Photons in a Box Contribute Weight

[cbd1]

It is said that if you add photons into a box and close it, the weight of the box will be increased. My question is: How?

Photons are understood to be massless, which is what allows them to travel at c. But, when photons are absorbed by a material body, they do add mass to that body. Now, when photons are in a box, but not absorbed by it, they are still lone photons, which are supposed to be massless. How then do they contribute to a net force downward by the box on the scale?

(My understanding is that photons have mass equivalence in their energy by E=mc^2 [which makes them contribute to spacetime curvature], but that they do not actually individually have inertial mass.)

The only way I can figure it is that the light in the box follows spacetime curvature, making there be statistically more radiation pressure on the bottom of the box than on the other sides -- assuming the insides of the box are 100% reflective.

 

[cbd1]

Is it possible that the box will not actually weigh more in experiment? I suppose "possible" would have to be "yes" as the experiment cannot feasibly be done. So, the equations tell us that the photons will add weight to the box; but, in reality, they possibly could not.

Still, if they do, how?

 

[bcrowell]

(My understanding is that photons have mass equivalence in their energy by E=mc^2 [which makes them contribute to spacetime curvature], but that they do not actually individually have inertial mass.)

No, gravitational and inertial mass are always equal. If they were ever unequal, the equivalence principle would be violated, and the whole structure of GR would be destroyed. When we say that photons have no mass, we're referring only to rest mass, and what we mean is that in the equation $m^2=E^2-p^2$, the constant m is zero; this simply means that a photon's momentum is equal to its energy, p=E (in units where c=1).

The only way I can figure it is that the light in the box follows spacetime curvature, making there be statistically more radiation pressure on the bottom of the box than on the other sides -- assuming the insides of the box are 100% reflective.

Yes, that's right. And the only way you can have radiation pressure is if radiation has inertia.

 

[humanino]

The only way I can figure it is that the light in the box follows spacetime curvature, making there be statistically more radiation pressure on the bottom of the box than on the other sides

Yes, that's right.

To my mind, as I have said in another thread discussing this very same topic, one should be cautious of "cheating" explanations. The reason there is more pressure at the bottom of the box is because the gas is falling. The fact that there is more pressure at the bottom of the box is not an explanation why the gas is falling. It is interesting to note that consistency holds between the pressure exerted and the effect of gravitation on the gas. But it is important to keep in mind that when there is no box and no concept of pressure, a single photon escaping the gravitational field of a star will also be red-shifted. The point is that gravitation has as a universal source energy-momentum and anything carrying energy-momentum (with or without mass) falls along the 4-geodesics consistently computed from the total energy-momentum around.

Take for instance the gravitational effect on a single hydrogen atom. It will be different from the gravitational effect of a single mass equalling the sum of the masses of a free proton and a free electron, the difference is about 13.6 eV. Right ? What is the explanation in terms of a virtual photon flying around exchanged between the electron and the proton ?

I think bcrowell is aware of those caveats, and that's why he added

And the only way you can have radiation pressure is if radiation has inertia.

 

[cbd1]

Yes, that's right. And the only way you can have radiation pressure is if radiation has inertia.

So, finally, I should be content with the understanding that photons do not possesses the quality of mass, but that they do possesses momentum. Is there a way that they could have momentum and not inertia? By my understanding something has to have rest mass to have inertia ?

By the means of the hydrogen atom having more weight than just the proton and the electron; what is your explanation for this? Could it be interpreted that the electron has more energy when bound than when free?

[My apologies for not taking in simply that radiation does have inertia: I am just honestly trying to understand it for myself. I thought I had this understood before, and now it is just not making sense for me.]

 

[humanino]

By the means of the hydrogen atom having more weight than just the proton and the electron; what is your explanation for this? Could it be interpreted that the electron has more energy when bound than when free?

The hydrogen atom is lighter than the free electron and proton separately, because there is a binding energy of 13.6 eV contributing negatively, that 13.6 eV is the energy it takes to pull out the electron from the proton "electromagnetic potential well". You can picture this energy that you need to put in the system classically, to go from the bound state to the 2 free asymptotic states "at infinity".

