# Redshift Of Light Due To The Curvature Of Spacetime In A Closed Universe

Relativity

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### #18 A-wal

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Posted 25 November 2015 - 09:01 PM

Light can't , the observers angle is shifted.

I have no idea what that's supposed to mean. Light is redshifted by gravitation so it is redshifted by following a curved path through spacetime.

The difference is that, for gravitational redshift to occur, light must travel from a place with lower gravitational potential to a place with greater. The redshift depends only on the difference in gravitational potential at the source and receiver, not that of other places through which the light travels, nor whether its path is deflected by gravitational lensing or other means.

Your question suggest to me, A-wal, that you’re confusing the curvature of spacetime, which is a property of points on a 3 spacelike + 1 timelike dimensional manifold, with the curvature of a path in 3 dimensional space, of which an example is the path of light deflected by gravitational lensing. These are very different things.

Yes, I'm very confused by this. Gravitational lensing occurs because light moves through spacetime that's length contracted and time dilated. Gravitational lensing occurs because light moves through spacetime that's length contracted and time dilated. There's no lensing in this case because the light is coming from the origin so the time dilation and length contraction are even in all directions so it has no reason to favour a particular direction and all you get is redshift. You could look at as energy being equal in all directions so it cancels out, whereas light origination away from the source of gravitation will have its path curved towards it.

You haven't described a difference, all you've done is stated that they are different. I don't see how gravitational lensing isn't caused by light traveling on a curved path through spacetime. How can it not be? There's no such thing as curved space. Time dilation and length contraction always happen together, you can't have one without the other. How can gravitation cause redshift of light coming from the source of the gravitation but not cause redshift when the light comes in at an angle to the source?

I still don't see how redshift can be finite at a relative velocity of the speed of light but infinite at the event horizon of a black hole, where the object is accelerated to a relative velocity of the speed of light. Both of these seem like blatant examples of shifting the goal posts. How could the fact that light came from somewhere other than the source of gravitation affecting its path cause it to escape the effects of time dilation and length contraction stretching its wavelength and how could the redshift of an object be infinite at a relative velocity of the speed of light but infinite if gravity did the accelerating? Regardless of the method the object used to reach that velocity the amount of time dilation and length contraction at the speed of light has to be the same, infinite!

I uncertain to what you’re referring, A-wal, but I wouldn’t call a model a theory, because they’re very different things.

A scientific model is a way of calculating some measurable feature of physical reality that’s hard or practically impossible to calculate exactly using approaches. For example, there’s no know exact way of calculating in general the position of 3 or more bodies with nonzero mass using Newton’s theory of universal gravity, but it’s easy to calculate them approximately using a model in which you calculate the force on each body, apply it as constant (or changing linearly) for some duration to calculate the bodies’ velocities, then apply the velocities to calculate their position (for example, with my GRAVSIM4 program, which we’ve used for various simple orbital mechanics discussions).

Scientific theories provide ideas that can be used to write models, and models can be used to solve practical problems, but theories and models are different kinds of things.

All theories are models but not all models are theories. General relativity for example is a theory that models gravitation as a curvature of spacetime. It shouldn't be that hard to turn this into an actual theory seeing as most of it is already done. I'd start by showing that curved spacetime and flat spacetime are equivalent by using the Rindler coordinate system to show that special relativity can be described as objects following straight paths in curved spacetime when they accelerate and gravitation can be described as objects following curved paths in flat spacetime and the Rindler coordinate system and Schwarzschild coordinate system are equivalent if you just drop the ridiculous assumption that gravitational acceleration is an inertial frame of reference. I'd model it in a closed four dimensional universe to show that it creates a black hole on the opposite side from the frame of reference of any observer and that the observed galactic redshift is gravitational redshift. And it will be called the what you get if it's done properly theory of relativity!

Newtonian mechanics and Relativity are theories that describes exactly the positions of bodies for a given instance under the influence of gravity and arbitrary well-defined forces, as measured from any reference frame with any possible velocity. They are not models making it easier to calculate these positions, nor are they ad-hoc adjusted to better agree with observations of actual reality.

Newtonian mechanics has been show to not agree with observations, but in most case not so badly that it does not remain a very useful theory. Relativity has not been show to disagree with observations, provided that those observations are of large bodies.

No, it matches 10% of the observations the other 90% is the ad hoc inclusion of never before seen form of matter needed to make the other 10% valid. Some people think that dark matter is evidence that the inverse square model is only an approximation and that this only becomes apparent at large scales. I don't. The strength of gravity is proportional to the volume of space that it fills. In one dimension it wouldn't weaken with distance, in two dimensions it's strength would halve every time the distance is doubled and in three dimensions it's an inverse square. If gravity really does fall off at a lesser rate then in one dimension it would strengthen with distance.

