General Questions about Special Relativity

[NoahsArk]

Because of the very good responses here, I have a better understanding of how relativity of simultaneity works. If clocks are lined up inside a rocket side by side in a row, like a row of seats, and there are several rows of clocks going from the back to the front of the rocket, then the clocks in any particular row will be synchronized in the stationary frame as well as in the rocket's frame. However, clocks belonging to different rows will not be synchronized according to the stationary frame. Also, all clocks in the rocket, no matter what row they are in, will be ticking at the same rate, its just that the different rows won't be synchronized in the stationary frame.

The why part of this I still don't understand. In the example with the rows of clocks, none of the clocks have any motion relative to the rocket. In all the examples that I've seen about relativity of simultaneity ("R.O.S"), there is motion of the clock relative to the rocket- either in the same direction that the rocket is moving or in the opposite direction. Here are two contrasting examples, both of which should involve R.O.S, but only the first example makes sense to me as to why it's occurring. The first example is a little repetitive, but I need to use it to contrast with the second:

1) From the middle of the rocket, two beams of light shoot out towards opposite ends of the rocket. Someone inside the rocket will observe the two beams hitting the opposite ends simultaneously. Someone in the rest frame will observe the beam hitting the back end first. This makes sense because the person in the middle of the rocket sees both beams traveling an equal distance at speed C. The person in the rest frame sees the beam traveling a longer distance to get to the front of the rocket. Given that C is constant, it's logical that the stationary observer will see the beam hitting the back end (which involves shorter travel), sooner than the front end.

2) A rocket is moving while two events happen at the back and front of the rocket simultaneously from the rocket frame. Say the event is just a flash of light where, unlike in example one above, there is no movement toward either end of the rocket (for example, if two people, one in the back and one in the front, both had a flash light pointing upwards, and they each turned the flash light on and off). In this example, we could also use, instead of a flash light, a ball being dropped on both ends, or two people clapping their hands on both ends, etc. From the stationary observer's point of view, the event that happened in the back of the rocket did not involve any extra distance of travel compared to the event in the front. This is in contrast to the beams of light in the first example where the only reason R.O.S. occurred was due to the different distances that had to be traveled before the first event (the beam hitting the back) and the second event (the beam hitting the front) could occur.

Am I missing something fundamental?

 

[Ibix]

Take your first example and add two clocks at the front and rear of the rocket. In the rocket frame the clocks strike 12 at the instant the light pulses arrive.

If the clocks are not out of sync in the other frame (for which the pulses arrive non-simultaneously) then they will show different times when illuminated by the pulses, but the same time in the rocket frame. That would be inconsistent. You can easily set up a clock-stopping device to go off when the light pulses arrive, and they can't stop at different times in diffetent frames...

 

[Mister T]

(My emphasis)

Only in frames moving in the same direction as the rocket. In frames moving in a different direction the clocks will not be synchronised.

Right. I should have said "both frames". I was trying for simplicity but went too far!

 

[Mister T]

The why part of this I still don't understand. In the example with the rows of clocks, none of the clocks have any motion relative to the rocket. In all the examples that I've seen about relativity of simultaneity ("R.O.S"), there is motion of the clock relative to the rocket- either in the same direction that the rocket is moving or in the opposite direction.

Imagine that there is a mock-up of the rocket at rest in the stationary frame. It's an identical copy of the rocket, so it also has rows of clocks. It points in the same direction in which the rocket moves, and lies along the line of that motion. To observers at rest in the real rocket, the clocks in the mock-up are in motion relative to them. All the clocks in the mock-up were synchronized in their rest frame. Observers at rest in the rocket (rocket observers) will agree that clocks in each row of the mock-up are synchronized, but they will observe that the clocks in each row are not synchronized with the clocks in other rows.

Also, by the way, rocket observers will conclude that mock-up clocks are ticking at slower rate than their own clocks. And, mock-up observers will conclude that rocket clocks are ticking at a slower rate than their own clocks.

In this example, we could also use, instead of a flash light, a ball being dropped on both ends, or two people clapping their hands on both ends, etc. From the stationary observer's point of view, the event that happened in the back of the rocket did not involve any extra distance of travel compared to the event in the front.

The traveling of the beams are not events. The arrival of the beams are events. (Events occur at a single location in space and a single clock-reading. They have no extension in space and they last for no duration of time.)

This is in contrast to the beams of light in the first example where the only reason R.O.S. occurred was due to the different distances that had to be traveled before the first event (the beam hitting the back) and the second event (the beam hitting the front) could occur.

