Beginner question about special relativity

In summary, the conversation discusses the concept of two rectangular coordinate systems sharing the same x-axis, with one system moving at a constant speed towards positive x while a beam of light travels along their x axes. The book suggests that at x=ct and x'=ct', the equation x-ct=M(x'-ct') holds true for some constant M. However, the individuals are confused about the value of M and why it cannot be limited to 1. The expert summarizer explains that M can be any value and the equation will still be true.
  • #1
neginf
56
0
Saw this in a book last night. I hope I read it right and am remembering it right.

If two rectangular coordinate systems share the same x-axis and one is moving at a constant speed towards positive x and a beam of light is traveling along their x axes going towards the positive, then at the beam is at x=ct and x'=ct', one for each system.

The book says then x-ct=M(x'-ct') for some constant M.
What I don't get is doesn't x-ct=0=x'-ct' mean M is 1?

What am I not understanding about this?
 
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  • #2
You can't add a variable to one side of an equation without adding it to both sides. A variable can end up being something other than one later on so that is why it is not done.
 
  • #3
neginf said:
Saw this in a book last night. I hope I read it right and am remembering it right.

If two rectangular coordinate systems share the same x-axis and one is moving at a constant speed towards positive x and a beam of light is traveling along their x axes going towards the positive, then at the beam is at x=ct and x'=ct', one for each system.

The book says then x-ct=M(x'-ct') for some constant M.
What I don't get is doesn't x-ct=0=x'-ct' mean M is 1?

What am I not understanding about this?
Why do you limit the solution to M=1?

M can be any value and the equation is still true, isn't it?

0 = M(0) is true for any value of M, correct?
 
  • #4
Thank you both. x-ct=x'-ct'=0 so x-ct=anything*(x'-ct').
 

What is special relativity?

Special relativity is a theory developed by Albert Einstein that describes 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 for all observers.

What is the difference between special relativity and general relativity?

Special relativity deals with the laws of physics in inertial frames of reference (objects moving at a constant velocity), while general relativity extends these laws to non-inertial frames (objects accelerating or in the presence of gravity). General relativity also includes the concept of curved spacetime.

How does special relativity affect our daily lives?

Special relativity has many practical applications, such as in GPS technology, particle accelerators, and nuclear power plants. It also helps us understand the behavior of objects traveling close to the speed of light, such as spacecrafts and high-speed particles.

What is time dilation in special relativity?

Time dilation refers to the phenomenon where time passes slower for an object moving at high speeds compared to an observer at rest. This is due to the dilation of time in the moving object's reference frame. This effect has been observed and confirmed through experiments.

Can special relativity be proven?

Special relativity has been extensively tested and has consistently been shown to accurately describe the behavior of objects at high speeds. However, like all scientific theories, it is always open to further testing and refinement.

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