Cosmological Redshift and Expansion

[Mohdje]

The ultimate cause is always that the inner product of the light's four momentum with the four velocity of the emitter is different from that with the four velocity of the receiver. In curved spacetime this is usually all the cause that there is - there is no non-arbitrary way to divide the frequency change into different "causes".

However, in some spacetimes with symmetries it is possible to divide this effect into components. For example, in Schwarzschild spacetime it is possible to identify hovering observers, and then to divide the frequency change into a part due to the altitude difference ("gravitational redshift") and a part due to velocity relative to the hovering observers ("kinematic redshift"). And in the FLRW spacetimes used in cosmology you can pick out comoving observers who see the CMB as uniform, then separate the frequency shift between any two observers into a shift due to their motion relative to their nearby comoving observers (their "peculiar velocity") and the frequency shift between those comoving observers (the cosmological recession velocity or expansion of the universe, depending on how you want to see it).

I don't know of any other relevant breakdown of the frequency shift.

And I don't know either. All I meant was that Doppler shift and cosmological redshift lead to the same results, but they have different mechanisms. The first works on the motion between the observer and the observed, while the second works on the wavelength of light in spacetime. They are both different because they complement each other. If we say that the shift is the same, I agree with you here because it has the same results, which is the effect of objects receding. But I also disagree with you because the mechanisms are different, and here we are talking about known models, not new ones.

 

[Ibix]

All I meant was that Doppler shift and cosmological redshift lead to the same results, but they have different mechanisms.

But they don't, really. That's my point. Both are due to the different inner products between four vectors, and you can only divide the cause of that difference by imposing a definition of "at relative rest" that is a personal choice.

 

[Mohdje]

But they don't, really. That's my point. Both are due to the different inner products between four vectors, and you can only divide the cause of that difference by imposing a definition of "at relative rest" that is a personal choice.

If it's a personal definition, do you have any proof of it?

 

[Ibix]

If it's a personal definition, do you have any proof of it?

Proof of what?

 

[Mohdje]

Proof of what?

Didn't you say it was a personal definition? If so, you must have proof of its validity.

 

[Ibix]

Didn't you say it was a personal definition? If so, you must have proof of its validity.

The personal choice I was referring to is the choice of what "not moving relative to each other" means. That is a part of a choice of coordinate system, which is not a thing that can be proved, any more than you can prove that a metre is the correct unit of distance. It also has no effect on measurements or predictions of measurements - in this context it's simply a choice of how much of a given object's redshift to ascribe to motion and how much to the passage of the light through spacetime.

If you make a decision to use co-moving coordinates (which everyone does in a cosmological context) then that fixes the split of the redshift. But you could choose a different coordinate system and you'd get a different split. It's no more mysterious than you and I facing each other across a table. If it's a long table and we're near one end, I would say the bulk of the table is on the right while you'd say it's on the left. Neither of us is wrong, and neither of us can prove our choice right. We're just using different coordinates.

 

[Mohdje]

The personal choice I was referring to is the choice of what "not moving relative to each other" means. That is a part of a choice of coordinate system, which is not a thing that can be proved, any more than you can prove that a metre is the correct unit of distance. It also has no effect on measurements or predictions of measurements - in this context it's simply a choice of how much of a given object's redshift to ascribe to motion and how much to the passage of the light through spacetime.

If you make a decision to use co-moving coordinates (which everyone does in a cosmological context) then that fixes the split of the redshift. But you could choose a different coordinate system and you'd get a different split. It's no more mysterious than you and I facing each other across a table. If it's a long table and we're near one end, I would say the bulk of the table is on the right while you'd say it's on the left. Neither of us is wrong, and neither of us can prove our choice right. We're just using different coordinates.

Your point is valid, and I agree with you, but you're explaining a completely different idea. Scientists always rely on Earth as an observer, but you're explaining the idea of observer independence, meaning every celestial body can be considered an observer. This is difficult to implement with current models. Regarding the relative differences in orientations, as you mentioned, there's the redshift and the blueshift, and you're talking about something that's very difficult to confirm. So I agree with you here, but that's not the only reason for the shift in the end.

 

[Ibix]

you're explaining the idea of observer independence

No I'm not. I'm explaining that comoving sources only having cosmological redshift and no kinematic frequency shift is a matter of definition. It follows from the choice of FLRW coordinates, which are just that: a choice. You can make other choices, and then you split the observed redshift a different way.

every celestial body can be considered an observer. This is difficult to implement with current models

It really isn't. The basic model is that the universe is the same everywhere so switching location is trivial.

Regarding the relative differences in orientations, as you mentioned, there's the redshift and the blueshift, and you're talking about something that's very difficult to confirm.

