Do photons warp space like the equivalent energy as mass would?

[bcrelling]

I understand that in GR mass is considered a distorting of space-time.

If you had a teleporter which transmitted an object's energy perfectly as photons to be reconfigured at a perfect reciever at the destination location, whilst in transit as a (very high energy) light pulse, would the same gravity be excerted by the light pulse as the equivalent rest mass?

 

[HomogenousCow]

No, Einstein's third law prohibits teleporters.

 

[bcrelling]

No, Einstein's third law prohibits teleporters.

I can't find any reference to "Einstein's third law". I assume your referring to the idea that nothing can travel faster than the speed of light? I might have caused confusion by referring to a "teleporter"(which you assumed ment instantaneous transmission, however this hypothetical machine transmits objects as light- and so the object's information and energy travel at light speed and no faster.

 

[pervect]

I understand that in GR mass is considered a distorting of space-time.

If you had a teleporter which transmitted an object's energy perfectly as photons to be reconfigured at a perfect reciever at the destination location, whilst in transit as a (very high energy) light pulse, would the same gravity be excerted by the light pulse as the equivalent rest mass?

Not really. It'd look a bit like the Aichelburg-sexl ultraboost while in transit.

http://en.wikipedia.org/w/index.php?title=Aichelburg–Sexl_ultraboost&oldid=77376500

Has a short summary, including the metric, and a reference to the original paper.

 

[bcrelling]

Not really. It'd look a bit like the Aichelburg-sexl ultraboost while in transit.

http://en.wikipedia.org/w/index.php?title=Aichelburg–Sexl_ultraboost&oldid=77376500

Has a short summary, including the metric, and a reference to the original paper.

Thanks- unfortunately the maths is a little beyond me!

Does this mean that there is at least some gravitaional effect excerted by photons in transit?

 

[pervect]

Yes - the field of a narrow light pulse would approach that of an impulse function that propagates as a plane wave.

The impulse function means that passing through the wavefront is a bit like getting hit with a baseball bat - it's the same sense of the word "impulse", the field approaches a plane discontinuity or plane wave.

 

[bcrelling]

I thought of a new scenario, which I should have asked in the first place!

1kg of mass is converted into energy as photons. The photons are trapped inside a box(of negligiable mass) with totally internally reflective sides.

Now does this box of light exert the same gravity as the original 1kg mass?

 

[pervect]

I thought of a new scenario, which I should have asked in the first place!

1kg of mass is converted into energy as photons. The photons are trapped inside a box(of negligiable mass) with totally internally reflective sides.

Now does this box of light exert the same gravity as the original 1kg mass?

Externally to the box, the gravity will be the same before and after the conversion to photons.

Inside the box (lets say you put an accelerometer just inside the surface and find a way to keep it from melting while you measure the proper acceleration while you hold it motionless) the gravity will NOT be the same after the explosion. It will , in general, increase.

I"m idealizing things a bit - assume that you let the box reach some sort of "steady state" after the explosion, and that nothing including gravity waves escapes during the explosion (the lack of spherically symmetrical gravity waves will help!).

The stresses in the box are important to the calculation - the "massless" box will contribute to the gravitational field via virtue of the tension in it. Note th at any material than can support a tension greater than its density must be exotic matter. Since the box is presumed massless, but capable of holding up under immense tension, the "box" must be made out of exotic matter.

Even though you have what appears at first glance to be the same box - the presence of tension in the box gives it different gravitational effects than the box without tension in its walls. This allows the inside gravity to change (increase) while the outside gravity remains the same.

(By gravity, I mean what one measures with an accelerometer, the Newtonian sort of gravity, because I think that's what people are asking about).

 

[bcrelling]

Externally to the box, the gravity will be the same before and after the conversion to photons.

Inside the box (lets say you put an accelerometer just inside the surface and find a way to keep it from melting while you measure the proper acceleration while you hold it motionless) the gravity will NOT be the same after the explosion. It will , in general, increase.

I"m idealizing things a bit - assume that you let the box reach some sort of "steady state" after the explosion, and that nothing including gravity waves escapes during the explosion (the lack of spherically symmetrical gravity waves will help!).

The stresses in the box are important to the calculation - the "massless" box will contribute to the gravitational field via virtue of the tension in it. Note th at any material than can support a tension greater than its density must be exotic matter. Since the box is presumed massless, but capable of holding up under immense tension, the "box" must be made out of exotic matter.

