Understanding Inertial reference frames

[Chestermiller]

Your quote, "All inertial frames agree on the spaciotemporal distance between any two points" is correct. Your question, therefore doesn't make sense, "how come the spaciotemporal distance between any two points p and q will disagree?" I don't know why you are asking that."

George sir, please pardon me, unknowingly i just retyped the same sentence, really very very sorry sir.

My question is: In all inertial frames, the temporal distance between p and q (time dilation) and on the spatial distance (length contraction) will vary (between any two observers am i right sir?), which is understood sir, but how come the spaciotemporal distance between any two points in all inertial frames agree?

They agree because of the unique geometry of 4D spacetime (which the Lorentz Transformation reveals). Think about a group of right triangles, all sharing a common hypotenuse, but each of which has different lengths for the other two sides. The square of the distance between the two ends of the hypotenuse is equal to the sum of the squares of the other two sides for each and every one of the triangles, by virtue of the Pythagorean theorem. The (distance) interval between events in 4D spacetime is analogous to the hypotenuse of the triangles, and the distance and time intervals for the events, as reckoned from various frames of reference, is analogous to the other two sides of the triangles. In many respects, the relativistic relationship is the 4D spacetime version of the Phthagorean theorem, albeit with a minus sign in the equation for the time "direction."

 

[bahamagreen]

Just wondering...

What is the crucial difference between an IRF with clocks and rulers (objects in it) and a coordinate system which is empty (no objects)? Is it called something else?

Let's assume that I am at rest wrt the galaxy, so that is my IRF.

I can imagine a coordinate system (call it "A") with its origin moving wrt the galaxy so as to cross it in one second by my clock... this is just imagining a coordinate system without objects in it, so there are no physical features subject to c, Lorentz, etc., it is just an empty coordinate system passing by very fast.

I am only defining / imagining this "A", not measuring anything in it (it has no objects).

So I can define a coordinate system that moves wrt the my IRF >c.

Since "A" has no objects, it has no clocks or rulers... does this conflict with the definition of a coordinate system (does a coordinate system imply clock and ruler measures)?

Can I assume "A" is a coordinate system because I can define its moving origin (which is not an object) even though there are no clocks and rulers in "A" (undefined metric)?

Now, if an IRF does not require objects in it, then what is "A"?

 

[ghwellsjr]

You can't have two IRF's moving at c or greater with respect to each other. Everything that is in one is also in the other.

 

[bobc2]

Whoops, I don't want to spread misinformation. What part(s) in particular did I get wrong there?

Hi m.e.t.a., I wasn't sure you caught my earlier post since it was a little delayed. Here is the quote again from my modern physics course textbook: "Concepts of Modern Physics" by Arthur Beiser (McGraw-Hill Book Co.). On Page 33 there is an inset with a short biography of Hendrik A. Lorentz. Here is a quote from that section of the textbook:

"...Lorentz (and independently, the Irish physicist G. F. Fitzgerald) suggested that the negative result of the Michelson-Morley experiment could be understood if lengths in the direction of motion relative to an observer were contracted. Subsequent experiments showed that although such contractions do occur, they are not the real reason for the Michelson-Morley result, which is that there is no "ether" to serve as a universal frame of reference."

This textbook seems to agree with you on this issue, notwithstanding the views of many on this forum.

 

[DrGreg]

Hi m.e.t.a., I wasn't sure you caught my earlier post since it was a little delayed. Here is the quote again from my modern physics course textbook: "Concepts of Modern Physics" by Arthur Beiser (McGraw-Hill Book Co.). On Page 33 there is an inset with a short biography of Hendrik A. Lorentz. Here is a quote from that section of the textbook:

"...Lorentz (and independently, the Irish physicist G. F. Fitzgerald) suggested that the negative result of the Michelson-Morley experiment could be understood if lengths in the direction of motion relative to an observer were contracted. Subsequent experiments showed that although such contractions do occur, they are not the real reason for the Michelson-Morley result, which is that there is no "ether" to serve as a universal frame of reference."

This textbook seems to agree with you on this issue, notwithstanding the views of many on this forum.

