Matrix Theory: Relativity Without Relative Space or Time

[Music] Let us consider a classic relativity scenario. Your friend gets on a rocket ship and blasts off towards Mars at nearly the speed of light. During this journey, his clocks tick slower, his lengths contract, and when he arrives at his destination, he has aged less than everyone back on Earth. But that's not the only side to this story. Because from your friend's perspective, events transpired somewhat differently. His clocks actually ticked at a normal rate, and it was in fact the distance between Earth and Mars that was contracting, allowing him to reach his destination in a shorter time. Meanwhile, before he reaches Mars, he perceives that less time has actually elapsed on your clock since you were traveling at near the speed of light relative to him. Only once he decelerates to land on Mars will his and your perception of time and space once more be reconciled.

This is the theory of relativity in a nutshell. A theory often described by the average person as totally trippy. Though mathematically consistent, the theory offers no vision of a shared reality for its observers, and upon its conception, it ushered in a reign of conscious-centric solipsism, an unphysical ratio signation that has endured uncontested for nearly a century and a quarter. Well, today, get ready to unplug because it turns out there is a completely physical explanation, one devoid of any notion of relative space or time, that we can give to this picture.

This is dialect, and welcome to Matrix [Music]. Theory there exists before you a pencil that one day inexplicably shrinks. Now you'd like to use physics to explain why this pencil shrunk, but coming up with an explanation is, well, difficult. You see, you'd have to posit some sort of physical mechanism or maybe chemical process to account for this contraction, which would involve a lot of speculation and theorizing, and gosh, that sounds like hard work. But then you have a brilliant idea: why do physics when you can just do math?

That is, you realize you can assert that nothing physical actually happened to the pencil at all, and instead of the pencil shrinking, it was in fact the background that grew. See, the pencil started out at 5 units of length relative to the background, but once the background grows, it now only spans four units of length. So it was the coordinates that actually shrank, not your pencil. Indeed, you claim that the length of your pencil is absolute or invariant. Then you fix a local background to it such that your background never grows, your pencil never shrinks, and you never have to do any physics. Woo! Job well done!

But now, along comes another observer with a pencil that also inexplicably shrinks from 5 to 4 units. You demand they give a physical explanation for this, but they aren't having it. If you don't have to do physics, why should they? Indeed, they claim their pencil is the invariant one, and yours is the one that actually shrank. You see, they assert that because your pencil shrank, you grew your background to compensate for this shrinking and that you are using this inflated background to see their own pencil, which of course now appears to span fewer coordinates.

Now, this catches you off guard at first, but being clever, you realize you can turn this argument around on them and say no, your pencil never shrank. Rather, as you first asserted, their pencil did, and they are the one wielding an inflated background to thus see your own pencil as shortened. Now, in the absence of any global background, there will be no way to know which of you is telling the truth. Worse, if you manage to bring the pencils side by side for comparison, they are found to be the same length, meaning each of you can now claim that the other's pencil physically grew upon leaving its frame, causing its observer's respective inflated background to deflate and thus for them to see a corresponding growth in the opposite pencil. Indeed, in this construct where all observers are equally entitled to not doing physics, one beholds in lieu of any actual explanations just symmetry, perfect, beautiful mathematical [Music] symmetry.

What is? How do you [Music]? Special relativity is undoubtedly a mathematically beautiful symmetric theory, but there has always been another explanation; that is the Lorenzian one. The one which posits the existence of an all-pervading ether through which light travels as a wave at a constant velocity. According to this interpretation, clocks in motion with respect to the ether physically tick more slowly, while objects in motion physically contract. Formalistic, this yields a theory that is equivalent to Einstein's, capable of making all the same mathematical predictions as well as explaining all the same experimental findings.

Despite this equivalence, for much of history, these theories have been viewed as dichotomous opposites, distinct and competing interpretations such that one can only be championed at the expense of the other. But this bad blood has led almost everyone to overlook something extraordinary and critical: Einstein and Lorenz's theories are not merely just formalistic equivalents; rather, they are in fact two indispensable halves of a greater whole. Taken apart, neither achieves true logical coherency, but together, they can produce a theory with unrivaled explanatory power.

To understand this union, let us start by observing that what makes Lorenz's Theory unique is its fundamentally ontological nature. That is, it offers us a hypothesis about what constitutes the real world, meaning the world whose existence is not relative to our perception of it. Indeed, prior to Einstein, every advancement in physics generally required making such a hypothesis to explain the workings of the universe. A physicist or natural philosopher was expected to propose some sort of physical content which existed outside of the mind and would serve as the causal mechanism for observable phenomena. Mathematics was then employed to help make these models precise and better describe such phenomena.

Since Einstein, however, the offering up of physical content is no longer in vogue, and math, instead of aiding in the description of observable phenomena, now serves as the cause of those phenomena. Relativity initiated this trend, for as Einstein himself admitted, special relativity was never a theory about reality; rather, it was only ever a theory about measurement, a convenient mathematical framework. But by failing to offer any physical content, the theory's mathematics was soon latched onto as being its content.

