Relativity And Simple Algebra

[Amplituhedron]

Ralf,

 

You want to banish length contraction from special relativity. In my view, you are going about this all wrong. The problem is twofold. First, you disdain philosophy. Second, you think that maths are the the be all and end all of reality. Both are (philosophical!) presuppositions, and both are false.

 

Science is simply shot through with philosophy: theory undertermination, adjustment of auxiliary hypotheses, the demarcation problem, the pessimistic meta-induction, and on and on. Science can no more be separated from philosophy than the Cheshire cat’s grin can be separated from the cat itself.

 

As to math, it appears, per Sabine Hossenfelder, that you are Lost in Math. You are confusing prescription with description. You seem to think that math prescribes reality, whereas in fact it describes it. In this, mathematics, a deductive enterprise which describes the findings of an inductive enterprise (science), is a proper subset of the Tarskian, or Correspondence Theory, of truth: that truth lies in descriptive propositions of the world, but one must never confuse description, with prescription. When one says, “The sun is rising,” one must never think that the true proposition, “the sun is rising,” makes the sun rise.

 

Einstein originally derived special relativity, and later general relativity, conceptually, via gedakens — thought experiments. The math, in both cases, came later, and is merely descriptive of the concepts. Also note that Einstein, a student of the philosopher Hume, conceived himself as a natural philosopher — harking back to the time when science (quite properly!) was conceived as an extension of philosophy, and not, as so many wrongly suppose, including Steven Hawking, a replacement of philosophy. (The “shut up and calculate” mob, particularly with respect to QM, is indicative of the current abandonment of the search for truth, an abandonment anathema to Einstein.)

 

As a matter of sheer wonderment, Hawking wrote a book in which, on Page One, he declared, “Philosophy is dead,” and then went on to write a tome that was entirely philosophical, which included positing the philosophy of “model-dependent reality,” from which he derived the “conclusion” that there is an actual reality in which the moon is literally made of Roquefort cheese! How he, or his editors, could not spot the blatant contradiction in his claim about philosophy totally eludes me. It just proves very smart people can also be very stupid.

 

In the case of special relativity and length contraction, one simply must turn to philosophy! One must see that SR can be formulated in epistemological terms, but also in ontological terms. Both epistemology and ontology are subsets of metaphysics, which just IS part of philosophy!

 

From the standpoint of epistemology, SR can be successfully formulated, or mathematically described, on the assumption that the world consists of 3D objects, which “move through” time. However, 3D objects evolving through time is already an ontological presupposition.

 

If SR is epistemically formulated in the manner, then two different observers in relative motion will disagree on the length of a 3D object, which is length contraction. Therefore, one will have to conclude that the same object has two different lengths. 

 

You object to this “two different lengths” for the same object. Fine. Then, reformulate SR as a matter of ontology, and not epistemology, and see what happens.

 

Forget about math, though not entirely. Imagine that space is 2D — a Euclidean plane. So we have some math right there, some elementary geometry.

 

We place a 2D object on the surface of the plane: a rectangle, or seal. We also place two lines — 1D — traveling as diagonals with respect to each other.

 

It can easily be shown that these two lines, which we can also think of as world lines in relative motion, will see the existent seal differently — they will disagree on its length (this is length contraction).

 

But — the diagram shows, obviously, that they are not seeing the whole 2D seal — rather, they are seeing two different one-dimensional cross sections of it.

 

The whole seal does not change.

 

They are disagreeing, not on the length of the seal as such, but on the length of their relative cross-sections of it.

 

Thus, their disagreement is entirely epistemological, and not ontological. If they could step out of their parochial view of things, they would realize that the seal does not change. There is no length contraction. There are simply two different epistemological interpretations of an existent, ontological object that does not change.

 

To suppose otherwise, is to suppose that the seal is not 2D, but 1D. But it isn’t! This is the difference between epistemology and ontology: Ontologically, the seal cannot be both a line, and a plane, at the same time. This violates elementary logic that goes back some 2,000 years: Aristotle’s Law of Non-Contradiction. The object in question must be either a seal or a line. It cannot be both. The claims are mutually exclusive, and jointly exhaustive.

 

Now throw in the third dimension, and the rest falls out. The seal becomes a rod in Minkowski spacetime, in which all its moments in time are simply given, just like all its locations in space. Thus there is no length contraction. Two different observers in relative motion are seeing two different 3D cross sections of an existent 4D rod that does not ever change. End of story.

