The basics of Physics — is Gravity amenable to Quantization?
— Article massively edited; 31.10.2015.
This is a very detailed and long article, but written in a very simple language, as it seems to me, describing such concepts as; the basis of expectations of “Quantization of Gravity with other forces” which is colloquially known as Einstein’s dream of GUT — or, Grand Unified Theory, and whether such is possible or not and what we may be missing.
The Gravitational Force follows such equations, according to the work of Einstein and such a theory is called as General Relativity Theory. The equation here describes the detailed behavior of the gravitational force and energy fields, in terms of field vectors and tensors.
- This article also describes briefly Pseudo Forces — check a detailed description here
- In detail the basis of Physics Formalism — check another discourse here, and
- What are waves and particle — (a link to an extensive discussion will be provided, upon further review), the discussion is in terms of a Formal POV of Physics — ‘slightly”, but much can be based and expanded on such.
This would be one of the most well written article by me as I would think.
A prism disperses light. This is to be understood as a wave effect of light. Waves are defined by wavelengths, which is a measure of the spatial period after which a particular amount of wave disturbance or energy phase occurs. Here Light has 7 different colors or wavelengths. As such each will have different momentum. When white light go through a prism their deviations are different and all the different waves are split differently.
So lets get back to the discussion of our original topic of interest.
The basics of Physics — is Gravity amenable to Quantization?
I like to speak first; about a development of Physics, in this article, that follows a chronological path, rather than, how we look at the cumulative understanding, in modern times, upon which we base our statements and help ourselves be inconsistent, because we forget or rather are oblivious; to the deeper framework, in which things were developed.
— Today I want to focus on Gravity. But before I talk about Gravity; I would like to speak something, on Physics itself.
Modern Physics evolved from Classical Physics in various detours.
— It involved old efforts at unification of forces, physical insights and recasting laws of nature and laws of transformation of these laws and quantities. Remember that laws are simply interrelationship between various physical quantities. When we say physical, we automatically hint at them being real, that is physical quantities have to be found in our Universe, as opposed to simply being hypothesized.
Newton and Galileo are both considered to be great Physicists, of our modern times, for science, which is counted to be from CE 1600. Newton and Galileo came several centuries apart. They were dealing with the similar kind of Physics, so to say.
Contrary to that, if we review deeper, we will see that thats a very superfluous remark. In-fact if we are to talk about old modern Physics wrt new modern physics, we see that there was a great deal of unification and advancement of understanding, of physical properties of our world, right from Galileo’s time to Newton’s and later and even much before Galileo.
eg One can not ignore the fact that there is nothing trivial in the unification of frictional forces to sliding forces, to rolling forces, to how a mechanical gear works, to the motion of planets and cosmic objects. In our view, now, they have been unified to a smaller set of forces, but the unification came from the understanding — of a vast deal of forces and phenomena.
Another point in making would be, how — towards the end of his brilliant life, Newton was dealing with the concept of Rotational or so called non-inertial forces. In-fact, this was the early days of a newer advancement of Physics, known by then, which was formulated by Newton, mostly to a form called as Galilean transformation and Newtonian mechanics. The said forms of Newton’s formulations were valid only for inertial frames of references — check the linked article for a deeper insight of the concept; of validity of such in inertial frame of reference.
Galilean Transformation; Galilean Transformation predicts that one adds up the speeds in a simple manner. speed_of_ball_wrt_ground = speed_of_ball_wrt_car + speed_of_car_wrt_ground. Check here to see how speeds are added in the Einsteinian realm of Physics.
While Newton understood the non-inertial or rotational forces, he did not understand them exactly and might not have found anything in the external environment, to associate with. This was what was circumscribed by Mach’s Principle later. For a brief overview, read the article, by the same name, in the linked post.
Centrifugal and Centripetal Force are examples of rotational forces. The centrifugal is exact opposite of the centripetal force. The centripetal force is a real force, whereas the centrifugal force is a pseudo force.
The effort by Newton, to understand Rotational forces — a particularly interesting example of Pseudo forces, as they can be said, is akin to how Einstein wanted to understand a grand unification of all fundamental forces known as GUT or Grand Unified Theory. This aspiration to unify all major forces of nature, is today, as unfounded, as it was ever, although the efforts to achieve so, aren’t.
Here is the list of 4 major or as they are called as; fundamental forces, of nature.
