Do moving massive objects drag curved spacetime with them?

[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.