Your friend says that it is easy to travel faster than the speed of light; you just need to find

Your friend says that it is easy to travel faster than the...

Key Concepts

Special Relativity

Special relativity, formulated by Einstein, is the framework that explains how the laws of physics are the same in all inertial frames and how measurements of space and time vary between observers moving relative to each other. It introduces key ideas like time dilation and length contraction, which are critical for understanding why exceeding the speed of light is not simply a matter of choosing a different reference frame.

Invariance of the Speed of Light

A central tenet of special relativity is that the speed of light in vacuum is constant and independent of the motion of the emitter or the observer. This invariance means that no matter how one changes the observer’s frame of reference, the speed of light remains the same, making it impossible to simply 'pick' an observer in which you would measure a speed higher than that of light.

Reference Frames and Observer Dependence

While measurements such as time intervals and distances can vary between different observers (reference frames), the laws that govern these measurements—including the speed of light—remain fixed. Any notion of 'traveling faster than light' by switching observers overlooks the fact that the transformation between frames (via the Lorentz transformation) preserves the cosmic speed limit.

Causality

Exceeding the speed of light could lead to violations of causality, where cause and effect might be reversed in some reference frames. This would pose significant problems for the logical consistency of physical theories and our understanding of temporal sequences, which is one of the primary reasons why the speed of light is considered an insurmountable limit for any form of information or matter.

Transcript

00:01 In this problem, you have to suppose that you have a friend who tells you that all that you need to do in order to go faster than light is to find the right observer.

00:13 So, for example, suppose that we have an object represented here by this red square, he's traveling with a speed, which is half the speed of light.

00:29 Okay, everyone agrees that this speed is attainable.

00:37 And this speed is relative, is measured relative to a certain observer, s.

00:43 Now consider that we take another observer, okay, s prime, according to whom the s observer is moving to the right with a speed of c divided by two.

01:02 Okay.

01:06 What newtonian physics tells us is that the speed v -prime that will be observed by the s -prime observer is equal to the speed.

01:19 And actually, instead of writing c over 2, i'm going to consider that s has a speed greater than c -over -2, let's say that it's 3c over 4.

01:30 So v prime is equal to the speed of the s observer, which is 3, c over 4, divided plus the speed of the object in the s reference frame.

01:44 And this is equal to 5c over 4.

01:48 This is according to newtonian physics.

01:51 And this answers the first question, which asks us to give physics -based reasons why your friend would, would think such a thing.

02:03 Okay, so the reason basically is because newtonian physics allows it.

02:14 So newtonian physics allows it.

02:25 And then we have to say whether or not we agree with him.

02:30 Notice that the law of transformation of velocities is not the same in relativistic theory as it is in newtonian physics...

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