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Could someone provide a practical description of tensors of first & second order, etc.? Trying to get this relativity thing (A.R., Absolute Relativity is looking good) & i'm hitting a roadblock with my limited understanding of differential linear algebra.Thanks in advance...

A point worth keeping in mind is that a distinction is to be made between a mathematical value and a function whose domain is a set of such mathematical values and whose range is another set of such (or perhaps a different type of) mathematical values, the function expressing the mapping between one and the other.

We may thus speak of the velocity of an object as a vector, and we may loosely speak of the windspeed as a vector, but to be semantically precise, the latter should be spoken of as a vector function of position because it does not necessarily have a single value, but a whole set of values varying from place to place.

Quote from: Atomic-SA point worth keeping in mind is that a distinction is to be made between a mathematical value and a function whose domain is a set of such mathematical values and whose range is another set of such (or perhaps a different type of) mathematical values, the function expressing the mapping between one and the other.What does this have to do with the definition of tensors?

An example of a second rank tensor is the Newtonian tidal force tensor. See: http://www.newenglandphysics.org/physics_world/mech/07_tidal_force_tensor/tidal_force_tensor.htm [nofollow]This tensor determines the forces on an object in a non-uniform gravitational field.

if i have rocket boots holding me stationary in that potential field, what's happening to that acceleration?

To use your rocket boots you are simply countering the instantaneous velocity at your altitude with an input of constant energy. Thus you are creating an artificially engineered 'inertial' frame of reference. However, this is still an accelerating frame of reference.

Yeah; i'm asking how that presents mathematically. If free fall is a straight line on a geodesic(?); stationary in a potential gradient must be a non-straight line in some respect... mustn't it?

I have two questions wrt equivalence: if i'm accelerating at 9.8 m/s2, why am i not going the speed of light? I'm old enough, to be sure. And; if i'm experiencing a force but *not* accelerating; am i traveling in a circle in some sense?

How does this relate to geodesics? & if i have rocket boots holding me stationary in that potential field, what's happening to that acceleration?

if i'm accelerating at 9.8 m/s^{2}, why am i not going the speed of light? I'm old enough, to be sure.

It is being eaten up by spacetime bending in the other direction.

However (and it's big however!), Einstein showed that you can never accelerate a massive object to reach the speed of light - no matter how hard you accelerate, or for how long.

The point of the thread is to further understanding of gravity as understood by G.R..

Atomic-S' reply is inline with my train of thought; i was gonna mention.

Gravity is a 'acceleration field/spacetime shape resolution' issue; ..

I'm merely trying to understand if I missed something that was obvious to others and not to me.

Quote from: Arthur Geddes Atomic-S' reply is inline with my train of thought; i was gonna mention.I'm confused here my dear sir. Please explain how so? I only ask because I can't see how its related since its almost completely unrelated to tensor analysis.

I asked Atomic-S What does this have to do with the definition of tensors? but he chose not to answer my question. Perhaps if you describe the train of thought that you mentioned above then I'll understand. Thanks.

Quote from: Arthur Geddes Gravity is a 'acceleration field/spacetime shape resolution' issue; .....actually tidal gradients in the gravitational field. In the language of general relativity, spacetime curvature.

Quote from: Arthur Geddesif i'm accelerating at 9.8 m/s^{2}, why am i not going the speed of light? I'm old enough, to be sure.If we apply some physics from early high school, you would expect your velocity to be: v = at where: v: velocity at time t a: acceleration (9.8m/s2 in this example) t: elapsed timeAccording to this formula, to reach the speed of light v=c=3x10^{8} m/s would take t=3x10^{8}/9.8 = 3x10^{7} seconds = 347 days, or just under a year.However (and it's big however!), Einstein showed that you can never accelerate a massive object to reach the speed of light - no matter how hard you accelerate, or for how long.These concepts normally come up at the end of high school or early university physics.We don't notice it with our daily lives here on Earth, but when you accelerate objects close to the speed of light, strange things occur: time slows down, and mass increases, so it gets harder and harder to get closer to the speed of light. Oddly, this is not visible to the person being accelerated.Such peculiarities are very familiar to physicists at the LHC, who try to get particles traveling as close as possible to the speed of light so they can do experiments at very high energies.See: ...sorry, you cannot view external links. To see them, please REGISTER or LOGINSo you may feel old, but you are not nearly old enough to reach the speed of light, when accelerating at 9.8m/s^{2}!

From the original post: "Trying to get this relativity thing..."QuoteAhhh! I understand now. For some reason I thought you only had special relativity (SR) in mind because people almost always study SR before they study general relativity (GR). Thanks for making that clear.

Ahhh! I understand now. For some reason I thought you only had special relativity (SR) in mind because people almost always study SR before they study general relativity (GR). Thanks for making that clear.

can gravity force an object to reach light speed at the event horizon of a black hole?

Quote from: JeffreyHcan gravity force an object to reach light speed at the event horizon of a black hole?For a "distant observer", an object can reach just over c/3 before it disappears inside the event horizon.If you scroll down to the graphs and equations on the following web page, you will see that the answer is "yes and no", all depending on your frame of reference....sorry, you cannot view external links. To see them, please REGISTER or LOGIN