At the time I made an attempt to build my theory from scratch, I'll like to sort through the garbage and try again, keeping in mind what I believe now (i.e. the relevance of DeBroglie matter waves).
To prepare for reading this document, I'd like to warn the reader in advance of a few important things.
Regarding basic Geometry / Physics
For math and modern some of modern physics, I won't be going into much detail since my goal here is not to teach the material. The people who already understand it won't need a refresher course, and for the people who don't yet know the material, I only want to express the ideas in an intuitive way, to get us quickly to my own ideas. I'll be describing my own ideas in a lot more depth, using genuine formulas.
It is dangerous to try and work with existing modern theory, since much of it has a vast amount of experimental evidence behind it, except for the bleeding edge science (which is out of my reach anyway).
Therefore, what I'll do instead is this: rather than invent my own premises and work against existing theories, I'm simply going to fail to assume that the premises of existing theories are correct. By doing this, I ought to be led to an incomplete model of the universe, if I'm educated enough and being rigorous in my work.
I emphasize "ought to", because here's where my own ideas come in. I believe I can explain more phenomena by using less of what is taken as true in modern physics.
To pull this off, I'll need to be stepping very carefully in the presentation of the relevant modern physics and of my own ideas. It is therefore worthwhile to read the whole document in order, rather than skipping the easy bits. The later sections depend very heavily upon a critical and thoughtful take on ideas that we may normally take for granted.
Despite the fact I'll be trying to make the Wiki legible to laypeople, I want to conclude the Wiki by presenting formulas. (I'm using this Wiki as motivation to actually build them.)
The paper will start out discussing content that one would find in a grade-school science class.
It will next discuss topics that go into quantum physics, but I won't be going into the math here so most adults should still be able to grasp the ideas (maybe).
Finally, I'll present my own research, which will only be understandable to those who have actually studied quantum physics in school or professionally, even if only a little bit.
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Although the term may frighten mathophobes, it's pretty easy to understand with just our everyday intuitions alone.
An infinitely small dot is zero-dimensional. It does not extend out in any direction.
If you smear the dot straight in a single direction, the line you create is one dimensional. The line can be measured with, say, a ruler. Just as there are infinitely many numbers, so too is a mathematical dimension actually defined as an infinitely long line.
Now, there are only two relevant "ways" to smear the infinitely long line:
Along its own direction
In any other single direction
If you smear it along its own direction, you still have an infinitely long line and nothing has changed. It's as if you did nothing at all.
If you smear it in any other direction (and assuming you keep smearing to infinity), you create something that looks like an infinitely large, utterly flat piece of paper. This is called a plane, and it is two dimensional because it stretches in two directions.
I'd like to talk about linear independence now, another math term that isn't as scary as it sounds.
Let's say you're trying to build new dimensions. It is important to note that, as I mentioned above, moving the line in the same direction (or the negative of the same direction) as the original line will never help. In fact, when you're smearing the new line, any movement along the direction of the original line implies that part of the movement is "wasted" because part of the smearing moves in first dimension, which we were already aware of.
To make your smearing worthwhile in the discovery of a new dimension, you must move the line in such a way that its movement in the original dimension is zero. This might sound impossible, but it's easy for the second and third dimensions. You just build a perfectly rectangular corner.
We can now measure locations on it much more easily, just by measuring distances along the two lines relative to their intersection. These lines are called "linearly independent".
Euclidean Space = Three-Dimensional Rectangular Space
We can use the same logic discussed above one more time and build a third line. This creates a three-dimension volume. It is called a Euclidean space simply to honor its Greek founder, considered the father of geometry.
This logic can also be generalized to spaces with more than three dimensions. However, note that it seems impossible to actually visualize (i.e. create or imagine) such a space. Take a three-dimensional Euclidean space, and try to draw a linearly independent line, i.e. a line that doesn't have a component along at least one of the existing three dimensions. It just can't be done.
The concept of Euclidean Space is an important foundation for many ideas in modern physics, so I'll be studying it in more depth in later sections.
Other kinds of spaces can be created, and I'll touch on that in the section on General Relativity, but I won't go into any depth since I'm starting with a failure in assuming that General Relativity is a correct model of gravity.
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Galileo observed that within his laboratory in the hold of a boat moving slowly down a quiet river, all experiments functioned identically to how they would in a laboratory he'd set up on land. If there were no windows on the boat, how would he know whether the room is moving relative to the surface of the Earth?
Galilean Relativity is a statement about inertia; i.e. the way in which objects "naturally" move, in the absence of forces. It suggests that an object, sufficiently removed from the influence of forces, will either remain stationary or else move at a constant rate in a straight line.
Galileo's laboratory on the boat allows objects to move as they naturally would (excluding gravity, of course). A fish in a fishbowl doesn't have to swim any harder in any direction as it would have if the bowl were stationary on the shore. Compare this to a fishbowl on a quickly turning or accelerating car. The fish and the water it's swimming in could very easily get dumped on the car rider's lap.
Frames of reference that allow natural movement are called "inertial reference frames", and such frames form the basis of Einstein's Relativity, but we'll get to that later.
The Galilean Transformation
The Galilean Tranformation, like any transformation", is a mathematical trick that allows you to change your perspective. For example, if one observer is on a riverbank, and another observer is on the boat as it floats slowly, unswervingly down the river, then the Galilean perspective allows one observer to predict how the movement of objects will be perceived of the other observer. Note that this only applies in day-to-day circumstances (i.e. at speeds significantly less than the speed of light).
The transformation can be calculated as follows:
Let each observer be at the origin (i.e. zero point) of his own coordinate systems. Also let the boat be moving with the speed v in the direction i.
Galileo's Addition of Velocities
Maxwell's speed of light and Einstein's revelation
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Maxwell's Major Achievement
James Clerk Maxwell was studying the laws of electricity and magnetism and noticed heavy similarities between the different laws. In short, he discovered that they weren't just twins, but different facets of the same law. It is through his work that we know there is only a single force, known as electromagnetism, at work rather than the two separate forces of electricity and magnetism.
The part of his work that is relevant here is that the equations he was working with described photons (i.e. particles of light) as moving at a speed of approximately 300,000,000 meters per second.
This speed didn't appear to be relative to anything. At the time, physicists assumed it was relative to the "aether", a mysterious absolute background of space. If you were at rest relative to the aether, supposedly you were "truly" at rest.
The Problem with the Speed of Light and Galileo's Addition of Velocities
What happens if a photon is launched forward from a moving train? If a photon's speed can't get larger (or even smaller), then this seems to break Galileo's Addition of Velocities or else photons can't really move at a fixed speed.
Several experiments were performed in attempt to measure our speed relative to the aether, most notably that of Michaelson and Morley. Against all expectations, the experiments returned negative results and slowly physicists came to realize that the aether was a myth, implying there was no absolute background. At about the same time, Einstein had a revelation and was able to reconcile the fixed speed of light with the addition of velocities.