Even though you have what appears at first glance to be the same box - the presence of tension in the box gives it different gravitational effects than the box without tension in its walls. This allows the inside gravity to change (increase) while the outside gravity remains the same.

(By gravity, I mean what one measures with an accelerometer, the Newtonian sort of gravity, because I think that's what people are asking about).

Thanks for your insightful reply.
That's interesting what you say about the issue of tension in the box. On dimensional analysis, I realized that pressure(effectively surface tension of the box N/m²) has the same units as energy density (J/m³).

For simplicity's sake, let's consider the box to be a sphere.

Does it follow then, that the photon pressure against the walls of the (spherical)box is equal to the energy density of the space enclosed within it?

If so, is it also true that the photon pressure multiplied by the volume will give us the energy content of the box?

 

[Bill_K]

Does it follow then, that the photon pressure against the walls of the (spherical)box is equal to the energy density of the space enclosed within it?

One-third. Standard result from statistical mechanics: for a photon gas, PV = (1/3)U where U is the internal energy.

 

[Dale]

I thought of a new scenario, which I should have asked in the first place!

1kg of mass is converted into energy as photons. The photons are trapped inside a box(of negligiable mass) with totally internally reflective sides.

Now does this box of light exert the same gravity as the original 1kg mass?

If the box is spherical then outside the box, yes, nothing would change. This follows from Birkhoff's theorem.

 

[PAllen]

Back to the original question, I don't think the most instructive exact metic would be the Aichelburg-sexl, given earlier. Instead, I think it would be the Bonnor beam:

http://en.wikipedia.org/wiki/Bonnor_beam

The 'gravitational' behavior of such beams is covered more in:

http://arxiv.org/abs/gr-qc/9811052

A fundamental fact is the for a static body, a very well defined mass can be given in GR (Komar mass). However, I don't believe any of the common mass definitions in GR will apply to a Bonnor Beam. Very crudely, the key difference is that for a massive body, while energy is coordinate dependent, no coordinates will show energy less than some minimum. For a light beam, there are frames for which (in SR treatment), the energy can be made arbitrarily small. Carried over to GR, this implies fundamental differences in the type of curvature produced by matter versus radiation, and fundamental problems defining a meaningful (curvature based) mass or energy.

All of this endorses the original one word answer: NO, the gravity would not be the same, to whatever extent this question can be given any meaning.

---

However, I think the focus on the object's energy as light is mistaken in the first place. If one were to implement some form of light based teleporting, it would be information you want to transimit, not energy. Thus, the beam character would be determined by the amount of information needed to represent the state of the object, and how it is encoded in the beam. Even in the rest frame of the deconstructed object, this would probably have little to do with the total energy equivalent of the original body. [edit: For example, it takes very little information to describe a 1 kg perfect crystal of one element at absolute zero; quite a bit more to describe the state of a 1 kg kitten].

 

[bcrelling]

One-third. Standard result from statistical mechanics: for a photon gas, PV = (1/3)U where U is the internal energy.

Thanks
I just found that there's also enthalpy- the total energy of a thermodynamic system
H = U + PV

Considering that the total energy is the sum of the internal energy and the box itself, does it follow that our box must have a mass of 3kg to contain 1kg(energy equivalent) of photons?

 

[bcrelling]

Back to the original question, I don't think the most instructive exact metic would be the Aichelburg-sexl, given earlier. Instead, I think it would be the Bonnor beam:

http://en.wikipedia.org/wiki/Bonnor_beam

The 'gravitational' behavior of such beams is covered more in:

http://arxiv.org/abs/gr-qc/9811052

A fundamental fact is the for a static body, a very well defined mass can be given in GR (Komar mass). However, I don't believe any of the common mass definitions in GR will apply to a Bonnor Beam. Very crudely, the key difference is that for a massive body, while energy is coordinate dependent, no coordinates will show energy less than some minimum. For a light beam, there are frames for which (in SR treatment), the energy can be made arbitrarily small. Carried over to GR, this implies fundamental differences in the type of curvature produced by matter versus radiation, and fundamental problems defining a meaningful (curvature based) mass or energy.

All of this endorses the original one word answer: NO, the gravity would not be the same, to whatever extent this question can be given any meaning.

---

However, I think the focus on the object's energy as light is mistaken in the first place. If one were to implement some form of light based teleporting, it would be information you want to transimit, not energy. Thus, the beam character would be determined by the amount of information needed to represent the state of the object, and how it is encoded in the beam. Even in the rest frame of the deconstructed object, this would probably have little to do with the total energy equivalent of the original body. [edit: For example, it takes very little information to describe a 1 kg perfect crystal of one element at absolute zero; quite a bit more to describe the state of a 1 kg kitten].

