Transformation Vs. Physical Law

[Austin0]

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.

Hi I agree completely with this statement and it is the perfect example as it can't get any more physical than that.

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.

But I think this might be a bit ambiguous. yes in this case they have instantaneous relative velocity throughout the trip but the end result depends on total spacetime distance traveled not on the relation during any segment.
I know you know this and that was your point but it could appear you were suggesting that relative velocity wasn't a factor in determining the aging [to someone who didn't understand world lines]
To determine the difference in rates requires relative velocities.wrt some frame.yes??

 

[Nugatory]

or even the simple following basic mathematics principle,
which is A+A = 2A, that is, suggesting A+A is not same as 2A, because he never uses multiplication when he uses addition and vice-versa, is entirely incorrect.

Is this thread a Socratic dialog with us as the students at the knee of a master Sophist? Or have we met the King of Trolls and fallen into his snares? Either way, it's an amazing thing to read from the beginning.

 

[universal_101]

Argument of what? Apparently you missed my post #95 (as well as #120). Already in classical mechanics are physical effects associated with the transformations*; thus your denial is simply wrong. Physical laws result in the validity of certain transformation equations between reference systems, so that they are related. If you know the effect (the transformation equations) then you can draw some conclusions about physical laws and causes.

I never denied the association of the physical effects with the transformations, I'm questioning them.

*PS I had in mind Newton's law but did not elaborate, however I see that now there is a fresh thread on that (simple explanation in post #10):
https://www.physicsforums.com/showthread.php?t=610258
Do you really claim that this is wrong?

No, We all know the Newton's law is invariant under Galelien transformation.

It's about both the physical laws and the resulting transformation equations (emphasis mine):

"Poincaré has objected to the existing theory of electric and optical phenomena in moving bodies that [..] the introduction of a new hypothesis [will be] required [..] each time new facts [are] brought to light. Surely, this course of inventing special hypothesis for each new experimental result is somewhat artificial. It would be more satisfactory, if it were possible to show, by means of certain fundamental assumptions [..] that many electromagnetic actions are entirely independent of the motion of the system. [..] I believe now to be able to treat the subject with a better result. The only restriction as regards the velocity will be that it be smaller than that of light."
- Lorentz 1904

"It is known that Maxwell's electrodynamics—as usually understood at the present time—when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena. [..] [SR is] a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell's theory for stationary bodies."
- Einstein 1905

Seems like you are suggesting that I'm just as incorrect as the Poincare, well may be I'm incorrect but even then Lorentz and Einstein are only partially verified experimentally, since we don't have any experiment confirming Length contraction as a physical effect. Does that trouble you even the slightest ? or do I need to ignore the Length contraction as a physical effect.

 

[Austin0]

which is A+A = 2A, that is, suggesting A+A is not same as 2A, because he never uses multiplication when he uses addition and vice-versa, is entirely incorrect.

Physics implies causality principle, i.e. If we have an effect then we must have a cause, atleast in the domain of classical physics.

Therefore, the effect(Time Dilation of unstable particles) must have a cause(where it comes from). Since, atleast you are accepting that we do have to involve gamma factor in order to understand these effects. How do you understand, the use of this gamma factor which is a part of the transformations, to produce the effects is question.

As I explained, you simply misunderstood what I was trying to ask, and not for introducing personal war of words, but it does not interests me a bit, how easily you make your perspective of other people, just by reading posts from a forum.

Where does gravity come from? we can describe the effects. Predict accurately how particles react in its presence but neither Newton or GR tells us where it comes from.
Well time dilation comes from the same place.

 

[universal_101]

Where does gravity come from? we can describe the effects. Predict accurately how particles react in its presence but neither Newton or GR tells us where it comes from.
Well time dilation comes from the same place.

You are confusing Time Dilation as an assumption, it is not. Assumption is electrodynamics(interaction of charges) just like gravity(interaction of masses), where we assumed certain things in order to satisfy experiments and observations.

Whereas, Time Dilation falls under the banner of electromagnetic phenomenon. That is, it is in no sense an assumption but an effect of there being an assumption(i.e. electromagnetism).

Your argument would be valid if I would have been questioning the existence of charges or electromagnetism.

So, if you think that Time Dilation is not an effect of relative motion under the laws of electromagnetism(Maxwell's Equations), but an entire theory of it's own, then only your argument is valid.

 

[Austin0]

QUOTE=Austin0;3940936]Thank you for your explication but as I fully understood the meaning of the interval and the metric I am afraid it completely missed the point.
That point being the meaning of the word invariant. In this context it simply means constant,unchanging, across all inertial coordinate systems
This necessarily implies the existence of other frames.
Would you disagree?

It does not apply to other coordinate systems within a single frame. I.e. changing from orthogonal to polar coordinates for eg.

It does not apply to local measurements as they apply within the frame.

It takes local coordinate measurements and outputs a value that is meaningful and constant in all other frames.

As that output value is related to the input values by the gamma factor it would appear it was a de facto transformation, semantic quibbles notwithstanding.
Yes[/QUOTE]

Yes, I would disagree. The length of the hypotenuse of a triangle is, by Pythagorus, equal to √(A² + B²), where A is the length of one leg, and B is the length of the other leg. Do you think that that definition implies the existence of other frames? The invariant interval in SR, τ = √((ct)² - x²) is a geometric relationship, just like the length of the hypotenuse of a right triangle. It doesn't have anything to do with "frames". The metric doesn't have anything to do with frames. Curved surfaces have associated metrics, and that doesn't have anything to do with frames.

Well you completely disregarded the meaning of the word invariant.

τ = √((ct)² - x²) this expression itself implicitly assumes and requires an orthogonal coordinate structure.

You have two points floating in space in front of you.

On this alone how do you define or express a metric? You can not even assign a distance of any kind without a ruler. I.e. a one dimensional coordinate system.