[sluggo]

Amp;

 

Science IS philosophy augmented with math, its verification tool.

In the decade prior to 1900, there were a few people working on a relativity theory.

Lorentz, Poincare, and Einstein among them. Typically the one who publishes first gets the credit, in this case Einstein. His version incorporated ideas from others, Maxwell’s equations, and Lorentz’s coordinate transformations. Einstein made his version as simple as possible by eliminating redundant ideas. Here I’ll insert an alternate interpretation of the 2nd postulate, ‘events don’t move’. This means light is emitted ‘as if’ from a fixed position in space, and independently of any moving objects, which is equivalent to a fixed medium/ether. He doesn’t need an ether, and has a basis for an invariant interval.

His idea of simultaneous measurements are correct, but incomplete as the graphic in the next post shows.

[sluggo]

You use spacetime graphics, so you should understand this obvious comparison.

I don't attempt to remember every post, so will repeat it.

A and B have a mirror M on the end of a rod of length d.
In the A frame, the length of the rod is ct=d.
The red hyperbola, aka calibration curve, denotes the same A-time where it intersects the time line of a moving observer. Gamma=g.
Left:
Bt=2gt at the return signal, event D. B assuming a pseudo rest frame (because there is no absolute rest frame), perceives his signal to M as equal out and back, giving d=gct, greater than d.
Right:
With length contraction, B measures the B rod as ct=d.
A measures the length of the B rod as d/g.
B measures the length of the A rod (on the Bx axis) as d/g.
The results are reciprocal only if the B frame is affected by lc.

 

[ralfcis]

I see where we differ. For me, time is independent of space but for Relativity it is not. I only need to consider proper time which does not require any clock syncing. So by the equation

 

(ct')² = (ct)² - x²

 

with the concept that all clocks tick at the proper rate within their own frame, Alice and Bob will both age 1 yr per yr during constant relative velocity but any disruption of that constant velocity will change that ageing rate for the duration of the disruption after which the normal ageing rate will resume but with a permanent difference in their proper time ages. 

 

For example, if Alice goes out at .6c, her proper time age is always joined to Bob's by the hyperbolas that represent the equation above. When Alice is 1, Bob is one; 2, 2; 3,3 etc in proper time. Of course their perspective times are governed by gamma Y. So from Bob's perspective at t=10, Alice is 8. But it's not the same 8 as the 8 if Alice turns around at the 3 ly mark. To say Alice =8 is meaningless in Relativity without including the space coordinates with the time coordinate.

 

But for me, in proper time, Alice and Bob have no proper time age difference if they remain in constant velocity. If Alice turns around at the 3 ly mark, she will age 2 yrs less than Bob when she reaches age 6 and Bob 8. She will always be 2 yrs less than Bob from that point on. So when Bob is 9, she will be 7; 10,8; 11,9 etc. Relativity has no concept of this type of age difference, it only has coordinate values for time that are dependent on perspective. All you have to do is trace out the worldlines and they both say Alice is 8  from Bob's perspective at age 10. For relativity this means the age difference is 2 for both but for me the proper time age difference is 0 and 2 and it's regardless of their perspectives.

 

So the question is how does relativity see the rate of proper time ageing change and for what duration. The answer I got was the Rindler metric but I have a far simpler algebraic method. I'll have to ask this question again on the PSX.

Edited November 29, 2019 by ralfcis

[ralfcis]

If I may just go back to what you guys were telling me to check if I've misunderstood you. You're saying our ability to see the 4-D universe is one dimension short so we can only see slices of 4-D. To me, we perceive 2-D space with time giving us the sense of 3-D space. Without time we'd just see a motionless flat screen in front of us. But I see time as the slicer outside of 3-D space. We can see the whole length of an object but we can only see the present time slice of that object (with some sensory persistence of past time slices). The future is not available and neither is the past without memory. So there is no continuity in time, (it's an infinitesimally small sliver), like there is in space. Time is above space and not part of it. This is where Relativity and I part ways. I'm working on the STD's to show what I mean mathematically.

