Velocity Postulate: Given the existence of space and time, there also exists a quality called motion. Motion is quantified by the property of velocity which is the ratio of duration in time to displacement in space.

[spacetime version: Given the existence of spacetime, there also exists a quality called motion. Motion is quantified by the property of velocity which is the ratio of displacement along the time axis to the displacements along the space axes.]

Velocity Uniqueness Theorem: It is a fundamental quality of motion that there can exist at most one instantaneous velocity magnitude ||v|| shared between any pair of observers.

Equivalency corollary: Given a velocity value |v| shared between a pair of observers, each observer must be able to calculate that velocity value from the standpoint of his own FoR and from the standpoint of the other observer's FoR. Furthermore, all four of these velocity values must be identical..

Relativity corollary: All velocities shared between all pairs of observers must be less than the velocity of light.

The author pauses here to ask if there is a chump among you who would like to dispute the foregoing?

On 23-May-22 12:21 pm, patdolan wrote:

> Velocity Uniqueness Theorem: It is a fundamental quality of motion that there can exist at most one instantaneous velocity magnitude ||v|| shared between any pair of observers.

If that's a theorem, where's the proof?

Sylvia.

patdolan <patdolan@comcast.net> wrote:

> Velocity Postulate: Given the existence of space and time, there also
> exists a quality called motion. Motion is quantified by the property of
> velocity which is the ratio of duration in time to displacement in space.

Given Euclidean geometry there exist a quality called 'angle'.
It is the same for all Euclidean observers,
and it is independent of coordinates,

Jan

On Monday, 23 May 2022 at 10:31:55 UTC+2, J. J. Lodder wrote:
> patdolan <patd...@comcast.net> wrote:
>
> > Velocity Postulate: Given the existence of space and time, there also
> > exists a quality called motion. Motion is quantified by the property of
> > velocity which is the ratio of duration in time to displacement in space.
> Given Euclidean geometry there exist a quality called 'angle'.
> It is the same for all Euclidean observers,
> and it is independent of coordinates,

And given the newsgrroup sci.physics.relativity there
exists pseudomathematical mumble.

On Monday, May 23, 2022 at 12:18:43 AM UTC-7, Sylvia Else wrote:
> On 23-May-22 12:21 pm, patdolan wrote:
>
> > Velocity Uniqueness Theorem: It is a fundamental quality of motion that there can exist at most one instantaneous velocity magnitude ||v|| shared between any pair of observers.
> If that's a theorem, where's the proof?
>
> Sylvia.
This is a most excellent point that you make, Sylvia Jones. The velocity uniqueness theorem may in fact have to be elevated to postulate level. But whether theorem or postulate, one thing is certain: given the validity of the LTs and SR, the velocity uniqueness theorem is certainly wrong. I will prove it directly.

Two observers, Stan and Townes. Using his co-moving coordinate system Stan determines that Townes is one light year away and traveling at .867c in his direction. Stan now calculates what Townes will say Stan's velocity is according to Townes' co-moving coordinate system.

Stan immediately perceives that Townes' co-moving coordinate system is contracted by a factor of two and that Towne's clock is ticking at half the rate of his own clock. These phenomena are not some sort of illusion. In Stan's FoR Townes really does measure that he moves two meters towards Stan for every one meter that Stan moves towards Townes. Furthermore, Stan measures that Townes' clock ticks off only half as much time as his own during the simultaneous distance intervals in the preceding sentence. When Stan and Townes pass one another, Stan watches Townes' hand moving at half speed as he writes down two light years distance divided by 0.5767 years to calculate Stan's velocity as 3.468c.

Sure, Townes will measure another velocity for Stan in his own FoR. But we are watching from Stan and Townes calculate velocity from Stan's FoR. [this also implies that SR is a "Many Worlds" theory.]

What has been accomplished: We have demonstrated that given the LTs and SR, the velocity two observers share between themselves can never be unique.

There is more to spin out but the author pauses here for his mathematical inferiors to catch the drift of his thought before proceeding.

On Monday, 23 May 2022 at 18:12:46 UTC+2, patdolan wrote:

> Two observers, Stan and Townes. Using his co-moving coordinate system Stan determines that Townes is one light year away and traveling at .867c in his direction. Stan now calculates what Townes will say Stan's velocity is according to Townes' co-moving coordinate system.

Nobody can calculate the output of a human brain.
It's a pure bullshit.
Instead calculations a relativistic idiot is offering
arm waving and assertions that it will surely be
as he says.

On Sunday, May 22, 2022 at 7:21:46 PM UTC-7, patdolan wrote:
> Velocity Postulate:

In physics, in terms of any operationally-defined system of coordinates x,t, and for any given trajectory x=f(t), at any given event, the quantity dx/dt is defined as the "velocity" of that trajectory at that event. This is the definition of the word "velocity", it is not a postulate.

> [spacetime version...

There is no separate "spacetime version" distinct from the standard historical definition of the word "velocity", as given above.

> ... there can exist at most one instantaneous velocity magnitude ||v|| shared
> between any pair of observers.

That doesn't make sense. Velocity is as defined above, dx/dt in terms of any specified system of coordinates. There are infinitely many systems of coordinates, and entities have infinitely many different velocities, depending on which system of coordinates you are referring to. What you might be trying to say is that for two standard systems of inertial coordinates S and S', with aligned space axes, objects at rest in S' have velocity v in terms of S, and objects at rest in S have velocity -v in terms of S'. But these are by no means the only possible coordinate systems that can be defined, and hence those objects have any other velocities in terms of many other coordinate systems. It is necessary always to specify the coordinate system when referring to a velocity.

> Given a velocity value |v| shared between a pair of observers...

Translation: Given two systems of standard inertia-based coordinates S and S' with mutual velocity v...