The thing that is fundamental about the metric is the signiture and that falls out of the gamma function. Out of the intrinsic structure of the world.It has nothing to do with historical precedent.
Without this fundamental aspect of reality there would be no Minkowski metric or gamma function and we would be living in a Galilean/Newtonian world.


gamma + Cartesian 4 D coordinates ===> Minkowski metric
gamma + Galilean transforms ====> Lorentz transforms
How do you possibly imagine anyone arriving at the metric without the knowledge of the gamma aspect of reality?

Yes, it certainly does. In cartesian coordinates, the metric tensor is defined by
(in 2-D spacetime):

g_tt = 1
g_xx = -1/c²
g_yy = -1/c²

(all other components are zero)

In polar coordinates, we have:
g_tt = 1
g_rr = -1/c²
g_θθ = -r²/c²

So the invariant interval is

ds² = dt² - dr²/c² - r²dθ²/c²

You have misunderstood.
Of course within a frame every possible coordinate system will have a relevant version of the Minkoiwski metric. We are in the middle of a discussion regarding the -version for cylindrical coordinates right now. So it should be obvious that this is not what I meant.
Within a frame transformation of events between different coordinate systems does not invlove the Minkowski metric.
It only comes into play when regarding things moving relative to the frame. I.e. different coordinate frames.

Within a Minkowski 2 D chart :
Regarding the rest frame the geometry is purely Euclidean with the Euclidean metric in a Cartesian chart. Yes? the normal Pythagorean relationships apply, yes?

It is only regarding the moving frame that the Minkowski metric with it's specific form of the Pythagorean operation applies ,,,,Yes?
Applying that metric returns the proper time value for a segment of the moving particles world line.
That time is related to the time of the rest frame described by the vertical interval of the triangle by the gamma factor Yes?

So it accomplished a geometric gamma transformation or do you disagree?

 

[universal_101]

gamma + Cartesian 4 D coordinates ===> Minkowski metric
gamma + Galilean transforms ====> Lorentz transforms
How do you possibly imagine anyone arriving at the metric without the knowledge of the gamma aspect of reality?

Thanks Austin, And i think this nails it.

That is, we don't need to present the metric or transforms as the physical aspects behind the physical relativistic effects.

In other words, Minkowski metric or spacetime should come under electromagnetism or electromagnetic effects of relative motion. But not as a physical law in themselves. And this is what some people are trying to suggest(by saying we don't need relative velocity to determine differential ageing), that spacetime itself is kind of a physical law.

 

[harrylin]

Yes, I would disagree. The length of the hypotenuse of a triangle is, by Pythagorus, equal to √(A² + B²), where A is the length of one leg, and B is the length of the other leg. Do you think that that definition implies the existence of other frames? The invariant interval in SR, τ = √((ct)² - x²) is a geometric relationship, just like the length of the hypotenuse of a right triangle. It doesn't have anything to do with "frames". The metric doesn't have anything to do with frames. Curved surfaces have associated metrics, and that doesn't have anything to do with frames.

The "frames" of SR are not things that necessarily "exist"; instead they are imaginary entities that represent differing measures of lengths and times or frequencies by means of really existing tools ("rods" and "clocks"). Obviously both the invariant space-time interval and the Lorentz transformation relate to the same "x" and "t"; as a matter of fact, Poincare introduced that invariant interval in the context of the Lorentz group in his 1906 paper (see my citation in post #126).

 

[harrylin]

[..] it could appear you were suggesting that relative velocity wasn't a factor in determining the aging [to someone who didn't understand world lines]
To determine the difference in rates requires relative velocities.wrt some frame.yes??

Exactly. The main point of modern versions of the twin "paradox" is to explain to students that when using SR the relative velocity (in terms of varying distance/time) between particles is not what determines the outcome; instead one has to relate the velocities to inertial reference systems (or to at least one inertial system that may be freely chosen).

 

[harrylin]

I never denied the association of the physical effects with the transformations, I'm questioning them. [..] We all know the Newton's law is invariant under Galelien transformation.

Then the issue is not really in the headline of your thread, "Transformation Vs. Physical Law"?

Seems like you are suggesting that I'm just as incorrect as the Poincare,

?? I see nowhere where I suggested that Poincare was incorrect. What made you think so? Lorentz, Einstein and likely everyone else agreed with his criticism. Some people even consider him to be the real inventor of SR (see for example http://en.wikipedia.org/wiki/Henri_Poincaré#Assessments for an entry point to the debate).

well may be I'm incorrect but even then Lorentz and Einstein are only partially verified experimentally, since we don't have any experiment confirming Length contraction as a physical effect. Does that trouble you even the slightest ? or do I need to ignore the Length contraction as a physical effect.

Maybe you are incorrect about what? You presented a point of view with which half of the people here seem to agree as well as a few erroneous claims that were debunked without comment by you (apparently you don't understand your errors). It doesn't trouble me much if a theoretical effect is too small to be directly measured with current technology (I already referred you to the first indirect experiment). That gives some slack for possible alternative theories, but very little.
Do you think that Newton should have been troubled by the fact that he could not test his theory to very high precision, so that he could not detect its flaws as we can nowadays? Most people are happy to have a better theory than before, and that works rather well.

 

[universal_101]

Then the issue is not really in the headline of your thread, "Transformation Vs. Physical Law"?

Well the headline transformation is Lorentz and not Galelien. And it makes me doubt how much of my point of view, or my problem, do you understand.

?? I see nowhere where I suggested that Poincare was incorrect. What made you think so? Lorentz, Einstein and likely everyone else agreed with his criticism. Some people even consider him to be the real inventor of SR (see for example http://en.wikipedia.org/wiki/Henri_Poincaré#Assessments for an entry point to the debate).

Seems like I misinterpreted your post there, but then what was your intent.