It seems that there is no question on the matter: photons have a gravitational effect

With reference to quantum mechanics:-
Surely this makes them detectable, what's is there to stop there wave-function being collapsed by the gravitational interaction with other matter?


For example: a double slit experiment with a super high energy photon, there is no theoretical upper limit for the frequency of a photon, which being proportional to its energy means we could potentially transmit our 1kg of energy in a single photon. Now wouldn't this photon's path be detectable by shear force of gravity?

 

[Bill_K]

However, I don't believe any of the common mass definitions in GR will apply to a Bonnor Beam. Very crudely, the key difference is that for a massive body, while energy is coordinate dependent, no coordinates will show energy less than some minimum.

Surely the Bondi "mass" is in reality the fourth component of an energy-momentum vector quantity, and could be applied to Bonnor's solution, which carries both energy and momentum.

 

[PAllen]

Surely the Bondi "mass" is in reality the fourth component of an energy-momentum vector quantity, and could be applied to Bonnor's solution, which carries both energy and momentum.

The Bonnor beam is not asymptotically flat, as I understand the definition. Derivations of Bondi mass I've read assume asymptotic flatness. If you constructed some sort of chopped Bonnor beam (rather than an infinitely long beam), then Bondi and ADM mass should apply.

 

[PAllen]

It seems that there is no question on the matter: photons have a gravitational effect

With reference to quantum mechanics:-
Surely this makes them detectable, what's is there to stop there wave-function being collapsed by the gravitational interaction with other matter?


For example: a double slit experiment with a super high energy photon, there is no theoretical upper limit for the frequency of a photon, which being proportional to its energy means we could potentially transmit our 1kg of energy in a single photon. Now wouldn't this photon's path be detectable by shear force of gravity?

That's an interesting speculation. I know Penrose pushes ideas gravitational collapse of the wave function, and the minority view that collapse of the wave function should be considered 'real'. It seems to me that such a high energy photon would be well into the domain where some consistent QG theory must be used. Thus, who knows what would happen?

 

[Dale]

I understand that in GR mass is considered a distorting of space-time.

If you had a teleporter which transmitted an object's energy perfectly as photons to be reconfigured at a perfect reciever at the destination location, whilst in transit as a (very high energy) light pulse, would the same gravity be excerted by the light pulse as the equivalent rest mass?

There is a bit of an inherent problem with the question. The source of gravity in GR is not mass, it is stress-energy. Mass has stress-energy, and so does light. The stress-energy for mass is not the same as the stress-energy for light, so there will be differences. However, in certain idealized cases (e.g. spherical symmetry) the curvature outside the mass is the same as the curvature outside the light (although it is different within).

 

[Samshorn]

For example: a double slit experiment with a super high energy photon... Now wouldn't this photon's path be detectable by shear force of gravity?

That's one of the traditional arguments in favor of the belief that gravity must be quantized, because (for example) in a two-slit experiment the two possible paths of a particle or photon are in superposition, and hence (so the argument goes) the distinct gravitational fields must also be in superposition, so there must be a quantum theory of gravity... although no one knows how to construct such a theory in a self-consistent way.

Thus, the beam character would be determined by the amount of information needed to represent the state of the object, and how it is encoded in the beam. Even in the rest frame of the deconstructed object, this would probably have little to do with the total energy equivalent of the original body. For example, it takes very little information to describe a 1 kg perfect crystal of one element at absolute zero; quite a bit more to describe the state of a 1 kg kitten.

That's an interesting comment... but it's notoriously difficult to understand the absolute "information content" of physical entities. Consider a classical non-rotating spherically symmetrical black hole, which in a sense can be fully characterized by just a few parameters. However, if we believe the black hole formed by the unitary evolution of the wave function of a billion kittens that coalesced in a gravitational collapse, we know that quantum information is conserved by unitary evolution, so the seemingly simple and nearly informationless black hole must contain all the information of all those kittens. This leads to the famous "information paradox" when we try to merge classical general relativity with quantum field theory. I think the question of whether information is actually lost in the formation of a black hole (or anything else) is still controversial. I don't know if this kind of consideration has any relevance to the formation and information content of perfect crystal at absolute zero... but it might. "Information" is a tricky subject.