Astronomy

Contradiction between Theory of Relativity and Newton's Law of Universal Gravitation?

Contradiction between Theory of Relativity and Newton's Law of Universal Gravitation?

Newton's Law of Universal Gravity states that an object will accelerate constantly as it falls. Let's assume an object falling into a black hole. According to Newton's Law, when it reaches the event horizon it must be traveling atc, because c is the escape velocity at the event horizon. Therefore, after it passes the event horizon, it must continue to accelerate pastc, yet theory of relativity states that it's never gonna happen. So, in this condition, what will the object do?


A) Don't take Newton's law too seriously in the relativistic regime.

According to Newton's Law, when it reaches the event horizon it must be traveling at $c$, because $c$ is the escape velocity at the event horizon.

This is true, assuming the particle freefalls from rest at infinity, but the details are quite different from Newtonian theory. For orbits in Schwarzschild spacetime, the effective potential is $$V = -frac{GM}{r} + frac{l^2}{2r^2} - frac{GMl^2}{c^2r^3} ext{,}$$ where $lequiv L/m$ is the specific angular momentum of the orbit. The last term offers relativistic corrections that have no analogue in Newtonian gravity, so in general Newton's law cannot be counted on when near the horizon of the black hole.

But for radial freefall, $l = 0$, and we a total orbital specific energy: $$mathcal{E} = frac{1}{2}left(frac{mathrm{d}r}{mathrm{d} au} ight)^2 - frac{GM}{r} ext{,}$$ which has exactly Newtonian form. In particular, a particle freefalling from rest at infinity will have $$left|frac{mathrm{d}r}{mathrm{d} au} ight| = sqrt{frac{2GM}{r}} ext{,}$$ so at as it nears the horizon ($r o 2GM/c^2$), we have $|mathrm{d}r/mathrm{d} au| o c$, just as Newtonian theory would predict.

However, the motion is only roughly analogous to what's prescribed by Newton's law, because there are very important differences in the interpretation of those quantities. Specifically, (1) the $ au$ refers to the proper time of the orbiting particle, not coordinate time $t$, and certainly not any absolute time as Newtonian theory proper, and (2) the $r$ refers to the Schwarzschild radial coordinate, which is defined such that a sphere at this coordinate have surface area $4pi r^2$, and this is not the radial distance to the center.

B) Coordinates have no intrinsic meaning.

Therefore, after it passes the event horizon, it must continue to accelerate past $c$, yet theory of relativity states that it's never gonna happen.

Suppose I fling a particle along a straight ruler, and that ruler is marked in feet. So if, for example, my particle goes five marked units along the ruler in a nanosecond, that's clearly a problem, because the particle must be superluminal ($capprox 1,mathrm{ft}/mathrm{ns}$).

Now suppose the ruler is not marked in feet, and I don't tell you how it's marked. Is it a problem that the particle goes five units in a nanosecond? Without knowing what the marks are, the statement of this sort of "coordinate speed" is not even meaningful. Finally, suppose I tell you how the ruler is marked, but its marks do not actually measure the distance along the ruler. Then is it a problem that it goes through five of those marks in a nanosecond?

The moral is simply this: by themselves, coordinates are simply labels to identify events. One can pick coordinates such that the coordinate speed is arbitrarily large or small, and it doesn't matter, because coordinates are not physical things. The universe does not come with its own coordinates; they're just labels we put on things.

However, what can give coordinates meaning is the metric tensor, which relates coordinates to actual lengths or durations, so that, for example, the Schwarzschild radial coordinate has a set meaning in terms of surface areas. Finally, the Schwarzschild coordinates are pathological near the horizon. They are not defined across the horizon (technically, the Schwarzschild coordinates are actually two entirely different coordinate charts disconnected by the horizon). You can see this in the Schwarzschild metric (units of $G = c = 1$): $$mathrm{d}s^2 = -left(1-frac{2M}{r} ight)mathrm{d}t^2 + left(1-frac{2M}{r} ight)^{-1},mathrm{d}r^2 + r^2(mathrm{d} heta^2+sin^2 heta,mathrm{d}phi^2) ext{,}$$ where the metric coefficients in the Schwarzschild chart are undefined at the horizon $r = 2M$.

C) "So, in this condition, what will the object do?"

It will cross the event horizon and meet its end at the singularity.

Here's the same Schwarzschild geometry in Gullstrand-Painlevé coordinates: $$mathrm{d}s^2 = -mathrm{d}t^2 + left(mathrm{d}r + sqrt{frac{2M}{r}},mathrm{d}t ight)^2 + r^2(mathrm{d} heta^2+sin^2 heta,mathrm{d}phi^2) ext{.}$$ In this coordinate chart, space is moving towards the singularity at the estate velocity $sqrt{2GM/r}$, and the particles are carried along with it. In a related coordinate chart, Lemaître coordinates, particles freefalling from rest at infinity have zero coordinate speed, with $mathrm{d}r/mathrm{d}t = 0$, where here $r$ is the Lemaître radial coordinate. (Edit: corrected example mistakenly attributing this property to the GP chart.)

You can pick any coordinate chart that's well-behaved at the horizon, and any such chart will show it moving across the horizon with no trouble. But the Schwarzschild coordinates do not give such a chart, because they're undefined at the horizon.