> ...each observer must be able to calculate that velocity value from the standpoint
> of his own FoR...

It's pointless to talk in terms of "what an observer must be able to calculate", because on observer could be someone like you, who can't calculate his way out of a paper bag. The propositions of physics are objective facts, not assertions about anyone's ability to calculate things. What you need to say is that given the velocity of an object in terms of one coordinate system, and given the relationship between that coordinate system and some other coordinate system, the velocity of the object in terms of that other system is fully specified.

> and from the standpoint of the other observer's FoR. Furthermore, all four of these velocity values must be identical.

Four? Again, a given object at a given event has a specific velocity in terms of any specified system of coordinates. So far you are just talking about two systems of coordinates, and you seem to b tacitly assuming they are inertial coordinate systems, which we can call S and S', and each object has a velocity in terms of those two coordinate systems (not four). As noted above, an object with dx/dt = 0 has d'x/dt' = -v, and an object with d'x/dt'=0 has dx/dt = v. If those are the four velocities you are talking about, they are not identical, two are zero and one is v and the other is -v.

> Relativity corollary: All velocities shared between all pairs of observers must be less than the velocity of light.

No, that's isn't a corollary, and it isn't the relativity principle. It's a complete non-sequitur from what you have said.

> Stan now calculates what Townes will say Stan's velocity is according to Townes' co-moving coordinate system.

If the "co-moving coordinate systems" you are referring to are standard inertia-based coordinate systems S and S' in which the two objects are at rest, then the object at rest in S' has velocity v in terms of S, and the object at rest in S has velocity -v in terms of S'. These are objective facts. Of course, we can refer to other systems of coordinates... for example, we could use the time coordinate from S and the space coordinates of S', or vice versa, and these resulting hybrid coordinate systems would have different velocities, but these are not standard inertial coordinate systems. Again, there are infinitely many coordinate systems (in fact, there are infinitely many in which a given object is at rest), and every object has infinitely many velocities, depending on which system of coordinates you are referring to. So nothing that you are saying makes any sense.

On Monday, 23 May 2022 at 21:04:21 UTC+2, Stan Fultoni wrote:
> On Sunday, May 22, 2022 at 7:21:46 PM UTC-7, patdolan wrote:
> > Velocity Postulate:
>
> In physics, in terms of any operationally-defined system of coordinates x,t, and for any given trajectory x=f(t), at any given event, the quantity dx/dt is defined as the "velocity" of that trajectory at that event.

A common sense prejudice, refuted by your insane gurus
with their inflation nonsense.

On Monday, May 23, 2022 at 12:04:21 PM UTC-7, Stan Fultoni wrote:
> On Sunday, May 22, 2022 at 7:21:46 PM UTC-7, patdolan wrote:
> > Velocity Postulate:
>
> In physics, in terms of any operationally-defined system of coordinates x,t, and for any given trajectory x=f(t), at any given event, the quantity dx/dt is defined as the "velocity" of that trajectory at that event. This is the definition of the word "velocity", it is not a postulate.
>
> > [spacetime version...
>
> There is no separate "spacetime version" distinct from the standard historical definition of the word "velocity", as given above.
>
> > ... there can exist at most one instantaneous velocity magnitude ||v|| shared
> > between any pair of observers.
> That doesn't make sense. Velocity is as defined above, dx/dt in terms of any specified system of coordinates. There are infinitely many systems of coordinates, and entities have infinitely many different velocities, depending on which system of coordinates you are referring to. What you might be trying to say is that for two standard systems of inertial coordinates S and S', with aligned space axes, objects at rest in S' have velocity v in terms of S, and objects at rest in S have velocity -v in terms of S'. But these are by no means the only possible coordinate systems that can be defined, and hence those objects have any other velocities in terms of many other coordinate systems. It is necessary always to specify the coordinate system when referring to a velocity.

Stownes, you never take the time to read. Or you just can't get beyond the cookie cutter thinking you've ingested. So you react in a knee jerk fashion like an animal striking at a perceived threat.

To have infinitely many coordinate systems is tantamount to having infinitely many observers. In this problem I have limited the observers/coordinate systems to only two, Stan's and Townes' co-moving coordinate systems. Think that over. These two coordinate systems/observers have but one single velocity magnitude |v| that they share between each other, according to the LTs. Of course, now that I have proved that this is not the case....
>
> > Given a velocity value |v| shared between a pair of observers...
>
> Translation: Given two systems of standard inertia-based coordinates S and S' with mutual velocity v...
>
> > ...each observer must be able to calculate that velocity value from the standpoint
> > of his own FoR...
>
> It's pointless to talk in terms of "what an observer must be able to calculate", because on observer could be someone like you, who can't calculate his way out of a paper bag. The propositions of physics are objective facts, not assertions about anyone's ability to calculate things. What you need to say is that given the velocity of an object in terms of one coordinate system, and given the relationship between that coordinate system and some other coordinate system, the velocity of the object in terms of that other system is fully specified.
> > and from the standpoint of the other observer's FoR. Furthermore, all four of these velocity values must be identical.
> Four? Again, a given object at a given event has a specific velocity in terms of any specified system of coordinates. So far you are just talking about two systems of coordinates, and you seem to b tacitly assuming they are inertial coordinate systems, which we can call S and S', and each object has a velocity in terms of those two coordinate systems (not four). As noted above, an object with dx/dt = 0 has d'x/dt' = -v, and an object with d'x/dt'=0 has dx/dt = v. If those are the four velocities you are talking about, they are not identical, two are zero and one is v and the other is -v.
> > Relativity corollary: All velocities shared between all pairs of observers must be less than the velocity of light.
> No, that's isn't a corollary, and it isn't the relativity principle. It's a complete non-sequitur from what you have said.
> > Stan now calculates what Townes will say Stan's velocity is according to Townes' co-moving coordinate system.
> If the "co-moving coordinate systems" you are referring to are standard inertia-based coordinate systems S and S' in which the two objects are at rest, then the object at rest in S' has velocity v in terms of S, and the object at rest in S has velocity -v in terms of S'. These are objective facts. Of course, we can refer to other systems of coordinates... for example, we could use the time coordinate from S and the space coordinates of S', or vice versa, and these resulting hybrid coordinate systems would have different velocities, but these are not standard inertial coordinate systems. Again, there are infinitely many coordinate systems (in fact, there are infinitely many in which a given object is at rest), and every object has infinitely many velocities, depending on which system of coordinates you are referring to. So nothing that you are saying makes any sense.

