Why Does Light Fall? Exploring Special Relativity

[oldman]

Light does gravitate --- there is plenty of sound evidence for this, such as gravitational lensing in astronomy. Gravity makes space refract, it seems.

What theoretical explanation can be offered for this observation? The equivalence principle is often used, but invoking a principle smacks of avoiding something you don't really understand.

Does special relativity require that light gravitates (because photons have measurable energy -- hence inertial mass -- and experiment shows that inertial masses gravitate) ? And if not, why not?

 

[Xnn]

Einstein's theory of special relativity does not address gravitation.

On the other hand, the theory of general relativity does.

 

[danb]

Light does gravitate ... Gravity makes space refract

Gravity makes space curved. Light travels in "straight" lines, where "straight" means "as straight as possible given the curvature of space itself". The curvature of a light beam is the curvature of the medium it passes through; it's not a property of the light beam.

 

[Wallace]

What theoretical explanation can be offered for this observation? The equivalence principle is often used, but invoking a principle smacks of avoiding something you don't really understand.

I'm not sure I follow this line of reasoning. General Relativity stems entirely from a few foundations, including the equivalance principle. If you understand the equivalance principle then you understand why GR predicts gravitational lensing. If someone invokes the principle of inertia to explain why you need to apply the brakes on your car to stop moving (as opposed to just taking your foot of the accelerator) does this mean they don't understand why you need brakes? No, if you understand the principle of inertia you can invoke it to explain an example of its operation.

 

[Ich]

The equivalence principle is often used, but invoking a principle smacks of avoiding something you don't really understand.

You really got it backwards. The principle has not been invoked to explain a posteriori some experimental facts that would otherwise contradict the theory.
GR is based on that principle, and GR predicts bending of light. It has been measured after the theory has been fully developed.
On small scales the principle states that falling objects are free floating, with no forces acting on them. Thus they move just like in free space. You don't have to explain that light does nothing interesting if nothing acts on it.
It's rather the ground that is accelerating upwards, that's why the "relative acceleration" (as measured in the ground system) is naturally independent of the properties of the free floating objects.
The trick is to make this principle work on large scales also, that's where spacetime curvature comes into play.

 

[Phrak]

The equivalence principle is often used...

What's the equivalence principle?

 

[Wallace]

In simple terms the equivalance principle states that an accelerated reference frame is equivalent to an un-accelerated reference frame in a gravitational field. Ich's post #5 gives some further exposition of this.

The example given when I had GR lectures in grad school was to imagine you are in a box that you cannot see out of. You can do a bunch of experiments with pendulums, dropping balls etc and you infer that you must be simply sitting on the surface of the earth, since you measure a graviational acceleration of 9.8 m/s/s. But, think about the possibility that you are instead in deep space (vaccum) and your box is being accelerated at a constant rate of 9.8 m/s/s by some kind of rocket. All of your experiments will give exactly the same result.

Einsteins leap was to realize not that these two situations are indistinguishable, but rather than they are identical. As Ich suggested, if you imagine again you are sitting on the surface of the Earth, then in fact in the language of GR you are continually being accelerated upwards at 9.8 m/s/s by the force exerted by the surface of the Earth on your feet.

In Newtonian physics we think of gravity as causing acceleration, but in GR in the language of the equivalence principle you are only 'accelerated' if your motion if altered by something other than gravity.

Now, in relation to light, you can imagine in the rocket in space example, that if you have a small window that allows just a single beam of light into the side of your box, you will observe the path of the light to be curve. Hence by the equivalence principle we must see the same effect in the presence of a gravitationl field, hence we see gravitational lensing.

 

[George Jones]

As usual, I don't have very much to say, and will only give a reference that might be relevant,

http://arxiv.org/abs/gr-qc/9909014.

Steve Carlip often does have interesting things to say.

 

[oldman]

Einstein's theory of special relativity does not address gravitation.

On the other hand, the theory of general relativity does.

You're quite right, Xnn. Taken on its own, SR says nothing about gravity. But if you add in the results of Eotvos-type experiments, it can be used, as I summarised, to persuade people that light gravitates. Nice (but inaccurate?) for simple minded folk who don't appreciate the equivalence principle (EP) and all that goes with it. I guess that SR used this way will give answers out by a factor of 2, as Newtonian calculations do. Do you know if this is so?

