Scenario in an attempt to understand relativity

[ghwellsjr]

You haven't made it clear but I think you are agreeing that the mirrors are attached to a rigid structure and so are you and when you accelerate, you have only one rocket and you, the rigid structure, the mirrors and the rocket all accelerate together (but not so fast that everything gets destroyed by the g-force).

Ack! No! :-)

You are correct when you say if the mirrors accelerate together, you mean that you put individual rockets on each mirror and accelerate each of them with no rigid connectors between them.

Yes, if I measured them out into a circle, then accelerated *unconnected* and they remained in a circle then they are not in the ellipse needed to make the light appear to travel at the same speed for me as it does for you. That is the problem the length contraction idea. From my point of view my ruler did not change when I accelerated, so I should measure the speed of light to be c, but I would not because the length contraction needed to make the circle an eclipse does not happen because the mirrors are not connected. From my point of view, light would not be measured to be c is as supposed to be the case.

But, if you measured the mirrors out into a circle and then accelerated them unconnected, then after you were done accelerating and you measured the shape of the mirrors with the same ruler you used before, you would see that they were no longer in a circle. Instead, it would look to you like a stretched out ellipse. Your ruler is a rigid object so it will contract along with you and everything else that is rigid, that's why you cannot tell that it has contracted.

Also, I think we should be able to detect the delay between the particles that make up an object narrowing and all the particles moving toward the center to fill the space. The longer the object is, the longer it takes the edges to finish moving in. I know we can measure time dilation in a moving clock, and I know we can measure time dilation due to gravity just one foot closer to the earth!
http://news.nationalgeographic.com/news/2010/09/100922-science-space-time-einstein-relativity-aging-gravity-earth/

You say "we should be able to detect the delay between particles"...did you mean the gap between the particles? The problem is that anything we use to measure distances will also be subjected to exactly the same length contraction which makes it impossible to directly tell that it is happening. But the fact that light clocks or any other kind of clock experiences time dilation as you pointed out, and the fact that the orientation of the clock does not effect the time dilation, indirectly proves that it must be happening.

 

[CosmicVoyager]

"But, if you measured the mirrors out into a circle and then accelerated them unconnected, then after you were done accelerating and you measured the shape of the mirrors with the same ruler you used before, you would see that they were no longer in a circle. Your ruler is a rigid object so it will contract along with you and everything else that is rigid, that's why you cannot tell that it has contracted."

Okay. So my ruler will shrink, but not from my point of view. Hmm...so if my ruler narrows but the circle does not, then to me the circle appears to get wider. I am having trouble picturing what the effect of that would be, but according to the animation what is needed is for the circle to be narrower from the other person's, your, point of view, which it is not if I measured it out while at rest relative to you."You say "we should be able to detect the delay between particles"...did you mean the gap between the particles?"

I mean that the particles that make up the object get narrower. This increases the space between them. The object narrows as the forces binding the particles together pull the particles together to fill the space."The problem is that anything we use to measure distances will also be subjected to exactly the same length contraction which makes it impossible to directly tell that it is happening."

There would be a delay as the object as a whole finishes contracting, and a delay in the effects of that contraction. The further the edges, the longer the delay. So briefly, at the edges, one would not measure the speed of light to be c."But the fact that light clocks or any other kind of clock experiences time dilation as you pointed out, and the fact that the orientation of the clock does not effect the time dilation, indirectly proves that it must be happening."

I have researched and everything I read says length contraction has not been proven experimentally. There are experiments planned such as the Space Interferometry Mission.

I don't know what you mean about the clock orientation. Why would you expect the orientation of the clock to matter if there is no length contraction?

 

[Rap]

Every time I have responded to something you posted, it is because you were going in the direction of not explaining things in *one* illustration of the spacetime continuum.

But it is *one* illustration of the spacetime continuum. That 3D spacetime continuum, as I have described it contains two world lines at angles to each other. Yours and the other persons. That's all.

Let me ask - what do you mean when you say "universe"? There is the spatial universe that you see now. Then there is spacetime, which contains the universe, past, present and future. What do you mean when you say "universe"?

"Your 2D piece of paper is a slice through the 3D spacetime. Everything in your paper happens "now" to you, as it moves through spacetime. Another person with another piece of paper is moving through spacetime at a different angle."

That is just telling what I already know. That there are two perspectives. If you can't put them together, then there is a contradiction. The universe is in one state or another. Otherwise, there would have to be different universe for every particle.

Again, what do you mean by "universe"?. If you mean spacetime, then yes, it is in only one state. There is only one spacetime. If you mean the spatial universe that you experience "now", then there are an infinite number of separate universes, all coherently tied together by the fact that they are slices through the unvarying spacetime.

