How exactly does energy become mass?

[Dale]

Regarding "pure energy". I don't think it is important, but I would say that mass at rest is "pure energy", not light. If you look at the four-momentum you see that energy is the timelike component and momentum is the spacelike component. So mass at rest is (m₀c,0) which is purely energy, while a photon is (p,p) which is energy that is "maximally contaminated" with momentum.

 

[lightarrow]

lightarrow, again, depending on what you call a mass.

I have 1kg of matter and 1kg of antimatter.
I annihilate them and get a huge flash of light.
There is no hardronic matter left.
(lets forget about the neutrino) do you agree that the total mass of light flash is 2kg?

Yes, but only because in this case p = 0 (or you can always find a ref. frame where it's 0). For a *single* photon that's false and the mass is exactly zero.

 

[Phrak]

Apples and Oranges

Tomatoes and Potatoes

E^{2} = m_{p}\!^{2} c^{4} + c^{2}p^{2}
E = m_{i}c^2

m_{i}
and
m_{p}
are not the same vegetable.

 

[lightarrow]

Tomatoes and Potatoes

E^{2} = m_{p}\!^{2} c^{4} + c^{2}p^{2}
E = m_{i}c^2

m_{i}
and
m_{p}
are not the same vegetable.

There is only one kind of mass in SR.

 

[cesiumfrog]

There is only one kind of mass in SR.

lol. And I suppose you wish to assert that it is the "rest" kind, rather than the "relativistic" kind?

 

[lightarrow]

lol. And I suppose you wish to assert that it is the "rest" kind, rather than the "relativistic" kind?

just a few posts before (n.59) I said it's better called "invariant" mass.
You are one of those who still talk about relativistic mass?

 

[cesiumfrog]

I said ..

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.

 

[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.

I think that each physicist has his own problems with mass, energy and momentum in special relativity theory. Because I have no physicists next room to me, please consider my own problem. Equation m=gm(0) (1) (m relativistic mass, m(0) rest mass, g Lorentz factor) is derived in many textbooks and papers but we can consider that it is the equations that fits best experimental results. Multiply both its sides by c in order to obtain
cm=cgm(0) (2).
Even if cm and cm(0) have the physical dimensions of momentum they have no physical meaning because tardyons could never reach the speed c.
Multiply both its sides’ by cc in order to obtain
ccm=ccgm(0 ). (3)
ccm and ccm(0) have the physical meaning of energy. Introducing the notation E=ccm for relativistic energy and E(0)=ccm(0) for rest energy (3) becomes
E=gE(0) (4)
Equations (3) and (4) tell us that mass and energy have the same physical properties in special relativity theory among others they conserve.
Consider a high sensitivity balance. Put on its pans identical bodies the balance being in a state of equilibrium. Irradiate with electromagnetic energy one of the two bodies for a given time interval. Stop the irradiation after a given time interval and you will see that the balance is inclined at the side where the irradiated body is located. Using usual terminology we could say that the irradiated body has received energy from the radiation and that its mass has increased. But we could also say that that the body has received energy and its energy has increased or that the electromagnetic energy gave up mass which contributed to the increase of the mass of the irradiated body.
Please tell me if I have interpreted correctly your point of view.

 

[jostpuur]

This is not inconsistant with particle physics, nor energy in transit as photons. Measure the photons on a scale, they have inertial mass.

What do you mean with inertial mass of a photon?

You've heard of light sails, right? Photons have inertia. They exert a force on the sail. I turn, the sail changes the momentum of the photon. Bounce enough light off a scale, it will measure an applied force.

The response to lightarrow should have been, that the comment was about inertial mass of several photons, not of a single photon.

Or was the comment about inertial mass of several photons? At least I interpreted it like that. On the other hand I was trying to interpret it so that it is right. An appropriate approach IMO, compared to the opposite one, in which interpretable claims are interpreted so that they are wrong.

 

[lightarrow]

The response to lightarrow should have been, that the comment was about inertial mass of several photons, not of a single photon.

Yes, several photons and *not traveling in the same direction*. If he talks about light sails, it's more about photons traveling in the same direction than the other way round.

 

[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[/color] 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 asymmetric? (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).