In case there's still any confusion over this:

1. The M-M experiment disproved the original version of ether using simple velocity addition
2. Lorentz subsequently formulated a modified version of ether to explain the M-M result (therefore the M-M result disproved the first version of the ether, but not Lorentz's version)
3. Lorentz's theory provided no method of detecting the speed of his supposed ether, and actually gave the correct answer no matter what value you assumed you were moving through the ether
4. Einstein's theory explained the M-M result without assuming the existence of something that could not be detected. Nowadays virtually everyone (who is knowledgeable in the area) accepts Einstein's theory and no-one takes Lorentz's theory seriously. I'm pretty sure this is also the position of the experts on this forum who occasionally mention Lorentz's theory as a counterexample to propositions put forward by other users (by virtue of the point below).
   [*]Nevertheless, although there's no evidence to support Lorentz's theory over Einstein's, there'e no evidence to disprove it either, so you can't say it's been disproved. Suitably formulated versions of Lorentz's theory are mathematically equivalent to Einstein's theory in terms of measurements you can measure directly (without any theoretical interpretation or recalculation).
   

 

[bahamagreen]

You can't have two IRF's moving at c or greater with respect to each other. Everything that is in one is also in the other.

That's why I asked the questions about the relationship between the coordinate system without objects and the IRF with clocks and rulers...

On your last line - wouldn't that require all IRFs share the same light cone?

 

[harrylin]

[..] no-one takes Lorentz's theory seriously. I'm pretty sure this is also the position of the experts on this forum who occasionally mention Lorentz's theory as a counterexample to propositions put forward by other users [..]

That's - literally! - a bold claim without scientific evidence. Many physics journals have a similar policy as this forum so that they can't be used for statistical analysis of your claim. An anonymous poll would be a proper way to asses your claim.

 

[ghwellsjr]

You can't have two IRF's moving at c or greater with respect to each other. Everything that is in one is also in the other.

That's why I asked the questions about the relationship between the coordinate system without objects and the IRF with clocks and rulers...

Are you saying my answer didn't satisfy you?

On your last line - wouldn't that require all IRFs share the same light cone?

I would never think to ask this question so I'm not sure if any answer I give would address your concern. In fact, I would never think to ask your previous questions. Where do you get these questions from? Don't you see an IRF as a coordinate system defined with imaginary rulers and synchronized clocks as prescribed by Einstein in his 1905 paper introducing Special Relativity? And don't you see this coordinate system as incorporating all objects, clocks, rulers, and observers that you want to consider? And don't you see the Lorentz Transformation as how you get the coordinates for another IRF moving with respect to the first one? And don't you see both IRF's as reaching out to infinity in all directions? How could one not include everything that the other one includes?

 

[bahamagreen]

The questions came from considering your own previous post in this thread which stated that an IRF did not have to contain any objects. This lead me to wonder if the constraints on an IRF stem from constraints on the objects themselves or constraints of geometry, or if the presence of objects changes the constraints on geometry.
I posed a strictly geometric coordinate system to compare to another coordinate system with objects (IRF) to consider the difference between them - to see what circumstances would prevent a coordinate system without objects from being an IRF.
The questions were presented to clarify my thinking about this distinction.

Now I see three versions:
Strictly without objects
With imaginary objects
With real objects

Positing imaginary objects (rulers and clocks) would seem to imply further positing principles and effects of those objects not necessarily present in a strictly object free coordinate construction.

I'm not challenging the IRF concept; I'm trying to see what about it makes it different from an empty coordinate system. At this point it appears to me that the difference is the presence of objects, even imaginary ones.
For example, previous to the universe there were no IRFs, but there were any imaginable coordinate systems.

"And don't you see both IRF's as reaching out to infinity in all directions? How could one not include everything that the other one includes?"

Infinity is a long way off; too far to make a measurement or observation, twice as far if you have to wait for a returning signal. I'm thinking an IRF that reaches to infinity and includes everything would need to include all objects of the universe itself. This seems like a "stretch" wrt the expansion...

 

[harrylin]

[..] Positing imaginary objects (rulers and clocks) would seem to imply further positing principles and effects of those objects not necessarily present in a strictly object free coordinate construction.

