Understand Special Relativity and Time paradox

[zonde]

I don't think anybody invented any law of physics without first having raw data on which to invent that law. I agree that the law should be further testable and new experiments invented to test the theory in areas that the original raw data didn't cover but that's a side issue and not related to the point or the argument that Bondi or I are making.

The problem with raw data is that there is a lot of it. And generally different observers don't share too much of it (usually none). But physical laws work for all observers (they share them so to say).

And what is the argument that Bondi is making?

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.

But I do not see how it explains this statement of yours:

The PoR is based on observable raw data that among other things concludes that things will be reciprocal between two inertial observers

unless you admit that it is plain wrong.

 

[zonde]

Seems like I left this post without answer.

What things? Can you be specific?

Form Einstein's 1905 paper:
Chapter 1. Definition of Simultaneity starts with:

Let us take a system of co-ordinates in which the equations of Newtonian
mechanics hold good. In order to render our presentation more precise and
to distinguish this system of co-ordinates verbally from others which will be
introduced hereafter, we call it the “stationary system.”

and it ends with:

It is essential to have time defined by means of stationary clocks in the
stationary system, and the time now defined being appropriate to the stationary
system we call it “the time of the stationary system.”

So we can write out such statements:
- in "stationary system" equations of Newtonian mechanics hold good;
- time of "stationary system" is defined using Einstein's simultaneity convention.

This suggests that Einstein's simultaneity convention is essential for equations of Newtonian mechanics to hold good.

I invite you to read the wikipedia article on the One-Way Speed of Light concerning Lorentz ether theory and Edwards' theory. Both of these use a clock synchronization convention that is different from Einstein's and yet they get the same physical laws. These examples should be enough to show you that clock synchronization conventions are arbitrary, meaning that we are not compelled by any raw data to select one over the other. We have a different kind of good reason to select Einstein's; as he stated, it's simple.

Lorentz ether theory does not propose it's own clock synchronization convention. At least I didn't found it.

Edwards' theory introduces parameter q. But it does not claim that physical laws are the same as you vary q. It claims however that experimental predictions won't change as you vary q.

For reference, this discussion started with this claim:

You will get the same physical laws that you would get with Einstein's convention as long as you do it in a consistent way.

 

[ghwellsjr]

The problem with raw data is that there is a lot of it. And generally different observers don't share too much of it (usually none). But physical laws work for all observers (they share them so to say).

And what is the argument that Bondi is making?

I summarized it in post #305 at the top of this page:

Let me see if I can summarize Bondi's argument. He says that if you have two inertial observers, A & B, in relative rest but separated by a great distance, and one of them, A, sends repetitive signals to the other, B, there will be no Doppler shifts. Then a third inertial observer, C, traveling from A to B will observe some Doppler shift ratio from A which will be less than one and which we can call DSR1. Then if that traveler creates his own repetitive signal(s) at the same rate he receives them from A and sends them to B, we know they will travel side by side on their way to B. When they get there, B will observe them both arriving at the same rate but the ones that were sent by C were sent with Doppler shift ratio that is the reciprocal of DSR1. We know that the speed that C is traveling away from A is the same as the speed that C is traveling toward B and so the Doppler shift ratios for the same speed coming and going are reciprocals of each other.

And http://archive.org/stream/RelativityCommonSense/Bondi-RelativityCommonSense#page/n45/mode/1up is that link again.

Of course they will see the same Doppler shift.

But I do not see how it explains this statement of yours:

The PoR is based on observable raw data that among other things concludes that things will be reciprocal between two inertial observers

unless you admit that it is plain wrong.

I will admit that my choice of the word "reciprocal" could be confusing to someone whose native tongue is not English, especially since I used it again later with an almost opposite meaning. A better word would have been symmetrical.

 

[ghwellsjr]

Seems like I left this post without answer.


Form Einstein's 1905 paper:
Chapter 1. Definition of Simultaneity starts with:

Let us take a system of co-ordinates in which the equations of Newtonian
mechanics hold good. In order to render our presentation more precise and
to distinguish this system of co-ordinates verbally from others which will be
introduced hereafter, we call it the “stationary system.”

and it ends with:

It is essential to have time defined by means of stationary clocks in the
stationary system, and the time now defined being appropriate to the stationary
system we call it “the time of the stationary system.”