Maybe you are incorrect about what? You presented a point of view with which half of the people here seem to agree as well as a few erroneous claims that were debunked without comment by you (apparently you don't understand your errors). It doesn't trouble me much if a theoretical effect is too small to be directly measured with current technology (I already referred you to the first indirect experiment). That gives some slack for possible alternative theories, but very little.

As I stated several times, Length contraction must be a physical effect if Time Dilation of Muons were to be explained using Minkowski spacetime, if you disagree please say yes or no.

And No, any indirect experiment will not do, for the same reason. But when you say " a small theoretical effect" , it makes me question, if we can easily measure the Time Dilation and increased mass or relativistic energy, then how come Length contraction is a small effect to detect.

And I don't want to talk about alternate theories, but would certainly like to know, how can one understand all the effects that are present and absent in electrodynamics.

Do you think that Newton should have been troubled by the fact that he could not test his theory to very high precision, so that he could not detect its flaws as we can nowadays? Most people are happy to have a better theory than before, and that works rather well.

I think Yes, Newton should have been troubled if his equations would have been suggesting the presence of an effect which he was unable to confirm experimentally or observations(for more than 100 Years). But since there was No problem of that sort, it all went great.

 

[harrylin]

Well the headline transformation is Lorentz and not Galelien. And it makes me doubt how much of my point of view, or my problem, do you understand.

That's perhaps the problem: your title is, as I stated "Re: Transformation Vs. Physical Law" and not as you state, "Lorentz and not Galelien" - as you can see when you look at the top of this page?!

Seems like I misinterpreted your post there, but then what was your intent.

I showed you that your claim that "Special relativity is not about the electromagnetism but it's transformation" was erroneous, by proving that, as I wrote, "It's about both the physical laws and the resulting transformation equations".

As I stated several times, Length contraction must be a physical effect if Time Dilation of Muons were to be explained using Minkowski spacetime, if you disagree please say yes or no.

Yes and I even gave you a link to very strong indirect evidence for length contraction. Surely you know the evidence for clock slowdown. If you disagree, please tell what theory explains the Kennedy Thorndike experiment with time dilation but without length contraction.

And No, any indirect experiment will not do, for the same reason.

What reason? Any indirect experiment will do for the reason that I just gave.

But when you say " a small theoretical effect" , it makes me question, if we can easily measure the Time Dilation and increased mass or relativistic energy, then how come Length contraction is a small effect to detect.

Plug in the numbers and you find out yourself. In addition, clocks can be made very stable and they accumulate time and the dynamic mass of small particles can easily be detected in particle experiments, but how would you detect their length? And as all moving lengths measurements are somewhat indirect, what kind of experiment would you consider sufficiently direct? Anyway, a theory is appreciated for its predictions that do have practical use, and not for predictions that don't have practical use.

[..] I think Yes, Newton should have been troubled if his equations would have been suggesting the presence of an effect which he was unable to confirm experimentally or observations(for more than 100 Years). But since there was No problem of that sort, it all went great.

That's not what I meant. Newton made assumptions which we now know to be slightly wrong, as they are only accurate at low speeds while he assumed that it was valid for all speeds. Should he have been troubled by the fact that he could not fully verify his theory?

 

[GeorgeDishman]

As I stated several times, Length contraction must be a physical effect if Time Dilation of Muons were to be explained using Minkowski spacetime, if you disagree please say yes or no.

You haven't made clear how you think "physical effect" differs from any other kind of effect, what exactly do you mean by that phrase?

And No, any indirect experiment will not do, for the same reason. But when you say " a small theoretical effect" , it makes me question, if we can easily measure the Time Dilation and increased mass or relativistic energy, then how come Length contraction is a small effect to detect.

They are all small effects because usually speeds are small compared to the speed of light but all can be measured. As more than one person has said before, length contraction is directly measured by the Michelson Morley experiment.

And I don't want to talk about alternate theories, but would certainly like to know, how can one understand all the effects that are present and absent in electrodynamics.

They can all be understood as geometric effects in Minkowski spacetime but it is not clear if you include those in your term "physical effects".

I asked before but you never replied, if one person walks directly from A to C while another goes via B and they have the same stride length, they will take a different number of strides. What is your understanding of that physical effect, or do you not consider the reason to be "physical"?

 

[stevendaryl]

Of course within a frame every possible coordinate system will have a relevant version of the Minkoiwski metric. We are in the middle of a discussion regarding the -version for cylindrical coordinates right now. So it should be obvious that this is not what I meant.
Within a frame transformation of events between different coordinate systems does not invlove the Minkowski metric.

That's not correct. Fundamentally, a metric tensor g(A,B) is a function that takes two vectors A and B and returns a real number, the "dot-product" of A and B. This meaning does not in any way depend on frames, or transformations. The metric determines the length of a vector via:

length(A) = √g(A,A)

If you have two neighboring events e₁ and e₂, then there is an associated vector, the spacetime separation between the events dX. Then the invariant distance between the events is given by:

ds = √|g(dX,dX)|

The meaning of the invariant interval has nothing to do with frames, or coordinate systems, or transformations. It's a geometric quantity, like the length of a line segment. As a matter of fact, in the specific case where e₁ and e₂ take place at the same time in some frame F, ds is equal to the distance between those events, as measured in that frame.

 

[universal_101]

You haven't made clear how you think "physical effect" differs from any other kind of effect, what exactly do you mean by that phrase?

A Physical effect is that which can be measured independently, that is the to observe the effect we don't need to include any assumptions or the indirect ways, which is done in the MMX experiment and it's extended version, the KT experiment.

They are all small effects because usually speeds are small compared to the speed of light but all can be measured. As more than one person has said before, length contraction is directly measured by the Michelson Morley experiment.

No, MMX does not prove/verify anything other than the "Non-Existence of aether". Any thing else that you say it proves is just the basis of the theory(SR) in order to understand the Experiment. That is, length contraction in MMX is part of the theory itself and not the proof of it.

