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Proof that Aleph Zero Equals Aleph One, Etc.

ABSTRACT: According to the current dogma, Aleph-0 is less than Aleph-1, but is there evidence to the contrary? Is it really true that ...

Showing posts with label fermions. Show all posts
Showing posts with label fermions. Show all posts

Monday, May 25, 2020

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?"

Sunday, September 3, 2017

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.