He kept the assumption that the speed of light is fixed and independent of the speed of the source, but introduced a new transformation known as Special Relativity. In other words, changing from the perspective of a person on land to the perspective of a person on a moving train is not as simple as merely adding the velocity of the train.
Technically the transformation was created by a fellow named Hendrik Lorentz, and so the equations are known as the Lorentz transformations, but Lorentz created the equations to try and save the concept of an aether. Einstein was the first person to correctly interpret the actual physics, and determine that it was measurements of space and time that change when you go from the perspectives of a person on land to the perspective of a person on a moving train. Although it seems counter-intuitive, these changes are just enough to allow both perspectives to measure photons as moving at the same speed.
Einstein's Special Relativity
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The Mechanics of Special Relativity
Einstein's premise might sound counter-intuitive at first. A common example used to demonstrates how it works is of a lightbulb on the floor of a rocketship, where the lightbulb is visible to an outside observer and a passenger in the rocket. The height of the rocketship is 1 unit high. (1 unit is chosen to make the math easier, but it would work with any distance).
Relative to the passenger, who is stationary relative to the lightbulb, a beam of light travels from the floor to the ceiling over a distance of 1, the height of the ship.
Relative to the outside observer, the light must travel a longer distance to compensate from the distance travelled.
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Einstein was unsatisfied with the fact that Special Relativity failed to be a general transformation for all kinds of movement; i.e. it left out the rather large class of non-inertial movements, or those movements that involve acceleration or rotation.
Through some logic, he took gravitation and inertia to be equivalent, and used this as a springboard to come up with the General Theory of Relativity. I won't discuss the theory at all except to point out a few things, as follows.
Minkowski took Einstein's theory of General Relativity and built a larger mathematical basis for it, forming a single unit called spacetime, where the dimensions of space and time are each just facets of this unit.
However, the structure is almost a Euclidean space in nature. Although one of the dimensions is "complex" (in mathematical terms), it otherwise functions as a rectangular space so that beams of light move in a straight line and so do objects with mass if they are sufficiently far away from other objects with mass.
As suggested by Einstein's General Relativity, the presence of mass and energy will warp and bend the surrounding space. As objects pass through warped space, they will follow the curves in the same way that the paths of rolling balls on a trampoline will be bent towards each other as they pass by closely.
In describing this structure, physicist John Archibald Wheeler is famously quoted as saying "Spacetime tells matter how to move; matter tells spacetime how to curve."
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Before describing why I prefer the one to the other, I'll first describe each experiment. The descriptions will be rough because I'm only interested in expressing the core "fuzziness" of Quantum Physics, rather than in treating these experiments scientifically.
The Cat in the Box
This experiment was first posed by Erwin Schrodinger, one of the major players in Quantum Physics. He first posed the experiment to express the absurdity of quantum physics.
The experiment goes like this:
Take a particle that may or may not decay into another particle. How long it takes to decay is random, being 50% likely after a given time T.
Take this particle and hook it up to a detector, and hook the detector up to some gaseous toxin. When the detector discovers that the particle has decayed, it releases the toxin into the air.
Put the whole contraption in a box, so that outside observers don't know what's going on in the box.
Put a cat into the box too.
After the given time T, there is a 50% chance that the cat will be found dead, and a 50% chance that the cat will be found alive.
What if we don't check? It is often stated that until we check, the cat is both dead and alive.
The reason I don't like this experiment is that it is easy to assume that, although we haven't checked, there really is one answer "in reality". In other words, that the cat inside the box is either already dead OR still alive, and that our checking under the box simply adds to our knowledge this existing fact.
However,despite the famousness of this example, the knee-jerk assumption of how it works doesn't truly demonstrate the inherent fuzziness in quantum physics works. Let's now talk about the double-slit experiment.
The Double-slit Experiment
In the double-slit experiment, we shoot electrons at two slits and measure where they hit a screen placed on the other side.
Initially, the goal of the experiment was to try and determine if the electron travels through space like a particle or a wave.
If it travelled like a particle, it was imagined that it would travel in a straight line through either one slit or the other (or else miss entirely and hit the barrier with the two slits).
If it travelled like a wave, it was imagined that the travelling of the electron would form a pattern in space much like you'd see by dropping a stone into a pond. Ripples would expand outward from the launch point. When the ripples made it through the two slits, they would continue to expand but create a pattern against the back wall of high and low intensity; i.e. where the waves from the two slits would add together or cancel out.
So what actually happens?
Both actually, depending on the conditions of the experiment. If you "don't peek" and allow the electrons to go where they may, they create the waveform pattern, suggesting they travel as a wave.
If you "peek" and try to check which barrier each individual particle is moving through before they make it through the barrier, they travel like baseballs and appear to move through space in one direction, through one slit or the other, but not both.
It's as if the experimenter has some weird mystical control over the behaviour of the electrons, which defies common sense.
Our New Weapon in Science
Going back to the cat-in-a-box example, by the same argument, the cat would truly have no official is-only-dead or is-only-alive state until we have tested the experiment by opening the box. Its state is both-dead-and-alive, which utterly defies common sense.
I'm not going to get into the implications, instead just leaving the topic behind by saying "it's weird".
Later, I'm going to be re-examining physics from the ground up. The discovery of this fuzziness in Quantum Physics, i.e. in reality itself, grants us an extraordinary, thought-provoking tool to use in our analysis of the foundations of modern physics.
What I do want to take away from this experiment is that the state of a particle does not even necessarily exist in any absolute, observer-independent way.
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Newton's First Law, in brief
To remind, Newton's First Law sets down Galilean Relativity as a law of mechanics. It states that an object either at rest or moving unaccelerated in a straight line will continue in this way relative to any and all other objects at rest or moving unaccelerated in a straight line, unless its motion is altered by a force.
Revisiting General Relativity
Newton's First Law was first written when space was assumed to be flat (i.e. curveless) and time was universally constant, long before General Relativity. Einstein first proposed spacetime with General Relativity, but he actually didn't damage Newton's First Law which is why it has been kept. If a spaceship is floating around Earth in an orbit without using its engines, it is moving in a curve only because it is moving with the curvature of spacetime. If spacetime curved in a different way, the rocket would be impelled to move that way instead. This is a consequence of the equivalence, as proposed by Einstein, between inertia and gravitation. The foundation of inertia is Newton's First Law.
This question will seem arbitrary and fruitless at first, but please bear with me: how do we know Newton's First Law, really Galilean Relativity, is true?
Newton backed up his First Law with a thought experiment; he asked what would happen if you shot a cannonball with successively more powerful cannons. With enough power, it would shoot off into space, with its path of movement eventually becoming a straight line as it escaped Earth's gravity.