I mention this because my understanding is that your initial motivations are related to understanding the proton mass. The proton mass is a fairly more advanced problem, one aspect being that there is no free state of the constituents. In the case of quarks, the energy stored in the system will grow with the distance, and the quarks are permanently confined inside hadrons (also called infrared slavery, the evil brother of asymptotic freedom). So there is a quantum mechanical balance between the light quarks trying to escape out of the region in which they are trapped which is smaller than their Compton radius (Heisenberg inequality), and the growing (positive) energy of the system as they fly apart. In this case, our classical pictures are of much less help.

 

[starthaus]

(My understanding is that photons have mass equivalence in their energy by E=mc^2 [which makes them contribute to spacetime curvature],

Not exactly. Photons contribute to the equivalent mass of a system via their momentum. This is a rather involved calculation that you can see https://www.physicsforums.com/blog.php?b=1928 (second attachment)

 

[bcrowell]

So, finally, I should be content with the understanding that photons do not possesses the quality of mass, but that they do possesses momentum.

They don't have *rest* mass.

Is there a way that they could have momentum and not inertia?

To me, the definition of having inertia is the ability to exchange momentum.

By my understanding something has to have rest mass to have inertia ?

No, light has inertia but no rest mass.

By the means of the hydrogen atom having more weight than just the proton and the electron;

It has less weight, not more.

what is your explanation for this?

Mass and energy are equivalent, so less energy is equivalent to less mass.

Could it be interpreted that the electron has more energy when bound than when free?

No, the binding energy is not just a property of the electron, it's a property of the whole system.

 

[lightarrow]

It is said that if you add photons into a box and close it, the weight of the box will be increased. My question is: How?

Photons are understood to be massless, which is what allows them to travel at c. But, when photons are absorbed by a material body, they do add mass to that body. Now, when photons are in a box, but not absorbed by it, they are still lone photons, which are supposed to be massless. How then do they contribute to a net force downward by the box on the scale?

There is no big difference with the case of photons absorbed by a material body (black body). If a single photon has energy E_ph then the box energy is increased of a quantity n*E_ph so its mass has increased of a quantity n*E_ph/c², because the box stayed at rest (for objects at rest you can use the relation E = mc²).

Furthermore, the fact photons are massless shouldn't make you think that a system of more than one photon is massless: mass *is not* additive.

Consider a system of two photons traveling in opposite directions and with the same energy E_ph. The system's energy is 2E_ph (energy *is* additive), but the system's momentum is zero, ok?

Then you apply the relation:

E² = (mc²)² + (cp)²

which is valid for every object or system with total energy E, total momentum p and total mass m.

In our case we have:

(2E_ph)² = (mc²)² + 0

so: m =/= 0. A system of two equal photons traveling in opposite directions *HAS* mass.

If the two photons have not the same energy, or are not traveling in opposite directions but however travels in different directions, or both things, you can always find a frame of reference where they have the same energy and are traveling in opposite directions, so the system of two photons still have mass.

 

[humanino]

A system of two equal photons traveling in opposite directions *HAS* mass.

I tried to make more or less the same analysis for cbd1, so I would like to thank you. I will repeat this experimental simple fact which I mentioned then : the neutral pion with mass 0.135 GeV/c^2 decays in two photons. We use those two photons to calibrate calorimeters in many experiments with calorimeters and neutral pions.

 

[Naty1]

It is said that if you add photons into a box and close it, the weight of the box will be increased

But the act of closing the lid does not account for the increase.

And if you add the same photons to a smaller box, or compress the size of the box after adding the photons, the weight will increase more...due to an increase in frequency and ultimately electron degeneracy pressure...

 

[cbd1]

Thanks to all for filling me in on these things. This is my understanding at this time:

Photons do not have rest mass. And, because rest mass is required to give resistance into a change in motion, i.e. inertia, the photon does not technically have inertia. This does not mean, however, that the photons do not have momentum; their momentum is equal to their energy; so they do have momentum, which is equal to their energy's mass equivalence. (By this, the momentum works in conservation of momentum for radiation pressure, even though they do not, by my description, have inertia.) And, to add, even if two photons are traveling in opposite directions and their total momentum equals 0, they will still contribute to the mass of a system.

Now, if photons are considered in a system, their mass equivalence contributes to the rest mass of the system, even though they do not individually have any rest mass. I think this (besides, perhaps the interpretation of "inertia") agrees with what has been said by the more experienced contributors -- I, of course, could be misunderstanding yet again.

