diff --git a/src/coordinax/_src/operators/galilean/spatial_translation.py b/src/coordinax/_src/operators/galilean/spatial_translation.py
index 3caab77f..d834e19a 100644
--- a/src/coordinax/_src/operators/galilean/spatial_translation.py
+++ b/src/coordinax/_src/operators/galilean/spatial_translation.py
@@ -23,6 +23,7 @@
 from coordinax._src.vectors.d2 import CartesianPos2D
 from coordinax._src.vectors.d3 import CartesianPos3D
 from coordinax._src.vectors.d4 import FourVector
+from coordinax._src.vectors.private_api import spatial_component
 
 ##############################################################################
 # Spatial Translations
@@ -345,8 +346,15 @@ def call(
     # Translate the velocity (this operator will have no effect on the
     # velocity).
     # 1. convert to a Quantity in Cartesian coordinates.
+    qvec = spatial_component(qvec)
+    pvec = eqx.error_if(
+        pvec,
+        qvec._dimensionality() != pvec._dimensionality(),  # noqa: SLF001
+        "The position and velocity vectors must have the same dimensionality.",
+    )
+
     q = convert(qvec.vconvert(qvec._cartesian_cls), u.Quantity)  # noqa: SLF001
-    p = convert(pvec.vconvert(pvec._cartesian_cls, q), u.Quantity)  # noqa: SLF001
+    p = convert(pvec.vconvert(pvec._cartesian_cls, qvec), u.Quantity)  # noqa: SLF001
     # 1.5 cast to float dtype  # TODO: more careful casting
     q, p = q.astype(float, copy=False), p.astype(float, copy=False)
     # 2. create the Jacobian of the operation on the position
diff --git a/src/coordinax/_src/vectors/d4/spacetime.py b/src/coordinax/_src/vectors/d4/spacetime.py
index badfc3cd..17c42a15 100644
--- a/src/coordinax/_src/vectors/d4/spacetime.py
+++ b/src/coordinax/_src/vectors/d4/spacetime.py
@@ -229,7 +229,7 @@ def __str__(self) -> str:
 
 
 # ===============================================================
-# Constructors
+# Vector API
 
 
 @dispatch  # type: ignore[misc]
@@ -280,10 +280,6 @@ def vector(cls: type[FourVector], obj: AbstractQuantity, /) -> FourVector:
     return cls(t=obj[..., 0] / c, q=obj[..., 1:], c=c)
 
 
-# ===============================================================
-# Vector Convert
-
-
 @dispatch  # type: ignore[misc]
 def vconvert(
     spatial_target: type[AbstractPos3D], current: FourVector, /, **kwargs: Any
@@ -304,8 +300,26 @@ def vconvert(
     return replace(current, q=vconvert(spatial_target, current.q, **kwargs))
 
 
+@dispatch  # type: ignore[misc]
+def spatial_component(x: FourVector, /) -> AbstractPos3D:
+    """Return the spatial component of the vector.
+
+    Examples
+    --------
+    >>> import unxt as u
+    >>> import coordinax as cx
+
+    >>> w = cx.FourVector(t=u.Quantity(1, "s"), q=u.Quantity([1, 2, 3], "m"))
+    >>> print(spatial_component(w))
+    <CartesianPos3D (x[m], y[m], z[m])
+        [1 2 3]>
+
+    """
+    return x.q
+
+
 # ===============================================================
-# Converters
+# Plum API
 
 
 @conversion_method(type_from=FourVector, type_to=u.Quantity)  # type: ignore[misc]
diff --git a/src/coordinax/_src/vectors/private_api.py b/src/coordinax/_src/vectors/private_api.py
new file mode 100644
index 00000000..e90260f5
--- /dev/null
+++ b/src/coordinax/_src/vectors/private_api.py
@@ -0,0 +1,21 @@
+"""Copyright (c) 2023 coordinax maintainers. All rights reserved."""
+
+__all__ = ["spatial_component"]
+
+from typing import Any
+
+from plum import dispatch
+
+from .base import AbstractPos
+
+
+@dispatch.abstract
+def spatial_component(x: Any, /) -> Any:
+    """Return the spatial component of the vector."""
+    raise NotImplementedError
+
+
+@dispatch
+def spatial_component(x: AbstractPos, /) -> AbstractPos:
+    """Return the spatial component of the vector."""
+    return x