- Gravitational Force
- Electromagnetic Force
- Weak Nuclear Force
- Strong Nuclear Force
In-fact, the efforts to understand a grander unification, are what have taken most of the Physics community’s muscles and minds. The super-symmetry theory and string theory are both an effort in that direction. But there are very basic characteristics, that have been strikingly missing, from such an effort. Some of it I will try to mention here, as they occur to me.
One can also compare, Newton’s efforts at Rotational forces or Pseudo forces, with Feynman’s efforts and disinterest at String Theory. Feynman was a much deeper and insightful scientist, than most other greatest scientists the world has ever known, including Einstein and Newton.
Feynman would formulate answers in the mind, much before anyone would and would show his dispassion, as an expression for “likelihood” that a problem is workable or not. In my opinion, it means, to understand with a greatly cultivated hindsight, why is something related greatly to the basics that, it has been ignored, that it won’t work out, as has been believed.
Feynmanisque dispassion takes depth, not a propensity to show one’s knowledge.
Richard Feynman, one of the most celebrated scientist of last CE was an American born Theoretical Physicist, who contributed to several branches of modern Physics, most notable being QED; the theory of light and electric charged particles.
So, much of Physics from CE 1600 until CE 1900 came in leaps and bounds, through heuristics and through elaborate formalism, through specifics and details and through Eagle-view, through insight and through serendipity. They were passed on, from generation to generation via unification of various kinds.
It only happens that Relativity and Quantum Mechanics are but a specialized unification, in some senses, of this unified formalism of classical mechanics, after the latter’s expansion and addition to newer insights.
So before we go to the formalism of classical mechanics or rather all of Physics itself, here are a few words about Pseudo Forces. A Pseudo force would be one which represents itself as an additional impact or force, once a framework defined on the basis of other forces, can’t explain this force. So first such pseudo forces are to be recognized and tested with the laws of the framework. eg One may not call Dark Force to be a pseudo force, once its recognized, unless, it is not explained by the laws of Physics as we know.
That is, some force may simply be an unknown force, than be a pseudo force. For it to be a pseudo force, it must make the laws inconsistent, even after it’s complete identification and the laws need to be modified to accommodate it. So pseudoness comes from the laws of Physics, than from the force itself. There should be no real correspondence of such forces. That is pseudo forces do not really propagate as an effect of space time and nature. They are rather a mis-adjustment of the real forces, due to definition of frames of references and formulation of the laws.
In Newtonian Mechanics, with simple one dimension, it was recognized that, pseudo forces would come with a –ve sign to real forces, because the pseudoness eg comes from the frame of reference to be defined as an accelerated frame and the Newton’s laws were later understood to be valid only for non-accelerated frames. The article that explains these ideas in great detail has already been linked above.
In any case once our laws are valid for some aspects or some systems we are safe. Anything more can be and will be generalized. The rotational forces are to be understood as Pseudo forces, in the framework of more complicated coordinates, than just a simple 1-dimensional frame of reference. With such newer and newer generalizations and insights theory of Relativity became a more complicated and advanced theory and field of study, but it never really broke up as such with classical mechanics.
Nomenclature of branches of Physics and advancement of understanding
Sitting in 2012 if we surmise that Relativity includes Quantum Mechanics, one would say, well ! — they have been merged from how one has to employ them, eg say in Standard Model of Particle Physics or Standard Model of Cosmology.
But to say Relativity predicts Quantum Mechanics, I can say; Classical Mechanics predicts Quantum Mechanics and prove it in the same sense one would have said Relativity predicts, that actually Classical Mechanics predicts it. Why not research and think a bit more than make superfluous remarks. Our Physics audience is already very confused.
Here is why I say that: so, if we can prove Quantum laws from Relativistic laws, I can prove the same from classical laws.
Classical mechanics already dealt with attributes of Quantum Mechanics. Quantum laws came about because the waves and particles are now predicted from the same differential equation. Classical mechanics was already dealing with waves and particles, but separately. There were two differential equations for each, one for waves, one for particles.
Quantum mechanics made it imminent that these two phenomena of waves and particles be dealt by the unification of both differential equations and in-fact it was achieved. This is dealt in much detail in another article — “Why is Energy Conserved?”— where formalism of Physics is explained.
