Paper: A causal mechanism for gravity

[joigus]

Yanchilin, Yanshmilin.

Haven't we been over this before? c² or phi.

You need more variables!!!

[rjbeery]

I have some questions regarding black holes. Which forum channel would be appropriate, and do we happen to have any astrophysicists on this forum?

[Strange]

4 minutes ago, rjbeery said:

I have some questions regarding black holes. Which forum channel would be appropriate, and do we happen to have any astrophysicists on this forum?

I would say the Relativity section, probably: https://www.scienceforums.net/forum/10-relativity/ 

Unless it is more about their formation and role in galaxies, in which astronomy might be better: https://www.scienceforums.net/forum/7-astronomy-and-cosmology/

There are at least two or three people with a good level of knowledge.

[rjbeery]

In this paper, we show that the time dilation field of mass-energy is sufficient to predict gravitational effects on light. Essay written for the Gravity Research Foundation 2021 Awards for Essays on Gravitation.

 

Free-falling into Black Hole

We start with a black hole, B, possessing a Schwarzschild radius (rs) of 3000 m, giving it a mass of roughly one solar-mass (~2*10^30 kg). We take a body, A, of negligible mass, initially resting at a great distance (PEi = KEi = 0), and allow it to free-fall towards B.

To calculate A’s coordinate velocity at a given distance, r, from the center of B, we start with

(1)

(2)

(3)

(4)

(5)

so

(6)

Integrating gives us:

(7)

We evaluate the equation for the final 1000 meters of A’s path before reaching the event horizon (i.e. r = 4000..3000, see Fig 2)

(8)

(9)

So

(10)

Here we take note of the proper velocity of A at r = 4000 (see Fig 2)

(11)

We also note that

(12)

where t0 is the proper time of events for A, tf is the coordinate time of those same events (for a distant observer), and the radical value is the time dilation factor which approaches 0 as r approaches the event horizon at rs.

 

Light passing through a graded refractive index

A refractive index of a medium is defined as the dimensionless number

(13)

where v is the measured velocity of light through that medium. In other words, n can be treated as the reciprocal of an apparent time dilation factor (from the remote observer’s point of view). If we consider a gravitational field as the medium being traversed, then we can use (12) to represent that medium’s refractive index as

(14)

where ys is analogous to the Schwarzschild radius of B above.

We see that as a light ray R approaches a height of ys the “time dilation factor” approaches zero, and n diverges to infinity. Light in this area is effectively frozen, and, for all intents and purposes, the horizontal boundary of y = ys is an event horizon. Now we take Snell’s Law

(15)

where k is a constant determined by the initial angle and location in the medium of an incident ray. Combining (14) with (15) we now have

(16)

so

(17)

In Figure 1 we are considering theta to be the angle between R and the normal to the x-axis, therefore

(18)

We can combine (16-18) to get

(19)

We now want to determine k. Since we know from (11) that the body A is approaching B at a velocity of .866025c at r = 4000 (see Fig 2), we choose theta such that the light ray R is approaching B at the same rate at y = 4000. A light ray with a vertical component moving downward at .866025c is doing so at pi/6 radians off the y-axis

(20)

(21)

(22)

All such k-values will be unity when the vertical component of R is equal to a radial free-fall velocity, such as A’s, at a given height. Plugging k = 1 into (19) we have
 

(23)

We now calculate the length of R’s spatial path from y = 4000 to the so-called event horizon ys = 3000.

(24)

(25)

(26)

(27)

(28)

So

(29)

which is the same value we calculated in (10).

 

Gravity and refraction equivalence

We can verify the relationship between (8) and (27) by adjusting (7)

(30)

(31)

(32)

where of course the constants of integration are irrelevant to the integral.
 

Conclusion

In conclusion, we have shown that the time dilation field of mass-energy predicts gravitational effects on light. Parsimony and equivalence would suggest that this mechanism is sufficient to explain gravitational forces on massive objects as well, possibly in the form of EM mass.

 

[swansont]

42 minutes ago, rjbeery said:

In this paper, we show that the time dilation field of mass-energy is sufficient to predict gravitational effects on light.

!