So we can write out such statements:
- in "stationary system" equations of Newtonian mechanics hold good;
- time of "stationary system" is defined using Einstein's simultaneity convention.

This suggests that Einstein's simultaneity convention is essential for equations of Newtonian mechanics to hold good.

Go back to the introduction:

...the phenomena of electrodynamics as well as of mechanics possesses no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good.1 We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate...

Lorentz ether theory does not propose it's own clock synchronization convention. At least I didn't found it.

Edwards' theory introduces parameter q. But it does not claim that physical laws are the same as you vary q. It claims however that experimental predictions won't change as you vary q.

For reference, this discussion started with this claim:

You will get the same physical laws that you would get with Einstein's convention as long as you do it in a consistent way.

It is not necessary to make a claim about the propagation of light in order to establish physical laws.

Isn't it significant to you that if you establish an Inertial Reference Frame according to Einstein's Special Relativity that for an inertial observer moving in that IRF light will not propagate at c relative to him and yet all the physical laws for him are still valid? This is because, the propagation of light is not measurable, it is not detectable, so how could it have any influence or bearing on any raw data or derived physical laws?

 

[BruceW]

In order to prove, without actually doing the experiment, that an observer traveling at one speed (0.5c in the OP's case) by going away from an inertial observer and then returning at the same speed, will age less than the inertial observer, it is only necessary to assume that nothing in the experiment will look any different to any of the observers if conducted at any other state of inertial motion for all observers (that's the Principle of Relativity as demonstrated in the case of LET that the ether wind could not be detected) and that the propagation of light, although it can be different in every state of inertial motion, is the same for different sources of light (which is certainly true under LET). This is important in Bondi's argument so that the light from C takes the same time to reach B as the light that from A takes to reach B after it passes C.

How about if we assumed Galilean relativity, and used ideas such as 'local time' and 'length contraction' as part of the theory of EM. So in this way, EM would transform in a Lorentzian way, but non-EM phenomena would not necessarily transform in a Lorentzian way. (Or to put it another way, EM is affected by the ether, and other phenomena may or may not be).

I know that this would disagree with experiment. But what I am trying to do is show that Bondi's explanation of the twin paradox using just relativity is also using other assumptions. And 'relativity principle' could mean more than one thing. A more rigorous definition of Einstein's relativity is needed for the twin paradox to be explained really.

p.s. I have not read Bondi's explanation, but I think I understand it from ghwellsjr's brief explanation.

 

[ghwellsjr]

How about if we assumed Galilean relativity, and used ideas such as 'local time' and 'length contraction' as part of the theory of EM. So in this way, EM would transform in a Lorentzian way, but non-EM phenomena would not necessarily transform in a Lorentzian way. (Or to put it another way, EM is affected by the ether, and other phenomena may or may not be).

I know that this would disagree with experiment. But what I am trying to do is show that Bondi's explanation of the twin paradox using just relativity is also using other assumptions. And 'relativity principle' could mean more than one thing. A more rigorous definition of Einstein's relativity is needed for the twin paradox to be explained really.

p.s. I have not read Bondi's explanation, but I think I understand it from ghwellsjr's brief explanation.

Bondi's explanation of the twin paradox did assume more things. But I was using only the very first part of Bondi's explanation which showed that the two Doppler shift factors for approaching and retreating at the same speed are reciprocals of each other. And from that we can prove that the Stay-At-Home twin is older than the traveling twin. I'm not saying by how much or even what the relationship is between speed and Doppler factor. Just which one is older. Just the question the OP asked.

So with that in mind, do you still think that we need more than:

1) the Principle of Relativity, which in this application simply means that two inertial observers moving with respect to each other will see the same Doppler shift in each other

2) the fact that light from A to B propagates at the same speed as the light from C to B

If you disagree, please state where the problem is in what I have just said. We don't need to get involved with transforms or simultaneity or synchronization or length contraction.

 

[Dale]

Edwards' theory introduces parameter q. But it does not claim that physical laws are the same as you vary q. It claims however that experimental predictions won't change as you vary q.

That is the same as claiming that the physical laws are the same. You seemed to have missed my previous post on this topic. Claiming that experimental predictions won't change as you vary q is in fact claiming that the physical laws are the same as you vary q.

 

[ghwellsjr]

So, I take it that we are on the same page with the sketch below representing our traveling twin in his rocket during the turnaround.

