We understand mass in the practical life, as an amount of substance. About light we say that it has no rest mass. But substance it has in a way, I mean, it carries electromagnetic field.
Sometimes appears in the literature the phrase "movement mass". For instance, a body moving with a velocity V in free space, carries the energy E = mc2, where m is named movement mass and is equal to m0/(1 - V2/c2)-½ , where m0 is the rest-mass. So, for a moving body, the relationship between the energy and movement mass is E/c2.
The photon is never at rest, it has no rest-mass, but carries the energy ħω. Is there any problem in considering ħω/c2 the photon's movement mass? (I was told some time ago that there is a problem but I don't remember what it was.) In short, a pulse of photons would curve the space around itself and make a neighbor body bend its trajectory as in the presence of a mass ħω/c2 ?
By the way: what you know about Eddington's experiment during the solar eclipse? Did indeed the light rays bend? I was told, but without further explanations, that the experiment was proved unconclusive. What is known to you?
H.G. Callaway
In the videos all the confinements have some aspect of symmetry, which connects them to principles of QFT. The symmetries can be presented without the confinement examples, but the confinements cannot be related to physical systems without the symmetries. In this way the symmetries can be thought of as being more fundamental.
The masses of single free electrons have been measured, leading to ideas that the electrons might be comprised of smaller parts inside with fractional electric charges.
In other threads I have suggested the vacuum of space has properties of limitations on polarization potential that prevent space from containing fractional electric charges separated from each other by more than one vibrational wave length. It gives a possible explanation to how a Higgs field in the vacuum can contribute to confinement and bestow mass.
Yes this is just the Eddington observation from 1919. The gravity curvature of the photon space interacts with the curvature of the sun gravity.
Also in black holes the photon cannot escape for the same reason taken to excess.
The STOE suggests mass is hods (most elementary particle) in a structure that captures a constant amount of plenum (ether, quantum vacuum, spacetime, etc.) per hod. The hod holds the plenum density to 0 and thus is the source of gravity. hods movement creates waves. The plenum has inertia (to support wave action)and the captured plenum is the inertial mass of a body.
This model of light as a column of hods in a simulation demonstrated interference in the Young's and Hodge's experiments (which rejects wave models of light).
> Is there any problem in considering ħω/c2 the photon's movement mass?
I don't think there is a problem, jut that this is not what people usually mean by mass. This could lead to confusion.
> In short, a pulse of photons would curve the space around itself and make a neighbor body bend its trajectory as in the presence of a mass ħω/c2 ?
I do not think it is quite that simple. People have considered the gravitational field due to laser beams and pulses, usually in the setting of linearised gravity.
Have a hunt on the arXiv.
Dear Sofia,
SW: Is there any problem in considering ħω/c2 the photon's movement mass?
That would just be giving energy a different and potentially confusing name.
I recommend learning the energy-momentum relationship:
(mc2)2 = E2 - (|p| c)2
where
- m is the invariant mass
- E is the total energy
- p is the momentum vector and |p| indicates the norm or magnitude
If you set p to zero, you get the usual mc2 = E which emphasise that this is only applicable to particles at rest.
For a photon, E = |p| c so m=0. That is what is tested experimentally.
If you put two photons moving in opposite directions inside a mirrored box though, the sum of their momenta is zero but the sum of their energies is positive so the pair has mass even though each has none. It's hard to understand that without using the relation above.
Graphically you can draw any particle as a vector in energy/momentum space, the first graphic shows some useful names for a single particle. Adding the vectors for two photons is then simple, the second graphic shows that.
Dear Sofia,
>
this is the issue of the "relativistic mass", there is no confirmed relation as such m0/(1 - V2/c2)-½ , it is considered wrong.
What is verified in accelerators is that the relativistic momentum is mV/(1 - V2/c2)-½ , proportional to the magnetic field B of the magnets bending the trajectory of a massive particle.
being constant the charge of the body and the radius q*r=K in a syncrotron it is
|B|=|k|*m |v| /√(1-v2/c2)
the strength of the magnetic field B, the controlled quantity, has to be proportional to the relativistic momentum.
The expression E=mc2 is always meant with "m" as the rest mass and it should be better written as E0=mc2 which is the rest energy.
And as George mentioned, although he wrote it with the wrong sign:
E0 2 = E2 - (|p| c)2 hence E2 = E02 + (|p| c)2 where p=m0 V/(1 - V2/c2)-½
in a Inertial reference frame the total energy of a body is given by:
its rest energy plus its squared relativistic momentum times the speed of light.
since there is no possibility for a photon to stay at rest in a IRF but always with speed c in vacuo, the mass at rest of the photon is not defined, which is not exactly the same thing as saying that its rest mass is 0, which although is the generally accepted value.
When the photon leaves a body it is just a wave-function which brings some information, so while travelling I don't know if it makes sense to say that it has any mass. The photon does not have a gravitational mass, it is not "attracted" by the gravitational field, although according to the fermat principle and General relativity and experiments, the light path gets bent in presence of gravitation.
not while it is in "motion" (if of motion we can speak), in principle only when it is absorbed. It is the way around...
Dear Stefano,
Stefano: "The expression E=mc2 is always meant with "m" as the rest mass and it should be better written as E0=mc2 which is the rest energy."
I think that I understand what you say. I'll say in my own words. For a moving body with rest-mass m0, the energy is E = (p2c2 + m02c4)-½ , contributed as you said by both the energy incapsulated in the rest-mass, and the kinetic contribution. But it is not clear where from took the people the expression (p2c2 + m02c4)-½ = mc2.
Stefano: "there is no confirmed relation as such m0/(1 - V2/c2)-½, it is considered wrong."