On Monday, May 23, 2022 at 1:02:57 PM UTC-7, patdolan wrote:
> > > Velocity Postulate:
> >
> > In physics, in terms of any operationally-defined system of coordinates x,t, and for any given trajectory x=f(t), at any given event, the quantity dx/dt is defined as the "velocity" of that trajectory at that event. This is the definition of the word "velocity", it is not a postulate.
> >
> > > [spacetime version...
> >
> > There is no separate "spacetime version" distinct from the standard historical definition of the word "velocity", as given above.
> >
> > > ... there can exist at most one instantaneous velocity magnitude ||v|| shared
> > > between any pair of observers.
> > That doesn't make sense. Velocity is as defined above, dx/dt in terms of any specified system of coordinates. There are infinitely many systems of coordinates, and entities have infinitely many different velocities, depending on which system of coordinates you are referring to. What you might be trying to say is that for two standard systems of inertial coordinates S and S', with aligned space axes, objects at rest in S' have velocity v in terms of S, and objects at rest in S have velocity -v in terms of S'. But these are by no means the only possible coordinate systems that can be defined, and hence those objects have any other velocities in terms of many other coordinate systems. It is necessary always to specify the coordinate system when referring to a velocity.
>
> To have infinitely many coordinate systems is tantamount to having infinitely many observers.

Nope, you are mistakenly conflating "observers" with coordinate systems, one of the most common newbie mistakes. Every object is at rest in terms of infinitely many coordinate systems, with distinct temporal foliations, so there is no unique system of coordinates in which an object is at rest.

> In this problem I have limited the ... coordinate systems to only two, [the two objects]
> co-moving coordinate systems.

I already spoonfed you your unexamined stipulations, pointing out that you are (unwittingly) referring to the standard inertial coordinate systems, S and S', in which the two object are respectively at rest.

> Given a velocity value |v| shared between a pair of observers...
Translation: Given two systems of standard inertia-based coordinates S and S' with mutual velocity v...
> ...each observer must be able to calculate that velocity value from the standpoint
> of his own FoR...

It's pointless to talk in terms of "what an observer must be able to calculate", because an observer could be someone like you, who can't calculate his way out of a paper bag. The propositions of physics are objective facts, not assertions about anyone's ability to calculate things. What you need to say is that given the velocity of an object in terms of one coordinate system, and given the relationship between that coordinate system and some other coordinate system, the velocity of the object in terms of that other system is fully specified.

> and from the standpoint of the other observer's FoR. Furthermore, all four of these velocity values must be identical.

Four? Again, a given object at a given event has a specific velocity in terms of any specified system of coordinates. So far you're just talking about two systems of coordinates, and you seem to be tacitly assuming they are inertial coordinate systems, which we can call S and S', and each object has a velocity in terms of those two coordinate systems (not four). As noted above, an object with dx/dt = 0 has d'x/dt' = -v, and an object with d'x/dt'=0 has dx/dt = v. If those are the four velocities you are talking about, they are not identical, two are zero and one is v and the other is -v.

> Relativity corollary: All velocities shared between all pairs of observers must be less than the velocity of light.

No, that isn't a corollary, and it isn't the relativity principle. It's a complete non-sequitur from what you have said.

> Stan now calculates what Townes will say Stan's velocity is according to Townes' co-moving coordinate system.

Again, if the "co-moving coordinate systems" you're referring to are standard inertia-based coordinate systems S and S' in which the two objects are at rest, then the object at rest in S' has velocity v in terms of S, and the object at rest in S has velocity -v in terms of S'. These are objective facts.

Of course, we could refer to other systems of coordinates... for example, we could use the time coordinate from S and the space coordinates of S', or vice versa, and the resulting hybrid coordinate systems would have different velocities, but these are not standard inertial coordinate systems. Again, there are infinitely many coordinate systems (in fact, there are infinitely many in which a given object is at rest), and every object has infinitely many velocities, depending on which system of coordinates you are referring to. So nothing that you are saying makes any sense. Now do you understand?

