Are laws of nature really the same in all reference frames? [Archive]

Bjarne

Sep24-11, 03:10 PM

Let’ say; “A” can see and measure a stone falls to the earth let’s say 10 meter per 1 Earth-second.
“B” lives at Mercury and can see the same thing.
But “B” would do not see the exactly the same, because seen from “B’s” viewpoint time / distance is not the same as for “A”.
Let us say time at Mercury would tick half so fast compared to a clock at the Earth.

B would not agree it took the stone 1 second to move 10 meter – but have seen that the stone only was moving ½ -mercury second.
B will therefore also not see the stone falling 10 meter (as A saw it was falling in one Earth-second), but only that the stones was falling 5 Mercury-meter.

It must matter whether the stone was falling 10 meter (from A’s viewpoint) in a certain period, - or only 5 meter (B’s viewpoint), - So the problem is now, how can all laws of nature be the same for all observers.

If distances not are changing proportional the same rate as time, - A and B would not agree of the speed of light. Hence distance always must change proportional with time, right?.

Both A and B would therefore observe the “same” speed of the stone, - even though a process on Mercury would take relative double so long time measured with a Earth-clock.

It is simple math to understand that the speed of the stones anyway “seems” to be the “same” for both of A+B, - but in fact it is not, simply because time is different, and distance too.

For example if we on Earth (A) see a photon traveling from the Moon to the Earth, and it take 1 second, - the same event (according to the example) would seen from Mercury only take ½ second.
But because distance seen from the Mercury viewpoint (between the Moon and the Earth) is only the half compared to the earth viewpoint, - a photon would hence after one Mercury-second have travelled the double distance meassured 1 second, - with a Earth-clock.
Which mean that after 1 Mercury second the photon must have traveled 600,000 Earth-km measured in 2 second with a Earth clock. (Since 2 Mercury-second = 1 Earth-seconds)

Let’s return to the real world to make that more clear.
After 1 orbit of the Milkyway, a clock at Mercury (B) would REALLY have “lost” 6 years compared to a clock at the Earth (A).

The point is that when time/distance not is the same for A and B, how can the laws expressed by Newtonian and Keplerian equations be the same everywhere.

At least the gravity constant “G” seems to must be adjusted all the time, since distance is changing all the time.
Otherwise the result of gravity will not be right by our feeds compared to ours noses.
How can a person that not share ours time-distances share (our) gravity constant (G) ?

For example;
A person living at mercury and another at the Earth could never agree about the distance - our Sun - travels the MilkyWay, - simple because time is not the same these two places.
Evidence is atomic clock wouldn’t lie on these two planets.

When 2 such observers cannot agree about distances /radius/ diameter of the Milkyway, - how is it possible for both to use the excact same gravity equations ?

If we exaggerate and say that a clock on Mercury ticks half so fast as on Earth, - this would mean that after 1 orbit of the Milkyway we on earth have travels 377,000 Light years, but a person living at Mercury would say the orbit only is the half.

Therefore 2 such observers must also get two different result of how strong gravity of the Milky way really is ?

How can we then say that the laws of Newtonian/Keperian gravity are the same for both observers?

ghwellsjr

Sep24-11, 04:51 PM

When we say the same laws apply, we're talking about formulas but the numbers we plug into those formulas and the results can be
different on each planet, except everone will measure the same value for the speed of light.

Bjarne

Sep25-11, 02:43 AM

The Point is that the gravity constant "G" cannot be the same, at different planets (etc), even not the same by your feed as by your nose, since time and distance not are the same.

I you would live on Mercury you would also measure the "same" speed of every motion included light, but when you would compared such speeds, with how an observer on earth would see the same event these are not the same speed because distances of Mercury are shorter.

For example according to the example mentioned above, - after 1 Mercury-second the photon must have traveled 300,000 Mercury-km - but at the same time (period) it have travel 600,000 Earth-km
This is because 2 second measurement with a Earth clock is 1 Mercury-second measurement with a Mercury clock .

The observer on Mercury would hence say 600,000 Earth km is only 300,000 Mercury-km, and therefore in fact the photon must REALLY be moving double so far measured with a Earth-Meter stick compared to a Mercury meter-stick. ( but still the "same" speed/ distance seen from the perspective of both observers (without comparing).

This must mean that the observer plays the "primary role", - the Universe plays a secondary role.
Or that; - the Universe is like the eyes (clocks) see it, and not opposite.

ghwellsjr

Sep25-11, 09:21 AM

Bjarne

Sep25-11, 03:36 PM

You are right, the gravity constant, "g", is not the same on different planets, it's not even a constant on earth but changes slightly from location to location due to differences in the mass density of the earth at different locations and due to changes in elevation,
"g" is not part of the question.

but the gravitational constant, "G", does not change due to any local considerations.
I geuss you would write that.

I would suggest you look up the articles in wikipedia on these two "constants" if you want to learn about them.
But these issues have nothing to do with different laws at these different locations.
The laws are the same, but but G can’t be, - it seems to mathematical impossible.

You have expressed concerns about the effects of gravity on measurements which is a very complex subject and requires an understanding of General Relativity.

I can't see why it should be "so complex"
The essence is 2 clocks are ticking differently, -; this is all we so fare need to know.
We have 2 clock and 2 different observers. One observer could be you, - the other a man and a clock on Mercury.
How long distance would the Sun travel seen from the perspective of these two observers (in 377,000 years / orbit the MW) - and wich distance is the “right distance” ?.

After 1 orbit of the Milkyway (MW) these 2 observers could impossible agree about what the radius / diameter circumference or the MW is.
If time is different and speed of light must be the "same” for all observers - left is only that distances not can be the same.
It seems to me to be a simple mathematic necessity.
So why make this simple event more difficult as is possible can be?

I would suggest that you focus first on understanding Special Relativity because that is so much easier and I think that once you can see how different observers traveling with respect to each other (no gravity involved) can both measure the speed of light to be the same, even though they each measure the other one's clocks and rulers to be different than their own. That, after all, is what this forum is for, understanding relativity.

I believe I know a lot about it, - but still we only dealing with simple facts; - 2 observers/clocks ticking with different rate cannot agree how the distance is of the MW.

Doesn’t matter whether the reason to the different time rate is GR or SR, - distances cannot be the same, and hence the Keplerian and Newtonian laws of gravity , - yes are the same, - but G cannot be, - since distances is the main factor of gravity.

In the meantime, I'd like you to think about your comment regarding seeing a photon traveling from the moon to the earth and I would like to ask you, how can anyone see a photon?

Don't take it literary..
The principle is what count.
When time not is the same distances can also not be, - and hence "G" can also not be.
On the one hand speed seems to be the same for both observer, - on the other hand, - so soon you compare how the distance difference (measured by 2 different relativistic observers) is , the observer with the slow clock must measure a shorter comparable distance, - in a certain period common for both.

So on the one hand, any observer will see (measure) light (a photon) travels 300,000 km/h, -but only because of distances not can be the same, - on the other hand that picture is wrong so soon you compare what have happen in a certain period.

I think we shall be carefully not to use relativity as a junkyard for things that not make sence, and allow export to such junkyard so soon something is “so complex” that probably nobody has understood it.

So fare I see this question, there MUST be a simple logical mathematical explanation, doesn’t, matter whether the clock ticks different due to gravity (GR) or fast motion (SR)..

“If you can't explain it simply, you don't understand it well enough”.
Albert Einstein

ghwellsjr

Sep25-11, 09:34 PM

You have stated that you believe you know a lot about SR but yet you have said:
Hence distance always must change proportional with time, right?
But while time dilates (gets longer), length contracts (gets shorter) so it's not proportional, it's an inverse relationship. Furthermore, it's only distance in certain directions that is contracted. How do you explain this?

bobc2

Sep25-11, 09:39 PM

Bjarne,

Why not try approaching it with a simpler comparison. Have A and B initially together in the same inertial reference system (on earth, out in space away from everything..., you pick it), and each is furnished with a laboratory on separate identical space ships. They can perform any of the basic experiments historically used to describe our physical laws.

Now, they take off in opposite directions at relativistic speeds (it really doesn't matter whether they go at the same speeds relative to the original rest frame or not). Each one performs a number of different experiments and then return to their original rest frame to compare their results. Their results will be the same.

So, yes--the laws of physics are the same in all inertial reference frames.

Also, if you have them land on distant planets (ignoring the inhabitable environments) and perform experiments, they will come up with the same results such as Newton's law of gravitation; they will find that masses attract with a force inversely proportional to r^2 with the same Newton gravitation constant, G. They will both find F = ma. The ratio of e/m will be the same, etc.

They probably won't have any more luck with experiments aimed at unification of general relativity and quantum mechanics than anyone has had so far.

Bjarne

Sep26-11, 12:52 AM

You have stated that you believe you know a lot about SR but yet you have said:

But while time dilates (gets longer), length contracts (gets shorter) so it's not proportional, it's an inverse relationship. Furthermore, it's only distance in certain directions that is contracted. How do you explain this?

Once again, there are no reasons to limit this question to Special Relativity.
The fact is that a clock on board on Mercury really is ticking slower as one at Earth.
Hence an observer (a clock) on Mercury must have "lost" 6 years due to GENERAL relativity, (compared to a clock at the Earth) after one MW orbit of the solar system.

This give you 2 simple possibilities

1.)
An observer on Mercury must have seen the Sun (orbit the MW) faster as an observer at the Earth have observed the same event (faster as the 250 km/s - the speed we on Earth observe the Solar system (the Sun) is orbiting the MW) - I don't believe you can sell that to anyone because that would in the end violate that “c” always is the same.

2.)
That distance is not the same for both observers. - This is logic math since an observer on Mercury would see the Sun complete 1 orbit of the MW in less time (6 years less) as seen from the Earth.

ghwellsjr

Sep26-11, 02:24 AM

Once again, there are no reasons to limit this question to Special Relativity.
The title of your thread is "Are laws of nature really the same in all reference frames?". You are referring to Einstein's first postulate for Special Relativity and it is true only for inertial reference frames. It is not true in accelerating frames which is what you have on the surface of planets and which is handled by General Relativity.

You have stated:
Doesn’t matter whether the reason to the different time rate is GR or SR,

...doesn’t, matter whether the clock ticks different due to gravity (GR) or fast motion (SR)..

But it does matter because in SR, time dilation is reciprocal and in GR it is not. It's only the reference frames in SR where the laws of nature are the same. Under the influence of different gravity fields, the laws are different. To put it another way: a scientist inside a box in any inertial frame cannot determine which kind of an inertial frame he is in, they are all the same due to the reciprocal nature of time dilation (among other things). But if you put him in an accelerating box, or in a box on the surface of a planet, he will be able to tell the difference between the boxes because they can have different accelerations and the time dilation is not reciprocal between two boxes on different planets (or on the same planet at different elevations).

A.T.

Sep26-11, 04:18 AM

Under the influence of different gravity fields, the laws are different.
It's not that they are different, but rather that in GR inertial frames don't extend infinitely. So in GR the equivalence of inertial frames only applies to local experiments.

zonde

Sep26-11, 08:49 AM

It's not that they are different, but rather that in GR inertial frames don't extend infinitely. So in GR the equivalence of inertial frames only applies to local experiments.
Under relativity inertial frames are constructed so that physical laws stay the same.

Now you say that inertial frames are not extendable globally. To me this statement seems equivalent to the statement that physical laws are not the same globally.

ghwellsjr

Sep26-11, 09:54 AM

It's not that they are different, but rather that in GR inertial frames don't extend infinitely. So in GR the equivalence of inertial frames only applies to local experiments.
I thought I made it very clear in my post that I was addressing the non-inertial frames on the surfaces of planets which is what Bjarne is using in his argument against Einstein's first postulate of Special Relativity. How does your post help Bjarne?

ghwellsjr

Sep26-11, 09:58 AM

Under relativity inertial frames are constructed so that physical laws stay the same.
You've got it backwards: Under relativity, physical laws are constructed so that they stay the same in different inertial frames, if they are not already that way.

Bjarne

Sep26-11, 03:34 PM

The title of your thread is "Are laws of nature really the same in all reference frames?".
You are referring to Einstein's first postulate for Special Relativity and it is true only for inertial reference frames.
It is not true in accelerating frames which is what you have on the surface of planets and which is handled by General Relativity.

Now you confuse me.
My concern is mainly if ALL laws of nature (equations) ALWAYS the same for all observer.
OR is (for example) gravity - and here I mean G (the gravity constant) an exception´.
Above you wrote; "G", does not change due to any local considerations"
I am now not sure what you really mean, - Is "G" ALWAY constant. - Yes or no ?

But it does matter because in SR, time dilation is reciprocal and in GR it is not. It's only the reference frames in SR where the laws of nature are the same. Under the influence of different gravity fields, the laws are different.
So is it true that G is not the same by your feed as by you nose ?
Yes of no ?
If the answer is no, then try to explain how 2 observers located in different space-time (caused by gravity) obviously not would be able to agree how long time one MW orbit take, - and therefore logical also not agree what the radius of the MW really is , - and therefore also not agree what G really is ? - What I mean is; - there are no common answers. G cannot be a constant - OR WHAT ?

To put it another way: a scientist inside a box in any inertial frame cannot determine which kind of an inertial frame he is in, they are all the same due to the reciprocal nature of time dilation (among other things). But if you put him in an accelerating box, or in a box on the surface of a planet, he will be able to tell the difference between the boxes because they can have different accelerations and the time dilation is not reciprocal between two boxes on different planets (or on the same planet at different elevations).
I prefer first to finish the easy part (the GR part) before confusion the discussion with SR.
So fare according to this context I believe a clock (observer) on Mercury don't care why time ticks slower, - exactly as we don’t care why our clock is slower as a clock on Neptune, I mean how much time dilation is due to GR and SR - the point will still be is G ALWAYS constant ?

Yes or no.

A.T.

Sep26-11, 04:41 PM

Now you say that inertial frames are not extendable globally.

Yes, not in curved space time.
To me this statement seems equivalent to the statement that physical laws are not the same globally.
No, this not equivalent. You can go anywhere and perform a local experiment in an inertial frame there, and then you get the same results. That is what "physical laws are the same globally" means.

JordanL

Sep26-11, 04:49 PM

Yes, not in curved space time.

No, this not equivalent. You can go anywhere and perform a local experiment in an inertial frame there, and then you get the same results. That is what "physical laws are the same globally" means.

In other words, globally there is local consistency, at the cost of locally there being global consistency?

EDIT:

Actually, consistency is the wrong word. What I suppose I meant was that globally there is local continuity of physical laws, instead of locally there being global continuity of physical laws. That's, as far as I understand it, rather the entire point of SR.

ghwellsjr

Sep26-11, 04:51 PM

Now you confuse me.
It's no wonder you are confused when you don't read my posts. Let me reiterate:
My concern is mainly if ALL laws of nature (equations) ALWAYS the same for all observer.
The title of your thread is "Are laws of nature really the same in all reference frames?". You are referring to Einstein's first postulate for Special Relativity and it is true only for inertial reference frames. It is not true in accelerating frames which is what you have on the surface of planets and which is handled by General Relativity.

OR is (for example) gravity - and here I mean G (the gravity constant) an exception´.
the gravity constant, "g"
...
the gravitational constant, "G"

Above you wrote; "G", does not change due to any local considerations"
I am now not sure what you really mean, - Is "G" ALWAY constant. - Yes or no ?
the gravitational constant, "G", does not change due to any local considerations.

So is it true that G is not the same by your feed as by you nose ?
Yes of no ?
the gravity constant, "g", is not the same on different planets, it's not even a constant on earth but changes slightly from location to location due to differences in the mass density of the earth at different locations and due to changes in elevation

If the answer is no, then try to explain how 2 observers located in different space-time (caused by gravity) obviously not would be able to agree how long time one MW orbit take, - and therefore logical also not agree what the radius of the MW really is , - and therefore also not agree what G really is ? - What I mean is; - there are no common answers. G cannot be a constant - OR WHAT ?
The effect of different gravity constants "g" on different planets will not cause scientists on those planets to arrive at different values of the gravitational constant "G". We have the same problem here on earth where g varies but you have to take that into consideration when calculating constants that are independent of your local situation. The value of "G" is not dependent on any particular local circumstance.

I prefer first to finish the easy part (the GR part) before confusion the discussion with SR.
So fare according to this context I believe a clock (observer) on Mercury don't care why time ticks slower, - exactly as we don’t care why our clock is slower as a clock on Neptune, I mean how much time dilation is due to GR and SR - the point will still be is G ALWAYS constant ?

Yes or no.
I have said G is constant, g is not constant.

Is the reason that you think GR is easier than SR because things like time dilation and length contraction are not reciprocal?

Bjarne

Sep27-11, 02:50 AM

I have said G is constant,

We did not got to the point. I mean we have a missing link here.
Let us forget everything about SR and only consider the consequence of GR and hence time dilation caused by gravity for 2 observers orbiting the MilkyWay.

These 2 observers, one on the Earth and one on Mercury measure the orbit of the Sun round the Milkyway, by multiplying time and speed.

Now...
The observer on Earth will claim 1 orbit of the MilkyWay took exactly 1,19E16 Earth-second.
But the observer on Mercury would say that the orbit toke 194,000,000 s (6 earth-year) less according to his clock.

This time difference is only caused by GR...

http://www.science27.com/forum/td2.jpg
Time dilation on Mercury relative to the Earth = 0,000000016 s. ( due to GR)
Time per year = 60*60*24*365 = 31,153,000 s.
Orbit of the MW = 314,000 Light Years (at the periphery).
Earth-Time to orbit the MW (250 km/s) = 377,000,000 years. (at the periphery).
Total Earth-second to 1 MW orbit = 377,000,000 * 365*24*60*60 = 1,19E16 seconds.
Lost" of Mercury-time in years = 1,19E16 s. * 0,000000016 s. = 194,000,000 s.

So after 1 MikyWay orbit the clock on Mercury have "lost" 194,000,000 seconds ( = 6 earth-years) relative to a clock on the Earth.

Now here is the simple question.
Is the circumference of the Milkyway the same for these 2 observers, so long we only speak about the mentioned time dilation due to GR ?

If the answer is yes, - how is this possible when the rate of time not is the same ?

This only can mean a mathematical meltdown, right ?

I mean since speed multiplied with the time one orbit takes must result to = Distances.

The only possible outcome I can see is that distance not can be the same, - so how can the law of gravity / the equations (and G) be the same?

I don’t understand why it is necessary to complicate that simple question - more as necessary, - .

Distances cannot be the same so far I can understand this simple logic , - this is to me the only logical answer, - and this must mean G have a problem.

It is not enough to say this is wrong, I must know why it should be wrong.

Is the time rate on Mercury, - the way a clock would count it, - only an illusion ?
Is speed seen from a Mercury perspective different?
Is Mass seen from a Mercury perspective not the same as on Earth
Or WHAT , - if not distance ?

JordanL

Sep27-11, 03:29 AM

All this example shows is that the same measurement if we attempt it from different reference frames will yield different results, which is rather the point of them, isn't it? Distances, speeds and times are not absolute, they are relative... which is why it is called relativity. You cannot say the distance is shorter, because that has no meaning. It only appears so from particular reference frames.

Bjarne

Sep27-11, 03:33 AM

zonde

Sep27-11, 06:13 AM

It is not enough to say this is wrong, I must know why it should be wrong.

Is the time rate on Mercury, - the way a clock would count it, - only an illusion ?
Is speed seen from a Mercury perspective different?
Is Mass seen from a Mercury perspective not the same as on Earth
Or WHAT , - if not distance ?

It should be that G is numerically different.
G is global constant. And if it is global constant then locally it should be different at different gravitational potentials due to time dilation.
Or maybe it is more reasonable to find out if it's GM product that's different or not and then talk about G and M separately.

Gravitational time dilation should be real effect as you can observe it in static setup.
I suppose that observations are consistent with distances being the same.

Anyways question seems quite interesting.

EDIT: Ah, but certainly speed is different from Mercury perspective due to time dilation. So the question is if it is enough to make picture consistent.

zonde

Sep27-11, 06:22 AM

No, this not equivalent. You can go anywhere and perform a local experiment in an inertial frame there, and then you get the same results. That is what "physical laws are the same globally" means.
If you perform Cavendish experiment at different gravitational potentials will it give the same results?
Hmm, only it is performed in non-inertial frame as almost all of the physics experiments. Then maybe discussion about inertial reference frames is not very useful?

ghwellsjr

Sep27-11, 03:33 PM

We did not got to the point. I mean we have a missing link here.
Let us forget everything about SR and only consider the consequence of GR and hence time dilation caused by gravity for 2 observers orbiting the MilkyWay.
OK, will do.
These 2 observers, one on the Earth and one on Mercury measure the orbit of the Sun round the Milkyway, by multiplying time and speed.

