Energy as Dimension

In relativity, energy and momentum are sometimes treated as a 4 vector, similar to treating space and time as a 4 vector.

 

Some related structures: the "mass shell" and "relativistic phase space".

 

In fact, i am not quite understand your definition/meaning of "Deimension".

 

You can regard energy as being one of the states of a system, which makes energy a part of a phase space

http://en.wikipedia.org/wiki/Phase_space

Example: The orbits of planets around the sun can be described by a phase space consisting of the energy and momentum of the planets (plus a few other variables).

Motion is usually regarded as a change of position with time, so it would generally be the wrong word to describe the rate of change of energy with time, for instance. (A possible exception would be in the context of some phase space of which energy is one of the variables, one might then talk about motion in this abstract phase space).

 

The E would be superfluous. Using only (x,y,z,t) you can already say that no two objects can have identical coordinate values. If, instead, you substituted E for one of the space-time coordinates, you would lose uniqueness and things like the Pauli exclusion principle. Might look at enegy as a state variable, a suggested above - "The energy of the universe is constant. Its entropy tends to a maximum." Clausius, 1865
-Jim

 

Correct, and in relativity that means a change of space-time position with regards to proper time.

 

i was actually thinking about this while i was pondering over superstring theory, and was surprised at how this would fit into the superstring theory.

As we all know, superstring theory tells us that the universe is made up of fundamental blocks of vibrating strings of energy. And that the frequency of the vibration of these strings determine the physical composition of the particle or sub particle. And for each positive vibrating string, there is a counterpart of it (anti-matter).

Now, we also know that there has to be a total of 11 dimensions (10 space and 1 time) in order for the superstring theory to work (a possible 12th dimension has emerged recently) and that these dimensions are in the form of a theoretical shape called the Calabi-Yau shape (the reason that we cannot see these extra dimensions is because they are so minute. Imagine you were holding a piece of paper from afar. It would seem like it only had 1 dimension, length; but if you were small enough and you climbed onto the piece of paper, you would actually find out that is it in fact 3 dimensional, length, width, thickness). And the strings travel through these shapes, and the vibrational patterns of the string is also determined by the Calabi-Yau shape.

Which leads on to the exciting part. As we know, we cannot create, destroy or alter any dimensions. And we also know that we cannot create, destroy or alter energy. We may be able to change the FORM that energy travels through, but not alter it.

Now, if energy was a dimension, then the vibrating strings would be a dimension as well. And since they are the fundamental blocks that create this universe, it leads us to believe that they are the fundamental dimension of the universe. For example: Since that energy is our first and fundamental dimension, a string that it creates would be seen as a two dimensional object; and this has been proven by theoretical calculations (since it cannot harvest any 3 dimensional properties and isn't a 1 dimensional object); and these strings form sub-particles, which later form particles, then atoms etc. which are all 3 dimensional objects.

I am still working on this theory, and I know it is an utterly mad idea, but aren't most good ideas, mad? Anyways, this is just my point of view. I'd be glad to hear some rebuttals =).

 

It does fit in string theory, but in a completely different way from what you said. "This opens the possibility that we can associate the extra dimensions suggested by the Holographic idea with energy scale." http://arxiv.org/abs/0909.0518