Special relativity question - reference frames

In summary, the scenario involves observer S' in frame S' with objects A', B', and C' at rest. S' is moving in the +x direction with respect to frame S at speed v. At t'=0, a light flash occurs at B' and expands outward as a spherical wave. According to an observer in S', the wave fronts do not arrive at A' and C' simultaneously, with the flash arriving first at C' due to the longer distance it has to travel. The difference in arrival times can be calculated using the Lorentz transformation, which takes into account the constant speed of light. On the other hand, an observer in S would see the flash reach A' and B' simultaneously, since
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Homework Statement


Suppose that A', B' and C' are at rest in frame S', which moves with respect to S at speed v in the +x direction. Let B' be located exactly midway between A' and C'. At t'=0, a light flash occurs at B' and expands outward as a spherical wave.

1. According to an observer in S', do the wave fronts arrive at A' and C' simultaneously? What about an observer in S?
2. If you answered no, what is the difference in their arrival times and at which point did the front arrive first?

Homework Equations



None, just Einstein's postulates of special relativity.

The Attempt at a Solution



Alright, so I *think* that the flashes would not arrive at A' and C' simultaneously according to an observer in S'. Because S' is moving in the +x direction, from the instant the flash occurs it has to travel a little further to get to C' than to A'. However, when I did out the math it told me that it would arrive at C' first.

This is what I tried. (I'm not sure if its right, should I be using a Lorentz transformation instead?)

t(b'-> c') = L/(c+v)
t(b' -> a') = L(c-v)
[tex]\Delta[/tex]t = L/(c-v) - L/(c+v)
[tex]\Delta[/tex]t = 2Lv/(c[tex]^{2}[/tex] - v[tex]^{2}[/tex])

I feel like I'm not understanding something about the fact that the speed of light always being a constant.

Furthermore, the observer in S would see the flash reach A' and B' simultaneously, right?
 
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  • #2
Since the observer in S sees S' as moving at v, it would cover a distance equal to vt, and thus the light wave would have to travel a distance of L+vt to get to A' and C'. Thanks in advance!
 

1. What is the basic premise of special relativity?

The basic premise of special relativity is that the laws of physics are the same for all observers in uniform motion. This means that the laws of physics are independent of the reference frame or perspective from which they are observed.

2. How does special relativity differ from classical mechanics?

Special relativity differs from classical mechanics in that it incorporates the concept of space and time being relative to the observer's frame of reference. This means that the perception of time and space can vary depending on the observer's velocity and position in space.

3. What is the significance of the speed of light in special relativity?

In special relativity, the speed of light is considered to be the same for all observers, regardless of their relative motion. This is a fundamental principle of the theory and has significant implications for concepts such as time dilation and length contraction.

4. How does special relativity account for the effects of gravity?

Special relativity does not directly account for the effects of gravity. However, it serves as the foundation for the more comprehensive theory of general relativity, which does incorporate gravity and its effects on space and time.

5. Can special relativity be applied to all situations?

Special relativity is most applicable to situations involving objects moving at high speeds, close to the speed of light. It is not as accurate for situations involving massive objects and gravity, for which general relativity is a better framework.

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