[MikeFontenot (OP)]

The best way of understanding the concept of a "NOW" moment in special relativity is to first get an understanding of Einstein's array of clocks, yardsticks, and "helper friends" (HF's) in an inertial reference frame. He said that all the clocks in that reference frame could be synchronized by sending light pulses between the various clocks, and by making use of the fact that in ANY inertial frame, any light pulse will move at 186,000 miles per second, according to all stationary observers in that frame.

So how do we use that fact to get a "NOW" moment (extending throughout all space), according to some particular inertial observer (call him the "PO") in that frame? To make it simple, we can arrange for all HF's to always have the same age as the PO. If the PO wants to know the current age of some particular distant person (DP) when the PO is age "T", he just needs to ask the HF who happens to be momentarily colocated with the DP at that instant, "What was the age of the DP when you were "T" years old?".

If we use the above procedure for several different inertial reference frames (that are moving with respect to one another), the PO's in those different frames (when they are momentarily co-located) will get DIFFERENT answers to the question "How old is that distant person, right NOW. But each of the PO's MUST conclude that the answer he got is completely real and meaningful to him, because it is based ONLY on the assumption that the speed of a light pulse is always equal to 186,000 miles per second in ANY inertial reference frame. If that assumption were wrong, then all of special relativity would collapse.

But what about for an ACCELERATING observer (the AO)? Can a "NOW" moment be defined for him? The answer is YES! He can ALSO surround himself with an array of clocks and HF's, separated by constant distances. Those clocks (and the corresponding HF's ages) CAN'T be synchronized with his clock and his age (because they all run at different rates), but he IS able to calculate what the reading of each HF's clock (and each HF's age) is at any instant of his (the AO's) own age. That DOES establish a "NOW" moment (extending throughout all space) for him, and that "NOW" moment MUST be completely real and meaningful to him.

When you use the above procedure, the result is the same as that given by the Co-Moving-Inertial-Frames (CMIF) simultaneity method. So the easy way to get the answer is to just use the CMIF method (and that is what Brian Greene is using in his "alien" scenario in his NOVA program to determine simultaneity at a distance). What the array of clocks method does is GUARANTEE that the result given by the CMIF method must be considered to be completely real and meaningful to the AO.

The derivations of the above results are given in three viXra papers. The "overview" (short) paper is titled

"Is the Equivalence Principle Schizophrenic? ... And a Summary, and a Correction", https://vixra.org/abs/2206.0133

Michael Leon Fontenot

[Kartazion]

I think the the "now" in the interpretation of relativity is when you stop time at instant t during the events of the studied system, and you start to calculate and reflect on the data collected from the events of this instant t and predict thanks to equations the evolutions of the system.

[MikeFontenot (OP)]

Relativity of simultaneity is a direct consequence of Lorentz invariance.

I'm not certain what you mean by Lorentz invariance.  Does that just refer to the fact that any given light pulse will be measured to be traveling at 186,000 miles per second in ALL inertial reference frames?

 Since Lorentz invariance has been demonstrated to extremely high precision experimentally, then we know by consequence that relativity of simultaneity is also a physically real phenomenon. It's not an illusion.

It's definitely not an illusion.  But it's been my experience that many physicists don't seem to consider it to be fully meaningful and "real".
I think it's commonly believed that if different momentarily-co-located observers come to different conclusions about the current age of the same distant person, then that IMPLIES that those results cannot be meaningful or real.  But I'm convinced that each of those different conclusions IS meaningful and real, TO THAT OBSERVER.

And I believe that the ability to determine simultaneity at a distance, by using arrays of clocks (and helper-observers) as I have described, shows that simultaneity at a distance MUST be considered to be fully meaningful and real to each observer (both in the inertial observer case AND in the accelerated observer case).

If the inertial observer were to conclude that his determination of the current age of the distant person isn't real or meaningful, he would also have to conclude that the speed of light is NOT 186,000 miles per second in his frame, which violates the fundamental assumption of special relativity.

