The Mathematical Construct of Space Time is a Metaphor and it Does Not Curve Because Metaphors do not Curve and They Certainly Do Not Contain Atmospheres
Time is Not a Tangible Entity:
People with little physics training often like to think that Space Time is a real thing, and that the idea of Space Time fabric is some kind of tangible object. You can thank a lot of Hollywood science fiction movies for drumming this myth into people’s minds. Hollywood has done a great job of blurring the lines between real science and science fiction for many decades, and the nuclear fallout is people’s belief in a Space Time continuum. There is nothing like repetition to convince people that mathematical metaphors are real things.
First of all, Time cannot curve, obviously, because it possess no geometric properties. Time is merely a perceptual and conceptual metaphor, and not a solid thing. Concepts and metaphors do not curve. The curvature tensor in General Relativity is just a mathematical concept, where Time is not a tangible thing. In Einsteinian Relativity, Time was always a mathematical abstraction.
Space is Real But Outer Space is an Unproven Hypothesis:
In General Relativity, Gravity is nothing more than a deformation in the shape of space-time itself. It's the warping in the fabric of space-time due to the mass of an object. The Moon is said to revolve around the Earth not because of some invisible force but, because it rolls along a curve in the fabric of space-time that the Earth creates. This is followed by all the matter in the universe. The objects with more mass create larger curvatures within which the lighter objects rolls around it. Space has properties and mass as the matter does.
None of this is proven, however. We really have to buy into the concept as mentioned earlier that Space Time is real, and that it is the ultimate frame of the universe which surrounds us without any proof. It's kind of invisible to us. In the theory, the center of mass of an celestial object deforms Space Time and creates a bend towards it's center, and so small objects like ourselves are constantly being pulled towards the center. That is why it's called the “Gravity Well”'. Nevertheless, it only exists in Hollywood movies and in mathematics and not in the real world.
Further, Space Time in General Relativity was merely a way of visualizing and bringing into existence a kind of pseudo force of gravity in imaginary Outer Space to explain away The Second Law of Thermodynamic in relation to atmosphere being contiguous to a vacuum without it expanding outwards to fill the available volume of the comparatively low pressure existing in that imaginary vacuum without violating The Second Law of Thermodynamic. The Second Law of Thermodynamics has been proven to be a Law of Physics thousands of times in empirical experiments, whereas Space Time has never been proven to exits not even once using proper scientific methodologies that employ independent control variables.
It is 100% theoretical hypothesis.
There is not truly a fabric of Space Time, and this imaginary fabric does not actually curve. The math simply explains a mathematical derivation of an imaginary pseudo-Riemannian Manifold as it traces geodesics in imaginary Outer Space. Einstein created the idea of Space Time fabric and its curvature using math and pseudo- geometry to concoct a pseudo-Riemannian Manifold phenomenon in Outer Space that nobody can see, measure, detect, or verify. Throw into this imaginary pseudo-Riemannian narrative a lot of Hollywood science fiction movies with Black Holes, theoretical physicists with a penchant for hypothesis instead of testable science, and voila!, you have a pièce de resistance of imaginary Physics.
Subsequently, the entire narrative of Space Time curvature is discussion found in philosophy rather than empirical physics. As such, Space Time curvature is a philosophical position, not a testable scientific quotient. Similarly, Newton’s Gravity is also a tour de force of descriptive mathematics, but at no time does it give a causal antecedent to the math. It merely describes acceleration and motion, but not what causes that acceleration and motion.
Even Newton said this in his letter to Bentley in February 1693:
“That Gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters any competent faculty of thinking can ever fall into it.”
--Sir Isaac Newton: Letters to Bentley, February 1693
Even Sir Isaac Newton claimed that no force could act at a distance through Outer Space to affect the behaviors between two “Planets”. He said that his gravitational attraction equations were descriptions of how celestial bodies behave, but not any proof of Gravity existing between “Planets” in a vacuum as a causal force behind his descriptive mathematics.
The Fundamental Flaw of General Relativity:
Fundamentally, physics does not answer what is really happening but rather provides frameworks that predict observations to some satisfying degree of precision. One hope is that a “final” theory would be able to provide exact predictions to what we know from experiment, but ultimately all we know is the agreement of experiments with theory.
Specifically, General Relativity is one current mathematical model that explains the perceived force of gravitation as curvature. Theoretical physicists call this theory correct, but it has never been tested experimentally. Such a theory is typically interpreted as being hypothetical for the purpose of further inquiry, but strictly speaking, such a claim is pseudoscience as it is unfalsifiable. Hence if you are looking for a pure General Relativity answer, then Space Time is hypothetical curved because that is effectively the premise behind the speculative mathematics. .
