Effect of Gravity on the Speed of Light

[finbarLay]

I know from my physics lessons many years ago that a gravitational field can bend the path of light, but what is the effect of gravity on a photon when it is heading directly at a star. "If" the speed of light cannot be exceeded, what happens ?

 

[Naty1]

Hi Finbar:

The speed of light is constant, but different observations may vary. So decriptions can sometimes be confusing: it is space and time that vary, and these affect our perceptions/measurements/observations.

For example, a clock runs slower on Earth than in free space due to differences in gravity [gravitational potential]. So if you observe that clock from outer space you get one elapsed time, one tick rate; if you then move to Earth right next to the clock, you see a different tick rate. Similar difference for the 'speed of light'. [So, for example, GPS clocks on Earth and satellites must continually be synchronized back together. Wikipedia discusses this.]

If the speed of light is observed locally, right where you measure, one will always measure its speed as 'c'. But in curved spacetime, where gravity is present, distant observers will measure [observe] different speeds. That's a measurement/observation effect; Light always moves at 'c' in free space.

Also keep in mind you can't actually "see" light in outer space; all you can "see" is the light
when it actually reaches you [locally] in a finite time. So the stars you 'see' tonight emitted that light a long time ago...they are no longer even in the positions in which they appear and the color you observe is different than if you were right near the star! But your observation 'is what it is'.


more here: http://en.wikipedia.org/wiki/Speed_of_light

PS: you can also search "speed of light" or similar in these forums and see many prior discussions...

 

[bahamagreen]

I raised the same issue in a recent thread that went nowhere...

When light is traveling in a straight line, it only has one kind of speed - the direction of which is aligned with the straight line of travel. There is no lateral component... if there was then the straight line speed would have to be <c, right?

When light curves there are now two different aspects of its speed - that component which still represents its alignment with its path forward (the speed component tangential to the curve), and a second component that includes the lateral translation into the curve (the component that is normal to the tangential component). Is this correct?

The resulting speed of the light should be the vector sum of these two components, right?

So, is c that vector sum or is c only the tangential component?
If c is the sum, then the tangential component would be <c.

My questions assumes the above is correct about the nature of curved light... is it?
If so, what bearing does that have on the idea that light has no specific direction or location between emission and absorption? Or does it "really" have a path? And if not, what is the apparent curvature of the path indicating otherwise?

 

[finbarLay]

Thank you both for the replies.
I think I was thinking that the extra pull of gravity would come into it somewhere.
I have had a look at wiki and seen that the speed of gravity is theorized at being the same as the speed of light. I had assumed the gravitational force was instantaneous.

 

[tom.stoer]

Gravitational curvature results in "tilting" of light cones, but in local reference frames c is curvature-independent and remains constant; globally velocity measurements are ambinguous in GR, therefore velocities of distant objects are not uniquely defined. For light this results in the so-called Shapiro delay which appears as refractive index n(x) which seems to result in c < 1.

 

[Naty1]

When light curves there are now two different aspects of its speed - that component which still represents its alignment with its path forward (the speed component tangential to the curve), and a second component that includes the lateral translation into the curve (the component that is normal to the tangential component). Is this correct?

That's ok as a simple start, but not really accurate for many reasons that emerge from our understanding of relativity, thanks to Einstein. That's a geometric explanation of a lot of stuff. For example the 'path' you refer to is really spacetime, that is space and time curvature. It also is not a clear explanation of how light always follows a [null] geodesic which means it always follows the straightest line possible.

Nor does it suggest why the speed of light never varies...that you can never catch up to it no matter how hard you try.

Instead, I would say something like gravitational curvature affects our distant perceptions of light. Light doesn't change velocity [speed] but changes frequency [color] and the path thru space and time.

Try reading about Shapiro delay, that Tom posted about, in Wikipedia...it will give some insights. And do a search in these forums, if interested, for many discussions on the "speed of light".

 

[bahamagreen]

Let me try it another way...

Two cases:

1] Light source and light target, both at relative rest, X distance apart with nothing between them. The light path is straight, is X long and takes X/c to go from source to target.

2] Light source and light target, both at relative rest, X distance apart with a mass between them.

Is case 1 presented correctly?
For case 2, is the bent light path >X long?
Does it take (>X)/c to go from source to target?.

 

[Naty1]

I had assumed the gravitational force was instantaneous...

Not in these sense you mean, but gravitational attraction toward an object moving with a steady velocity IS towards its instantaneous position...analogous to a charged test particle in an electromagnetic filed pointing toward the source’s instantaneous position rather than its retarded position. This effect does not mean that the electric nor gravitational field propagates instantaneously; as in Maxwell’s theory, if a source abruptly stops moving at a point, a test particle will continue to accelerate toward the extrapolated position of the source until the time it takes for a signal to propagate from from the source at light speed.

