Transformation Vs. Physical Law

[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.

$$\frac{dn}{d\tau}=-\lambda n$$Poof!

 

[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.

 

[universal_101]

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.

I don't understand how did you solved the problem, the radioactivity law that you posted, alone is incapable to explain the time dilation of Muons in the cyclotrons. You must somehow, introduce the gamma factor to calculate the Time Dialtion of moving Muons.

Now, when and where you would introduce this gamma factor in the radioactivity law, will be the point of my question.

And for the locking part, I think this thread has lost it's objective already, so go for it.

 

[universal_101]

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." ?

I apologize for the confusion regarding beta rays, I think I used the term beta at the wrong place.

I was trying to say that recently beta decays(involving weak nuclear forces) are found to depend on the Earth-Sun distance, and the decay of Muons are also mediated by the weak nuclear force.

 

[harrylin]

universal, I'm sorry but I can't make any sense of your last posts. Can you refer to any textbook or publications on which you (think to) base your ideas?

PS I referred to posts 100 and 101 - and with "publications" I don't mean Arxiv (see the rules).

 

[universal_101]

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.

Actually, the reference is for the variation in the decay rates of beta decays, which involve the weak nuclear forces, and it is this same force which mediates the decay of Muons. So, it is the extended view that, Muons too could depend on the Earth-Sun distance.

And the dependence of the nuclear decay rates(beta) is well-known nowadays. There are plenty preprints on arxiv.

 

[ghwellsjr]

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.

In the specific example of the Twin Paradox which we are discussing, where one twin remains inertial and the other one travels in both directions at the same speed, I'm not saying that you cannot use that speed to calculate the difference in aging, you can. And you can generalize the question to show that the age difference is a function of just the value of gamma which can be calculated from the value of the relative speed.

But you don't have to analyze it that way. You can also generalize it using just the Doppler for the outbound portion of the trip, whatever that happens to be and the knowledge that it will be the reciprocal on the inbound portion of the trip, and calculate the same answer using the process I described above. It's not that one way is wrong and the other way is right, they're both right. But the first way requires the establishment of a frame with coordinate times defined according to Einstein's synchronization process whereas the second way does not have that requirement. I'm only trying to get you to see that the second way does not require any transformation tools as you claimed in posts #34 and #45.

If you don't understand my argument, please ask specific questions, don't just disregard what I am saying.