Total % of Photons Redshifted While Moving Away From a Black Hole?

[metastable]

No, because the deceleration due to gravity is independent of the outward speed.

I'm confused on this point. Doesn't it take a much greater amount of force (from the lab frame) for a given change in velocity when the particle is relativistic (from the lab frame), compared to much lower velocities (from the lab frame)?

 

[PeterDonis]

Doesn't it take a much greater amount of force (from the lab frame) for a given change in velocity when the particle is relativistic (from the lab frame), compared to much lower velocities (from the lab frame)?

There is no force on any of the ships; they are in free fall.

Gravity is not a force in GR.

 

[metastable]

There is no force on any of the ships; they are in free fall.

What do we call the effect that causes 2 ships to change speed at different rates during the time of flight of a particular photon? Tidal gravity?

 

[PeterDonis]

What do we call the effect that causes 2 ships to change speed at different rates during the time of flight of a particular photon? Tidal gravity?

If you mean ships at different altitudes, yes, the change in their relative speed is a manifestation of tidal gravity, i.e., spacetime curvature. This is an effect of spacetime geometry and does not affect the ships being in free fall.

 

[metastable]

For Illustration:

https://www.av8n.com/physics/spacetime-welcome.htm
"3.19.3 General Case


Now let’s consider a particle that is neither super-slow (slug) nor super-fast (photon). That is, the particle has some nonzero mass, but it is moving fast enough that the classical approximations do not apply. The situation is shown in figure 36. Here (as in other figures in this section), the red ring represents the speed of light. The pink disk serves as a reminder of what the velocity vectors were doing originally, when the blue frame was not moving relative to the red frame."

Figure 36: Aberration : Fast but Not Massless

 

[PeterDonis]

For Illustration

Nobody is disputing how aberration works.

 

[pervect]

Is there still some disagreement about what the outcome would be?

I haven't been following the thread but I'll make a few remarks about why I'm confused about what the question is.

Let me recap. In the scenario there is a black hole with a radius of the observable universe

This is oddly over-specific. Why is the radius of the black hole that of the observable universe? Are you imagining that this black hole is in our universe (which seems hard to analyze and also probably paradoxical), or in an idealized uiverse with nothing but the black hole? In the later case, you can omit talking about how big the black hole is, and just say you have "a black hole", or better yet, "a Schwarzschild black hole".

and a fleet of coasting, co-moving ships with a variety of heights above the black hole and a variety of separation distances between them, but they are in a region of space roughly 2 black hole radii from the geometric center of the black hole

I think others have commented before that comoving is kind of hard to understand. It means something specific in the case of our universe, but it's unclear if you're talking about that or not, and whether or not you're using the standard understanding of what "comoving" means. If I felt positive I could follow your language to understand what it was you were asking, I might give it a shot, but at the moment I'm really not clear on what the question is, because of the way you describe it. So I can't tell what it is I would be agreeing with.

Anyway, the first step towards progress in my mind would be you modifying and/or expanding your question to use language that we both could understand. Of course, we both have to understand the question to avoid confusion. I'm just not sure how to get to that point where we both understand what the question actually is.

 

[metastable]

Why is the radius of the black hole that of the observable universe?

This parameter sets the scale of the gravitational redshift effects with respect to given distances and times traveled by the spacecraft .

Are you imagining that this black hole is in our universe (which seems hard to analyze and also probably paradoxical), or in an idealized uiverse with nothing but the black hole?

I'm imagining just outside the observable universe, but still within the total universe... & close & large enough to still observably affect events within the observable universe. For the idealized example the universe is simplified to just the black hole, the spacecraft , and the cosmological expansion parameter = 0 in the scenario.

I think others have commented before that comoving is kind of hard to understand

I mean comoving in the sense the vector of the spacecraft is extremely similar and the relative speed of the craft is insignificant compared to their speed with respect to the black hole. I am also "aware" of the separate astronomical definition of comoving in which all of the redshift is explained by cosmological expansion.