I'm not challenging the IRF concept; I'm trying to see what about it makes it different from an empty coordinate system. At this point it appears to me that the difference is the presence of objects, even imaginary ones.
For example, previous to the universe there were no IRFs, but there were any imaginable coordinate systems.

Sort of... Inertial reference frames are based on the relativity principle, and laws of nature can only be tested by means of real measurement instruments (such as "clocks and rulers") which obey laws of physics. In that context, proposing reference systems without at least hypothetical measurement instruments that follow the existing laws of the universe would not make sense.

Infinity is a long way off; too far to make a measurement or observation, twice as far if you have to wait for a returning signal. [..]

Good point, however you forgot such things as stellar aberration. Also on that point SR has to conform with observations. In order to verify this, one positions far away stars inside an inertial reference system.

 

[bobc2]

In case there's still any confusion over this:

1. The M-M experiment disproved the original version of ether using simple velocity addition
2. Lorentz subsequently formulated a modified version of ether to explain the M-M result (therefore the M-M result disproved the first version of the ether, but not Lorentz's version)
3. Lorentz's theory provided no method of detecting the speed of his supposed ether, and actually gave the correct answer no matter what value you assumed you were moving through the ether
4. Einstein's theory explained the M-M result without assuming the existence of something that could not be detected. Nowadays virtually everyone (who is knowledgeable in the area) accepts Einstein's theory and no-one takes Lorentz's theory seriously. I'm pretty sure this is also the position of the experts on this forum who occasionally mention Lorentz's theory as a counterexample to propositions put forward by other users (by virtue of the point below).
   [*]Nevertheless, although there's no evidence to support Lorentz's theory over Einstein's, there'e no evidence to disprove it either, so you can't say it's been disproved. Suitably formulated versions of Lorentz's theory are mathematically equivalent to Einstein's theory in terms of measurements you can measure directly (without any theoretical interpretation or recalculation).
   

That's a pretty fair way to characterize the situation, DrGreg. You provided much better context than I was able to. And I fully agree with your assessment, "no-one takes Lorentz's theory seriously." This view was affirmed in the Paul Davies book as well (that most physicists accept the Einstein interpretation of SR--thus reject the LET), and I'm sure many physicists have followed Einstein's lead on this view. Of course Beiser's statement that the Lorentz theory has been disproven may have related to his initial theory (as I think you are implying), although I assume that all of the revisions had been completed by the time Beiser authored his text. I wish that Beiser had cited references for the tests that proved LET invalid. I've been trying to identify the history of revisions to LET in order to understand its status. I know that from Vandam's posts that he is convinced that the LET is not a valid theory at this point in time--leaving the block universe as the only reasonable interpretation of special relativity.

Thanks for your input.

 

[DrGreg]

...no-one takes Lorentz's theory seriously. I'm pretty sure this is also the position of the experts on this forum who occasionally mention Lorentz's theory as a counterexample to propositions put forward by other users...

That's - literally! - a bold claim without scientific evidence. Many physics journals have a similar policy as this forum so that they can't be used for statistical analysis of your claim. An anonymous poll would be a proper way to asses your claim.

Well, to be fair, I suppose I should have prefaced the words quoted above with "the impression I get from all the literature and discussion I've seen is that..." The second sentence begins with "I'm pretty sure that...", so, again, it's not a proven fact (and I expect anyone who vehemently disagrees with my assessment will speak up and say so). Point 5 in my post #37 still stands.

 

[DrGreg]

That's a pretty fair way to characterize the situation, DrGreg. You provided much better context than I was able to. And I fully agree with your assessment, "no-one takes Lorentz's theory seriously." This view was affirmed in the Paul Davies book as well (that most physicists accept the Einstein interpretation of SR--thus reject the LET), and I'm sure many physicists have followed Einstein's lead on this view. Of course Beiser's statement that the Lorentz theory has been disproven may have related to his initial theory (as I think you are implying), although I assume that all of the revisions had been completed by the time Beiser authored his text. I wish that Beiser had cited references for the tests that proved LET invalid. I've been trying to identify the history of revisions to LET in order to understand its status. I know that from Vandam's posts that he is convinced that the LET is not a valid theory at this point in time--leaving the block universe as the only reasonable interpretation of special relativity.