... if you understand the principle of inertia you can invoke it to explain an example of its operation.

Thanks, Wallace, for this and your second post. But I'm afraid that my prejudice against principles (useful though they are) carries through to the inertia priniple as well. I don't really know what inertia is or what causes it. It's just a 'law' --- one that works pretty well, I must admit.

You really got it backwards. The principle has not been invoked to explain a posteriori some experimental facts that would otherwise contradict the theory.

I probably have got it backwards, as you say, or have put my thinking confusingly. But the fact that light gravitates is often introduced via the EP (e. g. by Rindler in section 1.21 of his Relativity and by Wallace in this thread (his post#7). I'm just suggesting that there is no need to rely on a principle (my prejudice) if one can offer a simpler rationale via something more readily understood, namely SR.

Thanks for the reference, George. Carlip's section 3: General Covariance and the Weight of Light is indeed relevant to the guess I made when replying to Xnn above.

 

[Wallace]

Thanks, Wallace, for this and your second post. But I'm afraid that my prejudice against principles (useful though they are) carries through to the inertia priniple as well. I don't really know what inertia is or what causes it. It's just a 'law' --- one that works pretty well, I must admit.

At the risk of getting overly philosophical, I think you are asking of empirical science something that it cannot provide. The best we can do is postulate principles and laws and then test them as rigourously as we are able. The only way we can ever 'explain' a principle or law is via a more fundamental principle or law, but then that principle is left 'unexplained'. I'm afraid I don't see how this infinite regression can be terminated by empirical science. Science is just a series of tested principles.

There is a whole story we could get into about empiricism vs Artistotelean deductovism (sp?) but it's been a long time since studied the details and I normally only bang on about this kind of stuff after a few beers.

 

[Bob S]

Light falls and gains energy in a gravatational field as shown by Pound and Rebka in their famous Mossbauer Effect experiment with iron-57 about 1959.

 

[Naty1]

Light does gravitate ...What theoretical explanation can be offered for this observation?

For me, the danb's answer in Post # 3 is just fine. Of course you can, as usual, keeping asking "why" and quickly get to unanswerables...yet I think general relativity is about as good a theory as is available.

On the other hand, it could be argued that the "theoretical explanation" depends on which model you'd prefer to use...particle, electromagnetic wave, quantum, etc...then the answer might be framed different ways. It would be interesting to reconcile them.

In Post #9, Oldman expresses displeasure with certain laws and principles and while I understand that (because we may not know why they work) feeling, that's really true of most of physics...if math predicts and measurement confirms, then we have a tool even though we might not understand exactly why...even if we start as Einstein did with an equivalence principle, we may never know exactly why it works...it's just a good guess...

And since nobody really knows what light nor gravity is, asking why one effects the other may be futile for the purist...

 

[atyy]

Does special relativity require that light gravitates (because photons have measurable energy -- hence inertial mass -- and experiment shows that inertial masses gravitate) ? And if not, why not?

Special relativity does not require that light gravitates, because it is possible to make a relativistic theory of gravity in which the trace of the energy tensor (instead of the energy tensor itself) is gravitational mass. The trace of the energy tensor of light is zero, so light would not gravitate. However I don't know if the equivalence principle requires that light gravitates, since this alternative relativistic theory also satisfies some form of the equivalence principle. See the comments on Nordstrom's second theory:
http://www.einstein-online.info/en/spotlights/equivalence_deflection/index.html
http://arxiv.org/abs/gr-qc/0405030
http://arxiv.org/abs/gr-qc/0611100

 

[oldman]

At the risk of getting overly philosophical...I normally only bang on about this kind of stuff after a few beers.

I agree with all you say here, and don't want to get philosophical. I remember that Henry Ford said that "History is bunk" and can only wonder if he had more pungent views on philosophy which I could also agree with. And I regret that this kind of communication can't involve sharing a few beers.

For me, the danb's answer in Post # 3 is just fine. Of course you can, as usual, keeping asking "why" and quickly get to unanswerables...yet I think general relativity is about as good a theory as is available... ...And since nobody really knows what light nor gravity is, asking why one effects the other may be futile for the purist...