They can all be understood as geometric effects in Minkowski spacetime but it is not clear if you include those in your term "physical effects".

If you reread the first few pages of the thread then I think, it would be clear that I'm questioning the use of transformation to explain Time Dilation of Muons, which is a physical effect.

I asked before but you never replied, if one person walks directly from A to C while another goes via B and they have the same stride length, they will take a different number of strides. What is your understanding of that physical effect, or do you not consider the reason to be "physical"?

As long as the difference in the number of strides or the path can be measured independently of everything else, it is a physical effect.

 

[stevendaryl]

If you reread the first few pages of the thread then I think, it would be clear that I'm questioning the use of transformation to explain Time Dilation of Muons, which is a physical effect.

This discussion has gone on for a long time, so I don't think there is much hope that anything I could say will clear things up, if they haven't been cleared up already. But I disagree with your way of putting things.

The physical effect is that in the frame of the muons, the number of muons left after T seconds is given by 2^-T/τ, where τ is the half-life of the muon.

Lorentz transformations come into play because you want to calculate T: how many seconds have elapsed in the frame of the muons? If you know that the muon went from x₁ at time t₁ to x₂ at time t₂, then you compute T via:

T = √(δt² - 1/c² δx²)

where δx = x₂ - x₁, and δt = t₂ - t₁.

This is a geometric computation, analogous to the case in Euclidean geometry: A line segment runs from the point (x₁, y₁) to the point (x₂, y₂). You calculate the length L via:

L = √(δx² + ² δy²)
where δx = x₂ - x₁, and δy = y₂ - y₁.

 

[harrylin]

A Physical effect is that which can be measured independently, that is the to observe the effect we don't need to include any assumptions or the indirect ways, which is done in the MMX experiment and it's extended version, the KT experiment. [..]

Again: what kind of moving length measurement would satisfy your desire?

If you reread the first few pages of the thread then I think, it would be clear that I'm questioning the use of transformation to explain Time Dilation of Muons, which is a physical effect. [..]

At least we solved that issue - you don't need to think that transformations "explain" physical effects.

 

[universal_101]

Again: what kind of moving length measurement would satisfy your desire?

I don't need to be satisfied, but it is very easy to see that we don't have any direct confirmation on Length contraction, as I posted earlier.
"No, MMX does not prove/verify anything other than the "Non-Existence of aether". Any thing else that you say it proves is just the basis of the theory(SR) in order to understand the Experiment. That is, length contraction in MMX is part of the theory itself and not the proof of it."

At least we solved that issue - you don't need to think that transformations "explain" physical effects.

No, it is not solved, and by the way what do you think causes the relativistic physical effects, spacetime, metrics (if not transformations) !?

 

[zonde]

A Physical effect is that which can be measured independently, that is the to observe the effect we don't need to include any assumptions or the indirect ways,

Measurements always relay on some kind of interpretation. It can only be more primitive or more advanced but it is always there.

So are you sure that the answer you want to get is possible at all?


Speaking about physical effects. When we accelerate body or particle or whatever our experience says that it happens in single particular way (we assume certain level of idealisation here of course, we do not talk about car crash tests). But if we ask why acceleration of body happens in this particular way we have to allow other hypothetical ways how this could happen.

So can you say what other hypothetical ways for (physical) transformation of body undergoing acceleration this physical law should exclude?

 

[harrylin]

[..] It is very easy to see that we don't have any direct confirmation on Length contraction, as I posted earlier. [..]

And as I posted earlier, I first asked you what you would consider a "direct confirmation" of length contraction. It may be that what you ask for is even conceptually an impossibility - like saying that no square ball has been found (in which case we should say "so what"). Or, alternatively, it could be that experimental evidence does exist that you would find sufficiently "direct". As long as you don't specify it, we can't really help you with that.

No, it is not solved,

Hmm that's strange, as several times I as well as several others actually agreed with your opinion in your first post - see for example my posts #95 and #120. To recapitulate:

You:
"If the number of unstable particles reaching the Earth is invariant under Lorentz transformation. Then this phenomena must be explained by a physical law and not by the transformation itself. 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."

Me:
#95 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.
#120 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.
#218 you don't need to think that transformations "explain" physical effects.

and by the way what do you think causes the relativistic physical effects, spacetime, metrics (if not transformations) !?

As to the question what causes relativistic physical effects, that's inherently the same question as what causes physical phenomena, including electromagnetism. And that's a field of speculation and perhaps even more of personal opinion (or philosophy). It's not scientifically relevant what someone's personal opinion is but sometimes physicsforums has polls about such opinions (should we have one now? how to set it up? ). I've seen such interpretations as "it's just the way nature is"(shut up and calculate), "it's due to the relativity principle/the Lorentz transformation"(mathematical interpretation), "it's caused by Spacetime"(geometric or block universe interpretation) or "it's caused by the Vacuum"(ether interpretation), and no doubt there are more.

 

[Dale]

Wouldn't it be more correct to say it was true in general but not necessarily true in certain limited cases like rotating frames

Sorry about that, it is a bit of scientific jargon, but the phrase "in general" means "in the most general case", or in other words, something which is true "in general" is always true. What you mean is "typically", which is something that is true in the most common or usual case, but may not be true in some exceptional cases. Something which is true "in general" is true both in the typical case and also in the exceptional cases.

We are talking about SR , inertial frames, Not GR or accelerating frames which are outside the topic of this thread and discussion.

I wasn't. For a law to be a law it needs to be true in general, not just in special cases. I.e. a law of physics should be true even in the presence of gravitation and even in accelerating frames.

See also http://math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html regarding SR and accelerating frames.

 

[Dale]

A Physical effect is that which can be measured independently, that is the to observe the effect we don't need to include any assumptions or the indirect ways,

Then there are no physical effects. Nothing can be measured independently.

