# (Alpha) General relativity is self-inconsistent

Zanket could also look out the window at a rotating body, such as the Earth or a distant pulsar, and notice their rotation frequency will seem to increase when timed by his cesium clock or light clock. The Earth would rotate several times in 24 hours of his clock as he approached closer to the event horizon. That can not be explained in an inertial frame, only in a non-inertial frame that is freefalling due to gravity.

OK, imagine you and I are in black boxes a million miles apart travelling through space at some steady velocity. You start to fall into a black hole, but you feel no acceleration. You remain in your inertial reference frame, and to you there are no forces at work. There is no "force of gravity". But when I observe you, I see that you're accelerating away from me. To me you're in a non-inertial reference frame, and I claim that the force of gravity is accelerating you. Your paragraph above mixes these two viewpoints. That's the basis of the contradiction in terms.
There is a contradiction in terms there. That’s a problem in physics. Contradicting terminology is allowed to stand uncorrected. There is a force of gravity; it’s one of the four fundamental forces of nature known to date. What is the force of gravity? It’s nothing but the tidal force, and that is the force at work in your example above. It is incorrect to say that “To me you're in a non-inertial reference frame”. The frame that snugly surrounds me is still an inertial frame, but the frame we share is noninertial, as indicated by the tidal force that accelerates us away from each other. An inertial frame is a frame that is in free fall and that is small enough that the tidal force throughout it is negligible.

Gravity is said to be not a force only in the context that nothing pulls me down. Gravity is a pull is the Newtonian viewpoint. In the Einsteinian viewpoint, things fall by default, without being pulled down. That is, space itself falls. If something is not falling then either it has enough velocity to offset the fall (like it’s orbiting) or it is noninertially accelerating (thrusting).

Going back to my scenario above, imagine that the black hole was suddenly removed and your freefall ceased. (Please can we ignore any accelerations or "gravity waves" caused by this). Thereafter both you and I would agree that you are back in an inertial reference frame, travelling at some steady but higher velocity. If the black hole reappears briefly to accelerate you some more, we would disagree about your inertial reference frame, then when it disappeared we would agree again.
I say that our respective individual inertial frames stay inertial (at least until I get close enough to the singularity), regardless of the presence or absence of the black hole, and the frame we share is noninertial when the black hole is present, and inertial when it’s absent. Freefall doesn’t cease when the black hole is absent. Freefall doesn’t mean that you’re falling; it means that you’re floating.

I feel happier about circular orbits. Again "neglible" looks like a problem. If it's neglible and yet spans the horizon how can the horizon be inside the frame? You're saying there's no difference here and yet the very presence of the horizon says there is a difference here. How can I explain this? In your freefall inertial reference frame, there was no action at a distance force. The thing that was causing you to accelerate with respect to me has to be local to you and every single atom of your body. Yes, the tidal force might be very small and your acceleration might be changing only slightly. But in my eyes you are definitely accelerating in a given direction. There is a definite non-uniformity and it is local to you, in what you consider to be your "uniform" local frame. The gravity is the non-uniformity. Hence a uniform gravitational field is a uniform non-uniformity, and is contradiction in terms.
A frame we share may well be noninertial. It is noninertial when the tidal force in the frame is significant. But the frame that snugly surrounds me can be inertial even as I cross the horizon, for a sufficiently large black hole. Throughout that frame the tidal force may be negligible, and when it is, the gravitational field on my body is uniform, which is shorthand for negligibly nonuniform.

I say gravity is not "curved spacetime", but instead is a gradient in c across your local frame that you don't notice but I do.
I say that gravity is spacetime curvature, because gravity is the tidal force, which is synonymous with spacetime curvature.

See my paragraphs above regarding viewpoint. If you stick to your reference frame, there's no force acting on you, no "force of gravity", no gravity. If we shift to my viewpoint, everything changes.
That’s how GR is designed to work. In either of our individual frames, the tidal force is negligible, so either of us can accurately conduct experiments of SR, or other experiments that would otherwise be ruined by a significant tidal force that could even physically stretch our equipment. We cannot conduct such experiments across the frame we share, because the tidal force is significant across that frame. If I don’t look out the window of my small ship, I may be able to claim that there’s no gravity in my ship. But if I do a precise enough experiment within my ship, I will detect some tidal force within my ship, and know that gravity is present even within my ship.

No problem. But if you say they are flat, all the letters end up looking like this _.
You can make an outline of a curved letter using small enough flat lines.

No problem. It's straight and it's curved. Ain't relativity fun!
Just like the Earth’s surface is flat locally but curved globally (in which case it’s curved even locally; the curvature may be too small to detect).

