4 ms·

Lorentz invariance appears naturally in practically all theories with waves - its violation would be a huge surprise. To see it, understand STR, the perfect mo

by eln1 10y ago

Lorentz invariance appears naturally in practically all theories with waves - its violation would be a huge surprise. To see it, understand STR, the perfect model is sine-Gordon: just many coupled pendula - we get particles ("kinks") with rest mass, which are created/annihilated in pairs, the mass grows exactly like in STR and is released while annihilation ... while moving these particles undergo Lorentz contraction (speed is limited by speed of massless waves) and oscillating particles ("breathers") slow down (time dilation) - exactly like in STR. https://en.wikipedia.org/wiki/Sine-Gordon_equation https://en.wikipedia.org/wiki/Sine-Gordon_equation "Universe model with a drill" ;) https://www.youtube.com/watch?v=nl5Qq5kUbEE https://www.youtube.com/watch?v=nl5Qq5kUbEE Animation of kink-antikink annihilation: https://en.wikipedia.org/wiki/Topological_defect#Images https://en.wikipedia.org/wiki/Topological_defect#Images

hansen 10y ago
There are lots of non-relativistic models using waves. Nothing special about them. The most compelling argument for relativity is causality. You can reconstruct spacetime – up to conformal transformations – just from the causality relations. I can’t even imagine what physics would be like w/o causality.
- eln1 10y ago
  If you restrict the speed of propagation of interactions (of massless waves), you nearly automatically get STR ... like in sine-Gordon model - speed of massive kinks becomes limited, and kinks are being contracted to zero while approaching this limit.
- dcudjejxice 10y ago
  Can you please explain or provide a link? This sounds fascinating.
  - hansen 10y ago
    http://aip.scitation.org/doi/abs/10.1063/1.523436 http://aip.scitation.org/doi/abs/10.1063/1.523436 ED: This is the starting point of the Causal Set [1] program. Don’t ask me for details, I don’t know any. But the wikipedia article looks interesting. Seems they are trying to figure out how causality restricts models with some level of discreteness. [1] https://en.wikipedia.org/wiki/Causal_sets https://en.wikipedia.org/wiki/Causal_sets
  - cyphar 10y ago
    This was covered in my undergraduate (second-year) SR course. The idea is that if you accept that Maxwell's equations apply in all inertial frames (speed of light is constant) and that causality is conserved in all frames, the result is that Newtonian mechanics requires adjustments for effects that are called "special relativity".
- valarauca1 10y ago
  GR does not imply causality nor does it enforce it. In fact GR works in a non-causal universe without a problem. 2 very sensitive measurements conducted within the past year seem to suggest (if GR is true), that we are in a universe that lacks causality. 2/3 LIGO detections imply one of the merging pair of black holes should be a naked singularity. GR allows naked singularities. It models them fine. GR just stops being globally deterministic. If you look up the history of GR some mathematicians in 50's made some really weird proposals for non-causal universes that would appear locally causal. But there isn't a way to test this. So it is more pure mathematics or philosophy then physics.
  - eaq 10y ago
    > 2/3 LIGO detections imply one of the merging pair of black holes should be a naked singularity. Where did you get this impression? All of the LIGO results are consistent with "standard" GR black holes whose event horizons merge.
    - andrewflnr 10y ago
      Possibly referring to this? http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.116.171101 http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.116.... Background: https://en.wikipedia.org/wiki/Gravastar https://en.wikipedia.org/wiki/Gravastar
      - eaq 10y ago
        Thanks for the links. I find it unfortunate that often in science (and especially with the LIGO data) much is written about what could possibly be lurking in the data but isn't actually favored over our current understanding. This creates more interest, but can obfuscate what the real situation in the field is. In this case, while Gravastars are certainly something many scientists actively do and should consider, there is no real evidence from the LIGO data that favors the hypothesis of "we are in a universe that lacks causality" over the observation of the merger of two Kerr black holes.
        10y ago
monochromatic 10y ago
SRT?
- eln1 10y ago
  I've meant special relativity.
noobermin 10y ago
I feel like this is a common misconception amongst some physicists. Lorentz invariance doesn't "appear naturally" in modern theories depending on how you develop it. Usually, one chooses a lagrangian that yields a lorentz invariant action and so all physical laws and thus solutions are lorentz invariant consequently. Lorentz invariance is a fundamental assumption...upheld by experiment. Those theories will then admit solutions (usually linearized ones (read quantized)) that appear as waves.

