# Scenario in an attempt to understand relativity

by CosmicVoyager
Tags: attempt, relativity, scenario
P: 159
 Quote by Rap ...
I do not follow this explanation :-(

I was expecting an explanations using four physical dimensions with 4d objects like hypercubes.

I do not see how to translate it into a specific such as the one in my first post or the one ghwellsjr gave. I am wondering if this can be illustrated with the universe as a plane with 2d objects on it and other planes being time.

This just seems to be a graph of how things appear, and not an explanation for how it is that they can appear hat way, not how observers moving at different speeds could measure something (light) to be the same speed like ghwellsjr animation was.

"spacetime is not a Euclidean space. The distance between two points in Euclidean space is the square root of x^2+y^2+z^2 no matter what your axes are, but in spacetime, the spacetime distance between two points is the square root of x^2+y^2+z^2-t^2 (x,y,z in light years, t in years) no matter what your axes are."

So it really isn't distance. Time is not a physical dimension. Time is concept. I line representing time is a graph of changes in the arrangement of objects. And if you were to add a fourth axis it should add the same distance as adding a second and third do.

Also, if time were a fourth dimension that the universe was in then there are two possibilities, both of in which the above explanation does not work:

Possibility A - Everything in the universe is moving through time. The past and the future are empty. Objects could not be at a different place in time than other objects because they would disappear from the slice of time that the rest of the universe is in.

Possibility B - Objects are four dimensional and extend backward in time. They are *extremely*, if not infinitely, long and connect to each other in the past. If this were the case then we should experience all of time at the same time and not just one slice of it, since we are four dimensional objects that are everywhere in time.
P: 789
 Quote by CosmicVoyager "spacetime is not a Euclidean space. The distance between two points in Euclidean space is the square root of x^2+y^2+z^2 no matter what your axes are, but in spacetime, the spacetime distance between two points is the square root of x^2+y^2+z^2-t^2 (x,y,z in light years, t in years) no matter what your axes are." So it really isn't distance. Time is not a physical dimension. Time is concept.
No - it IS a distance. Time IS a physical dimension. Its just that the 4-dimensional space in which things exist (spacetime) is not Euclidean. The geometry of things on the surface of a sphere is not Euclidean: the sum of the angles of a triangle on the surface of a sphere do not add up to 180 degrees. The distances in spacetime are not all positive real numbers. So what?

 Quote by CosmicVoyager Also, if time were a fourth dimension that the universe was in then there are two possibilities, both of in which the above explanation does not work: Possibility A - Everything in the universe is moving through time. The past and the future are empty. Objects could not be at a different place in time than other objects because they would disappear from the slice of time that the rest of the universe is in.
There is no unique "slice of time" that the universe is in. This is the whole point - the world is four dimensional, objects are four dimensional, and different people make different slices. Your slice is yours, mine is mine. I make a "slice of time" and the universe looks a particular way. You make a different slice, it looks different. Its the same four-dimensional universe, but different slices. Some things that I call "now", you might call "later". A ruler is a four dimensional object. How long is it? One person takes a slice of the 4-D ruler and gets an answer. Another person takes a different slice, gets a different answer. It makes no sense to ask "how long is the ruler?". You have to ask "by whose slice?". This is what the Lorentz contraction is all about.

