Does Gravity Bend Light or Curve Space-Time?

[Almeisan]

Does gravity bend light by pulling at the photons or does gravity curve the space-time the light travels through, making it appear that the light is bend?

I thought it was the latter but I wasn't able to confirm it. I also run into a problem with black holes. A black hole must curve space-time back into itself to be a black hole if the latter is correct.

Anyone? Thanks.

 

[Garth]

Does gravity bend light by pulling at the photons or does gravity curve the space-time the light travels through, making it appear that the light is bend?

I thought it was the latter but I wasn't able to confirm it. I also run into a problem with black holes. A black hole must curve space-time back into itself to be a black hole if the latter is correct.

Anyone? Thanks.

It is the latter. "gravity curves the space-time the light travels through"

You can cobble together Newton and SR and treat photons as having a mass equivalent to their energy that is then attracted towards the Sun by a Newtonian gravitational force; but you only obtain half the observed value of angle of deflection, you haven't taken space curvature into account, which doubles that value to the full GR deflection.

There is no problem with BHs, inside the event horizon the curvature tips the outgoing light cone over so that it does not reach out to the outside world.

I hope this helps.

Garth

 

[Almeisan]

So in the case of a black hole space-time doesn't have to curve back into itself for it to be able to tip the light cone back into itself?

If space-time around a black hole is tipped back into itself then that would separate the space-time of the BH from the rest of the galaxy?

Or am I applying everyday logic that has no validity?

 

[Garth]

You have to solve the equations of the Schwarzschild or Kerr metrics and work out where the null geodesics go. It is not easy to imagine without expert help, you might find Robert Wald's "Space Time and Gravity" helpful, or go the whole way and read his "General Relativity".

Garth

 

[pervect]

So in the case of a black hole space-time doesn't have to curve back into itself for it to be able to tip the light cone back into itself?

If space-time around a black hole is tipped back into itself then that would separate the space-time of the BH from the rest of the galaxy?

Or am I applying everyday logic that has no validity?

The Schwarzschild r-coordinate is a time coordinate inside the event horizon (though it's a space coordinate outside the horizon). Inside the event horizon of a black hole, time points towards the center (r=0).

This can be thought of as "tipping light cones" as well, robphy has a diagram he likes to post that I'm too lazy to look up at the moment.

Light can still reach the inside of a black hole from the outside, so the space-time in a black hole is not totally "separate" from that of the outside world.

However, no event inside the black hole event horizon can affect anything outside the event horion, because no signal can propagate from the interior through the horizon.

 

[Zanket]

Or am I applying everyday logic that has no validity?

IMO, there's a lot easier way to intuit what's theorized than thinking of tipping light cones. The event horizon of a black hole is just where everything inflows at c. Search for “free-fall coordinates” here for a decent explanation.

 

[qtron]

bending light in the lab.

Probably discussed before?
Wish to know if I can bend white light, or any visible light, in the lab, without using optics. IE, using strong magnets or electro-magnetic radiation/fields.
PLEASE help!

 

[Jheriko]

So in the case of a black hole space-time doesn't have to curve back into itself for it to be able to tip the light cone back into itself?

If space-time around a black hole is tipped back into itself then that would separate the space-time of the BH from the rest of the galaxy?

Or am I applying everyday logic that has no validity?

I think the problem you are having is that you are visualising in 3d still. The black hole doesn't need to bend space-time in on itself to bring something back to a position that it was previously at.

Imagine that some light is trapped in a black hole, and that it is confined to a plane and orbiting in a circle for simplicity. If we plot what happens over time in 3d, using the plane that the light is orbiting into reduce the 3d position down to 2d, then we can see a different view of the space time, and the light traces out a spiral path through it. There is no closed loop in time.

 

[notknowing]

It is the latter. "gravity curves the space-time the light travels through"

You can cobble together Newton and SR and treat photons as having a mass equivalent to their energy that is then attracted towards the Sun by a Newtonian gravitational force; but you only obtain half the observed value of angle of deflection, you haven't taken space curvature into account, which doubles that value to the full GR deflection.

There is no problem with BHs, inside the event horizon the curvature tips the outgoing light cone over so that it does not reach out to the outside world.

