Originally posted by @metal-brain "the observer in the test volume cannot tell that their clock is running slowly without consulting a second observer in an inertial frame and away from a gravity well - or on a planet with a non-varying clock rate. If the first observer is in an accelerated frame because they are accelerating in a flat background then their clock should be running slowe ...[text shortened]... ilation cannot provide a full account of it."
What 20 independent components? Please explain.
Kind of. The principle of equivalence has an observer unable to distinguish between a kinematic acceleration and a gravitational acceleration, but the clock hypothesis does distinguish between the two. Our "observer in a box" who knows they are accelerating but doesn't know whether it is due to changing velocity or a gravitational field can't tell if his clock is changing rate without consulting a second observer who knows their own state of motion relative to the Local Group of galaxies. It's not immediately obvious to me whether this is a problem for the principle of equivalence or not.
A vector has four independent components, three space like and one time like. A tensor is a generalization of the concept of a vector. A general tensor of rank two in a four dimensional space has sixteen independent components and can be written out like a matrix. However, most of the physically interesting ones have symmetry properties that reduce the number of independent components, for example the electro-magnetic field is a tensor of rank two that is anti-symmetric and has six independent components - three correspond to the electric field and the other three the magnetic field. The Riemann curvature tensor is a tensor of rank four which has various symmetries that reduce the number of independent components from 256 to 20.
My argument is essentially technical and is that any theory based around space-time being curved has to be able to account for the degrees of freedom space-time has. The full curvature tensor has too many independent components for a single scalar (along with boundary conditions) to adequately describe it. Roughly, I don't think you'll be able to predict enough using just time dilation.
Originally posted by @deepthought Kind of. The principle of equivalence has an observer unable to distinguish between a kinematic acceleration and a gravitational acceleration, but the clock hypothesis does distinguish between the two. Our "observer in a box" who knows they are accelerating but doesn't know whether it is due to changing velocity or a gravitational field can't tell if ...[text shortened]... describe it. Roughly, I don't think you'll be able to predict enough using just time dilation.
Does that get simpler inside a black hole where gravity may be trillions of times greater?
Originally posted by @moonbus Nothing causes gravity. Nothing causes electricity either.
Gravity exists, therefore it has a cause. Electricity exists, therefore it has a cause. I admit a failure in my imagination here. Things are caused or else they never happened.
Originally posted by @sonhouse Does that get simpler inside a black hole where gravity may be trillions of times greater?
Which, the statements about the equivalence principle or the mathematical structure of the theory? The theory doesn't change just because conditions are extreme.
Originally posted by @deepthought Which, the statements about the equivalence principle or the mathematical structure of the theory? The theory doesn't change just because conditions are extreme.
Structure of the theory. Could you explain these bits of the structure?
Originally posted by @sonhouse Structure of the theory. Could you explain these bits of the structure?
I think I get your question now - and apart from the way an observer in a box is going to have problems communicating with an external observer from the inside of a black hole, no it makes no difference, it's just the field is much stronger.
Regarding the structure of the theory, I was referring to the mathematical objects in the theory, specifically the Riemann tensor, and that the number of components it has doesn't change depending on where one is. For that to change the number of dimensions of spacetime would have to be position dependent and that seems unlikely.
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22 Mar '18 15:28
Originally posted by @deepthought I think I get your question now - and apart from the way an observer in a box is going to have problems communicating with an external observer from the inside of a black hole, no it makes no difference, it's just the field is much stronger.
Regarding the structure of the theory, I was referring to the mathematical objects in the theory, specifically ...[text shortened]... e number of dimensions of spacetime would have to be position dependent and that seems unlikely.
Doesn't the singularity collapse spacetime itself?
Originally posted by @deepthought Kind of. The principle of equivalence has an observer unable to distinguish between a kinematic acceleration and a gravitational acceleration, but the clock hypothesis does distinguish between the two. Our "observer in a box" who knows they are accelerating but doesn't know whether it is due to changing velocity or a gravitational field can't tell if ...[text shortened]... describe it. Roughly, I don't think you'll be able to predict enough using just time dilation.
"space-time being curved has to be able to account for the degrees of freedom space-time has"
That doesn't make any sense to me. Why wouldn't time dilation account for it?
Freedom? How would the degrees be restricted?
"The full curvature tensor has too many independent components for a single scalar (along with boundary conditions) to adequately describe it."
Why are you calling it "scalar"? How would it lack direction?
Originally posted by @metal-brain "space-time being curved has to be able to account for the degrees of freedom space-time has"
That doesn't make any sense to me. Why wouldn't time dilation account for it?
Freedom? How would the degrees be restricted?
"The full curvature tensor has too many independent components for a single scalar (along with boundary conditions) to adequately describe it."
Why are you calling it "scalar"? How would it lack direction?
Think about this: You have a flat space, then some magic machine starts a time dilation.
Then the spacetime fluid starts compressing or expanding, whichever way the time varied.
But here, there is no curve, it is more like a balloon expanding or contracting and the physical shape is exactly the same no matter what time dilation does.
On what do you base your time dilation causative theory?
Originally posted by @metal-brain "space-time being curved has to be able to account for the degrees of freedom space-time has"
That doesn't make any sense to me. Why wouldn't time dilation account for it?
Freedom? How would the degrees be restricted?
"The full curvature tensor has too many independent components for a single scalar (along with boundary conditions) to adequately describe it."
Why are you calling it "scalar"? How would it lack direction?
A scalar is something like air pressure - it's described by a single number at each point. A vector is something like the electric field, which needs 3 numbers at each point to describe it.
Originally posted by @sonhouse Think about this: You have a flat space, then some magic machine starts a time dilation.
Then the spacetime fluid starts compressing or expanding, whichever way the time varied.
But here, there is no curve, it is more like a balloon expanding or contracting and the physical shape is exactly the same no matter what time dilation does.
On what do you base your time dilation causative theory?
There is a curve. I don't see why you are assuming there is no curve.
Spacetime fluid? I take it that you accept spacetime is discrete and buy into the superfluid theory. It seems I am not the only one who has unconventional theories.
Time dilation is spherical and it varies from close to the surface of the earth to far away. You thinking that time dilation and gravity are different because that is what you were taught. I'm saying time dilation is gravity. They are the same thing.
Originally posted by @deepthought A scalar is something like air pressure - it's described by a single number at each point. A vector is something like the electric field, which needs 3 numbers at each point to describe it.
Why do you think time dilation is scalar? You have not made any convincing point to establish that. You just say it without explanation.
Originally posted by @metal-brain Why do you think time dilation is scalar?
The word 'scalar' in physics usually means a quantity that can be described by a single real number representing magnitude but without reference to direction (else it is a 'vector' ).
Originally posted by @metal-brain There is a curve. I don't see why you are assuming there is no curve.
Spacetime fluid? I take it that you accept spacetime is discrete and buy into the superfluid theory. It seems I am not the only one who has unconventional theories.
Time dilation is spherical and it varies from close to the surface of the earth to far away. You thinking that ti ...[text shortened]... ause that is what you were taught. I'm saying time dilation is gravity. They are the same thing.
"There is a curve'' is not an argument favoring your theory. For one thing, for a theory to be validated, you need to produce predictions that would be different from GR. What are your predictions in this area? So far you have shown nothing more than an opinion.
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21 Mar '18 03:44
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