I’m suspicious of Dowdye’s paper, because I suspect he’s a crank with a religious agenda. Here’s what lead me to this suspicion: Comments from Dowdye and reviewers rejecting his article submission to scitizen.com; Dowdye’s website, “Extinction Shift Principle”; Dowde’s scienceinthebible.net “about the author” page.

I hate religion (not spirituality in general) with a passion but I someone's spiritual beliefs have no direct baring on anything they present as scientific. His paper has to be judged purely on its own merit. I'm not saying his paper has any merit but if it does it's extremely interesting and it wouldn't surprise me if evidence that physicists find inconvenient gets swept under the carpet. Besides, it wouldn't make sense for somebody with a Christian ideology agenda to chose this of all things to attempt to refute. General relativity is a foundation of the big bang model which is well and truly a creationist model.

Halton Arp showed that redshift isn't only caused by distance when he showed that some supposedly distant and mega powerful quasars are actually closer and far less energetic by demonstrating repeatedly that quasars are physically connected to host galaxies. This doesn't even disprove the big big model, it's just inconvenient so it gets ignored and denied despite the fact that apparently anyone with a decent telescope can see for themselves that he was right. I should be careful here because I don't know the evidence first hand but I wonder how they'd get the limited attention they have if their evidence or conclusions aren't valid.

I don't trust physicists because the vast majority of them aren't truth seekers, they're partyline towers. I know from my own limited interactions with them that they're deceitful, manipulative, and outright dishonest they can be. I wouldn't put it past them to cover up evidence. The more I have contact with them the more convinced I am that they've just memorised what they know rather than having any actual understanding of it because most of the time they're completely incapable of defending their assumptions but will cling to them regardless of how convincing the refuting evidence is. I can give a dozen reasons why no object can ever fall past an event horizon and none of them have ever been able to refute even a single one.

Mainstream Physics Rules Of Engagement
Okay so you've achieved your objective and proved you can parrot back from memory a bunch of meaningless equations based on illogical and demonstratively false assertions to earn yourself a PHD, but what do you do if an individual with independent thought and critical thinking skills dares to challenge what you've memorised but don't comprehend? After all, they have the advantage of being able to think dynamically in real time and use their minds to actually analyse the subject matter due to the fact that their mind isn't already made up. Fear not, just follow this simple guide and you won't have to worry about it. Remember, you're the one with a PHD (don't forget to keep mentioning this) so your words are right until proven wrong, which won't happen if you just stick to these rules.

Rule 1. Try to never answer direct questions. Instead always misdirect by pointing out something that's related but not actually relevant so as to make it appear that the other person has overlooked something.

Rule 2. Always go on the offensive. Truth isn't half as important as appearances to most people, so make it look like the other person is under pressure and people will tend to assume that you're right. Never under any circumstances allow the other person to establish the offensive position. Be as confrontational as you like because you're the mainstream physicist so they're the one who will get the warnings for being rude, not you.

Rule 3. Always attack personally rather than attacking arguments that you know you can't refute so that you can establish dominance and prevent the other person from gaining credibility.

Rule 4. Make things seem much more complicated than they actually are. Try to create the impression to the readers that the other person lacks a full understanding by expressing the mathematical relationships in purely scientific terms even though plain English would make the same statements just as clear and concise. You can even repeat exactly what the other person said in a more complicated way and it will look like they made a mistake and you corrected them. Use equations from time to time as well. Most people can't follow them so it will make you look clever, even if they're not strictly relevant to the other persons argument.

Rule 5. If all else fails just don't answer. Instead say something like 'Your assertions are based on false assumptions and half understood facts and I don't even want to waist any more of my time trying to teach someone who is on such a low level and has already proved that they're not capable of understanding counterintuitive physics.' Always remember to implant the idea that anything you can't argue is counterintuitive if understood correctly. This will make sure that anyone who starts to question what you're saying will instantly right off their doubts as a misunderstanding.

Follow these very simple rules and always remember to be as condescending as possible and you'll be able to argue your point without actually addressing the other persons objections or engaging in any kind of meaningful debate.

### #19 CraigD

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Posted 25 November 2015 - 11:57 PM

Yes, I'm very confused by this. Gravitational lensing occurs because light moves through spacetime that's length contracted and time dilated.

I failed to correct this when you wrote it earlier. Length contraction applies only to bodies with nonzero velocity relative to an observer, not for bodies at locations with different gravitational potential than the observer’s location. That is, an observer in a place with higher gravitational potential observes a clock in a place with lower to tick slower, but they do not observe a measuring stick to be shorter.

While the formulas for the angle of deflection of gravitational lensing and gravitational time dilation,
$\theta = 2 \frac{r_s}{r}$
$\frac{t_0}{t_f} = t_f \sqrt{1 - \frac{r_s}{r}}$
where $r_s = \frac{2 G m}{c^2}$
have a $\frac{r_s}{r}$ term in common, I wouldn’t say gravitational time dilation causes gravitational lensing, but rather that both are caused by gravity.

