Gravity & Curvature: Explaining Geometrical Orbit of Particles

[Jorrie]

Sorry Jorie, I don't think you understand what you are talking about. You say space need not be curved for gravitational effects to appear. This seems very wrong to me, even in your oddly worded statement. Gravity IS the product of curved space, plain and simple.

Maybe we are both just guilty of expressing ourselves badly - you probably meant "Gravity IS the product of curved spacetime…..", not just curved space
Now the interesting thing is that the weak equivalence principle alone is enough to create gravity – and it is without space curvature, just like in the small, uniformly accelerating lab. The weak equivalence principle manifests itself as gravitational redshift and also produces half of the gravitational bending of light. The other half is produced by space curvature. Tidal gravity, on the other hand, only appears in a curved spacetime environment.
It is from this point of view that I disagreed with the statements made in the OP.
Jorrie

 

[pmb_phy]

Sorry Jorie, I don't think you understand what you are talking about.

Jorrie seems well versed in GR in my opinion.

You say space need not be curved for gravitational effects to appear.

This is true depending on what one means by "gravitational effects." In Einstein's GR gravitational effects consist in part of gravitational acceleration, gravitational redshift. There is no requirement for spacetime to be curved for these effects to exist.

Gravity IS the product of curved space, plain and simple.

You've arrived at this conclusion by defining gravitational effects to be identical with tidal acceleration. So you haven't demonstrated anything other than you are using a definition which differs from Einstein.

If you can point out a local region of space where a non-uniform gravitational field exists that is not somehow curved, please do so, otherwise you are wrong.

This is nonsensical since Jorrie already clarified that tidal acceleration and spacetime curvature are identical, i.e. different names for the same phennomena. Thus there is no spacetime curvature in a uniform g-field because a uniform g-field is defined by requiring that the Riemann tensor vanishes in such a field.

I suggest you read a book on Relativity, or if you have, reread it.

Sorry but it appears quite clear that Jorrie knows what he's talking about. I recommend that you pick up the works of Einstein on GR and read them carefully and focus your attention on how Einstein defines gravity in GR.

A lab accelerating upwards will experience an effect that is equivalent to gravity, but your one correct point is that the graviational effect in the lab will be uniform and not dissipated by the inverse-square law like real gravity would. Cudos on 1/4.

The term "real gravity " is based on a biased view on gravity, i.e. that gravity is identified by spacetime curvature. In this view a uniform gravitational field is a contradiction in terms and it makes no sense to speak of gravity, never mind referring to a uniform field.

Pete

 

[pervect]

I suppose you mean the t-coordinate instead of the z-coordinate.

dtau = (1+gz)*dt

So dt/dtau = 1/1+gz

This is a function of z, i.e. a function of height. g here is a multiplicative constant for z, the acceleration of the spaceship, in case that isn't clear.

As far as space-time coordinates goes, there are many possible choices for coordinate systems. The fact that SR is Lorentz covariant says that we will get the same answer, in the end, regardless of which one of them we choose.

However, the path to the unique answer may not always appear to be the same on a popular level - i.e. we wind up talking about "gravitational time dilation" in some coordinates, and not in others. This is unavoidable if we use the coordinate approach - only a highly abstract approach, using geoemtric entities rather than coordinates, can avoid this.

 

[MeJennifer]

dtau = (1+gz)*dt

So dt/dtau = 1/1+gz

This is a function of z, i.e. a function of height. g here is a multiplicative constant for z, the acceleration of the spaceship, in case that isn't clear.

I see.

However, the path to the unique answer may not always appear to be the same on a popular level - i.e. we wind up talking about "gravitational time dilation" in some coordinates, and not in others. This is unavoidable if we use the coordinate approach - only a highly abstract approach, using geoemtric entities rather than coordinates, can avoid this.

Well it seems to me that transforming the local coordinates to space-time will give resolve these "abiguities". Comparing coordinate time with proper time will be an indication if there is any time "dilation". The terms "time dilation" and "length contraction" are prone to confusion IMHO, because they only have a meaning when you compare coordinate systems.