Age Relative? Time, Speed and Paradox Explored

[4newton]

Fredrik:
Now we are on the same page. I have no problem with you drawing.

The point is that the one way time to reflection is different in different directions. This is a difference within the same frame. You will need to contort space a great deal to make the times come out equal.

You have two choices. You can keep the idea that clocks are absolute and modify the rest of nature to maintain consistencies or you can accept the fact that there is a more basic nature of time and that other functions of nature do not change except with applied action.

The concept I have given you simplifies the idea of space and time and has no paradoxes. It also allows you to proceed with understanding the larger universe, force, energy…

If you maintain the first choice you will have a hard time understanding anything more, as is the current problem in physics today.

 

[Fredrik]

Now we are on the same page. I have no problem with you drawing.

Are you absolutely sure that you agree with this drawing? I'm very surprised by your answer, because this is just what I've been saying all along, and you've had objections every time. (All of them were either wrong or irrelevant, and usually made no sense).

For example, you have previously said that what I'm saying is wrong because you can have more than one light synchronized clock in the same moving frame and they wouldn't agree with each other. (I can't tell if this one is wrong or irrelevant, because it doesn't make sense to me).

Why have you changed your mind? Are you sure you understand what I'm saying? One of the things I'm saying is that "space" is not the same set of events to different observers.

Haven't you been saying the exact opposite the whole time?

 

[russ_watters]

Frigga:
Fredrik seems to agree that this takes place but he does not think it is a paradox. Everyone else realizes that if SR say that all physical laws are the same in all inertial frames and that your clock is based on physical laws. Then clocks after some time in one inertial frame disagree with clocks in another inertial frame contradict the first statement. To be nice we call that a paradox. SR is right in most cases just as Newton’s laws were right. It is these small “paradoxes” that should lead us to find a more true understanding of the universe. This is just as Einstein did with Newton.

As others have said and you refuse to accept, the paradoxes are not paradoxes in SR, they are paradoxes in Newtonian physics. SR is what allows us to resolve the paradox. It should be perfectly obvious that if there is a paradox in a theory, the theory doesn't work and needs to be fixed.

And the part that you are calling the paradox is, in fact, the resolution to the paradox. The paradox is in the ages of the twins, not the way the theory reads.

 

[4newton]

Fredrik:
Either I or you or both of us have not been able to understand each other. I have another drawing to bring our current understanding together. I did not understand that you where talking about a y space line. You had that line labeled as x’.

I have now included your y-space line at the angle you show. All distances are in comparison to Fig. 1.
Line GJ is the time-distance for light to reach the ring in the forward x direction with the frame moving in the x direction. Line GH is the time-distance for the light to reach the ring in the y direction within the same frame.

The time it take the light to reach H is (t3)=(t5)/2 and in this frame moving at one half the speed of light. It is 1.2 times longer than the time in Fig. 1 AB or t1. The time it takes the light to reach J is 1.7 times longer than t1.

Clocks synchronized at G and moved to the ring before the frame is in transition may test this. All clocks being in the same frame will agree on the time. After the light reaches the ring and the clocks are stopped then the clocks can be brought together and the above times will be verified.

How does SR resolve this difference?

 

[4newton]

russ_watters:
I don’t have a disagreement with SR. I agree that SR can define time as clock time for all observers. It still is true that if you go through the two clocks experiment they will not agree. The question is, are the drawings I have presented representing reality including SR. If you think they do not please let me know where they differ.

If we can agree on the representation of reality then we can proceed to the next step.

 

[Fredrik]

I have another drawing to bring our current understanding together.

Let's not bring any more drawings into this. We should focus on the details of the one we've been discussing recently. (There's also no need to draw the y direction).

I did not understand that you where talking about a y space line. You had that line labeled as x’.

What are you talking about?! I stated very clearly that the lower green line (which is the same line that I labeled x' in another drawing) is in the t-x plane, which is perpendicular to the y axis.

The horizontal black line is the x axis. That's where the t and y coordinates are zero. (Remember that the unprimed coordinates are used by observer A). It is also the direction that observer A (if he's facing the y direction) would call "right".

The lower green line is the x' axis. That's where the t' and y' coordinates are zero. (Remember that the primed coordinates are used by observer B). It is also the direction that observer B (if he's facing the y direction) would call "right".