I don't see how gravitational lensing isn't caused by light traveling on a curved path through spacetime

The curved light path associated with gravitational lensing can be completely described in 3 spacelike dimensions, which we could call a curved path through space – that is, its timelike dimension can be ignored. Describing the curvature of the path that a body follows thought the 3 spacelike and 1 timelike dimensions requires all 4 dimensions.

My ability to explain – or even much understand – this is limited, though, because I can’t actually do the mathematical formalism of 4D spacetime. I’d like to, and since it can be done using fairly simpler matrix arithmetic, which I can do, am hopeful that I can self-educate myself to be able to. I don’t feel I understand physics for which I can’t do the math, largely because my approach to understanding physics involved calculate specific examples.

I don't trust physicists because the vast majority of them aren't truth seekers, they're partyline towers

I have a hard time imagining how you’d quantify what fraction of members of a profession are truth seekers, or what it means to tow a party line in science, give that scientists aren’t members of parties in the way that politicians and voters are. Can you provide links or references backing up your claim that the vast majority of physicists aren’t truth seekers, A-wal

Most of the physicists – that is, people with PhDs in physics – have been teachers - though, given the increasingly dismal job market in basic science, I’m meeting a startling number of them working as non-scientific computer programmers. I wouldn’t describe any of the teachers as either truth-seekers or party line towers – rather, they seemed to me interested mostly in rousing students to think about and learn physics. I’d describe the computer programmers as disillusioned, even depressed, because they worked very hard in school to be professional physicists, but are not. Sadder still are those who would have liked to teach science, but couldn’t afford to.

From what I’ve read of the history of physics and science in general, though, all noteworthy seekers of truth about the physical universe have been scientists, most of them physicists. So while it may be that most physicists are not truth-seekers, I think most successful seekers of truth about eh physical universe are physicists. While many people without much scientific training may seek truth about the physical universe, I don’t think they’re able to find it. Desire does not guarantee ability.

### #20 A-wal

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Posted 26 November 2015 - 09:43 AM

I failed to correct this when you wrote it earlier. Length contraction applies only to bodies with nonzero velocity relative to an observer, not for bodies at locations with different gravitational potential than the observer’s location. That is, an observer in a place with higher gravitational potential observes a clock in a place with lower to tick slower, but they do not observe a measuring stick to be shorter.

That can't be right. Of course they observe a measuring stick in a place with higher gravitational potential to be shorter! Singularities are infinitly length contracted. If you were to observe an object falling towards a black hole it would get progressively more length contracted at the same rate that it gets progressively more time dilated. ) = event horizon.

Length contraction:   )   I---I     )  I--I     ) I-I     )I

Time dilation:   )   I     )  I-I     ) I--I     )I---I

While the formulas for the angle of deflection of gravitational lensing and gravitational time dilation,
$\theta = 2 \frac{r_s}{r}$
$\frac{t_0}{t_f} = t_f \sqrt{1 - \frac{r_s}{r}}$
where $r_s = \frac{2 G m}{c^2}$
have a $\frac{r_s}{r}$ term in common, I wouldn’t say gravitational time dilation causes gravitational lensing, but rather that both are caused by gravity.

Same thing. Gravitation is length contraction and time dilation, it is curved spacetime, it is acceleration. I don't think there's any distinction between the four. I know that isn't the standard view because I've included acceleration which is described differently in some ways when it's caused by gravity but in the standard view the other three are the exact same thing. In general relativity gravitation is the curved spacetime caused by time dilation and length contraction. Anything (including light) that moves through time dilated and length contracted spacetime will follow a curved path relative to an observer that isn't moving through time dilated and length contracted spacetime. How can a massive object cause its to be redshifted due to the light's path curved path through spacetime but not not cause other light moving through the same time dilated and length contracted spacetime to follow a curved path? How can any light moving through time dilated and length contracted spacetime be affected by length contraction, but only affected by time dilation if it happens to be light coming from the source of gravitation? That makes no sense!

I have a hard time imagining how you’d quantify what fraction of members of a profession are truth seekers, or what it means to tow a party line in science, give that scientists aren’t members of parties in the way that politicians and voters are.

Not officially.

Can you provide links or references backing up your claim that the vast majority of physicists aren’t truth seekers, A-wal

Yes, but it would only be links to extremely frustrating conversations I've had on other boards that lead to right the mainstream physicist rules of engagement and links to scientists that provide evidence that contradicts the standard model and are automatically labeled as cranks because they've dared to challenge doctrine regardless of their evidence for doing it. I used to think crank meant somebody who makes invalid arguments based on underlying misconceptions, like a crackpot. I now realise that it's a code word for somebody who has the knowledge and evidence to back it up making claims that refute any models that team consensus science regard as settled.