Your basic concern of this whole thread seems to be that some things are more conveniently described in terms of a transformation. We have a set of equations called laws of physics. Those equations have a large variety of features. Some experiments are sensitive only to a small subset of those features, so they can be explained by reference only to those features. Notable examples are conservation principles and transformation symmetries.

Just because you can explain some given experiment using one of these principles or symmetries does not imply that the laws of physics are flawed.

 

[stevendaryl]

Then there are no physical effects. Nothing can be measured independently.

Your basic concern of this whole thread seems to be that some things are more conveniently described in terms of a transformation. We have a set of equations called laws of physics. Those equations have a large variety of features. Some experiments are sensitive only to a small subset of those features, so they can be explained by reference to those features. Notable examples are conservation principles and transformation symmetries. Just because you can explain some given experiment using one of these principles or symmetries does not imply that the laws of physics are flawed.

I think that the way that reasoning in relativity works is often like this:

• The laws of physics have the same form in any inertial coordinate system.
• Therefore, choose a coordinate system that makes your particular problem easiest to solve.
• Then, transform the answer into whichever coordinate system you want the answer in.

universal_101 seems to think that because you solve the problem using transformations, that you are using transformations instead of physical laws to solve the problem. That's not true at all.

 

[universal_101]

I think that the way that reasoning in relativity works is often like this:

• The laws of physics have the same form in any inertial coordinate system.
• Therefore, choose a coordinate system that makes your particular problem easiest to solve.
• Then, transform the answer into whichever coordinate system you want the answer in.

universal_101 seems to think that because you solve the problem using transformations, that you are using transformations instead of physical laws to solve the problem. That's not true at all.

Ofcourse, it should work like this, but we are not using it like this when we are explaining Muons and motion, consider the following reasoning and assertion.

• Since, Number of Muons reaching Earth is invariant, and therefore, any law that explains this invariant event, must not be dependent on any transformation tool. {Yes or No}
• If Yes , Gamma factor is used to explain this invariant physical effect. {Yes or No}
• If Yes , Gamma factor is a transformation tool in Special relativity. {Yes or No}

This explains the use of a transformation tool for an invariant physical effect, to which I have problem understanding.

In case, you still think one of the above points is NO, let's discuss it.

 

[universal_101]

Then there are no physical effects. Nothing can be measured independently.

The adjective independently was used to reflect the invariant nature of the events. And should not be confused with the dependence on the equipment.

Therefore, Ratio of the Number of Muons, starting from ionosphere to reaching Earth, can be measured independently or as invariant.

Or, an Experiment done in lab, the number of Muons created at one end and the number of Muons reaching the other end can be measured, independently or as invariant.

 

[harrylin]

[..]

• Since, Number of Muons reaching Earth is invariant, and therefore, any law that explains this invariant event, must not be dependent on any transformation tool. {Yes or No}
• If Yes , Gamma factor is used to explain this invariant physical effect. {Yes or No}
• If Yes , Gamma factor is a transformation tool in Special relativity. {Yes or No}

This explains the use of a transformation tool for an invariant physical effect, to which I have problem understanding.

In case, you still think one of the above points is NO, let's discuss it.

Your "therefore" doesn't make sense to me, and your last point misses the point which we made that gamma is contained in the transformation laws because it is also part of natural law. I tried to explain that to you by mentioning the classical transformation laws, but apparently it needs to be not just mentioned but rubbed in:

According to your reasoning, in classical mechanics:

• Since, Number of Muons reaching Earth is invariant, and therefore, any law that explains this invariant event, must not be dependent on any transformation tool. {Yes or No}
• If Yes , factor 1 is used to explain this invariant physical effect. {Yes or No}
• If Yes , factor 1 is a transformation tool in Classical relativity. {Yes or No}

What would you answer?

 

[universal_101]

Your "therefore" doesn't make sense to me, and your last point misses the point which we made that gamma is contained in the transformation laws because it is also part of natural law. I tried to explain that to you by mentioning the classical transformation laws, but apparently it needs to be not just mentioned but rubbed in:

According to your reasoning, in classical mechanics:

• Since, Number of Muons reaching Earth is invariant, and therefore, any law that explains this invariant event, must not be dependent on any transformation tool. {Yes or No}
• If Yes , factor 1 is used to explain this invariant physical effect. {Yes or No}
• If Yes , factor 1 is a transformation tool in Classical relativity. {Yes or No}

What would you answer?

If classical relativity stands for Galilean relativity, then it simply cannot/does not explain the Number of Muons reaching Earth. That's why we use Special relativity and its transformations.

 

[GeorgeDishman]

Ofcourse, it should work like this, but we are not using it like this when we are explaining Muons and motion, consider the following reasoning and assertion.

• Since, Number of Muons reaching Earth is invariant, and therefore, any law that explains this invariant event, must not be dependent on any transformation tool. {Yes or No}

No, the logical deduction from that is that any use of a transformation tool must keep the number the same. That is different from suggesting that the tool cannot be used.

• If Yes , ...[/QUOTE]

Not applicable.

• If Yes , ...[/QUOTE]

Not applicable.

In case, you still think one of the above points is NO, let's discuss it.

By all means.

 

[GeorgeDishman]

A Physical effect is that which can be measured independently, that is the to observe the effect we don't need to include any assumptions or the indirect ways, which is done in the MMX experiment and it's extended version, the KT experiment.

That's a difficult definition. If I boil watter in a kettle, does it's temperature rise? I could measure it with a termometer but then I am inferring a rise of temperature indirectly from the expansion of a column of red-dyed fluid.

In the MMX, there is nothing more indirect than that, we measure the length of an arm by comparing the time it takes light to travel from one end to the other and back. This is not dependent on a transform, the measurements all take place in the rest frame of the equipment.