[OverUnityDeviceUAP]

If I may just go back to what you guys were telling me to check if I've misunderstood you. You're saying our ability to see the 4-D universe is one dimension short so we can only see slices of 4-D. To me, we perceive 2-D space with time giving us the sense of 3-D space. Without time we'd just see a motionless flat screen in front of us. But I see time as the slicer outside of 3-D space. We can see the whole length of an object but we can only see the present time slice of that object (with some sensory persistence of past time slices). The future is not available and neither is the past without memory. So there is no continuity in time, (it's an infinitesimally small sliver), like there is in space. Time is above space and not part of it. This is where Relativity and I part ways. I'm working on the STD's to show what I mean mathematically.

You're both complicating it and not realizing how simple your reality is. Feeeeeel

[sluggo]

Ralf;

 

(ct')2 = (ct)2 - x2

 

 

 

That is just another rearrangement of ct' = t/gamma, which is much simpler, don't you think.

 

My last post was for Amp who also misses the point of the 1st postulate, which says, for any inertial frame (moving at constant speed), any experiment performed in that frame will produce the same results, regardless of speed. Imagine if you had to know where the center of mass was for our galaxy, before you could calculate the trajectory of a space probe. It wouldn't be possible. The more interesting question is not who ages more, but why is the local (proper) time the same for all observers, and the physics the same. There has to be a reason based on physical processes.

 

 

To say Alice =8 is meaningless in Relativity without including the space coordinates with the time coordinate.

 

 

You have to know where they are, when you compare clocks.

 

I posted 3 graphics on PSX, only 1 was accepted. Posts are reviewed, which is just another label for censorship. I cancelled my enrollment. They rate answers, with the foolish notion that 'truth' can be established by opinion polls! So much for forums. Twelve yrs is enough to discover the collective attitudes, and interpretations using cartoon physics.

 

I'm with the Einstein view of time as distinct from space.

[ralfcis]

https://photos.app.goo.gl/eJM1jmLgPBUUtzEp8"That is just another rearrangement of ct' = t/gamma, which is much simpler, don't you think."

 

My favorite form of the equation is c² = v_x² + v_t² but I use the form that is most useful and in this case I need x² in the equation.

 

For Alice leaving Earth at .6c, the equation 

 

(ct')² = (ct)² - x²

 

for t'= 4 is the purple hyperbola which looks like this:

 

https://photos.app.goo.gl/eJM1jmLgPBUUtzEp8

 

Yes I've put too many lines again in the diagram. If you extend the hyperbola from -c to c, every velocity line from the origin intersects the hyperbola at proper time 4. This is a universally common time that needs no clock sync method to co-ordinate perspectives, the perspectives can be derived from this basis and I'll show how.

 

The equation for the hyperbola works thusly:

x= 3, t=5, so t' = sqrt(5² - 3²) = 4 which are the endpoints of the blue line of Bob's perspective simultaneity.

 

Instead of redrawing everything to figure things out from Alice's stationary perspective, you replace x with x/Y, t with t' and t' with t'': 

x/Y = 2.4, t'=4 so t''=sqrt(4² - 2.4²) = 3.2 which are the endpoints of the red line of Alice's perspective simultaneity.

 

The same equation could have been used for Bob if you separate Bob's Y =1 from Alice's Y = 5/4. (A similar separation for DSR will happen later on for the new equation for t'.)

 

When Bob and Alice reach 4 on their clocks, they will send yellow and pink light signals to each other to figure out what their relative times are after they have travelled the 4 yrs. There is no coordination between them except the agreement they made at the origin and their belief that atomic clocks keep accurate time (a concept that was not available to Einstein when he came up with his clock sync method). They also agree to move at .6c relative velocity, something they can check using the broadcast TV picture of their atomic clock readouts which they will receive running at half speed, because of the Doppler shift ratio (DSR), compared to their on-board clocks.

 

For now there is no implication of a type of simultaneity for when the light signals are sent. In fact, there is no perspective simultaneity except for a half speed 1/3c observer who will see the same time for both. That is the green line of perspective simultaneity. 

 

From Alice's perspective (red line), Bob will send his pink light signal a full Alice year after she sends her yellow one. With the gamma factor Y and the fact her line of simultaneity intersects Bob at t=3.2, he will release his pink light signal .8 Bob yrs (=Alice yr/Y) after Alice releases her yellow. All this is shown between the thin lavender line from t=4 to t'=5 and the thick red line from t=3.2 to t'=4. 