Now...
The observer on Earth will claim 1 orbit of the MilkyWay took exactly 1,19E16 Earth-second.
But the observer on Mercury would say that the orbit toke 194,000,000 s (6 earth-year) less according to his clock.

This time difference is only caused by GR...

http://www.science27.com/forum/td2.jpg
Time dilation on Mercury relative to the Earth = 0,000000016 s. ( due to GR)
Time per year = 60*60*24*365 = 31,153,000 s.
Orbit of the MW = 314,000 Light Years (at the periphery).
Earth-Time to orbit the MW (250 km/s) = 377,000,000 years. (at the periphery).
Total Earth-second to 1 MW orbit = 377,000,000 * 365*24*60*60 = 1,19E16 seconds.
Lost" of Mercury-time in years = 1,19E16 s. * 0,000000016 s. = 194,000,000 s.

So after 1 MikyWay orbit the clock on Mercury have "lost" 194,000,000 seconds ( = 6 earth-years) relative to a clock on the Earth.

Now here is the simple question.
Is the circumference of the Milkyway the same for these 2 observers, so long we only speak about the mentioned time dilation due to GR ?
No.
If the answer is yes, - how is this possible when the rate of time not is the same ?

This only can mean a mathematical meltdown, right ?
The answer was no, so these don't need to be answered.
I mean since speed multiplied with the time one orbit takes must result to = Distances.

The only possible outcome I can see is that distance not can be the same, - so how can the law of gravity / the equations (and G) be the same?
They're not.
I don’t understand why it is necessary to complicate that simple question - more as necessary, - .

Distances cannot be the same so far I can understand this simple logic , - this is to me the only logical answer, - and this must mean G have a problem.

It is not enough to say this is wrong, I must know why it should be wrong.

Is the time rate on Mercury, - the way a clock would count it, - only an illusion ?
No.

Is speed seen from a Mercury perspective different?
Yes.

Is Mass seen from a Mercury perspective not the same as on Earth
It's not the same.

Or WHAT , - if not distance ?
Everything is different.

Bjarne

Sep28-11, 01:18 AM

Bjarne
Is speed seen from a Mercury perspective different??
Ghwellsjr
Yes
Bjarne
So when we measure the speed of the Sun to travel 250 km/s, - an observer on Mercury (or on the surface of the Sun) would measure it to be a little more than this? - is this what you saying ? If so Why ?

Now imaging the same 2 observers measure the speed of a photon, we on Earth would measure it to be; “c” - would an observer on Mercury also measure that to be faster?

Can the speed difference, - significant or almost completely solve the "mathematical meltdown" described above, - or is this value almost irrelevant in this context?

Does the speed difference, - have anything to do with the cause of the the "mathematical meltdown" described above ?

Bjarne
Is Mass seen from a Mercury perspective not the same as on Earth
Ghwellsjr
It's not the same.
Bjarne
I mean is let’s say the mass of the Sun is exactly 2E30 Kg.
Are you saying an observer on Mercury not would agree ?
If so, - why?
What about the mass of the Milkyway? - would the 2 observers also disagree ?

Can the mass difference significant contribute to solve the "mathematical meltdown" described above, - or is it almost irrelevant in this context?

Does the mass difference, - have anything to do with the cause of the the "mathematical meltdown" described above ?

Ghwellsjr
Everything is different
What more as (time) speed and mass is different ?

zonde

Sep28-11, 03:57 AM

Let's try to put it down in less chaotic way.

As two observers observe the same sequence of physical events the only thing they can change is their representation of this sequence i.e. coordinate system.
Relative time dilation between two observers is real as we can establish delay in sequence of signals with static distance. So first of all we have different scale for time dimension for two observers.
Distances should be the same as speed of light locally is changing in a way that is consistent with unchanging distances.
Result of this is that orbital speed around MW for observer on Mercury is faster by the same factor as time is delayed.

Now we calculate GM-product μ using the same formula for both observers.
v_m^2=\frac{\mu_m}{r}
v_e^2=\frac{\mu_e}{r}
As speed is faster for Mercury observer but distances are the same for both observers we have that GM-product is bigger by that speed scaling factor squared. As GM-product have dimensions of time squared in denominator it seems that we have consistent picture so far.

Now if we assume that G is the same for both observers then mass unit for Mercury observer should be smaller by speed scaling factor squared.
This seems plausible as lowering mass in gravitational potential should convert part of the rest mass into kinetic energy.

Does this reasoning seems fine?

Bjarne

Sep28-11, 01:50 PM

ghwellsjr

Sep28-11, 03:31 PM

Bjarne
So when we measure the speed of the Sun to travel 250 km/s, - an observer on Mercury (or on the surface of the Sun) would measure it to be a little more than this? - is this what you saying ? If so Why ?
Someone on the surface of another planet with a different mass than Earth could measure it a little or a lot more or less than ours because their rulers are different lengths than we would if they're based on the same standards that ours are based on and this is because of your stipulation:
Let us forget everything about SR and only consider the consequence of GR and hence time dilation caused by gravity for 2 observers orbiting the MilkyWay.

Now imaging the same 2 observers measure the speed of a photon, we on Earth would measure it to be; “c” - would an observer on Mercury also measure that to be faster?
No, everyone measures the speed of light to be "c".

Can the speed difference, - significant or almost completely solve the "mathematical meltdown" described above, - or is this value almost irrelevant in this context?

Does the speed difference, - have anything to do with the cause of the the "mathematical meltdown" described above ?

I thought your issue about a mathematical meltdown would only apply if I answered "yes" to your previous question but since I answered "no", I don't know what you mean by a mathematical meltdown and again, everyone measures the speed of light to be exactly the same value "c" so there's no mathematical meltdown that I can see.

Bjarne
I mean is let’s say the mass of the Sun is exactly 2E30 Kg.
Are you saying an observer on Mercury not would agree ?
If so, - why?

Yes, he would say the sun had a different mass because all his measuring devices are different due to the difference in gravity between the Earth and Mercury.

What about the mass of the Milkyway? - would the 2 observers also disagree ?

Yes, they would disagree about everything.

Can the mass difference significant contribute to solve the "mathematical meltdown" described above, - or is it almost irrelevant in this context?

Does the mass difference, - have anything to do with the cause of the the "mathematical meltdown" described above ?

You're going to have to explain to me what this mathematical meltdown is. I didn't know such a thing could be possible.

What more as (time) speed and mass is different ?
Everything measureable and observable is different:
Temperatures
Colors
Ages
Sizes
Shapes
Frequencies
Pressures
Forces
Directions
I'm having a hard time trying to think of something that wouldn't be put on the list.

Bjarne

Sep28-11, 04:16 PM

You're going to have to explain to me what this mathematical meltdown is. I didn't know such a thing could be possible.
.

Let's simplify the scenario
Ignore that the observers are orbiting different planet with different mass.
And ignore the influence of SR

Let's say the 2 clocks are orbiting the Sun without the planets Mercury and the Earth.
One clock (A) 50 billion km away and the other (B) 150 km away.
So the problem and the calculation shown above are still the same.

Both observers would see the Sun complete 1 orbit of the Milkyway at the same time.
But observer A would have "lost" 194,000,000 s. relative to B

If the orbit speed of the Sun = 250 km/s -for both observers / clocks, - observer A would calculate a shorter orbit of he Sun than B would - That would violate the laws of gravity.

If the speed not was the same for both – (first I must ask WHY should it not ?)
That would also violate the laws of gravity.
And it would rise the question; how can the Sun move with 2 different speed ?

So WHY can these 2 observers impossible agree about which measurement of the orbit of the Sun is the correct one?

Passionflower

Sep28-11, 04:49 PM

their rulers are different lengths than we would if they're based on the same standards that ours are based on and this is because of your stipulation:
...
No, everyone measures the speed of light to be "c".

You seem to be making a lot of definite statements, could you back them up?

Perhaps you would like to explain a bit more by what you mean, for instance our meter is defined by the speed of light, however you claim the speed of light is everywhere the same even in locations with a different gravitational potential. But you at the same time claim that rulers are different lengths.

JordanL

Sep28-11, 05:01 PM

Let's simplify the scenario
Ignore that the observers are orbiting different planet with different mass.
And ignore the influence of SR

Let's say the 2 clocks are orbiting the Sun without the planets Mercury and the Earth.
One clock (A) 50 billion km away and the other (B) 150 km away.
So the problem and the calculation shown above are still the same.

Both observers would see the Sun complete 1 orbit of the Milkyway at the same time.
But observer A would have "lost" 194,000,000 s. relative to B

If the orbit speed of the Sun = 250 km/s -for both observers / clocks, - observer A would calculate a shorter orbit of he Sun than B would - That would violate the laws of gravity.

If the speed not was the same for both – (first I must ask WHY should it not ?)
That would also violate the laws of gravity.
And it would rise the question; how can the Sun move with 2 different speed ?

So WHY can these 2 observers impossible agree about which measurement of the orbit of the Sun is the correct one?

Speed is a measure of distance over time. As both distance AND time are different in the two frames, the speed is different as well. (Also, a minor point, but I believe you mean velocity. Speed is different from velocity in physics.)

ghwellsjr

Sep28-11, 05:35 PM

Let's simplify the scenario
Ignore that the observers are orbiting different planet with different mass.
And ignore the influence of SR

Let's say the 2 clocks are orbiting the Sun without the planets Mercury and the Earth.
One clock (A) 50 billion km away and the other (B) 150 km away.
So the problem and the calculation shown above are still the same.
Still the same? From the beginning of this thread, you have been talking about observers on the surface of solar system planets (non-inertial) and so I wondered how you could think orbiting at different distances from the sun (inertial) could be the same. That prompted me to go back and look at your post #18 and now I understand what's going on here.

I'm afraid I have made a big mistake. When I was getting ready to study your post #18, I went to the Thread Tools and used the "Show Printable Version" to print out your thread. The printable version did not print your graphic but instead showed the URL from which it was taken. So I go to www.science27.com and I see that you are promoting your own personal theory in violation of the forum rules.

Bye, bye.

zonde

Sep28-11, 11:08 PM

I have not fine-read the last post (I have not much time yet), but the first that strike me is;

How can our Sun move with 2 different speed? - Something must be wrong.
Of course our Sun can't move at two different orbital speeds. But our measurements of that speed can be different.

First sentence in my explanation was:
"As two observers observe the same sequence of physical events the only thing they can change is their representation of this sequence i.e. coordinate system."
If you would use two clocks that tick at different speeds then with the same measuring rods your speed measurements will be different.

The next is that; even if it did, “what would be causing that” ?
It would also mean that the 2 observer not could agree about the strength of gravity of the Milkyway.

Remember the point is only; the motion of the Sun , - and how two different space-time observers can agree about that.

Bjarne

Sep29-11, 01:28 AM

Still the same? From the beginning of this thread, you have been talking about observers on the surface of solar system planets (non-inertial) and so I wondered how you could think orbiting at different distances from the sun (inertial) could be the same. That prompted me to go back and look at your post #18 and now I understand what's going on here.

I'm afraid I have made a big mistake. When I was getting ready to study your post #18, I went to the Thread Tools and used the "Show Printable Version" to print out your thread. The printable version did not print your graphic but instead showed the URL from which it was taken. So I go to www.science27.com and I see that you are promoting your own personal theory in violation of the forum rules.

Bye, bye.

I am NOT promoting my own personal theory in one single word.
I am using my own webhotel to load graphics, and as you self wrote it was accidentally that you at all discovered that I had personally websites / theory.
It sounds to me that you say; that only people that not have a personally theory are allowed to ask (skeptical) questions to science, - at this forum.

I asked the question because I want to understand nature, as well as I want to understand my own theory.
Is that really "forbidden" ?

When "my thought" that something must be obvious wrong, with the way different observers understand the orbits (speed/distance) of the sun , - you had have the change to lead me back to the right track, and you still have. But I am afraid such track even not exist. But I am not sure.

Bjarne

Sep29-11, 01:49 AM

Of course our Sun can't move at two different orbital speeds. But our measurements of that speed can be different.

First sentence in my explanation was:
"As two observers observe the same sequence of physical events the only thing they can change is their representation of this sequence i.e. coordinate system."
If you would use two clocks that tick at different speeds then with the same measuring rods your speed measurements will be different.

First at all I want to say that we can simplify the scenario even more, to avoid confusion.

Because we could say that the 2 clocks are following the Sun’s orbit around the Milkyway.
(Technical we could say the orbiting clocks have devices (small rockets) on board to counteract the gravity from the Sun.

Seen from our perspective both the Sun and the two clocks (all 3 objects) are therefore orbiting the Milkyway in the excact same radius to the center of the Milkyway) .

The one clock is 50 billion km. behind the Sun, and the other 150 billion km.

This should eliminate he last confusion according to the Special relativity influence, since all relative speed now are the same.

Back to yours suggestion;
As I understand you now I can only understand it like that speed not is comparable “the same” – which then also mean that also comparable distances not can be the same, - right?

I think we have a serious mathematical problem here and wonder how such a simple obviously unsolved mystery possible can have existed the last 100 years without any explanation. ?

I mean the math should be simple.
We know the 2 relative time rates and I believe we also know the speed, - the logical result (so far I can understand it) hence should be that B impossible can travels the same distance, simple because speed multiplied with time = distance.

I mean how difficult can that really be ?

zonde

Sep29-11, 06:43 AM

First at all I want to say that we can simplify the scenario even more, to avoid confusion.

Because we could say that the 2 clocks are following the Sun’s orbit around the Milkyway.
(Technical we could say the orbiting clocks have devices (small rockets) on board to counteract the gravity from the Sun.

Seen from our perspective both the Sun and the two clocks (all 3 objects) are therefore orbiting the Milkyway in the excact same radius to the center of the Milkyway) .

The one clock is 50 billion km. behind the Sun, and the other 150 billion km.

This should eliminate he last confusion according to the Special relativity influence, since all relative speed now are the same.

Back to yours suggestion;
As I understand you now I can only understand it like that speed not is comparable “the same” – which then also mean that also comparable distances not can be the same, - right?

I think we have a serious mathematical problem here and wonder how such a simple obviously unsolved mystery possible can have existed the last 100 years without any explanation. ?

I mean the math should be simple.
We know the 2 relative time rates and I believe we also know the speed
We don't know the speed. We measure speed i.e we make some observations and then come up with some number.
Two observers will come up with different numbers from their respective observations. Just because these numbers are different doesn't mean that they live in different worlds. It just means that they use different units for their measurements. In particular case it is time unit that is different.

- the logical result (so far I can understand it) hence should be that B impossible can travels the same distance, simple because speed multiplied with time = distance.

I mean how difficult can that really be ?

Bjarne

Sep29-11, 02:51 PM

We don't know the speed. We measure speed i.e we make some observations and then come up with some number.
Two observers will come up with different numbers from their respective observations. Just because these numbers are different doesn't mean that they live in different worlds. It just means that they use different units for their measurements. In particular case it is time unit that is different.

If speed is different for the 2 observers, - classic laws of gravity would not (as I see it) be the same. - I mean how could these?

Or the gravity of the galaxy would not be the same for the 2 observers. That too would sound absurd.

What should possible cause two different speed, or different influence of gravity?

darkhorror

Sep30-11, 12:50 AM

If speed is different for the 2 observers, - classic laws of gravity would not (as I see it) be the same. - I mean how could these?

Or the gravity of the galaxy would not be the same for the 2 observers. That too would sound absurd.

What should possible cause two different speed, or different influence of gravity?

Lets say we are both on earth. I decide that a foot is 24 inches. You come along and ask for 2 feet of lumber. I cut to me what is 2 feet of lumber. Now to you a foot is 12 inches. You measure the lumber i just cut(with a foot being 12 inches), and you tell me it's too long and that it's 4 feet. I say no it's clearly 2 feet. Is the lumber really 4 feet and 2 feet at the same time? Yes it just depends on which foot measurement you use.

That isn't really a good example but it might help you see the point people are trying to make.

Bjarne

Sep30-11, 02:05 AM

Lets say we are both on earth. I decide that a foot is 24 inches. You come along and ask for 2 feet of lumber. I cut to me what is 2 feet of lumber. Now to you a foot is 12 inches. You measure the lumber i just cut(with a foot being 12 inches), and you tell me it's too long and that it's 4 feet. I say no it's clearly 2 feet. Is the lumber really 4 feet and 2 feet at the same time? Yes it just depends on which foot measurement you use.

That isn't really a good example but it might help you see the point people are trying to make.

So what you are saying is; if observer A and B would compare their meter sticks, the size must be different and therefore they also measure different distance?

So when time shrink, the meter stick extend?
And this explains that the math is correctm, - for both, - when 1 orbit of the MilkyWay is completed?

JordanL

Sep30-11, 04:50 AM

Bjarne

Sep30-11, 03:23 PM

Ah, alright. I just went back and reread how this thread began:

Bjarne: The answer is yes, the laws of nature would be found the same in all reference frames. However, the measurements taken of your surroundings, and thus your inputs into your equations, would be different. Because the measurement is different, your receive a different answer for your reference frame. However, because of your different reference frame, you received the right answer for you.

That was actually the point of the idea... that we had spent hundreds of years making equations and laws that only worked for Earth and our reference frame. GR and SR together were a set of rules that would give the right answer even if your measurements turned out different.

Try to be more exact.
We can very simple multiply speed and time and get the result = distance

Why can a "stranger" living in a different space-time (caused by GR) - according to the mentioned example, not do the exact same as we can ?

Why seems reality to be limit to a certain place on Earth. ?

WHAT exactly should a observer that not shares our time-rate then exactly do if he also want to make such speed * time calculations. ?

How are the rules for him?

Shall he just pretend he is moving faster as us, even though there are absolutely no reason to believe so ?

Is his meter sticks really longer than ours and distance therefore shorter for him?

WHAT exactly would you tell him?.

I mean not only words, but how are the rules / law exactly according to the examples I have mentioned?

How can such relative huge dilemma have surveyed in 100 years without anyone have wonder; what happens here?

I believe we have no clue how to explain that, right ?

This could be a bad sign.

russ_watters

Sep30-11, 03:32 PM

Bjarne

Sep30-11, 04:01 PM

The rules for another observer are exactly the same as for us. No pretending needed and no issue of who's measurement is "really" right - the whole point of Relativity is that both measurements are right.
According to last the mentioned exsample;

We know observer B’s clock is "losing" 6 earth-years relative to A’s clock. after one Milkyway orbit,
We also know that both clocks’ orbits the milkyway (MW) the same radius from the center of the MW.
And we know that both clocks complete an orbit of the MW in the same period.
Both clocks follows the Sun, - The only difference that counts is that B is closer to the Sun as A is , hence B is stronger affected by gravity from the Sun as A, - ( none of the clocks are orbiting the Sun, and none on board of a planet).

Questions
So is the speed of observer B the same as the speed of A( 250 km/s) ?
Does both observer A and B agree the speed is the same ?
Are A's and B's meter-stick comparable the same ?
Will both observer A and B agree about how long the circumstance of the Milkyway is ?
If both observer A and B agree that speed and distance is the same for both (but the time rate not) , how can it be that speed multiplied with time not would show the same result for observer B as it would for observer A ?

It seems to be that we say that our reality is more real than these”out there”
I mean this is also how science was in the Middle Ages, - something must have change since.
I am not satisfied with words, but to know WHAT exactly is going on here.

darkhorror

Sep30-11, 05:39 PM

russ_watters

Sep30-11, 05:47 PM

*So is the speed of observer B the same as the speed of A( 250 km/s) ? As you must know, this question is incomplete. Speed is measured between two points and you've only listed one point for each of the two speeds you are looking for. You need to specify what you are measuring the speeds relative to and who is doing the measuring. Don't bother fixing this question, though - I'm not interested in playing games with made-up/impossible numbers and it really isn't important to your original point. Does both observer A and B agree the speed is the same ? Maybe. But again, this isn't really all that important. What is important is this:

If both observers faithfully follow the principle of Relativity as stated in your title and, as it requires, ensure they are clear and consistent about what frames of reference they are doing the measurements from, or measure from one and properly transform to the other, they will agree on what is happening. Are A's and B's meter-stick comparable the same ? Again: If they follow the principle of Relativity and are clear on the choices of reference frames (and the definition of a "meter") they most certainly will. They might say: "From here, your meter looks smaller than mine, but since I know our relative speeds, I calculate that if I was to go over to you and measure your meter it would be the same as mine." Will both observer A and B agree about how long the circumstance of the Milkyway is ? Same answer as above. If both observer A and B agree that speed and distance is the same for both (but the time rate not) , how can it be that speed multiplied with time not would show the same result for observer B as it would for observer A ? The wording of the question violates Relativity by mixing and matching observations from different reference frames without properly accounting for the differences. So we can answer this way: if A and B don't properly apply the principle of relativity, they may not believe that the laws of the universe are the same in all reference frames. Or put another way: if a person doesn't understand how to use a law, they will misuse it and may assume that the law is wrong when, in fact, it was just their use of the law that was wrong. That appears to be the basis of your issues with Relativity.

