Dear all,

I have enjoyed a rather violent debate with many views and controversies. A lot of confusion seems to be related to various interpretations of fundamental equations like the Klein Gordon or Dirac equation. These equations exhibit symmetries and if one is lucky they can be used to predict new phenomena or particles like positrons etc. 

Nevertheless it might be confusing to use "loose language" without employing a more careful attitude. For instance one problem is the uni-direction of time, despite the essential reversible formulation of the basic equations of physics, Newton, Schrödinger, STR. This has led to the popular notion of arrows of time. I have listed and discussed seven of them in the paper enclosed below (and Sergey, an arrow associated with gravitation is not so absurd!).

I have asked before about the CPT theorem, see also reference below. As far as we know today CPT is a law of nature, but since we do not yet agree on how to include gravity one cannot be fully sure of this.

So back to the question. The symmetries of e.g. the "Klein-Gordon", points at particles and antiparticles that have different parities regarding time and space and charge, and which we might detect experimentally in our uni-directed space-time.

Of course we can use any language we want as long as we agree on what we mean and not allow ourselves to read too much into interpretations. After all mathematics is the most succinct language for science and it permits formulations were words are not sufficient.

Because that statement implies the system is unstable-the vacuum, about which the particles are excitations, is unstable. Standard exercise, in the relevant chapter in any textbook on quantum field theory.

Dear Rajat,

Are your worries perhaps related to the CPT theorem?

Dear Rajat,

you refer to the formal assumption in scattering theory that incoming particles can be considered also as outgoing antiparticles.

Unfortunately, this formal symmetry has nothing to do with the naive idea that particles must go in the positive time arrow and antiparticles go instead in the opposite arrow time.

This belief is completely wrong !

In fact, the above change between particles and antiparticles refers only to the so-called crossing symmetry in quantum reactions. With respect to an observer, whether particles or antiparticles walk in the positive time arrow !

There is nothing in Physics that can go in the past !

This fact completely answers to your intriguing question.

My best regards,

Agostino

We read that energy has no direction?

Answer to your question can be obtained from  physics as well as from  philosophy. So far as Feynman-Stuckelberg interpretation of negative energy is concerned, a negative energy solution of the Dirac equation corresponds to a positron which then runs apparently backwards in time and vice versa. But, it can never be 100% as the third law of thermodynamics states.

From the philosophical point of view, marching ahead (for success/ victory), needs positive energy and  trailing behind (failure/ defeat) is due to accumulation of  negative energy (in thought and action). Really, entropy increases with direct proportion to the  negative in thought and action so far as body, mind and senses are concerned. That's why we don't (or can't) have negative energy particles with forward time sense and positive energy particles with backward time sense.Therefore the Upanishad declares: 'neti neti.... charaibeti charaibeti..."  means  'not this not this ... march ahead march ahead....'

My understanding is as follows. 

If particle mass is complex number with negative coefficient of the imaginary part, such as "m=m_0-ie", the Dirac equation can not have positive energy solution which propagates backward in time, nor negative energy solution which propagates forward in time, under the boundary condition that the wave function does not blow up at t = +/- Infinity.

Namely, Theta(-t)Psi(E) and Theta(t)Psi(-E) can not satisfy the boundary condition, but Theta(t)Psi(E) and Theta(-t)Psi(-E) can, where Theta(t) is a step function: (Theta(t)=1 for t>0 and =0 for t

I think it is best to remember that statements like this, like the CPT theorem, are statements that are built on the assumption of the framework of QFT.  For example, if CPT is wrong then, field theory with Lorentz invariance built in, is not the framework for such a universe.  It is possible since QFT is just a formal computational scheme and has never had an adequate conceptual foundation.  Interacting QFT is actually known to be inconsistent.  Nevertheless, it has been very useful.  

The usual arguments that one cannot have negative energy go back to the Dirac picture of the Fermi sea where negative states must be filled to prevent such a decay that Nicholas alluded to.  This is not strictly necessary.  If one does not have any couplings that can lead to such a decay or symmetry excludes it, then theses states cannot be reached.  The whole "backwards in time" thing is a computational tool Feynman employed but maybe is not worth taking to seriously in the conceptual foundations of the theory.  

It might be worth remembering that, in the construction of the U-matrix, one introduces the backwards in time integrations to make the integrals easier, without messy time ordering dependencies.  These are handy but not part of the original foundation of the theory.  They just make easier integrals.  

Dear All,

it is well known that the time-component of the relativistic 4-momentum of a particle, at rest with respect to an observer, is proportional to the rest-mass of the particle. On the other hand in relativistic mechanics the rest-mass is a positive parameter, like in the classic mechanics. Therefore in relativistic mechanics particles point in the future.

On the other hand negative energies in quantum mechanics exist as a consequence of the quantum energy conservation law. But in the quantum world particles cannot be considered point-like objects, and one cannot directly apply relativistic mechanics in the quantum world.  However, observed quantum processes are always directed in the future since this direction is induced by the absolute frame intrinsic in the universe, as I have already clarified in some other threads.

Thus I must insist.

There is nothing in Physics that can go in the past !

Regards,

Agostino

P.S.: Dear Charles bold fonts are useful to emphasize some misunderstandings ...  

No Charles !

You are doing a big confusion between relativistic mechanics, that works at the macroscopic level, and quantum world.

The proof of your misunderstanding is in your claim:

'Because negative energy means going backwards in time, the creation of a negative energy particle is seen as the annihilation of positive energy. This is the meaning of an antiparticle.'

In fact, it is well known that the mass of an antiparticle is the same (positive) of the corresponding particle.