So it was rather a fact of convenience, that was achieved by unification, so Quantum Mechanics is merely a more convenient form of Classical Mechanics. While the general lay man idea is opposite, Physicists think Quantum Mechanics is more convenient and its precise as well.
What was being dealt with separately, can now be and must be, for other reasons, dealt as the same thing.
Unification is not always that unnecessary. Classical Mechanics is like having different mobiles for one’s wife and one’s girl friends. But Quantum Mechanics is like calling them from the same mobile. Its far too convenient and the wives and girlfriends find it ok. Its the reality of nature that we’re gonna have both and Quantum Mechanics is more respectful, of the laws of nature, at-least in the realm in which its its necessary, rather than optional, that facet is clear.
With the rotational forces identified as Pseudo Forces, the modifications that were necessitated, were simpler — or perhaps they seem so now, after great deal of analysis. But on the other side, they triggered such a field of advancement as Relativity.
Relativity is simply an advancement of Galilean transformations into Lorentzian Transformation, an equivalence of various quantities — couple weeks ago I set onto writing “whats equivalence” but never really started it, Relativity is simply generalizations and simple mathematical insights such as “one not only differentiates speed but also mass”, why let mass be a constant, mass and speed occur in momentum together and there was no reason in the past as to why mass be considered constant.
It is difficult to guess, exactly where, Einstein’s insights make the ideas of Relativity so deeply advance compared to the Newtonian Mechanics the latter including the advancement of Rotational Forces. But the fact is Relativity is a classical mechanics theory. One can simply distinguish Relativity from Newtonian Mechanics, by saying; Newtonian Mechanics as old classical Mechanics and Einsteinian Relativity — special and general, as new classical mechanics.
In the formalism of Physics, there is no strict definition, as-to what to be called classical and what not, if we are attentive in the next 500 years, quantum Mechanics may be together with rest of it prior to it, called classical Mechanics. The word “canonical” represents the classic nature of a theory, although in the most formal methods of it, as applied to the terminology of Classical Mechanics. Classical represents “as in the literature” and canonical represents “as in the methods; a standard formal way of doing something”.
Relativity and Quantum Mechanics can together be called New Mechanics and its also called Modern Physics. But in this nomenclature “modern physics” the unprepared, can mix it, with the definition given in the true sense of history and formalism of Physics.
Thus we have Classical Physics and Non-Classical Physics.
- Classical Physics: Newtonian Mechanics — old classical and Einsteinian Relativity — new classical.
- Non-Classical Mechanics: Quantum Mechanics and QFT, QCD, String Theory, Super Symmetry, Standard Model.
- Modern Physics: Einsteinian Relativity — new classical and Non-Classical Mechanics — above, QFT etc.
But then there are parts of Relativity which are thought to be non-classical — this is a misunderstanding. One can say Doppler effect of light was known in classical Mechanics much before Relativity but Relativity successfully explained Doppler effect, thats because; Relativity is merely classical Mechanics with added orders of correction * and a few more generalizations.
* To the 2nd, 3rd order and more and the order of correction is the only way Relativity is different from classical Mechanics and there may be just one or two more ways, in which. Also Relativity had elements of quantum mechanics, much like classical mechanics had elements of Relativity, who is asking to comfortmentalize Physics this way, lets just call it Physics, if one is confused but lets not make it erroneous.
Actually the elements of a new theory are always to be found in old fields of study, from which they are developed. In the end everything must be quite simplified, but the tracts of development can’t be changed and a historical record will contain the complicacies, these tracts and the nomenclature etc.
What-if we made a mistake?
We have to refer to historical development and find out. Some of my recent research-articles point out some chronic misunderstanding about Relativity.
- eg the principle of equivalence and time dilation, two major understandings of Relativity I have shown to be old-classical — Newtonian-Galilean, in nature; with exactness coming from Relativity — Einsteinian, because of order and precision in the latter.
- Similarly the idea that space-time is warped, is not Relativistic in the Einsteinian sense, but a very simple geometrical concept, whose exactness again comes from Einstein’s great insightful work.
Formalism of Physics.
Now lets turn to whats the formalism of Physics. This is quite in detail, described in the following article: Why is energy conserved?
The idea that Relativity is a classical Physics theory is quite well known, although, it has elements in it, that makes it look like; it isn’t. So the recapitulation of the formalism of Physics — as linked above, makes it clear, why so. Very popular ideas of Relativity can in-fact not be Einsteinian, in the strict sense, but Einstein was the first to have these insights in their manifest and explicit form to higher orders of accuracy.
