A body at rest has rest Energy, so it should also have rest Momentum.
Lao Tzu said, “Gravity is the root of lightness; stillness, the ruler of movement”(重为轻根，静为躁君)*. The meaning of this statement can be extended in physics to mean that "big-G determines how light or heavy an object is, and rest-m determines how easy or difficult it is to move".
According to the mass-energy equation** [1], E=mc^2, any object with mass m has "rest energy" [1], regardless of its inertial frame†. Note that E here is meant to be the energy lost when radiating the photon γ, which is absolute and unchangeable in any inertial frame. The mass-energy equation has been experimentally verified [2] as the correct relation.
According to special relativity [3], the mass of the same object is different in different inertial frames, m' = βm. Therefore, the energy of conversion of m of an object into photon γ is different in different inertial frames. This issue has been discussed in [4], but there is no consensus. Our view is that the "rest energy" is theoretically not Lorentz invariant, and the existence of a minimum value is a reasonable result. The most rational explanation for this is that the minimum corresponds to an absolutely static spacetime, i.e., absolute spacetime(Later we will show that absolute space-time and relative space-time are not in conflict). Analytically, this is one of the reasons why absolute spacetime should exist. The constant speed of light is another reason.
In all cases in physics, energy and momentum coexist and have a fixed relationship, not independent metrics. The energy-momentum ‡ of a photon, E=hν[5], P=h/λ[6]; the energy-momentum relation of Newtonian mechanics, E=P^2/2m; and the relativistic energy-momentum relation, E^2=c^2p^2+m^2c^4. Therefore, it is assumed that if there is a body of mass m that has "rest energy", then it should also have "rest momentum". There is a "rest momentum", and the rest momentum cannot be zero. The rest energy is not intuitive, and the rest momentum should not be intuitive too. The calculation of the rest momentum is the same as the calculation of the rest energy. The nature of mass looks more like momentum; after all, energy is a sign of time, while momentum is a sign of movement. Therefore, instead of calling it the principle of equivalence of inertial mass and rest-energy[1], it should be called the principle of equivalence of inertial mass and rest-momentum.
When positive and negative electrons meet and annihilate [7], -e+e→γ+γ, radiating two photons in opposite directions. Their energy is conserved and so is their momentum. Energy is a scalar sum, while momentum is a vector sum. It seems that the "rest momentum" inside the object should be zero. However, one could argue that it is actually the momentum of the two photons that is being carried away, but in opposite directions. The momentum of the two photons should not come out of nothing, but rather there should be momentum of the two photons, also in some balanced way, and probably playing a very important role, such as the binding force.
Our questions are:
1) Since energy and momentum cannot be separated, should an object with "rest energy" necessarily have "rest momentum".
2) Elementary particles can be equated to a " energy packet ", and energy is time dependent. If an elementary particle is also equivalent to a "momentum packet", the momentum in the packet must be related to space. Does this determine the spatio-temporal nature of the elementary particles? And since momentum is related to force, is it the force that keeps the "energy packet" from dissipating?
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Notes：
* Lao Tzu，Tao-Te-Ching，~500 BCE. This quote is a translation of someone else's. There are some excesses that I don't entirely agree with. Translating classical Chinese into modern Chinese is just as difficult as translating classical Chinese into English.
** There is a historical debate about the process of discovery of the mass-energy equation, and digging into the history shows that there were discoverers and revisers both before and after Einstein, see literature [8][9]. Important contributions came from Poincaré, F. Hasenöhrl, Planck et al. Their derivations do not have the approximation of Einstein's mass-energy equation. And there is also a debate about the interpretation of the mass-energy equation. Notable debates can be found in the literature[10].
† There is a question here, i.e., is the rest mass Lorentz invariant? That is, is the rest mass the same in different inertial systems? Why?
‡ Einstein questioningly emphasized that energy and momentum seem to be inseparable, but did not explain it.
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References：
[1] Einstein, A. (1905). "Does the inertia of a body depend upon its energy-content." Annalen der physik 18(13): 639-641.
Einstein, A. (1935). "Elementary derivation of the equivalence of mass and energy." Bulletin of the American mathematical society 41(4): 223-230.
