More on general relativity

I’m going to go back to the subject of an earlier post, from a different direction.

In discussing the Twins Paradox, Banesh Hoffmann, in his book Relativity and Its Roots, says”

“Actually, the twins cannot legitimately be treated reciprocally, as in the preceding paragraph. There is a crucial difference between them that is best seen by making the reversal of direction of the spaceship after one year an abrupt one—say, one taking 30 seconds. Then the traveler would experience a deceleration force of about a million times the pull of earth’s gravity, and he would at once be squashed flat against the wall of his spaceship. But when we look at the situation relative to the travelling twin with the stay-at-home twin now the apparent traveller, the stay-at-home twin would nonetheless experience no such lethal force, while the traveller still would.”

But there’s a problem with this. The instant acceleration or deceleration is brought into the picture, the immediate thought should be, “Okay, at this point, I have to look at it from the perspective of general relativity.”

So you should then immediately go to the paragraph in Relativity where Einstein says:

““My body of reference (the carriage) remains permanently at rest. With reference to it, however, there exists (during the period of application of the brakes) a gravitational field which is directed forwards and which is variable with respect to time. Under the influence of this field, the embankment together with the earth moves non-uniformly in such a manner that their original velocity in the backwards direction is continuously reduced.”

Once you do this, the contention that the twins cannot be treated reciprocally is refuted. They can be treated reciprocally. The twin in the rocket simply claims that a gravitational field, whose existence coincides with the rocket twin turning the rocket’s steering wheel, causes the entire universe to swing around 180 degrees so that the rocket is once again facing the Earth.

And both the rocket twin and the rest of the universe experience this gravitational field, since according to Einstein, “Under the influence of this field, the embankment together with the earth moves non-uniformly…” Meaning that the gravitational field apparently called into existence by the turning of the rocket’s steering wheel (or the firing of its maneuvering rockets, however you want to look at it) acts upon the Earth, and by extension, the entire universe. And obviously the same gravitational field acts upon the rocket twin as well, since according to both Einstein and Hoffmann, the rocket twin feels a ‘jerk.’ There’s no getting rid of that pesky ‘jerk.’

So looking at it from the rocket twin’s viewpoint, both he and the Earth twin are subjected to the same gravitational force during the turn-around, in conflict with Hoffmann’s assertion that “when we look at the situation relative to the travelling twin with the stay-at-home twin now the apparent traveller, the stay-at-home twin would nonetheless experience no such lethal force, while the traveller still would.” Bringing general relativity into the situation, as is proper, shows that they’re both subjected to the same force.

How can it be said that the stay-at-home twin, considered as the one traveling, experiences no force? Einstein clearly, explicitly says that the stay-at-home twin, considered as the one traveling, does experience a force. Let me repeat Einstein’s exact words yet again: “Under the influence of this field, the embankment together with the earth moves non-uniformly in such a manner that their original velocity in the backwards direction is continuously reduced.” Again, repeat after me: from either the viewpoint of the train or the rocket, “under the influence of this field, the embankment together with the earth moves non-uniformly in such a manner that their original velocity in the backwards direction is continuously reduced.”

When the rocket twin is considered at rest and he turns the rocket’s steering wheel, a gravitational field comes into existence that acts upon the entire universe, rotating it around the rocket and causing the Earth and consequently the entire universe to begin moving past the rocket.

This is relativity! I am not misunderstanding this or misquoting anything! Mathematics are not necessary! This is simply the logical application of Einstein’s own ideas.

Here is the logical analytical path that must be followed, not according to me, but according to relativity’s own “rules”:

Special relativity claims that time dilation is reciprocal. Okay. So far so good. Bring in the twins and the rocket. Time dilation should be reciprocal, and each twin should be aging faster than the other. But it’s not, relativists claim, because acceleration is involved. Okay. Must switch to general relativity then, since special relativity only applies to uniform motion. So far so good. Bring in general relativity. In doing so, we immediately find that the twin situation is still reciprocal, despite earlier protestations that situation wasn’t reciprocal due to acceleration.

The problem is that most scientists apparently don’t follow this logical pathway, as they should.

Now, someone will probably object that I’m falling into a trap that Einstein warned about just a few paragraphs earlier:

“Before proceeding farther, however, I must warn the reader against a misconception suggested by these considerations. A gravitational field exists for the man in the chest, despite the fact that there was no such field for the coordinate system first chosen. Now we might easily suppose that the existence of a gravitational field is always only an apparent one.”

