Vectors and the Speed of Light?

In summary, the speed of light cannot be broken using vectors as the usual relativistic velocity addition formula only applies to velocities along the same line. The Lorentz Transformation also plays a role in this limitation. It is a fixed constant for all observers and cannot be exceeded, regardless of the frame of reference.
  • #1
ryuunoseika
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Can the speed of light be broken using vectors? Why not? Where does the Lorentz Transformation come into play?

E.g. I accelerate to 3/4 the speed of light North and then to 3/4 the speed of light East. Am I traveling faster than the speed of light at 45 degrees North-East?
 
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  • #2
If you travel 1 m/s for 1 hour to the north and the 1 m/s for 1 hour to the east, how fast did you travel? 1 m/s or 1.414 m/s?
 
  • #3
ryuunoseika said:
Can the speed of light be broken using vectors?

No.

The usual relativistic "velocity addition" formula applies only when the velocities are along the same line.

For adding velocities that are at an angle with each other, see for example the section The velocity addition formula for non-parallel velocities on this page.
 
  • #4
Can the speed of light be broken using vectors? Why not?

the speed of light is fixed for all obsevers. for all frames of reference.
 

1. What is a vector in physics?

A vector in physics is a quantity that has both magnitude (size or amount) and direction. It can be represented by an arrow, where the length of the arrow represents the magnitude and the direction of the arrow represents the direction of the vector.

2. How is the speed of light related to vectors?

The speed of light, denoted by the letter "c", is a constant in physics that represents the speed at which light travels in a vacuum. It is also a vector quantity, meaning it has both magnitude and direction. The direction of the speed of light is always perpendicular to the direction of the electric and magnetic fields of an electromagnetic wave.

3. Can vectors be used to describe the motion of light?

Yes, vectors can be used to describe the motion of light. Since light is an electromagnetic wave, it has both an electric and magnetic field that are perpendicular to each other and to the direction of the wave's motion. These fields can be represented as vectors, allowing us to use vector equations to describe the motion of light.

4. How is the speed of light calculated using vectors?

The speed of light can be calculated using the equation c = λv, where c is the speed of light, λ is the wavelength of the light, and v is the frequency of the light. This equation uses vectors, as the wavelength and frequency are both vector quantities. By plugging in the values for λ and v, we can calculate the speed of light in a specific medium.

5. Are there any limitations to using vectors to describe the speed of light?

Yes, there are limitations to using vectors to describe the speed of light. Vectors only work in linear systems, meaning they cannot accurately describe the behavior of light in curved spacetime. This is where the theory of relativity comes in, which uses tensors (a more complex mathematical concept) to accurately describe the behavior of light in curved spacetime.

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