Friday, August 14, 2020
The Beautiful Destruction of the Graviton
ABSTRACT:
In his paper titled "Aberration and the Speed of Gravity," S. Carlip argues that gravity propagates at light speed, and, its "action at a distance" and the lack of observed aberration is canceled by velocity dependent interactions. However, the underlying assumption of his thesis is that gravity is caused by gravitational radiation propagating at light speed. Another assumption held by much of the physics community is the quantization of gravitational waves will lead to a spin-2 massless particle known as the graviton. In this paper, I show why gravitational waves and gravitons are not the root cause of gravity. Gravity emerges from an entangled relationship between spacetime and matter.
Modern physics has two conflicting ideas: 1. gravity propagates at light speed, and 2. the equivalence principle. Why are these two ideas in conflict? The first proposes that gravity works in the following manner: a person holds a pen in his hand and drops it. Before it hits the floor, however, the floor must emit gravitons that propagate at c to create a field of gravity, so the pen can receive the gravitational information; otherwise, the pen won't fall.
The second idea is often set forth using a thought experiment where the person holding the pen is in a spaceship. The thrust of the engines cause the floor to accelerate toward the pen when the pen is dropped; otherwise, the pen would float freely in space and never make contact with the floor. In this scenario, no gravitons or gravitational field are needed. The floor is on a collision course with the pen and does not need to send a signal to the pen to let it know it's coming. According to Einstein, this is indistinguishable from gravity. Therefore, this great idea and the one that precedes it create a paradox: the first idea implies a force is causing the pen to fall, so a force-carrying particle is necessary. The second idea implies there is no force.
That begs the question: does gravity require gravitons? Let's examine what may be a source of gravitons and strong evidence that gravity's velocity is c: gravitational waves. Equation 2 below is a gravitational-wave equation:
From equation 2 we derive equation 3 which emphasizes that c is a component of rest-mass energy and not propagation speed.
Does gravity exist if there are no gravitational waves? To find out, we take angular frequency to zero. The time (t') it takes for no waves to propagate a distance r is also zero. The final result is equation 5:
Where there are no gravitational waves there is zero angular frequency and zero strain measured at distance r, but on the left side of equation 5 we see Newtonian gravity is not zero. Thus, the magnitude of gravitational acceleration does not depend on the magnitude of gravitational waves nor their quanta. Further, a zero time delay (t') implies action at a distance.
A comparison between electric waves and gravitational waves reveals why photons are observable and gravitons are not. The wave equation i below represents an electric field (photons) propagating at c. Equations ii through iv demonstrate how the removal of the electric field (photons) leads to no electromagnetic force:
By contrast, if the gravitational field (gravitons) is removed, Newtonian gravity still exists:
What's been shown so far is not surprising when you consider problems surrounding the hypothetical graviton:
1. Since electromagnetic force is around 1037 times greater than gravity, one might imagine a graviton with 1037 times the Compton wavelength of an electron. The graviton's wavelength would span much of the known universe! Not exactly quantum scale.
2. Or, one could imagine one graviton (with the same Compton wavelength as an electron and same speed as a photon) per 1037 photons. If it takes 1037 photons one second to interact with X number of atoms, the graviton would take 1037 seconds to interact with X number of atoms--many orders of magnitude longer than the age of the universe! Further, each graviton interaction would have the same strength as a photon interaction or electromagnetic force.
3. One expects gravitons to spread out to form a field. It is not clear how the gravitons of a black hole can escape each other (if they have a light-speed limit) and not clump together due to mutual attraction (caused by their spin, angular momentum, mass-energy equivalence, etc.).
4. Gravitational wave wavelengths are inconsistent with hypothetical graviton wavelengths.
5. There's a renormalization problem.
6. The graviton has never been observed.
Assuming gravitons are not the root cause of gravity, what exactly is? If we begin with the spacetime metric (equation 6), we can derive equations 9 and 10 below:
Imagine, for the sake of argument, there is a graviton propagating at velocity c. Equation 9 shows if the graviton's energy (E) changes, the spacetime must also change instantaneously; otherwise the constant c would have a different value during the time it takes the graviton to emit another graviton which then transports information to surrounding spacetime. In other words, if the speed of gravity is limited to c, there would be a time lag where c is no longer c! The same holds for Planck's reduced constant at equation 10. The very constants physics relies on would fail to be constant if gravity is required to propagate an information-carrying particle no faster than c.