I've said elsewhere that I consider this to be a hypothetical situation. You cannot in reality fall through the horizon, because at this point time dilation becomes infinite. My rule of thumb says that infinities don't happen in reality, so we should look to see if the mathematics needs some refinement. Hence I say c goes to zero at the horizon. This means a collapsing star takes forever to collapse, and none have finished collapsing yet. Hence they're frozen stars.
According to GR, they only look frozen from the perspective of someone above them. Someone who falls toward them would find no surface and would fall all the way to the central singularity.

A star you see that is ten light years away may have gone supernova nine years ago. You wouldn't know by looking at it.

Sorry Zanket, I have to go, so I can't answer your post properly. But for now:

There is a contradiction in terms there. That’s a problem in physics. Contradicting terminology is allowed to stand uncorrected. There is a force of gravity; it’s one of the four fundamental forces of nature known to date. What is the force of gravity? It’s nothing but the tidal force, and that is the force at work in your example above.

Sorry Zanket, that's not quite right. The tidal force is the change in the "force of gravity". You can fall towards a very large black hole, accelerating at 19.6m/s/s so the force of gravity is twice that at the surface of the earth. But the tidal force might be the same. The gravity is the local gradient, the tidal force is the change in that gradient.

It is incorrect to say that “To me you're in a non-inertial reference frame”. The frame that snugly surrounds me is still an inertial frame, but the frame we share is noninertial, as indicated by the tidal force that accelerates us away from each other. An inertial frame is a frame that is in free fall and that is small enough that the tidal force throughout it is negligible.

Again, sorry, we don't share a reference frame. We did before you started falling into that black hole, but now our reference frames are separating. Yours remains inertial to you but not to me, and vice versa. A reference frame that spans the both of us is another contradiction in terms.

A frame we share may well be noninertial. It is noninertial when the tidal force in the frame is significant. But the frame that snugly surrounds me can be inertial even as I cross the horizon, for a sufficiently large black hole.

No it can't. The horizon is some form of change. Your inertial reference frame is the same across its width. You're saying "something is different" whilst you're also saying "everything is the same". It's that contradiction in terms again.

According to GR, they only look frozen from the perspective of someone above them. Someone who falls toward them would find no surface and would fall all the way to the central singularity.

And it would take them forever to do it. They haven't got there yet, and never ever will. That central singularity is beyond the end of time. It's never going to happen. So it doesn't happen. [/QUOTE]

Sorry Zanket, I have to go, so I can't answer your post properly. But for now:
That’s okay, I took almost a month to answer yours! I have to do this quick too:

Sorry Zanket, that's not quite right. The tidal force is the change in the "force of gravity". You can fall towards a very large black hole, accelerating at 19.6m/s/s so the force of gravity is twice that at the surface of the earth. But the tidal force might be the same. The gravity is the local gradient, the tidal force is the change in that gradient.
I disagree, if only because the definition of “gravitation” by Taylor and Wheeler is “Effect of mass-energy on spacetime, evidenced by the relative or tidal accelerations of free test particles”. In other words, the only evidence of the force of gravity is the tidal force. An object’s fall is not due to a force, at least according to Einstein. Only the tidal force on it is a force (which can break the object apart as it falls). I don’t see any reason to disagree with those physicists.

Again, sorry, we don't share a reference frame. We did before you started falling into that black hole, but now our reference frames are separating. Yours remains inertial to you but not to me, and vice versa. A reference frame that spans the both of us is another contradiction in terms.
I disagree. Nothing says that a frame has to be inertial. An inertial frame is a frame in free fall and throughout which the tidal force is negligible. Then a noninertial frame is a frame that is either not in free fall or in which the tidal force is significant. Any two observers who can see each other can share a noninertial frame.

No it can't. The horizon is some form of change. Your inertial reference frame is the same across its width. You're saying "something is different" whilst you're also saying "everything is the same". It's that contradiction in terms again.
As I fall across the horizon, I needn’t notice anything extraordinary at all, according to GR, even with the finest instruments. I could have crossed a horizon while typing this sentence. The singularity could be a trillion light years away.

And it would take them forever to do it. They haven't got there yet, and never ever will. That central singularity is beyond the end of time. It's never going to happen. So it doesn't happen.
They will cross the horizon, you just won’t see it happen. You are free to cross the horizon yourself to prove to yourself that they are not above the horizon anymore, regardless of what you saw when you were above the horizon. I don’t believe this, mind you; I’m just paraphrasing GR. GR’s prediction of an event horizon is its undoing, the OP shows.

We'll have to agree to differ on this Zanket.