Proposed Experiment - Speed of Light

[DanAil]

TL;DR Summary

Experiment using Light.

One of the reasons to suggest that light might be bent by gravity is the assumption that light is behaving as the other objects that bend their trajectories by gravity. On a similar ground, we could suggest that as the objects are experiencing Gravity Assist, then the light could be also impacted by that. With Gravity Assist, an object flying near by a massive body (like a star or a planet) could gain or lose momentum adding the velocity of the massive body to the velocity of the object. This effect has been used for decades in flight dynamics to accelerate or slowdown space probes and reach celestial objects in the solar system. In the case with light, the eventual impact of the Gravity Assist will be in gaining or losing energy expressed with changing its frequency/wavelength.

We could use the inner planets in the solar system – Mercury or Venus – and determine if the light changes its frequency when passing near them. The suggested setup is the following using as example Mercury (orbital velocity ~48km/s vs. ~35km/s for Venus):

1. Use a spectroscope/spectrograph and record the spectrum of a star that appears near the Mercury when the planet is moving directly towards the observer.

2. After Mercury moves away from the initially observed star, then record again the spectrum of the same star and compare it with the previous one. An eventual difference/shift in frequency would hint that gravity assist effects are also applicable to light. In that case the frequency could be increased (blue shift) when the star appears near Mercury.

3. The same two points above should be performed with another star when Mercury is moving directly away from the observer. In that case, the frequency of the light could be reduced (red shift) by Mercury.

There are probably many technical details to be considered, but that is the general idea. Wondering what would be the outcome - would light experience Gravity Assist?

 

[Dale]

Summary:: Experiment using Light.

One of the reasons to suggest that light might be bent by gravity is the assumption that light is behaving as the other objects that bend their trajectories by gravity

One of the other reasons to suggest that light might be bent by gravity is because it has actually been observed to do so.

 

[DanAil]

Bending of the light is confirmed - no question about that! Gravity Assist however increases/decreases the velocity of the objects. Obviously, we do not expect light to increase its speed, but it could change its frequency. Would it be possible to be influenced that way by massive bodies?

 

[PeterDonis]

would light experience Gravity Assist?

Yes, as your own post shows:

In the case with light, the eventual impact of the Gravity Assist will be in gaining or losing energy expressed with changing its frequency/wavelength.

Look up "gravitational redshift".

Also look up "Shapiro time delay". Yes, light is kinematically affected by gravity, or more precisely by spacetime curvature. As you note, the effects don't show up in locally measured speed because that is always $c$ for light. But they do show up in other ways.

 

[DanAil]

Look up "gravitational redshift".

Also look up "Shapiro time delay".

Sorry, 'gravitational redshift' and 'Shapiro time delay' are completely different phenomena. Please lookup 'gravity assist' - it is about an object gaining (or loosing) the velocity of the heavy body. As already suggested - with Light it could be expressed with increasing (or decreasing) frequency.

 

[PeterDonis]

Sorry, 'gravitational redshift' and 'Shapiro time delay' are completely different phenomena.

I think you need to take a step back and rethink what you intend to be asking about. See below.

Please lookup 'gravity assist' - it is about an object gaining (or loosing) the velocity of the heavy body.

I know what gravity assist is as far as objects with nonzero rest mass are concerned. And if you are going to define "gravity assist" as just that phenomenon alone, then obviously there can be no such thing as "gravity assist" for light, so we can just close this thread since there is nothing to discuss.

Or else we can assume that you are using the term "gravity assist" with respect to light not in the strictly literal sense just described, but as a general term to mean "ways that gravity can affect the momentum or energy, i.e., the wavelength or frequency, of light". That is how I am interpreting your question. If you would rather we interpreted your question in the strict sense I gave above, which would, as noted, lead to this thread being immediately closed, you have only to say so.

As already suggested - with Light it could be expressed with increasing (or decreasing) frequency.

And what do you think "gravitational redshift" is?

 

[Bandersnatch]

@PeterDonis I believe the question is not just about the effects on light from climbing in and out of gravity wells, but whether light can exchange momentum with a moving body in a manner analogous to momentum exchange in gravity assist. I.e. it's neither of the two effects you referenced.

 

[DanAil]

And what do you think "gravitational redshift" is?

'Gravitational redshift' is when the light is coming out of a gravitational well - it is originating from that well (e.g. a star) and in that case it is decreasing its frequency. In the case of Gravity Assist the light is not originating from the heavy body, but just passing near by it, and if it moves in the same direction as that heavy body it could gain energy and increase its frequency.