 Quote by CosmicVoyager Possibility B - Objects are four dimensional and extend backward in time. They are *extremely*, if not infinitely, long and connect to each other in the past. If this were the case then we should experience all of time at the same time and not just one slice of it, since we are four dimensional objects that are everywhere in time.
But our consciousness does not experience things that way. Our consciousness experiences successive slices of the 4-D universe. If you ask why, then that is a real problem, I don't think anyone knows the answer to that. In that sense, relativity is using equations that tell us what we experience without knowing why. But its not just a bunch of equations, or, if they are, its amazing that they describe a four dimensional space in every bit of detail as the equations we use for our 3-dimensional space, geometry, physics, topology, everything. Searching for a true paradox in the geometry of spacetime is like searching for a paradox in Euclidean geometry. Very, very difficult. All paradoxes boil down to not understanding the geometry of spacetime. All contradictions are indeed apparent, as long as they are based on measurements.
 P: 159 "it IS a distance. Time IS a physical dimension. Its just that the 4-dimensional space in which things exist (spacetime) is not Euclidean." Okay. I'm glad you made that very clear, so there is no ambiguity on that point. It is very important. "There is no unique "slice of time" that the universe is in. This is the whole point - the world is four dimensional, objects are four dimensional, and different people make different slices. Your slice is yours, mine is mine. I make a "slice of time" and the universe looks a particular way. You make a different slice, it looks different. Its the same four-dimensional universe, but different slices. Some things that I call "now", you might call "later". A ruler is a four dimensional object. How long is it? One person takes a slice of the 4-D ruler and gets an answer. Another person takes a different slice, gets a different answer. It makes no sense to ask "how long is the ruler?". You have to ask "by whose slice?". This is what the Lorentz contraction is all about." Okay, I'm trying to visualize how all the slices fit together, how they are connected. When one drags a one dimensional line at a right angle perpendicular to itself repeating it over and over, a two dimensional plane is created. And when one drags a plane at a right angle perpendicular to itself, a three dimensional cube is created. When you refer to the fourth dimension, you mean dragging the cube at a right angle perpendicular to itself and getting many cubes with each point in a cube connected to the points in the same place in the previous an next cubes? An entire hypercube can be represented in 3D with a line of cubes and realizing which points are connected. When you say every particle has its own slice, you mean one of those cubes? I can't figure out how to account for observed phenomena with a line of cubes of space where each one is only touching two others just as a each 2D plane in a 3D cube are touching two others. It seems like it would require more dimensions (and I still don't see how to do it LOL) Is it possible to illustrate the same effects with a 2D plane as space and the 3D cube it is in as time?
PF Gold
P: 4,743
 Quote by CosmicVoyager As I said above, "If I were to measure out the distances between my mirrors when I am stationary to you, and I and all of the mirrors were to accelerate together, then they should still be arranged in a circle because as the mirrors narrow, the space between them increases since they are not connected." To which you replied, "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 but if you mean they are fastened to some kind of structure and you have only one rocket that accelerates the entire structure together, then the mirrors will move closer together." If I measured them out into a circle, then accelerated 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.
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). This will allow the rigid frame and the mirrors to take on the elliptical shape (when viewed from the original frame prior to acceleration). But note that you also will take on an elliptical shape and your ruler that you use after acceleration will change its length depending on its orientation so that when you are measuring the vertical distance between the top and bottom mirrors, you will get the same reading as when you measure the horizontal distance between the left and right mirrors. Because everything that has accelerated with you is experiencing length contraction along the direction of acceleration (and of motion with respect to your starting condition), then you cannot tell that any length contraction is going on with you.
 Quote by CosmicVoyager Anyway, Janus replied saying, "Length contraction is not something that "physically" acts on objects. It means that reference frames in motion with respect to each other measure the length differently. In other words, if there are two points in space that are 1 meter apart according to you, for someone traveling parallel to the line joining them, these two points will be closer together, regardless of the fact that there is no physical connection between those points or even if there is any physical objects at those point. So in your above examples, the distances between the discreet objects also length contract." To which I replied, "Okay, this is what I was afraid of. It seems to me this "length contraction" idea is just a convenient mathematical correction to compensate for something we have no explanation for, made up so that things will work out in calculations so that it can be predicted how things will *appear* in different circumstances. It is not really happening. Rulers are not contracting. And space is certainly not expanding and contracting based on how fast an object is moving. So it is extremely misleading to say objects flatten the faster they go. The correct answer for how it is that the speed of light can be measured to be the same regardless of one's speed is "No one knows. We only know how to calculate what the results of measurements will be."
I believe Janus was trying to reassure you that your lengths don't contract just because someone else accelerates or just because two other observers watching you are traveling at different speeds.

You are correct that Special Relativity does not explain how things contract or times dilate because it is merely a mathematical theory. But that doesn't mean there aren't other theories that explain the reality of length contraction or time dilation. The purpose of Special Relativity is to integrate measurements that two observers in relative motion make or between the states before and after a single observer accelerates, without regard to explaining any mechanism.

