I am sorry. I apologize for my poor English.

Below explanation is answer for Marcoen's questions. Please refer to below answer.

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Question1: For example, if one would apply contact forces to a body with negative inertial mass (assuming there is such a thing in a world where also positive inertial mass exists). If I would push such a body away from me, it would accelerate towards me, or not? Doesn't this sound so implausible that we can dismiss the idea of negative inertial mass? I would be interested in your thoughts about this.

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Answer: For gravity, there is the influence of attractive force between objects with the same signs, but it does not come into existence, when applying this to electromagnetic force as it is. Charges with the same signs exchange repulsive force with each other, although this phenomenon is very weird, considering the case of gravity.

Most of people have strong aversion of negative mass, but no law of physics says there is only positive mass in nature.

I think that implausible phenomena in nature are phenomena against physical laws such as the law of conservation of energy or momentum, not our thoughts.

We are necessary to watch carefully the fact that sort of physical laws such as law of energy conservation or law of conservation of momentum do not deny negative mass.

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Question2 : In your essay you write that "negative mass has repulsive effects towards each other so it cannot form any structure". However, two bodies with negative inertial mass and like electrical charges would attract each other: the Coulomb force on the first charged particle, exerted by the second equally charged particle, is directed away from the second particle, so the first particle would accelerate towards the second because of its negative inertial mass. So why would atomic structures (e.g. hydrogen-like) be impossible in a universe?

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Answer : As examined the equation of motion for negative mass, it is marked in form of F = -ma(m > 0), when attraction is applied together with nuclear force(when usually nuclear force is attraction, but has the form of repulsive core), and assuming nuclear force has the form of F = -Q(r) r^, Q(r) is the function of distance r, thus nuclear force is in the form of attraction worked in the direction of -r^. Because they form a binding structure together, regardless of the form of force~

Here, for the force worked on negative mass m,

F = - ma = - Q(r) r^

a = (Q(r)/m) r^

The term of acceleration is positive, so the effect of increasing distance r, namely repulsive effect appears. This means that negative mass hard to form the structure like atom(massive nucleon, baryon, particle consists of multi elementary particle), because nuclear force has not binding negative mass when it is applied to negative mass. Also, gravity has not binding negative mass (repulsive).

We have to open up a lot of possibilities about negative mass(energy) and also, consider the possibility that negative mass does not make electromagnetic interaction.

In a particular case, negative mass can form the structure such as atoms, but in general, it seems it is difficult for it to form a large-scale structure like stars or galaxies.

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Question3 : If small particles with negative inertial mass would exist everywhere in the universe, would not we then observe a constant incoming flow of these particles on earth?

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Answer : In my article,

If negative mass and positive mass were came into being together at the beginning of universe, since positive mass has attractive effects with each other, so it forms stars and galaxy. In addition, negative mass has repulsive effects towards each other so it cannot form any structure and may spread out almost uniformly across the whole area of universe.

Therefore, positive masses and negative masses are completely offset in the whole universe, but there is a local area where positive masses exist more than negative masses.

Owing to the effect of negative mass and positive mass, negative mass disappears near massive positive mass structures (such as the galaxy and galaxy clusters, etc.) after meeting positive mass. However, negative mass, which came into existence at the beginning of universe, can still exist in a vacuum state outside of general galaxy.

The current structure of the galaxy is a structure that survived in the pair-annihilation of positive mass and negative mass and, since negative mass existed outside of this galaxy structure, therefore it has not been observed at the Earth.

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    Question4 : how can we in principle detect a particle with negative inertial mass? In other words: how can we prove its existence?

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    1. Theoretical calculation

    After making new Friedmann eq., on the assumption that negative mass and positive mass coexist, we have to explain dark matters and dark energy using it, predict new phenomena and compare them with one another.

    Dark matter and dark energy come from one origin!

    "Pair creation model of negative mass(energy) and positive mass(energy)" insists that dark matter is not different from dark energy each other, dark matter is the effect of centripetal force by negative mass out of galaxy, and dark energy is that positive gravitational potential term in total potential energy.

    "Pair creation model of negative mass and positive mass" insists that dark energy is a gravitational potential energy(with positive value) between negative mass and positive mass.

    As a matter of fact, through numerical calculation using a computer, the distribution having a similar value to the predicted rate of WMAP was revealed.( Refer to 6~7P)

    We get a result at almost zero energy state.

