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I've noticed that spacetime diagrams are often used to explain certain situations in special relativity such as the Twin's Paradox, for example: spacetime diagram

In describing these diagrams, people will often say things like "the stationary twin's world line is along the y-axis; his position is constant in space, moving only in time." Of course, this is all relative, the twin could still be moving but he isn't in his frame of reference. My question, however, has to do with the statement "moving only in time." Lets say an object is truly stationary with respect to the three dimensions of space, why must the object be moving through time as the statement seems to imply? Does an object need to be moving to exist or can we not experience time without motion?

I've also heard people ask "if gravity is induced by the curvature of spacetime, how can an object experience gravity if it isn't moving through space?" In response to this, I hear arguments similar to that above "a still object is still moving through time and so will still experience gravity." Is this to imply all objects are moving through time even if they aren't moving through space? And if an object doesn't move with respect to space or time will it not experience gravity and will it even exist? I guess I am confused by what it means to be "moving" through time, is this the same as moving through the three dimensions of space and is it possible to not move through time?

Appreciate any responses. I realize this question is a bit informal, I'm just hoping to get a better concept of what is actually going on and not get lost in all the formality.

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    $\begingroup$ Do you cease to exist when you stop moving? $\endgroup$ – sammy gerbil Mar 14 '17 at 6:55
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    $\begingroup$ velocity is a consequence of space-time, without time component you are just a picture standing still. In newtonian physics space alone is absolute, time alone is absolute, but from the standing point of special relativity space-time (together) is absolute. From the general relativity point of view space-time CAN'T be something that can act upon an object but can't be acted upon. So in GR the space-time is the field and can be acted upon. To conclude, objects are in field and require field to co-exist (and are made up of field, in the view of the GR). $\endgroup$ – Mihai B. Mar 14 '17 at 8:38
  • $\begingroup$ Its really nomenclature, Just a description language. We know that time always goes forward. It's not a deep observation. Physics sometimes describes the position of an object as where it is in space, say x for 1 spatial dimension, at some time t. You can describe the trajectory as x(t). Or graph it as you did. You could also describe it in configuration space, say x and y, and you have an (x,y) at any time. If it moves it's a curve in that space. If it doesn't it's a point. All of those are real. There is no bias or mystery there. $\endgroup$ – Bob Bee Mar 15 '17 at 3:30
  • $\begingroup$ As for gravity at a point, it is indeed curvature. With respect to whatever is causing that curvature (say the earth or a black hole), yes somebody at that point will move, i.e., their position will change with time. You move in geodesics in spacetime, and a point particle will feel a curvature wrt the body that created it. There's always at least two points, you and the body that created the curvature. If you never saw it you would not know you are moving, you'd be free falling and feel nothing. And you'd say there is no gravity. But if you were an extended object, you'd feel a tidal force. $\endgroup$ – Bob Bee Mar 15 '17 at 3:40
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    $\begingroup$ An object in SR is by definition a forward-timelike-directed curve, (perhaps together with some other data like a rest mass, depending on exactly what you're studying). A point does not meet this definition. So every object "moves" for exactly the same reason that every even number must be divisible by 2 --- that's what the words mean. $\endgroup$ – WillO Mar 15 '17 at 4:08
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In GR a (non-extended) object not moving either in space nor time would just be a point in spacetime, what is called an event. That is not really an object, since it has no structure and no dynamics. For dynamics you need time.

As soon as you describe an object as something that "exists", which implies that it relates to something else that "exists" too (else what do "existence" means ?) you are talking about relations and thus, dynamics.

Now of course "existence" is no proper physics terminology. What I mean is that without time nothing can change, so the motion-in-time notion is simply a metaphor for change itself. Even if you say "nothing happens, the situation is always the same", the statement implies several moments in time, and then it is time itself that "moves": change happens on the observer's side.

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As for your question as to why we need to describe everything ine terms of its motion, it's a simple answer. It's useful in a lot of cases, but physics does not care if it's moving or not, through space or time. Even an event that happened at one point in space and at one time is something physics can describe and study. The simple version is that those graphics and descriptions are just description 'languages', graphic, I words, or in math. Just really nomenclature.

We know that time always goes forward. It's not a deep observation. Physics sometimes describes the position of an object as where it is in space, say x for 1 spatial dimension, at some time t. You can describe the trajectory as x(t). Or graph it as you did. You could also describe it in configuration space, say x and y, and you have an (x,y) at any time. If it moves it's a curve in that space. If it doesn't it's a point. All of those are real. There is no bias or mystery there, nothing deep there. What may be dep may be what happens in the different cases.

Your second question about curvature at a point is a good observation. But it also has a good explanation. For gravity at a point, it is indeed curvature. Now the question is 'in whose reference frame'. With respect to whatever is causing that curvature (say the earth or a black hole), yes somebody at that point will move, i.e., their position will change with time. You move in geodesics in spacetime, and a point particle will feel a curvature wrt the body that created it - meaning in the reference frame of the source of the gravity. In those cases there is always at least two points, you and the body that created the curvature and is measuring your motion.

If you never saw it you would not know you are moving, you'd be free falling and feel nothing. And you'd say there is no gravity. That is what we call your observation in your local inertial frame. But if you were an extended object, like a human with a body, and the gravity was very strong like near a black hole you'd feel a tidal force, i.e., a force pulling your legs away from your torso and your waist circumference getting smaller (but you're not getting less massive). If the field was weak you might not feel that tidal force, and think you're just floating in space. But once you got closer to the source of the field you'd see it, and see yourself going towards it. If the thing was a black hole once you got closer you'd see your body getting spaghettified moRe and more. Your certainly would feel the curvature then. So, it's a matter of how much, how close and when you start feeling it, but it is there.

Hope this answers your questions physically and straightforwardly.

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