All physics happens in spacetime. What we call a particle is a curve in spacetime. If the particle decays into two other particles, then that curve separates into two distinct curves in spacetime. It doesn't matter how you slice it, those curves are the single picture of what is going on. They do not depend on you or somebody else to observe them to decide which way they are going to twist and turn. As an observer, you take a slice thru spacetime, and say "that is what I experience". Another person takes another slice, and they say "that is what I experience". The curves don't know and don't care who, if anybody, is observing them.

He created a mathematical system to predict how things will *appear* to be under different circumstances. It is abstract.

When I say that the distance between two points is the square root of x^2+y^2+z^2, is that an abstract mathematical system? Or is it a description of the geometry of space?

"They do not have to be on the same paper!"

I disagree. To make sense they do. For everything to be in the same universe they do. There is only one universe. If you read my original post, the point of it is to point out that according to what you are saying, the photon in question would have to be in two different places at the same time, or that space would have to different lengths at the same time.

But this is the very problem I am trying to explain. Try this - space does not have a length. 3D space does not have a length. If you put two dots on a wall in 3D space, and take a picture of them, then you can talk about the distance between the dots on the picture. If you take a picture from a different angle, you can talk about the length between them on the second picture. Finally, you can go out and measure the distance between the dots on the wall. When you say "or that space would have to different lengths at the same time" its like saying your camera must take two different pictures at the same angle. The distance between the dots on the wall is independent of which angle you look at them from. In the same way, the spacetime distance between two events is the same for every observer, no matter how they are moving.

Read your statement again - "or that space would have to different lengths at the same time". It is proof that you do not yet understand relativity. There is no such thing as "the same time" for the two different observers. There is no such thing as "the same angle" for the two different pictures taken at different angles.

Saying "there is no unique "space of the universe" is like metaphysics. That is saying there is no objective reality. That every particle sees different contradictory states of the universe. There must be no contradictions. There has to be way to show why the speed of light *appears* to move the same speed relative to any observer. Otherwise there would have to be a different universe for every particle.

Again, what do you call "the universe"?. Here you seem to be calling the universe as the space of the universe as you see it now. There IS objective reality in the theory of relativity. That objective reality is spacetime. Every particle sees different, BUT NOT CONTRADICTORY, spatial universes. Just because they give measurements of space and time intervals which do not agree, does not mean that they are in contradiction, any more than the two photographs are in contradiction because they give two different pictures when taken at two different angles.

In one place you seemed to be saying what I am saying:
"You are both in the 3D spacetime, spacetime never changes. Your 2D piece of paper is a slice through the 3D spacetime."

So show that single spacetime. If mine is a slice and someone else's is a slice, then combine the slices into one picture.

The single spacetime, for you and the other observer consists of two lines in spacetime that are not parallel. That is the one picture you are looking for. The two lines and the spacetime in which they exist are the one picture.

 

[CosmicVoyager]

( I have replaced plane and cube with 2D grid and 3D grid. That is more accurate since spacetime might be bent))

When I say "universe" I mean all existing matter, energy, and space (and time if it is physical and not abstract.). This would be a line of 3D grids, each 3d grid being a location on the time axis. Or analogously, a series of 2D grids.

If the universe appears to be different, if things appear to be in different location, then it must be just that, *appearance*."unvarying spacetime."

When you say "unvarying spacetime", do you mean there is a 4-dimensional universe of matter, energy, and space (and the 4th dimension, time) that can be represented with single illustration? (If we could draw in in 4D. Instead we have to repeat a 3D space over and over with a line of 3D grids, or use a 3D analogy.) Because you keep giving multiple illustrations. Can you make a single illustration of two observers and a light source in 4D or a 3D analog? If not, then you are not saying there is unvarying spacetime.

If there is a single unvarying spacetime, then it should be possible able to show what is going on with two observers and a light source a single series of 2D grids, that is, with a single 3D grid.

 

[ghwellsjr]

"But, if you measured the mirrors out into a circle and then accelerated them unconnected, then after you were done accelerating and you measured the shape of the mirrors with the same ruler you used before, you would see that they were no longer in a circle. Your ruler is a rigid object so it will contract along with you and everything else that is rigid, that's why you cannot tell that it has contracted."

Okay. So my ruler will shrink, but not from my point of view. Hmm...so if my ruler narrows but the circle does not, then to me the circle appears to get wider. I am having trouble picturing what the effect of that would be, but according to the animation what is needed is for the circle to be narrower from the other person's, your, point of view, which it is not if I measured it out while at rest relative to you.

The effect of the mirrors accelerating with their own rockets and thus ending up farther apart than they should be (along the direction of acceleration) to form the correct ellipse is that you would no longer see the light returning back to you from all the mirrors at the same time. The reflections from the top and bottom mirrors would arrive first and the reflections from the mirrors along the direction of acceleration would arrive last, with the other mirrors in between. You would not conclude that you were in the center of the expanding sphere of light. Until, of course, you checked the dimensions of your setup and discovered that the mirrors were no longer arranged in a perfect circle.

"You say "we should be able to detect the delay between particles"...did you mean the gap between the particles?"

