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
Like.
You need only homogeneity to show that ##a## does not depend on coordinates. You use isotropy to show that ##a## can only depend on the... -
MMike_bb reacted to Sagittarius A-Star's post in the thread Graduate Is photon frequency intrinsic or observer-dependent? with Like.
Yes, because it is massless.
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MMike_bb replied to the thread Undergrad Why does coordinate dependence violate homogeneity in spacetime intervals?.Ibix, What do you think about following reasoning? If the space is homogeneity and isotropy we can use the fact that arbitrary point...
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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.
Apologies, I've reused the prime for something and confused myself about what you were asking. Restating my argument, consider two...
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MMike_bb replied to the thread Undergrad Why does coordinate dependence violate homogeneity in spacetime intervals?.I'm already starting to doubt that this is true. But I thought following way: if we have ##dx_1## and ##x_1+dx_1##; ##dx_2## and...
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MMike_bb replied to the thread Undergrad Why does coordinate dependence violate homogeneity in spacetime intervals?.If it so then why do we need proof L&L?
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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##...
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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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