# Thread: Special Relativity Primer discussion

2.

3. Originally Posted by Janus
It is important to focus on the need for an inertial reference frame in special relativity (and in Newtonian mechanics) and recognize what an inertial frame is and what it is not.

The definition as "a frame that is not accelerating" is interesting but it is not verifiable. Accelerating with respect to what ?

The answer is that an inertial reference frame is one in which the equations of special relativity (or of Newtonian mechanics) apply. It that simple and that abstract.

It can be show from the definition that 1) any reference frame in uniform motion to an inertial fram is also inertial and 2) if two reference frames are inertial then each is in uniform motion with respect to the other. In particular, if one can find one inertial reference frame then the set of all inertial reference frames is the set of frames in uniform motion with respect to that one.

So, is there an example of a true physical reference frame ? Probably not. It certainly is not one fixed with respect to the Earth, as is clear from the need for fictitious forces lke "coriolis force" to describe large-scale motions, and this is also seen by noting that the Earth revolves (accelerates) around the Sun. Similarly the sun revolves around the galaxy center and the galaxy undergoes non-uniform motion within the local group, etc. etc. etc.

So the notion of an inertial reference frame is an idealization, but a useful idealization. It is also a very good approximation for many reference frames, depending on the particular problem at hand. For many purposes a reference frame fixed to the Earth is essentially inertial. For others a reference frame fixed with respect to the sun is inertial. But ultimately an inertial reference is a mathematical idealization and an convenience.

Most importantly, in a given problem one starts with the postulation of an inertial reference frame and any and all other inertial reference frames must be in uniform motion with respect to that one. If you have two reference frames and one is accelerating with respect to the other, then it is quite impossible for both to be inertial -- and you can apply special relativity only in an inertial reference frame.

4. I also don't see it mentioned that the example at the end where 14 years for the traveler is 98 years for earth is in the case that the traveling speed is about 98.97% of the speed of light. which means that the distance traveled is about 48.5 light year away from earth and back again.

5. Originally Posted by DrRocket
Originally Posted by Janus
It is important to focus on the need for an inertial reference frame in special relativity (and in Newtonian mechanics) and recognize what an inertial frame is and what it is not.

The definition as "a frame that is not accelerating" is interesting but it is not verifiable. Accelerating with respect to what ?

The answer is that an inertial reference frame is one in which the equations of special relativity (or of Newtonian mechanics) apply. It that simple and that abstract.

It can be show from the definition that 1) any reference frame in uniform motion to an inertial fram is also inertial and 2) if two reference frames are inertial then each is in uniform motion with respect to the other. In particular, if one can find one inertial reference frame then the set of all inertial reference frames is the set of frames in uniform motion with respect to that one.

So, is there an example of a true physical reference frame ? Probably not. It certainly is not one fixed with respect to the Earth, as is clear from the need for fictitious forces lke "coriolis force" to describe large-scale motions, and this is also seen by noting that the Earth revolves (accelerates) around the Sun. Similarly the sun revolves around the galaxy center and the galaxy undergoes non-uniform motion within the local group, etc. etc. etc.

So the notion of an inertial reference frame is an idealization, but a useful idealization. It is also a very good approximation for many reference frames, depending on the particular problem at hand. For many purposes a reference frame fixed to the Earth is essentially inertial. For others a reference frame fixed with respect to the sun is inertial. But ultimately an inertial reference is a mathematical idealization and an convenience.

Most importantly, in a given problem one starts with the postulation of an inertial reference frame and any and all other inertial reference frames must be in uniform motion with respect to that one. If you have two reference frames and one is accelerating with respect to the other, then it is quite impossible for both to be inertial -- and you can apply special relativity only in an inertial reference frame.
I should have included the "where Newton's law apply" part. I think I intended to, but started thinking about what I going to write about next and left it out. ( I tend to do that, my mind runs ahead of what I'm typing. I've caught myself leaving out parts of sentences.)

But that is where this discussion part comes in. It allows others to add to, clarify or ask questions about points.

6. Note: Waveman28's posts and subsequent replies have been moved to the trash. Anyone who want's to continue that discussion can find it here:

http://www.thescienceforum.com/Wavem...ion-19055t.php

7. Originally Posted by mitchellmckain
I also don't see it mentioned that the example at the end where 14 years for the traveler is 98 years for earth is in the case that the traveling speed is about 98.97% of the speed of light. which means that the distance traveled is about 48.5 light year away from earth and back again.
I would have included them if I thought that they added to the understanding of the example. But since I did not discuss any of the actual math involved, I didn't see these numbers as being necessary.

If I had taken a mathematical approach, then yes, I would have included them in the example. But like I said in the thread, I wanted to avoid that. (Not that I have anything against the math myself.)

If my attempt to teach it in this manner ignites even a glimmer of extra understanding for someone, then it time well spent.

8. Originally Posted by Janus
Originally Posted by mitchellmckain
I also don't see it mentioned that the example at the end where 14 years for the traveler is 98 years for earth is in the case that the traveling speed is about 98.97% of the speed of light. which means that the distance traveled is about 48.5 light year away from earth and back again.
I would have included them if I thought that they added to the understanding of the example. But since I did not discuss any of the actual math involved, I didn't see these numbers as being necessary.

If I had taken a mathematical approach, then yes, I would have included them in the example. But like I said in the thread, I wanted to avoid that. (Not that I have anything against the math myself.)

If my attempt to teach it in this manner ignites even a glimmer of extra understanding for someone, then it time well spent.
I understand that. It wasn't a criticism. Just thought that this discussion thread would be a good place to offer that info for any who might be helped by it. It is after all good for people to know that that what you gave was just an example for a specific velocity, right?

Hey... kudos for any attempt to explain this stuff in a different way, because that is what will help a greater variety of people.

9. Originally Posted by mitchellmckain
Hey... kudos for any attempt to explain this stuff in a different way, because that is what will help a greater variety of people.
With waveman28 chiming in I think there is little need to worry about having a variety ...... of something.

10. Here's a presentational suggestion.

You made quite a point in the beginning to distinguish the astronauts from the inertial frames (in case they were under acceleration) but you then use the A and B label for both. May I suggest you give the astronauts names Alice and Bob and then refer to various frames associated with Alice as A, A' etc (in case of acceleration) and similarly with Bob.

Similarly you should label the whole gif animation for each frame A and B while the moving objects in the animations Alice and Bob. If that's not too much trouble.

BTW Nice graphics what software do you use to generate these?

One other point: I think the twin paradox is best presented in a symmetric format. Once the relativity effect is explained you can then boost either twin to catch up with the other to show the effect is physical and not just an optical illusion.

11. Originally Posted by jambaugh
Here's a presentational suggestion.

You made quite a point in the beginning to distinguish the astronauts from the inertial frames (in case they were under acceleration) but you then use the A and B label for both. May I suggest you give the astronauts names Alice and Bob and then refer to various frames associated with Alice as A, A' etc (in case of acceleration) and similarly with Bob.

Similarly you should label the whole gif animation for each frame A and B while the moving objects in the animations Alice and Bob. If that's not too much trouble.

BTW Nice graphics what software do you use to generate these?

One other point: I think the twin paradox is best presented in a symmetric format. Once the relativity effect is explained you can then boost either twin to catch up with the other to show the effect is physical and not just an optical illusion.
The whole point in resolving the twin paradox is that it is NOT symmetric. That is precisely the point in making sure that one is working in an inertial reference frame. Only one twin, the "stay-at-home" twin has a chance of being in an inertial reference frame. The traveling twin clearly feels acceleration at departute, at the turn-around point, and at return. His reference frame is not inertial and you cannot apply special relativity in that frame and expect to have valid results.

12. one question concerning Length Contraction - i know it may show a lack of understanding of the entirity of 'Special Relativity' but surely Length Contraction is an optical illusion and space time is never really contracted or expanded but is a result of the light taking longer or shorter to reach the observer???

the person on the ground is at the same point relative to the train in either reference frame when the light hits him which hits him in the same way, the two are identical............................

