Understand Special Relativity and Time paradox

[ghwellsjr]

Correct--I never said it was.

But you are saying it is enough if you also assume speed of light to be the same, as measured by any inertial observer?

I was very careful to say in post #7 and every other time since then when commenting on this topic that no one is measuring the speed of light. All the observer can do is measure that the flashes of light coming from two different co-moving sources travel together at the same speed but he cannot tell what that speed is.

I still disagree with this,

Are you sure you disagree with what I actually said?

...for the same reason:

Sure, you can go down a line of reasoning from this which does correctly explain the twin paradox, but such a line of reasoning is not obvious, only plausible.

Again, for right now, I'm not talking about the Twin Paradox. Do you still disagree? And if so, you need something more than that the line of reasoning is not obvious. And if you understand the argument, it is not just plausible, it is incontrovertible proof.

Try not to associate this with the Twin Paradox or any explanation of the Twin Paradox. This is something entirely different involving three inertial observers. Do you understand the situation I have described? Do you agree with everything I said? Are there any questions or doubts?

Yeah, it all seems fine. You were saying the speed of light is independent of the speed of the source.

In the limited scenario which I borrowed from Bondi, I'm assuming the Principle of Relativity and I'm adding the observable assumption that the speed of light is independent of the speed of the source and proving that the outbound Doppler is the inverse of the inbound Doppler when the speeds are the same. That's what we are focusing on right now. Do you have any problem with that conclusion? Even if it is not obvious, do you see it as incontrovertible proof?

 

[ghwellsjr]

I have looked at the link you provided and I don't see that there is any confusion about the word "reciprocal" as there it is written explicitly as 3/2 vs 2/3.

So let me say my objection differently. Find in the link you provided page 77/78. There is a sentence:
"Accordingly, by Brian's watch the flashes will not arrive every 6 minutes, but at longer intervals, simply because each flash has greater distance to cover than the preceding flash."
We don't know how Brian's watch is working. That's the very thing we are trying to find out. So let's suppose that flashes will arrive at shorter intervals and next sentence will read:
"For a suitable speed, which we need not work out now, we may suppose that the flashes are received every 4 minutes by Brian's watch."
instead of 9 minutes. Do we run into any contradictions further along the line?

We don't have to go further along the line--you just presented a contradiction right there. That suitable speed which would produce flashes at 4 minute intervals at Brian's watch would have to be negative which would only work if he started out some distance from Alfred but since he starts out colocated you have presented a contradiction.

You can't argue that we don't know how Brian's watch is working. We have to assume that all watches are working identically in order for them to be observing symmetrical Doppler shifts and you already agreed in post #316 that they will see the same Doppler shift:

I'm not asking you about the twin situation because we don't have two inertial observers in that situation. I'm asking you for any two inertial observers with relative motion. Do you doubt that they will see the same Doppler shift in each other, even if the experiment is repeated under different states of inertial motion for both of them? And if they ever saw a different Doppler shift, do you doubt that that would violate the Principle of Relativity?

Of course they will see the same Doppler shift.

 

[zonde]

We don't have to go further along the line--you just presented a contradiction right there. That suitable speed which would produce flashes at 4 minute intervals at Brian's watch would have to be negative which would only work if he started out some distance from Alfred but since he starts out colocated you have presented a contradiction.

You can't argue that we don't know how Brian's watch is working. We have to assume that all watches are working identically in order for them to be observing symmetrical Doppler shifts and you already agreed in post #316 that they will see the same Doppler shift:

I have identified my problem with Bondi argument. He implicitly relies on Doppler shift. And if we pretend that we don't know about SR then it's classical Doppler shift not relativistic. But classical Doppler does not respect PoR.

And you are arguing exactly from the same position. You are using some Doppler-like phenomena even so you have not demonstrated how it is consistent with PoR.
And that is the very thing that SR does, like it or not.

 

[zonde]

The Principle of Relativity predates SR and is part of the classical context.

It is no argument.
In classical context PoR might have been slightly different PoR than the one you mean. In particular it was not applied to wave phenomena.
You see, the words stay the same but their meaning changes. And as a result your argument fails.

I was only using his proof that the Doppler ratios are inverses for coming and going at the same speed. And then I only expressed the Doppler that one twin sees. That is sufficient to prove which twin is older when they reunite. But the limited assumptions that I made are warranted in a classical framework.

SR works because it accurately reflects the Doppler effects--not the other way around. The horse is the Doppler effects, the cart is SR. Don't get the cart before the horse. The Doppler effects occur no matter what theory we invent to explain them.

You are using the same name for classical Doppler and relativistic Doppler. If you would identify in your argument these two equally valid effects by different names it would be easy to see that your argument is faulty.

 

[ghwellsjr]

I have identified my problem with Bondi argument. He implicitly relies on Doppler shift. And if we pretend that we don't know about SR then it's classical Doppler shift not relativistic. But classical Doppler does not respect PoR.

And you are arguing exactly from the same position. You are using some Doppler-like phenomena even so you have not demonstrated how it is consistent with PoR.
And that is the very thing that SR does, like it or not.

It is no argument.
In classical context PoR might have been slightly different PoR than the one you mean. In particular it was not applied to wave phenomena.
You see, the words stay the same but their meaning changes. And as a result your argument fails.


You are using the same name for classical Doppler and relativistic Doppler. If you would identify in your argument these two equally valid effects by different names it would be easy to see that your argument is faulty.

Like virtually all other classical principles and laws, the formulation for the Principle of Relativity had to change as a result of new experiments performed on wave phenomena, for example, the Michelson Morley Experiment. The words and meanings of all these principles and laws remained the same, they just required more complicated formulas to correctly express them. The classical formulation for the Principle of Relativity is the Galilean Transformation and it works well at low speeds. But at high speeds the correct formulation is the Lorentzian Transformation which works at any speed (less than the speed of light, of course).

The classical Doppler formulation is no exception. It had a simplified formula, which is still used today, just like F=ma is still used today, but we realize it is only a very good approximation and useful because the more complicated formula won't make any difference in our computation, as long as the speeds are small compared to the speed of light. However, there is a more complicated formulation that works at all speeds which you can read about here.

But I don't want to get sidetracked on this issue as it has no relevance to Bondi's argument concerning the inverse relationship of the Doppler shifts for coming and going at the same speed.

Tell me something zonde, do you understand the argument, whether or not you agree with it?

 

[PeterDonis]

You are using the same name for classical Doppler and relativistic Doppler.

There is no "classical Doppler". What we call the "relativistic" formula for the Doppler effect does not actually require SR. It only requires Maxwell's Equations. Those equations are Lorentz invariant, so of course the Doppler formula derived from them is consistent with SR. But you don't need SR to derive it.

 

[PAllen]

There is no "classical Doppler". What we call the "relativistic" formula for the Doppler effect does not actually require SR. It only requires Maxwell's Equations. Those equations are Lorentz invariant, so of course the Doppler formula derived from them is consistent with SR. But you don't need SR to derive it.

I think there is a distinction worth making here. The principle of relativity as used to derive SR includes different phenomena than the same principle pre-SR. The SR principle includes more phenomena. Note that Doppler for sound in air does not follow the principle of relativity, and this is not a violation because air is material, and you can obviously detect your state of motion relative to some matter. In the same sense, circa 1850, a common belief was that POR did not apply to either light Doppler or speed of light, for the same reason. To the extent one believed aether was an exotic form of matter, this did not imply a violation of galilean POR.

 

[ghwellsjr]

I think there is a distinction worth making here. The principle of relativity as used to derive SR includes different phenomena than the same principle pre-SR.

Yes, it's the same principle. Just because Einstein applied it to all phenomena whereas other people didn't, doesn't change the principle. And by itself, there is no Special Relativity. SR requires another principle which includes the propagation of light which I was purposely excluding from my discussion of how to prove that the traveling twin ends up younger.

The SR principle includes more phenomena.

No, you just said it was the same principle. There's only one Principle of Relativity.

Note that Doppler for sound in air does not follow the principle of relativity, and this is not a violation because air is material, and you can obviously detect your state of motion relative to some matter.

That's like saying the addition of velocity doesn't follow the Principle of Relativity. Just because some people choose not to apply it to some particular phenomenon doesn't change the principle. In fact, the reason they don't apply it to particular phenomenon is because they don't believe that phenomenon adheres to the principle that never changes. But more importantly, Doppler for sound in air does follow the Principle of Relativity if you use the correct formulation as the link in my previous post shows. Same thing with the addition of velocity. You have to apply the correct formulation.

In the same sense, circa 1850, a common belief was that POR did not apply to either light Doppler or speed of light, for the same reason. To the extent one believed aether was an exotic form of matter, this did not imply a violation of galilean POR.

There is only one Principle of Relativity. It never changes. Just because some people in the past did not believe it applied to certain phenomenon, doesn't change the principle.

What you are calling galilean PoR just means his formulation of the transformation was incorrect, or more precisely, it only applied at low speeds which means it excluded light.

The issue that zonde is concerned about is whether the Principle of Relativity plus the principle that light from two sources with relative motion propagates at the same speed is enough to prove that the traveling twin will come back younger. Can I get some help on that score instead of this side track?

 

[Alain2.7183]

But if the second reversal immediately follows the first reversal, shouldn't the net effect be that the home twin ends up with the same age as before the first reversal?

And if the net effect of the two back-to-back reversals is that the home twin's age is the same after the second reversal as it was before the first reversal, then that means that the decrease in the home twin's age during the second reversal must be equal to the increase in the home twin's age during the first reversal, because they have to sum to zero. So that seems to imply that either both of the two results are valid, or else they are both invalid. Is my reasoning wrong somewhere here?

