Posts from the ‘quantum mechanics’ Category
July 18, 2012
In simpler words symmetry means nature of force and unitarity means Oneness or unchangeability of the force. So symmetry and unitarity are mutually found.
Take this example. A man is driving on a highway from a shopping mall and reaches home. Its the same man that was in the mall that is now at home. So the underlying force didn’t change the man into eg a bear. This “nature” of the objects is called a symmetry and quantitatively this is to be described by forces that are unitary. That is the force thats involved didn’t change the shape and size of the man. shape, size, appearance are therefore unitary. But the man sweat off, changed clothes, lost some pizza weight etc and thus one needs a new force to explain such change. This is a symmetry breaking. The changes are a symmetry breaking. The constancy is a symmetry.
Now think of an electron. The force here is such that the electron will change into something else. It may or may not change, just like the man. In one case a force that describes the electron is a symmetry force. In another its a broken symmetry. Broken symmetries can be added to symmetries to describe the whole picture and this new definition is called unification.
The unitarity is the fact that many variables change but in a way the over all change is zero.
[mainly energy does not change, but also carries to other conserved variable, in Quantum Mechanics probability is connected to energy density hence energy conservation or unitarity is probability conservation, that is, if you normalized probability distribution you will have that so for all time evolution. Normalized probability is 1 which is why the name unitarity. Unitarity force would mean normalized force when all force must add to unit-force ]
When thats so its called a symmetry. electron scattering off a proton is a symmetry or a unitarity group because its still the electron. But electron changing into say a photon by making out with a positron would be a breaking of that symmetry if these two processes are to be defined by two different forces.
July 17, 2012
July 15, 2012
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.
I am not going into history so much to capitulate every tiny bit of knowledge that were to be understood or misunderstood because I am not writing a book here, but a simple blog with a simple few things in mind which I forget over time if I were not to write them. I forget them even when I write them. Its a perspective changing article often but I myself can’t remember all of it. Its like a magic wand that I have got, I play it and it gives some insight then I become an ordinary fella. But for my peace and the peace of many other that are related to me I better confess that I am like a magician. I do it but I do not understand the deeper consequences or causes of what causes them in the first place. But we are mired in so much darkness and so much prejudice we are often carrying forth that we continue to forget the truer aspects of certain things where we focus.
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 this website: http://mdashf.org/2012/02/12/machs-principle/]
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.
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?[http://mdashf.org/2012/07/01/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” http://mdashf.org/2012/06/30/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.
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. [check: http://mdashf.org/2012/07/01/why-is-energy-conserved/]
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] http://mdashf.org/2012/07/12/whats-up-with-gravity/
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.
July 12, 2012
The recent findings of the Higgs aka the Goddamn particle aka the God particle has thrown into prominence a few fundamental problems of Physics. Whats next is the buzz word. There are a bunch of fundamental problems in Physics that can be thought to bear with this. People are saying in a language of particle-physics which particle next? Graviton or aphotitons/Unlitons? The later is a name for the purported Dark-Matter particles if you care to name them like that. Its one matter that Higgs has not been found as such in terms of formal claim but a Higgs-like. But Hawking has conceded defeat to a bet woth 100$ while thats not a way to think Higgs is confirmed I also stand by it that: Higgs-like is a Higgs-lead or in other words there is hardly anything that I can think now that will debilitate the chances of Higgs or Higgs-somes. As a particle experimentalist its my 6-th sense [one sense per quark] that this is Higgs and this will be confirmed.
But Unlitons is a quite different issue. One can ask if Higgs gives mass to Gravitons? Does Higgs gives mass to Unlitons? These two will perhaps be the same question if you have Quantum Gravity in mind: Ina situation where GUT is a success every particle would necessarily mean Gravitons and Unlitons which will perhaps only be gravitational.
But the important question remains what are Gravitons ?
What are particles? What are Fields? What are waves? What exactly is a Graviton?
OK then lets start from basics.
Lets invite Newton over a dinner and ask him this: Sir Issaac Newton? Whats Gravity?
Heila hypothesis na fingo. A Gravity is an inverse square law Force and an inverse proportional energy. You call this force Gravity and divide that by the mass of the object that experience the force and you get a field. Lets imagine these objects are particles cos “I ain’t talkin” about waves. Huygens would be but he is such a brag. CAn you pass that soup please, up close?