    (Zero rest mass energy: |m_positive| = |-m_negative|)

    Matter (U_posiposi) : -83.2 (Ratio:1)

    Dark Matter (U_neganega) : -459.6 (Ratio:5.52)

    Dark Energy (U_negaposi) : 1286.9 (Ratio : 15.46)

    2. Computer simulation

    1) Big bang simulation

    We set up each model from the birth of universe to the present, and calculated GPE using computer simulation in each level.

    As a result, we could verify that "pair creation model of negative mass and positive mass" explains inflation of the early universe and decelerating expansion, and present accelerating expansion in time series.

    This simulation is showing incredible results.

    It not only explains the total energy of the universe, flatness, and the essence (Total zero energy, pair creation of negative energy and positive energy) of the process of birth of the universe, but it explains inflation, decelerating expansion in the early stage, accelerating expansion(dark energy) in the late stage, and dark matter through the only term, negative energy. Moreover, this negative energy is one that is essentially required by the law of energy conservation.

    - The Change of Gravitational Potential Energy and Dark Energy in the Zero Energy Universe :

    http://vixra.org/abs/1110.0019

    - Dark energy - Accelerating expansion of distant galaxy due to negative mass :

    http://www.youtube.com/watch?v=71nMvwUhHwE

    - Inflation, accelerating expansion with pair creation of negative and positive mass :

    http://www.youtube.com/watch?v=SRUqQM2FfNU

    Therefore, a larger-scale, precise experiment is needed.

    2) Bullet cluster simulation

    Have a nice day!

    ---Hyoyoung Choi

    a month later

    • [deleted]

    • Post #14

    Hi Hyoyoung!

    Great to see you here! I had the negative mass interpretation thread on BAUT forum where I found your videos originally. Very glad to see you have posted an essay here. I am still figuring out the best way to present my own ideas, which are closely linked to your own.

    Here is a simple proof against General Relativity (and is an interpretation of your negative mass and energy) (note that the addition sign is not working on my preview so I have substitued the oplus symbol)

    The most general equation formed from the metric guv and the Riemann tensor is [math]\Lambda g_{\mu\nu}\oplus G_{\mu\nu}=R_{\mu\nu}-\frac{1}{2}R g_{\mu\nu}[/math] In keeping with this essay contest, lets change the symbols for the cosmological constant and the Einstein tensor so that we do not confuse what these are thought to physically represent and thus leave only a mathematical meaning. Then we can have [math]\Omega g_{\mu\nu}\oplus L_{\mu\nu}=R_{\mu\nu}-\frac{1}{2}R g_{\mu\nu}[/math] Let the condition [math]R_{\mu\nu}=0[/math] apply. This then becomes [math]\Omega g_{\mu\nu}\oplus L_{\mu\nu}=0[/math] so that [math]L_{\mu\nu}=-\Omega g_{\mu\nu}[/math] If we then also require [math]\Omega g_{\mu\nu}=0[/math] we obtain [math]L_{\mu\nu}=R_{\mu\nu}-\frac{1}{2}R g_{\mu\nu}[/math] This is a special case which results in the Einstein tensor since [math]\Omega g_{\mu\nu}=L_{\mu\nu}\oplus G_{\mu\nu}[/math] and for [math]\Omega g_{\mu\nu}=0[/math] then [math]G_{\mu\nu}=-L_{\mu\nu}[/math] which we can substitute in by pulling a -1 out of the Luv coefficients. Thus Einstein putting a multiple of the metric with his tensor (the cosmological constant) ruined the mathematical rigor of the field equation. He should have flipped his Einstein tensor around first. Therefore, in keeping with your work, [math]\Omega g_{\mu\nu}\oplus L_{\mu\nu}=R_{\mu\nu}-\frac{1}{2}R g_{\mu\nu}[/math] is the negative mass and energy field interpretation of GR (classical gauge theory). The positive mass and energy equation is only valid with no cosmological constant. Let me know what you think, I look forward to more of your simulations!

    Regards,

    Jeff Baugher

      15 days later

      For the observation or evidence of negative mass(energy)

      In 1998, an observation by both the HSS team and SCP team obtained a negative mass density from inspected field equations over 70years.(field eq. has a Lamda=0)

      SCP(Supernova Cosmology Project) team : If Lamda=0, Omega_M= - 0.4(±0.1)

      http://arxiv.org/abs/astro-ph/9805201 refer to 7P

      HSS(The High-z Supernova Search) team : If Lamda=0, Omega_M = - 0.38(±0.22)

      http://arxiv.org/abs/astro-ph/9805201 refer to 14P

      However, the two teams which judged that negative mass and negative energy level could not exist in our universe based on "the problem of the transition of the energy level of minus infinity" and they instead revised the field equation by inserting the cosmological constant.