I will just add that the reason why hardly anyone takes Lorentz's theory seriously is not that it's proven to be factually wrong (because it isn't), but just that Einstein's is considered much better, on grounds of philosophy, interpretation and Occam's razor.

(By the way, in passing, I don't accept that acceptance of the 4D mathematical model of spacetime commits anyone to the philosophical interpretation that the real universe in which we live is a "block universe" (I'm never entirely clear what that really means) or, more specifically, of "determinism". A deterministic model approximation doesn't require the real thing to be deterministic. But that's off-topic for this thread.)

 

[harrylin]

[..] (and I expect anyone who vehemently disagrees with my assessment will speak up and say so). Point 5 in my post #37 still stands.

I suggested to start a poll to find out - a similar poll on interpretation of QM has been very interesting. And I forgot to clarify that for the rest I agree with your points 1-5.

[..] I wish that Beiser had cited references for the tests that proved LET invalid.[..]

If a valid disproof existed then I'm sure that some of us would know about it (ADDED: technically speaking, SR was disproved with GR but that can't be the point; and the phrase "there is no "ether" to serve as a universal frame of reference" could simply mean DrGreg's Point 3!). However, discussing that is a little off topic in this thread.

 

[ghwellsjr]

The questions came from considering your own previous post in this thread which stated that an IRF did not have to contain any objects.

And which post was that?

This lead me to wonder if the constraints on an IRF stem from constraints on the objects themselves or constraints of geometry, or if the presence of objects changes the constraints on geometry.
I posed a strictly geometric coordinate system to compare to another coordinate system with objects (IRF) to consider the difference between them - to see what circumstances would prevent a coordinate system without objects from being an IRF.
The questions were presented to clarify my thinking about this distinction.

Now I see three versions:
Strictly without objects
With imaginary objects
With real objects

Positing imaginary objects (rulers and clocks) would seem to imply further positing principles and effects of those objects not necessarily present in a strictly object free coordinate construction.

I'm not challenging the IRF concept; I'm trying to see what about it makes it different from an empty coordinate system. At this point it appears to me that the difference is the presence of objects, even imaginary ones.
For example, previous to the universe there were no IRFs, but there were any imaginable coordinate systems.

"And don't you see both IRF's as reaching out to infinity in all directions? How could one not include everything that the other one includes?"

Infinity is a long way off; too far to make a measurement or observation, twice as far if you have to wait for a returning signal. I'm thinking an IRF that reaches to infinity and includes everything would need to include all objects of the universe itself. This seems like a "stretch" wrt the expansion...

The IRF's defined in Special Relativity are approximations to the real world. Since SR ignores the effects of gravity and there is no place in the real world devoid of the effects of gravity, we have to limit its application in the real world. Clearly, applying it to our entire galaxy as you did in post #34 or going back to the Big Bang as you did in post #41 is not appropriate.

What I have been doing in this thread is trying to help the OP understand that IRF's can handle accelerating objects, there is never any need to use an accelerating Frame of Reference.

 

[Vandam]

I will just add that the reason why hardly anyone takes Lorentz's theory seriously is not that it's proven to be factually wrong (because it isn't), but just that Einstein's is considered much better, on grounds of philosophy, interpretation and Occam's razor.
)

I wanted to post a link here to my thread on LET, but that has been deleted by moderation. My thread on LET is locked for no reason and I am not allowed to make a link to that thread.
Therefore I consider my presence on this forum as a waste of time, so I have asked moderation to close my account. Even if they don't, I consider my particitation as terminated. Please take note of that.
A special thanks to one member of this forum: BobC2, the only support I found for Block Universe on this forum. He's probably the only one who understands Special Relativity. Bob, thanks for your support, and good luck with these guys...

 

[harrylin]

[..]My thread on LET is locked for no reason and I am not allowed to make a link to that thread. Therefore I consider my presence on this forum as a waste of time [..] terminated. [..]good luck with these guys...

Moderation* can at times be very displeasing. Good luck to you too!