Therefore my bold fonts underline your misunderstanding that really believe that antiparticles go in the past. In this way, you believe also that there exists an antiuniverse going in opposite time direction of our universe, after the Big Bang ! ...

Of course you can believe what you like but such stupidities are not supported by Science !

'Homines quod volunt credunt ...'

I was always confused why antiparticles were introduced this way.  One can just introduce them with a Dirac field with negative mass and use the "negative energy" solutions.  It does the same thing and is more direct with no mention of actual negative energy or backwards in time solutions.  Weinberg thought the Dirac sea was a historical artifact that should be abandoned but it still colors our discussions in ways that don't help clarify anything.  

@Charles, all I mean is that the Dirac equation i\gamma\partial\psi-m\psi has positive and negative energy solutions but the equation with m->-m gives negative and positive energy solutions respectively.  For electrons you can use the first equation with boosted positive rest solutions u and for positrons you can use the second set, v, in the standard rep, which are also positive energy.  As long as you wire these correctly to the em field in the lagrangian this works.  I have argued that the operator approach is just an equivalent formulation to this.  It is not a different theory than QED.  It only introduces it without the usual confusing talk about time directions and negative solutions.  

Initially you will remember Dirac hoped his solutions were for electrons and protons but had to face that the negative energy states could not be protons.  Even trying to treat them as antiparticles he had to confront that the energy of positrons are positive.  The rules for operators and the vacuum state make everything work but there are less ad hoc ways to get there. 

Charles, quantum electrodynamics is supported by Science, but what you claim is not quantum electrodynamics ... it is a wrong interpretation !

However, it is also clear that your claims are nonsense. Let me go in some details.

1) Your reply:

'... the fact that the mass of the antiparticle is equal to the mass of particle follows directly from what I said, and is not a counter example to it.'

This is a nonsense. In fact whether both particle and antiparticle have the same positive mass \mu_0, it follows that for both, at the rest, the 4-momentum is given by p=\mu_0 \partial x_0. Therefore for a particle and its antiparticle p points in the future.

2) You have some big confusion about particles and antiparticle ! In fact you write:

'As you rightly say, your stupidities are not supported in science. '

I have talked about your stupidities, namely your belief that antiparticles go in the past. This of course should imply that there exists an antiuniverse going in the past ... Of course this big stupidity produce some trouble in your mind ... Thus you prefer to skip on such absurd conclusions that necessarily follow from your point of view, and to simply reciprocate my accusation.

3) Quantum electrodynamics as well as all quantum processes, are well encoded by nonlinear quantum propagators in quantum super Yang-Mills PDEs. [I refer to my quantum gravity theory.] Therein the time does not exist , thus your ridiculous belief that antiparticles go in the past does not apply.

However, with respect to an observer, namely considering the observed quantum super Yang-Mills PDEs, observed nonlinear quantum propagators therein, rightly encode observed quantum processes. Then it is possible to understand that such observed quantum processes evolve into the future of the observer ... as it must be !...

4) Unfortunately many nonsense arise from a naive mixing of relativistic mechanics of point-like particles and quantum mechanics. This perverse mixing produces all the well-known nonsense of the old QFT.

I regret that you try to defend what it is indefensible. On the other hand whether QFT should be a complete theory, it should not be necessary to formulate a quantum gravity theory ... as I made !

Regards,

Agostino

@ Charles Francis

 With your last post you have clarified to all serious users you are unable to read my works !

 No ! You are not a serious user !

 You like too much write on RG !

 But when you have not enough mathematical background to understand serious scientific documents, it should be better to stay silent !

 'Asinus asinum fricat ...'

Charles, I looked to your works and unfortunately I must confirm that you have not enough mathematical background in Algebraic Topology, (Co)bordism Theory  and PDEs Geometry.

This mathematics is fundamental to understand my works. In particular you have not mathematical background in Algebraic Topology in quantum super PDEs. Really this last mathematics has been formulated and developed by me in a long series of already published works, thus it can be justified that you are not expert therein. But in order to be able to read my works in this sector it is necessary to be introduced on the previous quoted mathematics.

Therefore your claim:

'... Of course this does mean that I am unable to read your works, because they are not mathematically sensible.'

simply proves that you have not enough mathematical background to understand what my works on the quantum gravity say...

@ Charles Francis

thanks for your last post !

Now it is clear to all serious users that you are not in this category !

To discuss with you it means to lose time ... You do not aim to understand ... since you are unable to enter in technicalities ... you play with words and insult ...

This is the worst behaviour that an user can adopt !

 'Asinus asinum fricat ...'

Dear All,

Yes I well understood Stam's opinion that believes antiparticles going into the past with respect to an observer !

I instead confirm my opinion:

There is nothing in Physics that can go in the past with respect to an observer !

This is also proved in my quantum gravity theory.

My best regards,

Agostino

Dear Rajet!

In my opinion the current understanding of the reality especially of the world of particles (smallest dimensions) and the whole universe (largest dimensions) is rather an incomprehension. All the theories are only transfers or applications of known facts (mechanics, electrostatics, electrodynamics etc.) to totaly new observations resp. dimensions. It is rather that the well known facts in physics are special cases of the laws of nature in the microcosm.

"Forward" or "backward" time direction are theoretical inventions to describe reality like a mthematical derivation. You can prove that particles and antiparticles have inverse structures. Feynman and others are not the end of wisdom.

My Regards!

Hans

No Stam !

Unfortunately you continue to play with words ... and to use old QFT ...

I am glad to read that now you recognize that antiparticles must go in the future ...

