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.
Saturday, November 3, 2018
What Einstein Didn't Tell You About Time
According to Einstein, if you are sitting in your chair, you are moving more through time and less through space, so time is moving faster for you than it is for a speeding jet. Unlike you, the jet is moving more through space and less through time. If a particle is completely at rest, it moves exclusively through time. If a particle is propagating at the speed of light, it is moving exclusively through space. Below is a Minkowski diagram illustrating the point. The vertical arrow represents the particle at rest and the horizontal line represents a photon. The diagonal arrow could be anything going less than light speed but not at rest.
Now, think about how we humans measure time. We see repeating patterns like day and night, the four seasons, the moon's phases. We then assign time units to these patterns. But imagine a universe where there are no patterns or events, where everything is at rest. How could time be measured? Who would do the measuring?
According to Einstein, everything in that universe is moving through time only, but how can we verify that? There are no clocks to track the alleged passing time. Consider his thought experiment where he has a clock consisting of a light beam oscillating in a boxcar. In the diagram below we mimic that thought experiment with an imaginary photon oscillating vertically inside a box:
The photon is moving at light speed, so special relativity says it experiences no time, but we do. Why? Because we see something happening. We see something that is not at rest. We decided to make that moving photon our clock. Ironically, in order to have time or know time exists, we need something to move through space.
Here's another irony: If all the particles in our imaginary universe were to change to a new overall state, we would say time has moved forward. If all the particles returned to a previous state, we'd say time has gone backwards. If you grow older, time is progressing; if you grow younger, time is regressing. Now, suppose you didn't age or grow younger? Suppose all particles stopped changing states? We would no doubt say time has stopped.
But how can that be? Didn't Einstein say when particles are at rest they move through time?
What gives a sense of time is ongoing change and/or repeated patterns. Time feels real when stuff is happening. When nothing happens, it is as if time has stopped. When things happen faster, it's as if time has sped up, when things slow down, time seems slower. However, if the photon box moves through space, the photon does not appear to complete the cycle as fast, so from our point of view, time has slowed:
But here's the thing: do all clocks slow down when they move faster through space? We will demonstrate the answer to this question is definitely NOT a "yes." First, let's define the variables we will be using:
Here's a new thought experiment: We take a photon clock like the one illustrated above. We have it oscillate in a larger box at velocity u. The larger box is moving at velocity v. Let's assume both velocities are well below the speed of light. We use the Pythagorean theorem to calculate the combined velocity. Below is a diagram for visual reference:
Of course the photon in the smaller box is still moving at velocity c, but this is no longer the clock we want to track time with. We decide to use the larger clock with the small box ticking off the time at a steady rate of velocity u. The question is, what happens to this new rate of time when velocity v is increased? To figure this out requires a little math. We start with equation 1 below which gives the relative mass of the entire system. From there we derive equation 9:
Equation 9 is just Einstein's full energy equation. Let's assume energy is conserved and the combined velocity of v and u is held constant. If we increase velocity v, u must decrease accordingly. So far, our new clock is consistent with relativity's prediction that time slows when velocity v is increased.
Now suppose we add energy to the system. Since both v ad u are well below light speed, we can use the additional energy to increase v without decreasing u! The system mass will increase, but time stays the same!
And what of the photon clock? It slows down as expected. What we now have are three time rates: t', t, and u. We can relate them as follows:
If we only change velocity v, velocity u can remain steady while time t' changes. However, if the combined velocity of u and v is light speed, when v increases, u must decrease.
So to keep our new clock ticking at the same rate, we must keep our combined velocity below light speed. That shouldn't be too hard.
Below we derive equations 16 and 17. These equations express u in terms of time rather than velocity:
Thus when when something moves through space it doesn't necessarily move less through time, and vice versa.
Tuesday, October 23, 2018
How Entropy, Temperature and Chemical Reactions Impact Time Dilation
How do we measure time? Normally we take some event that happens over and over again, and, we assign it a time unit. For example, the complete rotation of the earth we call a day. We can take that time unit (or any fraction thereof) and assign it to other events--that may or may not be periodic--such as a chemical reaction, for instance. We say the chemical reaction happened in time t.
What if that chemical reaction were to slow down? Can we say its rate of time has slowed? If we define time as the rate of change, then the change in the rate of chemical reactions, entropy, or the earth's rotation would indeed impact the rate of time.
Consider the famous twin paradox, where one twin boards a rocket that hurls him into outer space close to light speed. According to Einstein, his time slows, he ages more slowly than his twin back on earth. His body's biochemical reactions are slower, entropy is reduced--at least that is the implication.
When he arrives back on earth, he will be younger than his twin brother. But his twin has a plan: while he's out in space, his twin cryogenically freezes himself. His twin will be thawed out by the time he gets back to earth. If his twin's plan works, they will both be the same age. Now, did the twin on earth reduce his time rate? Can the rate of time be reduced by means other than high velocities and mass density? This post shall address these questions, but first, let's define the variables we will use:
Let's start with entropy. If we somehow reduce the rate of entropy, will the time rate also be reduced?