As far as the other topic, of the mass of a H atom, the system has less mass than the individual particles. And my next question: Assuming the proton has no change in its mass equivalence when the electron is bound to it, *could the loss in energy (mass equivalence) of the atom be interpreted as a loss in the electron's energy? (Since this amount of energy lost is the amount that would be required to be added to the electron to free it from the system again, giving it back its total free energy, an therefore mass equivalence?) In other words, can the loss in energy of the system (atom's mass) be considered to be due to a loss in the electron's energy, which is lost due it being bound?

 

[bcrowell]

And, because rest mass is required to give resistance into a change in motion, i.e. inertia, the photon does not technically have inertia.

No, rest mass is not required to give resistance to a change in motion. A photon does have inertia. For example, when a photon bounces off of a mirror, the mirror recoils from the collision.

And my next question: Assuming the proton has no change in its mass equivalence when the electron is bound to it, *could the loss in energy (mass equivalence) of the atom be interpreted as a loss in the electron's energy?

The assumption is wrong, and what's the point in trying to figure out what's true under a false assumption? The binding energy is a property of the whole system, not of one particle or the other.

 

[cbd1]

No, rest mass is not required to give resistance to a change in motion. A photon does have inertia. For example, when a photon bounces off of a mirror, the mirror recoils from the collision.

Could this example not be a result of the conservation of momentum?

Here is a way which shows that photons do not have inertia like other objects: When a photon enters a substance, like the atmosphere, from being in the vacuum of space, it slows from c. This, then, would have to be interpreted as a loss of inertia. Then, if the photon were to exit the atmosphere again and go back out into the vacuum of space, it will go back to traveling at c. It would seem then, that if the photon abides by inertia, it has somehow gained inertia spontaneously from nothing. This is something that objects with inertia do not do; an object with inertia would continue its path at the same speed, due to its resistance to change in motion.

With this, can you give other examples of rest mass not being required to give resistance to change of motion?

The assumption is wrong, and what's the point in trying to figure out what's true under a false assumption? The binding energy is a property of the whole system, not of one particle or the other.

You say "the whole system" as if that makes a simple cover to say that neither the proton or the electron lose energy, but that "the system" does. Wouldn't the loss of mass when the proton and electron become bound have to be described as a loss of rest mass in both the proton and the electron, with the degree of which between them being uncertain? The following is my logic.

If you take an unbound proton and an unbound electron in a system by themselves (with only vacuous space otherwise), they have total mass x. Then, upon their binding, they have total mass < x in the H atom. Is there any other thing in the system in which the energy/mass can be lost from? Unless you somehow add negative energy to the system when they bind, you must agree that the proton and the electron cannot still have both of their full beginning masses while in the atom.

 

[JesseM]

As far as the other topic, of the mass of a H atom, the system has less mass than the individual particles. And my next question: Assuming the proton has no change in its mass equivalence when the electron is bound to it, *could the loss in energy (mass equivalence) of the atom be interpreted as a loss in the electron's energy?

I think it would be valid to consider the difference in mass to be equal to the decrease in potential energy of the electron when it is moved from far away (unbound) to close to the proton (unbound). My understanding that the inertial mass of any bound system in SR (its resistance to acceleration in its own rest frame, which could be measured by putting it on a scale) is always equal to (sum of rest masses of all its constituent parts) + (sum of kinetic energies of all its constituent parts) - (amount that the potential energy of the parts is lower than the potential energy of the same parts if they were moved far apart), with kinetic and potential energies calculated in the rest frame of the bound system.

 

[bkelly]

While I cannot follow everything here, this is an interesting thread. It makes me wonder what would be the effect if the inside of the box were perfectly reflective. Put a laser in one corner and aim it so that the photons would bounce around almost forever. Turn on the laser. If you want, get the power for the laser from an external device so we don't have to worry about the energy consumption within a battery having an affect on the mass change. Now what happens to the mass of the box when the laser shines?

 

[humanino]

If you want, get the power for the laser from an external device so we don't have to worry about the energy consumption within a battery having an affect on the mass change.

But you do have to worry about it : your laser plugged into an outside source of power pumps energy in the box. Fill your box with energy, yes the mass increases.