Note that the x and x' axes do not coincide. At event G (the origin), both observers are at the same point in space, facing the same direction (we assume, as part of the definition of the observers A and B), but an event (like a phone ringing) that's on B's right in his "now", is in observer A's future. It hasn't happened yet to A. It will happen (on his right hand side) some time in the future.

If you are at all serious about learning relativity, there's something you should know: There is no way that you will ever understand relativity without understanding this. This fact (that the x and x' axes do not coincide) is the most important fact in all of SR.

I don't know how you could misunderstand my drawing like that. I hope you will understand it now. Perhaps you had problems because you've forgotten one basic fact from geometry: If two lines intersect, there's exactly one plane that contains them both.

Do you understand this now? Do you agree that the x' axis must be where I've drawn it, or would you put it somewhere else?

 

[Fredrik]

We were talking about paradoxes earlier. A lot of people seem to have misunderstood what a paradox is, so I will try to explain it.

A paradox in a physical theory is a prediction about the outcome of an experiment that disagrees with another prediction made by the same theory. A theory that contains a paradox is logically inconsistent, and would be thrown out with the garbage. There are no paradoxes in SR. (If there were, we would probably have to throw out all of mathematics).

The "twin paradox" might seem to be a paradox of SR, but it isn't. A correct application of the theory will always yield the result that the astronaut twin is younger when he gets back. People who don't understand the theory very well might come to a different conclusion, but that's only because they are making mistakes.

 

[4newton]

Fredrik,
If you insist on only looking at the observer clock being absolute then you must change the shape of space as you have done. This of course is not correct except in the view of the moving observer. Space for all other observers has not changed. If you look at
http://physics.syr.edu/courses/modules/LIGHTCONE/LightClock/
You can see my space-time drawing in motion. As you can see this is not only just my idea of space-time. This is not basically anything new in presenting space-time and is well supported.

I think we have wasted enough time on points of view. If you can not find anything wrong, except the point of view, in my drawing representing observation then I will go on to space-time and the Big Bang.

You have not commented on the one-way speed of light being reflected at different times by the ring. I assume you have no disagreement. You have not disagreed with the fact that you can have a spatial rest frame where there is no spatial transition. This is a point that russ_watters and I had a disagreement on. Russ do we now agree that there is a spatial rest frame?

I think the idea of simultaneous events will be much clear when considered with the Big Bang.

 

[Alkatran]

http://casa.colorado.edu/~ajsh/sr/paradox.html

Read the entire site. Then click "forward to Centre of the lightcone", continue reading and moving forward, or back if necessary, until you understand why we're right (according to experiment).

 

[Garth]

http://casa.colorado.edu/~ajsh/sr/paradox.html

Read the entire site. Then click "forward to Centre of the lightcone", continue reading and moving forward, or back if necessary, until you understand why we're right (according to experiment).

Great link, thanks.

Garth

 

[russ_watters]

You have not disagreed with the fact that you can have a spatial rest frame where there is no spatial transition. This is a point that russ_watters and I had a disagreement on. Russ do we now agree that there is a spatial rest frame?

If by "spatial rest frame" you mean an absolute/universal reference frame from-which to measure all velocities, distances, and times, of course not!

 

[4newton]

These illustrations of course point up the fact that you have space with different dimensions in two different reference frames located at the same center point in space-time. In order to accept this you must discard the fact that static objects always have the same spatial difference between them regardless of your reference frame. The distance between the Earth and the sun does not change just because you are in motion.

You must abandon the idea that clocks directly tell real time. You must think of a clock as just another variable in space-time. If time is another dimension as everyone seems to claim then you must follow the rules for dimensions.

 

[Garth]

These illustrations of course point up the fact that you have space with different dimensions in two different reference frames located at the same center point in space-time. In order to accept this you must discard the fact that static objects always have the same spatial difference between them regardless of your reference frame. The distance between the Earth and the sun does not change just because you are in motion.

You must abandon the idea that clocks directly tell real time. You must think of a clock as just another variable in space-time. If time is another dimension as everyone seems to claim then you must follow the rules for dimensions.

