Transformation Vs. Physical Law

[ghwellsjr]

yes I understand your point regarding reciprocity and the relative length of time in each phase. And certainly agree.
But to suggest you can apply this principle to the twins question to explain the difference in final age, without invoking the gamma factor inherent in the relativistic Doppler equation, is a different story. Wouldn't you agree?

The story I am discussing now does not look at the relative length of time in each phase for both twins but only for the one that turns around. His two times are equal and knowing the Doppler factors are reciprocal allows him to derive the value of gamma without invoking any other considerations.

 

[Samshorn]

I said if two inertial observers start off approaching each other (from far apart) and then pass each other so that they are then receding, they will continue at the same speed, won't they?

But an inertial observer doesn't constitute a basis for defining a velocity. For that we need an extended system of space and time coordinates. And if the velocities are going to correlate with the Doppler shift in the expected way we need them to be defined in terms of a standard inertial coordinate system. Of course, we can simply decline to consider any actual numerical velocities, but then we forfeit the ability to provide any quantitative answers to real world questions, and we don't have a physical theory at all. At some point we need to connect numerical velocities with the predicted quantitative effects.

Moreover, the assertion that every pair of inertial observers will each see the (presumed) standard frequency shifted by reciprocal factors when approaching and receding is tantamount to the assertion of not only source independence, but also directional independence and frame independence, meaning we are asserting the complete invariance of light speed in terms of any and every system of standard inertial coordinates.

Naturally we aren't required to explicitly construct such coordinates, but they are implicit in those premises. If two twins are directly approaching a central transmitter from opposite directions (all unaccelerated) and they see equal frequencies, we must say they have equal speeds relative to the rest frame coordinates of the transmitter. They pass the transmitter simultaneously and again see equal frequencies and therefore have equal speeds, so they implicitly define a system of space and time coordinates based on light synchronization. (We say they are at equal distances when they have received equal numbers of pulses.)

I have thought about how we can demonstrate that the two Doppler factors (coming and going at the same speed) are reciprocals and I found the answer in Hermann Bondi's book, http://archive.org/details/RelativityCommonSense, pages 77 to 80. So we can figure it out either by experiment or by analysis.

Bondi doesn't provide an analytical derivation of reciprocal Doppler factors, he simply assumes it (or rather, he assumes relativity and, tacitly, lightspeed invariance, from which it trivially follows, along with all the rest of special relativity), and spends a few pages trying to disguise the fact that he's simply assuming these things. Also, you can't on your terms "figure it out by experiment" either, because the thing to be figured out involves quantitative velocities (if it is to have any physical significance), and you can't even define velocities without some system of space and time coordinates.

 

[universal_101]

Actually, no, I don't see any contradiction.

Do you doubt the validity of time dilation as a function of relative motion as it is described in the Lorentz math??

Exactly, since to account for the differential ageing of unstable particles in different frames, we must use a physical law and not a part of a transformation.

This is the center point of the debate, in special relativity it is the Lorentz transformations which are used to explain the differential ageing. But instead we should have a physical law explaining these differences, which then can be validly transformed for any other inertial observing frame using Lorentz transformation.

 

[Austin0]

The story I am discussing now does not look at the relative length of time in each phase for both twins but only for the one that turns around. His two times are equal and knowing the Doppler factors are reciprocal allows him to derive the value of gamma without invoking any other considerations.

Perhaps you could explain this trick?
Reciprocity of Doppler by itself ,without the gamma factor , does not imply aging differential.

So you are assuming that factor behind the scene , applying that to Speedo's hypothetical
observations and then asserting that Speedo, if he were mathematically inclined, could derive the Lorentz transformation directly from these observations.

Are you really claiming that the gamma is not involved or necessary to the explanation?

 

[universal_101]

No, I don't agree.

The clock time of a twin depends only on their *own* worldline. It is completely irrelevant what the other twin is doing. Relative velocity does not come into it, except implicitly when we choose a frame in which to do the calculation. This does not have to be one of the twins frames.

The difference in age is the only time both twins come into the calculation.

This must be a new physics, since what you are suggesting is that, difference in the ages of the Twins after the trip, is independent of their relative velocity during the trip.

I mean, its alright to disagree with me or anyone for that matter, but rejecting everything that I post is gravely unscientific.