You have to remember that prior to Einstein's paper in 1905 describing Special Relativity, virtually all scientists believed in a universal absolute ether rest condition in which, and only in which, the speed of light was a constant in all directions and in which all dimensions and time intervals were stable and absolute. This is like the green man in my animation and his perfect circle of mirrors. But they assumed that we, on the surface of earth, were traveling through this stationary ether at some unknown speed and in some unknown direction, but our lengths must be contracting and our clocks must be ticking slower than normal in order to account for how we would always measure the speed of light to be exactly the same value as we would if we were stationary in the ether. We are like the red man in my animation. The theory these early scientists developed accounted for how clocks would tick more slowly and lengths would be contracted in the direction of motion through the ether. And they were constantly trying to figure out how to measure or detect this inevitable motion through the ether, without success.

What Einstein did was say that as long as you are not accelerating, you can assume that you are stationary in the ether rest condition and there will be no way to detect that you aren't. So this relieved the scientists of any compulsion to measure or detect any motion through the ether and allowed them to proceed with physical theories without concern about identifying any ether.

But this raises a question: suppose there really is an ether and suppose we are traveling through it at a very high speed in some direction, just by being stationary on the surface of the earth. We won't be able to tell, but we would certainly understand in principle that we would be experiencing length contraction and time dilation. Now suppose that we get in our rocket and take off at a very high speed into space and it just so happens by pure chance that we are traveling into the either such that our speed through the ether was now less than it was before, in fact, let's pretend that we are now stationary in the ether. What would we say about length contraction and time dilation? Well, if we assumed that we were at rest in the ether when still back on earth, we would have to now say that our lengths were contracted and our times dilated. But, since we are imagining that we really were traveling through the ether before and now we are at rest in the ether then our lengths would be longer and our clocks would tick at a faster rate. This explains why we can never say in an absolute sense that when you see something traveling at a high speed that it is experiencing length contraction and time dilation as it may be the other way around for all we know.

Again, please, if any of this is confusing or doesn't make sense or has apparent contradictions, then just ask.
 P: 159 [QUOTE=ghwellsjr;3208581]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. 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/n...gravity-earth/
 P: 159 "You are correct that Special Relativity does not explain how things contract or times dilate because it is merely a mathematical theory." That is what I suspect! "But that doesn't mean there aren't other theories that explain the reality of length contraction or time dilation." That is what I want to know! "The purpose of Special Relativity is to integrate measurements that two observers in relative motion make or between the states before and after a single observer accelerates, without regard to explaining any mechanism." That is what I was saying.
P: 789
 Quote by CosmicVoyager Okay, I'm trying to visualize how all the slices fit together, how they are connected. When one drags a one dimensional line at a right angle perpendicular to itself repeating it over and over, a two dimensional plane is created. And when one drags a plane at a right angle perpendicular to itself, a three dimensional cube is created. When you refer to the fourth dimension, you mean dragging the cube at a right angle perpendicular to itself and getting many cubes with each point in a cube connected to the points in the same place in the previous an next cubes? An entire hypercube can be represented in 3D with a line of cubes and realizing which points are connected. When you say every particle has its own slice, you mean one of those cubes? I can't figure out how to account for observed phenomena with a line of cubes of space where each one is only touching two others just as a each 2D plane in a 3D cube are touching two others. It seems like it would require more dimensions (and I still don't see how to do it LOL) Is it possible to illustrate the same effects with a 2D plane as space and the 3D cube it is in as time?
Yes, except that you would not say the 3D cube is time, you would say that the direction you are dragging the 2D square is the time direction and the 3D cube is a cube in spacetime.

Now somebody else tilts the piece of paper and drags it in a perpendicular direction. They create a different cube in spacetime. The direction they are dragging it in is their time direction. You are both dragging your square pieces of paper through the same spacetime, but your cube is tilted with respect to their cube.