The beams of light used to show ROS are not the cause of the ROS. They are used simply as a teaching tool to convince us that ROS is a valid phenomenon. In other words, they're a heuristic.

 

[NoahsArk]

Take your first example and add two clocks at the front and rear of the rocket. In the rocket frame the clocks strike 12 at the instant the light pulses arrive.

If the clocks are not out of sync in the other frame (for which the pulses arrive non-simultaneously) then they will show different times when illuminated by the pulses, but the same time in the rocket frame. That would be inconsistent.

If I am understanding you correctly, what you said means that if someone in the stationary frame took a picture of the beam illuminating the clock at the front end, and the person in the rocket frame also took a picture of the beam illuminating the front end, then, if they got together and compared pictures, the pictures would reflect different times on the clock which would be inconsistent. That makes sense, but from what I've seen so far, special relativity in general produces many inconsistent results, and is largely about different observers in different relative states of motion observing reality differently. For example, if the person in the stationary frame took a photograph that showed two clocks from the different rows, those clocks would show different times, whereas if the person in the rocket frame took the same photo, the clocks would show the same time. Isn't this also inconsistent, but at the same time what we'd expect?

Also, in the first of the two examples that I used, there is a physical explanation for why R.O.S. is occurring. Is there a physical explanation about why it should occur in the second example?

 

[NoahsArk]

Also:

The beams of light used to show ROS are not the cause of the ROS. They are used simply as a teaching tool to convince us that ROS is a valid phenomenon. In other words, they're a heuristic.

That also relates to my question on if there is a physical explanation for it.

 

[Ibix]

but from what I've seen so far, special relativity in general produces many inconsistent results

No. The results are never inconsistent - unexpected to Newtonian intuition, yes, but never inconsistent. You said that different frames describe reality differently, which is a good way to put it. Now rig one of the clocks so that the spaceship explodes if it is illuminated at exactly 12. Unless the clocks are de-synchronised, then, one frame says BOOM, one frame doesn't. Is that "different ways of describing reality"?

For example, if the person in the stationary frame took a photograph that showed two clocks from the different rows, those clocks would show different times, whereas if the person in the rocket frame took the same photo, the clocks would show the same time. Isn't this also inconsistent, but at the same time what we'd expect?

If you're using a small camera with a view of both clocks then you are not taking a photo of the clocks as they were when you took the photo - light had to travel from the clocks to the camera. The different frames will have different reasons for why the picture shows asynchronous clocks (clocks in sync, but unequal light travel times; or clocks out of sync, but with equal light travel times), but they will expect the picture to show asynchronous clocks.

Also, in the first of the two examples that I used, there is a physical explanation for why R.O.S. is occurring. Is there a physical explanation about why it should occur in the second example?

Because you can always add light pulses being exchanged and show that the results are inconsistent if simultaneity is preserved.

A better explanation is that spacetime is four dimensional. A choice of frame is a choice of how you split it into space and time, and when you make a different choice you get a different definition of "the same time". I strongly recommend looking up Minkowski diagrams. You might also want to have a play with my interactive diagrams tool: http://www.ibises.org.uk/Minkowksi.html

 

[Orodruin]

special relativity in general produces many inconsistent results

No it does not. Special relativity does not predict inconsistent results.

Isn't this also inconsistent,

No.
Inconsistency would mean disagreement on the same measuring process such as the classical formulation of the twin paradox, which is not an inconsistency of the theory though - just a faulty application of it.

 

[David Lewis]

...if someone in the stationary frame took a picture of the beam illuminating the clock at the front end, and the person in the rocket frame also took a picture of the beam illuminating the front end...

The camera shows you what you see, not what is happening.

 

[Mister T]

That also relates to my question on if there is a physical explanation for it.

The only thing prompting that question in your mind is a prejudice. If simultaneity were absolute would you be asking for a physical explanation of that? No, because your intuition, based on your experiences, tells you that simultaneity is absolute. So you seek no explanation of it. But in fact those experiences are limited to scenarios where the effects of the relativity of simultaneity are so small they don't make themselves apparent.

If you were an engineer working with the synchronization of the atomic clocks that are part of the GPS the effects of relative simultaneity would be so apparent that ignoring them would lead to positioning errors in the system large enough to render it useless. GPS could tell you what country you're in, but not what street intersection you're passing through.

 

[Nugatory]

For example, if the person in the stationary frame took a photograph that showed two clocks from the different rows, those clocks would show different times, whereas if the person in the rocket frame took the same photo, the clocks would show the same time.