The gist is that the gravitational field experienced by the rocket (the one that rotates the entire universe around the rocket) only exists from the viewpoint of the rocket. It’s only an apparent field, since it only exists for the twin in the rocket. This is the reason why he’s the only one who feels the jerk.

But Einstein’s warning was against supposing that this means that all gravitational fields are merely apparent. That’s not what I’m doing here, so I’m not falling into the trap Einstein is warning about.

So with that objection out of the way, let me finish. But keep that objection in mind, because I’m going to use it against itself.

Bringing general relativity into the Twins Paradox as we must since acceleration is involved, we find that the situation is indeed reciprocal, despite the claim that it wasn’t, because the rocket twin is “compelled by nobody to refer this jerk to a ‘real’ acceleration.” He is free to attribute the acceleration he feels in turning around to a gravitational field rotating the universe around his rocket.

But this is only an apparent gravitational field, not a real one, in light of Einstein’s warning about the trap, as outlined above. The rocket twin is free to interpret the acceleration as a gravitational field acting upon the entire universe…but it isn’t really. It’s only an apparent field, existing only for the twin in the rocket.

You might think this means that all gravitational fields are merely apparent if you choose the correct reference frame (Einstein’s trap). But it doesn’t mean that. Because only “those of quite special form” are apparent. For example, you can’t choose a reference frame from which the Earth’s gravity vanishes (meaning it’s only an apparent gravitational field).

So how do we know which gravitational fields are merely apparent? Apparently (no pun intended) the only apparent (i.e. not real) gravitational fields are those that exist solely from the viewpoint of an observer that is actually in motion, but is pretending that he isn’t.

And thus we’re once again handed a way of determining absolute motion.

Back to Einstein’s warning against the trap of regarding all gravitational fields as apparent: what is the chest Einstein mentions, and what was the coordinate system first chosen?

The coordinate system first chosen was a location in space so far removed from any gravitational field that it satisfies the requirements for Galilean relativity. The chest is basically just a rocket under constant acceleration relative to this first hypothetical Galilean frame. The man in the chest, says Einstein, is experiencing what he believes to be a gravitational field, since he regards himself as being at rest.

Einstein’s point is that the man in the chest thinks he’s experiencing gravity, but there’s no gravitational source in the Galilean frame.

And this, I think, is one of the fundamental errors of general relativity. Einstein establishes that gravitational mass and inertial mass are equivalent, if not one and the same. And so acceleration and gravitation can be treated equivalently.

But, Einstein warns, obviously gravitation and acceleration are not the same, because you can choose frames where the apparent gravitational field can be made to vanish entirely, which will show that it was really only ordinary acceleration. But you can never choose frames where certain types of gravitational fields will vanish entirely, and these are actual gravitational fields rather than apparent ones.

Of course, that’s not what Einstein explicitly says, but it’s the actual meaning of what he says, when he warns not to fall into the trap of thinking all gravitational fields are merely apparent.

Basically, it is doublespeak. Gravitation and acceleration are equivalent, so they can be treated as if they’re the same, but they’re not really the same, because they’re two different things.

And it’s obvious that they’re two different things. If I push or pull an object at a constantly increasing rate, obviously it is not gravity acting upon the object. Yet Einstein says we should treat the two as if they’re the same. But, he warns, only up to the point where we’re unable to treat them as if they’re the same. We secretly know which objects are really moving and which really aren’t, but everyone is free to pretend that we don’t really know which are really moving. It’s absurd!

So what it boils down to is that the Twins Paradox isn’t really a paradox because it’s never in doubt which twin is actually traveling. And how do we know which twin is actually traveling? Because there are unequal reference frames, in direct violation of relativity (some contain actual gravity, others merely apparent gravity)! Because relativity tells us it’s okay to pretend that completely different forces are actually the same force. Certain types of acceleration may be due to gravity, but not all types of acceleration are due to gravity, but we can pretend that all types of acceleration are due to gravity, as long as doing so doesn't lead to physical impossibilities, such as two twins each being younger than the other. Thus we can pretend that the each twin is aging more slowly than the other, until we try to reunite them.

In other words, relativity appears to be a valid principle, until you push it too far and discover that it’s actually invalid. Just as certain gravitational fields are merely apparent, relativity itself is merely apparent.