      We must to know that not the equation has disposed the value, but our thought disposed the value.

      Moreover, we considered vacuum energy as the source of cosmological constant Lamda, but the current result of calculation shows 10120, which is unprecedented even in the history of Physics.

      However, if "the problem of the transition of the energy level of minus infinity" does not occur, and thus negative and positive mass can coexist, what would happen?

      It is well known that a cosmological constant can respond to the negative mass density.

      peff = -Lamda/4piG

      Lamda is positive, so peff is negative.

      ==================

      Have a Nice day!

      --- Hyoyoung Choi

      • [deleted]

      • Post #16

      Dear Choi,

      I like your division to negative and positive part.

      I thinking about it in my two essay

      http://www.fqxi.org/community/forum/topic/946

      http://fqxi.org/community/forum/topic/1413

      Don't worry about broken English.....

        Dear Yuri Danoyan

        Thank you very much!

        I will read your paper, and if I have an opinion on your essay, I will post it.

        Have a nice day!

        --- Icarus2

        Dear Jeff Baugher!

        I am glad to see your essay at here and good luck in the contest.

        --- Hyoyoung Choi

        Dear Hyoyoung,

        This is a good idea you have. Who knows if it will turn out to be right, but it is clear, based on a simple motivating principle, and has a lot of explanatory potential. I have a couple of questions.

        1. Would you expect particles of negative mass to interact with particles of positive mass nongravitationally? The reason I ask is because I am trying to think of how one might try to observe such a thing in the laboratory.

        2. A similar "gravitational segregation" argument has been used before to try to explain the matter-antimatter asymmetry in the observable universe. (I mention this briefly in my essay here On the Foundational Assumptions of Modern Physics.) The idea is based on the fact that the nature of the gravitational interaction between matter and antimatter particles has never been conclusively established since gravity is so weak, and some people have speculated that antimatter itself may have an anti-gravity effect. Do you think it's possible that the negative-mass particles you are proposing might be ordinary antimatter?

        Take care,

        Ben Dribus

          Dear Ben Dribus,

          I am sorry. I apologize for my poor English. I am not sure that below thought be helpful to you.

          We have to open up a lot of possibilities about negative mass(energy).

          1. Negative mass hard to form the structure greater than the atom.

          As examined the equation of motion for negative mass, it is marked in form of F = -ma(m > 0), when attraction is applied together with nuclear force(when usually nuclear force is attraction, but has the form of repulsive core), and assuming nuclear force has the form of F = -Q(r)^r, Q(r) is the function of distance r, thus nuclear force is in the form of attraction worked in the direction of -^r. Here, for the force worked on negative mass m,

          F = -ma = -Q(r) ^r

          a = (Q(r)/m) ^r

          The term of acceleration is positive, so the effect of increasing distance r, namely repulsive effect appears. This means that negative mass hard to form the structure like atom(massive nucleon, baryon, particle consists of multi elementary particle), because nuclear force has not binding negative mass when it is applied to negative mass. Also, gravity has not binding negative mass(repulsive)

          But, we can see that the negative mass can form its binding structure if there is any repulsive interaction among the negative mass, from the characteristics of negative mass.

          In addition, negative mass and positive mass can form binding structure and atomic structure in theory.

          For example, it can form atomic structure if the positive mass is located in the center, and the negative mass is located in the surrounded area, and both are rotating.

          2. Without giving that kind of characteristics of "the observation result that seems to be that dark matter does not emit or absorb photons" from the first, can this kind of result be induced from other basic principle?

          The process of negative mass emitting photon

          (-E) -hv < -E

          -E: Initial energy of negative mass, (E>0)

          The relational expression above means that if negative mass emits photon(with positive energy), then the energy after emitting gets lower than the energy before emitting.

          Negative mass is stable at the state of high energy(Refer to my essay!), so the voluntary transition that negative mass emits photon and succeeds to the lower energy level does not exist. Therefore, negative mass explains the result of the current observation that dark matter does not emit photon from the fundamental principle.

          ======

          2. A similar "gravitational segregation" argument has been used before to try to explain the matter-antimatter asymmetry in the observable universe. (I mention this briefly in my essay here On the Foundational Assumptions of Modern Physics.) ~

          ======

          I am glad to see your essay and greatly enjoyed reading your essay

          There are two ways on antigravitation.

