Why Time is More Than Real

"Reality is merely an illusion, albeit a very persistent one."--Albert Einstein

It is apparent from the above quote that reality distinguishes itself from ordinary illusions by its persistent nature. Reality is true even if you choose not to believe in it. Thus, if we are trying to settle the question whether time is real, we should examine time to see, if like reality, it too is a persistent illusion.

The time variable is very persistent and ubiquitous in so many physics equations. On that basis we can claim it's real, but just how real is it compared to things like matter, energy, mass, distance, force, your neighbor's barking dog? It's not like we can grab time out of the air, hold in hand and look at it like a hunk of clay. However, like clay, time can be stretched or compressed depending on how close to the speed of light you are traveling. How is that possible if time is just a product of human imagination? Surely any relative differences in time would also be limited to the human imagination and not an empirical reality.

When examining time, one has to make the distinction between how we measure time and time itself. One popular argument claims that if all particles in the universe stopped changing their states and came to rest, time would stop and cease to exist. This seems reasonable. If nothing happens, how would we experience the "flow of time"?

But what if the "flow of time" is just our experience when we measure time? If your watch stops, you don't assume that time has stopped. You only assume your ability to measure and experience "the flow of time" has stopped. So it seems reasonable to assume that time continues even if every particle comes to a grinding halt. Think of a stalled universe as one big watch that stopped.

So what exactly is time if not a flowing, evolving, ever-changing environment of entropy? The following equation, for me, is a real eye-opener and has forced me to rethink time:

E is energy and psi is the wave function, tp is the Planck time, G, c, and h-bar are the gravitational constant, light speed and Planck's constant, respectively. The above equation shows that it doesn't matter how much or little energy there is, or whether states change frequently or not at all, whether they go forward or backward. No matter what values you plug in for E and psi, you get forward time, specifically, the Planck time. Imagine having zero energy, zero change and still having a Planck time. How is that possible? Thought experiment time:

Imagine a universe with no energy, no distance or space, no charges, no masses, no momentum, no oscillators--just a single zero-dimensional point, a singularity. According to the above equation, time still exists. Why? Because the singularity is persistent--it is real. What exactly is this singularity? It's literally nothing ... except time at a single reference frame, at a single point. No clocks, no observers, just pure time.

Time is so essential to reality, that no "persistent illusion" can persist without it. Time can persist without anything else we would deem real, but nothing we deem real can persist without time. The words "reality," "existence," "persistence," "presence" all imply the passage of time. At this juncture, one could argue that time is not only real, but reality's most essential component. And, when we perform the above thought experiment, we witness time in its purest form.

So if you ever encounter a skeptic who believes time isn't real, that particles exist without time, ask the following question (but don't hold your breath):

"How long do particles exist without time?"

A Quantum Gravity Lagrangian without the Graviton

According to Einstein, mass, momentum and energy cause spacetime to curve and curved spacetime tells matter how to move. Since gravity is considered one of the five fundamental forces (interactions), it ought to have its own boson--the graviton.

Unfortunately, particle physicists have had no luck finding this very elusive particle. Is it possible the graviton does not exist? If so, how does gravity work? That's what we will explore today. First, we define some variables:

Imagine a universe devoid of gravitons. Such a universe has mostly photons (radiation), and a little bit of matter here and there. The vacuum of space isn't much of a vacuum. We use Einstein's energy equation (equation 2) to describe the mass, energy and momentum in this universe.