I don't think you understood my point at all. GR is quite clear that coordinate choices are choices with no physical consequences (obviously), and that if you choose to explain the redshift of some distant galaxy in terms of cosmological redshift and kinematic redshift then you made a coordinate choice underlying that. You could have made another. It would make no difference to the actual measurements; it is merely a matter of definition.

Circling back to your original interjection, my point is that you have your explanation backwards. You are taking a coordinate-independant description of redshift in terms of the inner products of four vectors and parallel transport, adding your choice of coordinate system, dividing the effect according to your choice, and calling your choice of division "the ultimate cause". An ultimate cause that depends on your personal choices isn't very likely. You do have a perfectly valid description of the physics, but it's one among many, all of which follow from the coordinate free approach.

 

[Mohdje]

No I'm not. I'm explaining that comoving sources only having cosmological redshift and no kinematic frequency shift is a matter of definition. It follows from the choice of FLRW coordinates, which are just that: a choice. You can make other choices, and then you split the observed redshift a different way.

It really isn't. The basic model is that the universe is the same everywhere so switching location is trivial.

I don't think you understood my point at all. GR is quite clear that coordinate choices are choices with no physical consequences (obviously), and that if you choose to explain the redshift of some distant galaxy in terms of cosmological redshift and kinematic redshift then you made a coordinate choice underlying that. You could have made another. It would make no difference to the actual measurements; it is merely a matter of definition.

Circling back to your original interjection, my point is that you have your explanation backwards. You are taking a coordinate-independant description of redshift in terms of the inner products of four vectors and parallel transport, adding your choice of coordinate system, dividing the effect according to your choice, and calling your choice of division "the ultimate cause". An ultimate cause that depends on your personal choices isn't very likely. You do have a perfectly valid description of the physics, but it's one among many, all of which follow from the coordinate free approach.

My question is very simple: are you sure the universe is symmetrical to even pose this question?
I agree with everything you said except for one point: that the universe is symmetrical.

 

[Ibix]

My question is very simple: are you sure the universe is symmetrical to even pose this question?

Whether the universe has any symmetry at all is irrelevant to the description of frequency shift in terms of four vectors. It's highly relevant to the decomposition into cosmological redshift and kinematic redshift (or any other coordinate-dependant description) like the one you seem to prefer - so it is you that needs to answer this question.

The universe is observed to be isotropic around our location on the large scale. Galaxies appear to obey Hubble's Law. Together that implies an FLRW universe. Am I certain? Nothing in science is certain. However, the bar for an alternative explanation is extremely high - general relativity is well tested in regimes we can directly and indirectly test, and less direct consequences of FLRW models (I'm thinking of Big Bang nucleosynthesis here) are in line with observation. So I've no particular reason for doubt beyond a scientist's required skepticism.

But, as I say, it's your explanation that requires symmetries, not mine.

 

[Mohdje]

لا، لستُ كذلك. أنا أوضح أن المصادر المتحركة التي لها انزياح أحمر كوني فقط، دون أي انزياح تردد حركي، هي مسألة تعريف. هذا ناتج عن اختيار إحداثيات FLRW، وهي مجرد اختيار. يمكنك اختيار إحداثيات أخرى، وعندها ستقسم الانزياح الأحمر المرصود بطريقة مختلفة.

ليس الأمر كذلك حقاً. النموذج الأساسي هو أن الكون متماثل في كل مكان، لذا فإن تغيير الموقع أمر بسيط.

لا أعتقد أنك فهمت قصدي على الإطلاق. تنص النسبية العامة بوضوح على أن اختيار الإحداثيات هو اختيار لا يترتب عليه أي تبعات فيزيائية (بالطبع)، وأنه إذا اخترت تفسير الانزياح الأحمر لمجرة بعيدة بدلالة الانزياح الأحمر الكوني والانزياح الأحمر الحركي، فقد اتخذتَ اختيارًا للإحداثيات ضمنيًا. كان بإمكانك اختيار إحداثيات أخرى، ولن يُحدث ذلك أي فرق في القياسات الفعلية؛ إنها مجرد مسألة تعريف.

بالعودة إلى مداخلتك الأصلية، فإنّ تفسيرك معكوس. أنت تستخدم وصفًا للانزياح الأحمر لا يعتمد على الإحداثيات، وذلك بدلالة الضرب الداخلي لأربعة متجهات والنقل المتوازي، ثم تضيف نظام الإحداثيات الذي اخترته، وتقسم التأثير وفقًا لاختيارك، وتسمي هذا التقسيم "السبب النهائي". من غير المرجح أن يكون السبب النهائي مرتبطًا باختياراتك الشخصية. صحيح أن لديك وصفًا صحيحًا للفيزياء، لكنه واحد من بين العديد من الأوصاف، وكلها تنبثق من منهج لا يعتمد على الإحداثيات.