          -------

          Model-1 :

          Inertial mass < 0, (Active and Passive) Gravitational mass < 0.

          The principle of equivalence is valid. My model is a model-1.

          In my article, I show that negative mass(energy) provides an explanation for dark matter and dark energy.

          Model-2 :

          Inertial mass > 0, (Active and Passive) Gravitational mass < 0.

          The principle of equivalence is not valid. Some people have speculated that antimatter itself may have an anti-gravity effect.

          Model-2 has a merit. Model-2 can also explain anti-gravitational effect(accelerating expansion). And it explains asymmetry between matter and antimatter.

          -------

          In the model-1,

          At the Earth, negative mass will fall the Earth.

          If negative mass and positive mass were born together at the beginning of universe, positive mass has attractive effect each other, so it forms star and galaxy structure now, but negative mass has repulsive effect each other and nuclear force cannot form nucleons by binding negative mass, so they cannot make massive mass structure like star or galaxy.

          The current structure of the galaxy is a structure that survived in the pair-annihilation of positive mass and negative mass and, since negative mass existed outside of this galaxy structure, therefore it has not been observed.

          In the model-2

          Antimatter will grow away from the Earth.

          If matter and antimatter were born together at the beginning of universe, matter has attractive effect each other, so it forms star and galaxy structure now, and antimatter has attractive effect each other, so it forms star and galaxy structure now. And antigravity exist between the galaxy and anti-galaxy.

          However, if we considering the random creation, uniformly distribution and dark energy effect, anti-galaxy(or anti-galaxy cluster) must be existed at neighborhood. So, maybe, we must observe it(anti-galaxy or pair annihilation in large scale).

          =====

          Do you think it's possible that the negative-mass particles you are proposing might be ordinary antimatter?

          =====

          In my opinion, model-1(original negative mass) is pessimistic. Model-2 is affirmative than model-1!

          On the asymmetry of matter and antimatter,

          [ My conjecture ]

          Positive energy(mass) and negative energy(mass) was pair-created in zero energy state. -->

          Positive energy creates the matter and antimatter with same amount.-->

          Negative energy(mass) prefer to the antimatter than matter. Because that antimatter has a little different physics quantity(it is a secret.^^") -->

          Pair annihilation of negative energy and antimatter > Pair annihilation of negative energy and matter -->

          Therefore, matter and antimatter have an asymmetry.

          Have a nice day!

          --- Hyoyoung Choi

          Hyoyoung,

          Thanks for the detailed reply! In particular, I'm glad you raised the point that inertial mass could be either negative or positive in this context. I hadn't even considered the possibility of negative inertial mass. Take care,

          Ben

          Thank you very much!

          I wish you good luck in the contest.

          --- Hyoyoung Choi

          6 days later

          Thank you very much!

          I enjoyed reading your essay(THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY). I will think more about your point of view.

          Good luck in the contest.

          --- Hyoyoung Choi

          6 days later

          Dear Hyoyoung,

          The force in the second Newton law is [math]F = ma [/math] where mass of a body m > 0, a is acceleration of the mass. This force is acting to mass m from the source of force. According to third Newton law there is the force of inertia [math]F_i = -F =- ma [/math] which is acting to the source of force. The reason for the force of inertia is action of fluxes of gravitons to the mass substance during of acceleration of the mass. We see that the force of inertia and the acceleration are opposite. Then we have [math]F_i = -F =- ma= m_i a [/math] where [math]m_i =-m[/math] is the negative mass of the body. So negative mass is a property of inertial forces.

          Sergey Fedosin

          4 days later

          After studying about 250 essays in this contest, I realize now, how can I assess the level of each submitted work. Accordingly, I rated some essays, including yours.

          Cood luck.

          Sergey Fedosin

          If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is [math]R_1 [/math] and [math]N_1 [/math] was the quantity of people which gave you ratings. Then you have [math]S_1=R_1 N_1 [/math] of points. After it anyone give you [math]dS [/math] of points so you have [math]S_2=S_1+ dS [/math] of points and [math]N_2=N_1+1 [/math] is the common quantity of the people which gave you ratings. At the same time you will have [math]S_2=R_2 N_2 [/math] of points. From here, if you want to be R2 > R1 there must be: [math]S_2/ N_2>S_1/ N_1 [/math] or [math] (S_1+ dS) / (N_1+1) >S_1/ N_1 [/math] or [math] dS >S_1/ N_1 =R_1[/math] In other words if you want to increase rating of anyone you must give him more points [math]dS [/math] then the participant`s rating [math]R_1 [/math] was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

          Sergey Fedosin

          a month later

          In the essay by Choi I am finding some very interesting and possibly important points. But one has to bear in mind that negative energies are usually considered as unphysical. An interaction between positive energy and negative energy states can make transitions between those states, so that positive energies increase to plus infinity, and negative energy fall to minus infinity, while the system's total energy remains constant. Such an instability is generally considered as very problematic, and people have good reasons for rejecting any theory that involves negative energies.