Ok so we learned that there are energy, fields and forces for a particle which experiences these given a position and time for the particle around another huge particle thats producing this force.
How does the particle know where in the world the particle is wrt the Huge central or primary object? Its not like there are signs around this primary object where like a speed limit is written on a highway the energy and field values would be written. The secondary or small particle now has to talk with the primary object to know where its situated wrt the primary. How does it do it?
Newton thought it does so by action-at-a-distance. The effect of the force would be known instantaneously. Galileo did an experiment on speed-of-light and found such a behavior of light. Forces in his days were perhaps thought to transmit to infinite distances with infinite speeds, in other words the fact that you are here and you experience the effect of the primary means the primary has sent the action to your places instantaneously because while you are experiencing the primary you have signed no bonds that you will be stationed there and not relocate. I mean there are so many good things in life to be enjoyed. But you moved slightly and how would you know whats the effect of the primary, you need to know it instantaneously and you do experience the effect. So its only built into such an understanding that forces/fields/energy transmit themselves at infinite [or at the will] speeds. Monsters and epic manga can have such a scheme but we shall not judge Galileo or Newton for they were our only hope in those times to first flinch and then savior modern science from the clutches of a society that was predominantly anti-scientfic as they are now at-least in the way in which philosophical debates are made against ideas of Higgs, a scientific particle because its been named “God-particle”.
Ok so the force transmits at will. But now we know that thats not possible. We actually knew that since much more than a century. Waves of electric and magnetic phenomena travel at tremendous speed but not infinite at will speeds. So the kinds of fields the electric or magnetic phenomena are associated with travel at finite speeds. Those forces are not infinite so Gravity can’t be either.
One thing, when the electric and magnetic phenomena were understood, that came up was they satisfy a set of equations called Maxwell’s equation. These equations can be easily moulded into a form known as wave equations of motion. The objects that are particles such as the ones that experience Gravity as per Newton, satisfy a different kind of equation of motion known as the particle equations of motion.
So there are equations of motion which better be known as particle equations of motion [Newton’s 2nd law is one example]. There are wave equations of motion. And the form of these equations of motion are differential equations of motion. When solved with appropriate information regarding a physical system they give us answers that we are often familiar with eg how a tennis ball will fly when you hit it with a bat or how a magnet will produce electricity if its rotated with “much” force.
These wave equations which therefore satisfy the waves known as electromagnetic waves because eg a radio device can send such signals of em waves are in terms of two fields known as Electric Field E or Magnetic Field B. But these equations are ready enough to be treated in the framework in which Einstein wanted to test every physical law. They are Lorentz-invariance ready. The speed of these waves were like for any wave equation [eg sound waves satisfy sound-waves equation of motion and this equation gives the value of speed of sound waves in various medium and vacua]. The Maxwell waves or em waves were found to have a speed equalling to 3×10^8 m/s which is called speed-of-light because light was known to be an undulation of E and B in a way satisfying the Maxwell’s equation. In other words E produces B and B produces E as per validity of these equations.
But their preparedness for Lorentz Invariance is a bit calling for much more attention. Here the E and B cast/map themselves into Einstein’s equation of [particles, waves] motion called Einstein Field equation where the fields are Tensors. So some quantities of Newtonian mechanics [Old Classical Mechanics] cast themselves into what are called 4-vectors and some into Tensors so that these quantities when looked at from another frame of reference would retain some sort of invariance. Or in other words when a transformation of frame of reference is effected lets say energy is the same in two different frame of references if the frames of references differ by speed and thats wrt a passage of time. But this time the Energy is in the sense of a magnitude of a 4-vector which is conserved wrt the passage from one frame to another but only energy is conserved wrt a passage of time. These 4-vectors and Tensors then constitute equations and constraints among themselves which are consistent with old classical mechanics or Newtonian mechanics. Einstein’s special and general theory of relativity can be said to new classical mechanics.
