Calculating Spatial Separation Using Lorentz Transforms: Homework Solution

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In summary, the problem asks for the spatial separation between two events in an inertial frame with a time interval of 6 seconds, given that the same events have a time interval of 4 seconds in another inertial frame. The Lorentz Transforms can be used to solve this problem, specifically by finding the invariant quantity of the spacetime interval, which involves both time and position. It is recommended to review the relevant section in the textbook for further understanding.
  • #1
Mugen Prospec
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Homework Statement



Two events occur at the same place in a certain inertial frame and are separated by a time interval of 4 seconds. What is the spatial separation between these two events in an inertial frame in which the events are separated by a time interval of 6 seconds?

Homework Equations



Lorentz Transforms

The Attempt at a Solution



I really have no idea where to start. I know its not that hard I am just drawing a blank
 
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  • #2
Mugen Prospec said:

Homework Statement



Two events occur at the same place in a certain inertial frame and are separated by a time interval of 4 seconds. What is the spatial separation between these two events in an inertial frame in which the events are separated by a time interval of 6 seconds?

Homework Equations



Lorentz Transforms

The Attempt at a Solution



I really have no idea where to start. I know its not that hard I am just drawing a blank

Hint: What quantity involving both time and position is invariant under Lorentz transforms?
 
  • #3
I know the speed of light is invariant. The way I worked it was putting it through the Lorentz time transform solving for v. then put that v in the x Lorentz transform
 
  • #4
Mugen Prospec said:
I know the speed of light is invariant. The way I worked it was putting it through the Lorentz time transform solving for v. then put that v in the x Lorentz transform

Sure, [itex]c[/itex] is Lorentz invariant, but it doesn't invole time or position, so that doesn't help. What about the spacetime interval [itex]\delta s^2[/itex]?
 
  • #5
Could you give me maybe a walk through on how to find that or even the problem. I am really at a loss, I missed a week of classes because i was sick.
 
  • #6
Mugen Prospec said:
Could you give me maybe a walk through on how to find that or even the problem. I am really at a loss, I missed a week of classes because i was sick.

I'm not here to teach a week of coursework. Read the section in your text that talks about spacetime intervals and then try the problem.
 

FAQ: Calculating Spatial Separation Using Lorentz Transforms: Homework Solution

What is the purpose of calculating spatial separation using Lorentz transforms?

The purpose of calculating spatial separation using Lorentz transforms is to account for the effects of time dilation and length contraction in special relativity. This allows for accurate measurements of distance and position in reference frames moving at different velocities.

How do Lorentz transforms affect spatial separation?

Lorentz transforms affect spatial separation by altering the measurements of distance and position in reference frames moving at different velocities. This is due to the fact that time and space are relative in special relativity, and the relationship between them is described by the Lorentz transforms.

What is the equation for calculating spatial separation using Lorentz transforms?

The equation for calculating spatial separation using Lorentz transforms is x' = γ(x-vt), where x' is the transformed distance, x is the original distance, v is the relative velocity between the two reference frames, t is the time interval between measurements, and γ is the Lorentz factor.

Can Lorentz transforms be used for any type of spatial separation?

Lorentz transforms can be used for any type of spatial separation, as long as the reference frames are moving at different velocities relative to each other. This includes measurements of distance, position, and even angles in special relativity.

Are there any limitations to using Lorentz transforms for calculating spatial separation?

There are some limitations to using Lorentz transforms for calculating spatial separation. These include the assumption that the reference frames are moving at constant velocities, and that the effects of gravity are negligible. Lorentz transforms also do not account for the effects of acceleration on spatial separation.

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