[2] Rainville, S., J. K. Thompson, E. G. Myers, J. M. Brown, M. S. Dewey, E. G. Kessler, R. D. Deslattes, H. G. Börner, M. Jentschel, P. Mutti and D. E. Pritchard (2005). "A direct test of E=mc2." Nature 438(7071): 1096-1097.
[3] Einstein, A. (1905). "On the electrodynamics of moving bodies." Annalen der physik 17(10): 891-921.
[4] Is there a minimum value of m in the mass-energy equation E=mc^2? https://www.researchgate.net/post/NO7_Is_there_a_minimum_value_of_m_in_the_mass-energy_equation_Emc2；
[5] Planck, M. (1900). " " Verh. Deutsh. Phys. Ges 2: 237.
[6] Einstein, A. (1917). Physikalisehe Zeitschrift xviii: p.121
[7] Li, B. A. and C. N. Yang (1989). "CY Chao, Pair creation and Pair Annihilation." International Journal of Modern Physics A 4(17): 4325-4335.
[8] Ives, H. E. (1952). "Derivation of the mass-energy relation." JOSA 42(8): 540-543.
[9] Sharma, A. (0000). "The past present and future of the Mass Energy Equation DE =Dmc2." http://www.mrelativity.net/Papers/8/Sharma4.htm.
[10] Peierls, R., J. Warren and M. Nelkon (1987). "Mass and energy." Physics Bulletin 38(4): 127.
Dear Chian Fan.
I'm sorry to say, but your questions 1) and 2) are meaningless from my point of view.
"Rest mass" does not exist in nature, because it is not a physical entity, but just a mathematical technique necessary in relativistic mechanics.
In the same way, I cannot support the concept of a "wave packet" for small (elementary) particles, since such particles cannot be a wave in any way, no matter what they say about them. Particles only look like a wave, since they are forced to move in the surrounding space with a period equal to the quantum of action h. As required by the Schrödinger equation. A small particle cannot be at rest under any circumstances. The de Broglie formula h=pλ tells us that we cannot determine the exact position of a particle and thereby fix its rest point. And if the position of the particle is inaccurate, we will not be able to say with certainty what the particle is doing in the region of space under consideration: is it somehow moving or is it still “resting”.
Yours, Dulin Mikhail.
Dear Chian Fan
I really appreciate your quote of Lao Tzu about gravity and its relation to motion. Because at nearly the same moment (~500 BCE) – at the other side of the world – the ancient Greek philosopher Aristotle described the concept of the unmoved mover, an abstraction that relates all the dynamics in our universe to one influence that is created by a “rest frame”. Aristotle was influenced by Parmenides of Elea who described the concept of an underlying reality that creates observable reality (actually Parmenides is the “father” of the concept of quantized space as a dynamical field structure).
Every quantum of energy has momentum. Momentum represents a dynamical influence so energy is not only a “metric” to describe a certain amount of change but it is also the “power” to create change. The confusion in relation to momentum is that the concept originates from classic physics and described the hierarchy of mutual relations (influences) between matter objects in relation to motion and the direction of motion.
Energy and momentum (the vector part) represent the dynamical properties of the universal electric and corresponding magnetic field (together termed electromagnetic field). Thus “energy packet” and “momentum packet” (actually vector packet) are corresponding manifestations of a local concentration of energy. The force that keeps the “energy packet” of a proton (stable particle) from dissipating is thought to be a manifestation of the (weak part) of the strong force.
Nevertheless, I understand the opinion of Mikhail N Dulin but I interpreted the aim behind your questions a bit different.
With kind regards, Sydney
It can't, by definition of what ``rest'' means: ``Rest'' means velocity=0, therefore momentum=0.
Dear Mikhail N Dulin
Sincerely welcome your any comments.
you wrote, "I cannot support the concept of a "wave packet" for small (elementary) particles, since such particles cannot be a wave in any way”.
Wave packet is the most flexible term to describe particles, taking into account both particles and waves. It is not a "definition". The "energy packet" is first used by Einstein and Schrödinger themselves. We can think of the "wave function" as an "energy packet", or a "momentum packet". You think it conflicts with the uncertainty principle. I will talk about my own views on the Uncertainty Principle later.
