You mean negative energies, right ?

Dear Adil,

Thank you for your reply.

We know that anti-particles are associated with  the absence of negative energy particles which cause problems: the probability density of the KG equation  becomes negative, it seems to me that considering a negative mass for anti-particles(negative energy states) resolves the issue.

Dear Faical,

It is impossible to have particles with negative mass (it's unphysical). The presence of solutions to the Klein-Gordon equation with negative-energies is due to the fact that the relation between energy and momentum, in Relativitistic theory, is non-linear, i.e E^2 = p^2 + m^2 (in natural units). This relation admits two solutions; one with positive and the other one with negative energy for each value of the three-momentum. Bear in mind that the mass (the parameter m in this equation) is always positive. Furthermore, the solutions of Klein-Gordon equation are states of the Hilbert space. So you can not say, as in classical physics, that you can simply discard those solutions, you need all of them to form a complete basis in the Hilbert space.

Then, you have the problem of negative density of probability which doesn't arise because of the negative energy states only (which is actually a secondary reason) but from the fact the Klein-Gordon equation contains two derivatives with respect to time. The solution of this problem was provided by Dirac who derived a relativistic equation containing one derivative with respect to time. He solved the negative-energy puzzle by introducing anti-electron (positron) which was later discovered by Anderson.

Finally, second quantization avoids all these problems.

Cheers, 

Dear Adil,

Thank you for your reply.

Dubbing negative mass as nonphysical has no physical reason (that I know), in fact negative mass is as possible as positive mass, it's  just we didn't observe it yet as the case of imaginary mass it's possible but again not observed yet. I don't think anyone can discard negative mass or imaginary mass just by choice as the Poincaré group representations allow them.

In the Klein-Gordon equation, and the corresponding Lagrangian, the mass parameter m only occurs in the squared form m2. Instabilities are related to m2 being negative. The positive (negative) frequency solutions of the Klein-Gordon equation are associated with creation (annihilation) fields, not particles/anti-particles (the Klein-Gordon equation may describe particles which are their own anti-particles). Not all irreducible representations of the Poincare group can be associated with elementary particles.

Dear Kåre,

Thank you for your reply.

A positron state is the charge conjugate of the negative energy electron this is what I meant by "associated". 

"Not all irreducible representations of the Poincare group can be associated with elementary particles."

why is that? even continuous spin massless states could exist.

Dear Faical,

I agree with Mr. Kare about his point. In fact, we have only few irreducible representations that can be associated with elementary particles. i.e corresponding to m > 0 and for E > 0 to m = 0.

Best

It is just a matter of convention whether the electron is called the particle and the positron the antiparticle. It could just as well been taken that the positron was the particle and the electron the antiparticle. There are just more electrons, and it was discovered first so we chose it as the particle.  It is nonsense to think of either one of them as having negative mass.

Dear Jerrold,

Thanks for your reply,

Of course it's a convention, but why is it nonsense? 

Trying to give either the electron or the positron negative mass is nonsense.

No, because the concept of the negative mass doesn't exist, for example the positron her mass is positive, but it's the anti-particle of the electron. :) I'm not a specialist of the particle physics, science, but the negative mass it's the physics singularity at this moments =D

In relativity theories we distinguish between the rest mass m_o and the relativistic mass m. My conclusion is that the rest mass is always positive but the relativistic mass can have positive or negative sign. This difference in sign is only because of the difference in the direction of the velocity vector of the particle. This is consistent with the fact that the relativistic mass come into picture because of the relative motion between coordinate systems of two particles. This is discussed in detail at eqns. (1) and (2) in following quantum gravity theory and at eqn.(2.35) in the quarkonium article.

Article Quarkonium and hydrogen spectra with spin-dependent relativi...

Article Periodic quantum gravity and cosmology

You are not allowed to think to negative mass, negative energies, nor negative frequencies : the tribal group-think of the tribe forbids you to think.

Too, you are not allowed to distinguish the micro-time of any particle from the macro-times, which are statistical emergences. The tribal group-think of the tribe forbids it.

However, in the real world, huge infrared photons are captured by a tiny CO molecule, provided they have precisely the resonant frequency of this tiny molecule. But you are not allowed to write the geometry of this convergence to the absorber : the tribal group-think of the tribe forbids you to think that.

In the real world, in an Aharonov-Bohm experiment, the electron that was split in two parts, one passing above the micro-solenoid,  and one part passing below, however converge onto a small spot of the target, only a few atoms wide. But the tribal group-think of the tribe forbids you to think that.

If you dare to trespass the interdictions, you will be excluded from the club !

http://jacques.lavau.deonto-ethique.eu/Physique/Microphysique_contee.pdf

http://jacques.lavau.deonto-ethique.eu/Physique/4e_couverture.pdf

The concept of particles and anti-particles originated from the relativistic theory of the electron formulated by  P.A.M. Dirac. In his  interpretation of the  the electron-hole theory, Dirac suggested that the hole which appears in the negative energy see as a result of the interaction with electromagnetic radiation, has the same mass as the electron but opposite charge and represented the anti-particle to the electron.

There is no such thing as negative mass.

if so, then one could generalze dirac`s ideas and consider the results of 4.degree equations, i.e. 2 of them were complex ones.

The test is gravity: antiparticles respond exactly like particles in a gravitational field, so their mass (like all mass) is positive. Negative mass would be inverse gravity, therefore a global, not just linear, charge. The leading candidate for negative mass would be dark energy, the energy of space itself. So far we have no way to test for that. We have a space-time continuum, but no space-mass continuum, probably because that's not a continuum but perhaps the first broken symmetry in the Big Bang. All speculation at this point.

Dear Smith,

Thank you for your reply.

Yes negative mass particle has anti-gravity behavior, but it's not that easy to detect it:

Of course if an antiparticle has negative mass we have to rethink its charge since the behavior of any charged massive (anti)particle in a electromagnetic field depends on the ratio e/m .

dear Virginia, +1,-1,+i,-i are inverse 2 by 2; +i is not the inverse of -1 (e.g.)