 

Let's do some more examples from outside perspectives above .6c: (may be very difficult to follow)

 

From a .8c perspective (not shown) and using the above technique, the lower line of .8c perspective simultaneity would extend from t= 2.6 to t' = 4 and the upper from t=4 to t'=6.2. So Bob would release his pink light signal 1.4 Bob yrs (or 2.2 Alice yrs) after Alice releases hers. 

 

From a 1c perspective (not shown) and using the above technique, the lower line of 1c perspective simultaneity would extend from t= 2 to t' = 4 and the upper from t=4 to t'=8. So Bob would release his pink light signal 2 Bob yrs (or 4 Alice yrs) after Alice releases hers. 

 

end of examples

 

From Bob's perspective (blue line), Alice will send her yellow light signal a full Bob year  after he sends his pink one. With the gamma factor Y and the fact his line of simultaneity intersects Alice at t'=3.2, she will release her yellow light signal .8 Alice yrs (=Bob yr / Y) after Bob releases his pink. All this is shown between the thin blue line from t=4 to t'=3.2 and the thick blue line from t=5 to t'=4. 

 

Let's do some more examples from outside perspectives below 0c: (may be very difficult to follow)

 

From a -.8c perspective (not shown) and using the above technique, the lower line of -.8c perspective simultaneity would extend from t'=2.1 to t=4  and the upper from t'=4 to t=7.4. So Alice would release her yellow light signal 1.9 Alice yrs (or 3.4 Bob yrs)  after Bob releases his. 

 

From a -1c perspective (not shown) and using the above technique, the lower line of -1c perspective simultaneity would extend from t'=2 to t=4  and the upper from t'=4 to t=8. So Alice would release her yellow light signal  2 Alice yrs (or 4 Bob yrs) after Bob releases his. 

 

If you can read math you can see that the above examples illustrate an aperture of perspective simultaneity which closes at the green line of 1/3c simultaneity and opens widest at c (between the thick and thin pink lines) and -c (between the thick and thin yellow lines) for this example. 

 

We use this information as the basis for rewriting the equation

 

t'=sqrt(t² - x²)

 

to

 

t' =xDSR/Yv. (a long and complicated derivation)

 

Again DSR must be separate for Bob (DSR =1) and Alice (DSR=1/2 for receding and DSR=2 for approaching.)

 

All this is leading up to the discussion of how to use light signals to tell their relative time to each other. Relativity would say the yellow light signal is 3 ys long which hits Bob at 8 so he must have been 5 (from his perspective) when Alice was 4. I'm saying that's just one tiny part of the correct answer because it only shows 1 perspective. If you use the green universal line as the basis for a universal simultaneity from which all other perspectives can be derived, you can make the light lines come up with a better answer. That better answer is

 

t' =xDSR/Yv where Bob's perspective t=Yt' and Alice's perspective t'' = t'/Y.

 

Let's show how this works by throwing numbers at it in the next post.

Edited December 1, 2019 by ralfcis

[OverUnityDeviceUAP]

I'm convinced that later in his life, Einstein came close to the truths regarding post-Newtonian approximations but it was actually William Sidis who achieved my level of imagination regarding nature, however, he never lived long enough for it to be punched coherently into the entangled electrons of our thought patterns and there were no parallel operating systems such as sycamore for him to survive through when WJS had his stroke.

[ralfcis]

Ok I'm going to put you on ignore so if you directly address the topic of this thread, I won't be able to answer or see it.

[ralfcis]

So we saw in the last post that perspectives each have a different opinion of whether the pink or yellow light was sent first. Bob's perspective at t=4 when he turns on his pink light tells him when he receives Alice's yellow light that he was 5 when she turned it on.  The main equation of t'² = t² - x² (the correct form is t'² = t² - x²/Y² where Y=1 for Bob's and 5/4 for Alice's perspectives) tells us that Alice's clock was only running at 80% of Bob's because of the distance separation increasing between her and Bob. Her velocity through time, from Bob's perspective,  had to decrease as her velocity through space increased so that the total of the two velocities did not exceed c according to the form of the main equation c² = v_x² + v_t².

 

One could conclude that space separation is either the cause of time dilation/length contraction or that relativity of simultaneity is the cause and get into a century of debate over what's really happening. Time is not ticking any differently for Bob or Alice in their frames so why bother with the confusing results of perspective simultaneity. The proper times are instantaneously simultaneous. Bob and Alice are both 4 when the light signals are sent simultaneously in proper time according to the formula:

 

t' =xDSR/Yv where Bob's perspective t=Yt' and Alice's perspective t'' = t'/Y where DSR =1 for Bob and 1/2 for Alice separating from Bob at .6c.