"the same spatial distance" is in fact in SR the space-time interval, in time units this is the proper time, or the "real time" told by an inertial clock that is moving along the geodesic that joins the two events. This is invariant between "different frames". The space distance and the time interval between two events as measured in a particular frame do change "just because you are in motion", they do change when measured in different inertial frames in relative motion with each other.
You obviously haven't read the entire site Alkatran posted for us - it is standard SR, "read, mark, learn and inwardly digest".
Garth

 

[Fredrik]

If you insist on only looking at the observer clock being absolute then you must change the shape of space as you have done.

As usual it's not easy to understand how you misunderstood me this time. Are you saying that I'm treating the time on B's clock as more fundamental then A's clock? I would never do that.

I haven't changed the shape of space. Space is always a plane in 2+1 dimensional relativity. I'm just saying that different observers disagree about what plane that is. (Note that this is not a paradox).

I haven't changed space. I'm not saying that the x'-y plane is space in any objective way. The x-y plane is still "space" to A (but not to B).

You have not commented on the one-way speed of light being reflected at different times by the ring. I assume you have no disagreement.

You're just saying that if the mirror is far away it will take some time before the light reaches it. That's trivial and irrelevant.

I understand that you've been trying to say something else too, but I'm not sure what that is.

You have not disagreed with the fact that you can have a spatial rest frame where there is no spatial transition.

That sentence doesn't even make sense, but I'm guessing that you are trying to say that some objects can be stationary in some objective sense. That's not the case, so if that's what you mean, I disagree.

The distance between the Earth and the sun does not change just because you are in motion.

If you change your velocity, that will obviously not change any objective facts about the Earth and the sun, but spatial distance is not even something that can be defined in an objective way. If you measure the distance between the Earth and the sun before and after you change your velocity you will get different results. This is because you're not measuring the same thing. You're measuring two different things and calling them both "distance".

You must abandon the idea that clocks directly tell real time. You must think of a clock as just another variable in space-time.

I have probably misunderstood this, because I actually agree with it. The problem is that you think there is a "real" time. (If there's a preferred rest frame, then a clock that is stationary in that frame defines a preferred time).

Edit: At first glance, it may seem that I disagree with Garth about "real" time, but I don't. He is of course right about proper time. Proper time is invariant so it makes sense to call it "real".

It would make sense to explain the relationship between proper time, coordinate time and clock time here, but I don't have the time (no pun intended) to do it now. Perhaps tomorrow.

 

[4newton]

russ_watters

If by "spatial rest frame" you mean an absolute/universal reference frame from-which to measure all velocities, distances, and times, of course not!

That is not what I had in mind in my question. I was only thinking about transition in time without any spatial transition.

However, don’t you consider the Big Bang as the reference point for our universe?

I have been reading some of your post and it is interesting that we think alike on many points. I feel that we are coming together on more and more ideas I hope we can reach more agreements. I place great value on your viewpoints.

 

[Alkatran]

russ_watters


That is not what I had in mind in my question. I was only thinking about transition in time without any spatial transition.

However, don’t you consider the Big Bang as the reference point for our universe?

I have been reading some of your post and it is interesting that we think alike on many points. I feel that we are coming together on more and more ideas I hope we can reach more agreements. I place great value on your viewpoints.

The big bang expanded a point to the current universe. The center isn't fixed... it's everywhere (this is what I've been told).

Or think about it this way: if two people are moving at different speeds, will they measure the center to be in the same place? Chances are it doesn't matter what speed you're moving at the center stays fixed (just a guess!)

 

[russ_watters]

russ_watters

That is not what I had in mind in my question. I was only thinking about transition in time without any spatial transition.

However, don’t you consider the Big Bang as the reference point for our universe?

Yet another misunderstanding you have of what a theory in physics says: the Big Bang theory says nothing of the sort. In fact, it says exactly the opposite. Wait, this isn't all an elaborate cover for Geocentrism, is it?

 

[Fredrik]

If by "spatial rest frame" you mean an absolute/universal reference frame from-which to measure all velocities, distances, and times, of course not!

That is not what I had in mind in my question. I was only thinking about transition in time without any spatial transition.

If there is such a thing as "transition in time without any spatial transition" in any absolute sense, it would imply the existence of the absolute frame that Russ is talking about.

