I Do moving massive objects drag curved spacetime with them?

[hnaghieh]

don’t understand what you’re trying to say here - I know what “relative velocity”, “orthogonal”, “timelike worldline”, “frames”, and “deviation” mean, but you have strung these words together in a way that makes no sense.

I apologize for lack of clarity in my statement. I assumed you were referring to minkowskie’s geographical representation of time like and space like worldlines as orthogonal axies on a spacetime diagram. And That he represented the respective coordinate axies of a reference frame with a relative motion with respective to the former as lines with acute angles with respect to the former orthogonal lines. Hence I called those acute angled lines as deviation from orthogonal lines representing a relative velocity of the two respective frames. I hope this clarifies a little.

 

[hnaghieh]

The “motion of a frame“ cannot be determined

This is Galilean principle of relativity. Precursor to Einstein’s principle of relativity. Not related to “color love”or “weight of an idea “ which are not physical parameters. It simply means motion is relative not absolute. We Need a frame of reference in order to give its magnitude or its direction. Once the frame of reference is chosen(which means the units of measurement is chosen) then we can physically measure it. Without that reference frame we will not be able to measure relative parameters.

 

[hnaghieh]

(you can either put a detector taking time-stamped photos at these points,

This is the crucial point. A detector making “time” measurement can not make “space” at the same time with unrestricted accuracy because of finite velocity of light. These two parameters (time and space)are orthogonal parameters. In the time it takes for the signal to reach the detector, the moving object has moved a definite amount which is the limit of accuracy of the measurements for the times of the two end points. Einstein called them “A”time and “B” time. There is no common and absolute AB time. (In quantum domain there is a further source of indeterminacy due to size of the signal used to determine spatial meaurmets of an entity).

 

[hnaghieh]

Vectors are not components of tensors. Vectors are invariant objects just like tensors; they are best thought of as one-index tensors.

I totally agree and apologize for sloppy statement. Instead of just “vector” i should have put The words “components of vector “ in the parentheses. What I meant was components of tensor, as well as the components of vectors, are coordinate frame dependent.

 

[hnaghieh]

The “motion of a frame“ cannot be determined for about the same reason that I cannot determine the color of love or the weight of an idea - the notion is meaningless because frames aren’t things that can move. A frame is a mathematical convention for assigning coordinates to points in spacetime (these points are called “events” in the language of relativistic physics) and mathematical conventions aren’t things that move around in space.

Yes, I know you’ve heard people use the term “a moving reference frame” or “a frame moving relative to me” or similar... but that just shows that natural language isn’t always used precisely. It would be more accurate to say “a reference frame which assigns coordinates to events in such a way that the spatial coordinates of my position are a function of the time coordinate”.

Until you have resolved your confusion about what frames do and don’t do, you will find it very difficult to make sense of relativity. At this point all I can do is repeat my recommendation of the Taylor and Wheeler book.

One of The people I have heard using these terms: “a moving reference frame” or “ a frame moving relative to me” is the great inventor of all this. Mr Albert Einstein in his celebrated paper “on the electrodymamics of moving bodies”

 

[pervect]

In order to make any calculation we need data or measurements. In order to have measurements we need units of measurements(yard sticks and clocks). Yard sticks and clocks are frame dependent in the sense that two reference coordinate systems in relative motion will have different units (due to relativistic effects on the yard sticks and clocks, etc) when they compare each other’s measurements of a world event they will not agree on their measurement or the laws of nature unless they know the transformation relationship connecting their coordinate frames units of measurements ( Lorentz transformations).

I agree with much , though not all, of this. Let me try and give you the outline of a modern, relativistic perspective.

Distances as measured by yardsticks are frame dependent quantities, agreed. The time interval measured by a single, specific clock is, however, a frame independent quantity.

Time intervals measured by combining the results of more than one clock via some synchronization scheme are frame dependent, because the synchronization scheme is frame dependent.