 Dear Pistea,

Thank you for your reply.

Do you mean a 8 components spinor or a what we might call a quadrispinor?

Thanks, Faical. Spin is the clue but I'm looking for +/- global spin as the ultimate pair of "canonical conjugates." I've assumed spinors are still mass-based, am I wrong?  What I'm looking for is something like a Majorana seesaw mechanism with maximally "unequal" masses (since the negative conjugate would be dark energy/space as global expansion to mass's global contraction). But as it stands apparently not even Majorana theory will give us negative mass/energy as a global phenomenon, and linear math won't do it. For example, in a gravitational field my "negative majon" would expand instead of contracting (as both particles & antiparticles do, although stabilized as standing waves). This invokes an energy level currently out of reach as the first break in symmetry, possibly the Big Bang itself as the moment when mass "falls out of space." To test for negative mass might take a particle collider with half the energy of the universe. Even supermassive black holes can't match that ante, by the second law of thermodynamics. In any case, the space majon would be the ultimate "anti-spinacle" not as antimatter but as antigravity. If so the quantum gravity guys might capture it, at least mathematically, not just as antimatter but the inverse direction of space-time. I'm hoping for developments in quantum gravity for this one.

Dear Virginia,

Thank you for your reply

I find it interesting that you mentioned the seesaw mechanism.

Agree, Faical, I think something like it is the ultimate charge.

Antiparticles are particles that travel back in time. Observers cannot perceive travel back in time. Therefore they interpret the back traveling particle as a new type. Also, the antiparticle can reflect against a historic time instant and travel forward in time again. In this way, at a given instant the same particle can exist multiple times.  Observers interpret the reflection points as creation/annihilation events.

https://doc.co/PJ4XPQ

Dear Hans;

Thank you for your reply.

There is a problem with considering antiparticle as particles traveling backward in time. because this implies that the charge conjugation transformation that transforms particles into antiparticle must be the same as the time reversal transformation which manifestly not the case.

Faical> why is that? even continuous spin massless states could exist.

Yes, there are unitary representations corresponding to this case. For some reason there does not seem to be any corresponding physical objects (or maybe one has not looked carefully enough?). I believe it would require infinite-component fields to describe  them, so it certainly is a good thing than humankind does not have to deal with that mess :-)

This Mathematical Question is similar to the Physics Question of asking if Matter-Antimatter interactions yield antigravitation.

I emphasized Mathematical Question because it only pays attention to the Math. It doesn't even bothered to ask if there is a region in the Universe (SDSS has the data) where there is a clump of Antimatter Mass that is repelling surrounding Matter.

The other observation would be if there is a visible source of Gamma Rays resulting from matter-antimatter annihilation.

Why would you explore an interpretation of Mathematical equations without checking to see if the interpretation has support in Reality?

PS_ The answer to those questions is NO.

I dwelt on this problem for some time. I reached the conclusion that Gravitation is a Van der Waals like force and thus it is always attractive.

Dear Marco,

Thank you for your reply.

Van der Waals forces are short range forces while gravity is infinite range.

If antimatter has negative mass there can't be overall neutral clumps of antimatter

Dear Christian,

Thank you for your reply.

 I mean exactly the mass appearing in the Klein-Gordan equation and I don't challenge the equivalence principal.

It appears that there are regions in the Universe where something has been repelling surrounding Matter.

CERN experiments have tried to measure the effect of the Earth's gravity on anti-hydrogen, but the results are not (yet) accurate enough. 

http://www.space.com/28368-will-galactic-bubbles-reveal-dark-matter.html

Dear Kåre,

What is called Fermi bubble named after the Fermi telescope who discovered them are thought to be remnants of the activity of supermassive black holes in the center of galaxies.  The (G)bar experiment at CERN is promising it tests the Equivalence principle.

http://home.cern/about/updates/2017/03/raising-gbar-antimatter-exploration

@ Hans van Leunen and Faical Barzi. It was an idea of Wheeler, reported by Feynman.

Here we have a constraint : the anti-electron emitted backward in time by the absorber in cathode ray tube, or in an electronic microscope, must be deflected the same way by the electric and magnetic fields, than the electron with positive mass emitted by the emitter. Because they are just two equivalent descriptions of the same physics.

Similarly, the antiphoton is deflected by gravity exactly as the direct photon.

The inversion of the micro-time does the job.

Dear Jacques;

So a  charge conjugation+time reversal transformation (CT) equal keeping (e/m) the same? 

No. Anti-particles have the same mass as particles. CPT changes the sign of additive charges, doesn't change the sign of non-additive charges. Mass is an additive charge in Newtonian gravity only.

Dear Stam,

Thank you for your reply.

"Anti-particles have the same mass as particles" I think this is an assumption not a fact. "CPT changes the sign of additive charges, doesn't change the sign of non-additive charges. Mass is an additive charge in Newtonian gravity only." this phrase is not clear could you elaborate of indicate a detailed answer.

No it's not an assumption, that anti-particles have the same mass as particles-it's a consequence of the CPT theorem.

Mass is one of the two invariants of the Poincaré group (the other's spin). The CPT transformations commute with Poincaré transformations, so they don't affect mass and spin; and they affect ``internal'' symmetries, according to the rules that apply for the group. For electric charge the group law is addition, for the other charges the rules are more complicated.

One shouldn't confuse mass, that's a Lorentz invariant quantity, with energy, that's the time-like component of the energy-momentum 4-vector. In the particles rest frame, which exists, provided its mass is non-zero, the energy is equal to the mass, since the 3-momentum vanishes. 

@Stam

"Mass is one of the two invariants of the Poincaré group" isn't it the square of the mass that is an invariant?

 It doesn't matter-taking the square doesn't change anything: if m is invariant, m2 is, too and vice versa. And the mass is non-negative for matter to be stable at all.

@Stam

True, but the converse is false.  "And the mass is non-negative for matter to be stable at all." I think (in)stability depends on the other interactions and on the mass having an imaginary part.