This is a reasonable logical proof and Newton's First Law is actually depended upon in lots (and lots) of experiments. In fact, virtually every mechanical experiment depends in some way, more or less, upon this law.
Photons and Accelerating Electrons
A corollary of Newton's First Law is that acceleration is a different mode of movement that can be felt, or more scientifically, that it has a potentially measurable effect upon the body undergoing accelerated movement.
Continuing along the same vein as the silly question: my body is built from a vast, complex configuration of basic particles. I have absolutely no trouble believing that the acceleration of my body can be detected as the particles all interact with each other and transmit the acceleration through the whole of my body. When I'm in a car and that car corners quickly, I feel it.
However, would an electron "feel" when it is being accelerated?
As it turns out: yes. When electrons are accelerated, they absorb or emit photons of light. I won't go into detail, but the lightning bolts we see during thunderstorms are an example of this process.
Photons themselves seem to obey Newton's First Law more or less. They have no rest mass, meaning that there is no point of view you can adopt in which a photon is relatively stationary, but they travel through space following "straight" paths (i.e. the geodesics of spacetime).
Killing the Silly Question
Though Newton's First Law was proposed well before the discovery of quantum physics, it genuinely seems to have a basis in reality because, in addition to thought experiments "proving" it, a lot of evidence confirms it, such as that provided by electrons and photons.
I mentioned at the beginning that I would not challenge existing physical law. As such, I will not challenge Newton's First Law. What I will do is this: in spite of all the evidence in favor of Newton's First Law, later I will "forget" it and instead see if I rediscover it in the work that follows.
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Time versus Momentum
Time is a variable that seems to fundamentally underlie most of the rest of physics. However, in Quantum Physics..
Note, you'll find that there are four quantities for relational momentum. The classical mind would reduce them to two quantities, but in a quantum space, they may be four distinct values at a given moment:
A.1 - your relational momentum relative to me, from your perspective
A.2 - your relational momentum relative to me, from my perspective
B.1 - my relational momentum relative to you, from your perspective
B.2 - my relational momentum relative to you, from my perspective
This is also true for relative position.
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Here we start transitioning into ideas of my own.
Please note: as I have mentioned earlier, rather than challenge any particular existing physical theories, what I'll do is simply take a few and "forget" them. If I'm sufficiently thorough, I ought to come up with modern science as we know it now.
Incongruity of General Relativity with Quantum Physics, Revisited
As I mentioned in General Relativity, modern physics suggests that time is a dimension similar (but not equivalent) to a dimension of space. This isn't exactly intuitive, but General Relativity has produced some decent results despite the fact it hasn't yet fit into Quantum Physics.
Quantum Physics, on the other hand, has some very weird features that seem to run counter to the modern definition of time as a dimension. For example, there is Quantum Entanglement, called "spooky action at a distance" by Einstein, where particles interact with each other faster than the speed of light, which is impossible according to Special Relativity.
What is Time?
It begs the very sincere and serious question: what is time? If General Relativity may be incorrect, then so may be our definition of time.
I'm not going to suggest an answer. However, I'd still like a working definition of time, even if I don't know what time "really" is. I'll have to step carefully, given that Newton's First Law and General Relativity fail to make sense without a proper definition of time coming first.
Loss of Time in a Classical Universe
In a classical universe, every particle has a precise location and a precise momentum which exists in reality. Though we cannot measure the precise values, increasing the strength of our technology always produces better answers.
In this imaginary universe, if I remove time, I'm forced to stop dead.
Without a definition of time, the particles do not move relative to each other, and so there is no change. It is like a Medusa's gallery, with everything becoming a statue, locked in its position due to the absence of time.
Here, I can't even begin to build a working definition of time with what's left.
First Failed Attempt to Kill Time in an Einstein / Minkowski Universe
A modern physicist will tell you that there are some indications that elements of the universe are classical (such as the as-yet intractable problem of the observer, demonstrated by the double slit experiment). However, there is no denying that the universe is otherwise largely ruled by Quantum Physics.
In classical space, the dimensions of time and space were fundamentally separate, so we could easily rip away time as we would a dimension of space. This is true even with our modern definition of spacetime.
However, in quantum physics, every dimension of space (i.e. set of relative positions) is intimately connected to a dual dimension of momentum (i.e. set of relative momentums). The knee-jerk reaction is to assume that, if we try to forcefully recreate an existence without what we think of as time, then we should get a Medusa's Gallery as we would in a classical universe; i.e.:
the relative position of any particle can be precisely known and
the relative momentum of any particle is precisely zero
Heisenberg demonstrated that both of those statements cannot be true simultaneously for a single given particle, which hints that a universe that is capable of change without a definition of time may be possible. However, momentum can no longer be defined because it depends on the existence of the Einstein / Minkowski notion of time.
Momentum Ratios and Relational Momentum
The momentum for objects with mass is traditionally defined as: p = mv = m * (dx / dt).
This equation has a long history and has been thoroughly tested beyond all rational doubt. To continue on my mission to remove time, I need to define something that can do the job of a momentum variable that is congruent with this equation but steps around the need to define time.
One tricky way to do it is to define a momentum ratio and just cancel out time in the ratio.
Take the ratio of classical momentums of particle A and particle B. We get pA/pB = ma * (dxa/dta) / mb * (dxb/dtb)
If the span of "time" between measurements of both A and B is the same, we can eliminate dta and dtb because dta = dtb.
We're left with pA/pB = ma*dxa / mb*dxB, which can be reduced to two separate statements: pA = ma*dxa, and pB = mb*dxb. The statements can be generalized to a formula I'll call relational momentum: p = m * dx. This formula looks similar to classical momentum, but we have to remember that the equation is meaningful only in specific situations.
Namely, it only provides the momentum of an object or particle in terms of the momentum of another object or particle. We lose a definition of momentum defined absolutely against a dimension of time, in favour of a much more relational definition (thus, the name "relational momentum").
As hoped, relational momentum can be defined in a universe without the Galilei/Newton or Einstein/Minkowski definitions of time. The next step is to see if it can be used in most or all places that the traditional momentum variable could be used. Success in this endeavor will allow us to replace all physical formulae that include instances of a time variable with some variation that instead includes relational momentum variables.
It may sound like I'm being optimistic. Maybe so, but please follow me down this path of logic. Also note: I will not be using relational momentum interchangeably with classical momentum.
To see if relational momentum can take the place of regular momentum in Heisenberg's Uncertainty Principle (HUP), we have to find out how the HUP first came about, what role it fills, and what boundaries it faces.
YADDA YADDA YADDA
Given the lack of dependence upon a dimension of time in this version of Heisenberg's Uncertainty Principle, we can consider the relationship between position and relational momentum. Ignorant "common sense" may still drive us to think that, without time, the universe will have both of the following properties:
the relative position of any particle can be precisely known and
the relational momentum of any particle is precisely zero.
