[Halc]

Now we are coming to the nub of the matter. You claim that the acceleration due to a rocket is “different” from the acceleration due to gravity.  How could this be?

It is different.  Einstein considered gravity to be a curvature in the fabric of spacetime, and hence objects in freefall actually trace straight (geodesic) lines in their non-euclidean spacetime.  Thus freefall is equivalent to being inertial outside the gravitational field.  One just floats around and cannot tell which of the two situations one is in.
The accelerating case is where an actual force is being applied.  Gravity isn't such a force, it is just curvature.  So the force (of 1G say) is exerted upward by my rocket engines or by the ground underneath me. Either will cause my coffee to stay in its cup. Again, I cannot tell (via local test) which of the two situations I'm in.
That's the summary of the equivalence principle.

When an object is experiencing acceleration it doesn’t matter what kind of force is giving rise to that acceleration or what machine is responsible for it. If an acceleration is present it should have some effect on the spaceship and on its passengers also.

Agree.

In the space station the astronauts are under the influence of a constant acceleration of around 8.4m/s²  why should you claim that this does not affect the astronauts?

Einstein would claim they're not accelerating, but tracing a straight worldline.  Only in a non-local coordinate system (that of Earth instead of the space station) is the space station accelerating.  This may be difficult to visualize if you cannot conceive of 4 dimensional coordinates, let alone non-euclidean 4 dimensional coordinates.

In effect what you are saying, namely that there is a difference in acceleration due to gravity and that due to a rocket engine

Yes, there is very much a difference, since there is a trivial local test to distinguish one from the other.

is a complete right about turn to what the equivalence principle states, namely that there is no difference between the force caused by gravitation and that caused by an acceleration.

A misstatement of the principle.  It equates acceleration by non-gravitational force (a rocket engine say) to force exerted by the floor under me preventing the natural trajectory (a straight line) that gravity would otherwise take me.  There is a non-gravitational force in both cases.

In my example, in a space craft far from anywhere else, the passengers are weightless, they are free falling around space, so the application of an acceleration would have no effect on them. As long as they are weightless, acceleration should not affect them.

They would not be weightless if the spaceship was accelerating like that.

Or can you claim that these astronauts have weight?

Yes of course they would.  They could stand on a bathroom scale (a weight scale, not a mass scale) and it would read their weight.  A weight scale measures force.  A mass (balance) scale measures mass, a very different thing.

[Kryptid]

In the space station the astronauts are under the influence of a constant acceleration of around 8.4m/s2  why should you claim that this does not affect the astronauts?

It does affect the astronauts. I never said that it wouldn't. It's just that it affects the space station in an equivalent manner. If both the astronauts and the space station are accelerating at completely equal rates, then the astronauts can't tell whether they are standing still or in free fall.

In my example, in a space craft far from anywhere else, the passengers are weightless, they are free falling around space

Only if the spacecraft isn't accelerating.

so the application of an acceleration would have no effect on them.

Of course it would affect them. The difference is that, unlike the case of free fall in a gravitational field, the spacecraft and the astronauts are not accelerating at the same rate. The engines accelerate the rocket, which pushes the floor of the ship up against the feet of the astronauts. The ship's floor "feels" the acceleration before the astronauts' feet do, and their feet feel it before their heads do. This is because force propagates through material objects at a finite speed.

Do you think that all 10 Gs of a launching spacecraft come from the Earth's gravity or something? No. 9 of those Gs felt by those astronauts came from the spacecraft's acceleration.

[McQueen (OP)]

Halc: Einstein would claim they're not accelerating, but tracing a straight worldline.  Only in a non-local coordinate system (that of Earth instead of the space station) is the space station accelerating.  This may be difficult to visualize if you cannot conceive of 4 dimensional coordinates, let alone non-euclidean 4 dimensional coordinates.

If you don’t mind, I think I would like to decide what I can visualise or not visualise for myself. Not be told that something like the acceleration given to the space station, does not exist when seen from another non-euclidean point of view!  That kind of navel gazing you can keep to yourself if you don’t mind!

Halc: Either will cause my coffee to stay in its cup.

The space station is accelerating when viewed from our view point and not some non-euclidean( your words) point of view. Have you seen an astronaut trying to brush his teeth on the space station?

Halc:  Yes, there is very much a difference, since there is a trivial local test to distinguish one from the other.