I mean that the particles that make up the object get narrower. This increases the space between them. The object narrows as the forces binding the particles together pull the particles together to fill the space.

I still don't know why you use the word "delay". Delay has to do with time or speed and I don't see anything in your comments that have to do with either one of those. I'm also not sure if you are expressing a problem that you want someone to help resolve for you or if you are just making an observation.

"The problem is that anything we use to measure distances will also be subjected to exactly the same length contraction which makes it impossible to directly tell that it is happening."

There would be a delay as the object as a whole finishes contracting, and a delay in the effects of that contraction. The further the edges, the longer the delay. So briefly, at the edges, one would not measure the speed of light to be c.

If you are suggesting that during the time when you are starting and stopping an acceleration that the measurement of the speed of light will be compromised, then yes, that is true.

"But the fact that light clocks or any other kind of clock experiences time dilation as you pointed out, and the fact that the orientation of the clock does not effect the time dilation, indirectly proves that it must be happening."

I have researched and everything I read says length contraction has not been proven experimentally. There are experiments planned such as the Space Interferometry Mission.

I don't know what you mean about the clock orientation. Why would you expect the orientation of the clock to matter if there is no length contraction?

A light clock formed with a circle of mirrors would behave the same way no matter its orientation because it is symmetrical. But suppose you had a conventional light clock with just two mirrors and a burst of light bouncing back and forth between them, marking off equal time intervals. Now don't you agree that if the mirrors are oriented so that the burst of light is traveling along the direction of motion and then you rotated it 90 degrees, that it will keep a different time if there is no length contraction?

What would constitute a proof of length contraction for you? If someone were to construct and arrangement of mirrors like I show in the animation and no matter how they accelerated, they always see the light from all mirrors arriving simultaneously, would that be proof of length contraction? If not, what would an experiment be like that you would accept?

 

[CosmicVoyager]

"The effect of the mirrors accelerating with their own rockets and thus ending up farther apart than they should be (along the direction of acceleration) to form the correct ellipse is that you would no longer see the light returning back to you from all the mirrors at the same time. The reflections from the top and bottom mirrors would arrive first and the reflections from the mirrors along the direction of acceleration would arrive last, with the other mirrors in between. You would not conclude that you were in the center of the expanding sphere of light."

Right. Right."Until, of course, you checked the dimensions of your setup and discovered that the mirrors were no longer arranged in a perfect circle."

Ah. So if I am moving faster. My ruler will be shorter along the direction of motion then it was when I was moving slower and placed the mirrors. So the circle will appear narrower to me. Hmm.

*edit* I have thought about this a little while and I think it works out! So I have a scenario that reconciles the apparent contradictions! Yay! Time dilation and length contraction. Now the question is is that what is really happening? There might be other explanations that also fit the data."I still don't know why you use the word "delay". Delay has to do with time or speed and I don't see anything in your comments that have to do with either one of those. I'm also not sure if you are expressing a problem that you want someone to help resolve for you or if you are just making an observation."

I mean that though the narrowing of the particles that make up the object happens at the same time as the acceleration, the entire object is not fully contracted instantly because the particles at the ends have a longer distance to travel. The further from the center, the longer it will take for a particle to move to it's new position. So though you have reached the speed for a particular amount of contraction, the length of the object will briefly be longer and measurements will be off."A light clock formed with a circle of mirrors would behave the same way no matter its orientation because it is symmetrical. But suppose you had a conventional light clock with just two mirrors and a burst of light bouncing back and forth between them, marking off equal time intervals. Now don't you agree that if the mirrors are oriented so that the burst of light is traveling along the direction of motion and then you rotated it 90 degrees, that it will keep a different time if there is no length contraction?"

I see."What would constitute a proof of length contraction for you?"

Well I have thought of a direct way. If you have two objects of different lengths side by side with either their forward edges or backward edges aligned, and accelerate them together, then edges should get out of alignment. Because they are both contracting toward their centers the same *percentage*, which is a different length for each object. For example, if one is 1000 units long and the other is 100 units long, and the center of the shorter object is 50 units from the edge of the longer object, and they both contract 50%, the edge of the longer object will move in 250 units while the edge of the shorter object only moves in 25 units.

 

[CosmicVoyager]

@ghwellsjr

Conclusions.

So when it is said that the speed of light is constant we mean that, unlike massive particles, light is not affected by the speed of it's source. It always travels at the same speed regardless of how fast the thing that emitted it is going.

But, it is also constant in another way. We would expect that if we are moving light should be measured to be traveling at a different speed. But, due to time dilation and length contraction, we *also* measure light to be traveling at c *relative* to us.

Failure to make this distinction can be a cause of confusion.

I can't wait to explain this to others!

Thanks so much for your animation. It much easier to understand than trying to put it into words. Oh yeah, what software did you use for the animation?

So light would be an absolute reference frame if it were not for time dilation and length contraction. Your true speed is how fast you are traveling relative to light, but unfortunately you can't tell how fast you are traveling relative to light! LOL

People saying the speed of light is 1 might have something to do with this.