We're still restricted by Heisenberg's Uncertainty Principle to say that both cannot be true "simultaneously" (where "simultaneous" is defined in relation to the changing states of particles in the universe, not in time). Since either statement can be true for a given particle but not both simultaneously, we are forced out of believing in the possibility of a Medusa Gallery universe.
The one counterargument I can see is if all particles in the entire universe have a relational momentum of zero. They'd be frozen relative to each other, but they couldn't ever know each others' positions within the universe. I can't honestly answer this one, but it is a boundary case and seems to be very wound up in the effect of the observer (described in the Two Slit Experiment).
Since I freely admit I that I cannot explain the effect of the observer, I'll leave this case out of it, and be comfortable in the knowledge that all other cases imply a universe that is capable of change even in the absence of Newton or Einstein / Minkowski time. I'll call this a Quantum Relational universe.
Past memories, fuzzy present, and future probabilities
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We saw in the previous section "Stepping Around Time" that we could build the basic framework of a changing universe even without invoking an imaginary dimension of time. I called it the quantum-relational universe.
This framework does not yet give us a definition of the experiential time that we encounter in our day to day lives. The universe may be changing but it seems to be a massive jumble of particles jumping in and out of existence.
The "Arrow of Time": the Modern Take
Before moving on, I want to talk about the "Arrow of Time", or namely, the inherent directionality that time seems to have. This directionality is highlighted when I, say, run a movie backwards. In all but very, very specific scenes, it is obvious to the audience which way time is moving. Bullets go back into guns, fallen people stand back up, people levitate backwards onto building-tops and so on. It is easy to understand the concept, but actually understanding how it comes about is much more difficult.
Therefore, I'll draw a parallel by talking about space. Think of this example of the relativity of position and movement: why is it more reasonable to say that the Earth is floating around the sun than it is to say that the sun is floating around the Earth?
For a long stretch of human history, we believed that everything orbited Earth, but when astronomers in the time of Galileo attempted to make mathematical models, the models became very complex, and increased in complexity as their technology allowed them to know more about the movements of objects in space.
However, Galileo took the position that the solar system was indeed a solar system, and objects floated around the Earth. This proposition makes the calculations of movements of objects in the solar system vastly simpler. That said, my original question remains. The answer is: it doesn't matter to the laws of physics whether you imagine the Earth to be moving around the sun or the sun to be moving around the Earth. As long as your calculations are followed rigidly, they will produce correct answers in both cases. Luckily, astronomers are not so masochistic and therefore choose models of the universe that are as simple as possible (while still producing correct predictions).
The point I'm trying to reach is the relativity of observers in space. One position is functionally equivalent to another. The modern view is that this is true of time as well. In Minkowski spacetime, all objects are always moving through spacetime at the speed of light. By being at rest relative to another object, you are both moving fully through time at the speed of light. When you start moving through space relative to each other, each participant sees himself moving through time fully at the speed of light but observes the other participant as having traded in some "time speed" to get some "space speed".
In modern times, with the introduction of Minkowski's spacetime, this leads us to a reasonably convincing explanation of where an arrow of time comes from. Just as it is no more reasonable to say the Earth is moving and the Sun is still than it is to say the Sun is moving and the Earth is still, so too is it no more reasonable to say that one participant is moving through time at the speed of light and the other participant is moving through space and time, than it is to say visa versa. It's just a matter of perspective, and both perspectives are correct.
In the case of the two participants moving through time, unlike the movement of the Earth and Sun, neither has preference based on easier mathematics.
Working in a Quantum-Relational Universe
Surprisingly, we may be able to simulate an arrow of time that is built upon a quantum-relational universe. Before I describe it, I would like to stress: this simulation of the arrow of time produces an experience that is similar or equivalent to what might come out of the arrow of time from modern physics, but the mechanics of the simulation are vastly different! The "engine" behind the simulation needs to be extremely different in order to be able to function without a Newton or Einstein / Minkowski definition of time to drive it.
The core of the simulation is change. Change in the quantum-relational universe occurs because each particle is not quite certain where any other particle is, nor how much relational momentum it has (i.e. momentum in relation to itself). However, as mentioned earlier, every particle has a definite statistical probability of being at some given location moving with some given relational momentum. If particle B is likely going to be detected further down a pathway through space (defined by its relational momentum) by particle A, then as change in the universe occurs through the observer effect, particle B will likely be detected further down that pathway.
Obviously my previous statement is tautological; if true, then true. I use it to drive the point home.
Quantum Physics already maps for us a set of probabilities for where particles will be detected in space and what their relational momentums will be. The universe's inherent fuzziness is enough to drive everything in it to (approximately) follow the paths of likeliest probability (in most instance).
In this simulation of time, the future is then simply the tree of probabilities that the universe could follow as it changes due to its own quantum fuzziness. The future doesn't actually exist nor is it predefined beforehand because the randomness of quantum physics seems to be something that can't be woven out whatsoever. (On the other hand, if one subscribes to the idea of multiple universe, maybe all possibilities play themselves out in independent universes. I won't consider that possibility since, for now, we can only be aware of our own.)
The Fuzzy Present
By destroying a future that is fully mapped out along a dimension, we've past the point of no return. We need to discover the meaning of "present" and "past" for this example to be a true simulation of time.
The "present" is a difficult thing to get your hands on in a quantum universe. The observer effect, highlighted in the Double-Slit Experiment, makes it something of a mystery because there may be no single, fixed reality for the observed state of any given particle. This makes the present rather fuzzy though highly predictable for a single observer.
Einstein's Special Relativity further muddies the mix as well. What I detect to be a simultaneous pair of events may not be detected by you as simultaneous. Our ingrained idea of the present as a sharply-defined "now" clashes with a loss of simultaneity.
However, in a fuzzy quantum universe, a present "now" that is also fuzzy a bit into what we think of as the past and future is compatible. If an observer detects an event, then that event is within the present of the object at the moment of detection, even if the apparent time-order of detection clashes with the time order as detected by another observer. Furthermore, the locations and relational momentums of the two particles upon the moment of their mutual detection is random, though highly predictable.
As mentioned, the boundary between the past and the present is muddled because of the fuzziness of the present, but the past state of a particle as detected by an observer is any state no longer in its present.
The past is a completely different beast than the future. Though the future was non-existent, any given future at least had the potential to become the state of the present.
The past is also non-existent. However, to move back into the past, you would have to reverse the relational momentums of each and every particle in the universe, and even then you'd likely not reach an exact duplicate of the past you remember because quantum fuzziness forces you to keep rolling the dice as the present changes. The probability of the universe reaching a previous state is virtually (if not exactly) zero.
