
#163
Feb2712, 08:34 AM

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P: 16,485

Consider the difference between geometry on a sphere and geometry on a plane. On a plane, two straight lines which are parallel at one point remain parallel and never intersect. On a sphere, two neighboring lattitude lines are straight lines which are parallel at the equator and intersect at the poles. On a plane the sum of the interior angles of a triangle are 180°, but on a sphere the sum of the interior angles of a triangle are greater than 180°. This is the kind of thing that is meant by "curvature". A rubber band which is stretched into a triangle shape on a flat table still has interior angles which sum to 180°, regardless of the stretching of the band. 



#164
Feb2912, 03:38 AM

P: 344

Let’s return to the example,  the ISS and the Earth orbiting the exact same orbit around the Sun. – And both exactly 1 orbit. Both places / both observers (A & B) will locally agree that it will take 1 year,  31536000 second. They will also agree about their orbit local speed is average exactly 30000 m/s
Observer B on the Earth, orbiting the exact same orbit round the Sun will also say that that it took 31536000 earthsecond to complete one orbit and the Earthspeed was exact averagely 30000m/s. But according to the Shapiro delay experiments we know that the comparablespeed between the ISS and the Earth not is the same,  (even though it locally is the same) . For exsample,  if it was possible for A and B to reflect a light beam on the Sun and get it back, it would take the exact same local time, and the exact same local speed. But the comparable time and speed would not be the same. Let us now say that the comparable speed difference is proven to be 50% . Option 1. The only way we mathematical can understand what happens here is that distances also must be 50% comparable different. This is simple logic. Then both local and comparable different reality can both be true at the same time.  (Seen from both observer A+B+E). Option 2. is that we from Earth would see the ISS orbiting the Sun double as fast as the Earth (according to the exaggerated exsample) . That would contradict that an external observer (E) would see both objects moving with the same (his) speed and using the same (his) time to complete one orbit. If you disagree, to both these options,  can you please be more detailed according to;




#165
Feb2912, 05:09 AM

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P: 16,485

As far as how I would describe the different paths, I would use a 4D coordinate system. I would then write the different paths in terms of parameterized worldlines in the coordinate system. Probably the ecliptic coordinate system with the GPS time coordinate would be the easiest. If you write "comparable time" then I know what you mean since we already discussed it. But we have not discusses "comparable distances" nor "comparable speeds", so don't bother to use those terms when you have not defined them. When you say "comparable speed" what experiment are you thinking about performing to compare the speed? Again, you put an undefined term in bold as though that helps to convey meaning. It does not, it is simply irritating. What is a "comparable distance difference" and how would you measure it? Please do not use the word "comparable" or any related word in our further discussions unless you have clearly defined the experiment you would perform to make the comparison. 



#166
Feb2912, 06:07 AM

P: 344

The conclusion is then,  it seems more to discover,  but whether it is possible, is then a different question. Thanks’ a lot for your patience, and detailed explanation. 



#167
Feb2912, 06:52 AM

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#168
Feb2912, 07:28 AM

P: 344

Hence the options are whether speed and /or distance does "the same", and whether that happens proportional. Which is the most likely option.
I know you twist these words,  but I also think you know what i mean. 



#169
Feb2912, 08:52 AM

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P: 16,485

Note, this is not a personal criticism, this is a common problem when you are learning a new and difficult subject, the concepts are not clear and words often have subtly different meanings in the new context. It is just a simple fact that you need to be aware of and have patience with. People will be willing to help you, but you need to recognize that communication about this topic is inherently difficult. You need to ask people to define terms when you are confused and you need to be willing to define terms when asked. GR is mathematically guaranteed to be a selfconsistent framework. So, any time that you use an English description and come up with some inconsistency you immediately know that you are not correctly translating between the math and the English. That is typically due to using a poorly defined term or due to making a statement which is well defined and gramatically correct in English but is not mathematically correct. Here, we have the first case. You use words like "comparable", "the same", "stretch", etc. but without a rigorous definition. Any inconsistencies you come up with are due to that, not due to the theory. 



#170
Feb2912, 10:34 AM

P: 344

On the one hand I have heard that when people not get confused first time they hear about reality they haven’t understood it, so I am maybe legally excused (even though it is not first time).
On the other hand it must also be possible to explain it to grandmother according to Einstein. I think I begin to understand a lot more, especially what we don't know. Still I would be happy to hear some ideas / opinions (if any) about how the third factor, “distance” in space time, and whether these too possible can be a changing factor too (in the same way as time) I mean how this factor most likely can be globally understood,  there must at last have been speculations about it, what is the opinion of the majority,  are there different theories, etc.. or is that what we don’t know a dead end. If possible explained in a “grandmother adaptable language” first at all, then later I believe it is easier to understand the math behind, if any. 