I can see and agree that 'Objects with relative motion to a frame are contracted in length as measured from the frame' - the motion towards one beam of light and away from another causes this - eventually if the train went faster than light or then i could think i wouldn't see it..............but this is only an illusion due to light, the train is moving and passing a greater amount of mass in the direction it is travelling then where it is coming from so effectively speeding the time light takes to pass over the mass and reach the observer................

but in this context time never slows down & space never contracts - one atomic clock on earth and one in space are actually on the same time, it just takes longer to compare the two as you travel between them from your reference frame (a signal delay in simpler terms)............

neither person ages more or less than the other - the fact that one is moving towards or away from the other compensates for this so if one is moving closer to the other the speed at which he travels makes up for the distance he has to travel and arrives there at the same age as the other person............

with reference to above post by DrRocket it makes sense as I have to accept that I am in an reference frame and subject to its characteristics and as a result am unaware of what is happening around me and so will always be 'out of sync' with my environment & therefore unable to calculate it correctly so i need to compensate for it & effectively 'make a guess'.....special relativity as a tool helps me explain that but the information i am taking in will always be wrong & 'out of sync with time'..............again much like a signal delay (which due to the mass it is travelling through will also change & distort, further ruining my chances of finding out what it actually is or even was at point of origin)........

13. Originally Posted by fatman57
one question concerning Length Contraction - i know it may show a lack of understanding of the entirity of 'Special Relativity' but surely Length Contraction is an optical illusion and space time is never really contracted or expanded but is a result of the light taking longer or shorter to reach the observer???

the person on the ground is at the same point relative to the train in either reference frame when the light hits him which hits him in the same way, the two are identical............................

I can see and agree that 'Objects with relative motion to a frame are contracted in length as measured from the frame' - the motion towards one beam of light and away from another causes this - eventually if the train went faster than light or then i could think i wouldn't see it..............but this is only an illusion due to light, the train is moving and passing a greater amount of mass in the direction it is travelling then where it is coming from so effectively speeding the time light takes to pass over the mass and reach the observer................

but in this context time never slows down & space never contracts - one atomic clock on earth and one in space are actually on the same time, it just takes longer to compare the two as you travel between them from your reference frame (a signal delay in simpler terms)............

neither person ages more or less than the other - the fact that one is moving towards or away from the other compensates for this so if one is moving closer to the other the speed at which he travels makes up for the distance he has to travel and arrives there at the same age as the other person............

with reference to above post by DrRocket it makes sense as I have to accept that I am in an reference frame and subject to its characteristics and as a result am unaware of what is happening around me and so will always be 'out of sync' with my environment & therefore unable to calculate it correctly so i need to compensate for it & effectively 'make a guess'.....special relativity as a tool helps me explain that but the information i am taking in will always be wrong & 'out of sync with time'..............again much like a signal delay (which due to the mass it is travelling through will also change & distort, further ruining my chances of finding out what it actually is or even was at point of origin)........
Relativistic effects such as Time dilation, length contraction and the Relativity of Simultaneity, are what are left over after the signal delay effect you are talking about is accounted for.

For example, you have a train 1 km long (as measured by someone on the train), and you have two observers with synchronized clocks stationed 1 km apart (as measured by the observers) along the railway track. Each observer notes the time at which the ends of the train passes him from West to East.

If length contraction were not "real", then the West observer should record the same time for the passing of the rear of the train as the East observer records for the passing of the front of the train. But this is not what happens.

The East observer will not record the passing of the the front of the train until after the West observer has recorded the passing of the rear of the train. This can only happen if the train is less than 1km in length in the ground frame.

Note that this measurement of the length of the train in no way depends on light signal delay between the train and ground.

14. Originally Posted by fatman57
one question concerning Length Contraction - i know it may show a lack of understanding of the entirity of 'Special Relativity' but surely Length Contraction is an optical illusion and space time is never really contracted or expanded but is a result of the light taking longer or shorter to reach the observer???
Actually it is the opposite.

As Janus demonstrated, the contraction of length is real.

However, there is an optical illusion that goes along with this due to the finite speed of light. Penrose did an analysis of what an observer would see, based on light signals from something going past at relative velocities.

You would expect that from, length contraction, a circle on a relativistic train passing an obsever would look like an ellipse with the major axis vertical. But in fact the circle will look like a circle, due to the optical illusion that results from the actual finite speed of light.

15. section 2. postulates:
The 2nd animation is not B's view of the 1st.
You merely swapped A for B, which ensures their accounts are equal.
In pic 1, B is moving toward the light emission,
in pic 2, B is static. The doppler shift would not be the same for B in both cases, yet it should be.
What you should show is B's perspective compared to A's, and what the differences are.

16. Originally Posted by phyti
section 2. postulates:
The 2nd animation is not B's view of the 1st.
You merely swapped A for B, which ensures their accounts are equal.
In pic 1, B is moving toward the light emission,
in pic 2, B is static. The doppler shift would not be the same for B in both cases, yet it should be.
What you should show is B's perspective compared to A's, and what the differences are.
These animations do not deal with Doppler shift, which is a different concept from what I'm presenting. For this discussion all we are concerned with is the travel of the leading edge of the pulse, and for that, the animation are accurate representations of A and B's perspectives of the same flash.

The fact that B sees a Doppler Shift doesn't change this.

17. Originally Posted by DrRocket
The whole point in resolving the twin paradox is that it is NOT symmetric. That is precisely the point in making sure that one is working in an inertial reference frame. Only one twin, the "stay-at-home" twin has a chance of being in an inertial reference frame. The traveling twin clearly feels acceleration at departute, at the turn-around point, and at return. His reference frame is not inertial and you cannot apply special relativity in that frame and expect to have valid results.
But you can formulate the seeming paradox in a symmetric way:

Alex and Bob take off in space-ships traveling in opposite directions.
From Alex's perspective Bob is traveling at say 0.8c and his clock is running slow so after a few years Alex perceives that Bob is younger.
From Bob's perspective Alex is traveling at 0.8c and his clock is running slow and so after a few years Bob perceives Alex as younger.

Q: Which twin is really younger?
A: The question is ill posed "really younger" implies an absolute time frame or requires an unambiguous choice of inertial frame. Alex is "really younger" in Bob's inertial frame and Bob is "really younger" in Alex's frame.
(Now you can break the symmetry at this point.)
If Alex decides to turn around and catch up with (i.e. accelerate so he is no longer moving relative to) Bob then Alex will in fact be younger when they meet because he has entered Bob's inertial frame wherein Alex's clock was running slow.
It Bob decides to turn around and catch up with Alex then Bob will be younger since he has entered Alex's inertial frame.

That is what I mean. Hanging it on acceleration per se is not appropriate nor instructive. One could always hypothesize a gravitational force accelerating one or both of the twins so that neither actually feels the acceleration. The key is not the acceleration or the non-inertial nature. The key is the geometry of space-time and the relativity of time.

It is also instructive to consider what one twin sees as he accelerates to catch up with his brother. This also provides an excellent starting point for describing accelerated observers in SR.

Note as one twin accelerates toward the other he must see the other's clock speed up in proportion to the distance (and of course the magnitude of the acceleration). This is how the two twin's observations can be reconciled as one catches up with the other. The acceleration must reconcile the differences due to the entire period over which the twins were traveling in their inertial frames seeing each others clocks slowed. The waiting period can be arbitrary while the amount of acceleration (delta vee) is fixed. The record of how long they waited is in the distance between them.

One can begin to ease into GR by noting that the twin accelerating toward his sibling perceives himself as deeper in a gravity well via equivalence principle. This distance dependence shows that the effect is not purely a function of acceleration but rather a matter of the geometry of space-time paths (whether curved or straight). I think the asymmetric presentation can confuse this point for the new student of relativity. I recall it distracted me way back when I first tried to understand the TP.

