Is there a relation between light and gravity?

Michio Kaku said, on a special about time that I watched recently, that time slows down for an observer approaching the speed of light. This I had heard before. But he also said that time slows down for an observer in a strong gravity well, and that time in a black hole’s singularity would cease to exist, just as it would if you were riding a photon. If this is the case, then is there some relation between light and gravity? Maybe an equation that describes both and can be solved for either? If not, why not? Why would they have identical effects but have no relation to one another?

Related question: if a luminous object were moving away from us at the speed of light, would we be able to see it? Would photons travelling opposite its direction basically be standing still?

The photons would still be traveling at the speed of light, which is a constant. I believe they would be severely red-shifted. The luminous object can’t travel at the speed of light, but it can approach it. This can be seen in particle accelerators, where as the particles are repeatedly accelerated, they gain energy/mass but their speed changes very little once it gets close to the speed of light.

It’s acceleration that causes time to appear to slow down, and being in a gravity well is the same as accelerating-- that’s one of the incredibly simple, but genius, ideas that Einstein had. Remember the thought experiment about being in an elevator that is accelerating and how the observer could not tell the difference between that and being under the influence of gravity?

Okay, but one is not accelerating once one has reached the speed of light or the black hole’s singularity, are they? It is that point at which people observe one to be frozen in time, right? So, when you’re reached c or reached the infinitely dense point, how does acceleration still have a bearing on time?

I understood that the mysterious gravitons most likely travel at the same speed as photons, which suggests a relationship to me.

Gravitons are hypothetical particles. Plenty of theoretical models of the universe don’t need gravitons, and many of those models don’t permit gravitons, either.

They would be moving at the speed of light. A stationary observer would see them moving at the speed of light. And an observer on the moving object would also see them moving at the speed of light relative to the moving object.

At first this seems like a paradox. The moving object is travelling almost the speed of light itself. So any photons coming off the back of it should be stationary. You’d think it would be like throwing a baseball off the back of a moving train. The forward velocity of the train should cancel out the backwards velocity of the baseball.

The thing to remember is that time is moving more slowly for the observer on the moving object. And velocity is simply distance divided by time. The slowing of time experienced by the moving observer cancels out the paradox. Both observers see the light moving at the speed of light relative to themselves because they’re measuring that speed with stopwatches running at different rates.

First of all, just to be clear (some would say “needlessly pedantic”) time doesn’t slow down for Observer A close to c; he (or she) will experience time passing at the rate within his own reference frame regardless of speed or acceleration. Observer B in an inertial reference frame outside will perceive time to be moving slower in the accelerated frame than in his own surroundings, and Observer A inside the accelerated frame will perceive things outside to be going really fast, per the Lorentz transformations.

I have to admit I don’t know what the presenter means by “the singularity would cease to exist,” however, once Observer A has passed the event horizon–the point at which the intensity of the gravitational field is so strong that no possible trajectory can escape–we can’t really say anything useful about what happens to him. Hypothetically, Observer A will perceive things outside of his frame to happen faster and faster while in fact being subject to relativistic transformation will be moving slower and slower, incrementing toward complete motionless (inside the frame) as he approaches c; indeed, aside from the fact that all incoming light is going to be compressed and blueshifted into X-ray or gamma ray range, frying him to a crisp, he’ll be able to see the end of the universe in the blink of an eye. And if we take a rotating black hole (which most if not all most likely are) you have an additional zone called the ergosphere, in which relativistic frame dragging–warping of space–occurs. This can result in some really funny results in which, from the perception of external Observer B, Observer A goes faster than light. He’s not, really; it’s just that the space through which he travels is being moved (which can occur at any speed), and when you add all of that together you can get velocities that are greater than c in flat space, which the area around a large massive object (especially a rotating one) is not. However, the reality is that with any singularity smaller than a galactic mass the tidal forces from extreme gravity gradients would shear Observer A into component atoms long before he got around to observing anything cool.

