Is the standard view of gravity in general relativity accurate?

[The_Obsessive_One]

I am not sure that this is the best place for this but I have a question about general relativity. The standard view of gravity, under general relativity is a bowling ball on a tarpalleine (however that is spelt), distorting the tarpalleine, and causing any object on the tarpauline to fall down the incline towards it. Fair enough, but how litterally accurate is this view? Space is four dimensional, one of time, and three of space, so if we follow the bowling ball image the three dimensional space time matrix is distorted into another dimension, a fifth dimension, to produce gravity, or is gravity, under special relativity, an entirely three dimensional phenomona.

 

[selfAdjoint]

I am not sure that this is the best place for this but I have a question about general relativity. The standard view of gravity, under general relativity is a bowling ball on a tarpalleine (however that is spelt), distorting the tarpalleine, and causing any object on the tarpauline to fall down the incline towards it. Fair enough, but how litterally accurate is this view? Space is four dimensional, one of time, and three of space, so if we follow the bowling ball image the three dimensional space time matrix is distorted into another dimension, a fifth dimension, to produce gravity, or is gravity, under special relativity, an entirely three dimensional phenomona.

It is actually incorrect, in that it assumes an outside source of gravity to produce the curvature, whereas GR asserts that gravity IS the curvature. The only thing this model provides is a reduced dimension view of the curvature itself. If you can think of the curved sheet without the ball, and imagine the tracks of particles forced to move on the surface, you will get a better idea of what Einstein was talking about.

 

[RandallB]

Space is four dimensional, one of time, and three of space, so if we follow the bowling ball image the three dimensional space time matrix is distorted into another dimension, a fifth dimension, to produce gravity, or is gravity, under special relativity, an entirely three dimensional phenomona.

You don't need the fifth dimension. You might be confusing parts of your three dimensional experience, with the parts of the four dimensions of GR.

Think of it like this:
You see 3D: x,y,z
Plus a thing you called time (not a dimension) that tells you things ‘change or move’ within that 3D space.

Now GR has 4D: A, B, C, D

No one of your x, y, or z matches up with anyone of the A, B, C, or D

The presence mass causes ABCD to warp in specific ways to create the xyz you experience. Be careful not to expect to be able to tie coordinates in x to something like coordinates in A.

 

[Crazy8s]

We don't need any dimensions at all. Dimensions are only used to describe points in space, imaginary or not. You can most certainly use that concept of the 5th dimension (the one with the bowling ball...) to illustrate, and measure, the effects of gravity around massive objects. X and Y are every bit as irrational as that 5th dimension. Be careful how you apply logic to one thing that is irrational when doing so undoes something equally irrational that you use all the time. Machinists use X, Y and Z all the time, but X and Y only exist within the mind.

 

[RandallB]

the 5th dimension (the one with the bowling ball...) to illustrate, and measure, the effects of gravity around massive objects.
>>> exist within the mind.

It’s the 4D of GR that is “the one with the bowling ball...” not 5D.

In these threads, we try to stick with facts and established theories here not (only exist within the mind) Metaphysics.

 

[Crazy8s]

It’s the 4D of GR that is “the one with the bowling ball...” not 5D.
In these threads, we try to stick with facts and established theories here not (only exist within the mind) Metaphysics.

For clarification, please explain how X and Y are fact, and not imaginary. It is my understanding that X is a straight line with no other characteristics other than it that stretches infinitely. It has no depth or height, so it can only be imagined. Y is the addition of shape to that line, or simply a bisect of X that can have a shape or stretch indefinitely, and also only resides within the imagination. Z adds depth, which gives it tangibility, with exception thrown to motion to actually allow for "touching" of it. This is not metaphysics, religion, zen, or any other type of philosophy, unless you consider physics to be philosphy. (which in most respects, it is...)

Within GR, space-time does not mean tying two indifferent entities together. Space and time are two different entities, and would represent two different dimensions, if they were to be used to measure locations or motion. I suggest you revisit your textbooks for further clarification of what space-time is.

Please understand that this is not intended to be confrontational or even argumentative. I only wish to further my understanding of the things unknown.