But all your problems arise from the fact that you continue to apply relativistic mechanics to quantum particles, considered as point-like objects. In other words you are talking about old QFT. What you do not understand is that particles going in the past are nonsense even if they have negative energy.

I tried to advise you that such a nonsense can be solved with observed nonlinear quantum propagators of my quantum field theory, but you continue to play the wiseacre against me.

At this point my patience ends !

Good luck ...

No Stam !

I do not joke ! It's no joke !...

You are neither able to understand the mathematical structure of the old QFT. In fact in such a case you should be able to see the nonsense of quantum particles going in the past of an observer. The Feynman-Stuckelberg interpretation of negative energy solutions in QFTs, is an example of absurdities produced by that theory, ... well known from long time. Other examples are Feynman diagrams in strong interactions and their use in calculating scattering amplitudes therein ...

and you pretend also to play the wiseacre on my quantum gravity theory !  ... and also on other subjects (Riemann hypothesis) that nothing have to do with this thread !

'Asinus portans mysteria ...'

Dear All,

let us take seriously what Charles Francis believes, namely that all quantum particles with negative energy fly in the past of our universe.

Therefore, in a very far past, before the Big Bang, there exists an universe of negative energy !

For sure these are breaking news !!!

Thanks Charles ...

Maybe all this pre-big bang negative energy may explain the current negative energy in the discussion.

Dear Louis,

unfortunately for Charles there is a more serious justification to the dark energy/matter and expansion universe !

This is a boundary effect induced by the Planck epoch. Please look to my paper:

http://arxiv.org/abs/1206.4856.

Then you can understand that the reality is more complex and serious than the fantasy supported by Charles about particles with negative energy ...

He believes in flying ass ... ...

Charles, what you write

'... we know very well your ability to put random mathematical words in front of each other in your papers ...'

 means that you do not understand mathematics, since you consider it a set of 'random mathematical words'...

By now I am sure that you do not understand mathematics ! ...

Furthermore:

' ... you cannot understand even the simplest things said by other people ...'

for sure whether they are like your last:

'... all it amounts to is "green ideas sleep furiously".'

Let us look at the simplest explanation.

Using the uncertainty relation Δ E Δ t ~ h/2π we see that the R.H.S is positive. We have to set the scale such that zero energy is vacuum energy. Negative energy means less than the vacuum energy that is Δ E is negative. Therefore as the R.H.S is positive Δ t is also negative. This is a mathematical result which  is quite counter intuitive. So it is difficult to express it in plain words; but the best way to say is that the negative energy state is traveling back in time.

This not a rigorous mathematical argument where squares of uncertainties are calculated using a relation like  (Δ X)2=- 2 Then one uses the positive square root of  the quantity (Δ X)2  as the magnitude of uncertainty. This is rightly pointed out by Charles below.

Dear Biswajoy,

unfortunately your justification does not work !

In fact you use a naive Heisenberg uncertiantly relation (HUR), even if usual one ...  , it is also wrong ...

Really the correct HUR referred for two observables f, f' (read two operators for simplicity) is the following

\sigma2(f)e .\sigma2(f')e \ge 1/4||2

where \sigma2(f)e is the variance of f in the state e\otimes e. Since the variance is a nonnegative number then the HUR is always a nonnegative number on both sides. In particular this holds also in the case that f represents the quantum energy and f' the quantum time. For more information see the following references.

[1] https://books.google.it/books?hl=it&lr=&id=O5IbRdY7gqQC&oi=fnd&pg=PA307&dq=Geometry+of+PDE's+and+Mechanics+by+Prastaro+A.&ots=J5NLZFOWjH&sig=cBqqa4P-Td9UMqJQRebPlKCFFbY#v=onepage&q=Geometry%20of%20PDE's%20and%20Mechanics%20by%20Prastaro%20A.&f=false (pag. 603.)

[2] http://arxiv.org/abs/1205.2894 (pag. (II)31).

Let me add that negative quantum energies are justified in quantum world ... but in QFT, where particles are point-like objects and one directly adopts relativistic mechanics, one has nonsense like particles going in the past with respect to an observer. These problems are instead solved in my quantum gravity theory where one has extended quantum objects.

My best regards,

Agostino

Hi All,

I must thank all respondents here for their cold reasoning (and some hot exchanges/discussion) as well. I was away on a rip, so could not see all these interesting remarks/answers/suggestions. 

However, the following may please be kept in mind:

(1) The relativistic energy formula E2=p2c2+m02c4 formula (1905-Einstein) does not forbid the negative square-root, a priori.

(2) Dirac proposed his equation for the electron (including existence of positron) on the basis of such an argument that negative energies must not be impossible of existence. that the negative energy solutions must be evolving backwards in time was Feynman-Stuckelberg's contribution, due to non-observation of a backward time-arrow in a physical sense.

(3) The backward evolving (advanced waves) have been utilized in Feynman-Wheeler electrodynamics (1940-49) and the theory has been quantized by PCW Davies(1971-73). which provide an alternative to traditional retarded wave Classical Maxwellian electrodynamics and its quantized version QED.

(4) The backward evolving states (bras) have been utilized to propose another alternative to standard QM in the Two-State-vector Formalism (1964) of Aharonov et al.

(5) The advanced waves have been utilised by J. G. Cramer to put forth the Transactional Interpretation (1980-86)of QM.

(6) The possible reality of a negative time arrow has been proposed in Phys. Rev. Lett. 113, 181101 (2014) - Identification of a Gravitational Arrow of time, by J. Barbour.

Thus it is clear that every 20 years or so this issue of the negative time direction has kept coming back only to subside, just for the next two decades or so!

My very best regards to one and all.

