Lorentz Transformation: Solving Homework Statement

Other than that, your calculations are correct. To summarize, in a different inertial reference frame, two events that are separated by 3 seconds in the original frame are separated by 4 seconds. The invariant space-time interval is used to solve this problem, and the final answer is 7.9x10^8 meters.
  • #1
yellowputty
9
0

Homework Statement



Two events occur at the same place in an inertial reference fram S, but are separated in time by 3 seconds. In a different frame S', they are separated in time by 4 seconds.

(a) What is the distance between the two events as measured in S'?
(b) What is the speed of S relative to S'?

Homework Equations



I'm presuming:

t' = gamma*(t-ux/c^2)

The Attempt at a Solution



I have the answer, and a hint saying to use the interval S^2, but I have no idea what that means, and where I start. When I look and the relevant Lorentz equations, they involve velocity, and I do not have a velocity here.

Could you please point me in the right direction?

Thank you in advance.
 
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  • #2
The hint is implying that you use the invariant space-time interval to solve this problem. The following quantity is called the space time interval:

[tex](\Delta s)^2= (\Delta x)^2 + (\Delta y)^2 + (\Delta z^2) - (c\Delta t)^2[/tex]

This quantity is a Lorentz scalar and is thus invariant over Lorentz transformations (it is the same in all inertial frames). So, in one dimension this means:

[tex](\Delta x)^2- (c\Delta t)^2=(\Delta x')^2- (c\Delta t')^2[/tex]

Can you use this the solve the problem?
 
  • #3
G01 said:
The hint is implying that you use the invariant space-time interval to solve this problem. The following quantity is called the space time interval:

[tex](\Delta s)^2= (\Delta x)^2 + (\Delta y)^2 + (\Delta z^2) - (c\Delta t)^2[/tex]

This quantity is a Lorentz scalar and is thus invariant over Lorentz transformations (it is the same in all inertial frames). So, in one dimension this means:

[tex](\Delta x)^2- (c\Delta t)^2=(\Delta x')^2- (c\Delta t')^2[/tex]

Can you use this the solve the problem?

Do I find [tex](\Delta t)[/tex] by doing SQRT[(4^2)-(3^2)] = ROOT 7

Then at they are both at the same coordinates in the inertial reference frame, we can ignore x , y and z. Therefor S equals the root of (c^2)*(ROOT 7) = 7.9x10^8m

Is this correct?
 
  • #4
yellowputty said:
Do I find [tex](\Delta t)[/tex] by doing SQRT[(4^2)-(3^2)] = ROOT 7

Then at they are both at the same coordinates in the inertial reference frame, we can ignore x , y and z. Therefor S equals the root of (c^2)*(ROOT 7) = 7.9x10^8m

Is this correct?

You should only have one factor of c in your final line, since you take the square root of c^2 when solving for the answer.
 

Related to Lorentz Transformation: Solving Homework Statement

What is the Lorentz Transformation?

The Lorentz Transformation is a mathematical formula used in the theory of relativity to describe how physical quantities, such as time, length, and momentum, change between two reference frames that are moving relative to each other at a constant velocity.

Why is the Lorentz Transformation important?

The Lorentz Transformation is important because it allows us to understand how the laws of physics behave in different reference frames, particularly in the context of objects moving at high speeds. It is essential in the theory of relativity and has been confirmed through many experiments and observations.

How do you solve a homework statement involving Lorentz Transformation?

To solve a homework statement involving Lorentz Transformation, you will need to apply the appropriate equations and principles of the theory of relativity. This may involve converting between different reference frames, calculating time dilation or length contraction, or solving for other physical quantities. It is important to carefully read and understand the given information and use the correct equations and units in your calculations.

What are the key concepts to understand when working with Lorentz Transformation?

Some of the key concepts to understand when working with Lorentz Transformation include the concept of a reference frame, the idea of time dilation and length contraction, and the relationship between space and time in the theory of relativity. It is also important to understand the differences between special and general relativity and how they apply to different situations.

Are there any common mistakes to avoid when solving problems involving Lorentz Transformation?

One common mistake to avoid when solving problems involving Lorentz Transformation is using the wrong equations or not correctly converting between units of measurement. It is also important to carefully consider the given information and not make assumptions about the reference frames or other variables. It may also be helpful to double-check your calculations and make sure they are consistent with the principles of the theory of relativity.

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