“Could we consider anti-particles as having negative mass?”

- no. Inertial mass is the measure of inertia of material objects, including particles;  when the particles are some uninterruptedly running close-loop logical algorithms;  i.e. particles [including photons] are some gyroscopes that rotate with a 4D [in the 4D sub-spacetime of Matter’s absolute [5]4D Euclidian spacetime] rotation rate ω [“ω” means a vector], having the energy E= ћω.  Thus the phenomenon “inertia” is a consequence of that any gyroscope resists to attempts to change the value and/or direction of ω.

The difference particles and antiparticles isn’t principal in this case, it is simply as that the directions of the rates are opposite [for given type of particles and equal their energy, of course, if the energies are different than the rates aren’t co-linear, but that is inessential in this case]; the particles are, say “right-handed” gyroscopes, when antiparticles are “left-handed” ones.

And

“…One shouldn't confuse mass, that's a Lorentz invariant quantity, with energy, that's the time-like component of the energy-momentum 4-vector…”

- that isn’t relevant in this case, since “the energy-momentum 4-vector” in Minkowski space aren’t adequate to the reality – Matter’s spacetime is as that is pointed above [Euclidian, etc.], by no means that is imaginary, in fact, Minkowski  space.

In the real spacetime, in the 4D sub-spacetime particles move with 4D speeds having identical absolute values be equal to the speed of light, so having 4D  momentums P=mc and energies E= ћω =Pc. In this sub-spacetime indeed particles and antiparticles, that are closed-loop algorithms with a direct and opposite command sequences, move correspondingly in opposite [in the coordinate time, “zero” dimension] temporal directions and the zero components of momentums of particles and antiparticles are opposite.

At that the zero components of the 4 energy-momentums of particles and antiparticles in Minkowski space are obligatorily positive and so indeed always have the same direction. Thus, for example, the famous Feynman’s guess that antiparticles move in negative direction in the time contradicts with the SR, though Feynman is correct and this fact has the explanation [in the informational physical model] above.

More see https://www.researchgate.net/publication/273777630_The_Informational_Conception_and_Basic_Physics  DOI: 10.5281/zenodo.16494

Cheers

Article The Informational Conception and Basic Physics

Lorentz invariant interactions can't change a Lorentz invariant quantity. That's what matters. The interactions where antimatter is relevant are Lorentz invariant. 

Antimatter is just a form of matter, with different internal charges, that's all. Mass and spin are not internal charges. 

@Stam

We don't know if antimatter breaks the Equivalence Principle or not. So saying anything factual about the sign of antimatter's mass is too early. 

“…Antimatter is just a form of matter, with different internal charges, that's all…”

if that would be “all”, then the thread’s question would  not exist; when this question is quite natural:

- again, in accordance with QED, more concretely in accordance with the Feynman’s postulate, antiparticles move in 4D Minkowski space in time in the negative direction, i.e. have negative zero components of  their “the energy-momentum 4-vectors” , which in the reality in the SR is simply “4-momentum”, (E/c, P) [“P” means a vector, here – 3D spatial momentum vector].

This zero the 4-momentum’s component is E/c=mc/(1-V2/c2)½;  and so evidently it can be negative only if the  [invariant] mass, m,  is negative.

On another hand indeed in the SR the invariant mass is postulated as be always positive, and so the Feynman’s postulate contradicts with the SR.

That’s indeed all [relating to the question].

The solution of this puzzle – see SS post and the link in the post above, i.e. that happens because of the Minkowski formalism, and thus the SR as a whole, isn’t adequate to the objective reality; that is true in many other logical and physical aspects else, though.

Cheers

Dear Faical,

let me give a short comment on your question from one angle: If antiparticles have a negative gravitational mass that should eventually be detected with antimatter produced in laboratories. So no matter what any theory says it is an experimental question which should be decidable within the next decade experimentally with lets say anti Hydrogen. There is an experimental setup exactly for this at CERN which has not produced dependable results yet: http://home.cern/about/experiments/aegis

With best wishes

Dear Sergey,

Thank you for your reply.

In the model you replaced the resistance to changing the momentum in 3d to a resistance to changing the angular momentum in 4d I think that doesn't say much and it's just a playful visualization.

Dear Daniel,

Thank you for your reply.

I agree that the last word comes from experiments, but also theories tell what experiments to do and experiments tell what theories are true. I am concerned that some assumptions will bias the experiments.

There is a lot of positron physics that is well understood. If the positron had negative mass, this would influence the mass balances in radioactive decay.

If you postulate that antimatter might have negative mass you either have to postulate that the positron is no antimatter or that positron is an exemption. Both possibilities would mean a new definition of antimatter that is radically different from the current concept. So different that I don't think it would make sense to re-use the established nomenclature for something completely different from that what we call antimatter today.

Dear Erik,

Thank you for your reply.

Do you really think a beta plus decay could reveal something about the sign positron mass?

Yes I agree the charge conjugation transformation should be redefined by including a "mass reversal"

The nuclear masses are known with high precision, and the transition (decay) from one to another must fulfill mass/energy conservation. If you account for the released energy in a beta plus decay, a mass corresponding to 511 keV will be missing, so this is the rest mass of the positron. Otherwise, if the positron had negative mass, the mass balance would be the same for both a)beta plus decay and b)electron capture (EC). In fact, we can see EC always when we have any positive mass difference between mother nucleus and daughter nucleus by the decay, but beta plus we see only in cases, where this difference is ≥1022 keV, that is 2 electron masses (or, so to say, one elcrron mass and one positron mass).

@Erik

Yes, if the positron mass were equal and opposite to the mass of the electron the beta plus will be more favorable than EC which it seems not the case. but again aren't we confusing negative mass and negative energy?

Dear Faical,

“…In the model you replaced the resistance to changing the momentum in 3d to a resistance to changing the angular momentum in 4d I think that doesn't say much and it's just a playful visualization…”

-  that isn’t so by a few reasons. First of all – when somebody writes something relating to a physical variable [here inertial] “mass” , this somebody before should understand – what is mass? , including – what is the inertia and, since experimentally the other mass is introduced in physics, i.e. “gravitational mass” – why they are equal, at least at statics.