*These civilities are also off-topic but I hope that nobody minds good manners

 

[bahamagreen]

bahamagreen:The questions came from considering your own previous post in this thread which stated that an IRF did not have to contain any objects.

ghwellsjr:And which post was that?

bahamagreen: Your post #4...
"In fact IRF's do not require any objects in them to be inertial."(ghwellsjr)

I'm confused by this, too:

From your #47: "Clearly, applying it to our entire galaxy as you did in post #34 or going back to the Big Bang as you did in post #41 is not appropriate."

But in your #40: "And don't you see both IRF's as reaching out to infinity in all directions? How could one not include everything that the other one includes?"

 

[ghwellsjr]

When I said, "IRF's do not require any objects in them to be inertial", I meant that an IRF could contain only non-inertial objects, as my example of the Earth and the Moon in circular motion around each other shows.

Regarding the other questions--we're just imagining a spaceship far removed from earth--as far away as you like--there's no limit.

 

[saipathudut]

OM SAI RAM

Even if there were only one planet, our Earth, in the entire universe and so there is no sense in which it is moving, there still would not be an absolute inertial reference frame. The rest state of the Earth would define one valid IRF but so would any other frame moving at a constant velocity with respect to the Earth.

You could imagine a spaceship traveling away from the Earth and a great distance away, traveling at a constant speed so that it was inertial and it could define another IRF, just as valid as the IRF defined by the Earth's rest state. But then you could image the same IRF without the spaceship and it would still be a valid IRF. IRF's do not require any object in them to be at zero velocity.

In fact IRF's do not require any objects in them to be inertial. We could image an IRF with just the Earth and the Moon in circular motion around each other, constantly acceleration.

George sir, this is saipathudu here. Personal problems plagued my life and even before the moment of my death, my thirst to learn relativity would go on...now i came back rejuvenated, but i fear whether you will believe my words and my THIRST TO LEARN THIS AT ANY COST AT THIS CRITICAL JUNCTURE OF MY LIFE. I just need your "INVALUABLE ASSISTANCE" to me to learn this really tough subject.

i want to start from the beginning. George sir and all others who replied my queries regarding this IRFs, am really indebted. This time i am determined to learn it out by putting in my EVERYTHING...Please George sir AND ALL OTHERS...HELP ME OUT.

Firstly...these words...Earth's rest state...really i got stuck here...

then this statement George sir

"IRF's do not require any objects in them to be inertial", I meant that an IRF could contain only non-inertial objects, as my example of the Earth and the Moon in circular motion around each other shows."

if IRF's contain only non-inertial objects, what about non-IRFs? What will they consist of? What are they?...Without understanding this moot point, i was unable to make any headway George sir...Please throw light into this question sir...Hope to hear from you all my tutors...and especially from you Mr. George...

Regards,
saipathudut/srinivasant

OM SAI SRI SAI JAYA JAYA SAI

 

[Nugatory]

"IRF's do not require any objects in them to be inertial", I meant that an IRF [STRIKE]could[/STRIKE] might contain only non-inertial objects, as my example of the Earth and the Moon in circular motion around each other shows."

if IRF's contain only non-inertial objects, what about non-IRFs? What will they consist of? What are they?...

(I've made one correction to the above, to fix something that might be misleading to readers for whom English is not their first language).

Any frame of reference, whether it is inertial or not, may contain no objects, only inertial objects, only non-inertial objects, or both.

 

[bahamagreen]

Let me ask something IRF related that I have not been able to find anything about. Keeping in mind the "mechanics holds good" part of the IRF includes conservation of momentum...?

When vacuum fluctuation pair production occurs, do the velocities of the particles indicate they obey conservation so the origin of their departure (COM) is at rest wrt the observer, or do the particles indicate by differential velocities wrt the irf observer that by conservation, the origin of their departure is in relative motion wrt the observer?

In other words, taking SR into account, are the fluctuations themselves underlying pair production thought of as having any allowable sub c velocity wrt the IRF observer?

 

[ghwellsjr]

OM SAI RAM



George sir, this is saipathudu here. Personal problems plagued my life and even before the moment of my death, my thirst to learn relativity would go on...now i came back rejuvenated, but i fear whether you will believe my words and my THIRST TO LEARN THIS AT ANY COST AT THIS CRITICAL JUNCTURE OF MY LIFE. I just need your "INVALUABLE ASSISTANCE" to me to learn this really tough subject.