From what I’ve read of the history of physics and science in general, though, all noteworthy seekers of truth about the physical universe have been scientists, most of them physicists.

Think about what you just said.

So while it may be that most physicists are not truth-seekers, I think most successful seekers of truth about eh physical universe are physicists.

Or philosophers. It used to mean the same thing. Now philosophy (the ability to use reason to apply physics to the real universe) has been removed and is even stigmatised.

While many people without much scientific training may seek truth about the physical universe, I don’t think they’re able to find it. Desire does not guarantee ability.

And a lack of formal education doesn't guarantee failure. It just guarantees failure of the chance for their work to be judged fairly, on merit. In fact formal education is almost a guarantee of failing to find any new truths because it conditions people to accept ideas based on conformity rather than understanding.

### #21 A-wal

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Posted 28 November 2015 - 04:23 AM

Light does get time dilated by gravitational lensing because if it didn't then it would be following a curved path through curved spacetime, not a straight one.

Objects do appear length contracted if they're in a stronger gravitational than the observer because if objects were able to reach an event horizon they'd be infinitely time dilated and length contracted because they'd be infinitely accelerated and moving at the speed of light relative to any distant (even a Plank length's distance) observer.

I can't upload any more sketches, apparently I've reached the limit even though I've only uploaded a few. Meh, I'll do it without them.

As viewed from outside the gravitational effects (far enough away that the effects are negligible). ) = event horizon.

Length contraction:
)                                                                                                                                I--------I
)                                                                I-------I
)                                I------I
)                I-----I
)        I----I
)    I---I
)  I--I
) I-I
)I

Time dilation:
)                                                                                                                                I
)                                                                I-I
)                                I--I
)                I---I
)        I----I
)    I-----I
)  I------I
) I-------I
)I--------I

That's the Schwarzschild coordinate system. Any coordinate system that allows the free-faller to reach the event horizon (infinite acceleration and the speed of light relative to every inertial observer in the frigging universe) is a direct contradiction of the Schwarzschild coordinates that never allow an object to reach an event horizon in any amount of time. You need to work out what happens to the black hole from the free-faller's perspective. The free-falling object doesn't get length contracted and time dilated from there own perspective so the space between the free-faller and the event horizon is larger and the black holes life span is shorter from the free-faller's frame of reference. So the black hole and the event horizon are the exact same thing. Singularities are singular in time as well as space and only appear to have length in time and space when they're viewed from a distance, which is always.

The event horizon moves outwards at the speed of light when a black hole forms it's not really expanding, it's a a singularity, so the first any observer will know about it is a fully formed black hole that's event horizon is moving inwards at the speed of light but slower from a distance because of length contraction and time dilation. A four dimensional object that expands at a constant rate creates half of a sphere and when it's reached its maximum size it contracts at the same speed (speed of light, making it uncatchable) and creates the opposite shape making a full hypersphere. A singularity is an infinitely small hypersphere that expands in all four dimensions at the same rate as distance increase and become less pronounced as a square of the distance.

As viewed by the free-falling observer. . = singularity (if it was half way up instead of near the bottom of the )).

.                                                                                                                                )                                                                I--------I
.                                                                                                                               )                                                        I--------I
.                                                                                                                             )                                                I--------I
.                                                                                                                         )                                        I--------I
.                                                                                                                 )                                I--------I
.                                                                                                 )                        I--------I
.                                                                 )                I--------I
. )        I--------I
I--------I

Do you recognise that? It's the Rindler coordinates. The Rindler horizon works exactly the same way when an object accelerates towards the speed of light (infinite acceleration) free from gravitation. I didn't reverse engineer this. I worked these coordinates out ages ago before I'd even heard of the Rindler coordinate system and it's identical. All you need to do is switch the direction to see the horizon (light) chasing the accelerator. --- = rate of acceleration.

.                                                                                                                                )                                                                I--------I  ->
.                                                                                                                               )                                                        I--------I  -->
.                                                                                                                             )                                                I--------I  ---->
.                                                                                                                         )                                        I--------I  -------->
.                                                                                                                 )                                I--------I  ---------------->
.                                                                                                 )                        I--------I  -------------------------------->
.                                                                 )                I--------I  ---------------------------------------------------------------->
. )        I--------I  -------------------------------------------------------------------------------------------------------------------------------->
I--------I ---------------------------------------------------------------------------------------------------------------------------------------------...

Both together. ) = event horizon or the speed of light relative to an accelerator free from gravitation (same thing), ( = Rindler horizon.

.                                                                                                                         )                                        I--------I                                        (

.                                                                                                                 )                                I--------I                                (

.                                                                                                 )                        I--------I                        (

.                                                                 )                I--------I                (

. )        I--------I        (

I--------I

This is what would happen if an object were able to cross the event horizon.

