because of the linearity of addition, 2 spirals of half the diameter will have the same total arclength projections in both directions. Or n spirals of diameter 2r/n will still have the same size projections. In the limit, as n approaches infinity, the arc length from pole to pole is still πr sec(tilt), but the initial diameter of a single spiral at the equator reduces as 1/n, and asymptotically approaches 0. So, what we have is a line which is longer than it looks, longer than it measures, and while the displacement between the endpoints is the same in all cases, the effective radius of the spiral depends on the secant of the tilt angle. All we have to do is identify the relative velocity as c sin(tilt) with an associated Lorentz factor of sec(tilt) = γ, and you've got special relativity's time dilation or length contraction. The arclength remained constant, but the tilt angle changed, causing the spiral to tighten up, and the measured distance from pole to pole to shrink, because the arclength is invariant.

3D rotational symmetry carries a single radius vector to all the other locations on the surface of the unit radius sphere. Since none of these directions is privileged, it is only necessary to model one of them. Before getting into the details of the spirals, let's consider the spherical shells alone. We have a main axis that is horizontal. It represents every radius vector. The sphere between the origin and the shell is the cosine projection of the larger sphere, using the origin as the stereographic projection point. Similarly, any sphere anywhere represents a stereographic projection of a larger sphere along an axis of symmetry. And we can always rotate an axis of symmetry to be parallel to our baseline. Then the stereographic projection ray tilts away from the axis of symmetry and rotates around it. Since the smaller sphere is the cosine projection of the larger one, the larger one is the secant projection along the same ray. The interesting thing is that when we project both curves with the same projection cosine, the smaller shell turns into the larger shell, and the larger shell turns into the tangent plane. And if we treat the tangent plane as the cosine projection of the baseline coordinate, the curve that projected it is the unit hyperbola. The important thing to note is that all these geometries incrementally morph into each other just by using fractional powers of the scale factor, γ.

Applying this geometry to velocity, the point on the hyperbola has the coordinates of 4-velocity. The cosine projection of the Proper velocity in time is the constant velocity of c. The point on the tangent represents Proper velocity in space. This represents total relativistic velocity of an inertial frame. The cosine projection of Proper velocity is Newtonian velocity. The sine projection is responsible for excess relativistic momentum. The point represents an arbitrary, inertial laborarory frame. It is the cosine projection of the vector to the point on the hyperbola: (γc,βγc) cos(θ) = (c,βc) = (c,v). This vector illustrates the gudermannian. The slope of the line through these two points is the same at both of them. At the extreme end, the coordinates are (c*cosh(w),c*sinh(w)), while the coordinates of the lab frame are (c,c sin(θ)) = (c,v). The slope at the endpoint is sinh(w)/cosh(w) = tanh(w), while the slope at the lab point is sin(θ)/1. When θ = gudermannian(w), tanh(w) = sin(θ).

The abscissa here is the rapidity, w, and it is allowed to range from minus infinity to plus infinity. These two extreme points map to minus π/2 to plus π/2. All the finite values of w between those two limits map to tilt angles of less than π/2 in magnitude.

New graphic

The complexified unit. It is a curved hyperplane, a cone. In spite of rationalizations about subjective and objective reality, the measurements made by a co-moving observer are different from measurements made by any moving observer. If you believe in the reliability of measurements, then these two observers are simply not measuring the same thing. And yet they are. The resolution of this paradox is that the unit they are trying to measure is more than 1 dimensional. The moving observer is measuring the displacement vector between the two endpoints. The co-moving observer is measuring the distance along the vector. This distance is identical to the displacement projection when relative velocity is << c. But, like Newtonian physics, this statement is only true for those very small velocities.

I started by claiming that the Euclidean unit is actually multi-dimensional.. The hyperplane, to my surprise, doesn't even need to be a plane. It is any n-1 dimensional structure embedded in n dimensions. Like a plane in a volume, or a line in a plane, or even a point on a line. I add another wrinkle by allowing a curved 2D surface. In the embedding space, it takes 3 coordinates to unambiguously locate a point, whereas it only takes two coordinates to locate the point in the hyperplane. The defining equation of the hyperplane behaves, for all practical purposes, like a third coordinate. Which brings us to the cone.

In addition to its magnitude (or altitude), a cone is also characterized by the opening angle, the tilt of the wall of the cone relative to the axis of symmetry. Relative to this vector, a cone is just the surface of rotation of the tilted vector around the axis of symmetry. A point on the cone can be located by a length along the wall of the cone, and a rotation from some reference direction. But, although it is the same for every point on the wall of the cone, it implicitly selects a conical surface on which the other two coordinates locate a point. In 3D, points on the cone have an altitude, and the two dimensions that it takes to locate a point in the base. A word of caution here. This is NOT a light-cone. It is simply a cone.

To illustrate (and there is nothing sacred about the choice of axes or labels) let the axis of symmetry be the z axis. Eventually, this will be the direction of a relative velocity vector, but for this part of the discussion, it is just the label for the axis of symmetry. The corollary is that the normal plane to this axis is the (x,y) or (R,θ) plane. This angle specifies rotation around the axis of symmetry. In terms of these parameters, the opening angle of the cone is the arctan of the ratio of the radius of the base of the cone to the z coordinate of the base, call this φ. Then, in terms of φ and r (r² = x²+y²+z²), z = r cos(φ) and R = r sin(φ) (R² = x²+y²). φ is independent of θ, so we need both of them, but we only need one of r or R. Rotation around the axis is trivial. Thanks to rotational symmetry, the cross-section through the z axis of the cone is the same for any angle, θ.

Although φ is also a rotation angle, it has much richer texture. When φ=0, the cone degenerates into a vector of length r, the altitude of the cone. The radius of the base is 0, so the 0-phase cone is just a 1 dimensional vector. At φ=±π/2, the walls of the cone are perpendicular to the z axis, because r cos(φ) = 0. The fully open cone degenerates into a flat disk of area πr², and circumference 2πr. The area of the cone walls is directly proportional to the ratio of the circumference of the base to 2πr. As a function of φ, the circumference of the base of the cone is
2πR = 2πr sin(φ). The area of the base is πR² = πr²sin²(φ). There is an interesting identity here. The area of the disk is πr². So the area of the annulus that is the difference between these two circles is πr²-πr²sin²(φ) = πr²cos²(φ) = π(r cos(φ))², the area of a circle with radius equal to the altitude of the cone. Then the sum of the area of these two perpendicular circles is just πr², the area of the disk. When the sine and cosine contributions are equal, φ = π/4, and the two circles are both embedded in the unit diameter sphere, which has the same surface area as the disk. So, even though the 0-phase cone has no surface area at all, its complement, the area of a disk with the altitude as a radius is maximum and it equals the area of the flattened cone. The sum of the two areas is constant as the opening angle varies.

Op 29-okt.-2021 om 23:07 schreef Tom Capizzi:
> It occurred to me that

.... we are waiting for a paradigm shift?
What do you think... are we?