 

[lightarrow]

Could this example not be a result of the conservation of momentum?

Here is a way which shows that photons do not have inertia like other objects: When a photon enters a substance, like the atmosphere, from being in the vacuum of space, it slows from c.

No, photons cannot travel at speeds lower than c. The electromagnetic wave can (for what concern phase speed or group speed).

you say "the whole system" as if that makes a simple cover to say that neither the proton or the electron lose energy, but that "the system" does.

Infact it's exactly this way.

Wouldn't the loss of mass when the proton and electron become bound have to be described as a loss of rest mass in both the proton and the electron, with the degree of which between them being uncertain?

No. Consider, to make an example, a fixed region of space filled with electrostatic field. That region has energy and also has mass. So you don't need to ascribe energy or mass to particles only.

 

[lightarrow]

While I cannot follow everything here, this is an interesting thread. It makes me wonder what would be the effect if the inside of the box were perfectly reflective.

Where is the difference with the question we are discussing? The box acquires mass as soon as photons enter in it, we don't have to wait for photons to be absorbed by the box' walls (or the OP wouldn't even have made the question )

Put a laser in one corner and aim it so that the photons would bounce around almost forever. Turn on the laser. If you want, get the power for the laser from an external device so we don't have to worry about the energy consumption within a battery having an affect on the mass change. Now what happens to the mass of the box when the laser shines?

See up. Consider however that the initial mass of the box shoud be much greater of the order of the laser energy/c², otherwise the box will recoil, and its increase of mass would be lower than that value.

 

[bcrowell]

Could this example not be a result of the conservation of momentum?

Here is a way which shows that photons do not have inertia like other objects: When a photon enters a substance, like the atmosphere, from being in the vacuum of space, it slows from c. This, then, would have to be interpreted as a loss of inertia.

This is the same as the example of the light wave bouncing off the mirror. You've just substituted the atmosphere for the mirror.

Then, if the photon were to exit the atmosphere again and go back out into the vacuum of space, it will go back to traveling at c. It would seem then, that if the photon abides by inertia, it has somehow gained inertia spontaneously from nothing.

It exchanged momentum with the atmosphere.

This is something that objects with inertia do not do; an object with inertia would continue its path at the same speed, due to its resistance to change in motion.

No, this is incorrect. Having "inertia" doesn't mean that an object can never change its motion.

With this, can you give other examples of rest mass not being required to give resistance to change of motion?

I don't understand what you're asking here, or how it relates to the argument you made above.

You say "the whole system" as if that makes a simple cover to say that neither the proton or the electron lose energy, but that "the system" does. Wouldn't the loss of mass when the proton and electron become bound have to be described as a loss of rest mass in both the proton and the electron, with the degree of which between them being uncertain?

No.

The following is my logic.

If you take an unbound proton and an unbound electron in a system by themselves (with only vacuous space otherwise), they have total mass x. Then, upon their binding, they have total mass < x in the H atom. Is there any other thing in the system in which the energy/mass can be lost from? Unless you somehow add negative energy to the system when they bind, you must agree that the proton and the electron cannot still have both of their full beginning masses while in the atom.

The binding energy is negative, and it's equivalent to a certain negative amount of mass.

 

[cbd1]

No, photons cannot travel at speeds lower than c. The electromagnetic wave can (for what concern phase speed or group speed).

The speed at which light propagates through transparent materials, such as glass or air, is less than c. When it exits, it returns to c. Will you argue that light is no longer a photon when it travels through glass?

Infact it's exactly this way.

JesseM has made a point against this. The loss in energy can be considered a loss in the electron's potential mass.

No. Consider, to make an example, a fixed region of space filled with electrostatic field. That region has energy and also has mass. So you don't need to ascribe energy or mass to particles only.

Are you positing that the electrostatic field in the region is what loses mass? Further, the electrostatic field in space (vacuum energy/zero-point field) cannot have inertia: This is actually additional evidence that that rest mass is required for inertia.

I would still like to see more examples of where rest mass can be absent in anything with inertia.

 

[cbd1]

This is the same as the example of the light wave bouncing off the mirror. You've just substituted the atmosphere for the mirror.