Contradiction between Theory of Relativity and Newton's Law of Universal Gravitation? - Astronomy

Einstein's generalization of Newton's theory of gravitation in the general theory of relativity led not only to small quantitative differences between gravitational effects in the relativistic theory and the Newtonian theory, but also to essentially new phenomena and effects peculiar to the relativistic theory and absent in the Newtonian theory. This difference is so large that the gravitational interaction in Einstein's theory even altered the attraction-only property, characteristic of Newton's theory, the law of universal gravitation, and became both attractive and repulsive. It is notable that the nature of the repulsion in gravitational interaction already appears in the simplest case of a spherically symmetric isolated body. Einstein's equations admit for a spherical body a solution whose physical interpretation uniquely indicates the repulsive nature of a gravitational field inside the body, if the number of particles that make up the body is sufficiently large. The structure of such a body, density distribution of the number of particles, mass, and pressure, is determined in the equilibrium state by the pressure of the substance, the gravitational attraction of peripheral layers toward the center, and the gravitational repulsion of inner layers of matter away from the center. As a result of the gravitational repulsion of matter away from the center inside the body there appears a cavity, free of the matter making up the body and its electromagnetic radiation. If the body is cold, then the volume of the world tube of the cavity can differ from zero. In the opposite case, the world tube of the cavity reduces to the world line of the center, which is inaccessible to particles of matter and to electromagnetic radiation. Gravitational repulsion, on the other hand, is a result of the existence of a field singularity at the center of the body, whose world line is time-like.


Why Newton’s law of gravitation is declared Wrong.

We all know the Newton and his famous law of universal gravitation and the story of falling apple. Newton proposed his law of gravitation on 5 July 1687, it doesn’t mean that before it there was no gravity. Newton’s law of gravitation supported the Galileo galilei concept of earth revolving around the sun not the sun around the earth. This law totally revolutionized the physics and physics started growing tremendously. By using newton’s law of gravitation many things are proved. But after 332 years scientist declared newton’s law of gravitation is wrong. So let’s discuss why?

Even though the Newton’s law of gravitation is not correct but by using it we discovered eighth planet Neptune. We also use Newton’s law of gravitation in many cases. More than 100 years after path-breaking discovery of theory of general relativity by Albert Einstein, Now scientists declared Newton’s law of gravitation is wrong. Newton’s universal law of gravitation was published on 1687. So do the wrong ( derivations,laws ,theory,etc ) things in such a way that it would takes years, for people to prove it was wrong. Here wrong things means theories, laws ,derived equation, etc. Even today newton’s law of gravitation is useful.

According to newton’s law of gravitation, gravity is a force which is directly proportional to product of their masses and inversely proportional to square of distance between them. Newton describes gravity as a instantaneous force.

Newton’s law of gravitation explains many things then why Einstein started to think once again what is gravity let’s find out. While Working on the theory of relativity Einstein find that there is a limit for velocity in the universe. The limit for velocity is equal to velocity of light. Nothing can travel faster than the speed of light even light itself.

Portrait of physicist Albert Einstein, sitting at a table holding a pipe, circa 1933. (Photo by Lambert/Keystone/Getty Images)

As early describes according newton gravity is a instantaneous force. So if Sun suddenly disappeared earth will start moving in a straight line according to newton’s law of gravitation. But light takes 8 minutes and 19 seconds to reach earth from the Sun. So this instantaneous force is breaking the law of limit velocity i.e. nothing travel faster than the light. So Einstein started to think once again what is gravity and describes gravity as curve in spacetime fabric. So if Sun suddenly disappeared than we will come to know it after 8 minutes and 19 seconds and earth will start to move in straight line.

Gravity and general relativity concept. Curved spacetime caused by gravity of Sun. 3D rendered illustration.

According to Einstein’s general theory of relativity gravity is not a force but a curve in spacetime fabric. More massive objects create more curve in spacetime. Curvature is responsible for the circular motion of earth around the Sun. Motion of moon around the earth. This explains the gravity more precisely than newton’s law of gravitation. Theory of general relativity could not explain the gravity under a black hole but explains the existence of black holes and white holes.

According to Einstein’s theory of general relativity, Gravity also has effect on time and light. The massive objects bends the ray of light passing near by it. Near more gravitational objects time runs slower. For example times runs faster on mount Everest as compared to the surface of earth, because on surface of earth gravity is more than mount everest.

Now Question arises if Newton’s law of gravitation is wrong then why we do study it?

The answer is very simple, newton’s law of gravitation is perfect approximation of Gravity in Einstein theory of relativity. The calculation in Newton’s law of gravitation is very easy whereas in Einstein’s theory of relativity it is very tough. Hence, In classical physics we use Newton’s law of Gravitation.

Thanks for reading share with your friends and family and tell them the law they learned in a school is declared wrong.


Contents

Initially, the term theory of everything was used with an ironic reference to various overgeneralized theories. For example, a grandfather of Ijon Tichy – a character from a cycle of Stanisław Lem's science fiction stories of the 1960s – was known to work on the "General Theory of Everything". Physicist Harald Fritzsch used the term in his 1977 lectures in Varenna. [7] Physicist John Ellis claims [8] to have introduced the term into the technical literature in an article in Nature in 1986. [9] Over time, the term stuck in popularizations of theoretical physics research.

Antiquity to 19th century Edit

Many ancient cultures such as Babylonian astronomers, Indian astronomy studied the pattern of the Seven Classical Planets against the background of stars, with their interest being to relate celestial movement to human events (astrology), and the goal being to predict events by recording events against a time measure and then look for recurrent patterns. The debate between the universe having either a beginning or eternal cycles can be traced back to ancient Babylonia. [10] Hindu cosmology posits that time is infinite with a cyclic universe, where the current universe was preceded and will be followed by an infinite number of universes. [11] [12] Time scales mentioned in Hindu cosmology correspond to those of modern scientific cosmology. Its cycles run from our ordinary day and night to a day and night of Brahma, 8.64 billion years long. [13]

The natural philosophy of atomism appeared in several ancient traditions. In ancient Greek philosophy, the pre-Socratic philosophers speculated that the apparent diversity of observed phenomena was due to a single type of interaction, namely the motions and collisions of atoms. The concept of 'atom' proposed by Democritus was an early philosophical attempt to unify phenomena observed in nature. The concept of 'atom' also appeared in the Nyaya-Vaisheshika school of ancient Indian philosophy.

