Special Relativity spacetime intervals HW help

In summary: Can someone explain what I did wrong?The Kahless takes off from Kronos at t=5/4(4-0)=5 and it catches up to the Federation ship at x=0. The Kahless overtakes the other ship at x=+1.
  • #1
Nivek43
2
0

Homework Statement


The Tale:
The Klingon home world of Kronos is located at x=0. At time ct=-4 , a wonderful event occurs: Federation emissaries negotiate a peace treatywith the Klingons, bringing many years of warfare to an end! As part of this treaty, the Federation agrees to share its vast research database with the Klingons. As soon as the peace treaty is signed (x=0, ct=-4), the Fed. negotiators board their ship and set out from Kronos in the +x direction at speed .6c.

Armed with new knowledge, the Klingon scientists get to work...and before long, they are on the verge of a profound discovery: with a clever modification of their warp drive, they can make a faster-than-light warship! At time ct=0, the scientist K'pril solves the final piece of the puzzle: he solders the essential wire in place of the great warship Kahless, and the Klingon High council immediately launches the Kahless from Kronos. THe newly modified warship races off at velocity 3c in the +x direction, intent on destruction.

The Klingon high command chuckles with glee when their observers report the first success of the Kahless: the complete destruction of a Federation outpost at position x=+1.

The Kahless continues on its way without any change in course... and because of its tremendous speed, it soon catches up with the Fed. negotiators! The dreadful warship instantly powers weapon, and vaporizes the negotiators' ship.

The story above describes 4 events (underlined), some of which involeve a ship traveling faster than light-speed.

1. Plot the four events as seen by the scientists on Kronos and the world-lines for Kronos, Fed. neg., and Kahless.

2. Then plot the four events and world-lines in the frame of the fed. negotiators.

Homework Equations


I=(ct)^2-x^2-y^2-z^2
Lorentz Transformations.

The Attempt at a Solution



Now I think I can plot the first 3 events for the first part. I'm just having trouble with calculating the destruction of the negotiators. I tried doing something with spacetime intervals I=(ct)^2-x^2-y^2-z^2 but I can't seem to be getting anywhere. If someone could provide some hints that would be wonderful.
 
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  • #2
Nivek43 said:
I'm just having trouble with calculating the destruction of the negotiators.
When the Kahless takes off, where is the Federation ship? How long does it take for the Kahless to overtake the other ship? What time and place does that happen? (Use Kronos coordinates to start with.)
 
  • #3
I think I may have gotten the first part, but I'm feeling uncertain. I did t'=5/4(4-0)=5 and then x'=5/4(0-.6*4)=-3. This doesn't make sense to me, I used the lorentz transformations with t' and x' being in the reference frame of the Negotiators. And then x=0 because the people on Kronos see the two events happen at the same position and then used t=4 because the duration between the two events in the scientists' eyes is 4. But that negative length is screwing me up.
 

1. What is the concept of spacetime intervals in special relativity?

Spacetime intervals in special relativity refer to the distance between two events in both time and space. It takes into account the fact that time and space are relative and can be affected by the speed of an observer.

2. How is the spacetime interval calculated in special relativity?

The spacetime interval is calculated using the Minkowski metric, which takes into account the differences in time and space measurements between two frames of reference. This metric is based on the concepts of time dilation and length contraction.

3. What is the significance of the spacetime interval being invariant?

The invariance of the spacetime interval is a fundamental concept in special relativity. It means that the interval between two events will be the same for all observers, regardless of their relative motion. This is essential in maintaining the consistency of physical laws in all frames of reference.

4. How does the concept of spacetime intervals affect our understanding of time and space?

The concept of spacetime intervals challenges our traditional understanding of time and space as absolute and independent entities. It highlights the interdependence of time and space and the fact that they can be affected by an observer's perspective.

5. Can the spacetime interval ever be negative?

No, the spacetime interval cannot be negative in special relativity. This is because the Minkowski metric includes a negative sign for the time component, which ensures that the spacetime interval will always be positive or equal to zero.

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