To answer the concern if the topic of this thread is about "ways that gravity can affect the momentum or energy of light" - in my opinion it is more than that.

And please, there is no need for anyone in a discussion to feel offended by a statement that the 'gravitational redshift' and 'Shapiro time delay' are completely different phenomena - we just need to read their definition to understand and confirm that.

If the opinion is that there is no Gravity Assist for light, then that is great. Thank you for your comment!

 

[PeterDonis]

'Gravitational redshift' is when the light is coming out of a gravitational well

Yes.

it is originating from that well

Not necessarily. It could have come into the well from somewhere else and be climbing out again. There is a blueshift going in and a redshift coming out, but depending on where your source and detector are located, the two might not be the same. IIRC solar system experiments have been run confirming this effect for radio waves from space probes to Earth that pass by other planets or the Sun.

the light is not originating from the heavy body, but just passing near by it, and if it moves in the same direction as that heavy body it could gain energy and increase its frequency.

And IIRC, for appropriate locations of space probes, a planet or the Sun, and the Earth, yes, a net frequency increase has been observed for radio waves for exactly this reason.

To answer the concern if the topic of this thread is about "ways that gravity can affect the momentum or energy of light" - in my opinion it is more than that.

What more?

If the opinion is that there is no Gravity Assist for light

Until you define exactly what you mean by "gravity assist", we can't possibly answer this question either way. On the definition I proposed (effects of spacetime curvature on the momentum and energy of light), the answer is obviously that yes, there is "gravity assist".

 

[PeterDonis]

@PeterDonis I believe the question is not just about the effects on light from climbing in and out of gravity wells, but whether light can exchange momentum with a moving body in a manner analogous to momentum exchange in gravity assist. I.e. it's neither of the two effects you referenced.

Gravitational redshift/blueshift is not just for light climbing out of the gravity well of its source. See my post #9 just now.

 

[Dale]

Bending of the light is confirmed - no question about that! Gravity Assist however increases/decreases the velocity of the objects. Obviously, we do not expect light to increase its speed, but it could change its frequency. Would it be possible to be influenced that way by massive bodies?

Oh, I misunderstood your point. I thought you were trying to say that this would support the idea of light deflection.

I think what you describe would happen. But you would probably need a neutron star or black hole for it to be detectable. That is just a guess, with no calculations to support it

 

[PeterDonis]

I think what you describe would happen. But you would probably need a neutron star or black hole for it to be detectable.

No, you don't. As I said in earlier posts, frequency shifts of radio signals passing close to massive bodies as they travel from a space probe to Earth have already been observed in the solar system. Here is a reference I have found for one such experiment:

https://ilorentz.org/research/vanbaal/DECEASED/ART/gr-test.pdf

Note that focusing on "velocity increase", or correspondingly blueshift, in these cases is misguided since velocity and frequency are of course both frame dependent. The velocity "increase" in a standard gravity assist is for an observer with a particular state of motion (usually at rest relative to the Sun). Similarly, a blueshift of a particular light signal due to passing close to a massive body is for an observer with a particular state of motion. One can always find such an observer for any such maneuver.

 

[Orodruin]

Gravity Assist however increases/decreases the velocity of the objects.

This depends on the reference frame. There is no intrinsic velocity of an object. The same is true for light. Any light signal may be observed to have any frequency, you just need to change the motion of the observer. The 4-momentum of the light obviously changes but that is a rather moot statement since the 4-momenta at different times are nit colocated in spacetime and you technically need to be at the same spacetime event to compare two 4-momenta.

 

[vanhees71]

Here are my 2cts explaining free em. waves in GR spacetime:

https://itp.uni-frankfurt.de/~hees/pf-faq/gr-edyn.pdf

It's however only discussing the Hubble-Lemaitre redshift of FLRW spacetime. It's, however, easy to also treat the standard effects in Schwarzschild spacetime (deflection of light on the Sun, gravitational red/blue shift, Shapiro effect) using this formalism. When I find the time, I'll add some section on these topics too.

 

[DanAil]

I believe the question is not just about the effects on light from climbing in and out of gravity wells, but whether light can exchange momentum with a moving body in a manner analogous to momentum exchange in gravity assist. I.e. it's neither of the two effects you referenced.

