Cosmological Redshift in Simulated Universe

[Devin-M]

TL;DR Summary

How would observers distinguish between doppler and gravitational redshift in a simulated universe?

Suppose we have a simulated universe in which the observable portion (a collection of galaxies) is climbing out of a gravitational well at a very high fraction of the speed of light. The gravitational well is caused by a very large, accreting black hole outside of the observable portion. The observable portion is collapsing under its own self gravity so the galaxies move towards each other. Due to the collapse, observers would expect to see other galaxies blue shifted. However because the observable part climbs out of the gravitational well at very close to light speed with respect to the accreting black hole, the searchlight effect causes most emitted photons in the observable portion to move away from the black hole and climb out of the gravitational well causing redshift.

If the observers see galaxies that are moving toward them gravitationally redshifted in such a scenario, do they have any way to ascertain that the galaxies are coming towards them, despite the light they are observing from those galaxies being gravitationally redshifted?

 

[Ibix]

I'm not at all sure that this scenario is self-consistent. I don't think it's at all clear that one can have a black hole outside an observable region that has a gravitational effect on anything in the observable region. I don't see how such a thing could form - I think you'd need a finite age universe and/or some form of accelerating expansion, and a giant black hole with effects across an observable region it's not inside. I think you'd need to demonstrate that this can even be specified mathematically.

If you simplify it to a cloud of free-falling dust travelling away from a black hole, I don't see why you'd expect any redshift visible from inside the dust cloud. You might see some anisotropy due to tidal gravity from the black hole, but that's it.

 

[Devin-M]

If you simplify it to a cloud of free-falling dust travelling away from a black hole, I don't see why you'd expect any redshift visible from inside the dust cloud.

I was expecting to see redshift since nearly all emitted photons move away from the BH due to the relativistic aberration / searchlight effect, thereby becoming gravitationally redshifted.

 

[Ibix]

Yeah, but the clocks you've got are travelling along with the light, so their gravitational time dilation varies too.

More precisely, you're basically describing a closed box experiment with clocks exchanging light pulses while the whole thing is in free-fall. If you could detect gravitational redshift in such a circumstance it would violate the equivalence principle. You might (if your experiment is sensitive enough) detect anisotropy due to tidal gravity, but that's it.

Again, I'm assuming the simplified form of the setup discussed in the last paragraph of #2.

 

[Orodruin]

You cannot distinguish the two by measurement. It is a separation that - although made based on the symmetries of the expanding universe - is arbitrary to some extent. Mathematically it boils down to the same thing.

 

[Devin-M]

the clocks you've got are travelling along with the light, so their gravitational time dilation varies too.

In the scenario, if the clocks were ticking faster as they climb the gravity well wouldn’t that make any measured redshift even greater? Or do I have it backwards?

 

[Ibix]

It's not that simple. You want to frame things in terms of a coordinate system at rest with respect to the black hole - fine. But then you need to keep track of gravitational time dilation, kinematic time dilation, and Doppler effects for different clocks in your dust cloud. All three are changing over time because the cloud is being slowed by gravity in this coordinate system. And then you need to convert everything into proper time timelines for all the clocks so you can say what they see. And it immediately falls into numerical computation to describe the results - well within reach of a laptop, but still messy.

It's much easier to note that the equivalence principle allows you to say that the dust cloud cannot see any difference from free fall in flat spacetime over a small region. So observers moving in the cloud simply see some blue shift from the inward motion of the particles in the cloud. If the region you work in is not small enough there are corrections to that due to tidal effects from the black hole, which would lead to the anisotropy I mentioned.

The mechanics of exactly how all the light flight times, intercept calculations and time dilations all cancel out from the first perspective to give the second is more messy than it's worth, IMO, but you can do it if you wish. It's really only repeated application of the Schwarzschild orbital mechanics equations that you can find in Chapter 7 of Carroll's notes (equations 7.43, 7.44, 7.47 and 7.48). Probably worth reading George Jones' comment here before attempting the numerical integration.

 

[Devin-M]

I'm not at all sure that this scenario is self-consistent. I don't think it's at all clear that one can have a black hole outside an observable region that has a gravitational effect on anything in the observable region. I don't see how such a thing could form - I think you'd need a finite age universe and/or some form of accelerating expansion, and a giant black hole with effects across an observable region it's not inside. I think you'd need to demonstrate that this can even be specified mathematically.

If the BH was large enough, and also the collection of galaxies or dust cloud was large enough and climbing fast enough, would this cause the light from galaxies / dust distant enough from an observer within the “collection / cloud” to become too redshifted to be observable, and also cause light emitted from the region in the vicinity of the large BH also to be too redshifted to be observable?

 

[Ibix]

If the BH was large enough,

Black hole size doesn't really change anything here, except the timescale over which an object travelling at near light speed remains within its gravitational reach.

would this cause the light from galaxies / dust distant enough from an observer within the “collection / cloud” to become too redshifted to be observable

No, for the reason already stated. Observers travelling in the cloud see no effects of the hole unless the cloud is large enough to see signs of the anisotropy of the hole's gravity. If the hole is large enough that gravitational effects are significant over a period of thousands of years (as measured by the cloud) of travel at near light speed then tidal effects would have to be almost nothing.

and also cause light emitted from the region in the vicinity of the large BH also to be too redshifted to be observable?