18. Originally Posted by jambaugh
Originally Posted by DrRocket
The whole point in resolving the twin paradox is that it is NOT symmetric. That is precisely the point in making sure that one is working in an inertial reference frame. Only one twin, the "stay-at-home" twin has a chance of being in an inertial reference frame. The traveling twin clearly feels acceleration at departute, at the turn-around point, and at return. His reference frame is not inertial and you cannot apply special relativity in that frame and expect to have valid results.
But you can formulate the seeming paradox in a symmetric way:

Alex and Bob take off in space-ships traveling in opposite directions.
From Alex's perspective Bob is traveling at say 0.8c and his clock is running slow so after a few years Alex perceives that Bob is younger.
From Bob's perspective Alex is traveling at 0.8c and his clock is running slow and so after a few years Bob perceives Alex as younger.

Q: Which twin is really younger?
A: The question is ill posed "really younger" implies an absolute time frame or requires an unambiguous choice of inertial frame. Alex is "really younger" in Bob's inertial frame and Bob is "really younger" in Alex's frame.
(Now you can break the symmetry at this point.)
If Alex decides to turn around and catch up with (i.e. accelerate so he is no longer moving relative to) Bob then Alex will in fact be younger when they meet because he has entered Bob's inertial frame wherein Alex's clock was running slow.
It Bob decides to turn around and catch up with Alex then Bob will be younger since he has entered Alex's inertial frame.

That is what I mean. Hanging it on acceleration per se is not appropriate nor instructive. One could always hypothesize a gravitational force accelerating one or both of the twins so that neither actually feels the acceleration. The key is not the acceleration or the non-inertial nature. The key is the geometry of space-time and the relativity of time.

It is also instructive to consider what one twin sees as he accelerates to catch up with his brother. This also provides an excellent starting point for describing accelerated observers in SR.

Note as one twin accelerates toward the other he must see the other's clock speed up in proportion to the distance (and of course the magnitude of the acceleration). This is how the two twin's observations can be reconciled as one catches up with the other. The acceleration must reconcile the differences due to the entire period over which the twins were traveling in their inertial frames seeing each others clocks slowed. The waiting period can be arbitrary while the amount of acceleration (delta vee) is fixed. The record of how long they waited is in the distance between them.

One can begin to ease into GR by noting that the twin accelerating toward his sibling perceives himself as deeper in a gravity well via equivalence principle. This distance dependence shows that the effect is not purely a function of acceleration but rather a matter of the geometry of space-time paths (whether curved or straight). I think the asymmetric presentation can confuse this point for the new student of relativity. I recall it distracted me way back when I first tried to understand the TP.
I totally disagree.

The symmetric twin problem that you propose is a different problem from the usual twin paradox. It is not a bad problem, but it is different.

Moreover the separated traveling twins have no means to compare their ages unless and until they meet at some point in space-time. GR ultimately allows only comparison of world lines at coincident points. Unlike the case for special relativity, in GR there is NO global set of coordinates, and hence no independent global concept of either space or time.

If you stick to special relativity, then you must also stick to the basic requirements of special relativity. The most fundamental of those requirements is that the Lorentz transformatin be applied only within the context of an inertial reference frame. That requirement breaks the implied "symmetry" of the paradox and permits a simple resolution.

If you want to invoke general relativity that is OK too, It is perhaps better. But you then need to work in the context of path-dependency of "time", and the point must be made that "time" is a coordinate-dependent concept and one can only compare the end-points of two world lines at a point of intersection. The critical point in this context is that neither "time" nor "spatial length" are invariant, hence ther is no unambiguous definition of either with regard to distinct points in space-time. You have to look at integrals along world lines.

The GR explanation is certainly the deeper one. But to truly explain the physics in the language of GR requires a level of sophistication and mathematics that is difficult to get across to the usual audience that one has when the "twin paradox" is discussed. In that context it is easier, and I think more clear, to make the point that a fundamental premise of special relativity is that one must work in inertial reference frames and only in inertial reference frames. In the usual twin paradox there is only one inertial reference frame.

The beauty of general relativity is that is does away with the need for any distingushed class of reference frames. That is a tremendously important philosophical point, snce in fact there is no such thing as a truly inertial reference frame. "The fixed stars" are a fiction. That was a bothersome point to Einstein, and is at least one reason for his pursuit and development of the general theory.

19. Originally Posted by DrRocket
I totally disagree.

The symmetric twin problem that you propose is a different problem from the usual twin paradox. It is not a bad problem, but it is different.
No it is a manifestation of the same phenomenon. It is the symmetry in the time dilation which is counter intuitive and lead the naive to think "paradox". Max von Laue pointed out that Langevin's explanation which you use over emphasizes the effect of acceleration on the "traveling twin".

The only distinction between my presentation and yours (given the modified "catch up" below) is that I'm choosing to formulate it in a different inertial frame (i.e. the center of mass frame for the twins on the first leg).
Moreover the separated traveling twins have no means to compare their ages unless and until they meet at some point in space-time. GR ultimately allows only comparison of world lines at coincident points. Unlike the case for special relativity, in GR there is NO global set of coordinates, and hence no independent global concept of either space or time.

If you stick to special relativity, then you must also stick to the basic requirements of special relativity. The most fundamental of those requirements is that the Lorentz transformatin be applied only within the context of an inertial reference frame. That requirement breaks the implied "symmetry" of the paradox and permits a simple resolution.

If you want to invoke general relativity that is OK too, It is perhaps better. But you then need to work in the context of path-dependency of "time", and the point must be made that "time" is a coordinate-dependent concept and one can only compare the end-points of two world lines at a point of intersection. The critical point in this context is that neither "time" nor "spatial length" are invariant, hence ther is no unambiguous definition of either with regard to distinct points in space-time. You have to look at integrals along world lines.

The GR explanation is certainly the deeper one. But to truly explain the physics in the language of GR requires a level of sophistication and mathematics that is difficult to get across to the usual audience that one has when the "twin paradox" is discussed. In that context it is easier, and I think more clear, to make the point that a fundamental premise of special relativity is that one must work in inertial reference frames and only in inertial reference frames. In the usual twin paradox there is only one inertial reference frame.

The beauty of general relativity is that is does away with the need for any distingushed class of reference frames. That is a tremendously important philosophical point, snce in fact there is no such thing as a truly inertial reference frame. "The fixed stars" are a fiction. That was a bothersome point to Einstein, and is at least one reason for his pursuit and development of the general theory.
I think you misunderstand my point about hooking into GR. The description of what the accelerating brother sees while catching up with his twin is completely within the domain of SR. (It should also be treated in your presentation.) However it can provide a starting point for the introduction of GR and its predictions. In short it is just the right example to present the EP.

(Within SR) The twins once moving in a common inertial frame can either slowly and symmetrically move toward each other or throw slow moving clocks with records of departure times and speeds at each other. Thus they can synchronize their clocks and compare durations. But if you dislike this than fine, allow that "catch up" in my presentation means docking instead of just achieving a common inertial frame.

Again the critical issue is not the effect of acceleration but the symmetric time dilation during free fall in distinct inertial frames. Simply saying "it is the twin who experienced acceleration who is younger" confuses this point. Agreed, the symmetry must be broken to resolve cases where one twin is standing next to his older (or younger) twin. Indeed it is the illusion of symmetry in the question "which twin is younger" due to the absence of explicit reference to which definition of time which creates the "paradox" in the mind of the student. Leaving in the real symmetry as far as possible better focuses the student's attention (with suitable guidance) on this critical point.

Go ahead with the traditional form Einstein presented. At least point out that had the "stay at home twin" decided to catch up with his brother then the effect is reversed. This shows the full relativity of the effect instead of it appearing to be a function of velocity in some absolute reference frame.

I take it that the point of the primer is to clarify SR rather than providing a historic presentation. The "you should"s I am using are aimed at this. Possibly I am mistaking the intent of the document.

20. Originally Posted by jambaugh
[his shows the full relativity of the effect instead of it appearing to be a function of velocity in some absolute reference frame.
On this I can agree completely. A large part of most problems with "paradoxes" is the inherent, usually unrecognized, reliance on some absolute reference frame, for either time or space.