Neither the frame dependent distances, nor the frame dependent non-proper time intervals measured by multiple clocks are invariant quantities.

When you specify both of these frame dependent quantities, though, and combine them into a 4-vector, the 4-vector itself is regarded as frame independent, even though the components of the 4-vector are frame dependent.

The reason the 4-vector is regarded as frame independent is that if you know all the components in one frame you can, as you mentioned, use the Lorentz transform to find the components in any other frame. So, the 4-vector itself is regarded as a "geometric entity" that exists regardless of a specific choice of frame. The actual measurements that some observer made in some particular frame are not the 4-vector, but the components of the 4-vector in the observer's frame. Knowing the components of the 4-vector, and the specifics of the observer, one knows the four-vector.

Working with frame independent objects is a very powerful technique that makes errors much less likely. All the information you need to find the physical measurements are collected together into one place.

To give a specific example relative to the previous discussion. In special relativity, the electric field and the magnetic field are not tensors. They are parts of a larger object that is a tensor, the Farday tensor, which is a rank 2 tensor.

Knowing the electric fields at a point according to one observer doesn't let you know what the electric fields at that point are for another observer. Knowing both the electric and magnetic fields at that poitn according to an observer gives you the components of the Farday tensor, and you can use the approrpriate generalization of the Lorentz transform to find the electric and magnetic fields at that point for any observer you choose.

 

[PeterDonis]

would that also be true for a pair of compact objects in orbit?

Do you mean in orbit about each other? That's a different spacetime geometry, and "frame dragging" is not really a useful concept for that case.

 

[PeterDonis]

Yard sticks and clocks are frame dependent

No, they are not. Objects like this can be represented by 4-vectors and tensors, i.e., by frame invariant objects.

You really, really need to spend some time learning about the formulation of relativity using vectors and tensors. The classic reference for this is the GR textbook by Misner, Thorne, and Wheeler, which is a heavy lift but which makes it abundantly clear how it all works.

 

[PeterDonis]

the laws are not coordinate dependent, but their components (based on a specific measurement by a specific yard stick etc ) is coordinate dependent

No. The components of vectors and tensors are indeed frame-dependent, but they are not the same as actual results of measurements by actual physical things like yard sticks. Confusing these two very distinct and different things is unfortunately a common error, but it is nevertheless an error. You will continue to be confused unless you correct this error in your thinking and learn how results of actual measurements by actual physical things like yard sticks are actually represented in physics: by invariants.

 

[PeterDonis]

This is Galilean principle of relativity. Precursor to Einstein’s principle of relativity.

The principle of relativity does not mean what you think it does. You are trying to apply the words without a proper understanding of the underlying concepts.

 

[PeterDonis]

Distances as measured by yardsticks are frame dependent quantities, agreed. The time interval measured by a single, specific clock is, however, a frame independent quantity.

Unfortunately, I think these two statements taken together, while I see what you mean by them, are highly likely to increase the OP's confusion rather than decrease it.

The spacelike interval between two particular spacelike separated events is invariant, just as the timelike interval between two particular timelike separated events is invariant. (Here I am assuming the interval is being measured along a unique geodesic between the two events, to avoid a lot of technicalities that are out of scope for the OP at this point in the discussion.) A particular timelike interval has an obvious physical interpretation as the time measured by a clock that travels between the two events (along the geodesic between them). So it's easy to see how the invariance of a timelike interval is physically realized.

It's harder to see how the invariance of a spacelike interval is realized, because nothing moves on spacelike worldlines, so a measurement of any spacelike interval requires at least two timelike worldlines to be involved (one passing through each endpoint of the spacelike interval). This seems to introduce frame dependence, but it actually doesn't. It just means that we have to specify two worldlines instead of one. But worldlines are invariants, and if we specify two worldlines, say of the two endpoints of a ruler, and pick a pair of spacelike separated events, one on each worldline, that invariant spacelike interval will have a physical interpretation that can be described as "distance measured by the ruler". The interpretation won't be as intuitively obvious as the one for a timelike interval, but it will still be enough to support the invariance of the interval.