 

[atyy]

Whereas, a transformation, let's consider a co-ordinate transform in geometry first, then we can simply extend the concept for the Lorentz Transformation. In geometry the shape of any object(circle, parabola, line) does not depend on the position of the origin of the co-ordinate system, even though the co-ordinates(x,y,z) of these objects can change.

Exactly. However, if one is able to specify a coordinate system, then one can use the coordinates to describe events. In special relativity as in geometry, both the coordinate-system invariant and the coordinate-system descriptions are useful, with the proviso that when using the latter the coordinate system must be specified.

 

[universal_101]

If we assume the Principle of Relativity for light, we are assuming that what each twin sees of the other one is symmetrical and not dependent on their relative speed in any medium.

This is incorrect, 2 and 1/2, 3 and 1/3, or any other form like x and 1/x are inversely symmetrical, but saying that these values, for example, 2,3 and x is independent of the relative velocity makes them arbitrary. I mean if they does not depend on the relative velocity, then how come you choose one over the other and say they are different, since 2 and 3 are obviously different.

 

[Austin0]

Exactly, since to account for the differential ageing of unstable particles in different frames, we must use a physical law and not a part of a transformation.

This is the center point of the debate, in special relativity it is the Lorentz transformations which are used to explain the differential ageing. But instead we should have a physical law explaining these differences, which then can be validly transformed for any other inertial observing frame using Lorentz transformation.

I don't know what you think physical law means. As far as I can see they don't really explain much. They simply describe phenomena in exact terms and provide a basis for predicting certain aspects of those phenomena.
So GR predicts certain cases of time dilation but no particular explanation of the mechanism. The Lorentz math predicts certain other cases of time dilation also with no explanation of mechanism. If you want, you can say GR is a law and the Lorentz math a transform but in this case that is a distinction without a difference.
A semantic quibble not worth pursuing. The function and utility are exactly the same.
I would say that the Lorentz math was fundamentally a physical law and only secondarily a transformation but that is also a semantic question not worth any effort.
So i think you might be better served directing your intelligence towards more interesting questions and subjects, just mHO

 

[Nugatory]

This must be a new physics, since what you are suggesting is that, difference in the ages of the Twins after the trip, is independent of their relative velocity during the trip.

No, he is suggesting (correctly) that the age of each twin is independent of their relative velocity. I could shoot one of the twins dead while the rocket is in flight and the aging of the other twin would be not be affected in the least.

Each twin's age depends only on the path that twin takes through space-time. So I compute the age of twin one at the reunion by looking at twin one's path through space-time; twin two and the relative velocity don't enter into this computation at all. Then I compute the age of twin two at the reunion by looking at twin two's path through space-time; twin one and the relative velocity don't enter into this calculation at all.

And now that I know their ages at the moment of reunion... I know what the difference in their ages is.

 

[universal_101]

Each twin's age depends only on the path that twin takes through space-time.

That path is calculated/based/defined by their relative velocity.

 

[Nugatory]

That path is calculated/based/defined by their relative velocity.

It is not.

If it were, I wouldn't be able to calculate the aging of anyone who didn't have a twin... Surely you aren't suggesting that an only child suspended in the midst of empty space (so that's there's no relative velocity because there's nothing to be relative to) won't age, or that I can't calculate the aging? All we need to do is to look at his wristwatch.

But if I can calculate the aging of the isolated only child without considering his velocity relative to a twin that he doesn't even have... Clearly I can do the same for either twin, just by ignoring the other twin and the relative velocity between them.

 

[universal_101]

Exactly. However, if one is able to specify a coordinate system, then one can use the coordinates to describe events. In special relativity as in geometry, both the coordinate-system invariant and the coordinate-system descriptions are useful, with the proviso that when using the latter the coordinate system must be specified.

Agreed, but the invariant events, cannot depend on which coordinate system we use, and it is this use of the coordinate system which I'm questioning.

That is, how many events(differential age of the twins) would take place is concluded by using the gamma factor of a transformation.

Now, it is this use of the gamma factor to produce difference in the ages of the Twins, make it necessary to have real Length contraction phenomena, to which we don't have any experimental support.