Therefore, the past truly is a memory.
The "Arrow of Time": the Timeless Take
To bring everything together; in our quantum-relational simulation of time:
time does not exist, except for the present
although the present is singular for a given observer, it is chosen from a large number of random though predictable possibilities
the present, taken as a sum of "now" moments across all observers, slips slightly into the future and past
different observers need not necessarily gather the same results from the large number of random possibilities
despite the previous statement, the probability of a given future state for a particle is the same across all observers, mapped into the relative state of the observer
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Our Model, So Far..
In Stepping Around Time, we've seen how change inexorably emerges within a Quantum Relational universe; the relative positions of quantum particles must change through their relational momentums since, by Heisenberg's Uncertainty Principle, those values cannot be simultaneously precisely fixed for a given particle from the perspective of any observer. We've also seen how the relational momentums have a probabilistic "direction" which one could call a fuzzy kind of Arrow of Time. All of this is despite the fact that our model has been constructed without a dimension or property of time in and of itself.
Incompatibilities With Modern Science - Newton's FIrst Law
Though we have particles with relative positions and relational momentums in the universe and, from that, a simulation of time and movement, we can't yet assume that Newton's First Law will simply pop out of the model.
One might try to blindly reinterpret Newton's First Law in the context of a Quantum Relational universe by asserting that for an object far removed from all other objects in the universe, the relational momentum of that object can equivalently be said to be zero or any constant value, both resulting in an identical situation when it comes to the laws of physics.
This fails quite miserably for a few reasons.
First of all, relational momentum is defined relationally. The relational momentum cannot be said to even exist in the absence of another object. By using relational momentum in our model, we are utterly barred from asking questions about the properties of a lone object in the universe. We must always assume there are at least two. Therefore, it makes no sense to examine the behaviour of a single object "sufficiently far away from all other objects in the universe".
Furthermore, an "inertial reference frame" becomes impossible to really define in our model; let's say two objects start at some closest distance of approach and then move in a parallel way (i.e. parallel as if drawn on a flat sheet of paper) in opposite directions. From this, our model comes into serious conflict with Newton's First Law. In Newtonian space, parallel movement is simple. One object moves in an arbitrarily-defined positive direction along a line in space, and another object moves in the negative direction along the parallel line in space.
For us, it's not so simple. We can only talk about the relationship between objects and not the space they exist in. Two objects can never really be said to move in a parallel direction if they only have themselves as reference points. Parallel according to whom? If you try to force the objects in a supposedly parallel direction, the only effect observable by the objects is that they move farther away from each other along the line connecting them. This becomes their reality since, again, we cannot talk about the space they exist in.
Counterarguments come into play when you start talking about objects with non-zero size and consequently their orientations and relative rates of rotation. However, the Law ought to work the same way with zero-dimensional objects with mass if it is a correct description of the universe, so I won't talk about "big" objects yet and instead continue to focus on incompatibilities at the level of zero-dimensional particles.
Incompatibilities With Modern Science - General Relativity
Another big difference between our model and the definitions of modern physics is highlighted when we consider General Relativity and its description of gravity and non-inertial movement.
In General Relativity, a constant acceleration is equivalent to the application of an appropriate gravitational field. Einstein's example is of a chest being accelerated in space by a rocket pulling it with a rope, far away from all other objects in the universe (so that their gravitational fields don't interfere with the experiment). If the acceleration is constant, the person in the chest has no way to determine whether he is being accelerated at a constant rate or is stationary in a gravitational field. (Note that this is a very similar logic used by Galileo to determine the equivalency of inertial reference frames: experiments performed in the lab function the same way regardless of whether the laboratory is on land or on a smoothly moving, non-accelerating vehicle.)
Acceleration in General Relativity is a real, measurable effect. Let's say you have two rockets but they're powered by specialized warp drives that look the same whether they're active or not. Two people, one on each rocket, see each other accelerating by relative to each other. Since neither rocket appears to be causing an acceleration thanks to their special engines, how can the rocket riders determine which of their ships is doing the accelerating? In one ship, the person floats freely around the ship. In the other, the person and all his gear and equipment will be pushed towards one side of the rocket. The latter astronaut is therefore in the accelerating reference frame and is experiencing the equivalent of a gravitational pull.
Acceleration works differently in our model.
In Quantum Relational space, the following scenarios are isomorphic and therefore identical in this context for two particles alone in space:
two stationary particles
one stationary particle, the other orbiting in a circle
one stationary particle and another moving along any random paths at any random varying speeds
The reason that the scenarios are identical in our model is that the apparent movement is always collinear, as judged by the zero-dimensional participants, and their relational momentums become utterly arbitrary since they can only measure their relative distance by using each other as a reference point in the first place.
(Note that there is a boundary condition here, when the particles approach so closely that absorption occurs. Clearly they can no longer be said to be two separate particles in that instance. I'll discuss this later.)
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It might be tempting to throw up our hands and reject the model outright at this point, because all of our experience and innumerable experiments are in favour of Newton's First Law and General Relativity, and the incompatibilities of our model are scary. However, I suggest we continue down this path just to see what's at the end of it, since it may be enlightening even if it's an incorrect model of reality. Let's start from the very bottom and work our way up.
As discussed, objects in a Quantum Relational space are only capable of influencing each other based on their relativepositions and relational momentums. In a tricky sort of way, we can define a type of "clock" that is better likened to a sun-dial than a wristwatch. We tend to conceive of wristwatches as running with the flow of "true time", time as a dimension or as a fundamental property of the universe. However, the clock we'll define is different since it measures time by comparing the relative positions of moving objects. We are able to get away with this in a Quantum Relational universe since, as discussed, objects can change their positions despite the lack of a dimension of time thanks to their relational momentums.
Revisiting the Common Sense Definition of "Stationary"
To continue the journey, we need to define the word "stationary" in Quantum Relational space in a way conformable to the way we already think of the term.
For a short while, I'll begin by using the word "stationary" in its traditional sense just to point out a problem with its usual definition; i.e. perfectly (relatively) stationary with precisely zero momentum.
You may remember from the Double-Slit Experiment that, as I shoot an individual electron at a barrier with two slits, I can never know both its actual location and momentum to infinite accuracy simultaneously, I can only know the probability of its location anywhere in space and the probability of it having a given momentum.
Let's build two Double-Slit Experiments side by side and fire electrons at as close to simultaneously as we can. For someone stationary beside the experiment, they might wonder how the electrons view each other: before the electron waveform passes through the double-slit, wouldn't the electrons see each other as having relatively zero momentums, i.e. being relatively stationary?
No. Even before the electrons pass through the barrier with double-slits, they travel as a probabilistic wave. If the electrons were to observe each other, they would find each other being almost relatively stationary with relative momentums that areapproximately (but not exactly) zero.