I hope this helps.

Garth

I have looked at Einsteins original 1911 paper on the bending of light in which he used the fact that light is slowed down in a gravitational field and where he used Huygens principle to derive the deflected angle and which resulted in a deflection angle which was a factor two too low. It is easy to show that the factor 2 was missed because the speed of light (in a gravitational field) as seen by a distant observer was only based on gravitational time dilatation. If one takes into account both gravitational time dilatation and gravitational length contraction, the additional factor 2 comes out correctly (without having to solve the Einstein field equations).

 

[pervect]

One usually solves for the motion of light (or for that matter test particles) by using the geodesic equations. This is not the only way to solve for the motion of light - as you mention, there is the possibility of using Huygen's principle (mathematically the Hamilton-Jacobi method). I haven't read the original Einstein paper of which you speak (if I have, I've forgotten it), but this is mentioned for instance by MTW on pg 1102.

Neither of these approaches for finding the motions of particles involves solving Einstein's field equations if one already has the metric. Of course, the field equations are generally needed to find the metric in the first place. In this example the EFE were used to get the Schwarzschild metric.

Another interesting point is that the fact that particles follow geodesics in the first place can be proved from the field equations in GR (rather than having to be assumed as a separate assumption). See for instance MTW pg 471. Given a region of space-time containing nothing but electromagnetic fields and the Maxwell stress-energy tensor, Maxwell's equations "pop out" of the Einstein field equations - they don't have to be separately assumed.

This is drifting away from the main point. The main point is that there is a very close link between what you are calling "gravitational length dilation", and what Garth is calling "the curvature of space.

 

[notknowing]

This is drifting away from the main point. The main point is that there is a very close link between what you are calling "gravitational length dilation", and what Garth is calling "the curvature of space.

Yes, you are right in that. I wonder whether one could derive the gravitational length contraction by using only the equivalence between acceleration and gravitational field. For time dilatation, simple arguments (both in special relativity and in general relativity) give the correct relations. Have you ever seen a "simple" derivation of gravitational length contraction (in the same "spirit" as for time dilatation) ?

 

[pervect]

Consider the Rindler metric (in geometric units)

(1+gz)^2 dt^2 - dx^2 - dy^2 - dz^2

This metric is a vacuum solution to Einstein's field equations, and can be thought of as the (not necessarily unique) metric associated with an accelerated coordinate system.

Because the coefficient of dx^2, dy^2 and dz^2 is unity, there is however no "gravitational length contraction" at all in this metric - if I understand your usage of the term correctly (it's possible I'm misunderstanding something here).

So if I'm following your usage correctly, Schwarzschild coordinates have gravitational length contraction, but Rindler coordinates do not.

The discussion is complicated by the fact that defining gravitational length contraction by looking at the metric coefficients is a coordinate dependent notion, so the same space-time can have gravitational length contraction in one set of coordinates, and not have it in another.

 

[kmarinas86]

It is the latter. "gravity curves the space-time the light travels through"

You can cobble together Newton and SR and treat photons as having a mass equivalent to their energy that is then attracted towards the Sun by a Newtonian gravitational force; but you only obtain half the observed value of angle of deflection, you haven't taken space curvature into account, which doubles that value to the full GR deflection.

There is no problem with BHs, inside the event horizon the curvature tips the outgoing light cone over so that it does not reach out to the outside world.

I hope this helps.

Garth

Does this extra factor of two only apply to light and not massive objects, and if so, why?

 

[pervect]

A particle moving at almost the speed of light will be deflected in almost the same manner as a particle moving at the speed of light - i.e. a neutrino, having a very small rest mass, moving at almost the speed of light, will follow essentially the same trajectory as a photon (which has zero rest mass).

 

[notknowing]

Consider the Rindler metric (in geometric units)

(1+gz)^2 dt^2 - dx^2 - dy^2 - dz^2

This metric is a vacuum solution to Einstein's field equations, and can be thought of as the (not necessarily unique) metric associated with an accelerated coordinate system.

Because the coefficient of dx^2, dy^2 and dz^2 is unity, there is however no "gravitational length contraction" at all in this metric - if I understand your usage of the term correctly (it's possible I'm misunderstanding something here).

