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.

Why There is Something Rather Than Nothing

Why is there something rather than nothing? Mathematicians use zero to represent nothing. The concept of zero goes way back to ancient Egypt. The hieroglyph known as 'nfr' indicated "emptiness." Aryabhatta, an Indian mathematician, introduced zero in the 5th century AD.

I was first introduced to zero in the first grade. Our teacher, Mrs. White, taught us that 2 - 2 = 0. Later in life I was introduced to the Lagrange equation, where potential energy is subtracted from kinetic energy. Of course if kinetic energy equals potential energy, you get zero on the right side of the equation.

It's safe to say that all my life I've been brainwashed to believe you can have something, take it away, and end up with nothing: zero. And I'm not alone; philosophers have asked, "Why is there something rather than nothing?" as if nothing were a viable possibility.

The closest thing to nothing measured by the Wilkinson Microwave probe is about 6E-10 joules per cubic meter. The energy density of the vacuum of space is close to zero, but not quite. So the question arises, what is the probability of ever having nothing? In the case of the Lagrange equation, what is the probability that a universe could have the same amount of kinetic energy as potential energy?

Suppose we label kinetic energy "positive," and potential energy "negative." Let's assume all energy is made up of discrete quanta. We take all that quanta (an infinite amount) and put it inside a big cosmic hat. We reach in and pull some out. What is the probability we pulled out the same amount of positive quanta as negative quanta? Or what is the probability we pulled out zero quanta?

The probability we pulled out zero quanta is easy to figure out. Since there is an infinite number of quanta, the probability is 1/infinity--which is virtually zero. So we are virtually guaranteed to have more than zero quanta outside the hat. To have zero net energy, we need an even number of quanta, and equal amounts of negative and positive quanta.

If the quanta number is odd, the probability of netting zero is zero. For example, if we pulled out five quanta from our cosmic hat, the closest combination to zero would be three positives and two negatives--or vice versa. If we pulled out four quanta, there's a possibility we could have two positives and two negatives. The equations below enable us to calculate the probability of netting zero:

Equation 2) takes into account that there's a 0.5 probability that the number of quanta (n) could be even, so the probability that is calculated in equation 1) is cut in half. Thus, in equation 2's denominator, there is 2^(n+1) instead of 2^n.

The above equations show that the larger the number of quanta (n), the less likely we will have zero net energy. But shouldn't the net energy get closer to zero as we add more quanta to the mix? If we flip a coin, we get heads or tails. If we assign a value of minus one to heads and plus one to tails, we get plus one or minus one--never zero. But suppose we toss a trillion coins? We should get an equal amount of heads and tails (or pretty close).

We know if we increase the number of coins, the variance or deviation from zero is reduced.

Equations 3) and 4) clearly show, that as the number of coins (or quanta) increases, the smaller the variance becomes. The sum of coins or quanta converge to zero. This seems to contradict our earlier finding via equations 1) and 2). Let's crunch some numbers and put the data in a couple of tables to see what we get.

The first table above contains data for odd numbers of quanta. We see that the variance (v) decreases as expected. It gets closer to zero as more quanta are added. (This is also true in the second table for even numbers of quanta.) We see in the last two columns the probability of having exactly zero net energy is zero due to an odd number of quanta.

The second table shows an interesting paradox: As the variance decreases, so does the probability of having exactly zero net energy. This paradox is illustrated in the graphs below:

So, the closer we are to zero, the less likely we will have precisely zero--this is why there is something rather than nothing.

Would Chance Exist If We Knew All There is to Know?

This post is a continuation of the previous post "What We Didn't Know About Time Travel Could Surprise Us."

It is commonly believed that if we went back in time, history would repeat itself exactly as before if we started with the same initial conditions. It is also commonly believed that chance is a function of our ignorance. If we knew everything that goes into a coin toss, we could predict the outcome 100% of the time. Today we put these beliefs to a rigorous test.

For illustrative purposes, and to keep our first test simple, let's cut our 3D universe down to 2D. Imagine a pencil balanced on its tip. It can fall either right or left. A hand grabs the eraser end and tilts the pencil to the right at some unknown angle that's less than 90 degrees. Which way will it fall? Notice we are not completely informed. We don't know the exact angle of the tilt. Any estimate we make can be way off; yet, we can predict the outcome with 100% accuracy.

The pencil will always fall to the right. This demonstration shows that our ability to make 100% accurate predictions is not dependent on perfect knowledge. There are many things we don't know, like the tilt's angle, but our ignorance does not deter us. More importantly, it does not create a chance environment. Thus the so-called correlation between ignorance and chance breaks down here.

Since it is possible to be ignorant and make 100% accurate predictions, is it also possible to know all there is to know and be uncertain about an outcome?

Imagine a simple universe that contains a particle called B. As time (t) passes, B can move either right or left. Which way will it move? We don't know--so B's movements seem random to us. If we knew what causes B to move right or left, we could predict B's moves and the randomness would disappear, right?

We get all the scientists together and give them a big fat grant. Their mission (if they choose to except it) is to find the initial condition(s) that cause B to move as it does. They discover particle A. When particle A moves right, B moves right. When particle A moves left, B moves left. Perfect! We simply watch A to see how it moves, then we can predict how B moves.

The randomness is gone ... or is it? What causes A to move right or left? Well, nothing. "A" is the "initial condition." Nothing causes it. Nothing precedes it--or it would not be initial. So when A moves, it is completely random.

The above example demonstrates that you can have complete knowledge; i.e., know the initial condition(s) and still have randomness. But suppose the initial condition A moved left the first time history unfolded. We go back in time and A moves left again. Will history unfold the same way?

Let's see. If A has gone left, then B will move left. So far, so good. But which way will B move next? We can't look at A; it has done its job of initiating the universe's evolution. B moves on its own--either right or left. We don't know which direction now that A is out of the picture. So we can't predict with certainty that history will repeat itself because it doesn't have to--even when we know the initial condition with absolute certainty!

Since we no longer can predict B's movements, does that mean we are ignorant? Not if our thought-experiment universe consists only of A, B, time, space, and the rule that particles can go right or left. If that's all there is to know then we know it all--except what B will do next.

We don't know what B will do next because chance is not a function of ignorance in this case--it is a function of more than one option. If, for example, B could only move left, we could be as ignorant as a retarded cockroach and still predict B's movements with 100% precision. On the other hand, we could be geniuses with access to supercomputers and have no clue what B will do next if B can move in a gazillion number of ways (or exist in a gazillion number of varied states).

Finally, history need not repeat itself even if the initial conditions are the same as before and we have perfect knowledge of them.