[jeffreyH (OP)]

If a body is falling freely towards a black hole will time dilation cancel the tidal forces so that the equivalence principle remains in tact?

[evan_au]

time dilation cancel the tidal forces

Tidal forces near a black hole are very real - you will be spaghettified near a stellar-mass black hole.
https://en.wikipedia.org/wiki/Spaghettification

the equivalence principle remains intact?

I expect that Einstein's equivalence principle will be intact outside the event horizon.
But it talks about tests "in a laboratory", where this laboratory has to be "small".
When you are talking about a black hole with an event horizon only 30km in diameter, this laboratory has to be very small, or the results will be distorted by tidal forces.

By the way, nobody today is really sure what happens inside an event horizon; even if we did find a "tame" black hole to experiment on, nobody outside the black hole will be really sure what happens inside the event horizon...

See: https://en.wikipedia.org/wiki/Equivalence_principle#The_Einstein_equivalence_principle

[Bored chemist]

"Does the equivalence principle hold near black holes?"

Define "near" in this context.
If you mean "inside the event horizon" then the answer is  we simply don't know.

Outside that limit, how would a system know that it was "near" a black hole so it knew to change its behaviour?

[jeffreyH (OP)]

Well you could ask how does a system know it has to follow a curved spacetime?

[yor_on]

spin?

[Bored chemist]

Well you could ask how does a system know it has to follow a curved spacetime?

I could ask that, and the answer is that it is "in" the curved spacetime, so it can sense it and act accordingly.
Now, can you explain how it knows it's near, but not in, a black hole
Are you invoking some sort of "action at a distance"?

[PmbPhy]

If a body is falling freely towards a black hole will time dilation cancel the tidal forces so that the equivalence principle remains in tact?

I don't see how you get that.

There are two forms of the equivalence principle known as the strong form and weak form. The weak for refers to uniform gravitational fields so you can't apply that to curved spacetimes. The strong form says that any physical law which can be expressed in tensor notation in SR must have the same form in a locally inertial frame of a curved spacetime.

The later is consistent with the notion that if you limit your observations of an experiment in a small enough region of spacetime in a locally inertial frame of reference your observations can be described by SR. I noticed that Evan referred to a small region of space. Its really with a small region of spacetime. Its easy to imagine an experiment which is confined to a small region of space but which manifests the spacetime curvature. For example: place a ball at rest any place within the international space station and record its position as a function of time. At first the ball seems to remain at rest but will undergo a complete cycle back and forth within the time it takes for the station to make one orbit.

Regarding black holes: there's nothing special that goes on near or even at the event horizon as observed by an inertial observer. In fact you can imagine a black hole which has enough mass to make the spacetime as flat (but never zero) as you'd like at the horizon. In fact the book Exploring Black Holes by Taylor and Wheeler often refer to them in that text.

[jeffreyH (OP)]

Well you could ask how does a system know it has to follow a curved spacetime?

I could ask that, and the answer is that it is "in" the curved spacetime, so it can sense it and act accordingly.
Now, can you explain how it knows it's near, but not in, a black hole
Are you invoking some sort of "action at a distance"?

Why would the system need to sense curvature and act accordingly? Does a particle have a choice in the matter? What if it decided to not act accordingly?

[Bored chemist]

You are missing the point.
Something can only interact with another thing if there is a mechanism for communication between them.

There would be no mechanism by which a black hole could communicate when it was "near" a body in order for the behaviour of that body to change (eg to stop following the equivalence principle)

[PmbPhy]

I see comments/questions here regarding how a particle "knows" something or other. Those kinds of questions have no place in science.

Regarding Something can only interact with another thing if there is a mechanism for communication between them. I assume that you're talking about a particle in a field which is generated by a source and some mechanism for the source to "communicate" with the particle. Is that what you mean? If so then the answer is that a source creates a field and the field at the location of the particle acts on the particle.

[jeffreyH (OP)]

You are missing the point.
Something can only interact with another thing if there is a mechanism for communication between them.

There would be no mechanism by which a black hole could communicate when it was "near" a body in order for the behaviour of that body to change (eg to stop following the equivalence principle)

Well the escape velocity always approaches light speed at the event horizon of a black hole due to the potential of the field at that point. So this tells the particle something concrete and constant for all black holes. No field can propagate away from the horizon. That is a pretty definite reason for a particle to act accordingly. It is the region approaching the horizon that is more interesting.