 

So when Alice sends out her light signal at t'=4, Bob calculates his proper time age was also simultaneously 4. (x=3 (length of yellow line), DSR=1, Y=5/4, v=3/5, Yv=3/4, 3/.75 = 4). And when Bob sends out his light signal at t'=4, Alice calculates her proper time age was also 4. (x=6 (length of pink line), DSR=1/2, Yv=3/4 , 3/.75 = 4). Bob's perspective of Alice's red t'=4 is t=t'Y = 4 * 5/4 =5. Alice's perspective of of Bob's blue t'=4 is t''=t'/Y = 4/ 5/4 = 16/5 = 3.2.

 

The thick green perspective simultaneity line sees the light signals being sent off simultaneously and the thin green 1/3c velocity line will receive those light signals simultaneously where all 3 intersect. The pink line has to travel twice as far and take twice as long to reach the yellow line at the point of intersection. The most important result is that both perspective lines of simultaneity from Bob and Alice agree that the light signals sent proper time simultaneously, meet at t=6 and t'=6 simultaneously from both perspectives as shown here:

 

https://photos.app.goo.gl/bUQJssnJN539HYsb9

 

As I learned on the PSX, Relativity defines age difference from a perspective time. So from Bob's perspective at t=5, he is 1 year older than Alice. This is backed up by the results of Bob's age when Alice's yellow signal reaches him. I say all this is unimportant and is easily calculable from Bob's proper time age of 4 when Alice is 4. The proper time age difference between Bob and Alice, no matter how long the constant velocity journey, is always 0. They age at the same proper time rate. Of course, the farther they separate, the greater their perspective age difference which is not real. How do we know this.

 

A yellow light signal from Alice at t'=2 will reach Bob at t=4. You can use the formula and plug in x=1.5, DSR=1, Yv = 3/4 and you will get the result that Alice travels 2 more years when Bob gets her light signal. She and Bob will both be instantaneously, simultaneously proper time 4  when Bob gets the signal. There is no proper time age difference and the perspective age difference is not real. It is an illusion of perspective and it contradicts Alice's illusion of perspective of Bob's time. All light clocks tick off time at the same rate and your perspective is fooling you into believing they don't. Time is only really affected if the constant velocity is changed and that's a whole 'nother story.

Edited December 2, 2019 by ralfcis

[ralfcis]

Ok now back to answering Sluggo.

 

"who also misses the point of the 1st postulate"

 

Are you saying I miss the point of the 1st postulate also?

 

"You have to know where they are, when you compare clocks."

 

Not really required to establish proper time age difference if you believe space is invariant to relativistic effects. I see no need to introduce the concept of length contraction but relativity's philosophy does.

 

"I'm with the Einstein view of time as distinct from space."

 

Huh? Einstein's view is spacetime not time distinct from space.

 

Lately the answers have been pretty good on the PSX. I'm not crazy about judging answers on the most popular misconceptions. I'm not happy that if you don't know the answer to your question you will get heavily dinged for lack of research. I need to keep my points to ask more questions.

Edited December 2, 2019 by ralfcis

[ralfcis]

So the question remains if time dilation and length contraction don't exist, how does a muon make it to earth when it doesn't have enough time to cross the atmospheric thickness. The answer is in the new formula for t' re-written like this:

 

Yv = x/t'

 

The gamma velocity of the muon is much greater than its regular velocity hence it can cross the great atmospheric distance to earth in what little time it's given. It's as simple as that, no time dilation, no length contraction. Please before you state there's no velocity greater than c, try to remember v=x/t while Yv=x/t'. There's a big difference between the two equations for velocity.

 

Next I'll be redefining the twin paradox using the new formula and explaining why relativity's concept of perspective age difference just doesn't cut it.

 

If only I could present all this on the PSX but I'd be banned quicker than they could realize they'd have no idea what I was talking about. 

Edited December 2, 2019 by ralfcis

[sluggo]

Ralf;

 

Yv = x/t'

 

but t' = t/Y

 

so x = vt

 

You're just rearranging terms.

Associating Y with v instead of t.