Dirk Vdm

On Friday, October 29, 2021 at 5:15:15 PM UTC-4, Dirk Van de moortel wrote:
> Op 29-okt.-2021 om 23:07 schreef Tom Capizzi:
> > It occurred to me that
> ... we are waiting for a paradigm shift?
> What do you think... are we?
>
> Dirk Vdm
to Dirk:
how fast does it have to happen to be a paradigm shift as opposed to an evolution?

Tom Capizzi <tgcapizzi@gmail.com> wrote:
> On Friday, October 29, 2021 at 5:15:15 PM UTC-4, Dirk Van de moortel wrote:
>> Op 29-okt.-2021 om 23:07 schreef Tom Capizzi:
>>> It occurred to me that
>> ... we are waiting for a paradigm shift?
>> What do you think... are we?
>>
>> Dirk Vdm
> to Dirk:
> how fast does it have to happen to be a paradigm shift as opposed to an evolution?
>

Going to publish it?
Posting here isn’t publishing it.

--
Odd Bodkin — Maker of fine toys, tools, tables

On Friday, October 29, 2021 at 2:07:27 PM UTC-7, tgca...@gmail.com wrote:
> It occurred to me that my exposition of Euclidean Relativity was exceptionally insane.

Agreed

Tom Capizzi wrote:

> On Friday, October 29, 2021 at 5:15:15 PM UTC-4, Dirk Van de moortel
> wrote:
>> Op 29-okt.-2021 om 23:07 schreef Tom Capizzi:
>> > It occurred to me that
>> ... we are waiting for a paradigm shift? What do you think... are we?
>> Dirk Vdm
> to Dirk:
> how fast does it have to happen to be a paradigm shift as opposed to an
> evolution?

Australian cop kills an unresisting man on the street
https://www.bitchute.com/video/dTSeVrBAzm1w/

they already have death camps, take care.

On Friday, October 29, 2021 at 2:07:27 PM UTC-7, tgca...@gmail.com wrote:
> It occurred to me that my exposition of Euclidean Relativity was unintentionally
> skewed into Cartesian coordinates.

Suppose that, in terms of some system S of inertia-based coordinates x,t, the position of one end of a solid rod at any given time t is x=vt and the position of the other end is x=vt+L for some constants v and L. In terms of S, the speed of the rod is v and its spatial length is L. Do you agree?

On Friday, October 29, 2021 at 6:48:05 PM UTC-4, Townes Olson wrote:
> On Friday, October 29, 2021 at 2:07:27 PM UTC-7, tgca...@gmail.com wrote:
> > It occurred to me that my exposition of Euclidean Relativity was unintentionally
> > skewed into Cartesian coordinates.
> Suppose that, in terms of some system S of inertia-based coordinates x,t, the position of one end of a solid rod at any given time t is x=vt and the position of the other end is x=vt+L for some constants v and L. In terms of S, the speed of the rod is v and its spatial length is L. Do you agree?
No. Its displacement in S is L, but its spatial length is γ(v)L. Of course, nobody else calls it spatial length, so I could be wrong about what you mean. What I mean is its length in a frame in which it is at rest. It always measures shorter to a an observer in a relatively moving frame.

Tom Capizzi <tgcapizzi@gmail.com> wrote:
> On Friday, October 29, 2021 at 6:48:05 PM UTC-4, Townes Olson wrote:
>> On Friday, October 29, 2021 at 2:07:27 PM UTC-7, tgca...@gmail.com wrote:
>>> It occurred to me that my exposition of Euclidean Relativity was unintentionally
>>> skewed into Cartesian coordinates.
>> Suppose that, in terms of some system S of inertia-based coordinates
>> x,t, the position of one end of a solid rod at any given time t is x=vt
>> and the position of the other end is x=vt+L for some constants v and L.
>> In terms of S, the speed of the rod is v and its spatial length is L. Do you agree?
>
> No. Its displacement in S is L, but its spatial length is γ(v)L. Of
> course, nobody else calls it spatial length, so I could be wrong about
> what you mean. What I mean is its length in a frame in which it is at
> rest. It always measures shorter to a an observer in a relatively moving frame.
>

Perhaps if you understood the terms length and displacement.

--
Odd Bodkin -- maker of fine toys, tools, tables

On Friday, October 29, 2021 at 4:57:17 PM UTC-7, tgca...@gmail.com wrote:
> > Suppose that, in terms of some system S of inertia-based coordinates x,t, the position of one end of a solid rod at any given time t is x=vt and the position of the other end is x=vt+L for some constants v and L. In terms of S, the speed of the rod is v and its spatial length is L. Do you agree?
>
> No. Its displacement in S is L, but its spatial length is γ(v)L.

Ah, we've identified the source of the communication difficulties. In both colloquial English and scientific usage the spatial distance between the simultaneous positions of the ends of a rod in terms of a given system S of inertial coordinates is called the spatial length (or just the length) in terms of S. What you are calling the spatial length, γ(v)L, is what everyone else calls the 'rest length' of the rod, which is the spatial length of the rod in terms of the inertial coordinates in which the rod is at rest. This clears up all the confusion about length contraction.

> The accepted term for that distance is the "spatial length", or just "length" of the rod in terms of S.

If you're referring to γ(v)L, that is what's called the rest length of the rod, which is the spatial length of the rod in terms of the inertial coordinates in which the rod is at rest. The rod is not at rest in S, so the spatial length of the rod in terms of S is not the same as its rest length. The spatial length of the rod in terms of S, in the stipulated conditions, is simply L.

> Of course, nobody else calls it spatial length, so I could be wrong about what you mean.

In most discussions people use shorthand terminology like "length" rather than spelling out that they are referring to the spatial length in terms of some specified system of coordinates. The only reason for being careful to specify *spatial* length is to be sure of avoiding confusion over colloquial phrases like "length of time", etc., and to emphasize that it refers to the spatial distance between the simultaneous (in terms of S) positions (in terms of S) of the ends of the rod. The decomposition of spacetime intervals into space and time components depends on the frame. Most people take all this for granted when speaking informally, but I think in this discussion it's essential for us to be very explicit to avoid misunderstanding. So, when we say length in terms of S, we mean the difference in the space coordinates at equal time coordinates of the system x,t.

For example, if in terms of S at time t=3 the leading end of a rod is at x=10 and the trailing end is at x=4, we say the rod has spatial length 10-4=6 at time t=3 in terms of the x,t inertial coordinate system S.

> What I mean is its length in a frame in which it is at rest.

Yes, that's called the rest length of the rod, which is the spatial length in terms of inertial coordinates in which it is at rest, just as 0 is the speed of the rod in terms of its rest coordinates, but the length in terms of the inertial coordinate system S is L and the speed is v.

