# Light has Gravity?

Howdy,
Does light exert gravity? last i heard, eletro-magnetic radiation doesn't have mass, and thus no gravity, yet it is apparently effected by gravity.
How can something which has no mass be effected by gravity?
does that mean that gravity is a pattern in space itself?

cesiumfrog
does that mean that gravity is a pattern in space itself?
That's an excellent way of thinking about it.

I'd like to leave it at that, but I'd feel hypocritical if I let you draw the correct conclusion from compromised reasoning. Light does exert it's own gravity, and whether it has mass is largely just a question of semantics (it certainly has momentum).

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anantchowdhary
How can something which has no mass be effected by gravity?
does that mean that gravity is a pattern in space itself?

Light certainly is affected by gravity.And the reason can be understood by the equivalence principle.

Imagine you are in an elevator, and suddenly someone from outside shines light into the elevator (let the elevator be transparent!).If you start accelerating upwards,you will see the light bending towards the floor.

The same happens in a gravitational field as the equivalence principle is valid locally

Light does exert it's own gravity, and whether it has mass is largely just a question of semantics (it certainly has momentum).
hrmm, interesting.
i will try to find the studies which show that light has gravity. I'll probably use a search engine- can you point me to any particular experiments? Are you telling me that a "wavicle" which travels at a constant speed (c) has momentum? Are you saying that because electrons jump shells when photons impact them? I don't personally think its the same phenomena as momentum if that's the reason.

cheers,

anantchowdhary
Oh yes the wave traveling at c(it has energy) has momentum.

And the reason isn't because of the electron jump,it is because mass and energy both curve spacetime.

Also,an interesting fact:You could create a black hole if u focussed enough light to curve spactime very very much(high energy density)

Cheers!

Homework Helper
last i heard, eletro-magnetic radiation doesn't have mass, and thus no gravity
This is an invalid step. In relativity, gravity does not necessarily depend on mass.

Gold Member
Howdy,
Does light exert gravity? last i heard, eletro-magnetic radiation doesn't have mass, and thus no gravity, yet it is apparently effected by gravity.
How can something which has no mass be effected by gravity?
does that mean that gravity is a pattern in space itself?

Light is affected by gravity : in general relativity, gravity is understood in terms of curved space-time. So that a photon is always moving in a straight line, but it bends because space-time itself is bent.

Light exerts gravity : in general relativity, gravity is coupled to energy density and momentum flow, not only mass like in Newtonian gravity. An electromagnetic wave will exert its own gravity, though extremely weak and not currently measurable. Gravity exerted by massive bodies is much higher because of their huge energy content (see the c squared term in Einstein formula).

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Light certainly is affected by gravity.And the reason can be understood by the equivalence principle.Imagine you are in an elevator, and suddenly someone from outside shines light into the elevator (let the elevator be transparent!).If you start accelerating upwards,you will see the light bending towards the floor.The same happens in a gravitational field as the equivalence principle is valid locally
So the effect on light in a moving frame of reference is the same effect that gravity has on it within a stagnant reference? Thats really interesting, even though i don't understand why it is equivalent... Light appears to be bent from a moving frame of reference, but is it really bent the same as in a gravity field?
thanks,

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Oh yes the wave traveling at c(it has energy) has momentum. And the reason isn't because of the electron jump,it is because mass and energy both curve spacetime. Also,an interesting fact:You could create a black hole if u focussed enough light to curve spactime very very much(high energy density) Cheers!

Wow, that is amazing! I'm still having difficulty with the momentum concept... ie momentum= mass X velocity... c is the constant velocity, but whence cometh the mass? do you just substitute mass for the equivalence in pure energy by Einstein's conversion? Also, a black hole is a singularity... wouldn't you have to focus the light on a massive object to create a black hole? IN other words. Without something to stop it, where would the black hole form- near the source?

