**Ask a monkey a physics question thread**

[Renton]

I think you misunderstood what I said. The physics thread guy said that gravitational time dilation of a mass approaching an event horizon is identical to the the time dilation experienced by an object traveling at velocity approaching c. I mean comparing them as analogues, not that the gravitationally dilated mass is also experiencing SR effects.

This doesn't intuitively seem correct to me. The principle of equivalence only relates gravitational acceleration to actual acceleration, right?

Anyway this seems like an easy thing to check mathematically. Isn't there a simple formula for the amount of common time elapsed per second in a gravitational field of X strength? What strength does that need to be in order for time dilation to be infinite?

Re: my instantaneous usage, what I meant was that from the point of view of a being approaching the EH, a nanosecond of time would be equal to trillions of years of common time outside of the gravitational field of the black hole.

[MadMojoMonkey]

I think you misunderstood what I said. The physics thread guy said that gravitational time dilation of a mass approaching an event horizon is identical to the the time dilation experienced by an object traveling at velocity approaching c. I mean comparing them as analogues, not that the gravitationally dilated mass is also experiencing SR effects.

Ahh. Yes. I agree with him.

In both cases, there is a limit approaching infinite time dilation. In one case, it's due to the velocity approaching c. In the other case, it's due the extreme curvature in the local space-time caused by the black hole's mass density. (Local means the "nearby" volume around the observer, with no holes in the volume, in this case.)

The time dilation is the same, whichever the cause. In that regard, they are perfectly indistinguishable.

All time dilation is understood through Einstein's Relativity. I'm not sure whether it came in the GR or SR bit.

This doesn't intuitively seem correct to me. The principle of equivalence only relates gravitational acceleration to actual acceleration, right?

Ugh. I mean, maybe you're right, but it's a complicated subject that's hard to wrap up in one sentence.
The phrase "actual acceleration" gets my undies in a bind, but I think I know what you mean.

"We assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system."
-Albert Einstein

He was saying that the force of 1g near Earth's surface is indistinguishable from a force of 1g caused by an accelerating reference frame (like, say a magic elevator powered by the hand of God). He went on to say that this is only possible if the amount of "gravitational mass" a body has is identical to the amount of "inertial mass" a body has. Which everyone largely thought was rudimentary and went without saying.

He also said something like, "Let's assume that the conservation laws we observe are the same everywhere." Again, mostly nods of agreement.

Then he said, "So time dilation and space contraction, then, right?" That kicked the lid off, so to speak, of the steaming pile of ignorance that was waiting to be smelled (smelt?).


So, yeah... that's what the principle states. The implications are subtle and astounding, though.

Anyway this seems like an easy thing to check mathematically. Isn't there a simple formula for the amount of common time elapsed per second in a gravitational field of X strength? What strength does that need to be in order for time dilation to be infinite?

Re: my instantaneous usage, what I meant was that from the point of view of a being approaching the EH, a nanosecond of time would be equal to trillions of years of common time outside of the gravitational field of the black hole.

Well, I'm a layman at full-scale GR calculations, first off. Actually, that kind of makes me sound like I have some understanding, which I do not. I have seen the equations, but I don't even know the math behind quaternions, which is the language of GR.

My gut says that it would require infinite spacetime curvature to cause infinite time dilation.
Just like it would require infinite acceleration to cause the same.
Infinite spacetime curvature would imply infinite mass-energy density over some region, presumably infinitesimally small. This is the so-called singularity, which may or may not exist within a black hole. I am unsure of the current theories around singularities.

That said, I agree with your hyperbole of "trillions of years" as a nice work around. I have it in my head, though that it's the opposite, really. That the observer sees their own time passing as "normal" and that the "distant" times they observe are always slowed, never sped up.

Is Kingnat in the house? Any help here?

[Renton]

That said, I agree with your hyperbole of "trillions of years" as a nice work around. I have it in my head, though that it's the opposite, really. That the observer sees their own time passing as "normal" and that the "distant" times they observe are always slowed, never sped up.

Waitaminit now. My interpretation of gravitational time dilation:

Person A observing the black hole from a weak gravitational field. Experiences time at 1 sec/sec.

Person B at 1 nanometer from the EH of a black hole. Experiences time at 1 sec/sec.

Person A observes Person B's clock ticking very slowly at 1/X B's seconds per A's seconds, where x is approaching zero.

Person B observes Person A's clock ticking very quickly at X A's seconds per B's second, where 1/x is approaching infinite.

Is this wrong?

[MadMojoMonkey]

Waitaminit now. My interpretation of gravitational time dilation:

Person A observing the black hole from a weak gravitational field. Experiences time at 1 sec/sec.

Person B at 1 nanometer from the EH of a black hole. Experiences time at 1 sec/sec.

Person A observes Person B's clock ticking very slowly at 1/X B's seconds per A's seconds, where x is approaching zero.

