Can you solve the T and U paradox? Spacetime diagrams and explanations needed!

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In summary, the attempt at a solution is that in special relativity there is no such thing as a rigid object. This is the key to the paradox because just because one part of an object is moving, it doesn't mean all the other parts are. Similarly, just because one part of an object isn't moving, it doesn't mean the other parts of that object aren't moving either.
  • #1
KiyoEtAlice
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URGENT! T and U paradox

Sorry I know I posted this already, but I realized that it isn't really introductory physics:

Homework Statement


I'm really confused about how I should do this problem and this is urgent so if anyone can help, it would be very much appreaciated. Thanks.

T and U Bar paradox (This is my assigned homework, it is an edit of question 6-5 from a textbook called Spacetime Physics, it's one of my teacher's collection so I don't know anything more):

A U shaped structure made of the strongest steel contains a detonator switch connected by wire to one metric ton of explosive TNT. A T-shaped structure made of the same strong steel fits inside U, with the long arm of T not quite long enough to reach the detonator switch when the two collide. Therefore there will be no explosion.

But, look at the same situation in the rest frame of the T structure . In this frame the arm of the T has its rest length, while the two arms of the U-structure are Lorentz-contracted. Therefore the arm of the T will certainly strike the detonator switch and there will be an awful explosion.

Q: ==> Make two spacetime diagrams (the bigger the better) representing the motion of the objects in the T frame and in the U frame. Take the relative speech to be 87% of the speed of light --then the contraction is half of the rest length. Label the front and back of the T structure P and Q respectively and A and B the front and back of the U structure. Determine from your diagram whether there will be an explosion or not. And explain Why your diagram gives your answer.


2. Homework Equations
**I've attached the image of this paradox that I found on the net to make things clear (and yes the image is right). Please help me out on the drawings and explanation, I'm not really sure how to do it. Note: the diagram is not the solution, it is just another version of the diagram that goes with the question.


3. The Attempt at a Solution
Well, I am completely blank at this. I know how it should be like, and I know that it wouldn't explode.

Thanks!
 
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  • #2


The key to this 'paradox' is that in special relativity there is no such thing as a rigid object. That is, just because one part of an object is moving, it DOESN'T mean all the other parts are. Similarly, just because one part of an object isn't moving, it doesn't mean the other parts of that object aren't moving either.
 
  • #3


Mute said:
The key to this 'paradox' is that in special relativity there is no such thing as a rigid object. That is, just because one part of an object is moving, it DOESN'T mean all the other parts are. Similarly, just because one part of an object isn't moving, it doesn't mean the other parts of that object aren't moving either.

Okay I get it thanks! But I don't know how to fraw spacetime diagrams, can anyone teach me how I should do it for my question?
 
  • #4


:cry: Does anyone know how to draw it? Please help me if you do because I'm more stuck than ever and it's due very soon :(
 

1. What is the T and U Paradox?

The T and U Paradox is a paradox in thermodynamics that arises when trying to reconcile the second law of thermodynamics with the reversibility of microscopic physical laws. It states that while macroscopic systems tend to increase in entropy (disorder) over time, the underlying microscopic laws are reversible and do not govern the direction of time.

2. Why is solving the T and U Paradox important?

Solving the T and U Paradox is important because it helps us better understand the fundamental laws of the universe and their implications for the behavior of matter and energy. It also has practical applications in fields such as engineering and cosmology.

3. What are some proposed solutions to the T and U Paradox?

Some proposed solutions to the T and U Paradox include the theory of quantum mechanics, which introduces the concept of wave function collapse and non-deterministic behavior at the microscopic level, and the theory of cosmological inflation, which suggests that the universe underwent a period of rapid expansion that could explain the arrow of time.

4. Can the T and U Paradox be fully solved?

Currently, the T and U Paradox remains an unsolved problem in physics. While there are proposed solutions and theories that attempt to explain it, there is no consensus on a definitive solution. It is possible that a complete resolution may require a deeper understanding of the laws of physics or the discovery of new fundamental principles.

5. What are the implications of solving the T and U Paradox?

If the T and U Paradox were to be fully solved, it would have far-reaching implications for our understanding of the universe and our place in it. It could lead to advancements in technology, a deeper understanding of the nature of time, and insights into the origins and fate of the universe.

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