Depends what's emitting the light.

 

[Devin-M]

I was imagining the radius of the cloud on the order of 46 billion light years, the radius of the BH on the order of 4600 billion light years. The location of the cloud somewhere around 1.5 to 2.5 BH radii from the center of the black hole. If we assume a single Hydrogen Alpha photon is emitted directly away from the center of the black hole by an object traveling on the order of 99.999999999% the speed of light away from the BH, how long before that photon loses enough energy to where it is undetectable to a distant but same speed observer (in the frame moving along with the cloud)?

Can a (simulated) black hole be large enough that photons which escape the event horizon lose so much energy as they are climbing away that they are redshifted to undetectability to distant observers?

 

[Ibix]

You are trying to use a complicated perspective to understand something really quite simple:

the equivalence principle allows you to say that the dust cloud cannot see any difference from free fall in flat spacetime over a small region. So observers moving in the cloud simply see some blue shift from the inward motion of the particles in the cloud.

You can't avoid the equivalence principle by messing around with black hole size.

I feel like I'm repeating myself now.

 

[PeterDonis]

Can a (simulated) black hole be large enough that photons which escape the event horizon

No photons escape the event horizon.

lose so much energy as they are climbing away that they are redshifted to undetectability to distant observers?

Light that is emitted radially outward from an object that is "hovering" a very small distance above the horizon of any black hole will be redshifted to undetectability to distant observers.

However, what you proposed is light emitted by an object that is not "hovering", but traveling outward itself at a very high velocity. It is not clear that that light will be redshifted to undetectability to distant observers, because of the huge blueshift due to the outward velocity of the source.

You would need to look at actual math.

 

[Devin-M]

If the 46B ly radius, 99.99….% light speed cloud was not expanding or collapsing, could the simulated black hole be of such a size where a hydrogen alpha photon emitted from the edge of the cloud would be shifted to microwaves when observed by someone at the center (neither emitter or observer moves with respect to each other, but both move relative to BH)?

 

[PeterDonis]

If the 46B ly radius, 99.99….% light speed cloud was not expanding or collapsing, could the simulated black hole be of such a size where a hydrogen alpha photon emitted from the edge of the cloud would be shifted to microwaves when observed by someone at the center (neither emitter or observer moves with respect to each other, but both move relative to BH)?

@Ibix already answered this: as far as observers within the cloud itself and moving with the cloud are concerned, the black hole is irrelevant, by the equivalence principle. There is no redshift or blueshift for an observer moving with the cloud, because they're moving with the cloud--the cloud is at rest relative to them. How the cloud is moving relative to the black hole is irrelevant.

 

[Devin-M]

So the photons being observed are losing energy as they move away from the black hole, but because the observer’s clocks are ticking faster as they move away from the BH, no redshift is observed. Did I say that correctly?

 

[Ibix]

Did I say that correctly?

No. You forgot the kinematic time dilation and the Doppler effect (both source and receiver are moving). If you factor them in correctly as well as the gravitational time dilation, then you would predict no redshift.

 

[jedishrfu]

Since the OPs questions have been answered and the thread has run its course we will now close it.

Thank you all for participating here.

 

[Devin-M]

I’m still a bit confused because in my OP, the “cloud” moves away from the “hole” at nearly the speed of light so most if not all the photons emitted by the cloud move away from the hole due to relativistic aberration.

But if the cloud is initially at rest to the hole and a flash of light is emitted in all directions, roughly half the light moves toward the hole and half away, half being blue shifted the other half red shifted.

Which observers can tell the difference between these 2 scenarios (half vs all light moves away from hole)?

 

[PeterDonis]

Moderator's note: Thread reopened to address the OP's question in post #18.

 

[Ibix]

Which observers can tell the difference between these 2 scenarios (half vs all light moves away from hole)?

In the frame where the dustcloud is at rest, half the light moves towards the hole and half away. This is true in all cases assuming the emission point is at the same distance from the hole. In the frame where the black hole is at rest (if this is not the same as the dustcloud rest frame) then more or less (depending on direction of motion) of the light moves towards the hole than away.

So observers in the dustcloud cannot tell the difference between your two scenarios unless they can detect the black hole.

 

[Devin-M]

I’m referencing this diagram.

If the shuttle moves away from the hole, and flashes light in all directions, most of this light moves away from the hole due to relativistic aberration I thought.

https://www.physicsforums.com/attachments/img_1121-jpeg.352768/

 

[PeterDonis]

I’m referencing this diagram.

That diagram, applied to your scenario, is in the rest frame of the hole, not the rest frame of the dust cloud. @Ibix in post #20 correctly explained the difference between the two.

 

[Devin-M]

So can any observers note the difference in gravitational red/blueshifting of the light between v=0 and v=0.99c shuttle relative to hole emitting a flash of light?

 

[Ibix]

So can any observers note the difference in gravitational red/blueshifting of the light between v=0 and v=0.99c shuttle relative to hole emitting a flash of light?

