Connection between Lorentz covariance and special relativity

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Discussion Overview

The discussion revolves around the relationship between Lorentz covariance and special relativity, specifically whether all phenomena related to special relativity can be derived from the invariance of the spacetime interval and the covariant nature of the equations involved. The scope includes theoretical implications and the foundational aspects of spacetime structure in the context of special relativity.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant states that the equation s² = t² - x² - y² - z² is covariant and that the interval "s" is invariant, questioning if everything in special relativity can be derived from these facts.
  • Another participant suggests that deriving "everything" depends on the definition of "everything," indicating that the spacetime structure can be fully derived from these facts.
  • A further clarification is made that if all phenomena of special relativity can be predicted from the spacetime structure, then the answer would be affirmative, contingent on the covariant nature of other physical laws, such as Maxwell's Equations.
  • It is noted that while spacetime is fundamental, it is not the entirety of the physical laws governing phenomena.

Areas of Agreement / Disagreement

Participants express a general agreement on the derivation of spacetime structure from the stated facts, but there is no consensus on whether all phenomena of special relativity can be fully explained solely based on these principles, as it depends on the interpretation of "everything."

Contextual Notes

The discussion highlights the dependence on the definitions of terms like "everything" and the necessity for other physical laws to maintain covariance, which may not be universally accepted or defined in the same way by all participants.

fezster
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s2 = t2 - x2 - y2 - z2

This equation is covariant (Lorentz covariance). The interval "s" is invariant (Lorentz invariance).

Can you derive everything in special relativity from these facts? Or am I mistaken about that?
 
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fezster said:
Can you derive everything in special relativity from these facts?

It depends on what you mean by "everything". You can derive everything about the spacetime structure, yes.
 
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PeterDonis said:
It depends on what you mean by "everything". You can derive everything about the spacetime structure, yes.
When I say everything, I mean can we explain all the phenomena that arises due to special relativity on the basis of just these facts.

So, if we can predict all the phenomena of special relativity from the spacetime structure, and everything about spacetime can be derived from these facts, then the answer would be yes. Is that right?
 
fezster said:
if we can predict all the phenomena of special relativity from the spacetime structure, and everything about spacetime can be derived from these facts, then the answer would be yes. Is that right?

Yes, as long as you also stipulate that all of the other laws of physics must be covariant (for example, Maxwell's Equations governing the electromagnetic field). This is not a problem because we have covariant forms of all those other laws. But it should be noted that spacetime, by itself, is not everything.
 

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