Instead, it is the Time Dilation of unstable particles(using LT) which is directly challenged by the recent new findings, of dependence of the nuclear decay rates on the Earth-Sun distance, which includes beta decaying particles(Muons).

 

[universal_101]

It is not.

If it were, I wouldn't be able to calculate the aging of anyone who didn't have a twin... Surely you aren't suggesting that an only child suspended in the midst of empty space (so that's there's no relative velocity because there's nothing to be relative to) won't age, or that I can't calculate the aging? All we need to do is to look at his wristwatch.

But if I can calculate the aging of the isolated only child without considering his velocity relative to a twin that he doesn't even have... Clearly I can do the same for either twin, just by ignoring the other twin and the relative velocity between them.

To calculate the difference in the age of two twins, we need two twins to compare

 

[atyy]

Agreed, but the invariant events, cannot depend on which coordinate system we use, and it is this use of the coordinate system which I'm questioning.

That is, how many events(differential age of the twins) would take place is concluded by using the gamma factor of a transformation.

Now, it is this use of the gamma factor to produce difference in the ages of the Twins, make it necessary to have real Length contraction phenomena, to which we don't have any experimental support.

Instead, it is the Time Dilation of unstable particles(using LT) which is directly challenged by the recent new findings, of dependence of the nuclear decay rates on the Earth-Sun distance, which includes beta decaying particles(Muons).

Do you believe in energy?

 

[Mentz114]

The clock time of a twin depends only on their *own* worldline. It is completely irrelevant what the other twin is doing. Relative velocity does not come into it, except implicitly when we choose a frame in which to do the calculation. This does not have to be one of the twins frames.

The difference in age is the only time both twins come into the calculation.

This must be a new physics, since what you are suggesting is that, difference in the ages of the Twins after the trip, is independent of their relative velocity during the trip.

But I've said we only need both twins if we want to compare their worldlines. The proper length of a worldline depends only on that worldline - not on a relative velocity.

You keep moving the argument around. Do you still think there is a paradox buried in all this ?

 

[ghwellsjr]

If we assume the Principle of Relativity for light, we are assuming that what each twin sees of the other one is symmetrical and not dependent on their relative speed in any medium.

This is incorrect, 2 and 1/2, 3 and 1/3, or any other form like x and 1/x are inversely symmetrical, but saying that these values, for example, 2,3 and x is independent of the relative velocity makes them arbitrary. I mean if they does not depend on the relative velocity, then how come you choose one over the other and say they are different, since 2 and 3 are obviously different.

I didn't say that the Doppler factor is not dependent of the relative speed between the twins, I said it's not dependent on each twin's relative speed in any medium. I'm also saying that the speed is not important to being able to derive the difference in aging. All we need is the knowledge that the two Doppler factors are reciprocals, and that the traveling twin spends the same amount of time traveling away as he does toward the other twin based on his own clock.

For example, with Dopplers of 2 and 1/2, the average of them is 1.25 which means that as the traveling twin kept his eye on the stationary twin's clock through the entire trip, he first saw it ticking at 1/2 the rate of his own, then for the return trip, he watched it tick twice as fast as his own. You can confirm that at a relative speed of 0.6c, the relativistic Doppler factors are 2 and 1/2 and that gamma equals 1.25.

Another example, with Dopplers of 3 and 1/3, the average is 5/3 or 1.667, and this occurs with a relative speed of 0.8c which produces a gamma of 1.667.

The point is that we don't need to know the value of the speed in order to calculate the age difference which happens to be equal to gamma.

 

[ghwellsjr]

The story I am discussing now does not look at the relative length of time in each phase for both twins but only for the one that turns around. His two times are equal and knowing the Doppler factors are reciprocal allows him to derive the value of gamma without invoking any other considerations.

Perhaps you could explain this trick?
Reciprocity of Doppler by itself ,without the gamma factor , does not imply aging differential.

So you are assuming that factor behind the scene , applying that to Speedo's hypothetical
observations and then asserting that Speedo, if he were mathematically inclined, could derive the Lorentz transformation directly from these observations.

Are you really claiming that the gamma is not involved or necessary to the explanation?

I never said that it is possible to derive the Lorentz transformation. Gamma is not the Lorentz transformation, it just happens, among other things, to be equal to the ratio of the accumulated times for the two twins and it can be derived just from the reciprocal Doppler factors.