To summarize, even supposedly "stationary" particles cannot be truly stationary in the way that we're used to thinking of the term. The word "stationary", in the sense of a Medusa-gallery with perfectly unmoving statues with precisely relatively fixed locations, is a myth.
Stationary Relative to Self
Despite the loss of the term "stationary", there is something we can do to push forward.
Although this does not constitute a complete, new definition of "stationary" yet, we can comfortably define any particle as being stationary relative to itself. Although its actual location and relational momentum are random, its waveform does not change relative to its own waveform.
Careful! As I have discussed at length, in Quantum Relational space, no single particle can really be said to exist in the absence of a reference particle against which we can define its properties. Therefore, my definition of a particle being stationary relative to itself doesn't actually hold.
However, consider this: when we do finally build a complete definition of the word "stationary", other particles will then be granted the ability to define themselves as stationary relative to other particles, and if they are stationary relative to each other then our day to day sense of the word "stationary" suggests that we ought to define each particle as being stationary relative to itself. This idea can be extended so that it works even when a particle defines itself as moving and defines another particle as stationary.
A Look at the Origin
Before continuing with our reconstruction of the word "stationary", we will take a look at the word "origin". Origin is simply another word for "the point of reference". In any Cartesian coordinate system, it is the zero point in all dimensions. It is tied in very tightly with the concept of a reference frame.
In both classical and modern physics, the choice of origin may be defined as an arbitrary point "in space" rather than an actual particle. In General Relativity, although the properties of space are dependent upon the distribution of mass and energy within space, it remains true that we can talk about reference frames independently of any reference particles.
For Quantum Relational space, I will insist that for any given reference frame, we must always choose a particle as our origin.
You might question my reasons for doing so. It seems logical to assume that, regardless of whether or not a particle isactually placed at the origin, simply flagging a location as origin is sufficient. I agree with this logic in part and will admit that it works just fine in General Relativity.
However, this is a dangerous step to take in Quantum Relational space. The language of General Relativity is spacetime, i.e. location and duration, but the language of the Quantum Relational model is relative location and relational momentum. Reducing momentum to mass and velocity and then forgetting about mass means we're likely to lose something in translation. It is therefore important to transform the relational momentums properly in addition to transforming the relative locations.
Besides, it is a short journey from granting a point in space an identity to granting space itself its own identity which, as I have repeatedly advised, simply cannot be done in Quantum Relational space.
Therefore, it just easier to keep track of the origin by simply allowing a particle to exist there, once and for all. Each frame of reference will have its own origin particle O and the particle will always be stationary within the frame (with "stationary" being defined as I have rebuilt it so far; i.e. stationary relative to itself, so to speak).
"Stationary" - Completing the Definition
So far we chosen to define particles as stationary relative to themselves and we've chosen to always use an origin particle in our reference frames, defined to always be stationary at the zero point of the reference frame.
Note that if we decide to start adding more particles, there are an infinite number of isomorphisms as those particles start moving. As I mentioned in Incompatibilities with Modern Science, we get an infinite number of isomorphisms even with two particles, even when one particle is defined as a permanent origin.
Therefore, whether a particle is stationary in the frame comes down to our choice. We can freely define any particle as stationary relative to the origin, granting it the same qualities as we would grant a particle which is "stationary relative to itself"; i.e. a waveform which is unchanging relative to its own waveform.
Note that although we are initially free to define a particle as stationary relative to the origin, any subsequent choices are restricted and become increasingly restricted depending on how many particles whose movements we have assigned. If the origin is stationary in the frame and a secondary particle is stationary at (0, 1) on a two-dimensional Cartesian coordinate system, then we may no longer be able assert that a third particle is stationary.
For example, say that you have three particles in the frame: origin O, particle A and particle B. We may be equally justified in asserting that:
(i) A is stationary at (0, 1) while B is running off to infinity along the negative x-axis
(ii) A is approaching the origin at an infinitely decreasing rate while B is stationary at (0, -1)
any other isomorphic scenario, possibly with the particles approaching or receding from the origin at variable rates
However, in this example, we could never assert that, for example, both particles A and B are approaching the origin.
Inertial versus Non-inertial
The irksome quality of the definition as I have given the word "stationary" is that there is no quantitative difference between inertial and non-inertial. The allowance of isomorphisms that I've woven into the definition of the word imply that the difference becomes merely arbitrary choice between what is stationary, what is moving inertially, and what is moving non-inertially.
This quite effectively kills any hope we may have had of recovering Galilean Relativity, Newton's First Law, Special Relativity and General Relativity. Basically, major portions of modern physics are destroyed.
As I suggested at the beginning, I would still like to continue down this path of logic to see what results we'll find, though they may be incorrect. We can still hold quantum physics to be true, because it is far less dependent upon Newtonian physics.
Building a Clock Simulation
For now, I'm going to restrict my considerations to a one dimensional universe.
Even in one dimension, the clock is a bit of a complicated device. We'll require a total of three separate particles, excluding any other particles that may actually want to make use of the clock. They are -
the origin, O: the relationships of the moving parts of the clock will be defined in relation to the origin in this frame of reference. In other words, although some parts of the clock move, the clock structure itself is effectively stationary in the frame.
the gnomon particle G: we will arbitrarily define the gnomon to be stationary at a fixed distance from the origin in this frame of reference. It indicates the length of a "clock tick" (as well as defining dimensional length and orientation in a one dimensional Euclidean space). The word "gnomon" is, to quote Wikipedia, an ancient Greek word meaning "indicator", "one who discerns," or "that which reveals."
the shadow or clock particle Φ: This particle travels along the axis in the direction from O to G at a rate defined all other particles as constant. It measures the passage of time (or at least the passage of the simulation of time in this context), serving the same function as the shadow on a sundial.
Unlike particles O and G, which can be chosen at random from the particles available, the shadow particle Φ must be expressly chosen so that it has following relationship to the other two clock particles: it travels along the axis in the direction from O to G (its actual location being irrelevant) and its relational momentum is such that the ratio of distances from it to O and from it to G is always u/u-1 for some u. The distance variable u is defined by all other particles to be increasing at a constant rate as the universe changes naturally, i.e. as "now" advances.
The purpose of enforcing the u/u-1 ratio is so that the scenario is isomorphic to one where O is stationary at x=0, G is stationary at x=1, and Φ is travelling at a constant rate in the positive x-direction. In this way, the clock "ticks" every time the shadow particle measures a distance ΔΦ = |u - (u-1)| = 1, so all particles can measure durations using it.
I'd like to repeat the point made earlier that, without Newton's First Law, we have no way to know beforehand which particles are "really" stationary and which are "actually" moving or accelerating. As discussed, in Quantum Relational space these decisions are arbitrary and, for all we know, the "speed" of the clock could vary or go in reverse.