And in the same sense that we considered the sequence of instantaneous rockets as presented in the stay-at-home twin's frame, we can also recognize the sequence of hyperplanes of simultaneity indicated by the Lorentz-Poincare' transformations to the traveling coordinates.

The sequence of instantaneous 3-D rocket volumes that the traveling twins is living in are clearly not the same physical 3-D rocket volumes that are depicted in the sketch above. The physical 3-D rocket that the traveling twin lives in is unique to him and represented uniquely in his coordinates.

There is no point in compounding your argument to include a non-inertial observer when you haven't come to grips with your argument for an inertial observer:

If someone tells you that it takes 8 minutes and 20 seconds for light to get from the sun to the earth, you should realize that they are assuming (whether they know it or not) the common sun-earth inertial rest frame to be able to make that statement. Furthermore, that statement relies on the definition of a frame in Special Relativity such that it takes the same length of time for light to get from the Earth to the sun as it does for the light to get from the sun to the earth. Unless we make an assumption like this, we cannot and should not think that there is intrinsic in nature a meaning to the idea of simultaneous space that stretches between the Earth and the sun or between any other locations.

When we see an event on the sun such as a solar flare and note the time on our clock, we know that any definition of a frame or any theory that attempts to explain how light propagates will affirm that we did see that flare at that time but any claim that the solar flare actually happened 8 minutes and 20 seconds earlier is nothing more than a concept of simultaneity that we put into nature, not one that we take out of nature.

ghwellsjr, I tend to feel that nature has put the relativity of simultaneity into our physics and into our reality. Nature gave us a speed of light that is the same for all inertial frames. That is something that we experience because nature put in the photon worldlines so as to bisect the angle between X4 and X1 (thus, the Lorentz-Poincare'-Minkowski-Einstein simultaneous spaces). Nature gave us the worldlines to follow through space-time along with the simultaneous space in which to experience nature. These simultaneous spaces, for each different observer, are unique. Further, nature manifests the laws of nature through the continuous sequence of simultaneous spaces we experience as we move along our worldines. If you were one of the ficticious hyperdimensional observers looking at the block universe (pedagogically speaking--refer to earlier post with the hyperdimensional observers), these Lorentz simultaneous spaces would not have the same significance as for one of us 3-dimensional creatures. However, even the hyperdimensional creature could make out patterns of 4-dimensional objects that can be identified as unique patterns, from which laws of physics could be derived. And those laws would be recognized as associated with the Poincare' group of transformations.

You are simply asserting that there are preferred (or unique) reference frames with complete disregard for one of the main tenets of Special Relativity that there is no preferred (or unique) reference frame. Can we deal with your claim in the simple inertial case because your more complicated non-inertial case clouds the issue?

You don't seem to realize or you are unwilling to accept that coordinates have no physical significance and that's because we invent the coordinates in order to make sense out of nature--nature does not compel us to use any particular definition of coordinates, not even the one that Einstein came up with that forms the basis of Special Relativity.

 

[zonde]

Let me see if I can summarize Bondi's argument. He says that if you have two inertial observers, A & B, in relative rest but separated by a great distance, and one of them, A, sends repetitive signals to the other, B, there will be no Doppler shifts. Then a third inertial observer, C, traveling from A to B will observe some Doppler shift ratio from A which will be less than one and which we can call DSR1. Then if that traveler creates his own repetitive signal(s) at the same rate he receives them from A and sends them to B, we know they will travel side by side on their way to B. When they get there, B will observe them both arriving at the same rate but the ones that were sent by C were sent with Doppler shift ratio that is the reciprocal of DSR1. We know that the speed that C is traveling away from A is the same as the speed that C is traveling toward B and so the Doppler shift ratios for the same speed coming and going are reciprocals of each other.

Therefore, in the twin scenario, since the traveling twin spends the same amount of time going and coming at the same speed, we can simply average the two Doppler shift ratios and we will get a number greater than one, meaning the traveler sees the other twin's clock running faster than his own.

And http://archive.org/stream/RelativityCommonSense/Bondi-RelativityCommonSense#page/n45/mode/1up is that link again.

There is something wrong with Bondi argument. Look, the frequency that observer C is receiving and retransmitting can be whatever and this Bondi argument about two ratios being reciprocal of each other will work just the same. So we just plug in such a frequency that we can easily see that result comes out wrong, say we take frequency higher than that transmitted by observer A so that traveling twin will be certainly older than stay at home twin after reunion, and we can check that Bondi argument still works.

