Intuitions for Relativity

This section builds intuitions about relativity and spacetime.

Einstein’s theory of relativity describes how space and time are related based on the logical consequences of two core postulates:

1. The laws of physics are the same in all inertial reference frames.
2. The speed of light is the same in all inertial reference frames and is not affected by the speed of its source.

Demystifying Terms

The term inertial reference frame simply refers to a frame of reference where all objects follow Newton’s first law of motion:

Objects at rest remain at rest, and objects in motion remain in motion at a constant velocity in a straight line, unless acted upon by an external force.

For example, the inside of a car moving along a road at constant velocity and the inside of a stationary house are inertial reference frames.

The special in special relativity refers to the fact that it is a special case of general relativity: situations when objects are moving at constant velocities in a vacuum. When the theory is extended to follow what happens when objects accelerate, it is called general relativity.

From here on out, we will not worry about distinguishing between special or general relativity. They describe the same phenomena.

Here we will ignore the effects of light passing through a medium for the sake of brevity, but know that the physics still holds. This video provides an excellent intuition about how the speed of light can be constant and also how light moves “slower” through a medium.

TLDW; The “true” speed of light is still constant in any medium. The “slower” speed is a sort of illusion caused by “phase kicks” between the light and the medium as electromagnetic waves propagate through the medium.

Having the right mindset

When learning about relativity, it is important to approach the problem from a scientific perspective. The only way to learn about the universe is to make predictions and then test those predictions with measurements.

It is unsatisfying to say “let’s just accept that this is true” but, that’s part of the genius behind Einstein’s work. Einstein asks “What would happen if this is actually true?” Then he follows the logic to see the consequences of that truth and considers what must happen in order for our observations to be consistent with that truth.

Scientists have used this approach to make predictions about the universe for centuries. The predictions are then tested with measurements. If the measurements match the predictions, then we have evidence that suggests the prediction is true. Why is it true? We don’t know. Science cannot answer that question.

Every test science has invented to test relativity is true has shown that the observation matches the predictions made from following Einstein’s theory. We have to accept that we don’t know why because we can’t test which answer might be correct. It is an unanswerable question right now. Maybe someday there will be an invention that lets us know more about the universe but right now this is as far as we get.

More resources

Here are some excellent videos to get started:

• Special Relativity Intuitions
  • Speed of light is constant in all reference frames
  • Everything moves at the speed of light
  • Time dilation and length contraction
• General Relativity Intuitions
  • How gravity bends light even though it has no mass
  • Gravity comes from time curving space
  • Curved spacetime changes trajectories of light and matter

The textbook

OpenStax has multiple textbooks with sections on relativity:

• College Physics 2e
• University Physics Volume 3
• Astronomy 2e

In the coming chapters we’ll see how relativity affects equations of motion for events measured between inertial reference frames. The majority of this work is based on the Relativity chapter in OpenStax University Physics Volume 3. We’ll be using the same notation and examples as the OpenStax book, but I’ll be adding some additional commentary and examples to help solidify the concepts.