) I--------I (      I)------(I        I--)--(--I        I---)(---I        I--(--)--I        I(------)I      ( I--------I )

The Rindler horizon is the point past which light will never catch up to the accelerating object at it's present rate of acceleration, and it's just overtaken them! See how silly it is?

Good innit? Now all I've got to do to call it a theory is add a bunch of pointless equations that don't provide any actual explanations or context.

Edited by A-wal, 28 November 2015 - 02:36 PM.

### #22 CraigD

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Posted 01 December 2015 - 10:46 PM

I failed to correct this when you wrote it earlier. Length contraction applies only to bodies with nonzero velocity relative to an observer, not for bodies at locations with different gravitational potential than the observer’s location. That is, an observer in a place with higher gravitational potential observes a clock in a place with lower to tick slower, but they do not observe a measuring stick to be shorter.

That can't be right. Of course they observe a measuring stick in a place with higher gravitational potential to be shorter!

You’re right – I was wrong. Per General Relativity, a measuring stick at a place with a lower gravitational potential (ie: closer to a large mass) is observed to be shorter than one further away from the mass.

The question "which is shorter: a measuring stick closer to the source of gravity or a farther one?" is more complicated than it sounds.

This stackexhange Q&A page gives, I think, a good if technical sense of how complicated. My approach is to start with a thought experiment showing why length contraction due to relative velocity (that is, per Special Relativity) is not complicated.

Place 2 identical measuring sticks side by side, with zero relative velocity.

Move the sticks far apart

Accelerate one or both toward one another to a speed of 0.28 c

When they are side by side with relative speed 0.28c, an observer traveling with one of the sticks measures the length of the other. They find the other stick is 0.96 times ($\sqrt{1-0.28}$) as long as theirs.

Next, try to imagine an equally simple experiment to measure the length of the 2 sticks at different distances from the center of a large – let’ say 115 km and 150,000,000 km - dense body – let’s say a 2 solar mass, 11.5 km radius neutron star. From the Schwarzschild metric, we can calculate that the stick at 115 km is about 0.9485 times as long as the one at 150 million km. It’s hard to figure out a way to measure this, though. You can’t put the sticks side by side, because their length depends on their position. You can measure them by the arc they subtend, but must account for gravitational lensing, a complicated calculation.

Singularities are infinitly length contracted.

Per the Schwarzschild metric, gravitational time dilation and length contraction are infinite at the event horizon of a black hole.

But don’t confuse event horizon, which have nonzero surface area and enclose nonzero volumes and masses, with singularities, which are theoretical bodies with zero volume and nonzero mass.

Getting back to the question of whether the curving of light due to gravitational lensing causing it to be redshifted, here’s a simplified explanation of why it isn’t:
As light from a distant star approaches a massive body (a galaxy, black hole, etc) that deflects it, it is blueshifted. As it moves away from the body, it is redshifted. The amount of blueshift is about the same as the amount of redshift, so the net red or blueshift measured by a distant observer is about zero.

### #23 A-wal

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Posted 03 December 2015 - 03:29 AM

The question "which is shorter: a measuring stick closer to the source of gravity or a farther one?" is more complicated than it sounds.

It's as simple as an object accelerating at the same increasing rate of acceleration that it would be if it were falling towards an event horizon and an inertial observer measuring its length as it does. As a free-falling object gets closer to the horizon time dilation and length contraction approach infinity at the same rate as they do when an an accelerator approaches the speed of light from the perspective of an inertial observer. This is exactly what the Schwarzschild coordinates show and it means that free-falling objects can never reach an event horizon in a finite amount of proper time because no matter how long the black hole lives any objects falling towards it will still be outside the event horizon when it dies. There's no way to switch to coordinate system that allows a free-falling object to reach an event horizon without directly contradicting the Schwarzschild (and Rindler, as they can also be used to describe free-fall because it's just acceleration) coordinates.

My approach is to start with a thought experiment showing why length contraction due to relative velocity (that is, per Special Relativity) is not complicated.

Place 2 identical measuring sticks side by side, with zero relative velocity.

Move the sticks far apart

Accelerate one or both toward one another to a speed of 0.28 c

When they are side by side with relative speed 0.28c, an observer traveling with one of the sticks measures the length of the other. They find the other stick is 0.96 times ($\sqrt{1-0.28}$) as long as theirs.

You mean ($\sqrt{1-(0.28^2)}$). So each will view the others clock as ticking at 0.96 times as fast as their own because time dilation and length contraction are always equal. This is purely down to which observer's frame of reference you use, coordinate dependent td and lc. Acceleration causes actual td and lc, it's what's responsible for the age difference in the twin paradox when they meet back up. One way of looking at it is when one the inertial observers accelerates into the others frame of reference they have to use the new frame's measurements and in that frame they were the ones that were time dilated and length contracted, not the observer who remained inertial, so it turns coordinate dependent td and lc into actual td and lc because the amount of td and lc each observer initially measured the other to be will always be the same as the amount of true td and lc that will be experienced if one observer accelerates into the other frame.

