What does it mean for two events to be simultaneous in a given frame?

Is simultaneity absolute in special relativity?

State the Lorentz time-difference formula for frames moving along the \(x\)-axis.

Two events occur at the same place in \(S\) with \(\Delta t=2.00\,\mu\mathrm s\). If \(S'\) moves at \(0.600c\), find \(\Delta t'\).

Two events are simultaneous in \(S\) and separated by \(300\,\mathrm m\) along \(+x\). Frame \(S'\) moves at \(0.500c\). Find the sign of \(\Delta t'\).

Why is the relativity of simultaneity not just a delay caused by light travel time?

Two events are simultaneous in \(S\), separated by \(900\,\mathrm m\). Frame \(S'\) moves at \(0.600c\). Find \(\Delta t'\).

Two lightning strikes hit the front and back of a train at the same time in the track frame. Explain why the train frame can disagree.

Find the speed \(v\) for which two events with \(\Delta x=600\,\mathrm m\) and \(\Delta t=1.00\,\mu\mathrm s\) are simultaneous in \(S'\).

Two events have \(\Delta x=900\,\mathrm m\) and \(\Delta t=1.00\,\mu\mathrm s\) in \(S\). Frame \(S'\) moves at \(0.600c\). Find \(\Delta t'\).

For two events simultaneous in \(S\), derive the moving-frame time separation.

Two events have \(\Delta x=300\,\mathrm m\). What value of \(\Delta t\) in \(S\) would make them connected by a light signal?

Explain why two events at the same place in one frame cannot have their time order reversed by another inertial frame.

Two events are separated by \(\Delta x=1.20\,\mathrm{km}\) and are simultaneous in \(S\). Find \(\Delta t'\) for \(v=0.750c\).

A frame \(S'\) moves in the negative \(x\)-direction relative to \(S\). If two events are simultaneous in \(S\) with \(\Delta x>0\), what is the sign of \(\Delta t'\)?

Show that if two events can be connected by a light signal, no inertial frame can make them simultaneous.

Use \(\Delta t'=\gamma(\Delta t-v\Delta x/c^2)\) to explain why only separated events can show relativity of simultaneity.

A student argues that if observers disagree on simultaneity, one observer must be wrong. Give a relativistic correction.

Two events have \(c\Delta t=400\,\mathrm m\) and \(\Delta x=1000\,\mathrm m\). Can their order be reversed by changing inertial frame?

Derive the condition for a frame in which two events are simultaneous, and state when that frame is physically allowed.