[ralfcis]

That's exactly what I'm doing and look at the results, look at the new philosophy. I've taken time dilation and length contraction out of the equation and showed a "new" way of looking at velocity itself, a way to get around the limit of c. I've replaced Einy's clock sync method with a clock signalling method that is free to depend on the universal accuracy of the clocks themselves. I've even noticed this morning that light signals before the event can predict a future time relationship once the light signal reaches or triggers the event. As I gave in the example, Alice sending a light signal to Bob when she's 2 will trigger Bob to send his light when both of them are 4 and she can send her light signal proper time simultaneously with his. You can plan out a cascade of causal events through an objective proper time present instead of the subjectivity of individual perspective presents.

 

This math method works the same for determining what was their common proper time present in the past. This is where a tiny change in understanding totally obliterates Einy's theory. The light sent from Alice when she's 4 will hit Bob when he's 8 and relativity concluded he was 5 when she was 4 from his perspective. I've shown this conclusion is unimportant as well as being an illusion; no age difference, time itself is not being slowed , velocity is being augmented. If you use my formula to calculate what was Bob's proper time instead of his perspective time you can see his perspective time isn't real. All of math is about re-writing equations to get meaning from them, you have totally missed the meaning of a very simple math paradigm shift. Too bad for you is all I can say.

 

PS. I've also obliterated relativity's definition of age difference. No wait, I'm just about to go into the details of how I did it.

Edited December 2, 2019 by ralfcis

[OverUnityDeviceUAP]

That's exactly what I'm doing and look at the results, look at the new philosophy. I've taken time dilation and length contraction out of the equation and showed a "new" way of looking at velocity itself, a way to get around the limit of c. I've replaced Einy's clock sync method with a clock signalling method that is free to depend on the universal accuracy of the clocks themselves. I've even noticed this morning that light signals before the event can predict a future time relationship once the light signal reaches or triggers the event. As I gave in the example, Alice sending a light signal to Bob when she's 2 will trigger Bob to send his light when both of them are 4 and she can send her light signal proper time simultaneously with his. You can plan out a cascade of causal events through an objective proper time present instead of the subjectivity of individual perspective presents.

 

This math method works the same for determining what was their common proper time present in the past. This is where a tiny change in understanding totally obliterates Einy's theory. The light sent from Alice when she's 4 will hit Bob when he's 8 and relativity concluded he was 5 when she was 4 from his perspective. I've shown this conclusion is unimportant as well as being an illusion; no age difference, time itself is not being slowed , velocity is being augmented. If you use my formula to calculate what was Bob's proper time instead of his perspective time you can see his perspective time isn't real. All of math is about re-writing equations to get meaning from them, you have totally missed the meaning of a very simple math paradigm shift. Too bad for you is all I can say.

 

PS. I've also obliterated relativity's definition of age difference. No wait, I'm just about to go into the details of how I did it.

Stop diluting yourshelfs

[ralfcis]

You may remember my STD of the muon example:

 

https://photos.app.goo.gl/XGouFnSGGsGhVKkr9

 

We can now concoct a much better understanding than Einstein's of what's going on without relying on the illusory concepts of time dilation or length contraction and replacing them with proper time and relativity of proper time simultaneity. Notice above the green line of proper time simultaneity, we get a triangle that has 2 sides of 2.165 usec. Even though one looks much shorter than the other, both represent the same proper time of 2.165 usec. The longer one looks longer because:

 

 Even though the muon has 2.2 usec to cross the atmospheric thickness of 5.9 km, it can do it at Yv=x/t' or 9.14 * .994c * 3e6 = 9.08c. Again, please try to understand this is not superluminal speed. The earth view is of course limited to .994 c for the muon speed so  our clock starts from 0 to 2.165 usec but the relativity of proper time simultaneity means our clock waits 17.62 usec to start. t=Yt' = 9.14 * 2.165 usec =19.8 usec which is 17.62 + 2.165. 2.165 is the proper time both sides share for the life of the muon but it's the relativity of proper time simultaneity that gives us the total value of t = Y t'. There's no time slowing, it's the start of the timing that is delayed by relativity of proper time simultaneity. That's what's really happening, not time dilation and length contraction (which are both products of relativity of simultaneity).

 

Understanding it's a staggered start with the earth's perspective of velocity to be limited to v=x/t while the muon actually moves at a much higher velocity (from its perspective) of Yv=x/t' will now make the concept of age difference quite clear as I'll show next.

Edited December 4, 2019 by ralfcis