Many people has done this question: if gravity (and other forces) on the field theory are boson, why not the time is a field too with his own particle?.
Let be using the same rasoning that Einstein do with the electro-magnetic field. If there’s something (now we know it’s a particle that carry the force) that curves de space and attracts and repels with some conditions, why not the gravity is working in the same way and it’s something (remember, now we know it’s a particle) that bends the space and attracts (and now we know -at least in a mathematical way- that can be a negative gravity) “things”?.
Well using the same rasoning you can think that it can be “something”, maybe a particle, that bends the time and attracts you to the future and like Einstein and before says that time is a dimension, that dimension relay in a, we call it, time field theory. And, at least, there’s not only four (well three if we consider the electro weak force as one force and not two) force but five: electronical, weak, strong, gravity and time.
Considering time as a fundamental force means, as I say before, that it must be a particle that carry time. If graviton hasn’t been detected yet (because it need too much energy, because on string theory it influences in all dimensions but in “ours” it’s very light), if so, time particle will need more energy that the gravity one.
So, using time as a field change all the concepts and equations used before like Dirac field, Scrödinger equations and so on. If we consider time as a constant all this ecuations become all we know but if we consider it as a field it changes radically (like you can see on this paper).
It’s very interesting that you thought about it because if time is a field and in ours “dimensions” time it’s a representation of a multidimensional field in an unidimensional line (because for us it’s unidimensional) it will explain so many things in other physics fields and open too many questions because separating time of space that it’s so great.
Remember that this concept it’s not new, people is working with them for example in this paper about how this equations can change the way we thougt gluon works or in this where speaks about the information theory is affected with the time field or these where how the system geometry is affected by the time field.
At this time, I’m trying to find more about this topic because it sounds fantastic 🙂
We are in early stages about this creating the math base that will lead us to a great future. It’s a perfect time to be a physicist.