Transformation Vs. Physical Law

[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.

 

[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.

 

[universal_101]

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?

EDIT : http://www.sciencedirect.com/science/article/pii/S092765050900084X, how about this one.

 

[harrylin]

http://arxiv.org/abs/0808.3283, there you go.

Sorry I posted at about the same time as you and I referred to your earlier posts 100 and 101. But note that Arxiv cannot generally be used as knowledge base for discussions here, see the rules:
https://www.physicsforums.com/showthread.php?t=414380

EDIT : http://www.sciencedirect.com/science/article/pii/S092765050900084X, how about this one.

That looks better! :-)

 

[Dale]

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.

This is false. That law, alone, is in fact capable of explaining the decay of any large bunch of radioactive particles (i.e. n must be large) in an accelerator.

You must somehow, introduce the gamma factor to calculate the Time Dialtion of moving Muons.

Why must I do that when the law works fine as written?

Sure, if you want then you can rewrite the law in terms of coordinate time for some specific frame, and if that specific frame is inertial then the rewritten law will have a gamma factor in it. But if you do that then you are looking at a rewritten special case of the law as applied to a specific frame, not the general coordinate-independent form of the law itself.

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

I am not a mentor so I cannot lock it.

 

[Dale]

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.

The decay rates of muons was found to agree with the forumla I posted above in the following experiments using a highly relativistic storage ring:

Bailey et al., “Measurements of relativistic time dilation for positive and negative muons in a circular orbit,” Nature 268 (July 28, 1977) pg 301.

Bailey et al., Nuclear Physics B 150 pg 1–79 (1979).

 

[universal_101]

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.

George, I really appreciate your arguments, but even in the second way we end up using the gamma factor.

What I have problem with is, Do we have any way to get the gamma factor from a physical law, instead of the relativistic Doppler which we get from the Lorentz transformation.

That is, the relativistic Doppler is a transformation tool, is it not.

 

[universal_101]

This is false. That law, alone, is in fact capable of explaining the decay of any large bunch of radioactive particles (i.e. n must be large) in an accelerator.

Of-course, the law can explain the decay of Muons in cyclotrons, but to use the same law for lab particles, we must incorporate gamma factor in that law. Because, we are trying to understand the decay rates of both the frames with the same law and then compare them to get the gamma factor.

But if you think, that comparing the decay of Muons in lab and in cyclotrons does not involve the gamma factor. Please post some calculations for the same.

 

[ghwellsjr]

George, I really appreciate your arguments, but even in the second way we end up using the gamma factor.

What I have problem with is, Do we have any way to get the gamma factor from a physical law, instead of the relativistic Doppler which we get from the Lorentz transformation.

That is, the relativistic Doppler is a transformation tool, is it not.

Doppler is something that you observe. You can't avoid it. Just like when you hear the pitch of the siren of an emergency vehicle take a sudden drop as it passes you, the same thing happens with light. It doesn't matter if you have a theory to account for it or not, it's still going to happen. In fact, it's the raw data that we get from making these measurements that a theory has to account for. Special Relativity accounts for it perfectly but the theory doesn't make it happen.

If we could actually travel at relativistic speeds, the difference in clocks would be readily apparent even without any theory and then we would have to develop a theory to explain the facts. Gamma was developed prior to Special Relativity but SR also derives it.

And my point in bringing up gamma was not to show an alternate way of deriving it but merely to show that since we know that gamma is the correct answer based on SR with regard to the simple twin paradox, and the Doppler analysis arrives at the same numerical answer in all cases without resorting to SR, it shows that we don't need transformation tools to solve the age difference in the simple twin paradox scenario. So we are not using the gamma factor, we're just showing that we get the same answer as we would if we did use the gamma factor.

 

[Dale]

Of-course, the law can explain the decay of Muons in cyclotrons, but to use the same law for lab particles, we must incorporate gamma factor in that law.

Nonsense. Where precisely would you put gamma in? Wherever you would add it to the formula given it would give you wrong answers. The formula is correct as written for any reference frame (inertial or non-inertial), in any spacetime (flat or curved), and for any particle worldline (stationary or moving).

But if you think, that comparing the decay of Muons in lab and in cyclotrons does not involve the gamma factor. Please post some calculations for the same.

I can certainly do exactly that, but it will have to be later in the day. In the meantime, please identify precisely where in that formula you think gamma is missing so that I can describe the errors that you would get by inserting it there.

 

[Samshorn]

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.

For any standard system of inertial coordinates x,y,z,t, consider a burst of muons moving from the location x1,y1,z1 at the time t1 to the incrementally nearby location x2,y2,z2 at the time t2. If there are n muons at the first location, how many of them will have decayed by the time the burst reaches the second location?