So it has been proven that light curves spacetime around itself?! Wow, i really have been out of the loop!
peace and grace,

This is an invalid step. In relativity, gravity does not necessarily depend on mass.
Ah, thanks for the correction. What does gravity depend on? Heres a silly question:
The other fellow says its energy density, so, hypothetically, if i were in deep space traveling by a laser beam with the focused energy of a million suns, would i be sucked into it? (me being the only substantial matter around)
cheers,

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Light is affected by gravity : in general relativity, gravity is understood in terms of curved space-time. So that a photon is always moving in a straight line, but it bends because space-time itself is bent.
Light exerts gravity : in general relativity, gravity is coupled to energy density and momentum flow, not only mass like in Newtonian gravity. An electromagnetic wave will exert its own gravity, though extremely weak and not currently measurable. Gravity exerted by massive bodies is much higher because of their huge energy content (see the c squared term in Einstein formula).

If the gravity of light cannot currently be measured, then how do you know it's there? Light fills the entire universe, which means that if it does exert gravity, there's a lot of it, but no focal point of attraction. Since light appears to be moving constantly, where would the focal point of gravity be?
forgive my ignorance,

Gold Member
What does gravity depend on?
On energy density and momentum flow.

Wow, that is amazing! I'm still having difficulty with the momentum concept... ie momentum= mass X velocity... c is the constant velocity, but whence cometh the mass?
From the general energy formula $$E=\sqrt{p^2c^2+(m_0c^2)^2}$$ you can set $$m_0=0$$ and find that the momentum of the photon is $$p=E/c$$. E is the photon energy, equal to its frequency times Planck's constant.

wouldn't you have to focus the light on a massive object to create a black hole? IN other words. Without something to stop it, where would the black hole form- near the source?
It should form in any volume of space happening to contain enough photons with enough energy.

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Staff Emeritus
This is an invalid step. In relativity, gravity does not necessarily depend on mass.

Yes. To amplify this point a bit, in GR, one can say that energy, momentum, and pressure (and not just mass) causes gravity. Specifically, the density of energy and momentum and also pressure are components of an entity calledthe "stress-energy tensor" that appears on the right hand side of Einstein's equation. This "stress energy tensor" can be regarded as the "source" of gravity in General relativity.

Since light has energy and momentum, it causes gravity. The idea that only "mass" causes gravity is a carryover from Newtonian theory, things are different in GR.

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On energy density and momentum flow.
From the general energy formula $$E=\sqrt{p^2c^2+(m_0c^2)^2}$$ you can set $$m_0=0$$ and find that the momentum of the photon is $$p=E/c$$. E is the photon energy, equal to its frequency times Planck's constant.It should form in any volume of space happening to contain enough photons with enough energy.
Ah, i see. the momentum of a massive object is its mass X velocity, but the momentum of a wavicle is its energy divided by its velocity. Hrmm that means the momentum is very small... so this has been measured and not just theorized by manipulating equations?
Also, has the gravity of a beam of light been measured in a lab? Can u reference me?
thanks, you have been most helpful,

anantchowdhary
gravity exerted by a light beam is extremely small.I don't know of any instance where it has been measured though!

Yes. To amplify this point a bit, in GR, one can say that energy, momentum, and pressure (and not just mass) causes gravity. Specifically, the density of energy and momentum and also pressure are components of an entity called the "stress-energy tensor" that appears on the right hand side of Einstein's equation. This "stress energy tensor" can be regarded as the "source" of gravity in General relativity.Since light has energy and momentum, it causes gravity. The idea that only "mass" causes gravity is a carryover from Newtonian theory, things are different in GR.
interesting. here are a bunch of related questions, hope you don't mind!
so light exerts pressure and momentum? If light doesn't have mass, yet exerts gravity, then mass isn't really a source of gravity... its just extreme energy density. Yet, mass particles seem distinct from photons... but maybe I'm off. What do they both have in common, such that both exert gravity? Does a photon occupy space?
hrm so there's energy density, momentum, and pressure- but the latter 2 depend on the former, which means that gravity depends on energy, right? Is electromagnetic energy the only kind which exerts gravity?
Pressure is caused by particle density and energy- does the same go for light? Could you knock me off a chair with a beam of light?
Light is thought of as an oscillating magnetic/electric field. Does either one of those exert gravity or have momentum? Why should they when combined?
sry, don't mean to pummel with questions,
i'm just trying to figure things out,
cheers,

gravity exerted by a light beam is extremely small.I don't know of any instance where it has been measured though!
wait... you are telling me that nobody has ever measure the gravity of light, yet its a huge tenant of modern physics theory? How does that equate? It seems easy enough to make a big laser beam and measure its gravity...
Isn't there more light in the universe than anything else- like the cbr?! You'd think it would all add up to quite a bit of gravity...
cheers,

Staff Emeritus
Mass is the source of gravity in Newtonian theory, but not in GR.