When the OP talks about "distance measured by the ruler" in two different frames, he is talking about two different spacelike intervals. Yes, these two intervals will have different lengths. But that doesn't mean the intervals themselves are not invariant. The length of each interval is invariant. They're just different.

I know this all is obvious to you, but I don't think it's obvious to the OP, and given how this thread has gone up to now, I think it's worth belaboring points like this to try to make clear what is going on.

 

[hnaghieh]

Unfortunately, I think these two statements taken together, while I see what you mean by them, are highly likely to increase the OP's confusion rather than decrease it.

The spacelike interval between two particular spacelike separated events is invariant, just as the timelike interval between two particular timelike separated events is invariant. (Here I am assuming the interval is being measured along a unique geodesic between the two events, to avoid a lot of technicalities that are out of scope for the OP at this point in the discussion.) A particular timelike interval has an obvious physical interpretation as the time measured by a clock that travels between the two events (along the geodesic between them). So it's easy to see how the invariance of a timelike interval is physically realized.

It's harder to see how the invariance of a spacelike interval is realized, because nothing moves on spacelike worldlines, so a measurement of any spacelike interval requires at least two timelike worldlines to be involved (one passing through each endpoint of the spacelike interval). This seems to introduce frame dependence, but it actually doesn't. It just means that we have to specify two worldlines instead of one. But worldlines are invariants, and if we specify two worldlines, say of the two endpoints of a ruler, and pick a pair of spacelike separated events, one on each worldline, that invariant spacelike interval will have a physical interpretation that can be described as "distance measured by the ruler". The interpretation won't be as intuitively obvious as the one for a timelike interval, but it will still be enough to support the invariance of the interval.

When the OP talks about "distance measured by the ruler" in two different frames, he is talking about two different spacelike intervals. Yes, these two intervals will have different lengths. But that doesn't mean the intervals themselves are not invariant. The length of each interval is invariant. They're just different.

I know this all is obvious to you, but I don't think it's obvious to the OP, and given how this thread has gone up to now, I think it's worth belaboring points like this to try to make clear what is going on.

When the OP talks about "distance measured by the ruler" in two different frames, he is talking about two different spacelike intervals. Yes, these two intervals will have different lengths. But that doesn't mean the intervals themselves are not invariant. The length of each interval is invariant. They're just different.

No. I am talking about an invariant spacetime interval viewed from two different reference fame which have a relative velocity with respect to each other.

 

[PeterDonis]

I am talking about an invariant spacetime interval viewed from two different reference fame which have a relative velocity with respect to each other.

If you are, then much of what you have said about that invariant spacetime interval is simply false, since much of what you have said asserts that that interval is frame-dependent, and invariants are not frame-dependent.

I strongly suggest that you take a step back and think very carefully about what you are saying, and re-read very carefully what others have said to you in this thread.

 

[hnaghieh]

No. I am talking about an invariant spacetime interval viewed from two different reference fame which have a relative velocity with respect to each other.

The observer in each frame will determine that interval or “distance “ if you prefer, in their rest frame using rods and clocks of their frame (propertime and proper length). When they compare they don’t agree what the length of that distance is unless they know the relationship between their rods and clocks. (Transform laws)

 

[hnaghieh]

If you are, then much of what you have said about that invariant spacetime interval is simply false, since much of what you have said asserts that that interval is frame-dependent, and invariants are not frame-dependent.

I strongly suggest that you take a step back and think very carefully about what you are saying, and re-read very carefully what others have said to you in this thread.

