In a language like Japanese,
the notion of existence as being along a worldline in spacetime
is built right into its verbal morphology, with (for instance)
"being at", "coming" and "going" being represented by the same
word.

xixj_0@yahoo.com (John Tapper) wrote:

The four-dimensional continuum of one temporal and three spatial
coordinates in which any event or physical object is located.

For historical research, who changed the dimensions from 3 to 4?

Can I dare ask why?

It was always 4. The premise is built into the structure of
human language, itself. The belief in reality ultimately being
spacetime, rather than space "moving in time" is the essence of
Vedantic philosophy and the essence of its remote offshoot (Zen,
e.g., the famous "flag isn't moving, the mind is" koan); the
essential point underlying Zeno's philosophy, and a foundation
underlying Diodorian and Aristotle's temporal logic formalisms,
a key aspect of St. Aquinas' world view (who also stated that
God's existence is fundamentally at the level of spacetime,
not *in* time), among other places. In a language like Japanese,
the notion of existence as being along a worldline in spacetime
is built right into its verbal morphology, with (for instance)
"being at", "coming" and "going" being represented by the same
word.

Newton's theory was also a theory of spacetime, regardless of
whether it was spelled out as such or not. In particular, the
structure underlying Newton's spacetime is an instance of
what's known today as a Fibre Bundle -- in this case an E(3)
bundle (each fibre being a 3-D Euclidean space), on a E(1)
base space (the time line).

In fact, the same method used to represent gravity geometrically
in Relativity as (primarily) a curvature in time, in spacetime;
applies equally in the Newtonian spacetime. There, the curvature
takes place entirely in the time direction, represented by how
adjacent E(3) fibres are sewn up together. The way fibres
are connected in a fibre bundle is given by its "connection".
In Newtonian space, a connection consists precisely of a
prescription at each point of an acceleration (i.e., gravity).
This tells how a line, that is laid out like an embroidery
across fibres -- which would otherwise be straight (in
accordance with Newton's first and second laws) would curve
over time (i.e. accelerate). The warping is in the warping
of the connections of the adjacent layers to one another.
In place of Einstein's field equations, which relates the
curvature of [space]time with something involving matter
distributions; in Newton's Physics, you'd have Poisson's
equations, which relates the acceleration field corresponding
to the connection to the matter distribution.

So, warped spacetime has nothing to do with Einstein either.
The same geometrical interpretation involving curvature in time
applies to Newton's spacetime too.

xixj_0@yahoo.com (John Tapper) wrote:

The four-dimensional continuum of one temporal and three spatial
coordinates in which any event or physical object is located.

For historical research, who changed the dimensions from 3 to 4?

Can I dare ask why?

It was always 4. The premise is built into the structure of
human language, itself. The belief in reality ultimately being
spacetime, rather than space "moving in time" is the essence of
Vedantic philosophy and the essence of its remote offshoot (Zen,
e.g., the famous "flag isn't moving, the mind is" koan); the
essential point underlying Zeno's philosophy, and a foundation
underlying Diodorian and Aristotle's temporal logic formalisms,
a key aspect of St. Aquinas' world view (who also stated that
God's existence is fundamentally at the level of spacetime,
not *in* time), among other places. In a language like Japanese,
the notion of existence as being along a worldline in spacetime
is built right into its verbal morphology, with (for instance)
"being at", "coming" and "going" being represented by the same
word.

Newton's theory was also a theory of spacetime, regardless of
whether it was spelled out as such or not. In particular, the
structure underlying Newton's spacetime is an instance of
what's known today as a Fibre Bundle -- in this case an E(3)
bundle (each fibre being a 3-D Euclidean space), on a E(1)
base space (the time line).

So, warped spacetime has nothing to do with Einstein either.
The same geometrical interpretation involving curvature in time
applies to Newton's spacetime too.

In article <c38f0627.0311041507.3a675427@posting.google.com>,
John Tapper <xixj_0@yahoo.com> wrote:

Just interested in the history of the word "spacetime" as becoming one
word.

http://dictionary.reference.com/search?q=spacetime (these guys put a
hyphen)
space-time (spstm)
n. Physics
The four-dimensional continuum of one temporal and three spatial
coordinates in which any event or physical object is located.

For historical research, who changed the dimensions from 3 to 4?

I believe that would be Minkowski.

Can I dare ask why?

Because meaningful vector operations can be performed on four-vectors.
The magnitude of a position four-vector, for instance, makes sense,

A = (ct,x,y,z)

d^2/d(x^u)^2 phi = 0

where c is a wave propagation speed, not necessarily that of light, or
invariant.

In article <c38f0627.0311041507.3a675427@posting.google.com>,
John Tapper <xixj_0@yahoo.com> wrote:

Just interested in the history of the word "spacetime" as becoming one
word.

http://dictionary.reference.com/search?q=spacetime (these guys put a
hyphen)
space-time (spstm)
n. Physics
The four-dimensional continuum of one temporal and three spatial
coordinates in which any event or physical object is located.

For historical research, who changed the dimensions from 3 to 4?

I believe that would be Minkowski.

Can I dare ask why?

Because meaningful vector operations can be performed on four-vectors.
The magnitude of a position four-vector, for instance, makes sense,

A = (ct,x,y,z)

|A|^2 = c^2 t^2 - x^2 - y^2 - z^2

which is a statement of the metric of the space; it is the equivalent of
length and is the quantity that's preserved under a Lorentz
transformation. Galilean transformations preserve lengths which don't
include time.

... = c^2 t^2 - x^2 - y^2 - z^2

But I think it's interesting that in some late 19th century studies of
rotating objects, a four-dimensional formalism was developed for
mathematical convenience, with no physical significance ascribed to it.

And even a Newtonian wave equation has the form of

d^2/d(x^u)^2 phi = 0

where c is a wave propagation speed, not necessarily that of light, or
invariant.

And the plane wave that shows up in quantum mechanics,

psi ~ exp[i(px - Et)/hbar]

Looks a lot like a four-momentum dotted into a four-position. It's almost
like there's something about nature that wants a four-dimensional
description even if your kinematics don't support it.

John Tapper wrote:

For historical research, who changed the dimensions from 3 to 4?

Can I dare ask why?

You need three spatial co-ordinates and one time co-ordinate to
completely specify an event.

Bob Kolker

I assume that it's
called Minkowski space for a reason, so you might consider adding that
name to your searches.