Moderator Note

Merged with existing thread

 

[rjbeery]

swansont, I feel that this paper is a completely different angle on a similar subject. Please consider letting it remain in its own thread.

equation (19) should read:

[swansont]

Since time dilation and deflection of light are both effects that derive from GR, it seems unsurprising that they would be correlated.

1 hour ago, rjbeery said:

I feel that this paper is a completely different angle on a similar subject.

Effects based on time dilation being the cause, and gravity as refraction. No, you don’t get a new thread.

[rjbeery]

4 minutes ago, swansont said:

Since time dilation and deflection of light are both effects that derive from GR, it seems unsurprising that they would be correlated.

Effects based on time dilation being the cause, and gravity as refraction. No, you don’t get a new thread.

On 5/15/2020 at 7:45 PM, swansont said:

Explain how time dilation makes me fall down. 

You asked for an explanation 11 months ago, and now you seem to be saying that it's obvious.

[swansont]

2 hours ago, rjbeery said:

You asked for an explanation 11 months ago,

Really? Provide a link to the post.

2 hours ago, rjbeery said:

and now you seem to be saying that it's obvious.

No, I didn’t say it was obvious. I said it would be unsurprising.

 

[rjbeery]

6 hours ago, swansont said:

Really? Provide a link to the post.

No, I didn’t say it was obvious. I said it would be unsurprising.

 

I copied your post above, but here's a direct link: https://www.scienceforums.net/topic/122084-paper-a-causal-mechanism-for-gravity/page/2/?tab=comments#comment-1141752

I'll be curious to see if others find this result unsurprising as well. I think it is very significant.

 

[swansont]

9 hours ago, rjbeery said:

I copied your post above, but here's a direct link: https://www.scienceforums.net/topic/122084-paper-a-causal-mechanism-for-gravity/page/2/?tab=comments#comment-1141752

I'll be curious to see if others find this result unsurprising as well. I think it is very significant.

 

I was asking for the causal mechanism (i.e. how time dilation is a force), not an explanation of what you were deriving.

I was just thinking of the case where one has a constant gravitational acceleration, and the fractional frequency shift is gh/c^2, so g is right there in the equation, as my thought for why I would be unsurprised that time dilation might have a correlation with another effect that depends on g. It seems it would be trivial to rearrange the equation. The general description is that time dilation depends on the gravitational potential. So basically you're surprised that the gravitational potential depends on gravity and that you could parameterize some other effect that depends on gravity. OK.

[rjbeery]

11 minutes ago, swansont said:

I was asking for the causal mechanism (i.e. how time dilation is a force), not an explanation of what you were deriving.

I was just thinking of the case where one has a constant gravitational acceleration, and the fractional frequency shift is gh/c^2, so g is right there in the equation, as my thought for why I would be unsurprised that time dilation might have a correlation with another effect that depends on g. It seems it would be trivial to rearrange the equation. The general description is that time dilation depends on the gravitational potential. So basically you're surprised that the gravitational potential depends on gravity and that you could parameterize some other effect that depends on gravity. OK.

According to this paper, "constant gravitational acceleration" would not induce forces at all. I mean, intuitively, we would expect it to (because we are accustomed to using g for convenience) but, as the paper outlines, time dilation would be constant in a field of "constant gravitational acceleration" and therefore would not refract light. If gravitational forces still existed in such a field then equivalence would be broken.

Also, you are asking for the causal mechanism, but that is literally what the paper is about. Time dilation is the mechanism. If you're driving on a dirt road and you hit the shoulder of sand, your car turns in that direction; drop a straw in water (where light moves more slowly) and the straw appears to "bend down". It's all the same thing.

[swansont]

12 minutes ago, rjbeery said:

According to this paper, "constant gravitational acceleration" would not induce forces at all. I mean, intuitively, we would expect it to (because we are accustomed to using g for convenience) but, as the paper outlines, time dilation would be constant in a field of "constant gravitational acceleration" and therefore would not refract light. If gravitational forces still existed in such a field then equivalence would be broken.

So much for your earlier claim that this is consistent with GR.

Can you derive the time dilation effect without using GR, and making it consistent with this claim?

i.e. that there is no time dilation with constant g. Can you predict the Pound-Rebka experimental results?

 

Quote

Also, you are asking for the causal mechanism, but that is literally what the paper is about. Time dilation is the mechanism. If you're driving on a dirt road and you hit the shoulder of sand, your car turns in that direction;

Yes, and there are Newtonian forces acting on the car that make it do this.

