Understanding Inertial reference frames

[saipathudut]

Hi to all,

I am a new one to this physics forum and i have a doubt regarding Inertial Reference frames.

In an article of IRF, it is given as "There is no absolute inertial reference frame, meaning that there is no state of velocity which is special in the universe."

Can anybody please help me understand the above sentence regarding IRF?

 

[Rooted]

I understand it to mean that there is no place in the universe that can be used as a 'stationary point', if you like. Any 'rest frame' can be seen from another reference frame to have a non-zero velocity.

 

[saipathudut]

Thanks Mr. Rooted for clearing my doubt.

Since the entire universe is moving, there is no inertial reference frame or stationary point or rest frame or the one with zero velocity. Isn't it so, Mr. Rooted sir?

 

[ghwellsjr]

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.

 

[Muphrid]

Hi to all,

I am a new one to this physics forum and i have a doubt regarding Inertial Reference frames.

In an article of IRF, it is given as "There is no absolute inertial reference frame, meaning that there is no state of velocity which is special in the universe."

Can anybody please help me understand the above sentence regarding IRF?

It means that any observer, regardless of their velocity, only needs to know about the difference of their velocity from others' to make conclusions about what others see. It's the same way that only voltage differences in EM theory matter; i.e. there is no absolute voltage that someone needs to know about to recover physical consequences.

Another way this is posed is to say that the universe is "isotropic," meaning that all directions for worldlines through spacetime are equivalent. This means that you can rotate your coordinate system and it doesn't change what happens on a physical level. A boost (which move between reference frames) is just a certain kind of rotation.

 

[saipathudut]

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.

Mr. George, firstly i thank you very much for spending your invaluable time to answer my question sir. With respect to the words i have bolded, how can we say that Earth is in a rest state and that it is a valid IRE. Our planet is rotating around itself and at the same time rotating the sun. Since velocity is a vector quantity, change in direction means change in velocity which means Earth is accelerating and hence Earth is not an IRE.

 

[Muphrid]

Mr. George, firstly i thank you very much for spending your invaluable time to answer my question sir. With respect to the words i have bolded, how can we say that Earth is in a rest state and that it is a valid IRE. Our planet is rotating around itself and at the same time rotating the sun. Since velocity is a vector quantity, change in direction means change in velocity which means Earth is accelerating and hence Earth is not an IRE.

He was saying in particular, in the case that the Earth is all there is in the universe. Outside of that (and not neglecting rotation), one would most precisely talk about an instantaneous inertial reference frame of some point on the Earth.

 

[ghwellsjr]

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 accelerating.

Mr. George, firstly i thank you very much for spending your invaluable time to answer my question sir. With respect to the words i have bolded, how can we say that Earth is in a rest state and that it is a valid IRE. Our planet is rotating around itself and at the same time rotating the sun. Since velocity is a vector quantity, change in direction means change in velocity which means Earth is accelerating and hence Earth is not an IRE.

You're right. That's why I said just before the part that you bolded, "if there were only one planet, our Earth, in the entire universe and so there is no sense in which it is moving" which means I'm imaging that there is no Sun and no rotation of the Earth around itself. I was responding to your comment in post #3 because I wanted to make sure you understand that it is not because everything in the universe is moving that there is no absolute IRF because even if there nothing were moving in the universe, there still would be no absolute IRF.

But then I wanted to make sure you understand that an IRF is not dependent on anybody within it being inertial so I asked you to imagine just the Earth and the Moon accelerating around each other so that neither is inertial.

 

[saipathudut]

Thank you Mr. Muphrid and Mr. George for helping me out in this concept. I really appreciate you both from the bottom of my heart.

Mr. George please pardon me for not interpreting your answer correctly.

I will get back to you if i get any doubts in this aspect.

 

[m.e.t.a.]

Hi, saipathudut. There isn't much I can add, but if you want to learn more, you might find the aether theory interesting. This is the long-obsolete theory that the Universe is pervaded by a medium (the aether) which we can think of as a kind of stationary scaffold against which all velocities may be measured. The aether theory was famously disproved by the Michelson-Morley experiment. Having disproved the existence of the aether, it follows that there is no such thing as absolute velocity—because the concept of absolute velocity requires the aether frame as a stationary reference. Put another way: suppose you are the passenger of a windowless spaceship undergoing zero acceleration. How do you determine your "absolute velocity"? The answer is that you can't: with no aether, there is no "master" reference frame to measure your velocity against. I hope this helps in some way!