On Monday, May 23, 2022 at 3:41:07 PM UTC-7, Stan Fultoni wrote:
> On Monday, May 23, 2022 at 1:02:57 PM UTC-7, patdolan wrote:
> > > > Velocity Postulate:
> > >
> > > In physics, in terms of any operationally-defined system of coordinates x,t, and for any given trajectory x=f(t), at any given event, the quantity dx/dt is defined as the "velocity" of that trajectory at that event. This is the definition of the word "velocity", it is not a postulate.
> > >
> > > > [spacetime version...
> > >
> > > There is no separate "spacetime version" distinct from the standard historical definition of the word "velocity", as given above.
> > >
> > > > ... there can exist at most one instantaneous velocity magnitude ||v|| shared
> > > > between any pair of observers.
> > > That doesn't make sense. Velocity is as defined above, dx/dt in terms of any specified system of coordinates. There are infinitely many systems of coordinates, and entities have infinitely many different velocities, depending on which system of coordinates you are referring to. What you might be trying to say is that for two standard systems of inertial coordinates S and S', with aligned space axes, objects at rest in S' have velocity v in terms of S, and objects at rest in S have velocity -v in terms of S'. But these are by no means the only possible coordinate systems that can be defined, and hence those objects have any other velocities in terms of many other coordinate systems. It is necessary always to specify the coordinate system when referring to a velocity.
> >
> > To have infinitely many coordinate systems is tantamount to having infinitely many observers.
> Nope, you are mistakenly conflating "observers" with coordinate systems, one of the most common newbie mistakes. Every object is at rest in terms of infinitely many coordinate systems, with distinct temporal foliations, so there is no unique system of coordinates in which an object is at rest.
>
> > In this problem I have limited the ... coordinate systems to only two, [the two objects]
> > co-moving coordinate systems.
>
> I already spoonfed you your unexamined stipulations, pointing out that you are (unwittingly) referring to the standard inertial coordinate systems, S and S', in which the two object are respectively at rest.
> > Given a velocity value |v| shared between a pair of observers...
>
> Translation: Given two systems of standard inertia-based coordinates S and S' with mutual velocity v...
>
> > ...each observer must be able to calculate that velocity value from the standpoint
> > of his own FoR...
> It's pointless to talk in terms of "what an observer must be able to calculate", because an observer could be someone like you, who can't calculate his way out of a paper bag. The propositions of physics are objective facts, not assertions about anyone's ability to calculate things. What you need to say is that given the velocity of an object in terms of one coordinate system, and given the relationship between that coordinate system and some other coordinate system, the velocity of the object in terms of that other system is fully specified.
> > and from the standpoint of the other observer's FoR. Furthermore, all four of these velocity values must be identical.
> Four? Again, a given object at a given event has a specific velocity in terms of any specified system of coordinates. So far you're just talking about two systems of coordinates, and you seem to be tacitly assuming they are inertial coordinate systems, which we can call S and S', and each object has a velocity in terms of those two coordinate systems (not four). As noted above, an object with dx/dt = 0 has d'x/dt' = -v, and an object with d'x/dt'=0 has dx/dt = v. If those are the four velocities you are talking about, they are not identical, two are zero and one is v and the other is -v.
> > Relativity corollary: All velocities shared between all pairs of observers must be less than the velocity of light.
> No, that isn't a corollary, and it isn't the relativity principle. It's a complete non-sequitur from what you have said.
> > Stan now calculates what Townes will say Stan's velocity is according to Townes' co-moving coordinate system.
> Again, if the "co-moving coordinate systems" you're referring to are standard inertia-based coordinate systems S and S' in which the two objects are at rest, then the object at rest in S' has velocity v in terms of S, and the object at rest in S has velocity -v in terms of S'. These are objective facts.
>
> Of course, we could refer to other systems of coordinates... for example, we could use the time coordinate from S and the space coordinates of S', or vice versa, and the resulting hybrid coordinate systems would have different velocities, but these are not standard inertial coordinate systems. Again, there are infinitely many coordinate systems (in fact, there are infinitely many in which a given object is at rest), and every object has infinitely many velocities, depending on which system of coordinates you are referring to. So nothing that you are saying makes any sense. Now do you understand?

Stownes has muddied the water a bit. So now may be a good time for a clarifying concept put forward by a master mathematician/scientist.

To that end we now introduce the concept of the reciprocating velocities ratio. To calculate the reciprocating velocities ratio between a pair of FoRs imagine two observers, Stan and Townes, at rest at the origins of their respective co-moving FoRs. Stan now calculates the reciprocating velocities ratio for Townes in a Galilean universe.

1) Using his own co-moving FoR Stan finds that Townes is moving towards him at .867c.

2) Then Stan uses the Galilean Transformations to determine that Townes, at rest at the origin of his own FoR, will measure that Stan is moving towards him at .867c also.

3) Stan takes the ratio of these reciprocating velocities and finds it is equal to 1.0

Stan now repeats the calculation of the reciprocating velocities ratio in an Einsteinian universe:

1) Measuring by means of his own FoR Stan, at rest at the origin, finds that Townes is moving towards him at .867c.

2) Then Stan uses the Lorentz Transformations to determine that Townes, at rest at the origin of his own Lorentz-contracted & time-dilated FoR, will simultaneously measure that Stan is moving towards him at 3.468c.

Keep in mind that in the uncontracted-undilated version of his FoR, a version of Townes will find that Stan is moving towards him at .867c. But that Townes is not the same Townes in Stan's FoR moving towards Stan at .867c. A many-worlds camel thus sticks its nose under the Special Relativity tent.

3) Stan takes the ratio of these reciprocating velocities and finds that it is equal to gamma^2 in an Einstein-Lorentz Universe. Recall that in a Galilean Universe the ratio is always 1.0

On Monday, May 23, 2022 at 7:00:14 PM UTC-7, patdolan wrote:
> 1) Using his own co-moving FoR Stan finds that Townes is moving towards him at .867c.

Translation: Stan is at rest (at the origin, say) in the standard inertial coordinate system S, and Townes is at rest (as some negative x' value) in the standard (aligned) inertial coordinate system S' moving with speed v = sqrt(3)/2 in terms of S.

> 2) Townes, at rest at the origin of his own FoR, will measure that Stan is moving
> towards him at .867c also.

Well, if they are both at rest at the spatial origins of inertial coordinate systems, and they are approaching each other, and their origins coincide (standard configuration), they must be at negative time coordinates. You are again conflating observers/objects with coordinate systems, which is leading you into the error explained in the previous message.