That's why an accelerating observer approaches the speed of light in their own frame of reference as acceleration increases at the same rate as they approach the speed of light in an inertial observer's frame of reference as their velocity increases, like this:

I                                                                                                                                I--------I
I                                                                I--------I
I                                I--------I
I                I--------I
I        I--------I
I    I--------I
I  I--------I
I I--------I
II--------I

This represents both a consistent increase of acceleration at every step from the accelerator's frame of reference and a consistent increase of velocity at every step from an inertial frame of reference.

Next, try to imagine an equally simple experiment to measure the length of the 2 sticks at different distances from the center of a large – let’ say 115 km and 150,000,000 km - dense body – let’s say a 2 solar mass, 11.5 km radius neutron star. From the Schwarzschild metric, we can calculate that the stick at 115 km is about 0.9485 times as long as the one at 150 million km. It’s hard to figure out a way to measure this, though. You can’t put the sticks side by side, because their length depends on their position. You can measure them by the arc they subtend, but must account for gravitational lensing, a complicated calculation.

You can put the sticks side by side by making one of them hover outside the event horizon by constantly accelerating in the opposite direction to counteract the gravitation and the other free-fall past it. As they pass each other the length contraction and time dilation of the falling object as measured by the hoverer will be exactly the same as if it were measuring from a distance where the strength of gravity is negligible. It's also no different to if the object were moving at that speed relative to an inertial observer. The increasing rate of acceleration of the falling object is exactly equivalent to if the passing object were accelerating in the same way. Two free-falling objects at different distances is hard because they're accelerating at a different rate and the difference is constantly increasing.

Per the Schwarzschild metric, gravitational time dilation and length contraction are infinite at the event horizon of a black hole.

But don’t confuse event horizon, which have nonzero surface area and enclose nonzero volumes and masses, with singularities, which are theoretical bodies with zero volume and nonzero mass.

I'm not confusing them, they're the same same thing. A singularity from a distance has length in all four dimensions. It's only a singularity in its own frame of reference. The infinite length contraction and time dilation at the horizon makes the horizon infinitely small in space and makes it move through time infinitely fast, giving it zero length in time and space, a singularity. Any object approaching an event horizon would see the size of the black hole decreasing. They wouldn't be able to catch up with it in the same way that a Rindler horizon can't catch up to an accelerating object. There's a nice prediction there. Work out the amount of time dilation and length contraction at a black hole's event horizon (moving at the speed of light locally) and you can work out how fast the horizon will be moving inwards from any observed distance, so you can work out how quickly black holes loose their mass.

Getting back to the question of whether the curving of light due to gravitational lensing causing it to be redshifted, here’s a simplified explanation of why it isn’t:
As light from a distant star approaches a massive body (a galaxy, black hole, etc) that deflects it, it is blueshifted. As it moves away from the body, it is redshifted. The amount of blueshift is about the same as the amount of redshift, so the net red or blueshift measured by a distant observer is about zero.

That's inertial blueshift and redshift as the object moves towards and away from the source of gravity. They cancel each other out so the gravitational redshift is what's observed. That doesn't get cancelled out because it's caused by acceleration. Any light that follows a curved path through space time will be redshifted because that's exactly what causes gravitational redshift. The redshift of distant galaxies is gravitational redshift because of the curvature of the universe. 90 degrees (a quarter of the way around) is an event horizon and its size is determined by the combined mass of everything on the opposite side of the sphere, so the sphere's size depends on the overall mass of the universe.

Edited by A-wal, 04 December 2015 - 10:15 AM.

### #24 A-wal

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Posted 16 December 2015 - 05:06 AM

Getting back to the question of whether the curving of light due to gravitational lensing causing it to be redshifted,...

Whether or not gravitational lensing causes redshift isn't the real question. If the universe is a closed four dimensional sphere as I fully expect it should be then the redshift of distant galaxies isn't a product of gravitational lensing, it's gravitational redshift. If the universe is closed in four dimensions then everything in the universe can be thought of as existing on the surface of a hypersphere and (assuming the distribution of matter in the universe is basically uniformly spread) from the perspective of any observer that looks across space at quarter of the way round the sphere (90 degrees) in every direction would be an event horizon just as the four dimensions are curved to 90 degrees at the event horizon of conventional black holes. This means that everything past that point (on the opposite side of the sphere) would funnel into a singularity with a mass of half of the total mass of the universe.

This model makes two explicit predictions. Objects would tend to appear more redshifted the further away they are from any observer and there would be an apparent black hole of immense proportions at the furthest point that can be observed. Both of these effects are observed in reality, the second being dark flow.

