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I was chatting to someone recently about the motion of objects and whether they propagate through spacetime or not. They were/are convinced that motion through spacetime is simply not possible arguing something along the lines of the following:

They also referred me to this blog post: http://scienceblogs.com/goodmath/2008/01/17/the-nasty-little-truth-about-i/ which even after reading the first line immediately set off my "

My opinion is that objects

I think the problem in understanding is related to self-referential definitions of time that crop up, indeed time is a very difficult quantity to define without any self reference, but it doesn't mean that it isn't a physical quantity.

I have to admit, I'm starting to doubt myself a bit. Is my understanding correct here, or is this other person correct?

If someone could clarify this and also provide a convincing argument I'd much appreciate it.

"Objects move through space. If you depict an object in spacetime, you have a world-line. The world-line doesn't move through spacetime, it simply extends across spacetime.

Physicist's portrayal of this seems to come from their feeling that because the magnitude of a massive particle's velocity four-vector is traditionally normalized to have magnitude ##c##, it makes sense to describe the particle, to a nonmathematical audience, as "moving through spacetime" at ##c##. This is simply inaccurate. A good way to see that it's inaccurate is to note that a ray of light doesn't even have a four-vector that can be normalized in this way. Any tangent vector to the world-line of a ray of light has a magnitude of zero, so you can't scale it up or down to make it have a magnitude of ##c##. For consistency, Greene would presumably have to say that a ray of light "moves through spacetime" at a speed of zero, which is obviously pretty silly.

The reason we normalize velocity four-vectors for massive particles is that the length of a tangent vector has no compelling physical interpretation. Any two tangent vectors that are parallel represent a particle moving through space with the same velocity. Since the length doesn't matter, we might as well arbitrarily set it to some value. We might was well set it to 1, which is of course the value of ##c## in relativistic units. But this normalization is optional in all cases, and impossible for massless particles."

"Objects move through space. If you depict an object in spacetime, you have a world-line. The world-line doesn't move through spacetime, it simply extends across spacetime.

Physicist's portrayal of this seems to come from their feeling that because the magnitude of a massive particle's velocity four-vector is traditionally normalized to have magnitude ##c##, it makes sense to describe the particle, to a nonmathematical audience, as "moving through spacetime" at ##c##. This is simply inaccurate. A good way to see that it's inaccurate is to note that a ray of light doesn't even have a four-vector that can be normalized in this way. Any tangent vector to the world-line of a ray of light has a magnitude of zero, so you can't scale it up or down to make it have a magnitude of ##c##. For consistency, Greene would presumably have to say that a ray of light "moves through spacetime" at a speed of zero, which is obviously pretty silly.

The reason we normalize velocity four-vectors for massive particles is that the length of a tangent vector has no compelling physical interpretation. Any two tangent vectors that are parallel represent a particle moving through space with the same velocity. Since the length doesn't matter, we might as well arbitrarily set it to some value. We might was well set it to 1, which is of course the value of ##c## in relativistic units. But this normalization is optional in all cases, and impossible for massless particles."

They also referred me to this blog post: http://scienceblogs.com/goodmath/2008/01/17/the-nasty-little-truth-about-i/ which even after reading the first line immediately set off my "

*crackpot alarm" ,*and continuing to read the post further confirmed this.My opinion is that objects

*do*propagate through spacetime. My reason being that, although an objects worldline is a fixed trajectory through space, it is not remaining at a single point on that trajectory, it is moving along it. To move along its worldline the object must have some velocity associated with it - even if it remain stationary in space it will still be moving in time.I think the problem in understanding is related to self-referential definitions of time that crop up, indeed time is a very difficult quantity to define without any self reference, but it doesn't mean that it isn't a physical quantity.

I have to admit, I'm starting to doubt myself a bit. Is my understanding correct here, or is this other person correct?

If someone could clarify this and also provide a convincing argument I'd much appreciate it.

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