Mike_bb's latest activity
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MMike_bb reacted to Matterwave's post in the thread Undergrad Why does coordinate dependence violate homogeneity in spacetime intervals? with
Agree.
If you go with the L+L derivation you only need to prove ##ds^2=ds'^2## because ##ds'## is arbitrary. Note the quote "in any other... -
MMike_bb replied to the thread Undergrad Why does coordinate dependence violate homogeneity in spacetime intervals?.And then we prove that ##ds'^2=ds_1^2=ds_2^2=....## for other intervals in all inertial frames.
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MMike_bb reacted to Ibix's post in the thread Undergrad Why does coordinate dependence violate homogeneity in spacetime intervals? with Agree.
I think so, yes.
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MMike_bb replied to the thread Undergrad Why does coordinate dependence violate homogeneity in spacetime intervals?.From this we have that ##ds'^2=ds^2##, right?
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MMike_bb reacted to Ibix's post in the thread Undergrad Why does coordinate dependence violate homogeneity in spacetime intervals? with
Like.
Homogeneity of space means invariance under purely spatial translations. Thus if you have two events whose coordinates are ##x_a##... -
MMike_bb reacted to PeterDonis's post in the thread Undergrad Why does coordinate dependence violate homogeneity in spacetime intervals? with Like.
By analogy, "homogeneity of time" would mean invariance under time translations. And "homogeneity of space and time", which is what...
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MMike_bb reacted to Ibix's post in the thread Undergrad Why does coordinate dependence violate homogeneity in spacetime intervals? with Like.
I agree. I suspect L&L simply haven't got as far as defining spacetime yet (note the use of "fictitious four-dimensional space" just...
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MMike_bb replied to the thread Undergrad Why does coordinate dependence violate homogeneity in spacetime intervals?.In other source "homogeneity of space and time" means homogeneity of space and homogeneity of time. Not a spacetime.
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MMike_bb replied to the thread Undergrad Why does coordinate dependence violate homogeneity in spacetime intervals?.Landau & Lifshitz' Classical Theory of Fields (pp.14-15)
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MMike_bb posted the thread Undergrad Why does coordinate dependence violate homogeneity in spacetime intervals? in Special and General Relativity.Hello! I have a problem with understanding homogeneity of the space. In the book Landau&Lifshitz it was written that two spacetime...
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MMike_bb reacted to Sagittarius A-Star's post in the thread Undergrad Why can coefficient "a" between spacetime intervals depend on velocity between systems? with Agree.
It is from Wolfgang Rindler. https://www.amazon.com/Introduction-to-Special-Relativity/dp/0198531818?tag=pfamazon01-20 For details...
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MMike_bb replied to the thread Undergrad Why can coefficient "a" between spacetime intervals depend on velocity between systems?.Yes, it helps!
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MMike_bb reacted to Sagittarius A-Star's post in the thread Undergrad Why can coefficient "a" between spacetime intervals depend on velocity between systems? with Agree.
Maybe this helps: Source: https://en.wikipedia.org/wiki/Differential_(mathematics)#Introduction Approaches for making the notion of...
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MMike_bb replied to the thread Undergrad Why can coefficient "a" between spacetime intervals depend on velocity between systems?.I have this source only: I can't give rigorous definition of the term "differential" because its depend on context.
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MMike_bb replied to the thread Undergrad Why can coefficient "a" between spacetime intervals depend on velocity between systems?.Sagittarius A-Star, Hello! I argued with one person that "differentials" (as is mentioned in the book) = "infinitesimally small...