Rajat

@ Charles Francis,

I see now that there is another your post against my work ! ...

It is clear to all serious users that you falled in a deep depression ... since you are unable to read my papers ...

Unfortunately I cannot give you some online lecture to help you about ...

I cannot lose other time answering to your ridiculous posts addressed to me.

'... Nondum matura est; nolo acerbam sumere ...'

(Aesopo, The Fox and the grapes)

To all RG users.

« Ἀλώπηξ λιμώττουσα, ὡς ἐθεάσατο ἀπό

τινος ἀναδενδράδος βότρυας κρεμαμένους,

ἠβουλήθη αὐτῶν περιγενέσθαι

 καὶ οὐκ ἠδύνατο.

 Ἀπαλλαττομένη δὲ πρὸς ἑαυτὴν εἶπεν·

 «Ὄμφακές εἰσιν.» Oὕτω καὶ

 τῶν ἀνθρώπων ἔνιοι τῶν πραγμάτων ἐφικέσθαι

 μὴ δυνάμενοι δι' ἀσθένειαν τοὺς καιροὺς αἰτιῶνται. »

(Aesopo, The Fox and the grapes.)

Well, Charles,

the wrong translation now allows to all RG users understand to whom  fable applies ...  

'Lupus in fabula ...'

Dear All,

Again ...

'lupus in fabula ...'

Dear All,

with respect to the subject of this thread and Feynman-Stueckelberg interpretation of antiparticles it is worthy to point out again the following.

1) QFT is considered the relativistic formulation of QM. This has been made by assuming that quantum particles are point-like objects travelling in the Minkowski space-time M and by considering fields as operators on some Hilbert space defined on M. This is an unnatural marriage since M and point-like particles are classical objects, instead fields live in a noncommutative structure. In other words classical objects (point-like particles) should yet satisfy a classical logic encoded by classical differential equations, instead quantum objects (fields) must satisfy a quantum logic encoded by quantum PDEs. This illogical mixing has been in some sense 'solved', by the quantization of classical field PDEs. But this process has forgotten that point-like particles should satisfy ordinary differential equatioms ... therefore the quantization of classical field PDEs, have left point-like particles untouched. In fact in the QFT quantum particles continue to be considered classical objects uniquely constrained by SR.

2) Despite this incomplete aspect, QFT has obtained great successes in QED and quantum electro-weak interactions. In fact perturbative methods applied therein have allowed to rise very good approximations of physical reality. In this framework a central role has played the Feynman-Stueckelberg interpretation of antiparticles, shortly resumed by the so-called Feynman diagrams.

3) Unfortunately perturbative methods cannot be applied to other fundamental interactions, thus the beautiful Feynman diagram method fails, hence also QFT was considered few useful for a long period around 60's. In fact in that times central attention was focused on dispersion methods of scattering amplitudes for strong reactions. That was the gold-time of great results by Regge, Fubini, Veneziano and their Torino school on the scattering amplitude structure theory. Even if in that theory strong interactions are simulated by black-boxes where one knows only input and output and evaluations on the scattering amplitudes are essentially obtained by dispersion relations, the underline general framework remains QFT, hence S matrix, Dyson perturbative method and Feynman-Stueckelberg interpretation of antiparticles, continue to be handled therein. Really in 1964 the Standard Model of classification of quantum particles by Gell-Mann (1969 Nobel Prize) and Zweig, given new insights in the perception of scattering amplitudes. Regge poles were in that context a new original parametrization for such amplitudes.

4) After 80's the central attention in scattering theory returned on QFT and their perturbative methods thanks to the great results on the unification of electromagnetic and weak force, obtained by Glashow, Salam, and Weinberg, (1979 Nobel Prize), and experimentally verified by Rubbia discovering bosons W+, W− e Z, (1984 Nobel Prize).

5) The more recent experimental results on the discovering of Higgs particle (CERN 2015) and neutrino oscillations (first predicted by Bruno Pontecorvo in 1957, and  2015 Nobel Prize to Takaaki Kajita and Arthur B. McDonald), from a side confirmed SM but also opened the necessity to a new interpretation of the concept mass-acquisition mechanism in QFT. Furthermore, taking into account also the necessity to reconcile Einstein's GR and QM, and the new cosmological observations that from one side appear confirm GR (gravitational waves) and from another point out the necessity to justify so-called dark/matter energy, give us a new impulse to find a more general theory that could enclose QFT and GR as particular cases.

6) In particular was evident that the problems connected to the old interpretation of quantum particles as point-like objects, it requires the necessity to introduce string theory and M-theory. Even if these approaches appear enclose graviton particles and to restore attention on Regge poles in scattering amplitudes (Veneziano's works), they remain classical theories that necessitate to be quantized. Further advancements were obtained by relating string theory with QFT and supergravity (Witten, Polchinski, Susskind, Maldacena, ....).

In this general framework the Feynman-Stueckelberg's interpretation to see incoming antiparticles in a reaction as outgoing particles and vice versa, is the graphical reperesentaion of the crossing symmetry in quantum reactions. This has nothing to do with the wrong interpretation that antiparticles and negative energy quantum particles go in the past of an observer. These fantasies are wrong interpretations of quantum phenomena seen with the classical relativistic mechanics. Similar big mistakes were made about causality of tachyons. In fact it is possible to prove that tachyons, namely quantum particles with negative square mass, respect microscopic causality. This is clearly forbidden in classical relativistic mechanics of particles. (For information see the following link at pag. 338:

https://books.google.it/books?hl=it&lr=&id=YWj1iWIb7vcC&oi=fnd&pg=PR7&dq=%22A.+Prastaro%22&ots=AL-8IwVmsC&sig=Qq5NGbH_yOgF5wyZWrFDhEvW6Tc&redir_esc=y

By conclusion in the quantum world one cannot directly adopt relativistic mechanics of point-like particles, neither in the hybrid form adopted by the QFT.