If the somebody doesn’t understand the inertial/gravitational masses phenomena, all what is possible are some ad hoc suggestions that are used as postulates in physical theories at fitting the theories with experimental data. The examples in this case – Newtonian mechanics and Higgs field, though in the first case Newton simply introduced, without explanations what they are, those masses, when  the Standard Model with Higgs field contains the “explanation” of what is the inertial mass, which is rather questionable, and, besides, from this explanation by no means  follows the answer – what is the gravitational mass, etc.

Your approach is similar to the above, so you simply claim, in fact, that “to changing the momentum in 3d” is the real explanation of the inertia/mass, when  “to a resistance to changing the angular momentum in 4d”  isn’t real, without explanations – why that is so?.

These explanations indeed seems rather similar, but from “the changing of the momentum resistance”  immediately and inevitably  follows your suggestion that the inertial mass can be negative. Indeed, even if a pair of particle+antiparticle, both having the rest masses, is at absolute rest in the 4D sub-spacetime of the Matter’s [5]4D Euclidian absolute spacetime, the particle and antiparticle have 4D momentums (m0c,0,0,0) an (-m0c,0,0,0) [“c” means a 4D vector].

 Bu that is not because of the masses above have opposite signs, but because of they move in the [coordinate] time dimensions with opposite, c and –c speeds, when both masses are positive, just because of the resistance to attempts to change the value and/or 4D direction of the 4D particles/ “gyroscopes” rotation rates ω , which  is the same – the gyroscope is “right-handed” or “left-handed” [and so both masses have equal signs];  as that is well known for usual 3D gyroscopes.

Again more see the paper in the link in SS post on 5-th page.

Cheers

As you have posed the question in the framework of a relativistic QFT, we can assume that by the term "mass" you refer to the coefficient of the quadratic terms in field operators. Particle to antiparticle transformation in this language is a CPT transformation on the field operators.

For scalar bosons a CPT transformation leads to φ(x) →φ†(-x), whereas for vector bosons A(x) → - A† (-x). Such transformations keep the mass term invariant in the Lagrangian density functional of a Klein Gordon theory. Which means that mass terms in Kelin-Gordon equation are invariant under CPT transformation. This theory does not feel any effect of such a transformation on the fields. Klein Gordon theory cannot distinguish between particle and anti particle. A few years after the advent of Klein Gordon equation, Dirac wrote down a relativistic theory which could successfully describe an antiparticle.

Now let us address your question in terms of the no-go theorem, which is based on the fact that second order Casimir invariants of the Poincare group namely  PμPμ and WμWμ  commute with generators of internal symmetries. A minutes thought will tell you that, then, any multiplet of an internal symmetry generator will have a special property that each member of the multiplet should have same mass and intrinsic spin. Suppose now you consider a (isospin I=1, I3=-1,0,1) triplet of mesons, (π+ π0 π-), they should have same mass. Being mesons, by definition they also satisfy Klein Gordon equation. But π+ is the anti particle of π-, we have just seen that they must have the same mass. 

I hope it helps.

“…consider a triplet of mesons, (π+ π0 π-), they should have same mass…”

in this triplet π+ and π- mesons indeed have the same masses, but π0’s mass is lesser [near 5 MeV]. At that π0, as a whole particle, doesn’t move in the coordinate time dimension [[it is at the temporal rest; as, say, photon; if this meson has “equal number of gluons and antigluons” also, though] of the 4D sub-spacetime of Matter’s absolute [5]4D Euclidian spacetime, though all its 4 quarks move in this dimension, if being at the absolute 3D spatial rest, with the speed of light; quarks and antiquarks move in opposite directions;

when π+ and π- consist of non-symmetrical combination of their quarks and so all, i.e. both, u and d  quarks in the mesons move in  positive temporal directions,  both, u and d  antiquarks move in the negative temporal directions; and, since seems masses u and d quarks are different, so π+ and π- as mesons as a whole move, rather probably  in the opposite, temporal directions also, though having the zero components of the mesons’ 4D momentums being lesser then m0c, where m0 is the mesons’ rest masses.

Cheers

When we consider negative masses and negative flow of the micro-time, we do not describe new particules. Simply we do the complementary description of the same ordinary particles in the same flight, just more appropriate from the absorber side.

In 1932, Anderson discovered a really new particule : the positron with a positive mass.

Positive mass and negative mass can exist in the same space-time

All this time, the field of Physics did not seriously consider the possibility of existence of negative mass (energy) in a general state. The standard explanation of negative mass is that the state of low energy is stable when a negative energy level exists and that the lowest state of energy is minus infinity. Thus, this means that all positive mass emits energy and it will transit to the energy level of minus infinity and the universe will collapse.

However, at the present, our universe exists without collapsing, so the explanation for this has become strong proof of the nonexistence of the negative mass and negative energy level of. Thus, we have considered this to be obvious common sense and have taught this to students. At the center of this background, there is the fundamental principle that “State of low energy is stable”.

In this article, we will reveal that this principle is an incomplete, and that it is stable at a low energy state in the case of positive mass. However, it is stable at a high energy state in the case of negative mass. Due to this, “the problem of transition to minus infinite energy level” does not occur, and the existence of negative mass is therefore possible. Moreover, we will show that negative mass provides an explanation for dark matter and dark energy, which are the biggest issues posed to cosmology at the present.

5.Negative Mass Is Stable at the State of High Energy.

 If negative mass exists, is it stable at a lower energy state?

Fig.01

 F = (-m_) a     (m_ > 0)

 a = - ( F/m_ )

 The acceleration of negative mass is opposite to the direction of force. Therefore, the negative mass has harmonic oscillation at the maximum point and it is also stable at the maximum point.

