Confusion in special relativity - total newbie

In summary, the conversation discusses a problem in Special Relativity where Frame S has a speed of 0.7c along the x axis relative to Frame S'. The clocks are adjusted so that t=t'=0 at x=x'=0 and an event occurs in S at t1=3x10^7s at x1=40m. The task is to find the time at which the event occurs in S'. The solution involves using the equations \beta=0.7 and \gamma=1.4003 to find x'=\gamma(x-t\beta c) and then plugging in the given values to get x'=-32.21m. The conversation then discusses whether this answer is correct and suggests using a
  • #1
I'm sure it's a stupid question but this is my first crack at SR so help would be great.

Homework Statement


Frame S' has a speed of 0.7c along the x axis relative to frame S. Clocks are adjusted so t=t'=0 at x=x'=0.

An even occurs in S at t1 = 3 x 10^7s at x1 = 40m. At what time does the event occur in S'?


Homework Equations


[tex]\beta = 0.7[/tex]
[tex]\gamma = 1.4003[/tex]
[tex]x' = \gamma (x - t\beta c)[/tex]


The Attempt at a Solution



[tex]x' = \gamma (x - t\beta c) = (1.4003)(40 - (3 * 10^7)0.7 c) = -32.21m[/tex]

Is this answer correct? It seems to me it can't possibly be right! What am I doing wrong?
 
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  • #2
iamaelephant said:

The Attempt at a Solution



[tex]x' = \gamma (x - t\beta c) = (1.4003)(40 - (3 * 10^7)0.7 c) = -32.21m[/tex]

Is this answer correct? It seems to me it can't possibly be right! What am I doing wrong?

Why do you think this cannot be right? Think of where the origin of S' is wrt S when the event happens.

BTW, you have a direct formula for finding the time, which is the actual question.
 
  • #3




First of all, congratulations on taking on the challenge of learning about special relativity! It can be a confusing topic, but with patience and practice, you will gain a better understanding of it.

Now, let's take a look at your attempt at a solution. The equation you used, x' = \gamma (x - t\beta c), is correct. However, there are a few things you need to keep in mind when using this equation.

Firstly, the value of \gamma is actually 1/\sqrt{1-\beta^2}, which in this case is approximately 1.4. So when you substitute the values into the equation, it should look like this:

x' = (1/\sqrt{1-0.7^2})(40 - (3*10^7)*0.7*c) = 40m

The answer you got, -32.21m, is incorrect because you used the wrong value for \gamma.

Secondly, when using the equation x' = \gamma (x - t\beta c), you need to make sure that the units for x and t are consistent. In this case, the units for x are in meters and the units for t are in seconds. So you need to convert the time t1 = 3 x 10^7s to meters by multiplying it by the speed of light, c. This will give you a value of t1 = 9 x 10^14m.

Substituting this value into the equation, x' = (1.4)(40 - (9*10^14)*0.7*c), you will get an answer of 40m, which is the correct answer.

So in conclusion, your answer is correct, but you made a small mistake in using the value of \gamma and you also needed to convert the time to meters. Keep practicing and you will become more comfortable with using special relativity equations. Good luck!
 

1. What is special relativity?

Special relativity is a theory developed by Albert Einstein in the early 20th century that explains the relationship between space and time. It states that the laws of physics are the same for all observers in uniform motion, and that the speed of light is constant in all inertial frames of reference.

2. What causes confusion in special relativity?

The concepts of time dilation, length contraction, and the relativity of simultaneity can often be confusing for those new to special relativity. These ideas challenge our common sense understanding of space and time and require a shift in perspective to fully grasp.

3. How does special relativity impact our daily lives?

Special relativity has many practical applications in our daily lives, such as in GPS technology and particle accelerators. It also has a profound impact on our understanding of the universe and has led to advancements in fields such as cosmology and astrophysics.

4. Is special relativity the same as general relativity?

No, special relativity and general relativity are two different theories. Special relativity deals with the relationship between space and time in the absence of gravity, while general relativity includes the effects of gravity and describes the curvature of spacetime.

5. Can special relativity be proven?

Special relativity has been extensively tested and confirmed through numerous experiments and observations. Its predictions have been verified and it is considered one of the most successful and well-supported theories in physics.

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