Exploring Special Relativity: Two Events in Two Reference Frames

In summary, the problem involves two events occurring in different reference frames and the question is whether or not they can occur simultaneously in a moving reference frame. The correct answer is c.), which states that the events can only occur simultaneously in the moving frame if the separation between them is greater than the speed of light. This is because in a space-time diagram, the events must occur on a spatial axis for them to be simultaneous in the moving frame. This requires the separation between the events to be space-like, which is represented by the condition x/t > c.
  • #1
yxgao
123
0
gre problem: special relativity, two events in two reference frames

34. In an inertial reference frame S, two events occur on the x-axis separated in time by [tex]\Delta t[/tex] and in space by [tex]\Delta x[/tex]. in another inertial reference frame S', moving in the x-directon relative to S, the two events could occura t the same time under which, if any, of the following conditions?

a.) For any values of [tex]\Delta x[/tex] and [tex]\Delta t[/tex].
b.) Only if |[tex]\Delta x[/tex]/[tex]\Delta t[/tex]| < c
c.) Only if |[tex]\Delta x[/tex]/[tex]\Delta t[/tex]| > c
d.) Only if |[tex]\Delta x[/tex]/[tex]\Delta t[/tex]| = c
e.) Under no condition


Answer: c.)


Can someone explain why? It would help if you refer to specific equations that prove the answer is correct.

Thanks!
 
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  • #2
Being a dinosaur I don't write in lateX. I am condemned to Mathtype, which is not available here. So you'll get few equations from me.
Draw a space-time diagram in the frame where the two events are on the x-axis. Let the first event be at the origin and the second event at coordinates x.t (both in meters). The question asks for a frame moving along the x-axis in which the two events are simultaneous. Events that are simultaneous will live on a spatial axis. So take the origin of the moving frame at the first event and the moving x-axis on the line joining the two events. They are simultaneous in this moving frame. Since a spatial axis is space-like, so must the separation be between the two events. Back in the old frame this requires x/t>c, which is your answer c).
If you have understood this, which of your answers would you take if the question was altered so that the two events occurred at the same place in the moving frame?
 
  • #3


The correct answer is c.) Only if |\Delta x/\Delta t| > c.

This is because of the principle of relativity, which states that the laws of physics should be the same in all inertial reference frames. In this problem, we have two events occurring in two different reference frames, S and S'. In order for the time and space intervals to be the same in both frames, the ratio of \Delta x/\Delta t must be greater than c, the speed of light. This is because according to special relativity, time and space are not absolute, but are dependent on the observer's frame of reference. Therefore, in order for the laws of physics to remain the same in both frames, the ratio of \Delta x/\Delta t must be greater than c.

To further understand this, we can use the Lorentz transformation equations, which describe how measurements of time and space change between two inertial frames of reference. These equations show that as an object's speed approaches the speed of light, time and space intervals will appear to be different in different reference frames. So in order for the two events to occur at the same time in both frames, the ratio of \Delta x/\Delta t must be greater than c.

In summary, the correct answer is c.) Only if |\Delta x/\Delta t| > c because of the principle of relativity and the Lorentz transformation equations, which show that the ratio of time and space intervals must be greater than c in order for the laws of physics to remain the same in different reference frames.
 

1. What is special relativity?

Special relativity is a theory developed by Albert Einstein that explains how objects move and interact at high speeds, near the speed of light. It is based on two main principles: the principle of relativity, which states that the laws of physics should be the same for all observers in uniform motion, and the constancy of the speed of light, which states that the speed of light is the same for all observers regardless of their motion or the motion of the light source.

2. What is the difference between special and general relativity?

Special relativity deals with the physics of objects moving at constant speeds in a straight line, while general relativity deals with the physics of objects moving in non-uniform or accelerated motion. Additionally, special relativity only applies to objects in the absence of gravitational forces, while general relativity takes into account the effects of gravity on space and time.

3. How does time dilation work in special relativity?

According to special relativity, time is relative and can appear to pass at different rates for different observers. This is known as time dilation. As an object approaches the speed of light, time slows down for that object relative to a stationary observer. This means that two events that appear to occur simultaneously for one observer may not appear simultaneous for another observer traveling at a high speed.

4. What is length contraction in special relativity?

Length contraction is a consequence of special relativity that states that objects appear to shrink in the direction of motion when moving at high speeds. This means that an object's length will appear shorter to an observer traveling at a high speed compared to an observer who is stationary.

5. How does special relativity affect our everyday lives?

Special relativity has important implications in various fields, including physics, astronomy, and engineering. It helps us understand the behavior of particles at high speeds and has been confirmed by numerous experiments. It also plays a crucial role in technologies such as GPS, which relies on precise timing and the effects of time dilation to accurately calculate positions. Special relativity has also led to advancements in nuclear energy and particle accelerators.

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