So if I'm following your usage correctly, Schwarzschild coordinates have gravitational length contraction, but Rindler coordinates do not.

The discussion is complicated by the fact that defining gravitational length contraction by looking at the metric coefficients is a coordinate dependent notion, so the same space-time can have gravitational length contraction in one set of coordinates, and not have it in another.

Hi, thanks, but this is not what I had in mind. I meant some simple derivation (without a pre-knowledge of the metric) using some simple set-up with light pulses bouncing of mirrors (as used for instance in some derivations for time dilatation). PS : I found the original paper (see below) of Einstein on Internet. I is of course in German (I have lived for 12 years in Germany, so for me that is no problem) but English translations should certainly exist.

http://www.physik.uni-augsburg.de/annalen/history/papers/1911_35_898-908.pdf

I wonder whether such a paper would be accepted today: it is not full of maths, it contains revolutionary ideas, it is not written in Latex and it contains some typographic errors and a reference without the year of publication ...

 

[notknowing]

Hi, thanks, but this is not what I had in mind. I meant some simple derivation (without a pre-knowledge of the metric) using some simple set-up with light pulses bouncing of mirrors (as used for instance in some derivations for time dilatation). PS : I found the original paper (see below) of Einstein on Internet. I is of course in German (I have lived for 12 years in Germany, so for me that is no problem) but English translations should certainly exist.

http://www.physik.uni-augsburg.de/annalen/history/papers/1911_35_898-908.pdf

I wonder whether such a paper would be accepted today: it is not full of maths, it contains revolutionary ideas, it is not written in Latex and it contains some typographic errors and a reference without the year of publication ...

Consider the Rindler metric (in geometric units)

(1+gz)^2 dt^2 - dx^2 - dy^2 - dz^2

This metric is a vacuum solution to Einstein's field equations, and can be thought of as the (not necessarily unique) metric associated with an accelerated coordinate system.

Because the coefficient of dx^2, dy^2 and dz^2 is unity, there is however no "gravitational length contraction" at all in this metric - if I understand your usage of the term correctly (it's possible I'm misunderstanding something here).

So if I'm following your usage correctly, Schwarzschild coordinates have gravitational length contraction, but Rindler coordinates do not.

The discussion is complicated by the fact that defining gravitational length contraction by looking at the metric coefficients is a coordinate dependent notion, so the same space-time can have gravitational length contraction in one set of coordinates, and not have it in another.

Hi, I just found a very simple derivation of gravitational length contraction, without pre-knowledge of the metric. It is only based on the equivalence between acceleration and gravitation (rougly speaking). So, combining then gravitational time dilatation and gravitational length contraction, one can use this to the correct of speed of light in a gravitational field and the bending of light (around the sun for instance) can then be described by a simple refractive effect and it would give exactly the same result as the light bending obtained by general relativity. So, one could hold the alternative view that gravitation modifies the properties of the surrounding vacuum (such as electrical permittivity and magnetic permeability) such that the speed of light (and other things) is modified as a consequence of this. The mathematical equations would remain the same but the interpretation is very different. One replaces effectively "curvature of spacetime" by "modification of the quantum vacuum".

 

[Jheriko]

So, one could hold the alternative view that gravitation modifies the properties of the surrounding vacuum (such as electrical permittivity and magnetic permeability) such that the speed of light (and other things) is modified as a consequence of this. The mathematical equations would remain the same but the interpretation is very different. One replaces effectively "curvature of spacetime" by "modification of the quantum vacuum".

Right, but doesn't the new interpretation derive from GR in the first place... in which case, why go to all of that bother when you already have a perfectly good theory with a simpler interpretation?

I am not even sure if your idea is correct in the first place... AFAIK modifying electrical permittivity to create gravitational effects would require that other effects be observed.

 

[notknowing]

Right, but doesn't the new interpretation derive from GR in the first place... in which case, why go to all of that bother when you already have a perfectly good theory with a simpler interpretation?

I am not even sure if your idea is correct in the first place... AFAIK modifying electrical permittivity to create gravitational effects would require that other effects be observed.