What I am saying is, when you make the first cube in spacetime, the infinite plane containing that sheet of paper is your "time slice" through spacetime. When somebody else tilts the paper, the plane of that piece of paper is their "time slice" through spacetime. Different people experience different slices. The direction you move your paper is perpendicular to your paper. That is your "time direction". The direction the other person moves their paper is perpendicular to their paper. That is their "time direction".

Take a pencil and make a point in the middle of your paper. That represents you. Your paper always stays motionless with respect to you as you move through time and your point draws out a line. That line is called your "world line". The other person makes a point on their paper, that's them. Their paper always stays motionless with respect to them, and the line that their point traces out as they move their paper is their "world line". But what happens when you move the plane of your paper through the other person's world line? It moves on your piece of paper! The other person is moving with respect to you! If they look at your world line on their piece of paper, your world line moves on their piece of paper, so they say you are moving with respect to them. Thats why we say that if two people are moving with respect to each other, their "time slices" and "world lines" are tilted with respect to each other.
 P: 159 I am struggling to understand what you are saying. Further questions depend on the answer to this question: I meant for the 2D plane to represent our 3D universe. Did you realize that? Is that how you are using it? I ask because you talk about me moving the piece of paper in one direction or someone else moving the peace of paper in another direction. You seem be saying I am outside the universe moving it. I wanted to know if you could show how objects move in the 2D plane for space and through 3D for time. "the infinite plane containing that sheet of paper is your "time slice" through spacetime. When somebody else tilts the paper, the plane of that piece of paper is their "time slice" through spacetime." It sounds like you are saying we are holding the universe or that we are in different universes. I need an illustration that shows two objects or people moving at different speeds measuring the speed of light from the same source. An illustration that reconciles the apparent contradiction that they measure it to be the same speed. Like this animation tries to do http://www.youtube.com/watch?v=dEhvU31YaCw What I mean by "like this animation" is that it shows both people in the same universe, and how it might be that light appears the same speed to both. "Take a pencil and make a point in the middle of your paper. That represents you. Your paper always stays motionless with respect to you as you move through time and your point draws out a line. That line is called your "world line". The other person makes a point on their paper, that's them." They need to be on the same paper! lol Or at least the same cube. The paper is the space of the universe. If they are on separate paper it is like they are in different universes and there is no reconciliation of their views. I'm trying to see how their apparently opposing views can exist in the same universe, in the same space time continuum. You said there are 3 dimensions of space and a 4th of time. The 2D plane is supposed to represent our 3D space. If you are moving the paper in any way other than dragging it exactly perpendicular, more than 4 dimensions are needed.
P: 789
 Quote by CosmicVoyager I meant for the 2D plane to represent our 3D universe. Did you realize that? Is that how you are using it? I ask because you talk about me moving the piece of paper in one direction or someone else moving the peace of paper in another direction. You seem be saying I am outside the universe moving it. I wanted to know if you could show how objects move in the 2D plane for space and through 3D for time.
Yes, thats exactly how I meant it. The whole plane in which your 2D piece of paper sits represents the 3D universe as you see it now, and the 3D space that it is moving through represents spacetime. The direction that your piece of paper is moving is your time direction. Your paper, as it moves perpendicular to itself represents the universe, as you see it, moving through spacetime.

 Quote by CosmicVoyager "the infinite plane containing that sheet of paper is your "time slice" through spacetime. When somebody else tilts the paper, the plane of that piece of paper is their "time slice" through spacetime." It sounds like you are saying we are holding the universe or that we are in different universes.
You are both in the 3D spacetime, spacetime never changes. 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. Their piece of paper makes a different slice through spacetime. Everything in their piece of paper happens "now" to them. Yes, you experience spacetime differently from them. If two firecrackers, go off at the same time, according to you, the other person will say no, they did not go off at the same time, one went off before the other.

 Quote by CosmicVoyager I need an illustration that shows two objects or people moving at different speeds measuring the speed of light from the same source. An illustration that reconciles the apparent contradiction that they measure it to be the same speed. Like this animation tries to do http://www.youtube.com/watch?v=dEhvU31YaCw What I mean by "like this animation" is that it shows both people in the same universe, and how it might be that light appears the same speed to both.
Don't worry about the speed of light right now. That comes later. Right now you have to understand about how different people experience spacetime and why, and I think you are on the right track, but not there yet.