> 3) Stan takes the ratio of these reciprocating velocities and finds it is equal to 1.0

Again, given two systems of inertial coordinates S and S' in standard configuration, if S' is moving at velocity v in terms of S, then S is moving at velocity -v in terms of S'. This would be true in your hypothetical universe with S and S' related by Galilean transformation, and it is true in the actual universe with S and S' related by Lorentz transformation. Duh.

> 1) Measuring by means of his own FoR Stan, at rest at the origin, finds that Townes
> is moving towards him at .867c.

Again, this is specified as part of the condition, i.e., S' is moving at speed v in terms of S.

> 2) Then Stan uses the Lorentz Transformations to determine that Townes, at rest
> at the origin of his own Lorentz-contracted & time-dilated FoR, will simultaneously
> measure that Stan is moving towards him at 3.468c.

Nope, everyone agrees, and can verify by measurement, that objects at rest in S' are moving at speed v in terms of S, and objects at rest in S are moving at speed -v in terms of S'. Again, this would be true in your hypothetical universe with S and S' related by Galilean transformation, and it is true in the actual universe with S and S' related by Lorentz transformation. Duh.

> In the uncontracted-undilated version of his FoR...

There are not multiple versions of the two systems of coordinates that you are referring to, there is S and S', and the objects have the stipulated speeds in terms of those two systems. If you wish to define another system of coordinates (as explained in the previous message), you are free to do so, but that doesn't change the speeds of the objects in terms of S and S'.

Remember, the coordinates of any event in terms of a given system of inertial coordinates S are the readings on a grid of standard rulers and clocks at rest and inertially synchronized in S. Likewise for S'. These readings are what they are, empirically, without any reference to how S and S' are related to each other. After making these measurements, we note that S and S' are related by a Lorentz transformation. This accounts both for the reciprocal velocities and for all the effects of time dilations, length contraction, and skew of simultaneity. Do you understand this now?

On Monday, May 23, 2022 at 8:01:28 PM UTC-7, Stan Fultoni wrote:
> On Monday, May 23, 2022 at 7:00:14 PM UTC-7, patdolan wrote:
> > 1) Using his own co-moving FoR Stan finds that Townes is moving towards him at .867c.
> Translation: Stan is at rest (at the origin, say) in the standard inertial coordinate system S, and Townes is at rest (as some negative x' value) in the standard (aligned) inertial coordinate system S' moving with speed v = sqrt(3)/2 in terms of S.
>
> > 2) Townes, at rest at the origin of his own FoR, will measure that Stan is moving
> > towards him at .867c also.
> Well, if they are both at rest at the spatial origins of inertial coordinate systems, and they are approaching each other, and their origins coincide (standard configuration), they must be at negative time coordinates. You are again conflating observers/objects with coordinate systems, which is leading you into the error explained in the previous message.
> > 3) Stan takes the ratio of these reciprocating velocities and finds it is equal to 1.0
> Again, given two systems of inertial coordinates S and S' in standard configuration, if S' is moving at velocity v in terms of S, then S is moving at velocity -v in terms of S'. This would be true in your hypothetical universe with S and S' related by Galilean transformation, and it is true in the actual universe with S and S' related by Lorentz transformation. Duh.
> > 1) Measuring by means of his own FoR Stan, at rest at the origin, finds that Townes
> > is moving towards him at .867c.
> Again, this is specified as part of the condition, i.e., S' is moving at speed v in terms of S.
> > 2) Then Stan uses the Lorentz Transformations to determine that Townes, at rest
> > at the origin of his own Lorentz-contracted & time-dilated FoR, will simultaneously
> > measure that Stan is moving towards him at 3.468c.
> Nope, everyone agrees, and can verify by measurement, that objects at rest in S' are moving at speed v in terms of S, and objects at rest in S are moving at speed -v in terms of S'. Again, this would be true in your hypothetical universe with S and S' related by Galilean transformation, and it is true in the actual universe with S and S' related by Lorentz transformation.. Duh.
>
> > In the uncontracted-undilated version of his FoR...
>
> There are not multiple versions of the two systems of coordinates that you are referring to, there is S and S', and the objects have the stipulated speeds in terms of those two systems. If you wish to define another system of coordinates (as explained in the previous message), you are free to do so, but that doesn't change the speeds of the objects in terms of S and S'.

Stownes,

I'm finding it difficult to follow your argument in terms of S and S' then translating it into my terms of Stan and Townes. Please recast your entire post interns of Stan and Townes. Thank you.
>
> Remember, the coordinates of any event in terms of a given system of inertial coordinates S are the readings on a grid of standard rulers and clocks at rest and inertially synchronized in S. Likewise for S'. These readings are what they are, empirically, without any reference to how S and S' are related to each other. After making these measurements, we note that S and S' are related by a Lorentz transformation. This accounts both for the reciprocal velocities and for all the effects of time dilations, length contraction, and skew of simultaneity. Do you understand this now?

On Monday, May 23, 2022 at 8:13:12 PM UTC-7, patdolan wrote:
> I'm finding it difficult to follow your argument in terms of S and S' then translating
> it into my terms of Stan and Townes. Please recast your entire post interns of Stan
> and Townes.

Again, among the many conceptual mistakes you are making is the conflating of people with coordinate systems. Repeat after me: People are not coordinate systems. You are stipulating that any object (or person) at rest in S' has velocity v in terms of S, and any object (or person) at rest in S has velocity -v in terms of S'. This is independent of whether S and S' are related to each other by Galilean transformation or Lorentz transformation. Now do you understand?