Another important point to bear in mind is that, given two identically-constructed rods of rest length L0 and moving with relative speed v, each rod has the spatial length L0*sqrt(1-v^2) in terms of the inertial coordinates in which the other rod is at rest. Likewise each of two relativity moving clocks runs slow by the factor sqrt(1-v^2) in terms of the inertial coordinates in which the other is at rest. Do you agree?

On Friday, October 29, 2021 at 9:15:41 PM UTC-4, Townes Olson wrote:
> On Friday, October 29, 2021 at 4:57:17 PM UTC-7, tgca...@gmail.com wrote:
> > > Suppose that, in terms of some system S of inertia-based coordinates x,t, the position of one end of a solid rod at any given time t is x=vt and the position of the other end is x=vt+L for some constants v and L. In terms of S, the speed of the rod is v and its spatial length is L. Do you agree?
> >
> > No. Its displacement in S is L, but its spatial length is γ(v)L.
> Ah, we've identified the source of the communication difficulties. In both colloquial English and scientific usage the spatial distance between the simultaneous positions of the ends of a rod in terms of a given system S of inertial coordinates is called the spatial length (or just the length) in terms of S. What you are calling the spatial length, γ(v)L, is what everyone else calls the 'rest length' of the rod, which is the spatial length of the rod in terms of the inertial coordinates in which the rod is at rest. This clears up all the confusion about length contraction.
>
> > The accepted term for that distance is the "spatial length", or just "length" of the rod in terms of S.
>
> If you're referring to γ(v)L, that is what's called the rest length of the rod, which is the spatial length of the rod in terms of the inertial coordinates in which the rod is at rest. The rod is not at rest in S, so the spatial length of the rod in terms of S is not the same as its rest length. The spatial length of the rod in terms of S, in the stipulated conditions, is simply L.
> > Of course, nobody else calls it spatial length, so I could be wrong about what you mean.
> In most discussions people use shorthand terminology like "length" rather than spelling out that they are referring to the spatial length in terms of some specified system of coordinates. The only reason for being careful to specify *spatial* length is to be sure of avoiding confusion over colloquial phrases like "length of time", etc., and to emphasize that it refers to the spatial distance between the simultaneous (in terms of S) positions (in terms of S) of the ends of the rod. The decomposition of spacetime intervals into space and time components depends on the frame. Most people take all this for granted when speaking informally, but I think in this discussion it's essential for us to be very explicit to avoid misunderstanding. So, when we say length in terms of S, we mean the difference in the space coordinates at equal time coordinates of the system x,t.
>
> For example, if in terms of S at time t=3 the leading end of a rod is at x=10 and the trailing end is at x=4, we say the rod has spatial length 10-4=6 at time t=3 in terms of the x,t inertial coordinate system S.
> > What I mean is its length in a frame in which it is at rest.
> Yes, that's called the rest length of the rod, which is the spatial length in terms of inertial coordinates in which it is at rest, just as 0 is the speed of the rod in terms of its rest coordinates, but the length in terms of the inertial coordinate system S is L and the speed is v.
>
> Another important point to bear in mind is that, given two identically-constructed rods of rest length L0 and moving with relative speed v, each rod has the spatial length L0*sqrt(1-v^2) in terms of the inertial coordinates in which the other rod is at rest. Likewise each of two relativity moving clocks runs slow by the factor sqrt(1-v^2) in terms of the inertial coordinates in which the other is at rest. Do you agree?

I don't think so. The transformation is symmetrical in the sense that both observers will get the same measurements as each other. And from the center of mass frame, with each reference moving at equal speed in opposite directions, this almost makes sense. But at relativistic velocities, the Lorentz factor differs by far more than a factor of 2 as the sum of equal and opposite velocities is less than double either one. Furthermore, the fact that each observer perceives the same measurement as the other normally applies to only one frame, while the other is considered at rest. The predictions are only correct in fact for one of the two frames. After all, only one of the twins ages less. On the other hand, I claim that in the absence of crushing force, all lengths are invariant in magnitude, so that the truth is neither rod shrinks at all. There is a phase angle between two relatively moving frames, defined by the velocity as v = c sin(phase). When we compare two Euclidean units, one from each frame, the measurement is just the dot product of the two factors. Since these two factors are units, their magnitudes are 1, and their dot product is the scalar product of the two magnitudes and the cosine of the phase angle between them. I should point out that the dot product is commutative, so it doesn't matter which frame is moving and which frame is stationary. It also explains why each observer sees the other as shrunken. They are each seeing the other through the same filter, so the filter distorts reality the same way for both. When the measurement is 100% of the dot product, that means the measurement is 100% the cosine of the phase angle. Knowing this we should never accept a relatively moving measurement as anything more than raw data. It must be scaled by the Lorentz factor to compensate for the cosine factor. Then if both observers do the same thing, the truth is exposed. Both observers calculate that their rods are the same length after all. And like parallel mirrors, these projections bounce back and forth without shrinking.

On Friday, October 29, 2021 at 6:45:13 PM UTC-7, tgca...@gmail.com wrote:
> On Friday, October 29, 2021 at 9:15:41 PM UTC-4, Townes Olson wrote:

> > Another important point to bear in mind is that, given two identically-constructed rods of rest length L0 and moving with relative speed v, each rod has the spatial length L0*sqrt(1-v^2) in terms of the inertial coordinates in which the other rod is at rest. Likewise each of two relativity moving clocks runs slow by the factor sqrt(1-v^2) in terms of the inertial coordinates in which the other is at rest. Do you agree?
> I don't think so. The transformation is symmetrical in the sense that both observers will get the same measurements as each other.

We are dealing with a Dingle. Hopeless.

On Friday, October 29, 2021 at 6:45:13 PM UTC-7, tgca...@gmail.com wrote:
> > Another important point to bear in mind is that, given two identically-constructed
> > rods of rest length L0 and moving with relative speed v, each rod has the spatial
> > length L0*sqrt(1-v^2) in terms of the inertial coordinates in which the other rod is
> > at rest. Likewise each of two relativity moving clocks runs slow by the factor
> > sqrt(1-v^2) in terms of the inertial coordinates in which the other is at rest. Do
> > you agree?
>
> I don't think so. The transformation is symmetrical in the sense that both
> observers will get the same measurements as each other.

Please note that the word "observer" is used in relativity discussions as shorthand for "in terms of a specified system of inertial coordinates". Yes, the relations between the coordinate systems are reciprocal, i.e., each rod's length in terms of its rest coordinates is its rest length L0, and each rod has length L0*sqrt(1-v^2) in terms of the other rod's rest coordinates. So they are symmetrical in that sense.

> The predictions are only correct in fact for one of the two frames. After all,
> only one of the twins ages less.

That's a misunderstanding. The elapsed time along any world line with increments dt and dx is sqrt(dt^2 - dx^2), and this agrees exactly with my statement that each clock runs slow in terms of the inertial coordinates in which the other clock is at rest AND it agrees exactly with different in total elapsed proper time for the twins.