No, MMX does not prove/verify anything other than the "Non-Existence of aether". Any thing else that you say it proves is just the basis of the theory(SR) in order to understand the Experiment. That is, length contraction in MMX is part of the theory itself and not the proof of it.

Not at all, you get the same conclusion using either SR or LET.

I asked before but you never replied, if one person walks directly from A to C while another goes via B and they have the same stride length, they will take a different number of strides. What is your understanding of that physical effect, or do you not consider the reason to be "physical"?

As long as the difference in the number of strides or the path can be measured independently of everything else, it is a physical effect.

That's somewhat different from the way I've seen the term used before. The same is true of the changes in coordinate values resulting from the use of the Lorentz Transforms so by your definition, the gamma factor is a "physical" effect. The analogy of taking different paths works quite well (other than for the sign in the equations) for understanding SR, it's just extended to 4D instead of 3D so whatever categorisation you think applies to this analogy probably applies to the Lorentz Transforms too.

 

[harrylin]

If classical relativity stands for Galilean relativity, then it simply cannot/does not explain the Number of Muons reaching Earth. That's why we use Special relativity and its transformations.

Also according to classical mechanics (with "Galilean relativity") there should be an invariant number of muons arriving at the Earth. But as that distracts you from my question, we can replace it with the number of raindrops reaching the earth. Thus, again:

According to your reasoning, in classical mechanics:

Since, Number of Raindrops reaching Earth is invariant, and therefore, any law that explains this invariant event, must not be dependent on any transformation tool. {Yes or No}
If Yes , factor 1 is used to explain this invariant physical effect. {Yes or No}
If Yes , factor 1 is a transformation tool in Classical relativity. {Yes or No}

What would you answer?

 

[universal_101]

Also according to classical mechanics there is an invariant number of muons arriving at the Earth. But as that distracts you from my question, we can replace it with the number of raindrops reaching the earth. Thus, again:

According to your reasoning, in classical mechanics:

Since, Number of Raindrops reaching Earth is invariant, and therefore, any law that explains this invariant event, must not be dependent on any transformation tool. {Yes or No}
If Yes , factor 1 is used to explain this invariant physical effect. {Yes or No}
If Yes , factor 1 is a transformation tool in Classical relativity. {Yes or No}

What would you answer?

The number of raindrops, which started their journey are same which reach to the Earth surface, but with Muons this is not the case, they seem to change their half-life when they are moving to reach the Earth.

That is, I'm not questioning a particular number of Muons, but their ratio to the number of Muons which started their journey to the number of Muons which reached the Earth.

It is the ratio which is in question, not the numbers at one particular stage.

 

[universal_101]

No, the logical deduction from that is that any use of a transformation tool must keep the number the same. That is different from suggesting that the tool cannot be used.

Does that mean, there is nothing wrong with, the use of a transformation tool to explain number of Muons reaching Earth ?

Well if that is what you are suggesting, then aside from mathematics, where is the physics that let you use a transformation tool to explain a physical effect.

Or do you even doubt the physicality/invariant property of the number of Muons reaching Earth, itself !?

 

[harrylin]

The number of raindrops, which started their journey are same which reach to the Earth surface, but with Muons this is not the case, they seem to change their half-life when they are moving to reach the Earth.

That is, I'm not questioning a particular number of Muons, but their ratio to the number of Muons which started their journey to the number of Muons which reached the Earth.

It is the ratio which is in question, not the numbers at one particular stage.

In the part on which I commented you were not questioning the muons ratio but the gamma factor in the context of transformation vs. physical law. You suggested that the gamma factor can't be part of a physical law because it's also part of the transformation equations. So, what about the factor 1 in classical mechanics, how can that be part of physical law if it's also part of the transformation equations?

 

[universal_101]

That's a difficult definition. If I boil watter in a kettle, does it's temperature rise? I could measure it with a termometer but then I am inferring a rise of temperature indirectly from the expansion of a column of red-dyed fluid.

In the MMX, there is nothing more indirect than that, we measure the length of an arm by comparing the time it takes light to travel from one end to the other and back. This is not dependent on a transform, the measurements all take place in the rest frame of the equipment.

I'm quoting my previous post, which clarifies the above confusion.

The adjective independently was used to reflect the invariant nature of the events. And should not be confused with the dependence on the equipment.

Therefore, Ratio of the Number of Muons, starting from ionosphere to reaching Earth, can be measured independently or as invariant.

Or, an Experiment done in lab, the number of Muons created at one end and the number of Muons reaching the other end can be measured, independently or as invariant.

Not at all, you get the same conclusion using either SR or LET.

LET cannot be applied to MMX, because it is not falsifiable, i.e. we cannot detect ether.
And Nobody likes a physics theory based on purely mathematics.

That's somewhat different from the way I've seen the term used before. The same is true of the changes in coordinate values resulting from the use of the Lorentz Transforms so by your definition, the gamma factor is a "physical" effect. The analogy of taking different paths works quite well (other than for the sign in the equations) for understanding SR, it's just extended to 4D instead of 3D so whatever categorisation you think applies to this analogy probably applies to the Lorentz Transforms too.

Exactly, I'm suggesting that gamma factor is a physical effect, and there seem to be experimental indication of it. (The paper I quoted earlier)

 

[universal_101]

In the part on which I commented you were not questioning the muons ratio but the gamma factor in the context of transformation vs. physical law. You suggested that the gamma factor can't be part of a physical law because it's also part of the transformation equations. So, what about the factor 1 in classical mechanics, how can that be part of physical law if it's also part of the transformation equations? Please prove that you're not just trolling.

How in the world are you going to separate the ratio of Muons and the gamma factor. This is exactly what Dalespam was arguing and presenting his mathematics for, to prove they are unrelated, but apparently did not go far.

The ratio of Muons is defined by gamma factor,

The only way I know of producing gamma factor is using Transformations(Lorentz).

