[geordief (OP)]

I understand that space and time are interchangeable and that there is a conversion factor ,c that allows one to see one as a function of the other.

Would I be on the right track if I was to interpret these  understandings in the following way?

We do not travel through space  and neither (more intuitively) do we travel through time.


We just travel (follow entropy?)  and our progress relative to our environment is measured either in terms of spatial intervals or  temporal  intervals.

Would that interpretation be anyway along  the right lines?

[Halc]

Would I be on the right track if I was to interpret these  understandings in the following way?

We do not travel through space  and neither (more intuitively) do we travel through time.

I'd say you travel through space. I'm here at km-12, and an minute later I'm at km-13, which is travel of one km of space in one minute. That's what travel is.
Spacetime has time built in, and one cannot travel through it. Rather any object traces a worldline through it, but since it is present at all locations along that wordline, nothing moves through it. It isn't travel.

[geordief (OP)]

I'd say you travel through space. I'm here at km-12, and an minute later I'm at km-13, which is travel of one km of space in one minute. That's what travel is.
Spacetime has time built in, and one cannot travel through it. Rather any object traces a worldline through it, but since it is present at all locations along that wordline, nothing moves through it. It isn't travel.

Is that, though tracing a line in terms of the model or in terms of what the object is "actually" experiencing? (hope I didn't just drop down the rabbit hole)

[Halc]

I'd say you travel through space. I'm here at km-12, and an minute later I'm at km-13, which is travel of one km of space in one minute. That's what travel is.
Spacetime has time built in, and one cannot travel through it. Rather any object traces a worldline through it, but since it is present at all locations along that wordline, nothing moves through it. It isn't travel.

Is that, though tracing a line in terms of the model or in terms of what the object is "actually" experiencing? (hope I didn't just drop down the rabbit hole)

Most objects don't experience such things, but you experience moving through space over time because such an experience makes you far more fit than the same creature that doesn't interpret it this way.

[geordief (OP)]

Most objects don't experience such things, but you experience moving through space over time because such an experience makes you far more fit than the same creature that doesn't interpret it this way.

Are you saying that it is a practically infinitely close approximation that serves us extremely well since we are not relativistic biological creatures?

[Halc]

Are you saying that it is a practically infinitely close approximation that serves us extremely well since we are not relativistic biological creatures?

No, I made no mention of approximations or relativity.

I'm saying that travel means (by definition) a change in the unique location in space, and not being in some original location after the change occurs.

A worldline through spacetime doesn't meet this definition, so spacetime isn't something through which we travel. I live at this house yesterday, and if you look at the event of (this house, Aug 20) or the event (this house, Aug 24), you'll probably find me at those events. If it was travel, I'd only be at one location in spacetime, event (house, Aug 22) and you'd not find me at the house at those other locations in spacetime. But I'm present at mutliple events arranged in a worldline, and thus my worldline is just a line, not something that changes.

[BilboGrabbins]

But they do. A particle moving through space more than time is called a Braydion. A particle moving in time more than space is a Tardyon. A particle moving faster than light is called a Tacyhon.  It's all about relativity.

[Eternal Student]

Hi everyone.  I hope all is well.

A particle moving through space more than time is called a Braydion. A particle moving in time more than space is a Tardyon.

   Minor note:   I think Bradyon   and   Tardyon    are synonyms.   They mean the same thing, not different things.   Personally I like the name  Tardyon    - these are the particles that are "tardy".

- - - - - -
   Original Question:    Why do objects travel through space-time and not space and time?
Answer:   The English language is a bit sloppy.   People do say that we travel through space.  They also say that we travel through time - every second I have travelled 1 second into the future.   Finally, they also say we travel through spacetime but they probably shouldn't.   Halc has presented some good reasons for not thinking about spacetime or travel through spacetime in this way.

Would I be on the right track if I was to interpret these  understandings in the following way?
    We do not travel through space  and neither (more intuitively) do we travel through time.

