Is the spacetime model necessary between frames that are relatively stationary?

[geordief]

Suppose we have two frames of reference that only differ  in that they are separated  by a fixed distance 

And suppose each frame makes measurements of an object that is moving relatively to both at any speed between 0 and c.

Is the concept of spacetime necessary for each frame to make that measurement and so that they agree in every case?

I am asking this because it has been said (was it by Minkowski?) that our previous till then  understanding of space and time must be replaced with a new amalgam  of the two (spacetime)  and I am wondering if this is because all frames of reference  are relatively in motion  in practice or whether the reason is deeper than that.

[MigL]

Because of the finite speed of light ( information ), objects ( events ) are separated by time as well as distance.
At small distances the time separation is  trivial, so we can safely ignore it.

[swansont]

26 minutes ago, geordief said:

Suppose we have two frames of reference that only differ  in that they are separated  by a fixed distance 

This is only one frame. They must be moving with respect to each other to be different frames.

[geordief]

1 hour ago, swansont said:

This is only one frame. They must be moving with respect to each other to be different frames.

Well OK ,but can I repeat the question with just that one frame and the fixed distance between the location of the taker of the  measurements in the same frame? (I would have said "observer"  but I suspect that might have different meanings ...)

If you just have the one frame is there any way to find the concept of spacetime useful  as opposed to the pre relativistic separation of it into space and time?

[swansont]

7 hours ago, geordief said:

Well OK ,but can I repeat the question with just that one frame and the fixed distance between the location of the taker of the  measurements in the same frame? (I would have said "observer"  but I suspect that might have different meanings ...)

If you just have the one frame is there any way to find the concept of spacetime useful  as opposed to the pre relativistic separation of it into space and time?

Any time or length measurement will be the same, but there will be length contraction of the object, and it will experience time dilation. Two observers measuring the decay of muons, for example, will get the same answer for the half-life, but it won’t agree with the lab frame measurements. Without relativity you could not reconcile the discrepancy.