My best regards,

Agostino

Charles, by now I am not more surprised that you show to do not understand what I write ... since whether I write 'YES' you say that I written 'NO' ...

However SR is largely used in QFT and scattering theory therein, (e.g., Mandelstam invariants).

On the other hand also you, in a previous post use SR and Dirac equation in the same context.

'... in relativity we have E2 =  m2 - p2, so there is an indeterminacy in the sign when you take the square root. The negative energy solutions do not come from the conservation law, but from the solution of the Dirac equation and the form of the quantum field operator. Because negative energy means going backwards in time, the creation of a negative energy particle is seen as the annihilation of positive energy. This is the meaning of an antiparticle. It is seen by the form of the field operators that the creation of positive energy going forwards in time and negative energy going backwards in time are one and the same process.'

I know very well QFT to think that quantum particles could travel like classical particles in the Minkowski space time. But many tools of the SR are used in QFT. The same Feynman diagrams appear encoding reactions between point-like particles, that even if do NOT represent real space-time trajectories in the Minkowski space-time, use SR. In fact at each interaction vertex both the energy and momentum are conserved, (but the length of the energy momentum four vector is not equal to the mass).

All this is interpreted by my last statement in the last my post.

By conclusion you continue to play the wiseacre against what I write, but you simply prove any day more your squalid attitude to play the fox role in the Aesopo's fable.

'Errare humanum est, perseverare autem diabolicum ...'

Dear All,

it is by now clear that Charles Francis does not know what he says !

In fact his last post proves that he is not able to understand the contradiction of using SR, namely the relativistic mechanics of point-like particles, in a noncommutative framework of quantum operators. Really he writes:

' Just because special relativistic formulae are used, it does not follow that we are talking of classical pointlike objects in Minkowski space-time. '

This CONTRADICTION is just one of the main defects producing the incompleteness of QFT.

In fact my quantum gravity theory is formulated in a complete noncommutative framework and quantum particles are extended objects in noncommutative PDEs.

I surely do not use SR in the form adopted by QFT.

Therefore my criticism on the old QFT is not only in negative, but I have given also the solution to how go beyond it without occurring in its contradictions.

Regards,

Agostino

No Charles !

Whether you write E2 =  m2 - p2  it means that you use relativistic mechanics of point-like particles. Doesn't it ?

Demonstrating that you have no grasp of special relativity at even an elementary level only serves to prove  to all users that you do not understand what you say.

'Errare humanum est, perseverare autem diabolicum ...'

'No it doesn't, and certainly not classical particles in Minkowski spacetime'

Let me know in which sense you use E2 =  m2 - p2  in QFT please, Charles ...

Until now I was your angel ... but my patience is ending ...

My paper "Challenge to the special theory of relativity" has disproved STR theoretically.

Dear All,

last post by Charles is his self declaration of incompetence:

'...  I am not prepared to give you ...'

He believes that launching offensive words against some serious criticism it is enough to hide his complete inadequacy ...

It is clear that to discuss with such a type of user it is impossible ...

Dear Rajat,

 I have already given my answer to your question. At page 6 I have given a more extended panorama on some related problems and clarified the incompleteness of the QFT that is related to your intriguing question.

 Regards,

 Agostino

 'Only two things are infinite, the universe and human stupidity, and I'm not sure about the former.'

(Albert Einstein)

 Charles Francis, have you read my paper which has been published on an international peer-reviewed journal? If you haven't done so, please read it and then make your comments. I would like to have a real debate with you.

 Charles Francis, your reasoning is poor. I am to challenge the relativistic spacetime model while you have already assumed that the spacetime model is correct. Then, how can we debate?

Xinhang Shen,

As many other criticisms of relativity you want to violate the principle of relativity, but it is OK to agree on what we disagree.

It seems that even Rajat’s post on 5-th page didn’t help and the debates continue rather far away from the thread’s question. Though that is quite natural since they go mainly inside mainstream physics…

Rajat,

Your question in the reality is so long because of all approaches you mentioned were in the framework of the SR dogma that the real Matter’s spacetime is the 4D Minkowski space with rather strange either imaginary the 1D time or the 3D space coordinates and imaginary distances. What is, of course, unreal – Matter’s spacetime is [5]4D banal Euclidian manifold, where all coordinates and distances are real values; the spacetime is absolute and cannot be impacted / transformed by any material object or non-material “observer”.

 At that (briefly, more see https://www.researchgate.net/publication/273777630_The_Informational_Conception_and_Basic_Physics) in Matter two logical Rules/ possibilities “Time” act – “true time” and “coordinate time”.  Both relate to some changes of material objects and systems of the objects, at that they establish, including, that every changes obligatorily are accompanied by “time intervals”, i.e. – a changing object always “moves in time”.

But the times aren’t identical. The “true time interval” accompanies any change – a change of the internal state of an object   or a change of its position in 3D space. Because of all/every material object constantly change their internal states and, sometimes, the positions, all/ every objects always move in the true time. Because of the informational system “computer Matter” operates with standard and stable operations rate, all the objects move in the true time with identical speed that is equal to the speed of light. In certain sense it is possible to establish in the Matter’s spacetime the true time as “5-th dimension”, where all Matter always is placed in one true time point (more correct in one elementary interval); thus this time “isn’t interesting for physics” till now in most of physical situations.