Archimedes was possibly the first philosopher to have described nature with axioms (or principles) and then deduce new results from them. Any "theory of everything" is similarly expected to be based on axioms and to deduce all observable phenomena from them. [14] : 340

Following earlier atomistic thought, the mechanical philosophy of the 17th century posited that all forces could be ultimately reduced to contact forces between the atoms, then imagined as tiny solid particles. [15] : 184 [16]

In the late 17th century, Isaac Newton's description of the long-distance force of gravity implied that not all forces in nature result from things coming into contact. Newton's work in his Mathematical Principles of Natural Philosophy dealt with this in a further example of unification, in this case unifying Galileo's work on terrestrial gravity, Kepler's laws of planetary motion and the phenomenon of tides by explaining these apparent actions at a distance under one single law: the law of universal gravitation. [17]

In 1814, building on these results, Laplace famously suggested that a sufficiently powerful intellect could, if it knew the position and velocity of every particle at a given time, along with the laws of nature, calculate the position of any particle at any other time: [18] : ch 7

An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.

Laplace thus envisaged a combination of gravitation and mechanics as a theory of everything. Modern quantum mechanics implies that uncertainty is inescapable, and thus that Laplace's vision has to be amended: a theory of everything must include gravitation and quantum mechanics. Even ignoring quantum mechanics, chaos theory is sufficient to guarantee that the future of any sufficiently complex mechanical or astronomical system is unpredictable.

In 1820, Hans Christian Ørsted discovered a connection between electricity and magnetism, triggering decades of work that culminated in 1865, in James Clerk Maxwell's theory of electromagnetism. During the 19th and early 20th centuries, it gradually became apparent that many common examples of forces – contact forces, elasticity, viscosity, friction, and pressure – result from electrical interactions between the smallest particles of matter.

In his experiments of 1849–50, Michael Faraday was the first to search for a unification of gravity with electricity and magnetism. [19] However, he found no connection.

In 1900, David Hilbert published a famous list of mathematical problems. In Hilbert's sixth problem, he challenged researchers to find an axiomatic basis to all of physics. In this problem he thus asked for what today would be called a theory of everything. [20]

Early 20th century Edit

In the late 1920s, the new quantum mechanics showed that the chemical bonds between atoms were examples of (quantum) electrical forces, justifying Dirac's boast that "the underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known". [21]

After 1915, when Albert Einstein published the theory of gravity (general relativity), the search for a unified field theory combining gravity with electromagnetism began with a renewed interest. In Einstein's day, the strong and the weak forces had not yet been discovered, yet he found the potential existence of two other distinct forces, gravity and electromagnetism, far more alluring. This launched his thirty-year voyage in search of the so-called "unified field theory" that he hoped would show that these two forces are really manifestations of one grand, underlying principle. During the last few decades of his life, this ambition alienated Einstein from the rest of mainstream of physics, as the mainstream was instead far more excited about the emerging framework of quantum mechanics. Einstein wrote to a friend in the early 1940s, "I have become a lonely old chap who is mainly known because he doesn't wear socks and who is exhibited as a curiosity on special occasions." Prominent contributors were Gunnar Nordström, Hermann Weyl, Arthur Eddington, David Hilbert, [22] Theodor Kaluza, Oskar Klein (see Kaluza–Klein theory), and most notably, Albert Einstein and his collaborators. Einstein searched in earnest for, but ultimately failed to find, a unifying theory [23] : ch 17 (see Einstein–Maxwell–Dirac equations).

Late 20th century and the nuclear interactions Edit

In the twentieth century, the search for a unifying theory was interrupted by the discovery of the strong and weak nuclear forces, which differ both from gravity and from electromagnetism. A further hurdle was the acceptance that in a TOE, quantum mechanics had to be incorporated from the outset, rather than emerging as a consequence of a deterministic unified theory, as Einstein had hoped.

Gravity and electromagnetism are able to coexist as entries in a list of classical forces, but for many years it seemed that gravity could not be incorporated into the quantum framework, let alone unified with the other fundamental forces. For this reason, work on unification, for much of the twentieth century, focused on understanding the three forces described by quantum mechanics: electromagnetism and the weak and strong forces. The first two were combined in 1967–68 by Sheldon Glashow, Steven Weinberg, and Abdus Salam into the electroweak force. [24] Electroweak unification is a broken symmetry: the electromagnetic and weak forces appear distinct at low energies because the particles carrying the weak force, the W and Z bosons, have non-zero masses ( 80.4 GeV/c 2 and 91.2 GeV/c 2 , respectively), whereas the photon, which carries the electromagnetic force, is massless. At higher energies W bosons and Z bosons can be created easily and the unified nature of the force becomes apparent.

While the strong and electroweak forces coexist under the Standard Model of particle physics, they remain distinct. Thus, the pursuit of a theory of everything remains unsuccessful: neither a unification of the strong and electroweak forces – which Laplace would have called 'contact forces' – nor a unification of these forces with gravitation has been achieved.

Conventional sequence of theories Edit

A Theory of Everything would unify all the fundamental interactions of nature: gravitation, the strong interaction, the weak interaction, and electromagnetism. Because the weak interaction can transform elementary particles from one kind into another, the TOE should also predict all the various different kinds of particles possible. The usual assumed path of theories is given in the following graph, where each unification step leads one level up on the graph.