Thank you @Bandersnatch - this was a perfect statement that summarized the objective of the proposed experiment.

 

[DanAil]

I think what you describe would happen.

The 4-momentum of the light obviously changes

Thank you all for your input!

It would be good to get more comments, but at this point it appears the predominant opinion to be that Gravity Assist will also impact Light. We ultimately might have to perform such or similar experiment to confirm.

Now that makes me thinking - if the result of the experiment is positive, there could be an impact on the interpretation of our cosmological observations. Simple example: Two galaxies appear almost on the line-of-sight with the Earth - galaxy one (G1) is 1 billion light wars away, and galaxy 2 (G2) is 2 billion light wars away. Both are of course receding from us with different velocity (red shifting), however as we measure the red shift of G2 we need to consider the fact that the redshift of G1 will need to be added to the redshift of G2. And this is not only with galaxies, but with any significant (could be invisible) matter between the observer and the observed object. Does that make sense?

 

[PeterDonis]

Gravity Assist will also impact Light. We ultimately might have to perform such or similar experiment to confirm.

We already have. The effect has already been confirmed for radio waves in the solar system. See the reference I gave in post #12.

 

[PeterDonis]

as we measure the red shift of G2 we need to consider the fact that the redshift of G1 will need to be added to the redshift of G2.

While in principle this could occur, yes, in practice the effect will be negligible compared to the cosmological redshifts of the galaxies. It will even be smaller than the solar system effects measured in experiments like the one I referenced in post #12, because in the solar system we on Earth are at a significantly different potential in its gravity well as compared to the space probes whose radio waves we are measuring; whereas relative to galaxy G2 in your example, both galaxy G1 and us here on Earth are basically at infinity, so at least to a first approximation we expect the ingoing and outgoing frequency shifts to cancel.

 

[DanAil]

Sorry, still not completely clear on what is being suggested. Very simple example:

We record the spectrum of a star and calculate that it appears to move away from us with velocity 200 km/s.

When Mercury moves directly away from us with ~48 km/s and is very close to the line of sight to the same star, we obtain again its spectrum and calculate that the star now appears to be moving away with ~248 km/s.

Is that what everyone is assuming will happen?

 

[PAllen]

Sorry, still not completely clear on what is being suggested. Very simple example:

We record the spectrum of a star and calculate that it appears to move away from us with velocity 200 km/s.

When Mercury moves directly away from us with ~48 km/s and is very close to the line of sight to the same star, we obtain again its spectrum and calculate that the star now appears to be moving away with ~248 km/s.

Is that what everyone is assuming will happen?

No, not at all. To any achievable precision, 200 km/s redshift will be measured both times.

 

[Orodruin]

Sorry, still not completely clear on what is being suggested. Very simple example:

We record the spectrum of a star and calculate that it appears to move away from us with velocity 200 km/s.

When Mercury moves directly away from us with ~48 km/s and is very close to the line of sight to the same star, we obtain again its spectrum and calculate that the star now appears to be moving away with ~248 km/s.

Is that what everyone is assuming will happen?

Mercury is waaaaay too light to make a light signal turn 180 degrees. But no, even if you replace Mercury by something denser (like a small black hole) you need to be more careful with your numbers as they are not correct even for a classical gravity assist.*

The frequency shift would be the same as if you had a mirror moving away at the same speed. This comes down to a factor which is the square of the Doppler factor to the mirror’s rest frame, i.e, (c-v)/(c+v).

*: In a classical 180 degree gravity assist you gain twice the velocity of the assisting body.

 

[Halc]

Keep in mind that 'gravity boost' is frame dependent. The voyager probe actually loses energy to Jupiter in some frames as it passes by.

1. Use a spectroscope/spectrograph and record the spectrum of a star that appears near the Mercury when the planet is moving directly towards the observer.

Seems plausible to me, but the light needs to change direction significantly to get a measurement you want. Mercury, at any speed, isn't going to cut it because light going by it will (in Earth's frame) be bent slightly to the side but without any significant change in energy. So getting a real experiment is going to be difficult, but it's in principle easy to imagine with a strong gravity source.

So imagine a black hole coming at you at some nonzero speed. It doesn't have to be fast, just approaching (or receding). A light shines near it from our general direction and it makes a full U-turn at the black hole and reflected exactly back at us with the same change in wavelength that you'd get had it been a moving mirror. That's gravity boost of light in the observer frame. It really does acquire a bit of momentum from the black hole.