 

[ghwellsjr]

And if the net effect of the two back-to-back reversals is that the home twin's age is the same after the second reversal as it was before the first reversal, then that means that the decrease in the home twin's age during the second reversal must be equal to the increase in the home twin's age during the first reversal, because they have to sum to zero. So that seems to imply that either both of the two results are valid, or else they are both invalid. Is my reasoning wrong somewhere here?

If you stick with a single Inertial Reference Frame, then you never have to concern yourself with such brain bending issues. Why do you care about trying to figure out anything with a non-inertial accelerating frame?

Someone, please tell me. Why doesn't an analysis using an IRF satisfy?

 

[PAllen]

Yes, it's the same principle. Just because Einstein applied it to all phenomena whereas other people didn't, doesn't change the principle. And by itself, there is no Special Relativity. SR requires another principle which includes the propagation of light which I was purposely excluding from my discussion of how to prove that the traveling twin ends up younger.

I guess it is more useful to think strictly of one POR, but it's implications then depend on what other laws nature is assumed to follow. If you believe a wave travels in some material medium, then to apply POR, you treat the motion of the medium in laws that respect POR. The POR plus this wave model has different consequences than POR plus a wave model where either a transmission medium doesn't exist or is undetectable.

The issue that zonde is concerned about is whether the Principle of Relativity plus the principle that light from two sources with relative motion propagates at the same speed is enough to prove that the traveling twin will come back younger. Can I get some help on that score instead of this side track?

There is another assumption involved. You have to assume either that Doppler is symmetric between two observers, or that Doppler follows the POR directly, without need to include motion of a transmission medium. Especially if you take the view that POR applies to sound in air, you must have some additional assumption about how light is different from sound, because speed independent of emitter velocity is true for sound in air, yet Doppler is asymmetric for sound in air.

 

[phyti]

another look:

B moving at .8c relative to A, experiences a clock rate (via gamma) of .6 relative to the A clock.

Fig. 1 shows observer B with instant acceleration at B-time 0 and 24, and instant deceleration at B-time 12. B receives 4 A-ticks outbound (blue) and 36 ticks inbound. The doppler rate is therefore 4/12=1/3 out and 36/12=3 back, i.e. reciprocal as expected. The notion of A aging rapidly when B reverses direction is false. The simultaneity axis (gray) reverses from A 7.2 backward to A 32.8 forward, to FUTURE events.

Fig. 2 is from B's perspective, showing A approaching at .8c and tick 4 received at B 12. B has yet to receive ticks 5 thru 40. The extreme time and space excursions such as event A tick 4 ocurring 36 ticks before B departs, are a result of the simultaneity convention in SR. It must be remembered that the convention is a stipulation, not physics, and therefore the time and space coordinates of the remote events are bogus. The only meaningful measurement is the round trip time for light. Any division of that time into separate out and return paths is speculation if an absolute observer speed is unknown.

Fig. 3 shows the fig.2 scenario without the SR convention and using relative light speed (magenta).Fig. 3 maintains temporal order where fig.2 does not. Using my own stipulation, if b is greater than 0, I don't expect equal out and return paths. From a momentum comparison, with m the mass of the B system and M the mass of the rest of the universe, mv does not equal Mv. It's more logical and realistic that enough energy is available to accelerate a single observer system to .8c. (Why do physicists always accelerate the particles and not the lab?)

Fig. 4 shows B experiencing an equivalent G-field during his deceleration period, while perceiving A to follow a curved return path.
https://www.physicsforums.com/attachments/55394

 

[ghwellsjr]

I guess it is more useful to think strictly of one POR, but it's implications then depend on what other laws nature is assumed to follow. If you believe a wave travels in some material medium, then to apply POR, you treat the motion of the medium in laws that respect POR. The POR plus this wave model has different consequences than POR plus a wave model where either a transmission medium doesn't exist or is undetectable.


There is another assumption involved. You have to assume either that Doppler is symmetric between two observers, or that Doppler follows the POR directly, without need to include motion of a transmission medium. Especially if you take the view that POR applies to sound in air, you must have some additional assumption about how light is different from sound, because speed independent of emitter velocity is true for sound in air, yet Doppler is asymmetric for sound in air.

I'm assuming what Einstein assumed in his first postulate, the PoR, plus part of what he assumed in his second postulate, but not the part that says light propagates at c. Are you now saying that the additional assumption I need is the part of Einstein's second postulate that I left out or that Einstein also needs another assumption?

 

[PAllen]

I'm assuming what Einstein assumed in his first postulate, the PoR, plus part of what he assumed in his second postulate, but not the part that says light propagates at c. Are you now saying that the additional assumption I need is the part of Einstein's second postulate that I left out or that Einstein also needs another assumption?

I'm saying you need some additional assumption. Any of several are sufficient. You have to say something about how light follows the POR. You need not assume 2 way light speed speed follows the POR, but you do need something. You can simply assume Doppler directly follows the POR (without having to allow for Aether speed). If Aether is assumed to be material, it is not a violation of POR to be able to detect your speed in relation to it.

 

[Dale]

And if the net effect of the two back-to-back reversals is that the home twin's age is the same after the second reversal as it was before the first reversal, then that means that the decrease in the home twin's age during the second reversal must be equal to the increase in the home twin's age during the first reversal, because they have to sum to zero. So that seems to imply that either both of the two results are valid, or else they are both invalid. Is my reasoning wrong somewhere here?

Did you read my earlier post? I already responded directly to this question.

Please don't ask a question if you are going to just ignore the answers. Please read my previous explanation as well as the material I linked to.

 

[PAllen]

Fig. 1 shows observer B with instant acceleration at B-time 0 and 24, and instant deceleration at B-time 12. B receives 4 A-ticks outbound (blue) and 36 ticks inbound. The doppler rate is therefore 4/12=1/3 out and 36/12=3 back, i.e. reciprocal as expected. The notion of A aging rapidly when B reverses direction is false. The simultaneity axis (gray) reverses from A 7.2 backward to A 32.8 forward, to FUTURE events.

The time reversal under discussion in this thread is to the right of your B world line, where the simultenaity lines per this convention intersect. Also note that if you make a sideways W shaped path for the B twin, you can have the intersecting simultaneity lines occur to the left of the B world line, covering part of the A world line (you don't have the central peak of the W go all the way back to the A world line).

Most of us here are saying a few things about this:

- there is no anomaly using any inertial frame, and no need to use anything else.
- the Einstein simultaneity convention was defined for inertial frames (which cover all of spacetime). Einstein never used 'lines of simultaneity' in this way.
- if you want to describe a convention for simultaneity from a non-inertial world line, you can use this or many other conventions, but not all conventions cover all of spacetime. It is perfectly reasonable for a simultaneity convention not to cover all of spacetime.
- SR does not replace universal absolute simultaneity with observer dependent absolute simultaneity. It says there is no objective simultaneity at all, only conventions. Relativity of simultaneity means nothing more than If two observers in relative motion use the same convention, they will get different results for which events are simultaneous.

 

[Austin0]

Quote by Austin0

Well I have no doubt that both symmetry and reciprocity are actualities in the real world. But that is only because I think that SR accurately describes that world.
In SR both these properties of the Doppler effect are not assumptions but can be directly derived and demonstrated through the application of fundamental kinematics.
In a classical context they are purely ad hoc assumptions . Assumptions which in themselves directly predetermine the end results.
As far as I can see Bondi does not derive them from first principles, he simply introduces them as assumptions.

I think the value of the exercise is the show there are multiple sets of physical assumptions that can lead the the same prediction (differential aging, in this case). As to which is adhoc in the pre-relativity sense, this is subjective. Neither Bondi's assumptions nor Einstein's were expected in the 1800s. Aether theories did predict that light speed should be source independent, but they also predicted that Doppler would not be symmetrical, and that motion through the aether could also be detected by measurements of the two way speed of light. Either of these is measurable. Both get at the issue of the aether becoming undetectable. Either, combined with other assumptions, can lead to SR. Since Doppler is part of what is seen in the twin scenario (extra signals not needed - they just have to be able to see each others clocks), it is instructive work from this. The twins are not making measurements light speed unless this is added. The one that turns around will have some difficulties measuring two way light speed as well.

I assume you realize that Einsteins arrived at SR by making 3 main assumptions (undetectability of inertial motion; constancy of two way speed of light; light speed independent of emitter velocity). He also added a convention that put the theory in a particular [arguably, the simplest] form. He could have chosen a different convention, and gotten a theory with slightly different equations, that made the same predictions. So it really boils down to which sets of unexpected assumptions to make. My view is it is useful to understand that there are multiple choices.

Well I certainly agree on the subjectivity of ad hocness.
This case for example:
I would say that the first postulate was not at all ad hoc. It was founded on the observed reality of inertial frame equivalence regarding applied physics, mechanics etc. The only assumption part of it was the projection that it would continue to apply in the domain outside our limits of experimental verification.Achievable velocity range.

Likewise with the second postulate. The independence from source. This was a sound logical deduction (not ad hoc) founded on established wave theory and also observation, as it also applies to sound .

I agree that the constancy of the two way speed of light would be ad hoc if it was a foundational assumption, as it's validity is dependent on the condition of length contraction and time dilation. But I see it rather as a derivative theorem, arising from the gamma function and resulting kinematics (not to mention observation I.e. the M-M results). Not a pure assumption
Unless my memory leads me astray , Poincarre had previously proposed a similar synch convention based on the same principles.
In this light the actual assumptions (the two postulates) were not themselves ad hoc or inconsistent with classical physics and so were not unexpected in the sense you mean.