However, precisely because the decisions are arbitrary, by simply asserting them, all duration measurements that are based on this clock will work out to be accurate relative to everything else that measures time with the same clock. These assertions are similar to the decision of where North points. As long as everyone agrees, we can all build consistent maps.
This reduces the question of whether each and every particle in the entire system is moving as it "really" would, down to the singular question of whether a few key particles (the origin and the gnomon) are moving as they "really" would for all time. The clock would then work best if we choose particles with relational momentums that match our expectations most closely. In other words, the best clocks consist of the particles most likely to operate like the parts of a clock.
In any case, we have enough that we can start constructing simulations of time-dependent laws of physics.
Reinventing the Wheel
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Velocity in Quantum Relational Space
Now that we have a clock, the next useful tool to construct is an equation of velocity. The equation of velocity is arguably the simplest in physics, defining movement in a straight line. The traditional equation of velocity is: v = x / t
Note that for this discussion, I will be dodging a rather major assumption about velocity as we currently understand it. Without Newton's First Law in place, we have no reason to think that the particles ought to be moving at constant rates or even in a single direction when in the absence of forces. This is even after we've taken time into consideration as it is modelled using the clock defined earlier.
Fortunately, I am able to cheat to define velocity in a way specialized for my purposes: though a particular particle may not rely on Newton's First Law to maintain a single velocity over a large distance, given that at least some kind of movement is possible in our Quantum Relational universe (as discussed in Stepping Around Time), I can consider a particle as having an infinitesimal velocity over an infinitesimal amount of distance, or at least I can consider its waveform as having a velocity since the particle itself is fuzzy. This instantaneous velocity is the only variable I'll need to consider for now.
The next problem with the traditional equation is the time variable, t, since the fundamental version of time does not exist in our Quantum Relational simulation. Instead, we need to use our own clock simulation. Time is therefore measured by the distance travelled by the shadow particle Φ, as compared to the standard unit of measure in a given reference frame, |O-G|.
A simple substitution will resolve the traditional velocity equation into one that is compatible with Quantum Relational space: dv = dx / dΦ.
As this new equation highlights, velocity is now simply a ratio of distances; namely, the distance covered by a particle as the shadow particle crosses an infinitesimal fraction of the distance |O-G|. The fact that both variables dx and dΦ are units of distance means that velocity actually turns out to be a unitless factor. You may rename the units of distance crossed by the shadow particle to be something else, such as "seconds", but I will avoid doing this. Although the results will appear more familiar and comfortable, I expect that this will introduce needless complication later.
The Assumptions behind the Galilean Transformation
Galilean Relativity and, its predecessor, Newton's First Law are based on the following assumptions:
time is fundamental, and is independent of its measurement
straight-line movement in space makes sense when talking about a lone object
constant, straight-line movement of an object is equivalent to the object being stationary when it comes to the universal laws of motion/mechanics
length measurements are not affected by the speed of a particle
Point #1 was somewhat modified by Einstein when he suggested that time itself was a dimension similar to space, but point #1 effectively survives in modern theory. Rather than having a universal time, we now have the concept of personal time.
I'll describe now in what way we are failing to make the above assumptions, point by point.
1) Time is fundamental
As should be obvious by now, time is not fundamental in Quantum Relational space. Instead, time is an emergent phenomenon that comes from:
the natural relative changes in the universe, which themselves come from the uncertainty in relative position and momentum between particles
arbitrary assignment of being "stationary" to certain particles, in order use them as a reference to measure time
This construction does not quite give us time as we know it in our day to day lives, but it's already very different from the idea of time being a fundamental quantity.
2) Straight-line movement makes sense
It should also be fairly obvious that, given our construction of Quantum Relational space up to now, the idea of a lone object moving in a straight-line in space doesn't make sense in it. We cannot talk about the properties of lone objects, nor can we talk about straight-lines in space without reference to anything.
One object can travel by another in a "straight line" only by some serious artificial movement. If we have other particles to define a Cartesian coordinate system, the two objects themselves will observe each other to be approaching at a decreasing rate, becoming momentarily relatively stationary, and then accelerating away from each other at an increasing rate.
3) Constant velocity is equivalent to being stationary
I want to highlight this point in particular, because it represents a huge divergence of the Quantum Relational model from modern physics.
As natural as it feels, nothing in our model of Quantum Relational space gives us any reason to believe that constant, straight-line movement and the state of being stationary are equivalent when it comes to the laws of physics, even taking into account point #2, that straight line movement only makes sense in reference to some particle.
Originally, it was taken to be true by Galileo based on plain experience, and it's an experience so ubiquitous that it seems ludicrous to disbelieve the assumption. However, I'm choosing not to trust experience now and am going to fail to make this assumption.
4) Length measurements are not affected by the speed of a particle
Einstein already tackled this assumption behind Newtonian physics, and brought science into a new age by taking the next step and inventing Special Relativity. I won't be discussing this point much more from now on, but it should be interesting to note that failing to make this assumption (i.e. by wondering how length measurements are affected by the speed of a particle) automatically implies that measurements of time in Quantum Relational space are highly suspect, since time is no more than a measurement of distance of the shadow particle in your clock.
The precise way in which time and space are affected is covered in the Lorentz transformation in modern physics. We'll have to rediscover on our own what happens in Quantum Relational space.
The Assumptions behind Einstein's Special Relativity
I'm not even going to try to reinvent Galilean Relativity at this point, because it turns out to be incorrect and is instead a limiting case of Einstein's Special Relativity anyway (i.e. the Lorentz transformation).
So lets jump right into trying to simulate Einstein's Special Relativity. We've abandoned the major assumptions of Galilean Relativity so let us now consider the assumptions behind Special Relativity.
According to ..................., these are:
The Principle of Relativity – The laws of physics should be the same for all observers in uniform motion. All uniform motion is relative.
The Principle of Invariant Light Speed – The behaviour of light is correctly described by Maxwell's Theory of electromagnetism. The speed of light is the same for all observers in uniform motion.
The Principle of Relativity is effectively Galilean Relativity which, as discussed above,
Gravitational & Inertial movement - Wave Relativity
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If we introduce a second dimension, we now get an even greater array of strange possibilities.
Let's arrange three objects named A, B, C. We'll call A the observer, so that he's the object doing the measuring and philosophizing. We'll only be arranging the objects in a 2D plane for now and the observer, object A, will be fixed at location (0, 0).
In arrangement Alpha, B is fixed, unmoving at (0, 1), and C is starting at (1, 0) and is moving in the +x direction at an increasing rate to infinity.
In arrangement Beta, B is placed at some (0, 1) and then travels towards (0, 0) at a decreasing rate to zero, with the limit at (0, 0). Object C is fixed at (1, 0).