 

[4newton]

041117-04

If there is such a thing as "transition in time without any spatial transition" in any absolute sense, it would imply the existence of the absolute frame that Russ is talking about.

The discovery of the Big Bang requires a change or at least extensions of relationships. It is true at this time that the Big Bang is the primary reference point. We know that it happen at some location in the unknown all. We also know that it took place about 15 billion years ago. If you had a clock at the time of the BB and looked at it today it would indicate 15 billion. This number is of course just for discussion.

This is where thing get interesting. Do all clocks that move out from the BB in all directions accumulate the same time, tick at the same rate? The answer must be yes. If this were not so, accumulated time and the rate of clocks would be different through out the universe. You could have places in the universe that transitions could take place in zero time. The whole universe would be chaos.

Observation of red shift tells us that the universe is uniform and consistent and that clocks that are not in spatial transition tick at the same rates everywhere in the universe. The same atoms produce the same spectral line everywhere.

From the BB all that is the universe is expanding outward in all directions. After the formation of mass objects the expansion of all objects continued in a line normal to the expanding surface.

Space is measured and spatial transitions take place between objects in the universe. From the standpoint that you are able to measure if you are moving to or away form objects then you may maintain a point without spatial transition in our universe.

If the whole universe is in spatial transition then the only way you could tell is by measuring the one-way speed of light.

From the above you can see that it is impossible to tell the absolute position of the universe in “whatever” but you are able to reference all positions from the Big Bang and you are also able to tell change of spatial position between objects in the universe.

The BB theory is even less egocentric than SR or any other theory. It makes us realize that nature has done a lot to make us feel important in the past and now maybe we are ready to know we are very small but are still considered important for a grand purpose.

 

[Alkatran]

This is where thing get interesting. Do all clocks that move out from the BB in all directions accumulate the same time, tick at the same rate? The answer must be yes. If this were not so, accumulated time and the rate of clocks would be different through out the universe. You could have places in the universe that transitions could take place in zero time. The whole universe would be chaos.

15 billion years according to proper Earth time I think.

It is NOT THE SAME AMOUNT everywhere!

Things move relative to each other, meaning they move faster/slower through time relative to each other, meaning they haven't measured to same time from the 'beginning'. (The moon is always moving relative to us, so it is moving slower through time according to us)

 

[russ_watters]

Two things:

-4Newton, since the BB happened everywhere, you cannot use it as a reference point.

-Alkatran, its slightly more complicated than that: The expansion of space is not motion, so it doesn't cause time dilation. But there are, of course, other motions going on that do.

 

[Alkatran]

Two things:

-4Newton, since the BB happened everywhere, you cannot use it as a reference point.

-Alkatran, its slightly more complicated than that: The expansion of space is not motion, so it doesn't cause time dilation. But there are, of course, other motions going on that do.

That's what I meant. I probably gave the wrong idea by saying "everywhere"

I figured the moon example would make it clear that I meant according to different observers.

 

[Fredrik]

The discovery of the Big Bang requires a change or at least extensions of relationships. It is true at this time that the Big Bang is the primary reference point.

A lot of things are different in a spacetime that has non-zero curvature and a big bang singularity. That's why I think it's a mistake to start talking about GR now. You don't even understand the basics of SR yet. You will not be able to understand stuff like simultaneity in GR unless until you have understood it in SR.

We know that it happen at some location in the unknown all.

No it didn't. The big bang theory says that the distance between any two points on any spacelike hypersurface goes to zero as the "time after the big bang" goes to zero. It doesn't say that there was a "bang" at some point in space.

 

[4newton]

Fredrik:

A lot of things are different in a space-time that has non-zero curvature and a big bang singularity. That's why I think it's a mistake to start talking about GR now. You don't even understand the basics of SR yet. You will not be able to understand stuff like simultaneity in GR unless until you have understood it in SR.

Let me try to explain to you your position on SR.
If back in the Middle Ages I walked on to your farm and asked you about your world. You would tell me that the world is flat and that the sun goes around the earth. I would than try to explain to you that the Earth is round like a ball and is spinning. I would also tell you that the Earth is really going around the sun.

You of course would insist that I don’t know what I am talking about and that until I accepted the idea that the Earth is flat and the sun goes around the Earth I could not possibly understand the way the world works.

