Twin Paradox: A Physical Explanation

The twin paradox: why the SR/GR equivalence reveals a lack of physical explanation

1. In special relativity: a correct calculation, but a fragile explanation

Special relativity (SR) explains the twin paradox by comparing the proper times along the two worldlines:
τ = ∫ √(1 − v²/c²)   dt.

The calculation is uncontroversial: the travelling twin ages less. But the real question is: what is the physical explanation?

Two options exist:

• Minimal reading: one simply notes that the proper times differ, without invoking any mechanism. This is correct, but it is not a physical explanation, only a mathematical description.
• Usual reading: one appeals to the relativity of simultaneity. One explains that, at the turnaround, the traveller’s planes of simultaneity “jump,” which produces the age difference. But if one gives these planes an ontological status, one is adopting the block universe: past, present, and future all equally exist in Minkowski spacetime.

Therefore: either we accept the block universe (but then deny the reality of the present), or we reject this view and SR then offers only a purely formal explanation, without physical content.

2. In general relativity: an attractive reformulation

General relativity (GR) at first seems to resolve this difficulty. Thanks to the equivalence principle, one can interpret the traveller’s acceleration as equivalent to the presence of a gravitational field.

The slowing of their time is then explained by gravitational time dilation:
dτ = dt   √(1 − 2GM/rc²).

This formula resembles the kinematic time dilation of SR:
dτ = dt   √(1 − v²/c²),
if one takes v to be the escape velocity at distance r.

In this way one obtains a more intuitive reading: the traveller has undergone the equivalent of a gravitational field, hence their slower ageing.

3. The problem of equivalence

But this is where the real problem arises: the two explanations (SR and GR) are numerically equivalent.

• In SR, it makes no difference whether the stay-at-home twin is on Earth (subject to gravity) or freely moving in space: the calculation gives the same age difference.
• In GR, the difference is reinterpreted in terms of gravity, but it leads to the same result as SR.

In other words:

• GR does not, in this case, provide a new physical explanation.
• It merely reformulates SR’s explanation in its own language.
• The equivalence of the two solutions shows that we remain within the same conceptual framework, where the time difference is not tied to any real physical structure, but only to an abstract geometry.

4. The real problem: the absence of a physical reference in SR

The real problem lies in the fact that, in special relativity, the calculated result does not allow us to determine which of the twins is really in motion with respect to the spatial structure. Motion in SR is defined only with respect to an arbitrary reference frame, with no anchoring in a real spatial structure.

This means that, from a strictly physical point of view, it is impossible to say which twin is in motion relative to a concrete space. This absence of reference to a real physical structure prevents us from giving a truly physical explanation of the phenomenon and limits the SR solution to a mere geometrical abstraction.

5. The additional gravitational correction and explanatory asymmetry

When one takes into account the fact that the stay-at-home twin is sitting on a massive planet, GR requires a second calculation: one must add the local gravitational time dilation due to the potential in which they are situated. The stay-at-home twin is thus placed in a real spatial configuration, while the traveller continues to be treated in purely kinematic terms.

This correction is not a simple technical refinement: it introduces a deep asymmetry. One twin is tied to a real spatial structure, but not the other. The explanation then becomes unstable: GR juxtaposes a calculation equivalent to that of SR with a potential correction that depends on the context. Explanatory coherence is lost.

Thus, far from surpassing SR, GR merely layers adjustments on top of it. It does not provide a unified mechanism but a partial assemblage, which shows that its explanation of the paradox is incomplete.

6. Philosophical consequence

This equivalence brings a shortcoming to light:

• If one rejects the SR block universe, then the SR explanation is not physical.
• But if GR is equivalent to SR for this problem, then its explanation is not physical either.
• One therefore cannot simply say: “GR provides the true solution.” No: as long as it remains equivalent to SR and demands asymmetric corrections, it merely reformulates the same problem in an unstable way.

7. The need for a third way

To escape this impasse, it is necessary to:

• Reject the block universe arising from SR’s relative simultaneity,
• Reject the idea that GR is sufficient to “save” the physical explanation of the paradox, since it is equivalent to SR and incomplete in its correction,
• Acknowledge that we need a different conceptual framework, based on absolute simultaneity and on motion defined with respect to a real spatial configuration.

In such a framework:

• There exists a universal present.
• The flow of time is not uniform for everyone, but it is always measured with respect to this common present.
• The variation in the flow of time depends on motion with respect to a relational spatial structure (and not merely with respect to another arbitrary observer).

8. Conclusion

The twin paradox is indeed solved mathematically by both SR and GR, but this very equivalence, combined with the need for asymmetric corrections, shows that neither of them provides a satisfactory physical explanation.

— SR leads to the block universe if one takes relative simultaneity seriously, or to a purely formal explanation if one rejects it.
— GR reformulates the problem in terms of gravity, but merely reproduces SR’s result while adding partial adjustments, without offering any additional intelligibility.

The only way to provide a coherent physical explanation is to posit an absolute simultaneity, in which time truly flows in a universal present, and in which motion must be referred to a real spatial configuration.