This is implausible as a real experiment since there's no controlled source of light with known frequency. You simply don't see the light at all when the black hole isn't there to reflect it. A neutron star might not be dense enough to effect a full U-turn of light, but it does bend the path significantly so you'd still get the slingshot effect, but again, no reference frequency to compare: You can't empirically measure the frequency of the same light without the boost since you don't really know (like you did with Mercury) which source produced the light. It's not like we can shine a laser at the nearest black hole and wait for the boosted signal to return. That's like the joke of taking a flash picture of exo-planets.

 

[PeterDonis]

Mercury is waaaaay too light to make a light signal turn 180 degrees.

That's not what the OP is thinking. He's thinking that the "gravity assist" from Mercury will cause a frequency shift that corresponds to an additional recession speed equal to Mercury's speed away from Earth. Which is still wrong, but it's a different wrong thing than the one you are describing here.

 

[Orodruin]

That's not what the OP is thinking. He's thinking that the "gravity assist" from Mercury will cause a frequency shift that corresponds to an additional recession speed equal to Mercury's speed away from Earth. Which is still wrong, but it's a different wrong thing than the one you are describing here.

Not sure I understand the intended setup from this description. A gravity assist, even a classical one, changes the direction of motion.

 

[PeterDonis]

Is that what everyone is assuming will happen?

No. Your mental model of "gravity assist" for light is wrong. You cannot assume that Mercury's speed relative to Earth gets converted directly into an additional redshift.

The rough order of magnitude of the effect even for the Sun is very small: as the reference I gave in post #12 shows, it is a few parts in 10 billion. Mercury's gravity is weaker by roughly the ratio of their masses, which is roughly 10 million, so we're talking roughly one part in $10^{17}$.

 

[PeterDonis]

The frequency shift would be the same as if you had a mirror moving away at the same speed. This comes down to a factor which is the square of the Doppler factor to the mirror’s rest frame, i.e, (c-v)/(c+v).

I don't see how this is applicable to the effect of a massive body's motion relative to Earth on light passing the body on its way to Earth.

 

[Orodruin]

I don't see how this is applicable to the effect of a massive body's motion relative to Earth on light passing the body on its way to Earth.

It is applicable if the deflection angle is 180 degrees. Without a deflection angle you should not get a frequency shift.

Edit: In fact, this is the reason the effects are small in the solar system setting. There is just no objects dense enough to cause very large light deflections. It is also applicable to classical gravity assist. If your satellite moves fast enough, there will not be sufficient time for gravity to act on it and deflect it appreciably, resulting in only a small velocity change and a small deflection. I’d assume OP would need to understand this as well. As I said in a previous post, classical gravity assist does not just add the velocity of the assisting body.

 

[PAllen]

So the set up to produce a major effect would be as follows:

Imagine a star you see directly south of you (south just a way of saying some direction), moving directly away from you at 200 km/s. There is also a small BH that is directly north of you, moving directly away from you, at 48 km/sec. Then, if you look near the the BH, you will see some light from the star apparently coming from the north (near the BH) that has been bent around the BH by 180 degrees. This light will have a spectral shift corresponding to very close to 296 km/s recession. These speeds are low enough to ignore relativistic velocity addition and nonlinear composition of Doppler, to a very good approximation.

 

[Ibix]

This may be naive, but could we get an idea of the scale of the effect by noting that this is weak field, so we can add potentials? The only one that is changing is the potential due to Venus. A pulse of light passing Venus when it's at its maximum angular separation from the Sun arrives here when Venus is approximately $R\pm vR/c$ away, where $R$ is the distance to Venus when the light passes it, $v$ is Venus' orbital speed, and where the sign depends which side of superior conjunction it is. Then I make the fractional change in the frequency$$\frac{\Delta\Phi}{c^2}\approx\frac{2GM}{Rc^2}\frac vc$$Putting some approximate numbers into that, I get one part in $10^{18}$ difference, give or take a couple of orders of magnitude.

 

[PeroK]

Is that what everyone is assuming will happen?

The simple answer is no. I can't imagine why you would expect that.

 

[Vanadium 50]

Huh...not sure why this flagged as new.

In addition to the fact that this is unnecessary (has been observed elsewhere under better conditions), and likely too small to see, let me point out another problem: the kinematics of gravity assist are the same as for reflection. Good luck seeing the effect you want over a reflection background that's a zillion times bigger.