Bjarne

Oct1-11, 02:45 AM

As you must know, this question is incomplete.
Speed is measured between two points and you've only listed one point for each of the two speeds you are looking for.
We have “two point”...
We have a orbit and thereby a circumstance of the milkyway (MW).
You can bend the orbit to a straight line.
So you do have “two points”.
A staring point that also is the final point when the orbit is completed.

You need to specify what you are measuring the speeds relative to and who is doing the measuring.
This is done too.
The Sun travels relative to a points of no motion, which is the center of the Milkyway.
The 2 clocks are according to the example mentioned above following the exact same orbit as the Sun.

Bjarne
Does both observer A and B agree the speed is the same ?
Maybe. But again, this isn't really all that important. What is important is this:
Russ
If both observers faithfully follow the principle of Relativity as stated in your title and, as it requires, ensure they are clear and consistent about what frames of reference they are doing the measurements from, or measure from one and properly transform to the other, they will agree on what is happening.
First at all notice we are only speaking about influence due to gravity (GR) not about SR
The orbits of the 2 clock’s are exactly the same (for all observers).
Observer A and B are doing the measurement from their own reference frame.
B's clock is really ticking slower as A's clock - because B is closer to the Sun as A and therefore comparable slower as A's clock.

Nothing prevent that A and B can compare time differences.
Think about; how do we determinate how long 1 meter is or what the speed of light.
Both obersver A and B would determinate that the exact same way, wouldn’t they?

Again: If they follow the principle of Relativity and are clear on the choices of reference frames (and the definition of a "meter") they most certainly will.
They might say: "From here, your meter looks smaller than mine,
If A's meter-stick is comparable shorter as B's it will not only "look" shorter.
B's reality is real, as well as A's (or our) reality also are real.
Therefore B's meter stick will really be shorter.
We are not speaking about "illusion" but about realities.

but since I know our relative speeds, I calculate that if I was to go over to you and measure your meter it would be the same as mine."
Now you are speaking SR
Both A and B is according to the example in the same SR-reference frame, since both exactly follows the motion of the Sun, hence SR do not apply, - only GR does.

Let me ask more simple and all-round.
Imaging you was orbiting the Sun with a meter stick 50 billion km from the Sun.
I was orbiting 150 billion km from the Sun also carry a meter stick.
Would both meter sticks comparable be the same length? .
What I am asking is 1 meter the exact same length if a observer far away ( not affected by gravity of the Sun) could se both meter stick and also was able to compare if our meter stick did have the exact same length, so long we are different places in the gravitational field of the Sun ?

Now let say that time in your orbit is 1 billion part slower for you, compared to my time rate.
Would your meter stick then proportional to that be 1 billion-part longer ? (or shorter ) – or exactly the same as mine, - still seen from a observer C far away and not affected by the gravity of the Sun.

The wording of the question violates Relativity by mixing and matching observations from different reference frames without properly accounting for the differences.Comparing relative differences, doesn’t matter whether we speak about time rate, speed or length, - is not necessary mixing these, and this is also not what I have done at all.

I am not mixing anything but asking what is the speed and distance /B] [B]difference between A’s and B’s reality according to the example, - if any ?
There must be a very simple answer to that question.

If you would say there is no difference between the reality of A and B (accept time), simple math would show you a mathematical contradiction, since time multiplied with speed can impossible result to the same distance for A and B. (since time for B is shorter)

So I am in fact trying to separate relative differences.

Mathematical either speed or distance cannot comparable be the same.
So what is the mathematical answer here?
Is speed comparable larger - or is it distance that is proportional and comparable shorter (and therefore the meter -stick propositional longer) ?

If nothing proves that (comparable) speed is affected (and hence comparable different), and you multiply less time (for B) with the same (comparable ) speed that is valid for A, - you will get a shorter distances for B.

So if you have no objection that we assume that speed is (comparable) the same for A and B, - then it is mathematical proven that distance (circumstance of the MW) for A and B NOT is comparable the same for A.

If you do not agree speed is comparable the same, what is the correct comparable speed for B, ?.

Yours assumption that I am mixing realities is not true. – I am ONLY comparing realities, and do in fact try to keep factors separated, by asking what the differences except time .

Is speed and / or distance comparable different according to the very simple example mentioned?

Please try to keep it simple.

Bjarne

Oct1-11, 02:57 AM

You are getting caught up in time, speeds, distances being absolute. You have to do the calculations with respect to each "observer." So you say you are moving at 250k/s you have to ask with respect to what. In your own frame of reference you aren't moving at all. In the earths you are moving at one speed, sun another,...

No both clocks are moving 250 km/s as well as the Sun
Both clocks’ follows the Sun
SR does not apply to the mentioned scenario.
So this is not the correct answer either.

darkhorror

Oct1-11, 12:05 PM

No both clocks is moving 250 km/s as well as the Sun
Both clocks’ follows the Sun
SR does not apply to the mentioned scenario.
So this is not the correct answer either.

250 km/s with respect to what?

Bjarne

Oct1-11, 02:23 PM

250 km/s with respect to what?

I geusss the same way how we measure speed in space.
That must be valid for us but also for an observer with a slow ticking clock.

darkhorror

Oct2-11, 11:26 AM

I geusss the same way how we measure speed in space.
That must be valid for us but also for an observer with a slow ticking clock.

The way we measure speed in space is we see how fast we are going with respect to something else. If I am in space with respect to me my velocity is 0. With respect to the earth it might be .5c. With respect to something else it might be 250km/s.

Saying something is moving 250km/s is meaningless unless you say what it is with respect to.

zaybu

Oct2-11, 12:06 PM

Now you confuse me.
My concern is mainly if ALL laws of nature (equations) ALWAYS the same for all observer.
OR is (for example) gravity - and here I mean G (the gravity constant) an exception´.
Above you wrote; "G", does not change due to any local considerations"
I am now not sure what you really mean, - Is "G" ALWAY constant. - Yes or no ?

A consequence of Relativity is that we seek laws that are Lorentz invariant: meaning, if we have an equation A = BC + D in one frame of reference, then using the lorentz transformation laws to another frame of reference, we get A' = B'C' + D'. Note that not all equations will have this property, and certainly not certain observables. That's why we have time dilation, length contraction or that if two events are simultaneous in one frame, they might not be silmutaneous in a different frame. Now there are constants that are taken to be the same in every frame, that is, Lorentz invariant, notably the speed of light c, Planck's constant h-bar, and G -- Newton's constant in his law of universal gravitation.

Hope this helps.

Bjarne

Oct2-11, 04:13 PM

The way we measure speed in space is we see how fast we are going with respect to something else. If I am in space with respect to me my velocity is 0. With respect to the earth it might be .5c. With respect to something else it might be 250km/s.

Saying something is moving 250km/s is meaningless unless you say what it is with respect to.

250 km/s is the speed of the Sun's motion orbiting the MW
I don’t know how they did that measurement.
It is not with respect to “something” I believe, - but only to the center of the MW, where you have relative no motion.
If we can do such measurement, other observers in the Solar system can also. But I am not sure the result for a different space-time observer would be the same.

Bjarne

Oct2-11, 04:23 PM

A consequence of Relativity is that we seek laws that are Lorentz invariant: meaning, if we have an equation A = BC + D in one frame of reference, then using the lorentz transformation laws to another frame of reference, we get A' = B'C' + D'. Note that not all equations will have this property, and certainly not certain observables. That's why we have time dilation, length contraction or that if two events are simultaneous in one frame, they might not be silmutaneous in a different frame. Now there are constants that are taken to be the same in every frame, that is, Lorentz invariant, notably the speed of light c, Planck's constant h-bar, and G -- Newton's constant in his law of universal gravitation.
Hope this helps.

This is very a general "answer"
I belive many really are confused.
I am not sure that the right answer exsist ?

Try to be more specific and if you can try to answer some of all the questions.
I seem that many have mysophobia to answer concrete, for example show the simple content of the equation for B

Alle the content of the equation for A we can say we know, - A could share the same time rate as here on Earth, so it is only the stranger B, - that is the problem / challenge.

How is speed for B
How is comparable speed between A and B
What is the distance of the MW-orbit for B
How is the comparable distance between of the MW orbit for A and B
Is B's meter stick comparable smaller than A's – or longer – or the same length ?
Is a meter stick comparable smaller – or longer – or the same length, at the surface of the Sun compared to 100 billion km away, - du to gravity (GR) ?

We are only discussion GR not SR

darkhorror

Oct2-11, 04:46 PM

250 km/s is the speed of the Sun's motion orbiting the MW
I don’t know how they did that measurement.
It is not with respect to “something” I believe, - but only to the center of the MW, where you have relative no motion.
If we can do such measurement, other observers in the Solar system can also. But I am not sure the result for a different space-time observer would be the same.

It IS with respect to something that is one of the basic parts of relativity. To say you are moving at a certain km/s without saying anything else is meaning less. You are saying we are moving at 250 km/s with respect to the center of the MW. This also means the center of the MW is moving at 250km/s with respect to earth.

So are you trying to get the results from a frame of reference that is at the center of the MW galaxy?

zaybu

Oct3-11, 07:10 AM

This is very a general "answer"
I belive many really are confused.
I am not sure that the right answer exsist ?

Try to be more specific and if you can try to answer some of all the questions.
I seem that many have mysophobia to answer concrete, for example show the simple content of the equation for B

Alle the content of the equation for A we can say we know, - A could share the same time rate as here on Earth, so it is only the stranger B, - that is the problem / challenge.

How is speed for B
How is comparable speed between A and B
What is the distance of the MW-orbit for B
How is the comparable distance between of the MW orbit for A and B
Is B's meter stick comparable smaller than A's – or longer – or the same length ?
Is a meter stick comparable smaller – or longer – or the same length, at the surface of the Sun compared to 100 billion km away, - du to gravity (GR) ?

We are only discussion GR not SR

Relativity is a difficult subject. Even simple cases are difficult to tackle. I would suggest that before looking at complex situations, you start looking at simple cases to begin with. Here are two simple cases:

1) Twin paradox. See: http://soi.blogspot.com/2011/09/twin-paradox.html
2) Faster than light violates causality. See http://soi.blogspot.com/2011/09/why-ftl-violates-causality.html

Bjarne

Oct5-11, 04:24 PM

It IS with respect to something that is one of the basic parts of relativity. To say you are moving at a certain km/s without saying anything else is meaning less. You are saying we are moving at 250 km/s with respect to the center of the MW. This also means the center of the MW is moving at 250km/s with respect to earth.

So are you trying to get the results from a frame of reference that is at the center of the MW galaxy?

I have not invented how to calculate the orbit speed of the MW
So how was it done then ?

Bjarne

Oct5-11, 04:29 PM

Relativity is a difficult subject. Even simple cases are difficult to tackle. I would suggest that before looking at complex situations, you start looking at simple cases to begin with. Here are two simple cases:

1) Twin paradox. See: http://soi.blogspot.com/2011/09/twin-paradox.html
2) Faster than light violates causality. See http://soi.blogspot.com/2011/09/why-ftl-violates-causality.html

Both the example in the link is about Special relativity.
That confusion is not necessary.
General relativity alone is enough.
Don’t make it more complicated as it is.

PAllen

Oct5-11, 05:28 PM

Both the example in the link is about Special relativity.
That confusion is not necessary.
General relativity alone is enough.
Don’t make it more complicated as it is.

General relativity is more complex that special relativity; further all of special relativity is contained in general relativity. Treating GR separately from SR is impossible.

Bjarne

Oct6-11, 02:05 AM

General relativity is more complex that special relativity; further all of special relativity is contained in general relativity. Treating GR separately from SR is impossible.

The point is; according to the example (above) the 2 clocks moves with the relative same speed, and is therefore in the same SR-reference frame. (but not same GR-reference frame) Which mean SR is not affecting the 2 clocks, only GR does.

zonde

Oct6-11, 04:06 AM

First at all I want to say that we can simplify the scenario even more, to avoid confusion.

Because we could say that the 2 clocks are following the Sun’s orbit around the Milkyway.
(Technical we could say the orbiting clocks have devices (small rockets) on board to counteract the gravity from the Sun.

Seen from our perspective both the Sun and the two clocks (all 3 objects) are therefore orbiting the Milkyway in the excact same radius to the center of the Milkyway) .

The one clock is 50 billion km. behind the Sun, and the other 150 billion km.

This should eliminate he last confusion according to the Special relativity influence, since all relative speed now are the same.

Back to yours suggestion;
As I understand you now I can only understand it like that speed not is comparable “the same” – which then also mean that also comparable distances not can be the same, - right?
Wrong, distances are the same.
Only clocks tick at different rate. Measuring rods are of the same length.

I think we have a serious mathematical problem here and wonder how such a simple obviously unsolved mystery possible can have existed the last 100 years without any explanation. ?

I mean the math should be simple.
We know the 2 relative time rates and I believe we also know the speed, - the logical result (so far I can understand it) hence should be that B impossible can travels the same distance, simple because speed multiplied with time = distance.

I mean how difficult can that really be ?

PAllen

Oct6-11, 08:46 AM

The point is; according to the example (above) the 2 clocks moves with the relative same speed, and is therefore in the same SR-reference frame. (but not same GR-reference frame) Which mean SR is not affecting the 2 clocks, only GR does.

In GR, there is really no such thing as a global inertial frame of reference. You are actually trying to selectively use SR for one purpose and GR for another. Specifically, in a situation where you can detect time difference due to gravity, and where inertial paths in spacetime are observed over a whole spiral (that's how an orbit looks in spacetime), you really can't model this in terms of a global inertial frame centered on an orbiting body. Further, to maintain the paths you describe, none of your bodies (except the sun) are following inertial paths.

Next, you should be aware that for both SR and GR it is wrong believe there is equivalence between inertial and non-inertial frames, or between two non-inertial frames (which is what you really have). Acceleration (deviation from inertial path) is an invariant feature, not a relative feature (it is characterized by proper acceleration).

In a nutshell, every aspect of your scenario is ill conceived. The only thing you can actually expect from your scenario is that if all laws are expressed in their general tensor form, then each observer can build a coordinate system in which they are at rest, and use said coordinate system and laws in tensor form to make valid physical predictions.

darkhorror

Oct6-11, 12:26 PM

I have not invented how to calculate the orbit speed of the MW
So how was it done then ?

Observations and calculations.

How it was measured has no bearing on what I was talking about.

I am trying to figure out what you mean to say or what you are thinking. Here are a couple questions for you.

Does it matter what frame of reference you are talking about when you say earth is moving at 250km/s? Or are we simply moving at that velocity no matter what frame of reference we take?

Bjarne

Oct6-11, 12:51 PM

Observations and calculations.

How it was measured has no bearing on what I was talking about.

So how would A and B measure the distance of the Milky way ?
We can say A is you and B have a slower ticking clock, due to gravity, we could say that A live in a skyscraper, and B in a cellar etc. Or we can use the example above.

I am trying to figure out what you mean to say or what you are thinking. Here are a couple questions for you.

Does it matter what frame of reference you are talking about when you say earth is moving at 250km/s? Or are we simply moving at that velocity no matter what frame of reference we take?
The orbit speed round the Milkyway is the same for both observes (A and B).
Hence it doesn’t matter

Bjarne

Oct6-11, 01:29 PM

In GR, there is really no such thing as a global inertial frame of reference.
I have heard that before, but it is irrelevant according to the example, since this is not what the example conclude. All questions are open. So far there are no mathematical / logical explanations.

You are actually trying to selectively use SR for one purpose and GR for another.
No, - I am only distinguishing between the cause of time-difference between the 2 observers, and whether the cause is SR or GR.

The scenarios I have shown SR do not apply since speed of both observers is the same.
Both clocks orbit the MW in the same radius.
The cause of time difference between the 2 observers is in this case is only caused due to gravity (GR) (General Relativity).

Specifically, in a situation where you can detect time difference due to gravity, and where inertial paths in spacetime are observed over a whole spiral (that's how an orbit looks in spacetime), you really can't model this in terms of a global inertial frame centered on an orbiting body.

I am not suggesting "a global inertial frame" but only asking simple questions.

We can assume that A’s reality is exact the same as ours.
Hence we know everything about A’s reality, as well how A has come to all his conclusions, - for example the circumstance of the Milkyway etc..

But when a clock is ticking slower due to the gravity of the Sun, for another observer (we call that observer B,) - then it is simple calculation that A’s reality cannot be valid for B.

The answer must be that A‘s reality must be exactly so real as B’s, and therefore we also must know how is comparable distances speed etc or B.

For example;
How is speed for B ?
How is comparable speed between A and B ?
What is the distance of the MW-orbit for B ?
How is the comparable distance between of the MW orbit for A and B ?
Is B's meter stick comparable smaller than A's – or longer – or the same length ?
Is a meter stick comparable smaller – or longer – or the same length, at the surface of the Sun compared to 100 billion km away, - du to gravity (GR) ?
seen from B’s reality

Further to, maintain the paths you describe, none of your bodies (except the sun) are following inertial paths.
I do not understand , above I wrote that we assume these clock's does, we assume these have small rocket engines on board and therefore counteracts the gravity of the Sun, - (but not counteract the time difference). and therefore orbits the MW without getting attracted to the Sun.

Hence 2 clocks orbit the Milkyway exactly as the Sun does.

The difference is that one clock (B) is closer to the sun and therefore ticking slower than the other clock (A).

This certainly , logically and mathematical MUST have SIMPLE consequence(s), since 1 complete orbit round the Milkyway take less time for B as it does for A.

Time multiplied with speed = distance.

Try instead exactly to answer some or all the questions.
There must certainly be “consequences” of time dilation.

There are no reasons to make the simple scenario more difficult or impossible as necessary.

In a nutshell, every aspect of your scenario is ill conceived.
Then the Universe must also be such ill place, since time really is ticking slower due to gravity and that must have consequences .

“If you can't explain it simply, you don't understand it well enough”.
Albert Einstein

DrGreg

Oct6-11, 02:20 PM

Asking for an answer in terms of GR-without-SR is meaningless. No such theory exists. The only theories available are either SR alone (without gravity), or else GR+SR (with gravity).The scenarios I have shown SR do not apply since speed of both observers is the same.This is not something that all observers agree to.

According to each of your two observers, the velocity of the other observer is zero. But according to a third observer who is falling freely directly towards the Sun, the two observers are not a fixed distance apart. According to this third observer, who within GR is an inertial observer (and the other two are not inertial), Lorentz contraction causes their distance to keep changing, i.e. they are not both moving at the same speed according to the third observer. According to this 3rd observer, this relative motion is the cause of the time dilation between the first two observers.

PAllen

Oct6-11, 03:00 PM

No, - I am only distinguishing between the cause of time-difference between the 2 observers, and whether the cause is SR or GR.

This is not possible.

I am not suggesting "a global inertial frame" but only asking simple questions.

Yes, you are asking about global coordinates but you don't realize it.

You are asking about analyzing the motion of the MW center from A or B point of view. This requires two global coordinate systems. Each of these coordinate systems is built from a non-inertial frame because thrust would be required to hold A and B in position against the Sun's gravity. They are different non-inertial frames because each would require a different amount of thrust.

Further, from A and B point of view the laws to be applied would be determining the elliptical motion of MW center around each of them. For each, this would be a complex application of GR field equations in a rather complex coordinate system. They would still find that their application GR would be successful.

You can pretend the problem is simple only by ignoring its essential features, and misapplying relativity.

Einstein also said: be as simple as possible, but no simpler.

Bjarne

Oct6-11, 03:30 PM

Yes, you are asking about global coordinates but you don't realize it.

You are asking about analyzing the motion of the MW center from A or B point of view. This requires two global coordinate systems. Each of these coordinate systems is built from a non-inertial frame because thrust would be required to hold A and B in position against the Sun's gravity. They are different non-inertial frames because each would require a different amount of thrust.
.