This is what I want to know, WHY is it considered wrong? See in continuation:
Sofia: "In short, a pulse of photons would curve the space around itself and make a neighbor body bend its trajectory as in the presence of a mass ħω/c2 ?"
Stefano: "not while it is in "motion" (if of motion we can speak), in principle . . . ".
It seems strange to me. It seems to contradict the 3rd Newton's law, the principle of action and reaction. This law should remain also in the relativity. A body with rest-mass attracts the photon, making its trajectory bend. But the effect should be mutual, i.e. also the photon should also attract the mass-possessing body. One might tell me to leave this picture of masses and attraction forces, and move to the Riemanian picture of curved spaces. No, I don't want, the two pictures should be equivalent, shouldn't they?
By the way: what you know about Eddington's experiment during the solar eclipse? Did indeed the light rays bend? I was told, but without further explanations, that the experiment was proved unconclusive. What is known to you?
With best regards
Dear Sofia,
>
being constant the charge of the body and the radius q*r=K in a syncrotron it is
|B|=|k|* [(m|v|)/√(1-v2/c2)], nobody allows us to separate the contributions into the parts "v" and "m*gamma", it is arbitrary hence wrong.
I don't know but it is wrong..
the body with rest mass does not attract the photon. This would occur with a massive particle.
Light is bent by the hypermedium itself not by the attraction of the body..it is like a form of a refraction index due to the fact that the mass alters the global refraction index, see Eddington. In this regard there is no violation of the 3rd law.
the Riemanian curved space-time is just an artifact which is able to account for static phenomena very well but it cannot be considered a satisfactory Physical picture..
Very powerful in describing the potentials at stake as a function of the distribution of the masses (the Schwarzschild solution is very well suited to explain the GPS offset behavior), but very disputable in explaining the transition from one configuration to another which is what evolution of systems is about. The evolution can be described on with PNA approximation not within the curved space-time itself since there is a "chunck" missing in that picture: the localisation of the gravitational energy...
Dear George,
Nice to hear of you!
Now, please!!! Do not indicate me references, I don't have words to say how restricted in time I am. Whoever wants to help me - and thanks for that - would better explain things in his/her own words.
"If you put two photons moving in opposite directions inside a mirrored box though, the sum of their momenta is zero but the sum of their energies is positive so the pair has mass even though each has none. It's hard to understand that without using the relation above."
With or without relations and figures I did not understand. Would you read Stefano's answer? Please be kind and read also my reply to him - I mention there the principle of action and reaction, that I see no reason why should it not be valid also in the relativity. So, of course the two photons have a total energy. The question is whether this energy has also the effect of a mass, i.e. attract neighbor bodies. Stafano says NO. But, by the principle of action and reaction, says that attraction should be mutual.
So, what you say?
Another thing: what you know about Eddington's experiment during the solar eclipse? Did indeed the light rays bend? I was told, but without further explanations, that the experiment was proved unconclusive. What is known to you?
(By the way, can you change sign in your formula as Stefano said? It's not (mc2)2 = E2 + (|p| c)2, the sign of (|p|c)2, should be negative.)
Best regards (P.S. You are the lovely copy of Charlton Heston)
Dear Jerry,
"Yes this is just the Eddington observation from 1919. The gravity curvature of the photon space interacts with the curvature of the sun gravity."
Do you mean the experiment during the solar eclipse of 29 May 1919 that tried to check the bending of the light trajectory? I was told by one of the professors in Technion that the experiment was proved unconclusive. What is known to you?
SQ: And as George mentioned, although he wrote it with the wrong sign
Well spotted Stefano, thanks. I've corrected the typo.
Dear Sofia, you wrote
SW: I think that I understand what you say. I'll say in my own words. For a moving body with rest-mass m0, the energy is E = (p2c2 + m02c4)-½, contributed as you said by both the energy incapsulated in the rest-mass, and the kinetic contribution. But it is not clear where from took the people the expression
(p2c2 + m02c4)-½ = mc2.
That is not the correct equation. You get
E = mc2
by starting with
E = (p2c2 + m02c4)-½
and setting p=0 because an object at rest has no momentum.
SW: This is what I want to know, WHY is it considered wrong?
It's not technically wrong but it is considered misleading because students start thinking that an object moving fast enough might increase its mass to the point where it becomes a black hole and silly things like that. The formula correctly calculates the total energy, not a variable mass.
SW: It seems strange to me. It seems to contradict the 3rd Newton's law, the principle of action and reaction. This law should remain also in the relativity. A body with rest-mass attracts the photon, making its trajectory bend. But the effect should be mutual, i.e. also the photon should also attract the mass-possessing body.
That's correct. If you shine a laser just past the Sun, the beam will be bent towards the Sun so the Sun must get pulled slightly towards the beam. However, two photons travelling on parallel paths won't get pulled towards each other.
SW: By the way, can you change sign in your formula ..
Yes, that's done. Just a typo from typing too quickly while chatting to visitors, sorry.
Dear Stefano,
When speaking of general relativity I am not on my ground. So, I have to ask all sort of things which may seem simple to other people. You say:
"Light is bent by the hypermedium itself not by the attraction of the body..it is like a form of a refraction index due to the fact that the mass alters the global refraction index, . . . "
Hypermedium? Hmmm! Isn't this another way of saying curved space?
"the Riemanian curved space-time is just an artifact which is able to account for static phenomena very well but it cannot be considered a satisfactory Physical picture."
Wow! But the curved space of which speaks Einstein in his general relativity is not the Riemanian one? In short, what is the difference between the two? (Please don't send me to references - no time for that - I prefer a few words/lines of explanation).
Best regards
Dear George,
". . . two photons travelling on parallel paths won't get pulled towards each other."
