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Ragnar
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How do we prove that the spacetime interval is invariant? Also why is it so important?
Have a look please atRagnar said:How do we prove that the spacetime interval is invariant? Also why is it so important?
Ragnar said:How do we prove that the spacetime interval is invariant? Also why is it so important?
The space-time interval serves the same role in (the geometry of) Special Relativity as the distance formula serves in Euclidean geometry.Ragnar said:Also why is it so important?
Do you teach or only use special relativity. If you teach I would send you a story..masudr said:The Lorentz transformation is defined so as to keep the spacetime interval invariant. More precisely, any [itex]\Lambda[/itex] such that
[tex]\Lambda \eta \Lambda = \eta[/tex]
where [itex]\eta = \mbox{diag}(1,-1,-1,-1)[/itex] is a transformation which keeps the spacetime interval invariant.
EDIT: in component form, using Einstein summation
[tex]\eta_{a'b'} = \eta_{ab}\Lambda^a\mbox{}_{a'}\Lambda^b\mbox{}_{b'}[/tex]
neutrino said:The first chapter of Spacetime Physics deals with invariant interval; the exposition is enlightening. You can download the first chapter of the first edition from Edwin Taylor's website: http://www.eftaylor.com/download.html#special_relativity
bernhard.rothenstein said:Do you teach or only use special relativity. If you teach I would send you a story..
Ragnar said:How do we prove that the spacetime interval is invariant? Also why is it so important?
Invariance of the interval is a fundamental concept in physics that states the distance between two events in space-time remains unchanged regardless of the observer's frame of reference.
Invariance of the interval is important because it is a fundamental principle in special relativity that helps us understand the fundamental nature of space and time. It also plays a crucial role in the formulation of physical laws and the prediction of events.
Invariance of the interval is closely related to the speed of light, as it is the only physical quantity that remains constant in all frames of reference. This means that the interval between two events remains the same regardless of the relative motion of the observer and the events.
Yes, the invariance of the interval has been extensively tested and proven through various experiments, including the famous Michelson-Morley experiment and the more recent measurement of the speed of light using atomic clocks on airplanes.
No, the invariance of the interval is a universal principle that holds true in all frames of reference and has not been disproven or found to have any exceptions so far.