The interval is invariant “same for all observers “ only with the appropriate transformation equations relating the frame depandant components of one frame with another frame with relative velocity.Under these appropriate transformation equations all observers agree. Because they know it was their units of measurements which were affected by their relative motion and they would need to account of these relativistic effects. Once they “transform “ their frame depending measurements all will be happy and all spacetime intervals will be the same for all observers but only if they transform their unit coordinate basis or unit vectors.

 

[hnaghieh]

two different spacelike intervals. Yes, these two intervals will have different lengths. But that doesn't mean the intervals themselves are not invariant. The length of each interval is invariant. They're just different.

Two different “ spacelike “ intervals can never be “invariant” just as two “ timelike “ intervals can never be invariant. It is only “spacetime “ intervals that are invariant under approximate transformation equations

 

[PeroK]

The observer in each frame will determine that interval or “distance “ if you prefer, in their rest frame using rods and clocks of their frame (propertime and proper length). When they compare they don’t agree what the length of that distance is unless they know the relationship between their rods and clocks. (Transform laws)

If someone measures a physical quantity they may do so without any knowledge of any other observers. They get a single answer.

An invariant quantity is one where everyone gets the same answer. No one need be aware of anyone else's measurements nor transform their data in any way.

 

[hnaghieh]

If you are, then much of what you have said about that invariant spacetime interval is simply false, since much of what you have said asserts that that interval is frame-dependent, and invariants are not frame-dependent.

I strongly suggest that you take a step back and think very carefully about what you are saying, and re-read very carefully what others have said to you in this thread.

Ok thank you all for your patience . I think I have my answer.

 

[hnaghieh]

If someone measures a physical quantity they may do so without any knowledge of any other observers. They get a single answer.

That is exactly what Newton said.

 

[hnaghieh]

That is exactly what Newton said.

Absolute space and absolute time.

 

[hnaghieh]

Absolute space and absolute time.

And Mr Albert Einstein said no. Sorry you are wrong.

 

[PeroK]

Absolute space and absolute time.

You are confused about invariant quanities and transformation laws.

Spacetime coordinates are not invariant but are related by the Lorentz transformation ( in SR).

The length of a spacetime interval is an invariant quanity.

In Newtonian physics time and length are invariant and spatial coordinates are related by the Galilean transformation.

 

[hnaghieh]

Spacetime coordinates are not invariant but are related by the Lorentz transformation ( in SR).

When did I ever say spacetime coordinates are invariant? What said was : under approximate transformation laws relating the coordinate basis of all coordinate systems in relative motion with respect to each other the spacetime distance will be invariant “ same for all observers” Just as you stated. The Newtonian time and length is absolute, which we could agree to be called invariant but only for all rest frame observers. In fact the introduction of the notion of a moving observer(or moving reference frame)was Einstein solution and genius.

 

[PeroK]

What said was : under approximate transformation laws relating the coordinate basis of all coordinate systems in relative motion with respect to each other the spacetime distance will be invariant “ same for all observers” Just as you stated. The Newtonian time and length is absolute, which we could agree to be called invariant but only for all rest frame observers. In fact the introduction of the notion of a moving observer(or moving reference frame)was Einstein solution and genius.

There is no transformation of an invariant quantity. By definition it is the same in all frames without transformation.

Einstein was hardly the first to consider moving reference frames!

 

[PeterDonis]

Two different “ spacelike “ intervals can never be “invariant” just as two “ timelike “ intervals can never be invariant. It is only “spacetime “ intervals that are invariant

"Spacelike" and "timelike" intervals are spacetime intervals. Those terms are basic terminology in relativity, as you would learn if you spent even a few minutes consulting a textbook.

I think I have my answer.

Then you shouldn't have gone on to post this noise:

That is exactly what Newton said.

Absolute space and absolute time.

And Mr Albert Einstein said no. Sorry you are wrong.

Unfortunately, you do not appear to be capable of actually reading what others are posting, you are ignorant of basic terminology regarding relativity, and you do not understand the basic concepts involved and seem incapable of learning them. Thus this thread is making no progress, so I am closing it.