Theory of everything
Quantum gravity
Space Curvature Electronuclear force (GUT)
Standard model of cosmology Standard model of particle physics
Strong interaction
SU(3)
Electroweak interaction
SU(2) x U(1)Y
Weak interaction
SU(2)
Electromagnetism
U(1)EM
Electricity Magnetism

In this graph, electroweak unification occurs at around 100 GeV, grand unification is predicted to occur at 10 16 GeV, and unification of the GUT force with gravity is expected at the Planck energy, roughly 10 19 GeV.

Several Grand Unified Theories (GUTs) have been proposed to unify electromagnetism and the weak and strong forces. Grand unification would imply the existence of an electronuclear force it is expected to set in at energies of the order of 10 16 GeV, far greater than could be reached by any currently feasible particle accelerator. Although the simplest GUTs have been experimentally ruled out, the idea of a grand unified theory, especially when linked with supersymmetry, remains a favorite candidate in the theoretical physics community. Supersymmetric GUTs seem plausible not only for their theoretical "beauty", but because they naturally produce large quantities of dark matter, and because the inflationary force may be related to GUT physics (although it does not seem to form an inevitable part of the theory). Yet GUTs are clearly not the final answer both the current standard model and all proposed GUTs are quantum field theories which require the problematic technique of renormalization to yield sensible answers. This is usually regarded as a sign that these are only effective field theories, omitting crucial phenomena relevant only at very high energies. [5]

The final step in the graph requires resolving the separation between quantum mechanics and gravitation, often equated with general relativity. Numerous researchers concentrate their efforts on this specific step nevertheless, no accepted theory of quantum gravity, and thus no accepted theory of everything, has emerged. It is usually assumed that the TOE will also solve the remaining problems of GUTs.

In addition to explaining the forces listed in the graph, a TOE may also explain the status of at least two candidate forces suggested by modern cosmology: an inflationary force and dark energy. Furthermore, cosmological experiments also suggest the existence of dark matter, supposedly composed of fundamental particles outside the scheme of the standard model. However, the existence of these forces and particles has not been proven.

String theory and M-theory Edit

Is string theory, superstring theory, or M-theory, or some other variant on this theme, a step on the road to a "theory of everything", or just a blind alley?

Since the 1990s, some physicists such as Edward Witten believe that 11-dimensional M-theory, which is described in some limits by one of the five perturbative superstring theories, and in another by the maximally-supersymmetric 11-dimensional supergravity, is the theory of everything. There is no widespread consensus on this issue.

One remarkable property of string/M-theory is that extra dimensions are required for the theory's consistency. In this regard, string theory can be seen as building on the insights of the Kaluza–Klein theory, in which it was realized that applying general relativity to a five-dimensional universe (with one of them small and curled up) [ clarification needed ] looks from the four-dimensional perspective like the usual general relativity together with Maxwell's electrodynamics. This lent credence to the idea of unifying gauge and gravity interactions, and to extra dimensions, but did not address the detailed experimental requirements. Another important property of string theory is its supersymmetry, which together with extra dimensions are the two main proposals for resolving the hierarchy problem of the standard model, which is (roughly) the question of why gravity is so much weaker than any other force. The extra-dimensional solution involves allowing gravity to propagate into the other dimensions while keeping other forces confined to a four-dimensional spacetime, an idea that has been realized with explicit stringy mechanisms. [25]

Research into string theory has been encouraged by a variety of theoretical and experimental factors. On the experimental side, the particle content of the standard model supplemented with neutrino masses fits into a spinor representation of SO(10), a subgroup of E8 that routinely emerges in string theory, such as in heterotic string theory [26] or (sometimes equivalently) in F-theory. [27] [28] String theory has mechanisms that may explain why fermions come in three hierarchical generations, and explain the mixing rates between quark generations. [29] On the theoretical side, it has begun to address some of the key questions in quantum gravity, such as resolving the black hole information paradox, counting the correct entropy of black holes [30] [31] and allowing for topology-changing processes. [32] [33] [34] It has also led to many insights in pure mathematics and in ordinary, strongly-coupled gauge theory due to the Gauge/String duality.

In the late 1990s, it was noted that one major hurdle in this endeavor is that the number of possible four-dimensional universes is incredibly large. The small, "curled up" extra dimensions can be compactified in an enormous number of different ways (one estimate is 10 500 ) each of which leads to different properties for the low-energy particles and forces. This array of models is known as the string theory landscape. [14] : 347

One proposed solution is that many or all of these possibilities are realised in one or another of a huge number of universes, but that only a small number of them are habitable. Hence what we normally conceive as the fundamental constants of the universe are ultimately the result of the anthropic principle rather than dictated by theory. This has led to criticism of string theory, [35] arguing that it cannot make useful (i.e., original, falsifiable, and verifiable) predictions and regarding it as a pseudoscience. Others disagree, [36] and string theory remains an active topic of investigation in theoretical physics. [37]

Loop quantum gravity Edit

Current research on loop quantum gravity may eventually play a fundamental role in a TOE, but that is not its primary aim. [38] Also loop quantum gravity introduces a lower bound on the possible length scales.

There have been recent claims that loop quantum gravity may be able to reproduce features resembling the Standard Model. So far only the first generation of fermions (leptons and quarks) with correct parity properties have been modelled by Sundance Bilson-Thompson using preons constituted of braids of spacetime as the building blocks. [39] However, there is no derivation of the Lagrangian that would describe the interactions of such particles, nor is it possible to show that such particles are fermions, nor that the gauge groups or interactions of the Standard Model are realised. Utilization of quantum computing concepts made it possible to demonstrate that the particles are able to survive quantum fluctuations. [40]

This model leads to an interpretation of electric and colour charge as topological quantities (electric as number and chirality of twists carried on the individual ribbons and colour as variants of such twisting for fixed electric charge).