Careful - a photograph does not capture a picture of the objects in it at the same time, it captures the light hitting the film at the moment that the shutter is open. This has two implications:

1) If the objects are at different distances from the camera when the light left them, the photograph may show them at different times. Consider an ordinary boring room maybe 3 meters across (so light takes about ten nanoseconds to cross it). You and I are standing at opposite ends of the room, wearing synchronized wristwatches and each holding a delicate glass object at the same height above the floor. At exactly noon we both drop our objects and of course they hit the floor at the same time. However, the light carrying the image from your object breaking will reach me about ten nanoseconds later than the light from my object breaking, so there is a moment in there in which I can snap a photo showing my glass broken and yours still falling, just a few microns above the floor.
Someone elsewhere in the room and closer to you than to me could take a photo that shows the exact opposite: your glass is broken and mine is about to hit the floor and break. We'd have to consider the positions of both cameras and the distances involved, and do a bit of calculating to find that in fact the two glasses hit the floor and broke at the same time (which will be about .4 seconds after noon for a one-meter drop).
2) If two cameras are at the same place at the same time, they will take the same picture because the same light is coming in through their open shutters. If they're moving relative to one another, the colors may be a bit different because of the doppler effect, but other than that they have to agree - if there's a clock face in the photo, the hands have to be pointing the same way in both photos.

 

[NoahsArk]

I wasn't taking into account the mechanism of the cameras in my example, and I maybe should've used a more accurate example to demonstrate. If instead of just one person in the stationary frame, there were two people taking pictures of two clocks from different rows (and the light travel time to each camera was the same for both people), and then later they met and compared photographs, the pictures would show different times and they'd know the clocks were out of sync. The same experiment could be done with two people in the rocket frame, and when they compared photographs their times would be the same. This result, to me, is an inconsistent result, but I'm taking it as a given that this result would occur.

If the same experiment were done in both frames, except this time with the two people in each frame each taking a picture of a different clock in the same row, both people from both frames would compare the pictures and agree that the clocks were in sync.

A better explanation is that spacetime is four dimensional. A choice of frame is a choice of how you split it into space and time, and when you make a different choice you get a different definition of "the same time". I strongly recommend looking up Minkowski diagrams. You might also want to have a play with my interactive diagrams tool: http://www.ibises.org.uk/Minkowksi.html

Thank you for sending that link. I could not open it though. Please let me know if there is another link to the site.

The only thing prompting that question in your mind is a prejudice. If simultaneity were absolute would you be asking for a physical explanation of that? No, because your intuition, based on your experiences, tells you that simultaneity is absolute. So you seek no explanation of it.

That brings up a more general issue in science I think, which is when is a phenomenon an axiom or postulate that can't be further proved. This relates to another question that I and many others who I've seen posting on the subject have about why the speed of light is constant. My intuition tells me that C should not be independent of the relative state of motion of the observer, and that if a beam of light is shot out from a rocket traveling at .5C, the beam should then be traveling at 1.5C for me if I am stationary relative to the rocket. I've heard answers, to the question of why C is constant, ranging from there is no reason, it's just what the experiments tell us, to it having to do with a deep symmetry in nature. Is the fact that C is constant just something we know inductively through experiment? If so, could it be that there is something in nature causing C to be constant, we just can't perceive it with our senses?

Regarding relativity of simultaneity, is that also something we just know through experiment, and we don't know a deeper reason for it?

 

[Nugatory]

This relates to another question that I and many others who I've seen posting on the subject have about why the speed of light is constant. My intuition tells me that C should not be independent of the relative state of motion of the observer, and that if a beam of light is shot out from a rocket traveling at .5C, the beam should then be traveling at 1.5C for me if I am stationary relative to the rocket. I've heard answers, to the question of why C is constant, ranging from there is no reason, it's just what the experiments tell us, to it having to do with a deep symmetry in nature. Is the fact that C is constant just something we know inductively through experiment? If so, could it be that there is something in nature causing C to be constant, we just can't perceive it with our senses?

There's a fairly straightforward intuitive argument for why the speed of light might be the same for all observers. We intuitively expect that the laws of electricity and magnetism, like all other laws of physics, don't change with the speed of the observer. There's also a fair amount of experimental support for that proposition: we get the same results for E&M experiments in June and December, and at noon and midnight, even though the rotation and orbit of the Earth means that our physics lab is moving at very different speeds. So far, there's nothing surprising here - it would be far more bizarre and counterintuitive if (for example) Coulomb's law needed a correction that changed with the seasons for the speed of the observer through space.