 

[selfAdjoint]

For clarification, please explain how X and Y are fact, and not imaginary. It is my understanding that X is a straight line with no other characteristics other than it that stretches infinitely. It has no depth or height, so it can only be imagined. Y is the addition of shape to that line, or simply a bisect of X that can have a shape or stretch indefinitely, and also only resides within the imagination. Z adds depth, which gives it tangibility, with exception thrown to motion to actually allow for "touching" of it. This is not metaphysics, religion, zen, or any other type of philosophy, unless you consider physics to be philosphy. (which in most respects, it is...)
Within GR, space-time does not mean tying two indifferent entities together. Space and time are two different entities, and would represent two different dimensions, if they were to be used to measure locations or motion. I suggest you revisit your textbooks for further clarification of what space-time is.
Please understand that this is not intended to be confrontational or even argumentative. I only wish to further my understanding of the things unknown.

This view of dimension has nothing to do with the way the word is used in physics, including relativity. A dimension is a degree of freedom of linear measurement, so you can orient your yardstick some particular way and measure length, orient it some other way and make another one, and make a third measurement in some third direction. And if no two of these are actually the same direction, then you find that all your measurements can be expressed as linear combinations of the three you chose, and this is what we mean by three dimensional. No mystical line, tangible or otherwise.

If your friend has made his own three choices, then to express his measurements in your coordinate system (assuming he was using a matching yardstick to yours) you have to perform a mathematical rotation. When you do this you find that the square of the length he measured - sum of the squares of the lengths in his three directions - is the same as the squared length you measure - sum of the squares of the lengths in your three directions. So the rotations preserve this sum of squares; the squares themselves vary from coordinate system to rotated coordinate system, but their sum is invariant.

 

[Crazy8s]

Physical dimensions

The physical dimensions are the parameters required to answer to the question where and when happened or will happen some event; for instance: When did Napoleon die? — On the 5 May 1821 at Saint Helena (15°56′ S 5°42′ W). They play a fundamental role in our perception of the world around us. According to Immanuel Kant, we actually do not perceive them but they form the frame in which we perceive events; they form the a priori background in which events are perceived.
[edit]

Spatial dimensions

Classical physics theories describe three physical dimensions: from a particular point in space, the basic directions in which we can move are up/down, left/right, and forward/backward. Movement in any other direction can be expressed in terms of just these three. Moving down is the same as moving up a negative amount. Moving diagonally upward and forward is just as the name of the direction implies; i.e., moving in a linear combination of up and forward.
[edit]

Time

Time is often referred to as the "fourth dimension". It is, in essence, one way to measure physical change. It is perceived differently from the three spatial dimensions in that there is only one of it, and that movement seems to occur at a fixed rate and in one direction.

The equations used by physics to model reality often do not treat time in the same way that humans perceive it. In particular, the equations of classical mechanics are symmetric with respect to time, and equations of quantum mechanics are typically symmetric if both time and other quantities (such as charge and parity) are reversed. In these models, the perception of time flowing in one direction is an artifact of the laws of thermodynamics (we perceive time as flowing in the direction of increasing entropy).

The most well-known treatment of time as a dimension is Einstein's theory of general relativity, which treats perceived space and time as parts of a four-dimensional manifold.


(this was cut and pasted from Wikipedia. If you feel it is wrong, I encourage you to update it to reflect what more closely represents itself as correct.)

 

[Crazy8s]

This view of dimension has nothing to do with the way the word is used in physics, including relativity. A dimension is a degree of freedom of linear measurement, so you can orient your yardstick some particular way and measure length, orient it some other way and make another one, and make a third measurement in some third direction. And if no two of these are actually the same direction, then you find that all your measurements can be expressed as linear combinations of the three you chose, and this is what we mean by three dimensional. No mystical line, tangible or otherwise.
If your friend has made his own three choices, then to express his measurements in your coordinate system (assuming he was using a matching yardstick to yours) you have to perform a mathematical rotation. When you do this you find that the square of the length he measured - sum of the squares of the lengths in his three directions - is the same as the squared length you measure - sum of the squares of the lengths in your three directions. So the rotations preserve this sum of squares; the squares themselves vary from coordinate system to rotated coordinate system, but their sum is invariant.

I think that in the way I described it, I left the door open to misinterpretation. I worked as a machinist for a number of years, and I think I see the cartesian coordinate system from a slightly different perspective.

 

[RandallB]

I suggest you revisit your textbooks for further clarification of what space-time is.
Please understand that this is not intended to be confrontational or even argumentative. I only wish to further my understanding of the things unknown.