Bilson-Thompson's original paper suggested that the higher-generation fermions could be represented by more complicated braidings, although explicit constructions of these structures were not given. The electric charge, colour, and parity properties of such fermions would arise in the same way as for the first generation. The model was expressly generalized for an infinite number of generations and for the weak force bosons (but not for photons or gluons) in a 2008 paper by Bilson-Thompson, Hackett, Kauffman and Smolin. [41]

Other attempts Edit

Among other attempts to develop a theory of everything is the theory of causal fermion systems, [42] giving the two current physical theories (general relativity and quantum field theory) as limiting cases.

Another theory is called Causal Sets. As some of the approaches mentioned above, its direct goal isn't necessarily to achieve a TOE but primarily a working theory of quantum gravity, which might eventually include the standard model and become a candidate for a TOE. Its founding principle is that spacetime is fundamentally discrete and that the spacetime events are related by a partial order. This partial order has the physical meaning of the causality relations between relative past and future distinguishing spacetime events.

Causal dynamical triangulation does not assume any pre-existing arena (dimensional space), but rather attempts to show how the spacetime fabric itself evolves.

Another attempt may be related to ER=EPR, a conjecture in physics stating that entangled particles are connected by a wormhole (or Einstein–Rosen bridge). [43]

Present status Edit

At present, there is no candidate theory of everything that includes the standard model of particle physics and general relativity and that, at the same time, is able to calculate the fine-structure constant or the mass of the electron. [3] Most particle physicists expect that the outcome of ongoing experiments – the search for new particles at the large particle accelerators and for dark matter – are needed in order to provide further input for a TOE.

In parallel to the intense search for a TOE, various scholars have seriously debated the possibility of its discovery.

Gödel's incompleteness theorem Edit

A number of scholars claim that Gödel's incompleteness theorem suggests that any attempt to construct a TOE is bound to fail. Gödel's theorem, informally stated, asserts that any formal theory sufficient to express elementary arithmetical facts and strong enough for them to be proved is either inconsistent (both a statement and its denial can be derived from its axioms) or incomplete, in the sense that there is a true statement that can't be derived in the formal theory.

Stanley Jaki, in his 1966 book The Relevance of Physics, pointed out that, because any "theory of everything" will certainly be a consistent non-trivial mathematical theory, it must be incomplete. He claims that this dooms searches for a deterministic theory of everything. [44]

Freeman Dyson has stated that "Gödel's theorem implies that pure mathematics is inexhaustible. No matter how many problems we solve, there will always be other problems that cannot be solved within the existing rules. […] Because of Gödel's theorem, physics is inexhaustible too. The laws of physics are a finite set of rules, and include the rules for doing mathematics, so that Gödel's theorem applies to them." [45]

Stephen Hawking was originally a believer in the Theory of Everything, but after considering Gödel's Theorem, he concluded that one was not obtainable. "Some people will be very disappointed if there is not an ultimate theory that can be formulated as a finite number of principles. I used to belong to that camp, but I have changed my mind." [46]

Jürgen Schmidhuber (1997) has argued against this view he asserts that Gödel's theorems are irrelevant for computable physics. [47] In 2000, Schmidhuber explicitly constructed limit-computable, deterministic universes whose pseudo-randomness based on undecidable, Gödel-like halting problems is extremely hard to detect but does not at all prevent formal TOEs describable by very few bits of information. [48]

Related critique was offered by Solomon Feferman [49] and others. Douglas S. Robertson offers Conway's game of life as an example: [50] The underlying rules are simple and complete, but there are formally undecidable questions about the game's behaviors. Analogously, it may (or may not) be possible to completely state the underlying rules of physics with a finite number of well-defined laws, but there is little doubt that there are questions about the behavior of physical systems which are formally undecidable on the basis of those underlying laws.

Since most physicists would consider the statement of the underlying rules to suffice as the definition of a "theory of everything", most physicists argue that Gödel's Theorem does not mean that a TOE cannot exist. On the other hand, the scholars invoking Gödel's Theorem appear, at least in some cases, to be referring not to the underlying rules, but to the understandability of the behavior of all physical systems, as when Hawking mentions arranging blocks into rectangles, turning the computation of prime numbers into a physical question. [51] This definitional discrepancy may explain some of the disagreement among researchers.

Fundamental limits in accuracy Edit

No physical theory to date is believed to be precisely accurate. Instead, physics has proceeded by a series of "successive approximations" allowing more and more accurate predictions over a wider and wider range of phenomena. Some physicists believe that it is therefore a mistake to confuse theoretical models with the true nature of reality, and hold that the series of approximations will never terminate in the "truth". Einstein himself expressed this view on occasions. [52] Following this view, we may reasonably hope for a theory of everything which self-consistently incorporates all currently known forces, but we should not expect it to be the final answer.

On the other hand, it is often claimed that, despite the apparently ever-increasing complexity of the mathematics of each new theory, in a deep sense associated with their underlying gauge symmetry and the number of dimensionless physical constants, the theories are becoming simpler. If this is the case, the process of simplification cannot continue indefinitely.

Lack of fundamental laws Edit

There is a philosophical debate within the physics community as to whether a theory of everything deserves to be called the fundamental law of the universe. [53] One view is the hard reductionist position that the TOE is the fundamental law and that all other theories that apply within the universe are a consequence of the TOE. Another view is that emergent laws, which govern the behavior of complex systems, should be seen as equally fundamental. Examples of emergent laws are the second law of thermodynamics and the theory of natural selection. The advocates of emergence argue that emergent laws, especially those describing complex or living systems are independent of the low-level, microscopic laws. In this view, emergent laws are as fundamental as a TOE.