Best Regards, Chian Fan
It's nice to hear from you about the notions of the ancient Greek pioneers, and your comments on quantum.
"The force that keeps the "energy packet" of a proton (stable particle) from dissipating is thought to be a manifestation of the (weak part) of the strong force." The force seems to be the most important and the most difficult to interpret in physics. "Unification" is often thought of as the unification of the four forces. This is worthy of discussion.
Best Regards, Chian Fan
Dear Stam Nicolis
Thank you for your comment. However, there are two problems here. First, we have a difficult to clarify the concept of "rest". How do we recognize what is "rest". Secondly, even if we recognize a state of rest, how do we recognize that there is no motion inside the particle, such as assuming that the particle is a tiny gyroscope, which used to be Compton's view. Until we understand the structure of elementary particles, there is insufficient evidence to completely reject intrinsic momentum. I think it still makes sense to continue the discussion.
Best Regards, Chian Fan
Once more: The rest frame is defined as that where the object's velocity vanishes. The only objects that don't have a rest frame are the objects that move at the speed of light, since they can only move at that speed and none other.
The reason is that the combination E^2-|p|^2c^2 is invariant under Lorentz transformations, can be shown to be non-negative and, thus, provides the definition of the mass of the object as m^2c^4. The fact that it's non-negative implies that, if m≠0, there exists a Lorentz transformation that brings the energy-momentum 4-vctor, (E,pc) to th form (mc2,0), which is the rest frame.
If m=0, such a transformation doesn't exist, but it is always possible to find a transformation to a frame where p=(E/c,0,0) or (0,E/c,0) or (0,0,E/c), all consistent with E=|p|c.
These are standard exercises in special relativity.
If the object has internal structure, it's the frame where the velocity of the center of mass vanishes. There's no such notion as ``intrinsic'' momentum.
The quarks and leptons don't have internal structure (nor do photons, the W, Z, gluons or the Higgs), at least up to the energies probed-they're points-and the way to probe for internal structure is known-that's how it was discovered that the proton and the neutron had internal structure: By scattering other particles off them at increasing energies and studying the out states. That's how quarks were discovered.
“Should an Object at rest have Rest Momentum?”
- to answer to this question it is necessary before to define scientifically what is “Rest”, and so “Rest Momentum”.
Really – see the Shevchenko-Tokarevsky’s informational physical model, see
https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics - the Matter’s spacetime is fundamentally absolute, fundamentally continuous, fundamentally flat, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct), where the ultimate base of Matter – the (at least) [4+4+1]4D dense lattice of primary elementary logical structures – (at least) [4+4+1]4D binary reversible fundamental logical elements [FLE], is placed;
- while everything in Matter is/are some specific disturbances in the lattice, which always constantly move/propagate in the lattice in (utmost universal “kinematical”) 4D space [and in parallel in the time ct-dimension] with metrics (cτ,X,Y,Z) with 4D velocities that have identical absolute values be equal to the standard speed of light, c, [bold means 4D vector], what is determined by the main parameters of FLE, i.e. “FLE size” , and “FLE binary flip time interval”, which are lP and tP, c=lP/tP.
Correspondingly practically all/ every “objects” – besides fundamental Nature forces mediators - moves in the 4D space with 4D momentums, P=mc and energies E=Pc; and the notion “rest” can be principally applied only to motion in 3D space, where yeah, “T-particles” that are created by cτ-directed momentums, and so can be at rest in 3D space [so have “rest mass”] – and which so can move in 3D space after be impacted by a space-directed momentums, having some 3D speed V, and 3D momentums p=mV.
A particle at every given time moment is constantly always moving as “FLE flipping point” in 4D space along some 4D “helix”, which has the radius, if a T-particle is at 3D space rest, be equal to its Compton length, λ=ћ/P=m0c; while the “particle-point” can be so randomly in 4D and 3 D space volumes with size ~λ. If a particle moves in 3D space with a speed V, another - “de Brogile” - helix is added, with radius λB=ћ/p and in 3D space volume size is ~λB.