From your point of view on the farm you have every proof that you are right. If you can not change the mind set that there are other points of view that may be more valid then yours then you will never leave the farm.

The question is, if the view of space-time I have presented is wrong where does it disagree with observation or experiment? You have never addressed this main point. If SR and the space-time I have drawn both account for experiment and observation, which view point, should be accepted? Should we accept a view that requires conflict with logic or one that is logical on all counts?

No it didn't. The big bang theory says that the distance between any two points on any spacelike hypersurface goes to zero as the "time after the big bang" goes to zero. It doesn't say that there was a "bang" at some point in space.

Could you please describe or draw this concept. If you have trouble drawing you may find Open Office of help
http://www.openoffice.org/
The program is free and it does have a drawing function and a conversion to PFD files.

R. G.

 

[4newton]

Russ:

-4Newton, since the BB happened everywhere, you cannot use it as a reference point.

That is an interesting viewpoint. Of course the logical extension of that is that the universe is still everywhere so nothing has changed. I think it is quite logical to understand that a balloon that is not inflated occupies a different space than when inflated. You will need to explain why the universe before expansion can not be compared with the universe today.

Is space real? Is time real? Does the universe exist? If the answer to any of these questions is no then there is no reason for physics.

R.G.

 

[4newton]

Alkatran:

15 billion years according to proper Earth time I think.

It is NOT THE SAME AMOUNT everywhere!

Things move relative to each other, meaning they move faster/slower through time relative to each other, meaning they haven't measured to same time from the 'beginning'. (The moon is always moving relative to us, so it is moving slower through time according to us).

If the time is not the same everywhere what time is it right now on an object 10 billion light years away. Remember that what is taking place there right now will take 10 billion years to reach us.
R.G.

 

[Alkatran]

Alkatran:
If the time is not the same everywhere what time is it right now on an object 10 billion light years away. Remember that what is taking place there right now will take 10 billion years to reach us.
R.G.

I just told you that different observers will measure different times as having passed. How would I know the entire history of some random object 10 billion light years away? Chances are it hasn't observed the same passage of time as the stuff that made the sun.

 

[Alkatran]

Russ:
That is an interesting viewpoint. Of course the logical extension of that is that the universe is still everywhere so nothing has changed. I think it is quite logical to understand that a balloon that is not inflated occupies a different space than when inflated. You will need to explain why the universe before expansion can not be compared with the universe today.

Is space real? Is time real? Does the universe exist? If the answer to any of these questions is no then there is no reason for physics.

R.G.

Take a perfectly round sphere and show me the center of it's surface area.

That's why you can't necessarily pinpoint the center of our universe.

 

[Alkatran]

Fredrik:
Let me try to explain to you your position on SR.
If back in the Middle Ages I walked on to your farm and asked you about your world. You would tell me that the world is flat and that the sun goes around the earth. I would than try to explain to you that the Earth is round like a ball and is spinning. I would also tell you that the Earth is really going around the sun.

You of course would insist that I don’t know what I am talking about and that until I accepted the idea that the Earth is flat and the sun goes around the Earth I could not possibly understand the way the world works.

From your point of view on the farm you have every proof that you are right. If you can not change the mind set that there are other points of view that may be more valid then yours then you will never leave the farm.

The question is, if the view of space-time I have presented is wrong where does it disagree with observation or experiment? You have never addressed this main point. If SR and the space-time I have drawn both account for experiment and observation, which view point, should be accepted? Should we accept a view that requires conflict with logic or one that is logical on all counts?Could you please describe or draw this concept. If you have trouble drawing you may find Open Office of help
http://www.openoffice.org/
The program is free and it does have a drawing function and a conversion to PFD files.

R. G.

Relativity is tested everyday. If the farmer had done a scientific test, such as measuring how far the horizon was, he would realize the Earth could not be flat.

What is the space time you have drawn?

 

[russ_watters]

If you like the flat-earth analogy and want to keep us on the flat-earth side, here's the comparison: We've led you by the hand to the edge of the world and you've looked over the edge at the nothingness below and still refuse to accept that the world is flat.

