Undergrad How does everything move at C through spacetime?

[Joe30174]

Tldr: relative to what are we traveling through spacetime at the speed of light. It must be relative to something not moving through space nor time, which doesn't exist. (And possibly light, not sure though because light doesn't experience traveling through time)

I understand we are talking about spacetime and not space. So if we were talking about an object at rest, it travels through time at the speed of light. If the object were to move, it would still travel through spacetime as a whole at the speed of light because the greater the magnitude of the velocity would lessen the speed of time it is traveling at. I understand viewing it on a spacetime diagram. But it still doesn't make sense.

What is this speed relative to? If an object is at rest relative to the examining object, they both equally travel through space and time together, meaning it is not traveling through space time at all, let alone the speed of light. If the relative object is moving in a direction, it is the combination of its displacement and time, which they are still both traveling through time.

If you were to draw numerous objects and their displacements on a 2d spacetime graph, relative to each other they arent traveling at the speed of light. Only relative to (0,0) if that's your starting point, or wherever you want to put that starting point. So your frame of referance is something that is not travelimg through time nor space. And there's nothing in the universe that exists that we know of.

On a 2d graph for, let's say north, south, east, and west, the frame of reference could be the earth. And that can make complete sense because relative to the earth, it is stationary and not moving in those directions. But adding time in there, the Earth is traveling through time at the same speed, or very slightly slower than a mobing object on earth. Me laying here on my bed, i didnt travel through time at the speed of light faster than the earth.

Or can (0,0), or the object that is not traveling through spacetime, be the universe as a whole. Which would mean it is possible to have an unbiased frame of referance to calculate everything else. Wether humans could ever do it or not, idk.

 

[Dale]

Hi @Joe30174

The whole “moving through spacetime at c” is a bit overblown by pop-sci authors such as Brian Greene. It has almost no physical significance.

Basically, in spacetime nothing “moves”. Instead, a moving point particle is represented by a single static “worldline” which traces out a curve in spacetime that corresponds to the position of the point at each moment of time. The geometry of these shapes is then related to motion: particles that collide have worldlines that intersect, the relative velocity is given by the angle of the collision, a fast object has a steep slope, a high acceleration is a sharp curve in the worldline, an inertial particle has a straight worldline, etc.

So, the geometric quantity that is referenced is simply the unit tangent vector to the curve. Since it is a unit vector it always has unit length, and unsurprisingly the unit in relativity is usually c. There is no implication of anything moving at c nor anything relative to which the movement needs to be referenced. It is simply a unit vector in a situation where the unit is c.

 

[m4r35n357]

I can't really blame anyone for interpreting the magnitude of a velocity vector as a speed. Would (the invariant) speed of spacetime be any better?

 

[PeterDonis]

I can't really blame anyone for interpreting the magnitude of a velocity vector as a speed.

But it isn't a velocity vector. It's a unit vector. It's the same at every single event on every single timelike worldline, including the worldlines of objects that are moving relative to each other. Interpreting this vector as a speed would require you to say that objects moving relative to each other have the same speed, which doesn't make sense.

Would (the invariant) speed of spacetime be any better?

No. Spacetime doesn't have a speed, and the unit vector is not attached to spacetime, it's attached to a particular point on a particular worldline.

 

[Ibix]

I've said before that I don't think four-velocity is actually a particularly helpful name for the concept. I get that velocity is a standard name for this kind of tangent to a curve, and I can see why the three dimensional $dx^i/dt$ going to the four dimensional $dx^\mu/d\tau$ makes the name almost irresistible. But although the four velocity has a lot in common with the three velocity, there are some fairly fundamental differences.

The key one here is that the magnitude of the three-velocity is interesting - it's a big part of a measure of how much the thing is going to hurt when it hits you (formal statements in terms of energy and momentum are available). But the magnitude of the four velocity is simply a statement of the relationship between your choice of units for spatial and temporal distances. It's physically uninteresting. All the interesting stuff is in the inner product with other four velocities.

 

[Dale]

But it isn't a velocity vector. It's a unit vector.

This is very important. The sum of two four velocities is not a four velocity for the same geometric reason that the sum of two unit vectors is not a unit vector.