Correspondingly that
“…. Particles only look like a wave, since they are forced to move in the surrounding space with a period equal to the quantum of action h. As required by the Schrödinger equation. A small particle cannot be at rest under any circumstances. The de Broglie formula h=pλ tells us that we cannot determine the exact position of a particle and thereby fix its rest point.…..”
- is essentially correct, but if it is as in this post above, first of all that if a T-particle is at 3D space rest, in this case [p=0] application of de Broglie formula results in evidently absurd inference that in such case particle can be in infinite 3D space volume, while it exists, again, only in a concrete volume with its Compton length size.
Cheers
Dear Chian Fan
Suppose we have a local mass (E = m c2).
If I remove 1 quantum of energy from the mass (m), what is going to happen?
That is difficult to answer but if I remove all the quanta of the energy of the mass, except 1 quantum of energy, it is reasonable to propose that the linear velocity of the reduced mass is the speed of light (c).
Now what will happen if I have a mass of only 1 quantum and I "attach" a second quantum at the first one? I suppose that the velocity to transfer both quanta is < c. Thus increasing the mass is decreasing its velocity in relation to vacuum space around (if the local conditions don't change).
Every quantum of energy has momentum too because the universal electric field and the magnetic field are corresponding fields. That means that a quantum of energy generates a vector within the magnetic field and visa versa. The consequence is that we cannot eleminate the momentum of a quantum of energy because there is always a vector (direction of transfer).
The confusion is that we still use the phenomenological point of view, although everything in the universe changes synchronously (conservation of energy and conservation of momentum). Thus what is rest? Is it the condition that the mass doesn't change, is it the condition dat vacuum space around doesn't change, is it the condition that the mass and vacuum space together don't change? All these 3 possibilities are not real because of the synchronisation of all the energy transfer in the universe. Thus what we mean with "rest" is just a choice, a kind of focus on a phenomenon as if it is an independent unity.
With kind regards, Sydney
Dear Chian Fan
Quite a deep analysis, with proper referencing.
You ask: "1) Since energy and momentum cannot be separated, should an object with "rest energy" necessarily have "rest momentum"."
From the electromagnetic perspective, as experimentally established by Lorentz in his 1904 article in his analysis of the Kaufmann data, the only difference between transverse increased mass m1 and longitudinal increased mass m2 – his Equations (30) – is the amount of unidirectional energy that propels the electron in its longitudinal direction of motion, an amount of momentum energy detectable longitudinally but not transversely, due to its strictly longitudinal interaction. Subtracting this momentum energy from m2, both the increased longitudinal and the transverse masses are equal and larger than the rest mass m0 of the electron.
When an electron is prevented from moving closer to an atomic nucleus, such as the electron captive in axial resonance about the mean ground state distance that separates it from the proton in a hydrogen atom, instead of sustaining the "velocity" of the electron as in the case of the Kaufmann experiments, its momentum energy simply exerts an equivalent "pressure" in the direction of the proton against the mutually repelling counter pressure exerted against each other by the magnetic fields of the electron and of the proton, due to their default parallel magnetic alignment, which default permanent parallel magnetic alignment is itself due to their different oscillating frequencies.
When a mass rests against the surface of the Earth, its "velocity" towards the center of the planet that would be expressed if possible, due to sum of the individual momentum energies of all elementary charged particles of which it is made that are vectorialy oriented towards the Earth is prevented from being expressed. Instead, this cumulative sum of momentum energies is expressed as the "pressure" – the weight – that the body exerts against the Earth. A 1 kg mass exerts a pressure of 9,8 newtons against the Earth.
So yes, from the electromagnetic perspective, the rest mass of an object prevented from moving still retains all of the momentum energy that the interaction between all the charges of which it is made and all the charges of the Earth mass is made induce in them, in excess of the rest mass proper of the body, which is invariant.
Put in perspective in this article, and in most other articles of the electromagnetic mechanics project. All historical formal references are provided, with direct links to those directly available on the internet, which is most of them:
Article Introduction to Synchronized Kinematic and Electromagnetic Mechanics
Best Regards, André
Chian Fan,
Both the rest mass and rest energy are Lorentz invariants but not conserved because each is the magnitude of the four-momentum resulting from a dot product.On the other hand, both the relativistic mass and relativistic energy are conserved but not invariant.