Then why are you telling me to go read something?
What part is your unknown?
Are you clear on GR. – is it 4D or 5D for you?

Do you understand “Background”?
For GR is it ‘Dependent’ or ‘Independent’ for you?
(you may need to do some reading here – try search threads)

As you clarify those ideas from your readings, (not likely you’ve got to that part yet if you think GR is 5D) read what I said in my post, not what you imagine I said.

Note that SR is 3D not 4D like GR, so they are different forms of relativity.

 

[JesseM]

Note that SR is 3D not 4D like GR, so they are different forms of relativity.

Both GR and SR are 4D, the difference is that SR deals only with flat 4D spacetime while GR deals with curved 4D spacetime (with the curvature related to the distribution of matter/energy).

 

[JesseM]

I am not sure that this is the best place for this but I have a question about general relativity. The standard view of gravity, under general relativity is a bowling ball on a tarpalleine (however that is spelt), distorting the tarpalleine, and causing any object on the tarpauline to fall down the incline towards it. Fair enough, but how litterally accurate is this view? Space is four dimensional, one of time, and three of space, so if we follow the bowling ball image the three dimensional space time matrix is distorted into another dimension, a fifth dimension, to produce gravity, or is gravity, under special relativity, an entirely three dimensional phenomona.

The "rubber sheet" metaphor can be misleading--for one thing, it makes people think of objects being pulled "down" into depressions in the sheet, but really the orientation of the depression is irrelevant, you could just as easily imagine gravity creating humps in the sheet rather than depressions. All that's important is that the curvature of the surface determines the shortest path between two points, known as the "geodesic" path--for example, on the surface of a sphere, the shortest path between points is always a segment of the great circle (like lines of longitude, or the equator) that passes between those points. And even this is potentially misleading--on a curved 2D surface like a rubber sheet, a geodesic is the shortest path between two points on that 2D surface, but in general relativity, a geodesic is actually the path between two points in in curved 4D spacetime with the largest value of the "proper time" (time as measured by a clock that follows that path). And one other potentially misleading issue is the one you mention--to picture a curved 2D surface, we normally imagine it sitting in some higher 3D space, something that's known as an "embedding" of the curved surface in a higher-dimensional space. But mathematically there's no need to use a higher-dimensional embedding space, it is possible to describe curvature using purely intrinsic features that could be observed by a being confined to the surface (like whether the sum of angles of a triangle drawn on the surface is more, less, or equal to 180 degrees), and general relativity uses only such intrinsic features to describe what it means for space to be curved (see this page on differential geometry, the mathematical basis for general relativity, which talks about the difference between intrinsic and extrinsic descriptions of curvature).

 

[Crazy8s]

Then why are you telling me to go read something?
What part is your unknown?
Are you clear on GR. – is it 4D or 5D for you?
Do you understand “Background”?
For GR is it ‘Dependent’ or ‘Independent’ for you?
(you may need to do some reading here – try search threads)
As you clarify those ideas from your readings, (not likely you’ve got to that part yet if you think GR is 5D) read what I said in my post, not what you imagine I said.
Note that SR is 3D not 4D like GR, so they are different forms of relativity.

Under certain examples of GR, when applied to different examples of quantum mechanics calls out for 26 dimensions. I am not even slightly prepared to go into detail about that. All I was referring to, with regards to the "5d", was accounting for motion, which I only referred to it as 4d because most people associate it as such. If 4d represents space-time, how do you account for motion within this "warpage" of space-time? This warpage of space via mass is independent of motion, which is what I referred to as needing to separate time from this warpage.

What I suggest to alleviate such confusion is to identify this warpage by using a distinct variable that describes the relationship of mass and the relative density of it versus space itself. By using this relationship, you can illustrate using the cartesian coordinate system exactly how much space is warped by mass. I am not a mathematician, and I am still trying to figure out exactly that formula. By seeing this concept as a variable, you can effectively use it to describe gravity associated with a singularity, providing you know it's density and volume. (not an easy thing to know...)

When you account for time as being simply motion, you can easily understand 5 different spatial dimensions that you can illustrate pretty much all known locations, as well as forces.

Or I am as my title suggests, crazy...

 

[RandallB]

Or I am as my title suggests, crazy...

I'll go for crazy.
You need to get clear that motion in SR is covered in 3D. (time is not a D)
Motion is covered in GR, including changing motion now, is 4D not 5D.
Don't go into QM's Multi D's till you get that.