 

[BruceW]

So with that in mind, do you still think that we need more than:

1) the Principle of Relativity, which in this application simply means that two inertial observers moving with respect to each other will see the same Doppler shift in each other

2) the fact that light from A to B propagates at the same speed as the light from C to B

If we define a principle of relativity that only says how light gets Doppler shifted, then no, this is not enough. From this, it is not clear how spacetime transforms between inertial frames, and so it is not clear that the twins would age differently.

If instead, you defined a principle of relativity that say that spacetime transforms in a Lorentzian way, and assume that age is a reliable 'clock', then I would say you have enough.

 

[PAllen]

If we define a principle of relativity that only says how light gets Doppler shifted, then no, this is not enough. From this, it is not clear how spacetime transforms between inertial frames, and so it is not clear that the twins would age differently.

If instead, you defined a principle of relativity that say that spacetime transforms in a Lorentzian way, and assume that age is a reliable 'clock', then I would say you have enough.

How is 'spacetime transforms in a Lorentzian way' relevant? That is a statement about transforming between a certain family of coordinates. What if nobody uses any coordinates? This fails to state a physical proposition at all, as worded.

My take on what else you have to assume is something that seems inconceivable to reject: that if, for a given observer not feeling any forces, a few co-located clocks operating by different principles remain in synch, then a different observer, seeing images of them, cannot see them differ. Make one of the clocks based on the frequency of a standard light emission.

 

[ghwellsjr]

There is something wrong with Bondi argument. Look, the frequency that observer C is receiving and retransmitting can be whatever and this Bondi argument about two ratios being reciprocal of each other will work just the same. So we just plug in such a frequency that we can easily see that result comes out wrong, say we take frequency higher than that transmitted by observer A so that traveling twin will be certainly older than stay at home twin after reunion, and we can check that Bondi argument still works.

I'm afraid I have irreconcilably confused things by using the word "reciprocal" with two different meanings in two places in my original description. See if it makes sense using the word "symmetrical" in the first instance and "inverse" in the second instance. If that doesn't clear up the confusion, then just read Bondi's explanation in the provided link.

 

[ghwellsjr]

So with that in mind, do you still think that we need more than:

1) the Principle of Relativity, which in this application simply means that two inertial observers moving with respect to each other will see the same Doppler shift in each other

2) the fact that light from A to B propagates at the same speed as the light from C to B

If we define a principle of relativity that only says how light gets Doppler shifted, then no, this is not enough. From this, it is not clear how spacetime transforms between inertial frames, and so it is not clear that the twins would age differently.

If instead, you defined a principle of relativity that say that spacetime transforms in a Lorentzian way, and assume that age is a reliable 'clock', then I would say you have enough.

I didn't say anything about the Principle of Relativity explaining how light gets Doppler shifted, only that it does in a symmetrical manner. And I didn't say anything about any transformations. That is irrelevant. Just focus on the symmetrical aspects of Doppler.

 

[bobc2]

I don’t understand the reluctance to acknowledge implications of simultaneous spaces and relativity of simultaneity. I assumed that after everyone agreed on the rocket’s momentary at-rest state (in the stay-at-home rest frame) that it would then be easier to visualize the other momentary positions of the rocket (exhibiting length contractions). Then, once having accepted the momentary analysis concept, it would not be difficult to imagine doing Lorentz transforms to arrive at similar momentary at-rest states for the rocket in momentary rocket rest frames.

In other words, we observe that just as the entire rocket comes to rest at some instant in the stay-at-home rest frame, the rocket is always at rest in some inertial frame. Those are the rocket rest frames to which I’ve been referring.

It is a mistake to insist that we can only analyze the situation using a single accelerated frame of reference, because if you insist on that you are confronted with impossible misplaced implications of horizons and other artifact. Comments about overlapping charts are completely misplaced and irrelevant to the analysis. We use just one chart at a time.

 

[Dale]

it would not be difficult to imagine doing Lorentz transforms to arrive at similar momentary at-rest states for the rocket in momentary rocket rest frames.

In other words, we observe that just as the entire rocket comes to rest at some instant in the stay-at-home rest frame, the rocket is always at rest in some inertial frame. Those are the rocket rest frames to which I’ve been referring.

Sure, those are not difficult to imagine. They are called momentarily co-moving (MC) inertial reference frames (IRF). I don't think that anyone has an issue with that concept, and certainly I do not.