Equation 2's first term represents the photon radiation; the second term is matter. Let's assume this universe is not entirely homogeneous and isotropic. There are places where there is more or less mass, more or less radiation. We compare two such places at equation 3:

Using a bit of algebra, we derive equation 7 below:

Equation 7 reveals an increase in net mass causes the second term's wave-number ratio to shrink. This correlates nicely with the slowing of time and with spacetime curvature. From 7 we can derive Newton's gravitational constant:

Wait! We derived Newton's constant? How is that possible without gravitons? Note the wave numbers we used to derive G are from photons, not gravitons. Doing some more algebra leads to the Lagrangian (L) below:

Equation 17 is the gravity Lagrangian for our universe filled with photons and a little matter thrown in. Still no graviton in sight. When we take partial derivatives with respect to momenta, here's what we get:

Equation 18 shows the photon radiation velocity in a gravitational field. Equation 19 shows the velocity of fermions (mass particles) and satellites in a gravitational field. These results are consistent with our current understanding of gravity. However, we arrived at these results without using gravitons, gravitinos, strings, d-branes, extra dimensions, sparticles and all the fairy dust modern-theoretical physics has to offer.

How to Conserve Dark Energy and the Rest

In the above video the Physics Girl discusses how the expanding universe causes galaxies to move apart, and in turn causes photon wavelengths to stretch out. As photon wavelengths grow, they lose energy. "Where does the energy go?" she asks.

Other physicists, including myself, have a different question: "Where does dark energy come from?" As the universe expands, there is apparently more dark energy and less photon energy? Perhaps energy is conserved after all. If nothing else, it can be mathematically demonstrated. First, let's define the variables:

Equation 1 below shows how photon energy (Ep) is a function of its wavelength (lambda). The bigger lambda gets, the smaller the photon energy.

Equation 2 is dark energy (Ed)--a function of energy density (pd) times volume (V). As volume gets bigger, so does dark energy.

Equation 3 below shows the universe's radius (r) depends on how much dark energy there is. Equation 4 shows photon wavelength depends on how little photon energy there is:

Consider the universe's history. It started out with little or no space (dark energy) and it was very hot (photon energy). Over time space grew and the universe cooled (more dark energy, less photon energy). One way to conserve energy is to multiply photon energy and dark energy together. This creates a constant: as one energy grows, the other shrinks, but their product is always constant. Below we do a little algebra to get the product of the two energies:

Now, one thing we note is both energies are motion energies. Neither is at rest. Given the fact both energies have momentum (p) (due to mass or mass equivalence) we can make a substitution and derive equation 7 below:

You might recognize the momentum-energy term on equation 7's left side. It appears in this famous equation:

Einstein's energy equation, in this instance, shall represent the universe's total momentum and rest-mass energy. If we make one more substitution we get this:

Equation 9 above says the universe's conserved energy is the square root of dark energy times boson energy plus rest-mass energy squared. It includes all matter, radiation and vacuum energy.

Update: Here's another take on this topic: Is dark energy adding energy to our universe? If so, where is the extra energy coming from? How about our universe? The equations below show dark energy increasing at the expense of radiation energy. Overall, energy is conserved.

The Essence of Time

What exactly is time? Is it just an abstract idea? Or does it exist independently of human imagination and perception? Atomic clocks reveal that the rate of time appears to run slower on the earth's surface than way out in space. Assuming time is a real entity, what is it made of? What is its essence? We start our investigation by defining some variables:

We know that nothing goes faster than light in a vacuum. If we add velocity (v) to velocity (c) we still get the speed of light (c).

Equation 1) above seems absurd. When we combine velocities, we should get a higher velocity than c ... unless ... the rate of time (t') shrinks. Equation 2) below works:

And from equation 2) we can derive the famous Lorentz equation:

When velocity (v) increases, time (t') shrinks, but something else happens that's also strange: mass (m') increases. We can verify this if we start with Einstein's energy equation below.

From equation 6) we can derive the relative mass equation:

Equation 13) confirms that when velocity (v) is increased, mass (m') increases. Now, let's take equation 10) and derive equation 14) below:

Equation 14) shows why increased velocity increases mass. When the velocity of a system increases, velocity (u) decreases. To conserve momentum, mass (m') must increase. We start with momentum (mc) and end up with (m'u). Of course m'u must always equal mc. But what exactly is this velocity u? I call it the velocity of time.