Now Einstein’s equations or New classical mechanics has in it both waves and particles. But nobody is yet alarmed that they will lead to quantum mechanics not even until 1930s when Qmech was not realized when Einstein himself became a vociferous critic of it and later recanted. he wanted to show that he had a tongue in mouth not a damn foot. He was not a fool but a great fella.
But what was recognized was perhaps unification such as space and time as space-time. Energy and momentum into Energy-momentum 4-vector. Which is why Einstein’s Relativity is called a 4-dim theory and our world suddenly became a hotspot for intellectual debate as people thought they might have had been ignorant of such a drastic character in the fabric of the Universe. Actually E and B were also realized to be an unified field. Or for not only particles there are fields but there are also fields for waves. From the wave equation of motion called Maxwell equations in the case fo E, B it was known that speed of such waves is 3×10^8 m/s. Einstein also espoused the idea of ultimate speed limit [speed of em waves] as there were no other forces known in those times that would have traveled so fast. All the Physics was understood by Einstein, hence he did not see any reason why he should not employ such an idea of limitations to relay of transmission of any kind. This might itself be the basis of Quantum Mechanics since something traveling at highest speed must have lowest mass as having mass would only take some amount of energy away. So we have something thats moving at speed of light and must have a mass of zero. Now waves are traveling at this speed but whoever ever has thought of a mass for waves? Einstein equivalenced mass and energy hence waves having energy must have mass. But the frame of references in which the speed of waves would be zero would be a frame where the mass of the waves would be zero. But perhaps nobody thought like that. Everyone was working on the theory and the understanding and many things gradually set into our understanding of it all. Even to this day this trend is going or we wouldn’t be asking numerous questions. Science!! such an affair. It pains you but you get the pleasure of knowing something thats not obvious but thats so immensely useful.
It was later realized that light not only propagates as wave but also as corpuscles. [There is a corpuscles theory of light of Newtonian kind, whats that? ] And this corpuscle called as photon can be said to have mass zero, but I don’t know if they did realize it or not. We are living in times when QMech is the order of the day and understanding of Relativity has been colored by QMech or the advance formalisms.
So here is the idea: Einstein’s framework/formalism of Relativity has in it both wave fields and particle fields in a way they are correlated by some constraints which were not as detailed by anyone’s work as they are now. They were unificated eg through Gauge symmetry [Phi, A fields are an advance way of saying E and B are the manifestation of the same field] But unification is not Quantum Mechanics.
So the Relativity of Einstein has particles of Gravity and waves of E and B etc. The fields of Gravity are particle fields, fields of Electricity and magnetism are wave fields. Being a wave has the advantage that you know the speed by default and there is one speed. They have to travel at a fixed speed. So as far as it goes we know Gravity fields as a particle field.
This then transpires to a very fundamental problem: is there a wave called Gravity wave. The basic properties of a field having a wave nature means extraordinary consequences. First off the particle nature of a field is default. [You have objects around you which experience this force or that force] So when there is wave nature to it it must mean that they together satisfy a wave and particle equation and hence must be a result of wave-particle equation and this is known as Schrödinger’s Equation, or a differential equation in qunatum mechanics in general. Then the field of this particle or wave can be quantized. Or in other words such fields/particles/waves are synonymous with each other. Having a particle automatically means a corresponding wave and vice versa. For a fundamental force this means a force carrier particle called as a Gauge Boson [0, 1, … spin] which travels at speed of light and a force experiencing or interaction sources/charges/currents that are Fermionic particles [1/2, 3/2 … spin]. Further a 0 spin Boson or force carrier is a scalar boson and spin 1 is a vector boson and so on. The Fermionic does not have such a special name but the fact that there are many kinds of Fermions. eg electron is a Fermion. Quarks are Fermion, protons are Fermions. But the Bosons are a very few kind, eg about 4 kinds that have been found, 1 purported that has not been and one Boson which is special because its not a carrier of force but gives mass to every other particle just like Your friend John gives beer to everyone who goes to his club.
So to have a force carrier or messenger for the Gravity particle-field so that the 2ndary or Gravity-force experiencing particle knows exactly where it is located wrt the source of the Gravity one must have a wave as well of this field. You either have a particle field a wave field or both and it has so happened that the 4 forces of fundamental nature that we know so far 3 have this characteristic: they have both wave and particle nature for their fields. They have therefore been quantized from a single equation of motion called the wave-particle field’s equation of motion.
