I The uniqueness of D=4

arivero
Gold Member
Messages
3,481
Reaction score
187
TL;DR Summary
Discussions about having 3 spacial dimensions
I have found an interesting rabbit hole, because I thought the question of why we live in 3+1 was mainly a matter of footnotes and off-press debates. But it seems if was touched early by Weyl, Ehrenfest and Whitrow

https://einsteinpapers.press.princeton.edu/vol13-doc/764
1726959309657.png


1726959746222.png


And then elaborated for Schwarzchild metrics by Tangherlini, who seems to be the root citation nowadays.

Is there any other relevant literature? What have you read on the topic? How does modern theory evade Eherenfest's arguments?
 

Attachments

Physics news on Phys.org
For higher dimensionality, it seems to me that one way is to have “extra dimensions” be microscopic.
 
robphy said:
For higher dimensionality, it seems to me that one way is to have “extra dimensions” be microscopic.
That is empirically, of course. But point is, mathematically? with extra dimensions the argument does not disappear; it has some extra discussion about what compactifcations are stable. The point of D=7+4...
 

Thread 'Is the variation of the metric ##\delta g_{\mu\nu}## a tensor?'

From $$0 = \delta(g^{\alpha\mu}g_{\mu\nu}) = g^{\alpha\mu} \delta g_{\mu\nu} + g_{\mu\nu} \delta g^{\alpha\mu}$$ we have $$g^{\alpha\mu} \delta g_{\mu\nu} = -g_{\mu\nu} \delta g^{\alpha\mu} \,\, . $$ Multiply both sides by ##g_{\alpha\beta}## to get $$\delta g_{\beta\nu} = -g_{\alpha\beta} g_{\mu\nu} \delta g^{\alpha\mu} \qquad(*)$$ (This is Dirac's eq. (26.9) in "GTR".) On the other hand, the variation ##\delta g^{\alpha\mu} = \bar{g}^{\alpha\mu} - g^{\alpha\mu}## should be a tensor...
View full post »

Thread 'I don't see how a black hole's event horizon can be crossed'

OK, so this has bugged me for a while about the equivalence principle and the black hole information paradox. If black holes "evaporate" via Hawking radiation, then they cannot exist forever. So, from my external perspective, watching the person fall in, they slow down, freeze, and redshift to "nothing," but never cross the event horizon. Does the equivalence principle say my perspective is valid? If it does, is it possible that that person really never crossed the event horizon? The...
View full post »

Hot Threads

Recent Insights

Back
Top