Right, - I remember
We will call the third observer C
The problem that C also cannot agree how "comparable distances" (between A and B) is doesn’t make the problem smaller, does it?
Still we have time rate difference, that must mean 2 (real) and different realities.
The many questions (concerning A and B) mentioned above is still unanswered.
Answering these must be possible also even though SR and GR are "connected"

PAllen

Oct6-11, 04:04 PM

Well, the reality is roughly as follows.

We don't have to verify physical predictions in A coordinates and B coordinates would come out the same because this follows purely from mathematical definitions and theorems. However, doing physical computations in these coordinates would be a bummer (the metric tensor would have a very complex form). So, confident of pure math, A and B would each translate their local measurements to a convenient coordinate system (MW central frame, presumably). This translation would be based on relativity. They would have to translate locally measured times, distances, angles, and red/blueshift. Once they translated their local measurements, they would compute in the MW center frame.

And no, I have no interest in carrying this out with your numbers.

[Addendum: A and B can determine how to transform their local measurements with local measurements plus GR. They measure their proper acceleration with an accelerometer. This along with a bunch of local redshift and other astronomic measurements give enough information. ]

Bjarne

Oct7-11, 02:21 AM

Asking for an answer in terms of GR-without-SR is meaningless. No such theory exists. The only theories available are either SR alone (without gravity), or else GR+SR (with gravity).This is not something that all observers agree to.

According to each of your two observers, the velocity of the other observer is zero. But according to a third observer who is falling freely directly towards the Sun, the two observers are not a fixed distance apart. According to this third observer, who within GR is an inertial observer (and the other two are not inertial), Lorentz contraction causes their distance to keep changing, i.e. they are not both moving at the same speed according to the third observer. .

We will call the third observer C.

When C is falling towards the sun and first passing A and next B he would off course accelerate faster (due to acceleration of the Sun) when passing B as he would when passing A.

So for C it would look like B is moving faster away from C than A.

But in fact C is moving relative to A and B, - and not A and B relative to C.

I mean any other observer as C (on the Earth or other places in the Universe) would not see that A or B is moving away from the sun, (or away from each other) but only that C is moving towards the sun.

According to this 3rd observer, this relative motion is the cause of the time dilation between the first two observers

I can’t see there really is "relative motion" between A and B ?

How can the reality (an illusion) of the third observer C have anything to do with the time-rate for A and B ?

zonde

Oct7-11, 04:57 AM

No, - I am only distinguishing between the cause of time-difference between the 2 observers, and whether the cause is SR or GR.
This is not possible.
It is possible to take gravitational time dilation as experimentally verified physical fact without any reference to SR or GR.

You are asking about analyzing the motion of the MW center from A or B point of view. This requires two global coordinate systems. Each of these coordinate systems is built from a non-inertial frame because thrust would be required to hold A and B in position against the Sun's gravity. They are different non-inertial frames because each would require a different amount of thrust.

Further, from A and B point of view the laws to be applied would be determining the elliptical motion of MW center around each of them. For each, this would be a complex application of GR field equations in a rather complex coordinate system. They would still find that their application GR would be successful.
Nobody is doing it like you describe. This is simply crap.
Orbital speed can be calculated by simple formula when ellipticity is zero (circular orbit).

You can pretend the problem is simple only by ignoring its essential features, and misapplying relativity.
Why are you inventing problems that are not there? Are you trying to confuse Bjarne? Why?

PAllen

Oct7-11, 08:01 AM

It is possible to take gravitational time dilation as experimentally verified physical fact without any reference to SR or GR.

But that's not relevant to how I understand the Bjarne's confusion. In fact, he understands that and that is source of his confusion: "How come A and B, using their raw measurements, come up with different results? Aren't they supposed to be the same? " He is questioning in what sense there is 'relativity' between A and B, where each can directly use their measurements and find equivalent results.

Nobody is doing it like you describe. This is simply crap.
Orbital speed can be calculated by simple formula when ellipticity is zero (circular orbit).

I agree nobody would actually do it like that (as I described in another post). However, this is the only sense in which one can talk about applying the same laws to the raw measurements by A and B. I was trying to get across that in going from 'free falling enclosed labs' to global measurements by non-inertial observers, the statement the 'laws of physics are the same for all observers' takes on a more complex, less useful form. The same laws apply only if expressed in general tensor form. Otherwise, in practice, you correct measurements to do computations in a convenient coordinate system where the expression of the laws is simplest.

Why are you inventing problems that are not there? Are you trying to confuse Bjarne? Why?

No, I am trying to directly address where I think his confusion is leading to incorrect expectations.

zonde

Oct8-11, 03:57 AM

But that's not relevant to how I understand the Bjarne's confusion. In fact, he understands that and that is source of his confusion: "How come A and B, using their raw measurements, come up with different results? Aren't they supposed to be the same? " He is questioning in what sense there is 'relativity' between A and B, where each can directly use their measurements and find equivalent results.

I agree nobody would actually do it like that (as I described in another post). However, this is the only sense in which one can talk about applying the same laws to the raw measurements by A and B. I was trying to get across that in going from 'free falling enclosed labs' to global measurements by non-inertial observers, the statement the 'laws of physics are the same for all observers' takes on a more complex, less useful form. The same laws apply only if expressed in general tensor form. Otherwise, in practice, you correct measurements to do computations in a convenient coordinate system where the expression of the laws is simplest.

No, I am trying to directly address where I think his confusion is leading to incorrect expectations.
Ok, how the question went?

First, the setup for consideration is such that we can investigate gravitational time dilation with other things unchanged.
Yes we can do that in physically meaningful way exactly as Bjarne described. And that's the right approach to understand something. Isolate that one factor as much as possible. That is exactly the thing that you do in real experiments.

Second, observers make astronomical observations about their movement relative to the center of MW and the distance to the center of MW.
Again, yes we can do that and we don't have to factor out anything related to our gravitational acceleration.
Astronomers on surface of Earth (gravitationally accelerated frame) perform observations all the time and the only thing they factor out is aberration but that's velocity not acceleration effect.

Third, we compare results for two observers.

So far question (actually background for question) is formulated in physically meaningful way. Do you agree with that?

PAllen

Oct8-11, 07:07 AM

Ok, how the question went?

First, the setup for consideration is such that we can investigate gravitational time dilation with other things unchanged.
Yes we can do that in physically meaningful way exactly as Bjarne described. And that's the right approach to understand something. Isolate that one factor as much as possible. That is exactly the thing that you do in real experiments.

Second, observers make astronomical observations about their movement relative to the center of MW and the distance to the center of MW.
Again, yes we can do that and we don't have to factor out anything related to our gravitational acceleration.
Astronomers on surface of Earth (gravitationally accelerated frame) perform observations all the time and the only thing they factor out is aberration but that's velocity not acceleration effect.

Third, we compare results for two observers.

So far question (actually background for question) is formulated in physically meaningful way. Do you agree with that?

No, not completely. My understanding of Bjarne's issue is that time measurements will be different (they set up the idea that they were sensitive to the time difference between their A and B). So measurements sensitive to time will be different. At this level of sensitivity, doppler measurements will also be affected. Then, of course, aberration will apply (angles, as I called it in one of my posts). My understanding of Bjarne's thesis was that all of this violated the idea of laws being the same for different observers. If you used these measurements to directly compute a distant velocity, it would come out different.

I wanted to focus on this being a false expectation. That it is expected that different observer's measurements may differ. And that for arbitrary observer's, the only form 'laws being the same' that you can expect is if they are expressed in general tensor form.

Bjarne

Oct8-11, 02:43 PM

PAllen

Oct8-11, 03:17 PM

All what we can be 100 % sure about is;

That the 2 clock will tick different, - experience shows this.
Both clocks will complete the orbit of the Milkyway in the exact same period (according to the scenario mention above).
And because of that either speed or distance must be different from the perspective of A as it is for B.

I see no reason to complicate that more than this.

I believe we first at all only need to look at this purely / simple mathematical.

Speed multiplied with time = distance, - this must be true both for A as well for B, - since there is no reason to believe that only our ( or A’s) reality is more true like others.

This leaves us with 2 simple mathematical options;

Option 1.
The orbit speed for the 2 clocks (and the Sun) must seen from the perspective of observer B be faster as for observer A. - (I don’t believe in that option, - since A and B do not change distance between them).

Option 2
B's meter stick is longer and therefore distances shorter. - This is the only explanation I can accept so far.

As I understand relativity; - there are no certain reality (also not ours), since time (and probably also “size / distance”) not is comparable the same.
I think before accelerating the speculation into too much complexity we should try to look at the must simple level, as just shown, and finish here first.

It is easy to see that the most direct interpretation is that speed of distant objects will be greater for the one closer to the sun. This simply follows from direct interpretation of doppler - they will be slightly more blue shifted. Thus, if interpreted without adjustment, distant objects should be viewed as going slightly faster than the 'further from sun' observer would conclude. This is consistent with the slower time, obviously. Measurements by other methods would be expected to generally agree, but not necessarily be exactly the same. One key point is that it is only in flat spacetime, for inertial frames, that all reasonable ways of measuring a distant velocity or large distance will agree. For your observers (non inertial, curvature present), if they interpret their measurements as if they were inertial, Minkowski, observers, different measurement methods for distant observations will disagree.

Bjarne

Oct9-11, 02:28 AM

It is easy to see that the most direct interpretation is that speed of distant objects will be greater for the one closer to the sun.
No
According to the example the 2 clock counteracts gravity from the Sun, - (they have small racket engine on board).

This simply follows from direct interpretation of Doppler - they will be slightly more blue shifted.
No there will be no Doppler effect due to speed difference of the 2 clocks; both clocks orbit with the exact same orbit-speed as the Sun, and with the exact same radius to the center of the Milkyway

This is consistent with the slower time, obviously.
You may have misunderstood that both clocks follows the orbit of the Sun, and is not approaching the Sun due to the gravity of the Sun, - because that gravity attraction is counteracted (by small rockets on board on the 2 clocks) . Therefore both clocks and the sun move in the exact same orbit around the Milky Way.

Measurements by other methods would be expected to generally agree, but not necessarily be exactly the same.

The 2 clocks (observers) are certainly meassuring different time-rate and can't therefore agree how distance (or speed) around the Milkyway.

All other observers (in the Universe) will observe that the Sun and the 2 clocks are completing 1 orbit of the Milkyway in the exact same period of (their) time.
This will not affect the motion (or time-rate) of the 2 clocks..

zonde

Oct9-11, 03:19 AM

No, not completely. My understanding of Bjarne's issue is that time measurements will be different (they set up the idea that they were sensitive to the time difference between their A and B). So measurements sensitive to time will be different. At this level of sensitivity, doppler measurements will also be affected. Then, of course, aberration will apply (angles, as I called it in one of my posts).
Certainly different time rate will affect measurements. And that's the point of example.
I think that aberration can be factored out if both observers translate their observations to rest frame of MW mass center. After they do that they should point in the same direction as where is MW mass center.

My understanding of Bjarne's thesis was that all of this violated the idea of laws being the same for different observers. If you used these measurements to directly compute a distant velocity, it would come out different.
Well, yes, there are problems Bjarne's position but my point was that you where adding confusion to the problem and not making it clearer.

I wanted to focus on this being a false expectation. That it is expected that different observer's measurements may differ. And that for arbitrary observer's, the only form 'laws being the same' that you can expect is if they are expressed in general tensor form.
Generalized form might not be the best starting point for clearing confusions. Special simplified cases where you can replace tensors with simple specific transformations might be better.

zonde

Oct9-11, 05:44 AM

Option 1.
The orbit speed for the 2 clocks (and the Sun) must seen from the perspective of observer B be faster as for observer A. - (I don’t believe in that option, - since A and B do not change distance between them).
It is a good idea to check your beliefs against observations in real world.
So it might be good to check out about Shapiro delay (http://en.wikipedia.org/wiki/Shapiro_delay)

Bjarne

Oct9-11, 06:11 AM

It is a good idea to check your beliefs against observations in real world.
So it might be good to check out about Shapiro delay (http://en.wikipedia.org/wiki/Shapiro_delay)

I agree gravitational time delay is real.

PAllen

Oct9-11, 08:04 AM

No

No there will be no Doppler effect due to speed difference of the 2 clocks; both clocks orbit with the exact same orbit-speed as the Sun, and with the exact same radius to the center of the Milkyway

Doppler may not have been the best word choice. I meant gravitational blue shift (sloppily, I sometimes use doppler for all kinds of frequency shift). All distant objects will appear slightly more blue shifted to the observer closer to the sun.

PAllen

Oct9-11, 08:12 AM

Option 2
B's meter stick is longer and therefore distances shorter. - This is the only explanation I can accept so far.

.

Actually, along with gravitational time dilation, there is also gravitational length contraction. According to the 'further from sun' observer, the closer observer's rulers are slightly short, rather than long.

Be that as it may, there is straightforward way the two can observers agree on their speed relative to the milky way center. Suppose each adopts as their distance standard (converting other ways of measuring distance to far away object to match this standard) c times light round trip time to object as they measure it. Then the closer to sun observer thinks the MW center is closer (less time for the round trip). They then figure a smaller circumference for the orbit. They divide the smaller circumference by the shorter time, and come up with the same speed as the 'further from sun' observer.

PAllen

Oct9-11, 10:55 AM

We will call the third observer C.

When C is falling towards the sun and first passing A and next B he would off course accelerate faster (due to acceleration of the Sun) when passing B as he would when passing A.

So for C it would look like B is moving faster away from C than A.

But in fact C is moving relative to A and B, - and not A and B relative to C.

I mean any other observer as C (on the Earth or other places in the Universe) would not see that A or B is moving away from the sun, (or away from each other) but only that C is moving towards the sun.

I can’t see there really is "relative motion" between A and B ?

How can the reality (an illusion) of the third observer C have anything to do with the time-rate for A and B ?

In GR, C is not accelerating at all. C is the inertial observer. A and B are accelerating at slightly different rates, as seen by C, their distance is shrinking over time (per C), they have a relative speed (per C). These are facts computable in special relativity alone (treating C as inertial, as required, and treating A and B as accelerating so as to keep distance constant per A. You can read all about this under the Bell spaceship 'paradox'. That A and B are the non-inertial observers is an objective, invariant fact - they experience a force that can be measured by an accelerometer, locally. C feels no force, therefore is inertial.

This concretely explains the idea that, within GR, there is no objective meaning to an SR effect versus a GR effect. Almost always, you can validly treat some effect as different mix of SR vs. gravitation effect by choosing different observers or coordinates.

There is yet another way to choose to treat gravitational time dilation as kinematic rather than gravitational (involving parallel transport of 4-vectors). However, I don't think you have the background for that.

zonde

Oct10-11, 03:23 AM

I agree gravitational time delay is real.
Shapiro delay does not measure time delay. It measures changes in coordinate speed of light.
To make some statements about time delay in context of Shapiro delay you have to make some assumption about distance measurements. And this assumption is that distances stay the same. When you assume this then Shapiro delay agrees with expected time delay.

Or looking at this from another side. From Shapiro delay we find out that coordinate speed of light is different at different gravitational potentials.
Now if local speed standard (c) is different for two observers then speed measurements for the same (global) physical situation should be different for two observers. Just like it is with time.

You can try to make prediction for coordinate speed of light using your Option 2 (B's meter stick is longer and therefore distances shorter). What it will be?

Bjarne

Oct10-11, 05:04 AM

Doppler may not have been the best word choice. I meant gravitational blue shift (sloppily, I sometimes use doppler for all kinds of frequency shift). All distant objects will appear slightly more blue shifted to the observer closer to the sun.
Gravitionel blue shift yes, but it has nothing with speed to do.

Actually, along with gravitational time dilation, there is also gravitational length contraction. According to the 'further from sun' observer, the closer observer's rulers are slightly short, rather than long.

[QUOTE=PAllen;3548070]Actually, along with gravitational time dilation, there is also gravitational length contraction. According to the 'further from sun' observer, the closer observer's rulers are slightly short, rather than long.
I can only understand it like that; if time is ticking slower, the meter stick must be proportional longer (for B) and distances hence seen from the perspective of B – shorter. But seen from a “outsider” distances is the same. Remember both observers complete the “same distance” seen from the perspective of observer C.

Be that as it may, there is straightforward way the two can observers agree on their speed relative to the milky way center. Suppose each adopts as their distance standard (converting other ways of measuring distance to far away object to match this standard) c times light round trip time to object as they measure it. Then the closer to sun observer thinks the MW center is closer (less time for the round trip). They then figure a smaller circumference for the orbit. They divide the smaller circumference by the shorter time, and come up with the same speed as the 'further from sun' observer.
Right but keep in mind that reality by your feet is not the same as by your head.
The meter stick cannot be the same comparable lenght both places, - can it ?

In GR, C is not accelerating at all.
Notice C is the third observer “invented” by DrGreg ( it is not “c” )
http://www.physicsforums.com/showpost.php?p=3543384&postcount=64
C is; “a third observer who is falling freely directly towards the Sun”. Off course C is then accelerating, due to acceleration due to gravity.

C is the inertial observer. A and B are accelerating at slightly different rates, as seen by C, their distance is shrinking over time (per C), they have a relative speed (per C). These are facts computable in special relativity alone (treating C as inertial, as required, and treating A and B as accelerating so as to keep distance constant per A. You can read all about this under the Bell spaceship 'paradox'. That A and B are the non-inertial observers is an objective, invariant fact - they experience a force that can be measured by an accelerometer, locally. C feels no force, therefore is inertial.

This concretely explains the idea that, within GR, there is no objective meaning to an SR effect versus a GR effect. Almost always, you can validly treat some effect as different mix of SR vs. gravitation effect by choosing different observers or coordinates.
There is yet another way to choose to treat gravitational time dilation as kinematic rather than gravitational (involving parallel transport of 4-vectors). However, I don't think you have the background for that.
As I see it and hopefully any other observer in the Universe, - C is really acceleration towards the Sun.
A and B is not affected due to the fact that C can have the illusion that it is A and B that is moving opposite.
I don’t understand the point.
C’s reality and the illusion that A and B is moving opposite, is not real for anyone else than C.
Why make a big point out of what only is an illusion. ?

You can try to make prediction for coordinate speed of light using your Option 2 (B's meter stick is longer and therefore distances shorter). What it will be?
Good exercise.
Let us now say that B’s clock tick half so fast like A’s (for simplicity reasons) - (still according to the example above) .
A and B would send a light beam to the same planet .
The light beam would reflect and return.
After the exact same period of time (seen by any external third observer “EX”) the light beam would return to both A and B.
Observer A would now say it took 1 (earth)-year, (31536000 s.)
But B would say it took half so much time.

Seen from observer EX perspective the distance the light was travelling to A and B is the exactly same.

The ONLY way both A and B can agree that the light was travelling with the “same” speed, is when B’s meter-stick is comparable double so long as A’s meterstick.
So simple is that.

This mean that speed is really “c” (300,000 km/h) seen from both the perspective of observer A , as well as from B’s reality.

BUT when you would compare the speed it would be a different history.

The only solution to that (as I can see) is that we cannot mix realities, but are forces to separate these.

And as I wrote this must mean a different comparable meter stick – that’s all, and the only simple mathematical solution.

Why not keep things simple, when they are simple?

zonde

Oct10-11, 07:18 AM

Good exercise.
Let us now say that B’s clock tick half so fast like A’s (for simplicity reasons) - (still according to the example above) .
A and B would send a light beam to the same planet .
The light beam would reflect and return.
After the exact same period of time (seen by any external third observer “EX”) the light beam would return to both A and B.
Observer A would now say it took 1 (earth)-year, (31536000 s.)
But B would say it took double so much time.

Seen from observer EX perspective the distance the light was travelling to A and B is the exactly same.

The ONLY way both A and B can agree that the light was travelling with the “same” speed, is when B’s meter-stick is comparable double so long as A’s meterstick.
So simple is that.
Yes, that's correct.

The only problem is that if we would make prediction for Shapiro time delay it would be zero because coordinate speed of light does not change in your case.
And yet we observe slowing down of coordinate speed of light when signal passes gravitating object at close distance. So your model does not agree with observations.

So what we do next?

Bjarne

Oct10-11, 12:46 PM

Yes, that's correct.
The only problem is that if we would make prediction for Shapiro time delay it would be zero because coordinate speed of light does not change in your case.

Right
Now we assume the meter stick always is comparable the exact same for both A and B.
Observer A and B will now in a certain period measure a photon traveling a certain distance (300,000 km).
Both observers agrees that this is what really happen.

