Does special relativity entail matter annihilation?

[zoltrix]

hello

Does special relativity entail matter annihilation ?

 

[Dale]

Special relativity is a theory of spacetime, not matter

 

[PAllen]

Well, but making QM relativistic required the prediction of antimatter.

 

[PeterDonis]

making QM relativistic required the prediction of antimatter

To be more precise, special relativity (Lorentz invariance) plus quantum mechanics plus the requirement that the spectrum of the Hamiltonian is bounded below (in more ordinary terms, that there is a minimum possible energy, usually taken to be zero), requires that there be antiparticles. Feynman gave an elegant presentation of the argument in his Dirac Memorial Lecture, given in the early 1980s, which was published in the book Elementary Particles and the Laws of Physics.

 

[zoltrix]

I have been discussing this topic with a friend
My friend claimed that the relativistic Energy equation :

E^2 = (pc)^2 + (mc^2)^2

entails matter annihilation thanks to the term m*c^2
I disagreed
The relativistic Energy, in my opinion, is somehow equivalent to the Newtonian mass
the inertia of a body in motion being me = E/c^2
m*c^2 must be understood as the contribution of the matter to the inertia of the body while pc is the contribution of the movement
What do you think ?

 

[Nugatory]

What do you think ?

I think you should listen to your friend.

 

[PeroK]

I have been discussing this topic with a friend
My friend claimed that the relativistic Energy equation :

E^2 = (pc)^2 + (mc^2)^2

entails matter annihilation thanks to the term m*c^2
I disagreed
The relativistic Energy, in my opinion, is somehow equivalent to the Newtonian mass
the inertia of a body in motion being me = E/c^2
m*c^2 must be understood as the contribution of the matter to the inertia of the body while pc is the contribution of the movement
What do you think ?

First, this isn't a scientific question until you define what you mean by "matter annihilation". What particular physical process is entailed by SR and the above equation?

If it's the existence of anti-matter, then that does not follow. There is not enough in the theory of SR alone to imply the existence of antimatter. See post #4 above.

Moreover, that equation does not in itself imply that there must be massless particles. Nor does it imply that rest mass need not be conserved in particle collisions; nor that particles must decay.

It turns out that there are massless particles and that particles can decay and rest mass is not conserved in collisions. These are experimentally verified phenomena and - although the theory allows them - there's no implication that they must exist.

A good countereaxmple to this is the magnetic monopole. There is nothing in the theory of electromagnetism that forbids these. For whatever reason, however, it appears that nature has chosen not to make use of the magnetic monopole.

 

[zoltrix]

well , I suppose that you can define the term "matter annihilation" without invoking "anti matter "
Matter annihilation means that the whole body can be changed to energy.
However Einstein wrote

dm = E /c^2

I did not write

E = m*c^2

so I suppose that the original meaning was :

If a body absorbs / emits energy then its mass increases/ decreases

There is no reason , in my opinion, to assume that the whole body can be annihilated

 

[Dale]

What do you think ?

I think that it would have been helpful for you to include this in the beginning.

Frankly, I don’t think that either your position or your friend’s position is well supported.

For your position, $E/c^2$ is not the inertia of a body. The non-specific term “inertia” can either refer specifically to the momentum or to the invariant mass. In neither case does it refer to the energy. The concept of relativistic mass has been discarded for several decades now.

For your friend’s position, that term is certainly suggestive of annihilation, but is insufficient on its own. As @PeterDonis mentioned you need also a theory of matter with some specific features.

 

[weirdoguy]

whole body can be changed to energy

Energy is a property of matter not a form of matter, so things cannot be "changed to energy". Also, energy is conserved during annihilation so there is no additional energy created.

 

[PeterDonis]

There is nothing in the theory of electromagnetism that forbids these.

Actually, there is: the Maxwell Equation $\nabla \cdot \vec{B} = 0$.

There are extensions of standard electromagnetism in which this equation no longer holds and in which magnetic monopoles can exist. Also monopoles occur naturally in various quantum field theories. But none of those theories are standard electromagnetism.

 

[PeterDonis]

Matter annihilation means that the whole body can be changed to energy.

That depends on how you define "energy". If you define it as "massless radiation", which is what I suspect you have in mind, then, as has already been pointed out, the equations you give do not, by themselves, imply that such a process is possible. They are consistent with such a process, but they do not tell you that such a process must exist. You have to look elsewhere to find that out.

 

[PeroK]

Actually, there is: the Maxwell Equation $\nabla \cdot \vec{B} = 0$.

The theory works just as well with a magnetic charge and magnetic current. Although, I guess it depends whether you consider that equation forbids magnetic monopoles or is a working assumption that they don't exist.

 

[PeterDonis]

The theory works just as well with a magnetic charge and magnetic current.

A theory that includes magnetic charge and current works well. But(a) it is not properly called "the theory of electromagnetism"; it is, as as I said, an extension of the standard theory of electromagnetism; and (b) there is no evidence of magnetic charge or current, so "works just as well" is a statement of mathematical consistency only, not physical relevance.

