Transformation Vs. Physical Law

[ghwellsjr]

Not true, as explained in detail in the other thread where you made that claim. First, the principle of relativity is founded on experimental evidence, just as much as is the invariance of light speed in terms of standard inertial coordinates, so it makes no sense to take one as a principle and the other as an "experimental" proposition. They are both experimentally founded propositions that we adopt as principles. Second, the independence of light speed on the motion of the source is necessary but not sufficient to derive relativistic Doppler, because it doesn't rule out directional dependence. You need, in addition to the principle of relativity, the full principle of lightspeed invariance, including isotropy of light speed (in terms of standard inertial coordinates). And taken together, these are sufficient to derive all of special relativity, including (but not limited to) relativistic Doppler.

I'm not trying to derive relativistic Doppler. I'm saying that since two inertial observers can experimentally determine that the Doppler based on light is the same for both of them as they approach each other and that it is the same for both of them as they recede away from each other and that these two Doppler factors are reciprocals of each other, then that is all they need to know to predict that if they enact the twin scenario where they depart from each other and remain inertial for a while and then one of them accelerates back toward the other one with the recprocal Doppler, their accumulated age ratio can be calculated from the Doppler factor.

I'm also saying that this analysis does not require any synchronization of remote clocks by any method or the establishment or definition of any frame of reference or coordinate system or any theory about transforming coordinates between different coordinate systems, which is what universal_101 is contending.

 

[Samshorn]

I'm saying that since two inertial observers can experimentally determine that the Doppler based on light is the same for both of them as they approach each other and that it is the same for both of them as they recede away from each other and that these two Doppler factors are reciprocals of each other, then that is all they need to know to predict ... their accumulated age ratio ... from the Doppler factor. I'm also saying that this analysis does not require ... the establishment or definition of any frame of reference or coordinate system...

Still not true. Your premise is that we can experimentally determine that the Doppler shift when receding at a certain speed is the reciprocal of the Doppler shift when approaching at the same speed. The problem is that you haven't thought about how they would deterime that they are approaching each other at the same speed that they were formerly receding from each other. They obviously can't use the Doppler shift, because that would be circular and devoid of physical content. In other words, they can't simply define their approach speed to be equal to their receed speed when the Doppler shifts are reciprocal. For that proposition to have physical meaning, they need some independent measure of speed, which comes from the systems of coordinates in which the homogeneous and isotropic equations of mechanics hold good. There is simply no way of getting the effects of special relativity without establishing the correlation (implicitly or explicitly) with inertia.

I'm also saying that this analysis does not require any ... theory about transforming coordinates between different coordinate systems, which is what universal_101 is contending.

Well, it obviously doesn't require any transforming of coordinates, but it does imply Lorentz invariance, which entails the covariance of the physical parameters under a certain class of transformations.

The answer to the OP is that the physical law describing the half-life of a sub-atomic particle moving in the x, y, and z directions by the amounts dx, dy, dz in the time dt is purely a function of the quantity sqrt[dt^2 - dx^2 - dy^2 - dz^2] where x,y,z,t are any single system of inertial coordinates. No transformation is involved. (But of course x,y,z,t do have to be coordinates in terms of which the laws of mechanics hold good.)

In fact, we find that every physical process and phenomenon (not just the half-lives of sub-atomic particles) has this same form, in the sense that the physical laws don't depend on the absolute values of x,y,z,t, nor even on the absolute values of dx,dy,dz,dt or their ratios, but only on the quantity dt^2 - dx^2 - dy^2 - dz^2. The fact that these physical laws work equally well in terms of any standard system of inertial spacetime coordinates implies that this quadratic quantity is the same in all of them. After noticing this, and then seeing it confirmed over and over again for all known physical laws, we begin to expect it to be true, even when trying to formulate the laws governing previously unknown phenomena. This property, called Lorentz invariance, is not itself a physical law, it is an attribute of all known physical laws.

It's useful to know about Lorentz invariance because it enables us to compute things very easily by taking a short cut. If we already know that a certain physical law (such as the law for the half-life of a particle) is Lorentz invariant, we know that we can compute things in any convenient system of standard inertial coordinates, and then very simply express the results in terms of any other system of coordinates using the Lorentz transformation (which happens to be the transformation that preserves that quadratic quantity appearing in the physical laws). But this is just a computational shortcut, used by people who know what they're doing. If it confuses the OP, he can just go ahead and do things the more laborious (and less insightful) way.