     The sad thing is that we can't re-define every phrase that is used in common English language.   People do say that an object travels through space.  We (scientists) have made this quite a precise idea.  We can measure positions and record how they change with time.    The ratio of the change in position  by  the corresponding change in time is called the velocity of the object   etc. etc.   This is established and it's hard to change everyones view on that now.
     It's easier if you tolerate phrases like "we travel through spacetime" and just don't worry about them too much.  The person almost certainly meant "we can plot our position in space as time progresses" and they probably weren't trying to say anything more profound than that.

Best Wishes.

[evan_au]

It is said that "The shortest distance between two points is a straight line".
- I have heard a similar-sounding comment made about spacetime (by Sean Carrol, who knows a lot more than I do - but he was "dumbing it down" with a metaphor)

From what I understood: The twin paradox comes about because the "stay at home" twin has a constant time space coordinate, and so has a "shorter" worldline through spacetime than the "leave home" twin, who goes on a long journey through space and back again, and thus has a "longer" worldline through spacetime.
- So the stay at home twin is older, because he took the shortest path.

What have I got wrong with this metaphor?

PS: I corrected an error pointed out below

[Eternal Student]

Hi Evan_au.

What have I got wrong with this metaphor?

    Nothing much.   Just remember that there are two quantities of interest.

One is often called the proper time  and written         for the differential   and    for the total change in proper time.   This is the thing that is more like time.  It considers differences in co-ordinate time as a positive contribution while differences in spatial co-ordinates are a negative contribution.

The other is written     dS   and   ΔS    and given various names like   the proper distance, the "spacetime distance" although I would prefer to call it the "Minkowski metric distance".   Anyway it's the thing that is more like Euclidean distance in 3-D space.   Differences in the spatial co-ordinates are a positive contribution.

The relationship between these two is that   .      One is the negative of the other.   It is nothing more complicated than this.

   The "spacetime interval"  between two events in spacetime is usually taken to be     and  that is a minimum when  ΔS is a maximum.   In the Sean Carroll example you have mentioned, they were probably using  dS   instead of  dT.
    Anyway,  straight paths connecting two events in spacetime have the greatest     but the smallest  ΔS.
 
    So the Twin paradox shows that the twin who remained on the earth was the only one who took a straight line path and then they have the biggest    =  proper time change = the time elapsed on the clock that stays with that twin.

I hope that makes some sense.

Late editing to fix most of the errors in the LaTex codes for the Mathematics.

[Halc]

The twin paradox comes about because the "stay at home" twin has a constant time coordinate

Actually, he has a constant spatial coordinate (at least in the Earth frame) and the time coordinate is the only one that varies (by a year).

and so has a "shorter" worldline through spacetime than the "leave home" twin

E-S has the gist of it. Minkowskian spacetime isn't Euclidean. In Euclidean spacetime, 4D distances would be computed as √(t²+x²+y²+z²) but spacetime intervals subtract the xyz from the time: s² = t²-(x²+y²+z²). So the straight line (Earth result in the longest interval, and the shortest interval (that followed by light) is where t² equals distance². So I'd say the travelling twin has the shorter worldline, as measured as an interval.
A spacelike worldline (where spatial separation is greater than temporal separation) results in a negative interval s², meaning s would be imaginary. Nothing can 'follow' such a worldline.

[Eternal Student]

Hi Halc.
   👍   I hadn't even spotted that evan_au had said constant time co-ordinate instead of constant spatial co-ordinate.

A spacelike worldline (where spatial separation is greater than temporal separation) results in a negative interval s², meaning s would be imaginary. Nothing can 'follow' such a worldline.

   Yes and that's one good reason to have  dτ   and   dS    with  (dτ)² = - (dS)²   just to avoid  imaginary numbers.   However, the thing Halc is calling  S  is what I was calling   τ.   
The Greek letter tau is the equivalent of the letter t for time and so it should have the time co-ordinate as the positive contribution and measures timelike intervals with real numbers  (IMO).
  (I've also edited a bit more of my previous post to fix some more errors and insert some  squares  ²  in some places).

Best Wishes.