On Monday, May 23, 2022 at 8:20:41 PM UTC-7, Stan Fultoni wrote:
> On Monday, May 23, 2022 at 8:13:12 PM UTC-7, patdolan wrote:
> > I'm finding it difficult to follow your argument in terms of S and S' then translating
> > it into my terms of Stan and Townes. Please recast your entire post interns of Stan
> > and Townes.
> Again, among the many conceptual mistakes you are making is the conflating of people with coordinate systems. Repeat after me: People are not coordinate systems. You are stipulating that any object (or person) at rest in S' has velocity v in terms of S, and any object (or person) at rest in S has velocity -v in terms of S'. This is independent of whether S and S' are related to each other by Galilean transformation or Lorentz transformation. Now do you understand?

Are you kidding? No one ever understands you Townes.

On Monday, May 23, 2022 at 8:40:42 PM UTC-7, patdolan wrote:
> > > I'm finding it difficult to follow your argument in terms of S and S' then translating
> > > it into my terms of Stan and Townes. Please recast your entire post interns of Stan
> > > and Townes.
> >
> > Again, among the many conceptual mistakes you are making is the conflating of people with coordinate systems. Repeat after me: People are not coordinate systems. You are stipulating that any object (or person) at rest in S' has velocity v in terms of S, and any object (or person) at rest in S has velocity -v in terms of S'. This is independent of whether S and S' are related to each other by Galilean transformation or Lorentz transformation. Now do you understand?
>
> Are you kidding?

No, my thorough and succinct debunking of your misconceptions is correct. Which part of it do you think is wrong or unclear?

On Monday, May 23, 2022 at 8:53:16 PM UTC-7, Stan Fultoni wrote:
> On Monday, May 23, 2022 at 8:40:42 PM UTC-7, patdolan wrote:
> > > > I'm finding it difficult to follow your argument in terms of S and S' then translating
> > > > it into my terms of Stan and Townes. Please recast your entire post interns of Stan
> > > > and Townes.
> > >
> > > Again, among the many conceptual mistakes you are making is the conflating of people with coordinate systems. Repeat after me: People are not coordinate systems. You are stipulating that any object (or person) at rest in S' has velocity v in terms of S, and any object (or person) at rest in S has velocity -v in terms of S'. This is independent of whether S and S' are related to each other by Galilean transformation or Lorentz transformation.. Now do you understand?
> >
> > Are you kidding?
> No, my thorough and succinct debunking of your misconceptions is correct. Which part of it do you think is wrong or unclear?
You seem to act cornered Townes, as if you realize I have cornered you. Why else would you appear under the fake name Stan Fultoni? This use of alia signals that you realize you can't match me and my arguments. Be brave and use my definitions when addressing my problems.

Again Stownes, there is nothing in your words which is clearly recognizable.. Please use my words.

On Tuesday, 24 May 2022 at 00:41:07 UTC+2, Stan Fultoni wrote:
> On Monday, May 23, 2022 at 1:02:57 PM UTC-7, patdolan wrote:
> > > > Velocity Postulate:
> > >
> > > In physics, in terms of any operationally-defined system of coordinates x,t, and for any given trajectory x=f(t), at any given event, the quantity dx/dt is defined as the "velocity" of that trajectory at that event. This is the definition of the word "velocity", it is not a postulate.
> > >
> > > > [spacetime version...
> > >
> > > There is no separate "spacetime version" distinct from the standard historical definition of the word "velocity", as given above.
> > >
> > > > ... there can exist at most one instantaneous velocity magnitude ||v|| shared
> > > > between any pair of observers.
> > > That doesn't make sense. Velocity is as defined above, dx/dt in terms of any specified system of coordinates. There are infinitely many systems of coordinates, and entities have infinitely many different velocities, depending on which system of coordinates you are referring to. What you might be trying to say is that for two standard systems of inertial coordinates S and S', with aligned space axes, objects at rest in S' have velocity v in terms of S, and objects at rest in S have velocity -v in terms of S'. But these are by no means the only possible coordinate systems that can be defined, and hence those objects have any other velocities in terms of many other coordinate systems. It is necessary always to specify the coordinate system when referring to a velocity.
> >
> > To have infinitely many coordinate systems is tantamount to having infinitely many observers.
> Nope, you are mistakenly conflating "observers" with coordinate systems, one of the most common newbie mistakes. Every object is at rest in terms of infinitely many coordinate systems, with distinct temporal foliations, so there is no unique system of coordinates in which an object is at rest.
>
> > In this problem I have limited the ... coordinate systems to only two, [the two objects]
> > co-moving coordinate systems.
>
> I already spoonfed you your unexamined stipulations, pointing out that you are (unwittingly) referring to the standard inertial coordinate systems, S and S', in which the two object are respectively at rest.
> > Given a velocity value |v| shared between a pair of observers...
>
> Translation: Given two systems of standard inertia-based coordinates S and S' with mutual velocity v...
>
> > ...each observer must be able to calculate that velocity value from the standpoint
> > of his own FoR...
> It's pointless to talk in terms of "what an observer must be able to calculate", because an observer could be someone like you, who can't calculate his way out of a paper bag. The propositions of physics are objective facts, not assertions about anyone's ability to calculate things.