The rate of time is the relative speed (u) of a photon or (c^2-v^2)^.5. If a system is moving at velocity (v) and we assume that system is at rest, then the photons in that system may still appear to be moving at c, but relative to v they have slowed to velocity u. Since photons are bosons, their relative speed (how fast they carry force) will determine how fast or how slow the system evolves. If the system is your watch, your watch will noticeably slow down if it moves at a significant fraction of light speed. This suggests that time is real and not just a concept. After all, the original concept of time was that the rate of time is fixed.

Below is a Feynman diagram where velocity v is zero, so velocity u equals velocity c. At the beginning of time (t), two electrons colide. Next, a photon is emitted, then the electrons fly apart.

In the next diagram imagine that the entire diagram is moving through space at velocity v. If we assume the diagram is at rest, the emitted photon will be relatively slower and the measure of time will also be slower:

The electrons in the above diagram are moving faster, but photons can't increase their speed, so, relative to the electrons, the photon is slower. This seemingly slow moving photon is the time we measure or proportionate to the time we measure. Now, just for fun, what happens if the electrons go faster than light?

Time reverses! Your watch is now running backwards. In the diagram above, the particles fly apart, then comes the photon, and finally, the particles collide.

Before we conclude that time is (or is proportionate to) the speed of photons relative to the other particles in a system, let's look at how gravity impacts time, and take a closer look at light, i.e., electromagnetic waves. Once again we define some variables:

We include the variables for permittivity and permeability. Taken together, they determine the speed of an electromagnetic wave. A photon's relative speed (u) has its own corresponding permittivity and permeability. Free space is a vacuum. That is where light has a velocity of c. If the permittivity of free space, for example, had a lower value, light would go faster. Increasing velocity v causes permittivity and permeability to increase (so does additional mass/energy). As a result, EM waves (light) slow down or are relatively slower. The mathematical proof below provides further insight into the essence of time:

Equations 23) and 24) show that time is the reciprocal of frequency. Equations 24) and 26) define the rate of time (with variable t[sub o] set to 1) in one of two ways: The ratio of the relative speed (u) of a photon to light speed (c); or, the ratio of permittivities and permeabilities. Both ways are equivalent. To put it more simply, time (at the quantum level) is the measure of the rate bosons can carry force between particles. If that process is disrupted by high speeds or increased mass/energy, that process will slow down. Anything that is a function of that process will also slow down--including your watch.

Update: Quantum particle-waves are transverse waves: their oscillations are perpendicular to their propagation direction. The following is a mathematical proof that shows that the Lorentz equations above work for transverse waves.

Equation 37) is the formula used to calculate the velocity of a transverse wave. We were able to derive it from the Lorentz equation for relative mass. This shows that the two are intrinsically connected. Equation 39) predicts what we expect: increased mass (m') reduces the time rate (t').

The Anti-time/Anti-matter Controversy

"Anti-matter looks like matter going backwards in time," is a quote I've been hearing lately. Here's a question that popped into my head: What does matter going back in time look like? The typical response is it looks like a rewinding video. However, if matter truly goes back in time it would simply vanish or would exist in the past, not the present or future. It would be unobservable. All we can see is it going in the opposite direction in forward time.

Case and point: positrons have been experimentally trapped for as long as 16 minutes. How is that possible if they go back in time? To exist for 16 minutes, they have to go forward in time for 16 minutes. If you ask me, anti-matter looks like matter with an opposite charge--FULL STOP.

Reverse time comes with its own set of problems. Click here to read about those. Not withstanding these problems, a case can be made for reverse time that doesn't take you back to your high school reunion. I call it anti-time.

Anti-time does not take you to the past, but rather, it makes the past possible. If there was no anti-time there would be nothing to cancel the current moment in time. The moments would pile up. You would not only be living in the present moment, but all your past moments as well. All your memories would be all too real. Hopefully, for your sake, they are good memories.