If you could elucidate I am sure a lot of people would be interested. In case you missed it, the whole argument from Einstein’s point of view is that gravitational force and force due to acceleration are indistinguishable.
“The recognition that gravity and accelerated motion are profoundly interwoven is the key insight that Einstein had one happy day in the Bern patent office.”

Yes of course they would.  They could stand on a bathroom scale (a weight scale, not a mass scale) and it would read their weight.  A weight scale measures force.  A mass (balance) scale measures mass, a very different thing.

There is nothing to measure they are all weightless! F = ma, if there is no weight to measure because they are in free fall, acceleration does not affect them as it would if they possessed weight. They possess mass but no weight!

Kryptid: Of course it would affect them. The difference is that, unlike the case of free fall in a gravitational field, the spacecraft and the astronauts are not accelerating at the same rate. The engines accelerate the rocket, which pushes the floor of the ship up against the feet of the astronauts. The ship's floor "feels" the acceleration before the astronauts' feet do, and their feet feel it before their heads do. This is because force propagates through material objects at a finite speed.

In case you have not noticed you are repeating yourself over and over again. How can the acceleration due to gravity differ from the acceleration from a rocket. In the space station, the astronauts are not affected by the acceleration because they are in free fall and weightless. My contention is that exactly the same reasoning would apply to weightless astronauts in a rocket propelled ship far from any source of gravity.

[Janus]

My point is that astronauts in my example (i.e., in a spaceship far from any gravitational influences), would also be weightless and in free fall and hence the force of acceleration exerted on the ship would not affect them. Ergo, Einstein’s equivalence principle is wrong.

Your conclusion is demonstratively wrong.  Take the Dawn space probe to Ceres for example.  It was put on a course to Ceres under a gentle constant acceleration provided by its ION engine.  This required quite precise maneuvering.   While you can design the Engine to produce a given thrust, there will always be variations.   While at Ceres, the craft made a number of maneuvers to change its orbit from time to time.  Due to the great distance of the Ceres and the time lag, they could not be directly done from the Earth. Instead a signal was sent telling the craft to change its velocity by a certain amount.  This means the craft needed a means of telling when it had made the proper velocity change.   This was done by an accelerometer, a device which measures how much acceleration the probe is undergoing by measuring the very effect you claim doesn't exist.
If you were right, the Dawn probe's accelerometers would have not functioned as designed, and the craft wouldn't have been able to perform the maneuver  as instructed.   As it happened, the probe performed exactly as expected.
The Apollo mission craft also made use of accelerometers in their computer guidance systems so that when they made mid-course corrections, the computer would know just how long to burn the engines to effect the exact right amount of correction.  Again, according to your belief, this shouldn't have worked, but it did.

When the facts run contrary to your position, it is time to re-evaluate your position.

[McQueen (OP)]

I will have to rethink my position.

[Kryptid]

How can the acceleration due to gravity differ from the acceleration from a rocket.

Your entire argument seems to hinge on them being different. Otherwise, Einstein was right when he called them equivalent.

In the space station, the astronauts are not affected by the acceleration because they are in free fall and weightless. My contention is that exactly the same reasoning would apply to weightless astronauts in a rocket propelled ship far from any source of gravity.

Let's say that the astronaut is floating around inside of a non-accelerating spacecraft. Then, the engines turn on and the spacecraft starts accelerating at 9.8 m/s². The astronaut will see the floor accelerating towards him at the same rate as if he was falling towards the ground in the Earth's gravitational field. Do you really not think he will feel a force once he hits that floor equal to the force he would feel if he had fallen to the ground on Earth from an equal distance?

[Bored chemist]

According to what you state , moving at this speed the astronauts should be plastered to one side of the walls of the space station. Unable to move.

And would you like to point out  anywhere I said anything like that?
Or is it just dross you made up?

I will have to rethink my position.

Good.
I just wonder, do you, in real life (as opposed to on the internet) go round telling people who are much better qualified than you that you are right and they are wrong (in spite of demonstrably not actually understanding the subject).
Do you then add that the most famous expert in the field is also wrong, but only you have noticed ?

How conceited are you?
I mean, I'm pretty self assured but even I would draw the line at that sort of thing.

[McQueen (OP)]

Bored Chemist:How conceited are you? I mean, I'm pretty self assured but even I would draw the line at that sort of thing.

Glad you have got a renewed zest for living! As far as I am concerned it was really worthwhile. Terrific!