SR has, for the past 80 years, passe ever test thrown at it. It has never once been found to describe the universe on the macroscopic scale inaccurately. The problem here is that you quite simply either don't understand it or understand it but refuse to accept it. Either way, the resolution to all this is entirely up to you.

 

[4newton]

Russ:

If you like the flat-earth analogy and want to keep us on the flat-earth side, here's the comparison: We've led you by the hand to the edge of the world and you've looked over the edge at the nothingness below and still refuse to accept that the world is flat.

I like your addition to my flat-earth analogy. You have told the same story that everyone was saying back in the Middle Ages. Just as it turned out then the Earth was not flat and today the theory of SR is not the end of the story. All the observations that prove SR also apply to my GST-07 drawing. I have asked before, where is the GST space-time wrong with respect to observation or experiment.

Just as the laws of Newton still apply so also does SR. SR is just a part of the whole picture. It is the view of the egocentric observer just like the farmer of the Middle Ages. The farmer at that time could prove to you by thousands of measurements that the sun went around the earth.

R.G.

 

[4newton]

Alkatran:

I just told you that different observers will measure different times as having passed. How would I know the entire history of some random object 10 billion light years away? Chances are it hasn't observed the same passage of time as the stuff that made the sun.

In order to consider any concept you must focus on the ideal and not be distracted by irrelevant input.
The objects both start out at the time of the BB and continue without any spatial transitions or influence each will follow a path in a straight line away from the event of the BB. See the attached drawing GST-08.

You will note that the time line, proper time or normal time, with respect to the speed of light must be on the same path as the objects direction out from the BB. The light cone for each object is 45 degrees to the path of the objects.

Object A takes the path C-A’-A and object B has the path of C-B’-B. At any time a light pulse may be sent from either object to the other. This is shown by light lines A’ to B and B’ to A. The length of each light path must be equal. Therefore from the point of any simultaneous events on either objects the light must arrive at the same time on the other object. The start of the simultaneous event may be all the way back to the BB. The point of the BB must be simultaneous for all events in the universe. By this method it is shown that at all times all events in the universe are simultaneous and that all objects in the universe have the same normal, or proper time.

Take a perfectly round sphere and show me the center of it's surface area.
That's why you can't necessarily pinpoint the center of our universe.

The center of a surface has nothing to do with the center of a sphere or hyper-sphere.

Relativity is tested everyday. If the farmer had done a scientific test, such as measuring how far the horizon was, he would realize the Earth could not be flat.
What is the space time you have drawn?

As I pointed out before, show me where the test of relativity fails in GST-07. I will again attach GST-07.

If the farmer were not so convinced that he was right he would think to run the test. As we know that did happen later as will all truths. Has scientific thought changed very much in all this time? I am not asking that any idea be accepted out of hand. But it is just as bad to fall back to the position that everyone knows for a fact. If these viewpoints are wrong point it out in some detail. Saying that it is against some other theory is starting with a closed mind. With that approach all you can produce, like the farmer, is corn. (or something)

R.G.

 

[Fredrik]

If back in the Middle Ages I walked on to your farm and asked you about your world...

I wouldn't be surprised if you actually believe that your analogy is correct, but for your sake I really hope you don't.

There's at least one important difference between you and a person trying to convince a farmer in the middle ages that the world is round: That person would be able to convince the farmer that he understands the meaning of the sentence "the world is flat". You however, have not convinced anyone that you understand special relativity. You have shown us over and over again that you don't understand SR.

If you're going to try to convince people that a theory is wrong, you should first learn what the theory actually says.

By the way, the farmer would have to be very ignorant or stupid, because it's been well known for more than 2000 years that the Earth is round. The ancient Greeks knew it, and were even able to estimate the size of the earth.

The question is, if the view of space-time I have presented is wrong where does it disagree with observation or experiment? You have never addressed this main point.

As far as I can tell, your "view of spacetime" is that space and time is exactly what people thought it was before special relativity was discovered. As Pervect explained very well in a post earlier in this thread, this view doesn't disagree with experiment, but requires that you think of a Lorentz contraction as an actual physical deformation of a moving object. But the really disturbing fact about this view is that you can easily combine "real" space and "real" time to form "spacetime", and then choose another hyperplane that we can think of as "space". Let's call this hyperplane "fake space" and the direction that's perpendicular to it "fake time". The problem with your view is that if someone were to assume that "fake space" and "fake time" is actually the real space and time, there's no way you would be able to prove him wrong.