But then in 1861 James Maxwell showed that you can calculate the speed of light in vacuum from these laws of electricity and magnetism. Thus the only way that the speed of light could be different for different observers would be if the laws of electrodynamics changed with the speed of the observer, and they clearly don't. This was the great unsolved physics problem of the second half of the nineteenth century: Common sense says that light should behave as you describe ("if a beam of light is shot out from a rocket traveling at .5C, the beam should then be traveling at 1.5C for me if I am stationary relative to the rocket") but it can't because that would be inconsistent with the laws of E&M.

What Einstein did was to show that there was a completely consistent physics that matched all experimental results, agreed with the past few centuries of experiments with electricity and magnetism: everything can be made to work if we just listen to the laws of electricity and magnetism when they say that the speed of light must be constant. The title of his 1905 paper introducing special relativity is "On the electrodynamics of moving bodies", because that was the problem that relativity solved. His extraordinary-looking results were accepted so quickly because they so clearly solved the problem that had been tormenting phsyicists for the past half-century.

 

[Nugatory]

Regarding relativity of simultaneity, is that also something we just know through experiment, and we don't know a deeper reason for it?

No. It's nice to see it demonstrated in the GPS system, particle lifetime measurements, and the like...

But once you accept the postulate that the speed of light is constant for all observers, relativity of simultaneity follows as surely as any theorem in high school geometry follows from Euclid's postulates of geometry. The experiments are telling us that the world behaves the way we've logically proven that it must if our postulate is correct.

 

[Ibix]

I wasn't taking into account the mechanism of the cameras in my example, and I maybe should've used a more accurate example to demonstrate. If instead of just one person in the stationary frame, there were two people taking pictures of two clocks from different rows (and the light travel time to each camera was the same for both people), and then later they met and compared photographs, the pictures would show different times and they'd know the clocks were out of sync. The same experiment could be done with two people in the rocket frame, and when they compared photographs their times would be the same. This result, to me, is an inconsistent result, but I'm taking it as a given that this result would occur.

If the same experiment were done in both frames, except this time with the two people in each frame each taking a picture of a different clock in the same row, both people from both frames would compare the pictures and agree that the clocks were in sync.

Those aren't inconsistent. When you say two people take pictures, you mean two people take pictures simultaneously . But then you have to ask: simultaneously for who? The people in the rocket frame or the people in the stationary frame? When you've answered that, you'll know whose clocks show the same time and whose don't.

If both frames take photos simultaneously in their own frames, both will be able to observe that the other didn't take photos simultaneously. So there's no inconsistency here.

I think @Nugatory quoted his daughter as saying that the trick with Special Relativity problems is to spot where they're trying to sneak "at the same time" past you and not let them. You keep sneaking it past yourself. The Lorentz transforms and some Minkowski diagrams will set you straight.

Thank you for sending that link. I could not open it though. Please let me know if there is another link to the site.

Ack - not sure what went wrong there. Try ibises.org.uk/Minkowksi.html.

 

[Grimble]

It is all due to Relativity! All Frames of Reference are equal. None is a preferred Frame.
Also, because no Frame is preferred, Spacetime is at rest as mapped from each and every Frame.

Take an Event: A flash of light. It happens at a particular location in space; at a specific instant in time. (In each frame the Space and time coordinates will be different depending on the origin and orientation of that frame)

Yet the one thing that we know; and to which all observers in whichever frame they observe from; is that after 1 second the light emitted at that event will form a sphere, with a radius of 1 light second, centred on the initial flash-of-light event.

Now the difficulties arise whether we are considering moving trains on embankments, lights in carriages, in Rockets etc.
Let us take the last as an example:
From the rocket's frame of reference, after 1 second the light will have reached either end of the stationary rocket; yet from the perspective of an independent observer relative to whom the rocket is moving, the light will reach the rear of the rocket before the front.

Both these view's are correct; the point is that it is all relative; from the perspective of the observer in the rocket, the light flash was in the middle of the rocket (which in his frame of reference is at rest) and the light took the same time to travel to each end of the rocket.
From the perspective of the independent observer, moving relative to the rocket, the light flash happened at a particular fixed point in space, which at that moment coincided with the centre of the moving rocket. The light traveled out from the point occupied by the centre of the rocket, as a perfect sphere, at rest relative to the independent observer, while the rocket moved away at the relative speed between the rocket and the independent observer.

What we do know is that from an event, i.e. a fixed point in space, at a particular moment in time, the light will spread outwards as a perfect sphere at the speed of light.
In every single frame of reference that will happen. In every frame of reference the origin is at rest, because that is the point from which spacetime is mapped using that frame of reference. For the real or virtual observer, permanently at the origin of any frame spacetime is at rest; it has to be because that is what is being mapped.
Therefore the speed of the light emitted at that event will travel at c relative to each and every observer.