 

[Crazy8s]

I'll go for crazy.
You need to get clear that motion in SR is covered in 3D. (time is not a D)
Motion is covered in GR, including changing motion now, is 4D not 5D.
Don't go into QM's Multi D's till you get that.

Only when using frames of reference. By using frames of reference, you are in all essence stopping time for that being measured.

This is an inherent problem with measuring time. Time is a constant, and stops for no one. With this we start getting into time dilation, and is certainly not for the meek to discuss.

With this, I stop contributing to the thread because it has, in many respects, lost focus from what it was originally intended to do.

 

[JesseM]

I'll go for crazy.
You need to get clear that motion in SR is covered in 3D. (time is not a D)
Motion is covered in GR, including changing motion now, is 4D not 5D.
Don't go into QM's Multi D's till you get that.

What do you mean that time is "not a dimension" in SR? What about the fact that time and space get mixed up in different observer's reference frames in SR, so that two events that take place in different places but at the same time in one frame will happen at different times in another frame? What about the fact that the coordinate-invariant spacetime interval between events depends on dt as well as dx, dy and dz, and it can be thought of as the analogue of distance in ordinary euclidean 3D space? What about the fact that in SR, the conservation of the energy-momentum 4-vector is more fundamental than conservation of energy or conservation of momentum individually?

Since you are disagreeing with the definition used by the entire physics community here, can you provide your own novel definition of what it means for time to be a dimension, and why it should be considered a dimension in GR and not SR?

 

[StatusX]

Spacetime is 4 dimensional because, roughly speaking, you need 4 coordinates to uniquely specify a point. In the same way, a sphere is 2-dimensional because a point is uniquely specified by its latitude and longitude. Now, the sphere has a metric which, in these coordinates, tells you the distance between two points separated by some (infinitessimal) latitude and longitude. From this metric you get all you need to know about the sphere, and thinking about it in this abstract manner, you have a 2D, non-euclidean space. But you can embed the sphere in euclidean space in such a way that the distance between neighboring points as given by the metric is the same as the euclidean distance, ie, dx²+dy²+dz². To do this, you need at least 3 dimensions.

Likewise, for curved spacetime you need more than 4 dimensions if you want to embed the space in euclidean space in such a way as to preserve distances. Even then, since the metric is Minkowskian (ie, the distance can be negative if the points are timelike seperated), you can only look at spacelike slices, or use some artificial embedding that makes negative distances positve. It is a very abstract form of geometry.

 

[RandallB]

What do you mean that time is "not a dimension" in SR? What about the fact that time and space get mixed up in different observer's reference frames in SR, so that two events that take place in different places but at the same time in one frame will happen at different times in another frame?

Since you are disagreeing with the definition used by the entire physics community here, can you provide your own novel definition of what it means for time to be a dimension, and why it should be considered a dimension in GR and not SR?

What you’re talking about in SR is simultaneity issues not 4D. As soon as you say 'spacetime' your talking about GR.

Einstein abandoned SR in 1908 because he saw he couldn’t answer gravity or acceleration with it before most others in physics recognized that.
Still took him 8 more years to come up with the new CONCEPT and math to use 4D with warping to solve the problem in the new GR.

It’s only few in the scientific community think GR can be derived from the formulas of SR.
IT CANNOT – I know I tried till I finally got it that SR and GR are two different CONCEPTS.
Although, the principals of SR do apply in a GR world. Fundamentally SR is 3D and GR is 4D and are not the same thing. SR was complete within itself long before 4D was needed.

Unfortunately quite a few people are still confused by not getting this clear.
The other thing many get messed up on is thinking Einstein just added one dimension (time) to the existing three. He didn’t it’s not any part the three “we see” that warp. It’s the interrelation of the four that warp with each other that create the reality of the three “we see”, from each of our reference points. This is when you start getting into "background" issues.

 

[JesseM]

What you’re talking about in SR is simultaneity issues not 4D.

Those "simultaneity issues" are part of what the term "spacetime" was invented to describe. Also, the fact that the invariant spacetime interval ds^2 = c^2*dt^2 - dx^2 - dy^2 - dz^2, which can be used to define the metric of flat spacetime, depends on the time coordinate is not a simultaneity issue.

As soon as you say 'spacetime' your talking about GR.

