Something vs. Nothing vs. Mixed States

Yes, we could ask, "Why is there something rather then nothing?" However, if we take quantum physics into account, we shouldn't limit ourselves to pondering something or nothing--we also need to ponder mixed states. Before we do, let's work out the probability of there being something or nothing using a kind of information theory. We can let '1' represent something, and '0' represent nothing.

Imagine a coin with a '1' on one side and a '0' on the other. We assume the probability of either side being face up is 0.5. However, the coin might favor one side over the other. How do we fix this? We get a trillion coins where one side might be more or less probable than the other. The probabilities could range from 0 to 1, but the average probability will be at or near 0.5 for each side. So it's safe to assume, if we perform the coin toss many many times (and switch coins), on average, we will get each side 50 percent of the time.

To make our analysis easier, let's assume we are using a coin that has the expected (average) value of 0.5 for each side. Half the time we are going to get a universe with something, and half the time we will get nothing. If we define "nothing" as absolutely nothing, we can improve our odds of getting "something" by adding additional coins. Let "n" in the last two equations below be the number of coins:

Using two coins yields the following results:

The [0 0] above is nothing. Those pairs above it have a '1'--so they are something. By only using a pair of coins we have improved the chance of getting something to 0.75. What happens if we use three coins?

The probability of getting something jumps to 0.875. If we use an infinite number of coins, the probability of getting something is one--a sure thing. The probability of getting nothing is zero.

Thus we have a reason why there is something rather than nothing. But what if what we call "something" is really something else: a mixed state? What exactly is a mixed state? You could think of it as being both something and nothing--an undecided state, a state with both ones and zeros. By contrast, a pure state has all ones or all zeros:

If we dare to ask where something or nothing came from, one answer is a mixed state. The mixed state evolves into a pure state. When we flip a coin, we don't know if it's heads or tails when it is in the air. We can say it's both heads and tails--a mixed sate. When it hits the ground and comes to rest, it's in a pure state.

Another example analogous to a mixed state is a ball sitting on a hill. It can roll down one side or the other. It stays in a mixed state until something disturbs it:

In the above diagram, the ball's state can evolve into the pure state of '1' or '0.'

So instead of imagining a universe with just something or nothing, imagine a universe filled with ones and zeros, and, to make things more interesting, let's add an additional state of '-1.'

Instead of coin tosses we have binary number sequences that continuously change over time (t). The above diagram is an example of a two-digit binary sequence. The diagram below models the evolution of these binary numbers:

The diagram above starts with the pure state of [1 1]. It then moves through mixed states to get to [0 0], then moves through more mixed states to get to [-1 -1], and so on. Basically we have something that resembles a sine wave. There is a problem, however: it is too predictable for our probabilistic universe. The evolution of states should be random:

The diagrams above are more realistic. The different states should have varied time duration(t00,t11,etc.). If, say, state [00] jumps to [11] without passing through [01] and [10], We say that these mixed states each have a zero duration. It is also possible for any state to have an exceptionally long duration.

So how do we get the predictable sine wave we started with? We take a trillion random waves and calculate the average time duration for each state. We can then add those average times together to get the total time and average wavelength:

Our predictable binary sine wave is really the expectation value of a bunch of random binary waves:

Now, our binary sine wave isn't very smooth nor continuous. It has a clunky, stair-step quality. We can make it smoother if we add more digits to the states:

In the diagram above, notice the wave with only one digit is the clunkiest. The smooth wave at the bottom has an infinite number of digits or at least a really big number of digits. So let's take the bottom wave and make it our official sine wave:

Sooner or later, our sine wave will interact with another wave (superposition). At one extreme the phase difference between the waves could be 180 degrees, resulting in destructive interference:

At the other extreme the phase difference could be zero degrees, resulting in constructive interference:

If we have a bunch of waves, the average or median phase between each pair will be 90 degrees. Thus, we end up with both a sine and cosine wave.

Having sine and cosine waves lead to wave functions and matter--the stuff we call "something."

However, as we have witnessed, the stuff we call "something" is really a mixture of both something and nothing: zeros and ones. The stuff we call "something" also oscillates between pure and mixed states.

You can find more on this topic if you click here.

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.