by eln1 10y ago

hansen 10y ago

There are lots of non-relativistic models using waves. Nothing special about them. The most compelling argument for relativity is causality. You can reconstruct spacetime – up to conformal transformations – just from the causality relations. I can’t even imagine what physics would be like w/o causality.

eln1 10y ago
If you restrict the speed of propagation of interactions (of massless waves), you nearly automatically get STR ... like in sine-Gordon model - speed of massive kinks becomes limited, and kinks are being contracted to zero while approaching this limit.
dcudjejxice 10y ago
Can you please explain or provide a link? This sounds fascinating.
- hansen 10y ago
  http://aip.scitation.org/doi/abs/10.1063/1.523436 http://aip.scitation.org/doi/abs/10.1063/1.523436 ED: This is the starting point of the Causal Set [1] program. Don’t ask me for details, I don’t know any. But the wikipedia article looks interesting. Seems they are trying to figure out how causality restricts models with some level of discreteness. [1] https://en.wikipedia.org/wiki/Causal_sets https://en.wikipedia.org/wiki/Causal_sets
- cyphar 10y ago
  This was covered in my undergraduate (second-year) SR course. The idea is that if you accept that Maxwell's equations apply in all inertial frames (speed of light is constant) and that causality is conserved in all frames, the result is that Newtonian mechanics requires adjustments for effects that are called "special relativity".
valarauca1 10y ago
GR does not imply causality nor does it enforce it. In fact GR works in a non-causal universe without a problem. 2 very sensitive measurements conducted within the past year seem to suggest (if GR is true), that we are in a universe that lacks causality. 2/3 LIGO detections imply one of the merging pair of black holes should be a naked singularity. GR allows naked singularities. It models them fine. GR just stops being globally deterministic. If you look up the history of GR some mathematicians in 50's made some really weird proposals for non-causal universes that would appear locally causal. But there isn't a way to test this. So it is more pure mathematics or philosophy then physics.
- eaq 10y ago
  > 2/3 LIGO detections imply one of the merging pair of black holes should be a naked singularity. Where did you get this impression? All of the LIGO results are consistent with "standard" GR black holes whose event horizons merge.
  - andrewflnr 10y ago
    Possibly referring to this? http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.116.171101 http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.116.... Background: https://en.wikipedia.org/wiki/Gravastar https://en.wikipedia.org/wiki/Gravastar
    - eaq 10y ago
      Thanks for the links. I find it unfortunate that often in science (and especially with the LIGO data) much is written about what could possibly be lurking in the data but isn't actually favored over our current understanding. This creates more interest, but can obfuscate what the real situation in the field is. In this case, while Gravastars are certainly something many scientists actively do and should consider, there is no real evidence from the LIGO data that favors the hypothesis of "we are in a universe that lacks causality" over the observation of the merger of two Kerr black holes.
      - 10y ago

monochromatic 10y ago

SRT?

eln1 10y ago
I've meant special relativity.

noobermin 10y ago

I feel like this is a common misconception amongst some physicists. Lorentz invariance doesn't "appear naturally" in modern theories depending on how you develop it. Usually, one chooses a lagrangian that yields a lorentz invariant action and so all physical laws and thus solutions are lorentz invariant consequently. Lorentz invariance is a fundamental assumption...upheld by experiment. Those theories will then admit solutions (usually linearized ones (read quantized)) that appear as waves.