So sorry to hear about your personal problems but glad to hear you are rejuvenated now.

However, I would not say that Special Relativity is a "really tough subject". General Relativity is, but not SR. If you think it is tough, it's because you are misunderstanding it so I encourage you not to be intimidated by the subject of SR.

i want to start from the beginning. George sir and all others who replied my queries regarding this IRFs, am really indebted. This time i am determined to learn it out by putting in my EVERYTHING...Please George sir AND ALL OTHERS...HELP ME OUT.

I started from the beginning of this thread and read all of your posts and all of my responses. I think it would be good for you to do the same. I think all your questions have already been answered.

Firstly...these words...Earth's rest state...really i got stuck here...

then this statement George sir

"IRF's do not require any objects in them to be inertial", I meant that an IRF could contain only non-inertial objects, as my example of the Earth and the Moon in circular motion around each other shows."

if IRF's contain only non-inertial objects, what about non-IRFs? What will they consist of? What are they?...Without understanding this moot point, i was unable to make any headway George sir...Please throw light into this question sir...Hope to hear from you all my tutors...and especially from you Mr. George...

Regards,
saipathudut/srinivasant

OM SAI SRI SAI JAYA JAYA SAI

I'm not saying that an IRF cannot contain objects that are inertial, I'm just saying that an IRF does not have to be linked to an inertial object. When we are imagining a scenario, we can use an IRF to describe the positions, velocities, and accelerations of as many objects and observers as we want. We are not required to describe any of them as being at fixed locations, at fixed velocities, or a fixed accelerations. Any IRF can handle any scenario we desire. Does that help?

Let's leave the subject of non-IRF's until after we have a firm grasp of IRF's, OK?

 

[saipathudut]

George sir...

So sorry to hear about your personal problems but glad to hear you are rejuvenated now.

However, I would not say that Special Relativity is a "really tough subject". General Relativity is, but not SR. If you think it is tough, it's because you are misunderstanding it so I encourage you not to be intimidated by the subject of SR.

I started from the beginning of this thread and read all of your posts and all of my responses. I think it would be good for you to do the same. I think all your questions have already been answered.

I'm not saying that an IRF cannot contain objects that are inertial, I'm just saying that an IRF does not have to be linked to an inertial object. When we are imagining a scenario, we can use an IRF to describe the positions, velocities, and accelerations of as many objects and observers as we want. We are not required to describe any of them as being at fixed locations, at fixed velocities, or a fixed accelerations. Any IRF can handle any scenario we desire. Does that help?

Let's leave the subject of non-IRF's until after we have a firm grasp of IRF's, OK?

First of all, George sir, please suggest me some good websites to learn "The Special Relativity"...This time i want to make sure that i successfully complete this endeavor and strike at the grass root level and want to be strong at the basics of this great subject...and also please guide me some fantastic, simple, and some wonderful books on "The Special Relativity" by great authors. George sir, i would be really very much grateful to you if you throw your invaluable assistance and guidance in this regard. I am really very much indebted all other members who tried to help me out in learning this subject. Also, George sir i am really very, very lucky to get a mentor like you and this reflects from the fact that you showed a lot of patience to explain my doubts.

Regards,
saipathudut/srinivasant

 

[ghwellsjr]

First of all, George sir, please suggest me some good websites to learn "The Special Relativity"...

I can't think of a better one than this one. I would recommend that you just read many threads on this forum, that's what I did for a year before I ever made my first post. You can learn a lot by following how others learned.

This time i want to make sure that i successfully complete this endeavor and strike at the grass root level and want to be strong at the basics of this great subject...and also please guide me some fantastic, simple, and some wonderful books on "The Special Relativity" by great authors.

The best book I can recommend is Einstein's which you can read online:
http://www.bartleby.com/173/

George sir, i would be really very much grateful to you if you throw your invaluable assistance and guidance in this regard. I am really very much indebted all other members who tried to help me out in learning this subject. Also, George sir i am really very, very lucky to get a mentor like you and this reflects from the fact that you showed a lot of patience to explain my doubts.

Regards,
saipathudut/srinivasant

Thanks.