But some of these ideas are essentially understood in terms of simple Newtonian formula. Einstein’s works are a powerful method, that formalizes these into a new field — known as Relativity Theory. So the exactness or higher order precision comes from Einstein’s work. Some of this is described in — “What is theory of Relativity” .
So to recapitulate the formalism of Physics, one defines something called an action which is an integral of the total energy wrt time. In-fact one would say its the Lagrangian which is integrated but one can also formulate everything in terms of Hamiltonian or total energy.
But this is because if we have kinetic energy [T] and potential energy [U] known or formulated, we can constitute either a Lagrangian or a Hamiltonian; which are simply different algebraic operations of T & U. Its like constraining something without directly spelling it out. A palatable parenthood lets say.
Its here that the elaborate formalism were formed by merging Heuristics etc into an unified formalism over the centuries — from Galileo to Newton and later.
eg One can understand various problems using only Newton’s laws, which are heuristics and formalism, but not the complete formalism, one does not go here onto energy and action which are later day unification. Newton’s 2nd law formulation is different from principle of least action and principle of least action is different from principle of stationary action.
All these physical principles lead to physical solutions, at a different level. But Principle of stationary action is the most general of them all and Newton’s law is perhaps the least.
There once was an interview of mine — not too far into past, when the interviewer continued to make a false bravado that Newtons laws are general formulation of the Lagrange’s formulation of mechanics. I only mentioned once that its the other way round. When he seemed visibly agitated, I stopped further insinuation. These are the people that are made into directors of programs in science in general and Physics in particular.
These facts came over the century, not in 1 year. Its a Grand Unification of a kind.
Now we have the action integral, defined from total energy, Lagrangian is a total energy although not in a mathematical sense, but in the sense of equivalence, because we can’t define Lagrangian, without knowing T & U which then go into defining Hamiltonian, T + U, the total energy. This is what I commented above, Lagrangian is a particular way of constraining the T and U, to lock them, without directly spelling the T or U.
So whats fundamental is T &U are known separately and then we make any combination, then our theory just becomes convenient or complicated — we can check back. But since we know them (T, U) separately, Einstein did a trick in his mind, he dealt with T first and made all necessary changes to Physics, as needed, by recognizing some general assumption, eg mass is not constant, but to be differentiated.
This way, he got Special Theory of Relativity.
Then he mapped these ideas and methods on to U = potential energy and its called General theory of Relativity.
Actually to call General Theory of Relativity as Gravitation, is to call US as a cowboy nation. Of-course cowboys are Americans, but what to do with Blondes? and Red heads? and Yankees and so on? OK to call it General Theory of Relativity or to call it a general theory of Potential energy, are almost equal.
The Lorentz transformations are first obtained by systems with only kinetic energy in mind: just speed of frame of references. But I slacked a little: the general theory is then all the changes onto kinetic energy and potential energy situations. This has been described in the article “What is theory of Relativity” with a diagram. The application to gravity is only a special case.
Now that we have action which is like a space-time total of Force, as Energy is a space-total of force, its aptly called action because action represents over all space-time the amount of force = inter-action present. Now that we know the total space-time action or force we can have only those trajectory or trajectories for which this action is the minimum or rather stationary.
Lets check for some consistency here, minimum = 1st derivative zero, stationary = 2nd derivative also zero? so we are a bit more careful that the action is really not changing from one path to another.
Let me drop here some good diagrams, that I had made in another article, to make matters clear, about some of the points I have been making, lets check the first and last diagram, to see, what it means to have a stationary trajectory, lets remember a trajectory is a set of generalized coordinates.
Energy — or more generally, action, distributes itself through an equation of motion, which is a differential equation, obtained by applying principle of stationary action onto Hamiltonian or Lagrangian Action Integral.
Why Gravity slows our clock? Anyway its a classical-gravitational-effect — not Einsteinian. Einstein simply predicted the exact form of slowing of a clock due to gravity. Gravity is a negative energy for participants of gravity, hence, a slowing of time.
The relation between force and energy. A force free region is a flat-in-energy region. On the other hand, gravity is a warped or curvy space, due to an inverse square force, energy is inverse of separation from source of gravity. Evidently energy is not flat anymore. The well represents such a fact of non-flat-ness of the gravitational energy. To experience gravity means to experience negative energy or an energy well. One loses energy in a gravity experience, hence clocks run slower, just like we would if we are tired and have lost our energy.