But the assumption of Doppler symmetry and reciprocity are clearly out of thin air and contradictory to classical physics.

I take your point that if presented as an exercise in the importance and effect of initial assumptions regarding the development of a theory, such a demonstration could be valuable and instructive. But that is not the perspective that Bondi or ghwellsjr are taking in their demonstrations.

They are proposing that symmetry and reciprocity are inherent properties of signal exchange and inertial motion and that differential aging (time dilation) can be expalined on that basis without need or reference to the gamma factor (time dilation)

But it appears that in fact those properties are a consequence of time dilation so the logical equivalence of their derivation is:
If it is true that A---( Doppler symmetry and reciprocity) are only possible on the condition of B ---(time dilation)

A only if B ... then (assuming ) Aand proving that A implies B is an empty tautology as far as I can see.

 

[PAllen]

Quote by Austin0

Well I certainly agree on the subjectivity of ad hocness.
This case for example:
I would say that the first postulate was not at all ad hoc. It was founded on the observed reality of inertial frame equivalence regarding applied physics, mechanics etc. The only assumption part of it was the projection that it would continue to apply in the domain outside our limits of experimental verification.Achievable velocity range.

Many physicists in the late 1800s believed the POR was valid at all velocities, but didn't apply to EM phenomenon because Aether was an exotic material medium. It is normally considered that the ability to detect motion through air is not a violation of the POR.

Likewise with the second postulate. The independence from source. This was a sound logical deduction (not ad hoc) founded on established wave theory and also observation, as it also applies to sound .

Agreed, as the wave theory of light culminating in Maxwell's equations were near universally accepted. However, Newton and Bradley (sans later data ) would have disagreed. Interestingly, Bradley's derivation of aberration relied on a Newtonian corpuscular model which did not have source independent velocity; and it remained a difficulty for wave models to account for aberration until SR (there were approaches involving introduction of Aether wind, or Aether dragging).

I agree that the constancy of the two way speed of light would be ad hoc if it was a foundational assumption, as it's validity is dependent on the condition of length contraction and time dilation. But I see it rather as a derivative theorem, arising from the gamma function and resulting kinematics (not to mention observation I.e. the M-M results). Not a pure assumption

Nonsense. It was the foundational assumption from which Einstein derived gamma and time dilation and length contraction. Which all goes to show how freely one can interchange consequences and assumptions.

But the assumption of Doppler symmetry and reciprocity are clearly out of thin air and contradictory to classical physics.

Can't argue about taste. Constant two way speed of light was unexpected. Exactly symmetric Doppler was unexpected. Both for exactly the same reason (naive Aether theory). Note that Bondi's contribution (which I wasn't aware of before gwellsjr's link) is that assuming Doppler phenomena directly follow the POR you get both symmetric Doppler and reciprocal Doppler for approach versus recession at the same speed.

I take your point that if presented as an exercise in the importance and effect of initial assumptions regarding the development of a theory, such a demonstration could be valuable and instructive. But that is not the perspective that Bondi or ghwellsjr are taking in their demonstrations.

They are proposing that symmetry and reciprocity are inherent properties of signal exchange and inertial motion and that differential aging (time dilation) can be expalined on that basis without need or reference to the gamma factor (time dilation)

Well they are right. Recall, gamma factor and time dilation are derived features in Einstein's 1905 paper. You can replace 2-way light speed follows POR with Doppler follows POR, and get differential aging. It is an assumption that Doppler directly follows POR, but I don't find it adhoc or unnatural.

But it appears that in fact those properties are a consequence of time dilation so the logical equivalence of their derivation is:
If it is true that A---( Doppler symmetry and reciprocity) are only possible on the condition of B ---(time dilation)

A only if B ... then proving that (assuming ) A implies B is an empty tautology as far as I can see.

I disagree. If you don't know about diffential aging, gamma factors, etc. You can assume Doppler follows POR and arrive at differential aging. By the way, time dilation is a coorinate dependent quantity, not a physical observable the way differential aging is.

 

[PeterDonis]

But the assumption of Doppler symmetry and reciprocity are clearly out of thin air and contradictory to classical physics.

This is not correct. Doppler symmetry and reciprocity are consequences of Maxwell's Equations, which were verified experimentally well before relativity was even considered.

 

[Austin0]

Quote by Austin0
...

You propose that in a classical context (pre SR) with a single postulate of constant finite signal propagation independent of the source or any medium, that time dilation and differential aging can be derived as well as symmetry and reciprocity of signal reception ratios. WOuld you say this was an accurate appraisal?

No.

I never proposed a single postulate of constant finite signal propagation... That is Einstein's second postulate. I said in post #7 that I was proposing only a portion of Einstein's second postulate, the part that says that the propagation of light is independent of the source but I was not identifying that speed as Einstein did and which is necessary to establish SR..

The constancy of propagation as I used it and in the 2nd P refers to the intrinsic property of the signal not referring to any specific quantification or measurement. Both you and Bondi implicitly apply this assumption when you attribute equal propagation between Alfred and Brian in both directions. If you will notice I also did not assign any specific value but only said it must be finite.
But this is all really inrrelevant to the question at hand.

This is probably a confusing issue. I would recommend that you look up the wikipedia article on the One-Way Speed of Light and look down to the section called "Experiments that can be done on the one-way speed of light". There you will see that it is possible to determine experimentally that light from two different sources with relative velocity propagate at the same speed but we cannot measure what that speed is. This is also assumed to be true both in a classical context (pre SR) where ether is affirmed and in a relativistic context (SR) where ether is denied. Bondi did not specifically state that he was adopting this assumption but it is obvious that he is..

There is absolutely zero confusion in my mind and all of this is well known and understood. But as it is also not germane to the issue. The only purpose I see in this digression is the unfortunately common one of implying that disagreement must stem from ignorance or misunderstanding.

Quote by Austin0

Well I have no doubt that both symmetry and reciprocity are actualities in the real world. But that is only because I think that SR accurately describes that world.
In SR both these properties of the Doppler effect are not assumptions but can be directly derived and demonstrated through the application of fundamental kinematics.
In a classical context they are purely ad hoc assumptions . Assumptions which in themselves directly predetermine the end results.
As far as I can see Bondi does not derive them from first principles, he simply introduces them as assumptions.

Yes, the Doppler effects of symmetry and reciprocity are actualities in the real world and SR accurately describes that world but SR is not what makes those effects real.

As long as we adopt the Principle of Relativity (apart from SR), then even in a classical context the correct conclusion can be drawn that the traveling twin's clock will accumulate less time than the inertial clock. The Principle of Relativity predates SR and is part of the classical context. Based purely on that principle plus the assumption that light from different sources propagates at the same speed but without identifying that speed (as explained previously) and even with a belief in an absolute ether, it can be proven that a non-inertial clock will accumulate less time than an inertial clock..

yes you continue making unqualified assertions that it can be "proven" without providing any additional support or explanation. As others have pointed out you are applying your own interpretation of the classical Principle of Relativity which in effect is indistinguishable from the SR version.

As far as symmetry and reciprocity are concerned; your assertion of their actuality is a mere assumption (which I happen to share) on your part.
This is not a fact of your direct observation nor of experimental observation as our technology is yet insufficient for definitive verification. SO your assumption , like mine , rests on your belief in the validity of a theory. Either SR or Bondi but
in either case a theoretical 'actuality"

Quote by Austin0

He assumes that the ratio observed by Alfred of signals received from Brian (traveling away towards Charles) is the reciprocal of the ratio observed by Charles of the Brian signals received (as Brian is approaching).

Likewise he assumes that the ratio observed by Alfred of Brian signals is symmetrical (equivalent) to the ratio observed by Brian of Alfred signals.
I submit both these assumptions are unwarranted in a classical framework.

Yes, Bondi does make more assumptions as he continues his discussion that includes Charles because he wants to eventually give a full explanation of the Twin Paradox which includes the Doppler that both twins see. But I didn't do that because that was not my goal. I was only using his proof that the Doppler ratios are inverses for coming and going at the same speed. And then I only expressed the Doppler that one twin sees. That is sufficient to prove which twin is older when they reunite. But the limited assumptions that I made are warranted in a classical framework..

here you again claim that Bondi proved that the Doppler ratios are inverse for coming and going.
What I saw was that from first principles he demonstrated that the ratio of signals received from Brian by David was the reciprocal of the ratio of signals received from Alfred by Brian.This is also consistent with classical kinematics.
He then simply assumes symmetry and from this then makes the ratio of signals received by Alfred from Brian equivalent to the ratio that was shown to be received by Brian from Alfred. Which is not consistent with classical physics.

Quote by Austin0

In SR both the symmetry and reciprocity of observed signal ratios is directly a consequence of time dilation.
Introduced through the gamma factor embedded in the Relativistic Doppler equation and the LT kinematics.

They are not inherent properties of signal exchange between inertial observers but can only occur with the necessary condition of time dilation taking effect.

it would seem then, that to adopt them as initial premises or assumptions is to implicitly introduce time dilation to derive time dilation. Also to invoke SR as these properties are only valid in that context.

SR works because it accurately reflects the Doppler effects--not the other way around. The horse is the Doppler effects, the cart is SR. Don't get the cart before the horse. The Doppler effects occur no matter what theory we invent to explain them..