Aaaa! That's interesting! But, how can we check it? The bending of the rays won't be too small to be observed? Or, it's the theory that says it? Stefano explained me in terms of hyperspace, and with an analogy, but if I can get additional arguments/explanations it's good.
Best regards
Dear Sofia,
>
Curved space-time/diffeomorfism is what a Riemannian geometry provides...
the Hypermedium is something which has to be "postulated" having the behavoiur described by Einstein Field Equations (EFE) but also the expected values of QED and QFT and QCD and it is what is looked for in these days to explain the behaviour of lensing of Dark Matter and the galaxy dynamics. So, the space-time is not the Hypermedium, space-time is "more or less" a correct mathematical description of what Physically an Hypermedium should provide (not few other very important properties do not belong to space-time ).
Also the YANG MILLS equations are actually expressed in pseudo Riemanian Geometry and in a very similar way to the EFE but the two systems do not merge at all.
I asked a question about it since very recently there is this this Cosmic Fluid postulated in order to provide an explanation about the behaviour of what is called as Dark matter...
https://www.researchgate.net/post/Is_Nature_based_on_a_perfect_hyperfluid_an_active_background_the_unique_responsible_of_all_the_interactions
>
the Einstein Field Equations of GR involve a space-time which gets deformed, is not flat as it is supposed to be in SR, it is pseudo Riemannian , but in any case this is not the point.
What the EFE express is the equality between a Stress Energy Tensor of the matter and the curvature expressed by two types of curvature the Ricci curvature Rµν and the scalar curvature R (Lagrangian density, or trace of the Ricci tensor)gµν is the metric tensor
EFE: Rµν − 1/2 Rgµν = 8πG*Tµν
This equation tell us how the curvature of space-time reacts to the presence of energy-momentum of matter, expressed by the stress tensor Tµν
These equations cannot by themselves express an evolution in time of a system of masses.
They correctly express the potentials of a configuration of mass/energy but, both numerically and theoretically, there is not an evolution law allowing different configurations (this reserve was expressed also by Gullstrand when he gave a negative opinion on GR for the Nobel prize of Einstein which was eventually taken for the interpretation of the Photoelectric effect) .
The post newtonian approximations allows calculate the evolution of the systems (binary star) because in EFE equations it cannot be localized the gravitational field energy which has to be the quantity to be exchanged in order to let the body accelerate. The equivalence principle, EEP forbids its localization...
https://www.researchgate.net/post/Is_the_non_locality_of_the_gravitational_energy_a_serious_problem_for_General_Relativity_GRT
Dear Sofia,
SW: The bending of the rays won't be too small to be observed? Or, it's the theory that says it?
It's what the theory says and it would be much too small to test in the lab but consider the light from a distant quasar. The photons that reach a telescope a few metres in diameter after travelling for billions of light years are on randomly scattered paths that are incredibly close so you might expect those in close proximity to be drawn together while those that start farther apart would get pulled away and further separated. That would produce bright spots on a darker background as seen say by a space telescope. The light might flicker as the instrument moved through those regions much like the flickering of stars seen from Earth. That doesn't happen so there is no reason to doubt the theory.
SW: Stefano explained me in terms of hyperspace, and with an analogy, but if I can get additional arguments/explanations it's good.
Special relativity was explained by Minkowski by recognising that the behaviour is consistent with spacetime being a 4-dimensional manifold with Riemann geometry. In general relativity, that remains true over small volumes but energy (most often in the form of mass, and also pressure) causes an intrinsic curvature of that geometry. Line follows what are called "null geodesics" through that curved spacetime. A geodesic is an extremal path like a great circle on the globe, I won't go into more detail as you are shot of time.
Stefano said:
SQ: the Riemanian curved space-time is just an artifact which is able to account for static phenomena very well but it cannot be considered a satisfactory Physical picture.
That is just his personal view, the rest of science considers that the geometrical explanation is valid. There are other theories of gravity that have been proposed of course but GR is what is accepted as a working hypothesis although many people assume it will be seen as emergent from some future deeper theory, but we don't have one yet so you are as well to go with what we know pro tem.
Dear George,
let's say most of Science... There are alternatives like the FGT (Field Gravitation Theory) of Yurij Barishev who developed and Idea of Thirring and Feynman which is equally valid for all the experiments but does not involve the geometrization and is not founded on the EEP.
GD: There are other theories of gravity that have been proposed of course ..
SQ: There are alternatives like ...
I already noted that, there are at least a dozen alternatives that I could probably dig out. However, so far all that differ from GR in any testable way have been shown to be a poorer fit to reality. Those that replicate GR for all known tests are only giving a different philosophical interpretation of the same physics so you can take your choice, it makes no difference. The point is that geometrical GR is as good as, or better than, any alternative, and much more available for anyone wanting to learn the subject.
GD:
not the FGT, they are currently testing it against the values got from neutron stars merging for in the calculation of gravitational waves...
It will be interesting to see how that works out, LIGO is going to be a very powerful source of data, but that is why I said "so far", there will be many tests done in the future using LIGO data and will will just have to wait to see which theories continue to give accurate answers.
You can expect to see more papers like this on the nature of neutron stars:
Preprint GW170817: Measurements of neutron star radii and equation of state
and this which seeks to falsify a broad sweep of the alternatives:
Article GW170817 Falsifies Dark Matter Emulators
GD
Not the STOE that reduces to GR with some simplifying assumptions and describes several problems that GR has such as Rotation curves without dark matter, better match of galaxy redshift, etc.
This model suggests photons have mass and the model better explains Young's and Hodge's experiments.
So, you say, GR does not apply to light interference experiments. Exactly, that is why STOE is better.