Yes, indeed, GR is a very good and precise theory but a stumbling block for a quantum gravity theory is precisely that GR is based on a purely geometrical description. By using a different interpretation (in terms of the quantum vacuum) one could come a step closer in realizing this goal.

 

[Jheriko]

I think that it is naive to assume that curvature is a stumbling block for quantum gravity and that it must be based on a background flat space-time.

If we don't make that assumption it doesn't hurt us, since flat is just a special case of curved we could "come out with" a flat space-time for a QG theory anyway.

There is a paper floating around somewhere that demonstrates that even if you do start from a flat space time with the weak field approximation, the flat space-time becomes physically unobservable and a curved space-time is 'induced' by the presense of a gravitational field... I will see if I can find it.

That and I'm sure that I have read in numerous places that the real issue is renormalisation, since all of the 'charges' (masses) are positive there are no known ways to remove the infinities from the renormalisation.

Renormalisation is something that should be done away with more than curvature in my opinion... it is a rather arbitrary process, the sort of thing I would do (have done) in a computer program to force something to give results in an expected range. The only valid use I see is to normalise *one* thing, e.g. a vector, to get a unit vector. Renormalising a whole field just seems wrong from my narrow perspective... in my opinion a better solution (probably not possible though) would be a wave equation which produces already normalised values. Sure, nothing would ever add up to 100%, but you would have the right answers and would have done away with an ugly feature.

 

[pervect]

The super-simple (perhaps over-simplified) version of what I've been trying to say is that while gravitation is always associated with time dilation, it may or may not be associated with length contraction. For instance, there is no length contraction due to gravity in the elevator gerdankenexperiment, (though there is time dilation).

 

[notknowing]

The super-simple (perhaps over-simplified) version of what I've been trying to say is that while gravitation is always associated with time dilation, it may or may not be associated with length contraction. For instance, there is no length contraction due to gravity in the elevator gerdankenexperiment, (though there is time dilation).

Hi Pervect, I don't agree with that. In a previous post (no 16), I mentioned that I found a very simple derivation of gravitational length contraction (which was no joke). This derivation was just based on an accelerated elevator. It is a simple derivation and if I find the time, I shall try to include it in Latex.

 

[notknowing]

Right, but doesn't the new interpretation derive from GR in the first place... in which case, why go to all of that bother when you already have a perfectly good theory with a simpler interpretation?

I am not even sure if your idea is correct in the first place... AFAIK modifying electrical permittivity to create gravitational effects would require that other effects be observed.

Please consider a theory by Puthoff (which I found recently) and which shows that thus concept really works :
http://arxiv.org/ftp/gr-qc/papers/9909/9909037.pdf
PS: Puthoff is not a cranck (many journal publications)

This makes GR a lot more understandable!

 

[MeJennifer]

The super-simple (perhaps over-simplified) version of what I've been trying to say is that while gravitation is always associated with time dilation, it may or may not be associated with length contraction. For instance, there is no length contraction due to gravity in the elevator gerdankenexperiment, (though there is time dilation).

Does the distance between the bottom and the top stay the same?
If not, then there is relative motion between them and thus it seems logical to assume there is a Lorentz factor involved.

Am I making a logical mistake here?

 

[pervect]

Hi, I just found a very simple derivation of gravitational length contraction, without pre-knowledge of the metric. It is only based on the equivalence between acceleration and gravitation (rougly speaking). So, combining then gravitational time dilatation and gravitational length contraction, one can use this to the correct of speed of light in a gravitational field and the bending of light (around the sun for instance) can then be described by a simple refractive effect and it would give exactly the same result as the light bending obtained by general relativity. So, one could hold the alternative view that gravitation modifies the properties of the surrounding vacuum (such as electrical permittivity and magnetic permeability) such that the speed of light (and other things) is modified as a consequence of this. The mathematical equations would remain the same but the interpretation is very different. One replaces effectively "curvature of spacetime" by "modification of the quantum vacuum".

Somehow I missed this the first go-around.

Where did you find "a derivation of gravitational length contraction"? It's possible that I don't understand what you mean by that term - if you mean what I thought you meant, though, the Rindler metric should serve as a counter-example, as I mentioned before.