Whereas, I'm suggesting that gamma factor must be introduced by a physical law and not by a transformation.

That is, it just happens to be that gamma factor of the Lorentz transformation, is the same gamma factor which should come from a physical law.

So, we should have a gamma factor introduced by an physical law(which ofcourse depends on relative motion), and not by a transformation.

I don't know if I gave enough proof !

 

[harrylin]

How in the world are you going to separate the ratio of Muons and the gamma factor. This is exactly what Dalespam was arguing and presenting his mathematics for, to prove they are unrelated, but apparently did not go far.

They are not unrelated as I and others showed. And I simply tried to make clear to you how your questions don't make sense to me by asking the same about classical physics, in order for you to clarify what you mean, show that you can be consistent, and hopefully correct your fuzzy questions. But apparently you simply refuse to clarify your questions.

The ratio of Muons is defined by gamma factor,
The only way I know of producing gamma factor is using Transformations(Lorentz).

That's not needed at all, as I stressed in a number of posts and others also stressed this.
Don't you know the gamma time dilation factor expressed as law for physical processes such as clocks and muons?

Whereas, I'm suggesting that gamma factor must be introduced by a physical law and not by a transformation.

It has been agreed and clarified many times in this thread that it makes sense to introduce the gamma factor as part of physical laws. By the way, that already was done in 1888 for the fields of charged particles.

That is, it just happens to be that gamma factor of the Lorentz transformation, is the same gamma factor which should come from a physical law.

No, exactly as I stressed in my last posts: it not "just happens to be" that factor 1 of the Galilean transformation, is the same factor 1 which also comes from a classical physical law. Different physical laws cause different transformations, and this has been clarified several times now (as much as possible without you doing any math).

So, we should have a gamma factor introduced by an physical law(which ofcourse depends on relative motion), and not by a transformation.
I don't know if I gave enough proof !

That's a matter of philosophy, as I stressed in one or two earlier posts. No proof needed or possible for philosophy. While you and I find it logical the brains of some other people are wired differently. And the math doesn't tell you.

 

[stevendaryl]

Ofcourse, it should work like this, but we are not using it like this when we are explaining Muons and motion.

consider the following reasoning and assertion.

• Since, Number of Muons reaching Earth is invariant, and therefore, any law that explains this invariant event, must not be dependent on any transformation tool. {Yes or No}
• If Yes , Gamma factor is used to explain this invariant physical effect. {Yes or No}
• If Yes , Gamma factor is a transformation tool in Special relativity. {Yes or No}

I think the questions are based on a misunderstanding. If I had to answer yes/no, I would say "no", "no", "no". Transformations can certainly be used for explanatory purposes--otherwise, they wouldn't be used in science. If I want to explain how a 2-meter board can fit through a 0.5 meter doorway, I would use geometry; I would show that what's important is not the length of the board, but the projection of that length onto the width of the doorway. Computing that projection involves the angle between the board and the width of the doorway. Alternatively, we could talk about this in terms of a transformation between two coordinate systems: one in which the board is aligned in the +x direction, and a second one in which the width of the doorway is aligned in the +x direction.

There is a similar type projection going on in the problem of muon decay. There are two "worldlines" that are relevant: that of the muons and that of the Earth. The amount of muons left at any time is a function of the "length" of the worldline of the muons. To compute what this elapsed time is, according to the Earth, you have to compute the projection of the muons' worldline onto the Earth's worldline.

In every SR problem, there is a part that is physical, having to do with forces and clock rates and so forth. The half-life of a muon is such a physical effect. Then there is a part that is geometric, having to do with the projection of some quantity onto a particular worldline, or something similar.

gamma plays the same role in relativity that cos(theta) plays in Euclidean geometry. It's involved whenever is projecting one worldline onto another.

 

[stevendaryl]

The only way I know of producing gamma factor is using Transformations(Lorentz).

Whereas, I'm suggesting that gamma factor must be introduced by a physical law and not by a transformation.

The gamma factor comes up in the geometry of spacetime, in exactly the same way that cos(θ) comes up in Euclidean geometry. If two straight sticks make an angle θ with respect to each other, then the projection of the length of one stick onto the other stick involves cos(θ).

If in a relativity problem, two worldlines have a different orientation in spacetime, then the projection of the length of one onto the other involves the factor gamma. It's really about projections, not about transformations. You can use projections to create a coordinate transformation, but projections make sense even before you choose a coordinate system.

 

[Dale]

The adjective independently was used to reflect the invariant nature of the events. And should not be confused with the dependence on the equipment.

Therefore, Ratio of the Number of Muons, starting from ionosphere to reaching Earth, can be measured independently or as invariant.

Or, an Experiment done in lab, the number of Muons created at one end and the number of Muons reaching the other end can be measured, independently or as invariant.

That is indeed reasonable, but the correct adjective is "invariant", not "independent".

The muon ratios you mention are invariant and are given by the law I cited at the beginning of the thread, without using any transform. So your question seems to have been resolved more than a hundred posts ago.

 

[Dale]

The only way I know of producing gamma factor is using Transformations(Lorentz).

See post 154 where I derive gamma directly from the metric without a Lorentz transform.

 

[harrylin]

That is indeed reasonable, but the correct adjective is "invariant", not "independent".

The muon ratios you mention are invariant and are given by the law I cited at the beginning of the thread, without using any transform. So your question seems to have been resolved more than a hundred posts ago.

Checking for it, I see that you already qualitatively clarified the whole matter in post #7 of this thread - that's more than 200 posts ago - and you stated that you already did so in an earlier thread.

And concerning the time tau, I thought that I gave that but if not, here it is for universal as given in 1905:

"the time marked by the [moving] clock (viewed in the stationary system) is slow [on the reference clock] by 1-√(1-v²/c²) seconds per second, or—neglecting magnitudes of fourth and higher order—by 1/2 v²/c²."

