How exactly does energy become mass?

[DrGreg]

Please tell me if I have interpreted correctly your point of view.

What you said sounds OK.

Although when you say "the electromagnetic energy gave up mass", I would say "the electromagnetic energy gave up relativistic mass" to avoid confusion. The electromagnetic energy has zero invariant mass, or rest mass. Nowadays most (but not all) people will assume "mass" means "invariant mass".

In your example when you consider both the radiation energy and the mass energy (mc²), the total remains constant -- radiation energy is converted to mass energy (manifested as an increase in temperature).

The total relativistic mass of the bodies and the radiation also remains constant. Not surprising because "relativistic mass" is really another name for "energy" (rescaled by c²). But the invariant mass is not constant: the irradiated body's mass increases but the radiation has no invariant mass.

 

[Phrak]

"The total relativistic mass of the bodies and the radiation also remains constant. Not surprising because "relativistic mass" is really another name for "energy" (rescaled by c2). But the invariant mass is not constant: the irradiated body's mass increases but the radiation has no invariant mass. "

It's also what Newton called mass. One of the most directly measurable experimental quantities. All this whop-la is over a change in definition by the particle physics guys.

 

[Dmitry67]

Also, as I understand, relativistic mass, not invriant is source of gravity
We had 2kg of matter/antimatter, we have now 2kg or relativistics mass of light (but 0kg invariant mass) but bodies far away are still gravitationally attracted to these 2kg and don't care if it is matter or light

 

[lightarrow]

Also, as I understand, relativistic mass, not invriant is source of gravity
We had 2kg of matter/antimatter, we have now 2kg or relativistics mass of light (but 0kg invariant mass) but bodies far away are still gravitationally attracted to these 2kg and don't care if it is matter or light

You are talking of the "flash" of light going freely in all directions without being confined in a region of space? Then I give you my compliments to have found a quantum theory of gravitation.

 

[Dmitry67]

Ok, let's say I explode my 2kg of matter/antimatter inside an ideal reflecting sphere so light is reflected over and over again and sphere does not heat. Let's assume that the sphere is thin enough so its mass is <<2kg

I have a body orbiting this sphere. After the explosion, the orbit of the body WILL NOT CHANGE. Or do you assume that at the moment of explosion the gravity from 2Kg will magically 'dissapear'? (after some delay, distance to the body/c of course) so the body will fly away? :)

 

[Phrak]

You are talking of the "flash" of light going freely in all directions without being confined in a region of space? Then I give you my compliments to have found a quantum theory of gravitation.

Gravitational charge doesn't disappear, because it's changed form.

 

[lightarrow]

Ok, let's say I explode my 2kg of matter/antimatter inside an ideal reflecting sphere so light is reflected over and over again and sphere does not heat. Let's assume that the sphere is thin enough so its mass is <<2kg

I have a body orbiting this sphere. After the explosion, the orbit of the body WILL NOT CHANGE. Or do you assume that at the moment of explosion the gravity from 2Kg will magically 'dissapear'? (after some delay, distance to the body/c of course) so the body will fly away? :)

If you had read my post more carefully, I asked about a non confined flash of light. Here you are instead talking about *confined* light. In this case light has mass (invariant mass) and so the system's mass doesn't obviously varies, and so the orbit of the body does not change.

 

[lightarrow]

Gravitational charge doesn't disappear, because it's changed form.

What is "gravitational charge"?
Anyway, a photon is not a classical object but a quantum one. To infer its gravitational properties you need a quantum theory of gravity and we don't have yet. Instead, for a system where light is confined, we can simply write E^2 = (mc^2)^2 + (cp)^2 to infer that light's energy implies (invariant) mass (without the need of a quantum description)

 

[lightarrow]

You said it, but that doesn't make it so.

I think rest mass is a good clear term because it describes what you would measure (the mass of the thing when it is at rest) and the manner in which it is distinguished from its natural alternative (the resistance of the thing to any applied forces, i.e., inertial mass dp/adt). I don't object to you calling it invariant mass but don't find it better since, as well as that term being less common in the literature, it strikes me as inelegant since invariant mass (of a potato say) does vary - with temperature (for example).

