Why we won't notice anything special when crossing the horizon?

[PeterDonis]

This violates the principle of equivalence

I'm not sure it actually does. Basically he is describing a mechanism for transferring energy at infinity from the robot to the batteries, keeping the total energy at infinity of the robot + battery system constant. The latter is what you are insisting on (correctly); however, energy at infinity is not the same as his usage of the term "weight", which he is defining as proper acceleration times locally measured (i.e., *not* "redshifted") rest mass.

Another way of seeing that his process doesn't violate the EP is to consider an alternative process that arrives at the same end state: we let the robot + battery system free fall from infinity to some finite r; at that finite r, we stop the robot + battery with an apparatus that captures all of its kinetic energy, bringing it to rest locally, and stores the captured energy in the battery.

 

[PAllen]

Pervect was talking about the bag of photons, and I agree with his argument. As for the battery, if you have some mechanism where as robot and battery are lowered, work done by them on some 'generator' as they are lowered via cable (for example) [thus converting PE to electrical energy], and this energy transferred to battery, then battery will increase in weight compared to robot (measured locally to the robot).

Alternatively, imagine free fall. everything has a lot of KE relative to some stationary observer. Imagine a magic process to convert all of said KE to energy of the battery, while stopping robot. Again, battery increases in weight compared to robot. However, bag of photons does not.

 

[PeterDonis]

Pervect was talking about the bag of photons, and I agree with his argument.

I agree too, as far as the bag of photons is concerned: basically, the bag of photons will behave the same as the robot in the robot-battery scenario.

Alternatively, imagine free fall. everything has a lot of KE relative to some stationary observer. Imagine a magic process to convert all of said KE to energy of the battery, while stopping robot. Again, battery increases in weight compared to robot. However, bag of photons does not.

Yes, this is what I described at the end of my last post, and I agree the bag of photons will act like the robot.

However, I also think that jartsa would agree that the bag of photons acts like the robot in these scenarios; I think that's the point he was making when he said the energy of the bag of photons goes to zero at the horizon. (He can correct me if I'm wrong, of course.) It's just saying that, by lowering an object (robot or bag of photons) closer and closer to the horizon, one can extract more and more of its energy at infinity and put it somewhere else (the battery just being one example of a somewhere else). This is true, but as I said a couple of posts ago, I don't see what it has to do with the other questions raised in this thread.

 

[jartsa]

I agree too, as far as the bag of photons is concerned: basically, the bag of photons will behave the same as the robot in the robot-battery scenario.
Yes, this is what I described at the end of my last post, and I agree the bag of photons will act like the robot.

However, I also think that jartsa would agree that the bag of photons acts like the robot in these scenarios; I think that's the point he was making when he said the energy of the bag of photons goes to zero at the horizon. (He can correct me if I'm wrong, of course.) It's just saying that, by lowering an object (robot or bag of photons) closer and closer to the horizon, one can extract more and more of its energy at infinity and put it somewhere else (the battery just being one example of a somewhere else). This is true, but as I said a couple of posts ago, I don't see what it has to do with the other questions raised in this thread.

Exactly!

And how is this related to anything?

Well let's see. I assume it would take energy to winch the robot up a short distance, I mean the force required woud not be zero. Rather the force would 1000 Newtons, if the robot weighed 1000 Newtons on the surface of the Earth, and the black hole has surface gravity of 1 g.

http://en.wikipedia.org/wiki/Surface_gravity#Surface_gravity_of_a_black_hole(the above mentioned winching up was perfomed from "infinity", using a long rope)

 

[PeterDonis]

I assume it would take energy to winch the robot up a short distance, I mean the force required woud not be zero. Rather the force would 1000 Newtons, if the robot weighed 1000 Newtons on the surface of the Earth, and the black hole has surface gravity of 1 g.

More precisely, if the proper acceleration required to "hover" at the radius, above the horizon, at which the robot starts being winched, redshifted to infinity, were 1 g. (This also assumes that the robot is winched up slowly enough that its motion can be approximated by a series of static states at gradually increasing radius, and that the distance through which the robot is winched is small enough that there is no detectable change in the redshifted proper acceleration.) No object can be winched up from the horizon itself, and the surface gravity is the redshifted proper acceleration at the horizon. The redshifted proper acceleration at any point above the horizon will be less.

I still don't see what this has to do with the rest of the thread.

 

[jartsa]

More precisely, if the proper acceleration required to "hover" at the radius, above the horizon, at which the robot starts being winched, redshifted to infinity, were 1 g. (This also assumes that the robot is winched up slowly enough that its motion can be approximated by a series of static states at gradually increasing radius, and that the distance through which the robot is winched is small enough that there is no detectable change in the redshifted proper acceleration.) No object can be winched up from the horizon itself, and the surface gravity is the redshifted proper acceleration at the horizon. The redshifted proper acceleration at any point above the horizon will be less.

I still don't see what this has to do with the rest of the thread.

Why did I say the winching distance must be short? Oh yes, I thought the gravity field is quite inform but the gravitating energy increases rapidly, so the force increases.

I forgot that "unifom" gravity field is not uniform.

So when everyting is taken into account the force is quite constant, over quite large distance, like there was some kind of force field that is quite uniform. Right?

Earlier in this thread me and PAllen were arguing about this matter.

 

[PeterDonis]

So when everyting is taken into account the force is quite constant, over quite large distance, like there was some kind of force field that is quite uniform. Right?

The term "uniform gravity field" is somewhat problematic, as you have seen. Strictly speaking, the term does not apply in the presence of an actual gravitating body; it applies to the apparent "gravity field" seen by a family of accelerated observers in flat spacetime that all maintain a constant proper distance from each other. The term "Rindler observers" is often used to describe such a family of observers. However, as you note, the acceleration felt by such a family of observers is actually not uniform; the observers "lower down" feel more acceleration than the ones "higher up".

In the presence of an actual gravitating body, tidal gravity is present, which makes the field of an actual gravitating body vary with distance in a different way than the apparent "field" seen by Rindler observers in flat spacetime. (Also, the variation with distance depends on the mass of the body, whereas there is only one possible variation with distance for the acceleration felt by Rindler observers in flat spacetime.) I believe the term "uniform field" was used to describe the flat spacetime case to emphasize the fact that there is no tidal gravity in flat spacetime; but it can be confusing to realize that even in the absence of tidal gravity, the "gravity field" seen by Rindler observers still varies with position.

Since you have set your scenario in the presence of an actual gravitating body, the criterion for being able to treat the force felt by an object as constant is that tidal gravity is negligible over whatever distance you are considering. The larger the mass of the body, the larger the distance over which the force can be treated as uniform.