The thing that you seem to fail to understand is that there is nothing particularly unique or special about the MCIRF. By the first postulate, any IRF is as good as any other IRF. The fact that it is MC is perhaps convenient for some particular calculation, but otherwise of no physical importance.

It is a mistake to insist that we can only analyze the situation using a single accelerated frame of reference, because if you insist on that you are confronted with impossible misplaced implications of horizons and other artifact.

I have not insisted that, nor have I seen anyone else here do that. Do you believe someone has, if so, please quote the post that made you believe that their opinion was that the situation could only be analyzed using a single accelerated frame of reference.

Comments about overlapping charts are completely misplaced and irrelevant to the analysis. We use just one chart at a time.

If only that were the case. Every MCIRF is a 4D chart which covers all of spacetime with an inertial frame. Where YOU introduce a non inertial frame is when you go from talking about 4D charts to talking about a sequence of 3D simultaneous spaces. That is something that YOU insist on bringing into the analysis, not anyone else.

A sequence of 3D simultaneous spaces is a simultaneity convention, and with a simultaneity convention you have the a reference frame. So YOU are the one making a non-inertial frame, and YOU are the one insisting that it has some degree of physical significance, not anyone else. All we are doing is pointing out the fact that the non inertial frame that YOU have constructed violates some of the basic mathematical requirements for such things.

Go back and look at our discussions to this point. You will see that you consistently switch from talking about 4D frames to 3D simultaneous spaces, and you will see that the objections you have been getting all stem from the inappropriate use of the 3D simultaneous spaces, not the 4D frames.

 

[PeterDonis]

It is a mistake to insist that we can only analyze the situation using a single accelerated frame of reference, because if you insist on that you are confronted with impossible misplaced implications of horizons and other artifact. Comments about overlapping charts are completely misplaced and irrelevant to the analysis. We use just one chart at a time.

Nobody is insisting on that. What others have been saying is that you can analyze the entire situation using a single *inertial* frame of reference. You, by contrast, insist on switching inertial frames from event to event. How is that supposed to help any? The only reason I can see for your insistence on doing this is to somehow justify your claims about simultaneous spaces; but you can't then turn around and use your claims about simultaneous spaces to justify switching inertial frames from event to event.

 

[BruceW]

How is 'spacetime transforms in a Lorentzian way' relevant? That is a statement about transforming between a certain family of coordinates. What if nobody uses any coordinates? This fails to state a physical proposition at all, as worded.

Hmm. For the moment, just considering an inertial frame (i.e. not the frame of the traveling twin), and if spacetime transforms in a Lorentzian way, then this gives us an invariant - the spacetime interval. So, using an integral along the worldline of the traveling twin, we can calculate the proper time along this worldline.

My take on what else you have to assume is something that seems inconceivable to reject: that if, for a given observer not feeling any forces, a few co-located clocks operating by different principles remain in synch, then a different observer, seeing images of them, cannot see them differ. Make one of the clocks based on the frequency of a standard light emission.

I conceive the inconceivable :) The point is that we must state the things that we are going to define as 'clocks', if we want to be saying that we have 'proved' something.

 

[BruceW]

I didn't say anything about the Principle of Relativity explaining how light gets Doppler shifted, only that it does in a symmetrical manner.

In that case, your principle of relativity is just saying that light gets Doppler shifted in a symmetrical manner. Which is not enough to explain the twin paradox. 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.

 

[ghwellsjr]

In that case, your principle of relativity is just saying that light gets Doppler shifted in a symmetrical manner.

Good--we're making progress.

Which is not enough to explain the twin paradox.

Correct--I never said it was.

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.

Can we forget about the Twin Paradox for awhile? Can we focus on what I am trying to do?

I want to add one more assumption which has experimental support and that is that the propagation of light is independent of the source of the light. So when observer C is moving away from observer A and toward observer B, and observer A sends a flash of light towards observer B, if observer C sends his own flash of light towards observer B at the instant that he sees observer A's flash of light arrive at his location, the two flashes of light will propagate at the same speed toward observer B and observer B will see them both arrive at his location at the same instant.

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?

 

[PAllen]

Hmm. For the moment, just considering an inertial frame (i.e. not the frame of the traveling twin), and if spacetime transforms in a Lorentzian way, then this gives us an invariant - the spacetime interval. So, using an integral along the worldline of the traveling twin, we can calculate the proper time along this worldline.