Any sort of energy can be said to "gravitate" in GR. Massive particles are different from photons, but as they both contain energy, they both contribute to gravity, since it is energy that causes gravity (along with the other things I mentioned).

It's not really very accurate to say that pressure is caused by particle density and energy density, but I'm not sure how much detail we want to get into at this point on the topic. Not only would we have to review the basic physical defintions of pressure, but to be totally accurate we'd have to explain some of the differences between the GR defintions and the usual engineering defintions - differences that don't matter, unless one is considering moving objects.

Note that you can get a "push" from light (see for instance interstellar "light sail" propulsion). I tend to think of this as being due to the momentum of the light, but I suppose one could technically call it due to light pressure (there is a pressure term in the region where light travels in both directions).

Unless you have a very good mirror, though, you will tend to be "fried" (or at least have have a hole drilled) by an intense laser beam rather than "pushed".

On the cosmological scale (i.e the scale of the entire universe) the gravity of radiation (i.e. photons) is not important at the current time. Early in the history of the universe this was not the case (at least in theory)- General relativity predicts a "radiation dominated" era in the first 400,000 years or so after the "big bang" as per the Wikipedia stub http://en.wikipedia.org/wiki/Radiation-Dominated_Era. You might also try looking for articles about the timeline of the Big Bang, they should also mention the radition dominated era.

The biggest contributor to the radiation density in the universe is the cosmic microwave background radiation. While it is very faint, it exists everywhere. In our particular local region, things like starlight and especially sunglight are more important, but on the average, it is the CMB that is the biggest contributor.

I'm a bit unclear on what actual experimental justification (if any) we have for the existence of a radiation dominated era in cosmology, but this is something that is predicted to have happened if GR is correct.

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country boy
Gravity is a mutual attraction, so in the classical sense the measurement of light bending around a star or galaxy is a measurement of light's gravity. But classical gravity and special relativity led to a bending around the Sun that was only half of what was measured. It is better to go with the purely GR approach and describe light paths as geodesics.

Gold Member
Ah, i see. the momentum of a massive object is its mass X velocity, but the momentum of a wavicle is its energy divided by its velocity. Hrmm that means the momentum is very small... so this has been measured and not just theorized by manipulating equations?
Also, has the gravity of a beam of light been measured in a lab? Can u reference me?
thanks, you have been most helpful,

As said above,

An electromagnetic wave will exert its own gravity, though extremely weak and not currently measurable. Gravity exerted by massive bodies is much higher because of their huge energy content (see the c squared term in Einstein formula).

which means that gravity depends on energy, right?
As said above, it depends on energy density and momentum flow.

Is electromagnetic energy the only kind which exerts gravity?
No, it is any kind of energy. In GR even the energy of gravitational waves exerts gravity, and even the energy of vacuum.

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anantchowdhary
wait... you are telling me that nobody has ever measure the gravity of light, yet its a huge tenant of modern physics theory? How does that equate? It seems easy enough to make a big laser beam and measure its gravity...
Isn't there more light in the universe than anything else- like the cbr?! You'd think it would all add up to quite a bit of gravity...
cheers,

Even if you have a lottttttt of energy from light it would be pretty difficult to measure the gravitational force.This is as each photon has some energy.Now,You can by no means change the energy of a photon unless you alter its frequency.Also when you bring a laser,the energy density is still the same.Think of it like this:

If you take a bucket of water and take out a glass of water or add some water into the bucket,would the density of the water change?No .