Dear friends,
I understand, from detailed explanations that I got - thank you all - that the photon won't attract a mass-possessing body. In short, to attribute "movement mass" to a photon is wrong. It suggests me, somehow analogously, that a body A won't attract a body B in relative movement with A, more strongly than in the case they are at rest with respect to one another. That also would prove that the phrase "movement mass" is meaningless. Am I right?
Dear Sofia,
SW: I understand, from detailed explanations that I got - thank you all - that the photon won't attract a mass-possessing body.
That's the opposite of what I said:
GD: That's correct. If you shine a laser just past the Sun, the beam will be bent towards the Sun so the Sun must get pulled slightly towards the beam.
SW: That also would prove that the phrase "movement mass" is meaningless.
I've never heard that term before, I guess it's the same as "relativistic mass" which if you look at the diagram I posted is just another name for total energy.
Dear Sofia,
Check out my book, Electromagnetic Gravity. Part 1, in my profile. You will receive answers to all your questions, in particular:
- photons are particles of matter (Nobel Prize A. Einstein 1921),
- when an annihilation reaction occurs between an electron and a positron, their mass passes into the mass of photons, the photon is the superpartner of the electron,
- the photon has transverse inertia (mass),
- the Sun attracts any mass, including the mass of a photon...
Yours
Valeriy Pakulin
PS
Do you believe that "photons would curve the SPACE around itself"?
SPACE is a purely philosophical object, isn't it?
No, George,
If we cannot say that a body A attracts a body B stronger when B is in movement with respect to A, then Stefano is right, i.e. denoting (m02c4 + p2c2)-½ as mc2 is wrong. E/c2 has indeed dimensions of mass, but that is elluding. Only if, as I said, the attraction between the bodies A and B were stronger by a factor (1 - V2/c2)-½ when they are in relative movement with velocity V, would justify naming m = E/c2 a mass. It seems that Stefano is right.
Dear Valeryi,
To tell me "read my material", puts me in an impossibility. I am asking all my acquaintances to be understanding and explain me their rationals in a couple of lines. My situation is a terrible lack of time, I can't describe it.
So, I ask you too, please be kind and explain in your own words, why do you think that E/c2 is a mass. I also invite you to read my post above the present one, referring to Stefano's and George's explanations.
With best regards,
Sofia
Sofia, I was pointing out that I previously said that when the path of light is gravitationally bent passing a mass, momentum is conserved so the mass is accelerated. You seemed to have taken the opposite meaning from what I said.
SW: ... Stefano is right, i.e. denoting (m02c4 + p2c2)-½ as mc2 is wrong.
Yes, I agree, that is what I have said several times. The correct equation is
E = ( (mc2)2 + (pc)2 )-½
Set p = 0 and you get E = mc2 for a massive particle at rest but you can't put them together to get:
mc2 = ( (mc2)2 + (pc)2 )-½
because you already assumed p=0.
SW: E/c2 has indeed dimensions of mass, but that is elluding. Only if, as I said, the attraction between the bodies A and B were stronger by a factor (1 - V2/c2)-½ when they are in relative movement with velocity V, would justify naming m = E/c2 a mass.
If you measure the gravitational pull of a hot brick versus when cold, you will find the gravity is slightly increased, by the same amount as increasing the mass by E/c2. Energy is part of mass when looked at that way, or you can say that the kinetic energy of the particles which is increased by raising its temperature also generates gravity. The energy content also affects the body's inertia as mass would.
The full story in GR is that the right hand side, the source of gravity, is the stress-energy tensor:
https://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor
The diagram on the right shows the components.
Dear Sofia,
I really laughed at your words. You do it like a woman: you ask me and do not want to listen to my answers, which I prepared for you in my book.
The body is the sum of particles. A particle is a vortex flow of gravitons of an electromagnetic field. The mass of a particle is the energy of gravitons. The graviton speed is c.
You write the Planck formula for the photon. A photon has two neutrinos. therefore E=mc^2, but not E=mc^2/2.
Sorry, this is more than two lines.
Yours
Valeriy Pakulin
Dear Valeriy,
Thanks for your lines, and I am glad for the amusement. I do want to listen to your words, I just explained my difficulty in reading long material at the present time. Were you ever been in the situation of being extremely pressed by time?
Now, you say,
"A particle is a vortex flow of gravitons of an electromagnetic field. The mass of a particle is the energy of gravitons. The graviton speed is c."
Where is the Higgs boson in this picture? If a particle is gravitons, and the gravitons give it mass, why do we need Higgs' boson? Do you deny the quantum field theory (QFT)?
"A photon has two neutrinos"
Can you indicate an experiment proving that? The photon is the gauge particle of the e.m. field, not of the weak interaction.
With best regards,
Sofia
Dear Sofia,
I feel sorry for you. You have a set of school stereotypes. In addition, you do not have time. Therefore, I will not retell you my book here.
Best
Valeriy
Philadelphia, PA
Dear Wechsler & readers,
I believe it is pretty standard, in explanation of classical GR, that,
"Mass-energy tells spacetime how to curve and spacetime tells mass-energy how to move."
In consequence, high densities of energy will curve spactime just as do high concentrations of mass.
The photon has momentum, but it has no mass. Though confined electromagnetic energy will result in something like inertia of the confining structure, explaining mass is something more complex. Right?
H.G. Callaway
Dear H.G. Callaway, and everybody
People more competent than I in matters of general relativity say that two photons do not cause to one another bending the trajectory. However, H.G. Callaway seems to have a different opinion:
"high densities of energy will curve spactime just as do high concentrations of mass"
To my understanding, how high is the density is an experimental issue, but, theoretically, low densities of energy should also curve the space-time, the effect being much weaker.