I think this is backwards. We start with the fact that, say, a specific clock has advanced an hour. This is objective fact. Everyone sees that this specific clock has advanced an hour between two firings of a flash bulb right next to it (identifiable events). Then we invent mathematical models like coordinates, metrics, invariants that allow objective facts to be treated as invariants. Physical assumptions must relate to measurements, not mathematical abstractions. Thus, Einstein assumed things like 'every inertial observer will measure the two way speed of light the same'; 'if two sources next to each other but at different speeds flash a lights, any observer will get the light from them at the same time; and 'no experiment can distinguish inertial motion from rest from withing a closed lab'. Your proposal to me lacks any character of being a physical assumption.

I conceive the inconceivable :) The point is that we must state the things that we are going to define as 'clocks', if we want to be saying that we have 'proved' something.

Such an assumption as I described is rarely stated; in fact numerous times, arguments like that are, without further justifications, assumed to refute a theory that predicts something like that. For example, we say there is a paradox to resolve if one observer is predicted to see a bomb explode and another observer sees no explosion. If the paradox can't be resolved, we treat this as ipso facto disproof of a theory.

 

[Austin0]

The problem with this as it stands is that the stay-at-home twin also sees two reciprocal "clock rates": he sees the traveling twin's clock ticking slower than his outbound and faster than his inbound, and the two rates are reciprocals of each other. In fact they are exactly the *same* rates as the traveling twin sees. So just this observation alone isn't sufficient to account for the different elapsed times.

The difference, as the Usenet Physics FAQ page on the Doppler Shift Analysis makes clear, is *when* each twin sees the change from slower to faster ticking of the other's clock. The traveling twin sees it when he turns around, halfway through the trip; the stay-at-home twin sees it only when the light signals emitted by the traveling twin at the turnaround reach him--i.e., much *later* than halfway through the trip.

*That* is the key asymmetry, the *observable* asymmetry, between the two twins. Your analysis in post #7 was fine as far as it went; it explains how the traveling twin can predict that the stay-at-home twin's clock reading will be greater than his. But it does *not* explain why the stay-at-home twin can't apply exactly the same reasoning. That requires including the observed asymmetry I just described in the analysis: this shows that the stay-at-home twin *does* apply the same reasoning, but he applies it to different observed data (observed change from redshift to blueshift is towards the end of the trip vs. halfway through). If you do the same calculation you described in post #7 for the stay-at-home twin, averaging the two reciprocal clock rates but with the correct weighting for the relative times (your formula assumed 50-50 weighting, but that's only valid for the traveling twin--for the stay-at-home twin the slower tick rate is weighted much more than the faster tick rate), you will get the stay-at-home twin's (correct) prediction that the traveling twin will have aged less when they meet.

I just want to point out that all the valid points you make here are well known to ghwellsjr
and have been completely covered by him in his analysis in previous threads.

 

[PeterDonis]

I just want to point out that all the valid points you make here are well known to ghwellsjr
and have been completely covered by him in his analysis in previous threads.

I know; see my post #294.

 

[Austin0]

I didn't say anything about the Principle of Relativity explaining how light gets Doppler shifted, only that it does in a symmetrical manner. And I didn't say anything about any transformations. That is irrelevant. Just focus on the symmetrical aspects of Doppler.

Bondi's brilliant analysis which only requires one additional piece of "raw data", that the propagation of light is independent of the speed of the source--
Bondi concludes that the rates at which the traveling brother sees the Stay-At-Home brother's clock ticking between coming and going at the same speed are reciprocals of each other and from this it is easy to conclude that the traveling brother can predict ahead of time that he will see his brother's clock accumulate more time than his own during the trip. See post #7.
.

. I'm trying to put ourselves in the situation before Einstein's theory of Special Relativity or even before Lorentz's Ether Theory, in fact before any theory. ... without invoking SR .

Bondi ...his brilliant scheme to identify the Doppler ratios as being reciprocal and the idea of averaging them to determine that the inertial observer would be older than the traveler.

In other words, you don't have to incorporate any theory that involves spacetime or transformations. .

Some comments on your and Bondi's demonstrations as I understand them.

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?

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.

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.

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.

So I would like to know if you see points that I am misunderstanding or am in error and if this makes any sense as I have outlined it.