Personally, I still like the concept of inertial (frequently called relativistic) mass because it:

• retains the classical meaning (inertia)
• sums additively (as is familiar).
• admits an elegant explanation of the most important equation in popular culture (identification of mass and energy as opposed to "no, stuupid, that equation needs to rewritten more complicated, with more squares and a momentum term..")
• was convenient in introducing SR (the transformation of the mass concept is the same as for time and length, and the dilation intuitively refutes acceleration past light-speed)
• is the charge corresponding to space-time symmetry (another link to momentum, of which we also have a classical notion).

Granted, my arguments are pedagogical/theoretical (why use the term rest-"mass" for something that behaves more differently from the classical notion of mass?) and there don't seem to be many practical applications where relativistic mass is more convenient (whereas rest mass is obviously appropriate for cataloguing fundamental properties in particle physics and so I accept that it is the one most frequently abbreviated as just "mass") but, given reality, it is ignoble to say mass has "only one kind" of meaning.

Where is the elegance and the pedagogical usefulness of introducing two different kinds of relativistic masses in the parallel and in the ortogonal directions with respect velocity?

 

[DrGreg]

In my view, it's a waste of time for anyone to try and persuade anyone else on this forum that "my definition of mass is right and yours is wrong". Both of the definitions I gave in post #58 are technically valid, and which one you use is a matter of choice, convention and fashion. People have entrenched views on this and, in my experience, are unlikely to change their mind. The important thing is to use clear unambiguous language so that when you post, others will understand which sort of mass you are talking about.

And the source of gravity is actually energy-momentum-stress rather than mass.

_____________________

And a further comment on post #67. Roughly speaking,

- invariant means a single measurement that all observers agree on;
- conserved means a value that does not change over time according to a single observer.

The invariant mass of a single object is invariant but need not be conserved. (Proper time and proper acceleration are other examples of invariant quantities.)

The total energy of a closed (i.e. isolated from external forces) system is conserved but is not invariant. Therefore, in the absence of potential energy, the sum of its relativistic masses is also conserved but not invariant.

Ditto the total momentum of a closed system is conserved but is not invariant.

The term "invariant mass" is slightly preferable to "rest mass" only because it seems odd to talk of the rest mass of a photon that is never at rest. Nevertheless "rest mass" is a very common term. Actually I think "proper mass" is even better, but not many people use that term.

 

[DaveC426913]

- conserved means a value that does not change over time according to a single observer.

...in a closed system.

 

[Dmitry67]

1
Anyway, a photon is not a classical object but a quantum one.

2
To infer its gravitational properties you need a quantum theory of gravity and we don't have yet. Instead, for a system where light is confined, we can simply write E^2 = (mc^2)^2 + (cp)^2 to infer that light's energy implies (invariant) mass (without the need of a quantum description)

1 As well as quarks, electrons and gluons in stars.
The quantum nature of ALL these objects does not prevent us from using GR even there is no theory of Quantum Gravity yet.

2 It does not matter. Again, we don't have a theory ofQG, but that theory MUST be compatible with GR at some conditions.

And GR does not allow for the gravity source to suddenly 'appear' or 'dissapear'. In GR you cna not define 1Kg in some point from nowhere at some point. For the very same reason light MUST attract other objects with exactly the same force as 2Kg before.

 

[Dale]

Also, as I understand, relativistic mass, not invriant is source of gravity

The source of gravity is the stress-energy tensor. Mass (both invariant and relativistic) is a scalar not a tensor.

That said, I think the remainder of your point is accurate.

 

[lightarrow]

1 As well as quarks, electrons and gluons in stars.
The quantum nature of ALL these objects does not prevent us from using GR even there is no theory of Quantum Gravity yet.

2 It does not matter. Again, we don't have a theory ofQG, but that theory MUST be compatible with GR at some conditions.

And GR does not allow for the gravity source to suddenly 'appear' or 'dissapear'. In GR you cna not define 1Kg in some point from nowhere at some point. For the very same reason light MUST attract other objects with exactly the same force as 2Kg before.

So you are able to write the gravitational field or the spacetime curvature produced by a single photon?

 

[Dmitry67]

So you are able to write the gravitational field or the spacetime curvature produced by a single photon?

If it is confined between mirrors, then yes.
Also, if it is moving far enough from the body, then it is also simple - body is attracted into the direction of the photon.

BTW this might be interesting for you:
http://www.users.csbsju.edu/~frioux/neutron/neutron.htm

 

[Phrak]

What is "gravitational charge"?