Therefore,energy over a very small region can exert more gravity than maybe a lottttttt of energy spread around a HUGE area.I hope my views are clear

Cheers!

cesiumfrog
Gravity is a mutual attraction, [..] better to go with the purely GR approach and describe light paths as geodesics.
But geodesics are only valid in the limit where you ignore the "mutual" part.

Any sort of energy can be said to "gravitate" in GR. Massive particles are different from photons, but as they both contain energy, they both contribute to gravity, since it is energy that causes gravity (along with the other things I mentioned).
does heat energy exert gravity?
another fellow said the energy of a vacuum does. that would be more like potential energy, no?

As said above...
sorry for the redundancy. just trying to nail the ideas into my skull.

As said above, it depends on energy density and momentum flow.
So energy density depends on the frequency and what else? Momentum flow... that is a propagating pattern in an infinite causation, no?
No, it is any kind of energy. In GR even the energy of gravitational waves exerts gravity, and even the energy of vacuum.
i thought gravitational waves from collapsing stars hasn't been proven yet... but yes i can kind of "see" how that fits.
now, the "energy of vacuum" is something you will have to explain in more detail for me! Vacuum is void, relative nothing. Something always tends towards it- thus entropy, diffusion, osmosis etc. How can the tendency of all things to fill non-thing- a tendency, exert gravity? That is fascinating!

Staff Emeritus
does heat energy exert gravity?
If you heat an object up, it will have more energy, and a greater gravitational field.
another fellow said the energy of a vacuum does. that would be more like potential energy, no?

If I'm decoding this correctly, you are asking if the energy in the vacuum causes gravity. The answer according to GR is yes - any form of energy should cause gravity. (And in some cases, such as dark energy, not only the energy of the vacuum is important, but it's pressure as well).

I should add that it appears that the contribution of any vacuum energy to gravity is very very low according to cosmological observations. The reason for the smallness of the effective value of vacuum energy as far as gravitation goes is a quantum gravity question that is not well understood at the current time.

MeJennifer
I should add that it appears that the contribution of any vacuum energy to gravity is very very low according to cosmological observations.
Well that could explain it. But is it not more likely that since the vacuum energy is more or less homogeneous the observable gravity effects are virtually non existent?

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Staff Emeritus
Well that could explain it. But is it not more likely that since the vacuum energy is more or less homogeneous the observable gravity effects are virtually non existent?

A homogenoeous field would have an observable cosmological effect on the cosmological decelleration factor q.

We have known since the late 1920s that the universe is expanding. Quantifying the expansion is done conventionally in terms of two numbers. H0, the Hubble constant, measures the current expansion rate of the universe, and q0 is the rate at which the expansion is slowing, or decelerating, because of the self-gravitational pull of all the matter in the universe. The standard cosmological solutions of Einstein's equations of general relativity are specified by H0 and q0. H0-1, the inverse of the Hubble constant, is a measure of the current age of the universe, while q0 is a measure of how long the universe will continue to expand.

While currently according to the concordance model there is thought to be a small negative value for 'q', we do not have a good theory which predicts the value of q from first principles. Explaining the observations for 'q' is very much an open question at the moment.

It is a prediction of general relativity (note that this is specific to GR) that a positive energy term in the stress-energy tensor of the vacuum (with no pressure terms) would cause a positive value for the cosmological deceleration parameter q. The most convincing way of demonstrating this unfortunately requires some knowledge of Einstein's field equations and a lot of math which I would'nt have time to go through at the moment anyway. So you'll have to trust me on this point, and if you don't trust me :-) ask Space Tiger in the cosmology forum about this issue for another opinion.

There are some other slants on the issue if one uses some darkhorse (though still peer reviewed) theories other than GR), but I don't want to hijack the thread in this direction. You can ask Garth in some other thread about "freely coasting cosmologies" if you like, though, or look up some of the past discussions. These cosmologies are unfortunately not compatible with Einstein's field equations.

Gold Member
Momentum flow... that is a propagating pattern in an infinite causation, no?

Momentum flow is pressure.

now, the "energy of vacuum" is something you will have to explain in more detail for me! Vacuum is void, relative nothing. Something always tends towards it- thus entropy, diffusion, osmosis etc. How can the tendency of all things to fill non-thing- a tendency, exert gravity? That is fascinating!

