# 4.4 Invariance | Summary and Q&A

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November 8, 2021
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MIT OpenCourseWare
4.4 Invariance

## TL;DR

In special relativity, time and length are relative and depend on the reference frame, but certain observables, such as the invariant interval, remain constant.

## Questions & Answers

### Q: How does special relativity explain the concept of time dilation and length contraction?

Special relativity proposes that the passage of time and the length of objects depend on the relative motion between the observer and the object. Moving clocks run slower and lengths are contracted in the direction of motion.

### Q: What are the observables that remain invariant in special relativity?

While time and length are relative, certain observables, such as the height and width of objects, remain unchanged. The difference in time and space between two events, known as the invariant interval, is also an observable that all observers can agree on.

### Q: Can the width or height of an object change when it is moving at high speeds?

No, according to special relativity. The width and height of an object are not affected by its motion. In a conversation between observers in different reference frames, they can agree on the height and width of the object.

### Q: What is the concept of the invariant interval in special relativity?

The invariant interval refers to the squared difference between the time and space intervals between two events. This property, expressed as c^2*(t^2 - x^2), remains constant and is an observation that all observers can agree on.

## Summary & Key Takeaways

• Special relativity has been experimentally verified through the absence of ether, the concept of the relativity of simultaneity, and the observed time dilation and length contraction of moving objects.

• The time and length of a moving clock are related to the time and length of a clock at rest through a gamma factor, while transverse dimensions remain invariant.

• Observables such as the height and width of objects are invariant, and the difference in time and space between two events, expressed as delta t and delta x, is an observable that all observers can agree on.

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