Yes, I agree here too. But I do prefer explanations based as far as possible on observation, that delay for as long as possible getting down to the level of principles, which I feel have an ex cathedra flavour.

As far as light falling (which one cannot doubt, as Bob S points out) and the fact that there are good reasons why:

.. Special relativity does not require that light gravitates, because it is possible to make a relativistic theory of gravity in which the trace of the energy tensor (instead of the energy tensor itself) is gravitational mass. The trace of the energy tensor of light is zero, so light would not gravitate...

I still don't understand why it is so wrong to reason, for introductory purposes only?, that light falls "because photons have measurable energy -- hence inertial mass -- and experiment shows that inertial masses gravitate". All good observational stuff far removed from philosophy and the history of Nordstrom's theories. But perhaps I'm just too simple-minded.

 

[JesseM]

I still don't understand why it is so wrong to reason, for introductory purposes only?, that light falls "because photons have measurable energy -- hence inertial mass -- and experiment shows that inertial masses gravitate". All good observational stuff far removed from philosophy and the history of Nordstrom's theories. But perhaps I'm just too simple-minded.

There's no logical connection between the idea that light gravitates and the idea that it falls in the presence of an external source of gravity (after all, the rate at which an object falls in an external field is totally independent of its own mass, and thus independent of its own gravitational pull). It's also not clear what you mean by "inertial mass" here--if you mean "rest mass" you're incorrect, since something with zero rest mass but nonzero momentum can have nonzero energy in relativity.

 

[JesseM]

What's the equivalence principle?

See http://www.aei.mpg.de/einsteinOnline/en/spotlights/equivalence_principle/index.html for a good overview.

 

[atyy]

I still don't understand why it is so wrong to reason, for introductory purposes only?, that light falls "because photons have measurable energy -- hence inertial mass -- and experiment shows that inertial masses gravitate". All good observational stuff far removed from philosophy and the history of Nordstrom's theories. But perhaps I'm just too simple-minded.

That light should fall because it has energy, and energy has mass is certainly a useful heuristic. However, it is only a heuristic, and not a requirement.

Edit: Your argument about the universality of free fall is an EP argument. Redshift and local light bending are required by the EP, global light bending is not required, that light should curve space is also not required.

 

[Phrak]

That light should fall because it has energy, and energy has mass is certainly a useful heuristic. However, it is only a heuristic, and not a requirement.

Thanks for pointing this out, atyy--here, and in a previous post. From a rather good source, and paraphrased, "it's difficult to conceive of a situation where the Newtonian equivalence principle is not equivalent to the Einstein equivalence principle." But just about anything with a stress energy tensor unlike common matter is a possible candidate to violate both.

 

[Al68]

Why does light fall?

The real question is, "Why does the surface of a massive body accelerate outward?" or "Why does Earth's surface accelerate upward?"

It's easily observed that Earth's surface accelerates upward with respect to any unaccelerated object (freefall) at the rate of 9.8 m/s^2, and we of course "feel" the force of this acceleration against our feet when we stand. It should be no surprise that we would see the path of a light ray "bend" relative to an accelerating reference frame, just like it would relative to an accelerating spacecraft .

 

[Phrak]

The real question is, "Why does the surface of a massive body accelerate outward?" or "Why does Earth's surface accelerate upward?"

And what would some dark energy do in the presence of some outwardly accelerating body. Would it be carried along? Would it accelerate outwardly faster than the Eath's surface?

 

[oldman]

There's no logical connection between the idea that light gravitates and the idea that it falls in the presence of an external source of gravity (after all, the rate at which an object falls in an external field is totally independent of its own mass, and thus independent of its own gravitational pull). It's also not clear what you mean by "inertial mass" here--if you mean "rest mass" you're incorrect, since something with zero rest mass but nonzero momentum can have nonzero energy in relativity.

About the "logical connection": I don't quite see the difficulty here.

I did mean inertial mass, not rest mass. I invoked experiments of the Eotvos type (which show that inertial mass is always numerically identical to gravitational mass) to associate relativistic energy with gravitating or falling photons. As you say, this energy is linked to momentum (and something experimentally observed, namely light pressure).