Having said that, I still can't understand why gravitational lensing wouldn't cause redshift. Gravitational lensing is caused by light moving through time dilated and length contracted space and gravitational lensing is caused by the exact same thing, so how can it not cause redshift?

I also know for a fact that it's not possible for any object to reach the event horizon of a black hole because at the horizon time dilation and length contraction become infinite as objects would be accelerated to the speed of light relative to the singularity (no amount of acceleration, gravitational or otherwise can do that) so everything else in the universe, including the black hole would be moving infinitely quickly through time from the the perspective of the falling object and regardless of how long the black hole lasts, it will be gone before any object can reach the event horizon. No object can reach an event horizon in a finite amount of proper time. That's just one of many reasons why no object can ever reach an event horizon, which is just one of many reasons why gravitational acceleration is equivalent to accelerating free from gravity, not equivalent to being inertial.

### #25 carpenter0

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Posted 20 February 2018 - 03:14 PM

I basically agree with A-wal but want to add a few ideas.

Redshift:

If I was to lay a 10 meter pipe 'perfectly straight', and joined it to another 'perfectly straight' section, then another etc so that a finite number of pipes would join up once it has circumnavigated the entire closed spherical universe. Then if I shine a light down the tube (in a 'straight line') it would result in it moving away from me in what I perceived as a straight line, but what in fact is a curve in spacetime.  If a person on the other side of the universe (14 billion light years in the distance) was to open the pipe to see the light I had sent in a 'straight line' around the curvature of spacetime, he would note that it was redshifted to the maximum (infinity) at precisely at the point opposite me on the sphere. The distortion caused by the curvature of space time prevents the light ever completing its journey around the curve back to its origin.

Universe does not expand or collapse:

Also, the universe does not expand or collapse because it is perfectly balanced. Every point appears to be the center and has neutral gravity at that point - similar to the center of the earth where things will appear weightless. The size of the sphere is dependent on the mass of the universe.  If mass does not change the size does not change.

Universe is eternal:

The universe has always existed and always will.  It simply recycles energy for eternity.  New galaxies forming, older ones dying, all spread roughly evenly throughout the space of the universe and it has always been like this through all eternity, past  present and future.  Black holes almost certainly have a role to play in the recycling system, they will form and then disperse.    How it came into being is a similar question to who made God. Always existed, and always will based on the law of conservation of energy - energy can neither be created nor destroyed, rather, it can only be transformed from one form to another.

### #26 Farsight

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Posted 21 February 2018 - 04:44 PM

I have no idea what that's supposed to mean. Light is redshifted by gravitation...

Actually, light isn't redshifted by a gravitational field. Einstein said this: "an atom absorbs or emits light at a frequency which is dependent on the potential of the gravitational field in which it is situated". The frequency didn't reduce as the photon ascends, it was lower when the photon was emitted, that's all. The ascending photon doesn't lose energy. You measure it to have lost energy because when I lift you up I do work on you and your rods and clocks, so I add energy to you and them. So the photon appears to have lost energy, even though it hasn't.

### #27 carpenter0

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Posted 22 February 2018 - 03:57 AM

Light traveling in what it perceives as a straight line (through curved space of the universal sphere) is noticeably distorted as it passes a gravitational field such as a large star on its journey to the observer.  https://en.wikipedia...iro_delay.gif      As far as I can see it is red shifted, when compared to light coming to an observer without a star in the way.

Edited by carpenter0, 22 February 2018 - 04:02 AM.

### #28 A-wal

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Posted 23 March 2018 - 02:48 PM

I basically agree with A-wal but want to add a few ideas.

Redshift:

If I was to lay a 10 meter pipe 'perfectly straight', and joined it to another 'perfectly straight' section, then another etc so that a finite number of pipes would join up once it has circumnavigated the entire closed spherical universe. Then if I shine a light down the tube (in a 'straight line') it would result in it moving away from me in what I perceived as a straight line, but what in fact is a curve in spacetime.  If a person on the other side of the universe (14 billion light years in the distance) was to open the pipe to see the light I had sent in a 'straight line' around the curvature of spacetime, he would note that it was redshifted to the maximum (infinity) at precisely at the point opposite me on the sphere. The distortion caused by the curvature of space time prevents the light ever completing its journey around the curve back to its origin.

No it would be at a quarter of the way round the sphere, look at the diagrams in the opening post. That's why I did the arrows from > to ^, it's the rotation of the light waves that would be causing them to red-shift. A 90 degree rotation would cause infinite red-shift, limiting visibility to a quarter of the way round the sphere in all directions so an observer could only see their half of the sphere.

It would mean that the universe would seem completely dark if we look a certain distance away in any direction and then presumably if it possible to look far enough past that we'd start to see objects on the other side of the sphere as blue-shift lowers from infinity as distance increases. That wouldn't be possible though because there'd always be an event horizon separating the two halves of the sphere. I'm not sure if this rotation could reverse charge, but if it could that would nicely explain why there's more matter than anti-matter, the anti-matter is on the other opposite side wherever the observer happens to be.