> I claim that in the absence of crushing force, all lengths are invariant in magnitude...

Are you arguing semantics, or physics? What everyone in the world means by the phrase "length in terms of S" is the spatial distance between the ends at equal times in terms of S. This agrees with how "length" has been defined throughout human history. We are not coming up with novel definitions and semantics. With the stated meaning, if the rod has rest length L, then it has length L*sqrt(1-v^) in terms of inertial coordinate system in which it is moving with speed v. This is not controversial, and is a direct consequence of Lorentz invariance, with which you have said you agree.

It all comes down to the meaning of the phrase "length in terms of inertial coordinate system S". Everyone in the world (except you) says this refers to the distance (in terms of S) between the ends of the rod at equal times (in terms of S). Given the Lorentz transformation between inertial coordinates, this implies length contraction, just as every scientist and text book says. Agreed?

On Friday, October 29, 2021 at 11:21:53 PM UTC-4, Townes Olson wrote:
> On Friday, October 29, 2021 at 6:45:13 PM UTC-7, tgca...@gmail.com wrote:
> > > Another important point to bear in mind is that, given two identically-constructed
> > > rods of rest length L0 and moving with relative speed v, each rod has the spatial
> > > length L0*sqrt(1-v^2) in terms of the inertial coordinates in which the other rod is
> > > at rest. Likewise each of two relativity moving clocks runs slow by the factor
> > > sqrt(1-v^2) in terms of the inertial coordinates in which the other is at rest. Do
> > > you agree?
> >
> > I don't think so. The transformation is symmetrical in the sense that both
> > observers will get the same measurements as each other.
> Please note that the word "observer" is used in relativity discussions as shorthand for "in terms of a specified system of inertial coordinates". Yes, the relations between the coordinate systems are reciprocal, i.e., each rod's length in terms of its rest coordinates is its rest length L0, and each rod has length L0*sqrt(1-v^2) in terms of the other rod's rest coordinates. So they are symmetrical in that sense.
> > The predictions are only correct in fact for one of the two frames. After all,
> > only one of the twins ages less.
> That's a misunderstanding. The elapsed time along any world line with increments dt and dx is sqrt(dt^2 - dx^2), and this agrees exactly with my statement that each clock runs slow in terms of the inertial coordinates in which the other clock is at rest AND it agrees exactly with different in total elapsed proper time for the twins.
>
> > I claim that in the absence of crushing force, all lengths are invariant in magnitude...
>
> Are you arguing semantics, or physics? What everyone in the world means by the phrase "length in terms of S" is the spatial distance between the ends at equal times in terms of S. This agrees with how "length" has been defined throughout human history. We are not coming up with novel definitions and semantics. With the stated meaning, if the rod has rest length L, then it has length L*sqrt(1-v^) in terms of inertial coordinate system in which it is moving with speed v. This is not controversial, and is a direct consequence of Lorentz invariance, with which you have said you agree.
>
> It all comes down to the meaning of the phrase "length in terms of inertial coordinate system S". Everyone in the world (except you) says this refers to the distance (in terms of S) between the ends of the rod at equal times (in terms of S). Given the Lorentz transformation between inertial coordinates, this implies length contraction, just as every scientist and text book says. Agreed?

No. Your definition of length is 1 dimensional. In hypercomplex geometry, coordinates are 2 dimensional. Even length has a magnitude AND a phase angle.. When the phase angle is included in the math, length contraction vanishes.. So, you are dedicated to dogma and I am not. I think we have each other's positions clear. Appeals to authority are a waste of time, too. Let me make it clear. I'm right, and the world is wrong. As my mother used to say, "Would you jump off a cliff because everybody else was doing it?" The only argument I will believe is if my premises lead to some contradiction. But since they predict identical results, no experiment will provide any contradiction. It must be by a logical argument about the interpretation. But that does not include quibbling about usage of words. In some cases I use definitions that are not 1st on the list. No crime there. When I find that I've misused a word, I just replace it. More often, I am trying to put a label on a process that does not yet have one, and I use the closest descriptor I can. Still no crime. No evidence of a contradiction. Nothing a good science editor wouldn't catch and correct. Nothing relevant to the validity of the argument.

On Friday, October 29, 2021 at 9:03:28 PM UTC-7, tgca...@gmail.com wrote:
> > It all comes down to the meaning of the phrase "length in terms of inertial
> > coordinate system S". Everyone in the world (except you) says this refers to
> > the distance (in terms of S) between the ends of the rod at equal times (in
> > terms of S). Given the Lorentz transformation between inertial coordinates,
> > this implies length contraction, just as every scientist and text book says.
> > Agreed?
>
> No. Your definition of length is 1 dimensional.

It isn't *my* definition of length, it is the meaning and definition of the word "length". It's pointless to dispute statements by re-defining the words to mean something other than what they are intended to mean. When people describe length contraction in the context of modern science, the phrase "length in terms of S" signifies the spatial distance between the ends at equal times, all in terms of S (a system of inertial coordinates). And length is a scalar ("one-dimensional") quantity. If you want to make up your own meanings for words, that's fine, but you can't logically conflate your usage of those words with how everyone else uses those words.

> The only argument I will believe is if my premises lead to some contradiction.

But you've been shown the contradictions in your statements several times, and you just ignore them. The basic problem is that you are willfully misconstruing the propositions of special relativity, and then critiquing your misconstruals.

> I think we have each other's positions clear.

Perhaps, but just to be sure, my position is that the propositions of special relativity are expressed in terms of words with their usual meanings, i.e., the definitions that everyone but you uses. For example, the word "length" is defined to mean what the word "length" has meant throughout human history (simultaneous distance between the end points). Granted, one can insist on re-defining the word length to mean (say) cranberry sauce, and thereby the propositions of special relativity (and many other branches of science) become gibberish, but that is just semantic silliness. In terms of the actual definitions of words corresponding to basic physical concepts, the propositions of special relativity are all correct. Do you agree?

