Is the speed of causation propagation linked to plank length?
Yes, more specifically the Planck length is derived from an equation involving the speed of light/causality.
Where C is light, h is reduced planck constant, and G is gravitational constant. Together they tell us the fundamental unit length of meaningful distinction, a very important yard stick for measuring the smallest distances.
Its more related to limits of knowability of events beyond a certain scale. Its easy an intuitive to think of it like spacetime is quantized like pixels on a grid with a minimum action requirement of time and energy to move between them. But its not that simple or at least that kind of granular discreteness is not proven (though there are digital physics frameworks that treat spacetime discrete like this)
The Planck length does not define the minimum distance something can move but rather the minimum scale of meaningful measurement that can make a bit of distinction between two microsstates of information. In essence it says that if theres two continuous computational paths that differ by less than a sub-plancks worth of distinction there is no measurable distinction difference between them and the paths get blurred together.
Its a precision limit that defines how exact we can measure interactions that happen within the distance between two points.
It’s possible that spacetime is continuous at a fundamental level, but the Planck length represents the scale at which quantum fluctuations of spacetime itself become so violent that the concepts of a ‘path’ or a ‘distance’ can no longer be defined in the classical sense, effectively creating discrete quantized limits for measurement precision.
Ultimately this precision bound limit is related to energy cost to actualize a measurement from a superposition and the exponetial increase in energy needed to overcome uncertainty principle at smaller and smaller scales. The energy required to actualize a meaningful state from a sub-planck length would be enough to create a kugelblitz black hole made from pure condensed energy.
This same logic applies to time, giving us the Planck time, the shortest meaningful interval. So, in a way, the Planck scale does define a fundamental limit on the ‘speed’ at which distinguishable events can occur.
As I understand, the speed of light in vacuum is bound by the speed of causality. So, light would go at infinite speed, if it could (it being massless means any acceleration should result in infinite speed), but instead it goes as fast as the universe allows, which is the speed of causality.
Speed of Causality is the absolute maximum speed. It’s the theoretical maximum that any cause could propagate an effect. Speed of Light in a (perfect) vacuum happens to be equal to the Speed of Causality.
Speed of light in a true vacuum.
Speed of light through any non-vacuum decreases.
The speed of causality remains the same.
is the speed of causality tied to speed of light in a vacuum, or independent of it?
Yes, more specifically the Planck length is derived from an equation involving the speed of light/causality.
Where C is light, h is reduced planck constant, and G is gravitational constant. Together they tell us the fundamental unit length of meaningful distinction, a very important yard stick for measuring the smallest distances.
is the plank length tied to the speed of events or is it just the shortest distance light can move
Its more related to limits of knowability of events beyond a certain scale. Its easy an intuitive to think of it like spacetime is quantized like pixels on a grid with a minimum action requirement of time and energy to move between them. But its not that simple or at least that kind of granular discreteness is not proven (though there are digital physics frameworks that treat spacetime discrete like this)
The Planck length does not define the minimum distance something can move but rather the minimum scale of meaningful measurement that can make a bit of distinction between two microsstates of information. In essence it says that if theres two continuous computational paths that differ by less than a sub-plancks worth of distinction there is no measurable distinction difference between them and the paths get blurred together.
Its a precision limit that defines how exact we can measure interactions that happen within the distance between two points.
It’s possible that spacetime is continuous at a fundamental level, but the Planck length represents the scale at which quantum fluctuations of spacetime itself become so violent that the concepts of a ‘path’ or a ‘distance’ can no longer be defined in the classical sense, effectively creating discrete quantized limits for measurement precision.
Ultimately this precision bound limit is related to energy cost to actualize a measurement from a superposition and the exponetial increase in energy needed to overcome uncertainty principle at smaller and smaller scales. The energy required to actualize a meaningful state from a sub-planck length would be enough to create a kugelblitz black hole made from pure condensed energy.
This same logic applies to time, giving us the Planck time, the shortest meaningful interval. So, in a way, the Planck scale does define a fundamental limit on the ‘speed’ at which distinguishable events can occur.
Thanks for this, I had no idea it was more a precision limitation
As I understand, the speed of light in vacuum is bound by the speed of causality. So, light would go at infinite speed, if it could (it being massless means any acceleration should result in infinite speed), but instead it goes as fast as the universe allows, which is the speed of causality.
Speed of Causality is the absolute maximum speed. It’s the theoretical maximum that any cause could propagate an effect. Speed of Light in a (perfect) vacuum happens to be equal to the Speed of Causality.
Is the speed of causation propagation linked to plank length?
Yes, it’s derived from 4 physical constants including c
Independent.