In the case of positive mass, it was stable at the minimum point at which energy is the low. However, in case of negative mass, stable equilibrium is a point of maximum value, not a point of minimum value.

~~~~~~~

As we have examined above, “the problem of transition to minus infinite energy level” does not occur, and thus positive mass and negative mass can exist in the same space-time. This is a very important result because it means that negative mass and negative energy can exist stably in our universe.

1.https://www.researchgate.net/publication/301696194_On_Problems_and_Solutions_of_General_Relativity_-_V3_Commemoration_of_the_100th_Anniversary_of_General_Relativity

2.https://www.researchgate.net/publication/263468413_Is_the_State_of_Low_Energy_Stable_Negative_Energy_Dark_Energy_and_Dark_Matter

Deleted research item The research item mentioned here has been deleted

Article Is the State of Low Energy Stable? Negative Energy, Dark Ene...

"Could we consider anti-particles as having negative mass?"

Excellent question. It depend on how we can interpret "negative mass". When admitting that "mass" is only macroscopally a scalar, but microscopally a vector, the electron-positron pair creation might have opposite mass vector orientations. The gravitational attraction of the pair to the Earth will then depend from all these orientations. 

I don`t think that mass is a scalar, while multipying by 1/Square-root(1-v²/c²)

Dark matter is Negative mass!

Negative energy(mass) is an object whose existence is required by the law of the conservation of energy.. The fundamental properties of negative mass can explain important characteristics of dark matter.

1) Additional centripetal force effects

2) Explanations derived from fundamental principles about the reason why dark matter does not have electromagnetic interaction

3) Repulsive gravity ensuring almost even distribution and lower interaction of dark matter

4) Accelerating expansion of the universe can be explained with negative mass

5) Gravitational lens effect by negative mass

- Dark matter is required by rotation curve of the galaxy. However, why is it not detected on the earth or the solar system?

: According to negative mass model, negative mass exists outside the galaxy, while additionally exerting centripetal force effects inside the galaxy, so it cannot be observed in the vicinity of the earth. Dark matter (negative mass) exists outside the galaxy, and there is only a gravitational effect in the galaxy.

- Negative energy does not have positive energy to produce charges, so it is very unlikely to have charges.

This inference also suggests that negative energy(mass) is unlikely have charges, because electrostatic self-energy is positive mass (energy), which provides an evidence about the fact that electromagnetic interaction does not occur.

- Lower interaction between dark matters and almost even distribution: occurring from repulsive gravitational effects between negative masses.

- The effect of concave gravitational lens by negative mass out of galaxy will be presented to an observer on the earth in the same form as the effect of convex gravitational lens which galaxy works.

Preprint Dark Matter is Negative Mass

Antiparticle are particles that move back in time. Elementary particles can zigzag in time.

as negative energy exists, then why shouldn`t exist negative mass? e=mc² and e m

“Antiparticle are particles that move back in time…”

That isn’t completely so. As that is shown in the Shevchenko and Tokarevsky’s informational model in physics, Matter’s spacetime is the absolute [5]4D Euclidian spacetime, where are two rules/possibilities/[i.e. dimensions] “times”: the “true time” [5-th the spacetime’s dimension, t] and the “coordinate time”, [zero-th dimension, τ]. Thus the coordinates of the spacetime points are (cτ, x, y, z, ct) were all coordinates are mutually independent, as in any other mathematical space.

However every Matter’s object [particle, body, galaxy, etc.] after Beginning constantly moves, because of the energy conservation law, with the 4D speeds that have identical absolute values be equal to the speed of light in 4D sub-spacetime (cτ, x, y, z) and, correspondingly with the speed of light along the ct-dimension/ axis. Correspondingly coordinates of material objects in the spacetime aren’t independent, are mutually independent, dx2+dy2+cdτ2=cdt2.

That exists in Matter because of the “true time” rule/possibility is absolutely fundamental and universal [any change of everything is accompanied (thus position in time increases and so anything what changes moves in time) by corresponding true time interval]. Thus the constant changes of material objects states, i.e. of the objects’ internal states and their spatial positions are accompanied by unidirectional “true time” intervals.

However the informational system Matter is a logical system that is based on some reversible logic, because of in this case changing of information isn’t accompanied by energy dissipation. Thus particles are some close-loop algorithms, when particles are the algorithms with “direct” commands’ order, and antiparticles are the same algorithms, but with reverse commands’ order.

The reverse order logically contradicts, in certain sense, with “true time”, since it is, in fact, some “reverse traveling in time”.

Just therefore Matter’s spacetime contains the zero dimension, where particles move along positive coordinate time axis direction, when antiparticles move in the negative direction.

However the rule/possibility “coordinate time” acts only when it is necessary, i.e. at changing of internal states of particles/antiparticles [at the algorithms running], and so the coordinate time intervals accompany [in parallel with the true time] only such changes, and not accompany changes of any particle spatial position.

That antiparticles move “in the negative temporal direction” was postulated in QED by Stueckelberg and Feynman yet in the 1940-th years, however that was only the great ad hoc guess, which, when used as some non-understandable mathematical method, allowed to build the adequate to the reality QED, in spite of that this guess contradicts with the special relativity, where there is only one temporal dimension in the Minkowski 4D space, where all, particles and antiparticles, move only in the positive direction.

Though

“…Elementary particles can zigzag in time.”

If that relates to ± direction [in the coordinate time only, in true time that is impossible principally], that isn’t so.

More see

https://www.researchgate.net/publication/273777630_The_Informational_Conception_and_Basic_Physics DOI 10.5281/zenodo.16494

Cheers

1. WHAT does

“…1. WHAT does

As long as you do not apply a sensible modeling platform, you can keep asking silly questions that have no bearing. Please define first a suitable modeling platform. For example "Modeling Platform"; http://vixra.org/abs/1804.0104

well, I do not believe that time is 1-dimensional! and: 2 complex numbers z1, z2, must not be z1z2 like Real numbers! so, what means back in a Complex Set?

anew: to make a zig-zag possible, one needs a Plane (at least a plane)

my questions are not silly, they are merely uncomfortable for those who do not (themselves) analyse things and do accept everything because einstein/ hawking said them.