On Saturday, 30 October 2021 at 03:15:41 UTC+2, Townes Olson wrote:
> On Friday, October 29, 2021 at 4:57:17 PM UTC-7, tgca...@gmail.com wrote:
> > > Suppose that, in terms of some system S of inertia-based coordinates x,t, the position of one end of a solid rod at any given time t is x=vt and the position of the other end is x=vt+L for some constants v and L. In terms of S, the speed of the rod is v and its spatial length is L. Do you agree?
> >
> > No. Its displacement in S is L, but its spatial length is γ(v)L.
> Ah, we've identified the source of the communication difficulties. In both colloquial English and scientific usage the spatial distance between the simultaneous positions of the ends of a rod in terms of a given system S of inertial coordinates is called the spatial length (or just the length) in terms of S. What you are calling the spatial length, γ(v)L, is what everyone else calls the 'rest length' of the rod, which is the spatial length of the rod in terms of the inertial coordinates in which the rod is at rest. This clears up all the confusion about length contraction.
>
> > The accepted term for that distance is the "spatial length", or just "length" of the rod in terms of S.
>
> If you're referring to γ(v)L, that is what's called the rest length of the rod, which is the spatial length of the rod in terms of the inertial coordinates in which the rod is at rest. The rod is not at rest in S, so the spatial length of the rod in terms of S is not the same as its rest length. The spatial length of the rod in terms of S, in the stipulated conditions, is simply L.
> > Of course, nobody else calls it spatial length, so I could be wrong about what you mean.
> In most discussions people use shorthand terminology like "length" rather than spelling out that they are referring to the spatial length in terms of some specified system of coordinates. The only reason for being careful to specify *spatial* length is to be sure of avoiding confusion over colloquial phrases like "length of time", etc., and to emphasize that it refers to the spatial distance between the simultaneous (in terms of S) positions (in terms of S) of the ends of the rod. The decomposition of spacetime intervals into space and time components depends on the frame. Most people take all this for granted when speaking informally, but I think in this discussion it's essential for us to be very explicit to avoid misunderstanding. So, when we say length in terms of S, we mean the difference in the space coordinates at equal time coordinates of the system x,t.
>
> For example, if in terms of S at time t=3 the leading end of a rod is at x=10 and the trailing end is at x=4, we say the rod has spatial length 10-4=6 at time t=3 in terms of the x,t inertial coordinate system S.
> > What I mean is its length in a frame in which it is at rest.
> Yes, that's called the rest length of the rod, which is the spatial length in terms of inertial coordinates in which it is at rest, just as 0 is the speed of the rod in terms of its rest coordinates, but the length in terms of the inertial coordinate system S is L and the speed is v.
>
> Another important point to bear in mind is that, given two identically-constructed rods of rest length L0 and moving with relative speed v, each rod has the spatial length L0*sqrt(1-v^2) in terms of the inertial coordinates in which the other rod is at rest. Likewise each of two relativity moving clocks runs slow by the factor sqrt(1-v^2) in terms of the inertial coordinates in which the other is at rest. Do you agree?

In the meantime in the real world, however, GPS clocks
keep measuring t'=t, just like all serious clocks always
did.

On Saturday, 30 October 2021 at 07:34:21 UTC+2, Townes Olson wrote:

> Perhaps, but just to be sure, my position is that the propositions of special relativity are expressed in terms of words with their usual meanings, i.e., the definitions that everyone but you uses.

Delusions, sorry.

> For example, the word "length" is defined to mean what the word "length" has meant throughout human history (simultaneous distance between the end points).

And what is "second", poor halfbrain?

On Saturday, October 30, 2021 at 1:34:21 AM UTC-4, Townes Olson wrote:
> On Friday, October 29, 2021 at 9:03:28 PM UTC-7, tgca...@gmail.com wrote:
> > > It all comes down to the meaning of the phrase "length in terms of inertial
> > > coordinate system S". Everyone in the world (except you) says this refers to
> > > the distance (in terms of S) between the ends of the rod at equal times (in
> > > terms of S). Given the Lorentz transformation between inertial coordinates,
> > > this implies length contraction, just as every scientist and text book says.
> > > Agreed?
> >
> > No. Your definition of length is 1 dimensional.
> It isn't *my* definition of length, it is the meaning and definition of the word "length". It's pointless to dispute statements by re-defining the words to mean something other than what they are intended to mean. When people describe length contraction in the context of modern science, the phrase "length in terms of S" signifies the spatial distance between the ends at equal times, all in terms of S (a system of inertial coordinates). And length is a scalar ("one-dimensional") quantity. If you want to make up your own meanings for words, that's fine, but you can't logically conflate your usage of those words with how everyone else uses those words.
> > The only argument I will believe is if my premises lead to some contradiction.
> But you've been shown the contradictions in your statements several times, and you just ignore them. The basic problem is that you are willfully misconstruing the propositions of special relativity, and then critiquing your misconstruals.
> > I think we have each other's positions clear.
> Perhaps, but just to be sure, my position is that the propositions of special relativity are expressed in terms of words with their usual meanings, i.e., the definitions that everyone but you uses. For example, the word "length" is defined to mean what the word "length" has meant throughout human history (simultaneous distance between the end points). Granted, one can insist on re-defining the word length to mean (say) cranberry sauce, and thereby the propositions of special relativity (and many other branches of science) become gibberish, but that is just semantic silliness. In terms of the actual definitions of words corresponding to basic physical concepts, the propositions of special relativity are all correct. Do you agree?

No. Your "history" is very narrow-minded. Arguing semantics instead of substance is irrelevant. You can make all the ridiculous strawmen you want. I simply apply a mathematician's definition and you go silly and talk about cranberries. Just google displacement vs. distance. They are clearly not the same thing. Whoever told you that words are only allowed to have 1 definition? When people point out that the meaning they assumed is not what I meant, I add enough detail to clarify the statement. Using definition 2 or 3 does not invalidate my argument. Replacing math definitions with food references is typical crackpot nonsense.

Tom Capizzi wrote:
> On Saturday, October 30, 2021 at 1:34:21 AM UTC-4, Townes Olson wrote:
>> On Friday, October 29, 2021 at 9:03:28 PM UTC-7, tgca...@gmail.com wrote:
>>>> It all comes down to the meaning of the phrase "length in terms of inertial
>>>> coordinate system S". Everyone in the world (except you) says this refers to
>>>> the distance (in terms of S) between the ends of the rod at equal times (in
>>>> terms of S). Given the Lorentz transformation between inertial coordinates,
>>>> this implies length contraction, just as every scientist and text book says.
>>>> Agreed?
>>>
>>> No. Your definition of length is 1 dimensional.
>> It isn't *my* definition of length, it is the meaning and definition of the word "length". It's pointless to dispute statements by re-defining the words to mean something other than what they are intended to mean. When people describe length contraction in the context of modern science, the phrase "length in terms of S" signifies the spatial distance between the ends at equal times, all in terms of S (a system of inertial coordinates). And length is a scalar ("one-dimensional") quantity. If you want to make up your own meanings for words, that's fine, but you can't logically conflate your usage of those words with how everyone else uses those words.
>>> The only argument I will believe is if my premises lead to some contradiction.
>> But you've been shown the contradictions in your statements several times, and you just ignore them. The basic problem is that you are willfully misconstruing the propositions of special relativity, and then critiquing your misconstruals.
>>> I think we have each other's positions clear.
>> Perhaps, but just to be sure, my position is that the propositions of special relativity are expressed in terms of words with their usual meanings, i.e., the definitions that everyone but you uses. For example, the word "length" is defined to mean what the word "length" has meant throughout human history (simultaneous distance between the end points). Granted, one can insist on re-defining the word length to mean (say) cranberry sauce, and thereby the propositions of special relativity (and many other branches of science) become gibberish, but that is just semantic silliness. In terms of the actual definitions of words corresponding to basic physical concepts, the propositions of special relativity are all correct. Do you agree?
>
> No. Your "history" is very narrow-minded. Arguing semantics instead of substance is irrelevant. You can make all the ridiculous strawmen you want. I simply apply a mathematician's definition

No you don't.