If you consider this system in your view, the photon exerts inertia onto the mirror, yet the photon travels away will all of it's inertia intact. Is it possible by the laws of physics to double the inertia in a system??

It exchanged momentum with the atmosphere.

So what you are saying is that the atmosphere gave the photon back its supposed inertia as a gift upon its leaving? I see it as the momentum of the photon is constant.

No, this is incorrect. Having "inertia" doesn't mean that an object can never change its motion.

I never made the argument that anything with inertia can never change its motion. What I am arguing is that an object abiding by inertia cannot gain inertia from nowhere, as would be required to happen when the photon exits the atmosphere and gains speed - if it were an object with inertia.

I don't understand what you're asking here, or how it relates to the argument you made above.

I will rephrase: Do you have any other examples in which rest mass can be absent in anything possessing inertia?

The binding energy is negative, and it's equivalent to a certain negative amount of mass.

If you are sure that it is negative mass that is being added to the proton and electron when they bind, I guess then we would not have to assume that either the proton or electron lost mass in some way. But, by my understanding nothing in the universe can have negative mass. Could you explain further how exactly the "binding *energy is negative*?"

 

[bcrowell]

Are you positing that the electrostatic field in the region is what loses mass?

This is basically how it's described in a classical field theory. However, there are some problems with that description, since the energy content of a point-charge's field is theoretically infinite. A classical field theory is not the only way to describe it. However, in all successful descriptions the binding energy is a property of the whole system, not one particle or the other.

Further, the electrostatic field in space (vacuum energy/zero-point field) cannot have inertia:

No, that's incorrect. First of all, an electrostatic field is not the same thing as a zero-point field. Second, an electrostatic field does have inertia. (It has energy, energy is equivalent to mass, and by the equivalence principle that mass is both gravitational and inertial.)

This is actually additional evidence that that rest mass is required for inertia.

It's getting kind of pointless to argue with you, since you have fixed ideas that you have set out to prove, and you don't listen when people try to correct your misconceptions.

 

[lightarrow]

The speed at which light propagates through transparent materials, such as glass or air, is less than c. When it exits, it returns to c. Will you argue that light is no longer a photon when it travels through glass?

Did you reead the FAQ in General Physics: "Do Photons Move Slower in a Solid Medium?" It will give you some hints. I say hints because the subject "photon" is not as straightforward as you believe (I used an euphemism).
Photons don't slow down. When you have read well that FAQ we can go on discussing that, if you like, but I advised you about the mined-field we would go into.

Are you positing that the electrostatic field in the region is what loses mass?

Something on which you could reason about: compute the electrostatic field's energy generated by two fixed opposite charges very far from each other (in the limit of infinite distance but it's not really necessary) and that generated when the two charges are near. Then compute the simple difference of potential electrostatic energy. You will find an interesting thing.

Further, the electrostatic field in space (vacuum energy/zero-point field) cannot have inertia: This is actually additional evidence that that rest mass is required for inertia.

No. What matter do you think is made of? Single atoms? Not exactly. A more correct answer would be: atoms *and* fields. But actually the answer is: you have to consider the entire *system*, as bcrowell tried to explain you.
Looking inside atoms what do you find? A nucleus, electrons *and* the fields which bind them. Looking inside the nucleus you would find that the binding energy of protons and neutrons has now a mass which is some percent of that of the same nucleons; looking inside a nucleon (a proton or a neutron) you would find that the field's mass is now comparable with that of the same quarks...
So, what is matter really made of, apart of fields?

 

[cbd1]

I would say that matter is energy which is confined into particles (fermions). Then, when these particles are extant, they can form bonds from fields of the various forces, which can indirectly add to or decrease the mass of the systems of particles, which have rest mass. However, be there no particles, there is no mass, only *mass equivalence*. When energy is composed into particles, allowing for rest mass, the energy can then be gravitationally accelerated and have inertia. However, were this energy not bound into particles (fermions), it will not be.

For this example of the photon in the box, we have not actually shown that the photons will give the box rest mass. We have shown that the box will push downward on a scale due to the photons following geodesic lines in spacetime and press radiation pressure on the bottom side. Yes, the box will have mass equivalence inside it however, considering the box is weightless, it will still not have inertia...

