Why is the invariance of light a problem?

[PAllen]

What if the ship is orbiting a BH with a mass that theoretically would provite the necessary pull?

Sure, but then you have a problem in strong field general relativity, not special relativity (and it would have to be a supermassive BH to have an moon sized orbit of .9c). Further, concepts of special relativity (specifically, global inertial frames) do not apply. Even though the rocket is in free fall, there is no corresponding inertial frame (except at an instant of time; not for an orbit) for it because these don't exist globally in general relativity.

If we assume the mass of the rocket is very small compared to the BH and is small enough to treat the rocket as a test body, then spacetime around the BH can be considered static (if it is a non-rotating BH). Then there is no concept of gravity traveling. The orbit is just a geodesic of the spacetime. It is true that by some definitions, the rocket could consider the BH as 'moving' at speed > c. However, so what? In general relativity, the speed of light being c and all bodies moving less than c is strictly a local property not a global one. Thus, the rocket would find that all physics in and right near the rocket over short periods of time would match those as if the rocket were in 'empty space'. Globally, GR predicts all sorts of effects different from SR.

 

[Dale]

what happens when energy from outside reaches inside?

It is still conserved. It may be transformed to another form, depending on the details, but the conservation of energy applies in all frames.

is Earth gravitational pull changed? if it is, the ship could not orbit I suppose.

An orbit in one frame is an orbit in all frames. They are called geodesics, and the math ensures that all frames agree on whether or not a given path is a geodesic.

And the very speed of the ship, shall it be meaured at the same time with two standards, one inside and one outside?

Yes. There is certainly nothing new in that. That has been the case since Galileo.

 

[Dale]

Moderator's note: I have deleted several off topic posts about $\epsilon_0$ and $\mu_0$, including my own. Let's not detract from the OP's discussion while he or she is actively involved.

 

[bobie]

An orbit in one frame is an orbit in all frames. They are called geodesics, and the math ensures that all frames agree on whether or not a given path is a geodesic.

Of course we know this flight is technically impossible, but just to explore what would happen:

If time is, say, 1/10 of the time outside the ships should get 1/10 of the regular acceleration
When the radio waves are picked up inside the ship they they get in at a shorter wave but the words jam ten times quicker, but they cannot understand English any more because their brain is 10 times slower, right?
They cross the moon 10 times in a second ( their second) so, as the know the the orbit is 2π c, they are moving at 10 c in their frame?

Thanks for your kind patience, Dalespam

 

[PAllen]

Of course we know this flight is technically impossible, but just to explore what would happen:

If time is, say, 1/10 of the time outside the ships should get 1/10 of the regular acceleration

I cannot attach any meaning to this statement. Please try to be specific, using accepted definitions.

When the radio waves are picked up inside the ship they they get in at a shorter wave but the words jam ten times quicker, but they cannot understand English any more because their brain is 10 times slower, right?

If a ship is orbiting (a supermassive BH; even for a neutron star, there is no orbit that is .9c) at .9c, radio waves sent from a far away ship would be received blueshifted by the orbiting ship. There is one factor affecting wavelength (shorter than at source), frequency (greater than at source), interval between signals (smaller than at source). It is not clear if you are suggesting these affects add up - they do not, they all correlate with the same factor. However, for people inside the orbiting ship (talking, turning on lights, etc.) everything is indistinguishable from if they were floating far away from any massive body. It is only signals received from far away that are received differently (as described above) from the way they emitted. Note, that if such a signal were slowed down by the given factor, then the English would be perfectly comprehensible.

Note, also, that we cannot talk about signals received from the BH, because that is impossible.

They cross the moon 10 times in a second ( their second) so, as the know the the orbit is 2π c, they are moving at 10 c in their frame?

Near a BH, geometry is non-euclidean, the ratio of circumference to radius is no longer 2 pi, and distance to a BH is challenging to define in a way that can be measured.

I suggest you accept my accelerating scenario and stick to SR rather than GR. There I already explained that the ship would consider the Earth (not the other way around as you keep saying) to be moving faster than c and this is no more surprising for such a non-inertial coordinates than a merry go round observer seeing distant mountains moving faster than c.

[edit: The question of how the ship would measure the speed of the moon, assuming the ship accelerating in a circle near the moon's orbit, passing it periodically, is actually quite complicated. If you measure the moon's passing locally, as it passes you, it will be .9c. This is accounted for by distance contraction. However, to model the moon's average speed over an orbit from the rocket point of view, you need a complete coordinate system. This is actually quite complicated for such a circular accelerating rocket, but it doesn't really matter what the result might be - there is no expectation that motion of bodies must be less than c in highly non-inertial coordinates. What is true, is that the moon would never overtake any light signal in any direction, in any coordinates. This is because in non-inertial coordinates, light may move many times faster than c]

Thanks for your kind patience, Dalespam

 

[russ_watters]

Of course yes, if it were so simple. But if you accept the assumption that all processes in the world can be altered in a tiny fraction of the world you are opening up a n endless Pandora-box of trouble.

Why do you believe that when others are saying exactly the opposite is true? How is needing a lot of different explanations simpler than only needing one?

What happens to processes (nearly all) that are time-dependent? forces like gravity and electric?
A ship orbiting the Earth at 9.9999.. c vould have no gravity, no atomic bonds, what would happen to radio communications? etc...

Nothing. That's the point: relativity is what enables them to always work the same way. That is in fact one of its postulates.

 

[Dale]

If time is, say, 1/10 of the time outside the ships should get 1/10 of the regular acceleration

I would have to work it out, it may be a different factor. However, the short answer is that coordinate acceleration can indeed differ from proper acceleration. All frames will agree on proper acceleration, but, obviously, different frames will disagree on the coordinate acceleration.

When the radio waves are picked up inside the ship they they get in at a shorter wave but the words jam ten times quicker, but they cannot understand English any more because their brain is 10 times slower, right?

Sure. I don't see why you think that a persons inability to understand a blue shifted transmission represents a problem for a physical theory.

They cross the moon 10 times in a second ( their second) so, as the know the the orbit is 2π c, they are moving at 10 c in their frame?

By definition they are at rest in their frame.

The math guarantees that an object which has a timelike worldline (slower than c in a coordinate independent sense) will have a timelike worldline in all frames. Similarly, an object with a lightlike worldline (traveling at c in a coordinate independent sense) will have a lightlike worldline in all frames.

Furthermore, if two timelike objects pass right next to each other then they will both agree on their relative velocity at the meeting.