Of course we could agree. We would know exactly why there is a difference between our clocks, and how big it is. No problem at all. Remember the GPS satellites? Their clocks are off due to speed, but we know this and can compensate for it. No problem at all.
Hans
The problem is that you ignore that because it is a fact that time is unique in all reference frames (due to both SR + GR) the law of gravity as you know it at the Earth can’t be the same at Mercury, or at the surface of the Sun, or at a satellite, or from the perspectives of an muon, - or in billion other reference frames , - but only apply for the Earth.
Each time you enter a new reference frame the gravity-constant "G" MUST change. – This should not surprise you, but is seems you are not aware.
Bjarne
Seen from the perspective of Mercury (or satellite muon etc…) either speed around the MW must be relative larger as on Earth, or distance round the MW relative shorter (proportional to the time dilation valid for the other traveler relative to the Earth) …
Hans
Well, yes, if they did not know about SR, and if they only measured distances by time, they would get a different result.
It is so simple Hans; there are no reasons to wrap it into unnecessary mysterious nonsense as necessary.
We are already dealing with the result of GR and SR, - which mean time is not the same.
We KNOW the clock on Mercury (etc..) ticks slower than here. This is starting point.
This give intelligent cow’s one option; distances MUST change proportional, also even you and RC obviously disagrees.
Here is the cow logic :
If we (the solar system) moves 100 second (around the MW) multiplied with 250 km/s (the orbit speed of the MW) – we have moved a distance = 25000 km.
The clock on Mercury counts the same event, - but the clock of Mercury is compared to the clock here “losing” time (let’s of simplicity reason say) it losing 1 second per 100 s.
Hence, - either Mercury must have moved faster around the MW as the Earth, - which we can ignore since then also light on Mercury must be faster as c.
The last (cow logic) option is the
distance Mercury have travelled around the MW is not 25000 km, - but only 99% of that distance, - which mean seen from the perspective of Mercury distances are shorter than at the Earth.
From any reference frame observe a event, for example a falling stone towards the Earth appears to happen with the same speed, even though time and distance not are the same.
(From a overall perspective there would be differences.)
Since everybody probably agree that ADG (acceleration due to gravity) (and all other kind of speed) seen from a Mercury perspective must be the same as on Earth, we can easy conclude that because distances in the MW not is the same (e.g.; for Mercury or a muon satellites etc) – the law of gravity (e.g; from the Milkyway) is also not the same.
Bjarne
It is also obviously that both larger orbit speed of the Sun, - and relative shorter radius of the MW, - in both cases would require stronger gravity to keep the Sun in orbit of the MW.
Hans
No. Absolutely not, and this is where you go wrong. I already mentioned it earlier: How time is from an observer's point of view has no influence on the sun, or the galaxy. The sun moves at the speed it does, and at the distance from the galactic centre it does, regardless of how somebody observes it.
I agree that the Sun and the reality on the Sun don’t care with the reality of a muon.
BUT the reality of the muon is ALSO TRUE.
The reality on the Earth is ALSO true.
The reality on Neptune is also true.
Since TIME and DISTANCES all these places are different, the law of gravity cannot be the same and therefore only valid in our own reference frame here on Earth, and not even other places in our own solar system, since motion definition not are the same.
To solve this we must at least change the gravity constant “G” each time we enter a new reference frame, and off course accept that distances always are changing proportional with time..
Think of this: If there is an absolute reference frame, then light must move according to that, right?
OK, we can test that (and we have). We are on a spaceship that travels through the galaxy at a speed of 250km/s. This spaceship is called Earth. In fact it also circles the sun at about 50km/s, so at times it travels about 300km/s. That is actually 1/1,000 c. So we can send an electromagnetic signal forward in our direction of movement, and measure its velocity (pretty simple, any reasonably competent radio amateur can do this). At the same time we can send a similar signal backwards, and measure its speed. Now, if EM waves were moving in an absolute reference frame, these two signals would be moving at different speeds: We would find that the forward signal moved at 0.999c and the backward signal moved at 1.001c, relative to us. This is quite a significant difference, and not difficult to measure.
First at all, my mission is
NOT to claim that the speed of light is changing in different ref-frames.
I agree "c" ALWAYS is 300.000 km/s
BUT light it is NOT traveling the same “”DISTANCE”” seen from an overall perspective.
Example;
You can measure the time a photon takes to reach the Moon, - let say 1 second.
Let’s now assume a muon also would measure that distance.
Now it would only take 1/10 of a s. for the photon to reach earth, seen form the muon-perspective.
Which natural means that the muon only can accept that the distance to the moon is 38,000 km away, - not 380,000 km , but since also time for the muon is 10 times slower the speed is still 300,000 km/s. So seen from a muon, the photon would reach a distance that is 3 million km/s per
our second.
As I say, that experiment has been made. In fact it is often done in universities as an exercise, so it has been done many, many times.
Guess what the result is, every time? The beams have exactly the same velocity.
Hans doesn’t matter how big a cake you have, - you can always share it in 300,000 pieces.
In the same way so soon time is “lost”, - distance is “winning” that “lost” back – which mean that the meter stick just gets proportional longer.
This doesn’t contradict ANYTHING - So what?
And this proves that there is no absolute reference frame.
No it doesn’t, it only proves that c is always 300,000 km/s in all reference frames.
This means that the time dilation factor is less than a microsecond per second. It makes absolutely no difference to out calculation of dark matter.
It shows something is wrong with some peoples understanding of relativity.
The laws of nature are not the same everywhere unless we are willing to change “G” all the time. Which in fact mean that the law of gravity (GM/r^2) not is the same by you feed as it is by your nose.
Don’t under-estimate this.