The debates do not make the point at issue clear. Possibly the only issue at stake is the right to apply the high-status term "fundamental" to the respective subjects of research. A well-known debate over this took place between Steven Weinberg and Philip Anderson [ citation needed ] . [54]

Impossibility of being "of everything" Edit

Although the name "theory of everything" suggests the determinism of Laplace's quotation, this gives a very misleading impression. Determinism is frustrated by the probabilistic nature of quantum mechanical predictions, by the extreme sensitivity to initial conditions that leads to mathematical chaos, by the limitations due to event horizons, and by the extreme mathematical difficulty of applying the theory. Thus, although the current standard model of particle physics "in principle" predicts almost all known non-gravitational phenomena, in practice only a few quantitative results have been derived from the full theory (e.g., the masses of some of the simplest hadrons), and these results (especially the particle masses which are most relevant for low-energy physics) are less accurate than existing experimental measurements. Even in classical mechanics there are still unsolved problems, such as turbulence, although the equations have been known for centuries. The TOE would almost certainly be even harder to apply for the prediction of experimental results, and thus might be of limited use.

A motive for seeking a TOE, [ citation needed ] apart from the pure intellectual satisfaction of completing a centuries-long quest, is that prior examples of unification have predicted new phenomena, some of which (e.g., electrical generators) have proved of great practical importance. And like in these prior examples of unification, the TOE would probably allow us to confidently define the domain of validity and residual error of low-energy approximations to the full theory.

The theories generally do not account for the apparent phenomena of consciousness or free will, which are instead often the subject of philosophy and religion.

Infinite number of onion layers Edit

Frank Close regularly argues that the layers of nature may be like the layers of an onion, and that the number of layers might be infinite. [55] This would imply an infinite sequence of physical theories.

Impossibility of calculation Edit

Weinberg [56] points out that calculating the precise motion of an actual projectile in the Earth's atmosphere is impossible. So how can we know we have an adequate theory for describing the motion of projectiles? Weinberg suggests that we know principles (Newton's laws of motion and gravitation) that work "well enough" for simple examples, like the motion of planets in empty space. These principles have worked so well on simple examples that we can be reasonably confident they will work for more complex examples. For example, although general relativity includes equations that do not have exact solutions, it is widely accepted as a valid theory because all of its equations with exact solutions have been experimentally verified. Likewise, a TOE must work for a wide range of simple examples in such a way that we can be reasonably confident it will work for every situation in physics.


And the winner is?

If you wanted to pick a referee in the big-small debate, you could hardly do better than Sean Carroll, an expert in cosmology, field theory and gravitational physics at Caltech. He knows his way around relativity, he knows his way around quantum mechanics, and he has a healthy sense of the absurd: he calls his personal blog Preposterous Universe. Right off the bat, Carroll awards most of the points to the quantum side. “Most of us in this game believe that quantum mechanics is much more fundamental than general relativity is,” he says. That has been the prevailing view ever since the 1920s, when Einstein tried and repeatedly failed to find flaws in the counterintuitive predictions of quantum theory. The recent Dutch experiment demonstrating an instantaneous quantum connection between two widely separated particles – the kind of event that Einstein derided as “spooky action at a distance” – only underscores the strength of the evidence.

Illustration by Owen Gildersleeve

Taking a larger view, the real issue is not general relativity versus quantum field theory, Carroll explains, but classical dynamics versus quantum dynamics. Relativity, despite its perceived strangeness, is classical in how it regards cause and effect quantum mechanics most definitely is not. Einstein was optimistic that some deeper discoveries would uncover a classical, deterministic reality hiding beneath quantum mechanics, but no such order has yet been found. The demonstrated reality of spooky action at a distance argues that such order does not exist.

“If anything, people underappreciate the extent to which quantum mechanics just completely throws away our notions of space and locality [the notion that a physical event can affect only its immediate surroundings]. Those things simply are not there in quantum mechanics,” Carroll says. They may be large-scale impressions that emerge from very different small-scale phenomena, like Hogan’s argument about 3D reality emerging from 2D quantum units of space.

Despite that seeming endorsement, Carroll regards Hogan’s holometer as a long shot, though he admits it is removed from his area of research. At the other end, he doesn’t think much of Smolin’s efforts to start with space as a fundamental thing he believes the notion is as absurd as trying to argue that air is more fundamental than atoms. As for what kind of quantum system might take physics to the next level, Carroll remains broadly optimistic about string theory, which he says “seems to be a very natural extension of quantum field theory”. In all these ways, he is true to the mainstream, quantum-based thinking in modern physics.

Yet Carroll’s ruling, while almost entirely pro-quantum, is not purely an endorsement of small-scale thinking. There are still huge gaps in what quantum theory can explain. “Our inability to figure out the correct version of quantum mechanics is embarrassing,” he says. “And our current way of thinking about quantum mechanics is simply a complete failure when you try to think about cosmology or the whole universe. We don’t even know what time is.” Both Hogan and Smolin endorse this sentiment, although they disagree about what to do in response. Carroll favours a bottom-up explanation in which time emerges from small-scale quantum interactions, but declares himself “entirely agnostic” about Smolin’s competing suggestion that time is more universal and fundamental. In the case of time, then, the jury is still out.

No matter how the theories shake out, the large scale is inescapably important, because it is the world we inhabit and observe. In essence, the universe as a whole is the answer, and the challenge to physicists is to find ways to make it pop out of their equations. Even if Hogan is right, his space-chunks have to average out to the smooth reality we experience every day. Even if Smolin is wrong, there is an entire cosmos out there with unique properties that need to be explained – something that, for now at least, quantum physics alone cannot do.

By pushing at the bounds of understanding, Hogan and Smolin are helping the field of physics make that connection. They are nudging it toward reconciliation not just between quantum mechanics and general relativity, but between idea and perception. The next great theory of physics will undoubtedly lead to beautiful new mathematics and unimaginable new technologies. But the best thing it can do is create deeper meaning that connects back to us, the observers, who get to define ourselves as the fundamental scale of the universe.

