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.
Newton and Galileo are both considered to be great Physicists of our modern times for science which is counted to be from the 1600. Newton and Galileo came several centuries apart. They were dealing with the similar kind of Physics so to say. But if you review deeper you 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 unificated to a smaller set of forces but they came from the understanding of a vast deal of forces and phenomena.
Another point in making would be how 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 Galilean transformation and Newtonian mechanics which were valid only for inertial frames of references. But while Newton understood the noninertial or rotational forces he did not understand them exactly and might not have found anything to associate with. This was what was called Mach’s Principle later. [Read the article by the same name in the linked post ]
The effort by Newton to understand Rotational or Pseudo forces as they can be called is akin to how Einstein wanted to understand a grand unification of all fundamental forces known as GUT or Grand Unified Theory. This is today as unfounded as it was ever although the efforts to achieve so aren’t. In-fact the effort to understand a grander unification are what have taken most of the Physics community’s muscles and minds. The super-symmetry theory, string theory are all 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. [Also compare Newton's efforts at Rotational forces or Pseudo forces with Feynman's efforts/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, 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. It takes depth not a propensity to show your knowledge]
So, much of Physics from 1600 until 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 unifications 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 [or call them Ceudo Forces]. A Pseudo force would be one which represents itself as an additional impact/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 You 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. In Newtonian Mechanics with simple one dimension it was recognized that pseudo forces would come with a -ve sign, 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. In any case once your laws are valid for some aspects or some systems you are safe. Anything more will be generalized. The rotational forces are to be understood as Pseudo forces in the framework of more complicated coordinates than justaa simple 1-dim. With such newer and newer generalizations/insights theory of Relativity became a more complicated and advanced theory/field but it never really broke up as such with classical mechanics. Sitting in 2012 if you 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 you said Relativity predicts that actually Classical Mechanics predicts it. Why not research a think a bit more than make remarks. Our Physics audience is already very confused.
[here is why I said that: so if you 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 come 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. Quantum mechanics made it imminent that these two phenomena of waves and particles be dealt by the unification of both differential equations and infact it was achieved. This is dealt in much detail in another article where formalism of Physics is explained, the article is perhaps "Why is Energy Conserved?" So it was rather a fact of convenience that was achieved by unification, so Quantum Mechanics is merely a more convenient form of Classical Mechnaics. (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 your wife and your girl friends. But Quantum mechnaics 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 you gonna have both and Quantum Mechnaics is more respectful of the laws of nature atleast 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], generalizations and simple mathematical insights such as “you not only differentiate speed but also mass”, why let mass be a constant, they 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 including the advancement of Rotational forces included into the latter. But the fact is Relativity is a classical mechanics theory. One can simply differentiate 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 you are attentive in the next 500 years quantum Mechanics may be together with rest of it prior to it, may be 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 the unprepared can mix it with the definition given in the true sense of history and formalism of Physics. We have Classical Physics and Non-Classical Physics. Classical Physics: Newtonian Mechanics and Einsteinian Relativity. Non-Classical Mechanics: Quantum Mechanics and QFT, QCD, String Theory, Super Symmetry, Standard Model.
But then there are part of Relativity which are thought to be nonclassical, 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 and more and thats the only way Relativity is different from classical Mechanics and there may be just one or two more ways in which. Plus Relativity had elements of quantum mechanics much like classical mechanics has elements of Relativity, who is asking you to comfortment-alize Physics this way, just call it Physics if you are confused but don't 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.
Now lets turn to whats the formalism of Physics. This is quite in detail described in this 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 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 you have kinetic energy [T] and potential energy [U] known or formulated you can constitute either a Lagrangian or a Hamiltonian which are simply different algebraic operations of T & U.
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. They all lead to physical solution at a different level. But Principle of stationary action is the most general of them all and Newton’s law is perhaps the least. They came over the century not in 1 year. Its a Grand Unification of a kind.
Now that you 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 you can't define Lagrangian without knowing T&U which then go into defining Hamiltonian.] So whats fundamental is T &U are known separately and then you make any combination, then your theory just becomes convenient or complicated, you can check. But since you know them 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. He got Special Theory of Relativity. Then he mapped these ideas/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. Ofcourse cowboys are Americans but what to do with Blondes? and Red heads? and Yankees and so on? OK 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 was described in the article “What is theory of Relativity” with a diagram ] The application to gravity is only a special case.
Now that you have action which is like a space-time total of Force as Energy is a space-total of force, its aptly called action because it represents over all space-time the amount of force=inter-action present. Now that you know the total space-time action/force you can have only those trajectory/trajectories for which this action is the minimum or rather stationary. [minimum=derivative zero, stationary = 2nd derivative also zero? so you 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, check the first and last diagram to see what it means to have a stationary trajectory, a trajectory is a set of generalized coordinates]
So now that you submit the action S to a calculus of variation [delS=0] you will obtain a differential equation called equation of motion which connects all variable from energy down to speed and distance and time in the form of this equation. The first diagram above 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 a change in space or time since there is a change in force or energy or more generally action S. Time can differ/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 your 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 you go on defining everything appropriately.
The attribute of classical physics is it allows waves and particle-systems but separately. The energy and force gives you definition of fields and potentials. So one may always say field/force/potential/energy for a physical problem. If one is there you may define the corresponding variable by 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 formalisms are 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. Such unifications are the exclusive regime of Quantum Mechanics.
But this form becomes one in Quantum Mechanics which is what Schrödinger’s equation is. But the catch is Relativity has in it the force and fields of waves which are a the same time the forces at the quantum scale, namely electromagnetic energy/force/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. Ofcourse the Quantum Gravity and other QG-GUT studies have to assume some forms of QFT parameters in teh framework of Relativity as an attempt to quantize it.
You will do really well to realize one concept, it came just a couple of days ago to me, if you have a fundamental force/field/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 quantums 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 [quantum mechanical] force. We guess that Gravity must be a QFT force in other words action must travel via a wave-particle quantum. But there is no evidence and 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/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 gravity waves/particles exist. This is a simple idea, you do 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: 1. they exist at the quantum scale 2. they have waves associated with them that we know and particles as well 3. 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 Pauli matrices ]
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.
**Gravity wave’s validity [Gravitational waves, since gravity waves is used sometimes in a different sense] can be understood by this 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:
1. earth and satellite are gross objects, large, how will they interact with the quantums? without being quantums themselves? That will constitute another force of quantum nature. ** see the whale in ocean analogy
2. the force of gravity might simply be conducted/convected [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 determines how fast will the objects respond, in other words what will happen to overdrafted 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] 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 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 through electromagnetically. Why then you think you must unify the Gravity Force with say electromagnetic force? It may simply be unnecessary and unviable 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] because here the force is convected/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 inverse square of separation to a practical infinity. But then why it has to be inverse square?
– 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 superstring theory. Although there is much controversy in the physics community over superstring theory, the recent discovery of the Higgs boson at CERN, opens the road to the discovery of supersymmetry 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 supersymmetry and superstring theory.
Dash: “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 fields 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/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 field 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 their. Or the em wave's energy can predict a consistent gravity theory and unificated. which is the goal but not reached] 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 field to predict the gravitons. Hence a gravity wave field is synonymous of 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.
The 2nd paragraph is speculation and the 3rd one: because you win a bet does not mean you have a theory when you say 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 superstring 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: 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 ununderstood 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 this article after this 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.