Transformation Vs. Physical Law

Nugatory

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

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

Nugatory

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

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

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

atyy

Do you believe in energy?

Mentz114

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

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

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

I believe in energy conservation.

Mentz114

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

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

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

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

'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

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

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.