This is an absurd interpretation of what I said. A straw horse. No one would propose that theory determined reality.
On the other foot:
Your claim to explain the asymmetry of aging by the asymmetry in the Doppler observations makes a direct connection between the two phenomena. This directly implies a causal connection and direction. Otherwise your initial claim is meaningless and invalid.

This unambiguously inverts reality. The Doppler effects, symmetry and reciprocity are the end of the line. They are consequences of , not causes of time dilation. Yes there is a correlation between the asymmetry of the observations and the asymmetry of the differential aging but this is a correlation without causation.
And is unsurprising because ultimately both the Doppler effects and the final aging are caused by the same thing: The time dilation factor intrinsically resulting from relative motion.. Do you disagree??
so actually the gamma factor does "explain" both the differential aging and the Doppler effects.

Even in an SR context , the Twins scenario, the effects directly resulting from relative motion (without the introduction of dilation) are neither symmetric nor reciprocal. Would you agree?

 

[PAllen]

This is not correct. Doppler symmetry and reciprocity are consequences of Maxwell's Equations, which were verified experimentally well before relativity was even considered.

If you assume Maxwell's equations are valid in any inertial frame, rather than that they are the simplest expression of laws of EM, true only in the Aether frame (similarly, sound is simplest to describe in the rest frame of air; yet this is not normally taken as a violation of POR).

Anyway, I strongly agree they are natural assumptions, but not the most common ones circa e.g. 1870.

 

[PAllen]

This unambiguously inverts reality. The Doppler effects, symmetry and reciprocity are the end of the line. They are consequences of , not causes of time dilation. Yes there is a correlation between the asymmetry of the observations and the asymmetry of the differential aging but this is a correlation without causation.
And is unsurprising because ultimately both the Doppler effects and the final aging are caused by the same thing: The time dilation factor intrinsically resulting from relative motion.. Do you disagree??
so actually the gamma factor does "explain" both the differential aging and the Doppler effects.

Even in an SR context , the Twins scenario, the effects directly resulting from relative motion (without the introduction of dilation) are neither symmetric nor reciprocal. Would you agree?

Time dilation and length contraction and Einstein simultaneity convention are part of the coordinate expression of a model to explain a range of measurable phenomena: symmetric and reciprocal Doppler, transverse Doppler, differential aging, invariant two way light speed. The phenomena exist even if we don't have a theory to explain them. Further, the phenomena, by themselves, have relationships. An important one is that symmetric and reciprocal Doppler (along with emitter speed independence of light transmission) implies differential aging ; it even quantifies as I will show in blog I am almost done with. Similarly, invariant two way light speed (along with a couple of undisputed assumptions) implies all the rest.

Time dilation and length contraction are the derived features of a model, that accommodates the truth of all these phenomena. These are derived from various possible sets of assumptions. It is the assumptions that should be taken to impy time dilation and length contractions given a convention for defining inertial coordinates, not vice versa.

 

[PeterDonis]

If you assume Maxwell's equations are valid in any inertial frame, rather than that they are the simplest expression of laws of EM, true only in the Aether frame

I realize a lot of people assumed this, but it isn't actually consistent with Maxwell's Equations. People in the late 1800's didn't fully understand what "Maxwell's Equations are Lorentz invariant" actually meant. They are only consistent if they are valid in any inertial frame. (More precisely, if you want to have any connection between Maxwell's Equations and mechanics at all, they have to be valid in any inertial frame; there is no way to have them only be valid in one chosen aether frame.)

 

[PAllen]

I realize a lot of people assumed this, but it isn't actually consistent with Maxwell's Equations. People in the late 1800's didn't fully understand what "Maxwell's Equations are Lorentz invariant" actually meant. They are only consistent if they are valid in any inertial frame. (More precisely, if you want to have any connection between Maxwell's Equations and mechanics at all, they have to be valid in any inertial frame; there is no way to have them only be valid in one chosen aether frame.)

Can you clarify what you mean? To me, it is logically possible (in some alternate universe) to posit that Maxwell's equations only hold in an aether rest frame (and would take some other form in other inertial frames). That, without having derived time dilation for a moving body, when an aether rest observer and a moving observer exchange light signals, Doppler will be asymmetric.

 

[PeterDonis]

To me, it is logically possible (in some alternate universe) to posit that Maxwell's equations only hold in an aether rest frame (and would take some other form in other inertial frames).

But this assumption would violate the classical PoR, because velocity appears in the Lorentz force law, which you have to use to combine Maxwell's Equations with mechanics. You would end up predicting a different motion for the same charged particle depending on which frame you did the computation in, so you could tell whether or not you were in the ether frame by measuring charged particle motion.

 

[PAllen]

But this assumption would violate the classical PoR, because velocity appears in the Lorentz force law, which you have to use to combine Maxwell's Equations with mechanics. You would end up predicting a different motion for the same charged particle depending on which frame you did the computation in, so you could tell whether or not you were in the ether frame by measuring charged particle motion.

In this universe, it would not be problem to detect motion relative to aether using EM phenomena, any more than it is a problem to detect motion relative to air. Put another way, Lorentz force law would take a different form in a frame moving relative to the aether.

 

[PeterDonis]

In this universe, it would not be problem to detect motion relative to aether using EM phenomena, any more than it is a problem to detect motion relative to air. Put another way, Lorentz force law would take a different form in a frame moving relative to the aether.

Hm. I'll have to think about this some more; I'm still not sure this can all fit together consistently, because there are also EM waves to be considered, and Maxwell's Equations do predict Lorentz invariance for those (just consider Einstein's thought experiment about trying to ride alongside a light beam).

 

[PeterDonis]

This unambiguously inverts reality. The Doppler effects, symmetry and reciprocity are the end of the line. They are consequences of , not causes of time dilation.

No, the statement you just made here is what inverts reality. The Doppler effect, including symmetry and reciprocity, is a direct observable. It is more fundamental than any theory we have about it. Time dilation is not a direct observable; it's a derived quantity that occurs in our theory.

both the Doppler effects and the final aging are caused by the same thing: The time dilation factor intrinsically resulting from relative motion.. Do you disagree??

Yes, because relative motion itself (which is a direct observable) is not the same as time dilation (which is not). I would agree that relative motion causes the Doppler effect and differential aging, but not that time dilation does.

 

[PAllen]

Hm. I'll have to think about this some more; I'm still not sure this can all fit together consistently, because there are also EM waves to be considered, and Maxwell's Equations do predict Lorentz invariance for those (just consider Einstein's thought experiment about trying to ride alongside a light beam).

But I think Einstein was implicitly assuming Maxwell's equations must hold in such frame, or nature should be familiar in such a frame. Phenomena involving sound, when traveling at the speed of sound, are radically different than in rest frame of air.

 

[Austin0]

Quote by Austin0

But the assumption of Doppler symmetry and reciprocity are clearly out of thin air and contradictory to classical physics

This is not correct. Doppler symmetry and reciprocity are consequences of Maxwell's Equations, which were verified experimentally well before relativity was even considered.

i understand that the gamma function is derived from Maxwell's equations. ANd have already stated that the symmetry and reciprocity of Doppler (like contraction and time dilation) are also derived within that structure with the gamma function as well as being fundamental properties of motion through spacetime. That is not the argument.
When you say verified experimentally what are you referring to?
.Were the Doppler properties derived directly from Maxwell or were they derived later with the inclusion of the gamma function?

There is no "classical Doppler". What we call the "relativistic" formula for the Doppler effect does not actually require SR. It only requires Maxwell's Equations. Those equations are Lorentz invariant, so of course the Doppler formula derived from them is consistent with SR. But you don't need SR to derive it.

What do you mean when you say"only requires Maxwell's Equations" Are you speaking literally and suggesting that the relativistic Doppler equation was directly derived from them?/
or are you talking about the Lorentz maths derived from them. The gamma function?
When you say "But you don't need SR to derive it" are saying you don't need the Lorentz math which is an integral part of SR?

 

[Austin0]

Quote by Austin0 View Post


This unambiguously inverts reality. The Doppler effects, symmetry and reciprocity are the end of the line. They are consequences of , not causes of time dilation. Yes there is a correlation between the asymmetry of the observations and the asymmetry of the differential aging but this is a correlation without causation.
And is unsurprising because ultimately both the Doppler effects and the final aging are caused by the same thing: The time dilation factor intrinsically resulting from relative motion.. Do you disagree??
so actually the gamma factor does "explain" both the differential aging and the Doppler effects.

Even in an SR context , the Twins scenario, the effects directly resulting from relative motion (without the introduction of dilation) are neither symmetric nor reciprocal. Would you agree?

Time dilation and length contraction and Einstein simultaneity convention are part of the coordinate expression of a model to explain a range of measurable phenomena: symmetric and reciprocal Doppler, transverse Doppler, differential aging, invariant two way light speed. The phenomena exist even if we don't have a theory to explain them. Further, the phenomena, by themselves, have relationships. An important one is that symmetric and reciprocal Doppler (along with emitter speed independence of light transmission) implies differential aging .

Well I not only agree with all of the above but have explicitly stated the same things in the course of this thread.
Eg.
YOU "Time dilation and length contraction and Einstein simultaneity convention are part of the coordinate expression of a model to explain a range of measurable phenomena: symmetric and reciprocal Doppler, differential aging,"
ME "so actually the gamma factor does "explain" both the differential aging and the Doppler effects."
Here I was explicitly referring to the time dilation aspect of the gamma factor. SO not only are we in agreement but you are supporting my point. Time dilation explains Doppler symmetry not the other way around.