Based on this observer A would say that the speed of light is exactly 300,000 km in one (of his) second.

But observer B would say OK I agree the distance the photon was travelling is 300,000 km ...
BUT I do not agree it took one second, - my clock shows it only took ½ second, so here the speed of light is 600,00km/s
Do you prefer that solution?
Hmmm… So what we do next?

And yet we observe slowing down of coordinate speed of light when signal passes gravitating object at close distance. So your model does not agree with observations.

I have never heard about Shapiro time delay. If it really is certain and confirmed knowledge, and not something only at a test level, - yes we have a one more problem/challenge..

So what we do next?
Hmmm speculate, but not too loud, suggestion could be wrong, and we would look stupid.
What do you think the answer is (except that distances / the meter stick always are comparable the same lenght) ?

PAllen

Oct10-11, 12:55 PM

Gravitionel blue shift yes, but it has nothing with speed to do.

The context was, suppose you don't know you're in a gravitational field, or what consequences that would have. What laws do you apply to your observations? If you apply either pure SR or Galilean physics (even accounting that you know you are accelerating), you would conclude different relative velocity for distant objects than you would if you were not subject to gravity (or subject to less gravity).

I can only understand it like that; if time is ticking slower, the meter stick must be proportional longer (for B) and distances hence seen from the perspective of B – shorter. But seen from a “outsider” distances is the same. Remember both observers complete the “same distance” seen from the perspective of observer C.

You claim to accept gravitation time dilation, per se. The same derivations that lead to it, also lead to gravitational length contraction. The thing that allows all of it to be consistent is that the observer that sees your clock slow and your rulers short also sees light going slower for you. When you put in the actual numbers, this observer 'understands' why you still measure the same value for light speed. (this comment was unrelated to observer C. It was in reference to how the 'outer' of A and B would view the inner. Observer C would be more complex, because they have relative motion to account for).

Right but keep in mind that reality by your feet is not the same as by your head.
The meter stick cannot be the same comparable lenght both places, - can it ?

The point is ultimately related to the fact that only for inertial observers in flat spacetime do you have the nice property that any 'reasonable' way of doing measurements comes out the same. For inertial observers in flat spacetime, radar ranging, parallax distance, luminosity distance, etc. all yield an equivalent distance scale. For either curved spacetime or non-inertial observers (even in flat spacetime), they disagree with each other. You can choose which to favor, getting different answers for where your results are 'unexpected'. My example shows, if you choose to favor radar ranging, you get shorter distances to remote objects, but the same speeds (well, there would be higher order differences, but let's not worry about that) for A and B.

There truly is no unique, preferred answer to large distances in GR (short of choosing a preferred global coordinate system). Actually, there isn't in SR either - distances are observer dependent.

Notice C is the third observer “invented” by DrGreg ( it is not “c” )
http://www.physicsforums.com/showpost.php?p=3543384&postcount=64
C is; “a third observer who is falling freely directly towards the Sun”. Off course C is then accelerating, due to acceleration due to gravity.

As I see it and hopefully any other observer in the Universe, - C is really acceleration towards the Sun.
A and B is not affected due to the fact that C can have the illusion that it is A and B that is moving opposite.
I don’t understand the point.
C’s reality and the illusion that A and B is moving opposite, is not real for anyone else than C.
Why make a big point out of what only is an illusion. ?

You are simply wrong here. In GR, all observers agree C is the inertial observer and A and B are the non-inertial observers. ('Accelerating', on the other hand, has very little relevance in GR if it is referring to coordinate acceleration, as you are; proper acceleration, computed in any coordinates, by any observer, says A and B are accelerating and C is not accelerting). On this, there is no 'relativity'. What is describe here is not an illusion at all, but the essence of relativity (note that C sees the distance between A and B shrinking over time; not sure you got that). The point (initially by Dr. Greg) is that the how much of an effect is related to gravity or SR effects is observer dependent. This is fundamental in GR, not an illusion to be ignored. And, in particular, for C, difference between A and B would be primarily the same effect as the SR bell spaceship 'paradox'.

zonde

Oct11-11, 01:23 AM

Right
Now we assume the meter stick always is comparable the exact same for both A and B.
Observer A and B will now in a certain period measure a photon traveling a certain distance (300,000 km).
Both observers agrees that this is what really happen.

Based on this observer A would say that the speed of light is exactly 300,000 km in one (of his) second.

But observer B would say OK I agree the distance the photon was travelling is 300,000 km ...
BUT I do not agree it took one second, - my clock shows it only took ½ second, so here the speed of light is 600,00km/s
Do you prefer that solution?
Hmmm… So what we do next?
This is different from how Shapiro experiment was performed.
There is only one observer who is sending radar signals so that sometimes they are passing close to the Sun and sometimes far from the Sun. When you make a correction for time delay depending on signal's closest passing distance from the Sun you can consistently describe orbit of observed object (Venus).
In your case speed of light is always the same because proportion "m/s" does not change.

I have never heard about Shapiro time delay. If it really is certain and confirmed knowledge, and not something only at a test level, - yes we have a one more problem/challenge..
From Wikipedia about Shapiro delay (http://en.wikipedia.org/wiki/Shapiro_delay):
"The time delay effect was first noticed in 1964, by Irwin I. Shapiro. Shapiro proposed an observational test of his prediction: bounce radar beams off the surface of Venus and Mercury, and measure the round trip travel time. When the Earth, Sun, and Venus are most favorably aligned, Shapiro showed that the expected time delay, due to the presence of the Sun, of a radar signal traveling from the Earth to Venus and back, would be about 200 microseconds,[1] well within the limitations of 1960s era technology.

The first tests, performed in 1966 and 1967 using the MIT Haystack radar antenna, were successful, matching the predicted amount of time delay.[2] The experiments have been repeated many times since then, with increasing accuracy."

Hmmm speculate, but not too loud, suggestion could be wrong, and we would look stupid.
What do you think the answer is (except that distances / the meter stick always are comparable the same lenght) ?
First of all speed of light globally is not the same everywhere.
Statement that "laws of physics are the same in all inertial reference frames" means that local experiments will give the same results. But global observations can be different.

PAllen

Oct11-11, 06:28 PM

Right but keep in mind that reality by your feet is not the same as by your head.
The meter stick cannot be the same comparable lenght both places, - can it ?

I realize I didn't directly answer this question. In theory, a meter stick by your feet would be slight shorter than one by your head (not longer as you have argued several times). Light would be slower at your feet compared to your head. Clocks would be slower at your feet than your head. The only one of these that has been experimentally verified is the clocks, because they have reached the precision to detect differences over 6 feet in the earth's field. The others will not be observable in the foreseeable future (of course, unforeseeable future could be only a few years away; never know when there is a breakthrough).

None of this is relates at all to the issue I was presenting (measuring distance over tens of thousands of light years using radar ranging distance as your definition, with other measuring methods calibrated to match). Especially because your own scenario had these measurements being done from lab held stationary (by thrust) with respect to the sun. Also, of course, there are no astronomic measurement that could be made at a precision where it mattered whether they were done at your head or your feet.

Passionflower

Oct11-11, 07:10 PM

In theory, a meter stick by your feet would be slight shorter than one by your head (not longer as you have argued several times).
Your claim that meter sticks are shorter closer to the EH, could you back it up with some math or at least a reference? And shorter tangentially or radially, or perhaps both?

What I can show you mathematically is that both the volume and radial distance between two shells is more than we would suspect if we would calculate it based on their areas. And the discrepancy increases for lower r-values closer to the EH.

PAllen

Oct11-11, 09:44 PM

Your claim that meter sticks are shorter closer to the EH, could you back it up with some math or at least a reference? And shorter tangentially or radially, or perhaps both?

What I can show you mathematically is that both the volume and radial distance between two shells is more than we would suspect if we would calculate it based on their areas. And the discrepancy increases for lower r-values closer to the EH.

Ah, but if delta r represents distance as perceived by an observer at infinity, and a local, stationary observer computes a proper distance (with their t=0 simultaneity) of something greater, that implies the local rulers look short to the observer at infinity (in the radial direction).

I've only seen this contraction discussed radially. Two references validating its existence (but not deriving it) are (search for contraction on of these pages):

http://www.upscale.utoronto.ca/PVB/Harrison/GenRel/GenRel.html

http://www.mathpages.com/rr/s6-01/6-01.htm

Passionflower

Oct11-11, 09:52 PM

Ah, but if delta r represents distance as perceived by an observer at infinity

1. How do you conclude that delta r is distance as perceived by an observer at infinity.
2. If so, how do you conclude that the observer at infinity has the ultimate saying about what the real length is?

r simply represents the, so called, reduced circumference and directly relates to the circumference and area of resp. a circle and sphere.

Are you perhaps saying that the increase in radius and volume between shells of lower r-values over the expected Euclidean values is not due to the fact that space is no longer Euclidean but due to the fact that rulers shrink?

, and a local, stationary observer computes a proper distance (with their t=0 simultaneity) of something greater, that implies the local rulers look short to the observer at infinity (in the radial direction).

What kind of computation did you have in mind?

wrt the first reference, I am sorry I must be slow but I do not see where it states anything that is relevant to what you said, could you tell me exactly what you think shows the reference that rulers shrink.

wrt to the second reference I am also at a loss, where exactly is this pointed out that rulers shrink?

PAllen

Oct11-11, 10:32 PM

1. How do you conclude that delta r is distance as perceived by an observer at infinity.
2. If so, how do you conclude that the observer at infinity has the ultimate saying about what the real length is?

r simply represents the, so called, reduced circumference and directly relates to the circumference and area of resp. a circle and sphere.

Are you perhaps saying that the increase in radius and volume between shells of lower r-values over the expected Euclidean values is not due to the fact that space is no longer Euclidean but due to the fact that rulers shrink?

What kind of computation did you have in mind?

wrt the first reference, I am sorry I must be slow but I do not see where it states anything that is relevant to what you said, could you tell me exactly what you think shows the reference that rulers shrink.

wrt to the second reference I am also at a loss, where exactly is this pointed out that rulers shrink?

With regard to the first reference, the following is said:

"Gravitational Length Contraction

Lengths of objects in gravitational fields are contracted according to the theory. The prediction has never been tested. For the keen, you may wish to derive this prediction using the same techniques used in the previous sub-section to derive gravitational time dilation. "

With regard to the second reference, there is the following:

"The factor of 2 relative to the equation of 1911 arises because in the full theory there is gravitational length contraction as well as time dilation. Of course, the length contraction doesn’t affect the gravitational redshift, which is purely a function of the time dilation, so the redshift prediction of 1911 remains valid"

Here is another discussion, but it is not at all rigorous:

http://www.relativity.li/en/epstein2/read/g0_en/g4_en/

"The smaller r is, the longer a segment in the radial direction will be when measured with local yardsticks. As seen from OFF: yardsticks shorten in the radial direction with increasing strength of the gravitational field! Thus, for the thickness of a spherical shell around M, a local surveyor determines a larger value than an observer in OFF. "

[EDIT: found better discussion of this:

http://www.mathpages.com/rr/s7-03/7-03.htm ]

Bjarne

Oct12-11, 01:25 AM

First of all speed of light globally is not the same everywhere.
Statement that "laws of physics are the same in all inertial reference frames" means that local experiments will give the same results. But global observations can be different.

I guess the different speed of light happens doesn’t matter whether the length of the rulers always is comparable the same or not.

Bjarne

Oct12-11, 02:20 AM

With regard to the first reference, the following is said:

"Gravitational Length Contraction

Lengths of objects in gravitational fields are contracted according to the theory.

Right
I agree (and "disagree").
Notice Observer “Ex” (external) will not see any length contraction.
Seen from the perspective of "Ex" the distance of the Milkyway would be the same for both A and B.

B is deeper inside the gravitionel field of the Sun. He will complete 1 orbit in less time as A.

If B shall have the right to claim that the orbit of the MW is shorter (length contraction), it is only possible if B’s ruler is comparable longer than A’s.

Do you understand that point? – It seems like a contradiction but it is not, but rather a mathematical necessity that B’s meter stick must be longer than A’s.
(You must also respect the mathematical reality of observer Ex, - Observer Ex must also have the possibility to understand other realities - relative to his own )

B and A’s perception of speed can also not possible be the same, simply because B’s clock is ticking slower.

We should not be allowed to mix realities, hence also not to force our (A’s) perception of speed into B’s reality.

So since B’s time-rate is ticking slower, - that alone should mean that B moves FASTER than A, - but because B’s ruler (seen from a mathematical point of view) must be longer the speed is the “same” – but not comparable the same.

Notice A and B will agree to complete the orbit of the MW in the exact same period, but they can impossible agree about distance / circumstance / time / rulers.

I appreciate your contribution to the thread and I understand most of what you have explained, but still I wish there was a simpler way to understand and compare how B's reality really is, as well as understand how would B’s ruler would be compared to A’s.

I think there still is more to discover to make that simpler, straight and logical.

zonde

Oct12-11, 05:48 AM

I guess the different speed of light happens doesn’t matter whether the length of the rulers always is comparable the same or not.
It matters. Length of rulers is related to local speed of light and local rate of clocks.

A.T.

Oct12-11, 08:24 AM

Are you perhaps saying that the increase in radius and volume between shells of lower r-values over the expected Euclidean values is not due to the fact that space is no longer Euclidean but due to the fact that rulers shrink?
I think these are just two different ways to say the same thing:

- The space in not Euclidean, so rulers measure more radius than expected based on the circumference, so the rulers appear to be shrunk when compared to identical rulers placed around the circumference.

This is equivalent to:

- The space-time in not Euclidean, so clocks measure less time than expected, so the clocks appear to be slowed down when compared to identical clocks placed around the circumference.

PAllen

Oct12-11, 09:20 AM

Right
I agree (and "disagree").
Notice Observer “Ex” (external) will not see any length contraction.
Seen from the perspective of "Ex" the distance of the Milkyway would be the same for both A and B.

Correct, some observer floating away from the milkyway would see these distances the same.

B is deeper inside the gravitionel field of the Sun. He will complete 1 orbit in less time as A.

If B shall have the right to claim that the orbit of the MW is shorter (length contraction), it is only possible if B’s ruler is comparable longer than A’s.

Do you understand that point? – It seems like a contradiction but it is not, but rather a mathematical necessity that B’s meter stick must be longer than A’s.
(You must also respect the mathematical reality of observer Ex, - Observer Ex must also have the possibility to understand other realities - relative to his own )

Here, you have confused several things. The length contraction I described had to do with local rulers as perceived by a distant observer. However, I never proposed a way to use local ruler measure for astronomic distances (it is possible, building a ladder of distances).

Totally independent of the issue of local rulers perceived from a distant free fall observer, I proposed a different, simple convention for astronomic distances (radar ranging, using local time, and assumption speed of light is isotropically c. It is only using this convention (rather than local rulers) that you end up with shorter distances to distant objects, and thus the same speed measured by A and B.

Note that whatever definitions are used, some measurements by A and B will differ (assuming each uses the same definitions). This is not unexpected or inconsistent with invariance of laws of physics.

Let's state what is really claimed by different relativity principles:

1) Galilean relativity: All laws take the same, simplest, form in any inertial frame. Note, this never meant that measurements are the same, only laws (equations) relating measurments. The main thing wrong with this was that its law for velocity transformation between inertial observers turned out to be experimentally incorrect. Between observers with relative acceleration, there is no simple relativity, and laws take more complex form.

2) Special relativity: Same principle as above, except the transformation law between different frames is different and consistent with experiment. In particular, there is no 'relativity' between observers undergoing relative acceleration.

3) General relativity gives you both less and more. The laws of special relativity only apply locally, for inertial observers, defined as those in free fall. There is no unique answer at all to such things as long distances or velocity of a distant object (whether for inertial observers or non-inertial observers). Instead there are only useful conventions you may choose, and procedures for making valid physical predictions based on whatever conventions you choose. There is a general formulation of laws such that whatever conventions are used by any observer, the laws in this form apply (but measurements are not the same). However, the same conventionality of coordinates means, in practice, you use transformation rules to convert your measurements to the most convenient coordinates for calculation.

Based on (3), your A and B observes each know they are non-inertial; they know the magnitude of their acceleration. Seeing the sun, and making measurements, they can determine the quali-local structure of spacetime. What each does, in practice, is convert their local measurements, using the predictions of GR to accomplish this, to milkyway center coordinates (each able to determine a different required clock adjustment, for example). They compute distances, speeds, etc. in this frame. Each one doing this ends up with the same predictions and values. This is all that is expected, and found to be true.

B and A’s perception of speed can also not possible be the same, simply because B’s clock is ticking slower.

You cannot make such a blanket statement. It depends on measurement conventions. I have shown that there exists a simple convention that has the property that A and B differ on distances and times such that speeds of distant objects come out essentially identical. Other equally valid measurement conventions will lead to different results. However, GR provides the precise rules allowing A and B to make the same physical predictions whatever consistent conventions they use, and compare results, as long as each knows the other's conventions. The requirement on consistency here are very broad (one-one mapping of spacetime, continuity conditions, etc.).

We should not be allowed to mix realities, hence also not to force our (A’s) perception of speed into B’s reality.

There is really one reality in GR - the spacetime manifold. There are many ways to label events in it, and many different physical processes for taking measurements, that can be used at different places, times, instrument speed etc. GR allows any of these to be used to probe the underlying reality. However, the underlying reality does not include statements such as a unique valid distance between distant objects, nor a unique valid relative speed between distant objects.

So since B’s time-rate is ticking slower, - that alone should mean that B moves FASTER than A, - but because B’s ruler (seen from a mathematical point of view) must be longer the speed is the “same” – but not comparable the same.

Notice A and B will agree to complete the orbit of the MW in the exact same period, but they can impossible agree about distance / circumstance / time / rulers.

That all depends on how they take and interpret measurements. Using raw local measurements, some of these must disagree (but not necessarily all of them, and many choices about which differ). However, if each converts their measurements to an agreed common coordinate convention, using the predictions of GR, they will agree on everything.

I appreciate your contribution to the thread and I understand most of what you have explained, but still I wish there was a simpler way to understand and compare how B's reality really is, as well as understand how would B’s ruler would be compared to A’s.

I think there still is more to discover to make that simpler, straight and logical.

Bjarne

Oct16-11, 06:56 AM

Here, you have confused several things. The length contraction I described had to do with local rulers as perceived by a distant observer.

My point is imaging you could jump between A and B’s reality, which difference would there be , except time ?

Well I have come to a new simpler conclusion.
When I would jump from A’s to B’s reality, I would see the exact same Universe.
The distance between the earth and the Moon, or any other distance would be exact the same everywhere.

But if we compare these 2 realities, - B’s reality would be a bit smaller. - Everything would be a bit smaller, also the ruler.
That could then also explain the cause of the Shapiro delay http://en.wikipedia.org/wiki/Shapiro_delay
Because speed of light must then be measured in the local surroundings.

Edit
No
I change my mind
This can't be true because then there would be no Shapiro delay, but rather opposite

PS
Any idea what is causing the Shapiro delay ?

Bjarne

Feb12-12, 01:11 AM

ghwellsjr

Feb12-12, 02:18 AM

Let's say the International Space station (ISS) was orbiting the Sun in the exact same orbit as the Earth.

A clock on board the ISS and the Earth would now tick different due to different gravity.

This mean that the laws of orbit gravity can't be the same these 2 places, simply because the time consumption to complete one orbit for both objects, - is larger for the ISS

So what is wrong?

I mean the law of nature must be the same everywhere, or ?

Is the answer that; - the length of one second not is the same both places , - or in other words that one second is "stretching" on board the Earth (compared to one second on board the ISS) and therefore longer compared to one second at the ISS ?

I mean the time to complete one orbit must be the same on board at both objects, but a clock on board the 2 objects would not show this.

There must be a simple way, basic to explain which factor(s) is (are) changing
You don't have to use the example of the ISS in the same orbit as earth but far removed to make your point. You can use the simple fact that atomic clocks near sea level at Greenwich tick at a different rate than identical atomic clocks at Boulder Colorado at an elevation of one mile. They would each say that the orbit of earth around the sun takes a different amount of time based on their own coordinate system.

But what is important is that they both measure the same value for the speed of light and in order to do that, they must use the time from their local clock, not some other time such as from GPS which gives the same time for every point on earth.

DaleSpam

Feb12-12, 06:49 AM

A clock on board the ISS and the Earth would now tick different due to different gravity.Yes.