My objection to things like discussion what is happening "while one twin is catching up" is that it really has no meaninng in GR, because in GR all that you can really talk about is what happens along world lines. So, while you can't talk about what happens "while he is catching up", you can talk about what happens after they meet in your formulation. In that situation your symmetry should apply.

One has to be very careful when mixing GR and SR. As Rindleer notes, GR shows us that SR is only a local theory. It provides the basis for the local charts that describe the space-time manifold in GR, but it does not provide a means for comparison between separated events.

From my perspective there are two issues:

1) SR comes equipped with the hypothesis that one is working in an inertial reference frame. It is important that one not attempt to apply the transormations of SR without first verifying that SR even applies -- i.e. you can't use theorems without verifying the hypotheses.

So, if one is dealing with special relativity and only with special relativity, I think that explanation is a good one. At the very least it should get across the idea that the formulation in terms of a "paradox" is not correct. I think that is very important. I am less sanguine about the actual resolution.

2) In GR, SR is no longer a global theory. It is an infitesimal approximation that permits development of the physics of GR on the manifold of space-time. Curvature of the space-time manifold eliminates the ability to formulate global coordinates, and therefore to be precise one can only compare world lines and objects that are invariant. Neither "time" nor "space" are invariant.

Using GR is probably a better way to treat the twin "paradox". It does require a bit more abstract thinking, and, I think, a more mathematically mature audience. I know of at least one person who is, or will be shortly, attempting to teach something along the lines of "special relativity from a general relativity perspective". I think that may be an interesting experiment, and one that I think has a good chance of success.

21. Janus:

But since the train observer is halfway between the ends of the
train, and the lightning struck the ends of the train, the light
should take an equal time to travel from either end to the
observer, thus the front strike must have taken place first.
The one way trip times do not have to be equal. It's the two way
(round trip) times that are equal.

(if we were to stop the train so that it was at rest with respect
to the ground, it would still be longer than the distance between
the char marks, though not as much as it measured in its frame
when they were in relative motion.)
If the train and tracks are in the same frame, both observers use equivalent rulers and measure the same train length and strike separation!

22. Originally Posted by phyti
Janus:

But since the train observer is halfway between the ends of the
train, and the lightning struck the ends of the train, the light
should take an equal time to travel from either end to the
observer, thus the front strike must have taken place first.
The one way trip times do not have to be equal. It's the two way
(round trip) times that are equal.
In the frame of the train the light has to take an equal time to travel an equal distance. Otherwise the 2nd postulate is violated

(if we were to stop the train so that it was at rest with respect
to the ground, it would still be longer than the distance between
the char marks, though not as much as it measured in its frame
when they were in relative motion.)
If the train and tracks are in the same frame, both observers use equivalent rulers and measure the same train length and strike separation!
The sentence you quoted was to meant to illustrate that it is length contraction as measured in the ground frame that causes the distance between the ends of the train and the char marks to be equal in the ground frame when there is relative motion between the two.
For example, if the char marks were 1 km apart and the relative velocity of the train and ground were 0.866c, then in order for the train to be measured as 1km in length from the ground frame, it would be 2km long in its own rest frame, or if the train and char marks were compared while in the same frame the length of the train would be twice the distance between the char mark.

This means that, when in relative motion, from the train frame, the char mark would be only 1/2 km apart( 1/4 the length of the train.)

23. The sentence you quoted was to meant to illustrate that it is length contraction as measured in the ground frame that causes the distance between the ends of the train and the char marks to be equal in the ground frame when there is relative motion between the two.
1. There is no length contraction.
2. The separation in the track frame is measured as 1 km. The train is measured as 1 km in the train frame. If the train is at rest on the track, all observers, using the same rulers will measure 1 km for both. How could it be any different?

24. Originally Posted by phyti
The sentence you quoted was to meant to illustrate that it is length contraction as measured in the ground frame that causes the distance between the ends of the train and the char marks to be equal in the ground frame when there is relative motion between the two.
1. There is no length contraction.
There is always length contraction between two relatively moving frames.

2. The separation in the track frame is measured as 1 km. The train is measured as 1 km in the train frame. If the train is at rest on the track, all observers, using the same rulers will measure 1 km for both. How could it be any different?
No. The length of the train is 1 km as measured in the ground frame. This is so that the ground observer notes that the each end of the train is adjacent to a lightning strike.

When the train is moving relative to the ground frame, it is length contracted in the ground frame. Ergo, it is longer than 1 km as measured in its own frame.

If you now put this same train in the same frame as the ground, so that all observers use the same rulers, then all observers in this frame will measure the distance between the char marks on the ground as being 1km and the length of the train as being greater than 1 km.

25. The image shows an event at E with light photons moving radially away at c.
Observer A can move toward or away from the event. The only case where the light moves from a point a constant distance from A is when A is not moving (relative to E). If the distance was constant for A while moving, the event would have to move with A, but events do not move (c is independent of the source).
In all cases the light speed is still c, only the closing speeds vary.

http://www.savefile.com/files/2157911

26. Originally Posted by phyti
The image shows an event at E with light photons moving radially away at c.
Observer A can move toward or away from the event. The only case where the light moves from a point a constant distance from A is when A is not moving (relative to E). If the distance was constant for A while moving, the event would have to move with A, but events do not move (c is independent of the source).
In all cases the light speed is still c, only the closing speeds vary.

http://www.savefile.com/files/2157911

Your image only shows one frame's perspective, for all three perspectives, including those of A when it has a relative velocity towards or away from E, you need two more S-T diagrams:

In all three light speed is c relative to the frame.

For the train example, With O1 being the ground observer and O2 being the train observer, the S-T diagrams for each frame look like this:

Again, the speed of light is c in both frames.

27. lesson 7 contains some confusing parts:

Because the Relativity of Simultaneity, the endpoint clock no longer reads the same time as the Earth clock but reads 48 yrs ahead.
The endpoint clock rate and reading are independent of the earth's motion.

due to Relativity of Simultaneity, it is the Earth clock that is ahead of the Endpoint clock. Since the Space twin is still right next to the Endpoint clock, it is the Earth clock that changes to read 48 years ahead of the Endpoint clock and thus now reads 97 yrs.
The previous reply applies, and, how can the earth clock read 97 yrs. when it is running slow for 1 yr?

You haven't explained how the earth clock while moving 14 lyr, and recording 2 yrs, still sends 98 annual signals! It would seem the earth clock ticks 98 times while the space twin clock ticks 14 times, i.e. it's running faster not slower.

28. Originally Posted by phyti
lesson 7 contains some confusing parts:

Because the Relativity of Simultaneity, the endpoint clock no longer reads the same time as the Earth clock but reads 48 yrs ahead.
The endpoint clock rate and reading are independent of the earth's motion.

due to Relativity of Simultaneity, it is the Earth clock that is ahead of the Endpoint clock. Since the Space twin is still right next to the Endpoint clock, it is the Earth clock that changes to read 48 years ahead of the Endpoint clock and thus now reads 97 yrs.
The previous reply applies, and, how can the earth clock read 97 yrs. when it is running slow for 1 yr?

You haven't explained how the earth clock while moving 14 lyr, and recording 2 yrs, still sends 98 annual signals! It would seem the earth clock ticks 98 times while the space twin clock ticks 14 times, i.e. it's running faster not slower.
You have to take the Relativity of simultaneity into account. On the outbound trip, according to the ship's frame the endpoint clock is ahead of the Earth clock. But then, the ship switches frames to one where the Earth clock is ahead of the endpoint clock (In the Earth/endpoint frame both clock always read the same.)

Here are some ST diagrams to illustrate. I reduced the ship speed to 0.5c because it makes things easier to see.

The first is from the Earth/endpoint frame. The dark blue line is the Earth world line, the light blue the endpoint world line, the green is the ship on the outbound leg and the red is the ship on the return leg. The yellow lines are a light signal traveling from earth to End point and back again.

After one year Earth time it sends a signal which arrives at the end point at the same time as the ship does.