Tom Capizzi <tgcapizzi@gmail.com> wrote:
> On Friday, October 29, 2021 at 6:48:05 PM UTC-4, Townes Olson wrote:
>> On Friday, October 29, 2021 at 2:07:27 PM UTC-7, tgca...@gmail.com wrote:
>>> It occurred to me that my exposition of Euclidean Relativity was unintentionally
>>> skewed into Cartesian coordinates.
>> Suppose that, in terms of some system S of inertia-based coordinates
>> x,t, the position of one end of a solid rod at any given time t is x=vt
>> and the position of the other end is x=vt+L for some constants v and L.
>> In terms of S, the speed of the rod is v and its spatial length is L. Do you agree?
>
> No. Its displacement in S is L, but its spatial length is γ(v)L. Of
> course, nobody else calls it spatial length, so I could be wrong about
> what you mean. What I mean is its length in a frame in which it is at
> rest. It always measures shorter to a an observer in a relatively moving frame.
>

And so you have different meanings for length and displacement than as they
are defined in first year physics.

--
Odd Bodkin — Maker of fine toys, tools, tables

Tom Capizzi <tgcapizzi@gmail.com> wrote:
> On Friday, October 29, 2021 at 11:21:53 PM UTC-4, Townes Olson wrote:
>> On Friday, October 29, 2021 at 6:45:13 PM UTC-7, tgca...@gmail.com wrote:
>>>> Another important point to bear in mind is that, given two identically-constructed
>>>> rods of rest length L0 and moving with relative speed v, each rod has the spatial
>>>> length L0*sqrt(1-v^2) in terms of the inertial coordinates in which the other rod is
>>>> at rest. Likewise each of two relativity moving clocks runs slow by the factor
>>>> sqrt(1-v^2) in terms of the inertial coordinates in which the other is at rest. Do
>>>> you agree?
>>>
>>> I don't think so. The transformation is symmetrical in the sense that both
>>> observers will get the same measurements as each other.
>> Please note that the word "observer" is used in relativity discussions
>> as shorthand for "in terms of a specified system of inertial
>> coordinates". Yes, the relations between the coordinate systems are
>> reciprocal, i.e., each rod's length in terms of its rest coordinates is
>> its rest length L0, and each rod has length L0*sqrt(1-v^2) in terms of
>> the other rod's rest coordinates. So they are symmetrical in that sense.
>>> The predictions are only correct in fact for one of the two frames. After all,
>>> only one of the twins ages less.
>> That's a misunderstanding. The elapsed time along any world line with
>> increments dt and dx is sqrt(dt^2 - dx^2), and this agrees exactly with
>> my statement that each clock runs slow in terms of the inertial
>> coordinates in which the other clock is at rest AND it agrees exactly
>> with different in total elapsed proper time for the twins.
>>
>>> I claim that in the absence of crushing force, all lengths are invariant in magnitude...
>>
>> Are you arguing semantics, or physics? What everyone in the world means
>> by the phrase "length in terms of S" is the spatial distance between the
>> ends at equal times in terms of S. This agrees with how "length" has
>> been defined throughout human history. We are not coming up with novel
>> definitions and semantics. With the stated meaning, if the rod has rest
>> length L, then it has length L*sqrt(1-v^) in terms of inertial
>> coordinate system in which it is moving with speed v. This is not
>> controversial, and is a direct consequence of Lorentz invariance, with
>> which you have said you agree.
>>
>> It all comes down to the meaning of the phrase "length in terms of
>> inertial coordinate system S". Everyone in the world (except you) says
>> this refers to the distance (in terms of S) between the ends of the rod
>> at equal times (in terms of S). Given the Lorentz transformation between
>> inertial coordinates, this implies length contraction, just as every
>> scientist and text book says. Agreed?
>
> No. Your definition of length is 1 dimensional.

It’s not his definition. It’s the definition understood and used in
physics. If you choose not to use it…

> In hypercomplex geometry,

Gobbledygook

> coordinates are 2 dimensional. Even length has a magnitude AND a phase
> angle. When the phase angle is included in the math, length contraction
> vanishes. So, you are dedicated to dogma and I am not.

I think what you are saying is that the definitions of length and
displacement in physics are dogma, and you don’t use those definitions.

> I think we have each other's positions clear. Appeals to authority are a
> waste of time, too. Let me make it clear. I'm right, and the world is wrong.

Well, so you are going to say that you reject meanings of basic terms in
physics and say that the world is wrong for using those definitions. Do you
think that’s innovative?

> As my mother used to say, "Would you jump off a cliff because everybody
> else was doing it?" The only argument I will believe is if my premises
> lead to some contradiction.

As this is not the basis for assessing truth in physics, it’s out of place
here.

> But since they predict identical results, no experiment will provide any
> contradiction. It must be by a logical argument about the interpretation.
> But that does not include quibbling about usage of words.

I’m sorry but if you are not using terms as they are defined in physics
then communication is impossible.

> In some cases I use definitions that are not 1st on the list. No crime
> there. When I find that I've misused a word, I just replace it. More
> often, I am trying to put a label on a process that does not yet have
> one, and I use the closest descriptor I can. Still no crime. No evidence
> of a contradiction. Nothing a good science editor wouldn't catch and
> correct. Nothing relevant to the validity of the argument.
>

--
Odd Bodkin — Maker of fine toys, tools, tables

Tom Capizzi <tgcapizzi@gmail.com> wrote:
> On Saturday, October 30, 2021 at 1:34:21 AM UTC-4, Townes Olson wrote:
>> On Friday, October 29, 2021 at 9:03:28 PM UTC-7, tgca...@gmail.com wrote:
>>>> It all comes down to the meaning of the phrase "length in terms of inertial
>>>> coordinate system S". Everyone in the world (except you) says this refers to
>>>> the distance (in terms of S) between the ends of the rod at equal times (in
>>>> terms of S). Given the Lorentz transformation between inertial coordinates,
>>>> this implies length contraction, just as every scientist and text book says.
>>>> Agreed?
>>>
>>> No. Your definition of length is 1 dimensional.
>> It isn't *my* definition of length, it is the meaning and definition of
>> the word "length". It's pointless to dispute statements by re-defining
>> the words to mean something other than what they are intended to mean.
>> When people describe length contraction in the context of modern
>> science, the phrase "length in terms of S" signifies the spatial
>> distance between the ends at equal times, all in terms of S (a system of
>> inertial coordinates). And length is a scalar ("one-dimensional")
>> quantity. If you want to make up your own meanings for words, that's
>> fine, but you can't logically conflate your usage of those words with
>> how everyone else uses those words.
>>> The only argument I will believe is if my premises lead to some contradiction.
>> But you've been shown the contradictions in your statements several
>> times, and you just ignore them. The basic problem is that you are
>> willfully misconstruing the propositions of special relativity, and then
>> critiquing your misconstruals.
>>> I think we have each other's positions clear.
>> Perhaps, but just to be sure, my position is that the propositions of
>> special relativity are expressed in terms of words with their usual
>> meanings, i.e., the definitions that everyone but you uses. For example,
>> the word "length" is defined to mean what the word "length" has meant
>> throughout human history (simultaneous distance between the end points).
>> Granted, one can insist on re-defining the word length to mean (say)
>> cranberry sauce, and thereby the propositions of special relativity (and
>> many other branches of science) become gibberish, but that is just
>> semantic silliness. In terms of the actual definitions of words
>> corresponding to basic physical concepts, the propositions of special
>> relativity are all correct. Do you agree?
>
> No. Your "history" is very narrow-minded. Arguing semantics instead of
> substance is irrelevant. You can make all the ridiculous strawmen you
> want. I simply apply a mathematician's definition