Criteria of Quantization of Forces.
Lets get back to the equation of motion, which we obtain by submitting the action S to calculus of variation [del_S = 0] we will thus obtain a differential equation, called equation of motion, which connects all variables, from energy down to speed and distance and time, in the form of this equation.
The first diagram above — diagram 1, explains how a given amount of energy or force transmits down to the level of change in distance and time. It goes through a path of generalized set of variables which are all, related to each other, hence a differential equation. So if energy is a function of space or simply time, we say space-time is not flat and time dilation and length contraction are simply an imminent change in space or time, since there is a change in force or energy or more generally; action S.
Time can differ or deviate slightly, due to various reasons and would reflect as a change in space or time, speed, momentum etc. There is nothing special or general relativistic here. Only when our Lagrangian is general enough to accommodate Relativistic ideas, the time dilation will be exactly what Einstein predicted from his work.
All laws of Physics are derivable from this formalism called action-principle or principle stationary action — and sometimes least action as a specific case.
Now this statement is not only valid for classical mechanics, but all of Physics; including Quantum Mechanics and QFT and what not. The only difference is we go on defining everything appropriately.
The attribute of classical physics is, it allows waves and particle-systems, but separately. The energy and force gives us definition of fields and potentials. So one may always say field, force, potential and potential energy for a physical problem. If one quantity is there, we may define the corresponding variable, by either differentiation or integration.
One has to be somewhat careful in what framework one is dealing the system. eg in a relativistic system, one has to be careful how one is defining the force etc. So there really is no difference in Relativity and Newtonian Mechanics, as far as formalism is concerned. One starts with equation of motion, of either a wave or a particle. One equivalences E, B, Energy, momentum, all forms of energy etc in Relativity, but not wave and particles. Wave-Particle unification is the exclusive regime of Quantum Mechanics.
So one has a different form of equation of motion for wave, than for particles and these two forms are present in classical mechanics — including Relativity, separately. Read more here.
But this form becomes one in Quantum Mechanics, which is what Schrodinger’s equation is. But the catch is Relativity has in it, the force and fields of waves, which are at the same time; the forces at the quantum scale, namely electromagnetic energy, force and fields.
So naturally when Relativity is extended, to fit into a wave-particle equation, it automatically unites the waves of em and particles as well. Its not a relativity attribute, but a QFT attribute. One does not have a gravity wave or gravity QFT parameters by default, in Theory of Relativity. Of-course the Quantum Gravity and other QG-GUT studies have to assume some forms of QFT parameters in the framework of Relativity; as an attempt to quantize it.
One will do really well to realize one concept, it came just a couple of days ago to me, if one has a fundamental force, field or energy, which propagates through waves — and at the quantum scale, its certainly going to be a quantum mechanical force — QFT therefore, wave-particle nature ascertains eg a force carrier quantum and source quantum etc.
Every force is a particle-force by default — although action-at-a-distance was sacrosanct in Newtonian scheme. Sans the Newtonian limitation, having a particle automatically means to have a wave.
How-else will action travel?
So if a force is not known to be associated with a wave, it simply means its not a QFT — or quantum mechanical, force.
We guess that Gravity must be a QFT force in other words its action must travel via a wave-particle quantum. But there is no evidence so far and the misunderstanding is Einstein’s theory predicts it. Its predicted by the very idea of physics, not even classical mechanics, as explained above what comes as a formalism of classical mechanics, is only a development of all we know, since primeval times, in terms of physical attributes, that we understand * see below.
Actually there is a catch: does gravity exist in vacuum?
Also gravity can simply permeate through a convection or conduction of space-time, rather than a wave-particle carrier of the force. These are not quantum mechanical force, by obvious observations. There has been no evidence, so far, that gravity exist at Q. Mechanical scales or in other words gravity waves and particles exist.
This is a simple idea, one does not jump to mathematics of the highest order, for no reason, for the heck of it. Even a greatly theoretical particle is one which comes along because there has been a great deal of physical validation that has gone into it. We quantize the QFT forces because we know 3 things about them;
- They exist at the quantum scale.
- They have waves associated with them, that we know and particles that we as well.