"An important one is that symmetric and reciprocal Doppler (along with emitter speed independence of light transmission) implies differential aging" ----yes i have repeatedly stated that given these assumptions you get differential aging.
That is not the question. Which is:Do the Doppler effects explain dilation or does dilation explain the symmetric Doppler effects?Do those effects cause dilation or does dilation cause those effects??

Time dilation and length contraction are the derived features of a model, that accommodates the truth of all these phenomena. These are derived from various possible sets of assumptions. It is the assumptions that should be taken to imply time dilation and length contractions given a convention for defining inertial coordinates, not vice versa..

As far as I know the gamma function, time dilation and length contraction were derived by Lorentz from the Maxwell math without need of any assumptions at all. is this not the case??

As such they are mathematical descriptions of fundamental phenomena and so precede and determine derivative theorems and coordinate conventions.

So i can't really understand a perspective where they are determined by something else other than the intrinsic properties of spacetime?

 

[PAllen]

But the assumption of Doppler symmetry and reciprocity are clearly out of thin air and contradictory to classical physics

No, this is not true. If Bradley's derivation of aberration was correct, one would expect symmetry in Doppler. If no one thought waves needed an aether, then Maxwells equations + POR should have led quickly to the Lorentz transform. Thus, any 'unnaturalness' of symmetry and reciprocity came from the belief that some form of medium was needed for wave propagation.

i understand that the gamma function is derived from Maxwell's equations.

It can be. But Einstein first derived it without any reference to Maxwell's equations. Lorentz, and others also derived it without reference to Maxwell's equations.

ANd have already stated that the symmetry and reciprocity of Doppler (like contraction and time dilation) are also derived within that structure with the gamma function as well as being fundamental properties of motion through spacetime. That is not the argument.
When you say verified experimentally what are you referring to?
.Were the Doppler properties derived directly from Maxwell or were they derived later with the inclusion of the gamma function?

Doppler properties follow directly from Maxwell if you assume Maxwell's equations hold in any inertial frame. You do not need to first derive the Lorentz transform or gamma.

What do you mean when you say"only requires Maxwell's Equations" Are you speaking literally and suggesting that the relativistic Doppler equation was directly derived from them?/
or are you talking about the Lorentz maths derived from them. The gamma function?
When you say "But you don't need SR to derive it" are saying you don't need the Lorentz math which is an integral part of SR?

Historically, I believe derivation of Lorentz transform preceeded relativistic Doppler equation. But history is not causation. It is a mathematical fact that Maxwell's equations holding in any inertial frame leads directly to relativistic Doppler, without need to derive the Lorentz transform.

 

[PAllen]

As far as I know the gamma function, time dilation and length contraction were derived by Lorentz from the Maxwell math without need of any assumptions at all. is this not the case??

No, this is not true. Lorentz believed (initially) that Maxwell's equations held only in the 'aeither frame'. He (and others, before Einstein) derived the length contraction, time dilation, and the Lorentz trasnform from analysis of experiments. I believe the only person before Einstein to realize that Maxwell's equations were invariant under the Lorentz transform was Poincare.

As such they are mathematical descriptions of fundamental phenomena and so precede and determine derivative theorems and coordinate conventions.

So i can't really understand a perspective where they are determined by something else other than the intrinsic properties of spacetime?

Spacetime is a human invention to describe our experience. If you want to boggle your mind, any number of BSM theories suggest the effective dimensionality of space is emergent; and that it may also depend on the scale on which you examine physics; and that (per some approaches) a continuous manifold is emergent, not fundamental.

 

[PeterDonis]

But I think Einstein was implicitly assuming Maxwell's equations must hold in such frame

He was assuming that whatever would be observed in his thought experiment would have to be a solution of Maxwell's Equations, yes. The fact that those equations have no solutions corresponding to a static EM wave (varying only in space, not time) clued Einstein into the fact that Maxwell's Equations were Lorentz invariant, not Galilean invariant. That conclusion does not depend on any additional mechanical assumptions; but I agree that that conclusion by itself is not enough to show that mechanics must be Lorentz invariant.

 

[PAllen]

He was assuming that whatever would be observed in his thought experiment would have to be a solution of Maxwell's Equations, yes. The fact that those equations have no solutions corresponding to a static EM wave (varying only in space, not time) clued Einstein into the fact that Maxwell's Equations were Lorentz invariant, not Galilean invariant. That conclusion does not depend on any additional mechanical assumptions; but I agree that that conclusion by itself is not enough to show that mechanics must be Lorentz invariant.

I agree with all of that, but I think plenty of physicists at the time were assuming that an EM field in a frame moving rapidly relative to the aether need not look anything like a solution of Maxwell's equations (it would be a solution of some more complex equation). Further, this need not be viewed as a violation of POR if you hold that aether provides a material 'absolute frame', in which EM follows Maxwell.

 

[DrGreg]

No, this is not true. Lorentz believed (initially) that Maxwell's equations held only in the 'aeither frame'. He (and others, before Einstein) derived the length contraction, time dilation, and the Lorentz trasnform from analysis of experiments. I believe the only person before Einstein to realize that Maxwell's equations were invariant under the Lorentz transform was Poincare.

I could be wrong, but I thought Lorentz was motivated to come up with his final form of the Lorentz transformation specifically to find a transformation to leave Maxwell's equations invariant. Length contraction and time dilation (relative to a supposed aether) had already been found, in order to explain the Michaelson-Morley result, but the final step of a time offset (what Lorentz called "local time" and equivalent to Einstein's relativity of simultaneity) was needed to get invariant Maxwell's equations.

 

[Austin0]

would you agree that on an essential level physics is a study of causality?

Quote by Austin0

This unambiguously inverts reality. The Doppler effects, symmetry and reciprocity are the end of the line. They are consequences of , not causes of time dilation.

No, the statement you just made here is what inverts reality. The Doppler effect, including symmetry and reciprocity, is a direct observable. It is more fundamental than any theory we have about it. Time dilation is not a direct observable; it's a derived quantity that occurs in our theory..

You will note that I was talking about causality here. Are you suggesting that The Doppler effect, including symmetry and reciprocity should considered as cause rather than effect simply because they are directly observable and time dilation is not?

yes in a sense observables are more fundamental,frame invariant, but observations in themselves have little meaning.
That meaning is also derived from our theory , yes?


Quote by Austin0

both the Doppler effects and the final aging are caused by the same thing: The time dilation factor intrinsically resulting from relative motion.. Do you disagree??

Yes, because relative motion itself (which is a direct observable) is not the same as time dilation (which is not). I would agree that relative motion causes the Doppler effect and differential aging, but not that time dilation does..

Note i did not say or imply that relative motion was the same as time dilation.
I said that time dilation resulted from relative motion.

relative motion---->time dilation------>Doppler effect and differential aging

You seem to be implying that time dilation and differential aging are unrelated phenomena. That because we cannot observe or quantify time dilation that it is not the same thing.
DO you doubt that differential aging is simply the cumulative result of time dilation?

 

[PeterDonis]

would you agree that on an essential level physics is a study of causality?

Causality is certainly one thing physics can study. I don't know that I agree that causality is all there is to it on an essential level. Physics is the study of whatever reality turns out to be; if reality includes causality, then physics studies causality. But if reality turns out not to include causality in some cases (for example, in quantum gravity theories causality may turn out to be an emergent property, not fundamental, and not present in all cases), then physics will not just be the study of causality on an essential level.

Are you suggesting that The Doppler effect, including symmetry and reciprocity should considered as cause rather than effect simply because they are directly observable and time dilation is not?

I didn't say the Doppler effect was a cause; later on in your post you quoted me as saying it is an effect, caused by relative motion. But the Doppler effect is indeed a direct observable and an invariant; time dilation is a frame-dependent convention. See further comments below.

observations in themselves have little meaning.
That meaning is also a derived from our theory , yes?

An observed Doppler shift does not seem to me to be a very "theory-laden" observation. There are some observations in physics that require a lot of theory to interpret--results from particle physics experiments like the LHC, for example--but we're not talking about those kinds of observations here. We're talking about pretty simple and straightforward ones.

relative motion---->time dilation------>Doppler effect and differential aging

Yes, I understand that this is your interpretation of the causality involved. Mine is:

relative motion --> Doppler effect and differential aging

Time dilation does not appear because it is frame-dependent, so it is a convention, not a "real thing" that needs to have a cause.

DO you doubt that differential aging is simply the cumulative result of time dilation?

I don't "doubt" this in the sense of thinking it's a purported factual statement that might not be true. I think it's "not even wrong" in the sense that it attributes causality to a frame-dependent convention.

 

[PAllen]

I could be wrong, but I thought Lorentz was motivated to come up with his final form of the Lorentz transformation specifically to find a transformation to leave Maxwell's equations invariant. Length contraction and time dilation (relative to a supposed aether) had already been found, in order to explain the Michaelson-Morley result, but the final step of a time offset (what Lorentz called "local time" and equivalent to Einstein's relativity of simultaneity) was needed to get invariant Maxwell's equations.

After a bit of research, yes, it appears you are correct. So perhaps Einstein was the first to show their derivation without any reference to Maxwell's equations.

 

[zonde]

The classical Doppler formulation is no exception. It had a simplified formula, which is still used today, just like F=ma is still used today, but we realize it is only a very good approximation and useful because the more complicated formula won't make any difference in our computation, as long as the speeds are small compared to the speed of light. However, there is a more complicated formulation that works at all speeds which you can read about here.

And this more complicated formulation of Doppler is explained using SR.