I hope you will understand that none of this reflects on your Doppler analysis of the Twins differential aging . I have a sincere appreciation of your presentation and think it is a great illustration (for those who question) that direct observation would correspond to abstract calculation.(surprise,surprise) I think it is a valuable contribution on it's owm merits without additional claims.

 

[PAllen]

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.

 

[bobc2]

Nobody is insisting on that.

DaleSpam Post #50:
Quote by bobc2: "I have not presented the turn-around in the context of non-intertial frames."
DaleSpam: "Yes, you did…"

DaleSpam Post #46:

I agree that the naive approach at defining a non-inertial frame is not nonsense in general, but only to the left of the crossover. At that point it violates one of the fundamental requirements of a coordinate system, and therefore it does become illogical. You can use this approach to make statements about the stay at home twin, but not the red guy. Your claims about the red guy's clock running backwards are therefore indeed nonsense.

Also, the Lorentz transform transforms between inertial frames, so it is reasonable to disregard it here where we are dealing with non inertial frames. And after you cobble together the various pieces the resulting transform is decidedly not the Lorentz transform anymore anyway.

PAllen Post #35:

…They relate points on the two world lines in a smooth, non-repeating way. Thus, there is no reason a rational traveler should ever believe the home clock is running backwards.

PAllen Post #75: Please note further that the derivation of simultaneity convention for inertial observers relies on:

- being inertial long enough to apply a clock synchronization method (establishing simultaneity), for clocks a given distance apart. It is also preferred only in the sense that all reasonable methods agree.

- A non-inertial observer has a different past than co-moving inertial observer. This means that physical synchronization methods they might use will come out different from the comoving inertial frame. They also won't agree with each other.

Post #190: …even as a mathematical convention, talking about blue's simultaneous spaces does imply an overall simultaneity convention for the blue world line. For this, there are mathematical requirements - any region where a proposed simultaneity convention for blue has intersecting surfaces is outside the domain of that convention. If you want to talk about a blue simultaneity for such a region, you must adopt a different convention that does not have intersecting surfaces…

What others have been saying is that you can analyze the entire situation using a single *inertial* frame of reference.

No. That was not my impression.

You, by contrast, insist on switching inertial frames from event to event. How is that supposed to help any?

That's what I just finished explaining in my last couple or so posts.

The only reason I can see for your insistence on doing this is to somehow justify your claims about simultaneous spaces; but you can't then turn around and use your claims about simultaneous spaces to justify switching inertial frames from event to event.

I just looked at the turnaround in the context of the sequence of Rocket rest frames, then looked at the implications. The sequence of Rocket rest frames (as explained in my last two posts, similar to Rindler and other sources) was a natural way to analyze the turnaround, then the other observations naturally followed.

 

[BruceW]

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 still disagree with this, 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.

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.

 

[zonde]

I'm afraid I have irreconcilably confused things by using the word "reciprocal" with two different meanings in two places in my original description. See if it makes sense using the word "symmetrical" in the first instance and "inverse" in the second instance. If that doesn't clear up the confusion, then just read Bondi's explanation in the provided link.

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?

 

[zonde]

That is the same as claiming that the physical laws are the same. You seemed to have missed my previous post on this topic. Claiming that experimental predictions won't change as you vary q is in fact claiming that the physical laws are the same as you vary q.

As you vary q you have to vary Newtonian equations as well. You have to vary both together and only then you get the same experimental predictions.

 

[BruceW]

I think this is backwards. We start with the fact that, say, a specific clock has advanced an hour. This is objective fact. Everyone sees that this specific clock has advanced an hour between two firings of a flash bulb right next to it (identifiable events). Then we invent mathematical models like coordinates, metrics, invariants that allow objective facts to be treated as invariants. Physical assumptions must relate to measurements, not mathematical abstractions.

hmm. Yes, ok, I would also need to say how the idea of 'coordinates' relates to physical measurements, if I wanted to show that the theory is consistent. On a slightly related topic, after going on google, I found this paper: http://synset.com/pdf/100_en.pdf Which essentially says that you can define SR by using the same axioms of classical mechanics, minus the axiom of simultaneity, and plus the axiom of speed of light being the same in all inertial frames. (They also go on to say about what happens if we relax the axiom of c being same in all inertial frames, but this is not really relevant to our discussion, I think).

 

[Dale]

As you vary q you have to vary Newtonian equations as well. You have to vary both together and only then you get the same experimental predictions.

