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Maybe I haven’t understood him right, but he said: > […] physical properties, like c, h […] which is false, c and ℏ aren’t “physical properties”. The numeric

by hansen 11y ago

Maybe I haven’t understood him right, but he said: > […] physical properties, like c, h […] which is false, c and ℏ aren’t “physical properties”. The numerical values we attach to them are merely a convention. In SI units c isn’t even something that is measured. The second is defined via a measurement, c has a fixed defined value (no measurement involved), and the meter is defined via the second and c. In natural units this is even simpler: ℏ = c = 1. The fine structure constant is another thing. It caries no dimension and encodes the strength of EM coupling. But as an interesting site note: These coupling constant are pretty complicated things, they actually depend on the energy/length scale of your experiment. The numbers you find in text books are just the low energy limits.

tremon 11y ago
Well, I did mean the physical properties behind the symbols, i.e. speed of light, energy quantum, gravitational constant. I understand that the numerical quantities we assign to those constants are arbitrary, but even though they're not dimensionless, the physical properties they represent are still considered constant, am I right?
- hansen 11y ago
  > the physical properties behind the symbols Maybe my interpretation is a bit mathematical and a physicist would disagree but I wouldn’t call the speed of light or the Planck constant a “physical property”. In case of the speed of light the actually geometric thing, that exists w/o resorting to some arbitrary choice of units, is causality. In the case of the Planck constant there are different equivalent properties that I would call “physical”, but it all boils down to representations of symmetries. The gravitational constant is more complicated and I’m not quite sure what to make of it. Setting it to 1 too means that we get rid of all units and we measure length in multiples of the Planck length. But so far there is no experimental evidence that the Planck unit is something special that could be interpreted as some purely geometric property. I wouldn’t call it something “physical” with what we know today.
  - tremon 11y ago
    the actually geometric thing, that exists w/o resorting to some arbitrary choice of units, is causality I can agree with that in principle, but continuing in that line of reasoning: what remains is that the effects of an event ripple outward at a certain speed (ignoring quantum entanglement for a moment). It is my impression that c represents the upper limit of event propagation speed, and as such I would classify it a physical property. I'm a bit hazy about the exact physical implications of h-bar, but I thought it represented the absolute lower bound of energy quantization. Whether that is a real fundamental property or a consequence of underlying structure is yet to be determined, I believe.
    - hansen 11y ago
      The term ’length’ in GR is pretty complicated and there is no such thing as a canonical spacial distance between two events. There is no canonical splitting of space-time into space and time, unless perhaps for very symmetric space-times. E.g. we use the free falling galaxies in an isotropic universe as a global clock and call the orthogonal complement ’space’, aka ’comoving coordinates’. Using the term ’speed’ in the sense of ’spatial distance per time’ implies some non-trivial conventions. So the most accurate way to describe light rays would be to say they are “light like curves” (the ones with zero velocity wrt the Lorentian metric) which are exactly the geometric entities that describe the causal past and future of events. So IMHO causality is the real physical property of space-time and the ’speed’ of light is just a convenient way to visualize it. ℏ is probably best described as fixing the units for angular momentum. The energy spectrum of QED is continuous. And using the properties of free particles feels a bit fishy as they are just an approximation.

by hansen 11y ago

tremon 11y ago

Well, I did mean the physical properties behind the symbols, i.e. speed of light, energy quantum, gravitational constant. I understand that the numerical quantities we assign to those constants are arbitrary, but even though they're not dimensionless, the physical properties they represent are still considered constant, am I right?

hansen 11y ago
> the physical properties behind the symbols Maybe my interpretation is a bit mathematical and a physicist would disagree but I wouldn’t call the speed of light or the Planck constant a “physical property”. In case of the speed of light the actually geometric thing, that exists w/o resorting to some arbitrary choice of units, is causality. In the case of the Planck constant there are different equivalent properties that I would call “physical”, but it all boils down to representations of symmetries. The gravitational constant is more complicated and I’m not quite sure what to make of it. Setting it to 1 too means that we get rid of all units and we measure length in multiples of the Planck length. But so far there is no experimental evidence that the Planck unit is something special that could be interpreted as some purely geometric property. I wouldn’t call it something “physical” with what we know today.
- tremon 11y ago
  the actually geometric thing, that exists w/o resorting to some arbitrary choice of units, is causality I can agree with that in principle, but continuing in that line of reasoning: what remains is that the effects of an event ripple outward at a certain speed (ignoring quantum entanglement for a moment). It is my impression that c represents the upper limit of event propagation speed, and as such I would classify it a physical property. I'm a bit hazy about the exact physical implications of h-bar, but I thought it represented the absolute lower bound of energy quantization. Whether that is a real fundamental property or a consequence of underlying structure is yet to be determined, I believe.
  - hansen 11y ago
    The term ’length’ in GR is pretty complicated and there is no such thing as a canonical spacial distance between two events. There is no canonical splitting of space-time into space and time, unless perhaps for very symmetric space-times. E.g. we use the free falling galaxies in an isotropic universe as a global clock and call the orthogonal complement ’space’, aka ’comoving coordinates’. Using the term ’speed’ in the sense of ’spatial distance per time’ implies some non-trivial conventions. So the most accurate way to describe light rays would be to say they are “light like curves” (the ones with zero velocity wrt the Lorentian metric) which are exactly the geometric entities that describe the causal past and future of events. So IMHO causality is the real physical property of space-time and the ’speed’ of light is just a convenient way to visualize it. ℏ is probably best described as fixing the units for angular momentum. The energy spectrum of QED is continuous. And using the properties of free particles feels a bit fishy as they are just an approximation.