Now, browsing in Wikipedia for seeing what is the content of the stress–energy tensor Tμν in Einstein's field equations,
https://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor#Identifying_the_components_of_the_tensor
I see that if the considered space-time region is vacuum in which travel electromagnetic waves,
T00 = c-2 (½ ε0 E2 + ½ μ0-1 B2).
So, the photon yes would curve the space-time, i.e. would act as a gravitational mass.
Do I missunderstand something? Can somebody "make light"?
What you are missing is that the effect between photons depends on the angle between the photons' direction of travel.
A laser beam passing the Sun has a mean energy density in the Sun's frame.
If you try to analyse two photons of the same frequency on parallel paths from an inertial frame, you can take the limit of increasing speed of the frame in the direction of the photons in which case Doppler means they have zero energy (in the limit) hence no effect.
For other directions or different frequencies, you can find a frame in which they are moving anti-parallel with equal frequency and that is the lowest total (frame-dependent) energy configuration.
Dear Sofia,
That is for the bounded EM fields which for sure produce stress according to mass energy equivalence. Radiation does not feel the gravitational attraction.
see Okun, Telegdi and Selivanov
http://www.itep.ru/science/doctors/okun/publishing_eng/em_12.pdf
GR explains the bending of light (and not only GR) as a global variation of the speed of light (coordinate) as a function of gravitation. It is the first and only way Einstein derived the light bending for the Sun, and that is the only reasonable way to do it since with the Equivalence principle the derivation is totally busted at least Synge and Fock would not support the derivation with the EP.
A global variation preserves the measurement of the speed of light measured locally as c.
If the photon itself curved the space time then c would not be locally the same.
You teach me that a photon in the gap between emission and absorption it is just a wavefunction which only at the absorption gets determined by the "relation" with the absorber.
In terms of three spatial coordinates xi, where i=1,2,3; we can write stress energy tensor component by component,
T00 is energy density
T0i is energy flux/c across a surface of xi= const
Ti0 is ith momentum density multiplied by c
Tij is the flux of i th momentum across a surface of xj= const
Evidently for the photon field stress energy tensor is non zero. Therefore photon does have gravitational interaction in Einstein's gravity, even though in the Newtonian gravity it cannot interact gravitationally. In other words it does induce a curvature. No wonder that indeed there exists observational evidences of gravitational lensing.
It seems that there are some confusion in the questions put by Sofia and I think it would useful to try to answer them clearly for avoiding what could be seen as interpretations.
What is mass?
The mass is one opposition to to change the state of motion, which is called inertia. In fact gravitation is also an interaction associate to the mass due to induce an acceleration field. The principle of equivalence of General Relativity assumes both concepts as the same for its definition.
A pulse of light has mass ħω/c^2?
No because the light cannot change its state of motion and never is provided of something as an acceleration.
Does the pulse curve the space around?
Yes, because the photon carry energy and momentum whose values depend of the frequency. Taking a simple calculus of the constants appearing in Einstein's equations it is straightforward to see that its value is absolutely negligable in comparition of a gravitational potential due to a planet or a star. The photon follows the geodesic of the pseudo-Riemann spacetime and never interact gravitationally among them for the same reason. Even a bosonic gass of photons with neutrinos, for instance, never fall in the stars or planets as the cosmic microwave background (CMB) shows.
In my response above I did refer to the classical electromagnetic field, because Einstein's gravity is a classical theory. I considered light as a classical electromagnetic field. In QED, calculation of stress energy tensor should be more complicated.
Einstein initially called the left hand side (lhs) of the field equation as describing "gravitational ether" (GE). The change of the term to "spacetime" was a mistake because it tends to confuse the situation. I like the deSitter interpretation. The mass Gravitational attraction is a right hand side (rhs) value and is a basic component of the universe. As deSitter said, there is no mass on the lhs. The position in space with mass is assumed to have a high GE value on the lhs (to avoid singularities which are a problem if an inverse transformation is to done to find rhs values). The GE is considered to be a imaginary Hilbert space (some consider it to be a Clifford space) with imaginary units and to carry inertia. I think it is better if it is a real Hilbert space with real existence (no i, ict, or ih -QM). The 2 components of the universe are them mass and the GE. Then the GE=0 where mass is and the GE slopes more naturally. Then Dark Matter , Dark Energy, are unnecessary as well as explaining many other observation that are currently mysteries of the standard model of cosmology.
Dear Daniel,
if one wants to be rigorous, attraction should occur also by two beams of light then, which should bend the space-time around them as you just said...
this occurrence is not the case since in Hubble for example which is a very very accurate telescope one should see light "cluttering" or we might expect it in 2021 with the James Webb telescope which is order of magnitude more powerful..
Light follows null geodesics to the maximum possible accuracy, but it is not able to determine or alter the geodesics which it crosses....
mass in principle is able to do it...so geodesic motion for a mass is an approximation since any mass entering a gravitational field of another mass changes its own gravitational field and the gravitational field of the other mass. This cannot be seen in the Newtonian approximation which is linear.
Dear Stefano,
The calculus are absolutely stupid but conceptually they exists. The coefficient in front of the energy-momentum tensor in Eistein's equations is around 10-4011 and if you consider the energy of a photon of 1000 TeV (which is gigant) you can see that its change of curvature is very far of a possibility of being measured. Thus the curvature of the spacetime due to a photon is nothing, but it is true that applying Einstein's equation can by calculated and don't give zero.
Dear friends,
I am getting here different answers, and as I don't belong to the domain of general relativity, for better understanding I need to ask additional questions.
So, please tell me, the EFE are linear in sources? I mean, assume that in the RHS of EFE there is a source T1μν and one gets the solution g1μν . Assume now that we write the EFE with another source T2μν and get the metric tensor g2μν . Finally, if we write the EFE with the source Tμν = αT1μν + βT2μν , where α and β are two complex numbers, the solution gμν won't be equal to αg1μν + βg2μν ?