For convenience, let dx denote the value of x2-x1, and so on for the other coordinates, and let dn denote the incremental change in the number of muons. The physical law states that

dn = -lambda*n*sqrt[dt^2 - (dx^2 - dy^2 -dz^2)/c^2]

The value of dn for that incremental segment must be invariant, i.e., independent of the choice of inertial coordinate system, because the number of muons at any given event obviously cannot depend on our choice of coordinate system. However, suppose we divide both sides of that equation by dt. Then the left hand quantity will be dn/dt, which is NOT an invariant quantity, because it DOES depend on our choice of the t coordinate. Therefore, when we divide by dt, both sides of the equation become coordinate dependent quantities. The right side becomes -lambda*n*(1/gamma). Hence the derivative of n with respect to t depends on gamma, which depends on v, which depends on the choice of coordinate systems, but this shouldn't surprise you, because the thing we are computing in that case is dn/dt, which is a coordinate dependent quantity.

This bothers you because you want t and dt to be invariants, as they would be if standard inertial coordinate systems were related by Galilean transformations. But if that were the case, energy would not have inertia, and E would not equal mc^2, and we would be living in a very different universe.

 

[GeorgeDishman]

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/Michels...ial_relativity

Every phenomena even those which are not discovered yet can be explained just by considering a supernatural power i.e. a GOD.

I didn't mention "God" or anything like that, I'm atheist. In fact I wasn't even addressing your question, Austin0 asked for an experiment which showed length contraction and I gave him a well-known historical example.

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,

The above experiment uses light to measure the length of one leg of the interferometer versus the other just like radar, it is as direct a confirmation of the phenomenon as can be obtained.

but it is assumed to be there in order to explain some relativistic effects.

As I said above, length contraction was identified in 1887, relativity wasn't published until 1905 so your suggestion is blatently erroneous.

Whereas, for the electromagnetism it is perfectly fine to use Length contraction ...

If you accept it is "perfectly fine" to use it in one case, it is necessary to use it in all similar cases, either it is a law or it isn't.

While we are talking, let me go back to your original question and ask you for some information so that I can better understand what you mean by "physical law". Suppose two friends walk over a flat salt lake, one goes directly from town A to town C while the other detours via town B on the way. They both have the same steady stride length but the guy who makes the journey directly takes fewer steps that his friend who takes the detour. The question is what "physical law" do you think explains that difference?

 

[russ_watters]

Universal101, you are using an incorrect formulation of the Principle of Relativity based on an incorrect belief about reality to try to create a self-reinforcing challenge to SR. The recursiveness of your argument is both silly and maddening:

You say that because time dilation is frame dependent, the transformation is part of the "physical law", therefore time dilation is a violation of the PoR.

Nevermind the fact that time dilation arises as a necessary consequence of the PoR; there are plenty of frame dependent concepts in physics. Anything having to do with motion has a frame dependency. The fact that (for example) you can transform velocity into another frame and arrive at a different value for kinetic energy of a moving object does not imply a violation of the PoR for kinetic energy. Why? Because the PoR requires you to work in one frame at a time and therefore mandates doing transformations to ensure all calculations are based in that chosen frame. Jumping frames to attempt to create a contradiction (what you are doing) is the violation of the PoR, not the frame dependency of (for example) a velocity calculation.

Put another way: The fact that you have to transform from one frame to another to make accurate calculations of velocity dependent phenomena (energy, momentum, time dilation, air pressure, etc.) isn't a violation of the PoR, it is the whole point of the PoR!

 

[ghwellsjr]

In fact I wasn't even addressing your question, Austin0 asked for an experiment which showed length contraction and I gave him a well-known historical example.

Universal_101 may be confusing his similar request in post #72:

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.

and which I gave him the same answer that you gave Austin0 in post #87:

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

 

[GeorgeDishman]

Universal_101 may be confusing his similar request in post #72:

and which I gave him the same answer that you gave Austin0 in post #87:

Ah, indeed, I had missed your mention of it. There seemed to be separate conversations going on as Austin0's question seemed a straightforward request for a pointer.

Anyway, hopefully Universal_101 will answer the question I asked which will make it easier to respond meaningfully to his question.

 

[zonde]

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.

This physical law is quite simple. Zigzag trajectory is longer than forth and back trajectory (with forth and back trajectory being projection of zigzag trajectory). You can use Pythagoras' theorem and derive gamma factor as length difference for two trajectories.

Some additional assumptions are required however.
Let's assume that say muons have some dimensional structure and decay rate of muons depend on their structure evolution at the speed determined by communication speed within that structure. Then decay rate of muons in motion will decrease by gamma factor as compared to muons at rest.

The only question left then is why muon in motion has to have the same dimensions in direction orthogonal to direction of motion as stationary muon. There is no answer to that question but we can simply assume that matter "likes" PoR and PoR is fulfilled when these dimension are equal.

 

[harrylin]

Universal, did I in post #95 - and I see that others gave similar answers - address your point or not? If not, why not?

Here's another way that this physical law about "time" was explained as based on one of the first convincing experiments (and I paraphrase to express the same in a more straightforward way) :

If a light beam is split into two beams that are brought together after traversing paths of different lengths, the resulting interference pattern will not depend on the velocity of the apparatus because the frequency of the light depends on the velocity as required by relativity.
- http://en.wikipedia.org/wiki/Kennedy-Thorndike_experiment

In other words (your words!), one may hold the opinion that this phenomenon is governed by a physical law and not by a transformation between points of view. This physical law is a necessary requirement for the transformation equations to work.

Does that help?