The second shows the same situation from the frame of the outbound leg. Note, that according to the ship, when the Earth clock reads one year and sends it signal, the endpoint clock only reads 1/2 of a year.
The light from Earth still arrives at the at the same time the ship and endpoint meet.

Now here is the ships frame during the return trip:

Note that while the Endpoint clock still reads 2 yrs at the instant the ship turns around, the Earth clock now reads 2.5 yrs. This is because the light from endpoint to Earth has to arrive at Earth when its clock reads 3 yrs (just like it does in the first S-T diagram). But since the Earth is rushing toward the Ship in this frame, and light always travels at c relative to the frame it is being measured from, the light only takes 1/2 year Earth time (.577 yr ship time) to meet up with the Earth.

29. Janus;
Thanks for the diagrams, I'll study them for now.

30. Fig.1 is the earth perspective of ship's trip.

Fig.2 and fig.3 are the ship's view of diverging and converging segments with the aid of the axis of simultaneity, which visually helps assign times for events.

Fig. 4 is the ship's perspective of the trip. The reason the earth clock jumps from 1.5 to 2.5 is the ship's instantaneous turnaround, otherwise the s-axis would rotate from 1.5 to 2.5 during the deceleration/acceleration.

The second clock was omitted since it's similar to the earth clock, but with the segments in different order.

twin-prdx-2

31. Originally Posted by Janus

Example, going back to our astronauts A and B. Assume that their relative velocity is towards each other (A see's B approaching him and B see's A approaching him).

A flash of light occurs at a point of light between them.
If both the observers start a stopwatch when they see the light, and when they meet and see, whose will be faster?

32. Originally Posted by basim
Originally Posted by Janus

Example, going back to our astronauts A and B. Assume that their relative velocity is towards each other (A see's B approaching him and B see's A approaching him).

A flash of light occurs at a point of light between them.
If both the observers start a stopwatch when they see the light, and when they meet and see, whose will be faster?
Neither. Since both were an equal distance from the flash each will measure the same amount of time on their watch between seeing the flash of their meeting up.

However, by each astronaut's reckoning, the flash reaches the other astronaut first, and therefore the other astronaut started his stopwatch first. Both astronauts agree that their respective watches read the same time when they meet. This means that the other astronaut's watch has to run slow.

For instance, according to A, the flash reaches B and B starts his watch, then the flash reaches A and he starts his watch. B's watch then runs slower than A's watch such that when they meet up both watches read the same time.

For B the reverse is true; A starts his watch first and it is A's watch that runs slow.

33. Just for the inevitable crowd that wants to debate the resolution of the Twin Paradox, this paper (see proposition 2.9) explains it in rigorous terms using general relativity, which is what is really needed to handle accelerated reference frames.

Janus -- you might want to add a link to this paper to your "sticky" on relativity.

http://arxiv.org/PS_cache/math/pdf/0603/0603190v3.pdf

34. Hello all. This is my first post in this forum. I've been active in the Space.com forums but their forum site apparently crashed in December and to this day continues to be "undergoing maintenance".

I've enjoyed reviewing the posts on Special Relativity in regard to concepts related to the so-called "twin paradox". As has been pointed out explicitly by Paul Langevin, Max von Laue, and Einstein himself as early as 1911, this is only an apparent paradox resulting from the assumption that the twins' situations are symmetrical and interchangeable, an assumption that is not correct.

My questions concerning Special Relativity have to do with what might be called the "world view" of photons and their properties as they fit in 4-dimensional spacetime that Special Relativity implies and that General Relativity describes in mathematical detail.

Specifically, it occurs to me that photons - by virtue of Lorentzian translation - must possess two related properties that I haven't seen discussed. As a layman, these properties (about which I might be entirely mistaken) puzzle me.

From our point of view an photon travels through "empty" space at the invariant speed of light. Special relativity says that anything traveling at this speed experiences a time dilation to the extent that time doesn't pass for the object itself (from our point of view). If a photon possesses any inherent wave-like or oscillatory properties, this property would appear to us - and to the emitting body, for that matter - to be "frozen in time". If this is so, I'm puzzled by the meaning of the term "frequency" when it's applied to the energy of a photon of light.

The other feature that puzzles me is related to length contraction along the axis of travel of the photon. From the photon's point of view all things in the universe along this axis are traveling towards it at the speed of light. If an observer on the photon were to somehow be able to measure the distance to these things - they would all appear to be zero (again, by Lorentzian translation). To the photon, a trip from emission to absorption between two electron shells would be the same as one to the farthest galaxy. In this context, the universe itself is "frozen in time" from the perspective of the photon.

By the above reasoning if we could somehow observe a photon in motion, it would appear to us to be at most a two dimensional object possessing (perhaps) height and width, but no depth or time, although it would be traveling through our four dimensional space-time which possesses three spatial dimensions as well as time.

I'm sure that these things over which I'm puzzled have been brought up and explained elsewhere (perhaps in another thread in this forum). If so, please direct me to the proper thread or source. It's also very possible that I'm making assumptions that are invalid or that my resoning is flawed. In this case please feel free to correct me.

Thanks,

Chris

35. Hi Chris - Reading your post, I suspect that you already know a bit more on this subject than I do (I'm just an interested passer-by), but one thing about your post does stand out to me.

I asked a similar question a while back, and what I learned is that a photon does not have a "worldview" nor does a photon have a "reference frame." The way it was explained to me was that those both require an object to have the capacity to be "at rest."

To have a valid reference frame, that frame is measured at rest, and the photon is never at rest (in fact, is by definition always moving at the speed of light).

There are many members here who are far better versed in this material than myself, and I suspect one of them may be able to come in and bring further clarity. Anyway, cheers... and welcome.

36. Originally Posted by CSMYTH3025
I've enjoyed reviewing the posts on Special Relativity in regard to concepts related to the so-called "twin paradox". As has been pointed out explicitly by Paul Langevin, Max von Laue, and Einstein himself as early as 1911, this is only an apparent paradox resulting from the assumption that the twins' situations are symmetrical and interchangeable, an assumption that is not correct.
Right. The "paradox" is quickly resolved by noting that special relativity applies only in an inertial reference frame and only the frame of the non-traveling twin is inertial.

Alternately one can use general relativity. The non-traveling twin in an inertial frame is in freefall, non-accelerating in general relativistic terms. Hence the world line of the non-traveling twin is a geodesic and therefore the proper time is maximal among all world lines with the same starting and ending spacetime points. The world line of the traveling, accelerating twin is not a geodesic and therefore has a smaller proper time.

Originally Posted by CSMYTH3025
My questions concerning Special Relativity have to do with what might be called the "world view" of photons and their properties as they fit in 4-dimensional spacetime that Special Relativity implies and that General Relativity describes in mathematical detail.

Specifically, it occurs to me that photons - by virtue of Lorentzian translation - must possess two related properties that I haven't seen discussed. As a layman, these properties (about which I might be entirely mistaken) puzzle me.

From our point of view an photon travels through "empty" space at the invariant speed of light. Special relativity says that anything traveling at this speed experiences a time dilation to the extent that time doesn't pass for the object itself (from our point of view). If a photon possesses any inherent wave-like or oscillatory properties, this property would appear to us - and to the emitting body, for that matter - to be "frozen in time". If this is so, I'm puzzled by the meaning of the term "frequency" when it's applied to the energy of a photon of light.
The frame of a photon is not a legitimate SR reference frame, but you can consider it as a limiting case. Your description of the limit is correct.

"Frequency" of a photon is just another word for energy. where is energy is frequency and is Planck's constant.

The photon, so far as in known is a point particle, like all elementary particles.

Originally Posted by CSMYTH3025
The other feature that puzzles me is related to length contraction along the axis of travel of the photon. From the photon's point of view all things in the universe along this axis are traveling towards it at the speed of light. If an observer on the photon were to somehow be able to measure the distance to these things - they would all appear to be zero (again, by Lorentzian translation). To the photon, a trip from emission to absorption between two electron shells would be the same as one to the farthest galaxy. In this context, the universe itself is "frozen in time" from the perspective of the photon.
This is a correct description of the limiting case, but remember that the reference frame of the photon is not a true reference frame.