You are adding your OWN definition, not any other mathematician’s
definition. Moreover, this is physics, not mathematics. “Cell” means
different things in EE and in biology and it’d be silly to conflate the
two.

> and you go silly and talk about cranberries. Just google displacement vs.
> distance. They are clearly not the same thing. Whoever told you that
> words are only allowed to have 1 definition? When people point out that
> the meaning they assumed is not what I meant, I add enough detail to
> clarify the statement. Using definition 2 or 3 does not invalidate my
> argument. Replacing math definitions with food references is typical crackpot nonsense.
>

--
Odd Bodkin — Maker of fine toys, tools, tables

Tom Capizzi <tgcapizzi@gmail.com> wrote:
> On Friday, October 29, 2021 at 9:15:41 PM UTC-4, Townes Olson wrote:
>> On Friday, October 29, 2021 at 4:57:17 PM UTC-7, tgca...@gmail.com wrote:
>>>> Suppose that, in terms of some system S of inertia-based coordinates
>>>> x,t, the position of one end of a solid rod at any given time t is
>>>> x=vt and the position of the other end is x=vt+L for some constants v
>>>> and L. In terms of S, the speed of the rod is v and its spatial length
>>>> is L. Do you agree?
>>>
>>> No. Its displacement in S is L, but its spatial length is γ(v)L.
>> Ah, we've identified the source of the communication difficulties. In
>> both colloquial English and scientific usage the spatial distance
>> between the simultaneous positions of the ends of a rod in terms of a
>> given system S of inertial coordinates is called the spatial length (or
>> just the length) in terms of S. What you are calling the spatial length,
>> γ(v)L, is what everyone else calls the 'rest length' of the rod, which
>> is the spatial length of the rod in terms of the inertial coordinates in
>> which the rod is at rest. This clears up all the confusion about length contraction.
>>
>>> The accepted term for that distance is the "spatial length", or just
>>> "length" of the rod in terms of S.
>>
>> If you're referring to γ(v)L, that is what's called the rest length of
>> the rod, which is the spatial length of the rod in terms of the inertial
>> coordinates in which the rod is at rest. The rod is not at rest in S, so
>> the spatial length of the rod in terms of S is not the same as its rest
>> length. The spatial length of the rod in terms of S, in the stipulated
>> conditions, is simply L.
>>> Of course, nobody else calls it spatial length, so I could be wrong about what you mean.
>> In most discussions people use shorthand terminology like "length"
>> rather than spelling out that they are referring to the spatial length
>> in terms of some specified system of coordinates. The only reason for
>> being careful to specify *spatial* length is to be sure of avoiding
>> confusion over colloquial phrases like "length of time", etc., and to
>> emphasize that it refers to the spatial distance between the
>> simultaneous (in terms of S) positions (in terms of S) of the ends of
>> the rod. The decomposition of spacetime intervals into space and time
>> components depends on the frame. Most people take all this for granted
>> when speaking informally, but I think in this discussion it's essential
>> for us to be very explicit to avoid misunderstanding. So, when we say
>> length in terms of S, we mean the difference in the space coordinates at
>> equal time coordinates of the system x,t.
>>
>> For example, if in terms of S at time t=3 the leading end of a rod is at
>> x=10 and the trailing end is at x=4, we say the rod has spatial length
>> 10-4=6 at time t=3 in terms of the x,t inertial coordinate system S.
>>> What I mean is its length in a frame in which it is at rest.
>> Yes, that's called the rest length of the rod, which is the spatial
>> length in terms of inertial coordinates in which it is at rest, just as
>> 0 is the speed of the rod in terms of its rest coordinates, but the
>> length in terms of the inertial coordinate system S is L and the speed is v.
>>
>> Another important point to bear in mind is that, given two
>> identically-constructed rods of rest length L0 and moving with relative
>> speed v, each rod has the spatial length L0*sqrt(1-v^2) in terms of the
>> inertial coordinates in which the other rod is at rest. Likewise each of
>> two relativity moving clocks runs slow by the factor sqrt(1-v^2) in
>> terms of the inertial coordinates in which the other is at rest. Do you agree?
>
> I don't think so. The transformation is symmetrical in the sense that
> both observers will get the same measurements as each other. And from the
> center of mass frame, with each reference moving at equal speed in
> opposite directions, this almost makes sense. But at relativistic
> velocities, the Lorentz factor differs by far more than a factor of 2 as
> the sum of equal and opposite velocities is less than double either one.
> Furthermore, the fact that each observer perceives the same measurement
> as the other normally applies to only one frame, while the other is
> considered at rest. The predictions are only correct in fact for one of
> the two frames. After all, only one of the twins ages less. On the other
> hand, I claim that in the absence of crushing force, all lengths are
> invariant in magnitude,

But as length is defined in physics this is experimentally false. Whether
you have a DIFFERENT meaning for length which by that meaning MUST be
invariant is irrelevant.