 

[Dale]

I've tried something similar before:

I didn’t see any indications that you were using a black hole of the given mass or a pair of ships at any specified radius or any of the other pieces of this question. I am not sure in what sense you think that calculation was similar to the scenario you describe here.

 

[metastable]

I didn’t see any indications that you were using a black hole of the given mass or a pair of ships at any specified radius or any of the other pieces of this question. I am not sure in what sense you think that calculation was similar to the scenario you describe here.

You are correct, I haven't yet attempted solving those particular formulas, but I thought it was similar in that it was a relativistic aberration equation. The point was I don't shy away from combining and rearranging equations...

^peak mechanical power is 10746.218459832w @ 8082.063923094534641801 motor rpm

A = meters per second = XX.XXX
B = drag coefficient = 0.75
C = frontal area = 0.6m^2
D = fluid density of air = 1.225kg/m^3
E = wind drag force in watts
F = sine of 5% slope = sin(atan(5/100)) = 0.04993761694389223373491
G = acceleration of gravity = 9.80655m/s^2
H = vehicle mass in kg = 90.7184kg = 200lb / 2.20462lb/kg
I = mechanical watts required for constant speed up slope with no wind drag
J = mechanical watts required for constant speed up slope including wind drag
K = H * G * F
L = (1/2) * D * C * B

E = ((1/2) * D * C * (A^2) * B) * A

I = H * G * A * F

J = E + I

J = (((1/2) * D * C *(A^2) * B) * A) + (H * G * A * F)

J = (1/2) * D * C * B * A^3 + H * G * F * A

J = (L * A^3) + (K * A)

^this can be rearranged to:

A=(sqrt(3) * sqrt(27 * J^2 * L^4 + 4 * K^3 * L^3) + 9 * J * L^2)^(1 / 3) / (2^(1 / 3) * 3^(2 / 3) * L) - ((2 / 3)^(1 / 3) * K) / (sqrt(3) * sqrt(27 * J^2 * L^4 + 4 * K^3 * L^3) + 9 * J * L^2)^(1 / 3)

we know:

J = 10746.218459832w peak mechanical
L = 0.275625 = (1/2) * D * C * B
K = 44.42622815547907982077 = H * G * F

therefore:

A=(sqrt(3) * sqrt(27 * 10746.218459832^2 * 0.275625^4 + 4 * 44.42622815547907982077^3 * 0.275625^3) + 9 * 10746.218459832 * 0.275625^2)^(1 / 3) / (2^(1 / 3) * 3^(2 / 3) * 0.275625) - ((2 / 3)^(1 / 3) * 44.42622815547907982077) / (sqrt(3) * sqrt(27 * 10746.218459832^2 * 0.275625^4 + 4 * 44.42622815547907982077^3 * 0.275625^3) + 9 * 10746.218459832 * 0.275625^2)^(1 / 3)

A=32.32551993764664323864 meters per second

 

[Dale]

The point was I don't shy away from combining and rearranging equations...

Ok. So why are you unwilling to work this specific problem?

 

[metastable]

Ok. So why are you unwilling to work this specific problem?

I look forward to attempting it. I think it's analogous to the "how fast can I go up slope also factoring wind drag with a certain amount of mechanical power" problem -- ie one could choose to calculate the speed from JUST wind drag OR the slope forces, but in this problem both factors are combined. Analogously, in a given problem we could look at the velocity redshift or gravitational redshift, but here we have to look at both.

What is a "10gev + 1ev kinetic energy" electron's initial velocity in m/s from the lab frame?

10gev + 1ev kinetic electron (lab frame)-->

B = 0.5109989461MeV = electron rest mass

Z = 10000.000001MeV = initial electron kinetic energy (lab frame) = 10gev + 1ev

E = Electron Total Energy

E = B+Z

E = 10000.5109999461MeV

E = B/sqrt(1-(V^2/C^2))

can be rearranged to:

E = B/sqrt(1-A)

A = V^2/C^2

E = B/sqrt(1-A)

can be rearranged to:

A = -1*((B^2-E^2)/E^2)

A = -1*((0.5109989461^2-10000.5109999461^2)/10000.5109999461^2)