I did not record the forum discussion thread in my notes, but there is a paper here that was used in the discussion: http://arxiv.org/abs/gr-qc/9909087

 

[Naty1]

Does it take (>X)/c to go from source to target?.

you need to qualify just what you mean, but in general, yes...the path is curved...so longer and time is slowed by the presence of the gravitational mass.

This is like the Shapiro delay Tom mentioned above...I know it's in Wikipedia.

 

[bahamagreen]

Thanks, Naty1; I'm glad to see your response.

I have read enough threads here to expect alarm when someone asks about light's reference frame, light's "sense" of time passing, etc... The Wiki page on Shapiro delay says it's a kind of gravitational time dilation.

How does time dilation of any sort have any effect on light? The Wiki page seems to differentiat between local and non-local paths, but must not all measures of light be local?

 

[tom.stoer]

What I tried to explain in post #5 is the following:

If you measure the speed of light passing point P and if your experimental setup is located at P as well, you'll find c. If you measure the speed of light passing point P and if your experimental setup is located at Q, you may find something else.

But this is due to the fact that velocity is no longer globally unique in GR; in an expanding universe you can't even define time, distance, energy, ... in a global and unique way; the statement "this galaxy is x lightyears away from us" becomes ambiguous.

 

[Chronos]

Light changes frequency in response to a gravitational field, not speed. A photon entering a gravitational field is blue shifted, then redshifted as it exits the field. The speed is always c.

 

[bahamagreen]

Every time I think I'm beginning to get a sense of what light is, I find out I don't... not even close!

Is this quick survey accurate?

Chronos: always c, only frequency may shift

tom.stoer: always c locally, may not be c measured non-locally

Naty1: may be <c (longer path, longer time)

Wiki (Shapiro):

"time delay effect"

"object take slightly longer to travel to a target and longer to return"

"a special case of gravitational time dilation"

"The speed of light is constant for measurements in a local reference frame. However, this is not true for non-local paths along which a gravitational field is present. The measured elapsed time of a light signal in a gravitational field is longer than it would be without the field..."

My intuition is that Relativity is not an existential theory (what is), but a theory about data (what we measure), and the transforms needed to square data from one frame of reference to another. In any regard, I am not seeing an agreement yet on what one would expect to measure here.

Is it correct to assume that time dilation and length contraction pertain only to frames of reference... only things for which a frame of reference applies?
If so, I am still curious how light may be subject to time dilation... if it is, how?; and would it also be subject to length contraction (is that what shifts the observed frequency?)?

 

[Mentz114]

My intuition is that Relativity is not an existential theory (what is), but a theory about data (what we measure), and the transforms needed to square data from one frame of reference to another. In any regard, I am not seeing an agreement yet on what one would expect to measure here.

(my bold)

In physics, the 'what is' coincides exactly with 'what is measured' ? There are no ghosts in physics.

 

[tom.stoer]

There are no ghosts in physics.

what about Fadeev-Popov ghosts?

 

[Mentz114]

what about Fadeev-Popov ghosts?

Is QFT still considered to be physics ?

 

[bahamagreen]

"In physics, the 'what is' coincides exactly with 'what is measured' ?"

That would be a tautology if the relationship was one to one. but does not relativity demonstrate this is a one to many relationship? A unitary reality, multiple frames of reference with different measures?

"There are no ghosts in physics."

Well then what about that "spooky action at a distance"? If you suggest virtual particles or messenger photons I'll just think, "A rose by any other name".

Mentz114, of course you are correct - the ghosts are still in our own minds.

 

[Naty1]

Post #15...

Is this quick survey accurate?

generally ok I think depending on just what you mean.

These are different aspects of relativity rather than different unrelated rules. Generally in relativity, relative speed and gravitational potential affect observations of time and distance...so, higher speed in different frames makes things appear slower in other frames [time dilation, frequency shift] distances forshortened [length contraction] and greater gravitational potential affects both by slowing time and curving space as potential and potential gradient increase. And accelerated rather than inertial observations may overlay other affects.

All these affects are suppressed [ minimized] when you make a local/incremental observation...there is no change in potential [time dilation], potential gradient [curvature], speed, etc,etc...because you are measuring right where you are...

 

[JPBenowitz]

That's ok as a simple start, but not really accurate for many reasons that emerge from our understanding of relativity, thanks to Einstein. That's a geometric explanation of a lot of stuff. For example the 'path' you refer to is really spacetime, that is space and time curvature. It also is not a clear explanation of how light always follows a [null] geodesic which means it always follows the straightest line possible.

Nor does it suggest why the speed of light never varies...that you can never catch up to it no matter how hard you try.