Originally Posted by CSMYTH3025
By the above reasoning if we could somehow observe a photon in motion, it would appear to us to be at most a two dimensional object possessing (perhaps) height and width, but no depth or time, although it would be traveling through our four dimensional space-time which possesses three spatial dimensions as well as time.
1. You cannot observe a photon in motion, even in principle. To detect a photon it has to interact with something. An object does not "posess" time. The clock that is meaningful to you is on your wrist.

2. Nothing travels through spacetime. only locally through space. It simply has a spacetime worldline.

3. In GR spacetime is all-encompassing. It is a single entity that contains all of space and all of time --past, present, and future -- all mixed together by curvature.
One needs to think about this a bit and adopt a rather different mind set to see what is going on in GR.

37. Hi Chris, good to see you here!

38. I remember rading a speculation a long time ago, but don't remember in what book or periodical, that there is only one photon in the whole universe and we see 'windows' of its travels through time and space. Each 'differnt' photon we see is actually the same photon from a different time. Maybe just nonsense, but interesting.

39. Originally Posted by SpeedFreek
Hi Chris, good to see you here!
Hi Speedfreek. Do you have any idea what's up with the SDC forums site? :?

On the subject of photons, thanks all for your input. I believe that Richard Feynman pointed out that the arrival of a photon (or other particle) at a detector is the weighted sum of all possible histories of the particle from emission to absorption. In this sense, the wave-like interference pattern of light in the "two slit" experiment is a manifestation of the probability of a photon arriving at the detector at a specific time rather than an indication of any wave-like property of the photon itself. Feynman seems very definite that photons are particles, not waves (a point well taken by DrRocket).

My half-baked musings about the nature of photons in motion are made in an effort to create for myself some sort of mental picture (or model) that might help me understand the interaction (of lack of interaction) between photons.

I'm a little perplexed by the comment that inow made that a photon doesn't have an inertial frame of reference. My confusion stems from the article on the "Oh-My-God-Particle" written by John Walker, which can be found here:
http://www.fourmilab.ch/documents/OhMyGodParticle/

This particle is estimated to have had a velocity of 0.9999999999999999999999951 c

Walker describes various transit times that this particle might experience, as well as various distances along it path of travel that it would "measure". I wonder what the "world view" of an observer on this particle might be - and, by extension, what the world view of an observer going slightly faster on a massless particle might be.

Chris

40. Originally Posted by CSMYTH3025
I'm a little perplexed by the comment that inow made that a photon doesn't have an inertial frame of reference. My confusion stems from the article on the "Oh-My-God-Particle" written by John Walker, which can be found here:
http://www.fourmilab.ch/documents/OhMyGodParticle/

This particle is estimated to have had a velocity of 0.9999999999999999999999951 c

Chris
0.9999999999999999999999951 c < c

There is a world of difference between almost c and c.

You cannot use a photon as the base for an inertial frame.

As I said, you can use it as a limiting but unreachable case if you are careful about it.

41. according to the second postulate of relativity......
the speed of light should be observed the same by anyone moving at any velocity(at any speed and direction)
but according to simultaneity,the speed of light is observed different by observers moving at speeds closer to that of light.....that is why an event does not appear to occur at the same time by observers moving at different velocities.
are not both these theories contradicting???
as the speed of light should be the same for 2 observers moving at different speeds and thus an event should appear to happen at same time to different observers moving at different speeds.is simultaneity wrong or second postulate of relativity?

42. [quote="Aakash Pandita"]according to the second postulate of relativity......
the speed of light should be observed the same by anyone moving at any velocity(at any speed and direction)
but according to simultaneity,the speed of light is observed different by observers moving at speeds closer to that of light.....that is why an event does not appear to occur at the same time by observers moving at different velocities.
are not both these theories contradicting???
as the speed of light should be the same for 2 observers moving at different speeds and thus an event should appear to happen at same time to different observers moving at different speeds.is simultaneity wrong or second postulate of relativity?

You are wrong.

43. Originally Posted by Aakash Pandita
according to the second postulate of relativity......
the speed of light should be observed the same by anyone moving at any velocity(at any speed and direction)
but according to simultaneity,the speed of light is observed different by observers moving at speeds closer to that of light.....that is why an event does not appear to occur at the same time by observers moving at different velocities.
are not both these theories contradicting???
as the speed of light should be the same for 2 observers moving at different speeds and thus an event should appear to happen at same time to different observers moving at different speeds.is simultaneity wrong or second postulate of relativity?
It is important to understant exactly what is meant by "the speed of light being the same". It means that someone will always get the same value for the speed of light relative to themselves.

Thus in the classic trian example, the embankment observer measures light as traveling at c relative to the embankment, and the train observer measures it as traveling at c realtive to the train.

Since the embankment observer is halfway between the lightning strikes and sees the flashes at the same time, the lightning strikes must have happened at the same time according to him since it would take an equal amount of time for the light from each strike to reach him.

Also, he will note that the light flashes will not reach the train observer at the same time as the train observer is moving to meet on flash and is running away from the other.

Now at this point it must be said that if the flashes do not reach the train observer at the same time according to the embankment, they do not reach him at the same time according to the train either. This is something both frames must agree on (otherwise physical contradictions would arise).

We now consider things from the train:

It has been established that the observer at the midpoint of the train does not see the flashes at the same time. We also know that he is sitting halfway between the ends of the train and that the lightning strikes hit the ends of the train. Using the second postulate, he measures the speed of light relative to the train to be the same in both directions, and thus light arriving from either end of the train must take equal times to make the trip.

So if he sees the flashes at different times, and the light flashes took equal amounts of time to reach him from each end of the train, then the lightning strikes could not have occured at the same time, according to him.

Thus the second postulate requires that simultaneity be relative and does not contradict it.

44. So,who was right,The man on the embankment or in the train?For the one on the embankment,the lightening will occur at the same time but for the one in the train,those strikes will not be simultaneous...

45. Originally Posted by Aakash Pandita
So,who was right,The man on the embankment or in the train?For the one on the embankment,the lightening will occur at the same time but for the one in the train,those strikes will not be simultaneous...
They are both right. That is the whole point.

46. but how could they both be right...???
either the events were simultaneous or were not....

47. Nope. That's the thing: simultaneity is relative, not universal. It's because time isn't universal, so it doesn't make much sense to be comparing timing here and timing there anyway.

48. o..thank you.....thank you very much

49. I have a small problem with events happening at the different times in different frames because of the physical differences in the two frames. In the 2nd railway animation in the frame of the railway rider the lightning on the right side occurred first causing (as is shown in the animation) the photons from that flash of light to be more dispersed than they seem to be in the ground frame which causes different interactions between photons when the two flashes hit. This difference is of coarse minute and not observable by the human eye, but nonetheless it does cause two different sets of events to occur.

I have a small problem with events happening at the different times in different frames because of the physical differences in the two frames. In the 2nd railway animation in the frame of the railway rider the lightning on the right side occurred first causing (as is shown in the animation) the photons from that flash of light to be more dispersed than they seem to be in the ground frame which causes different interactions between photons when the two flashes hit. This difference is of coarse minute and not observable by the human eye, but nonetheless it does cause two different sets of events to occur.
According to special relativity, the exact same set of events occur. All that changes is the spatial and temporal relationships between these events. If one takes the time to work out the differences, one finds exactly the same events occur.

51. Originally Posted by PhysBang
According to special relativity, the exact same set of events occur. All that changes is the spatial and temporal relationships between these events. If one takes the time to work out the differences, one finds exactly the same events occur.
In fact that is central. All inertial observers see the same events, and in the same order. What the Lorentz group does is to relate the time and spatial coordinates of one inertial observer to those of another for some given event.

The points of Minkowski spacetime are events. Those points are invariant. What is observer-dependent are the coordinate values assigned to the points.

