Spacetime Intervals and Four-Vectors · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

The distance everyone agrees on

Science · Quantum & Modern Physics · ages 19-20
Name ______________________   Date ____________

  1. A pair has negative s squared. What can frames disagree on?

    • The value of s squared
    • Whether light speed is c
    • The time order of the two events

  2. Two frames time the same event pair differently. What do they still share?

    • The time gap
    • The interval s squared
    • The space gap

  3. What is the position four-vector?

    • The bundle c t, x, y, z
    • The velocity divided by gamma
    • The interval times the mass

  4. s squared is 16 and positive for two flashes. What follows?

    • Only light could have visited both
    • One slow traveller could visit both, in an order all frames share
    • Neither flash could have any connection at all

  5. Two flashes are 5 s apart in time and 3 light s apart in space. Type s squared.

    Answer: ______________

  6. Why does frame dependent time order never break causality?

    • Signals travel faster than light
    • Effects always precede causes
    • Only pairs no signal could connect ever swap order

  7. Two distant flashes occur with spacelike separation. Could one have triggered the other?

    • No, since no signal could have connected them in time
    • Yes, since their order is frame dependent
    • Yes, if a fast enough ship carried the news

  8. For a timelike pair, some frame sees the effect before its cause.

    Circle one:   True   False

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Answer key

For grown-ups. Fold this page away before handing over the rest.

The distance everyone agrees on W1-mt_CYdi7Qpvrf-s1

  1. The time order of the two events · Spacelike pairs have no connecting signal, so their order is frame dependent.
  2. The interval s squared · Frames split space and time differently but compute one shared interval.
  3. The bundle c t, x, y, z · Time scaled by c joins the three space slots as one object.
  4. One slow traveller could visit both, in an order all frames share · Positive means timelike: a slow path can link them in a fixed order.
  5. 16 · 25 minus 9 is 16, a positive timelike interval.
  6. Only pairs no signal could connect ever swap order · Swappable pairs are exactly the ones nothing can link, so no cause ever trails its effect.
  7. No, since no signal could have connected them in time · Influence needs a signal, and spacelike gaps admit none fast enough.
  8. False · Every frame agrees on a timelike order, so causes always come first.
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