Question about this equation

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T = root((t2 - t1)^2 - (x2 - x1)^2) represents proper time as measured in any inertial frame, regardless of the frame in which (t2 - t1)^2 is measured. This is because T is an invariant, meaning it remains the same regardless of the frame of reference. In summary, T is proper time measured in someone's inertial frame, and (x2 - x1)^2 represents their movement through space. The equation is invariant and can be used to calculate proper time regardless of the frame of reference.
  • #1
Best of the Worst
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T = root((t2 - t1)^2 - (x2 - x1)^2)

As I understand it, T is proper time as measured in someone's intertial frame, and (x2 - x1)^2 is their movement through space... but in what frame is (t2 - t1)^2 measured?
 
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  • #2
t1,x1 and t2,x2 are both measured in somenone (anyone's) inertial frame.

Regardless of which inertial frame you chose to measure t1,x1,t2, and x2, the result T will be the same - it will be invariant.
 
  • #3
Awesome. Thank you kindly ;).
 
  • #4
Best of the Worst said:
T = root((t2 - t1)^2 - (x2 - x1)^2)

As I understand it, T is proper time as measured in someone's intertial frame, and (x2 - x1)^2 is their movement through space... but in what frame is (t2 - t1)^2 measured?
Please note that

[itex]\Delta[/itex]s2 = (t2 - t1)2 - (x2 - x1)2

may be either positive, negative or zero. [itex]\Delta[/itex]s2 may be either a proper time or a proper distance according to its sign.

Pete
 
Last edited:

What is this equation used for?

This equation is used to represent a relationship between different variables or quantities. It can be used to solve problems, make predictions, or analyze data in a specific field of study.

How do I interpret this equation?

To interpret an equation, you should first identify the variables and their corresponding values. Then, you can use the equation to calculate unknown values or understand how changes in one variable affect the others.

What assumptions are made in this equation?

Every equation has certain assumptions that need to be met for it to be valid. These assumptions can include things like a constant temperature or pressure, a linear relationship between variables, or the absence of certain external factors.

How was this equation derived?

The process of deriving an equation involves using mathematical principles and logic to manipulate existing equations and concepts in order to arrive at a new relationship between variables. This process often involves experimentation and data analysis in the specific field of study.

Can I use this equation in other contexts?

It depends on the assumptions and limitations of the equation. Some equations may only be applicable in certain situations or for specific variables, while others may have broader applications. It is important to understand the context and assumptions of an equation before using it in a different context.

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