Fortunately, the result given by the array of clocks is the SAME result as is given by the commonly used methods (the time dilation equation (TDE) method for an inertial observer, and the Co-Moving-Inertial-Frames (CMIF) method for an accelerating observer).  The TDE and the CMIF methods are MUCH easier, quicker, and more practical to use than the array-of-clocks method.  The VALUE of the array-of-clocks method is strictly that it GUARANTEES the meaningfulness of the results of the TDE and CMIF methods.

[Kryptid]

This whole thread has derailed from MikeFontenot's original post and is now focusing solely around Deecart's claims. As such, I'm splitting this into two threads.  Here is the new one: https://www.thenakedscientists.com/forum/index.php?topic=85310.0

Please keep relevant posts in the relevant threads.

[MikeFontenot (OP)]

The best way of understanding the concept of a "NOW" moment in special relativity is to first get an understanding of Einstein's array of clocks, yardsticks, and "helper friends" (HF's) in an inertial reference frame. He said that all the clocks in that reference frame could be synchronized by sending light pulses between the various clocks, and by making use of the fact that in ANY inertial frame, any light pulse will move at 186,000 miles per second, according to all stationary observers in that frame.

So how do we use that fact to get a "NOW" moment (extending throughout all space), according to some particular inertial observer (call him the "PO") in that frame? To make it simple, we can arrange for all HF's to always have the same age as the PO. If the PO wants to know the current age of some particular distant person (DP) when the PO is age "T", he just needs to ask the HF who happens to be momentarily colocated with the DP at that instant, "What was the age of the DP when you were "T" years old?".

If we use the above procedure for several different inertial reference frames (that are moving with respect to one another), the PO's in those different frames (when they are momentarily co-located) will get DIFFERENT answers to the question "How old is that distant person, right NOW. But each of the PO's MUST conclude that the answer he got is completely real and meaningful to him, because it is based ONLY on the assumption that the speed of a light pulse is always equal to 186,000 miles per second in ANY inertial reference frame. If that assumption were wrong, then all of special relativity would collapse.

But what about for an ACCELERATING observer (the AO)? Can a "NOW" moment be defined for him? The answer is YES! He can ALSO surround himself with an array of clocks and HF's, separated by constant distances. Those clocks (and the corresponding HF's ages) CAN'T be synchronized with his clock and his age (because they all run at different rates), but he IS able to calculate what the reading of each HF's clock (and each HF's age) is at any instant of his (the AO's) own age. That DOES establish a "NOW" moment (extending throughout all space) for him, and that "NOW" moment MUST be completely real and meaningful to him.

When you use the above procedure, the result is the same as that given by the Co-Moving-Inertial-Frames (CMIF) simultaneity method. So the easy way to get the answer is to just use the CMIF method (and that is what Brian Greene is using in his "alien" scenario in his NOVA program to determine simultaneity at a distance). What the array of clocks method does is GUARANTEE that the result given by the CMIF method must be considered to be completely real and meaningful to the AO.

The derivations of the above results are given in three viXra papers. The "overview" (short) paper is titled

"Is the Equivalence Principle Schizophrenic? ... And a Summary, and a Correction", https://vixra.org/abs/2206.0133

Michael Leon Fontenot

The material that I've posted above is actually NOT a new "theory".  I.e., it is NOT an ALTERNATIVE to special relativity.  The "array of clocks" construction, that establishes a "NOW" moment for an observer in an INERTIAL frame, was done by Einstein himself.

What I've done is to show that an analogous thing can also be done for an accelerated frame of reference in special relativity.  I.e., an array of clocks can also be set up for an accelerating observer.  That is possible by making use of a combination of the gravitational time dilation (GTD) equation, and the equivalence principle.  The only original work I've had to do, is to first realize that the existing GTD equation (the well-known exponential version) is incorrect, and then to derive the corrected version.