 

[Austin0]

Thanks for the view,

I agree that Lorentz transformation is more than just a transformation in modern physics. It is exactly what I'm questioning. It seems as if the transformation is multipurpose, it can be a physical law at times and also can be a transformation at other.

Do you see this contradiction of basic physics concept.

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??

If you don't then I don't understand why you think there is a problem. Is it the semantic question of whether time dilation is called a law or a transformation? You seemed to agree that it could be both so I am confused as to your point here.

 

[Austin0]

Still not true. Your premise is that we can experimentally determine that the Doppler shift when receding at a certain speed is the reciprocal of the Doppler shift when approaching at the same speed. The problem is that you haven't thought about how they would deterime that they are approaching each other at the same speed that they were formerly receding from each other. They obviously can't use the Doppler shift, because that would be circular and devoid of physical content. In other words, they can't simply define their approach speed to be equal to their receed speed when the Doppler shifts are reciprocal. For that proposition to have physical meaning, they need some independent measure of speed, which comes from the systems of coordinates in which the homogeneous and isotropic equations of mechanics hold good. There is simply no way of getting the effects of special relativity without establishing the correlation (implicitly or explicitly) with inertia.



Well, it obviously doesn't require any transforming of coordinates, but it does imply Lorentz invariance, which entails the covariance of the physical parameters under a certain class of transformations.

The answer to the OP is that the physical law describing the half-life of a sub-atomic particle moving in the x, y, and z directions by the amounts dx, dy, dz in the time dt is purely a function of the quantity sqrt[dt^2 - dx^2 - dy^2 - dz^2] where x,y,z,t are any single system of inertial coordinates. No transformation is involved. (But of course x,y,z,t do have to be coordinates in terms of which the laws of mechanics hold good.)

In fact, we find that every physical process and phenomenon (not just the half-lives of sub-atomic particles) has this same form, in the sense that the physical laws don't depend on the absolute values of x,y,z,t, nor even on the absolute values of dx,dy,dz,dt or their ratios, but only on the quantity dt^2 - dx^2 - dy^2 - dz^2. The fact that these physical laws work equally well in terms of any standard system of inertial spacetime coordinates implies that this quadratic quantity is the same in all of them. After noticing this, and then seeing it confirmed over and over again for all known physical laws, we begin to expect it to be true, even when trying to formulate the laws governing previously unknown phenomena. This property, called Lorentz invariance, is not itself a physical law, it is an attribute of all known physical laws.

It's useful to know about Lorentz invariance because it enables us to compute things very easily by taking a short cut. If we already know that a certain physical law (such as the law for the half-life of a particle) is Lorentz invariant, we know that we can compute things in any convenient system of standard inertial coordinates, and then very simply express the results in terms of any other system of coordinates using the Lorentz transformation (which happens to be the transformation that preserves that quadratic quantity appearing in the physical laws). But this is just a computational shortcut, used by people who know what they're doing. If it confuses the OP, he can just go ahead and do things the more laborious (and less insightful) way.

Hi regarding relative velocities in these scenarios. Isn't that always problematic if we are considering hypothetical real world situations?? But normally in a case like ghwellsjr's it is assumed we extended a virtual frame all the way to the destination to measure velocity exactly , no? We do make the assumption that approach is equivalent to recession.

Regarding the invariant interval, I understood it was a direct derivation from the Lorentz math. Is this incorrect?

 

[Austin0]

I'm not trying to derive relativistic Doppler. I'm saying that since two inertial observers can experimentally determine that the Doppler based on light is the same for both of them as they approach each other and that it is the same for both of them as they recede away from each other and that these two Doppler factors are reciprocals of each other, then that is all they need to know to predict that if they enact the twin scenario where they depart from each other and remain inertial for a while and then one of them accelerates back toward the other one with the recprocal Doppler, their accumulated age ratio can be calculated from the Doppler factor.

I'm also saying that this analysis does not require any synchronization of remote clocks by any method or the establishment or definition of any frame of reference or coordinate system or any theory about transforming coordinates between different coordinate systems, which is what universal_101 is contending.

Hi Firstly I don't agree or in fact even understand the OP's point, but I have to mention that the Doppler shift equation is itself derived from and expressing the fundamental transformation isn't it? With classical Doppler it seems to me there would be no age differential, no?