In Einstein's relativity,energy and momentum are inseparable even in the rest frame. This is due to the fact that unlike Newtonian mechanics where the momentum has three components and is called three-vector or three-momentum,the momentum has four components and is called four-vector or four-momentum in special relativity. As a consequence,in the rest frame,only the spatial components vanish while the time component remains nonzero and is equal to the rest energy E0 and is designated by P0.Thus, the four-momentum or four-velocity of an object or particle can never be zero in its rest frame,and Einstein is surely right.
Dear Chian Fan ,
This translation of Lao Tzu cannot be interpreted in the way you interpreted it. Better would be a translation that is truly related to Lao Tzu's Tao teachings!
Ordinary objects do not have 'rest momentum'. Rather, they have moments of inertia.
(The moment of inertia of an ordinary body becomes evident when it interacts directly, and mechanically with another body. or 'the relative state of rest and uniform motion of these objects in a straight line is not forced to change ' (''-Newton's first law - the law of inertia)
The inertia momentum of the body does not express its rest energy. The body's energy is related to its expression quantity and how is structured inside the body.
Have you thought about how Lao Tzu would feel about what you just wrote?
He would also be critical of me for getting involved in such a nonsense discussion.
Regards,
Laszlo
The scientific answer to the thread question is given in the SS post on page 1. Further, regrettably, mostly rather strange posts appeared, about, say, “unidirectional energy”, though energy is scalar; or, say, - though that is not so unphysically at all, moreover – in full accordance with mainstream physics, that:
“…unlike Newtonian mechanics where the momentum has three components and is called three-vector or three-momentum, [in the SR] the momentum has four components and is called four-vector or four-momentum in special relativity. As a consequence,in the rest frame,only the spatial components vanish while the time component remains nonzero and is equal to the rest energy E0 and is designated by P0……”
- however that for any normal human looks as again rather strange claim. First of all the “4-momentum” is defined on, really of course non-existent, 4D [mathematically] imaginary Minkowski space, which for some strange reason in the SR is postulated as real (?) Matter’s spacetime , where, including, if 3XYZ space coordinates are [mathematically] real, then the fourth, i.e. time coordinate, is [mathematically] imaginary, and so P0 is imaginary as well;
- and, besides, in this case is as P0=iE0/c, c is the standard speed of light, it isn’t equal to the rest energy E0, since, again – energy is scalar, and cannot be a [in this case “P0”] vector component.
Matter’s spacetime is, of course, fundamentally [mathematically] real, fundamentally absolute, fundamentally continuous, fundamentally flat, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct); etc. more see the SS post on page 1 and links in the post.
Cheers
Dear Stam Nicolis
Special relativity is a theory of motion; it is a derivative of relative motion. As such, it is only capable of depicting the external motion of an object, and provides no information or is ineffective when the object is at relative rest.
The concept that elementary particles do not have an "internal structure" can only be a stopgap strategy for current physics. It is not a theory, nor is it an experimental result. No one can define point particles that have no internal structure but have many external properties and yet are different. Please be wary of "definitive" physics.
BTW, the most intuitive stationary momentum that exists in a "mini gyro" is angular momentum [1].
Best Regards, Chian Fan
[1] https://www.researchgate.net/post/No9_Is_the_spin_of_an_electron_really_spin；
Chian Fan ,
I agree with you that rest matters should have rest momentum most probably angular momentum. I believe that all matters are confined photons so that the mass energy equilibrium holds naturally. All photon momentum is curled up and turned into angular momentum which is resistive to push like mini gyroscope you have mentioned.
Jixin
Dear Chian Fan ,
The next conclusion is connected to your previous comment:
Research Proposal Physico-metaphysical proof of the existence of graviton (Fiz...
So far, two people with PhDs have made veiled, arrogant criticisms... somewhat suggesting my stupidity. So far, there are four opinions. : one is a normal honestly worded opponent opinion. What's your opinion?
Regards,
Laszlo
P.S.: there is a thought that relates to your topic...