Well, vacuum is not nothing, nor a non-thing.. vacuum is space, which in GR is a thing like another.

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Does light exert gravity? last i heard, eletro-magnetic radiation doesn't have mass, and thus no gravity, yet it is apparently effected by gravity.

As several respondents already said, what matters here is that according to Maxwell's theory of electromagnetism, light beams carry EM field energy, and this field energy gravitates. Sometimes it is useful to think of gtr as a framework for incorporating gravitational effects into arbitrary theories, such as Maxwell's theory, so in gtr, we should expect that EM field energy will curve spacetime. This turns out to be true.

But you have to be careful not to misunderstand what this means. For one thing, it is possible to construct models showing that two parallel light beams will not attract each other, but two anti-parallel beams will attract one another. For another, I made a statement about what gtr predicts, not what has been confirmed in the laboratory. Unfortunately, this intriguing prediction about light beams is much too weak to hold out much hope of an experimental test in the near future.

does that mean that gravity is a pattern in space itself?

In gtr, gravitation is treated as the curvature of spacetime. Since curvature manifests itself in various patterns of test particle motion (for example), in some sense I guess you are not wrong. Some authors (see the textbook by Ohanian and Ruffini) even draw diagrams illustrating the pattern of tidal forces at different events.

Also, a black hole is a singularity...

Actually, the defining characteristic of a black hole is its event horizon, which is not a "geometric singularity" in the sense you probably mean. It is true that some of the best known models of black holes do feature curvature singularities deep inside their horizon(s), but while this is in some sense only to be expected, it is not really a definitive characteristic.

wouldn't you have to focus the light on a massive object to create a black hole?

Everything we know about gtr so far suggests that a black hole is formed whenever enough mass-energy is confined in a sufficiently small location (but figuring out the details involves the Cosmic Censorship Conjecture, one of the outstanding open problems in gravitation physics).

In principle, if you could somehow arrange for a huge spherical and collapsing shell containing EM energy to implode, it would form a black hole (see the discussion of Vaidya null dust in Frolov and Novikov, Black Hole Physics), but this is not the way in which astrophysical black holes are thought to form.

So it has been proven that light curves spacetime around itself?

Careful, this statement might be true or false or neither, depending upon how you qualify it (see my remarks above about theory versus experiment).

hypothetically, if i were in deep space traveling by a laser beam with the focused energy of a million suns, would i be sucked into it? (me being the only substantial matter around)

Again, I think you need to clarify what you mean by "sucked into". In the Bonnor beam model (see the version of a Wikipedia article I wrote which is listed at http://en.wikipedia.org/wiki/User:Hillman/Archive) [Broken], test particles which are released "from rest" outside the beam will indeed fall into the beam. In the Vaidya model in which a spherical shell of incoherent EM radiation implodes upon a locally flat shrinking ball-shaped region, an observer inside said region would notice the imploding shell as it collapses past his location, and might actually be inside the newly formed black hole even before the shell passes (this thought experiment illustrates the global nature of the event horizon, which as I said is the defining characteristic of a black hole).

If the gravity of light cannot currently be measured, then how do you know it's there?

I'll interpret that to mean: why should one believe that electromagnetic field energy gravitates? The best short answer is probably that for all kinds of reasons we know that gtr is very good gravitation theory (albeit, for all kinds of reasons we also expect that it has fundamental limitations, but these presumed limitations aren't directly relevant just here), and this theory unambiguously predicts that electromagnetic field energy gravitates. However, we haven't directly tested this in the lab, so I suppose it is conceivable that this prediction of gtr might somehow be wrong (even though I doubt you can write down a theory which reproduces gtr's many successes while differing on this one point).

Light fills the entire universe, which means that if it does exert gravity, there's a lot of it, but no focal point of attraction. Since light appears to be moving constantly, where would the focal point of gravity be?

I think you are asking what gtr says about the cumulative gravitational effect of all that EM field energy. Well, the best short answer is probably that for quite some time, in the simple FRW models, we have been in the "matter dominated epoch" in which the gravitational effect of EM radiation has been neglible compared to that of matter. But long ago, in the "radiation dominated epoch", this was not true. This point is not altered by current discussion of hypothetical "dark energy" and "dark matter", BTW, although these developments do affect the details of the "best fit" mixed matter-radiation-Lambda FRW models.