Let me say once again - it is all relevant!

We only have trouble dealing with this when we define one particular view, one particular frame of reference, and make everything relative to that.

 

[Mister T]

Regarding relativity of simultaneity, is that also something we just know through experiment, and we don't know a deeper reason for it?

Historically, it was predicted as a consequence of two postulates before it was ever detected experimentally.

The notion of deeper reasons is illusory. You can easily fool yourself into believing you understand something because it makes sense based on other stuff that you think you know to be true. In this case, the relativity of simultaneity makes sense based on what we know about other things. But that alone is not enough to convince us that it's valid. We also need experimental verification. And we have an overwhelming amount of that.

 

[NoahsArk]

not sure what went wrong there. Try ibises.org.uk/Minkowksi.html.

Thank you. That worked for me. I'm going to play around with it.

Historically, it was predicted as a consequence of two postulates before it was ever detected experimentally.

The notion of deeper reasons is illusory. You can easily fool yourself into believing you understand something because it makes sense based on other stuff that you think you know to be true. In this case, the relativity of simultaneity makes sense based on what we know about other things. But that alone is not enough to convince us that it's valid. We also need experimental verification. And we have an overwhelming amount of that.

How about the speed of light being constant, though? Isn't that something we only know from experiment and not something we deduced from other facts which were already known?

There's a fairly straightforward intuitive argument for why the speed of light might be the same for all observers. We intuitively expect that the laws of electricity and magnetism, like all other laws of physics, don't change with the speed of the observer. There's also a fair amount of experimental support for that proposition: we get the same results for E&M experiments in June and December, and at noon and midnight, even though the rotation and orbit of the Earth means that our physics lab is moving at very different speeds.

I have not taken a course in electricity and magnetism, and have just read about the concepts in layman's books. Would it help me to understand special relativity better if I studied electricity and magnetism more?

 

[Nugatory]

I have not taken a course in electricity and magnetism, and have just read about the concepts in layman's books. Would it help me to understand special relativity better if I studied electricity and magnetism more?

Not if your goal is just to understand special relativity - for that you can start with Einstein's postulates, and all of SR will follow from there. Studying E&M will help convince you that there is no reasonable alternative to these postulates, but you don't need that to consider the implications of those postulates.

In the common American undergraduate physics program you learn SR before you take on E&M.

 

[CPTinvariant]

New user, old nerd and I'm jumping in right here.

My own personal approach to this problem of getting some intuition for ideas of time dilation and length contraction went as follows.

1) Accept that we have no native intuition for such things nor any internal reference points for understanding such a thing. That this is exactly why it took centuries of science to spot this change in descriptions of space, time, matter and relative motion was needed.

It is a counter-intuitive set of results, to the extent that historically it required great contradictions to appear between two sets of very well respected laws to suggest the need for a new theory of space and time. Our experience gives way to a sense of emptiness the moment the rate of relative motion between two observers becomes so appreciable that relativistic effects apply - no human being has ever perceived their everyday world in such a way.

Where these effects are obvious, we have never been. Where they are hidden that's where we live our entire macroscopic lives.

Only in the analysis of small particles where these relative speeds are commonplace revealed the problem was a serious thing and could not be gotten rid of. So the ideas openly defy an intuition, we're just too big and we live in a nicely, gently curved space, so we cannot know anything about this kind of a problem with every intuition we have about space and time, not until it becomes a problem of self-consistency between two sets of very well-loved laws. Then we have two problems, one of them is getting rid of the wrong intuition and the other is not having a new one to put in place. Quite a problem!

But... 1) doesn't mean feeling the same thing as remaining forever uncomfortable with theory and that's because of the self-consistency of the theory and the development of intuition for that instead. So, there's also...

2) That such an intuition for the theory may be carefully developed in spite of not having direct experience of its most shocking effects.

My approach to this was to look at the mathematics a whole lot, look for geometric representations of the theory, read a great many sources, read the original papers by Einstein, Minkowski, etc, all the early relativists who were themselves also still looking to develop such an intuition and familiarity. That kind of sustained effort to get at the relativity theory seemed a worthwhile thing because it isn't like other theories of physics, being a theory of space and time itself, it matters to all coordinate exchange so that places it in a remarkably important place in all theoretical physics. So this thing is, whatever else can be said of it, fundamental to all the physics which comes after it and that's a thing worth persisting with and specifically it's worth persisting in developing intuition for the self-consistency of it, by hook or by crook.