 

[Dale]

Regarding the invariant interval, I understood it was a direct derivation from the Lorentz math. Is this incorrect?

If you start with the spacetime interval you can derive the Lorentz transform as a class of transforms that leaves the interval invariant. If you start with the transform you can derive the interval as a quantity that is invariant. It just depends what you want to consider a postulate and what you want to consider a derived result. The math doesn't care which direction you go.

I find a certain appeal to starting with the interval. After all, to me, the notion of distance seems more basic than the notion of coordinates.

 

[ghwellsjr]

I'm saying that since two inertial observers can experimentally determine that the Doppler based on light is the same for both of them as they approach each other and that it is the same for both of them as they recede away from each other and that these two Doppler factors are reciprocals of each other, then that is all they need to know to predict ... their accumulated age ratio ... from the Doppler factor. I'm also saying that this analysis does not require ... the establishment or definition of any frame of reference or coordinate system...

Still not true. Your premise is that we can experimentally determine that the Doppler shift when receding at a certain speed is the reciprocal of the Doppler shift when approaching at the same speed. The problem is that you haven't thought about how they would deterime that they are approaching each other at the same speed that they were formerly receding from each other. They obviously can't use the Doppler shift, because that would be circular and devoid of physical content. In other words, they can't simply define their approach speed to be equal to their receed speed when the Doppler shifts are reciprocal. For that proposition to have physical meaning, they need some independent measure of speed, which comes from the systems of coordinates in which the homogeneous and isotropic equations of mechanics hold good. There is simply no way of getting the effects of special relativity without establishing the correlation (implicitly or explicitly) with inertia.

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? I wasn't talking yet about the twin scenario.

But beyond that, 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.

I'm also saying that this analysis does not require any ... theory about transforming coordinates between different coordinate systems, which is what universal_101 is contending.

Well, it obviously doesn't require any transforming of coordinates, but it does imply Lorentz invariance, which entails the covariance of the physical parameters under a certain class of transformations.

The answer to the OP is that the physical law describing the half-life of a sub-atomic particle...

I wasn't addressing the initial issue (which was already thoroughly addressed and discarded by universal_101 in his other thread that got locked because it was going around in circles) but only his contention that transformation tools are required to explain the twin paradox, which I did in a way that I thought might make sense to him.

 

[ghwellsjr]

Hi Firstly I don't agree or in fact even understand the OP's point, but I have to mention that the Doppler shift equation is itself derived from and expressing the fundamental transformation isn't it? With classical Doppler it seems to me there would be no age differential, no?

I am not using the Doppler shift equation, if by that you mean the one that calculates the Doppler factor as a function of relative speed. I'm only saying that the approaching and receding Doppler factors are reciprocals for the same relative speed but we aren't concerned with what that relative speed is or how it relates to the Doppler factor. Of course, you can also confirm that this is true based on that Doppler shift equation, but that is immaterial for the analysis that I have given.

There are many ways to derive the equation but that is irrelevant to what I am saying. And yes, the classical Doppler shift equation won't work because it is not relativistic.

 

[Austin0]

Yes there is, you even say it is well known and DaleSpam gave you it mathematically.



No we don't, my point was that the law applies equally well in both the Earth frame and the particle frame. The value of the half-life obtained in the lab is in the particle's rest frame while we usually measure the thickness of the atmosphere in the Earth frame. It is inherent in the question you asked that that those are not the same hence applying the transform is one way to get both to the same frame. However, that isn't the only way. If you want to know the value of the particle half-life in the Earth frame, you must apply the time dilation factor but that can be obtained from many experiments, that of Ives and Stilwell for example, you don't need to use the Lorentz Transforms.



The Lorentz Transforms can be used to convert between the frames to check for consistency but they aren't needed to predict the particle numbers, both length contraction and time dilation can be obtained empirically from experiment as independent laws without using the transforms.

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

 

[Austin0]

I am not using the Doppler shift equation, if by that you mean the one that calculates the Doppler factor as a function of relative speed. I'm only saying that the approaching and receding Doppler factors are reciprocals for the same relative speed but we aren't concerned with what that relative speed is or how it relates to the Doppler factor. Of course, you can also confirm that this is true based on that Doppler shift equation, but that is immaterial for the analysis that I have given.

There are many ways to derive the equation but that is irrelevant to what I am saying. And yes, the classical Doppler shift equation won't work because it is not relativistic.