Also, has the gravity of a beam of light been measured in a lab?

No, and unfortunately there seems to be little chance of that happening any time soon.

Does a photon occupy space?

Is electromagnetic energy the only kind which exerts gravity?

No, any kind of mass-energy should gravitate. The energy of the gravitational field itself is treated different from all the others, incidently, but in a sense even this should gravitate (which can be understood as implying that the Einstein field equation must be nonlinear, which it is).

Pressure is caused by particle density and energy- does the same go for light?

Yes, but the contributions to the energy-momentum-stress tensor of a "non-null" EM field, a "null" or radiative EM field, a perfect fluid, and hypothetical scalar fields, are all rather different. See the versions listed at http://en.wikipedia.org/wiki/User:Hillman/Archive of articles I wrote on various kinds of exact solutions in general relativity.

Could you knock me off a chair with a beam of light?

In principle, yes, although you shouldn't expect to encounter such intense radiation on Earth.

wait... you are telling me that nobody has ever measure the gravity of light, yet its a huge tenant of modern physics theory? How does that equate? It seems easy enough to make a big laser beam and measure its gravity...

Well, you need to learn enough about gtr that you can plug some numbers into something like the Bonnor beam model in order to see why, while we can indeed make a big laser beam (e.g. at Lawrence Livermore Laboratory), we shouldn't expect to measure its gravitational effects.

does heat energy exert gravity?

You can probably answer this one yourself. Imagine an isolated ball in deep space, far from any other objects. Imagine that you use some laser beams to heat it up (carefully balancing so that the momentum they impart cancels) and then turn off the laser beams and measure the mass of the heated ball. Bearing in mind that heat is manifested by increased molecular motion inside the ball and that you just transferred a large amount of energy to the ball from someplace else, would you expect the gravitational mass of the heated ball to be larger?

So energy density depends on the frequency and what else? Momentum flow... that is a propagating pattern in an infinite causation, no?

You really need to slow down---now you seem to be confusing several distinct notions.

i thought gravitational waves from collapsing stars hasn't been proven yet...

Well, the existence of gravitational radiation has been established indirectly sufficiently firmly to earn two astronomers a Nobel prize (google the Hulse-Taylor pulsar)! No doubt you mean that gravitational wave detectors such as LIGO haven't yet directly measured the effects of a passing gravitational wave.

the "energy of vacuum" is something you will have to explain in more detail for me! Vacuum is void, relative nothing. Something always tends towards it- thus entropy, diffusion, osmosis etc. How can the tendency of all things to fill non-thing- a tendency, exert gravity? That is fascinating!

Physics is indeed fascinating, but you are confusing a whole buncha ideas here, and it would take a long time, I think, to sort it all out. Maybe you should just file this question away and continue your study of physics--- eventually, it will all sort itself out.

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Gravity is a mutual attraction, so in the classical sense the measurement of light bending around a star or galaxy is a measurement of light's gravity. But classical gravity and special relativity led to a bending around the Sun that was only half of what was measured. It is better to go with the purely GR approach and describe light paths as geodesics.
Hrm, since gravity is always mutually attractive, it represents a connection between all things. Is there any "thing" which isn't tied into gravity somehow?
You might have to bubba-ize geodesics for me. What i gather is that it describes the curved path of a photon relative to time, space, or nothing. This seems to build on rather than replace euclidean systems. Does a straight line exist in reality? Perhaps Light doesn't travel in a straight line, but does it exist?
thanks,

Well, vacuum is not nothing, nor a non-thing.. vacuum is space, which in GR is a thing like another.
How does one know that the energy is derived from the fabric of a spatial dimension, and not just the oodles of ghosting neutrinos and other phenomena?

Gold Member
How does one know that the energy is derived from the fabric of a spatial dimension, and not just the oodles of ghosting neutrinos and other phenomena?