Fast forward 120 years, and you have a shocking number of physicists who sincerely believe that it is hyperbolic manowski and geometry which causes rather than merely describes time dilation and length contraction. But the representation is not the reality, and we can see that Einstein's theory was, as opposed to being ontological in nature, rather merely epistemological. To unify it with Lorenzian ontology then requires advancing what is termed the Matrix hypothesis.

The hypothesis is simple; it posits that there is a real world, a world of physical causal content existing independent of our minds, but that our perception of that reality does not and may not ever align with the actual thing. Indeed, math measurement, language, abstraction—the things which modern physics asserts causes observable phenomena—these things, in truth, belong to the world of perception and consciousness, encasing our minds there like a womb, one to which we may be forever irrevocably plugged in.

[Music] In the real world, there exists the medium of the Ether and some singular frame in which it is physically at rest. Clocks that are set in motion with respect to this medium will tick more slowly, and objects set in motion will physically contract. This is the first half of the picture—the Lorenzian half. The second half of the picture is what happens when the observer is put in motion with respect to the medium. Here is where the observer enters the Matrix or, as a consequence of Einstein's Axiom, begins to construct a false projection of their reality that does not correspond to the actual one.

To understand this, let's imagine an observer traveling at near the speed of light relative to the medium. When they fire a beam of light in the direction of travel, this beam moves at a constant speed C through the medium. Relative to the observer, the beam thus travels very slowly, but thanks to the one-way speed of light problem, an observer has no way of knowing this. They can only make a judgment about what this speed of light was relative to them once the beam has bounced off of something and returned to them. What Einstein's Axiom stipulates then is that the simplest assumption mathematically the observer can make is that the light beam traveled at the same speed there and back relative to them.

But this assumption is only mathematical, not physical. And of course, back in the real world, the light beam did not travel at the same velocity relative to the observer there and back. The observer, therefore, has to adjust their notions of time and space in order to maintain this assumed isotropy. This is where the relativity of space and time comes from. It's not a metaphysically deep discernment of what reality is or is not; rather, it's a mathematical contrivance intended to sidestep our inherent uncertainty in the knowledge of the one-way speed of light.

To understand how this works, let's divide the world of two given observers into four essential partitions. In the first two partitions, each observer has their own local frame, which encompasses anything co-moving with them and which can be constructed using physical objects such as rulers and clocks. But these frames can't be used to make physical measurements for things in motion relative to them. For this, an observer needs a second frame—a background frame. This background frame is not physical but rather mathematical, and it is constructed via interpreting information from incoming light signals. Indeed, for this background frame to represent something physically real, the assumptions about the behavior of light which go into constructing it must correspond to the actual behavior of light.

So, say our two observers start out at rest with respect to each other and to the Ether. If they construct their backgrounds assuming that the speed of light is everywhere constant and isotropic, as it truly physically is in the Ether frame, then their local frames and their background frames will all perfectly align and everyone sees each other exactly as they are. But now if we put one of the observer's frames into motion, two things will happen. In accordance with Lorenz's Axiom, the lengths of the moving frame will physically contract, and the lengths of its temporal durations will dilate.

Let's consider first just the spatial aspect of the problem. Since the background of the unmoving observer remains unchanged, they see the moving observer as they truly are—physically contracted. But now the moving observer has a choice. If they accept that they are in a moving frame, meaning they accept that light behavior in their frame is anisotropic, then consequently they can maintain the validity of the original background, and they will agree that the unmoving observer is longer than themselves.

But if they want to maintain the idea that light behavior in their frame is still isotropic, that is, if they want to reject the notion that anything physical happened in their frame, then they will have to remap their shortened lengths back to the proper lengths they had in the original Ether frame. But remapping or growing their lengths means growing their background as well, and since the moving observer has to use this background to see the non-moving frame, the non-moving observer will now appear to be contracted relative to them, even though of course it's their own lengths which are truly physically contracted.

Less abstractly, we can reframe this by saying that as a moving observer's lengths physically contract, in order to offset this shrinking and continue maintaining the invariance of their proper length, the observer's notion of what constitutes length must consequently grow. Traveling at high velocities relative to the medium thus causes an observer to perceive lengths about them contracting, all the while in reality it's their own lengths which are physically contracting. Similarly for time, as a moving observer's temporal durations physically dilate, their notion of what constitutes time must consequently contract in order for them to maintain an invariant proper time, and thus relative to them, other clocks will run slow.

One may clearly recognize in this the mathematical principle of contravariance; that is, since any measurement involves both an amount and a unit, one can always compensate for a decrease in amount by increasing their notion of what constitutes the unit. Alas, this contravariant interplay between an observer's local and velocity dependent background means an observer can always claim that their shortened lengths or dilated times aren't actually physical but rather the consequence of other observers in motion wielding inflated backgrounds.

