The Probability of Backward Time, Forward Time and No Time

Is backward time possible? Yes it is, but what is the likelihood? What is the probability of going back in time? Imagine you have a three-sided coin. The sides are labeled -1, 0, and +1. Suppose we define time as follows: when the coin goes back to its previous state, it has gone back in time. When it goes to a new state, it goes forward in time. If it stays the same, there is no time.

Side 0 is the coin's current state, i.e., the present. Side -1 is the previous state--the past. Side +1 is the future. Below we calculate the probabilities:

At equations 2 through 4 we see the probability of going to the past is the same as going to the future, and staying in the present is just as likely. The coin above could be analogous to a simple quantum system; perhaps a single particle. Where the number of particles and states are few, backward time and "no time" are highly probable.

Now, let's make our simple system above more complex. Let's place the coin in a lattice with four cells. We decide that a change in state includes a change in position. If the coin moves to a new cell, it has moved forward in time. To move back in time, it must go back to its previous state which includes -1 and the cell it previously occupied. To have "no time" means no changes at all. Below is the relevant math. At equation 7 we normalize the total number of possibilities so the total probability is 1.

Here are the probabilities for our more complex system:

At equation 10, notice how the probability of forward time has increased to 10/12. At equations 8 and 9 we can see that backward time and "no time" have lost some ground--they are now less probable. Their likelihood decreases as we add more and more particles, states, and cells, and, the likelihood of forward time increases. Below are some general equations that determine the probability of past, present, and future.

But take note of equation 14. There's a question mark. Our model of time is incomplete. So far, we have only included what happens when the coin is tossed, i.e., when there is an interaction between, say, you and the coin. Assuming you toss the coin at a steady rate, there are three basic states: you toss the coin and get -1, you toss the coin and get +1, you toss it and get 0. But what happens if you don't toss it, i.e., if there isn't any interaction? Nothing changes and time stands still.

Thus there are two ways time can be zero: no interactions or an interaction where you get back the same state. To get the true probabilities of time, we need to take relativity into account. (The variables we will be using are defined below.) We know that time can slow down at high velocities and where there are large masses. The slowing of time implies that there are more instances where time is "no time" and fewer instances where time is moving forward or backward.

Equations 15 through 19 give us the relationships between mass, energy, velocity and time:

Equations 15 and 16 show how increased linear velocity (v) reduces the time rate (t') and increases the mass (m'). It follows that there is a correlation between reduced time rate and increased mass. It is understood that increased mass reduces the time rate, but how? Especially if it is at rest. Oscillators are the key. Equations 17 through 19, which involve Hooke's law and Einstein's mass-energy equivalence, show how oscillators increase mass.

If all variables, except angular velocity, are held constant at equation 19, It becomes apparent that increased angular velocity increases mass, or, mass is a function of angular velocity. Looking carefully at equations 15 through 19, it follows that increased linear velocity (v) causes increased angular velocity. In the case of both mass and linear velocity, there is increased angular velocity or oscillations. Could increased oscillations cause slower time? If so, that would explain why both linear velocity and mass slow time. Let's see if we can prove it:

Equation 34 clinches it! Increased oscillations cause a reduced rate of time. Anytime we add energy to a system, the oscillators oscillate more. Why does this reduce the time rate? Take a look at the left side of equation 34. It has the variable "u"--the 'relative' emission and absorption rate of gauge bosons within a system of harmonic oscillators. Bosons move no faster than light speed. They can't speed up when fermions speed up. When fermions are at rest, gauge bosons are relatively faster and carry force faster than when fermions are in motion (oscillating), so time is faster when fermions are at rest and slower when fermions are in motion.

Using our coin-toss analogy, if you can't increase your speed and have to chase the coin and catch it before you can change its state, you can change its state more often if the coin is at rest than if it is moving at high speed. So time, as we defined it earlier, has more instances of "no time" if the coin is hard to catch (i.e. time is slower). Also, at 34, notice the plus and minus sign in front of the radical. The square root can be negative as well as positive. This allows for backward time. The only question that remains is, "What are the odds?"

If slower time increases the instances of "no time" due to no interaction, we must reduce the probabilities of the other three possibilities: forward time, backward time, "no time" with interactions. To do this we use the Lorentz factor from equation 34.

Equations 36 through 38 show that forward time still dominates within complex systems due to more degrees of freedom. To get the probability of "no time" due to no interactions, we subtract the above probabilities from the total of 1:

This probability is zero when matter is at rest, and it grows when matter is in motion. We now have a complete probability distribution for backward time, forward time, and no time.

Update: What about the oscillations? Couldn't they count as changes of state? Sure, why not? But the net value of time would still be "no time." Take for example a pendulum. We decide if it swings right, time is going forward, but when it swings left, time goes backward and washes out the forward time, so time makes no progress until something more happens than mere oscillations.

Caveat: One could ask what is the duration of a no-time state or any time state for that matter. How long must each state last in order to count as a state? The obvious answer is more than zero arbitrary time units. So do changing states really make up time or does time make up changing states? Perhaps we've gone as far down the philosophical rabbit hole as we can go.