- We know that having a phenomena like that, is explainable, by simple mechanics: action principle or a differential equation with physical parameters.
There is no other reason to call for a differential equation. Why a differential equation why not eg a trigonometric or algebraic equation? — Not all algebraic equations eg will map into differential equation, just the Pauli matrices do.
We can not chose arbitrary equations and derive physically viable answers from them. So a theoretical particle is not strictly theoretical. And we can not for apparent reasons, extend this privilege to Gravity yet. We just can’t quantize gravity because we want to. We must find the above 3 criteria to be satisfied, by gravity and obviously gravity does not, yet.
* Gravity wave’s validity — Gravitational waves actually, since gravity waves is used sometimes in a different sense, can be understood by this following simple idea, irrespective of whether; it can be quantized or not.
A satellite is falling towards earth, because of earth’s gravity and it knows how far its located from earth how-else it would know it has to experience what amount of force. But … how does that information gets transmitted to the satellite? Most think therefore a wave-particle exists, that gets transmitted, to the satellite; to tell it what force it must experience.
But I think thats unfounded, because;
- Earth and satellite are gross objects, large, how will they interact with the quanta? without being quanta themselves? That will constitute another force, of quantum nature. * See the whale in ocean analogy, below.
- The force of gravity might simply be conducted or be convective — like water or a chain of iron, to another point in space-time. In that case a gravity force’s existence — as a QFT force, will be valid, if and when the large objects recede or approach each other and that determines how fast the objects will respond, in other words what will happen to over-drafted energy, since they may or may not have information that the objects have moved.
* To understand Gravity force and Gravitational waves think of this. A whale is moving in ocean. The Ocean is flat but because the whale is moving this flatness is no more there. There are now waves in the surface of ocean — and below of it. The whale’s gone. But the waves are there for some time. These waves are inducing much turbulence, to other small objects. These small objects are then moving towards or away from the whale, even after the whale has moved off.
Such a force need not come from a quantum scale.
Space-time is like ocean surface, and it extends across the ocean = Universe, far larger than the whale. The whale can move off, yet its wave impacts will be there for a relatively longer time. Its a large force, hence will live longer and deeper; gradually getting divided into small proportion. These forces are not coming from the molecules of the sea surface, although the energy gets dissipated into them and creates various auxiliary forces and converts into heat etc which can radiate electromagnetically.
Why then one needs to think one must unify the Gravity Force with say electromagnetic force? It may simply be unnecessary and nonviable, since the force does not have a quantum mechanical wave and a quantum mechanical particle.
In the above whale-in-ocean analogy one can see the force exists after the whale has moved off. Think of a whale which is in periodic motion in the ocean in a circle, it will start to swarm-in the smaller objects, in the ocean, along with it much like earth takes moons and satellites. Then the question arises, since how-long the whale has been in motion — or the earth is in motion, because here the force is being convective or is being conducted, not transmitted, its a huge force — in terms of scale, not in terms of strength.
Only if the Gravity force is present as a cumulative effect of many gravitational objects in space-time which can occur anywhere in the universe, does it create in the vicinity of any object; an impact which goes by the inverse square of separation to a practical infinity.
But then why it has to be inverse square?
Background of the discussion.
— This discussion ensued because of the following conversation — between Jon Vos Post and Synch and Synch and Me.
Gravitons are a prediction of quantum-gravity theories. Gravity waves are a prediction of Einstein’s General Relativity theory. These are separate issues. However, gravitons are required by super-string theory. Although there is much controversy in the physics community over super-string theory, the recent discovery of the Higgs Boson at CERN, opens the road to the discovery of super-symmetry partners, especially after the LHC is ramped up to its design energy of 14 GeV.
This may be two years in the future, of course.
Gordon Kane — who won $100 in a bet with Stephen Hawking over the Higgs Boson, has shown that there is an intimate connection between the Higgs Boson — or Bosons, and super-symmetry and super-string theory.
“Gravity waves are a prediction of Einstein’s General Relativity theory.” You said.
How is that?
Isn’t classical Gravity — Newtonian + Einsteinian, a particulate theory? The only waves we knew were electromagnetic and acoustic. In classical motion — Principle of action for either particles or waves, particles and waves are not mixed. They are mixed in quantum mechanics.
