Another relativistic dynamics question

In summary, the conversation discusses the Lorentz invariance of action and how it is required for a theory to have Lorentz invariance. The possibility of a non-Lorentz invariant action is also mentioned.
  • #1
snoopies622
846
28
Could someone please either derive or point me towards a derivation of the Lorentz invariance of action?

Thanks.
 
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  • #2
Thought I'd give this one bump before it left the front page altogether..
 
  • #3
I don't think it's derived so much as required. You could write down a non-Lorentz invariant action, but you wouldn't want to, because the resulting theory would lack Lorentz invariance, which is firmly established experimentally.
 
  • #4
So if a theory includes action that isn't Lorentz invariant, then it will inevitably have something else in it that's also not Lorentz invariant and is required to be according to the initial hypotheses of special relativity?
 

FAQ: Another relativistic dynamics question

1. What is relativistic dynamics?

Relativistic dynamics is the branch of physics that studies the motion of objects at speeds close to the speed of light. It is based on Einstein's theory of special relativity, which states that the laws of physics are the same for all observers in uniform motion.

2. How does relativistic dynamics differ from classical mechanics?

Relativistic dynamics differs from classical mechanics in that it takes into account the effects of time dilation and length contraction at high speeds. It also introduces the concept of four-vectors, which combine time and space into a single entity known as spacetime.

3. What is the Lorentz transformation in relativistic dynamics?

The Lorentz transformation is a mathematical expression that describes how the measurements of time and space differ between two observers in relative motion. It is a key component of Einstein's theory of special relativity and is used to calculate the effects of time dilation and length contraction.

4. How does relativistic dynamics explain the twin paradox?

The twin paradox is a thought experiment that illustrates the effects of time dilation in relativistic dynamics. It involves two twins, one of whom stays on Earth while the other travels at high speeds through space. When the traveling twin returns, they will have aged less than the twin who stayed on Earth due to the effects of time dilation.

5. What are some real-world applications of relativistic dynamics?

Relativistic dynamics has many practical applications, including in the design and operation of particle accelerators, GPS systems, and spacecraft. It also plays a crucial role in understanding the behavior of particles at high energies and in the study of cosmology and the early universe.

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