Tell me something zonde, do you understand the argument, whether or not you agree with it?

Hmm, you will have to be more specific. There is Bondi argument and there is your argument and your interpretation about Bondi argument.

I guess I understand Bondi argument just fine as he does not seem to be claiming much. He just says without any argument:
"Note that the Principle of Relativity, by insisting on the equivalence of all inertial observers, makes it quite clear that the ratio must be the same whichever of a pair of inertial observers does the transmitting."

As I already said he provides no explanation how it can be considered consistent with classical Doppler.

And he makes quite clear distinction between classical Doppler and relativistic Doppler contrary to you:
"It is trough this rule [PoR] that our work on light differs so sharply from the work on sound where, it will be remembered, the speed of transmitter and receiver relative to the air had also to be taken into account."


On the other hand your claim is that one can predict that the traveling twin will be younger than stay at home twin just from PoR and SR second postulate by some shorter route than SR.
So I have to "forget" SR and try to understand your argument. And this is a bit complicated as you keep referring to things that I learned from SR as given.

 

[ghwellsjr]

The classical Doppler formulation is no exception. It had a simplified formula, which is still used today, just like F=ma is still used today, but we realize it is only a very good approximation and useful because the more complicated formula won't make any difference in our computation, as long as the speeds are small compared to the speed of light. However, there is a more complicated formulation that works at all speeds which you can read about here.

And this more complicated formulation of Doppler is explained using SR.

Yes, and when writing a book to explain relativity, Bondi started with the simplified formula.

Tell me something zonde, do you understand the argument, whether or not you agree with it?

Hmm, you will have to be more specific. There is Bondi argument and there is your argument and your interpretation about Bondi argument.

In between the above two quotes of mine is this qoute which you left out:

But I don't want to get sidetracked on this issue as it has no relevance to Bondi's argument concerning the inverse relationship of the Doppler shifts for coming and going at the same speed.

That clearly provides that answer to your question.

I guess I understand Bondi argument just fine as he does not seem to be claiming much. He just says without any argument:
"Note that the Principle of Relativity, by insisting on the equivalence of all inertial observers, makes it quite clear that the ratio must be the same whichever of a pair of inertial observers does the transmitting."

As I already said he provides no explanation how it can be considered consistent with classical Doppler.

And he makes quite clear distinction between classical Doppler and relativistic Doppler contrary to you:
"It is trough this rule [PoR] that our work on light differs so sharply from the work on sound where, it will be remembered, the speed of transmitter and receiver relative to the air had also to be taken into account."On the other hand your claim is that one can predict that the traveling twin will be younger than stay at home twin just from PoR and SR second postulate by some shorter route than SR.
So I have to "forget" SR and try to understand your argument. And this is a bit complicated as you keep referring to things that I learned from SR as given.

Are you saying that there are two kinds of Doppler, classical which applies to sound and relativistic which applies to light and since I'm saying to "forget" SR then I must, by default, be limited to the Doppler that applies to sound and not to light?

 

[Austin0]

Quote by Austin0

would you agree that on an essential level physics is a study of causality?

Causality is certainly one thing physics can study. I don't know that I agree that causality is all there is to it on an essential level. Physics is the study of whatever reality turns out to be; if reality includes causality, then physics studies causality. But if reality turns out not to include causality in some cases (for example, in quantum gravity theories causality may turn out to be an emergent property, not fundamental, and not present in all cases), then physics will not just be the study of causality on an essential level.

"on an essential level"... in this context the word "an" inherently implies other essential levels,yes?

Quote by Austin0

Are you suggesting that The Doppler effect, including symmetry and reciprocity should considered as cause rather than effect simply because they are directly observable and time dilation is not?

I didn't say the Doppler effect was a cause; later on in your post you quoted me as saying it is an effect, caused by relative motion. But the Doppler effect is indeed a direct observable and an invariant; time dilation is a frame-dependent convention. See further comments below.

Your reaction to my quote below

Quote by Austin0

This unambiguously inverts reality. The Doppler effects, symmetry and reciprocity are the end of the line. They are consequences of , not causes of time dilation.

was

No, the statement you just made here is what inverts reality.

if you say I am inverting reality ,this would only be true if the inverse of what I said was true, Yes?

The Doppler effects, symmetry and reciprocity ---->time dilation

instead of time dilation----->Doppler effects, symmetry and reciprocity which is what I said.


Quote by Austin0

observations in themselves have little meaning.
That meaning is also a derived from our theory , yes?

An observed Doppler shift does not seem to me to be a very "theory-laden" observation. There are some observations in physics that require a lot of theory to interpret--results from particle physics experiments like the LHC, for example--but we're not talking about those kinds of observations here. We're talking about pretty simple and straightforward ones.

What could be simpler than a temperature reading?
But what does that bare value tell us about what is being measured other than that you may not want to stick your fingers in it?
What does the word temperature or heat even mean without a theory? A molecular model, mechanics,etc, etc.

With Doppler the theoretical context in this case is SR .

According to which it appears that the observed values are the result of two distinct factors ---relative motion and the dilation factor.
Now the quantitative evaluation of the relative effect of these components is of course conventional and not to be understood as having any absolute significance quantitatively.
but you seem to want to throw out this understanding completely. Not only the implication that time dilation is a phenomenon which exists independent of convention but also the fundamental kinematics involved in this analysis and understanding.

You missed this one;
Quote by Austin0

Even in an SR context , the Twins scenario, the effects directly resulting from relative motion (without the introduction of dilation) are neither symmetric nor reciprocal. Would you agree?

Quote by Austin0

relative motion---->time dilation------>Doppler effect and differential aging

Yes, I understand that this is your interpretation of the causality involved. Mine is:

relative motion --> Doppler effect and differential aging

Time dilation does not appear because it is frame-dependent, so it is a convention, not a "real thing" that needs to have a cause.

so do you think that there is no causality involved in relative rates of static clocks in a gravity field?
That those rates are not "real" ( don't occur) until a clock is transported and returned ?

That the returning twins age is only a "real thing" after he arrives and it becomes observable??

Do you think that the existence of phenomena is dependent on or determined by convention?

Quote by Austin0 View Post

DO you doubt that differential aging is simply the cumulative result of time dilation?

I don't "doubt" this in the sense of thinking it's a purported factual statement that might not be true. I think it's "not even wrong" in the sense that it attributes causality to a frame-dependent convention.

Well i think that you must agree that observation certainly does NOT cause phenomena. And propagation of signals of itself doesn't either.

Ultimately the asymmetry, the difference in signals received is solely dependent on the actual difference in the number of signals sent at the sources. YES?

This difference in number must be spread out over the course of travel ...Agreed?

This seems to lead to two inevitable inferences:

1)There must be differences in relative rates during that transit.
The fact that we can't quantify or locate these differences in a frame independent way during transit does not negate the conclusion they must occur somewhere in that course.
2) These differences occur at the sources. Simply mechanisms (observers and clocks) and relative motion. No other intermediate factors or influences. You agreed that differential aging was a consequence of relative motion, yes/
Well differential aging is a process occurring over time.
As a process it is a difference in rates (biological or mechanical) over intervals. Time dilation by definition ,,,yes"?

 

[PAllen]

This seems to lead to two inevitable inferences:

1)There must be differences in relative rates during that transit.
The fact that we can't quantify or locate these differences in a frame independent way during transit does not negate the conclusion they must occur somewhere in that course.
2) These differences occur at the sources. Simply mechanisms (observers and clocks) and relative motion. No other intermediate factors or influences. You agreed that differential aging was a consequence of relative motion, yes/
Well differential aging is a process occurring over time.
As a process it is a difference in rates (biological or mechanical) over intervals. Time dilation by definition ,,,yes"?

I can agree with (1) in following sense: any mapping from a parameter to each (twin) world line that meets the requirements of implementing a simultaneity convention will show a greater average rate of tau to the parameter for one of the twins.

With (2), I have a big problem. You say differential aging is a process occurring over time. Whose time? The only objective time is the time along each world line. If I draw lines on a piece of paper, we don't talk about length occurring over length. If two curves on a plane have different lengths, we don't say one of them accumulated length faster, or more length per length. We say nothing more than one is longer. That is all we can say of world lines.

 

[zonde]

But I don't want to get sidetracked on this issue as it has no relevance to Bondi's argument concerning the inverse relationship of the Doppler shifts for coming and going at the same speed.

That clearly provides that answer to your question.

But you understood that Bondi explained in detail inverse relationship of the Doppler shifts for coming sender and going receiver at the same speed that works just as well for classical Doppler as relativistic Doppler, right?
And when it cames to the point where one should invoke PoR (reverse sender and receiver) and two Dopplers are not equal any more all the explanations are cut short with this sentence:
"Note that the Principle of Relativity, by insisting on the equivalence of all inertial observers, makes it quite clear that the ratio must be the same whichever of a pair of inertial observers does the transmitting."

Are you saying that there are two kinds of Doppler, classical which applies to sound and relativistic which applies to light and since I'm saying to "forget" SR then I must, by default, be limited to the Doppler that applies to sound and not to light?

Yes

 

[PAllen]

Theories don't cause anything. They explain observations.

Doppler symmetry exists independent of theory, and, if observed, is sufficient to predict differential aging (which might then be observed). Doppler symmetry and reciprocity is sufficient to derive the gamma factor of differential aging, without deriving Lorentz transform or even assuming invariance of light speed (if you don't assume this, you allow that the c in gamma could be frame dependent and not necessarily isotropic).