If you don't mean what I thought you mean, I need a better explanation of what you do mean so I can follow your argument.

I was going to ask for a reference about your previous statements about interpreting GR as some sort of modification of the vacuum, but I see that the paper by Puthoff answers my questions. I'll have to read it and get back to you. While Puthoff is often on the fringe, this paper doesn't appear to be too wild on the surface. On the other hand, I'm not totally convinced that this particluar paper has been peer reviewed. In my 15 second evaluation I think it's worth a further look.

Unfortunately I'll be a bit busy for the next day or so, it may be a while before I get back to this.

 

[jtbell]

PS: Puthoff is not a cranck (many journal publications)

In the 1970s and 1980s, Harold Puthoff and his collaborator Russell Targ spent a lot of time studying and promoting the supposed psychic phenomenon of "remote viewing." They claimed that some people could describe locations accurately without ever having visited them or seen pictures or descriptions of them. This makes warning bells go off in my head whenever I see Puthoff's name mentioned.

 

[pervect]

Does the distance between the bottom and the top stay the same?
If not, then there is relative motion between them and thus it seems logical to assume there is a Lorentz factor involved.

Am I making a logical mistake here?

In the Rindler metric, the metric coefficeints for space are independent of height, however the metric coefficient for time is not.

I don't know how to put this in terms of "distance" offhand. Where did the "bottom and top" come from? I'm just pointing at an equation and comparing the Rindler metric to the Schwarzschild metric. In the former, only the g_tt coefficient of the metric depends on position, in the later both g_tt and g_rr depend on positon.

To measure distance in the Rindler metric, BTW, one would compute the length of the curve connecting the "top" and "bottom" (whatever they are) by a straght line in a hypersurface of constant rindler-time. IIRC this turns out to be the notion of simultaneity adopted by an inertial observer who is co-moving with the origin of the coordinate system.

 

[Chris Hillman]

In the 1970s and 1980s, Harold Puthoff and his collaborator Russell Targ spent a lot of time studying and promoting the supposed psychic phenomenon of "remote viewing." They claimed that some people could describe locations accurately without ever having visited them or seen pictures or descriptions of them. This makes warning bells go off in my head whenever I see Puthoff's name mentioned.

I agree that Puthoff's papers generally seem to be belong to "fringe physics", to put it kindly. Some of them are less disreputable than his work with Targ, but I haven't seen any recent papers coauthored by Puthoff which I would characterize as mainstream physics.

PS: Puthoff is not a cranck (many journal publications)

Unfortunately, notknowing, a CV listing a physics Ph.D., or even "many journal publications", is no guarantee that a given researcher would generally be considered by his peers to work in the mainstream of physics. In particular, with more experience, you will recognize that some journals function something like trashcans (publish the papers rejected by more useful journals), and authors who publish mostly in these journals tend to be generally considered to be operating on the fringes.

Ultimately, there is no substitute for having enough expertise (sufficient background knowledge and experience, sufficient mathematical and physical insight, and sufficiently good scientific judgement) to easily assess "controversial" papers yourself. The good news is that with sufficient expertise it is often easy to quickly recognize that an incorrect paper cannot be correct. The work comes in learning enough good physics/math to become expert in standard theories and methods; fortunately, this is a delightful and fulfilling experience!

 

[MeJennifer]

In the Rindler metric, the metric coefficeints for space are independent of height, however the metric coefficient for time is not.

I don't know how to put this in terms of "distance" offhand. Where did the "bottom and top" come from? I'm just pointing at an equation and comparing the Rindler metric to the Schwarzschild metric. In the former, only the g_tt coefficient of the metric depends on position, in the later both g_tt and g_rr depend on positon.

To measure distance in the Rindler metric, BTW, one would compute the length of the curve connecting the "top" and "bottom" (whatever they are) by a straght line in a hypersurface of constant rindler-time. IIRC this turns out to be the notion of simultaneity adopted by an inertial observer who is co-moving with the origin of the coordinate system.

Pervect, I was simply asking a question on what you wrote:

The super-simple (perhaps over-simplified) version of what I've been trying to say is that while gravitation is always associated with time dilation, it may or may not be associated with length contraction. For instance, there is no length contraction due to gravity in the elevator gerdankenexperiment, (though there is time dilation).