A careful examination of equation 9 reveals the graviton's energy, when divided by Planck's constant, has the same dimension as frequency, and the spacetime has the same dimension as wavelength. Frequency and wavelength have an entangled relationship. If you measure the value of one, you instantaneously know the value of the other.
In the case of our graviton, a change in its energy instantaneously updates its surrounding spacetime. Our graviton does not need to emit a graviton--and neither does any particle, planet, star, or black hole.
Thus, if the graviton is ever discovered, it is not the root cause of gravity. Gravity is the result of an entangled relationship between matter and spacetime. Matter has a certain energy and moves in certain ways because of a certain configuration of spacetime, and spacetime has a certain configuration because matter has a certain energy and moves in certain ways. Like frequency and wavelength, one does not exist without the other. This new hypothesis is consistent with "action at a distance" observations but inconsistent with the highly contraversial Jovian deflection experiment (see endnote 22).
Acknowledgements:
Amber Strunk. Education and Outreach Lead. LIGO Hanford Observatory.
References:
1. Parikh, Wilczek, Zahariade. 2020. The Noise of Gravitons. arxiv.org.
2. Feynman, R.P. 07/03/1963. Quantum Theory of Gravitation. Acta Physica Polonica. Vol. XXIV.
4. Carlip, S. 12/1999. Aberration and the Speed of Gravity. arxiv.org.
5. Van Raamsdonk, M. 05/17/2010. Building up spacetime with quantum entanglement. arxiv.org.
7. Gravitational Wave. Wikipedia.
8. de Rham, C., Tolley, A.J. 03/17/2020. Speed of Gravity. arxiv.org.
9. Carroll, S.M. 12/1997. Lecture Notes on General Relativity. Enrico Fermi Institute.
14. Nix, E. 08/22/2018. Who Determined the Speed of Light. History.com.
15. Speed of Gravity. Wikipedia.
16. Tests of General Relativity. Wikipedia.
17. Decross, M. et al. Gravitational Waves. Brilliant.com.
18. Lawden, D.F. 1982. Introduction to Tensor Calculus, Relativity and Cosmology. Dover Publications, Inc.
19. Stefanovich, E. V. 09/16/2018. A relativistic quantum theory of gravity. arxiv.org.
20. Light-time correction. Wikipedia.
21. Liénard–Wiechert potential Wikipedia.
23. Faber, J. A. 11/24/2018. The Speed of Gravity Has Not Been Measured From Time Delays. arxiv.org.
24. Yin Zhu. 08/18/2011. Measurement of the Speed of Gravity. arxiv.org.
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?"
Monday, May 11, 2020
Uncertainty Principle for Black Holes
The above video discusses black-hole mathematical singularity problems. The current laws of physics seem to break down once a particle crosses a black hole's event horizon. One mathematical singularity occurs at the Schwarzschild radius; another occurs at the black hole's center. That being said, we will show if Heisenberg's uncertainty principle is employed, the singularity problems vanish and the laws of physics are restored. First, we define the variables we will use:
Before we examine a black hole, let's look at an electron orbiting a hydrogen nucleus. If we know the electron's mass and its approximate velocity (close to light speed c),i.e., its momentum, then we don't know its exact position. Its position could be anywhere within the Bohr radius. The product of its uncertain position and momentum gives us a number close to Planck's reduced constant:
We can imagine the electron being anywhere within a spherical cloud extending as far as the Bohr radius:
Now, let's take the mass of a black hole. Let's assume it is greater than the Planck mass. At the black hole's Schwarzschild radius, equation 3 is true:
Next, we add a pinch of algebra to get equation/inequality 5--an uncertainty principle for the black hole.