 

[oldman]

That light should fall because it has energy, and energy has mass is certainly a useful heuristic. However, it is only a heuristic, and not a requirement.

Edit: Your argument about the universality of free fall is an EP argument. Redshift and local light bending are required by the EP, global light bending is not required, that light should curve space is also not required.

The universality of free fall is not only an EP argument, but an experimental fact. I prefer facts to principles -- but then, as I've admitted, this is just my prejudice!

 

[JesseM]

About the "logical connection": I don't quite see the difficulty here.

When you say "light gravitates", you mean that light has its own gravitational pull, no? Don't you agree that showing something has its own gravitational pull is conceptually distinct from showing it falls downward in an external source of gravity? An object with infinitesimal mass would have no measurable gravitational pull on other objects, for example, yet it would still fall downwards just like other objects in the presence of an external gravitational field.

I did mean inertial mass, not rest mass. I invoked experiments of the Eotvos type (which show that inertial mass is always numerically identical to gravitational mass) to associate relativistic energy with gravitating or falling photons.

How do you define "inertial mass", specifically? Normally I think it would be defined in terms of something like the force or energy required to change an object's velocity by a small amount from an initial rest state, but there is no frame where light starts out at rest, and it is also impossible to change light's velocity by any amount from the perspective of an inertial frame.

 

[oldman]

When you say "light gravitates", you mean that light has its own gravitational pull, no? Don't you agree that showing something has its own gravitational pull is conceptually distinct from showing it falls downward in an external source of gravity? An object with infinitesimal mass would have no measurable gravitational pull on other objects, for example, yet it would still fall downwards just like other objects in the presence of an external gravitational field.

How do you define "inertial mass", specifically? Normally I think it would be defined in terms of something like the force or energy required to change an object's velocity by a small amount from an initial rest state, but there is no frame where light starts out at rest, and it is also impossible to change light's velocity by any amount from the perspective of an inertial frame.

I now see what you're getting at, Jesse. Thanks for the reply. You are drawing a correct
distinction between active and passive gravitational mass. Observation shows that light has passive gravitational mass. I don't know of any experiment that shows it to have active gravitational mass. But this distinction is a fine one which I chose, foolishly, not to make. Sloppy!

I see also that I shouldn't have used "inertial" here for the reasons you state. But light certainly has electromagnetic energy and warms you when you stand in front of a fire. This energy must have mass --- otherwise why would the world be getting its knickers in a knot about the nuclear capabilities of rogue states? And I don't know of any kind of mass that doesn't fall.

For the fine distinctions the paper by Carlip
(kindly referred to me by George Jones in post #8) shows how intricate the matter of kinetic andelectromagnetic energy is. Carlip drew the conclusion that:

“We can thus tell our students with confidence that kinetic energy has weight, not just as a
theoretical expectation, but as an experimental fact.”

 

[cragar]

lets say we have a sphere that is mirrored and we have anti-matter and matter in there and the matter and anti-matter create a gravitational field when the collide they produce photons and the gravitational field would still be there.

 

[I. N. Stine]

By pure luck I happen to have a library book that can explain this question in the words of Albert Einstein himself!

The book is " Relativity". It is written by Albert Einstein. Usually there is a note in a book about what edition it is but I cannot find it. All I can find is "first Plume printing 2006".

Page 163 about half from the top of the page.

"It may be added that, according to the theory, half of this deflection is produced by the Newtonian field of attraction of the sun, and the other half by the geometrical modification ( "curvature" ) of space caused by the sun."

Here is Einstein's own words to explain why light bent down and fell during the eclipse! I admit that I don't really understand any of it but it impresses me.

I am sure that a lot of you know what Einstein meant by saying that half of the light falling was because of Newtonian field of attraction.

And all of you must know what he meant by saying that half of light falling was because of space, which I still cannot imagine as "something" instead of "nothing", curving.

Please, try to explain these things so that I have a chance to understand it. I really enjoy daydreaming about seeing time go fast and slow, and sizes of things stretch and stuff like that so that anything strange is possible. The real world is so hard and mean. Things just stay the same and hurt. Please help me understand how Relativity can let me imagine that everything is OK and good like in a dream.

Thanks so much!