I now have a major piece of the puzzle that will hopefully lead to answering the next questions which are why does time dilate and why does length contract? What Rap has been trying to explain might have something to do with this. I don't know.

 

[CosmicVoyager]

@ghwellsjr

Uh oh. I think I thought of another problem. What happens if the light source is moving with me? Would the animation me the same, or does the line emitted perpendicular to my direction of motion move along forward with me?

 

[Rap]

( I have replaced plane and cube with 2D grid and 3D grid. That is more accurate since spacetime might be bent))

When I say "universe" I mean all existing matter, energy, and space (and time if it is physical and not abstract.). This would be a line of 3D grids, each 3d grid being a location on the time axis. Or analogously, a series of 2D grids.

If the universe appears to be different, if things appear to be in different location, then it must be just that, *appearance*.

Ok, let's call that "spacetime" instead of "the universe". Under that definition, events are points in spacetime and are always in the same "location", they do not move, nor do they appear to move to any observer. If you draw a set of perpendicular axes in spacetime, you will say that an event has coordinates x,y,z,t. If someone else draws a different set of perpendicular axes in spacetime, they will read off different values of x,y,z,t, but as long as they realize that their coordinate systems are different, they will both agree that the event itself is at the same unvarying location in spacetime.

When you say "unvarying spacetime", do you mean there is a 4-dimensional universe of matter, energy, and space (and the 4th dimension, time) that can be represented with single illustration?

Yes, exactly right.

Can you make a single illustration of two observers and a light source in 4D or a 3D analog? If not, then you are not saying there is unvarying spacetime.

If there is a single unvarying spacetime, then it should be possible able to show what is going on with two observers and a light source a single series of 2D grids, that is, with a single 3D grid.

Yes. If a laser is a point in space, not being accelerated, then it is an unvarying straight line in spacetime. At some point it emits a photon. That photon will be an unvarying straight line segment in spacetime which starts at some point on the laser line and goes off to infinity. The point in spacetime at which it intersects the laser line is an event - that event is the emission of the photon from the laser. It has an unvarying position in spacetime. If the two observers are points in space, not being accelerated, then they are two unvarying straight lines in spacetime.

 

[ghwellsjr]

"Until, of course, you checked the dimensions of your setup and discovered that the mirrors were no longer arranged in a perfect circle."

Ah. So if I am moving faster. My ruler will be shorter along the direction of motion then it was when I was moving slower and placed the mirrors. So the circle will appear narrower to me. Hmm.

You got it backwards, if the mirrors end up in a perfect circle just like they started prior to your acceleration, then the circle will appear wider (along the direction of acceleration) to you when you measure it with your shortened ruler.

*edit* I have thought about this a little while and I think it works out! So I have a scenario that reconciles the apparent contradictions! Yay! Time dilation and length contraction. Now the question is is that what is really happening? There might be other explanations that also fit the data.

Ah, yes, the question of what is really happening. We can't answer that question in the sense of where is the light really traveling at c. My animation could just as easily have been depicted from the viewpoint of where you are stationary and I was moving in the opposite direction. Or we could depict it where we were both moving in opposite directions, but at a slower equivalent speed. It doesn't matter where we start, the net result of what each person can see and measure turns out to be the same no matter how we depict it (in a consistent way, of course). So we cannot tell where light is really moving at c.

"I still don't know why you use the word "delay". Delay has to do with time or speed and I don't see anything in your comments that have to do with either one of those. I'm also not sure if you are expressing a problem that you want someone to help resolve for you or if you are just making an observation."

I mean that though the narrowing of the particles that make up the object happens at the same time as the acceleration, the entire object is not fully contracted instantly because the particles at the ends have a longer distance to travel. The further from the center, the longer it will take for a particle to move to it's new position. So though you have reached the speed for a particular amount of contraction, the length of the object will briefly be longer and measurements will be off.

OK, but keep in mind that it also takes time to make your measurements. All measurements are dependent on light to travel across a distance to communicate information to us. We cannot know "instantly" during an acceleration what is actually happening. We can only know the final results of our measurements.

"A light clock formed with a circle of mirrors would behave the same way no matter its orientation because it is symmetrical. But suppose you had a conventional light clock with just two mirrors and a burst of light bouncing back and forth between them, marking off equal time intervals. Now don't you agree that if the mirrors are oriented so that the burst of light is traveling along the direction of motion and then you rotated it 90 degrees, that it will keep a different time if there is no length contraction?"

I see.

Good, I like progress.

"What would constitute a proof of length contraction for you?"

Well I have thought of a direct way. If you have two objects of different lengths side by side with either their forward edges or backward edges aligned, and accelerate them together, then edges should get out of alignment. Because they are both contracting toward their centers the same *percentage*, which is a different length for each object. For example, if one is 1000 units long and the other is 100 units long, and the center of the shorter object is 50 units from the edge of the longer object, and they both contract 50%, the edge of the longer object will move in 250 units while the edge of the shorter object only moves in 25 units.

