M2 - Space, time, and "spacetime"

Thought Experiment 1

You are inside a train:

• The train moves at a constant speed (no acceleration).

• The windows are blocked.

• You have no measuring devices that can detect motion relative to the outside.

Question:
How can you tell whether the train is moving or at rest?

Answer:
You can’t.

Motion at constant velocity and being at rest are physically equivalent. Everything behaves exactly the same as if the train were not moving.

Thought Experiment 2

You are inside a plane going 900 km/hr:

• You roll a ball at 10 km/hr

  • You observe the ball roll at 10 km/hr

  • An observer from the ground observes it going at 910 km/hr

Speed is not an intrinsic property of the ball

• It depends on who is measuring it

• Each observer uses their own reference frame

Reference Frame

Motion is not absolute—it only makes sense relative to something else

Imagine a book:

• On a table → not moving relative to the table

• On Earth → not moving relative to Earth

• Relative to the Sun → moving

• Relative to the galaxy → moving even faster

So is the book moving or not?

All answers are correct, depending on the reference frame.

Inertial Frame

Reference frames moving at constant velocity (no acceleration)

Einstein

Among the first to realize that motion can only be measured in a relative sense

• Special Relativity

Special Relativity

Deals with motion at constant speeds (no gravity involved).

• The laws of physics are the same for all reference frames that are moving at constant velocity.

• The speed of light (in a vacuum) is the same for everyone, no matter how fast they’re moving.

Speed of Light

Speed of light is the same for all inertial observers

• Motion of the source does not change light’s speed

• This contradicts everyday velocity addition

Same Speed of Light

To keep the speed of light the same for everyone:

• Time must change (time dilation)

• Distances must change (length contraction)

• Simultaneity must change

Space and time adjust so that everyone still measures ccc.

What each observer disagrees on

They agree on:

• Speed of light

They disagree on:

• Time intervals

• Lengths

• Whether two events happen at the same time

Time Dilation

A moving clock runs slower compared to a clock at rest, as seen by an outside observer.

• In other words, time “stretches” for the moving object from the perspective of a stationary observer.

Train Flashlight Example

Outside observer sees light emitted from flashlight travel diagonally (more distance)

special relativity says:

• speed of light_train = speed of light_ground

• distance_train / time_train = distance_ground / time_ground

• time_ground = distance_ground / distance_train (time_ground)

• time_ground > time_train

Outside observer sees time is slower on the train

Spacetime

Because the speed of light is the same for everyone, space and time must adjust together, forming the four-dimensional fabric we call spacetime