3 ms·

The speed of light is a dimensionful quantity -- it has dimensions of length over time. Dimensionful quantities cannot be measured, only dimensionless ones can

The speed of light is a dimensionful quantity -- it has dimensions of length over time. Dimensionful quantities cannot be measured, only dimensionless ones can be measured: we can only measure pure numbers. When we say we measure the speed of light, we are really measuring the ratio between that and some other arbitrary speed defined by our measurement device. Therefore, it makes little sense to ask how the speed of light changes over time; we can only ask this question after we specify how we measure, and then it's no longer a fundamental question.

HCIdivision17 12y ago
It may be a bit surprising that the speed of light is actually a consequence of universal constants interacting, and not merely measured via reference benchmarks [0]. At least for me, finding that Maxwell's equations distill an equation that happens to be a velocity in a vacuum was extremely gratifying. There's a notion that perhaps if the constants were different, then c would be different as well - both in scale and even dimensionally; this is, I think, what the parent is referencing. EDIT: I'd like to restate why c is neat. There's a lot of history to it, but it's sort of a form of a number ending up so important that it overtook the archetypical "and a constant c". I highly recommend the article from Phillip Gibbs that goes into this in depth [1]. Your comment actually shows up near the beginning of the long answer in the form of paragraph 5 of The Long Answer, so you'll likely enjoy the additional detail. [0] http://en.m.wikipedia.org/wiki/Maxwell's_equations#Vacuum_equations.2C_electromagnetic_waves_and_speed_of_light http://en.m.wikipedia.org/wiki/Maxwell's_equations#Vacuum_eq... [1] http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/c.html http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLigh...
- guygurari 12y ago
  These universal constants (vacuum permittivity and permeability) are themselves dimensionful quantities, so the same comment applies to them. They can only be measured by comparing to a reference, and there is no natural sense in which they can be said to change over time. By the way, these constants are no more 'universal' than the speed of light itself.
  - jsweojtj 12y ago
    The fundamental constant you're looking for is the fine-structure constant (often referred to as alpha). It's a dimensionless ratio of physical constants, and if its value changes, physics is different.
  - HCIdivision17 12y ago
    I mean, sure, it's going to be turtles the whole way down if you're looking to define the universe without resorting to physical quantities (that is, dimensioned units). We don't have anything like a Grand Unified Theory yet, wherein we define Physics by means of some elemental mathematics (in the form that we can bootstrap computation from lambda calculus via things like the Y Combinator [0]). Besides, we occasionally give dimensional names to dimensionless quantities (my favorite being the engineering unit the inverse radian) [1]. It's a useful abstraction, and it seems confusing to complain about it. So we resort to what we know, which is what we see. We can't see more than the surrounding universe, but we can try extrapolating from what seems to work. Attempting to stifle that inquiry seems a bit... I dunno, pointlessly antagonistic. This article shows science in action, doing what it does best: taking observations and reconciling them with other observations via theory, and then fixing theory to match. It seems our universe follows certain equations which are themselves dimensionful, so I'm not sure why we wouldn't attempt to benchmark the universe against itself - we don't have much else to use. Even dimensionless numbers are only marginally useful, like alpha; it may "exist" and manifest as our universe, but it's not especially predictive. [0] https://www.youtube.com/watch?v=FITJMJjASUs https://www.youtube.com/watch?v=FITJMJjASUs (one of my favorite videos - I still don't grok it, but I'm getting closer!) [1] http://arxiv.org/pdf/1409.2794.pdf http://arxiv.org/pdf/1409.2794.pdf

HCIdivision17 12y ago

It may be a bit surprising that the speed of light is actually a consequence of universal constants interacting, and not merely measured via reference benchmarks [0]. At least for me, finding that Maxwell's equations distill an equation that happens to be a velocity in a vacuum was extremely gratifying. There's a notion that perhaps if the constants were different, then c would be different as well - both in scale and even dimensionally; this is, I think, what the parent is referencing. EDIT: I'd like to restate why c is neat. There's a lot of history to it, but it's sort of a form of a number ending up so important that it overtook the archetypical "and a constant c". I highly recommend the article from Phillip Gibbs that goes into this in depth [1]. Your comment actually shows up near the beginning of the long answer in the form of paragraph 5 of The Long Answer, so you'll likely enjoy the additional detail. [0] http://en.m.wikipedia.org/wiki/Maxwell's_equations#Vacuum_equations.2C_electromagnetic_waves_and_speed_of_light http://en.m.wikipedia.org/wiki/Maxwell's_equations#Vacuum_eq... [1] http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/c.html http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLigh...

guygurari 12y ago
These universal constants (vacuum permittivity and permeability) are themselves dimensionful quantities, so the same comment applies to them. They can only be measured by comparing to a reference, and there is no natural sense in which they can be said to change over time. By the way, these constants are no more 'universal' than the speed of light itself.
- jsweojtj 12y ago
  The fundamental constant you're looking for is the fine-structure constant (often referred to as alpha). It's a dimensionless ratio of physical constants, and if its value changes, physics is different.
- HCIdivision17 12y ago
  I mean, sure, it's going to be turtles the whole way down if you're looking to define the universe without resorting to physical quantities (that is, dimensioned units). We don't have anything like a Grand Unified Theory yet, wherein we define Physics by means of some elemental mathematics (in the form that we can bootstrap computation from lambda calculus via things like the Y Combinator [0]). Besides, we occasionally give dimensional names to dimensionless quantities (my favorite being the engineering unit the inverse radian) [1]. It's a useful abstraction, and it seems confusing to complain about it. So we resort to what we know, which is what we see. We can't see more than the surrounding universe, but we can try extrapolating from what seems to work. Attempting to stifle that inquiry seems a bit... I dunno, pointlessly antagonistic. This article shows science in action, doing what it does best: taking observations and reconciling them with other observations via theory, and then fixing theory to match. It seems our universe follows certain equations which are themselves dimensionful, so I'm not sure why we wouldn't attempt to benchmark the universe against itself - we don't have much else to use. Even dimensionless numbers are only marginally useful, like alpha; it may "exist" and manifest as our universe, but it's not especially predictive. [0] https://www.youtube.com/watch?v=FITJMJjASUs https://www.youtube.com/watch?v=FITJMJjASUs (one of my favorite videos - I still don't grok it, but I'm getting closer!) [1] http://arxiv.org/pdf/1409.2794.pdf http://arxiv.org/pdf/1409.2794.pdf