Besides all particles (and so systems of particles – bodies, etc.) in Matter exist in two types – “T-particles” and “S-particles”, T-particles are created by [coordinate] temporarily directed momentums, S-particles (say, photons) – by spatially directed momentums. The coordinate time interval accompanies [roughly] only  internal changes of T-particles, and, so T-particles always move in this time and just the coordinate time is the 4-th coordinate of Matter’s spactime; when S-particles [roughly] move in the 3D space only. Since  all /every  particles move in the 4D spacetime with  identical (by magnitude) 4D speeds, T-particles having different 3D spatial speeds have different temporal speeds – as that Pythagoras prescribed, so when all particles are always simultaneously in one true time point, they are also in different coordinate time points.

Such – “two-time” scheme in Matter - is realized because of to transform some informational systems without the energy dissipation is necessary (main authors who discover this fact - see the links in the reference list of the paper above) for this system to be built by using reversible algorithms. And just the Rule/possibility to realize reversible algorithms is the coordinate time, when T-particles with “direct command order” are “particles” and move always in positive directions along the t-axis. T-particles with “reverse command order” are “antiparticles” and move always in negative directions along the t-axis.

That’s all, but returning additionally to the thread’s debates:

Nonetheless Minkowski space is adequate in certain degree to the reality since is a mathematical re-formulation of the Lorentz transformations, which are indeed valid in/ at many [“physical”] processes and interactions in Matter. Including in Minkowski space also two times exist – the “simply time“ which is the “coordinate time” and the “proper time”, which are some “mixes” of the real “times”. But in this space rather evident scalar – the energy – becomes be vector value, since it is the t-component of the 4-vector momentum. And since when an antiparticle indeed moves in the negative t-direction, for this fact in the SR and further in the QED  became be necessary to introduce some mathematical thick  - the Feynman-Stuckelberg interpretation of “negative energy”, which isn’t understandable – as in this thread – till now.

In the reality, again, the energy is the scalar, when the 4D momentum indeed can be t-positive/negative. When all interactions in Matter happen only in the 3D space and in the one true time moment, independently on the true time coordinates of interacting particles and so, for example when a pi-0 meson decays, its quarks and antiquarks aren’t in an one spacetime point, but in average they are on distances near 25-(-25)=50 nm – what is rather large distance relating to the spatial size of this particle.

And, for example, if there is the annihilation of an (electron +positron) pair, they can be on practically arbitrary  [c]t-distance in the spacetime, but the annihilation happens and results in, say two photons having (for very slow particles) total - and just “positive” energy 2x0.511 MeV - instead of zero if there would be the sum of “positive” and “negative” energies. But the sum of momentums that were for the particles equal by magnitude, but directed in opposite temporal directions is equal to zero and conserves after the annihilation as zero – as the sum of momentums of opposite spatially directed photons.

Again – more see the link above,

Cheers

Article The Informational Conception and Basic Physics

Though they next time cannot formulate any reasonable objections to a next SS’s post, some tireless and discipline downvoters  checked in again…

Cheers

For some unknown reason, nature doesn't admit causality violation. Both the positive energy particle moving backward in time and the negative ones moving forward violate causality. 

Abhik Sanyal ji! That is shifting the question one step back, as is usually done in science. what is that unknown reason that does not allow causality violation, if that is accepted to be the answer to the question.

Sergey,

The antiparticles have positive energy and are detected as such. There is no use taking antiparticles to have negative energy in forward time sense.

My question is why we don't have such entities although they are not forbidden explicitly by any principle. And if they are discovered tomorrow, no hell will break loose.

Rajat

Rajat,

“….My question is why we don't have such entities although they are not forbidden explicitly by any principle…”

-  sorry, I don’t understand what are those “entities”; and can only repeat what is in the SS post above – to discuss something that directly relates to the notion “Time” is necessary to understand – what is “Time”; and, besides, since in this case the problem – how the notion “Time” is realized in the system “Matter”, is necessary to understand – what is “Matter”. Here, of course, should be the understanding of the notion “Consciousness” since  just individual consciousnesses observe material processes and analyze the observations data, when, regrettably just some consciousnesses invent a lot of suggestions, dogmas, etc., including rather strange definitions of the two other notions above; but let this point be outside this discussion.

Since all notions above are Meta-physical and Meta-mainstream-philosophical notions, they can be properly defined and/or at least understandable on some satisfactory level only in the “The Information as Absolute” conception; the application of the conception in physics – see the SS post above and the RG link in the post, where briefly:

-in Matter two “times” act – the “true time” and the “coordinate time”, the coordinate time is 4-th coordinate of the Matter’s absolute [5]4D [1 temporal and 3 spatial] Euclidian  spacetime;

- after an impact with  huge portion of “energy” and “momentum” to something, appeared the system of material objects -“automata” - “Matter”,  where there is no dissipation of the energy outside and so all objects, or better in this case – particles, move constantly in the absolute spacetime (and “in an absolute inertial reference frame(s)”, ARF) in different 4D directions with identical by the absolute value, which is equal to the speed of light,  4D speeds, including – in positive and negative coordinate time directions. The coordinate time in that practically doesn’t differ from a spatial dimension, the differences exist of course, but again more – see the link;

  - at that T-particles can be “particles” and “antiparticles”, the first obligatory move in the positive (by convention) coordinate temporal directions, antiparticles – in the negative temporal direction in this spacetime, besides they can move and indeed most of them move in some 3D spatial directions. S-particles don’t move in the coordinate time and so move in the 3D space only. Nonetheless all particles move in the true time – “in the positive direction by convention” only  with the speed of light. That’s all or at least nearly all to understand the thread’s question.