SR is a theory which explains a whole range of phenomena in a unified way. That is what is great about it. But it doesn't cause anything. Within SR, you can, but in no way need to invoke time dilation to explain Doppler. If you look at SR as Einstein did, you have assumptions: (POR applies to all phenomenon including light = can't detect aether, if it exists (I am building in invariance of light speed into this); speed of light is independent of emitter speed). From these, plus a convention, you derive Lorentz transform and the full machinery of SR. Also, from these, without the convention, and without bothering to derive Lorentz transform or time dilation, you can derive symmetry and reciprocity of Doppler, and from that differential aging by gamma factor.

It thus seems tendentious to insist the time dilation is the explanation (let alone cause!) of Doppler symmetry and reciprocity.

 

[PeterDonis]

"on an essential level"... in this context the word "an" inherently implies other essential levels,yes?

I don't think I have anything to add to what I've already said on this point. I'm not interested in playing word games.

if you say I am inverting reality ,this would only be true if the inverse of what I said was true, Yes?

I said quite clearly what I thought the causality was, and I made it clear that my main point was that time dilation doesn't belong in the causal chain. If you have something substantive to say in response to that, fine. Again, I'm not interested in playing word games.

What could be simpler than a temperature reading?
But what does that bare value tell us about what is being measured other than that you may not want to stick your fingers in it?
What does the word temperature or heat even mean without a theory?

Um, that you shouldn't stick your fingers in it if it's hot? Temperature measurements have obvious pragmatic value even if nobody has a good theory to explain them. Which was, in fact, the case for a significant period of time after thermometers were invented. That did not prevent them from being used. Similar remarks apply to most observations; we can make them, and often make use of the data obtained, without having a theory about them.

With Doppler the theoretical context in this case is SR.

Not necessarily. The observations come first; they are logically prior to any specific theory that explains them. You are assuming that SR is the correct theory; on that assumption, of course you can turn the logic around and deduce all the observations from the theory. But we're talking about how you know which theory is correct; and you only know that by treating the observations as primary, not the theory.

According to which it appears that the observed values are the result of two distinct factors ---relative motion and the dilation factor.

No, that's not what SR says. Here's the formula for relativistic Doppler:

\frac{\omega}{\omega_0} = \sqrt{\frac{1 + v}{1 - v}}

where v is the relative velocity of the observer *towards* the source (i.e., positive v is velocity towards, negative v is velocity away). Now tell me, where in that formula does time dilation appear?

but you seem to want to throw out this understanding completely. Not only the implication that time dilation is a phenomenon which exists independent of convention but also the fundamental kinematics involved in this analysis and understanding.

What makes you think that? All I have said is that time dilation is a frame dependent convention. I haven't said relativistic kinematics is invalid.

so do you think that there is no causality involved in relative rates of static clocks in a gravity field?

That those rates are not "real" (don't occur) until a clock is transported and returned?

Now you're talking about a different scenario where a causal factor (gravity, spacetime curvature, whatever you want to call it) is present that wasn't present in the original scenario. What makes you think that what I said about causal factors in the original scenario applies to this new one? Please don't attribute positions to me that I have not taken.

To answer your questions as you pose them, obviously if gravity (spacetime curvature, whatever) is present, there is another causal factor involved; in the case of static objects (i.e., no relative motion), the causality would be:

varying gravitational potential --> differential aging

Since the situation is static, two observers at different altitudes can establish the same simultaneity convention by exchanging light signals; and when they do, they will find that the one who is higher up experiences more ticks of his own clock between two of the exchanged light signals than the one who is lower down. So there is a set of direct observables corresponding to differential aging in this case even though the two observers don't ever actually meet.

Note, by the way, that this is a key difference from the flat spacetime case; in flat spacetime it is impossible for two observers who remain at rest relative to each other to have differential aging. If two such observers in flat spacetime run the above experiment (exchanging light signals to establish the same simultaneity convention), they will find that both of their clocks tick the same number of ticks between light signals. And if they are in relative motion, they can't synchronize their clocks this way; so the only way they have of detecting differential aging is to actually meet up and compare clocks.

Well i think that you must agree that observation certainly does NOT cause phenomena.

As long as we're talking about classical physics, yes, this is true. More precisely, we can always make the effects of observation sufficiently small that they can be ignored; but observations are themselves physical phenomena (for example, receiving light signals from an object), so they do have some effect.

If we take quantum mechanics into account, of course, we can no longer always make the effects of observations negligible; but I don't think we need to open that can of worms here.

And propagation of signals of itself doesn't either.

Propagating signals *are* phenomena, aren't they? (More precisely, detections of such signals are.)

Ultimately the asymmetry, the difference in signals received is solely dependent on the actual difference in the number of signals sent at the sources. YES?

Difference compared how? There has to be some common standard for comparison. In the case of the standard twin paradox, the standard is that the two twins are together, then they separate, then they come together again; so at the start and end of the scenario they can directly compare their clocks. In the case of the static gravity field, the two observers can establish a common standard of simultaneity that serves as the standard for comparison. Once there is such a standard, then yes, you can compare how many times each observer's clock ticks (or how many light signals he emits) between two standard comparison points. But you have to have those standard comparison points to do it.

PAllen already commented on the rest of your post; I agree with what he said.

 

[ghwellsjr]

But you understood that Bondi explained in detail inverse relationship of the Doppler shifts for coming sender and going receiver at the same speed that works just as well for classical Doppler as relativistic Doppler, right?

Correct.

And when it cames to the point where one should invoke PoR (reverse sender and receiver) and two Dopplers are not equal any more all the explanations are cut short with this sentence:
"Note that the Principle of Relativity, by insisting on the equivalence of all inertial observers, makes it quite clear that the ratio must be the same whichever of a pair of inertial observers does the transmitting."

Are you saying that there are two kinds of Doppler, classical which applies to sound and relativistic which applies to light and since I'm saying to "forget" SR then I must, by default, be limited to the Doppler that applies to sound and not to light?

Yes

I can understand that if forgetting SR meant you had to forget relativistic Doppler, then the argument would be cut short. But this would only be true if forgetting SR meant you had to forget PoR which is not the case. Einstein's theory of Special Relativity is just one possible theory based on the Principle of Relativity but it requires another postulate stating that light propagates at c in all Inertial Reference Frames. That's what I was saying to forget which leads to forgetting SR but not PoR. I specifically said this in post #7 and Bondi specifically says this in his book. We are not identifying either the speeds of the traveler or light in this argument and we are not identifying the time that it takes for light to make any part of the trip. That would require a theory such as SR or the Relativistic Doppler equation relating the speed of the observers to the Doppler factor. But we are not deriving that equation, we're only pointing out a conclusion based just on the PoR and that the propagation of the light coming from two sources with relative motion is the same.

Again, I want to emphasize that I was answering the OP's question of which observer would be older. He accepted the PoR and wondered how the symmetry inherent in it could result in the observers accumulating different ages. DaleSpam answered his question and pointed out that the PoR applied to inertial referentials (as the OP called them) but that the traveler is not inertial. This showed the lack of symmetry but did not explain how you could conclude which one would be older. Of course a full blown explanation from SR would provide that answer or even a full blown explanation based just on Relativistic Doppler but I wanted to show that the answer could also be provided just from the PoR and the assumption that light propagated from two different sources at the same speed.

 

[ghwellsjr]

I said that time dilation resulted from relative motion.

Here is a spacetime diagram of a single clock at rest in its Inertial Reference Frame. The blue dots represent one second ticks of Proper Time on the clock:

Now here is another spacetime diagram created by transforming to an IRF moving at -0.6c with respect to the first IRF:

In both diagrams the Time Dilation of the clock can be calculated from the same formula relating Time Dilation to speed. Is this what you meant when you said that time dilation resulted from relative motion?

 

[Austin0]

Quote by Austin0

This seems to lead to two inevitable inferences:

1)There must be differences in relative rates during that transit.
The fact that we can't quantify or locate these differences in a frame independent way during transit does not negate the conclusion they must occur somewhere in that course.
2) These differences occur at the sources. Simply mechanisms (observers and clocks) and relative motion. No other intermediate factors or influences. You agreed that differential aging was a consequence of relative motion, yes/
Well differential aging is a process occurring over time.
As a process it is a difference in rates (biological or mechanical) over intervals. Time dilation by definition ,,,yes"?

I can agree with (1) in following sense: any mapping from a parameter to each (twin) world line that meets the requirements of implementing a simultaneity convention will show a greater average rate of tau to the parameter for one of the twins.

With (2), I have a big problem. You say differential aging is a process occurring over time. Whose time? The only objective time is the time along each world line. If I draw lines on a piece of paper, we don't talk about length occurring over length. If two curves on a plane have different lengths, we don't say one of them accumulated length faster, or more length per length. We say nothing more than one is longer. That is all we can say of world lines.

So are you saying that differential aging is not a process?
Doesn't the fundamental physical concept of process necessarily require an unspecified time interval??

Am i not correct in thinking that the basic mathematical description of processes are differential equations??
Can't we discuss them in their general form without parameterization or convention? What meaning does difference, or change with respect to , etc have without a finite time interval of some duration??
So your comments make sense as related to quantifying results but I was speaking in terms of general principles.

You say:

The only objective time is the time along each world line

. Here you are talking about along the world line ,acknowledging the passage of time.
So worldlines are curves on a plane and as such once drawn exist outside of time but don't we still have to assume that differential aging is not an instantaneous event but must occur spread throughout the time represented by those curves?

Theories don't cause anything. They explain observations.

