How does light from the past ever reach me?

[closet mathemetician]

If everything is moving at the speed of light in the time direction all the time, Then how does the light from an event in the past ever catch up and reach me?

 

[Dale]

Spacetime is not Euclidean.

EDIT: I realized, while this is true it is not pertinent.

 

[bcrowell]

If everything is moving at the speed of light in the time direction all the time,

This is apparently Brian Greene's idiosyncratic way of talking about spacetime in his popular-level book. I don't know of anybody else who describes it this way. Judging by the number of people who post about it, it seems to cause a huge amount of confusion. Things don't move through spacetime. Things move through space. When a thing moves through space, it has a world-line which is a curve in spacetime.

 

[ghwellsjr]

If everything is moving at the speed of light in the time direction all the time, Then how does the light from an event in the past ever catch up and reach me?

"Everything" is moving at the speed of light? Where'd you get that idea from? I thought things with mass could not move at the speed of light.

Please explain.

 

[closet mathemetician]

This is apparently Brian Greene's idiosyncratic way of talking about spacetime in his popular-level book. I don't know of anybody else who describes it this way. Judging by the number of people who post about it, it seems to cause a huge amount of confusion. Things don't move through spacetime. Things move through space. When a thing moves through space, it has a world-line which is a curve in spacetime.

You are right, that "moving through time" in, say, a two-dimensional spacetime is represented by a static line in the time direction that is not dynamic. I was playing loosely with the language. However, if I have velocity in space, then my worldline in spacetime has a slope between vertical and one (45 degrees), meaning that there must be two components of velocity, one in time and one in space, in other words, (c,v).

Furthermore, my velocity through space, v, can go from zero to c, (if I don't have mass) but my velocity in time is always c.

 

[bcrowell]

You are right, that "moving through time" in, say, a two-dimensional spacetime is represented by a static line in the time direction that is not dynamic. I was playing loosely with the language. However, if I have velocity in space, then my worldline in spacetime has a slope between vertical and one (45 degrees), meaning that there must be two components of velocity, one in time and one in space, in other words, (c,v).

Furthermore, my velocity through space, v, can go from zero to c, (if I don't have mass) but my velocity in time is always c.

The velocity four-vector's magnitude is always equal to 1, regardless of the speed at which the object is actually moving. The velocity four-vector's magnitude is not interpreted as the speed of the object.

 

[Dale]

Furthermore, my velocity through space, v, can go from zero to c, (if I don't have mass) but my velocity in time is always c.

No, in this interpretation it is the speed through spacetime (norm of the four-velocity) which is always c, not the timelike component of the four-velocity.

In any case, the most important point in this discussion so far is bcrowell's point that "Things don't move through spacetime." A moving point particle has a single 1D worldline in spacetime. You can draw a unit tangent vector (the four-velocity) at any point on this line. The fact that any worldline has a unit tangent vector of unit length is a tautological statement that has little value and no bearing on whether or not two worldlines intersect.

 

[JesseM]

"Everything" is moving at the speed of light? Where'd you get that idea from? I thought things with mass could not move at the speed of light.

Please explain.

As bcrowell said, this is Brian Greene's confusing way of explaining relativity in some of his books. For the math behind what he means behind "speed through spacetime", see my [post=430613]post #3 on this thread[/post].