There's also the obvious option on repeating useful thought experiments with subtle variations, just putting yourself in the situation being modeled and imagining yourself inside it. If we cannot have a physical intuition for these effects we need perhaps to try and develop an abstract sense of one, from sheer brute force of imagination.

Humans appear to be absolute naturals at this kind of thinking, so I decided that since we have daydreaming abilities, and reasoning abilities, those were worth coopting for doing a lot of repeated thought experiments to just drill the idea into my brain that this is how the world really is. That everything else I have experienced about time and space has been a kind of pleasant and simplified illusion which comes from living a provincial life, never moving very fast with respect to anything macroscopic, certainly not fast enough to peel away the veil and notice the illusion of absolute space and absolute time is just as much an illusion as an absolute rest frame.

You can see things in your imagination you cannot experience in real life and then check out what you've been thinking about for logical consistency with the theory and that way, over a span of some time, you can definitely train the imagination to have a partial intuition for the observations fitting theory, i.e., intuition for its self-consistency.

It is a kind of like building a jigsaw puzzle when you don't know what the final image looks like but you do know that locally, two pieces always have to fit in a way that makes sense of the images on just those two pieces and so you can still build a jigsaw without knowing anything at all about the global image it contains. So I decided that was a fair way to at least try to attack this kind of problem where there's just no real intuition to start with and everything has to be built up from local efforts of understanding this bit here and that bit there. So just feeding the visual cortex scenarios in which relative motions and such effects would become observable, I claim that's extremely useful, its importance cannot be overstated. And besides, it's amazing to think about and massive fun.

I know it's a kind of silly recommendation but I can still read Mr. Tompkins by Gamow and enjoy that. He wrote one story intended for kids but absolutely good to go as a fun read for adults, covering the special theory of relativity and that's a real gem as starting point for prepping the imagination for repeating interesting thought experiments.

3) just not really ever stopping. It's my view that anyone who says they have mastered this topic, is likely only fooling themselves. The subject is certainly all but bottomless, it is endlessly fascinating to ponder, SR might lose some of its initial mystery but I've been boggled by it for two decades now and its majesty and aura never really seem to fade.

 

[David Lewis]

"From the perspective of the independent observer, moving relative to the rocket, the light flash happened at a particular fixed point in space, which at that moment coincided with the centre of the moving rocket. The light traveled out from the point occupied by the centre of the rocket, as a perfect sphere, at rest relative to the independent observer, while the rocket moved away at the relative speed between the rocket and the independent observer." [emphasis added]

From the perspective of the independent moving observer:

1. Does the "particular fixed point in space" remain the center of the light sphere?
2. Does the rocket leave the particular fixed point in space behind?

 

[Chestermiller]

No. It's nice to see it demonstrated in the GPS system, particle lifetime measurements, and the like...

But once you accept the postulate that the speed of light is constant for all observers, relativity of simultaneity follows as surely as any theorem in high school geometry follows from Euclid's postulates of geometry. The experiments are telling us that the world behaves the way we've logically proven that it must if our postulate is correct.

I like to think of this differently. The empirical observations of GPS systems, particle lifetime measurements, measurements of the constancy and isotropy of the speed of light, and deductions of the latter from E and M are all explained by, and are all consequences of, the unique 4D geometry of spacetime. Each of these observations, not just the speed of light, enabled us to deduce what that geometry had to be.

 

[NoahsArk]

Thank you for the responses.

CPTInvariant thanks very much for the suggestions and for the helpful approach to thinking about SR.

There's also the obvious option on repeating useful thought experiments with subtle variations, just putting yourself in the situation being modeled and imagining yourself inside it. If we cannot have a physical intuition for these effects we need perhaps to try and develop an abstract sense of one, from sheer brute force of imagination.

That seems like a useful way to develop more intuition, and I'll try to read about more of those experiments to try. I also checked out the book by Gamow on Amazon and I'm going to order it!:)

 

[Dale]

From the perspective of the independent moving observer:

1. Does the "particular fixed point in space" remain the center of the light sphere?
2. Does the rocket leave the particular fixed point in space behind?

Yes to both

 

[David Lewis]

Many thanks, Dale, for your prompt answer.

 

[Mister T]

How about the speed of light being constant, though? Isn't that something we only know from experiment and not something we deduced from other facts which were already known?

It follows as a consequence of Maxwell's theory of electromagnetism, but experimental verification is needed to know that that is indeed the right way to interpret those laws of electromagnetism.

Nature behaves the way it behaves. Physical laws are generalizations from observations of those behaviors. As humans we like to pretend that Nature obeys the laws of physics, but that's an anthropomorphism.