Doppler symmetry exists independent of theory, and, if observed, is sufficient to predict differential aging (which might then be observed). Doppler symmetry and reciprocity is sufficient to derive the gamma factor of differential aging, without deriving Lorentz transform or even assuming invariance of light speed (if you don't assume this, you allow that the c in gamma could be frame dependent and not necessarily isotropic).

SR is a theory which explains a whole range of phenomena in a unified way. That is what is great about it. But it doesn't cause anything. Within SR, you can, but in no way need to invoke time dilation to explain Doppler. If you look at SR as Einstein did, you have assumptions: (POR applies to all phenomenon including light = can't detect aether, if it exists (I am building in invariance of light speed into this); speed of light is independent of emitter speed). From these, plus a convention, you derive Lorentz transform and the full machinery of SR. Also, from these, without the convention, and without bothering to derive Lorentz transform or time dilation, you can derive symmetry and reciprocity of Doppler, and from that differential aging by gamma factor.

It thus seems tendentious to insist the time dilation is the explanation (let alone cause!) of Doppler symmetry and reciprocity..

i am puzzled by the repeated implications that i think or have said anything indicating a belief that theories determine (cause) phenomena.
You say that Doppler symmetry exists independent of theory. WHile i share this belief it is through the theory. POR is itself a theory ,no??
you then say

if observed.

Has this been definitively determined by actual observation at relativistic velocities??

In any case I agreed from the beginning that given symmetry and reciprocity time dilation was an inevitable result. i have yet to see how this alone leads to the actual gamma factor (it didn't in bondi or the quick calcs I did) so would like to see how you arrived there in your your derivation when finished.

I think all the Lorentz effects exist independent of theory and would have been directly derived from observation eventually through increased clock precision, particle acceleration, actual relativistic travel etc.

SR is a theory which explains a whole range of phenomena in a unified way.

This is exactly how I see it and am simply trying to understand the full implications of that explanation in a coherent whole. You mentioned in another post the inherent limitations of our abstract constructs as far as correspondence to reality. WHile I certainly agree and at the end of the day it may be revealed that our current models have little or no correspondence to the actual universe , still we proceed with the assumption that there is some actual correspondence even into areas where there is no possibility of observation Eg. interior of a black hole.

You seem to be concerned here with the precedence of derivation of the theory itself. I am not disagreeing with anything you are presenting but I am looking at causality and time ordering on a more physical level.

Is it possible to arrive at an alternative explanation without being tendentious?? if so I guess in my case it is simply my personal limitations in communication which i will strive to improve ;-)

 

[Austin0]

Quote by Austin0

"on an essential level"... in this context the word "an" inherently implies other essential levels,yes?

I don't think I have anything to add to what I've already said on this point. I'm not interested in playing word games..

I was neither being argumentative nor playing word games. So i would like to clarify this matter as it bothers me you would think that.

Quote by Austin0

would you agree that on an essential level physics is a study of causality?

This was my original statement. It appears to me that to argue the contrary is necessarily equivalent to asserting that :

a study of causality is not an essential level of physics.

Causality is certainly one thing physics can study. I don't know that I agree that causality is all there is to it on an essential level. Physics is the study of whatever reality turns out to be; if reality includes causality, then physics studies causality. But if reality turns out not to include causality in some cases (for example, in quantum gravity theories causality may turn out to be an emergent property, not fundamental, and not present in all cases), then physics will not just be the study of causality on an essential level.

From you response it appears that you misread my statement as ...On the essential level, physics is a study of causality.

IF that had been my statement I would completely agree with your arguments but as actually stated that interpretation is essentially precluded.

So rather than trying to create an argument I was trying to indicate there was no real argument but only a semantic misinterpretation.
...
i have too high a regard for your input and this opportunity for discussion to seek out trivial and unnecessary arguments. I am sorry if my mode of expression seemed to imply otherwise.

Quote by Austin0

With Doppler the theoretical context in this case is SR.

Not necessarily. The observations come first; they are logically prior to any specific theory that explains them. You are assuming that SR is the correct theory; on that assumption, of course you can turn the logic around and deduce all the observations from the theory. But we're talking about how you know which theory is correct; and you only know that by treating the observations as primary, not the theory.

Certainly observations come first in construction of a theory regarding actual empirical observations.
But i was talking about the theory as it exists ...SR and how it provided context and meaning to the raw Doppler observations.

Quote by Austin0

According to which it appears that the observed values are the result of two distinct factors ---relative motion and the dilation factor.

No, that's not what SR says. Here's the formula for relativistic Doppler:

\frac{\omega}{\omega_0} = \sqrt{\frac{1 + v}{1 - v}}


where is the relative velocity of the observer *towards* the source (i.e., positive v is velocity towards, negative v is velocity away). Now tell me, where in that formula does time dilation appear?

It explicitly appears in the derivation presented in hyper Physics. so i think it is intrinsically embedded in the equation just as it is in the Addition of Velocities equation. Certainly there may be other possibly derivations that do not directly involve gamma but I think that in any case the implicit presence can be revealed through decomposition into gamma and the classical kinematic Doppler component.


I am asking this again:
Quote by Austin0

Even in an SR context , the Twins scenario, the effects directly resulting from relative motion (without the introduction of dilation) are neither symmetric nor reciprocal. Would you agree?

Quote by Austin0

but you seem to want to throw out this understanding completely. Not only the implication that time dilation is a phenomenon which exists independent of convention but also the fundamental kinematics involved in this analysis and understanding.

What makes you think that? All I have said is that time dilation is a frame dependent convention. I haven't said relativistic kinematics is invalid.

I think that because when i said"the observed values are the result of two distinct factors ---relative motion and the dilation factor." you said I was incorrect.that seems to imply you are dismissing the kinematic element as well??

I am unsure of what you mean when you say "time dilation is a frame dependent convention" in this specifically limited context (Doppler analysis)
The gamma factor between source and observer is as invariant as the Doppler factor ,yes??
SO are you disassociating the gamma factor from any connection to time dilation here??

Also,,,, observing inertial frames can directly apply the Doppler equation to arrive at the correct result but am I incorrect in thinking that they could instead directly do a kinematic and gamma analysis and arrive at the same end result??
SO although they would derive different quantitative results during the process they would all agree that the two factors validly applied as I am suggesting. yes?

Quote by Austin0

so do you think that there is no causality involved in relative rates of static clocks in a gravity field?

Quote by Austin0

That those rates are not "real" (don't occur) until a clock is transported and returned?

Now you're talking about a different scenario where a causal factor (gravity, spacetime curvature, whatever you want to call it) is present that wasn't present in the original scenario. What makes you think that what I said about causal factors in the original scenario applies to this new one? Please don't attribute positions to me that I have not taken.

Yes this is different. I was not attributing any position to you but just asking what that position was.

To answer your questions as you pose them, obviously if gravity (spacetime curvature, whatever) is present, there is another causal factor involved; in the case of static objects (i.e., no relative motion), the causality would be:

varying gravitational potential --> differential aging

Since the situation is static, two observers at different altitudes can establish the same simultaneity convention by exchanging light signals; and when they do, they will find that the one who is higher up experiences more ticks of his own clock between two of the exchanged light signals than the one who is lower down. So there is a set of direct observables corresponding to differential aging in this case even though the two observers don't ever actually meet.

In actuality i was somewhat expecting this response but did not presume. I share this view but it seems that others may question it. PAllen mentioned Singhe for one.

Actually in the static Sc case isn't the standard interpretation of this to be Doppler shift? SO in this case it appears you are making an analytical choice of interpretation of dilation even though it is also not directly observable in the sense you are talking about with relativistic Doppler observation.

AsI said I have no problem with this at all.
But this leads to another question.

Do you think that relativistic dilation from relative motion is a fundamentally different phenomenon from gravitational dilation?

Quote by Austin0

Well i think that you must agree that observation certainly does NOT cause phenomena.

As long as we're talking about classical physics, yes, this is true. More precisely, we can always make the effects of observation sufficiently small that they can be ignored; but observations are themselves physical phenomena (for example, receiving light signals from an object), so they do have some effect.

If we take quantum mechanics into account, of course, we can no longer always make the effects of observations negligible; but I don't think we need to open that can of worms here.

Yes no need for any more worms

Quote by Austin0

And propagation of signals of itself doesn't either.

Propagating signals *are* phenomena, aren't they? (More precisely, detections of such signals are.)

Of course propagating waves and observations of the same are phenomena. My point was that the propagation had no possible effect on the outcome. No change in transit,,,yes??

Quote by Austin0

Ultimately the asymmetry, the difference in signals received is solely dependent on the actual difference in the number of signals sent at the sources. YES?

Difference compared how? There has to be some common standard for comparison. In the case of the standard twin paradox, the standard is that the two twins are together, then they separate, then they come together again; so at the start and end of the scenario they can directly compare their clocks. In the case of the static gravity field, the two observers can establish a common standard of simultaneity that serves as the standard for comparison. Once there is such a standard, then yes, you can compare how many times each observer's clock ticks (or how many light signals he emits) between two standard comparison points. But you have to have those standard comparison points to do it.

You are addressing a separate question. Yes it is understood that comparison during transit is impossible in any frame independent way.
But I am talking about simple physical causality. Independent of observation.it would seem that the causality and temporal ordering were unambiguous.
Actual number transmitted----->Propagation----->Observation. that propagation and observation can have no possible causal influence on the numbers at the sources.

Would you propose that this could somehow not be the case?
That the asymmetry at the end was not a result of an actual different number of signals sent ?
sorry for my delayed response i have been a bit under the weather