So far, so good, but we run into a problem when we reduce radius r to, say, the Planck length:
The inequality at 6 clearly violates the uncertainty principle. The left side is required to be greater or equal to the right side--not less! The problem is caused by the momentum term containing nothing but constants (the Planck mass, c, and m).
If we are more certain about the position or size of the black hole's physical singularity, we need to be more uncertain about its momentum, so we need a momentum uncertainty factor represented by the Greek letter eta:
At 8 we see the uncertainty principle is restored. When radius r shrinks to a Planck or even a zero limit, eta blows up as it should.
Below we do some more algebra and derive 14:
At 14 we see the total energy on the right side never exceeds the total finite energy on the left side. A large momentum uncertainty (eta) cancels position certainty due to a small or zero radius. The inequality/equation at 14 also implies the black hole's singularity position is uncertain if the momentum is known. It could be located anywhere within a sphere bounded by the Schwarzschild radius. The most probable location being the center.
We can take what we have developed so far and apply it to an energy conservation technique used within a previous post titled "High Energy Quantum Gravity." At 15 below we take the total energy between two orbiting bodies and subtract the strong, weak and electromagnetic energies.
The gravitational energy that remains will have a radius (ro) independent of radius r. The total gravitational energy remains constant no matter the distance r. However, we've factored in eta to conserve the Heisenberg uncertainty principle if r shrinks below the Scharzschild limit. Equation 15 reveals that a small force over a large area is equal to a large force over a small area.
Now, let's take what we now know and apply it to the singularity problems that crop up in the Schwarzshild metric below:
At 16, the right side's first term is infinity if r = rs. This implies the spacetime interval (ds) is infinite at the Schwarzschild radius--which is ridiculous. If r = 0, the last term, proper time, is infinite--also ridiculous. But of course, we have the tools to vanquish these mathematical singularities. We know the following Lorenz equations are true:
From 19 to 23 we make some substitutions and simplify the metric at 24:
At 25 we factor in eta:
Now, the only time we get infinity is when r is infinity and kappa is greater than zero. This makes sense if you stop and think about it (see results below).
When the radius is equal to the Schwarzschild radius, the spacetime interval is finite and the proper time is zero. When the radius is zero, the spacetime interval is only the outside observer's time, which makes sense, since nothing can move through zero space (a single point). The proper time is also zero, which makes sense, since it implies that time began after the universe expanded beyond a single point. Thus the current laws of physics that previously broke down are now at least partially fixed.
Friday, March 27, 2020
High Energy Quantum Gravity
In the above video, Sabine Hossenfelder discusses one of the shortcomings of quantizing gravity. At high energies or short distances things go haywire and you get crazy big numbers or infinities. In this post I present one possible solution to this problem. It is not the only solution, and, only experiments will reveal which solution is correct, or, reveal that none are correct. Here is a list of variables we will be working with:
Let's start things off by taking two arbitrary masses (m',m) and creating a reduced-mass Schwarzschild radius:
At equation 2 below, we express the maximum energy of the gravitational field between the two masses. Notice at equation 3, if the radius between the two masses is taken to the zero limit, you don't end up with an infinity. Instead the maximum gravitational energy is conserved, and, said energy never exceeds the maximum energy available--which is always finite.
The equation at lines 2 and 3 can be written in a more familiar form of work (energy) equals force times distance (see 3a below):
If the distance (carrot r) is great, the gravitational force (mg) is small, but if the distance goes to zero, the force blows up to infinity, but ... the energy is conserved, since the infinite force is only along a zero distance.
The next step is to quantize what we have so far. Let's take equation 3a and use a scale factor (alpha). At equation 4, we multiply alpha by a time derivative of h-bar. That takes care of energy (E). On the right side of 4 we have alpha times the time derivative of momentum (p) times the distance. The time derivative of momentum is, of course, the force.
From 4 we derive Heisenberg's uncertainty principle for the singularity (reduced by the alpha factor):
What does equation 7 tell us? It indicates that if we know the exact position of a singularity, we are completely uncertain about its momentum, and vice versa.