Person B observes Person A's clock ticking very quickly at X A's seconds per B's second, where 1/x is approaching infinite.

Is this wrong?

I've been on this for long enough to report in.

I'm still a lot confused about the gravitational portion. I've even read some stuff that I don't fully understand about velocity transformations now... since the equivalence principle says that any force can be interpreted as a gravitational force, if that suits.

Here's the rub I'm dealing with. I am correct insofar as to say that an observer will always observe his own time as "normal." When observing things, if he's a clever physicist, he will know that what he observes can be different from what he calculates. This is because he's taking travel distances into account. He knows that everything he sees takes some amount of time between action and observation, and his calculations account for that.

OK. Some fuzziness around observations, but ultimately the calculations allow separated observers to agree on the cause of their observations.

Where I am lost is how an observer sees the other's clocks when the information is blue-shifted.

In the twin paradox, the blue shifted information arrives at increased frequency. The stationary twin sees his twin's clocks advance at a rapid pace, due to the fact that the traveling twin is approaching the stationary twin. There is a Doppler effect on the frequency.

So wait, what now? I thought that they would always see the other's clock tick more slowly, but this is not agreeing with the above information. So I have massive doubts.

I am trying to figure out where the notion that observers always see outside clocks tick more slowly is coming from. I thought it was tied to space contraction. I thought the dual effects of time dilation and space contraction served to make this effect.
I need to figure it out.

[dario.steaua]

never to eat chocolate before you play poker , is my advice!!!

[MadMojoMonkey]

Waitaminit now. My interpretation of gravitational time dilation:

Person A observing the black hole from a weak gravitational field. Experiences time at 1 sec/sec.

Person B at 1 nanometer from the EH of a black hole. Experiences time at 1 sec/sec.

Person A observes Person B's clock ticking very slowly at 1/X B's seconds per A's seconds, where x is approaching zero.

Person B observes Person A's clock ticking very quickly at X A's seconds per B's second, where 1/x is approaching infinite.

Is this wrong?

Ugh. I'm so out of practice these days.

You are correct. The Lorentz transformation goes both ways and the inverse transformation has a '+' sign, where the forward transform has a '-' sign.

The clocks on the ISS require re-synching with ground-based clocks, due to the combined effects of both special and general relativity.

Clocks in greater gravitational fields run more slowly, as you've said, than clocks in lesser gravitational fields.

Personal derp. Sorry it took so long to correct it, but I really wanted to be certain of why I was confused before I stated anything more on the topic.

[Renton]

Waitaminit now. My interpretation of gravitational time dilation:

Person A observing the black hole from a weak gravitational field. Experiences time at 1 sec/sec.

Person B at 1 nanometer from the EH of a black hole. Experiences time at 1 sec/sec.

Person A observes Person B's clock ticking very slowly at 1/X B's seconds per A's seconds, where 1/x is approaching zero.

Person B observes Person A's clock ticking very quickly at X A's seconds per B's second, where x is approaching infinite.

Is this wrong?

X approaches infinity in both observations. I think you got my meaning but I thought I'd fix the glaring typos here in case anyone else reads it and it confuses them.

[MadMojoMonkey]

X approaches infinity in both observations. I think you got my meaning but I thought I'd fix the glaring typos here in case anyone else reads it and it confuses them.

Yes, the relativistic time dilation would affect the clocks in the way you describe, with appropriate handling of infinities, that is.

(The following is based on a loose understanding of the effects of relativistic velocity. I'm assuming they apply to gravitational effects as well.)
When the relativistic factor becomes high enough, atomic interactions become somewhat impossible.

Imagine a single molecule of water, H2O. Assume that by some un-described means, it experiences a constant accelerating force.

At some speed, the exchange of photons which mediates the attraction of the covalent bonds will be left behind. Meaning that the molecule of water will just be one atom of Hydrogen and another atom of Hydrogen and an atom of Oxygen speeding along, moving too quickly to "catch" the photons that are "thrown" by the other atoms. They outpace the exchange particles.

E.g. Assume 2 capable people are playing catch with a beach ball. They keep throwing the ball back and forth as the wind slowly but unfailingly picks up. No matter what angle the 2 people stand at, relative to the wind, eventually the wind will become so strong that they can't play catch anymore. Either the wind will blow the ball too far off coarse to be caught, or the wind will be too strong for the person downwind to throw it upwind without it coming straight back to them.

In the analogy, the beach ball is the exchange particles between the atoms, and the wind is the spacetime that the atoms are rushing through.

At some speed, the atoms are no longer a molecule.

At some greater speed, the same thing happens to the atoms. The electric fields emanated by the protons and electrons become shaped like an elongated tear drop behind them. When this deformation reaches a tipping point, the atoms are no longer really atoms. They're just a bunch of fundamental particles whizzing along near eachother, completely oblivious to each other's existence.