          A treatment of negative energies must be carried out with great care. As a toy model, I have studied the 2-dimensional harmonic oscillator whose x-component has positive, and y-component has negative kinetic plus potential energy. There is no problem with stability in the absence of an interaction that mixes the x and the y component. Such a system is analogous to the Choi's system with negative mass that is stable on the top of the potential. Instability can arise in the presence of an interaction. I have found that for some interactions between x and y, the system can be stable, which means that the trajectory remains confined within a finite region of the (x,y)-space. This is shown in slides http://www-f1.ijs.si/~pavsic/IARD2012.pdf and paper http://arxiv.org/abs/arXiv:1210.6820 , where I also considered the cases of the quantum oscillator, the scalar field theory, and the Dirac field theory.

          The Dirac equation describes a spinor with positive and negative energy states. It can be generalized so that it describes not only one, but four such spinors. I will not go into details here. Let me only mention that this is related to the description of spinors as objects embedded in the Clifford algebra Cl(1,3). Since the latter algebra has 16 dimensions, also a generalized spinors is a 16-component object. Eight of those components have positive and the remaining eight components have negative energies.

          Can such a theory make sense? First recall that the occurrence of negative energy states was puzzling in the time when Dirac proposed his equation. In 1932, Fermi in wrote:

          "It is well known that the most serious difficulty in Dirac's relativistic wave equations lies in the fact that it yields besides the normal positive states also negative one, which have no physical significance. This would do no harm if no transition between positive and negative state were possible (as are, e.g., transition between states with symmetrical and antisymmetrical wave function). But this is unfortunately not the case: Klein has shown by a very simple example that electrons impinging against a very high potential barrier have a finite probability of going over in a negative state." [E. Fermi, Rev. Mod. Phys. Vol. 4, 87 (1932) ].

          Thus, Dirac' relativistic wave equation could have been put aside and ignored. Fortunately, this did not happen. The problem was solved by the Dirac sea of negative energy states.

          With the generalized Dirac equation the situation is analogous to that in 1932. Within the Clifford algebra framework, besides the negative energy states of the first 4-component spinor, we have also negative energy states of the second, third and forth spinor. Here one could also cure the problem by the sea of negative energies of all four types of quantized spinor fields. Alternatively, one can assume that there is the negative energy sea associated with two spinor fields, and the positive energy sea associated with the remaining spinor fields. The vacuum energy density of such 16-component field is zero. In such a setup we have positive energy states that are not filled, and also the negative energy state that are not filled. Such a system is unstable. The vacuum can instantly decay into an infinite number of positive and negative energy states particles.

          In the paper http://arxiv.org/abs/arXiv:1210.6820 we argue that such a catastrophic instantaneous explosion does not happen in a finite (closed) universe, with a minimal (e.g., Planck) distance. Then there exists a maximal absolute value of a particle's energy, and the momentum eigenvalues are discrete. The number of possible fermionic states is finite in such a universe. The vacuum then decays in a finite time into a finite number of positive and negative energy particles. This is reminiscent of Big Bang, and perhaps this could be an explanation of the origin of Big Bang.

          In Choi's essay there are classical considerations only. But it is known that the main problems with negative energies arise in quantum theory. In my paper "Quantum Field Theories in Spaces with Neutral Signature", http://arxiv.org/abs/arXiv:1210.6820, I address how such difficulties could be circumvented.

            • [deleted]

            • Post #30

            The links that stay in my previous post do not work properly.

            After having read the link help page more carefully, I am trying to insert the links again. Hopefully, the following links are correct:

            My talk at the IARD2012 conference in Florence, Italy:

            www-f1.ijs.si/~pavsic/IARD2012.pdf

            Paper "Quantum Field Theories in Spaces with Neutral Signature":

            arxiv.org/abs/arXiv:1210.6820

            Matej Pavsic

            www-f1.ijs.si/~pavsic

            10 months later
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