P.S. Try to envision all of this with the box being weightless. Send the box with the photons in it out into space. The velocity of the box will not matter, because all the photons in it will be flying at c anyway, supposedly having zero momentum over-all.

I would like very much to hear all of your thoughts on any of this.

 

[JesseM]

For this example of the photon in the box, we have not actually shown that the photons will give the box rest mass. We have shown that the box will push downward on a scale due to the photons following geodesic lines in spacetime and press radiation pressure on the bottom side. Yes, the box will have mass equivalence inside it however, considering the box is weightless, it will still not have inertia...

P.S. Try to envision all of this with the box being weightless. Send the box with the photons in it out into space. The velocity of the box will not matter, because all the photons in it will be flying at c anyway, supposedly having zero momentum over-all.

But the "inertial mass" of the whole box is its resistance to acceleration--if you try to accelerate it in deep space, photons bounce off the "bottom" inner side more often than the "top" inner side (top and bottom relative to the G-force experienced by anything in the box due to the acceleration), because the bottom is constantly accelerating towards the previous center of the box while the top is constantly accelerating away from it. Also, by the http://www.einstein-online.info/spotlights/equivalence_principle):

[PLAIN]http://physics.syr.edu/courses/modules/LIGHTCONE/anim/equv-m.gif

 

[Dead Boss]

However, be there no particles, there is no mass, only *mass equivalence*. When energy is composed into particles, allowing for rest mass, the energy can then be gravitationally accelerated and have inertia. However, were this energy not bound into particles (fermions), it will not be.

So how does this "mass equivalence" actually affect anything if it does not have inertia nor is it gravitationally attracted? How do you measure such
"mass equivalence"?

 

[lightarrow]

I would say that matter is energy which is confined into particles (fermions).

With the term "matter" here you intended "mass"? Or something else?
If you intended "mass" then the answer is: mass is energy confined in whatever "stationary" region of space you are considering. Nothing else.

Then, when these particles are extant, they can form bonds from fields of the various forces, which can indirectly add to or decrease the mass of the systems of particles, which have rest mass. However, be there no particles, there is no mass, only *mass equivalence*.

As Dead Boss wrote, this concept would'nt have much meaning if we couldn't measure it. But I know where these concepts come from: popularization or low level school lessons. It was not very clear for me too. All confusion comes from this (in)famous formula: E = mc². If you simply remember that the formula is valid *only* for a stationary object/system, then a lot of your confusion fades away. (With stationary here I mean: total momentum = 0).
If you give energy to a stationary box which remains stationary in your frame, then the energy E you give *IS* mass, independently of the way you give it this energy. (Nothing "mass equivalence").

For this example of the photon in the box, we have not actually shown that the photons will give the box rest mass.

Not correct, we have proved it.

 

[cbd1]

But the "inertial mass" of the whole box is its resistance to acceleration--if you try to accelerate it in deep space, photons bounce off the "bottom" inner side more often than the "top" inner side (top and bottom relative to the G-force experienced by anything in the box due to the acceleration), because the bottom is constantly accelerating towards the previous center of the box while the top is constantly accelerating away from it.

This makes a lot more sense of how the box will behave as though it has inertial mass, thank you. The gif brought a question to mind: A gravitational field accelerates all objects in it at the same rate. Does this also apply to light? It seems it could be considered as such if the light is traveling tangent to the gravitational field, for on Earth it would accelerate the ray towards the ground at 9.8m/s^2, like all other objects in free fall. However, if it is traveling straight towards the gravitational field, it cannot be as such. Thus, it seems photons must be treated differently than other objects when it comes to how gravity influences them--and therefore how we consider their inertial and gravitational mass. Right? (My logic is again leading me towards the idea that photons do not have inertial or gravitational mass like objects with rest mass do.)

Further, could this box (assuming the walls are weightless) theoretically be accelerated to the speed of light? If it is possible that it could be, then this box cannot have rest mass, as nothing with rest mass can reach the speed of light...

 

[Bussani]

The gif brought a question to mind: A gravitational field accelerates all objects in it at the same rate. Does this also apply to light? It seems it could be considered as such if the light is traveling tangent to the gravitational field, for on Earth it would accelerate the ray towards the ground at 9.8m/s^2, like all other objects in free fall. However, if it is traveling straight towards the gravitational field, it cannot be as such. Thus, it seems photons must be treated differently than other objects when it comes to how gravity influences them--and therefore how we consider their inertial and gravitational mass. Right? (My logic is again leading me towards the idea that photons do not have inertial or gravitational mass like objects with rest mass do.)