This essay originally appeared in issue 29 of Nautilus. To find out more, visit nautil.us

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What about gravity?

In 1907 Einstein realised that his theory was not complete. The principle of relativity was only applicable to observers moving with a constant velocity. It also did not fit with the Newtonian description of gravity.

Einstein, being a patent officer, did not have access to laboratory equipment. To compensate, he had to engage himself in thought experiments. He considered various scenarios in his head and worked through them step by step.

These thought experiments showed to him that gravity is not different from acceleration. So standing stationary on the Earth feels just the same as standing in a rocket ship accelerating at a constant 1G.

It also showed that the accelerated observer would observe that fundamental geometrical properties change. For example, that the number π (a mathematical constant) could no longer be defined as a ratio of a circle’s circumference to its diameter.

So it was not just time and space that lost their absolute meaning, but Einstein realised that also geometry itself was not absolute and could be susceptible to physical conditions.


General Theory of Relativity

As we have seen, matter does not simply pull on other matter across empty space, as Newton had imagined. Rather matter distorts space-time and it is this distorted space-time that in turn affects other matter. Objects (including planets, like the Earth, for instance) fly freely under their own inertia through warped space-time, following curved paths because this is the shortest possible path (or geodesic) in warped space-time.

This, in a nutshell, then, is the General Theory of Relativity, and its central premise is that the curvature of space-time is directly determined by the distribution of matter and energy contained within it. What complicates things, however, is that the distribution of matter and energy is in turn governed by the curvature of space, leading to a feedback loop and a lot of very complex mathematics. Thus, the presence of mass/energy determines the geometry of space, and the geometry of space determines the motion of mass/energy.

In practice, in our everyday world, Newton’s Law of Universal Gravitation is a perfectly good approximation. The curving of light was never actually predicted by Newton but, in combination with the idea from special relativity that all forms of energy (including light) have an effective mass, then it seems logical that, as light passes a massive body like the Sun, it too will feel the tug of gravity and be bent slightly from its course. Curiously, however, Einstein’s theory predicts that the path of light will be bent by twice as much as does Newton’s theory, due to a kind of positive feedback. The English astronomer Arthur Eddington confirmed Einstein’s predictions of the deflection of light from other stars by the Sun’s gravity using measurements taken in West Africa during an eclipse of the Sun in 1919, after which the General Theory of Relativity was generally accepted in the scientific community.


(Click for a larger version)
General relativity predicts the gravitational bending of light by massive bodies
(Source: Time Travel Research Center: http://www.zamandayolculuk.com/cetinbal/
HTMLdosya1/RelativityFile.htm)

The theory has been proven remarkably accurate and robust in many different tests over the last century. The slightly elliptical orbit of planets is also explained by the theory but, even more remarkably, it also explains with great accuracy the fact that the elliptical orbits of planets are not exact repetitions but actually shift slightly with each revolution, tracing out a kind of rosette-like pattern. For instance, it correctly predicts the so-called precession of the perihelion of Mercury (that the planet Mercury traces out a complete rosette only once every 3 million years), something which Newton’s Law of Universal Gravitation is not sophisticated enough to cope with.

Gravity Probe B was launched into Earth orbit in 2004, specifically to test the space-time-bending effects predicted by General Relativity using ultra-sensitive gyroscopes. The final analysis of the results in 2011 confirms the predicted effects quite closely, with a tiny 0.28% margin of error for geodetic effects and a larger 19% margin of error for the much less pronounced frame-dragging effect.

The General Theory of Relativity can actually be described using a very simple equation: R = GE (although Einstein's own formulation of his field equations are much more complex). Unfortunately, the variables in this simple equation are far from simple: R is a complicated mathematical object made up of 16 separate numbers in a matrix or "tensor" that describes the distortion of space-time G is the gravitational constant and E is another complicated number, also represented by a tensor, representing the energy of the object (or more accurately the 4-dimensional "energy momentum density"). Given that, though, what the equation says is simple enough: that what gravity really is is not a force but a distortion of space and time, and that the geometry of space and time depends not just on velocity (as the Special Theory of Relativity had indicated) but on the energy of an object. This makes sense when we consider that Newton had already shown that gravity depends on mass, and that Einstein's Special Theory of Relativity had shown that mass is equivalent to energy.

Stephen Hawking and Roger Penrose’s singularity theorem of 1970 used the General Theory of Relativity to show that, just as any collapsing star must end in a singularity, the universe itself must have begun in a singularity like the Big Bang (providing that the universe does in fact contain at least as much matter as it appears to). The theorem also showed, though, that general relativity is an incomplete theory in that it cannot tell us exactly how the universe started off because it predicts that all physical theories (including itself) necessarily break down at a singularity like the Big Bang.

The theory has also provided endless fodder for the science fiction industry, predicting the existence of sci-fi staples like black holes, wormholes, time travel, parallel universes, etc. Just as an example, the notionally faster-than-light “warp” speeds of Star Trek are based firmly on relativity: if the space-time behind a starship were in some way greatly expanded, and the space-time in front of it simultaneously contracted, the starship would find itself suddenly much closer to its destination, without the local space-time around the starship being affected in any relativistic way. Unfortunately, however, such a trick would require the harvesting of vast amounts of energy, way in excess of anything imaginable today.


What is the logic behind the Eddington expedition that proved Einstein's general theory of relativity?

The Eddington expedition in 1919 proved Einstein's general theory of relativity.