Not according to how every physicist in the world defines "spacetime". For example:

http://en.wikipedia.org/wiki/Spacetime

Treating space and time on the same footing and as two aspects of a unified whole was devised by Hermann Minkowski shortly after the theory of special relativity was developed by Albert Einstein. This unification is further exemplified by the common practice of expressing time in the same units as space by multiplying time measurements by the speed of light. The concept of spacetime is vital to this theory and also to general relativity, an extension of special relativity, that takes into account gravitation.

Or this:

http://www.physics.nmt.edu/~raymond/classes/ph13xbook/node40.html

In special relativity we find that space and time ``mix'' in a way that they don't in Galilean relativity. This suggests that space and time are different aspects of the same ``thing'', which we call spacetime.

If time and position are simply different dimensions of the same abstract space, then they should have the same units. The easiest way to arrange this is to multiply time by the maximum speed, , resulting in the kind of spacetime diagram shown in figure 4.3.

Or this:

http://www.einstein-online.info/en/navMeta/dictionary/s/

Already in special relativity, observer in motion relative each other will not, in general, agree as to whether two events happen simultaneously, or as to how great is the distance between two objects. They do, however, agree as to what events there are, although not to when and where they happen. This observer-independent totality of all events is called space-time. How space-time is split into space and time can differ from observer to observer.

Every-day space has three dimensions. Adding time adds another dimension - space-time has four dimensions, all in all.

We are used to the notion of a point in space - an object with but a single location, defined completely once its space coordinates are given. In spacetime, a spacetime point is an object defined completely once its space coordinates and its time coordinate are given - which makes a space-time point nothing but an elementary event.

The idea of space-time is, in addition to its role in special relativity, a building block of general relativity. Analogous to how a plane is flat, but the surface of a sphere is curved, in general relativity, curved or distorted versions of the simple, flat space-time of special relativity play a role. Space-time curvature, in general relativity, is intimately connected with gravity.

For an introduction to the basics of both theories of relativity, check out the chapters Special relativity and General relativity in Elementary Einstein. Sometimes, it can be helpful to view space-time in analogy to ordinary space - such analogies are explored in the spotlight topics Time dilation on the road (for time dilation) and Twins on the road (for the twin effect).

This use of "space-time" accords with Einstein's own use of the word, see this section of a book by Einstein entitled "The Space-Time Continuum of the Special Theory of Relativity Considered as a Euclidean Continuum."

So again, if you have your own definition of "spacetime", and of what it means for a theory to be 4D as opposed to 3D, then please provide it. If not, then probably the problem is just that you have misunderstood what physicists mean when they use these terms.

Einstein abandoned SR in 1908 because he saw he couldn’t answer gravity or acceleration with it before most others in physics recognized that.
Still took him 8 more years to come up with the new CONCEPT and math to use 4D with warping to solve the problem in the new GR.
It’s only few in the scientific community think GR can be derived from the formulas of SR.
IT CANNOT – I know I tried till I finally got it that SR and GR are two different CONCEPTS.

I have never said that GR can be derived from SR, although once you know GR, you can derive SR as a special case of GR, and note that in arbitrarily small regions GR reduces to SR.

However, this has nothing to do with the point about the proper use of "spacetime". GR does indeed involve some different concepts that aren't present in SR, but the basic idea of spacetime is not one of them (the idea that spacetime can be curved is, though).

Although, the principals of SR do apply in a GR world. Fundamentally SR is 3D and GR is 4D and are not the same thing. SR was complete within itself long before 4D was needed.

SR and GR are different, but the difference has nothing to do with one being 3D and one being 4D, at least not as any physicists would use these terms. So either you've made up your own terminology which disagrees with that used by all physicists, or you've just misunderstood what physicists mean by these terms.

 

[RandallB]

Mathematically “space-time” is not needed until you need to curve it. Using it on SR clouds the issue that SR is not 4D. SR can be handled with ‘classical’ thinking just fine. Physics didn’t leave the classical with SR, nor with QM first. It first went non-classical with GR, one of the reasons it was so hard to understand and accept.

When “wikipedia” says “general relativity, an extension of special relativity” they are wrong. GR is a much bigger conceptual step than that.

If you like, it’s my ‘opinion’ the phrase “space-time” should only be used where it’s needed or makes sense. That’s where it needs to curve, and that’s GR not SR. If you don’t want to accept the SR and GR are two different things – go ahead. Each to his own.