Depends what you mean. If a moving shuttle passes a stationary one and they both emit a light pulse, the only difference between the pulses is due to kinematic time dilation/Doppler effects.

If a single shuttle repeatedly emits flashes, observers travelling with the shuttle will always see them all the same (assuming they can't detect the tidal anisotropy). All other observers will see a changing Doppler shift, which they can partially attribute to changing gravitational time dilation if they wish.

 

[Devin-M]

The shuttle accelerates from 0 to 0.99c away from hole emitting flashes of light. As the shuttle accelerates, with each subsequent flash, a greater percentage of that flash’s light moves away from the hole due to relativistic aberration, correct?

 

[Ibix]

As the shuttle accelerates, with each subsequent flash, a greater percentage of that flash’s light moves away from the hole due to relativistic aberration, correct?

According to who? The answer is dependant on your choice of coordinates, but you keep writing like there's an absolute answer.

 

[Devin-M]

According to who?

To an observer hovering at fixed altitude above the event horizon, as the flashing shuttle accelerates away from the horizon, the hovering observer will see a greater percent of the light from the flashes move away from the black hole as the flashing ship accelerates away from the black hole. That’s because the relativistic aberration causes most of the light to be emitted by the shuttle to travel in the forward direction of motion when the shuttle is close to light speed according to the stationary observer (stationary to the hole).

 

[Devin-M]

“Relativistically, moving objects are beamed due to a variety of physical effects. Light aberration causes most of the photons to be emitted along the object's direction of motion.”

“The magnitude of the effect is illustrated by the AGN jets of the galaxies M87 and 3C 31 (see images at right). M87 has twin jets aimed almost directly towards and away from Earth; the jet moving towards Earth is clearly visible (the long, thin blueish feature in the top image at right), while the other jet is so much fainter it is not visible.[1]”

Only a single jet is visible in M87.

Source:
https://en.m.wikipedia.org/wiki/Relativistic_beaming

 

[Ibix]

To an observer hovering at fixed altitude above the event horizon, as the flashing shuttle accelerates away from the horizon, the hovering observer will see a greater percent of the light from the flashes move away from the black hole as the flashing ship accelerates away from the black hole. That’s because the relativistic aberration causes most of the light to be emitted by the shuttle to travel in the forward direction of motion when the shuttle is close to light speed according to the stationary observer (stationary to the hole).

Yes.

 

[Devin-M]

Which observers (besides the one stationary to the hole) can tell that as the shuttle moves faster away from the hole, a greater percent of the light from each flash is being gravitationally redshifted on account of a greater percentage of light moving away from hole (more percentage of light bent towards direction of travel close to light speed relative to hole)?

 

[Ibix]

Which observers (besides the one stationary to the hole) can tell that as the shuttle moves faster away from the hole, a greater percent of the light from each flash is being gravitationally redshifted on account of a greater percentage of light moving away from hole (more percentage of light bent towards direction of travel close to light speed relative to hole)?

There is no "can tell" here. No perspective is right or wrong here.

From the point of view of observers at rest with respect to the hole, the light pulses are increasingly beamed away from the hole.

From the perspective of the ship the hole is accelerating away and simply becomes a smaller target so less light hits the hole, but the same amount is launched within 90° of the line to the hole.

From other perspectives the beaming may be towards the hole and reducing, or the beaming may be at an angle to the hole.

In all interpretations actually measurable quantities (like the mass increase of the hole) are the same, but for different reasons and at different rates.

 

[Devin-M]

An observer could be in free fall and reach apogee after initially moving away from the hole, thus be momentarily hovering but also in free fall. If a flashbulb went off on board at apogee, could photodetectors also on board see some light moving towards the hole blueshifted and the some light moving away from hole redshifted?

 

[Ibix]

It does not matter how many times you ask that question. The answer will not change from the one given in #2, #4, #7, #11, and probably others.

 

[Devin-M]

Ok, so we’re invoking the equivalence principle to answer my original question, but on the wikipedia page for equivalence principle it says:

“Here local means that experimental setup must be small compared to variations in the gravitational field, called tidal forces. The test experiment must be small enough so that its gravitational potential does not alter the result.”

Source: https://en.m.wikipedia.org/wiki/Equivalence_principle

Can the equivalence principle really be used in the situation I described, where in the frame of the “cloud” a photon is traveling 46 Gly from edge to center, but in the frame of the “hole” the photon is traveling much farther because the cloud moves very close to the speed of light relative to hole. Is that really small and local enough and absent of tidal forces over the time of flight of the photons in question to use the equivalence principle?

 

[Devin-M]

very large, accreting black hole

I also should have been more specific about what I meant by the “accreting” black hole. I meant the “cloud” moves away from the center of the black hole very close to the speed of light, but the black hole is growing rapidly enough that the event horizon is approaching the cloud, even though the cloud moves away from the center of the hole. In other words the black hole’s event horizon is expanding faster than the cloud recedes from the center of the hole. So even though the cloud is moving away from the center of the hole, the event horizon is actually moving towards the cloud.