How could it be that the exponential equation (first written down in 1907 by Einstein himself) could be wrong all these years, without anyone noticing?  I THINK it's never been noticed before, because no one has ever happened to use it for large values of its argument (until I did).  And when I  did that, I got absurd results that violate a sacrosanct equation (the time dilation equation for an inertial observer).  In an argument between the time dilation equation for an inertial observer, and the exponential gravitational time dilation equation, the exponential gravitational time dilation equation loses.

[JanetSims]

I bet that even renowned scientists can get wrong, why not.

[Halc]

The material that I've posted above is actually NOT a new "theory".

You're calling the equivalence principle 'Schizophrenic' which is a form of science denialism. The topic is in new theories where it belongs.

The only original work I've had to do, is to first realize that the existing GTD equation (the well-known exponential version) is incorrect

It is not 'the well known version' nor is it 'sacrosanct' since I had trouble finding it anywhere. It is correct for the fairly obscure scenario in question. Still, your wording above suggests you have a new theory.

What I've done is to show that an analogous thing can also be done for an accelerated frame of reference in special relativity.  I.e., an array of clocks can also be set up for an accelerating observer.

I've not figured out what you're trying to do there. Clocks in an accelerated frame (say clocks situated at various points in a rigid accelerating ship) are going to stay in sync in neither the ship frame nor any inertial frame.

That is possible by making use of a combination of the gravitational time dilation (GTD) equation

What you're calling this GTD seems to appear in very few places anywhere. I looked on the wiki page by the same name, and it isn't mentioned. The general (and normalized) formula there is

T_d(h) = exp[ ∫₀^h g(h') dh' ]

Yea, I know, I need to put that in tex.

g(h) is a function of the geometry. It is constant in Einstein's 1907 paper. It is linear for said rigid accelerating object. It is a 2nd order effect for gravity of a spherical mass, so one can empirically determine one situation from the other by simply doing some non-local measurement like reading clocks at various altitudes.

I looked at the 1907 paper, which I find here (from wiki reference) http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_1907_Jahrbuch.pdf
This is a 1977 journal of physics English translation of the paper. Page 900 (right) lists the simplified (no 2nd order effects considered) equation as eqn 30. Just below that is the only reference to what you call 'the GTD', which Einstein didn't even bother to number. It seems to only apply to this uniform proper acceleration case (a sort of Bell's spaceship scenario), inappropriate for discussion of say clocks on different floors of a tall building where g(h) is not constant.

[MikeFontenot (OP)]

[Mod edit: Hijack split from
https://www.thenakedscientists.com/forum/index.php?topic=86093.0
merged with this topic since it is essentially the same discussion]

This thread only concerns the question of what events on Andromeda look like to someone on earth looking at it through a telescope.  But there is a far more interesting question: What do two people on earth, who are moving with respect to one another in the direction of Andromeda, conclude about the current time on Andromeda?  The answer, according to special relativity, is that the two people will disagree about what is currently happening on Andromeda.  (They ultimately don't disagree about the complete sequence of events that occur on Andromeda, they just disagree about what in that sequence is happening "right now".)

Roger Penrose advanced a form of this argument that has been called "the Andromeda paradox" in which he points out that two people walking past each other in the street could have very different present moments. If one of the people were walking towards the Andromeda Galaxy, then events in this galaxy might be hours or even days advanced of the events on Andromeda for the person walking in the other direction. [...]  Penrose highlighted the consequences by discussing a potential invasion of Earth by aliens living in the Andromeda Galaxy. As Penrose put it:

    Two people pass each other on the street; and according to one of the two people, an Andromedean space fleet has already set off on its journey, while to the other, the decision as to whether or not the journey will actually take place has not yet been made.

[Origin]

But there is a far more interesting question: What do two people on earth, who are moving with respect to one another in the direction of Andromeda, conclude about the current time on Andromeda? 

You should start a topic on that if you find it interesting instead of hijacking this one.

[MikeFontenot (OP)]

The answer to the original question is "No, obviously not."  It's a trivial question, with an obvious answer.