A result of the current un-testability of all aspects of a General Relativity Theory is explicitly seen in the newer theory of Teleparallelism (or more accurately the Teleparallel Equivalent of General Relativity, TEGR), which re-creates Gravity as the torsion of Space Time. Within this framework, Space Time has zero curvature. How do we know which one is “correct”? We do not, and cannot know because there is no consistent predictions between the two theories. As such, General Relativity amounts to a never-ending parade of speculative hypothesis which are unfalsifiable, and therefore, invalid in terms of real empirical scientific research. If you cannot truly test your hypothesis using proper independent variable controls, you have nothing more than an unproven hypothesis. And this has always been the flaw of General Relativity.
The Myth of Time Dilation in Atomic Clocks:
The defining feature of Special Relativity is that when you accelerate in any direction with acceleration, “a”, you see clocks ahead of you by some coordinate, “z”, tick faster by a proportion az/c2, and clocks behind you tick slower by the same proportion. You can derive the general Lorentz Transformation from this, which states that if you are accelerating, there is a surface behind you at coordinate z=−c2/a, where Time appears to stand still.
Additionally, there is the idea of Gravitational Time Dilation, and it is a consequence of General Relativity. It is very hard to explain in any sort of field approach since those typically have universal time coordinates, and so you would have to postulate that the mechanisms in the clock depend in complicated ways on the field. Similarly, strong sources of Gravity called Black Holes have a “wall of death”, intrinsically, when viewed from a far-off distance. Clocks that fall into them appear to tick slower and slower as they fall, when seen from a far-off distance. But though the clock seems from the greater distance to stop, General Relativity allows you to calculate from the in-falling clock's perspective, and in that perspective, nothing special happens at this surface. You just happen to pass through it after some time, and then no more of your light can reach the distant observers who were looking at you. So the natural language of the theory does not permit you to say objectively that the clock “stops”. Rather, it allows you to see things also from the clock's perspective where it does not stop. This would be even harder to do on a flat background.
Finally as kind of the simplest example of this, you would have to do some very nontrivial coupling of electromagnetism to a gravitational field to get a gravitational field to bend light rays the way that gravitational lensing is said to do. But that only happen in mathematical models, and not in reality.
But Did Einstein Actually Prove Time Dilation was Real?
In order to attempt to prove this theory of time dilation, two very accurate atomic clocks were synchronized and one was taken on a high-speed trip on an airplane. When the plane returned, the clock that took the plane ride was said to be slower by exactly the amount Einstein's equations allegedly predicted.
Here is Where Time Dilation Falls Apart:
Suppose we have two atomic clocks, A and B, which are known to be very accurate. Clock A is standing still while clock B zooms toward it, narrowly missing. As B passes A, we observe that they are perfectly synchronized. Clock B then continues to move away from A. Special Relativity tells us that because B is moving away from A, its time will be running slower than A, and will gradually fall behind time-wise.
But wait.
Is B moving away from A or is A moving away from B? Since velocity is purely relative, there’s no way of knowing. In this case, perhaps A should instead be running slower than B, or more properly, perhaps each should be running slower than the other. To suggest that two clocks could both run slower than each other is a logical absurdity, even within the speculative ideas that Special Relativity asks us to follow. It is the mathematical equivalent of saying: A>B and B>A, which is impossible.
To complicate the situation a little, let’s say there are three clocks: A, B and C. As before, A is standing still and B is moving to the right. C is meanwhile moving to the left of A with the equal and opposite velocity of B. Special Relativity tells us that C and B must be recording time more slowly than A, and A should slow down by the same degree relative to C and B. It also tells us that C should be going slower than B, by a greater degree than relative to A, and likewise B should slowdown the same amount relative to C.
Mathematically this is:
A>B and B>A and C>A and A>C and C>>B and B>>C
In other words, mounting logia paradoxes reveal the fallacious nature of the entire proposition very quickly.
Let’s take another case.
The Time Travelling Twins:
A story often told to demonstrate the implications of Special Relativity time-dilation is that of the travelling twins; also known as the twins paradox.
It goes something like this:
A pair of identical twins, named Alpha and Beta, decide to journey to a nearby star where a new planet has been discovered. The planet is 10 light years away from Earth and the twins have at their disposal a space ship that is capable of travelling at near the speed of light. However the ship is only big enough for one occupant. So it’s decided that Alpha should stay at home while Beta make the journey alone. They estimate the round trip should take about 20 years.
The journey begins. Once outside of Earth’s gravity, the ship accelerates at a comfortable rate of 9.8 m/s2 (equal to Earth’s gravity), and reaches light speed in just under a year. To fit within the Special Relativity speed limit, we’ll say that the ship’s top speed is 99.99% of light speed. The ship then cruises at a constant velocity for the next 10 years. As it approaches the planet, it then decelerates at the same rate until it stops.