Yes. But what you are doing is not changing the laws of physics, but rather expressing them in terms of new quantities.

 

[Dale]

DaleSpam Post #50:
Quote by bobc2: "I have not presented the turn-around in the context of non-intertial frames."
DaleSpam: "Yes, you did…"

Here I am insisting that YOU are unwittingly introducing a non-inertial frame; I am not insisting "that we can only analyze the situation using a single accelerated frame of reference".

DaleSpam Post #46:

I agree that the naive approach at defining a non-inertial frame is not nonsense in general, but only to the left of the crossover.

And here, are you seriously taking my statement that the "non-inertial frame is not nonsense in general" as me insisting "that we can only analyze the situation using a single accelerated frame of reference"?

Let me be clear. I am not insisting "that we can only analyze the situation using a single accelerated frame of reference". I am insisting that you have to use some frame of reference and that you have to follow the mathematical requirements in order to have a valid one. YOU are the one who brings in the non-inertial frame using the MCIRF simultaneity convention, and I am simply pointing out that in part of the spacetime it fails to meet the mathematical requirements.

I just looked at the turnaround in the context of the sequence of Rocket rest frames, then looked at the implications. The sequence of Rocket rest frames (as explained in my last two posts, similar to Rindler and other sources) was a natural way to analyze the turnaround, then the other observations naturally followed.

No, the other observations only follow when you transition from the 4D inertial frames to a sequence of 3D simultaneous spaces, which you have done repeatedly throughout this thread. In none of the 4D inertial frames does the red guy's clock go backwards at any point. You cannot have it both ways. Either you are looking at 4D inertial frames, in which case the clock never goes backwards, or you are looking at your 3D simultaneous spaces, in which case you are defining a simultaneity convention in a non-inertial frame which cannot cover the red guy.

 

[ghwellsjr]

I just looked at the turnaround in the context of the sequence of Rocket rest frames, then looked at the implications. The sequence of Rocket rest frames (as explained in my last two posts, similar to Rindler and other sources) was a natural way to analyze the turnaround, then the other observations naturally followed.

Your fundamental problem is that you continue to promote the idea that Einstein's simultaneity convention for establishing a rest frame is natural. It doesn't come from nature nor is it obvious. Simultaneity only seems natural and obvious to you because you ignore Einstein's argument that since it is not natural, he is free to establish any convention he wants (that is consistent with the data). His argument against Lorentz's concept (and practically everybody else's) of an absolute ether rest state is not because there is evidence against it, but simply that his theory will also work even if you believe there is an absolute ether rest state. We choose to adopt Einstein's theory only because it is simpler than Lorentz's. You have stated that you do not believe this, you believe that there is some fundamental flaw in Lorentz's Ether Theory and that it cannot be true because it violates some aspect of nature. As long as you continue to hold these false ideas, you will never be able to understand why your conclusions about simultaneity for accelerating observers are also mere conventions, just like they are for inertial observers.

 

[ghwellsjr]

Some comments on your and Bondi's demonstrations as I understand them.
...
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.

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.

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.

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.

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.

So I would like to know if you see points that I am misunderstanding or am in error and if this makes any sense as I have outlined it.

I hope you will understand that none of this reflects on your Doppler analysis of the Twins differential aging . I have a sincere appreciation of your presentation and think it is a great illustration (for those who question) that direct observation would correspond to abstract calculation.(surprise,surprise) I think it is a valuable contribution on it's owm merits without additional claims.

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.

And thanks for your continued affirmations of my efforts to explain SR.

 

[Alain2.7183]

I agree that the naive approach at defining a non-inertial frame is not nonsense in general, but only to the left of the crossover.

That seems to say that the rapid aging of the home twin, when the traveling twin reverses from outbound to inbound, is OK, but that if the traveling twin then reverses from inbound back to outbound, then the rapid decrease in the age of the home twin isn't OK. 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?

 

[Dale]

That seems to say that the rapid aging of the home twin, when the traveling twin reverses from outbound to inbound, is OK, but that if the traveling twin then reverses from inbound back to outbound, then the rapid decrease in the age of the home twin isn't OK

That is correct, a decrease in age is never OK.

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?

Even so. The problem is having any situation where the same event is mapped to multiple coordinates. This happens any time that the age decreases.

See Ch 2, especially p. 33-38
http://arxiv.org/abs/gr-qc/9712019