Twins paradox explained without forces

[md65536]

6 hours ago, Celeritas said:

Yes.  However, we assume the Einstein clock synchronization procedure is true to nature and hence correct, per Occam's Razor (until some future test proves otherwise).

Whether it's "true to nature" is neither testable nor even relevant! I'll repeat Einstein's argument: (emphasis mine)

Quote

"I maintain my previous definition nevertheless, because in reality it
assumes absolutely nothing about light. There is only one demand to be made
of the definition of simultaneity, namely, that in every real case it must supply
us with an empirical decision as to whether or not the conception that has to be
defined is fulfilled. That my definition satisfies this demand is indisputable.
That light requires the same time to traverse the path A -> M [the midpoint between A & B] as for the
path B -> M is in reality neither a supposition nor a hypothesis about the
physical nature of light, but a stipulation which I can make of my own freewill
in order to arrive at a definition of simultaneity."

 

6 hours ago, Celeritas said:

If a future test proves 1-way <> 2-way, well, then we'll be changing the LTs to accomodate.

That one-way is the same as two-way is by definition. See Einstein's 1905 paper, eg. translated at http://www.fourmilab.ch/etexts/einstein/specrel/www/
 where he writes:

Quote

We have not defined a common “time” for A and B, for the latter cannot be defined at all unless we establish by definition that the “time” required by light to travel from A to B equals the “time” it requires to travel from B to A.

There's no test that can invalidate a self-consistent definition! IF on the other hand, some test found that SR does not adequately describe reality, then some other definition of time, or a modified definition, might be used instead. For example in curved spacetime, in cosmology etc, that definition isn't used and there is no such definition of a common time (or simultaneity) for different locations throughout the universe.

If you think you're debating whether the LT or Einstein synchronization is "correct or incorrect", you're missing the point and wasting your time, because it's correct. But when you speak of what happens at a distant A when B does something locally, you are basing that off of definitions. What's happening at A is outside B's light cones, there is no causal effect, and arguments about what is "true to nature" are not supported by SR as written by Einstein. The difference in ageing when they meet is indisputable, testable, true to nature, geometrically measurable, etc. The time at A when B is far from it is NOT based on "nature", Occam's razor, experiment, etc., it is established by definition. Any true conclusions you make based off of that are true by definition, regardless of reality.

As for Occam's razor, if something like the simultaneity of events at A and B can neither be physically proven real nor proven inconsistent, wouldn't it be simpler to neither assume that they're real nor wrong, and accept that it might be just a definition that can "supply us with an empirical decision as to whether or not the conception that has to be defined is fulfilled" and not necessarily physical?

 

 

Also, I don't argue that acceleration plays no role in the twin paradox; B's path involves a turnaround that involves acceleration. I argue it plays no role in OP's experiment. But if you can agree that in the water boiling analogy (two twin cups of water A and B, B is poured into a kettle that's on the stove and it boils)... if you agree that "pouring the water causes it to boil" then I'll agree that "B accelerating causes the difference in ageing", because then I'll understand the intended interpretation of the statement. Please, can we just agree??? Otherwise, I think that the role of acceleration in the twin paradox is the same as the role of pouring the water; something that establishes the necessary conditions for the outcome of the particular experiment.

Edited February 5, 2020 by md65536

[Markus Hanke]

5 hours ago, Celeritas said:

and it is ultimately about the length of the worldlines over the interval

This is it, plain and simple.
If you have two events in spacetime (start and finish), with initial conditions being equal, there is precisely one unique inertial world line connecting these events. This is geometrically the longest possible world line, i.e. the one that accumulates the most proper time. Formally, this world line is a geodesic of the spacetime, meaning you have 

\(a^{\mu}=0\)

everywhere along it. The only way to obtain a different world line connecting these same events, with all other things remaining equal, is to violate the above condition - i.e. introduce proper acceleration at some point, which leads to a world line that is shorter than the inertial one. 

Of course you can decide to vary initial conditions as well between observers, in which case they will trace out different inertial world lines between the same events - but then you are no longer comparing like for like.

[Mordred]

Excellent post +1

[Celeritas]

32 minutes ago, Markus Hanke said:

This is it, plain and simple.
If you have two events in spacetime (start and finish), with initial conditions being equal, there is precisely one unique inertial world line connecting these events. This is geometrically the longest possible world line, i.e. the one that accumulates the most proper time. Formally, this world line is a geodesic of the spacetime, meaning you have 

aμ=0

everywhere along it. The only way to obtain a different world line connecting these same events, with all other things remaining equal, is to violate the above condition - i.e. introduce proper acceleration at some point, which leads to a world line that is shorter than the inertial one. 

Of course you can decide to vary initial conditions as well between observers, in which case they will trace out different inertial world lines between the same events - but then you are no longer comparing like for like.

I'm not sure why you posted this for me Markus?  I only re-iterated that the length of the worldlines dictates the relative aging in the stated twins scenario. I mean, I've been saying that all along here.  Wrt any of my prior posts, can you refer me to the part that made you think I did not realize that going non-inertial causes the lesser aging (or symmetry break).

Wrt your last line ... same thing.  I did mention that twin B's velocities (per A) are the result of its intial velocity and all the subsequent proper accelerations by B. I don't recall suggesting changing the motions of twin A or B wrt the defined twins scenario.

I understand everything you say here above.  If I had contradicted that anywhere, it went unbeknownst to me.

Best regards,

Celeritas

Edited February 5, 2020 by Celeritas

[Celeritas]

3 hours ago, md65536 said:

That one-way is the same as two-way is by definition. See Einstein's 1905 paper,

md65536,

I understand Einstein's convention, and that it is by definition. 