But one of the remaining force-field the Gravity force/field/energy has not been known to have a wave and particle character. The erroneous understanding that General Theory predicts Gravity waves is well: erroneous. The fact as I just explained above to have a wave nature of something is to by default meet by a particle-wave nature and hence quantization since particle nature is a must. This is so if you consider something a fundamental force. And Gravity is considered a fundamental force.
So there are two approaches to face this problem
1. Consider Gravity alone and let it have just wave nature, we already have its particle nature hence it must lead to quantization a la Quantum Field Theory [a way to let the forces or fields or energy to be quantized and satisfy the equations of motion for both particles and fields and have the properties of Quantum Mechanical systems] Then unify this resulting quantum-field with other fundamental forces which are Weak Force, Strong Force and Electromagnetic Force. Note that all these forces were dual Field forces [particle and wave] and they are unified. Unified means in the greater framework of a theory one could define just one variable which would give the different forces under different physical situations. Its an equivalence!! just like E and B were unified and is a same field in the greater frameworks. USA is a unification of 52 states. They are all equivalent wrt a certain privilege if the “Federation” makes it so. But its not unified with Mexico although Mexico has its internal equivalence which are not same as that of US. But given the definition of United Nations policy/pacts Mexico and USA are unified.
2. To unify the 3 forces described in 1 with Gravity and then look for clues to quantize Gravity. To say “quantize” is to mean an acronym for having both wave and particle nature of a variable such as Force, Field or Energy.
Its not necessary that any of the above two will be satisfied. But then how could we understand that a particle experiencing the force of gravity knows where it is present in the gravity field? We can’t allow the relay of information to surpass that of speed of light. That will invalidate everything else we know which have worked so well. This is a Physics problem and this does not come with a priori solutions or insights or ideas or answers.
One can only see deeper and deeper.
But what has been done so far as I understand is the wave nature has been imposed on Gravity Fields by considering such an equation of motion and then letting it quantize [which it must since now it satisfies such a differential equation]. This is called as an attempt at GUT, the vision of Einsteinian Era. But the whole idea of letting fields have both particle and wave nature is the most fundamental and central formalism and nature of Quantum Mechnaics [which is called Quantum Field Theory, since Force/Field are involved]. This is therefore called a Supersymmetry Theory since it has superseded all expectations of trying to stop loseends and find a happy marriage of what we know and what ought to be there and what its forms shall look like [eg missing particles: supersymmetry]. Its a 3some marriage.
So there are two ways of looking at the Gravity Force the GUT vision and the elegant formalism of QFT [call it Quantum Force Theory for once no !!] and GUT can’t necessitate a wave by its own nature without leading to QFT-supersymmetry. Supersymmetry can’t dictate terms to what we must or must not find as long as we don’t. eg Higgs was found as a characteristics of this central tenet of QFT hence people have started talking about supersymmetry GoldRush now. But its not clear whether General Relativity actually predicts Gravity waves. If it does you immediately quantize this wave-field and get the character of the particle called Graviton. No Classical theory has an apriori property of predicting if there must be a wave nature to an inherent field without first observing such a wave. You observe electro-magnetic field hence you can right away write some sort of equations that satisfy wave-motion. To predict such one must have a wave equation by default not by imposition. The imposition is necessitated as I explained to avoid action-at-a-distance which is a catastrophe as also explained. But we have not observed such Gravity waves, the there are experiments that are set up to circumvent this problem to bring some credit of observation to teh Physical problem. Any kind of observation helps in the type of physical problems that have no clue. But particle nature is by default.
The basic difference is a Gravity Force/Field is experienced by huge objects which are not operating in the quantum scales and for a unification with all other 3 forces which are quantum-scale forces one must be in such a scale. How can you have a quantum-particle communicate information to large objects such as a ball or a satellite or an earth?
And Gravity is not observed for quantum-particles, they have mass which is energy and their energy is satisfied for other forces so we do not know Gravity is a quantum-force or not that is, present at that scale as a smaller or larger value wrt the other forces. May be we can just live without unification and mind it without quantization.
Only finding something by observation can change such knowledge.