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?

 

[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

 

[Dale]

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 gave you physical laws for both the decay of unstable particles and the differential aging. Your point is completely refuted. I think that you know it is refuted which is why you have carefully avoided discussing the points I have made.

This thread is heading towards a lock for the same reason as the previous one. You are going around in circles as though you had not already received a complete answer.

 

[Mentz114]

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

Please don't think I'm badgering you, but we need to clear this up.

Muons are heavy unstable leptons that always decay quickly into other particles, whereas radioactive emmission of beta-rays is something else.

We can talk about rates of emission in the beta-ray case, but not decay because beta-particles don't decay.

In the muon case we can talk about decay, but not emission rates.

Did you mean to say

" ... the different number of (beta) particles (counted), or decay (times of muons), depending on the motion of these particles." ?

 

[Dale]

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 which I answered by providing coordinate independent laws of physics.

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).

Please post your reference here. The time dilation of muons was found by Bailey to follow the law I posted, which is compatible with special relativity.

 

[Dale]

the problem vanishes if we conclude the difference in the nuclear decay rates of moving Muons by using some physical law.

\frac{dn}{d\tau}=-\lambda nPoof!

 

[harrylin]

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.

Rejecting everything that you post would be unscientific if some of the things that you post were correct (which may be the case, I did not check). What Menz wrote is standard physics, while what you wrote is new (and wrong) physics.

In particular, the difference in the ages of the Twins after the trip does not depend on their relative velocity during the trip. For example if the one does not stay at home but the two take off at the same speed in opposite directions, turn around and meet again, then their relative velocity was much more; nevertheless their difference in age can be zero.

Each twin appears to age at a certain rate according to physical law, and the difference of these two rates gives you the difference in their ages when they meet again.

Now, to get back at your original question: sure the transformation equations provide us conditions that physical laws must conform with; or inversely, physical laws make that the transformation equations work. And that is already the case with classical (Newtonian) mechanics. Do you have a problem with that?

 

[atyy]

I believe in energy conservation.

Energy is not Lorentz invariant, and particle lifetime is energy dependent.

See Eq 3.16 of https://edit.ethz.ch/itp/education/lectures_hs10/PPPI/PPP1_3.pdf

 

[Nugatory]

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

Of course we do. But we don't need their relative velocity. We calculate the age of the first twin in isolation using only-child math; we calculate the age of the second twin in isolation using only-child math; and now we can compare the ages without ever having used any relative velocities.

 

[Dale]

In particular, the difference in the ages of the Twins after the trip does not depend on their relative velocity during the trip. For example if the one does not stay at home but the two take off at the same speed in opposite directions, turn around and meet again, then their relative velocity was much more; nevertheless their difference in age can be zero.

Excellent point! That is simple and clear once it is pointed out, but I completely missed it.

 

[universal_101]

Please explain exactly what this means.

Alright, here is another detailed try,

First of all, I think we all agree on the relativistic nature of electromagnetism. That is, Lorentz transformation successfully and validly explains the electromagnetic effects like, Doppler effect, Aberration of star light etc. In other words, we don't need any asymmetry, symmetry, or any pattern to undertake the explanation of electromagnetism unlike the Twin Paradox which requires to check symmetry or asymmetry of the relative motion of the Twins.

It can be shortly said as, Electromagnetism follows Principle of Relativity, whereas the Differential ageing of Twins does not, since even the infinitesimal small asymmetry in their motion can change the outcome of the whole experiment ! In other words, it does not follow Principle of relativity.

But even the Twin Paradox is based on the extended view of, the ability of the fast traveling Muons to reach the Earth. Or their ability to suppress their decay rates while in motion w.r.t the lab frame in cyclotrons. (For now we can avoid relativistic increase in mass, which I think has a different term and meaning nowadays)

Therefore, only effect that can be confirmed experimentally for unstable particles is only the change in decay rates due to their motion.

 

[universal_101]

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

Every phenomena even those which are not discovered yet can be explained just by considering a supernatural power i.e. a GOD. But the problem is it is not falsifiable, the same is the problem with using Length contraction, we don't have any direct confirmation of it, but it is assumed to be there in order to explain some relativistic effects.

Whereas, for the electromagnetism it is perfectly fine to use Length contraction, since electromagnetism comes under the Principle of relativity, and of-course the use of length contraction in electromagnetism is abstract and not physical.