P.S. Ms Rooted ;)

 

[harrylin]

[..] if you want to learn more, you might find the aether theory interesting. This is the long-obsolete theory that the Universe is pervaded by a medium (the aether) which we can think of as a kind of stationary scaffold against which all velocities may be measured. The aether theory was famously disproved by the Michelson-Morley experiment. Having disproved the existence of the aether [..]

Sorry that's wrong, as most participants here know. However, there was indeed the belief, based on ether theory, that it should be possible to determine a "truly stationary" or "absolute" reference frame, which thus would be "special" in that sense. The accumulation of negative experimental outcomes suggested to the contrary, that no such determination is possible. Knowledge of that historical development is certainly helpful to understand the statement in the OP.

 

[Naty1]

Knowledge of that historical development is certainly helpful to understand the statement in the OP.

Wikipedia probably discusses this and the experimental efforts of the 1920's ARE interesting. It was NOT known just that short time ago that there are no 'absolute inertial
frames'.

As has been discussed in these forums, there is no official universally agreed upon definition of 'frame of reference'. Even if there were, in general relativity [curved spacetime] we cannot even talk about relative velocities, except for two particles at the same point in spacetime.

PeterDonis posted a comment I really liked:

A "frame of reference" is a part of the structure of our models; but asking what it "really means" is implicitly assuming that there is something in reality itself that corresponds to it.

 

[m.e.t.a.]

Sorry that's wrong, as most participants here know.

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

 

[harrylin]

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

Just a little detail: the stationary ether concept is rather problematic in some aspects and thanks to SR it is widely deemed "superfluous" - which is very different from "disproved". One may say that Maxwell's ether theory was disproved because it upheld Newtonian mechanics - but that's outside of this topic.

 

[saipathudut]

You're right. That's why I said just before the part that you bolded, "if there were only one planet, our Earth, in the entire universe and so there is no sense in which it is moving" which means I'm imaging that there is no Sun and no rotation of the Earth around itself. I was responding to your comment in post #3 because I wanted to make sure you understand that it is not because everything in the universe is moving that there is no absolute IRF because even if there nothing were moving in the universe, there still would be no absolute IRF.

But then I wanted to make sure you understand that an IRF is not dependent on anybody within it being inertial so I asked you to imagine just the Earth and the Moon accelerating around each other so that neither is inertial.

Mr. George, let us consider three spaceships, say one at rest, second one is moving with constant velocity, and the third one is accelerating. Will all these three spaceships be IRFs? if that is the case, what about non-IRFs? can you please explain me in detail. i was really confused and unable to make any headway w.r.t. this concept.

 

[Muphrid]

For the accelerating ship, there exists an inertial reference frame in which the accelerating ship is instantaneously stationary, but obviously such a frame is different at other points in time. That's an instantaneous inertial reference frame.

 

[ghwellsjr]

Mr. George, let us consider three spaceships, say one at rest, second one is moving with constant velocity, and the third one is accelerating. Will all these three spaceships be IRFs? if that is the case, what about non-IRFs? can you please explain me in detail. i was really confused and unable to make any headway w.r.t. this concept.

Ships are not frames. A frame is a coordinate system in which we describe positions of objects as functions of time. So you can describe the motions of all three of your ships in a single IRF.

The first one is at some fixed location.

The second one is at some location at one time and at some other location at some other time. Since it is inertial, we can easily calculate where it is at any other time. Or you could describe its position with an equation such as x=0.5t (using units where c=1 so that it is traveling at 1/2 the speed of light).

The third ship can also be described with an equation such as x=0.1sin(t). Or you might say that it has different velocities at different times. Or you might provide a list of its location at particular times and say that it travels at a constant rate between those locations.

Sometimes, people refer to a frame by saying "the ship's frame" in which they mean that the ship is at rest in that particular frame, usually at the spatial origin of the coordinate system. If the ship is inertial, as your first two are, then the frame in which they are at rest will also be inertial. If you have two ships that are described in the same frame as your first two ships are, then you can use standard, well-defined features of Special Relativity to analyze what is going on with them relating to time dilation, length contraction and simultaneity, and you can use the Lorentz Transformation to convert the coordinates of the frame in which the first ship is at rest into the coordinates of a second frame in which the second ship is at rest.