سؤالي بسيط للغاية: هل أنت متأكد من أن الكون متناظر حتى تتمكن من طرح هذا السؤال؟

إن وجود أي تناظر في الكون من عدمه لا يؤثر على وصف انزياح التردد بدلالة أربعة متجهات. ولكنه ذو أهمية بالغة لتحليل الانزياح الأحمر إلى الانزياح الأحمر الكوني والانزياح الأحمر الحركي (أو أي وصف آخر يعتمد على الإحداثيات) كما يبدو أنك تفضله - لذا فأنت من يجب أن يجيب على هذا السؤال.

يُلاحَظ أن الكون متجانس الخواص حول موقعنا على نطاق واسع. ويبدو أن المجرات تخضع لقانون هابل. وهذا يُشير مجتمعًا إلى كون فريدمان-لايمر-روبرتسون-ووكر. هل أنا متأكد؟ لا شيء في العلم يقيني. مع ذلك، فإن معيار وجود تفسير بديل صعب للغاية - فالنسبية العامة مُختَبَرة جيدًا في نطاقات يُمكننا اختبارها بشكل مباشر وغير مباشر، والنتائج الأقل مباشرة لنماذج فريدمان-لايمر-روبرتسون-ووكر (أقصد هنا التخليق النووي للانفجار العظيم) تتوافق مع الملاحظات. لذا، ليس لدي سبب مُحدد للشك يتجاوز الشك العلمي المُتطلّب.

لكن، كما قلت، تفسيرك هو الذي يتطلب التناظرات، وليس تفسيري.

Whether the universe has any symmetry at all is irrelevant to the description of frequency shift in terms of four vectors. It's highly relevant to the decomposition into cosmological redshift and kinematic redshift (or any other coordinate-dependant description) like the one you seem to prefer - so it is you that needs to answer this question.

The universe is observed to be isotropic around our location on the large scale. Galaxies appear to obey Hubble's Law. Together that implies an FLRW universe. Am I certain? Nothing in science is certain. However, the bar for an alternative explanation is extremely high - general relativity is well tested in regimes we can directly and indirectly test, and less direct consequences of FLRW models (I'm thinking of Big Bang nucleosynthesis here) are in line with observation. So I've no particular reason for doubt beyond a scientist's required skepticism.

But, as I say, it's your explanation that requires symmetries, not mine.

Well, I see many contradictions in your statement. First, you say that we live in a FLRRW space, which is the space that most strongly dictates homogeneity, congruence, and symmetry. Second, I didn't assume anything; I didn't say that I need symmetry or not. Third, you say that multiplying by four is the most logical mathematical solution, but this mathematical description doesn't explain the precise physical mechanism and the curves that the photon goes through during its journey. Therefore, you are speaking mathematically, not physically.

 

[Ibix]

First, you say that we live in a FLRRW space, which is the space that most strongly dictates homogeneity, congruence, and symmetry.

I believe observation is consistent with this, yes. But it is your choice of decomposition of redshift that is reliant on it. My description works in any spacetime.

Second, I didn't assume anything; I didn't say that I need symmetry or not.

You might think that, but by decomposing redshift into a cosmological component due to expanding space and a kinematic component due to peculiar velocity you did assume it, whether you meant to or not. If you didn't want to assume that you would need to provide details of the spacetime and coordinate system you are using.

hird, you say that multiplying by four is the most logical mathematical solution,

I did not say that anywhere. If you wish to assert that I did, please provide an exact quote. Edit: I see renormalize's post above has proposed a reasonable explanation for this mistake.

this mathematical description doesn't explain the precise physical mechanism and the curves that the photon goes through during its journey.

All physical theories are mathematical at their base.

Also, note that light travels on geodesics, which are the curved spacetime generalisation of straight lines. If you are thinking of light following curved paths (such as in the usual description of gravitational lensing) you are once again making a choice of coordinate system and seeing the results of your personal choice as the fundamental explanation.

 

[Mohdje]

I believe observation is consistent with this, yes. But it is your choice of decomposition of redshift that is reliant on it. My description works in any spacetime.

You might think that, but by decomposing redshift into a cosmological component due to expanding space and a kinematic component due to peculiar velocity you did assume it, whether you meant to or not. If you didn't want to assume that you would need to provide details of the spacetime and coordinate system you are using.

I did not say that anywhere. If you wish to assert that I did, please provide an exact quote. Edit: I see renormalize's post above has proposed a reasonable explanation for this mistake.