All particles have always 4D momentums P=mc (“a” means a "vector a"), which are vectors;  and scalar energies in the absolute spacetime E=mc2. Since all particles are some closed loop algorithms, for all particles is valid E=h-bar*omega; and all energies in Matter’s ARF are “positive”. Outside this ARF  in concrete systems energy can be – and often is – considered as frame-dependent  and be defined only with an uncertain  additional constant. Thus, say, if for a free electron one establishes E=0, then this electron in, say, Hydrogen atom, has negative energy  -13.6 eV, but it at that doesn’t become be a positron. As well as in the reality there are no “forward/ backward time senses” – if there is the proper understanding what is the notion “Time” – in any other physical situation; excluding, of course, the T-particles/antiparticles motion - only in the coordinate time; and – there are no “negative/positive energy particles” as well.

Again, all approaches that you mentioned in the thread’s question (including  absurd “Gravitational Arrow of time”; any “time” hasn’t any arrow by [true] definition) appeared because of the authors remain in framework of the SR/GR, where, claimed as real Matter’s spacetime, Minkowski and pseudo Riemannian spaces are in the reality some “reflections in a false mirror” of the real Matter’s spacetime and so to make the theory be adequate enough to the reality it were required for the genial Dirac’s guess and further also very non-trivial Feynman-Stuckelberg interpretation.  Though in the reality all is rather simple.

On the other hand, if I erroneously understood your words in the quote above – it can be possible some additional consideration, though.

Cheers

Dear all,

I have enjoyed a rather violent debate with many views and controversies. A lot of confusion seems to be related to various interpretations of fundamental equations like the Klein Gordon or Dirac equation. These equations exhibit symmetries and if one is lucky they can be used to predict new phenomena or particles like positrons etc. 

Nevertheless it might be confusing to use "loose language" without employing a more careful attitude. For instance one problem is the uni-direction of time, despite the essential reversible formulation of the basic equations of physics, Newton, Schrödinger, STR. This has led to the popular notion of arrows of time. I have listed and discussed seven of them in the paper enclosed below (and Sergey, an arrow associated with gravitation is not so absurd!).

I have asked before about the CPT theorem, see also reference below. As far as we know today CPT is a law of nature, but since we do not yet agree on how to include gravity one cannot be fully sure of this.

So back to the question. The symmetries of e.g. the "Klein-Gordon", points at particles and antiparticles that have different parities regarding time and space and charge, and which we might detect experimentally in our uni-directed space-time.

Of course we can use any language we want as long as we agree on what we mean and not allow ourselves to read too much into interpretations. After all mathematics is the most succinct language for science and it permits formulations were words are not sufficient.

Luiz,

I do not quite get your point, since it is the precise boundary conditions that specify the propagator, e.g. the causal- the retarded- or the advanced propagator. Where is the beef?

“…Where is the beef?”

- indeed, here is no too much beef – since the existence of antiparticles and the Feynman-Stuckelberg interpretation are quite well understandable (see page 8 here), if somebody understands what are the space, the time, and the spacetime in Matter – as well what is Matter, though. Including if (s)he understands that real Matter’s spacetime isn’t [here] Minkowski space, which is nothing more then some convenient sometimes mathematical tool -  the real Matter’s spacetime  is [5]4D Euclidian manifold. And instead of to continue to solve next problems that arise at application of some unreal basic notions/variables to the real physical processes it would be much more useful to work aimed at reformulation existent theories in consistence with the reality…

Cheers

Dear Erkki,

In CPT, Is the time reversal a real reversal of time or is just motion/velocity reversal?

Rajat

@Rajat,

I understand your frustration.  The use of such formal tools and loose language leaves many people with an uneasy feeling about QFT.  Sometimes one hears some explanation for how causality is preserved based on operator commutation and one feels like it is all mumbo jumbo.  You can adopt the formalist perspective in terms of measurement operators and interpretations and then you can sleep easier.  Most of us can't.  We either walk away or keep looking for something more deterministic and better.  The quantum measurement problem has a resolution in terms of many dimensional deterministic equations but people hate it because it is not at all like the formulation they learned.  I am always adamant that the "right" way to approach the subject is with a well defined forward direction in time for all particles.  Of course, one can introduce negative time and such notions in the use of computation as long as it is in a mathematically consistent way but, with this other way, since it is not traditional, you will get pushback and even claims you are wrong (even when it is completely equivalent).  I know this is the right approach because when I introduce it to new people, not the people filtered by the traditional approach, they universally prefer and connect with it.  

Rajat – Charles Francis has already answered.

Rest mass and time cannot be negative. The positive or negative signs appearing in the energy momentum invariant has to do with the direction of the velocity vector and therefore the momentum or the relativistic mass can be positive or negative. For detailed discussion see section II and equations (1) and (2) in following article.

Article Periodic quantum gravity and cosmology

Hi All,

I am unable to access the internet regularly for the time being and so am a little late in coming back to this thread. Please bear with me.

Most of the responses here have been along the lines as stated in textbooks. Please note that the electromagnetic potentials were just a mathematical convenience for long, before it found its incontrovertible physical interpretation. Similarly. matrices remained a mathematical tool for physicists before they found their physical significance in Quantum theory and in other areas having matrix methods. The complex numbers also were taken to be just mathematical artifacts having no physical significance and we all know how significant they are in QM and QFT. 

My question is along the same lines. Can we find an interpretation, a significance for the two so-called unphysical time-energy quadrants, which we say are just mathematical in content. Is time-reversal just a mathematical transformation, or can we give it some meaning? Especially, in view of Charles Barbour's paper and the works that i have cited above.