Mass.

Anyway, a photon is not a classical object but a quantum one.

As is everything.

To infer its gravitational properties you need a quantum theory of gravity and we don't have yet. Instead, for a system where light is confined, we can simply write E^2 = (mc^2)^2 + (cp)^2 to infer that light's energy implies (invariant) mass (without the need of a quantum description)

That equation is about The Photon. It let's you put a zero in a table of particle masses. It's not well suited for photons, real or virtual.

 

[bernhard.rothenstein]

I think it's necessary to remind some participants that there is more than one definition of "mass" in relativity.

- invariant mass, or rest mass, or proper mass, which excludes the kinetic energy of the object's centre of momentum
- relativistic mass, sometimes called inertial mass, which includes the kinetic energy of the object's centre of momentum.

Be sure you know which sort of mass is being talked about.

Most modern physicists use "mass" to mean "invariant mass" but some people use "mass" to mean "relativistic mass".

Photons have zero invariant mass, but non-zero relativistic mass. The quoted Wikipedia article on the photon refers only to invariant mass, which is described simply as "mass", consistent with modern usage.

Whichever definition you choose, mass is a form of energy, like other forms such as kinetic energy, potential energy, heat energy, sound energy, etc. So mass doesn't get converted into energy, but it can be transformed from mass-energy to some other form of energy. The total energy from all sources (as measured by a single observer) remains constant.

Let generalize the problem. Consider that a clock K' is located at the origin O' of its rest frame I. It measures a time interval dt(0), has a mass m(0) an energy E(0), a temperature T(0) and an extension dx(0) in the direction of the x' axis. Are all of them REST, PROPER or INVARIANT physical quanties?
Measured from I they are dt, m, T and dx. Are they RELATIVISTIC physical quantities or there are better names?

 

[lightarrow]

If it is confined between mirrors, then yes.
Also, if it is moving far enough from the body, then it is also simple - body is attracted into the direction of the photon.

BTW this might be interesting for you:
http://www.users.csbsju.edu/~frioux/neutron/neutron.htm

Dmitry, I appreciate your attempt to avoid the direct question It's the second time I have to remind you that we are not talking about photons confined in a specific region of space. However, from this I understand that you don't have a simple answer to my question, so, I think it's better to stop it here or we will go in a loop...

 

[Dmitry67]

I just don't feel strong enough in GR formulas to answer this question.

But yes, let's imagine that we emited a super-powerful but short laser beam to infinity. It is so compact and heavy so it is a 'body' flying at v=c

The weird thing is that as gravity also moves at c, it arrives at the same time as light. So the effect of the gravitation becomes assymetric? (like for cherenkov's particles) - bodies do not attract to the incoming mass, but they are pulled towards it when 'body' is leaving.

Like in Cherenkovs case, that laser beam should lose momentum because it passes the momentum to all bodies around trying to pull them in the same direction. It makes the light in the beam redder...

But of course we need someone with a more deep knowledge of GR to check if this is a correct pucture or not...

 

[cesiumfrog]

imagine that we emited a super-powerful [laser pulse .. then it] should lose momentum because it passes the momentum to all bodies around trying to pull them in the same direction. It makes the light in the beam redder...

That's a great observation!

That said, I think this has gone off-topic. In principle we think we know everything about electromagnetic pulses/waves in curved space-time (that is, the coupling of the Maxwell and Einstein tensors). No quantum theory was necessary (provided we speak of classical flashes of light and macroscopic masses, rather than individual quanta of light and fundamental particles), and nor is confinement of the light (but note the rest mass of a system is not just the component rest masses).

 

[DrGreg]

Let generalize the problem. Consider that a clock K' is located at the origin O' of its rest frame I'. It measures a time interval dt(0), has a mass m(0) an energy E(0), a temperature T(0) and an extension dx(0) in the direction of the x' axis. Are all of them REST, PROPER or INVARIANT physical quanties?
Measured from I they are dt, m, T and dx. Are they RELATIVISTIC physical quantities or there are better names?

I'm assuming that your first mention of I should have been I', which I have corrected in the quote above.

I can't comment on temperature, as that's not a subject I've studied under relativity.