All physical theories are mathematical at their base.

Also, note that light travels on geodesics, which are the curved spacetime generalisation of straight lines. If you are thinking of light following curved paths (such as in the usual description of gravitational lensing) you are once again making a choice of coordinate system and seeing the results of your personal choice as the fundamental explanation.

You say that all theories are mathematical in essence, but this is a grave mistake. Mathematics is the most suitable tool for understanding physics and physical phenomena. Mathematics is meaningless without physics . If you were to create an equation that calculates different numbers simply by changing a variable, you would say, "This is physics." But in reality, we observe phenomena, explain them, and the final step is mathematics. Mathematics is the last step and depends on explaining the mechanisms. Even the displacement equation you defend is meaningless if it is not linked to a precise physical description that corresponds to the observed phenomena.

 

[berkeman]

Mathematics is meaningless without mathematics.

Is this a typo?

 

[Mohdje]

Is this a typo?

Yes, indeed
What I mean is that mathematics is meaningless without physics.
I must clarify an important point: I am not fluent in English and I use a translator, and this translator included in the keyboard sometimes makes mistakes.

 

[PeterDonis]

in a free fall frame it is primarily Doppler.

There is no local inertial frame that covers both observers.

 

[PeterDonis]

In the case of spectral shifts in GR, all the essential features of Doppler remain

I disagree, because I think one "essential feature of Doppler" is well-defined relative motion between emitter and receiver that has some well-defined relationship to the magnitude of the Doppler effect, and that's not present in all of the curved spacetime cases, and in cases where it is, it doesn't match what you're claiming.

In the gravitational redshift case, there is a well-defined notion of relative motion, and according to that notion, the two observers have zero relative motion, so there should be zero Doppler between them. But there is nonzero redshift, so whatever is accounting for the redshift, it can't be Doppler.

In the FLRW case, I would argue that there is no well-defined notion of relative motion between emitter and receiver to begin with; but even if you can find one, it doesn't match up with the cosmological redshift. As I've already pointed out, the cosmological redshift tells you by what factor the scale factor has increased. There is no well-defined relationship between that and any notion of relative motion between emitter and receiver.

 

[PeterDonis]

the frequency shift between those comoving observers (the cosmological recession velocity or expansion of the universe, depending on how you want to see it).

As I've pointed out, the frequency shift between comoving observers tells you by what factor the scale factor has increased, which bears no well-defined relationship to "recession velocity".

 

[PeterDonis]

this mathematical description doesn't explain the precise physical mechanism and the curves that the photon goes through during its journey

The "mechanism" is that the light travels on null geodesics of the (curved) spacetime geometry. That's all there is to it, according to GR. What more do you want?

 

[PeterDonis]

Saying that light travels on a null geodesic of curved spacetime is a geometric description of the path, not a physical mechanism.

This is your personal opinion, not physics. GR, as a physics theory, gives you what I said. No more.

 

[PAllen]

I disagree, because I think one "essential feature of Doppler" is well-defined relative motion between emitter and receiver that has some well-defined relationship to the magnitude of the Doppler effect, and that's not present in all of the curved spacetime cases, and in cases where it is, it doesn't match what you're claiming.

Frequently Doppler is used to define mutual rest, by absence of shift. Of course this is just one definition, but it is ONE. It generalizes uniquely and invariantly to any GR situation. Using this definition, then all aspect of SR Doppler carry over quantitatively to GR. You may say that it is victory by definition, but that’s the point - it is a definition that is physically observable, and general to all cases in GR.

In the gravitational redshift case, there is a well-defined notion of relative motion, and according to that notion, the two observers have zero relative motion, so there should be zero Doppler between them. But there is nonzero redshift, so whatever is accounting for the redshift, it can't be Doppler.

In the FLRW case, I would argue that there is no well-defined notion of relative motion between emitter and receiver to begin with; but even if you can find one, it doesn't match up with the cosmological redshift. As I've already pointed out, the cosmological redshift tells you by what factor the scale factor has increased. There is no well-defined relationship between that and any notion of relative motion between em

 

[PeterDonis]

It generalizes uniquely and invariantly to any GR situation.

Not in the gravitational redshift case, since the observers are at mutual rest in that case--at least by the only definition of "mutual rest" that I have seen applied to this scenario (constant round-trip light travel time), and have nonzero shift. That was my point.

Using this definition, then all aspect of SR Doppler carry over quantitatively to GR.

Can you give an actual reference (textbook or peer-reviewed paper) that uses (and justifies, in the light of the observation I made above) this definition of "mutual rest" (zero observed frequency shift of light) for observers hovering in the gravitational field of a spherically symmetric body?