52. I read the part on a frame of reference being different to a point of view, but I still don't really understand it. So, would the frame of reference of A just be a stationary point in space that doesn't move with A but is left behind meaning that within the frame of reference you see A moving away from A's frame of reference? No, that doesn't seem right- I'm getting confused, it doesn't help that we do absolutely no work on relativity (general or special) in physics for A-Level

53. Originally Posted by x(x-y)
I read the part on a frame of reference being different to a point of view, but I still don't really understand it. So, would the frame of reference of A just be a stationary point in space that doesn't move with A but is left behind meaning that within the frame of reference you see A moving away from A's frame of reference? No, that doesn't seem right- I'm getting confused, it doesn't help that we do absolutely no work on relativity (general or special) in physics for A-Level
Let's put it this way:

Let's say that you have a number of objects at rest with respect to an inertial frame of reference. They all have different points of view, but "are in" the same rest frame of reference.

Now have one of the objects move with respect to the others. It's point of view goes with it, but the rest frame of reference doesn't, it is now moving with respect to the original frame of reference. You can still have it as being at rest with respect to a frame of reference, but it will be a different rest frame of reference.

The point is that while a point of view is "attached" to the object, frame of references aren't. If you change velocity you change the rest frame of reference.

This comes into play with the twin paradox. The traveling twin changes velocity during the trip, and while his "Point of view" remains fixed to the ship during the entire trip, his is at rest respect to different inertial frames of reference at different points of the trip.

54. Ah, ok, I get it now. Thanks!

55. Wouldn't acceleration of objects create a "tidal" effect?

Some work is required to accelerate, some force must be at work (laws of motion).

This force will have a direction, a leading edge.

Remember objects turning into spaghetti falling (accelerating) into black holes.

56. Originally Posted by Eleven
Wouldn't acceleration of objects create a "tidal" effect?

Some work is required to accelerate, some force must be at work (laws of motion).

This force will have a direction, a leading edge.

Remember objects turning into spaghetti falling (accelerating) into black holes.
Spaghettification in black holes is indeed due to tidal forces, where the gravitational potential at your feet might be very different from the gravitational potential at your head.

How would this apply in an acceleration scenario?

57. [The inow post below should have come in before thise one]

What is causing the acceleration in your scenario?

There is no cause for acceleration in your scenario, which is impossible.
It is though your scenario is in a vacuum, away from logic and the laws of physics.

Nothing can accelerate without being acted upon by a force.......
That would an exception to the laws of motion.

The formulae for acceleration is E=ma^2, developed long ago by the phoenicians.

The E stands for energy, i.e. work is required to accelerate objects.

58. Originally Posted by Eleven
What is causing the acceleration?
It can't just happen, remeber the laws of motion?
Tell me how something can accelerate without being acted upon by a force.......

Originally Posted by SpeedFreek
Spaghettification in black holes is indeed due to tidal forces, where the gravitational potential at your feet might be very different from the gravitational potential at your head.

How would this apply in an acceleration scenario?

59. Actually, this thread is about Special Relativity, so let's not get diverted into a discussion about the equivalence principle, or whether your spacecraft could withstand the force of the acceleration without deforming. "Tidal forces" require a different thread, methinks.

60. Originally Posted by MagiMaster
Nope. That's the thing: simultaneity is relative, not universal. It's because time isn't universal, so it doesn't make much sense to be comparing timing here and timing there anyway.
Careful.

This thread is about special relativity, not general rrelativity. In special relativity there is a global set of coordinates, including time. There is in fact one such set for each inertial reference frame. "Relativity of simultaneity" refers to the fact that surfaces of constant time depend on the reference frame chosen -- different observers disagree on what events are simultaneous.

GR combines this local effect with a lack of global coordinates. It is curvature of spacetime that prevents comparing "time here' with "time there".

61. I'm sorry I didb't read the thread carefully. I thought you were discussing how we could tell if an object were accelerating....

62. The rest of the posts in this thread have been split off to pseudoscience. Please keep in mind that the intent of this thread is to aid in the understanding of SR, and not to serve as a soapbox for those who wish to dispute it.

63. An inertial coordinate system is defined as a system of space and time coordinates in terms of which the resistance to acceleration of any given object at rest is the same at every location and in all directions. In other words, we define inertial coordinate systems in such a way that the inertia of material objects is homogeneous and isotropic. Homogeneity implies that every material particle free of external influence moves at constant speed in a straight line (i.e., the space coordinates are linear functions of the time coordinate), and isotropy implies that if two identical material particles initially adjacent and at rest act to repel each other, they acquire equal speeds (i.e., derivatives of the space coordinates with respect to time) in opposite directions. Given one inertial coordinate system we can construct infinitely many others by means of arbitrary fixed translations and spatial rotations, which leave the speed of every object unchanged. Such an equivalence class of inertial coordinate systems is called an inertial reference frame.
It's important to note that the definition of an inertial reference frame given above not only identifies inertial motion with straight paths of constant speed, it also establishes an operational definition of simultaneity (i.e., the synchronization of times at spatially separate events), because inertial isotropy implies that we can use identical physical objects acting against each other to synchronize clocks equidistant from their center of mass (relying on either inertial oscillations or the equilibrium configurations of solid objects at rest to define distances). Unfortunately the terms “inertial coordinate system” and “inertial reference frame” are often defined in a weaker sense, based simply on homogeneity, without requiring isotropy. This weaker definition identifies inertial coordinate systems with unaccelerated coordinate systems. It is obviously permissible to make such a definition, but we must recognize that inertia need not be isotropic with respect to unaccelerated systems of coordinates. There is an unfortunate tradition in text books to define inertial coordinates merely as unaccelerated, i.e., such that (classically) Newton’s first law holds good, and then to immediately assert that all of Newton’s laws hold good with respect to such coordinates. This is not generally true, because the set of space-time coordinate systems in terms of which Newton’s first law holds good is much larger than the set of coordinate systems in terms of which all of Newton’s laws hold good. In order to identify the latter systems, we must stipulate not just inertial homogeneity but also inertial isotropy. A more suitable name for these systems of reference might be something like “inertia-based” rather than “inertial”, since the latter word is so suggestive of the word “unaccelerated”. On the other hand, the term “inertial coordinate system” is widely used to refer to systems for which inertia is both homogeneous and isotropic – even though it is rarely defined that way. We have chosen here to actually define the term in such a way that it corresponds to the most widely held meaning. See the note “What is an Inertial Coordinate System?” for a more detailed discussion of the sources of this troublesome linguistic and conceptual confusion.

Given the above definition of inertial reference frames, the principle of relativity asserts that for any material particle in any state of motion there exists an inertial reference frame – called the rest frame of the particle – with respect to which the particle is instantaneously at rest (i.e., the change of the spatial coordinates with respect to the time coordinate is zero). This principle is usually extended to include reciprocity, meaning that for any two suitably aligned systems S1 and S2 of inertial coordinates, if the spatial origin of S1 has velocity v with respect to S2, then the spatial origin of S2 has velocity -v with respect to S1. The existence of this class of reference frames, and the viability of the principles of relativity and reciprocity, are inferred from experience. Once these principles have been established, the relationship between relatively moving inertial coordinate systems can then be considered.