This mean that the laws of orbit gravity can't be the same these 2 places, simply because the time consumption to complete one orbit for both objects, - is larger for the ISS How do you get from the above correct statement to this incorrect conclusion? The law of physics which pertains to this situation is GR. What makes you think that GR states that both clocks should measure the same time?

Bjarne

Feb12-12, 04:06 PM

You don't have to use the example of the ISS in the same orbit as earth but far removed to make your point. You can use the simple fact that atomic clocks near sea level at Greenwich tick at a different rate than identical atomic clocks at Boulder Colorado at an elevation of one mile. They would each say that the orbit of earth around the sun takes a different amount of time based on their own coordinate system.
Correct
But the example of the ISS and the Earth orbiting the exact same orbit is at least for me easier to handle, because both such observers (these places) must be right, which mean the time one orbit takes can't be the same.

Hence there is a problem since the gravity-orbit-equations a ISS inhabitant and a Earth inhabitant will use, - will not give the same result.
For exsample to determinate their speed or orbit size.

So whos calculation will be wrong?
The Earth observer or the ISS observer?

Option 1 is the definition of 1 second cannot be universal.
Option 2, - this is what wrote about above, ( but now I have change my mind) and believe option 1 must be correct.

You don't have to use the example of the ISS in the same orbit as earth but far removed to make your point. You can use the simple fact that atomic clocks near sea level at Greenwich tick at a different rate than identical atomic clocks at Boulder Colorado at an elevation of one mile. They would each say that the orbit of earth around the sun takes a different amount of time based on their own coordinate system..
It is the same kind of problem, 2 observers (on the Earth), -one living in a cellar and another one in a skyscraper, - both would not be able to agree how long time it takes the light (e.g; from the sun) to reach a certain point of the earth.
So what is wrong, - which simple factor(s) must be flexible?

Is it the definition of how long 1 second is from place to place, - or is it distances or/and speed that not are the same in such 2 observer realities. ?

As I wrote I believe it is “one second” that cannot have a universal definition.
If that should be wrong WHAT is hen the correct answer?

The answer must as I see it be simple, logical and understandable - since we are discussion simple math, >> time multiplied with speed must = distance ( and not for exsample distances)

Bjarne

Feb12-12, 05:07 PM

How do you get from the above correct statement to this incorrect conclusion? The law of physics which pertains to this situation is GR. What makes you think that GR states that both clocks should measure the same time?

Because ………….
Let say one (atomic) clock is on board at the ISS and another on board of the Earth, both objects orbit the Sun in the exact same orbit.

Let’s say the clock on board the ISS ticks double so fast compared to a clock at the Earth (due to different gravity)
And exactly this is the problem, - because time is different these 2 places.

Hence many laws / equations cannot give the same result.
1 orbit of the Sun cannot at the same time be both 500 million km and also 250 million km.
This should be pretty simple, at least so long time multiplied with speed must = distance.
Due to time is not the same even in the same orbit, we have such principle problem (just not so exaggerated as the example shows,).

This means that either equation-constants, distances and/or speed, - or the definition of 1 second cannot be the same in different space-time realities.
Does the stable nailed definition of one second mean that we are mixing ingredients of different space-time realities?
As I see the difination of "one-second" cannot be universal, and if it really should be how can we know it is so?

It seems that “our definition” of 1 second simple cannot be used in other space-time realities..
I know this will confuse you, - but the point is that yes a process in a different space time reality can be either faster or slower as here at the planet.

How can equation and laws of gravity be exactly the same everywhere, something must give and take. Why doesn’t it seem to be answer to these questions?

Shortly spoken, let say 1 second is the same length everywhere, - but the process responsible for the definition of 1 second is not the same. Is that possible?

DaleSpam

Feb12-12, 05:15 PM

Hence there is a problem since the gravity-orbit-equations a ISS inhabitant and a Earth inhabitant will use, - will not give the same result.
For exsample to determinate their speed or orbit size.

So whos calculation will be wrong?
The Earth observer or the ISS observer?Why should either one be wrong? If the ISS and the Earth observers both use GR then the ISS observer can calculate what both he and the Earth observer can measure, and likewise with the Earth observer. Then they can each perform the measurements and see if they agree with the predictions. If they each do the math correctly then the ISS observer can calculate what the Earth observer will measure and vice versa. Assuming they mach with the observations, then in what way is anyone wrong?

DaleSpam

Feb12-12, 05:18 PM

Hence many laws / equations cannot give the same result. Please be specific. The relevant law is GR, so what is the specific difference between the Earth GR and the ISS GR? In what way is GR at all modified between the two frames?

Simply because two different observers measure something different does not mean that the law governing the measurement is different. For example, due to Doppler shift two different observers will measure different frequencies for a given light source, but that by itself does not imply that Maxwell's equations are different.

Bjarne

Feb12-12, 05:34 PM

Why should either one be wrong? If the ISS and the Earth observers both use GR then the ISS observer can calculate what both he and the Earth observer can measure, and likewise with the Earth observer. Then they can each perform the measurements and see if they agree with the predictions. If they each do the math correctly then the ISS observer can calculate what the Earth observer will measure and vice versa. Assuming they mach with the observations, then in what way is anyone wrong?

So long that time multiplied with speed, is a valid equation, both observer cannot agree about the circumstance of the same orbit.
Right?

So you can sit on the Earth and calculate the orbit of the Earth and you will get a certain result. – You will believe this is 100 % true.

A ISS inhabitant can do the same from his perspective, - and from the exact same orbit, he also will believe his result is absolute right about the circumstance just calculated.

But since time is not the same, (and I assume we agree speed is the same) – we have now 2 different circumstances, - these can’t be the same.

So who is wrong and who is right?

I mean do you believe the orbit of the Earth can be both 250 billion km and also 500 billion km ?

It doesn’t sound logical - and hence hard to buy.

DaleSpam

Feb12-12, 07:17 PM

So long that time multiplied with speed, is a valid equation, both observer cannot agree about the circumstance of the same orbit.
Right?

So you can sit on the Earth and calculate the orbit of the Earth and you will get a certain result. – You will believe this is 100 % true.

A ISS inhabitant can do the same from his perspective, - and from the exact same orbit, he also will believe his result is absolute right about the circumstance just calculated.

But since time is not the same, (and I assume we agree speed is the same) – we have now 2 different circumstances, - these can’t be the same.

So who is wrong and who is right?

I mean do you believe the orbit of the Earth can be both 250 billion km and also 500 billion km ?

It doesn’t sound logical - and hence hard to buy.There is a race track near my town. One driver, racing for team ISS, stays always on the outside edge of the race track, and the other, racing for team Earth, stays always on the inside edge of the race track.

Using their odometers they each measure the length of 100 billion laps around the same track. One obtains a length of 250 billion km and the other 500 billion km.

So who is wrong and who is right? I mean, do you believe that the track can be both 250 billion km and also 500 billion km? It doesn't sound logical - and hence hard to buy.

Therefore, the laws of physics must clearly be different on the inside of the track and the outside.

Bjarne

Feb13-12, 02:42 AM

There is a race track near my town. One driver, racing for team ISS, stays always on the outside edge of the race track, and the other, racing for team Earth, stays always on the inside edge of the race track.

Using their odometers they each measure the length of 100 billion laps around the same track. One obtains a length of 250 billion km and the other 500 billion km.

So who is wrong and who is right? I mean, do you believe that the track can be both 250 billion km and also 500 billion km? It doesn't sound logical - and hence hard to buy.

Therefore, the laws of physics must clearly be different on the inside of the track and the outside.

This is not an identical analogy, but can rather be compared to that the orbit of Venus have different circumference than the Earth (Edit; - I wrote circumstance above this is of course wrong- bad english) .

According to this example there are no logical problems, except when you mean that the radius to the Sun is different measured from the Earth to the sun compared to measured from the ISS and to the sun, - even though both objects, - ( the Earth and the ISS) both would obit the Sun in the exact same orbit (and with the exact same speed).

Is that what you mean?

DaleSpam

Feb13-12, 06:14 AM

Bjarne

Feb13-12, 06:29 AM

Of course the analogy is not exact, then it would not be an analogy.

The point is that you are measuring different things and calling them the same thing. The surface of the earth and the ISS are different locations on a curved surface. There is no logical reason to expect them to measure the same thing, and no logical reason to conclude that the laws of physics are different.

You have not demonstrated any conflict with GR nor with logic.

Either speed, distance and/or the definition of 1 second can then not be the same. It is a simple mathematical necessity. I haven't got an excact answer where the "camel is buried"

I am just asking the simple question; - how would these space time realities look like (what would be the comparable difference) if I could jump between them, and see the differences?

I am not an expert in his field, but it is easy to see that the full story can’t have been told so far.

I also did not got the answer (yes or no) to whether the orbit circumference for exsample of the Earth really can be 2 different sizes, (the same orbit), according to the exsample mentioned above..

And if this is so, how can the law of gravity apply for both without contradictions.

DaleSpam

Feb13-12, 06:49 AM

Either speed, distance and/or the definition of 1 second can then not be the same. It is a simple mathematical necessity.Is it a mathematical necessity? I certainly haven't seen any derivation that would show that.

Although without a derivation posted from you it is hard to tell where you are going wrong in your thoughts, it seems to me that the mistake could be that you are mentally sticking to flat geometry. Since the geometry of GR is curved, you can easily get shapes as described without any logical contradiction.

I also did not got the answer (yes or no) to whether the orbit circumference for exsample of the Earth really can be 2 different sizes, (the same orbit), according to the exsample mentioned above.The two paths are not the same, so the answer is "yes, two different paths may have different lengths".

Each path is a 1D line (a helix) in a 4D curved spacetime. You can easily come up with coordinate systems where the two paths have two coordinates which are identical and constant, and you can parameterize the paths by one of the remaining coordinates, but they will always be different in at least the final coordinate. They are simply different paths with different lengths, no contradictions nor confusions.

And if this is so, how can the law of gravity apply for both without contradictions.You certainly haven't demonstrated any conflict with the law of gravity. I don't even know what you think would be contradicted here.

A.T.

Feb13-12, 06:52 AM

I mean do you believe the orbit of the Earth can be both 250 billion km and also 500 billion km ?
Depends on the convention used to measure distance. If we use the convention that distance is measured with rulers at rest, then distance is frame dependent. This is true even without gravity.

Agerhell

Feb13-12, 07:19 AM

Bjarne

Feb13-12, 08:36 AM

There are a lot of posts in this thread, maybe this is already answered.

Basically in a gravitational field, you previously mentioned Mercury and the Earth and now the Earth and a satellite following the Earths orbit around the sun, the perceived velocity of light, using an external clock will be slower deeper in a gravitational field. However, for a local observer the rate ot time will slow down in a gravitational field by the exactly same amount, so locally c will always be perceived as invariant. That the velocity of light slows down in a gravitational field is known as "Shapiro Delay" as i see is already mentioned.

Regarding the guy on Mercury watching an object fall down on earth (from say A to B), his clock will tick another amount of ticks than an earthbound observer. However, due to the fact that light slows down with exactly the same factor as time in a gravitational field both observers will acually agree on the acceleration, if both use local rate of time and how long light travels per time unit locally as measures.

Regarding ISS and the Earth, if, lets say, the conditions are such that the rate of clocks onboard the ISS is 1 percent faster than the clocks on Earth. Under such circumstances the light will also travel 1 percent faster around the ISS (less Shapiro delay). They ISS observer and the Earth observer will basically disagree on how many clock-ticks an orbit around the Sun takes.

However if the, by radar say, measure the distance to the sun they will also disagree on the distance to the Sun, as measured in local seconds.

But I really do not understand what you point is...

Very good explanation.

So... when a clock due to gravity difference (in a different space-time reference frame) ticks let's say comparable 1% slower compared to the earth-space-time reference frame, - both the Time is now 1% slower , and the ruler and speed is now all 1% (edit >>) larger , if I understand this correct (?)

So when time is stretching, distances (and hence speed) is doing the same.

The first point?
I was just wondering how relative differences would look like if I could jump between such realities and see the comparable difference.

A second point …
Hmmm now the whole solar system (and the rest of the whole universe) is 1% larger one place compared to the same universe seen from the Earth space-time perspective (if we could and would compare them).

To be extreme the difference can be much larger than only 1% ..
So how can it be the same universe?
I mean, - It seems that the whole Universe is either shrinking or stretching just because of local (gravity) differences, - not because the whole universe is “so much” affected by the ISS or a fast moving muon a collapsing star or what so ever.

It seems it ‘all’ ( the optical transformation) happens “locally” (?).
Well I believe we just must say, - this is how it is.
Nothing is maybe what is seems to be… or?

DaleSpam

Feb13-12, 12:08 PM

Bjarne, please go back and read my post 111, particularly the second section. There I explain that the spacetime paths are different. The fact that different paths have a different length is no large surprise. When you measure different things you get different results, like if you measure my height and yours and find that they are 1% different.

The first point?
I was just wondering how relative differences would look like if I could jump between such realities and see the comparable difference. What different realities? Would you assume that reality is different because my height is different from yours?

A second point …
Hmmm now the whole solar system (and the rest of the whole universe) is 1% larger one place compared to the same universe seen from the Earth space-time perspective (if we could and would compare them).Would you claim that the universe is a different size for you than it is for me simply because our heights are different? Would you claim that rulers have changed size or that clocks have changed rates?

All of your confusion seems to stem from the incorrect assumption that the two different paths are the same and should therefore have the same length. Not only are they not the same path, there is also no symmetry that you can invoke here to claim that they should have the same length. Once you let go of that erroneous assumption then hopefully everything else falls into place.

Bjarne

Feb13-12, 01:24 PM

Bjarne, please go back and read my post 111, particularly the second section. There I explain that the spacetime paths are different. The fact that different paths have a different length is no large surprise. When you measure different things you get different results, like if you measure my height and yours and find that they are 1% different.

What different realities? Would you assume that reality is different because my height is different from yours?

Would you claim that the universe is a different size for you than it is for me simply because our heights are different? Would you claim that rulers have changed size or that clocks have changed rates?
.
When distances between the ISS and the Sun, and between the Earth and the Sun no longer are comparable the same, - even in the exact same orbit - the diameter of the Sun is also not, also not the diameter of the Earth or the Moon, or the diameter of New York, Cadillac’s, rulers or the distance to whatever else it may be.
I cannot imagine that some distances would change but not all. – Which mean that the whole universe also not can be the same for such 2 different space-time observers?

This cannot be so surprising, - So fare I understand a photon is everywhere at the same time,- or nowhere at the same time. – What I am saying is that distances do no linger exist. It is even wrong to say “the same time” because time doesn’t exist too from that perspective. Well this is off course an extreme perspective but this is the direction relativity goes isn’t it?

DaleSpam

Feb13-12, 01:33 PM

I cannot imagine that some distances would change but not all. There is no distance which has changed. Two different spacetime paths have two different distances.

Bjarne

Feb13-12, 01:37 PM

There is no distance which has changed. Two different spacetime paths have two different distances.
Right
You know what I mean anyway.

DaleSpam

Feb13-12, 01:57 PM

Right
You know what I mean anyway.Yes I know what you mean, but what you mean is illogical given the above. The fact that the lengths of two different paths are different does not imply any of the conclusions you have made about the laws of physics changing or anything else changing.

Bjarne

Feb13-12, 02:23 PM

Yes I know what you mean, but what you mean is illogical given the above. The fact that the lengths of two different paths are different does not imply any of the conclusions you have made about the laws of physics changing or anything else changing.

How would you define and limit the comparable distance difference to a "path" - for example the path of the ISS or the path of the Earth ?
For example where are the "borders” to what belong to the path and what is not the path. - Logical I would say it is everything or nothing, not only a path. It simply sounds wrong in my ears.

DaleSpam

Feb13-12, 04:16 PM

Perhaps it would help to talk a little about the curved geometry of this situation.

If we consider a spherical coordinate system centered on the sun then we can fix r to be the earth orbital radius and we can fix the azimuthal angle to be in the orbital plane. That leaves only the orbital angle and time. So we have reduced the problem from 4 dimensions down to 2 dimensions and we can consider curved 2D surfaces embedded in a non-physical flat 3D embedding space which would accurately represent the geometry of the situation.

So, our space is essentially a cylinder, and if there were no spacetime curvature then the cylinder would be flat, meaning that you could cut it and lay it out on a table smoothly without any bumps. However, there is spacetime curvature, specifically, there is a little "dent" on the cylinder which goes around the cylinder in a helical pattern.

Now, suppose we draw a vertical line along the cylinder and we measure the length of the path around the cylinder down in the bottom of the helical dent and the length of the path up on the top edge of the helical dent from one intersection with the line to the next.

We will find that those lengths are slightly different. This is not because our measuring device is different from the top to the bottom of the dent, nor that the laws of physics are different, but simply because we are measuring the length of a different path. Due to the curvature of the space the lengths are different even though in the original 4D space the paths have the same radius.

This is why understanding the concept of curved spacetime is essential to understanding gravity and how it can be represented in a self-consistent, non-contradictory manner. It becomes very difficult to describe verbally, and that is why the math is important.

Bjarne

Feb13-12, 11:32 PM

Let’s now (again) say that the time dilation is 50% at the ISS.
Again the ISS and the Earth is in the same orbit. Only gravity is different.

The mission is now a gravity experiment. Acceleration due to gravity (ADG) must be measured on board. On board is a ruler completely identical to one on Earth.

A stone is dropped from 1 meters altitude and reach the bottom.
From Earth we can observe the same event, - we will now say that ADG was exactly as we beforehand have calculated, it was 1 m/s. – But on board they do not agree, because it took the stone 2 second to reach the bottom.

So is the gravity constant “G” not the same.
Is it something wrong with the ruler, I mean is a 1 meter ruler no longer 1 meter ?
Is something wrong with the universal definition of one second?
And finally, how can we be sure what the problem is?

DaleSpam

Feb14-12, 05:57 AM

Bjarne

Feb14-12, 08:09 AM

Before we change topics, do you understand and agree with the above? I.e. do you understand and agree that simply measuring a different time for one orbit does not imply any of the universe-is-changing or laws-of-physics-are-changing conclusions? Do you understand the curved geometry presented?

Before we change topics, do you understand and agree with the above? I.e. do you understand and agree that simply measuring a different time for one orbit does not imply any of the universe-is-changing or laws-of-physics-are-changing conclusions? Do you understand the curved geometry presented?
I don’t understand how comparable space-time distances both can be the same and not the same at the same time.
As I understand it you say that the orbit path would be comparable different for the ISS compared to the Earth, - (even though the Earth would follow the exact same orbit).
This must mean that you also must agree that the radius to the Sun is comparable different too.
If there is a long train beside the "radius path" or "orbit-path" - this too must off course be comparable different, and hence also the rest of the Universe.
I mean before complicating it all, try to answer the very simple questions asked in post 122. Try to keep it so simple as possible, and let’s then start from there.

Let me show what I mean...

Question;
So is the gravity constant “G” not the same?
Supposed answer;
I guess it must be Yes.

Question;
Is it something wrong with the ruler, I mean is a 1 meter ruler no longer 1 meter?
Supposed answer….
I don’t know how you would answer.
But it is pretty logical that when the calculation-result of Acceleration Due to Gravity (ADG) at the ISS must be correct both seen from the Earth’s perspective and seen from the ISS perspective, - then the ruler on board must be 1 meter seen from the Earth perspective and 2 meter seen from the IIS perspective, so that the result of ADG in both cases is the same = 1m/s.

Take a look at the equation
MG/r^2 – We both agree that M and G is the same values both places, so the only factor we can adjust is now “r” ( the ruler) as I just did. – But this could be wrong, because we can also just say that the definition of one second is not the same. We do ONLY have these 2 option – so long GM is nailed.

When the laws of nature (e.g the equation MG/r^2) is universal, - for me it seems that (at least) one of these factors must be flexible.

You said (above) distances is not comparable the same, - so what do you mean?.
I have no idea how you can limit that to only be valid for the “path”
A falling stone follows its own path
A light beam also, and these are also affected, so how can you say comparable differences are limited to a certain path?

An third observer (let say on the Sun) would not see any difference to the paths, he would see both objects orbiting the same orbit/path.
So it makes no sense to say that the “path” is the key to any truth understanding.

At least try to answer this question; - What would be the comparable difference between the ruler on board the ISS and the one still on the Earth?

Question;
Is something wrong with the universal definition of one second?
Supposed answer;
I understand it is not, but I am not convinced.
How can we know which factor(s) is/are comparable different.
Yes a clock would be ticking different, but is it the definition of 1 second really universal ?