Dear Paul,

“…I do not believe that time is 1-dimensional! …anew: to make a zig-zag possible, one needs a Plane (at least a plane)…”

In Matter’s spacetime, again, two rules/possibilities [possibilities - as the dimensions/axes] act, the “true time”, t, and the “coordinate time”, τ, (see SS posts above and the papers that are linked in the posts); however these times are “bounded” in Matter by some way and act differently for T- [i.e. having “rest mass”] and S- [“restmassless”] particles. At that all/every, i.e. both, T-and S-particles, particles, which all/every constantly move in the 4D Matter’s sub-spacetime with 4D speeds of light, move along the t-axis with the speed of light also, however along the τ-axis only T-particles move.

When the T-particles are at absolute spatial rest, they move along the τ-axis with the speed of light, i.e. identically with their simultaneous motion along the t-axis.

If a T-particle is impacted by some spatial momentum [in macro physics practically all momentums are spatial momentums, the directed along the τ-axis momentums, when new T-particles are created, appear only in high energy physics], it moves in the 3D space also, though remain to move along the τ-axis with a speed that is lesser then the speed of light in Lorentz factor [thus the rate of internal processes in spatially T-particle/T-body becomes be lesser in the Lorentz factor, including, for example, clocks tick slower, comparing with when they are at the spatial rest]. However its speed along the t-axis remains be equal to the speed of light.

Thus T-particles formally can make only one “zig-zag” in the time: back and forth along the τ-axis. However that is impossible in Matter, particles and antiparticles move in the coordinate time only in their [opposite] directions. Though they can make any zig-zag in the 3D space.

S-particles, for example, photons, move in the 3D space only [and, of course, in the true time] with the speed of light. Since they so don’t move in the τ-axis, they cannot make some zig-zag in the coordinate time [and in the true time by definition], however can make any zig-zag in the 3D space.

“…what means back in a Complex Set?…”

Since in the Matter’s spacetime all dimensions, and so all motions of anything, are [mathematically] real, there is no necessity to consider some complex numbers in this case. In the special relativity it is postulated that the real Matter’s spacetime is indeed some [mathematically] imaginary 4D Minkowski space, which can be really “contracted”, “dilated”, etc., however these postulates are nothing else then some “fundamental” fantasies, which have no relation to the objective reality.

Cheers

dear Sergey, in my opinion time is variation of space AND variation of variation of space! there are 2 variables!! that is: complex number. or: f(v;a) a complex function. one cannot ignore that a variation of variation of space exists too. ergo: time depends on 2 vatiables.

A great question, not as simple as it seems.

We would need to recognize a new category of existence to allow the concept of negative mass. As things stand in physics, all particles have positive mass including antimatter, which responds to gravitational forces exactly as familiar matter does. So "negative mass" is not a concept that physicists allow. The downside of this failure of imagination (or nerve) is that it reduces the universe to a monism---mass---with no form of opposed energy. To an artist, that's equivalent to trying to paint in a sandstorm with a brush, canvas and paint all made of sand. Or a biologist trying to generate a zygote with just an egg, no sperm; or a programmer trying to write code with just 0's, no 1's. It can't be done. Reason enough cosmologists have not been able to offer a coherent explanation for how a complex Universe could emerge from nothing.

The simplest and most logical explanation would start with the definition of "nothing" as a chaos of equally mixed mass and space particles (something like a quark-gluon plasma at the highest level). At the Big Bang this symplasm differentiates into positive mass (matter and antimatter) and negative mass (space). Here we would define "space" exactly as "negative mass" traveling the opposite direction in time and space. For example in a gravitational field space would behave the diametric opposite of mass, expanding instead of contracting (and incidentally offering a logical source for inflation, beta decay and the Big Bang itself.) Complexity would then be defined as that configuration with the least free energy and highest degree of structural interaction between space and mass. All this is wholly compatible with the laws of thermodynamics once we understand that such a quintessential dualism (not just a duality) offers the missing option in the Second Law: an open system whereby energy for mass constitutes entropy for space and vice versa (one common example is the gas exchange in animal vs plant respiration). "Disorder" for one side thus supplies energy to the other in a reciprocal energy exchange. By the dynamics of broken symmetry, the overall game plan for the Universe then appears as increasing complexity defined as the ongoing process of differentiation of most opposed forces out of chaos (defined as their mutual con-fusion). All by the laws of thermodynamics. This is exactly what we see.

However, the concept of "cooperative antagonism" requires us to imagine that what we assume is our worst enemy just might be our best friend. As the artist and poet William Blake said, "Opposition is true friendship." But evidently theoretical physics operates under the same delusion as mysticism: eliminating opposition by merge both parties into one big entity destroying the identity of either side. The name of that process is dedifferentiation,* exactly what we see when we run the cosmic movie backwards to the Big Bang. Chaos is one example; so is Minkowski spacetime (https://en.wikipedia.org/wiki/Minkowski_space). I'm not saying that Minkowski and the other monist physicists are wrong; merely that if they can only explain half the Universe, maybe monism itself is flawed, not to say nonphysical. (No example of pure monism can be found anywhere in the known Universe; every action everywhere has its opposite and equal reaction.) Religion can get away with saying Let there be light; but even Genesis recognizes God's first act of creation was to separate the light from the darkness. That's art, that's science, that's truth, that's life itself. Unfortunately, it's not yet theoretical physics, but if it's the way the Universe operates, it's just a question of time.**

*Dedifferentiation in oncology is an ominous development and a hallmark of malignancy; it's the reverse process by which stem cells differentiate into their specialized organs. It runs the movie of life in reverse.

**It would help if artists understood the physics of their own line of work enough to explain it to science guys in their own terms. That this level of dialog is still undeveloped is not entirely the fault of the physicists who periodically make gestures toward the art side of the aisle. Like everything, it takes both sides.

I would suggest to have a look at the Janus Cosmological model which relates to negative mass particles. This could help to answser this question.

