Velocity in Spacetime / Russell

[Alan Grayson]

Russell; this is directed to you, primarily, since I am confident you can answer this question with ease. If a test particle is at rest from the perspective of some reference frame, it's claimed that this test particle is moving at velocity c along the time axis. But what exactly does this mean? And more important how is this possible since SR establishes that no material particle can move at exactly velocity c? TY, AG

[Russell Standish]

Any object will experience moving though spacetime at a rate of 1
second per second. The term often used for this is "proper
time". Since one second is c metres (c being just the conversion constant
between metres and seconds, you could also say it is moving through
spacetime at velocity c.

The other thing your refer as "no material particle can move at
exactly velocity c" has left out the phrase "in space". Relative to
any other object's path through spacetime, the angle of the test
object trajectory cannot be such that it is moving c metres through
space for every second it moves through time.


--

----------------------------------------------------------------------------
Dr Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders hpc...@hpcoders.com.au
http://www.hpcoders.com.au
----------------------------------------------------------------------------

[Alan Grayson]

On Tuesday, November 11, 2025 at 12:47:53 AM UTC-7 Russell Standish wrote:

On Mon, Nov 10, 2025 at 10:27:41PM -0800, Alan Grayson wrote:
> Russell; this is directed to you, primarily, since I am confident you can
> answer this question with ease. If a test particle is at rest from the
> perspective of some reference frame, it's claimed that this test particle is
> moving at velocity c along the time axis. But what exactly does this mean? And
> more important how is this possible since SR establishes that no material
> particle can move at exactly velocity c? TY, AG
>

Any object will experience moving though spacetime at a rate of 1
second per second. The term often used for this is "proper
time". Since one second is c metres (c being just the conversion constant
between metres and seconds, you could also say it is moving through
spacetime at velocity c.

If we label coordinate time along the time (y) axis, and use c as the conversion

factor, the claim is the particle is moving at light speed along the time axis,

while at rest along the space (x) axis. The only problem from my pov, is this

makes no sense whatsoever! I can't grasp what this means. AG 

The other thing your refer as "no material particle can move at
exactly velocity c" has left out the phrase "in space". Relative to
any other object's path through spacetime, the angle of the test
object trajectory cannot be such that it is moving c metres through
space for every second it moves through time.

[Brent Meeker]

On 11/11/2025 4:15 AM, Alan Grayson wrote:

On Tuesday, November 11, 2025 at 12:47:53 AM UTC-7 Russell Standish wrote:

On Mon, Nov 10, 2025 at 10:27:41PM -0800, Alan Grayson wrote:
> Russell; this is directed to you, primarily, since I am confident you can
> answer this question with ease. If a test particle is at rest from the
> perspective of some reference frame, it's claimed that this test particle is
> moving at velocity c along the time axis. But what exactly does this mean? And
> more important how is this possible since SR establishes that no material
> particle can move at exactly velocity c? TY, AG
>

Any object will experience moving though spacetime at a rate of 1
second per second. The term often used for this is "proper
time". Since one second is c metres (c being just the conversion constant
between metres and seconds, you could also say it is moving through
spacetime at velocity c.

If we label coordinate time along the time (y) axis, and use c as the conversion

factor, the claim is the particle is moving at light speed along the time axis,

while at rest along the space (x) axis. The only problem from my pov, is this

makes no sense whatsoever! I can't grasp what this means. AG 

The idea is that everything moves thru spacetime at the same speed, c.  Time along this path is one (proper) second per second.  But it doesn't move thru space at c and speed thru space is relative; each person can take themself to be stationary in space.



Brent

The other thing your refer as "no material particle can move at
exactly velocity c" has left out the phrase "in space". Relative to
any other object's path through spacetime, the angle of the test
object trajectory cannot be such that it is moving c metres through
space for every second it moves through time.

----------------------------------------------------------------------------
Dr Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders hpc...@hpcoders.com.au
http://www.hpcoders.com.au
----------------------------------------------------------------------------

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[Alan Grayson]

On Tuesday, November 11, 2025 at 2:28:50 PM UTC-7 Brent Meeker wrote:

On 11/11/2025 4:15 AM, Alan Grayson wrote:

On Tuesday, November 11, 2025 at 12:47:53 AM UTC-7 Russell Standish wrote:

On Mon, Nov 10, 2025 at 10:27:41PM -0800, Alan Grayson wrote:
> Russell; this is directed to you, primarily, since I am confident you can
> answer this question with ease. If a test particle is at rest from the
> perspective of some reference frame, it's claimed that this test particle is
> moving at velocity c along the time axis. But what exactly does this mean? And
> more important how is this possible since SR establishes that no material
> particle can move at exactly velocity c? TY, AG
>

Any object will experience moving though spacetime at a rate of 1
second per second. The term often used for this is "proper
time". Since one second is c metres (c being just the conversion constant
between metres and seconds, you could also say it is moving through
spacetime at velocity c.

If we label coordinate time along the time (y) axis, and use c as the conversion

factor, the claim is the particle is moving at light speed along the time axis,

while at rest along the space (x) axis. The only problem from my pov, is this

makes no sense whatsoever! I can't grasp what this means. AG 

The idea is that everything moves thru spacetime at the same speed, c.  Time along this path is one (proper) second per second.  But it doesn't move thru space at c and speed thru space is relative; each person can take themself to be stationary in space.

Thanks for your effort, but I don't get it. If an observer is at rest, it would mean he's moving at speed c along time axis, which makes no sense to me. Also, in your left diagram, I get (ds)^2 = (dt)^2 + (dx)^2 using Pythagorean theorem. Why no negative sign before spatial differential? And why is red rocket labeled T in right diagram? AG