 

[universal_101]

Do you believe in energy?

I believe in energy conservation.

 

[Mentz114]

The clock time of a twin depends only on their *own* worldline. It is completely irrelevant what the other twin is doing. Relative velocity does not come into it, except implicitly when we choose a frame in which to do the calculation. This does not have to be one of the twins frames.

The difference in age is the only time both twins come into the calculation.

This must be a new physics, since what you are suggesting is that, difference in the ages of the Twins after the trip, is independent of their relative velocity during the trip.

What I'm trying to say is that we don't need the relative velocity between the twins explicitly in the calculation. We could choose any inertial frame to parameterize the worldlines and still get the correct result.

Suppose I concede the point that the calculation could be done in one of the twins frames - what conclusion would you draw from that ?

Are you still saying that using a transformation to change frames invalidates the laws of dynamics ?

 

[universal_101]

I didn't say that the Doppler factor is not dependent of the relative speed between the twins, I said it's not dependent on each twin's relative speed in any medium. I'm also saying that the speed is not important to being able to derive the difference in aging. All we need is the knowledge that the two Doppler factors are reciprocals, and that the traveling twin spends the same amount of time traveling away as he does toward the other twin based on his own clock.

For example, with Dopplers of 2 and 1/2, the average of them is 1.25 which means that as the traveling twin kept his eye on the stationary twin's clock through the entire trip, he first saw it ticking at 1/2 the rate of his own, then for the return trip, he watched it tick twice as fast as his own. You can confirm that at a relative speed of 0.6c, the relativistic Doppler factors are 2 and 1/2 and that gamma equals 1.25.

Another example, with Dopplers of 3 and 1/3, the average is 5/3 or 1.667, and this occurs with a relative speed of 0.8c which produces a gamma of 1.667.

The point is that we don't need to know the value of the speed in order to calculate the age difference which happens to be equal to gamma.

You inherently used the relative velocity, when you talk about the reciprocity of the Doppler values, i.e. 2 and 1/2 etc. It is very surprising that you and other people here are claiming that difference in the age is independent of relative velocity.

 

[universal_101]

What I'm trying to say is that we don't need the relative velocity between the twins explicitly in the calculation. We could choose any inertial frame to parameterize the worldlines and still get the correct result.

Suppose I concede the point that the calculation could be done in one of the twins frames - what conclusion would you draw from that ?

Are you still saying that using a transformation to change frames invalidates the laws of dynamics ?

If the difference in the age is independent of the relative velocity, why does Muons moving at different speeds decay at different rates.

Please, don't say that, they do so because their worldlines are different, but there is no relation to the relative velocity.

Because the concept of the world-lines is abstract, and even difference in the world-lines of the two objects in a frame, is known as Lorentz transformation, whereas, we are talking about the difference in age which is invariant.

 

[Mentz114]

universal_101, how is the comparison of proper times, as it is done in the twins paradox relevant to the expression of physcal laws in one frame or another ?

In the case of the muon decay it has been pointed out that we can write the 'law' (equations ) governing detector counts in any frame with no inconsistency ?

[edit] I just saw this

If the difference in the age is independent of the relative velocity, why does Muons moving at different speeds decay at different rates.

I don't know what you mean by 'different rates'. The life-time of the muon is invariant. What changes between frames is the distance they travel as expressed in different coordinates.

 

[Austin0]

I never said that it is possible to derive the Lorentz transformation. Gamma is not the Lorentz transformation, it just happens, among other things, to be equal to the ratio of the accumulated times for the two twins and it can be derived just from the reciprocal Doppler factors.

'Derived just from the reciprocal Doppler factors" because those factors are found through a Lorentzian transform (relativistic Doppler) derived from and inherently containing the gamma factor , Or do you think this is not so??
SO when you say one twin sees the time on the other twins clock you are calculating what he sees using the transformed version of classical Doppler. yes?

I think Gamma cannot be derived simply from reciprocity of classical Doppler. Do you think otherwise? Because that is what you seem to be saying.

 

[universal_101]

I never said that it is possible to derive the Lorentz transformation. Gamma is not the Lorentz transformation, it just happens, among other things, to be equal to the ratio of the accumulated times for the two twins and it can be derived just from the reciprocal Doppler factors.