Quote

drop a straw in water (where light moves more slowly) and the straw appears to "bend down". It's all the same thing.

There is no force on the straw. You can't make a stronger straw and have it resist the bending, because the effect is not dependent on the straw; the straw doesn't actually bend. The light does.

In Newtonian terms, if I fall, it's because there is an acceleration that is the mechanism (gravity in this case), and thereby a force. If you can't tie your effect back to this concept, then how is it consistent with Newtonian physics (in the regime where Newtonian physics is valid)?

[rjbeery]

1 minute ago, swansont said:

So much for your earlier claim that this is consistent with GR.

Can you derive the time dilation effect without using GR, and making it consistent with this claim?

i.e. there is no time dilation with constant g? Can you predict the Pound-Rebka experimental results?

There's nothing controversial in the paper. It's very straightforward. If you think this paper is inconsistent with GR then you are perhaps misrepresenting what GR predicts.

I don't understand the second statement above. I'm not sure how (or why) I would want to derive time dilation without GR.

Lastly, time dilation would exist in constant g but it would also be constant, and therefore gravitational acceleration would not be present. Consider the inside of a massive, transparent Newton's shell -- time moves slowly, but everything is free-floating.

[swansont]

2 hours ago, rjbeery said:

There's nothing controversial in the paper. It's very straightforward. If you think this paper is inconsistent with GR then you are perhaps misrepresenting what GR predicts.

I don't understand the second statement above. I'm not sure how (or why) I would want to derive time dilation without GR.

The claim that there is no time dilation with constant g is inconsistent with GR. Thus, your claims are inconsistent with GR and can’t be based on it.

 

Quote

Lastly, time dilation would exist in constant g but it would also be constant, and therefore gravitational acceleration would not be present. Consider the inside of a massive, transparent Newton's shell -- time moves slowly, but everything is free-floating.

GR claims a frequency shift of gh/c^2, i.e. it varies with h, and you claim it’s constant. 

There is no gravity inside of the shell. g=0; it’s trivially constant, but it’s not the general case.

[rjbeery]

1 hour ago, swansont said:

The claim that there is no time dilation with constant g is inconsistent with GR. Thus, your claims are inconsistent with GR and can’t be based on it.

 

GR claims a frequency shift of gh/c^2, i.e. it varies with h, and you claim it’s constant. 

There is no gravity inside of the shell. g=0; it’s trivially constant, but it’s not the general case.

This isn't true; the frequency shift you're using is a Newtonian approximation. Compare this (the true equation):

to equation (12) in my paper above and you can see that they are clearly just taking the ratio of time dilation at both heights to determine blueshift.

[swansont]

22 minutes ago, rjbeery said:

This isn't true; the frequency shift you're using is a Newtonian approximation. Compare this (the true equation):

to equation (12) in my paper above and you can see that they are clearly just taking the ratio of time dilation at both heights to determine blueshift.

The difference between the equations is well below the precision of the measurement, but the more important issue is you’re claiming a different result. 

[rjbeery]

30 minutes ago, swansont said:

The difference between the equations is well below the precision of the measurement, but the more important issue is you’re claiming a different result. 

Have you done any calculations?

and

gh/c^2 = 2.5×10^(−15)

 

[swansont]

45 minutes ago, rjbeery said:

Have you done any calculations?

Lots of them

Quote

and

gh/c^2 = 2.5×10^(−15)

 

You can punch numbers into a calculator. What’s your point?

(also you should show your work in more detail. you only have one significant digit with .009; where did that come from and why isn’t there more precision?)

[rjbeery]

8 minutes ago, swansont said:

Lots of them

You can punch numbers into a calculator. What’s your point?

(also you should show your work in more detail. you only have one significant digit with .009; where did that come from and why isn’t there more precision?)

I can't tell if you're being intentionally obtuse, but .009 is the approximate Schwarzschild radius of the Earth. I used that for r_s in the calculation. The above math was my response to you saying

1 hour ago, swansont said:

The difference between the equations is well below the precision of the measurement, but the more important issue is you’re claiming a different result. 

where the ratio of time dilation factors (using rough estimates) is a difference of 3*10^(-15), compared to the gh/c^2 = 2.5*10^(-15). The fact that they could not (at the time) measure the time dilation difference at a distance of 22.5 meters, forcing them to use the approximation you listed, does not mean that the GR answer is anything but correct.