Dear George,
"If you try to analyse two photons of the same frequency on parallel paths from an inertial frame, you can take the limit of increasing speed of the frame in the direction of the photons . . . . ."
Of course, for deciding on a problem one begins with the simplest case, parallel trajectories of the photons and same frequency.
About the inertial frame, I believe that you pose wrongly the problem: I suppose no inertial frame, that gives the flat space metric. I'll write the EFE, and get the metric with the two photons serving as sources, i.e. appearing on the RHS, in Tμν.
Now, for the moment I don't know how the solution gμν would look like. In this thread I am LEARNING from you all. Let me tell you that before beginning this thread I was looking at the EFE as to a creature from safari.
With kind regards
Dear Sofia,
the EFE are totally non linear, that is why they are very difficult to treat and for the gravitational waves it had to be used a sort of a linearized version...
In regards to the photons and the gravitational field, imagine to make the experiment of the beam splitter, non linear Chrystal which divides the wave function and then at a huge distance there are two observers which are also at huge distance from eachother. The wavefunction collapses on one but non in the other, but the one who absorbs it decides to do it first ... how could the beam of light in that case stress the space-time?? What space time it stresses around it all the space.. in that case it is not possible to define where it is stressed, because the stress is a local property.. so basically for the known quantum non local properties it becomes impossible to say that light can stress the space-time.....
Dear Stefano,
"if one wants to be rigorous, attraction should occur also by two beams of light then, which should bend the space-time around them as you just said..."
Wait a bit. The photon can be contemplated only by an observer with respect to which the photon moves. For eliminationg the problem that the photon passes quickly through a point in space leaving vacuum after that, let's assume a very long wave-packet. It would keep for a while a non-zero energy at that point.
Now, you say that EFE are non-linear. Your example with the beam-splitter doesn't tell me much. Can you tell me WHICH term in EFE is responsible for the non-linearity? For instance, the RHS seems to me linear. Is the term containing the Ricci curvature tensor the cause of non-linearity? Or, is the scalar curvature? Or both?
Dear Sofia,
" Now, you say that EFE are non-linear. Your example with the beam-splitter doesn't tell me much. "
infact the beam splitter is not related at all the the form of the EFE but to the impossiblity of quanta of light to stress the space time while they "travel", since a direction may not be defined "a priori"...
In special relativity mass is energy in center of inertia frame (divided by c^2, but let c=1). So called "movement mass" is old term, which is used in school textbooks and popular science. "Movement mass" is just energy (multiplied by c^2, but let c=1).
Dear Sofia,
SW: About the inertial frame, I believe that you pose wrongly the problem: I suppose no inertial frame, that gives the flat space metric.
No, it gives a base geometry which is independent of your choice of coordinates and may be flat or have some intrinsic curvature. To get flat space, consider the two photons in empty space far from any significant mass.
SW: For eliminating the problem that the photon passes quickly through a point in space leaving vacuum after that, let's assume a very long wave-packet. It would keep for a while a non-zero energy at that point.
A photon is not a wave packet, it is a point particle. You can't mix classical versus quantum representations.
Dear Mikhail,
There are no "movement mass" as you wrote. The energy diveded by c2 is only valid for the rest mass.
Dear Gerorge,
It seems that each one of us spoke of something else.
Sofia: "About the inertial frame, I believe that you pose wrongly the problem: I suppose no inertial frame, that gives the flat space metric."
George: "No, it gives a base geometry which is independent of your choice of coordinates and may be flat or have some intrinsic curvature. To get flat space, consider the two photons in empty space far from any significant mass."
When we discuss what happens with the two photons I don't suppose an a priori metric, e.g. the inertial frame. The EFE would give me the metric. As to the coordinates, I have to choose some coordinates, e.g. t, x, y, z, otherwise how shall I solve the EFE? Though the metric may show that if x̄ is a geodesic line, ȳ isn't.
George: "A photon is not a wave packet, it is a point particle."
How so? If the wave-packet of the photon is long, as I say, WHERE EXACTLY inside the wave-packet is the point that you speak of? I don't think that the uncertainty principle would let you answer.
With kind regards
Dear Daniel,
From the EFE we learnt that mass is what makes the space-time curve. It is our full right to choose a frame of coordinates in which a certain body is moving with respect to us (of course, because of the body, the frame won't be inertial). We have no obligation to work with a frame in which the body is at rest.
Well, a moving body has the energy E = (p2c2 + m02c4)½, s.t. E/c2 plays in the EFE the role of a mass. Maybe, from other considerents, it doesn't behave as a mass, but in the EFE it does.
With kind regards
Dear Sofia,
When you talked of "the flat space metric" I presumed you meant the Minkowski metric in this context. Obviously there are other metrics that can provide a flat spatial part, in cosmology, it seems the large scale universe is flat but expanding for example.
SW: When we discuss what happens with the two photons I don't suppose an a priori metric, e.g. the inertial frame.
In discussing two photons, you could consider them in the Minkowski metric in deep space far from any mass but then use any frame you like. Inertial is easiest but any other frame is equally valid. Alternatively you could consider two photons as part of a beam being bent as it passes close to the Sun in which case you would be using the Schwarzschild metric, but again you still have a free choice of frame.
George: "A photon is not a wave packet, it is a point particle."
SW: How so?
A wave packet is a macroscopic burst of EM which contains a variety of frequency components frequencies so is like a large group of photons. As analogy I might say "a flock is not a bird".
SW: I don't think that the uncertainty principle would let you answer.