IT JUST HAPPENS ! No, just happens to be... does not come under the domain of the classical physics. On the other note, I myself think that it just happens to be equal to the gamma factor from the Lorentz Transformations, but again as I suggested the problem vanishes if we conclude the difference in the nuclear decay rates of moving Muons by using some physical law.

 

[universal_101]

I don't know what you mean by 'different rates'. The life-time of the muon is invariant. What changes between frames is the distance they travel as expressed in different coordinates.

First of all, you don't have any experimental proof of that change in distance, whereas, I do have the experimental evidence of different rates.

So, you cannot refute the notion of different rates, since, experimental proof is needed to claim otherwise.

 

[Mentz114]

First of all, you don't have any experimental proof of that change in distance, whereas, I do have the experimental evidence of different rates.

So, you cannot refute the notion of different rates, since, experimental proof is needed to claim otherwise.

I still don't follow you. What do mean by rate ? Are we talking about muon decay or beta-emission ?Here is a space time diagram of the muon being observed from the lab.
The muon is traveling at 0.8c wrt the lab.

The proper intervals are Creation -> anihilation = 2.51, lab clock start -> lab clock stop = 7.69

So the laboratory frame concludes that the life-time is 7.69. The distance traveled in lab coords is about 3.15.

I don't know if this is the scenario you are talking about.

 

[ghwellsjr]

Agreed, but the invariant events, cannot depend on which coordinate system we use, and it is this use of the coordinate system which I'm questioning.

And I'm offering you an explanation of the twin scenario that does not involve any coordinate system.

By the way, saying that invariant events cannot depend on which coordinate system we use doesn't make any sense. In Special Relativity, events are defined in terms of an inertial coordinate system. There is no such thing as an invariant event. Every event has certain coordinates according to a particular coordinate system. The same event can have different coordinates in a different coordinate system and for the standard configuration, we can use the Lorentz transformation to see what those coordinates are for the same event in many different inertial Frames of Reference.

In the twin scenario, the event of the twins separating and the event of the twins reuniting do not tell us anything about the difference in their ages. They do tell us the accumulated age for the stationary twin (because he is stationary) but they do not tell us anything about the age of the traveling twin and in fact there are no two events in any inertial frame that will give us this information.

That is, how many events(differential age of the twins) would take place is concluded by using the gamma factor of a transformation.

Can you show us an example of what you are talking about here?

Now, it is this use of the gamma factor to produce difference in the ages of the Twins, make it necessary to have real Length contraction phenomena, to which we don't have any experimental support.

Don't you consider the Michelson-Morley Experiment to be experimental evidence of length contraction? That's how Lorentz explained it.

Instead, it is the Time Dilation of unstable particles(using LT) which is directly challenged by the recent new findings, of dependence of the nuclear decay rates on the Earth-Sun distance, which includes beta decaying particles(Muons).

Can you provide a source link to these recent new findings?

 

[universal_101]

I still don't follow you. What do mean by rate ? Are we talking about muon decay or beta-emission ?


Here is a space time diagram of the muon being observed from the lab.
The muon is traveling at 0.8c wrt the lab.

The proper intervals are Creation -> anihilation = 2.51, lab clock start -> lab clock stop = 7.69

So the laboratory frame concludes that the life-time is 7.69. The distance traveled in lab coords is about 3.15.

I don't know if this is the scenario you are talking about.

Above is the traditional use of Lorentz transformation, and the validity of these transformations to explain the Time Dilation is only confirmed by the experiments, whereas the other part that needs the real length contraction has never been experimentally confirmed.

So, I think we can't use the above use of transformation to explain the different number of particles decay rates, depending on the motion of these particles.

 

[Mentz114]

... the different number of particles decay rates, depending on the motion of these particles.

Please explain exactly what this means.

 

[GeorgeDishman]

Hi
could you point me to the experimental tests revealing length contraction?
I have looked without coming across anything. Thanks

The Michelson-Morley experiment for example was originally explained using length contraction alone ("FitzGerald–Lorentz contraction") in 1889. Only later was time dilation included (Larmor in 1897 according to Wikipedia) but it didn't remove the need for length contraction.

http://en.wikipedia.org/wiki/Michelson–Morley_experiment#Length_contraction_and_special_relativity