See you in another thread someday.

 

[StatusX]

Just my 2 cents. It may be that, historically, GR was a radically new conception of space and time, and spacetime as a 4D manifold was not used in SR before the advent of GR. I'm not sure whether this is true or not. But in any case, it is clear now that SR is the special case of GR when spacetime is flat. There is no need to overcomplicate things by preserving the unrefined view that physicists had when SR was still a new theory.

 

[JesseM]

Mathematically “space-time” is not needed until you need to curve it. Using it on SR clouds the issue that SR is not 4D.

You've never answered my question, what criteria are you using to decide whether a theory 'is 4D' or not? If you disagree with the rest of the physics community's definitions on this, then you can't just rely on your own personal intuitions and gut feelings, you have to provide some sort of clear definition so we can all see that, given your definition, SR would indeed not 'be 4D' while GR would be. Otherwise you're just pontificating about nothing, using empty terminology that doesn't have any well-defined meaning.

SR can be handled with ‘classical’ thinking just fine. Physics didn’t leave the classical with SR, nor with QM first. It first went non-classical with GR, one of the reasons it was so hard to understand and accept.

Can you provide any sort of coherent definition of what you mean by "classical"? For instance, GR is deterministic, and it also allows you to have an objective self-contained picture of the entire universe without the need for any external observer, unlike QM (although some alternate 'interpretations' of QM would change this). Since both of those features of QM are part of why most physicists label QM as "non-classical", in this sense GR is more classical than QM. But usually "classical" seems to just be defined in a historical way, as a label for all physics before relativity and QM.

When “wikipedia” says “general relativity, an extension of special relativity” they are wrong. GR is a much bigger conceptual step than that.

Can you provide a coherent definition of what it means for one theory to be an "extension" of another? Most physicists would say that GR qualifies as an extension of SR for the simple reason that it reduces to SR in the case of flat spacetime with no matter or energy to curve it. Whether or not GR represents a major conceptual step beyond SR (I agree it does) wouldn't even enter into it.

If you like, it’s my ‘opinion’ the phrase “space-time” should only be used where it’s needed or makes sense.

What do you use to judge whether it "makes sense" if you don't even have a clear definition of the term in mind? Just gut feelings? You seem to rely on those quite a bit, in lieu of rational thinking or clear arguments.

That’s where it needs to curve, and that’s GR not SR. If you don’t want to accept the SR and GR are two different things – go ahead. Each to his own.

Nice strawman. I accept that they are quite different, I just don't think that the definitions of terms like "spacetime", "classical" and "extension" should be totally rewritten to reflect your personal preferences, as opposed to the meaning they have always had among physicists. And the fact is, the question of where these words apply has never been understood by physicists to have jack squat to do with whether or not SR and GR are "different" or not, that's just you making up your own private language and then criticizing other people for not using words the same way you do.

 

[Crazy8s]

Space and time are interrelated within Lorentz transformations to transpose measurements made by one observer into those of another observer, but the measurements of space and those of time are completely distinct. Space and time are not interchangeable as sometimes people imply using either SR or GR.

 

[selfAdjoint]

Space and time are interrelated within Lorentz transformations to transpose measurements made by one observer into those of another observer, but the measurements of space and those of time are completely distinct. Space and time are not interchangeable as sometimes people imply using either SR or GR.

But this mixing in the L transforms means that when Alice measures the length and time of something, her numbers will not agree with Bob's measurements, assuming he is moving relative to her (or she to him, as it's symmetric). So there isn't any TRUE and independent way to measure time and space apart from each other, and the concept of a four-vector, where they are components on the same level becomes important.

You want space and time to be philosophically different, but its difficult (I would suggest impossible) to make that mean anything where you don't have a preferred observer to do the splitting.

 

[Crazy8s]

But this mixing in the L transforms means that when Alice measures the length and time of something, her numbers will not agree with Bob's measurements, assuming he is moving relative to her (or she to him, as it's symmetric). So there isn't any TRUE and independent way to measure time and space apart from each other, and the concept of a four-vector, where they are components on the same level becomes important.
You want space and time to be philosophically different, but its difficult (I would suggest impossible) to make that mean anything where you don't have a preferred observer to do the splitting.