I'm assuming that when you say "accelerate them together" you mean that they are connected at some point, either at their common edge or at the other end of the shorter one or at the center of the shorter one or at any other point. Then this is no different than if you had marked off lines on the longer one at 100 unit intervals and asked about how those markings are any different than the ends of the shorter object next to it. Maybe I didn't understand your scenario but I think if you analyze it carefully you will see that you cannot learn anything about how connected things contract during acceleration.

Do you want to propose a different proof of length contraction than the one I suggested or would mine be good enough for you?

What would constitute a proof of length contraction for you? If someone were to construct and arrangement of mirrors like I show in the animation and no matter how they accelerated, they always see the light from all mirrors arriving simultaneously, would that be proof of length contraction? If not, what would an experiment be like that you would accept?

 

[CosmicVoyager]

I'm assuming that when you say "accelerate them together" you mean that they are connected at some point, either at their common edge or at the other end of the shorter one or at the center of the shorter one or at any other point. Then this is no different than if you had marked off lines on the longer one at 100 unit intervals and asked about how those markings are any different than the ends of the shorter object next to it. Maybe I didn't understand your scenario but I think if you analyze it carefully you will see that you cannot learn anything about how connected things contract during acceleration.

No, I don't mean connected. It would work if they were connected :-) By accelerate together, I mean at the same rate, starting at the same time.

So read again.

If you have two objects (They would each have two rockets attached on their sides at their midpoints.) of different lengths side by side with either their forward edges or backward edges aligned, and accelerate them at the same rate starting at the same time, then edges should get out of alignment. Because they are both contracting toward their midpoints the same *percentage*, which is a different length for each object. For example, if one is 1000 units long and the other is 100 units long, and the midpoint of the shorter object is 50 units from the edge of the longer object, and they both contract 50%, the edge of the longer object will move in 250 units while the edge of the shorter object only moves in 25 units.

I wish I could draw pictures on the screen with a stylus.

*edit* Added illustration.

 

[ghwellsjr]

@ghwellsjr

Conclusions.

So when it is said that the speed of light is constant we mean that, unlike massive particles, light is not affected by the speed of it's source. It always travels at the same speed regardless of how fast the thing that emitted it is going.

But, it is also constant in another way. We would expect that if we are moving light should be measured to be traveling at a different speed. But, due to time dilation and length contraction, we *also* measure light to be traveling at c *relative* to us.

Failure to make this distinction can be a cause of confusion.

I can't wait to explain this to others!

Thanks so much for your animation. It much easier to understand than trying to put it into words. Oh yeah, what software did you use for the animation?

So the light would be an absolute reference frame if it were not for time dilation and length contraction. Your true speed is how fast you are traveling relative to light, but unfortunately you can't tell how fast you are traveling relative to light! LOL

People saying the speed of light is 1 might have something to do with this.

I now have a major piece of the puzzle that will hopefully lead to answering the next questions which are why does time dilate and why does length contract? What Rap has been trying to explain might have something to do with this. I don't know.

Yes, you are correct when you say that "the speed of light is constant" has more than one meaning. The second one you mentioned:

But, it is also constant in another way. We would expect that if we are moving light should be measured to be traveling at a different speed. But, due to time dilation and length contraction, we *also* measure light to be traveling at c *relative* to us.​

is referring to the measured round-trip speed of light and is based on experimental evidence.

The first one you mentioned:

So when it is said that the speed of light is constant we mean that, unlike massive particles, light is not affected by the speed of it's source. It always travels at the same speed regardless of how fast the thing that emitted it is going.​

is Einstein's second postulate which is an arbitrary definition and cannot be proved but is the basis of his Theory of Special Relativity. He is stating that when you measure the round trip speed of light from a source to a mirror and back to a detector colocated at the source, you cannot tell if the time it took to get from the source to the mirror is the same as the time it took to get from the mirror back to the detector. Think of the two people in the animation: for the green one, the light takes exactly the same time to go from him to the mirrors as it does to go from the mirrors back to him but for the red man, it takes different amounts of time to go from him to the mirrors as it does to go from the mirrors back to him. In fact, depending on the mirror, it can take the same time (the ones on the top and the bottom) but for other mirrors, the times are significantly different. But because of length contraction and time dilation, he cannot tell that this is what is really happening. Neither person can tell which is really happening. So Einstein said, for any inertial observer (one who is not accelerating) he can define those two times to be equal, in other words that the speed of light is the same going out to the mirror and coming back. That is what is meant when it is said that the speed of light is the same in all directions. But this is referring to the one-way speed of light.

The net result of all this is that any inertial observer can assume that he is the green man and everything will work out for him just as if he really were stationary with respect to where light is really is traveling at c in all directions.