Universe does not expand or collapse:

Also, the universe does not expand or collapse because it is perfectly balanced. Every point appears to be the center and has neutral gravity at that point - similar to the center of the earth where things will appear weightless. The size of the sphere is dependent on the mass of the universe.  If mass does not change the size does not change.

Yea, overall gravity would have to be roughly equal in all directions.

Universe is eternal:

The universe has always existed and always will.  It simply recycles energy for eternity.  New galaxies forming, older ones dying, all spread roughly evenly throughout the space of the universe and it has always been like this through all eternity, past  present and future.  Black holes almost certainly have a role to play in the recycling system, they will form and then disperse.    How it came into being is a similar question to who made God. Always existed, and always will based on the law of conservation of energy - energy can neither be created nor destroyed, rather, it can only be transformed from one form to another.

Yes a hyper-spherical four dimensional universe is eternal, one of the dimensions is time. The further away an event is in space, the closer it is in the opposite direction and the further away an event is in time, the closer it is in the opposite direction as well. This doesn't cause a paradox because there's no way to get information from the future from the other side of an event horizon and again, doing it in increments doesn't count. You can think of it as time being on a loop and going round and round like a spinning wheel but in reality it's a static hyper-sphere. Our perception of progressive time is just that, our three and a half dimensional view because we only see in one direction of one of the four dimensions. This one-way perception is the only thing that makes time seem distinct from space, and so we remember the past but not the future.

I think it's also cyclical in another sense, it's a fractal. Every point contains all the information of the whole, if you zoom in or out far enough you end up back where you started.

Actually, light isn't redshifted by a gravitational field. Einstein said this: "an atom absorbs or emits light at a frequency which is dependent on the potential of the gravitational field in which it is situated". The frequency didn't reduce as the photon ascends, it was lower when the photon was emitted, that's all. The ascending photon doesn't lose energy. You measure it to have lost energy because when I lift you up I do work on you and your rods and clocks, so I add energy to you and them. So the photon appears to have lost energy, even though it hasn't.

No, red-shift shouldn't be based on the curvature gradient at the point of emission, it should be based on the overall curvature on the path that it traveled.

Light traveling in what it perceives as a straight line (through curved space of the universal sphere) is noticeably distorted as it passes a gravitational field such as a large star on its journey to the observer.  https://en.wikipedia...iro_delay.gif      As far as I can see it is red shifted, when compared to light coming to an observer without a star in the way.

Good, a curved path through space-time causes light to red-shift.

Black holes are four dimensional spheres as well. Singularities are infinitely small, in all four dimensions. They have no surface area and exist for no amount of time but their effect grows equally in all four dimensions as an inverse square as distance increases because they're infinitely time dilated and length contracted from their own perspective (although you can't really class something that has no size in all four dimension as having a perspective) but not from any distance and time dilation and length contraction decreases as you move away.

There's no real distinction between the singularity and the event horizon. The event horizon rushes outwards at the speed of light until it reaches it's maximum size but its gravitational influence moves out at the same rate so the it's at it's full size when it's observed, that's the first half of the sphere. From then on it's rushing inwards at a speed approaching the speed of light as the observer's distance decreases, that's the other half of the sphere. You can never catch the event horizon because you can never accelerate past the speed of light relative to it, it's just how a singularity appears from a distance. That's what the Schwarzchild and Rindler coordinate systems both show, one from the perspective of a distant observer and the other from the perspective of an in-falling observer. Any coordinate system that shows an object reaching the event horizon is in direct contradiction of these two legit coordinate systems because a change of perspective can't possibly change whether or not an event can occur and those coordinate systems show that an event horizon can never be reached because the proper time and acceleration required is infinite.

The Rindler horizon applies just as much to an object that's being accelerated by gravity as it always does, it doesn't matter what's doing the accelerating. Falling is not force free, acceleration is acceleration, it's a curved path in four dimensions. The event horizon and Rindler horizon would actually cross over if an object crossed an event horizon. The Rindler horizon is the point behind an accelerating observer where a signal moving at the speed of light could never catch them if they continue to accelerate at the same rate so that would make no sense.

Edited by A-wal, 30 March 2018 - 10:42 AM.

### #29 A-wal

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Posted 24 March 2018 - 06:11 AM

But the simplest way to show that objects can't cross an event horizon is that gravity is time reversible but if an object crosses an event horizon and you reverse the arrow of time then that object escapes from inside the horizon which is impossible. A time reversed black hole is still a black hole (and not a theoretical white hole) because gravity is still an attractive force if the clock ticks backwards but an object crossing an event horizon clearly breaks this symmetry.