[swansont]

56 minutes ago, rjbeery said:

I can't tell if you're being intentionally obtuse, but .009 is the approximate Schwarzschild radius of the Earth. I used that for r_s in the calculation. The above math was my response to you saying

where the ratio of time dilation factors (using rough estimates) is a difference of 3*10^(-15), compared to the gh/c^2 = 2.5*10^(-15). The fact that they could not (at the time) measure the time dilation difference at a distance of 22.5 meters, forcing them to use the approximation you listed, does not mean that the GR answer is anything but correct.

What? You have this backwards. A low-precision doesn’t force you to use an approximation. It allows you to, because any difference in their results requires more precision than you can measure.

Meaning that the difference between the two calculations lies somewhere out past the ~10^-16 precision that was measured. Trivially confirmable, too, if you’d bother to investigate (i.e. work through the algebra)

IOW, the effect is because of h, not because of the change in g. Because the potential varies as r, but g varies as r^2

 

 

[rjbeery]

3 hours ago, swansont said:

The difference between the equations is well below the precision of the measurement, but the more important issue is you’re claiming a different result. 

What different result were you referring to here?

To be honest, the things you're saying are just bizarre. This is from the Pound-Rebka wiki page:

In other words, treating g as constant is a known approximation, and the proper calculation is literally listed. I solved that exact calculation to show you that it does not produce a "different result". If we used exact values for r_s and altitude then it would produce an exact result.

Edited April 16, 2021 by rjbeery

[swansont]

25 minutes ago, rjbeery said:

What different result were you referring to here?

To be honest, the things you're saying are just bizarre.

No, you’re misreading them.

25 minutes ago, rjbeery said:

This is from the Pound-Rebka wiki page:

In other words, treating g as constant is a known approximation, and the proper calculation is literally listed. I solved that exact calculation to show you that it does not produce a "different result". If we used exact values for r_s and altitude then it would produce an exact result.

And the exact result and the approximation are equal at the level of precision of the experiment. They would differ if you carried the calculation out to a higher precision.

 

You’re the one saying that if g were constant there would be no time dilation, and you’re quoting a source that confirms you are incorrect. A constant g does predict time dilation varying with h.

 

[rjbeery]

1 hour ago, swansont said:

You’re the one saying that if g were constant there would be no time dilation, and you’re quoting a source that confirms you are incorrect. A constant g does predict time dilation varying with h.

 

I understand now. You think that, because the approximation has varying time dilation with a constant g, then that's proof that GR claims the same thing. This is false, and equivalent to saying that Newton's approximations prove that the speed of light is infinite.

[swansont]

15 hours ago, rjbeery said:

I understand now. You think that, because the approximation has varying time dilation with a constant g, then that's proof that GR claims the same thing. This is false, and equivalent to saying that Newton's approximations prove that the speed of light is infinite.

No, it's a claim from GR.

Take the GR equation and expand it. The first term is the contribution from constant g.

Regardless, the problem with Newton was with light, not gravity. GR reduces to Newtonian gravity when gravity is weak, which is the case here, so the results have to agree. The time dilation varies with the gravitational potential, and is going to  be gh/c^2 whether g is constant of varies with r.

GM/r is the gravitational potential (it's what shows up in the Schwarzchild radius equation, which is relativistic) and the time dilation is the potential divided by c^2

g = GM/r^2

so GM/r = gr

But over the height of a few tens of meters g is only going to vary by less than a part in 10^10, so this difference in g can safely be ignored in a result that's only good to 10% (as was Pound-Rebka) or 1%, as in the case of the later Pound-Snider experiment. You're only going to have to worry about the variation of g when you go to higher altitudes, such as in Vessot's gravity probe A experiment.

You can see that Pound and Rebka assume constant g

 

 

If there was no time dilation in constant g, then the frequency of light would not change with height, and this would violate conservation of energy, which is very much in conflict with mainstream physics

Also, the “no light deflection in constant g” is in direct opposition to the Einstein elevator example of the equivalence principle