@Preston Guynn
Unable to accept your argument in complex space.
Sorry
Yes, the imaginary part indicates that it’s unstable and is related to its decay rate.
What a crazy idea! If it is correct then sooner or later we will see the particles with quaternionic or even octonionic masses, why not? What will happen to the famous formula E=mc2 then? What can exists in mathematical mind does not necessarily is a part of physical reality. Anyway: why the limitation of \beta < 1? Could it be equal to -5?
Nothing happens to the relationnE=mc^2; the energy has an imaginary part, which indicates that the particle is unstable.
Quaternionic masses aren’t useful, because quaternions don’t commute and octonionic masses aren’t useful, because octonions aren’t associative. Energy describes invariance under time translations and translations are commutative and associative.
Once more, all unstable particles, by definition of what unstable means, have complex masses, with the imaginary part defining the decay rate. This isn’t anything new.
@Marek Wojciech Gutosky
Reconsider you argument in complex space .
Have we ever thought of complex space ?
Have we ever seen expt with spectral bifurcation in real space ?
If above two are feasible ,then why do you think complex mass idea is crazy ?
Why didn't you think it's validity for particle with v
@ all
arxiv : 1505.09724 v3
If possible read and comment.
I feel happy to have your comments.
The message from https://arxiv.org/abs/1505.09724 is:
'Article 1505.09724 not found'.
To Stam Nicolis: would you be so kind to say what might be the imaginary part of neutron's mass? And where from you know it? How about ordinary sandwiches, which are more or less unstable?
This is all standard stuff, cf. for instance http://fma.if.usp.br/~burdman/QFT1/lecture_26.pdf
(Cf. also here: https://inspirehep.net/literature/100753)
The imaginary part of the neutron's mass is proportional to its decay time. The way to compute it is described in the references linked to above (of course any textbook will discuss it).
Any unstable object can be described in a similar way, by a complex mass, whose imaginary part describes its decay rate and its real part its evolution.
This is, in fact, even more elementary, just consider a harmonic oscillator with a frictional term. The frequency is complex and its imaginary part describes the decay of the amplitude. There's nothing more than that here.
Indeed the statement of the question is incorrect, insofar as either ``partially real'' or ``complex'' suffices. A number is either real or complex.
Indeed, the classical harmonic oscillator's evolution with damping (namely its position) may be described as a real part of A*exp(i*\omega*t) with complex \omega. But is it a simpler description of what is usually observed? Or more obvious? It is correct, but very artificial.
By the way: some complex numbers are real (and still complex).
@Marek Wojctech
arxiv : 1505.09724v3
Search on
" An atavism on real spectra in non-hermitian ,non-PT symmetry in complex Hamiltonian "
If not give your e.mail address .
@Marek Wojociech
Unable to upload the arxiv file.
If interested give e.mail address.
All ideas in physics at first look crazy . But after expt verification, we never say the word crazy .
My suggestion is within the preview of Special Theory of relativity .
Hope you will give your email if interested to see arxiv paper only .
I ave already read the mentioned papers, which was found as 1905.09724.
Going back to the damped harmonic oscillator. Its damping comes from the environment and is not an intrinsic feature of the oscillator itself. Therefore introduction of its complex mass is not necessary at all. Why should we complicate simple things? The concept of complex mass will unavoidably produce complex energy in mentioned equation E=mc2. Remember that in this equation the mass is at rest, thus the frequency/friction have no physical meaning. How would you interpret then an imaginary part of energy??
Everything should be made as simple as possible, but not simpler. (A. Einstein, Autobiographical Notes).
In quantum field theory and not classical nuclear physics, both stable and unstable particles are called observable.While the mass of a stable particle is real,that of an unstable particle must be complex and thus must include the imaginary unit "i" since the mass of an unstable particle or a particle with finite lifetime can never be quantumly defined and its wave function decreases as time increases.Additionally,even though the rest mass of a stable particle is real,it must be renormalized;as a consequence, the classical rest mass in E=mc^2 is replaced by the renormalized mass,and the physical or observable mass is not anymore the classical rest mass but instead the quantum renormalized one.
For shut-up-and-calculate details, check "A Modern Introduction to QFT"by Maggiore or "The Physics of Time Reversal"by Sachs or "An Introduction to QFT"by Peskin and Schroeder.
Here's a useful link https://www.mat.univie.ac.at/~neum/physfaq/topics/unstable.html
Sooner or later I will be dead. This means I am an unstable object. Does it also means that my mass has imaginary component? How big? Note: I'm asking a physical question, not religious.
@Marek Wojcech
Nice query ,
If part of your mass is complex ,I feel you can not be dead . You will not act as an unstable
object but a part of your body will not be visible . ( I don't know how to create such objects ) .
You will be partially fit for a longer time to do your work efficiently .
I do not know how to convince you .
The special relativity relations have real and complex forms that are mirror images. In the complex forms v>c, but so is the Universe; in the Hubble relation v>c is permitted; the Universe can expand as fast as it wants, with no conflict with the complex forms of special relativity. It would seem the real forms are in conflict with nature.
@Warren Frisina
Only time will answer . I believe one day it will be proved . But no idea ,how to prove it .
Its not correct to associate a complex number with
a mensurable quantity, like mass! Only the MODULUS of the complex number may be used! Complex numbers are often used during intermediate calculations, and are very useful in minimizing the algebraic work, but they have no physical meaning by themselves
@ J.A.Souza
Pl. read PT symmetry & arxiv 1905.09724
after that we can discuss ,if you feel so .
@Muralidhar Kundeti
Please read my paper in arxiv :1905.09724 &
PT symmetry.
This idea of partially complex mass is a open question .
If PT symmetry can be experimentally verified with spectral bifurcation, then what is wrong with complex mass ?
@Andea Rossi
Thank you for recommending my question
on complex mass.
B.Rath
I think, in theoretical physics, what is important is the physically consistent interpretation of the results of a hypothesis within the framework of a given theory; the hypothesis itself is not so important.
Provided that a consistent physical meaning to complex masses can be given, then why not using them?
Since complex energies are well-interpreted and acceptable; why not complex masses too?
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