Obviously I am talking about the top and the bottom of the elevator in your example.
If the elevator accelerates exactly as in a gravitational field does the distance between the top and the bottom change?
If so, would it not be a logical assumption that since top and bottom are in relative motion with each other that there must be a Lorentz factor involved?

 

[notknowing]

Somehow I missed this the first go-around.

Where did you find "a derivation of gravitational length contraction"? It's possible that I don't understand what you mean by that term - if you mean what I thought you meant, though, the Rindler metric should serve as a counter-example, as I mentioned before.

I did not find it in literature. I made a simple derivation myself, though I must admit that I still miss a factor two somewhere .
Suppose you have a rocket (or elevator if you like) in free space. What I'm interested in is not the length Lorentz contraction, but a contraction due to acceleration itself. Therefore, to separate both effects, I assume that the rocket is initially at rest. If the effect is due to acceleration only, this assumption should not influence the result. Next, the rockets are switched on, which induce a push on the "back" of the rocket. An external observer is located at some distance in a line perpendicular to the velocity of the rocket.
At the moment the acceleration starts, the back of the rocket is set into motion, while the front of the rocket is absolutely still, since it takes a time L/c for the "push" to reach the top of the spacecraft (L is length of rocket). This is purely a consequence of the finite speed of light, to be distinguished from an elastic compression. Then, one just calculates the length the bottom has moved in the time T=L/c using Dx=a*t^2/2 (where a is the acceleration). The new length is then L-a(L/c)^2/2. Dividing this by L gives the contraction factor :
1-aL/(2*c^2). This can be considered as a Taylor expansion of SQRT(1-aL/c^2). Now, the corresponding term for aL in a gravitational field is GM/R, such that one obtains the contraction factor SQRT(1-GM/c^2 R). This is very similar (except for the factor 2) to the true length contraction SQRT(1-2*GM/c^2 R) in a gravitational field.

Rudi

 

[notknowing]

I agree that Puthoff's papers generally seem to be belong to "fringe physics", to put it kindly. Some of them are less disreputable than his work with Targ, but I haven't seen any recent papers coauthored by Puthoff which I would characterize as mainstream physics.



Unfortunately, notknowing, a CV listing a physics Ph.D., or even "many journal publications", is no guarantee that a given researcher would generally be considered by his peers to work in the mainstream of physics. In particular, with more experience, you will recognize that some journals function something like trashcans (publish the papers rejected by more useful journals), and authors who publish mostly in these journals tend to be generally considered to be operating on the fringes.

Ultimately, there is no substitute for having enough expertise (sufficient background knowledge and experience, sufficient mathematical and physical insight, and sufficiently good scientific judgement) to easily assess "controversial" papers yourself. The good news is that with sufficient expertise it is often easy to quickly recognize that an incorrect paper cannot be correct. The work comes in learning enough good physics/math to become expert in standard theories and methods; fortunately, this is a delightful and fulfilling experience!

After some further investigation, I found that the work of Puthoff is in fact a continuation of previous work, started already in 1921 (Wilson) and Dicke (1957). These theories were published in respected (not thrascans) journals such as Phys. Rev and Rev. Mod. Phys.. So, if Puthoff would belong to the almost-crackpots, then these people should belong to the same class ?! Further, I also found that Puthoff made a publication on this theory in
Phys. Rev. A 39, 2333 - 2342 (1989) (see http://prola.aps.org/abstract/PRA/v39/i5/p2333_1 ), again no trashcan journal.

Some remark about "mainstream physics": I would say that a good physicicst is someone who dares to step outside the "mainstream" and we should all be glad that such persons exist. Einstein was also not doing mainstream physics. Antiparticles were once also considered an absurditiy invented by a non-mainstreamer. Without such people, science would stagnate. It is unfortunate (in my view) that most journals are so defensive and conservative that they do not even want to consider the possibility that some new idea might be correct. This explains also why the arxiv website is so successfull. Even if this website contains indeed a lot of doubtfull papers, it also contains a lot of very valuable papers which for some reason were not acceptable by the journals.

Rudi