[Eddington] argued that the deflection, or bending, of light by the Sun’s gravity could be measured. because Einstein’s theory predicted a deflection precisely twice the value obtained using Isaac Newton’s law of universal gravitation. [Crommelin's] measurements were decisive, and were noticeably closer to the Einstein prediction than to the Newtonian.(Coles, 2019)

Suppose p is the statement"the measured deflection of light by the Sun's gravity matches Einstein's prediction", and q is the statement "the general theory of relativity is correct". To explain the reasoning behind the Eddington expedition, the conditional statement that needs to be used as a premise is q → p. The statement q → p is the only true one, and it allows for keeping the inference valid, which will be shown later.

The statement p → q reads as "if the deflection matches the prediction, then the theory is correct". When both component statements are analyzed, this conditional statement becomes problematic. The mere fact of deflection matching prediction does not necessarily lead to a correct theory. The theory can be false for other reasons even as deflection matches prediction. In the truth table for p → q, both the following rows are possible:

Therefore, using p → q as a premise in the inference is not very reliable.

As p → q appears shaky, the statement p cannot be established as a sufficient condition for statement q. However, the inverse of p → q offers some hope in explaining the expedition. The statement

q reads as "if the deflection does not match Einstein's prediction, the general theory of relativity is incorrect". This one looks solid, because once the deflection is found not to match the prediction, there is no other ground for the theory to continue to be correct. This idea is embodied in the following truth table row.

A conditional statement is logically equivalent to its contrapositive. Using this rule, the preceding explanation for the Eddington expedition can be further tested by evaluating the truth or falsity of conditional statement q → p. The statement q → p reads as "if the general theory of relativity is correct, the measured deflection matches Einstein's prediction". For this statement, reasoning appears solid, because any discrepancy between the deflection and the prediction would render the theory incorrect. This reasoning can be shown in the following truth table row.

Up to this point, it has been shown that q → p is a reliable statement. In other words, p is established as a necessary condition for q.

Lastly, processes of inference are used to derive the desired conclusion.

Very unintuitively, the inference uses modus tollens. As far as the Eddington expedition went, the second premise never surfaced, which is, the measured deflection was never found to differ from the predictions made by Einstein. Thus, only the first premise q → p stays relevant. Coupled with the analysis above that reveals the truth of q → p, the general theory of relativity is held to be correct.

A side note on this question: if one day the second premise of the inference block is found, the general theory of relativity will be discredited.

Reference: Coles, P. (2019). Relativity Revealed. Nature. 568. 306-307.


Einstein’s Theory of Relativity: Explained

Einstein’s Theory of Relativity is mostly known for its assertion that time travel is possible, but in reality this theory encompasses much more. The theory itself is actually split into Special Relativity and General Relativity.


Special Relativity
is based upon two postulates:
1) The laws of physics are the same for all observers in uniform motion relative to one another.
2) The speed of light in a vacuum is the same for all observers, regardless of their relative motion or the motion of the source of the light.

What are the consequences of these postulates? They are best explained with these YouTube videos which use excellent animation to show their points:

– Time Dilation and Time Travel:
Moving clocks are measured to tick more slowly than an observer’s “stationary” clock. The video below explains:

– Simultaneity of Events: It is impossible to say with absolute certainty that two events occur at the same time if the events occur in different spaces. The perception of when each takes place depends on the observer:


– Length Contraction:
This result of special relativity is only relevant when looking at objects moving at speeds above 30,000,000 m/s. At that speed, however, objects appear to be shorter than they what they appear as when stationary or moving at a slower speed. While this is interesting in itself, the real insight comes from realizing that if an observer sees an object moving at the speed of light (assuming this is physically possible), then the object will appear to have no length whatsoever. What follows is the idea that if an object has mass, it cannot move at the speed of light. Hence the speed of light, 299,742,458 m/s, is the universal speed limit for anything with physical mass. Anything moving at the speed is pure energy, which leads to the final conclusion of special relativity…

– Energy = (Mass)(Speed of Light) 2:
This equation explicitly shows that mass can be converted to energy and vice-versa. It also upholds the concept of Conservation of Matter and Energy because the equation shows that when matter disappears in some objects, it is only because it has been converted to energy which is equivalent to mass.

General Relativity is the geometric theory of gravitation put out by Einstein to argue against Newton’s Law of Universal Gravitation. Newton’s law was based on the idea that gravity could move faster than the speed of light, which Einstein obviously found to be false. Consequently, Einstein stated that gravity is instead a property of the geometry of space and time, also called spacetime. The only way for you to fully understand this is to watch the video below, and I promise that it will blow your mind. You will never think about gravity in the same way again.

The consequences of General Relativity are as follows:
1) Gravitation Time Dilation: time moves more slowly in gravitational fields than it does in fields lacking n gravitation pull. The mass of the effect is proportional to the strength of the gravity.
2) Beams of light are bent as they travel through gravitational fields, which explains the existence of black holes
3) Frame-Dragging: a rotating object with mass will drag along the spacetime that is around it. One example is light moving in the same rotational direction as the object will appear to move faster to a distant observer light moving in the opposite direction. Here is a 10-second clip illustrating this idea:


  1. The general theory of relativity was a new way of understanding
    1. the speed of light.
    2. gravity.
    3. mass.
    4. force.
    1. True
    2. False
    1. True
    2. False
    1. when emitted from a moving source
    2. when measured from an accelerating space ship
    3. when measured in the presence of an extreme gravitational field
    4. NEVER
    1. 3.0×10 8 m/s
    2. 1.5×10 8 m/s
    3. 4.5×10 8 m/s
    4. 0 m/s

    Use this resource to answer the questions that follow.

    1. If you have two objects and one of them is moving and one is standing still, what experiment can you do to determine which object is moving?
    2. If a person in a spaceship flies by a person on the earth and each person assumes that they are standing still and the other one is moving, which person is correct?