This segues into a direct answer to your question; light is massless, and is therefore permitted to move exactly and only at c per the tenets of special relativity. It also travels exactly in straight lines until it hits something. (A quantum field theorist would qualify this by saying that light takes all paths but it all averages out to follow a straight line, but they’re kind of an indeterminate bunch anyway.) However, these “straight lines” (physicists call them geodesics) lie upon the plenum of spacetime which is distorted by the presence of mass (which is just energy bound up in a particular form) and some other, more exotic forms of energy which may or may not actually exist. The conservative energy field created by the presence of mass is, of course, gravity, and so a concentration of gravitational energy will cause space to be distorted and thus light to bend around it, just as a marble will roll toward a bowling ball dropped in the middle of a mattress. (For those playing along at home, it is inadvisable to store your bowling ball in the middle of your bed mattress; this is only done by professionals for the purpose of illustration and should not be repeated without adult supervision.)

The set of equations that relate the presence of energy to the distortion of spacetime, and thus would describe the geodesic lines that light would follow, are called the Einstein Field equations, named after the eponymous scientist despite being independently developed by mathematician David Hilbert and his students. (To be clear, Einstein developed the fundamental concepts for GR, but Hilbert et al developed a great deal of the underlying math. Hilbert himself credited Einstein with the essential discoveries, while according himself only nominal credit for his work.) The EFEs are a descriptio of relations between a set of four symmetric tensors (stress-energy, Ricci, curvature, and the metric tensor); this is obviously somewhat beyond high school mathematics, and I’ll defer to Chronos or another professional physicist working with relativity theory to explain the relations in more detail, partially because I don’t want to trod on anyone’s prerogatives but mostly because I don’t have a modern physics text here at work and don’t want to futz up details in an area I haven’t studied in over a decade.

In reference to your final question regarding light emitted from an object moving at c, all light moves at c (though its local frame) regardless of the speed of the frame it was emitted from. This seems counterintuitive from normal experience, because when we through a baseball from a moving train we are told to add the velocity of the train to the velocity of the ball so that we can figure out just how fast it is going when it smacks some poor bystander in the head. (I sincerely hope that these types of problems are only performed in classroom problem sets.) Since this doesn’t happen with light, but we’re still stuck with having to deal with conservation of momentum and conservation of energy, we have to resolve this by changing the frequency of light (which is directly related to the energy of an individual photon). So your photons emitted by an object moving at close to c would be redshifted into oblivion, and photons emitted by an object moving at c would be entirely hypothetical, as they’d have a frequency of zero. This also ofters the conceptually problematic issue that if you are moving faster than c, the way to slow down is to shoot photons out the back, which is kind of like hitting the accelerator petal to slow down, something that Audi 5000 owners know to be distinctly ill-advised.

Here is a pretty clear nontechnical reference from our friends at Caltech on the fundamentals of general relativity and gravity, and here John Baez gives a layman’s overview of the Einstein Field equations. Enjoy.

Stranger

Strictly speaking what you’re talking about is the black hole’s event horizon, not it’s singularity.

Imagine two rockets zipping past each other in space at 99% of the speed of light. An observer on rocket A looks over at rocket B and notices that clocks on B are running slow. However, an observer on rocket B looking at rocket A will notice the same thing! In a situation where two observers are moving at constant velocities, the other clock will always run slow compared to mine – no matter which rocket I’m on.

Whose clock is right? They both are. No reference frame is priveleged over another.

If the pilot of rocket A decides to match speeds with rocket B (i.e. put them both in the same reference frame) he needs to accelerate. This acceleration breaks the symmetry of the situation. Now the pilot of rocket A notices that his clock is running slow compared to rocket B. When he finally matches speeds with rocket B he stops accelerating and both clocks tick at the same rate.

It turns out that being in a gravitional field is identical to accelerating. If I’m in a sealed rocket with no windows there is no way for me to tell the difference between sitting on the Earth or accelerating through space at 1G. I can feel myself being pulled down onto the deck, but I can’t tell whether its because of gravity or acceleration. They behave exactly the same way.

So … if I’m accelerating or in a gravity well I will observe my clocks running slow relative to outside clocks. If I’m moving at a constant velocity relative to another observer (or he’s moving at a constant velocity relative to me … same thing) I will observe his clocks running slow relative to mine.

I’ve always wondered about that. Gravity is (hypothetically) mediated by (as yet undetected) particles called “gravitons.” Would gravitons be present in an accelerating elevator?

While this is true, gravitons are essential to all theories of quantum gravity in unifying the current understanding of general relativity and quantum mechanics, and are accepted as being conceptually valid by the vast majority of physicists. Fundamental interactions in QM are mediated by exchanges of particles called gauge bosons, and the graviton was conceived to fit this role analogous to the photon in electrodynamic interactions, gluons in strong interactions, and the W and Z bosons in weak interactions. Since individual gravitons are so weakly interacting with matter, it is virtually impossible (with anything like modern instruments) to observe a single graviton-matter interaction, and so we can only deduce these properties from field interactions.

It is entirely possible, of course, that the whole business of fundamental interactions and force carriers is just yet another level of abstraction and there is something entirely different going on below the surface, but we’re just too primitive to figure it all out, what with our monkey paws, overgrown nerve cord brains, and pinhole camera eyes.

Stranger

I’m positive that Michio Kaku never said this. To expand on a point Stranger made, but one I feel can’t be overemphasized, since it is central to most people’s misunderstand of the subject, never ever changes for an observer.

Time always passes at one second per second. Weight is always a constant. Length and perception of objects never changes in any way.

No matter what speed you travel, everything in your reference frame always looks the same to you.

It is only to an outside observer not in your reference frame that anything looks different. To an outside observer, the passing of your time may slow, your weight may increase, your length may decrease.

You don’t notice this. We can prove this by noting that to the person in the other reference frame, *we * are the ones whose time has slowed, who weight has increased, whose length has decreased. Since we can be viewed from an effective infinity of other reference frames (a large finite number in actuality, of course) we are at all lengths and times and weights simultaneously.

We don’t notice because that’s not how reality works. It is obviously utterly crucial for any understanding of relativity to make this distinction.

It is also crucial to remember that no object with mass can travel at the speed of light. You cannot meaningfully talk about or answer any questions that begins with “once one has reached the speed of light.” You are always either accelerating asymptotically approaching the speed of light, decelerating from a higher speed, or moving in a uniform motion.

Nitpick: Mass is constant, not weight. (An important distinction in a discussion that involved gravity.)

Yes, I dithered over whether to use the more familiar term and finally decided to do so since my examples directly compared two unchanging gravity wells. Mass is the correct constant, though.

Thanks to everyone for the responses, corrections, and criticisms. Thanks especially to **Stranger ** for the informative links and commentary. The link to the Einstein field equations led me eventually to the Geometrized unit system in which both G and c are set to equal 1 (or G is set to equal 1/8π, which means, I guess, that G would be c/8π.)

But I don’t know how to solve the first form of the EFE shown at Wiki for G and c since the equation has three, rather than two, “sides”. Can one or another just be arbitrarily dropped? (Say, the middle one with K?)

Good post Stranger, but one small nitpick: The observer would have to be stationary just outside the event horizon in order for him to be fried by the blue shifted radiation.

At or inside the horizon his past light cone would completely close up.

I stand corrected. If A is inside the event horizon, he’s outrun his past. A neat trick if you can do it.

Stranger

Pfft. I know plenty of people who’ve managed to outrun their pasts. Their major problem is that they then proceed to create new pasts that they have to run from.

Bump. (Hope someone can help with this.)

All three “sides” to the equation are equal to the other two. The only reason you’re seeing three here is that they’re giving you both the condensed form and the definition of the constant K, kappa. Take another look at the second and third “sides” - the only difference is that kappa has been expanded in terms of other constants.