If you want to know why time dilates and lengths contract, you can look up the history of Special Relativity on wikipedia. Follow the links to Lorentz Ether Theory and you will see how those early scientists worked it out before Einstein came along.

 

[Rap]

If you have two objects (They would each have two rockets attached on their sides at their midpoints.) of different lengths side by side with either their forward edges or backward edges aligned, and accelerate them at the same rate starting at the same time, then edges should get out of alignment. Because they are both contracting toward their midpoints the same *percentage*, which is a different length for each object. For example, if one is 1000 units long and the other is 100 units long, and the midpoint of the shorter object is 50 units from the edge of the longer object, and they both contract 50%, the edge of the longer object will move in 250 units while the edge of the shorter object only moves in 25 units.

You have to be careful when you say "accelerate". Suppose the rockets have the same mass, and their engines give a constant and equal force. They are both at rest with respect to you, the observer. Then they fire their engines at the same time. Then the two pilots in each rocket will say that they are undergoing constant and equal acceleration, and since their back ends were aligned when they started, they will remain aligned.

The fact that they are aligned throughout the time the engines are firing is an invariant spacetime fact. That means that you, the observer left behind, and anyone else, will see the back ends aligned as well. You will not see them as having a constant acceleration, however. If they had constant acceleration, then there would be no stopping them from passing through the speed of light and beyond. So what you see will be a constantly decreasing acceleration, with the back ends aligned. Their lengths will contract, but the back ends will remain aligned.

 

[CosmicVoyager]

You have to be careful when you say "accelerate". Suppose the rockets have the same mass, and their engines give a constant and equal force. They are both at rest with respect to you, the observer. Then they fire their engines at the same time.Then the two pilots in each rocket will say that they are undergoing constant and equal acceleration...

Yes.

...and since their back ends were aligned when they started, they will remain aligned.

But they are different lengths and if they undergo the same percentage length contraction toward their midpoints, that is a different amount for each one, so the backends of each one should shift a different amount.

 

[Rap]

But they are different lengths and if they undergo the same percentage length contraction toward their midpoints, that is a different amount for each one, so the backends of each one should shift a different amount.

They always contract about their midpoint. You are assuming that the distance you observe between the midpoints of the rockets stays the same. But, to the pilots in the rocket ships, this means that the distance between their midpoints is increasing. Saying that some distance remains the same to you is not a spacetime invariant statement. Distances that you observe are not the same as other observers moving with respect to you will observe. Saying that two points on the rocket ships remain aligned IS a spacetime invariant statement. If you see them aligned, then all observers will see them aligned.

If the rockets start out with their midpoints aligned, they will stay aligned. If the rockets start out with their front ends aligned, they will stay aligned. Remember that for one rocket, if the pilot says that all points on his rocket accelerate the same, then you will say that they do not. To you, the back end of the rocket will have a different acceleration than the front end because of the ongoing Lorentz contraction.

 

[CosmicVoyager]

They always contract about their midpoint. You are assuming that the distance you observe between the midpoints of the rockets stays the same. But, to the pilots in the rocket ships, this means that the distance between their midpoints is increasing. Saying that some distance remains the same to you is not a spacetime invariant statement. Distances that you observe are not the same as other observers moving with respect to you will observe. Saying that two points on the rocket ships remain aligned IS a spacetime invariant statement. If you see them aligned, then all observers will see them aligned.

If the rockets start out with their midpoints aligned, they will stay aligned. If the rockets start out with their front ends aligned, they will stay aligned. Remember that for one rocket, if the pilot says that all points on his rocket accelerate the same, then you will say that they do not. To you, the back end of the rocket will have a different acceleration than the front end because of the ongoing Lorentz contraction.

I don't understand what you are saying.

And I'm saying that if you are on one of the ships you will see the end move out of alignment.

I have attached an illustration.

 

[Janus]

I don't understand what you are saying.

And I'm saying that if you are on one of the ships you will see the end move out of alignment.

I have attached an illustration.

One thing that you need to consider is that it takes time for the impulse of the engines firing at the middle of the ship to travel through the body of the ship to the two ends. This impulse will travel at the speed of sound for the material that the ship is made of.

In other words, the ends of the ship will not start moving at the same time as the middle does and since the ships are of different lengths, the delay between the engines firing and the ends moving will be different for each ship. This will be true as far as someone in the in the ship is concerned as well as someone that isn't.

Once the ships start to move, you then run into the issue of the Relativity of Simultaneity. Events that are simultaneous at the ends and middle in the ship are not simultaneous according to someone not moving with the ship. Not only that, but according to someone at the rear of the ship, time runs faster at the middle of the ship and even faster at the front of the ship. Again, since the ships are of different lengths to start, this difference in time between the ends of the two ship will be different.

All and all, this is a very complicated situation.

 

[Rap]

I don't understand what you are saying.

And I'm saying that if you are on one of the ships you will see the end move out of alignment.

I have attached an illustration.

