B Is SpaceTime just DistanceTime?

[FRANKENSTEIN54]

TL;DR Summary

Is SpaceTime just DistanceTime ?

Since "Space" is just a Distance between 2 objects , isn't "Space" just equal to Distance ? If so , then the term "SpaceTime" can be called DistanceTime . Which I think clarifies what is meant . And I think it's meaning is thus a Distance Time . In other words , it just refers to the TIME it takes to Travel some Distance . So "SpaceTime" is just a Distance travelled in some Time . Such as 60 MPH , 60 miles travelled in one hour . SpaceTime = 60 miles in One hour. SpaceTime = Speed . Make sense ?

 

[weirdoguy]

Since "Space" is just a Distance between 2 objects ,

It's not, and I don't know where did you get that it is. Distance is a number, space is a (sub)manifold. It's like saying red and apple is the same.

 

[Orodruin]

Make sense ?

None whatsoever. Spacetime - whether Minkowski or Galilean - is a four-dimensional affine space. It is not just ”distance per time”. That would be velocity.

 

[pervect]

TL;DR Summary: Is SpaceTime just DistanceTime ?

Since "Space" is just a Distance between 2 objects , isn't "Space" just equal to Distance ? If so , then the term "SpaceTime" can be called DistanceTime . Which I think clarifies what is meant . And I think it's meaning is thus a Distance Time . In other words , it just refers to the TIME it takes to Travel some Distance . So "SpaceTime" is just a Distance travelled in some Time . Such as 60 MPH , 60 miles travelled in one hour . SpaceTime = 60 miles in One hour. SpaceTime = Speed . Make sense ?

Space and distance are certainly very closely related, but using the words in a non-standard way as you suggest is just confusing and doesn't illuminate anything. Sorry.

As far as space-time goes, it's not what you think. I'm not sure of your background, but "The Parable of the Surveyor" discusses this at some length via an analogy. It's online at https://phys.libretexts.org/Bookshe...etime_Overview/1.01:_Parable_of_the_Surveyors

It may seem a bit long and rambling, but if you stick with it it should hopefully clarify a few things.

One of the lessons of the parable of the surveyor is why we consider a plane a two dimensional space. Could we treat east-west distances as being separate from north-south distance? Why do we unify them into a single entity, called "space", and not two seprate one-dimensonal quanties (north-south distance and east-west distance).

The short answer is "rotational symmetry". We can choose to use "true north" or "compass north", the way we break down distances (which are the same for all observers, which we call invariant), even though under such a change the "north-south" and "east-west" classification of the distances varies.

The argument for unifying space and time into space-time is similar. I won't go into the details unless prompted, but I'll mention that the underlying symmetry is called a "boost symmetry".

My main purpose in this post is to explain why the plane is two dimensional, and not two separate one dimensional quantities, and to provide a reference. If you want an exposition on how to go a bit further in understanding the concept of space-time as a unified entity rather than a separate "space" part and a "time part", I'll be happy to write more, but I'll wait for a sign of interest before I do the work to post. Much of what I would write is probablby handled at least as well (if not better) by Taylor in the quote I referenced, though.

 

[Dale]

I don’t think there is any intrinsic harm in the term distance time. Far worse terminology is already in use. However, the point of terminology is communication. Using standard terminology, even where it is poor, aids communication.

Sometimes, non-standard terminology can be adopted if it addresses a known problem with the standard terminology. For instance, this community has adopted the terminology “differential aging” to address the known problem distinguishing between the symmetrical time dilation in the Lorentz transform and the asymmetrical time dilation of the twin paradox.

In this case, spacetime is well established terminology, and distance time is neither established nor does it address any recognized problem with spacetime. I don’t see it being helpful in communication.

 

[FactChecker]

TL;DR Summary: Is SpaceTime just DistanceTime ?

Since "Space" is just a Distance between 2 objects , isn't "Space" just equal to Distance ?

Good question. That is wrong. Traditional "space" as Newton imagined it is three-dimensional. The space time in relativity has 4 dimensions. If you are considering a fast-moving object, the direction that it is moving in is distorted according to the familiar Special Relativity factors. The other directions are distorted differently. So the direction of the motion is important. To keep things simple, most discussion of relativity only considers the direction of motion as one dimension and time as the other. That might be what has you confused.

 

[Albertus Magnus]

Space-time is a termed used to emphasize that fact that in relativistic physics, space and time which were previously in classical thought two separate entities, are unified into one single geometric entity known as a manifold. Thus, in Newtonian physics distance between two points or events in the manifold are characterized by the Euclidean metric:
$$\Delta s^2=\Delta x^2+\Delta y^2+\Delta z^2.$$
By contrast, in relativistic physics distance is non-Euclidean and is evidenced in the departure from the Pythagorean theorem used to measure distance in the Euclidean case:
$$\Delta s^2= c^2\Delta t^2-\Delta x^2-\Delta y^2-\Delta z^2. (\text{where c is the speed of light})$$
Note that in the classical case time does not appear in the metric, unlike the relativistic case where time is treated similarly to the spatial coordinates, i.e. time is considered to be spatial as opposed to an independent parameter. Thus, one has space-time as opposed to the familiar classical conception of space and time.

 

[cianfa72]

None whatsoever. Spacetime - whether Minkowski or Galilean - is a four-dimensional affine space. It is not just ”distance per time”. That would be velocity.

Just to be clear: in the realm of GR, Spacetime is no longer an affine space. Namely, taken the spacetime as the set of events, one can't assign a meaningful affine structure on top (even though locally, i.e. on each tangent space, one can assign a vector space structure).

 

[Orodruin]

Just to be clear: in the realm of GR, Spacetime is no longer an affine space. Namely, taken the spacetime as the set of events, one can't assign a meaningful affine structure on top (even though locally, i.e. on each tangent space, one can assign a vector space structure).

Of course, but that is hardly at B-level.

 

[pervect]

I don't have any real argument with the idea that space can be thought of the study of distance. It's the way I think of it myself, though I have become aware that that's slightly oversimplified as mathematicians DO study concepts of "space" without distance. But for GR, it is convenient and sufficient (in my opinion at least) to think of space as the study of distance.

I often quote Taylor who once said "distances determine geometry".

Moving on to space-time, I would say that Taylor's treatment of spacetime in "the parable of the surveyor" that I recomended is at the I level rather than the B level - but I'm not aware of any simpler treatment that I would recommend.

The simplest way I can think of to put it at the moment - while space is basically motivated by the concept of distance, space-time studies something else. We call it the Lorentz interval, and it is a mathematical construct that can be applied to both space intervals and time intervals.

In normal space, we use the pythagorean theoerem, that the square of the hypotenuse is the sum of the squares of the other two sides. The Lorentiz interval, in the simple 2d case, is similar, except that that square of the hypotensue is the DIFFERENCE of the squares of the other two sides, one "side" being space, and the other side being "time".

 

[robphy]

In my opinion, if we use the intro textbook definition of "distance" (as the magnitude of a displacement vector or more generally as the arc-length along a path), then
"DistanceTime" fails to capture what "SpaceTime" does.
And as @Orodruin suggests, we don't need to bring in special relativity to make this point.
An intro 1D-space position-vs-time diagram has more information than what would be on a "DistanceTime" diagram.

In the context of Galilean physics in one-spatial dimension,
- a DistanceTime diagram won't distinguish two events with (t,x) coordinates (0,1) and (0,-1).
- a DistanceTime diagram won't allow vector addition (as suggested by the "affine" references by @Orodruin and @cianfa72).

It is not just ”distance per time”. That would be velocity.

I would call that average-speed.

 

[Dale]

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