Well sort of. A photon is a particle with a definite energy. Energy depends on frequency though Planck's relation E=hv. That implies a unique frequency, but any modulation produces sidebands, so a pure frequency cannot be modulated, it must a sine wave with the same amplitude for eternity. That implies it is infinitely long so cannot be localised. On the other hand, Einstein's work on the photoelectric effect showed that photons are created and absorbed in single events
Trying to draw analogies between classical and quantum physics can be very misleading.
Dear George,
"In discussing two photons, you could consider them in the Minkowski metric in deep space far from any mass but then use any frame you like. Inertial is easiest but any other frame is equally valid."
I don't want!!! I want to learn what is the metric produced by the two photons as if they were alone in the universe. This is the problem we posed.
"A wave packet is a macroscopic burst of EM which contains a variety of frequency components frequencies so is like a large group of photons. . . . . A photon is a particle with a definite energy."
NO, George, absolutely not. If we speak of two photons we don't speak of a large group of photons. We speak of only two photons. Each one is a wave-packet. For instance, the two photons may be a down-conversion pair. Each one of the photons is a wave-packet of a time-duration of ~ 100femto-seconds. If the wave-packet is short in time, it has a big uncertainty in energy. A wave-packet long in time has a much better defined energy. For a photon to have a precise energy its wave-packet has to be, theoretically, infinitely long in time.
". . . a pure frequency cannot be modulated, it must a sine wave with the same amplitude for eternity. That implies it is infinitely long so cannot be localised."
That's the problem I spoke of.
- The space can be curved by material body possessing mass of rest m_0. It means that the body gravitates (creates the gravitational field). Photon cannot create gravitational actin because it possesses only relativistic mass. Photons do not create gravitational field, but travel under effect of other gravitational fields.
Dear Sofia,
I think that you are in a conceptual circle of simple concepts. The photon has not mass, its dispersion equation is
E=pc never E=mc2
By the way,the relativistic mass is also zero because is the rest mass multiplied by gamma. But this doesn't forbid that they can contribute to the curvature of the spacetime following EFE equations: these equations depend of the energy momentum tensor and not on the mass.
Philadelphia, PA
Dear Baldomir & readers,
Now on to the main course? What is mass?
I suspect that going at that question more directly, given contemporary accounts, we might put some of the detailed puzzles aside.
I think that several contributors have already said substantially what you say below, but the contrary trend has been to look at the question in terms of the predicted effects on curvature or energy--basically some detailed puzzles which don't really question the basic answer provided by the Einstein equations. Surely, the gravitational effects of passing photons are going to be beyond experimental detection. At the least, one would think to look at extreme high energy phenomena.
H.G. Callaway
---you wrote----
By the way,the relativistic mass is also zero because is the rest mass multiplied by gamma. But this doesn't forbid that they can contribute to the curvature of the spacetime following EFE equations: these equations depend of the energy momentum tensor and not on the mass.
Daniel and Larissa,
H.G. Callaway is right!
Why do you devoid the photon of its electric and magnetic field? The photon energy is ħω = ½ ∫all the space {ε0E2 + (1/μ0)B2}dV. It has also energy-stress tensor as any e.m. field, and this tensor provides a Tμν tensor. You can say that the photon Tμν is negligible, but you cannot deny it conceptually. As H.G. Callaway says, if we would examine a burst of photons, say, from a star, the Tμν tensor yes would be significant.
With kind regards
For reference:
https://en.wikipedia.org/wiki/Electromagnetic_stress%E2%80%93energy_tensor
H.G. Callaway
Classical response. What is Mass?
Mass is the ratio between force and acceleration. This gets credit on most exams.
In relativity mass is property that curves space time in fields called gravity.
In quantum mechanics mass is a symmetry of particle interaction with local space time that allows an object to travel at less than light speed.
In many particle creations an additional skew symmetry results in antiparticles production in equal numbers to particles creation. CERN is doing experiments hoping to prove that mass of antiparticles in identical to mass of particles, attracted by Earth Gravity. Many researchers believe anti particles are attracted by gravity because of equivalence related to acceleration.
In a centrifuge it seems unlikely that positrons could express a negative mass in positive time. On the other hand if antimatter goes backward in time as Richard Feynman wrote in QED, then positrons could express a negative mass in negative time and not be detected as such in positive time measurements. In that regard the CREN experiment seems likely to find anti hydrogen attracted to Earth gravity in positive time even if it is repelled from Earth gravity in negative time.
Peter Higgs predicted a symmetry breaking at very high energy with help from a boson that arose from the vacuum often enough that our matter world could be created. Particle experiments have claimed possible success in finding the Higgs. with several candidate events. The alternative is that about half of the total cosmos might be antimatter separated from us by drifting backward in time.
The question of mass leads to a question of time. CERN also does experiments of time reversal including charge and parity as CPT. The question of mass is an old one and the answer changes slowly over time leading to newer questions and challenging of assumptions. The alternative to challenging the assumptions is the eventual extinction of humans. So humans are often called a race, or other times more than one.
Jerry
Your first 2 cover the bases. The equivalence principle does the rest.
Philadelphia, PA
Dear all,
Readers of this thread may find the following short video of interest:
https://www.youtube.com/watch?v=gSKzgpt4HBU&vl=en
(Ignore any advertisement that may be place before the video, svp.)
The title is "The True Nature of Matter and Mass," from Space Time, PBS Digital Studios. It runs about 8 Min. --excluding some discussion of the relation of the video to other themes in the video series.
The basic idea is that mass arises from the confinement of energy. There is first a discussion of inertial mas and later this is related to gravitational mass via the equivalence principle. Note in particular the thought experiment o the "photon box."
I would be interested to see comments or links to papers illustrating the thesis presented, which seems to arise from QFT.