I agree with Janus - acceleration of material bodies is complicated in special relativity. Accelerated bodies form curved lines in spacetime and there is no point in trying to explain the geometry of curved lines in spacetime until you understand the geometry of straight lines in spacetime. Go back to my post #39. Is there anything there that you don't understand?

 

[lugita15]

Okay, this sounds promising :-) So you are saying there *is* a way of reconciling the apparent contradictions. Could you or anyone explain the idea in detail like ghwellsjr did with his scenario, preferably with illustrations (but anything is welcome)? ghwellsjr's explanation almost worked. I am imagining the 2d to 3d equivalent of this 3d to 4d scenario, and I don't see how one's speed would cause one to see a higher dimensional object from a different angle.

What we think of as motion in 3D is really rotation in 4D. So different speeds in three dimensions correspond to different angles in 4D.

 

[CosmicVoyager]

I agree with Janus - acceleration of material bodies is complicated in special relativity. Accelerated bodies form curved lines in spacetime and there is no point in trying to explain the geometry of curved lines in spacetime until you understand the geometry of straight lines in spacetime. Go back to my post #39. Is there anything there that you don't understand?

Yes. I am having difficulty picturing it. I don't think I am going to understand what you are trying to explain in just words without an actual picture or animation. I would expect such animations to exist already.

An illustration as we discussed here:

When you say "unvarying spacetime", do you mean there is a 4-dimensional universe of matter, energy, and space (and the 4th dimension, time) that can be represented with single illustration?

Yes, exactly right.

Can you make a single illustration of two observers and a light source in 4D or a 3D analog?

Yes. If a laser is a point in space, not being accelerated, then it is an unvarying straight line in spacetime. At some point it emits a photon. That photon will be an unvarying straight line segment in spacetime which starts at some point on the laser line and goes off to infinity. The point in spacetime at which it intersects the laser line is an event - that event is the emission of the photon from the laser. It has an unvarying position in spacetime. If the two observers are points in space, not being accelerated, then they are two unvarying straight lines in spacetime.

I don't know the directions of the lines, and I don't see how the light appears to be moving at the same speeds to both observers. I need to see observers and light in 4D as a series of 3D grids, or in 3D series of 2d grids.

 

[CosmicVoyager]

What we think of as motion in 3D is really rotation in 4D. So different speeds in three dimensions correspond to different angles in 4D.

You are saying things are rotating in time? Go forward and back? I do not get that.

 

[lugita15]

You are saying things are rotating in time? Go forward and back? I do not get that.

No, you misunderstood me. Let's say two people Alice and Bob both have xy coordinate systems with the origins being the same but the x-axis of Bob's system is rotated by 10 degrees with respect to Alice's. Then if you have some weird-shaped object, the "shadows" or projections it casts on Alice's x-axis and y-axis, will be very different from the projections on Bob's axes. But some properties, like the area of an object and the distance between two points will be invariant in all coordinate systems.

What does this have to do with relativity? We have four mutually perpendicular, xyzt. And now Bob is moving at say 500 meters per second with respect to Alice. What does that look like geometrically? It turns out it corresponds to rotating Bob's x-axis and t-axis by some angle, just like in the previous case his x and y axes were rotated by some angles. It's a bit counterintuitive, but looking at and drawing spacetime diagrams might help. I suggest the book Spacetime Physics.

 

[Rap]

Yes. I am having difficulty picturing it. I don't think I am going to understand what you are trying to explain in just words without an actual picture or animation. I would expect such animations to exist already.

I don't know the directions of the lines, and I don't see how the light appears to be moving at the same speeds to both observers. I need to see observers and light in 4D as a series of 3D grids, or in 3D series of 2d grids.

Don't worry about how they see the light moving at the same speed right now. Just understand that this picture is unvarying, and it is the bottom line. Any physics, any geometry, any description of the universe, of what happens in the universe, how things interact, how all the lines connect up, all happen in this unvarying spacetime, independent of any observer.

For example, if an electron and a positron collide and emit a gamma ray, there are two straight lines that come together and meet. At the point that they meet, another line goes away from that vertex, and it is the photon. These three lines and the point at which they meet are absolutely fixed in spacetime. The angles between the lines are absolutely determined and fixed in spacetime.

You say you don't know the directions of the lines. How should I describe the directions of the lines? One way to describe the direction of a line is to establish a coordinate system. If we are in a 3D spacetime, we can choose three orthogonal axes, whose directions we know, and then we can describe the direction of the line. Otherwise you cannot talk about the direction of a line, you can only talk about the angle it makes with another line, and the plane of that angle.

Lets say an observer is a point in space, and in an "inertial frame". This means they exist as a straight line in spacetime. That line is their "world line". You can think of it as the observer traveling along this line. The 2D space that is orthogonal to that persons world line and passes through them is what they experience as their 2D space at that time. Everything in that 2D space happens simultaneously. Anything "above it" happens later, everything below it happens "before". Other observers that are moving at a constant velocity with respect to you have world lines that are separate from you and at an angle with respect to your world line. The 2D space orthogonal to their world line, passing through them, is what they experience as their 2D space "now". Everything on that plane is simultaneous to them. Obviously you and that person will disagree on what is simultaneous. If you see two events (like two firecrackers going off) and you say they happened in the same place, the other observer will say no, they happened in different places. But if you both understand relativity, you will both agree on what happened in spacetime, as you must.