Assuming we are measuring an object that is stationary relative to the I' frame, in Special (not General) Relativity:

- the relativistic mass relative to I' is the same as the rest/proper/invariant mass (all 3 mean the same)
- the energy relative to I' is the same as "rest-energy" or "rest-mass-energy"
- a time interval dt' is the same as proper time $d\tau$, provided we are talking about a single point in space (stationary relative to I')
- a distance interval dx' is the same as proper length or rest length

In the I frame, that same object is not stationary and so
- the relativistic mass relative to I is not rest mass
- the energy relative to I is not "rest-energy"
- a time interval dt is "coordinate time"
- a distance interval dx is "coordinate distance"

In general, coordinate measurements depend on a frame's synchronisation convention, whereas proper or invariant measurements do not.

In general relativity it gets more complicated.

 

[Phrak]

I just don't feel strong enough in GR formulas to answer this question.

But yes, let's imagine that we emited a super-powerful but short laser beam to infinity. It is so compact and heavy so it is a 'body' flying at v=c

The weird thing is that as gravity also moves at c, it arrives at the same time as light.

I don't quite know what you mean by this, but changes in the stress-energy tensor (gravity waves) propagate at c, for small perturbations in the stress-energy tensor from flat space. The stress-energy tensor itself (gravity) doesn't have a velocity.

So the effect of the gravitation becomes assymetric? (like for cherenkov's particles) - bodies do not attract to the incoming mass, but they are pulled towards it when 'body' is leaving.

Like in Cherenkovs case, that laser beam should lose momentum because it passes the momentum to all bodies around trying to pull them in the same direction. It makes the light in the beam redder...

But of course we need someone with a more deep knowledge of GR to check if this is a correct pucture or not...

As I said, I don't really follow, but for a bunch of massive objects circling the sun, for example, it's the lighter bodies that, on average, get sent to higher orbits or are ejected from the solar system. This is due to the sling-shot effect, and will on average increase the angular momentum of a lighter body at the expense of a heavier body. This makes some sense, if you think of a system that reaches equilibrium when each object has nominally the same angular momentum as the next.

As far as light is concerned, that's another animal, so I really don't know if light can be equated with lighter bodies.

 

[heldervelez]

I'm late to this discussion but no one said that the conversion of energy to mass needs a energy (photons) an intervenient mass (atom/particles). This intervenient mass (oscilator) absorbs energy changing to permited levels or configurations, and the surplus energy can be packed into other particle(s) or photon(s) leaving the system.
AFAIK photons can not be packed as particles without an intervenient mass. Is there any experiment against this?
In this context how could a radiation dominated world generate particles?

In the thread a power laser was mencioned and some gravitational effects on neutrons (Ultra Cold Neutrons)
An experiment could be done, I think, to prove or disprove, the assertion that light are sources of gravity (independently of GR saying so).
The experiment could involve the extreme power lasers of today and try to bend the trajectories of UCN beam.
Does anyone know of an experiment that proves that light is source of gravitational effects ?

 

[altonhare]

Mass is bound energy they are (in GR and SR) exactly the same thing with different units.

What binds the energy? Forces? Energy exerts forces on itself?

 

[gonegahgah]

Naty, a fusion reaction is supposed to release about .1% of the energy of the hydrogen atoms I think (instead of 1%). Fission releases a lot less energy (bigger atoms broken in two parts; only small part converted).

About this topic, we can create diamonds by applying lots of pressure to coal. Wouldn't something similar occur for the creation of matter? ie Super extreme pressure applied to energy to cause it to bind in sufficient quantity to form protons, electrons and neutrons?

 

[neopolitan]

A late entry.

As far as I can tell, the particle with the smallest stable mass is the electron. Is this actually the case, or just the "popular physics" answer? (I know the neutrino is said to have a very small non-zero mass, but with a halflife of about 10 minutes, it is not quite as stable as the electron.)

Is mass possibly a consequence of so much energy being concentrated in so little space? An electron has a mass equivalent to a photon with a frequency of 123 petahertz (10¹⁵Hz). This is, interestingly enough, a little above the frequency where radiation become ionising, somewhere in the middle of the x-ray range.

This would align with what some have said here (mass is energy, so there is no such thing as "pure energy") and possibly get towards what other have tried to say, there is energy without mass, if the concentration of energy is not sufficient to create the phenomenon we call mass.