Curiously, if time is what we use to describe movement, than how does space, which does not move, get measured as if it does? Have they found that space actually moves?

To my knowledge, many experiments have been performed to find out if space actually moves, and all of the ones I am aware of have shown that it does not. If I am mistaken, I sincerely would like to know.

 

[pervect]

Curiously, if time is what we use to describe movement, than how does space, which does not move, get measured as if it does? Have they found that space actually moves?
To my knowledge, many experiments have been performed to find out if space actually moves, and all of the ones I am aware of have shown that it does not. If I am mistaken, I sincerely would like to know.

You are correct that there is no way an observer can tell if he is moving relative to "space" by any known experiment. One can measure velocity relative to another object or observer, but not relative to "space".

The point that Self-Adjoint is making, however, has nothing to do with space moving.

Let's look at Euclidean geometry for a bit. If we have a north-south distance x, and an east-west distance y, then the Pythagorean theorem says that the total distance between two points is given by z^2 = x^2 + y^2.

We get the same distance z for any orientation of our coordinate axes - we can make north point in different directions, and when we take x^2 + y^2 we will still get a constant number, as long as we make sure that the x and y axes are perpendicular.

In relativity, the "distance" betwen two events is given (in units where c=1) by

s^2 = (distance^2) - (time^2)

s is the invariant Lorentz interval. It is the same for all observers, no matter how they are moving.

Space and time "mix together" in the formula for the Lorentz interval, much in the same way that north-south and east-west "mix together" under a rotation of coordinate axes.

If point A is one mile "due north" of point B, and we rotate the coordinate axes 45 degrees clockwise, then point A will no longer be due north, but it will be .707 miles north and .707 miles east.

We have "transformed" north-south distances into east-west distances by rotating the coordinate axes.

In relativity, we transform spatial distances into temporal distances by the Lorentz transform (which represents moving observers, rather than rotating observers).

This is discussed in considerably more detail in "Spacetime Physics" by Taylor & Wheeler, for instance.

A Lorentz transform (Lorentz boost) transforms one persons spatial distance into another persons time distance, and vica-versa. This is why physicists talk about a space-time continuum, and a 4-dimensional "space-time".

 

[robphy]

Mathematically “space-time” is not needed until you need to curve it. Using it on SR clouds the issue that SR is not 4D. SR can be handled with ‘classical’ thinking just fine. Physics didn’t leave the classical with SR, nor with QM first. It first went non-classical with GR, one of the reasons it was so hard to understand and accept.

When “wikipedia” says “general relativity, an extension of special relativity” they are wrong. GR is a much bigger conceptual step than that.

Historically, GR is an (i.e. one) extension of SR, namely one in which the underlying manifold is not necessarily R⁴ and the Lorentz-signature metric is not necessarily flat (i.e. has nonzero Riemann tensor). It may be that the word "extension" has implication of something minor [like adding a garage to a house]... however, it could also suggest that SR is merely a stepping stone to GR. Maybe the word "generalization" is more agreeable. Of course, it is possible that GR could have been formulated first and that SR was a "specialization".

If you like, it’s my ‘opinion’ the phrase “space-time” should only be used where it’s needed or makes sense. That’s where it needs to curve, and that’s GR not SR. If you don’t want to accept the SR and GR are two different things – go ahead. Each to his own.

Opinion noted.

Of course, it was in the context of SPECIAL Relativity that Minkowski introduced the notion of spacetime, which provides a starting framework to formulate relativity theories geometrically (Special- and Galilean- in non-curved case; General- and Newton-Cartan in the curved case). In SR, of course, this geometric formulation allows one to reason and interpret using Euclidean analogies. In GR, one uses Riemannian analogies. It should be pointed out that SR, Galilean, and Newton-Cartan can be seen as limiting cases of GR.

If by "space-time" you really mean "space-time manifold" (with emphasis on the not necessarily vector-space structure), I would agree that a discussion of "manifolds" is not needed for teaching SR. However, if by "space-time" you mean the four-dimensional [vector] space with its geometrical analogies introduced by Minkowski, I disagree... physical interpretations of SR guided by my suitably-modified Euclidean intuition is much better than by my [non-vector-] algebraic intuition. (Case in point: those tediously-obtained and seemingly-mysterious algebraic identities involving "the $$\beta$$ and $$\gamma$$ functions" are nothing more than hyperbolic-trig identities in spacetime.)