If the answer were "yes", that would require that, if you received two light pulses p1 and p2, at time t1 and t2 of your time on Earth (with t2 > t1), that when the pulses left Andromeda, p1 left AFTER p2 did.  I.e., it would require that the second pulse to leave Andromeda would have to overtake the pulse that left earlier, so that it arrives first at Earth.  That's nonsense.

[MikeFontenot (OP)]

The only remaining question, in my mind, about this thread is "What motivated the OP to ask his original question".  My guess is that he had heard (perhaps from people like me) that if a person (he) suddenly changes his velocity with respect to a distant person (her), accelerating in the direction AWAY FROM her, that he will conclude that she suddenly gets YOUNGER during his acceleration.  So I think the OP may have miss-applied that result, thinking that it applied to the conclusions of the inertial person who was NOT changing her velocity.  But it does NOT apply in that case.  Any INERTIAL person always concludes that any other person moving relatively to herself will be getting older more slowly than she is, but she will never say that they are getting younger.

Also, I think the OP may have been confusing the conclusions of an observer about the current time at a distant location, with what the observer can see through his telescope at that instant.  Those are two very different things.

[Origin]

The only remaining question, in my mind, about this thread is "What motivated the OP to ask his original question".  My guess is that he had heard (perhaps from people like me) that if a person (he) suddenly changes his velocity with respect to a distant person (her), accelerating in the direction AWAY FROM her, that he will conclude that she suddenly gets YOUNGER during his acceleration

My only question is how can you not know what your motivation was?  I mean you're the OP for Gods sake, see the little (OP) by your name?

[Origin]

Mike is referring to the topic from which his last three posts were split (at your suggestion no less).

I know, l think I'm funny.  I realize this is the minority opinion.  Sorry for the pointless hijack.

[MikeFontenot (OP)]

The material that I've posted above is actually NOT a new "theory".

You're calling the equivalence principle 'Schizophrenic' which is a form of science denialism. The topic is in new theories where it belongs.

I used the word Schizophrenic to characterize the fact that sometimes a scenario that makes sense in free space with constant accelerations, does not make sense when converted to a motionless scenario with a constant (and uniform) gravitational field.  So in that case, the equivalence principle isn't valid.  (I gave an example of that in the paper you're referring to.)  But in other scenarios, the equivalence principle IS valid.  That's why I called the equivalence principle "Schizophrenic".

As to whether my results should be called "a new theory":

My results DON'T describe a new theory of physics, different from special relativity.  My results just point out and correct a mistake that has been perpetuated for more than a century in special relativity.  The mistake was first made by Einstein in his 1907 analysis of an array of separated, equally-spaced and equally-accelerated clocks. For his entire analysis, he used a linear equation for the time dilation, but made a quick comment at the end of the analysis that the correct equation should actually be an exponential.  Other people (such as Rindler) adopted Einstein's exponential, and eventually it became "common knowledge".  But it had never before been used for large values of acceleration (in the highly non-linear portion of the exponential), until I used it to describe what happens when the acceleration gets extremely large, and the duration of the acceleration gets extremely short.

I did a series of separate (numerical) experiments, with increasingly large (constant) accelerations (from one experiment to the next), but with durations of the acceleration chosen for each experiment so that the total change in the velocity was always the same, from one experiment to the next.

When you do that, you find that the resulting change in the reading of the leading clock, relative to the trailing clock, does not converge to a finite limit ... it goes to infinity as the duration goes to zero.  But that implies that the traveling twin in the twin paradox is infinitely old at the reunion, which is of course incorrect: we know (from the time dilation equation [TDE] for an INERTIAL person [the home twin]) that both twins have a FINITE age at the reunion.  In a disagreement between the exponential time dilation equation of general relativity and the TDE for an inertial person, the TDE wins.  The exponential GTD equation is wrong.  And after I had proven that, I was eventually able to determine the correct gravitational time dilation equation.