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Yet, here we find Contemporary Theoretical Physics - specifically Einstein's General Theory Of Relativity - equating gravity with acceleration as - and which is - a 'pushing or repelling force'.
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*** Your quotes from Einstein and Newton might be correct but in my view your deductions are not.
How can you arbitrarily say that acceleration is "pushing or repelling force"? What is that statement a logical deduction of?
If you pull the elevator you cause acceleration and likewise if you push it.
Incidentally gravity is caused by forces that originate from the object and act towards its center and this to me is sufficient description for them to be referred to as pulling forces as opposed to pushing ones that are thought to originate from a source external to the object.
Roger