Calle
@casve.bsky.social
Essentially, the sources of your EM field are not necessarily causally related in space, but they are casually related in time
March 11, 2025 at 4:56 PM
Essentially, the sources of your EM field are not necessarily causally related in space, but they are casually related in time
If I understand you correctly I think the problem will be that you cannot determine the charge distribution throughout space from an initial spatial slice. The reason it works in time is due to something called the continuity equation. en.m.wikipedia.org/wiki/Charge_...
Charge conservation - Wikipedia
en.m.wikipedia.org
March 11, 2025 at 4:46 PM
If I understand you correctly I think the problem will be that you cannot determine the charge distribution throughout space from an initial spatial slice. The reason it works in time is due to something called the continuity equation. en.m.wikipedia.org/wiki/Charge_...
Whenever you measure a quantity you get a number defined by the unit of measure you use. Scientists can then employ a clever change of units to express the information in a way that is easier to work with. In this case natural units. en.m.wikipedia.org/wiki/Natural...
Natural units - Wikipedia
en.m.wikipedia.org
March 11, 2025 at 4:19 PM
Whenever you measure a quantity you get a number defined by the unit of measure you use. Scientists can then employ a clever change of units to express the information in a way that is easier to work with. In this case natural units. en.m.wikipedia.org/wiki/Natural...
For time on the other hand, an event can only be caused by a past event in time. It cannot be caused by a future event in time. To see this in the context of Maxwells equations I recommend looking at Jefimenko’s equations en.m.wikipedia.org/wiki/Jefimen...
Jefimenko's equations - Wikipedia
en.m.wikipedia.org
March 11, 2025 at 3:38 PM
For time on the other hand, an event can only be caused by a past event in time. It cannot be caused by a future event in time. To see this in the context of Maxwells equations I recommend looking at Jefimenko’s equations en.m.wikipedia.org/wiki/Jefimen...
I am not familiar enough with the theory of boundary conditions for PDEs to know the answer to that unfortunately. Though the way time differs from space afaik has to do with the fact that for space, an event can be caused by another event happening at any location in space. 1/
March 11, 2025 at 3:35 PM
I am not familiar enough with the theory of boundary conditions for PDEs to know the answer to that unfortunately. Though the way time differs from space afaik has to do with the fact that for space, an event can be caused by another event happening at any location in space. 1/
It turns out that you can rotate between spatial dimensions such that x -> -x without changing the right hand side of your equation. You cannot, however, rotate between t and x in a way that gives t -> -t while keeping the RHS unchanged. Therefore time moves in a specific direction
March 11, 2025 at 2:10 PM
It turns out that you can rotate between spatial dimensions such that x -> -x without changing the right hand side of your equation. You cannot, however, rotate between t and x in a way that gives t -> -t while keeping the RHS unchanged. Therefore time moves in a specific direction
Another question to ask might be “what transformations can I make to the coordinates such that the right hand side does not change?”. The answer to this is the transformations in the Poincaré group (there’s a wiki page on the Poincaré group that has more info on what those transformations are)
March 11, 2025 at 2:04 PM
Another question to ask might be “what transformations can I make to the coordinates such that the right hand side does not change?”. The answer to this is the transformations in the Poincaré group (there’s a wiki page on the Poincaré group that has more info on what those transformations are)
I should start by saying I’m still studying this and am by no means an expert but one thing to notice is that if you move over the spatial term to the left hand side the spatial terms (in 1, 2 or 3 spatial dimensions) will always have opposite sign to the time dimension 1/
March 11, 2025 at 2:02 PM
I should start by saying I’m still studying this and am by no means an expert but one thing to notice is that if you move over the spatial term to the left hand side the spatial terms (in 1, 2 or 3 spatial dimensions) will always have opposite sign to the time dimension 1/