A = 0.9999999973890676149262

A = V^2/C^2

can be rearranged to:

V = C*sqrt(A)

C = 299792458m/s

V = 299792458*sqrt(0.9999999973890676149262)

V = 299792457.608631081048

10gev + 1ev Electron V=299792457.608631081048m/s from lab frame

%C = 299792457.608631081048 / 299792458

%C = 99.9999998694533806347%

10gev + 1ev Electron V = 99.9999998694533806611% C

10gev + 1ev Electron V = 0.999999998694533806611C

------------------------

Conclusion

Q: What is the 10gev + 1ev electron's initial velocity in m/s from the lab frame?

A: The 10gev + 1ev electron initially travels 299792457.608631081048m/s from the lab's rest frame, which is 0.999999998694533806611C.

 

[metastable]

Will the relativistic aberration cause a higher and higher % of total photons to travel on vectors which increase in distance from the black hole over time, as the ships co-moving velocity increases in different scenarios?

In a given scenario (for example if 99.99999999999999% of total photons are moving away from the black hole), will the photons become redshifted from gravitational redshift during their flight times between craft?

^If yes, Will the measured gravitational redshift increase (as measured by an observer on one of the craft) as the separation distance between the craft increases in different scenarios (longer flight times between craft)?

A = cos(motion path angle relative to the vector from the observer to the source at the time when the light is emitted)
B = V
C = C
D = cos(angle observed to source)

D = (A-(B/C))/(1-((B/C)*A))

A = -1*(((-1*B)-(D*C))/(C+(D*B)))

A = cos(motion path angle relative to the vector from the observer to the source at the time when the light is emitted)
B = 299792457.6086310810085m/s
C = C = 299792458m/s
D = cos(angle observed to source) = 0 = cos(90deg)

A = -1*(((-1*B)-(D*C))/(C+(D*B)))

A = -1*(((-1*299792457.6086310810085)-(0*299792458))/(299792458+(0*299792457.6086310810085)))

A = 0.9999999986945338064792 = cos(0.00292766)

0.00292766 degrees = motion path angle relative to the vector from the observer to the source at the time when the light is emitted

-----------------------------------------
Conclusions

The angle of the source motion path relative to the vector from the observer to the source at the time when the light is emitted is 0.00292766 degrees if the source momentum vector appears to be 90 degrees to the lab-frame-observed emission vector at the time of viewing from the lab frame

Can I use:
Initial V=299792457.6086310810085m/s

A = cos(motion path angle relative to the vector from the observer to the source at the time when the light is emitted)
B = 299792457.6086310810085
C = C = 299792458m/s
D = cos(angle observed to source) = 0 = cos(90deg)

A = -1*(((-1*B)-(D*C))/(C+(D*B)))

A = -1*(((-1*299792457.6086310810085)-(0*299792458))/(299792458+(0*299792457.6086310810085)))

A = 0.9999999986945338064792 = cos(0.00292766)

0 degrees + 0.00292766 degrees = 0.00292766 degrees blueshifted towards black hole

180 degrees - 0.00292766 degrees = 179.99707234 degrees redshifted away from black hole

0.00292766 / 179.99707234 = 0.0016265% of photons gravitationally blueshifted when initial V = 299792457.6086310810085m/s

100 - 0.0016265 = 99.9983735% of photons gravitationally redshifted when initial V = 299792457.6086310810085m/s

 

[metastable]

0.00292766 / 179.99707234 = 0.0016265% of photons gravitationally blueshifted when initial V = 299792457.6086310810085m/s

100 - 0.0016265 = 99.9983735% of photons gravitationally redshifted when initial V = 299792457.6086310810085m/s

*correction:
0.00292766 / 180 = 0.00162647% of photons gravitationally blueshifted when initial V = 299792457.6086310810085m/s

100-0.00162647=99.99837353% of photons gravitationally redshifted when initial V = 299792457.6086310810085m/s

 

[PeterDonis]

@metastable, please stop including huge quotes in your posts of things you're not going to respond to. Particularly if they're just repeats of your previous posts.

