petrushka.googol Posted January 18, 2016 Posted January 18, 2016 Even if a particle is given infinite energy there exists no infinite path, either in a closed loop or open loop system, so infinite propagation is impossible.
Strange Posted January 18, 2016 Posted January 18, 2016 Why is infinite energy relevant? What is an "open loop" system? However, if the universe is infinite then a particle could, in principle, travel for an infinite distance (with no energy required). And even in a finite system, it is possible to have an infinitely long path. For example: https://en.wikipedia.org/wiki/Koch_snowflake
petrushka.googol Posted January 18, 2016 Author Posted January 18, 2016 Why is infinite energy relevant? What is an "open loop" system? However, if the universe is infinite then a particle could, in principle, travel for an infinite distance (with no energy required). And even in a finite system, it is possible to have an infinitely long path. For example: https://en.wikipedia.org/wiki/Koch_snowflake It is a thought experiment. Assume that the Big Bang generated infinite energy. By open loop system I am referring to the open loop architecture of the fabric of space-time. eg)saddle shaped It seems to be a matter of the frame of reference. can a path in space-time be truly infinite ? I think not. The path exists because it is mapped in space-time which is continuous yet finite. In a closed loop system the longest path will be that of zero displacement since the particle follows the geodesic to return to the origin.
Strange Posted January 18, 2016 Posted January 18, 2016 It is a thought experiment. Assume that the Big Bang generated infinite energy. Still not sure what the relevance of infinite energy is. can a path in space-time be truly infinite ? I think not. If the universe is infinite, then a path can be infinite. If the universe is finite but continuously expanding (which I guess is what you mean by "open") then I think that the expansion of the universe and means that there will always be locations that it will never be possible to reach (even at the speed of light) because they are carried away by expansion faster than you can approach them. Therefore the path is infinite.
StringJunky Posted January 18, 2016 Posted January 18, 2016 Even if a particle is given infinite energy there exists no infinite path, either in a closed loop or open loop system, so infinite propagation is impossible. The exact shape is still a matter of debate in physical cosmology, but experimental data from various, independent sources (WMAP, BOOMERanG and Planck for example) confirm that the observable universe is flat with only a 0.4% margin of error.[3][4][5] Theorists have been trying to construct a formal mathematical model of the shape of the universe. In formal terms, this is a 3-manifold model corresponding to the spatial section (in comoving coordinates) of the 4-dimensional space-time of the universe. The model most theorists currently use is the so-called Friedmann–Lemaître–Robertson–Walker (FLRW) model. Arguments have been put forward that the observational data best fit with the conclusion that the shape of the global universe is infinite and flat,[6] but the data are also consistent with other possible shapes, such as the so-called Poincaré dodecahedral space[7][8] and the Picard horn.[9] https://en.wikipedia.org/wiki/Shape_of_the_universe
petrushka.googol Posted January 21, 2016 Author Posted January 21, 2016 The Universe is infinite relative to the observer. It is a construct which is beyond the scope of the human mind and that is why it is infinite. Do we really know where the Universe ends ? Or where it begins ? Here we are dealing with an "infinity" rather than the "infinity of infinities". (true infinity). An infinite path does not exist since the Universe by it's very definition is a construct that we can measure and hence finite. (but tending to infinity). Hence the postulate stated in the OP follows.
Strange Posted January 21, 2016 Posted January 21, 2016 The Universe is infinite relative to the observer. ... An infinite path does not exist since the Universe by it's very definition is a construct that we can measure and hence finite. So is both infinite and finite. That makes sense. </sarcasm> It is a construct which is beyond the scope of the human mind and that is why it is infinite. That is not what infinite means. Maybe the word you are looking for is "incomprehensible". But we are doing a pretty good job of understanding the universe. We just don't know if it is finite or infinite. Do we really know where the Universe ends ? Or where it begins ? No.
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