#171
Apr1512, 05:50 AM

P: 344

'A' at 1st. floor and 'B' at 10th. Between the Sun and the Earth there is a measurement tape. Because time is ticking different for ‘A’ and ‘B’ they cannot agree about the speed and /or the distance to the Sun (the circumstance). Because ‘A’ and ‘B’ live at the same planet they cannot be travelling with different speed. Because ‘A’ and ‘B’ both can see the same measurement tape (between the Sun and the Earth) the distance (circumstance) of the Sun can also not be different. Because time multiplied with speed = distance (circumstance) we do in fact have a dilemma here. So now they must both be following the same path. The only logical possible explanation is that ‘A’ relative to ‘B’ lives in a completely transformed reality. This mean when time is stretching, then distances and speed is doing the same. Or ? 



#172
Apr1512, 06:13 AM

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P: 16,485

Hi Bjarne, welcome back! It has been quite a while.
Not only are the paths approximately 30 m different, but that 30 m is a significant difference since there is a measurable amount of time dilation between the two paths. 



#173
Apr1512, 06:43 AM

P: 344

Let’s say ‘A' and 'B' live at the North Pole i the same highrise flat Hence speed and orbit distance of the Earth,  must be the same for both observers. Speed of the Earth must be the same, since both are at the same planet. The planet cannot be moving with 2 different speeds at the same time. Distance is also the same.. The measurement tape between the Sun and the Earth would prove for both A and B, that distance is the same. This means ‘A’ and ‘B’ cannot say that these factors are different. Hence still the conclusion mentioned above,  that both speed and distance transform proportional with time,  seems to be the most and only logical. 



#174
Apr1512, 07:22 AM

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P: 16,485

Also, since Earth is not a point like object in this scenario, the Earth does not have a single path through spacetime unless you define one specific point as the reference point. For instance, suppose one police officer is on the side of the road and another is driving on the road and suppose that they each measure the speed of the same car at the same time. One may get 100 km/h and the other may get 0 km/h. Both are valid measurements of the speed of the car, but in different frames. 



#175
Apr1512, 10:44 AM

P: 344

A and B is in this example only observers to the Earth orbiting the Sun. Both can see the radius / circumstance of the orbit of the Earth and both agree that the orbit of the Earth (as just defined) really is the same for both observers,  simple because both can observe this is how the tape measure proves it to be. So both must agree that distance / circumstance of the radius/orbit of the Earth, is observed from both observers perspective to be the same. A and B and the Earth is all exactly following the same orbit, and hence in the same frame. We could also say that also at the North Pole of the Sun there was a similar building, and from each floor a tape measure to the building / same floors at Earth's North Pole. A and B would agree that all tape measure was the same length. How can you then say they are in different frames / moving relative to each other? 



#176
Apr1512, 05:42 PM

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P: 16,485

Besides, haven't you been assuming that A and B are different reference frames and therefore claiming that the laws of physics are different in different reference frames? It seems strange for you to change your position on this topic after this long when it hasn't been a point of disagreement until now. 



#177
Apr1612, 02:33 PM

P: 344

I also understand that A and B could move with different speed,  but since there is a different option, (mentioned above) that also can be true  it seems there is a chose between two options. I mean, we know that both time and speed is comparable different factors, but the fact that we don't know whether also distance are affected or not, must mean the complete picture still is an open question. I mean I believe that the laws of nature are the same in all space time reference frames. I am just wondering which possible changing (with distance and speed) possible can ‘follow’ time dilation. And this is really what confuses me.  If that was clearer, I think it would be much easier to understand general relativity. 



#178
Apr1612, 02:56 PM

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That is why it is so important to specify the experiment you are using to perform a measurement. If you are sufficiently clear about what it is that you are measuring then you can get a complete picture of that scenario, it is only when you ask ambiguous questions that you get ambiguous answers. If you get into the habit of thinking about how you can measure a quantity of interest then you will generally be able to ask better questions and get better answers. 



#179
Apr1712, 12:57 AM

P: 344

But still relativity and the fact that space curves is really strange. I mean our immediate understanding is that space is nothing How can nothing curve? And how can we know whether or not something happens to distances too, and if so what happens to distances,  and to the ruler? You say that speed is different seen from the perspective of A and B. But if distance also is a proportional variant still speed would be different, but the whole concept would too. What I am trying to say,  we cannot cut a piece of “curved space” in cardboard and say ,  This is like it really and objective looks like, this is how we can imagine what we are talking about. The nature of "curvature of space" is a difficult to relate to, even in our fantasy. It doesn’t make it easier when we cannot know for sure whether distances and the ruler not is affected or could be. So how sure can we be that "the theory" "is it",  or whether there is more to come ? I think many do have a problem to accept what seems to be huge contradiction, for example that A and B is moving with different speed. Even though eveybody can see this is not the case, since they live in the same building at the Noth Pole. Is our understanding really complete? The opposite of a fact is falsehood, but the opposite of one profound truth may very well be another profound truth.” Niels Bohr 


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