But when it comes to an accelerating frame or a non-IRF, there are no standard ways to handle them and you cannot use the Lorentz Transformation. I don't know why non-IRF's appeal to so many people since there is no advantage to using a non-IRF in Special Relativity and they don't provide any additional insight or information that you can't get from IRF's, but the topic does generate very long threads as this thread is bound to end up as.

 

[GrammawSally]

I don't know why non-IRF's appeal to so many people since there is no advantage to using a non-IRF in Special Relativity and they don't provide any additional insight or information that you can't get from IRF's,

The advantage is that it gives you the perspective of the person who's doing the accelerating. That's certainly what the accelerating person most cares about, not the perspective of some far-away inertial person.

 

[Muphrid]

The advantage is that it gives you the perspective of the person who's doing the accelerating. That's certainly what the accelerating person most cares about, not the perspective of some far-away inertial person.

Doesn't even an accelerating observer measures with respect to their instantaneous inertial reference frame at any given point on their worldline?

 

[saipathudut]

Ships are not frames. A frame is a coordinate system in which we describe positions of objects as functions of time. So you can describe the motions of all three of your ships in a single IRF.

The first one is at some fixed location.

The second one is at some location at one time and at some other location at some other time. Since it is inertial, we can easily calculate where it is at any other time. Or you could describe its position with an equation such as x=0.5t (using units where c=1 so that it is traveling at 1/2 the speed of light).

The third ship can also be described with an equation such as x=0.1sin(t). Or you might say that it has different velocities at different times. Or you might provide a list of its location at particular times and say that it travels at a constant rate between those locations.

Sometimes, people refer to a frame by saying "the ship's frame" in which they mean that the ship is at rest in that particular frame, usually at the spatial origin of the coordinate system. If the ship is inertial, as your first two are, then the frame in which they are at rest will also be inertial. If you have two ships that are described in the same frame as your first two ships are, then you can use standard, well-defined features of Special Relativity to analyze what is going on with them relating to time dilation, length contraction and simultaneity, and you can use the Lorentz Transformation to convert the coordinates of the frame in which the first ship is at rest into the coordinates of a second frame in which the second ship is at rest.

But when it comes to an accelerating frame or a non-IRF, there are no standard ways to handle them and you cannot use the Lorentz Transformation. I don't know why non-IRF's appeal to so many people since there is no advantage to using a non-IRF in Special Relativity and they don't provide any additional insight or information that you can't get from IRF's, but the topic does generate very long threads as this thread is bound to end up as.

George sir,

It is really very nice of you to respond quickly to my query for which i need to thank you time and again.

So from your answer, i came to understand to some extent George sir. Let us consider an object table in a room. Hence that room is a frame in which the object table is present. By using coordinates, we can determine the position of the table in that room. am i right sir?

I have a doubt regarding Minkowski spacetime George sir. That article is given as follows:

"All inertial frames agree on the spaciotemporal distance between any two points p and q. They will disagree on temporal distance between p and q (time dilation) and on the spatial distance (length contraction). They will disagree on how they split the spacetime into temporal and spatial parts.

My doubt is, "The measurements regarding length contraction and time dilation between two observers will however differ, but how come the spaciotemporal distance between any two points p and q will disagree?"

They will disagree on how they split the spacetime into temporal and spatial parts.. Can you please explain me about this point, Mr. George sir?

This is my doubt, Mr. George sir. Once again, i thank you for the support you are providing me to learn more.

 

[harrylin]

Doesn't even an accelerating observer measures with respect to their instantaneous inertial reference frame at any given point on their worldline?

That depends... certain measurements are difficult to do when considerably accelerating. It's more common and simpler to measure with respect to a single (approximately) inertial reference frame - as GPS and astronauts do!

 

[ghwellsjr]

George sir,

It is really very nice of you to respond quickly to my query for which i need to thank you time and again.

So from your answer, i came to understand to some extent George sir. Let us consider an object table in a room. Hence that room is a frame in which the object table is present. By using coordinates, we can determine the position of the table in that room. am i right sir?