Shortly Spoken
I am not convinced about anything so long it seems to be so complicated, - in a simple way - to explain what must be comparable space-time differences .

Agerhell

Feb14-12, 09:21 AM

I don’t understand how comparable space-time distances both can be the same and not the same at the same time.
As I understand it you say that the orbit path would be comparable different for the ISS compared to the Earth, - (even though the Earth would follow the exact same orbit).
This must mean that you also must agree that the radius to the Sun is comparable different too.
If there is a long train beside the "radius path" or "orbit-path" - this too must off course be comparable different, and hence also the rest of the Universe.
I mean before complicating it all, try to answer the very simple questions asked in post 122. Try to keep it so simple as possible, and let’s then start from there.

Let me show what I mean...

Question;
So is the gravity constant “G” not the same?
Supposed answer;
I guess it must be Yes.

Question;
Is it something wrong with the ruler, I mean is a 1 meter ruler no longer 1 meter?
Supposed answer….
I don’t know how you would answer.
But it is pretty logical that when the calculation-result of Acceleration Due to Gravity (ADG) at the ISS must be correct both seen from the Earth’s perspective and seen from the ISS perspective, - then the ruler on board must be 1 meter seen from the Earth perspective and 2 meter seen from the IIS perspective, so that the result of ADG in both cases is the same = 1m/s.

Take a look at the equation
MG/r^2 – We both agree that M and G is the same values both places, so the only factor we can adjust is now “r” ( the ruler) as I just did. – But this could be wrong, because we can also just say that the definition of one second is not the same. We do ONLY have these 2 option – so long GM is nailed.

When the laws of nature (e.g the equation MG/r^2) is universal, - for me it seems that (at least) one of these factors must be flexible.

You said (above) distances is not comparable the same, - so what do you mean?.
I have no idea how you can limit that to only be valid for the “path”
A falling stone follows its own path
A light beam also, and these are also affected, so how can you say comparable differences are limited to a certain path?

An third observer (let say on the Sun) would not see any difference to the paths, he would see both objects orbiting the same orbit/path.
So it makes no sense to say that the “path” is the key to any truth understanding.

At least try to answer this question; - What would be the comparable difference between the ruler on board the ISS and the one still on the Earth?

Question;
Is something wrong with the universal definition of one second?
Supposed answer;
I understand it is not, but I am not convinced.
How can we know which factor(s) is/are comparable different.
Yes a clock would be ticking different, but is it the definition of 1 second really universal ?

Shortly Spoken
I am not convinced about anything so long it seems to be so complicated, - in a simple way - to explain what must be comparable space-time differences .

I really do not get where you want to go with this discussion. Basically in a gravitational field of a planet or some other objects there are two effects:

1. Light slows down with a certain factor, sometimes named as "the Shapiro effect".
2. Time as measured with a local clock slows down with exactly the same factor, often called "gravitational time dilation".

This means that the locally measured velocity of light as "Distance travelled per time unit" will always be the same and equal to "c".

The fact that light and time slows down in a gravitational field has no "magical effects" as you seem to believe...

Assuming the guys on the Earth, Mercury, the ISS or whatever example you have made are decent physicisists they can do the math. These effects basically complicates things, especially for an instituion such as Nasa that has spacecrafts moving around that they are trying to communicate with using frequencies that may appear different and trying to get the spacecrafts to start their engines at exactly the right time although there are several factors that have influence on the clock of the spacecraft and relativity is also a factor when trying to decide how long time it will take a signal to get from the Earth to the space-craft...

So there is no magic, only the fact that light and time slows down in a gravitational field that complicates the computations. Of course for Nasa you also have gravitational redshift to put up with which might have to be described as a third effect...

DaleSpam

Feb14-12, 09:22 AM

I don’t understand how comparable space-time distances both can be the same and not the same at the same time..Of course, they cannot be both the same and not the same, that is nonsense and nobody is claiming that except you. They are simply not the same.

As I understand it you say that the orbit path would be comparable different for the ISS compared to the Earth, - (even though the Earth would follow the exact same orbit).Yes, they are two different paths with different lengths.

This must mean that you also must agree that the radius to the Sun is comparable different too.

If there is a long train beside the "radius path" or "orbit-path" - this too must off course be comparable different, and hence also the rest of the UniverseNo, the radius and the azimuthal angle coordinates are the same for both paths, as discussed above in post 121. Because the geometry is curved, the fact that the lengths of the two paths are different does not imply that the radius of the two paths are different.

We have a situation with curved geometry and you are making conclusions based on reasoning from flat geometry. Such conclusions will generally be wrong.

One other subtelty that you may not be aware of which may be important: there is a difference between a radial coordinate and the length of some spacelike path along the radial direction. I have been refering to the former, which is what I have assumed you meant by "radius".

Bjarne

Feb15-12, 12:56 AM

Ok
I understand much better now, thank’s...
But still I wonder that when calculation based on GM/r^2 would show a stone will fall let say 1m/s^2 a certain place (due to gravity) different space-time observer would say that they have seen the stone was falling ½ , - or - 2 m/s^2, - (because time ticks different).
So who is all right, and wrong, - and why?
GM is the same, - "r" should also be, so how is it possible that the results are different?
Yes, because of time is different, - but do that not mean that when we compare distances these cannot be the same?
Or that the GM/r^2 not is universal.
This is really what mostly confuses me.

A.T.

Feb15-12, 04:07 AM

1. Light slows down with a certain factor, sometimes named as "the Shapiro effect".
2. Time as measured with a local clock slows down with exactly the same factor, often called "gravitational time dilation".
...
Of course for Nasa you also have gravitational redshift to put up with which might have to be described as a third effect...
Is the gravitational redshift are third effect, or just a manifestation of 2?

DaleSpam

Feb15-12, 06:12 AM

Or that the GM/r^2 not is universal.This is essentially the correct one. Newtons law of gravitation is not, in fact, a law of nature. The law of nature (as far as we can tell) is the Einstein Field Equations. Newtons law is a reasonable approximation for certain situations.

The laws of nature are the same for the ISS and on the surface of the Earth, but GM/r^2 is not one.

Bjarne

Feb18-12, 07:03 AM

This is essentially the correct one. Newtons law of gravitation is not, in fact, a law of nature. The law of nature (as far as we can tell) is the Einstein Field Equations. Newtons law is a reasonable approximation for certain situations.

The laws of nature are the same for the ISS and on the surface of the Earth, but GM/r^2 is not one.

http://www.science27.com/images/img_1.jpg
Each time the radius of a circle doubles, the area quadruples.
Since, in this case, the circles share a common centre, the space the larger circle occupies, that the smaller circle does not, accounts for 75% of the larger circle’s area.
At the same time the force of acceleration due to gravity (ADG) always decreases by 75%.
Is this a coincidence, or rather expresses a relation between matter, space and gravity that we haven’t understood?

http://www.science27.com/images/img_17.jpg
So, - when the acceleration due to gravity decreases by 75 %, the distance square increment will increase inversely proportional by 75 %.
As we can see there is equal proportionality between space (square) increase, and gravity decrease and hence the proportional 1:1
Hence the equation GM/r^2 in fact seems to reflect a law of nature, also even though we can’t say we have understood why this seems to be so.

I am therefore not convienced that we in this case can conclude that : "The Newtons law (only) is a reasonable approximation for certain situations".
Rather it seems that the equation GM/r^2 is universal, and only can be understood so, - so long the proportional’s 1:1 is respected.

This mean that result of the equation only is valid in the particular space-time where the calculation apply.

Let us now say that ADG (acceleration due to gravity) must be calculated on a white dwarf.
Based on the known mass of the star all observers that would calculate the expected ADG of the star (at the surface), would (off course) come to the same result, - let’s say 1000m/s^2.

Let's say time is ticking 50% slower at the surface of the star compared to Earth.
How far would a stone accelerate the first 1 second?
Will a stone now fall 1000 meter the first second or for example 2000 meter, due to the slower time rate at the star? - or how far?

The answer must be; - because the definition of the second and the meter both are universal and of course also MG too (in the equation GM/r^2), - we are dealing with a mathematical equation with only 1 variant, - and this is time.

Purely mathematical we are then forced to conclude that when a Earth based observer is watching the stone that falls to the ground on the star, he must observe that the stone falls 1000 meter the first second, - but because time is ticking comparable slower locally on the star, locally observed it must fall 2000 meter the first second. (As you can see this puts the Earth in some kind of relativistic center).

Both observer are observing the same event in the same period of time (although time ticks different), - and the result is obvious different.
Off course this is a contradiction, both results cannot be true. The equation only allows one result and this is 1000 meter the first second.

Hence it is off course easy to conclude that the Newtonian equation only is an approximation.
But remember there is equal proportionality between space (square) increase and gravity decrease and hence the proportional 1:1 , - shown above. This proportionality doesn’t sounds like an insignificant coincidence.
The fact that the cause of this not is understood, and hence also not whether this is a reflection of a law of nature, or not, - should that not mean that we must be more carefully to violate what could be a law of nature?

Does that not mean that the equation instead maybe should be treated like was it a law of nature?
If so the consequences would be that the result of the equation GM/r^2 =(for example ADG = 1000 m/s^2) only is valid in the particular space-time where the calculation (the time rate) is connected to, - and that that distance always must stretch and shrink proportional with time dilation.

This is the only possibility (as I see it) that not would violate the nice equal proportionality between square and magnitude of ADG .

Would that be possible?

DaleSpam

Feb18-12, 08:15 AM

Each time the radius of a circle doubles, the area quadruples. If and only if the space is flat.

At the same time the force of acceleration due to gravity (ADG) always decreases by 75%.
...
Hence the equation GM/r^2 in fact seems to reflect a law of nature, also even though we can’t say we have understood why this seems to be so.
You are assuming your conclusion, this is called circular reasoning.

If it were true that the force of the acceleration due to gravity (weight) always decreased by 75% then GM/r^2 would be a law of nature. However, the fact is that if you make sensitive measurements you find that your assumption does not reflect reality.

Bjarne

Feb18-12, 01:18 PM

If and only if the space is flat.

No, ADG is always equal proportional with the square increase, and yes, only when you equal square with "space" – space must be flat. .
I am not saying we understand what the proportionality is reflecting, only that it is remarkable and deserves attention.

If it were true that the force of the acceleration due to gravity (weight) always decreased by 75% then GM/r^2 would be a law of nature. However, the fact is that if you make sensitive measurements you find that your assumption does not reflect reality.
What happens when the ADG equation only is valid as a "flowing equation" , only valid at a local point in space time, - as I wrote above?
Furthermore what happens when distances is proportional stretching / shrinking with time dilation ?
Anyway maybe there is more to discover, also not relativity always seems to give us the expected results.
http://www.nature.com/news/2011/111005/full/news.2011.575.html

DaleSpam

Feb18-12, 03:20 PM

No, ADG is always equal proportional with the square increaseThis is not true. It is approximately true in many cases, but it fails for others.

You need to stop assuming your conclusion, it is circular logic. And it is particularly bad when your assumption has been falsified experimentally.

Bjarne

Feb18-12, 03:28 PM

This is not true. It is approximately true in many cases, but it fails for others.

You need to stop assuming your conclusion, it is circular logic. And it is particularly bad when your assumption has been falsified experimentally.

The equation is true, and the ADG/Square proportionality result of that is also true.
That the equation "fails for others" etc... - to reflect measurement is a different story.

DrGreg

Feb18-12, 03:57 PM

The equation is true, and the ADG/Square proportionality result of that is also true.No matter how many times you say it is true doesn't make it true. Einstein and Schwarzschild proved it to be false.

The nearest equation general relativity can provide is
g = \frac{GM}{r^2\sqrt{1 - \frac{2GM}{rc^2}}}
That is only true in certain circumstances -- a non-rotating uncharged spherically-symmetric mass and an observer at rest relative to the mass and whose own mass is insignificant -- and even then, r isn't quite what you thought it was -- the circumference of a circle around the mass divided by 2π.

Agerhell

Feb18-12, 07:24 PM

If and only if the space is flat.

You are assuming your conclusion, this is called circular reasoning.

If it were true that the force of the acceleration due to gravity (weight) always decreased by 75% then GM/r^2 would be a law of nature. However, the fact is that if you make sensitive measurements you find that your assumption does not reflect reality.

Now, that was interesting Dalespam. Have you conducted any experiment and come to the conclusion that the gravitational force between two spherically symmetric objects is anything ells than F=GMm/r^2? Or at least maybe you can provide some more information regarding that experiment that you are refering to.

If the two spheres are moving with respect to each other in your experiment I may agree with your findings.

Bjarne

Feb19-12, 01:17 AM

No matter how many times you say it is true doesn't make it true. Einstein and Schwarzschild proved it to be false.

The nearest equation general relativity can provide is
g = \frac{GM}{r^2\sqrt{1 - \frac{2GM}{rc^2}}}
That is only true in certain circumstances -- a non-rotating uncharged spherically-symmetric mass and an observer at rest relative to the mass and whose own mass is insignificant -- and even then, r isn't quite what you thought it was -- the circumference of a circle around the mass divided by 2π.

You misunderstood what I wrote above.
I am not saying that relativity is wrong, but only that the proportionately between ADG and Square increase 1:1 , as a result of the equation itself, - is true ( in a classic sense).
That things are different in relativity is a different history.

I agree that the equation gives contradictory result when compared to relativity; at least we must expect the result of it to be limit to local space-time.

The point is only that I wonder whether the equation when put right together with other facts, for example Schwarzschild , and relativity , - could it maybe be so that the proportionality 1:1 reveals a aspect of a law of nature that we have overlooked, and that maybe not is in conflict with relativity, but instead forms a synthesis?

I don’t know, I am not an expert in this field, but I think the proportionality is remarkable, and maybe could be a clue to discover something that maybe could have been overlooked .

One thing is that time ticks different, and that space is really strange, but another question is; - are there more to discover in this field? Or have we fully understood the nature of space?
I mean we know matter is deforming space.
From a classical perspective we see that ADG and square increase is connected proportionally 1:1 , - this could at least be a clue to better understanding. So long we don’t know what this really reflect, if anything, it could be stupid to ignore it.
And it is particularly bad when your assumption has been falsified experimentally.
Which experiment do you have in mind ?

“The opposite of a correct statement is a false statement. But the opposite of a profound truth may well be another profound truth.” Niels Bohr

DaleSpam

Feb19-12, 12:44 PM

The equation is true, and the ADG/Square proportionality result of that is also true.Have you conducted any experiment and come to the conclusion that the gravitational force between two spherically symmetric objects is anything ells than F=GMm/r^2? Or at least maybe you can provide some more information regarding that experiment that you are refering to.Which experiment do you have in mind ?The equation a=GM/r² is the fundamental equation of Newtonian gravity, so any observation which falsifies Newtonian gravity falsifies that equation. Those observations include:

The anomolous precession of Mercury
The orbital decay of PSR1913+16
Geodetic precession (Gravity Probe B)
Gravitational lensing/deflection
Shapiro delay experiments

All of these experiments falsify Newtonian gravity. It is no use repeating the claim that a=GM/r² is a law of nature when nature disagrees.

Bjarne

Feb23-12, 09:22 PM

The equation a=GM/r² is the fundamental equation of Newtonian gravity, so any observation which falsifies Newtonian gravity falsifies that equation. Those observations include:

The anomolous precession of Mercury
The orbital decay of PSR1913+16
Geodetic precession (Gravity Probe B)
Gravitational lensing/deflection
Shapiro delay experiments

All of these experiments falsify Newtonian gravity. It is no use repeating the claim that a=GM/r² is a law of nature when nature disagrees.
I agree that the "problem" to the Newtonian equation is that because of space-time disturbing "r" in the equation is twisted by space-time, whereby the classic understanding not can be completely correct.
But after modifying from that influence I am not sure the equation is so bad (?).

Before digging deeper into this let us first finish what the Shapiro delay really must mean.

1 second at the ISS is still 1 second, but comparable to 1 second at the Earth it is "stretching" at the ISS.
Hence 1 second at the ISS is comparable longer.

Speed on board the ISS (e.g. the speed of light) is comparable slower as speed on the earth

I am often walking round a lake near my hometown.
If we would copy that lake and paste it into a low gravity planet, - it will still (locally) take me the 'same' amount of local time, - to walk around it.
My speed would also locally be the same, - but time (1 second and speed) would comparable to the same tour on Earth both be ‘stretching’ factors (comparable slower).

Anyway I assume I would not have any feeling of moving in slow motion, everything would be the 'same' both places.
So is it not true to say that also distances (the ruler) at the ISS, - is a relative proportional comparable stretching factor too, - so like both time and speed also are ?

Let say the size of the kitchen on board the ISS is identical to one in my house, but on board the ISS it is stretching proportional with time and speed.
But locally everything seems exactly the same as on Earth.
http://www.science27.com/images/kitc3.jpg http://www.science27.com/images/kitc2.jpg
(Sizes is off course exaggerated)
It would still take the ‘same’ time to walk (with the ‘same’ speed) from A to B, - doesn’t matter in which space-time that kitchen would be.

Do we know whether distance is a streching factor too?

Or its it only possible that also distances are comparable different in different space-time, - (without violating any laws of nature)?

I mean why is time really ticking comparable different?

Is it “because” also distances are comparable different?

If not also distances are affected it is hard even to imagine how my tour round the lake on a low gravity planet would be?

At least I would discover something is wrong, - due to 'slow motion'.
If distance also is stretching proportional factor together with time and speed, - everything would be “normal”.

Many experiments have been done when it comes to speed and time, - but what about local distances, why should they be comparable the same everywhere, (if that really should be so) ?

So what can we say for sure here ?

DaleSpam

Feb24-12, 04:07 PM

I agree that the "problem" to the Newtonian equation is that because of space-time disturbing "r" in the equation is twisted by space-time, whereby the classic understanding not can be completely correct.
But after modifying from that influence I am not sure the equation is so bad (?).I never said it was bad. In fact, I have repeatedly said that it is a close approximation in many circumstances.

Nevertheless, it is not a law of nature.

1 second at the ISS is still 1 second, but comparable to 1 second at the Earth it is "stretching" at the ISS.
Hence 1 second at the ISS is comparable longer.How exactly do you plan on making the comparison?

zonde

Feb25-12, 02:45 AM

Bjarne

Feb25-12, 02:54 AM

I never said it was bad. In fact, I have repeatedly said that it is a close approximation in many circumstances.
Nevertheless, it is not a law of nature.

Maybe, maybe not, - I am not convinced, but I have also not taken any decision.
Have we understood the full range of relativity?
Never say never.

Bjarne
1 second at the ISS is still 1 second, but comparable to 1 second at the Earth it is "stretching" at the ISS.
Hence 1 second at the ISS is comparable longer.
Dalespam
How exactly do you plan on making the comparison?

Sorry, - I mean the opposite
1 second at the ISS is still 1 second, (the definition is correct) but comparable to 1 second at the Earth, time (1 second) is "stretching" at the Earth.

Hence 1 second at the ISS is comparable shorter at the ISS.
When time (1 second) compared to time at a different space-time is "stretching" and speed can be said to doi the same (since speed of light always is the "same") - what prevent us from assuming that also distances are doing exactly and proportional the same,- so that also the 1 meter ruler still is one meter, but comparable stretching, exactly the same rate as speed and time. ?

So the question is, - is the "big kitchen" and "big lake" etc... (together and proportional with strech of time and speed) also "stretching" on the Earth, and comparable "shrinking" in lower gravity space time, as for example on board the ISS or on a low gravity planet etc…?

At least this would make sense, when I would imagine how it would be to jump to an (extreme) different time space reality and walk around. I would expect everything to be the same, - but not comparable the same. (except the magnitude of gravity).

DaleSpam

Feb25-12, 06:14 AM

When it is clear that there is significant domain where assumptions of the theory hold good you do not say that theory is falsified but instead you say that experiments have established it's domain of applicability.I am fine with this phrasing. Nevertheless, Bjarne's scenario dealing with gravitational time dilation is outside the domain of applicability of Newtonian gravity.

And because Newtonian gravity talk only about massive objects optical observations (Gravitational lensing, Shapiro delay) have nothing to do with it's predictions.I disagree here. While the gravitational force between a massive object and a massless object is 0 according to Newton's laws it doesn't take force to accelerate a massless object. So the acceleration of massless objects in Newtonian gravity is still given by a=GM/r².

DaleSpam

Feb25-12, 06:18 AM

I am not convincedThat is not an indication of a failure in physics or relativity.

