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## Transformation Vs. Physical Law

 Agreed , and I'm also not suggesting that the number of particles should depend on transformation.
Good, because it is invariant.

 What I'm suggesting is, it must be governed by a physical law instead of a transformation that which predicts how many particles should reach a particular destination.
The transformation does not predict how many many particles should reach a particular destination. The transformation changes the observers coordinates.

There is a physical law that decides the number, which law happens to be invariant under transformation .

 But at the first place, To calculate the number of unstable particles in any frame, we use the Lorentz transformation, don't we ?
Not necessarily. We can use the rest frame of the particle. We only use the LT when we want to see what happens in a different frame.

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 Quote by universal_101 Thanks for the view, 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.
No contradiction that I see... The transform describes certain aspects of physical law, namely how observations of time and space differ between observers in relative motion. It's very convenient to describe these differences in terms of coordinate transforms because we generally state our observations of time and space in terms of coordinate systems.

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 Quote by universal_101 Since, a transformation cannot keep the numbers invariant if this phenomena were to be actually explained by the transformation of observers. But as we all know, the transformation around this phenomena does keep the numbers invariant must imply that this phenomena is governed by a physical law and not by the transformation.
The transformation tells how different observers view the invariant event--the death of a character in the play, or the arrival of a given number of unstable particles at a given detector. So just as we expect the "transformation" from one audience viewpoint to another to keep invariant the death of the character in the play (while changing observer-dependent details such as the exact angle at which the character's face is viewed), we expect the transformation from one observer's viewpoint to another to keep invariant the number of unstable particles arriving at the detector (while changing observer-dependent details such as the time, according to that observer, that the particles take to travel from source to detector, or the distance between the two). As of course it does.

So your own analogy perfectly supports the facts of the Lorentz transformation; yet you talk as if you are somehow pointing out a problem. What problem?

 Quote by Mentz114 I have to say I admire your gall. You don't understand this stuff, which has been around for decades and examined by the best minds of our time - and still you think you've found a paradox.
If something is there for decades and so many people admire it, does not make that something correct or does it. I don't want to include history, which says otherwise.

But what I would really like to mention is that, to refute a theory we need just one experiment where as to give a theory the stature of fundamental fact there is NO limit on the Experiments.

And No, I'm not looking for paradoxes, instead I'm looking for solutions.

Thanks

 Quote by universal_101 But at the first place, To calculate the number of unstable particles in any frame, we use the Lorentz transformation, don't we ?
 Quote by Mentz114 Not necessarily. We can use the rest frame of the particle. We only use the LT when we want to see what happens in a different frame.
I don't think even using the rest frame of the particle, you can calculate the number of particles reaching Earth without using any kind of transformation of any property what so ever.

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 Quote by universal_101 If something is there for decades and so many people admire it, does not make that something correct or does it. I don't want to include history, which says otherwise.
Which something are you talking about ? Special relativity ?

 But what I would really like to mention is that, to refute a theory we need just one experiment where as to give a theory the stature of fundamental fact there is NO limit on the Experiments.
Sure. What experimental evidence have got ?

 And No, I'm not looking for paradoxes, instead I'm looking for solutions.

 ... instead I'm looking for solutions.
Solutions to what problem ? The fact that physical laws must be Lorentz invariant is not a problem.

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 Quote by universal_101 I don't think even using the rest frame of the particle, you can calculate the number of particles reaching Earth without using any kind of transformation of any property what so ever.
If you know the time in the rest frame of the particle, what could you possibly need to transform? That's the only variable in the formula DaleSpam posted (everything else is a physical constant or a known initial condition).

 Quote by PeterDonis The transformation tells how different observers view the invariant event--the death of a character in the play, or the arrival of a given number of unstable particles at a given detector. So just as we expect the "transformation" from one audience viewpoint to another to keep invariant the death of the character in the play (while changing observer-dependent details such as the exact angle at which the character's face is viewed), we expect the transformation from one observer's viewpoint to another to keep invariant the number of unstable particles arriving at the detector (while changing observer-dependent details such as the time, according to that observer, that the particles take to travel from source to detector, or the distance between the two). As of course it does. So your own analogy perfectly supports the facts of the Lorentz transformation; yet you talk as if you are somehow pointing out a problem. What problem?
The problem is, it is the audience viewpoint of one special position in audience, which is utilized in determining how many characters will die in a certain play.

That is, the number of particles reaching Earth are determined by the tools of transformation. This is a big problem, at-least to my understanding.

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 Quote by universal_101 Does this law explain or account for the number of particles reaching the Earth, without using any transformation.
Yes.