Between two observers then, if both refuse to acknowledge any physical difference between their local frames, what you will arrive at is a theory with perfect symmetry but zero physicality. You are thus trapped in the Matrix. But if you already know, how can I make a choice? Because you didn't come here to make the choice— you’ve already made it. You're here to try to understand why you made it.

At last, we're ready to go back to our initial scenario and ask what really happens when your friend gets on a rocket ship and travels to Mars. Well, essentially, there are two main cases we can consider. In the first case, we start by assuming the Ether is at rest with respect to the Earth and Mars. In this case, when your friend travels at near the speed of light, his clocks really do physically slow down, and so he arrives on Mars having aged less than you. He, meanwhile, only perceives the distance between Earth and Mars to be contracted in contravariant consequence to his own lengths actually physically having contracted. Likewise, he also only perceives your clocks ticking slowly in contravariant consequence to his own temporal durations being physically lengthened.

Now in the second case, we instead assume that the Earth and Mars are in motion with respect to the Ether, and moreover traveling through it at a velocity such that your friend is actually at rest with respect to the Ether during his trip. Now in this case, the distance between Earth and Mars is really physically contracted, but since you on Earth are in motion, you map that shorter distance as being longer than it is. Once your friend is at rest relative to the Ether, his lengths physically grow and consequently he no longer maps the distance between Earth and Mars as being longer than it is, and thus the real contracted distance between Earth and Mars is revealed to him. His clocks then tick in accordance with true time during his trip while yours tick slowly until he decelerates to land on Mars, during which he will be required to start remapping both lengths and times.

Once more, between these two cases, we can note that the end results are exactly the same, making it impossible to distinguish between them. That is, it's impossible to know whose time dilation and whose length contraction were physically real and whose were merely a result of coordinative constructions. This isn't some conspiracy, however, but rather the consequence of reaching an epistemological ceiling—a possible limit to our knowledge. To be an observer fundamentally means to live in a matrix of our consciousness's own making, and relativity was the first theory to fundamentally strike up against this fact: this Platonic barrier.

Indeed, Einstein's most striking insight was in recognizing that before we as observers can even make any empirical measurements at all, we have to make a choice of background, which in the context of special relativity means making an assumption about the behavior of light. Now, as we discussed in our prior video, the particular conclusion Einstein drew from this insight was unfortunately wrong. As contrary to what he wrote, it is possible to define time without assuming invariant isotropic light behavior. Moreover, as we further demonstrated, by adopting the right set of synchronicity values, observers can always agree on notions of space and time.

However, even if we impose a master frame upon all observers, we could never be certain whether such a frame were truly the Ether frame, meaning we can never be certain if the time dilation and length contraction we observe relative to that frame are physically real or merely correlative. But a lack of certainty doesn't imply we should consequently reject the notion of physical objective reality. Indeed, to believe a light beam magically alters its behavior based on who is observing it, as Einstein's postulate has always undeniably implied, is the height of pseudoscience. If we want to escape such solipsistic thinking, if we want to escape the matrix, then we need only acknowledge that there is indeed a real physical difference between any two inertial frames in motion and that it is in fact the phenomena of time dilation and length contraction which precisely reveals this difference to us.

With all this in mind, we can now summarize the essential tenet of Matrix Theory as follows: First, there exist two types of time dilation and length contraction—the real world physical time dilation and length contraction, and the Matrix world coordinative time dilation and length contraction. Einstein's theory treats only of the correlative type and consequently offers no explanation for the physical type. Lorenz's Theory alone treats only of the physical type and consequently offers no explanation for the correlative type. In combination, however, the theories demonstrate that it is precisely the physical time dilation and physical length contraction of observers in motion relative to the medium which, in leading them to wield inflated backgrounds, causes coordinative time dilation and coordinative length contraction.

Secondly, the mathematical principle of contravariance requires a symmetric interplay between the correlative Matrix world and the physical real world. The highly prized symmetry of relativity is thus not a feature of reality; rather, merely a feature of mathematics—that is, of our own consciousness. Similarly, the inability to detect the Ether, or equivalently the one-way speed of light problem, is a consequence of the fact that all measurement is relative to the Ether. Thus, the Ether itself cannot be measured without invoking circularity, and this is in fact the source of relativity.

But of course, the mystery remains: what is it about motion relative to the Ether that causes physical time dilation and physical length contraction to begin with? Here is where the power of Matrix Theory really begins to shine, because more so than offering us an escape from mathematical solipsism, more so than revealing to us the interdependency of the Lorenzian and Einsteinian worldviews, we'll find that with a little hard work, Matrix Theory unfurls the causal mechanisms for physical time dilation and physical length contraction right before our very feet. Indeed, we are about to discover where all a truly physical theory of wave mechanics can lead us. This has been dialect, stay [Music] tuned.