 

[NoahsArk]

Physical laws are generalizations from observations of those behaviors. As humans we like to pretend that Nature obeys the laws of physics, but that's an anthropomorphism.

Doesn't nature obey it though? Aren't the equations of physics not subject to change? If a certain object of a certain weight is dropped from a certain height, we can calculate exactly when it will hit the ground, and that should never change if all the conditions are the same.

Also, on the idea of the constancy of the speed of light, here is an example which I read to explain it: If a rocket is traveling at .75C with respect to me, and that rocket shines a beam of light, I would expect that someone in the rocket would measure the beam at .25C. However, if I know that his measuring sticks are four times smaller than mine, it will come as no surprise that his measurement of C will be equal to mine. For example, if the rocket were traveling at .75C and chasing a beam of light that traveled a distance of one light year, and the rocket traveled .75 light years, I would see the beam being .25 light years ahead of him. With his meter stick, though, he'd measure that .25 distance to be 1. That would make sense if it weren't for the fact that the lengths he is measuring also contracted, which would cancel out the effects of his meter stick being contracted. How to make sense of this?

 

[Orodruin]

Doesn't nature obey it though? Aren't the equations of physics not subject to change? If a certain object of a certain weight is dropped from a certain height, we can calculate exactly when it will hit the ground, and that should never change if all the conditions are the same.

But this is just an assumption on the repeatability of experiments. It is an assumption that has served us well and is well tested experimentally. Ideally though, a physical theory should make new predictions that you can test. If it does not match the new tests, we should be looking to replace it with something more accurate - as was done when Newtonian mechanics was surpassed by relativistic mechanics. It does not mean that Newtonian mechanics is wrong - within its limited region of applicability - but special relativity is more accurate. You have to differentiate how nature behaves with our description of how nature behaves, it is the latter we are all too fond of calling "laws of nature".

How to make sense of this?

You are not taking relative simultaneity into account. There is more to this than length contraction and you need to combine all relativistic effects, including the relativity of simultaneity, into account in order to make sense of it. I suggest any elementary textbook on relativity.

 

[Mister T]

Doesn't nature obey it though?

No. Nature behaves the way it behaves. It makes no anthropomorphic effort to obey anything.

Aren't the equations of physics not subject to change?

The laws of physics are indeed subject to change.

If a certain object of a certain weight is dropped from a certain height, we can calculate exactly when it will hit the ground, and that should never change if all the conditions are the same.

No. We cannot calculate anything exactly. The best we can ever do is an approximate measurement. All measurements are subject to uncertaintly based on the devices we use to make the measurements. There's no such thing as an exact measurement.

With his meter stick, though, he'd measure that .25 distance to be 1.

No, he wouldn't. He would measure it to be smaller, not four times larger.

 

[Nugatory]

How to make sense of this?

In post #3 of this thread, all the way back on the first page, I said "Back away from trying to intuitively understand length contraction and time dilation, work on nailing down your understanding of relativity of simultaneity." This new problem isn't making sense to you because you're forgetting the relativity of simultaneity again.

We could put a bomb triggered by the light flash at the 1.0 point (using your measurements), and another bomb triggered by collision with the ship at the .75 point (again, using your measurements). You will find that both bombs explode AT THE SAME TIME, meaning that the ship was at the .75 point AT THE SAME TIME that the light was at the 1.0 point. 1.0-.75=.25 so clearly the light was .25 light years ahead of the ship. However, the two explosions are not simultaneous in the ship frame, so the ship's measurement of the distance between them tells you nothing about how far ahead the light was in the ship frame - to do that measurement you'd need to find where the light was and where the ship was AT THE SAME TIME in the ship frame, measure the distance between those points.

 

[NoahsArk]

I suggest any elementary textbook on relativity

Thanks. I got the Wheeler book- Space Time Physics. Hopefully it will be covered there. It starts out with the space time interval ehich I think is an interesting place to start, because in the examples it seems like he assumes people already know that two observers in different frams can measure time differently.

Regarding the point about the way nature behaves vs our descriptions of it, does that mean we have laws, but they are refined and become more general as we get more info (e.g Galilean relativity vs. special relativity). Also, couldn't it be that there are laws that can't be refined or generalized further?

Nugatory, the example you used involves teo events in teo different places. I need to think more about how relativity of simultaneity relates to the measurement of objects. E.g. On the rocket the clocks in a different rows are out of synch w each other in the frame stationary w. Respect to the rocket. That relates to clocks though... Would this apply to just the distance between two points on the rocket when no events are involved?