Absolute energy-momentum and absolute reference frame
An important concept that needs to be made clear is whether the energy-momentum of an object is absolute or relative.
The energy-momentum of a photon (E=hν, P=h/λ) is absolute. This absoluteness is inherent in the photon, from the time it is separated from the light source. Implicit in this absoluteness is the notion that it must be for an observer in an "absolute reference frame", even though we do not know where the absolute reference frame is. For an observer in any other inertial frame, the photon would have to undergo a Doppler shift, changing its energy-momentum. This change, which depends on the inertial system, is not a real change. Rather, it only manifests itself when it interacts with the inertial frame in which the observer is located. As long as there is no interaction, the energy momentum of a photon is independent of the observer in any inertial frame.
Is the energy momentum of an electron absolute, or relative? The energy-momentum of an electron depends equally on the interacting inertial frame. But what is the energy-momentum of an electron before the interaction? What is the energy momentum of an electron as seen by an observer in the photon's "absolute reference frame"? Is it certain? There is no doubt that such a value must exist for it, and an absolute reference frame.
“…Absolute energy-momentum and absolute reference frame
An important concept that needs to be made clear is whether the energy-momentum of an object is absolute or relative.…..”
- really that is rather vague passage, since really relates to completely till now in mainstream physics subjective approach at studying of Matter, including in the mainstream the main measurements in any experiments are made in laboratory [inertial] frames, which are sets of scaled rules and specifically synchronized distant clocks, i.e. measurements of coordinates, distances and time intervals of/between studying objects/events/effects/processes.;
- while any real absolute frames don’t exist till now; moreover, the postulates that there exist no the absolute Matter’s spacetime and so that all/every inertial reference frames are absolutely completely equivalent and legitimate are basic postulates in the SR, which is quite standard theory in the mainstream.
That is another thing that the postulates above are fundamentally wrong, and so Matter’s spacetime is absolute [more concretely that rigorously shown in Shevchenko-Tokarevsky’s informational physical model, more see, e.g.,
https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics, and Matter’s spacetime is the fundamentally absolute, fundamentally continuous, fundamentally flat, and fundamentally “Cartesian”, [4+4+1]4D spacetime with metrics (cτ,X,Y,Z,g,w,e,s,ct)].
However the frames are really very essentially equivalent since that is in accordance with the extremely mighty Galileo-Poincaré relativity principle; and so measurements in real reference frames are as a rule completely legitimate, despite that all are principally only relative.
At that some parameters of what exists and happens in Matter are invariant, i.e. the measurements results are the same in all different inertial frames, however energy-momentum aren’t invariant, and their measured values are different in different relatively moving frames.
Really, since as that Poincaré showed in 1905, the Lorentz transformations, which follow from the relativity principle, form the “velocity group”, and so any frame is traceable to any “absolute”, i.e. that is at rest in the absolute 3DXYZ space of Matter’s spacetime above, frame.
Correspondingly at everyday physical practice the fundamentally possible, but really in the mainstream non-observable, absolute frames differ from the really used frames mostly only in that only in absolute frames all/every parameters of everything in Matter have - and can be measured so – real values, while in every moving in the space frame the measured values are principally unreal,
- however, again, that is only subjective problem of some humans that are physicists. Objectively everything in Matter exists and happens without any attention to somebody measures something or not, and to there exist somebodies or not, though.
Experimental measurements must be made only in “Lorentzian” frames, and, as that rigorously shown in the SS&VT model above, the results are completely adequate to the reality only if the studied objects/systems in Matter are rigid bodies that compose rigid enough systems. In other cases the results of measurements that are based on the frame equivalence postulate can be physically strange. Absolute frame are rigid by definition.
In system of free bodies the relativity principle action is limited, and so Lorentz transformations aren’t completely applicable, what allows to observe the absolute motion and to measure the absolute velocity of such systems, corresponding proposed yet in 2013-2016 experiments, see https://www.researchgate.net/publication/259463954_Measurement_of_the_absolute_speed_is_possible, can be made yet now.
More see the links above; returning to the thread question more concretely – the scientific answer see in the SS posts on the pages 1 and 2..
Cheers
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