Neutrinos, with their unstable mass might just be on the border, not quite enough to make a stable mass, but enough to start exhibiting the features of mass. (Electron neutrinos, at around 2.2eV are equivalent to a photon in lower end of ultraviolet range/upper end of the visual spectrum. UV is where radiation does become ionising - admittedly pretty much in the middle of the UV range, at the frequency used in tanning booths, otherwise known as "booths of leathery death". I assume that ionising radiation is radiation which has enough energy to smash bonds, but it is interesting to think that the energies involved are also representative of the smallest masses. Note also that radiation in the visible spectrum is also suspected to cause skin cancer, so while it might not be ionising by definition, this lower energy radiation does do something more than provide a rosy glow.)

Just an idea, and maybe a hopelessly vague retelling of something already in quantum and/or string theory.

cheers,

neopolitan

 

[JANm]

Hallo Neopolitan
Ok ionisation is declarable as electric difference from one case to the other. Bound Bound, Bound free and free bound, but infrared radiation from neutral molecules? Isn't that just mass-velocity relation, so changing velocity and emitting infrared?
greetings Janm

 

[neopolitan]

Hallo Neopolitan
Ok ionisation is declarable as electric difference from one case to the other. Bound Bound, Bound free and free bound, but infrared radiation from neutral molecules? Isn't that just mass-velocity relation, so changing velocity and emitting infrared?
greetings Janm

I am trying to understand your statement - neutral molecules can be made to emit infrared by accelerating them? I'm using "accelerating" here rather than "changing velocities" - is there as difference?

I think there may be, since the idea that one velocity inherently has more energy than another velocity seems to smack of an absolute frame. But if you have a neutral molecule undergoing acceleration, that is another matter. By accelerating, by applying force to the molecule you are doing something to its energy. The force could slow it down relative to you, so that would be reducing the relative energy. But it could speed it up relative to another frame.

I could see that molecules could emit radiation as a result of being accelerated (and decelerated). The energy represented by frequency and quantity of the radiation (frequency in your frame) plus the final velocity (in your frame) will be equal to the energy represented by the initial velocity (in your frame) plus the work done by the force (in your frame).

The result would be conservation of energy in the system (irrespective of frame).

As for the actual mechanism, if that is in fact anything like how it works ... I wouldn't like to guess.

cheers,

neopolitan

 

[neopolitan]

I did think of a mechanism. When accelerated (during the acceleration), a molecule would be compressed. On release of that acceleration, the molecule would relax, perhaps one of the phases, or both, would release radiation. At the particle scale, this could be due to delocalisation of energy, resulting a litte "bound" energy escaping to become "free".

But since I don't know much about neutral molecules emitting radiation when accelerated, my comments should not be taken too seriously

cheers,

neopolitan

 

[feynmann]

When two particles fuse, such as in the heart of stars, their combined mass is greater than their separate mass.

More later.

>>their combined mass is greater than their separate mass.
Does not make sense to me

 

[Dmitry67]

No, of course.
Mass of He4 is smaller then 2 neutron + 2 proton masses.

 

[ccollins919]

You could say that energy becomes mass when the wave collapses into particle form. As for pure energy, one might say that the closest thing to this might be the primordial first field that came into being after the big bang.

 

[JANm]

You could say that energy becomes mass when the wave collapses into particle form. As for pure energy, one might say that the closest thing to this might be the primordial first field that came into being after the big bang.

Energy becomes mass in: foton + molecule = triggered molecule?
and primordial first field: backgroundradiation?

It is a pity that of changes of energy levels of one electron we don't even know how this takes place which would be part of the answer to the posed question. I do believe that the formula's are there to calculate the amount of energy change.

I think that counts also for infrared emission. Process unknown yet calculation of amount: on one side of the equation Max Planck:
hf = 2 pi f hbar = omega hbar
(sorry have to learn more about the symbol-editor)
and on the other side delta m c^2.
The delta m coming out of the mass-velocity relation.
If it is right to use any inertial system, why not use the inertial system comoving with the backgroundradiation?

greetings Janm

 

[DaveC426913]

>>their combined mass is greater than their separate mass.
Does not make sense to me

Does it have to? These aren't billiard balls here. Don't look to the classical world.

 

[Gerinski]

Approaching the question from a different angle from what has been discussed until now, wouldn't it be another type of answer to say that "energy is supposed to become mass via the Higgs mechanism"?