I guess it depends whether you consider that equation forbids magnetic monopoles or is a working assumption that they don't exist.

It doesn't depend; standard EM does forbid magnetic monopoles. It's easier to see why if you express standard EM using differential forms. Then you have a potential 1-form $A$ and a field 2-form $F = dA$. Since $dd = 0$ (the "double exterior derivative" always vanishes), you must have $dF = 0$--and that forbids magnetic monopoles.

So it's not as simple as just "oh, put a magnetic source term into Maxwell's Equations". You have to break one of the fundamental properties of standard EM, that the field is the exterior derivative of a potential (since $dF \neq 0$ means it is impossible to find any potential $A$ such that $F = dA$). As I have noted, you can construct a mathematically consistent theory this way, but it's clearly not "the same theory" as standard EM, since it lacks a fundamental property that standard EM has.

 

[zoltrix]

For your position, $E/c^2$ is not the inertia of a body. The non-specific term “inertia” can either refer specifically to the momentum or to the invariant mass. In neither case does it refer to the energy. The concept of relativistic mass has been discarded for several decades now.

I don't think that the concept of relativistic mass has been discarded, its physical meaning was
Mass being no longer a measure of the quantity of matter of a body
The fundamental equation of the dynamics F = d(mt)/dt still holds if m = E/c^2
Whereas E is the total energy

 

[PeroK]

I don't think the concept of relativistic mass has been discarded,

I've never found it in any modern textbook. We sometimes get homework problems from students working from A.P. French's book, which dates from 1965 and uses relativistic mass. So @Dale is right, it's been gone from undergraduate textbooks for decades.

One issue is that once you move beyond SR to GR, particle physics and quantum field theory, relativistic mass is a dead end.

 

[weirdoguy]

I don't think that the concept of relativistic mass has been discarded

It is, at least in physics research. This insights article is a good start:
https://www.physicsforums.com/insights/what-is-relativistic-mass-and-why-it-is-not-used-much/

 

[zoltrix]

maybe the term relativistic mass is out of fashion but its physical meaning is still important in my opinion
Einstein demostrated the equivalence inertial and gravitational mass via the common factor E /c^2 while for Newton it was just an hyphotesis

 

[weirdoguy]

maybe the term relativistic mass is out of fashion

Term and quantity itself. Mass is defined as a norm of 4-momentum and therefore is invariant. There is no need for mass that is frame-dependent. We had plenty of threads about it, use "search" function and you'll find lenghty discussions about why it is not used.

 

[PeroK]

maybe the term relativistic mass is out of fashion but its physical meaning is still important in my opinion

It has no physical meaning, which is one of its problems. Any velocity you assign to a particle is frame-dependent, hence any relativistic mass is frame dependent. The particle itself has no idea what its relativistic mass is supposed to be - the particle doesn't undergo any physical change just because you choose to observe it from a different reference frame.

That's why it's a dead-end: if you approach GR with the notion that mass is frame-dependent, then you are off on the wrong foot immediately.

 

[zoltrix]

well I meant the following

quote

A common misconception that can be attributed to the concept of relativistic mass is that an object changes its internal structure by gaining mass when it travels at relativistic speeds. The object’s internal structure is independent of its velocity and it will always appear to be the same in its rest frame. The source of this confusion is that relativistic mass depends on the frame in which the object is observed and the concept of mass is typically regarded as a property of an object. See also our FAQ on the mass energy equivalence.

unquote

Mass and matter ( or bodies or objects ) are no longer related items in special relativity as they were in Newtonian physics
If modern texts scracth the word relative mass to avoid confusion that's understandable but physical concepts remain unchanged whatever words you want to use

Source https://www.physicsforums.com/insights/what-is-relativistic-mass-and-why-it-is-not-used-much/

 

[PeroK]

Mass and matter ( or bodies or objects ) are no longer related items in special relativity as they were in Newtonian physics

You'll be telling us next that if you go fast enough, you turn into a black hole!

 

[weirdoguy]

but physical concepts remain unchanged whatever words you want to use

The physical concept of relativistic mass has no serious meaning, as you've already been told. Are you here to learn, or to force upon us your own, incorrect understanding of physics?

 

[etotheipi]

You'll be telling us next that if you go fast enough, you'll turn into a black hole!

wait, that doesn't happen? years of training wasted!

 

[Dale]

I don't think that the concept of relativistic mass has been discarded,

You think incorrectly. Even as early as Einstein the concept of relativistic mass was not in favor: https://aapt.scitation.org/doi/10.1119/1.3204111 and Lev Okun expressed the "majority opinion" well throughout his career: http://www.stat.physik.uni-potsdam.de/~pikovsky/teaching/stud_seminar/einstein_okun.pdf and http://www.itep.ru/science/doctors/okun/publishing_eng/em_3.pdf

The concept of relativistic mass is analogous to those famous horse drawn carriages in New York city. Everyone knows about them but they aren't really practical and are pretty much only used by tourists. They might be good for impressing a girl on a date, but as a practical matter nobody who is trying to work wants to deal with the horse sh** that comes along with it.