Think carefully about these two arrangements. If you choose the rates of movement carefully, you produce isomorphicscenarios, where "isomorphic" means that the relative proportions of all components of each scenario are the same.
To modern astrophysicists (or even Galileo), this is merely an interesting mathematical trick with no bearing on reality since acceleration is measurable. Therefore, we can distinguish between the two arrangements. Is C detecting acceleration? Then we're dealing with arrangement Alpha. Is B decelerating? Then arrangement Beta is the case.
However, our model shows a solid deviation from Galilean Relativity. As I mentioned earlier, in our model, acceleration is a relationship between objects and cannot be detected absolutely. Therefore, the two arrangements are not just isomorphic butequivalent. There is no way to distinguish between the two situations in Quantum Relational space.
NOVEMBER 28, 2014 - backup of Blain Laboratory Introduction
So I just lost the original version of this particular post. Meh, it contained nothing I can't rewrite. ANYWAY, so the purpose of this post is to sum up what I've got so far. I've reached a critical point in my research.
When I began my journey, I treated the physical theories of science that already exist as "Innocent, until proven Guilty". Whenever I had a difference of opinion with a physical theory, it was significantly more likely that my opinion was based on too limited information than it was that the physical theory was incorrect. (Actually, it is more accurate to say that I made my own foray into understanding these theories, but treated physical theory as "the answer book" to show me where I was missing information or making mistakes in my assumptions.)
However, I have come to point where I'm confident that I know all there is to know about Special Relativity - what issues evoked a need for it, how it resolves those issues, the mathematical mechanics of how it works, and how the engine core of Special Relativity (both in theoretical terms and in mathematical mechanics) has spread out to General Relativity and by extension, all of Cosmology.
I have also identified what my instincts have been forcing me to seek out. A tiny (literally point-sized) gap in the mechanics, where the Lorentz transformation doesn't quite solve the problem it is meant to solve. Though tiny, the point-sized problem explodes into a major issue in General Relativity, defeating it as a proper theory of gravity. I also strongly expect that a correction to the theory will show dark matter, and possibly also dark energy, to be artefacts of General Relativity, an incorrect model of the universe.
This is why I'm now adopting a more offensive approach. Given that I can identify the location of the problem, I can then trace it through physics, and I can confidently say which physical theories can be left alone and which need to be recalculated.
My goals now consist of the following -
- Create a conceptual model of the corrected Special Relativity
- Build the mathematics corresponding to the conceptual model
- Rebuild the equations of relevant physical theories to match; i.e. mechanics and electrodynamics
- Extend the mathematics of the corrected Special Relativity into a general equation of gravity
Special Relativity is a touch incomplete.
The incompleteness is difficult to spot, and it will be easier to demonstrate if I first compare the Galilean transformation (where the velocity of a baseball relative to Earth is u+v, if the velocity of the train carrying the thrower is u) and the Lorentz transformation, used by Einstein to maintain the speed of light relative to all observers in different inertial reference frames.
Two notable effects of the Lorentz transformation are length contraction and time dilation. Lengths of the observed object (like a baseball thrown from a train) are shortened along the direction of motion and it experiences time ticking away at a longer relative rate than a person watching it standing on the Earth. That way, both the baseball and the person standing on Earth see the light leaving the train headlight at the same velocity.
For straight line movement at constant velocity, it is a single transformation but for non-inertial movement (i.e. accelerations, rotations, or revolutions), the situation is more complicated.
Rotations, as mentioned, do not appear to maintain inertia. Let us confirm by finding out what happens when a Galilean Laboratory is rotated about the center, and we'll fire a beam of light towards the center.
The perspective of the spinning person is also natural. As the ball comes towards them, the baseball veers left and right in their field of vision. Humans are equipped with biology so that we still generally understand we're spinning and ball is moving in a straight line, but if we're watching a video of that person's perspective, it's not necessarily obvious. Is the object onscreen moving left and right, or is the camera operator rotating around?
Einstein knew that an application of the Lorentz transformation was required here. He reasoned that the outer edges of the spinning Laboratory are moving at a greater velocity than the center, and therefore are subject to Special Relativity to a greater degree than the stationary center, and that the effects of Special Relativity are increasing from the center to the edges. The circumference of the Laboratory shrinks by length contraction, an effect of Special Relativity, and experiences time at a dilated rate compared with the center. By this, he reasoned that the spacetime of the laboratory "bubbles up". You might have seen videos online of how matter affects the fabric of spacetime by creating a dimple in the fabric.
If the Laboratory is rotating wildly back and forth, clockwise and counterclockwise, then it dimples and undimples spacetime with its movement. The Laboratory shrinks and expands again to its stationary size, and the edges of the Laboratory move slightly ahead in time before equalizing with the center again as a clockwise rotation turns into counterclockwise, and visa versa. In short, an observer on Earth sees the Laboratory undergoing some pretty spectacular effects in terms of length contraction and time dilation. However, an observer on Earth sees the beam of light head straight towards the center of the laboratory at the speed of light, exactly as required.
From the perspective of an observer inside the Laboratory, many experiments do not perform as expected, and some might even throw themselves against the outer edge of the Lab. An observer looking outside the Laboratory would see the universe itself shrinking and growing to normal size, and time dilating, as required by the Lorentz transformation to keep the speed of light constant for all observers. The path of the beam of light itself becomes difficult to calculate, with all the length contractions and time dilations going on around it, but it is a warped version of the path from Figure 1b.
Notice that in all of the previous examples, we used the Galilean Laboratory. It is large and spacious, and sensitive to rotations. When a beam of light approaches the Laboratory from the outside, the scientist in the lab can determine what part of the lab detected it. I'm now going to attempt these experiments with the Blain Laboratory, which is a single point rather than a large, spacious laboratory.
When the photon begins it's journey from the emitter (stationary on Earth) towards the Blain Laboratory, we are also stationary with respect to Earth, and so the photon travels at the speed of light as we expect. It hits the Blain Laboratory on-time and at the proper velocity.
However, something strange happens when we observe from the perspective of the Blain Laboratory. The Laboratory is zero-dimensional and therefore has no implicit orientation. With no implicit orientation, we cannot determine how Lorentz transformation applies. If the Blain Laboratory is stationary (i.e. not rotating), then the Lorentz transformation reduces to the regular Galilean transformation and light is travelling at the speed of light toward us, but we can't guarantee that. If the Blain Laboratory is rotating wildly (as in previous examples), then we need to know its precise pattern of rotation or else we cannot properly account for it to correct the speed of light, and we risk losing the correct speed of light. The physics inside the Blain Laboratory would be thrown into utter chaos.
We seem to be stuck in a sea of confusion. Fortunately, Einstein left us a lifeboat.
When I began my journey, I treated the physical theories of science that already exist as "Innocent, until proven Guilty". Whenever I had a difference of opinion with a physical theory, it was significantly m