1 second at the ISS is still 1 second, (the definition is correct) but comparable to 1 second at the Earth, time (1 second) is "stretching" at the Earth. Again, how exactly do you plan on making the comparison?

Bjarne

Feb25-12, 06:29 AM

Again, how exactly do you plan on making the comparison?

I don't understand the question..
Time, and hence 1 second is not comparable the same in different space time, - do you not agree to that?

DaleSpam

Feb25-12, 06:36 AM

I don't understand the question.I am asking for a detailed description of what experiment you are planning on doing in order to compare a 1 s on the ISS to 1 s on the earth, and how are you going to interpret different possible results of that experiment in terms of comparing the seconds?

Bjarne

Feb25-12, 08:01 AM

I am asking for a detailed description of what experiment you are planning on doing in order to compare a 1 s on the ISS to 1 s on the earth, and how are you going to interpret different possible results of that experiment in terms of comparing the seconds?
I cannot see the problem.
Clocks ticks different in different space time.
Let us say you were living in a relative very strong gravitionel field, compared to me.
Let’s say it will take 2 second on my atomic clock, - to observer one second ticking on yours atomic clock.

Opposite it will take you ½ second to observe 1 second ticking on my atomic clock.

The definition of 1 second is for both of us 9,192,631,770 cesium frequency cycles per second.

But it will take a comparable long second (relative double period “of time”) for your clock to reach this number, and only a relative comparable short (½) period, and hence a short second for me to count the same numbers of frequencies.

So the comparable second is not the same. I cannot understand how you seem not to agree to that.

DaleSpam

Feb25-12, 08:14 AM

Clocks ticks different in different space time. You are going in circles. I ask you how you are making the comparison and you simply assert that they are "different". Since "different" is a comparison where you find that they are not equal that still leaves the question of exactly how you are making the comparison.

Please answer the question. How are you comparing clock rates at different points in spacetime?

Let us say you were living in a relative very strong gravitionel field, compared to me.
Let’s say it will take 2 second on my atomic clock, - to observer one second ticking on yours atomic clock. What is the experiment you are proposing here? How do you "observer" the time ticking on your clock and mine?

Bjarne

Feb25-12, 11:17 AM

You are going in circles. I ask you how you are making the comparison and you simply assert that they are "different". Since "different" is a comparison where you find that they are not equal that still leaves the question of exactly how you are making the comparison.

Please answer the question. How are you comparing clock rates at different points in spacetime?
Satellites proves this every day

What is the experiment you are proposing here? How do you "observer" the time ticking on your clock and mine?
The same answer as above.
I cannot see any other option, - can you ?

Mentz114

Feb25-12, 11:40 AM

Bjarne, your answers are getting more and more feeble. I think you misunderstand what is meant by "the laws of physics are the same in all inertial frames" so I'll spell it out.

If an experiment is done in lab A to test the law f=ma using billiard ball type experiments and of course measuring with local clocks and rulers, then the result will be the same as in any other lab frame, where of course, they use their local clocks and rulers.

It matters not a jot if the local clocks and rulers are 'different', both frames will verify that f=ma is true, up to a small experimental error.

Going on about seconds or centimeters being different in different frames is irrelevant.

DaleSpam

Feb25-12, 01:58 PM

I cannot see any other option, - can you ?Sure, I can see at least 4 ways to compare two distant clocks:

A) Broadcast a reference signal, measure the frequency of the signal locally at each clock
B) Take a reference clock, physically transport it from one clock to the other and measure the rate of the reference locally at each clock
C) Agree on a standard physics experiment as a reference, perform it locally at each clock and measure the time for the experiment
D) Agree on an astronomical reference, and measure the time for the astronomical reference locally

Your suggested measurement of one year with two clocks is an example of D. Your mention of satellites probably refers to A. Mentz114's recent post refers to C, which encapsulates the principle of relativity. I came up with B on my own.

With D and A you will get that the Earth clock and the ISS clock run at different rates. With B and C you will get that the Earth clock and the ISS clock run at the same rates.

The beauty of GR is that it is a single law of physics which explains A, B, C, and D all together.

Bjarne

Feb26-12, 01:32 AM

Double .

Bjarne

Feb26-12, 01:32 AM

Sure, I can see at least 4 ways to compare two distant clocks:

A) Broadcast a reference signal, measure the frequency of the signal locally at each clock
B) Take a reference clock, physically transport it from one clock to the other and measure the rate of the reference locally at each clock
C) Agree on a standard physics experiment as a reference, perform it locally at each clock and measure the time for the experiment
D) Agree on an astronomical reference, and measure the time for the astronomical reference locally

Your suggested measurement of one year with two clocks is an example of D. Your mention of satellites probably refers to A. Mentz114's recent post refers to C, which encapsulates the principle of relativity. I came up with B on my own.

With D and A you will get that the Earth clock and the ISS clock run at different rates. With B and C you will get that the Earth clock and the ISS clock run at the same rates.

The beauty of GR is that it is a single law of physics which explains A, B, C, and D all together.

Off course I cannot disagree to that.
I was confused because I thought you did not agree to that, - when times ticks different, in different space-time, then each second also does, - whereby the comparable length off 1 second must be either stretching or shrinking. – So I expected a different kind of answer to your question, not easy to know what that possible could be.

DaleSpam

Feb26-12, 06:12 AM

whereby the comparable length off 1 second must be either stretching or shrinking.So I still don't know how you plan on doing the comparison. For the fourth or fifth time, what method are you using to do the comparison? Feel free to simply use one of my four or come up with your own, but be specific.

Mentz114

Feb26-12, 09:13 AM

Bjarne, I find your post #154 difficult to follow. It is not logically argued and poses more questions than it gives answers.

Have you seen this ?

http://www-istp.gsfc.nasa.gov/stargaze/Smass.htm

It is about experiments carried out on a space station.

There is a universe of evidence that the laws of nature are the same everywhere. We know that atoms continue to emit and absorb the same pattern of spectral lines which have been recognised in millions of astronomical bodies. On a large scale, the GR cosmological models explain most of what we can measure about the universe.

What you are proposing is 'new' physics. If the laws of nature really are laws of nature, they must apply everywhere. If there is experimental evidence to support it, then they must be modified, like relativity altered Newtonian concepts.

Your position is impossible to argue unless you can produce this experimental evidence.

Bjarne

Feb26-12, 10:48 AM

So I still don't know how you plan on doing the comparison. For the fourth or fifth time, what method are you using to do the comparison? Feel free to simply use one of my four or come up with your own, but be specific.
I cannot see this is neccesery
Either time is ticking different, or it is not.
According to relativity time is ticking different.
Many experiments and experiences confirm this.
So I still cannot see any point with the question.

DaleSpam

Feb26-12, 11:09 AM

I cannot see this is neccesery
Either time is ticking different, or it is not.
According to relativity time is ticking different.
Many experiments and experiences confirm this.
So I still cannot see any point with the question.No, according to relativity, if you use methods B or C to do the comparison then time is the same, and only if you use methods A or D to do the comparison then is it different. There is no "hidden reality" under which you can simply say time is different or it is not. There are only experimental measurements, and relativity correctly predicts those.

Bjarne

Feb26-12, 11:45 AM

B) Take a reference clock, physically transport it from one clock to the other and measure the rate of the reference locally at each clock
What do you mean by "measure the rate of the reference"

DaleSpam

Feb26-12, 11:54 AM

I mean to take the reference clock, place it locally next to the test clock (either the Earth clock or the ISS clock), and measure the duration of one "tick" of the reference clock using the local test clock.

Bjarne

Feb26-12, 12:52 PM

So I still don't know how you plan on doing the comparison. For the fourth or fifth time, what method are you using to do the comparison? Feel free to simply use one of my four or come up with your own, but be specific.

B + C is local measurement
A + D is comparable measurement
I agree to all that, but it has not much with the question to do.
I do off course mean A+D

Do we know (for sure) whether distances are comparable different too, so as time and speed is (see A+D), - in different space-time.
I have read that mass-energy conservation will changes the Bohr radius, which also must apply to relativity?

DaleSpam

Feb26-12, 07:18 PM

I do off course mean A+D Finally, a straight answer to such a basic question. It is a shame that it took so many posts to get to that.

Do we know (for sure) whether distances are comparable different too, so as time and speed is (see A+D), - in different space-time. I see how to compare the time on two distant clocks using methods A or D. How would you propose to compare the different distances?

Please, let's not waste another dozen or more posts chasing this down. Just describe your experimental method of comparing two spatially separated distances as clearly and succinctly as possible.

Bjarne

Feb27-12, 02:19 AM

Finally, a straight answer to such a basic question. It is a shame that it took so many posts to get to that.

I wrote comparable difference from the start.
It confused me you could misunderstand that so much.

I see how to compare the time on two distant clocks using methods A or D. How would you propose to compare the different distances?

Please, let's not waste another dozen or more posts chasing this down. Just describe your experimental method of comparing two spatially separated distances as clearly and succinctly as possible.
Good question.
I believe it is impossible.
Maybe only mathematical possible.
Already we compare space with a stretching rubber band, - or use the expression "curvature"
What does that mean?
Can we get closer to an understandable nature of that?
What happens with the ruler in such “bended” space? ( what do we know or not know)
At least seen from a mathematical perspective, is space stretching like the rubber band?

DaleSpam

Feb27-12, 08:34 AM

I wrote comparable difference from the start.
It confused me you could misunderstand that so much. Comparable doesn't have a well-defined meaning in terms of experiment. I.e. there is no experiment called the "comparable" experiment. Writing "comparable" over and over and over was not helpful to the conversation and was one of the main sources of delay. I am not a mind reader to know that by the word "comparable" you meant something like A or D and not something like B or C.

Good question.
I believe it is impossible. Then there is no use discussing about whether or not lengths change at different locations.

Already we compare space with a stretching rubber band, - or use the expression "curvature"
What does that mean?
Can we get closer to an understandable nature of that?
What happens with the ruler in such “bended” space? ( what do we know or not know)
At least seen from a mathematical perspective, is space stretching like the rubber band?The word "curvature" does not refer to space stretching like a rubber band. Curvature refers to deviations from (pseudo) Euclidean geometry.

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.

Bjarne

Feb29-12, 03:38 AM

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.

Sorry, but it is still very difficult for me to understand how, - reality differences’ - at all is possible (in this case) when distances not is affected too.

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

I have claimed that distance cannot be the same.
You have claimed that these 2 observers follows different path.

Do you mean these object follows 2 comparable different path?
Do you mean these path locally seems to be exactly the same ?
Or how would you describe the “different path”?

Because observer A (on the ISS) he will say it took exactly 31536000 ISS-second to complete one orbit, and the ISS-speed was exact averagely 30000m/s

Observer B on the Earth, orbiting the exact same orbit round the Sun will also say that that it took 31536000 earth-second to complete one orbit and the Earth-speed 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;

What you mean with that these 2 objects follows a “different path”?
How is this at all possible without assuming that comparable distance differences also must be a fact.?

This REALLY confuse me. – Sorry that I not is so quick to understand this.

DaleSpam

Feb29-12, 05:09 AM

Sorry, but it is still very difficult for me to understand how, - reality differences’ - at all is possible (in this case) when distances not is affected too.If you cannot come up with an experiment for comparing distances then it doesn't make sense to claim that distances are not affected. You cannot know anything about the distances if you cannot experimentally compare them, so you cannot claim that they are affected and you also cannot claim that they are not affected.

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.No, this is option D from my post 151. They will measure 1 astronomical year to be a different number of seconds.

They will also agree about their orbit local speed is average exactly 30000 m/sHow does each measure that?

I have claimed that distance cannot be the same.
You have claimed that these 2 observers follows different path.
These claims do not contradict each other.

Do you mean these object follows 2 comparable different path?
Do you mean these path locally seems to be exactly the same ?
Or how would you describe the “different path”?
You like to put the word "comparable" in bold as though somehow putting it in bold magically helps give it some meaning. What is a "comparable different path"? I have never heard the term and as far as I know it has no meaning.

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.

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) .How do you experimentally compare speeds?

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?

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 timeNo, this is not correct. This is known as Shapiro delay.

and the exact same local speed.This is true, the local speed of the light beam is c.

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% .Again, please define the experiment for comparing speeds.

Option 1.
The only way we mathematical can understand what happens here is that distances also must be 50% comparable different. Again, what experiment are you using to compare distances?

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.How would we measure the speed of the ISS and how would the external observer measure both the Earth speed and the ISS speed?

If you disagree, to both these optionsNeither of the options is clear enough for me to either agree or disagree with them.

What you mean with that these 2 objects follows a “different path”?
How is this at all possible without assuming that comparable distance differences also must be a fact.?

This REALLY confuse me. – Sorry that I not is so quick to understand this.They follow different paths because the coordinates of their path are different in any coordinate system you might choose.

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.

Bjarne

Feb29-12, 06:07 AM

Dalespam
They will measure 1 astronomical year to be a different number of seconds.

Yes off course, this was a blunder..

If you cannot come up with an experiment for comparing distances then it doesn't make sense to claim that distances are not affected. You cannot know anything about the distances if you cannot experimentally compare them, so you cannot claim that they are affected and you also cannot claim that they are not affected.

Ok so this is then still an open question. This is what confused me.
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.

DaleSpam

Feb29-12, 06:52 AM

Ok so this is then still an open question.I wouldn't even call it an open question yet. I would call it an undefined term. Until you have defined all of the terms you don't even have a properly formed question.

Thanks’ a lot for your patience, and detailed explanation.You are welcome. I will be glad to continue the discussion if needed.

Bjarne

Feb29-12, 07:28 AM

I wouldn't even call it an open question yet. I would call it an undefined term. Until you have defined all of the terms you don't even have a properly formed question..

Since we know the comparable length of one second is relative stretching or shrinking in different spacetime, for exsample relative to one of ours seconds, we know 1 of 3 factors.

Hence the options are whether speed and /or distance does "the same", and whether that happens proportional.

Which is the most likely option.

Is it that only speed follows the relative (proportional) stretch of time (and hence relative slowing or speeding)?
Or is distance also involved in the same relative proportional change?

Of course there could be other combination, according to what these 2 other factors does or not does, - but I think these 2 are the most likely.

I know you twist these words, - but I also think you know what i mean.

DaleSpam

Feb29-12, 08:52 AM

I know you twist these words, - but I also think you know what i mean.It is hard to claim that someone is twisting words which are undefined. I certainly do not know what you mean. In fact, I believe that you do not know what you mean either.

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 self-consistent 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.

Bjarne

Feb29-12, 10:34 AM

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.

Bjarne

Apr15-12, 05:50 AM

Bjarne Wrote
Either speed, distance and/or the definition of 1 second can then not be the same. It is a simple mathematical necessity. I haven't got an excact answer where the "camel is buried"

I am just asking the simple question; - how would these space time realities look like (what would be the comparable difference) if I could jump between them, and see the differences?

I am not an expert in his field, but it is easy to see that the full story can’t have been told so far.

I also did not got the answer (yes or no) to whether the orbit circumference for example of the Earth really can be 2 different sizes, (the same orbit), according to the example mentioned above..

And if this is so, how can the law of gravity apply for both without contradictions.

DaleSpam Wrote
The two paths are not the same, so the answer is "yes, two different paths may have different lengths".

Each path is a 1D line (a helix) in a 4D curved spacetime. You can easily come up with coordinate systems where the two paths have two coordinates which are identical and constant, and you can parameterize the paths by one of the remaining coordinates, but they will always be different in at least the final coordinate. They are simply different paths with different lengths, no contradictions nor confusions.

You certainly haven't demonstrated any conflict with the law of gravity. I don't even know what you think would be contradicted here.

Let’s say observer ‘A’ and ‘B’ live in a high-rise flat.
'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 ?

DaleSpam

Apr15-12, 06:13 AM

Hi Bjarne, welcome back! It has been quite a while.

Let’s say observer ‘A’ and ‘B’ live in a high-rise flat.
'A' at 1st. floor and 'B' at 10th.
...
So now they must both be following the same path. These two statements are mutually contradictory. If they are following the same path in spacetime then one cannot be on the 1st floor at the same time that the other is on the 10th floor. I.e. as described their spacetime paths are different by approximately 30 m or so, therefore they are not following the same path in spacetime.

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.

we do in fact have a dilemma here.Agreed. Which of the two mutually contradictory premises do you wish to keep?

Bjarne

Apr15-12, 06:43 AM

Hi Bjarne, welcome back! It has been quite a while.

These two statements are mutually contradictory. If they are following the same path in spacetime then one cannot be on the 1st floor at the same time that the other is on the 10th floor. I.e. as described their spacetime paths are different by approximately 30 m or so, therefore they are not following the same path in spacetime.

Not only are the paths approximately 30 m different, but that 30 m is a significant difference since there is, according to you, a measurable amount of time dilation between the two paths.

Agreed. Which of the two mutually contradictory premises do you wish to keep?

The observers are following different paths, yes, - but the observed, - the orbit of the Earth is not following 2 different paths..
Let’s say ‘A' and 'B' live at the North Pole i the same high-rise 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.

DaleSpam

Apr15-12, 07:22 AM

The observers are following different paths, yes, - but the observed, - the orbit of the Earth is not following 2 different paths.That isn't how clocks work. They only measure the length of their own path through spacetime, not some other objects path. A's clock measures the length of A's path through spacetime, not the length of B's path nor the length of Earth's path. Similarly for B.

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.

The planet cannot be moving with 2 different speeds at the same time.Why not? Speed is a frame variant quantity, so it can have as many different values at the same time as you have reference frames.

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.

Bjarne

Apr15-12, 10:44 AM

That isn't how clocks work. They only measure the length of their own path through spacetime, not some other objects path. A's clock measures the length of A's path through spacetime, not the length of B's path nor the length of Earth's path. Similarly for B.

Let's say it really was possible to tie a tape measure to the North Pole of the Sun and to the North Pole of the Earth in the other end.
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.

Why not? Speed is a frame variant quantity, so it can have as many different values at the same time as you have reference frames.
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.

A and B live at the North Pole in the same building ( ‘A’ at 1st and ‘B’ at 10th floor) . They are not moving relative to each other and also not relative to the Earth.
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?

DaleSpam

Apr15-12, 05:42 PM

Let's say it really was possible to tie a tape measure to the North Pole of the Sun and to the North Pole of the Earth in the other end.
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.I agree. By the way, I really like how you not only specified what you wanted to measure, but also the experiment to measure it.

They are not moving relative to each other and also not relative to the Earth.
A and B and the Earth is all exactly following the same orbit, and hence in the same frame.That would be true if spacetime were flat. I.e. in flat spacetime A not moving relative to B implies that A and B are at rest in the same frame. However, the spacetime is not flat, but is curved, and in curved spacetimes reference frames are local. For example, although the distance wrt each other is not changing (an indicator of the same frame in flat spacetime), signals from A are redshifted when received by B (an indicator of different frames in flat spacetime). So A and B are not considered to be using the same reference frame despite the fact that they are not moving relative to each other.

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.

Bjarne

Apr16-12, 02:33 PM

That would be true if spacetime were flat. I.e. in flat spacetime A not moving relative to B implies that A and B are at rest in the same frame. However, the spacetime is not flat, but is curved, and in curved spacetimes reference frames are local. For example, although the distance wrt each other is not changing (an indicator of the same frame in flat spacetime), signals from A are redshifted when received by B (an indicator of different frames in flat spacetime). So A and B are not considered to be using the same reference frame despite the fact that they are not moving relative to each other.

I understand this.
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.

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?
Did I ? - if so it was not my intention.
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.

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.
I think we don't disagree about anything, - if it is correct understood that we both agree, that what happen with speed and distance, in different space-time not is fully understood / proven.

And this is really what confuses me. - If that was clearer, I think it would be much easier to understand general relativity.

DaleSpam

Apr16-12, 02:56 PM

I understand this.
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.Actually, there are an infinite number of possible coordinate systems, and therefore an infinite number of choices, not just two. Any of them is valid.

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. Well, the reason that it was still open is that we hadn't defined a measure of distance. If you use your ruler-based measurement of distance then distance is frame-invariant.

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.

I think we don't disagree about anything, - if it is correct understood that we both agree, that what happen with speed and distance, in different space-time not is fully understood / proven.What happens according to the theory is fully understood, and many aspects (though not all) are also experimentally proven. However, because of the nature of GR it is very important to ask well-defined questions, and that is what can seem like it is not fully understood. I.e. it is not the theory but the question which is not fully understood.

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.

Bjarne

Apr17-12, 12:57 AM

What happens according to the theory is fully understood,
Right
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