Dear Paul,

"I don`t think that mass is a scalar, while multipying by 1/Square-root(1-v²/c²)"

Why the heck would you multiply by 1/Square-root(1-v²/c²)?

Best regards,

Thierry

Mathematically, we can consider antiparticles as particles that travel back in time. In the same way mathematicians can interpret pair creation and pair annihilation as time reversal of a single (anti)particle. During time reversal, many of the properties of the (anti)particle switch sign. Its mass stays the same.

We are observers and all observers must travel with time. So we cannot properly imagine what time reversal means.

dear Thierry, why not? increase vs. decrease, accelerate vs. slow down...

Dear Paul, if there is no fundamental physical substantiation, it is nonsense to apply factors to physical events in order to get a ad hoc "fit".

Since Einstein we know that mass is related to the capability of massive objects to deform the field that embeds them. See: Preprint Mass and Field Deformation

What's in a language, dear Hans! Don't charges "deform" fields?

dear Thierry, if dividing by sqrt(1-v²/c²) means something, then multiplying by the same should be the inverse.

I dont know if someone has already stated this, but if particle-antiparticle annihilation results in the energy release of the sum of both particles, then both particles must have equal energy, and equal sign of energy. A negative mass antiparticle should also have negative energy.

A short answer to this question: If there were particles within our present Universe with negative mass they would be expelled immediately due to negative gravity. This implies a Universe made by either positive of negative particles.

The case of Dark Energy, that is attributed to negative gravity, is another case that is no the proper place to discuss here. (This is related to the duality of our Universe ... .)

Anti-particles are the ones that have opposite charge and the same mass and spin. However, particles with opposite mass may be related to Super-Symmetry.

“…I dont know if someone has already stated this, but if particle-antiparticle annihilation results in the energy release of the sum of both particles, then both particles must have equal energy, and equal sign of energy. A negative mass antiparticle should also have negative energy…..”

- yeah, that is evidently so. And in the SR [kinetic] energy is always positive. Nonetheless just suggesting that there are some “see of negative energy”, i.e. in contrary with the SR, Dirac predicted antiparticles, which, of course, turned out to have positive energy.

This casus obtains explanation only in the Shevchenko-Tokarevsky’s informational physical model https://www.researchgate.net/publication/273777630_The_Informational_Conception_and_Basic_Physics DOI 10.5281/zenodo.16494; where it is shown that Matter’s spacetime is the absolute [5]4D Euclidian “empty container” with metrics (cτ,X,Y,Z,ct), where two times,” cτ” and “ct”, exist and act, and where the 4D sub-spacetime with metrics (cτ,X,Y,Z) is filled by dense lattice/ether of 4D fundamental logical elements; when particles, bodies, etc. are mostly some cyclic disturbances of the lattice.

All disturbances move in the 4D ether with 4D velocities that have identical absolute values be equal to the speed of light, c, [bold is 4D vector], having always momentums P=mc and energies E=Pc=mc2.

So energies and masses have, as that must be, always positive values. However momentums can have negative values in every of the 4 dimensions above. At that particles are close-loop reversible algorithms, which can run in direct and reverse modes, so the motion in the “coordinate time” cτ, of the algorithms with direct command sequence, i.e. of particles, is motion in positive cτ direction; motion of algorithms with reverse sequence, i.e. of the antiparticles, is motion in negative cτ direction;

- that, besides explanation of Dirac’s conjecture, is also the explanation of what is the ad hoc “Feynman–Stueckelberg interpretation” in QED, and why it is indeed adequate to the reality.

Cheers

Sergey Shevchenko To sum up, the negative energy states (negative mass) particles of the Feynman–Stueckelberg interpretation from the Dirac equation must travel backwards in time, right? Turns out that have only measured particles travelling foward in time.

I recently wrote a paper on this subject, which was published in Mod Phys Lett A back in January. See:

Article On the existence of exotic matter in classical Newtonian mechanics

Article On the existence of exotic matter in classical Newtonian mec...

Data Exotic Matter in Classical Newtonian Mechanics and General R...

We have to be very careful what we mean when we refer to "negative mass". There is more than one type of mass in Newtonian gravity, and the possible signs of the various masses allows for the existence of precisely four classes of particle, one of which represents ordinary matter and the remaining three of which represent matter with different kinds of negative mass.

The principle of equivalence does allow for the existence of negative mass particles in GR - which corresponds to one of the three classes mentioned above. However I argue that all four classes of particle must in fact exist even in GR.

I expect that antiparticles will be found to antigravitate, i.e. to fall upwards.

Sabbir Rahman If observed antiparticles have negative mass (and thus, gravitate), shouldnt the annihilation between one of those an a particle result in a zero energy release? Because a negative mass implies negative energy. And that is not what we observe in the annihilation process.

If you check the formulae in the paper, you will see that negative mass does not, in fact, imply negative energy. Indeed class A and class D particles have positive energy, while class B and class C have negative energy.

So even if the observed antiparticles are of class D and have negative mass, they still have positive energy, and so if they annihilate with an ordinary particle (i.e. of class A) there will be positive energy released.

On the other hand, if a class B particle (note that dark energy would be of class B) were to 'annihilate' with a class A particle (note that dark matter would be of class A), then it is possible that there will be no release of energy as class B particles have negative energy. (Note that this would correspond to annihilation of positive curvature with negative curvature, not matter with antimatter).

Since general relativity's prediction is A and B class, I would like to think that those are the ones that exist. The others seem to be an arbitrary choice interaction with no reason. Thus, if only class A and B exist, and annihilation would result in no energy release. Because we do observe energy released, I believe antiparticles (antimatter) are not class B and thus, they have positive mass.

Yes, that is correct. Antiparticles have positive energy and so can only be of class A or D. The general concensus appears to be that they are of class A, and would therefore fall downwards in the Earth's gravitational field.

It will be interesting to see the results of AEgIS and other related experiments to determine whether this is indeed the case. If you read my papers you will see that I have a number of theoretical reasons for expecting antimatter to be of class D and therefore to antigravitate.