 

[Nugatory]

Regarding the point about the way nature behaves vs our descriptions of it, does that mean we have laws, but they are refined and become more general as we get more info (e.g Galilean relativity vs. special relativity). Also, couldn't it be that there are laws that can't be refined or generalized further?

You might want to give this essay a try: http://chem.tufts.edu/AnswersInScience/RelativityofWrong.htm
(Start a new thread for any followup on this fork of the discussion, please)

 

[Nugatory]

Would this apply to just the distance between two points on the rocket when no events are involved?

An "event" is just a point in space at a particular time, so all measurements always involve events. If you say "here" and tap your finger on a point in space, you've just identified an event: the point where your fingertip was at the moment of the tap. If I say "one meter to my left, level with my navel, six meters straight in front, three minutes from now" that's an event even if nothing noteworthy happens at that spot three minutes from now.

All distance measurements involve two events: "the point where one end of the length being measured was at a given time" and "the point where the other end of the length being measured was at the same time".

 

[Mister T]

Regarding the point about the way nature behaves vs our descriptions of it, does that mean we have laws, but they are refined and become more general as we get more info (e.g Galilean relativity vs. special relativity). Also, couldn't it be that there are laws that can't be refined or generalized further?

If you just google richard feynman layers of an onion you'll find lots of references to this question. It may be that as scientific knowledge of one particular thing or another progresses we will keep refining our knowledge. Like peeling an onion to always find another layer below. Or it may be that as we peel it we eventually reach a core, something that can no longer be refined and is universally valid. The only way to find out is to keep looking. Nature will turn out to be the way it turns out to be. You can't know unless you investigate.

 

[Ebeb]

...
Also, on the idea of the constancy of the speed of light, here is an example which I read to explain it: If a rocket is traveling at .75C with respect to me, and that rocket shines a beam of light, I would expect that someone in the rocket would measure the beam at .25C. However, if I know that his measuring sticks are four times smaller than mine, it will come as no surprise that his measurement of C will be equal to mine. For example, if the rocket were traveling at .75C and chasing a beam of light that traveled a distance of one light year, and the rocket traveled .75 light years, I would see the beam being .25 light years ahead of him. With his meter stick, though, he'd measure that .25 distance to be 1. That would make sense if it weren't for the fact that the lengths he is measuring also contracted, which would cancel out the effects of his meter stick being contracted. How to make sense of this?

No, for the astronaut at that event, per his frame the light is not at distance 1 from him. It's at .66 ! In this post I explain you how it works.
Furthermore, your 'that distance' is a measurement between two events that are simultaneous for me, but not simultaneous for the rocket astronaut.
And the astronaut does not measure with a contracted tape measurer. Only for me, per my frames of simultaneous events, his measuring stick is contracted (due to different events of the measuring stick being simuiltaneous for him or me). For the astronaut, his wristwatch does not run slow and his measuring stick does not contract. What does happen is that for him my clock runs slow, and my measuring stick is contracted, but that's irrelevant for the measurements he performs.

Consider following 3 events:
Event 1: astronaut at his location after .75 lightyears: Let's say he is at star A
Event 2: light at star B (star B located further than star A)
Event 3: light at star C (star C located further than star B)

v = .75c
gamma = 1.5

1/ I stayed home on earth.
For me the distance from Earth to star A is .75 ly.
For me the distance from Earth to star B is 1 ly.
For me the distance between star A and B is .25 ly.
For me the distance from Earth to star C is 1.75 ly.
For me, events 1 and 2 are simultaneous. 1 and 3 are not.
For me, when my wristwatch shows 1, the rocket is at star A and the light is at star B.
For me, when the rocket traveled .75 ly, the light traveled 1 ly.
For me and for the astronaut, when the rocket is at star A, the astronaut's wristwatch shows .66 (content of event is absolute)!

2/ The astronaut frame:
For the rocket astronaut events 1 and 3 are simultaneous.
For him, when the rocket is at star A -and his wristwatch shows .66, the light is (already) at star C.
(Due to relativity of simultaneity of events, per my frame the light will be at star C when the rocket is somewhere between star B and C)
Per astronaut frame, the distance he traveled to star A is .5 ly (=.75/1.5). His clock indicates .66 (1/1.5), speed = .75c
For the astronaut the distance between star A and B is .166 lightyears. Between star B and C the distance is .5. From A to C = .66

At event 1, when the astronaut is at star A -and his wristwatch indicates .66- , per astronaut frame the light has traveled .66 ly from astronaut to star C. Hence per astronaut frame light speed is c, because .66/.66=1

You can find all this information in my spacetime diagram below: