# Speed of light, mass, time questions

CookingWithGas mentioned that “Gravity slows time. Velocity slows time.”
So what I want to know is what is the range of those effects?
The speed of light is an upper limit. I doubt “sitting still” is possible but perhaps it is in a given reference frame as a lower limit?
Is the mass of a black hole an upper limit and weightlessness a lower limit in terms of slowing time? If so, then we have a range correct? What units would this range of the effect of slowing time be expressed in? Perhaps the range is infinite for mass but not velocity (due to the speed of light limit)?

I’m not sure what you mean by “range” of effects. In general, it’s difficult to discuss these concepts in plain English because the terms that we use in normal discourse often do not precisely reflect the physics of the situation. For instance, speaking of “slowing time” is a misnomer; time isn’t a measurable quality except for the effects that occur during its passage. Someone subject to the effects of relativistic time dilation may find that their clock has “run much slower” than a clock that remains at a “stationary” inertial reference frame, but in fact both clocks “run” at the same rate locally; one, however, has taken a different route through space-time (two inextricably related concepts) in a non-local and non-equivilent frame of reference which is not inertially-linked to that of the “stationary” clock. Even this explanation is suspect; there are, according to Special Relativity, no privlidged “stationary” reference frames, and everything is in motion with respect to everything else. We can’t say anything about how fast or slow time “passes” or “moves” without describing it in terms of a subjective reference frame.

An object moving at c (the speed of light) will not experience “movement” through time; that is to say, a photon knows naught between its genesis and terminus. Massy particles, however, are incapable of being accelerated to this speed as they become exponentially more massive and harder to accelerate. Of objects infalling into a black hole, once they fall past the event horizon, we can no longer speak of them existing in any real sense; while they may still be accelerating (and if the singularity is massive enough, the tidal gradients may be gentle enough that it even survives without being torn to component atoms) they and all information about them is lost to the external universe for all time, as they enter a region of maximal entropy.

If you can get your hands on them, I recommend reading the relevent sections of The Feynman Lectures on Physics. Even if you can’t delve too deeply into the math, Feynman makes good strides toward explaining what happens in clear, simple English. Alternatively, you could check out Brian Greene’s The Fabric of the Cosmos, which (despite mostly being a pop-science book about superstring theory and cosmology) has some pretty good illustrations of phenomena pertaining to relativity physics.

Stranger

This is going to take a lot more explanation than I can handle.

But to start with, neither gravity nor velocity slows time. Nothing slows time. Time always proceeds for everyone inside a reference frame at 1 second per second. We don’t know of anything that can alter this.

What confuses people is that to an outside observer time can appear to slow in someone else’s reference frame. This is a consequence of relativity and the unchanging nature of lightspeed as a constant. If you speed off to the nearest star and back at near the speed of light, your clock and my clock will differ. Yours will appear to have gone slower. But you won’t notice anything at all. For you time went by normally at every instant and it was my clock that speeded up. Note the symmetry. If time slows down for one observer it must speed up for the other. But this is a comparitive effect. Time itself does not change.

This means we can’t talk about the “range” of the effect. It is not that kind of effect. It’s a matter of reference frames and reference frames can be at any distance or location, however near or far.

You also misunderstand the meaning of the mass of black hole. A black hole is a matter of density. It can be of any mass, from less than a proton to more than the universe. There are no upper or lower limits. All that is required is that the mass is sufficient for the volume to overcome the ability of particles to escape.

None of these effects have range. That’s like asking what is the range of being a Yankees fan. It doesn’t apply to the subject.

Well, it is possible to say the following: To a faraway stationary (in his frame) observer time comes to a stop at the event horizon of a black hole.

A clock that is somehow lowered close to the EH and then brought back to a hovering rocket will show an elapsed time that is less than the clock on the rocket.

When the clock gets back to the rocket it will run at the same rate as the rocket clock so I guess you could say the range runs from 0 to 1.

ETA. That should say stationary with respect to the BH not “in his frame”

There is a lower range for a stable black hole, at least if we take Hawking’s presumptions about black hole mechanics to be true. There’s also an upper limit on how massive a rotating black hole of a particular invariant mass can be; attempting to adding additional mass causes it to be cast out before entering the event horizon, preventing the formation of a naked singularity. (In theory you could create a non-rotating black hole, but in reality all naturally formed black holes will have a net spin.)

No black hole could weight more than the universe for obvious reasons. A “closed universe”, however, could be thought of as being enclosed within the event horizon of a black hole, unable to escape the closed boundary of the universe.

This is all just a minor nitpick on your otherwise excellent response.

Stranger

I think I’d say that a little differently Stranger. I think I’d say that for a given mass there’s a maximum angular momentum.

max angular momentum < M[sup]2[/sup]G/c.

I believe I was thinking something like “an upper limit on how much angular momentum a rotating black hole of a particular invariant mass can have…” but the fingers did something different, resulting in gibberish. Thanks for the correction.

Stranger

OK, OK, true, :o but it was just so much easier to say that gravity and velocity slow time.

Actually, no. If you have two reference frames A and B, and B’s time is slow relative to A’s, then A’s time is also slow relative to B’s. The reason that this doesn’t lead to a paradox is that if you have an observer in each reference frame, they can only directly compare times at a single point. In order for them to have two points in common, at least one of the observers has to change reference frames.

By way of analogy, suppose I’m standing up straight, and Ring is lying on his back on the floor (I hope you don’t mind, Ring; it’s easier with concrete examples). I call “up” the direction from my feet to my head, and define “height” as the distance from my downmost point to my upmost point. So I say that my own height is six feet, but Ring’s height is about eight inches (that being the distance from his back to his chest). So I say that Ring is shorter than me (but he’s six feet thick)

Meanwhile, though, Ring is in a different reference frame. He defines “up” as the direction from his feet to his head. So in his reference frame, he’s six feet tall, and I’m the one who’s only eight inches. So in his reference frame, I’m the one who’s really short (but really thick).

Now, really, we’re the same size, and if you take “height” and “thickness” and combine them in the right way, you’ll get a measurement that stays the same no matter what reference frame you measure them in. In the same way, when two observers are moving relative to each other, each one will observe the other guy’s clock to be running fast, and each will measure the other’s length as being less than it should be. But if you combine length and time in the right way, you’ll get a measurement which everyone agrees on, no matter what their reference frame.

But essentially wrong. Saying this may seem right as a very quick explanation, but it actually gives a conception of what is going on that is utterly incorrect. This is why using words and illustrative analogies to explain the non-intuitive concepts of modern physics is so very tricky and prone to misunderstanding.

Stranger

Damn that’s amazing, it is eight inches. It just goes to show if you’ve got a PhD you really do know some truly important stuff.

Also my wife in now convinced that I’ve lost my mind. She also said “honey that’s really not where you could use some more thickness.” I wonder what she meant by that?

Yes, I was going for the classic “twin” paradox, in which the traveling twin comes home and finds the other twin much older. This also requires general theory instead of special theory.

And I was also thinking of a black hole being more massive than the observable universe, to answer Stranger’s nitpick, but thinking about it I see why that can’t work.

Nitpicks aside, when an OP needs as much handholding as this one did, sometimes I think some of you true science types go overboard with the jargon. I would read Feynman’s biographies, e.g., but his lectures? So certainly not for anyone who could think CookingWithGas to be correct.

Sorry, CWG, but even as a simplification, that was really wrong.

Thanks for the answers. I guess I pictured time as something with a “flow” and a rate of “flow” because I have heard speculation of some particles moving backwards to our forwards.
My last questions are, if you are moving at the speed of light relative to me, what is the rate at which our clocks will diverge? Could this work if you traveled around me in a circle at the speed of light keeping the same distance?

The answer to that is, I’m not moving at the speed of light relative to you. I can’t be. It just doesn’t make any sense to try to define a reference frame moving at the speed of light.

Now, what I can do is move at ever-faster speeds, which approach (but never quite reach) the speed of light. As I approach the speed of light relative to you, the time dilation factor approaches infinity. It can never reach infinity, since I can never reach the speed of light, but for any finite number you name, I can name a speed less than the speed of light for which that’s the time dilation factor. Want a time dilation factor of a million? A billion? A googol? That’s possible.

Feynman showed that antimatter particles could be treated as regular matter particles moving backward in time. However, this is mostly a mathematical understanding and not very relevant to the questions you’re asking. Especially since we live in a regular matter universe in which antimatter is extremely rare.

The Feynman Lectures are really quite accessible (up to a point, anyway) and he often goes back to fundamental principles and makes it clear why an intuitive concept–like time “flowing”–is wrong. More than once I’ve copied or scanned lectures out of the book to describe behaviors in relativity or quantum mechanics to neophytes with confidence that the material would provide some value. Many of the lectures–despite being intended as an comprohensive introductory course for Caltech students–are pretty light on math and don’t require a working understanding of anything beyond algebra. There are certain concepts you can’t really get without going into the math, but where he can, he uses illustration and analogy to good effect.

However, at some point you’re going to blueshift the Cosmic Microwave Background to x-rays or hard gammas and you’ll get seriously fried by virtue of your own energy. Even before that, impact with a small grain will be enough impulse to utterly annihilate any normal material, so unless your vessel is made from a giant artificially strengthened molecule or some absurdly strong coughscrithcough material you won’t have to worry about the accuracy of anyone else’s timepieces.

However, if you were able to move at the speed of light, rate at which time would advance for you from someone in a different reference frame would be zero; your clock would be frozen. This would in fact be the case whether you’re going toward, or away, or even in circle, though the last case has some special complications, since it would require you to either be orbiting at the bleeding edge of an event horizon of a black hole with gravity bending your path, or continually thrusting and thus also non-inertial. You can’t do this, though, because you have (invariant) mass, which is a type of energy bound up into a state that has a natural resistance to being accelerated, and that resistance increases when you get to velocities that edge up on the speed of light; this is a converse to the dilation of time Chronos mentions, and scales by the same factor, except inverted.

Stranger

Sorry for the hijack, but what would prevent two objects with mass from traveling directly away from each other, each at 1/2 the speed of light? Wouldn’t that make each of them travel at the speed of light, relative to each other? Photons from one would never reach the other until they slowed down, right?

You can’t add relativistic speeds the way you do regular speeds. If you could, what would happen if your two bodies were each moving 2/3 of the speed of light?

I’m not going to try to reproduce the formula that you do need to use. You can find it here.

Your proton will catch up and with ease.

Nope. You would think this to be intuitively true from a classical perspective, but when you get into Special Relativity velocity between two inertial reference frames is no longer additive. Although this Wikipedia article on the topic is remarkably craptastical, the basic derivation is there. For two frames moving away from a fixed starting point in opposite directions at 1/2c, the resultant velocity difference between them is exactly 2/5c. Strange, but true, or rather, truly strange. Odd; perhaps even bizarre, and like the Spanish Inquisition, almost totally unexpected. And that’s just where the weirdness starts. Let me tell you about massive rotating cylinders with no endpoints…

Stranger

I don’t understand the math, but does it say that two objects traveling at 1/2 the speed of light directly away from each other WOULD see photons emitted from each other?

I thought relativistic speeds of more than C is what defines the “observable” universe from the unobservable part, because when relative velocity exceeds the speed of light, we will never see the object at the other end.