 Quote by CosmicVoyager "Take a pencil and make a point in the middle of your paper. That represents you. Your paper always stays motionless with respect to you as you move through time and your point draws out a line. That line is called your "world line". The other person makes a point on their paper, that's them." They need to be on the same paper! lol Or at least the same cube. The paper is the space of the universe. If they are on separate paper it is like they are in different universes and there is no reconciliation of their views.
There is no unique "space of the universe". They do not have to be on the same paper! This is what Einstein discovered! There will be no reconciliation of their views only if they fail to understand what is happening. Once they understand that spacetime is where everything happens, and they are only taking slices through spacetime, they will be able to reconcile everything.

If two people are moving with respect to each other, the slices through spacetime which they call "the universe as I see it now" are different. Spacetime is what it is, so yes, they can disagree on whether two firecrackers went off at the same time, or how far apart they were when they went off, but they will always agree that two firecrackers went off, because two firecrackers went off in spacetime, no matter what angle you look at it from.

 Quote by CosmicVoyager I'm trying to see how their apparently opposing views can exist in the same universe, in the same space time continuum. You said there are 3 dimensions of space and a 4th of time. The 2D plane is supposed to represent our 3D space. If you are moving the paper in any way other than dragging it exactly perpendicular, more than 4 dimensions are needed.
Your paper is moving perpendicular to its plane through spacetime. Someone else's paper is moving perpendicular to the plane of their paper through spacetime. You say "I'm trying to see how their apparently opposing views can exist in the same universe". The answer is "by understanding that they are experiencing slices through a 3-D spacetime"

You have two eyes. They give you slightly different 2-D views of the same scene. How can these two apparently opposing views be reconciled? By realizing that they are viewing a 3-D scene from slightly different angles. Thats how they are reconciled.

You have to get rid of the idea that what you call "the universe as it is now" is the same as what a person moving with respect to you calls "the universe as it is now". The fact that this causes disagreements about space and time is to be expected. But just like the disagreements between your two eyes, once you understand that another dimension is involved, all the disagreements are explained and everything is fine.
PF Gold
P: 1,847
 Quote by CosmicVoyager So show that single spacetime. If mine is a slice and someone else's is a slice, then combine the slices into one picture.
(In this reduced dimension model)
You just stack all your 2D space slices together and you get 3D spacetime.
I just stack all my 2D space slices together and I get 3D spacetime.
We both get the same single 3D spacetime even though we disagree on what the 2D space slices are.

(Add one to all the dimensions above for the real answer, of course.)
P: 159
 Quote by DrGreg (In this reduced dimension model) You just stack all your 2D space slices together and you get 3D spacetime. I just stack all my 2D space slices together and I get 3D spacetime. We both get the same single 3D spacetime even though we disagree on what the 2D space slices are. (Add one to all the dimensions above for the real answer, of course.)
You say "we both get the same single 3D spacetime". So the illustrations are identical? There is one arrangement of objects?

If not, another thread is discussing whether or not the speed of light is just measured to be constant relative to all observers.

In this thread I asking for a single arrangement of objects in spacetime and any relevant phenomena that shows why light *appears* to be the same speed relative to any observer.
PF Gold
P: 4,743
Quote by CosmicVoyager
 Quote by 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! :-)
 Quote by ghwellsjr 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.
 Quote by CosmicVoyager 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/n...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.
 P: 159 "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?
P: 789
 Quote by CosmicVoyager 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"?

 Quote by CosmicVoyager "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.

 Quote by CosmicVoyager 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?

 Quote by CosmicVoyager "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.

 Quote by CosmicVoyager 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.

 Quote by CosmicVoyager 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.
 P: 159 ( 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.
PF Gold
P: 4,743
 Quote by 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.
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.
 Quote by CosmicVoyager "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.
 Quote by CosmicVoyager "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.
 Quote by CosmicVoyager "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?
 P: 159 "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.

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