H.G. Callaway
H.G. Callaway
In the videos all the confinements have some aspect of symmetry, which connects them to principles of QFT. The symmetries can be presented without the confinement examples, but the confinements cannot be related to physical systems without the symmetries. In this way the symmetries can be thought of as being more fundamental.
The masses of single free electrons have been measured, leading to ideas that the electrons might be comprised of smaller parts inside with fractional electric charges.
In other threads I have suggested the vacuum of space has properties of limitations on polarization potential that prevent space from containing fractional electric charges separated from each other by more than one vibrational wave length. It gives a possible explanation to how a Higgs field in the vacuum can contribute to confinement and bestow mass.
Dear Sofia,
what you write ħω = ½ ∫all the space {ε0E2 + (1/μ0)B2}dV is quite undetermined since you imagine to make an integral all over the space... The stress tensor is a local property, while photons do not necessarily have "local properties". You know much better than me that we don't know what is a photon (a wave-function?) until we detect it and what we detect is just mass/energy.
In addition what seems to be missing in SR and GR is a reasonable accounting of angular momenta and photon is the quantum of angular momentum h * frequency.
So for the reasons above, to attribute a contribution to the stress tensor to a photon in between its emission and its detection (if occurs) it may not be the case at all. What is reasonable to be related to the stress tensor are instead the actual events of emission and absorption (if occurs) which exchange matter/energy with conventional matter.
E = mc2 applies to a particle at rest. The idea of "relativistic mass" (defined as E/c2 for a moving particle) is thoroughly misleading.
A photon is never “at rest” and has no mass. But it has energy ħω. According to Einstein’s gravitational theory all energy "curves space”. Accordingly, a photon or a “pulse of light” curves space.
Philadelphia, PA
Dear all,
Back to "What is mass?" and "confinement"?
What strikes me is the illustrations from he video based on the thought experiment of the "light box," and the claim that the mass of the proton or neutron arises chiefly from confinement of the quarks --the quarks themselves only contributing in a very small measure to the mass of the protons and neutrons. The confinement of quarks within protons or neutrons, etc. is an aspect of QCD and thus of QFT. Perhaps symmetries enter in to the theory of confinement related to the strong force, but at the least this is yet to be explained.
In the light-box example, the argument depends on the momentum of the photons bouncing off the sides of the accelerated box. Neither the box (by hypothesis) nor the photons have any mass, but the accelerated light-box exhibits inertia and thus inertial mass. It seems of special interest that photons carry momentum without mass, though any moving mass carries momentum. This suggest that momentum, and thus energy, are more basic in some sense. Momentum would seem to be a property of massless particles from which mass arises, since it contributes to inertial mass.
Decker has it that "but the confinements cannot be related to physical systems without the symmetries." How are the symmetries to enter into confinement?
Here's the video again:
https://www.youtube.com/watch?v=gSKzgpt4HBU&vl=en
(Ignore any advertisement that may be place before the video, svp.)
H.G. Callaway
---Decker wrote---
In the videos all the confinements have some aspect of symmetry, which connects them to principles of QFT. The symmetries can be presented without the confinement examples, but the confinements cannot be related to physical systems without the symmetries. In this way the symmetries can be thought of as being more fundamental.
Momentum is always conserved locally, both in linear and rotational forms. Energy can arise from momentum, but also can arise from heat, chemicals, and nuclear processes. Energy and mass together are conserved locally.
A special case of radiant EM energy being focused to a hot spot requires the third law of thermodynamics, because the spot can be hotter than the source with no other low temperature energy being given off somewhere in the process. The process is non random with respect to the focusing device.
Particles interact with the space they occupy. A symmetry in that interaction allows a particle to travel at less then light speed. The lack of symmetry in some aspect of the interaction enables the vacuum to transport the particle at light speed and no other speed.
The energy in vacuum is debated. GR requires a small cosmological constant. QFT requires the energy to be very great usually estimated as infinite. In other threads I have applied partition theory to the vacuum energy, which adds enough equations to make an exact calculation. The vacuum energy is very large but finite and not differing from the Dirac sea of energy by more than a factor of two. GR is satisfied because the partitions are balanced in positive and negative curving energies, related to the four fundamental forces.
Vacuum energy is important because it enforces the physical laws including the Higgs field which is far more powerful than most of the particle streams it interacts with. The vacuum energy has no rest mass to satisfy GR and must then travel at light speed in all directions equally to agree with Michaelson and Morley.
Now the explanation about symmetry can be given. The vacuum energy is finite, enormous, and symmetrical. When it collides with a particle unsymmetrically then the particle must move at light speed with the vacuum energy. When the collisions are symmetrical then the particle is not driven at light speed and is given the properties of mass. It is like the video example except the photons are outside the box instead of inside. Then mass can arise from exclusion as well as it may arise by containment.
QFT gives a different explanation to get mass from the Higgs field with infinite energy, does not embrace partition theory, and has not made peace with GR. IT still invokes symmetries in the Higgs field without which the math would be unmanageable, and mass could not be represented..
Quarks and fractional parts of electrons are confined inside their particles creating mass and are described fairly well. Another way to look at is that the fractional electrical charges are excluded by the vacuum using its enormous energy to reject them and prevent their separation by more than a vibrational wave length. In this representation the Higgs field outside the particles gives rise to the mass by excluding fragments with fractional electrical charges, and symmetrically in all directions.
Philadelphia, PA
Dear Decker & readers,
I notice that Professor Wechsler seems to have given up on this question in favor of others. Perhaps we have answered her question --as suited to her interest in it?
I see few takers on the theme of energy confinement in relation to the question, "what is mass?" Perhaps the theme can be taken up again at another point?
Kind regards to all.
H.G. Callaway
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