Instead, I would say something like gravitational curvature affects our distant perceptions of light. Light doesn't change velocity [speed] but changes frequency [color] and the path thru space and time.

Try reading about Shapiro delay, that Tom posted about, in Wikipedia...it will give some insights. And do a search in these forums, if interested, for many discussions on the "speed of light".

I'm pretty sure light cannot vary in local-reference frames because it would break causality according to s-t diagrams. Nonetheless, how can we justify the following:

m\tilde{\gamma} = \frac{h}{c\lambda} if \tilde{\gamma} is \infty and m = 0?

A photon's mass isn't approaching 0 and its gamma ratio isn't approaching infinity, it IS 0 and infinity.

However, let's consider that as the universe expands \lambda for electromagnetic radiation increases. So on the right hand side we can say that \lambda approaches infinity as T\rightarrow\infty thus, amongst friends the left hand side approaches 0 as the right approaches 0. But at any point in time this isn't so. So... I am confused.

 

[tom.stoer]

The l.h.s. in terms of the mass m is not defined for photons; if you consider an expanding universe it's true that light is red-shifted, i.e. λ goes to zero, and that the energy E of a photon approches zero (it is not conserved)

 

[JPBenowitz]

The l.h.s. in terms of the mass m is not defined for photons; if you consider an expanding universe it's true that light is red-shifted, i.e. λ goes to zero, and that the energy E of a photon approches zero (it is not conserved)

I am not sure what you mean for I.h.s. The mass isn't defined as in doesn't appear on the left hand side which would be consistent with the left hand side as energy isn't conserved therefore there isn't any mass conserved. Yet, the gamma factor still remains; still confused. Or do you mean mass is not defined as in there is perhaps some unknown operator on the left hand side producing a finite value on the left hand side?

0 x ∞ is of the indeterminate from which essentially, as I understand it means that you could theoretically construct a mathematical structure that converges to any particular value. If so, then depending on the left hand side there exists a unique mathematical structure such that it converges to that particular value.

(Btw where the hell are the limits in Latex?)

So we can re-express 0 * ∞ as Lim x \rightarrowc \frac{f(x)}{\frac{1}{g(x)}} and then construct it such that is satisfies the right hand side. However, does there exist a single mathematical expression such that it satisfies all possible values of the right hand side? If so what is its correlation to nature? If not what does this mean?

I thought I understood SR apparently I don't.

 

[tom.stoer]

I mean that the l.h.s is not defined for massless particles with m=0 and 'γ=∞'; mγ is simply not defined, so this relation only makes sense for massive particles. For arbitary mass m you have the relation

E² = (mc²)² + p²c²

For massless particles (rest mass m=0) this reduces to

E = pc.

The fact that the energy of a photon is not conserved is only due to the expansion of spacetime (in GR); the above mentioned problems arise already in SR with static, flat spacetime.

 

[PAllen]

Just a comment that there are different ways to look at the issue of energy loss due to expansion. See, for example, the following classic article by a top expert in the field (co-author of the famous Lineweaver papers and articles on expansion):

http://www.physics.uq.edu.au/download/tamarad/papers/SciAm_Energy.pdf

She specifically argues that, viewed properly, photons do not lose energy in expansion.

 

[JPBenowitz]

Just a comment that there are different ways to look at the issue of energy loss due to expansion. See, for example, the following classic article by a top expert in the field (co-author of the famous Lineweaver papers and articles on expansion):

http://www.physics.uq.edu.au/download/tamarad/papers/SciAm_Energy.pdf

She specifically argues that, viewed properly, photons do not lose energy in expansion.

Well, as the universe expands there is an increase in vacuum energy as it accelerates. If we want to take Thermodynamics seriously on both a cosmological and quantum scale the red-shifting on electromagnetic energy must be going somewhere.

 

[JPBenowitz]

I mean that the l.h.s is not defined for massless particles with m=0 and 'γ=∞'; mγ is simply not defined, so this relation only makes sense for massive particles. For arbitary mass m you have the relation

E² = (mc²)² + p²c²

For massless particles (rest mass m=0) this reduces to

E = pc.

The fact that the energy of a photon is not conserved is only due to the expansion of spacetime (in GR); the above mentioned problems arise already in SR with static, flat spacetime.

It may be possible to define them with converging limits and the cosmological red-shift. Are there any papers on this? I'm sure there is.

 

[tom.stoer]

The principle problem is that the definition of energy becomes problematic for expanding universes ...

 

[Naty1]

...what is the effect of gravity on a photon when it is heading directly at a star.

just in case the above posts aren't clear, the photon speed remains 'c' locally...but viewed from a distance in space the light will be blueshifted and will appear to slow. That's because as the star, the gravitational source, is approached space curves and time dilation occurs.