This effect must be valid in general: not only mechanical clocks slow down by a factor γ but any natural process, including the half-life of radioactive "clocks" such as muons.

Note also that the expression "viewed in the stationary system" is the reference for "laws of physics"; it's not a transformation equation, and universal can use that law for arriving muons with the Earth as "stationary system".

 

[GeorgeDishman]

Does that mean, there is nothing wrong with, the use of a transformation tool to explain number of Muons reaching Earth ?

A transformation changes numbers in one coordinate system into the equivalent numbers in another system. If you have first calculated the number in the muon frame, you can use a transform to convert any frame-dependent numbers (e.g. lengths and times) to the Earth frame. The number of muons reaching the Earth is an invariant so applying a transform will not change it.

Well if that is what you are suggesting, then aside from mathematics, where is the physics that let you use a transformation tool to explain a physical effect.

Physics is nothing but mathematics applied to measurable quantities. The basic physics we are using has been posted several times, it is the exponential equation which predicts the number of particles that decay in a given period based on the half-life of the muon. That equation is obviously just mathematics.

Using a transform simply converts that half-life to a different coordinate system.

Or do you even doubt the physicality/invariant property of the number of Muons reaching Earth, itself !?

No, I doubt that you have grasped that the question you are asking is the same as querying the "physical cause" for taking more strides to get from A to B via C than going directly from A to B. Most people think of that as a consequence of geometry rather than a "physical" effect but your definition of what you mean by "physical" is different to what I have seen before.

 

[universal_101]

See post 154 where I derive gamma directly from the metric without a Lorentz transform.

See my post #207, Which shows very clearly, that you are just juggling mathematics... and by NO means it can be said a derivation.

 

[Mentz114]

See post 154 where I derive gamma directly from the metric without a Lorentz transform.

See my post #207, Which shows very clearly, that you are just juggling mathematics... and by NO means it can be said a derivation.

No, you're wrong. The gamma factor emerges from the Minkowski metric with a simple rearrangement of the differentials. You cannot deny this - it is elementary mathematics.

 

[Dale]

See my post #207, Which shows very clearly, that you are just juggling mathematics... and by NO means it can be said a derivation.

Post 207 doesn't show anything "very clearly". And yes, as Mentz114 mentioned, my post 154 derives gamma without a coordinate transformation.

If you choose to call a correct derivation "just juggling mathematics" then so be it. It is still a correct derivation and completely refutes your claim.

 

[GAsahi]

There is really no reason not to either. Reparameterizations are common and well accepted.

You are totally missing (or willfully ignoring) the point: your derivation is not quite right, since the muons move in a cyclotron, r=R so dr=dz=0 meaning that d\tau^2=dt^2-r^2d\theta^2=dt^2(1-R^2 (\frac{d \theta}{dt})^2) meaning that d\tau^2=dt^2 (1-v^2)=(\frac{dt}{\gamma})^2. So, the correct result is d\tau = \frac{dt}{\gamma}.

 

[Dale]

So, the correct result is d\tau = \frac{dt}{\gamma}.

That isn't the only correct way to work the problem.

 

[universal_101]

That isn't the only correct way to work the problem.

Let me put it this way, consider the Newtonian mechanics,

Just because we can understand a particular event by using energy conservation(Least action principle), does not mean that there is NO Force involved in the event.

Whereas, you are suggesting, because we can calculate the correct results also by using spacetime metrics, it means that Time Dilation is independent of relative motion, i.e. independent of gamma factor.

 

[Dale]

you are suggesting, because we can calculate the correct results also by using spacetime metrics, it means that Time Dilation is independent of relative motion, i.e. independent of gamma factor.

What I have proven is that the mere fact that gamma shows up does not imply that there was a coordinate transform. I didn't make any claims about the independence of time dilation and relative motion.

Your entire complaint from the OP is that physical effects like muon decay should come from physical laws and not coordinate transforms. I gave the physical law for muon decay. You then complained that simply because gamma pops out of the law that it must be a transform. In fact, you said that the "only way I know of producing gamma factor is using Transformations(Lorentz)". So I showed you that it can be produced directly from the metric without any transform.

So now that you know that gamma can come from other sources than a coordinate transform it should be clear that your complaint is completely resolved.

Do you now accept that the decay of muons can be explained by a law of physics that is not a coordinate transform? If not, then what possible logical reason can you have for not accepting it?

 

[GeorgeDishman]

A Physical effect is that which can be measured independently, that is the to observe the effect we don't need to include any assumptions or the indirect ways, which is done in the MMX experiment and it's extended version, the KT experiment.

That's a difficult definition. If I boil watter in a kettle, does it's temperature rise? I could measure it with a termometer but then I am inferring a rise of temperature indirectly from the expansion of a column of red-dyed fluid. ..

I'm quoting my previous post, which clarifies the above confusion.

The adjective independently was used to reflect the invariant nature of the events. And should not be confused with the dependence on the equipment. ..

OK, then you should note that the null result of the MMX is invariant hence length contraction is a "physical effect" by your definition.

LET cannot be applied to MMX, because it is not falsifiable

That is incorrect, LET predicts a null result for the MMX, if a non-null result was found, LET would be falsified. However, you miss the point, the null result of the MMX is an invariant hence valid by your definition. It is indirect in that it uses a radar-like technique but you say that's not what you meant and such inference is an unavoidable part of most measurements anyway.

And Nobody likes a physics theory based on purely mathematics.

Physics is purely mathematics in which the variables are identified with measurable quantities.

Exactly, I'm suggesting that gamma factor is a physical effect, and there seem to be experimental indication of it. (The paper I quoted earlier)

Well "gamma" is just a mathematical shorthand for a commonly ocurring term, it is part of many "physical" effects. I'm not at all sure what it is that you are arguing about.