The fundamental equation of the dynamics F = d(mt)/dt still holds if m = E/c^2
Whereas E is the total energy

This is false.

Einstein demostrated the equivalence inertial and gravitational mass via the common factor E /c^2 while for Newton it was just an hyphotesis

This is also false.

One of the main reasons that the concept of relativistic mass has been abandoned is precisely because it tricks people into believing exactly those false concepts. The last reference above discusses both mistakes in detail.

 

[vanhees71]

I think once more there's a lot of confusion about "relativistic mass", "anti-matter/particles", and all that coming up in this thread.

Let's begin with "relativistic mass": The very fact that all the confusing comes up as soon as one uses this idea, which is amazingly persistent since Einstein's very 1st and most famous paper on SRT. If I remember right, in this paper Einstein even comes up with a "longitudinal and a transverse relativistic mass", which is due to the fact that he had not Minkowski's mathematical analysis of the theory in terms of invariant theory to his disposal, and Einstein pretty early abandoned the idea of "relativistic mass(es)". For some reason this notion still persists to be used even in some introductory modern textbooks and of course even more in popular-science textbooks.

Since Minkowski we know it's of great advantage to formulate everything in terms of four-tensor (or in QFT also $\mathrm{SL}(2,\text{C})$ spinor) quantities. Thus nowadays one exclusively uses the invariant mass, which is a scalar quantity and energy and momentum, which together form the components of a four-vector $(p^{\mu})=(E/c,\vec{p})$, and the relation to the space-time vector of a point particle (classical mechanics) is
$$p^{\mu}=m \frac{\mathrm{d} x^{\mu}}{\mathrm{d} \tau},$$
where we take time derivatives with respect to "proper time", which is defined by
$$\mathrm{d} \tau=\mathrm{d} t \sqrt{1-\vec{v}^2/c^2},$$
which makes this a scalar measure of time, and physically it's an "infinitesimal time-increment" as measured in a momentaneous inertial rest frame of the particle, and from this definition of the four-momentum it's clear that $m$ occurring in this definition is just the Newtonian mass, independent of the velocity of the particle. Further from this definition you also get that the invariant mass is just given in terms of eneryg and momentum by the covariant energy-momentum relation,
$$p_{\mu} p^{\mu}=(E/c)^2-\vec{p}^2=(m c)^2.$$

Now concerning "anti-matter". Historically it took a while, starting from Dirac's treatment of the spin-1/2 particles in terms of his famous equation for a (bi-)spinor field. The modern line of arguments goes as follows:

(a) Free elementary particles are described by a realization of an irreducible unitary (ray) representation of the proper orthochronous Poincare group.

(b) In order to be able to formulate a Poincare-covariant theory of interacting particles one needs a local formulation, i.e., a formulation in terms of field operators $\hat{\psi}(t,\vec{x})$ such that the Hamilton density should commute with any local observable at spacelike distances (microcausality).

This is realized by assuming that the representation of the Poincare group is defined as a unitary representation acting on the field operators in a local way, as for the corresponding classical fields.

Building up the free-particle theory this leads to a decomposition of the field operators which always include both an annihilation operator (in front of the positive-frequency modes) an a creation operator (in front of the negative-frequency modes). This implies that for any particle there should be an anti-particle with the same mass and an opposite Noether charge from the global symmetry under multiplication of the field operators with phase factors (except if you want to describe strictly neutral particles, where the annihilation operators are just the hermitian conjugates of the creation operators, and then there is no more conserved Noether charge anymore and thus you have neutral particles).

Further the creation and annihilation operators should either obey the bosonic or the fermionic commutation relations.

Finally, one should have a stable ground state, i.e., the Hamiltonian should be bounded from below. The locality, microcausality, and the existence of a stable ground state ("the vacuum") one necessarily gets the usual spin-statistics relation (half-integer-spin fields have to be quantized as fermions, those with integer spin as bosons), the CPT theorem, and the unitarity and Poincare-covariance of the S-matrix, which also obeys the cluster-decomposition principle.

If you then treat the interactions with the usual perturbation theory (which is the best you can do with such a relativsitic QFT to begin with), you find that the particle number is not conserved but that particles and antiparticles can be created and destroyed in scattering processes. E.g., in QED (in its most simple form describing electron and positrons as a bi-spinor field minimally coupled to massless vector bosons which are necessarily U(1) gauge fields and describing finally photons, which are strictly neutral), you also can have annihilation processes ending up only with photons in the final state. The most simple one is of course $\mathrm{e}^+ + \mathrm{e}^- \rightarrow 2 \gamma$. Then sometimes it's said that "the electron and positron are completely annihilated to pure energy". What the popular-science writers mean by that is simply that the photons are massless, i.e., their entire energy is "field energy" without any "rest-mass energy".

 

[mitochan]

Does special relativity entail matter annihilation ?

If I remember correctly Einstein predicted at the end of his first paper on special relativity that loss of mass would be observed in nuclear fission of Uranium.