Jon Osterman
Member
I'm still unclear to me as to why you don't see time as fundamentally different from space, and therefore energy as fundamentally different from momentum.
According to our understanding of physics, they are not so different.
Consider two events that happen, according to your point of view, at the same time, say 1m apart. You regard these as simultaneous. Now your friend is in a rocket travelling very fast, he passes you just as the events happen and he sees them too. Special relativity tells us that he doesn't see these events at the same time. In his reference frame they are not simultaneous, and they are actually closer together than 1m. What has happened is that part of the space-distance between the two events that you see, is seen by him as a time-difference. Which is which is actually a matter of which reference frame you are in. (In mathematical terms, your axis for time is not parallel to his.)
I understand that a given momentum necessarily implies a specific amount of energy, much like I suppose coordinates in three-D space allows us to calculate distances, but we still have what appears to be a fundamental difference between time and space and hence between energy and momentum.
The relation between energy and momentum is due to the relativistic length being conserved by the Lorentz transformation. A few posts ago, I wrote dt^2 - dx^2 - dy^2 -dz^2 = constant, which is a relation between time and space, but a similar relation holds for energy and momentum. E^2 - px^2 - py^2 -pz^2 = constant (ignoring factors of c). Interestingly, this constant quantity is the mass of a particle. This is why "a given momentum necessarily implies a specific amount of energy" as you say, E = sqrt( |p|^2-m^2). In the non relativistic limit, this turns into E = m + 1\2 m v^2.
If time and space are essentially just parts of the same thing, how could our brain possibly see them as different, both in terms of their nature and of their properties?
EB
This is an interesting question, but an unanswered one. This is asking, what sets the arrow of time? Why do humans (and presumably other animals) experience time as a continuous stream? No-one knows, and I personally have not seen a satisfying answer.