Dear Manuel Urueña Palomo ,

- sorry for so late comment to your post above, seems I missed corresponding RG acknowledgement.

“…To sum up, the negative energy states (negative mass) particles of the Feynman–Stueckelberg interpretation from the Dirac equation must travel backwards in time, right?…”

- to write something about “energy” and “mass” beyond many of standard applications in physics, i.e. when Meta-physics becomes be essential – as that is in the quotation above – is necessary to understand before – what are fundamental Meta-physical phenomena/notions “Energy” and “Mass” [and the fundamental Meta-physical phenomena/notions “Space” and “Time”, though]. Which can be, and are, properly defined only in the Shevchenko-Tokarevsky’s “The Information as Absolute” conception https://www.researchgate.net/publication/260930711_the_Information_as_Absolute DOI 10.5281/zenodo.268904,

where it is rigorously proven that there exist nothing else than some informational patterns/ systems of the patterns that are elements of the absolutely fundamental and absolutely infinite “Information” Set. Matter is nothing else than some informational system of a huge number of informational patterns/sub-systems, which are elements of the Set; and the term “absolutely fundamental” means: “exists/act on whole Set”, when [“simply”] “fundamental” relates to phenomena /notions that are fundamental in the system “Matter” only;

and where the utmost common definition of so absolutely fundamental phenomena/notion “Information” is given: Information is something that is constructed in accordance with absolutely fundamental Rules, Possibilities, Quantities, Actions, etc. that are elements of the corresponding set, in the conception the “Logos” set, and which [elements of the “Logos” set] “make something to be an information”

The Quantities “Energy” and “Mass”, the Rules/Possibilities Space and Time, and the Action “Change” are absolutely fundamental, i.e. “Logos” set’s elements.

Energy and Mass exist in any/every informational pattern/system [further “information”] because of the logical self-inconsistence of “Change”, including at creation some new information: at a change every state of changing information is simultaneously the previous, recent, and future states, what is logically wrong by definition of the change.

And to overcome this absolutely fundamental self-inconsistence it is necessary (i) – to spend some “energy”, and (ii) nonetheless that isn’t enough, and for any limited energy the states of changing information are on some level “illogical”, i.e. uncertain. Just that is observed at changes of parameters of physical informations on the QM level and the QM is adequate to the reality. That was discovered in outstanding Zeno aporias 2500 years ago, when Zeno, in fact, predicted QM.

Thus energy that creates any information, including any particle [which are 4D close-loop algorithms that constantly always run because of the energy conservation law] can be only positive, when the logical “resistance” of any information to changes is called “Inertia”, in physics, because of Matter is rigorously organized informational system in accordance with a set of universal fundamental laws/links/constants, corresponding Inertia has a measure “mass”. Mass so fundamentally is positive.

Matter in fundamental depth is based on simplest binary [in accordance with the outstanding von Weizsäcker’s “Ur hypothesis”] and reversive [with outstanding Fredkin-Toffoly finding] logic,

so Matter’s spacetime is absolute [5]4D Euclidian “empty container” with metrics (cτ,X,Y,Z,ct), i.e. that consists of 3D space – in accordance with Weizsäcker’s outstanding finding above, X,Y,Z dimensions; and 2 “times” , “ct”, i.e. “true time”, and “cτ”, i.e. “coordinate time” dimensions,

where all Matter’s informations, including particles and antiparticles, move with 4D velocities that have identical absolute values be equal to the speed of light, in the 4D sub-spacetime with metrics (cτ,X,Y,Z), and, simultaneously, in the 1D true time dimension with the speed of light.

The “additional” coordinate time dimension is used in Matter just to implement logically reverse algorithms, when particles move so in positive cτ-dimension, and antiparticles, which are reverse algorithms of particles, in negative cτ-dimension. Just so the ad hoc Feynman–Stueckelberg interpretation is adequate to the reality. However everything what changes, including particles and antiparticles, moves only in positive direction in the absolutely universal “true time” dimension.

So that

“…Turns out that have only measured particles travelling foward in time.….”

- indeed, everything moves “forward in the true time”, and, since humans are made from particles, forward in the coordinate time also. However, because of the above, i.e. because of that most of physics happens/proceeds in the 4D sub-spacetime above, the motion “back in the coordinate time” is essential at describing of event/effects/processes in Matter.

And just so, the ad hoc Dirac’s idea about “negative energy” and the ad hoc Feynman–Stueckelberg interpretation, turned out to be, though contradict with the rest physics, adequate to the reality conjectures.

More see https://www.researchgate.net/publication/273777630_The_Informational_Conception_and_Basic_Physics DOI 10.5281/zenodo.16494, the SS posts in https://www.researchgate.net/post/What_is_the_most_precise_definition_of_time_And_what_is_the_easiest_way_to_describe_time#view=5dc1c5712ba3a1862e764a2c are useful also.

Cheers

Sergey Shevchenko You could use the same reasoning for electric charges been only positive, and we know that is not true (see the similarity between electromagnetic and gravitational fields).

Metaphysical arguments break down when you consider modern physics (for instance, greek philosophers could never know that time is not absolute, or that the vacumm always contains particles). You need to use the modern theories we've got:

Negative mass works in general relativity, thus, It might be real. It is just that we have never observed it (we have never observed all cosmos).

You can also reverse time in general relativity. Time is just another dimension, in which you can go backwards by an antichronous transformation. We now know that time is not absolute, it slows down and even stops. Why to reverse in some place where the spacetime curvature allows it? There is no "true direction" of any spatial dimensions. It might be the same for the time dimension.

There are many insconsistences when you allow both a negative energy (or negative mass) to coexist in the same causally connected space time. First, annihilation when positive energy and negative energy collide, or even a runaway motion between a positive and a negative mass according to the predictions of general realtivity. But that is not enough reason to rule out their existence, since there are places in the cosmos where a spacetime is one-way causally disconnected from the rest, such as the interior of a black hole (which by the way, is the place where spacetime is more curved till clocks slow down and they stop, so it is one the best candidates for a time reversal to occur).