You can define a Reference Frame starting with a room but I wouldn't say the room is the frame because the frame extends out beyond the boundaries of the room and includes all of space. We can think about two points on the table, say on one edge and on the opposite edge and we can measure (or just pretend by assigning) the coordinates of those two points according to the Reference Frame. So even though the table might only be 2 meters long, if it is sitting in the middle of a room that is 10 meters long, the x-coordinates of those two points might by 4 and 6.

I have a doubt regarding Minkowski spacetime George sir. That article is given as follows:

"All inertial frames agree on the spaciotemporal distance between any two points p and q. They will disagree on temporal distance between p and q (time dilation) and on the spatial distance (length contraction). They will disagree on how they split the spacetime into temporal and spatial parts.

My doubt is, "The measurements regarding length contraction and time dilation between two observers will however differ, but how come the spaciotemporal distance between any two points p and q will disagree?"

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.

They will disagree on how they split the spacetime into temporal and spatial parts.. Can you please explain me about this point, Mr. George sir?

This is my doubt, Mr. George sir. Once again, i thank you for the support you are providing me to learn more.

It would help if you are quoting a post to provide a link. I hope the post uses the term "event" rather than "point" because "point" usually refers just to a spatial location, whereas "event" includes a time component.

So in our example, we can say that x_p=4 and x_q=6 and the time coordinates are both 0, t_p=0 and t_q=0.

But in another reference frame moving at, say, 0.6c along the x-direction of our previously defined frame, the x and t coordinates of those two events take on different values which we can determine from the Lorentz Transformation process. Those values would be:

x'_p=5 and t'_p=-3
x'_q=7.5 and t'_q=-4.5

As you can see, the spatial difference between those two events is now 2.5 meters instead of 2 and the temporal difference is 1.5 instead of 0. But the spaciotemporal distance (more often called the spacetime interval) is defined as √(Δx²-Δt²).

If you plug the previous values into this formula, you get for the initial frame:

√(2²-0²) = √(4-0) = √4 = 2

and for the moving frame:

√(2.5²-1.5²) = √(6.25-2.25) = √4 = 2

However, there is no significance to the fact that these two come out to the same value, it is merely a result of the mathematics of the Lorentz Transformation process.

 

[saipathudut]

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?

 

[ModusPwnd]

but how come the spaciotemporal distance between any two points in all inertial frames agree?

How come? It just does. That is the way we have observed the universe to work. Any explanation of 'why' would necessarily have to appeal to some other postulate of relativity and thus be just as fundamentally unsatisfactory.

 

[ghwellsjr]

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?

As I pointed out in my previous post, as long as you accept the Lorentz Transformation as a valid mathematical process to relate the coordinates of an event between two inertial frames, then the fact that the spaciotemporal distance between two of those events is frame invariant is nothing more than a mathematical curiosity.

Then the real question you want to ask is why is the Lorentz Transformation process valid? And I would answer that by saying that it is based on the definition of spatial distance and temporal distance that Einstein gave in his 1905 paper introducing Special Relativity. He said distance is what we measure with a rigid ruler and time is what we measure with a clock. Then it can be shown that the spaciotemporal distance between any two events (not points, please) falls into one of three categories without regard to any further definition of an inertial frame. In the first category, we can measure the distance between the two events with an inertial clock. In the second category, we can measure the distance between the two events with an inertial rigid ruler. The third category applies to two events that we cannot measure with either a clock or a ruler.

For example, for the two points on your table if we talk about two events that occur so close to the same time that we could not traverse a clock between those two events because it would have to travel faster than light, then we use the ruler to measure the distance. But if the two events were at the center of the table for when we light a candle and when the candle burns out, we would use a clock at that location to measure the distance between those two events. Finally, if we wanted to consider the first event as the lighting of the candle and the second event as the first light hitting the wall we could not measure that with either a clock or a ruler so we call it null meaning it doesn't have a distance. I realize that this is an oversimplification but if you read up on "spacetime interval" maybe you can understand it better.

 

[saipathudut]

It would help if you are quoting a post to provide a link. I hope the post uses the term "event" rather than "point" because "point" usually refers just to a spatial location, whereas "event" includes a time component.

Mr. George, in that pdf file, they were mentioning it to be points rather than events. As you said, it has included a time component, but they tend to call it point rather than event. Hence i am uploading that document for your reference sir to explain my confusion, George sir.

 

[ghwellsjr]

Aside from the minor differences in terminology that have already been pointed out, I don't see where your confusion lies. Maybe it would help for you to point to a specific comment in the pdf and/or in my posts that you find confusing or in conflict.

