Two particles each have a speed of 5 m/s. Particle A moves north; Particle B moves south. If their momenta are added as vectors, what is the total momentum of the system (assuming equal mass m)?
A10m kg·m/s northward, because both magnitudes add
B5m kg·m/s, the average of the two momenta
C0 kg·m/s, because the equal-and-opposite momenta cancel
DIndeterminate, because direction is not a real property of momentum
Each particle has momentum mv in opposite directions. As vectors, they sum to zero. This result — same speed but opposite velocities producing zero total momentum — demonstrates that direction in vectorial properties is doing real physical work, not merely labeling a scalar. If direction were just a notational convenience, combining two 'equal' momenta should yield something nonzero. The cancellation shows that directionality is intrinsic to what momentum is.
Question 2 Multiple Choice
A structural realist claims that vectorial properties like velocity and force are genuinely fundamental and cannot be reduced to a scalar magnitude plus a relation to a direction in space. What would be the main metaphysical implication?
APhysics could describe all phenomena using only scalar magnitudes, making direction a derived convenience
BVelocity and force would turn out to be the same property described from different reference frames
CThe world's fundamental ontology would contain built-in directedness that cannot be explained away by reference to external spatial relations
DSpatial directions would be purely conventional with no objective reality
If vectorial properties are irreducible, then direction is not something imposed on scalar magnitudes from outside (via relations to independently existing spatial directions) but is constitutive of the property itself. This means the world's fundamental inventory includes properties with inherent orientation — a kind of built-in directedness. This has implications for debates about spacetime realism and whether relational structure can be grounded in intrinsic properties.
Question 3 True / False
Two objects with the same speed but opposite velocities will have their momenta cancel to zero when combined, which shows that the directional component of velocity is physically substantive, not merely a notational label.
TTrue
FFalse
Answer: True
The cancellation of equal-and-opposite momenta is direct evidence that direction does real physical work. If direction were only a label, combining two 5 m/s magnitudes would yield 10 m/s. Instead, the actual result is zero — the directions genuinely determine how vectorial quantities combine. This is the key empirical point that distinguishes vectorial from scalar properties.
Question 4 True / False
Vectorial properties are simply scalar properties plus a directional relation to some feature of spacetime — direction adds no new intrinsic content to the property itself.
TTrue
FFalse
Answer: False
This is the reductionist position, and it is philosophically contested. If direction were just an extrinsic relation to spacetime structure, then vectorial properties would reduce to scalars plus relational facts about orientation. But the intrinsicalist alternative holds that the directional component is built into the property itself — that a force of 10 N northward is intrinsically different from 10 N southward, not merely differently related to space. Whether this reduction succeeds is a live debate in philosophy of physics with stakes for spacetime realism.
Question 5 Short Answer
Why might a philosopher argue that a particle's velocity cannot be fully analyzed as a scalar speed plus a relation to a direction in space? What would be at stake metaphysically if vectorial properties are genuinely irreducible?
Think about your answer, then reveal below.
Model answer: The argument is that direction is not an add-on but constitutive of the property: 60 km/h northward and 60 km/h southward are intrinsically distinct states with different causal consequences, and this difference cannot be captured by the scalar 60 km/h plus an extrinsic relation to spatial directions (which would themselves need to be grounded). If vectorial properties are irreducible, the world's fundamental ontology contains built-in directedness — properties that inherently point. This matters for spacetime realism (is spatial direction a genuine feature of reality?), for debates about intrinsic vs. relational properties, and for causal explanation (forces, momenta, and fields are fully characterized only by their direction, not just their magnitude).
The scalar-plus-relation reduction succeeds only if spatial directions themselves are independently real and can serve as the relata. Structural realists argue that what is real is precisely the relational/vectorial structure of physics — the directions are as fundamental as the magnitudes. Intrinsicalists push further: the direction may be intrinsic to the property, not derived from any spatial relation.