Is reality a mathematical construct?

"As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality."

"How can it be that mathematics, being after all a product of human thought, which is independent of experience, is so admirably appropriate to the objects of reality?"

Albert Einstein
Spacetime of special relativity. © K. Aainsqatsi at Wikipedia

1905 – The end of the Newtonian Universe

The publication of Albert Einstein’s special theory of relativity in 1905 should have marked the end of the Newtonian view of reality as a stage made up of permanent unchangable objects. Quantum physics just emerging at the time would further undermine that image. Yet apparently that end has not yet really sunk in. Many scientists who are not very skilled in physics still use the old billiard ball model of the universe as the model of reality

Special relativity is a special case of general relativity – also called the theory of gravity. This special relativity is a theory about observers moving uniformly with respect to each other – that is, without accelerating or decelerating – in which gravity plays no role. In order to achieve some understanding let’s put Alice and Bob back on the scene. That’s a bit easier to follow.

Each of those two will experience and also regard itself as at rest while the other is moving. Each will find that the other’s clocks run slower than their own one and that the other’s rulers are shorter than their own ones. This effect becomes larger as the difference in speed increases and only becomes noticeable when the difference comes close to the speed of light. But these differences are in principle always there. If Bob is standing along the highway and sees Alice driving past at 100 km/h, Alice’s clock will slow down from Bob’s viewpoint and her car will have become shorter. As far as he’s concerned, Alice has also gained a utterly tiny bit of weight. But Alice does not speed up or slow down, she considers herself and everything in the car at rest, and sees Bob passing by at 100 km/h. For her, Bob has gained a little weight, Bob’s clock runs slower and his waistline is shorter than when they walked an hour ago together.

For a more detailed explanation, read my post of October 18, 2020: Einstein and the speed limit of the universe

Not an illusion?

Space becomes curved by the presence of mass and according to the general theory of relativity we experience curved space as gravity . The image below attempts to clarify that effect – in vain as far as I am concerned. The mass of the earth distorts the two-dimensional texture of space. However, we live in in three dimensions and we cannot image a fourth dimension to make curves in three dimensional space. On top of that, to explain the dent the earth makes in the two-dimensional texture of space you still need gravity pulling the earth down. But mathematically it all makes perfect sense.

Gravity curving two-dimendional space time

‘These relativistic effects are not an illusion’ did a physics teacher assure us in a course in 2018, ‘They are real’. Relativistic effects have indeed been confirmed experimentally. Any GPS device has to take into account that the clocks in the satellites are running faster than on ground level – 38 microseconds faster in 24 hours. Also think of particle accelerators like the Large Hadron Collider in Geneva, where protons travel in an underground circular tunnel with a diameter of 8.4858 km at 99.996% the speed of light to collide eventually. In order to keep those protons in their circular orbits, the relativistic increase in their mass, a factor of 112, has to be taken into account to dynamically adjust the strength of the superconducting magnets according to their relativistic masses.

CERN – Large Hadron Collider (LHC)

Really?

What did the teacher mean by ‘real’ here? That it is a measured effect and therefore true? In our ‘real’ experience, it is apparently the case that massive objects moving relative to us exhibit behavior that we cannot reconcile with the way we understand our daily reality. That is a reality that is made up of tangible massive objects that only deform when we exert forces on them. But those forces are not there in objects that move at constant speeds relative to each other. Don’t forget that those speeds are relative to each other. From Bob’s point of view he is at rest but from Alice’s point of view he moves at 100 km/h and his rulers are shorter than hers. In short, this is utterly incomprehensible if we want to maintain and understand the idea of an objective world outside us made up of massive material objects.

The Relativity Express – pag. 9: At the same moment Agent X spots the steeple clock, leaps from his seat in disbelief and rushes to the car door to check the clock on the flatcar. Sure enough, it says 12:40, although the steeple clock reads 1:00. “Ye gods!” he shouts. ” That steeple clock must be wrong! It must be fast- or else it was set wrong! I know the train clock was correct back at the master time station.” The whole plan is in danger! In near- panic, X looks for the conductor to tell him that the world has gone mad; the clocks are all wrong.

Click on the picture for the full pdf.

Reality as a mirror reflection of the Cosmic Mind

Relativistic effects, on the other hand, are very well to comprehend if we alter our perspective on reality by starting to understand our observations as projections of the content of the cosmic mind. Those observations are the reflections of the contents of a cosmic consciousness in the mirrors of our individual minds. That one great cosmic consciousness observes itself by its reflections in those myriad mirrors that living beings are. So, we are mirors of the contents of the cosmic mind. That reflected content behaves according to mathematical laws because the content of the cosmic consciousness is very probably the source of the mathematical laws Einstein found so admirable appropriate. This is by no means a new idea. Now may begin to understand why mathematics, a product of the mind, corresponds so well to observed reality. The math and reality we experience are both products of the mind*. The reality we see reflected in that mirror of our mind is a mathematical construction.

Material infinities, are they possible?

Also consider black holes. When the possibility of black holes was first suggested, that idea was rejected by most physicists. Their rejection was based on the fact that, according to general relativity, a black hole had to be a singular point, which is a mathematical infinity. A point without dimensions containing an enormous amount of mass. In a Newtonian universe made up of a countable number of material objects, material infinities cannot exist. Yet these days black holes are generally described and taken as actually existing. We even have a photo of it. But most people still live in a material reality made up of finite numbers of massive objects. Thats twisted thinking.

The first photo of a black hole, existing in the Messier 87 galaxy.
© Event Horizon Telescope Collaboration, via National Science Foundation

The measurement problem of quantum physics goes away

That the world is a projection or reflection of the contents of cosmic mind has also been proposed by me in my book as a solution to the measurement problem in quantum physics. The measurement problem is, in a nutshell, the idea in quantum physics that every object is a coherent* non-material probability wave, extending in principle everywhere in space, that ends abruptly in the material manifestation of the object the moment it is measured . How the measurement mamages this cannot be explained by a purely material view of the universe. But, in the idea that the world is a projection of the contents of the cosmic consciousness, perception has become almost identical to creation. Material existence is, like its observation, also a mind phenomenon. In your mind, rulers can shrink just fine and clocks will tick slower without any problem. Think about dreaming.

A reading tip: Lothar SchäferInfinite Potential.

(*) A wave is a coherent phenomenon. How the quantum mechanic non-material probibility distribution comes to possess coherence cannot by explained by a material view of reality.

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