> so that the truth is neither rod shrinks at all. There is a phase angle
> between two relatively moving frames, defined by the velocity as v = c
> sin(phase). When we compare two Euclidean units, one from each frame, the
> measurement is just the dot product of the two factors. Since these two
> factors are units, their magnitudes are 1, and their dot product is the
> scalar product of the two magnitudes and the cosine of the phase angle
> between them. I should point out that the dot product is commutative, so
> it doesn't matter which frame is moving and which frame is stationary. It
> also explains why each observer sees the other as shrunken. They are each
> seeing the other through the same filter, so the filter distorts reality
> the same way for both. When the measurement is 100% of the dot product,
> that means the measurement is 100% the cosine of the phase angle. Knowing
> this we should never accept a relatively moving measurement as anything
> more than raw data. It must be scaled by the Lorentz factor to compensate
> for the cosine factor. Then if both observers do the same thing, the
> truth is exposed. Both observers calculate that their rods are the same
> length after all. And like parallel mirrors, these projections bounce
> back and forth without shrinking.
>

--
Odd Bodkin — Maker of fine toys, tools, tables

Townes Olson <townesolson7@gmail.com> wrote:
> On Friday, October 29, 2021 at 4:57:17 PM UTC-7, tgca...@gmail.com wrote:
>>> Suppose that, in terms of some system S of inertia-based coordinates
>>> x,t, the position of one end of a solid rod at any given time t is x=vt
>>> and the position of the other end is x=vt+L for some constants v and L.
>>> In terms of S, the speed of the rod is v and its spatial length is L. Do you agree?
>>
>> No. Its displacement in S is L, but its spatial length is γ(v)L.
>
> Ah, we've identified the source of the communication difficulties. In
> both colloquial English and scientific usage the spatial distance between
> the simultaneous positions of the ends of a rod in terms of a given
> system S of inertial coordinates is called the spatial length (or just
> the length) in terms of S. What you are calling the spatial length,
> γ(v)L, is what everyone else calls the 'rest length' of the rod, which
> is the spatial length of the rod in terms of the inertial coordinates in
> which the rod is at rest. This clears up all the confusion about length contraction.

This confusion about the meaning of length is what I’ve been telling him
for some time. He thinks the meaning you refer to is assigned in physics to
displacement, which is ALSO incorrect. He has failed to learn the meanings
of two basic terms in physics and he thinks he is being forward-thinking by
that failure.

>
>> The accepted term for that distance is the "spatial length", or just
>> "length" of the rod in terms of S.
>
> If you're referring to γ(v)L, that is what's called the rest length of
> the rod, which is the spatial length of the rod in terms of the inertial
> coordinates in which the rod is at rest. The rod is not at rest in S, so
> the spatial length of the rod in terms of S is not the same as its rest
> length. The spatial length of the rod in terms of S, in the stipulated
> conditions, is simply L.
>
>> Of course, nobody else calls it spatial length, so I could be wrong about what you mean.
>
> In most discussions people use shorthand terminology like "length" rather
> than spelling out that they are referring to the spatial length in terms
> of some specified system of coordinates. The only reason for being
> careful to specify *spatial* length is to be sure of avoiding confusion
> over colloquial phrases like "length of time", etc., and to emphasize
> that it refers to the spatial distance between the simultaneous (in terms
> of S) positions (in terms of S) of the ends of the rod. The
> decomposition of spacetime intervals into space and time components
> depends on the frame. Most people take all this for granted when
> speaking informally, but I think in this discussion it's essential for us
> to be very explicit to avoid misunderstanding. So, when we say length in
> terms of S, we mean the difference in the space coordinates at equal time
> coordinates of the system x,t.
>
> For example, if in terms of S at time t=3 the leading end of a rod is at
> x=10 and the trailing end is at x=4, we say the rod has spatial length
> 10-4=6 at time t=3 in terms of the x,t inertial coordinate system S.
>
>> What I mean is its length in a frame in which it is at rest.
>
> Yes, that's called the rest length of the rod, which is the spatial
> length in terms of inertial coordinates in which it is at rest, just as 0
> is the speed of the rod in terms of its rest coordinates, but the length
> in terms of the inertial coordinate system S is L and the speed is v.
>
> Another important point to bear in mind is that, given two
> identically-constructed rods of rest length L0 and moving with relative
> speed v, each rod has the spatial length L0*sqrt(1-v^2) in terms of the
> inertial coordinates in which the other rod is at rest. Likewise each of
> two relativity moving clocks runs slow by the factor sqrt(1-v^2) in terms
> of the inertial coordinates in which the other is at rest. Do you agree?
>

--
Odd Bodkin — Maker of fine toys, tools, tables

On Saturday, October 30, 2021 at 6:14:54 AM UTC-7, tgca...@gmail.com wrote:
> > The propositions of special relativity are expressed in terms of words with
> > their usual meanings, i.e., the definitions that everyone but you uses. For
> > example, the word "length" is defined to mean what the word "length" has
> > meant throughout human history (simultaneous distance between the end
> > points). In terms of the actual definitions of words corresponding to basic
> > physical concepts, the propositions of special relativity are all correct. Do you
> > agree?
>
> No. Your "history" is very narrow-minded. Arguing semantics instead of substance
> is irrelevant.

But *you* are the one who is playing semantic games rather than reasoning about substance. Look, in order to communicate, it is obviously necessary for people to agree on the meanings of the words they are using. You are redefining a word, and then making statements based on that redefinition, and you are frustrated when people say your statements are wrong.

Everyone else is using the word "length" with its actual meaning, i.e., if I hold up a meter stick (at rest in S) and note that the ends of a passing object coincide with the ends of the meter stick at a particular instant of time (in terms of S), then the length of the object in terms of S is one meter. You may not like using the word "length" to represent that, but if you like you can just spell out the meaning each time. It's just more convenient to have a word that signifies that meaning.

> You can make all the ridiculous strawmen you want.

That isn't a strawman (I am not claiming you think length is cranberry sauce), that is a reductio ad absurdum, meaning I am demonstrating that by redefining words we can make nonsense statements formally true. For example, if someone defined "length" to mean "ice cream cone", then length melts on a warm summer day. Yes, that's just semantic nonsense, but that's what *you* are doing.

> I simply apply a mathematician's definition...

I don't think that is true, you have given multiple inconsistent definitions. At times you use the word "length" to mean what everyone else refers to as "rest length", i.e., the real-valued scalar length [normal definition] of the object in terms of inertial coordinates in which it is at rest. But at other times you use the word "length" to refer to some complex-valued quantity that has no more to do with the normal meaning of the word "length" than cranberry sauce. Mathematicians are sticklers for consistency, and you are using "length" in very inconsistent ways, so you can't rightly claim to be using a mathematician's definition. If you have a single coherent and logically consistent definition of the "length" of a solid physical object, I'd like to hear it.

> When people point out that the meaning they assumed is not what I meant, I add
> enough detail to clarify the statement.

But, again, your clarifications are logically inconsistent (sometimes real-valued rest length, other times a complex-valued quantity that bears no relation at all to the normal meaning of the word). In essence, your clarifaction is like someone saying no no no, I'm using the word length to mean ice cream cone, and therefore my statement that length melts on a warm summer day is perfectly correct. To which everyone in the world responds "wow, that is a load of semantic silliness". (Again, not a straw man, a reductio ad absurdum.)

> Using definition 2 or 3 does not invalidate my argument.

You are just playing semantic games. In physics the spatial length of an object in terms of a specified system of coordinates x,t is the difference between the x coordinates of the ends of the object at equal values of the t coordinate. If you want to talk about some other quantity, then you should give it a different name to avoid confusion. And you should acknowledge that the propositions of special relativity (noting the specified meanings of the words) are all perfectly correct. Isn't that reasonable?