To demonstrate how anti-time works, let's start with a time-moment represented by an arrow:

The plus sign indicates that it is a positive, forward time-moment. The time-line arrow to the right is how we normally think of time: just a straight line going up in this instance. Now let's add a second time-moment and see what happens:

The first time-moment is canceled by an anti-time-moment (arrow pointing down). That leaves us with the present moment. We get a similar result when another time-moment is added:

But why isn't there an anti-time arrow to cancel the current time-moment? Well, at the beginning of time, there was no past, so time could only go forward, but once it went forward a little, there was some room to go back and still room to go forward--so we get a forward arrow followed by a backward arrow and another forward arrow, etc. As a result, we get time that has a forward bias.

This is a pretty bizarre theory! Can it be tested? Sure. Ask yourself, "Is history history or is it still happening?" If history is history, obviously something is cancelling those time-moments that would otherwise pile up. In mathematics we use a minus sign to cancel a plus sign, so it stands to reason that -time cancels +time leaving us only with the present.

Where is the Anti-matter Hiding?

Around the time of the Big Bang there was, according to one theory, unequal amounts of matter and anti-matter. When matter met anti-matter, they annihilated each other, albeit a little bit of matter was left over--that matter is the matter of our universe. Below is a Feynman diagram illustrating the process of matter-anti-matter creation and destruction.

According the above diagram, a particle (+A) and an anti-particle (-A) destroy each other and produce a boson (B). The boson then goes on to produce another +A/-A pair. This is all done in time (+t) and minus time (-t). (Anti-particles allegedly have anti-time.)

To my knowledge, the above theory has yet to be experimentally verified. It would be great if some scientist could show that a photon, for example, could produce an electron without the positron. That would surely establish why our universe is predominately matter.

The next best thing is to demonstrate that an anti-particle always comes with a particle, but in spite this, a universe could still end up with mostly matter or anti-matter. That is what we are going to demonstrate below.

(Note: What we call matter could very well be anti-matter. However, we are biased and like to think positive--so we label what we have "matter" and its opposite "anti-matter.")

Let's kick things off with a diagram of two electrically charged plates. Let's pretend the positively charged plate is matter and the negatively charged plate is anti-matter. The arrows represent the field lines. Let's also assume the plates are identical in every way except for the charge--this will be analogous to equal amounts of matter and anti-matter.

The arrows originating from the positive plate point away from the source. One arrow goes up and another goes down and through the negative plate:

The arrows originating from the negative plate behave in the opposite fashion:

Now let's add the arrows. Arrows pointing in opposite directions shall cancel each other. Arrows pointing in the same direction shall enhance each other.

Well would you look at that! The arrows didn't cancel each other out completely. We end up with two left over. So it is possible to start with equal amounts of opposite charge, put them together and not end up with zero. However, what if we had a second pair of plates that are reversed?

As you can see the arrows left over are pointing in the opposite direction. If we add those arrows to our original left-over arrows, we get zero.

So whether we get zero or left-over arrows depends on whether we have an odd or even number of plate pairs. An odd number will always give us left-over arrows. Even-numbered pairs will sometimes give us left-over arrows and sometimes not.

We could ask, what is the probability we will get an odd or even number of pairs? I'd say .50 is a reasonable estimate. (P1(a) stands for probability of getting an odd or even number of pairs. The "a" stands for annihilation.)

Let's assume our luck is bad and there are two pairs of plates. What is the probability (P2(a)) that the left-over arrows will be opposite and cancel each other?

How about .50? Finally, what is the total probability (P(a)) that we will end up with zero arrows? What is the probability (P(!a)) we will have something left over when matter and anti-matter annihilate each other?

It should be obvious our universe had at least a .75 (or 75%) chance of having some matter (anti-matter) left over. The odds improve when bigger numbers are crunched. For example, four pairs of plates have a .375 probability of cancelling each other out and yielding zero. That raises the chance of left-over matter to .78 (or 78%) (1- (.5 * .375)= .81; [.81+.75]/2=.78).