Beta then gets out, takes pictures, collects samples etc, and then climbs back into the ship for the journey home. The return journey follows the same pattern of acceleration, cruising, and deceleration as before, until it reaches Earth. A chart of the ship’s velocity would look like this:
Many years later, Beta’s ship returns to Earth. It lands gently and, as the roar of its mighty engines subside, a crowd of onlookers gather round. Twenty years have passed and Alpha is waiting anxiously by the docking bay for the return of his brother. As he stands waiting, we notice that he is visibly different. The sands of time have aged him: his face, hair, and body no longer hold the youthful looks he once had when Beta departed all those years ago.
The hatch opens, and as Beta steps out, Alpha notices that his brother has barely aged, looking much like the day when he left. In fact while everything on the Earth has moved twenty years forward in time, Beta has aged little over a year. All of the ship’s timekeeping instruments have likewise barely moved in comparison to Earth’s clocks.
Special Relativity tells us that Beta has experienced time-dilation. The closer Beta got to the speed of light, the slower his clocks ticked, and the slower he aged, relative to Alpha. Beta had no awareness of this because all his bodily functions, and even his thoughts, slowed similarly.
But hang on a minute. Was Beta moving away from Alpha or was Alpha moving away from Beta? Both classical mechanics and Special Relativity tell us that velocity has no absolute measure and can only be measured relative to something else. Beta looks out his rear window and sees Alpha moving away from him at the same speed as Alpha sees Beta’s ship move away from Earth.
Is the same as this:
So, why not have Alpha stay young and let Beta age instead? It’s the same thing. Or let’s take it to the extreme and say that, when the ship returns, they are both younger than each other? This is the same situation that I’ve described above with the moving clocks, albeit with one small difference.
The Effects of Acceleration
Opponents of the above argument may point out that we cannot simply reverse the roles of Alpha and Beta because they do have a difference; namely that Beta experienced acceleration whereas Alpha did not. That’s true. Beta experienced both acceleration and deceleration in shifting between rest and near-light speeds.
However, This Acceleration Cannot Account For The Time Differences For The Following Reasons:
1. Time dilation calculations are based upon velocity, not acceleration. If speed was not an issue, then it shouldn’t make much difference if the top speed was only 90% light speed instead of 99.99%. But the Lorentz factor for 0.9c (γ=2.3) is very different from 0.9999c (γ=71).
2. The acceleration/deceleration occurs over only brief periods of the trip. If acceleration was the deciding factor for time-dilation, then it should make no difference if the destination was 20 light years away instead of 10. Better yet we could simply remove the cruising portion of trip (i.e. immediately decelerate after reaching top speed, and get the same result.)
3. The acceleration experienced by Beta is mild. It is only Earth’s gravity strength. If acceleration of such mild degree could allow Beta to take 20 years off his life, then I propose we could sit in a spinning centrifuge for a few years to achieve the same. Since the direction of the acceleration is unimportant (the net acceleration of Beta’s journey was zero), it shouldn’t matter that the centrifuge’s acceleration is constantly changing direction.
The Reference Frames Argument
This leads us to the standard explanation of this anomaly, known as the ‘accelerated vs. inertial reference frames’ argument. Basically it states that Beta shifted into a different ‘time frame’ due to his initial acceleration – whereas Alpha did not accelerate and stayed in the same frame. This made Beta experience time dilation rather than Alpha. An important point about the argument is that acceleration is not what determines the degree of dilation – that is still done via velocity. Rather, acceleration is what enables dilation to occur.
From a logical perspective this makes no sense because it says nothing about the amount of acceleration required. Essentially it is saying that, while zero acceleration won’t change a ‘reference frame’, a non-zero acceleration of any amount changes it completely. For example Beta’s acceleration may be a billion-trillion times weaker than Earth’s gravity, yet that is all that’s needed to make Beta age 71 times slower than Alpha, rather than vice-versa. If acceleration was a determining factor in the degree of dilation then it should be incorporated into the LT describing it. But the fact is, it’s not.
And from a practical perspective the ‘frames argument’ fails completely. Because Alpha, left behind on earth, cannot stand perfectly still and will be accelerating all the time. As the earth rotates and orbits the sun he experiences acceleration. Even if both he and the earth were somehow completely motionless, the molecules in his body will be constantly vibrating with heat, and vibration involves acceleration. Therefore an argument that favours non-zero accelerating bodies over zero-accelerating ones could never apply in a real situation.
The Conclusion:
And so, Time Dilation, itself, proves to be just a fictional narrative based upon the equally fictional narrative of Space Time curvature. They are both anchored in mathematical paradoxes and illogical and imaginary hypothesis.
One defining feature of General Relativity is that when you are in free-fall you are in a flat Minkowski Space Time, hence if you are not in free-fall, you must be accelerating away from a planet and thus seeing clocks at higher elevations ticking faster than your clocks are. In mathematical physics, Minkowski space (or Minkowski spacetime) combines inertial space and time manifolds (x,y) with a non-inertial reference frame of space and time (x',t') into a four-dimensional model relating a position (inertial frame of reference) to the field (physics).