Because Einstein Equation draws on the equation of motion of a particle, despite of it having field tensors etc defined, it is easy to construe that it lends to gravity-waves. But I think — which I haven’t checked, the Einstein equations do not construct any waves. In general the old classical mechanics also had fields and/or forces but they are not waves unless the wave properties are introduced, which is introduced for em-waves in classical mechanics.
Since Einstein equivalenced Electric and Mag fields into em-waves you would think gravity is a wave. But thats not so. Gravity fields are only equivalenced to acceleration, hence energy of only gravitational kind. The em wave’s energy eg excluded from there. Or the em-wave’s energy can predict a consistent gravity theory and unificated — which is the goal but not reached, yet.
But one takes the gravity field equations of Einstein and tries to solve them as wave equations and particle equations at the same time and quantizes the fields to predict the gravitons. Hence a gravity-wave field is synonymous with a graviton. But gravity wave based field is different from gravity field. A gravity field is known from Galileo’s time, but we are still looking for a gravity wave-field. This wave or quantum, are yet unfounded.
Your 2nd paragraph is speculation and the 3rd one; because one wins a bet does not mean one has a theory, when one says something. Hawking likes to lose bets in order to sympathize with a better cause. But I am not belittling Kane. I am just unaware of his idea.
Synch: I know it’s a damn big discovery — Higgs, because if Gravitons exist they need that mechanism – you did mention something about an apple falling regardless of gravity. I take Wolfram more seriously then I do anyone – he has an intellect that is just out there.
Dash: I agree with Post’s idea that super-string theory may have it with the graviton. But I do not know anything about having it with Higgs — Kane’s idea, I just don’t know, his idea was popped up recently in the wake of Higgs I think, which does not matter anyway; if its a good idea.
Reg. Wolfram’s article, I did take it very seriously, I am quoting his idea as the concept that can be said as a central underpinning. But I think he dozed off a little to the last 3 paragraphs. Pun intended but seriously stopping experiments means having a lousy theory.
A graviton is a quantization of a simple field. A Higgs is a quantization of a field which is related to the field of every other particle. We haven’t asked if Higgs gives mass to Graviton or not?
Apple falling regardless of gravity has nothing as such to do with Higgs. I have a simple analogy why Higgs gives mass to other particles in a very recent article with “Higgs” in the title. Please have a look. Its very simple. Higgs is simply an idea where all particle’s mass-parameters are valid only through the mass of a Higgs. Such a complicated scheme is first made consistent and quantized to predict Higgs. Then we have a seen a Higgs-like just as of yet. — My bet would be its Higgs or at-least lead- Higgs.
But this later idea I am telling you from Stephen Wolfram’s recent article. Its a brilliant article. Except one major disagreement to his 1st of last 3 paragraphs, where he thinks we shall base our theories on experimental knowledge we have gained so far and not new results as this makes the process inefficient. I do not at all agree with this contention. Since he is in my list I did not tag him. But I mean no disrespect. His article is a brilliant reminder and informative and comprehensive. It was too long and I gathered to patience; to read it.
Post: Contradiction: “classical Gravity [Newtonian+Einsteinian]” as The General Theory of Relativity is anything but classical, predicts gravitational quadruple radiation, predicts black holes, allows time travel …
Dash: I disagree with your contradiction. This is why I often use the terms old classical mechanics for Newtonian Mechanics and new classical mechanics for Relativity. Relativity is classical Mechanics since its the same method of treatment through the principle of stationary action. The action in old Classical Mechanics lends to a differential equation of motion which describes waves and particles separately.
Relativity has this attribute although it can be called New classical Mechanics, since it advances the treatments and brings in many hitherto not-understood physical properties such as time dilation, universal speed limit, equivalence of mass and energy and E, B etc. It merely brings more precision or higher order effects — for Relativity special: Doppler effect of light, aberration, for general relativity: perihelion of mercury, black-holes.
But strictly speaking its a classical theory.
On the other hand the Quantum Mechanics can’t be said to be a classical theory, because here both wave and particle actions are merged into one, through just one differential equation. I have described why this misconception of gravity waves occurs, in the following article after a discussion with Synch. But black-hole — Schwarzschild solution, is a classical gravity concept … — in the stricter sense of the word there is only classical or quantum mechanics.
The simple answer why Relativity can be misunderstood to be a non-classical theory is; it describes the Maxwell equations or in other words deals with E/B fields which are QFT forces, hence quantum mechanical or non-classical.