Best Regards.

Rajat,

“….Is time-reversal just a mathematical transformation, or can we give it some meaning? Especially, in view of Charles Barbour's paper and the works that i have cited above..”

- again, in Matter, two Rules/possibilities “Time” and, in certain sense, 3 Rules/possibilities “Space” act, i.e. the time in Matter is “two faced” – it acts as the “true time” and the “coordinate time”, where the 1D coordinate time with 3D spatial coordinates, as the possibilities, constitute absolute 4D Euclidian empty container for Matter and so the coordinate time is essentially similar to a spatial coordinate;

the corresponding difference – particles can move in any, including +/- spatial direction, when all "particles" move only in the + coordinate time direction and all "antiparticles" move only in the - time direction; photons don't move in the coordinate time (more – see the SS post above in this thread and the links in the posts ).

Besides as the rules Time implicitly establishes that every change of some material object is accompanied by a “time interval” – only accompanied, neither Space, nor Time Rules are something active. There cannot be an active “time arrow”, including – an “Gravitational Arrow of time”. There is only constantly increasing – because of that Matter constantly changes – true time’s (and for every T-particle unique +/- coordinate time’s interval) interval,

when Matter evolves practically always simply from given state to utmost probable next state. In the reality instead practically senseless notion “arrow of time” would be much more correct to use the notion “arrow of probability”. That’s all.

When you ride in a car from a point A to point B the spatial distance to A constantly increases, but you don’t call this process “Gravitational Arrow of space”? – when the gravitation indeed is very essential if necessary to ride just from point A just to point B….

Cheers

Dear Sergey,

You say: coordinate time is essentially similar to a spatial coordinate. This is unfortunately not true. Adding time as a extra dimension to our 3D space will not become an Euclidian 4D space. The point is that the resulting Minkowski space is characterized by a non-positive metric and this adds all the extra properties of relativity, compared to non-relativistic dynamics.

This also imparts that the expression "arrow of time" becomes meaningful and innovative.

You are right Erkki. Time is not the same as a another space coordinate. It cannot be, even when multiplied by c. The inherent difficulty is the arrow of time. There is no arrow of space for any of the three spatial dimensions. Does this mean time and space must not be treated in the same footing.as is done in Relativity?

Good point Rajat,

Instead of "arrow of space" we always have a space and its parity partner – this is analogous to forward time and past time. In fact we do not know if antimatter might be "hosted" in a parity equivalent of our space. Chiral phenomena prompts the existence of such a space – this is why I brought in the question of CPT.  

Can we say that like the time arrow, the expansion of space defines an equivalent arrow of space, if we take the radial coordinate that is increasing proportional to a(t), the scale factor in standard cosmology?

Rajat,

In any case the difference here between time and space is their dimension and that the latter is odd in each case. To me any "arrow of space" must be related to a line element in the Einstein equations, like the Schwarzschild gauge.

Erkki,

“…coordinate time is essentially similar to a spatial coordinate. This is unfortunately not true….Adding time as a extra dimension to our 3D space [results in]  Minkowski space …”, etc.

- there is no any reasons – why if to a 3D Euclidian space a next dimension is added resulting in appearance of a 4D Euclidian space, then that is impossible because of the result will be the “Minkowski space”. Such result is evidently impossible/ non-sensical – Euclidian and Minkowski spaces are principally different.

As well as in the real Matter’s [5]4D Euclidian spacetime the 4-th dimension/coordinate principally differs from the 3 spatial ones – when every particle in Matter moves in the spacetime with 4D speed of light, a motion along this coordinate, which is sequential change of a T-particle’s internal state, including when the particle is at absolute spatial rest, is independent on spatial motion – and on the contrary -  there can by motion in 3D space only.

As well as, a next time – see earlier SS posts here – in Matter there are no any active “arrows of time”, though indeed for all particles – since they uninterruptedly move in the spacetime,  this motion is obligatorily accompanied by the increasing [from Matter’s Beginning] true time interval; but that is nothing more then an “witness”; this interval increases always – when there is some “arrow of time”, say, - “thermodynamic arrow”, and when there is no “arrows”, say at motion Earth around Sun.

Again – in the reality all what is “active” and has indeed “arrow” is Matter’s evolution from some highly nonequilibrium state at Beginning, when the next Matter’s state – and every material object’s and system’s of objects states – is practically always an utmost probable state/ states privided a present state/states.

Including the quoted here paper about “Gravitational Arrow of time”, where authors considered an evolutoion of a number of gravitating bodies in an nonequilibrium state and discovered this arrow of  time. Though authors could consider some more simple analouge, for example – a fall of a brick from a roof; and obtained conclusion of existence of Gravitational Arrow of time possibly would be even  more convincible.

More see the SS post above and URL links in the posts.

Cheers

Sergey,

I am not sure what you want to say? Do you agree with what I said or do you want to say something else. Please clarify.

Cheers

Erkki,

“Sergey,I am not sure what you want to say? Do you agree with what I said or do you want to say something else…”

-?

- the SS post above is a comment to your post above in this page (not only, of course); namely to

“…You say: coordinate time is essentially similar to a spatial coordinate. This is unfortunately not true. Adding time as a extra dimension to our 3D space will not become an Euclidian 4D space. The point is that the resulting Minkowski space…”

And the comment is seems as quite clear:  this [quoted] passage isn’t correct and why it is incorrect.

The rest in the SS post is comment why “the expression "…arrow of time" becomes meaningful and innovative…” isn’t correct…

Cheers

Sergey,

Yes you say that my comments are not correct, but not why in a way that I understand.