Photons have no rest mass, but they have momentum, and they follow a straight path through space. But gravity is the result of spacetime being bent, so the "straight path" the light is following is also going to be bent. So it's not that the light is being accelerated toward the ground in the sense that the light is getting faster or increasing in magnitude, but its direction can be changed, at least.

 

[cbd1]

So how does this "mass equivalence" actually affect anything if it does not have inertia nor is it gravitationally attracted? How do you measure such
"mass equivalence"?

Free light, while in flight, only has mass equivalence, and no rest mass. The photons, while in flight, only interact with the environment by their mass equivalence having effect on the curvature of spacetime to a degree of which is equal to their energy's *mass equivalence*. Light only exhibits qualities of inertial and gravitational mass when it collides with something or is absorbed/emitted by a system. It is not gravitationally attracted; rather, it follows geodesics in its flight path, which is always straight in spacetime, but appears to be deviated to us by gravity, because we see the universe in a Euclidean way, though it is not Euclidean.

For instance, my ideation involves that during inflation there was only free energy, having only mass equivalence, in the universe. Nothing interacted, though there was all the energy and mass equivalence then as there is today. It was only when particles (fermions) materialized that interaction began--and inflation ended, due to things then having the characteristic required to be gravitationally attracted (i.e. rest mass).

 

[Dale]

I would say that matter is energy which is confined into particles (fermions). ... However, be there no particles, there is no mass, only *mass equivalence*. When energy is composed into particles, allowing for rest mass, the energy can then be gravitationally accelerated and have inertia. However, were this energy not bound into particles (fermions), it will not be.

In addition to the excellent replies you have already received I would just like to point out that the W and Z bosons have mass also. So even if we are speaking of isolated fundamental particles (and not systems of 2 or more) then mass is not always associated with matter.

Also, you can easily see that EM fields have inertia from the fact that their Lagrangian is symmetric wrt spatial translations.

 

[DaTario]

I would say that if you have a ball bouncing inside a box, its mass (ball's mass) will contribute to the box' mass in a way which takes into account the specific shape of trajectory of the ball inside de box. Its collisions with the walls and so forth. But when ball and box are not touching, we could say that the box, at least during a small time interval, would behave as if it was empty (no mass contribution). Very similar must be the situation with light inside.

Best Regards

DaTario

 

[JesseM]

The gif brought a question to mind: A gravitational field accelerates all objects in it at the same rate. Does this also apply to light? It seems it could be considered as such if the light is traveling tangent to the gravitational field, for on Earth it would accelerate the ray towards the ground at 9.8m/s^2, like all other objects in free fall. However, if it is traveling straight towards the gravitational field, it cannot be as such.

Actually it does apply to light traveling vertically as seen in the accelerating reference frame where the box (or either of the rockets in the gif) is considered to be at rest. The idea that light always moves at c only applies to inertial frames, which in the context of gravity would mean a free-falling frame. In the accelerating frame, the speed of a vertical light ray does change, with the ray accelerating towards the "floor" at 9.8 m/s^2.

If you haven't read about the equivalence principle yet I'd definitely recommend doing so...

Further, could this box (assuming the walls are weightless) theoretically be accelerated to the speed of light?

You can't assume the walls are literally massless, just that the mass is so small it can be treated as negligible for the sake of the problem. But as long as the mass is not exactly zero, it's impossible to accelerate it to the speed of light (and I'm pretty sure there aren't any massless particles such that, if a group of them were traveling together and formed a closed shape like a box, they would reflect photons that hit the 'walls' and keep them inside)

 

[Passionflower]

So it's not that the light is being accelerated toward the ground in the sense that the light is getting faster or increasing in magnitude, but its direction can be changed, at least.

The (proper, e,g, measured locally) speed of light does not change in a gravitational field. The Schwarzschild coordinate speed of light decreases while for massive particles this coordinate speed depends on a critical speed which is $c/\sqrt{3}$, above this speed a test particle's coordinate speed will slow down, below it it will speed up.