 

[pervect]

This parameter sets the scale of the gravitational redshift effects with respect to given distances and times traveled by the spacecraft .

So, no really pressing reason, then?

I'm imagining just outside the observable universe, but still within the total universe... & close & large enough to still observably affect events within the observable universe. For the idealized example the universe is simplified to just the black hole, the spacecraft , and the cosmological expansion parameter = 0 in the scenario.\

The case that I can analyze doesn't have any "universe" other than a black hole. It's uncler if that's the case you're interested in.

I mean comoving in the sense the vector of the spacecraft is extremely similar and the relative speed of the craft is insignificant compared to their speed with respect to the black hole. I am also "aware" of the separate astronomical definition of comoving in which all of the redshift is explained by cosmological expansion.

That's still not very clear. It sounds like you could mean what I would call a static observer, but I am not at all confident.

A static observer would be one that has constant Schwarzschild r, theta, phi coordinates.

I see some references to "wind drag" and "relativistic aberration" in some of your posts that make no sense to me, so - I'm concluding that I don't understand your question.

We appear to lack a common vocabulary, and I don' see any sensible way to proceede without one.

 

[metastable]

So, no really pressing reason, then?

The black hole in the scenario is sized in such a way that the effects it causes in the scenario are still detectable while the black hole itself is completely outside the observable universe.

For Illustration (assume the fleet is a bit farther away from the circle in the middle than position A):

https://www.researchgate.net/figure/This-illustration-tries-to-show-schematically-a-hypersurface-at-time-T-with-our_fig4_313078586

"This illustration tries to show schematically a hypersurface at time T with our Observable Universe surrounded by other similar Observable Universes, arbitrarily positioned, some of them overlapping."

 

[Ibix]

The black hole in the scenario is sized in such a way that the effects it causes in the scenario are still detectable while the black hole itself is completely outside the observable universe.

That would seem to be a contradiction in terms.

 

[metastable]

That would seem to be a contradiction in terms.

But yes, the observable universe is a subset of some larger universe.

https://www.physicsforums.com/threads/is-the-universe-a-3-sphere-or-a-4-sphere.971938/post-6181121

 

[Ibix]

https://www.physicsforums.com/threads/is-the-universe-a-3-sphere-or-a-4-sphere.971938/post-6181121

So? You are describing something that's not observable (because it's not part of the observable universe), but is observable (because of its effects). So it's observable and not observable. I don't think you actually have a consistent scenario here.

 

[metastable]

So? You are describing something that's not observable (because it's not part of the observable universe), but is observable (because of its effects). So it's observable and not observable. I don't think you actually have a consistent scenario here.

Not observable via light (and also because it's a black hole)... but still observable via its gravity.

We can't "see" black hole mergers but we can measure the gravity waves.

 

[Ibix]

Not observable via light (and also because it's a black hole)... but still observable via its gravity.

It's not clear to me that this is a consistent model. If the black hole is eternal, then yes you can detect its gravity at any distance (in principle). However, such a universe does not have the concept of "observable universe". The observable universe is a concept in FLRW spacetimes, in which black holes may form but are simply a kind of extreme over-dense patch. They don't have a long-range gravitational effect different from any other kind of over-dense region.

We can't "see" black hole mergers but we can measure the gravity waves.

Gravitational waves (nitpick: gravity waves are a kind of surface wave on liquids) propagate at the speed of light. If we can observe them, we can observe light emitted at the same time.

 

[metastable]

However, such a universe does not have the concept of "observable universe". The observable universe is a concept in FLRW spacetimes, in which black holes may form but are simply a kind of extreme over-dense patch.

So the distances I refer to in my original post (black hole radius = observable universe radius and rough craft distance = 2 black hole radii from geometric center of black hole) should be taken to mean the distances are derived from estimates of the size of the observable universe in the actual observable universe.

 

[PeterDonis]

The black hole in the scenario is sized in such a way that the effects it causes in the scenario are still detectable while the black hole itself is completely outside the observable universe.

This model of yours is personal speculation, as you have already been told in at least one previous thread. Please do not post about it further or you will receive a warning.

Thread closed.