Since it is a law of physics and since all laws of physics are diffeomorphism invariant, we know that it is invariant under the Lorentz transform. But no transform is required in order to use it.

 Quote by PeterDonis If you know the time in the rest frame of the particle, what could you possibly need to transform? That's the only variable in the formula DaleSpam posted (everything else is a physical constant or a known initial condition).
I think you left the Length part, since in order to calculate how many particles reached, we must know how much they traveled.

And this length is to be transformed.

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 Quote by universal_101 I don't think even using the rest frame of the particle, you can calculate the number of particles reaching Earth without using any kind of transformation of any property what so ever.
If you do the calculation in the rest frame of the particle, only the coordinates of that frame are used. No transformation is used. As others have said above.

 I think you left the Length part, since in order to calculate how many particles reached, we must know how much they traveled.
Yes, measured in rest frame coordinates.

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 Quote by universal_101 I think you left the Length part, since in order to calculate how many particles reached, we must know how much they traveled. And this length is to be transformed.
No, it isn't. Remember we're talking about the rest frame of the particle: in that frame, the particles are at rest. So there is no "length" involved--only the particles' travel time (or, if you want to be really precise, since the particles are not moving but the source and detector are, in this frame: the time between when the source is co-located with the particles and when the detector is co-located with the particles, by the particles' clock).

Look at the formula DaleSpam posted, which explicitly uses the time in the particles' rest frame. Do you see any length in there?

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 Quote by universal_101 Does this law explain or account for the number of particles reaching the Earth, without using any transformation.
Yes.
I was tempted to add "of course", but obviously it's not obvious or you wouldn't be asking.

So here goes.... You find yourself riding a relativistic particle down from the top of the atmosphere. You see the surface of the earth rushing towards you at speed v=.999c, from a distance of 1 light-usec away. Note that neither this distance nor the speed came from any sort of transformation - you measured them directly.

Now, what is the probability that your relativistic but unstable steed will hit (be hit by) the surface of the earth before it decays? Calculate the time the particle needs to live, by dividing the distance by the velocity, and plug it and lambda (the half-life of the particle expressed in terms of the particle's proper time, which is the time that you are measuring - see, still no transforms) into the formula... And out pops your answer.

 Quote by PeterDonis No, it isn't. Remember we're talking about the rest frame of the particle: in that frame, the particles are at rest. So there is no "length" involved--only the particles' travel time (or, if you want to be really precise, since the particles are not moving but the source and detector are, in this frame: the time between when the source is co-located with the particles and when the detector is co-located with the particles, by the particles' clock). Look at the formula DaleSpam posted, which explicitly uses the time in the particles' rest frame. Do you see any length in there?
I thought it would be simple to explain the necessity of the use of the transformation even in the rest frame of the particles.

In order to pinpoint, how does one calculate when was the particle at source and when at the detector? The simple equation would have been, contracting the distance between the source and detector and dividing it by the relative velocity.

But you never mentioned how are you going to calculate when the particle was at source and how much time it took to reach the detector.

 Quote by Nugatory Yes. I was tempted to add "of course", but obviously it's not obvious or you wouldn't be asking. So here goes.... You find yourself riding a relativistic particle down from the top of the atmosphere. You see the surface of the earth rushing towards you at speed v=.999c, from a distance of 1 light-usec away. Note that neither this distance nor the speed came from any sort of transformation - you measured them directly. Now, what is the probability that your relativistic but unstable steed will hit (be hit by) the surface of the earth before it decays? Calculate the time the particle needs to live, by dividing the distance by the velocity, and plug it and lambda (the half-life of the particle expressed in terms of the particle's proper time, which is the time that you are measuring - see, still no transforms) into the formula... And out pops your answer.
You are using the increased half-life time of the particle, which is a transformation tool. Remember you would either use Time Dilation of half-life or the length contraction of the distance which the particle needs to travel. And these are not transformations but tools of it.

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 Quote by universal_101 You are using the increased half-life time of the particle
Where, exactly? $\lambda$ is the usual non-increased half life. It is not a function of speed.

 Quote by DaleSpam Where, exactly? $\lambda$ is the usual non-increased half life. It is not a function of speed.
So that everyone can see it, does the differential ageing of the twins after the trip can be explained without using transformation tools ?

No it cannot, the same applies to the number of particles reaching Earth. That is, No matter what, in the end the ratio of the number of particles reaching Earth to the number of particles survived in the lab, is always a function of the speed of the particles which reach in higher quantity.

What you guys are missing is the point that, we need to use that same law for lab particles also.

Thanks