By the way, the pdf is also using the terms "time dilation" and "length contraction" incorrectly, but I'm afraid that pointing that out may just add to your confusion.

 

[saipathudut]

You can define a Reference Frame starting with a room but I wouldn't say the room is the frame because the frame extends out beyond the boundaries of the room and includes all of space. We can think about two points on the table, say on one edge and on the opposite edge and we can measure (or just pretend by assigning) the coordinates of those two points according to the Reference Frame. So even though the table might only be 2 meters long, if it is sitting in the middle of a room that is 10 meters long, the x-coordinates of those two points might by 4 and 6.

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.

It would help if you are quoting a post to provide a link. I hope the post uses the term "event" rather than "point" because "point" usually refers just to a spatial location, whereas "event" includes a time component.

So in our example, we can say that x_p=4 and x_q=6 and the time coordinates are both 0, t_p=0 and t_q=0.

But in another reference frame moving at, say, 0.6c along the x-direction of our previously defined frame, the x and t coordinates of those two events take on different values which we can determine from the Lorentz Transformation process. Those values would be:

x'_p=5 and t'_p=-3
x'_q=7.5 and t'_q=-4.5

As you can see, the spatial difference between those two events is now 2.5 meters instead of 2 and the temporal difference is 1.5 instead of 0. But the spaciotemporal distance (more often called the spacetime interval) is defined as √(Δx²-Δt²).

If you plug the previous values into this formula, you get for the initial frame:

√(2²-0²) = √(4-0) = √4 = 2

and for the moving frame:

√(2.5²-1.5²) = √(6.25-2.25) = √4 = 2

However, there is no significance to the fact that these two come out to the same value, it is merely a result of the mathematics of the Lorentz Transformation process.

George sir, due to personal problems, i was unable to log in sir. Please pardon me sir for not responding to your posting.

"All inertial frames agree on the spaciotemporal distance between any two events" - the proof you have given above clearly made me understood the above sentence sir.

"They will disagree on the temporal distance between p and q (time dilation) and on the spatial distance (length contraction)." - of course, they will disagree as the static p will find the q's moving vehicle's length contracted and also will see the time running slowly in the q than his time. Isn't it George sir?

But at the same time, am unable to understand this point,"They will disagree on how they split the spacetime distance into temporal and spatial parts."

Thank you Mr. George sir for your support.

 

[ghwellsjr]

"They will disagree on the temporal distance between p and q (time dilation) and on the spatial distance (length contraction)." - of course, they will disagree as the static p will find the q's moving vehicle's length contracted and also will see the time running slowly in the q than his time. Isn't it George sir?

No, there is no sense in which p is static and q is moving. They are "events", an instant in time at a particular location in space. Each frame assigns numbers, or coordinates, to each event, one coordinate for the instant in time and three coordinates for the location in space.

But at the same time, am unable to understand this point,"They will disagree on how they split the spacetime distance into temporal and spatial parts."

Each frame can assign different numbers, or coordinates, to an event. So if we first consider two events and the numbers (or coordinates) assigned to them by one frame, and we calculate the difference in the corresponding numbers (or coordinates), we will get a set of four numbers, correct? Now if we do this again with the numbers (or coordinates) assigned by a second frame, we will get a different set of four numbers, correct? That's what we mean when we say that different frames "will disagree on how they split the spacetime distance [between two events] into temporal and spatial parts".

 

[bobc2]

Originally Posted by m.e.t.a.
[..] if you want to learn more, you might find the aether theory interesting. This is the long-obsolete theory that the Universe is pervaded by a medium (the aether) which we can think of as a kind of stationary scaffold against which all velocities may be measured. The aether theory was famously disproved by the Michelson-Morley experiment. Having disproved the existence of the aether [..]

Sorry that's wrong, as most participants here know. However, there was indeed the belief, based on ether theory, that it should be possible to determine a "truly stationary" or "absolute" reference frame, which thus would be "special" in that sense. The accumulation of negative experimental outcomes suggested to the contrary, that no such determination is possible. Knowledge of that historical development is certainly helpful to understand the statement in the OP.

Along these lines, here is a reference I found in one of my textbooks, "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 m.e.t.a. on this issue.

 

[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).
5. 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).