The question of whose space and time is "real" arises in your view of SR, not ours. We have accepted that it's a bad idea to think of space and time as two different things. No separation of spacetime into space and time is any more real than any other.

Could you please describe or draw this concept.

Most of the solutions of Einsteins equation are not as easy to visualize as Minkowski space. Fortunately, there is one solution with a "big bang" that is easy to draw. Remember that in a spacetime diagram that represents Minkowski space, horizontal lines represent space at different times, and their vertical position indicates what time that is. Later times are drawn above earlier times. In a spacetime diagram that represents a homogenous and isotropic universe with positive constant curvature, "space at different times" are drawn as circles with different radii. (If you would like to visualize two spatial dimensions, replace the circles with spheres). In this spacetime diagram, increasing time is not "up". It's "outward".

The visualization of this particular solution is where the analogy with a balloon being inflated comes from. The universe is not the interior of the balloon, it's the surface of the balloon. The big bang is not a point on the surface of the ballon, or an outward line from the center of the drawing, or any such thing. The big bang is the point at the center.

This is why it makes no sense to say that the big bang happened at some point in space. The big bang "event" is not even a point in spacetime, since the metric can't be defined at that point.

 

[Alkatran]

Well of course if you pick two objects which have the same speed they're going to agree about the amount of time passed!

Consider this:
Let's say, hypothetically, that the moon and Earth agree on how much time since the big bang. The moon is moving relative to the earth, and accelerating around us, so it's proper time != Earth proper time. That means a moment later, they WILL NOT AGREE on how much time since the big bang!

Ok, let's say the center of the 3d sphere is the center. How does that mean ANYTHING to the 2d people restricted to the surface area of the balloon? There's no point in their 2d space which is the center of the sphere, so THERE IS NO CENTER IN THEIR SPACE. Just as THERE IS NO CENTER IN OUR SPACE (according to the big bang theory).

 

[Fredrik]

Just as it turned out then the Earth was not flat and today the theory of SR is not the end of the story.

Of course it isn't, but you're not replacing SR with a better theory. You don't have a theory at all. You're not a scientific pioneer. You're just a guy who doesn't understand relativity.

The farmer at that time could prove to you by thousands of measurements that the sun went around the earth.

What are you talking about? Of course he couldn't.

All the observations that prove SR also apply to my GST-07 drawing. I have asked before, where is the GST space-time wrong with respect to observation or experiment.

I'm not going to comment every little detail in every one of of your drawings. It's a waste of time, because every time I show you something that you have done wrong or something that just doesn't make sense, you ignore most of what I'm saying and just make another drawing.

I will say a few words about this one, but I will not comment any more of your drawings until you've made some progress in the discussions about your previous ones.

"Line GJ is the time-distance for light to reach the ring..."

The word "time-distance" is something that you just made up. How can I comment stuff like this? Do you mean time? Do you mean distance? Do you mean something else? The time is t(J)-t(G). The distance is x(J)-x(G). The line GJH is just the world line of a photon that is reflected off the ring.

"Line GH is the time-distance for the light to reach the ring..."

There's no such word, but let's ignore that for the moment. Have you noticed that the light is actually reflected in the wrong direction? Since the ring has moved, the photon will hit a part of the ring that's not perpendicular to the y axis, and will therefore be reflected a little to the right, and miss the green line GK. At time t5, the photon will be to the right of the green line, and on this side of the x-axis (with a negative y coordinate).

"The time it take the light to reach H is (t3)=(t5)/2 and in this frame moving at one half the speed of light."

If we pretend that you didn't make the mistake I just described, and that there is a ray of light that actually takes the path GHK (where all three points have x coordinates that are consistent with x=vt) then we must have t3=(t5-t0)/2. (Apparently you have chosen t0=0). This is definitely less than t4.

So at least you got that right, but what's your point? This wouldn't prove anything you've said.

You've made a few more mistakes, like not considering the Lorentz contraction of the ring. You're assuming that it's moving in the x direction in this frame. That means that it must be shorter in the x direction than in the y direction.