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

On 24-May-22 2:12 am, patdolan wrote:
> On Monday, May 23, 2022 at 12:18:43 AM UTC-7, Sylvia Else wrote:
>> On 23-May-22 12:21 pm, patdolan wrote:
>>
>>> Velocity Uniqueness Theorem: It is a fundamental quality of motion that there can exist at most one instantaneous velocity magnitude ||v|| shared between any pair of observers.
>> If that's a theorem, where's the proof?
>>
>> Sylvia.
> This is a most excellent point that you make, Sylvia Jones. The velocity uniqueness theorem may in fact have to be elevated to postulate level. But whether theorem or postulate, one thing is certain: given the validity of the LTs and SR, the velocity uniqueness theorem is certainly wrong. I will prove it directly.
>
> Two observers, Stan and Townes. Using his co-moving coordinate system Stan determines that Townes is one light year away and traveling at .867c in his direction. Stan now calculates what Townes will say Stan's velocity is according to Townes' co-moving coordinate system.
>
> Stan immediately perceives that Townes' co-moving coordinate system is contracted by a factor of two and that Towne's clock is ticking at half the rate of his own clock. These phenomena are not some sort of illusion. In Stan's FoR Townes really does measure that he moves two meters towards Stan for every one meter that Stan moves towards Townes. Furthermore, Stan measures that Townes' clock ticks off only half as much time as his own during the simultaneous distance intervals in the preceding sentence. When Stan and Townes pass one another, Stan watches Townes' hand moving at half speed as he writes down two light years distance divided by 0.5767 years to calculate Stan's velocity as 3.468c.
>
> Sure, Townes will measure another velocity for Stan in his own FoR. But we are watching from Stan and Townes calculate velocity from Stan's FoR. [this also implies that SR is a "Many Worlds" theory.]
>
> What has been accomplished: We have demonstrated that given the LTs and SR, the velocity two observers share between themselves can never be unique.
>
> There is more to spin out but the author pauses here for his mathematical inferiors to catch the drift of his thought before proceeding.
>

If you misapply SR, which you are, then you'll reach wrong conclusions,
which you also are.

Sylvia.

On Monday, May 23, 2022 at 8:20:41 PM UTC-7, Stan Fultoni wrote:
> On Monday, May 23, 2022 at 8:13:12 PM UTC-7, patdolan wrote:
> > I'm finding it difficult to follow your argument in terms of S and S' then translating
> > it into my terms of Stan and Townes. Please recast your entire post interns of Stan
> > and Townes.
> Again, among the many conceptual mistakes you are making is the conflating of people with coordinate systems. Repeat after me: People are not coordinate systems. You are stipulating that any object (or person) at rest in S' has velocity v in terms of S, and any object (or person) at rest in S has velocity -v in terms of S'. This is independent of whether S and S' are related to each other by Galilean transformation or Lorentz transformation. Now do you understand?

Such ignorance. People are not coordinate systems. But people are co-moving observers when they are at rest at the origin of coordinate systems. This is so fundamental that I don't know if I should waste more time on a beginner like you Stownes. This is childish word play on your part. Do you even intend to argue honestly?

You always end your posts by asking if I understand. Answer me one simple question to let me understand if you are an honest arguer or a dishonest obscurantist. This simple question goes to the heart of your honesty and integrity. Here is the questions Stan Fultoni:

Are you now, or have you ever been Townes Olson?

On Monday, May 23, 2022 at 9:06:36 PM UTC-7, patdolan wrote:
> > > > Again, among the many conceptual mistakes you are making is the conflating of people with coordinate systems. Repeat after me: People are not coordinate systems. You are stipulating that any object (or person) at rest in S' has velocity v in terms of S, and any object (or person) at rest in S has velocity -v in terms of S'. This is independent of whether S and S' are related to each other by Galilean transformation or Lorentz transformation. Now do you understand?
> > >
> > > Are you kidding?
> >
> > No, my thorough and succinct debunking of your misconceptions is correct. Which part of it do you think is wrong or unclear?
>
> There is nothing in your words which is clearly recognizable.

Any mentally competent person with even a passing acquaintance with elementary physics would have no difficulty understanding what I've said. It may well be true that you do not understand a word of what I've said, but that is because of your limitations, not because the explanation is incorrect or even unclear. Your refusal to even ask for clarification speaks volumes: You don't want to understand.

> Please use my words... use my definitions when addressing my problems.

Your problems are due to the fact that your words and definitions are all self-indulgent infantile gibberish. I've explained this very clearly, giving detailed explanations of why each of your definitions and statements was wrong, and then I provided the correct statements. You're welcome. If you have any questions, feel free to ask. (As always, I suggest you wait until you sober up before replying.)

On Monday, May 23, 2022 at 9:29:52 PM UTC-7, patdolan wrote:
> People are co-moving observers when they are at rest at the origin of coordinate systems.

Yet again (please try to concentrate), every object is at rest at the origin of infinitely many different systems of coordinates, with different temporal foliations, so you cannot specify a coordinate system by just referring to a person or object. You absolutely must specify the coordinate system, such as the inertial coordinate system S in terms of which the person or object is at rest (at a specific event). Do you dispute this?

On Monday, May 23, 2022 at 9:37:54 PM UTC-7, Stan Fultoni wrote:
> On Monday, May 23, 2022 at 9:29:52 PM UTC-7, patdolan wrote:
> > People are co-moving observers when they are at rest at the origin of coordinate systems.
>
> Yet again (please try to concentrate), every object is at rest at the origin of infinitely many different systems of coordinates, with different temporal foliations, so you cannot specify a coordinate system by just referring to a person or object. You absolutely must specify the coordinate system, such as the inertial coordinate system S in terms of which the person or object is at rest (at a specific event). Do you dispute this?

I do not dispute it. In fact I have employed it. But your mind is too small to substitute Stan for S and Townes for S'. Do you dispute this?

Stwones, you simply will never understand math until you also understand linguistics and semiotics, the signifier and the signified.

You continue to offer me answers to everything but the one question I asked of you, Stan Fultoni:

Are you now, or have you ever been Townes Olson????