This is all spacetime geometry. You have to learn spacetime geometry, just like you learned plane or solid geometry. Its the same kind of thing, only a bit more complicated. Once you learn spacetime geometry, you will find that all the paradoxes are just the result of people not understanding spacetime geometry, treating special relativity like a bunch of recipes in a cookbook, which may or may not have any relationship to each other, all kinds of strange voodoo going on with no rhyme or reason. Once you understand spacetime geometry, its like solving a problem in plane or solid geometry. Do it step by step, and you are done.

 

[ghwellsjr]

I'm assuming that when you say "accelerate them together" you mean that they are connected at some point, either at their common edge or at the other end of the shorter one or at the center of the shorter one or at any other point. Then this is no different than if you had marked off lines on the longer one at 100 unit intervals and asked about how those markings are any different than the ends of the shorter object next to it. Maybe I didn't understand your scenario but I think if you analyze it carefully you will see that you cannot learn anything about how connected things contract during acceleration.

No, I don't mean connected. It would work if they were connected :-) By accelerate together, I mean at the same rate, starting at the same time.

So read again.

If you have two objects (They would each have two rockets attached on their sides at their midpoints.) of different lengths side by side with either their forward edges or backward edges aligned, and accelerate them at the same rate starting at the same time, then edges should get out of alignment. Because they are both contracting toward their midpoints the same *percentage*, which is a different length for each object. For example, if one is 1000 units long and the other is 100 units long, and the midpoint of the shorter object is 50 units from the edge of the longer object, and they both contract 50%, the edge of the longer object will move in 250 units while the edge of the shorter object only moves in 25 units.

I wish I could draw pictures on the screen with a stylus.

*edit* Added illustration.

Yes, you are right, if you have more than one rocket and each one is accelerating a different rigid structure with the same acceleration, then you will be able to see differences in their positions after the acceleration, unless the rockets are adjacent to each other.

But I thought we covered this issue earlier when discussing the accelerations of the individual mirrors in my animation. Why are we going over this again?

Is it that you are suggesting that this would be a good test of length contraction? If so, then, yes, except for the very practical matter that we cannot perform such a test because of the difficulting of individually accelerating massive objects and the problem of getting volunteers to go on these trips because we probably couldn't get them back, but even if we could, they'd probably be dead for a host of reasons (g-forces, impacts with debris in the way, so much energy required we'd have to make it a one-way trip, etc.).

Maybe you could think of a more practical experiment.

 

[ghwellsjr]

@ghwellsjr

Uh oh. I think I thought of another problem. What happens if the light source is moving with me? Would the animation me the same, or does the line emitted perpendicular to my direction of motion move along forward with me?

I addressed that issue way back on this post:

We have two observers, I, George, will be the first one and we'll assume that I'm stationary and I have a flash bulb that I have arranged to be energized when you, the CosmicVoyager traveling toward me in a straight line at half the speed of light arrive at my location. You carry a stop watch, as do I, which we both start at the moment of the flash. You continue on without stopping or slowing down. The very bright flash of light will expand outward from its starting point in a perfect sphere getting bigger at the speed of light. According to Special Relativity, I will measure myself to be in the exact center of the expanding sphere of light. That makes sense, doesn't it, since I set off the light and I'm not moving? But according to Special Relativity, you will also measure yourself to be in the exact center of the expanding sphere of light and that doesn't seem right, does it, because you are moving with respect to the source of the light? But would it make sense if you were the one carrying the light source and to have set it off when you arrived at my location? Maybe, but in this case, I, too, would measure myself to be in the center just like you would. And that doesn't seem right but it really doesn't matter what the speed of the source of the light is or the speed of the observers, they all will think they are in the center of the expanding sphere of light. This can only work if the speed of light is the same for all observers, do you agree with that?

And it wouldn't change the animation at all.

 

[LeeJeffries]

That is awesome! Thanks :-)

I will think about it some more and see if it raises any questions. I took a conceptual basic physics class which focused on understanding. I wish there was a conceptual relativity class, and a conceptual quantum physics class.

We know that time dilation is more than a technique to make things work out. We have actually measured it with pairs of high precision clocks. Is there a way to measure length contraction to know objects are actually getting thinner? Since density is increasing, it's gravity should be affected. You could pass in front or behind it closer to it's center since it is narrower and experience stronger gravity.

Sort of off-topic but addresses your first wish

If you search for TTC Quantum Mechanics, TTC Particle Physics and TTC Relativity you'll get some somewhat lengthy but very informative lectures from the teacher training company (I think that's what it stands for)