Recent observations indicating that the universe is undergoing an accelerated expansion tend to favor the hypothesis that the energy producing such expansion is associated with space itself (or perhaps with another field dubbed 'quintessence'). As if it was energy of matter (at least the ordinary one) or of radiation, then the energy density would decrease when matter (or radiation) would dilute into the expanding space.

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How does one know that the energy is derived from the fabric of a spatial dimension

I don't think anyone said that; in fact, I don't know what "energy is derived from the fabric of a spatial dimension" would even mean.

Is there any "thing" which isn't tied into gravity somehow?

Don't forget that questions like this are always theory-dependent, so you should mention which theory you are asking about. The default in this context is probably gtr, but strictly speaking some of the stuff you have been talking about lies outside the domain of gtr. In particular, gtr can model the effects of hypothetical dark energy via the cosmological constant, but (regarding dark energy) it can't hope to answer Pauli's question: "who ordered that?!"

You might have to bubba-ize geodesics for me. What i gather is that it describes the curved path of a photon relative to time, space, or nothing.

A geodesic is simply a path on a (possibly curved) manifold which is analogous to a straight line in ordinary euclidean space. More precisely, any curve (even in a curved manifold) has a "path curvature" defined at each point along the curve. A geodesic is a curve such that this quantity vanishes all along the curve. In gtr, a timelike curve is interpreted as a world line of a particle (representing the kinematical history of the particle), a null curve can be interpreted (more or less) as the world line of laser pulse,
and the path curvature is interpreted as the magnitude of the acceleration vector. Here, a curve is said to spacelike, null, or timelike according to whether its tangent vectors are everywhere spacelike, null, or timelike. A vector is said to be spacelike, null, or timelike--- well, see Taylor & Wheeler, Spacetime Physics, first edition.

This seems to build on rather than replace euclidean systems.

It generalizes notions already familiar to you (if you studied elementary differential geometry) from euclidean spaces.

Does a straight line exist in reality? Perhaps Light doesn't travel in a straight line, but does it exist?

Oh dear, now it sounds like you are veering off into philosophy or even mysticism. I hope you can clarify the question so that it can be interpreted as an unambiguous question about physics.

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Hullo Chris,
thanks for the time and effort it took to write such a large post. As you can see, I know just enough about physics to make me dangerous(in the annoying sense). Thanks for you patience, you've no doubt had to explain these things 1x10^38 times already. Assume that if i don't reply to one of your points, i agree or am silently intrigued.
interesting thread- anantchowdhairy sounds allot like me... so instead of "photon", you call it "a test particle with a null geodesiac" or something like that. hopefully, the forum guidelines link wasn't because i was violating the "overt crackpottery" rule...yet. Without the esoterica, jargon, and math, i have a hard time understanding the gtr concept of light and gravity... and why plow through an entire textbook when i can just ask you? (rhetorical)
You can probably answer this one yourself. Imagine an isolated ball in deep space, far from any other objects. Imagine that you use some laser beams to heat it up (carefully balancing so that the momentum they impart cancels) and then turn off the laser beams and measure the mass of the heated ball. Bearing in mind that heat is manifested by increased molecular motion inside the ball and that you just transferred a large amount of energy to the ball from someplace else, would you expect the gravitational mass of the heated ball to be larger?
to answer your question: i suppose so, yes... however, since heat describes a pattern in something else, i don't quite see how heating a ball and measuring shows that heat energy exerts gravity. For all i know, some of the energy of the laserbeam was converted into matter upon impact, accounting for the increased gravitational mass, so it would still be heavier after it cooled. I suppose, however, if the mass decreased as the ball cooled, that it was indeed the heat which caused the increase...
You really need to slow down---now you seem to be confusing several distinct notions.
Granted. I'm trying to understand the connectivity and universal principals of things. I'll be more clear in my next posts.
Physics is indeed fascinating, but you are confusing a whole buncha ideas here, and it would take a long time, I think, to sort it all out. Maybe you should just file this question away and continue your study of physics--- eventually, it will all sort itself out.
good advice, but there might be a tad more milk in this thread. one particular concept has arisen which inspires me, so i'll ask you about it in the relevant post.
cheers,