An inertial coordinate system is defined as a system of space and time coordinates in terms of which the resistance to acceleration of any given object at rest is the same at every location and in all directions. In other words, we define inertial coordinate systems in such a way that the inertia of material objects is homogeneous and isotropic. Homogeneity implies that every material particle free of external influence moves at constant speed in a straight line (i.e., the space coordinates are linear functions of the time coordinate), and isotropy implies that if two identical material particles initially adjacent and at rest act to repel each other, they acquire equal speeds (i.e., derivatives of the space coordinates with respect to time) in opposite directions. Given one inertial coordinate system we can construct infinitely many others by means of arbitrary fixed translations and spatial rotations, which leave the speed of every object unchanged. Such an equivalence class of inertial coordinate systems is called an inertial reference frame.
It's important to note that the definition of an inertial reference frame given above not only identifies inertial motion with straight paths of constant speed, it also establishes an operational definition of simultaneity (i.e., the synchronization of times at spatially separate events), because inertial isotropy implies that we can use identical physical objects acting against each other to synchronize clocks equidistant from their center of mass (relying on either inertial oscillations or the equilibrium configurations of solid objects at rest to define distances). Unfortunately the terms “inertial coordinate system” and “inertial reference frame” are often defined in a weaker sense, based simply on homogeneity, without requiring isotropy. This weaker definition identifies inertial coordinate systems with unaccelerated coordinate systems. It is obviously permissible to make such a definition, but we must recognize that inertia need not be isotropic with respect to unaccelerated systems of coordinates. There is an unfortunate tradition in text books to define inertial coordinates merely as unaccelerated, i.e., such that (classically) Newton’s first law holds good, and then to immediately assert that all of Newton’s laws hold good with respect to such coordinates. This is not generally true, because the set of space-time coordinate systems in terms of which Newton’s first law holds good is much larger than the set of coordinate systems in terms of which all of Newton’s laws hold good. In order to identify the latter systems, we must stipulate not just inertial homogeneity but also inertial isotropy. A more suitable name for these systems of reference might be something like “inertia-based” rather than “inertial”, since the latter word is so suggestive of the word “unaccelerated”. On the other hand, the term “inertial coordinate system” is widely used to refer to systems for which inertia is both homogeneous and isotropic – even though it is rarely defined that way. We have chosen here to actually define the term in such a way that it corresponds to the most widely held meaning. See the note “What is an Inertial Coordinate System?” for a more detailed discussion of the sources of this troublesome linguistic and conceptual confusion.

Given the above definition of inertial reference frames, the principle of relativity asserts that for any material particle in any state of motion there exists an inertial reference frame – called the rest frame of the particle – with respect to which the particle is instantaneously at rest (i.e., the change of the spatial coordinates with respect to the time coordinate is zero). This principle is usually extended to include reciprocity, meaning that for any two suitably aligned systems S1 and S2 of inertial coordinates, if the spatial origin of S1 has velocity v with respect to S2, then the spatial origin of S2 has velocity -v with respect to S1. The existence of this class of reference frames, and the viability of the principles of relativity and reciprocity, are inferred from experience. Once these principles have been established, the relationship between relatively moving inertial coordinate systems can then be considered.

64. Einstein not exist only classical IDEA will never DIE
www.maroszvsnewton.cba.pl/start.pdf ( it is only hot run for brain )

look how I write NEwton grawitation equations -
http://www.maroszvsnewton.cba.pl/new4a.pdf

65. Originally Posted by tesla2
Einstein not exist only classical IDEA will never DIE
I should point you to this thread:
Modern Tests of Relativity

Einstein's theories of Special and General Relativity do indeed exist, and have been repeatedly tested over the past 100 years.

I couldn't look at your pdf as the host site doesn't allow hotlinking, so all I get is a jpg message from the host.

But unless you take Einstein's ideas into account, I am unsure as to how you would write Newtons gravitation equations and have them predict the correct precession of the perihelion of the orbit of Mercury, or the correct amount of deflection of light around the Sun. Newtonian gravity gets both these calculations very wrong, whereas General Relativity gets them right.

66. sound.JPG
classical mech.
and below high speed C
Main question what happen with microphone or camera and rocket in time T
after signal reverse ( and making distance R )
V=0 mean base on light velocity or Sound velocity

light.JPG

67. You do know that light and sound obey different laws of physics? They do not act the same. The speed of light is invariant in all frames, while sound is not.

68. Yes You have right 100% sorr my mistake

below You have actual link after repair mistake

http://www.maroszvsnewton.cba.pl/mainrule.pdf

airplane 800 km will make 2R
airplane 400 km will make only R

below airplane in my pdf I copy picture from e-book about photography
brightness of picture has strong relation to distance R

Point where was sent master signal not move with airplane it is constant
point in space

base on point where was sent light signal You can measure airplane velocity

Do You see any mistake ????

everybody can make mistake thank You

69. Originally Posted by tesla2

Do You see any mistake ????
Yes. The real world doesn't work like that.

We know: we have tested it. Very, very accurately. To a few parts in a billion, not the 10% errors you joke experiment shows.

everybody can make mistake
But apparently not everyone can learn from them.

70. I seem to be misunderstanding the essence of SR. I read that in the mathematical formulation for SR, the Riemann Tensor is zero. Implications: Riemann Tensor = 0 --> No curvature --> Flat spacetime --> Absence of matter. So what is it describing exactly?

There's definitely a misconception in the above assumptions, unless I'm missing something. Note that I'm only a layman and the mathematics of relativity is beyond me. But I'm still wondering what significance a lack of curvature has in SR... Especially since "Matter bends space-time" is a popular notion, meaning that there's no matter being described in SR?

71. Originally Posted by epidecus
I seem to be misunderstanding the essence of SR. I read that in the mathematical formulation for SR, the Riemann Tensor is zero. Implications: Riemann Tensor = 0 --> No curvature --> Flat spacetime --> Absence of matter. So what is it describing exactly?
It is describing an empty universe.

Yes, really.

But in many situations, gravity is not much of a factor in the calculations, as it is such a weak "force". So the equations of Special Relativity can be used in, for instance, particle accelerators, or to calculate the time-dilation in the decay times of muons.

There's definitely a misconception in the above assumptions, unless I'm missing something. Note that I'm only a layman and the mathematics of relativity is beyond me. But I'm still wondering what significance a lack of curvature has in SR... Especially since "Matter bends space-time" is a popular notion, meaning that there's no matter being described in SR?
"Matter bends space-time" comes from General Relativity, rather than Special Relativity.

In the GPS system we use SR to calculate the component of time-dilation between the GPS satellite and the surface of the Earth due to the relative motion of the satellite (which is not in a genosynchronous orbit), and we use GR to calculate the time-dilation component due to the difference in gravitational potential between the satellite and the surface of the Earth.

72. Originally Posted by SpeedFreek
It is describing an empty universe.

Yes, really.
Sorry to be such a Socrates, but then what's the point if the universe is empty? Isn't one of the points of relativistic theory to describe physical phenomena that classical mechanics couldn't do accurately? (to be honest, I really can't tell if what you said is sarcasm or not)

In the GPS system we use SR to calculate the component of time-dilation between the GPS satellite and the surface of the Earth due to the relative motion of the satellite (which is not in a genosynchronous orbit), and we use GR to calculate the time-dilation component due to the difference in gravitational potential between the satellite and the surface of the Earth.
I always saw things as GR being an improved, more accurate model than SR. Is this true?

73. Originally Posted by epidecus
I always saw things as GR being an improved, more accurate model than SR. Is this true?
The reason that SR is SR and not just R is that SR, as you've just learned, assumes a gravity-free universe. So, SR's domain of relevance is limited to those situations that are well-approximated by zero gravity, as SpeedFreek pointed out.

GR goes beyond that limitation. So SR is a subset of GR.

This type of limitation is hardly unique to relativity. Our physical "laws" are actually applicable only within certain domains. Newtonian physics works just fine within its domain, but not outside it. Quantum theory doesn't accommodate gravity (although attempts continue), etc. Scientists are therefore careful to rely on theories only within the appropriate domains of relevance.

74. So is special relativity better to learn first rather than general relativity for a student?

Originally Posted by tk421
This type of limitation is hardly unique to relativity. Our physical "laws" are actually applicable only within certain domains. Newtonian physics works just fine within its domain, but not outside it. Quantum theory doesn't accommodate gravity (although attempts continue), etc. Scientists are therefore careful to rely on theories only within the appropriate domains of relevance.
And the most general system in describing all these domains would be the "theory of everything". Right?

75. Originally Posted by epidecus
So is special relativity better to learn first rather than general relativity for a student?
Yes if for no other reason than that the math is far far easier.

76. Originally Posted by epidecus
So is special relativity better to learn first rather than general relativity for a student?
And the most general system in describing all these domains would be the "theory of everything". Right?