On Monday, May 23, 2022 at 9:26:19 PM UTC-7, Sylvia Else wrote:
> On 24-May-22 2:12 am, patdolan wrote:
> > On Monday, May 23, 2022 at 12:18:43 AM UTC-7, Sylvia Else wrote:
> >> On 23-May-22 12:21 pm, patdolan wrote:
> >>
> >>> Velocity Uniqueness Theorem: It is a fundamental quality of motion that there can exist at most one instantaneous velocity magnitude ||v|| shared between any pair of observers.
> >> If that's a theorem, where's the proof?
> >>
> >> Sylvia.
> > This is a most excellent point that you make, Sylvia Jones. The velocity uniqueness theorem may in fact have to be elevated to postulate level. But whether theorem or postulate, one thing is certain: given the validity of the LTs and SR, the velocity uniqueness theorem is certainly wrong. I will prove it directly.
> >
> > Two observers, Stan and Townes. Using his co-moving coordinate system Stan determines that Townes is one light year away and traveling at .867c in his direction. Stan now calculates what Townes will say Stan's velocity is according to Townes' co-moving coordinate system.
> >
> > Stan immediately perceives that Townes' co-moving coordinate system is contracted by a factor of two and that Towne's clock is ticking at half the rate of his own clock. These phenomena are not some sort of illusion. In Stan's FoR Townes really does measure that he moves two meters towards Stan for every one meter that Stan moves towards Townes. Furthermore, Stan measures that Townes' clock ticks off only half as much time as his own during the simultaneous distance intervals in the preceding sentence. When Stan and Townes pass one another, Stan watches Townes' hand moving at half speed as he writes down two light years distance divided by 0.5767 years to calculate Stan's velocity as 3.468c.
> >
> > Sure, Townes will measure another velocity for Stan in his own FoR. But we are watching from Stan and Townes calculate velocity from Stan's FoR. [this also implies that SR is a "Many Worlds" theory.]
> >
> > What has been accomplished: We have demonstrated that given the LTs and SR, the velocity two observers share between themselves can never be unique.
> >
> > There is more to spin out but the author pauses here for his mathematical inferiors to catch the drift of his thought before proceeding.
> >
> If you misapply SR, which you are, then you'll reach wrong conclusions,
> which you also are.
>
> Sylvia.

Sylvia, it comes down to this: are length contraction and time dilation real? Or are they illusionary mirages and plays on light? A person whose brain, wristwatch and pocket calculator are all functioning at half the rate of yours and whose outstretched arm and ruler are half the length of yours simply can never accept that the velocity you assign him is the same as yours.

On 24-May-22 2:55 pm, patdolan wrote:
> On Monday, May 23, 2022 at 9:26:19 PM UTC-7, Sylvia Else wrote:
>> On 24-May-22 2:12 am, patdolan wrote:
>>> On Monday, May 23, 2022 at 12:18:43 AM UTC-7, Sylvia Else wrote:
>>>> On 23-May-22 12:21 pm, patdolan wrote:
>>>>
>>>>> Velocity Uniqueness Theorem: It is a fundamental quality of
>>>>> motion that there can exist at most one instantaneous
>>>>> velocity magnitude ||v|| shared between any pair of
>>>>> observers.
>>>> If that's a theorem, where's the proof?
>>>>
>>>> Sylvia.
>>> This is a most excellent point that you make, Sylvia Jones. The
>>> velocity uniqueness theorem may in fact have to be elevated to
>>> postulate level. But whether theorem or postulate, one thing is
>>> certain: given the validity of the LTs and SR, the velocity
>>> uniqueness theorem is certainly wrong. I will prove it directly.
>>>
>>> Two observers, Stan and Townes. Using his co-moving coordinate
>>> system Stan determines that Townes is one light year away and
>>> traveling at .867c in his direction. Stan now calculates what
>>> Townes will say Stan's velocity is according to Townes' co-moving
>>> coordinate system.
>>>
>>> Stan immediately perceives that Townes' co-moving coordinate
>>> system is contracted by a factor of two and that Towne's clock is
>>> ticking at half the rate of his own clock. These phenomena are
>>> not some sort of illusion. In Stan's FoR Townes really does
>>> measure that he moves two meters towards Stan for every one meter
>>> that Stan moves towards Townes. Furthermore, Stan measures that
>>> Townes' clock ticks off only half as much time as his own during
>>> the simultaneous distance intervals in the preceding sentence.
>>> When Stan and Townes pass one another, Stan watches Townes' hand
>>> moving at half speed as he writes down two light years distance
>>> divided by 0.5767 years to calculate Stan's velocity as 3.468c.
>>>
>>> Sure, Townes will measure another velocity for Stan in his own
>>> FoR. But we are watching from Stan and Townes calculate velocity
>>> from Stan's FoR. [this also implies that SR is a "Many Worlds"
>>> theory.]
>>>
>>> What has been accomplished: We have demonstrated that given the
>>> LTs and SR, the velocity two observers share between themselves
>>> can never be unique.
>>>
>>> There is more to spin out but the author pauses here for his
>>> mathematical inferiors to catch the drift of his thought before
>>> proceeding.
>>>
>> If you misapply SR, which you are, then you'll reach wrong
>> conclusions, which you also are.
>>
>> Sylvia.
>
> Sylvia, it comes down to this: are length contraction and time
> dilation real? Or are they illusionary mirages and plays on light?
> A person whose brain, wristwatch and pocket calculator are all
> functioning at half the rate of yours and whose outstretched arm and
> ruler are half the length of yours simply can never accept that the
> velocity you assign him is the same as yours.
>

As has been repeatedly pointed out, length contraction and time dilation
are a consequence of projections from one coordinate system to another.
They are special cases of the Lorentz transform, and people frequently
try to use them inappropriately in arguments, and reach mistaken
conclusions thereby. Whether or not they are real depends very much on
your precise definition of "real", and is a question for philosophy.

In your scenario, each person will use their own clocks and metre rules
to determine the relative velocity, and they will both reach the same
conclusion.

The real test of SR is whether its use results in the correct
predictions of what can be measured, and it does.

Sylvia.