What is the difference between curved spacetime and a field?

[alba]

Does GR use spacetime mainly in order to include SR?
Couldn't gravity be explained just with mass curving space and not spacetime?
Why can't we explain the trajectories by field lines in regular space and choose the warp the structure of space itself,which is a really tricky business? How can space be homogeneous and isotropic if it is at same time expanding (cosmology) ,being curved (GR) and contracted (SR) at same time?

 

[martinbn]

I think that there is no way to answer these questions in a way that will be satisfactory to you. All of them stem from not knowing enough about relativity. The way to change that is to study some more. I would recommend Geroch "General Relativity from A to B".

Take for instance your first question. It shows that you thing that space-time is something that GR uses. But it is not like that. Space-time is what it is and GR describes/models it in a particular way. In classical(non relativistic physics) you still have the notion of space-time, but its structure is very different. Penrose has a nice section on space-time from Aristotel to Einstein in "The Road to Reality".

 

[alba]

I think that there is no way to answer these questions in a way that will be satisfactory to you. All of them stem from not knowing enough about relativity. The way to change that is to study some more. I would recommend Geroch "General Relativity from A to B".

Take for instance your first question. It shows that you thing that space-time is something that GR uses. But it is not like that. Space-time is what it is and GR describes/models it in a particular way. In classical(non relativistic physics) you still have the notion of space-time, but its structure is very different. Penrose has a nice section on space-time from Aristotel to Einstein in "The Road to Reality".

That is not true, no one, scientist or philosopher, has ever remotely thought of time as a dimension, and a dimension that can be merged with space. Kant even ignored time as a category. Presently, nobody knows anything about time and space, can you give a reference/link where some scientist explaines what is time or space and how you bent, curve or contract space?

Of course I do not know SR or GR in details, but I hope that there is somebody who does not take them as gospel or dogmas and is prepared to discuss the basic concepts, which are not thechnical but theoretical.

 

[Jonathan Scott]

Space is what is measured by rulers. Time is what is measured by clocks. The same concepts are extrapolated to situations where we cannot do a measurement directly.

If mass only curved space, static objects wouldn't be accelerated by gravity.

To describe what happens a region of space-time where gravity is significant we cannot use local rulers and clocks, because different paths give slightly different measurements. We therefore choose a coordinate system which is approximates conventional space and time, then describe how local rulers and clocks behave in terms of a function of that coordinate system (for example using the "metric" which describes distances). The conventional terminology for this in General Relativity is to say that space-time is still what is described by local rulers and clocks. You could obviously switch the terminology and use "space-time" to refer to the chosen coordinate system in which case rulers would be curved relative to "space" and clocks would not exactly measure "time", but this doesn't change the physics.

When mass is present, space-time is curved in a way which is coordinate-independent, in that for example a closed space-like path constructed with rigid rulers and protractors around a mass will have a total angle that differs slightly from 360 degrees.

The expansion of the universe is not an expansion of local space, but rather that there is more space as the universe gets older. Consider the analogy of a toy car driving outwards on a flat disc of paper, where the current radius from the centre represents time and the circumference at that radius represents space. The paper is flat, so there is no force trying to move the wheels apart, but the total size of space is steadily increasing.

Contraction in special relativity is not a physical contraction, but rather a viewpoint effect similar to the way in which rotation makes things shorter in one direction and longer in another.

 

[alba]

Space is what is measured by rulers. Time is what is measured by clocks.

It would be wounderful it it were as easy as that. Unfortunaly, Jonathan,it is not.
But, just considering , for argument's sake, your definition as meaningful, how do you get from there that what you measure by clocks is/has a dimension and that it can be merged with what you measure by rulers? can all that we measure be merged with space? what would you say if I try to merge space with beauty, or honesty, we can device a system to measure those concepts.
Also how do you get to the conclusion that time can be dilated/contracted? There can never exist a proof of that.

But the point of my question is not to discuss or question the basic concepts of GR, my question is if gravity can be explained by curvature of space and not spacetime.

 

[A.T.]

Couldn't gravity be explained just with mass curving space and not spacetime?

Space geometry only affects object which are already moving through space. But gravity also affects objects which are initially at rest.

 

[Nugatory]

It would be wounderful it it were as easy as that. Unfortunaly, Jonathan,it is not.

Actually, it is that easy. That you don't find it so merely reinforces martinbnn's point above - you haven't learned the basics of relativity enough to sensibly discuss the subject.

how do you get from there that what you measure by clocks is/has a dimension and that it can be merged with what you measure by rulers? can all that we measure be merged with space? what would you say if I try to merge space with beauty, or honesty, we can device a system to measure those concepts.

"Dimension" has a precise mathematical meaning and we have an unambiguous mathematical theory that treats time as a dimension. This theory agrees with experiments with greater accuracy than any alternative. So the answer to your "how do we get from there...?" question is to learn that theory.

Also how do you get to the conclusion that time can be dilated/contracted? There can never exist a proof of that.

In science, proof comes from experiment and observation, and there are numerous experiments in which the effects of time dilation are observed. A representative few are described in the sticky thread at the top of this forum; the muon decay and Hafele-Keating are two of my favorites, and time dilation is also observed routinely in particle accelerators.

 

[Nugatory]

How can space be homogeneous and isotropic if it is at same time expanding (cosmology) ,being curved (GR) and contracted (SR) at same time?

As long as the curvature and expansion are the same at all points and in all directions spacetime is homogeneous and isotropic.

The length contraction in SR is a different phenomenon that cannot be understand as space being contracted. The easiest way of seeing this is to consider that length contraction in SR is symmetrical: if you and I are in relative motion, you will find my meter stick to be contracted and I will find yours to be contracted. This effect cannot be explained by contraction of space because there's only one space that we're both in - if it is contracted for one of us it has to be contracted for the other as well.

The questions in the original post have been answered so this thread can be closed.