If we take the Boltzmann constant (which has entropy units) and multiply it by the unit-less Lorentz factor's squared reciprocal, we derive equation 2 below:
Equation 2 shows that entropy is reduced when velocity (v) is increased. The time rate is also reduced. So far it appears we have a correlation between entropy and time. If equation 2 is valid, we should be able to use it to derive a more standard entropy equation:
Equation 6 above confirms the validity of equation 2. So we can say the twin in outer space, traveling near light speed, has reduced his entropy. Now the twin on earth wants to freeze himself, i.e., lower his body's temperature. Will this reduce his entropy? Equation 8 below confirms that it will. From 8 we derive equation 12 which shows lowering the temperature (T) reduces the time rate.
According to equation 12, the twin on earth will age more slowly. Does this imply the rate of his body's biochemical reactions will slow down?
Equation 13 is the Arrhenius equation, where k is the rate of a chemical reaction. When temperature T is reduced, so is the rate of the chemical reaction. From 13 we derive a new entropy equation at 19:
Equation 19 tells us that when the rate of a chemical reaction is reduced, so is entropy. And the reduced chemical-reaction rate reduces the rate of time:
So the age difference between the twins could be nil when the space twin arrives back on earth. If the earth twin cryogenically freezes himself, he may be younger than the space twin. Both twins have found a way to reduce their respective time rates, they have found ways to time travel into the future. Here are four ways to reduce the time rate:
Why Einstein's Time Theory Works So Well
Experiments involving mu-mesons confirm Einstein's special relativity theory and the value of the Lorentz factor. When a particle is moving fast along a straight line, its time slows down. But is this the only circumstance where time slows? This post will address that question and more. First we define the variables we will use:
Einstein's classic thought experiment involved a speeding train passing by an observer who sees the inside of a boxcar as the train whisks by. The rectangular diagram below represents the inside of the moving boxcar. A person inside the boxcar shines a light from the floor to the ceiling (see red line in diagram). If the train is at rest, the light beam goes straight up to the ceiling. When the train moves, the beam goes up at an angle as indicated in the diagram. Using the Pythagorean theorem, we can derive the Lorentz equation (see equation 7 below):
The train and the vertical light beam can be considered a clock. We can say that one unit of time passes when the beam goes from the floor to the ceiling and vice versa. The Lorentz factor is perfect for this clock. As the train moves faster, it takes longer for the light to reach the ceiling--thus our time unit takes longer, i.e., time slows down.
Now, suppose the light beam went from side to side instead of up and down? Would the Lorentz factor still work or does time behave differently? In the diagram below, we have the beam going from right to left. From that, we derive equation 12 below. Note that equation 8 is the velocity addition formula where the total velocity never exceeds light speed.
In the next diagram, the beam is moving left to right. From that we derive equation 18:
Let's take the average of the right sides of equations 12 and 18 at 19. Doing the math we see that the result at 20 is equal to the Lorentz equation at 21. So when the beam goes horizontally, time behaves the same way as when the beam is vertical. But what if the beam goes at an angle? It would have a horizontal and vertical component. At 22 we use sine and cosine for the vertical and horizontal components.
Equation 23 shows it doesn't matter whether the light beam is horizontal, vertical or some arbitrary angle. In any case, we get the Lorentz-equation value of time (t'). It appears the Lorentz factor works splendidly in flat spacetime and where particles, trains, light all move in straight lines. What about curves?
At 24 and 25 below we start with flat spacetime. At 26 we include the metric tensor. From there we derive equation 31:
Equation 31 confirms the Lorentz factor works in curved spacetime. Now what about crazy, oddball geometries (see diagrams below)? We can still derive the Lorentz equation (see equation 41).
Equation 41 will accommodate horizontal light beams, and beams going at any arbitrary angle or curve. At 42 below we calculate the horizontal component which is equal to the Lorentz equation at 41:
To cap things off, we use basic calculus for curves and squiggly lines to derive the Lorentz equation yet again (see 50 below):
We know that the velocity along a curve varies from point to point, so why is velocity (v) in the above equations unvaried? Because velocity v is the average velocity along the whole curve distance. We take the velocity at each point, add them all together, but that would give us infinity, so we need to divide by n, the number of velocities:
OK, so we've established the Lorentz factor works in all situations where a particle, train or whatever is moving at velocity v along any line. We know that mass can slow time as well as velocity. We also know that protons have their mass due to quark oscillations. So we can think of mass as oscillating velocity. The equations below show the relationships between time, mass, angular velocity and the Lorentz factor:
Update: Below are some diagrams (and calculus) that help one visualize how a light beam (or photon) moves along a curved horizontal component. The first diagram below shows the photon (red dot) moving from left to right along epsilon-x. Epsilon-x is also moving from left to right along x. The total distance covered is x + epsilon-x. The second diagram shows the same except the photon moves right to left. The total distance is x - epsilon-x.
In the next two diagrams, everything is the same except x and epsilon-x are now warped, distorted, curved, etc.
Below is a mathematical proof showing that the magnitudes of x and epsilon-x are invariant no matter how they are distorted:
