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

[Bjarne]

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.

 

[Dale]

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]

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?

 

[Dale]

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.

 

[Bjarne]

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.

 

[Dale]

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.]

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]

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, let's 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...

 

[Bjarne]

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, let's 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?

 

[Dale]

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]

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?

 

[Dale]

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]

There is no distance which has changed. Two different spacetime paths have two different distances.

Right
You know what I mean anyway.

 

[Dale]

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]

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.

 

[Dale]

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]

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?

 

[Dale]

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?

 

[Bjarne]

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]

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 traveled 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 spacecraft s moving around that they are trying to communicate with using frequencies that may appear different and trying to get the spacecraft s 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...

 

[Dale]

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 Universe

No, 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 referring to the former, which is what I have assumed you meant by "radius".

 

[Bjarne]

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.]

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?

 

[Dale]

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]

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.

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?

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?

 

[Dale]

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]

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

 

[Dale]

No, ADG is always equal proportional with the square increase

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.

 

[Bjarne]

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]

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]

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 referring to.

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

 

[Bjarne]

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

 

[Dale]

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 referring 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 anomalous 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]

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 anomalous 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.

(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 ?

 

[Dale]

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?