But before responding further, I need to revisit differing conventions-of-simultaneity, make sure I understand that properly.  I was thinking differing conventions would produce somewhat different LT solns, but now I'm thinking that's not the case.  Given the LT solns are no different, I suppose it would not matter if the convention was true to nature or not.  However, the LTs are simplest per Einstein's convention.  Also, it's hard to imagine the ray not bisecting the roundtrip in the proper frame of the emitter/reflector, given there are no preferred frames.

Best regards,

Celeritas

Edited February 5, 2020 by Celeritas

[md65536]

1 hour ago, Celeritas said:

I understand Einstein's convention, and that his is per definition.  Maybe I misunderstand the impact of differing time sync conventions tho? 

Let me ask you this first ... Based on what you've stated, you seem to be saying that the time sync convention does not matter, that (for the same scenario) the LT solns are the same no matter if 1-way = 2-way speed of light, or not.  Am I correct in that?  That for those differing conventions, the LTs will predict the very same time readouts for all intersecting moving clocks in flat spacetime, given the same scenario?

The point of the twin paradox setup is that it produces a result that's certain and independent of reference frame. You never *have* to compare distant clocks to resolve it. You don't need synchronized clocks, or a synchronization convention, or a definition of simultaneity. In that sense they don't matter. You don't need coordinate times or the LT to resolve the paradox. But if you try, using the LT, you always get consistent results.

If you used any alternative that was consistent with reality, it would give you the same results at the events where the twins meet. Any other result isn't consistent with reality. If you use some other transformation or system of coordinates or definition of time where the one-way speed of light is different in different directions, if it was consistent with reality you'd get the same age difference that SR predicts when the twins reunite, but generally a different coordinate time of events at the other clock while they're separated.

The coordinate times given by the LT would be different if they used a different definition of time other than Einstein's, where the time of a light signal between two locations is the same in either direction. You say "readouts" given by the LT, I guess you mean the calculated coordinate time in the distant clock's reference frame of the local event "now" ... the calculated coordinate time in the distant clock's reference frame, of an event at the distant clock's location, whose time in the local clock's reference frame is "now"???. At the intersections of two clocks' world lines, the "readouts" wouldn't depend on the one-way speed of light because the distance between the clocks would be 0, and the time of a light signal would be the same regardless. So I guess the answer, as best as I can understand your question, is "no", in general an alternative to the LT would give you different "readouts" everywhere except where the two clocks meet.

Edited February 5, 2020 by md65536

[Markus Hanke]

5 hours ago, Celeritas said:

I'm not sure why you posted this for me Markus? 

Apologies if it came across wrongly, the intention was not to make you aware of anything “wrong” you might have said. It wasn’t even directed at you as such, it was more of a general comment.
My intent was simply to point out that looking at the situation in terms of geometry of world lines is the easiest and most straightforward way to do it, since that geometry is a quantity that all observers agree on. This is as opposed to reference frames, observers, clocks etc, which makes the situation unnecessarily confusing. But maybe that is just me

[md65536]

6 hours ago, Markus Hanke said:

My intent was simply to point out that looking at the situation in terms of geometry of world lines is the easiest and most straightforward way to do it, since that geometry is a quantity that all observers agree on. This is as opposed to reference frames, observers, clocks etc, which makes the situation unnecessarily confusing. But maybe that is just me

Yes, we all agree on that! Celeritas, you're right on that.

 

However Markus, if you take clocks out of it you're no longer talking about the twin paradox, which concerns ageing. The geometric length of the world lines doesn't depend on the validity of the clock hypothesis (right?) but the twin paradox does. Back to OP's topic, the 3-clock variation also does not depend on the validity of the clock hypothesis. But in either case its fine because we assume the clock hypothesis is true in the twin paradox in any case, which means both OP's experiment and the geometric length measure the same ageing as does a clock that turns around (instantly, in this case corresponding to OP's setup).

The situation in terms of geometry is the easiest and most straightforward, leaving no room for debate or confusion about physical aspects, and the lack of effects due to acceleration (that aren't fully accounted for in terms of velocity) is by definition of geometric length (I think). In the twin paradox the lack of effects due to acceleration (that aren't fully accounted for in terms of velocity) is by assumption and experimental confirmation "to very high accelerations".

Edited February 5, 2020 by md65536

[dimreepr]

11 minutes ago, md65536 said:

if you take clocks out of it you're no longer talking about the twin paradox, which concerns ageing.

so you take time out of spacetime.

[Celeritas]

12 hours ago, md65536 said:

The coordinate times given by the LT would be different if they used a different definition of time other than Einstein's, where the time of a light signal between two locations is the same in either direction.

OK, thanks md.  Long ago, I tried deriving LTs using a non-midpoint reflection event in the k system.  I remember the derivation got rather ugly, fast.  It did not simplify very well at all.

12 hours ago, md65536 said:

The coordinate times given by the LT would be different if they used a different definition of time other than Einstein's, where the time of a light signal between two locations is the same in either direction.

Yes, that's the conclusion I came to, way back.  I was second guessing that last night, as it had been awhile.  I may have to try that derivation again, although I presume it's likely been long on the web somewhere, so maybe I'll look for that.

12 hours ago, md65536 said:

You say "readouts" given by the LT, I guess you mean ... the calculated coordinate time in the distant clock's reference frame, of an event at the distant clock's location, whose time in the local clock's reference frame is "now"???. At the intersections of two clocks' world lines, the "readouts" wouldn't depend on the one-way speed of light because the distance between the clocks would be 0, and the time of a light signal would be the same regardless. So I guess the answer, as best as I can understand your question, is "no", in general an alternative to the LT would give you different "readouts" everywhere except where the two clocks meet.

Wrt 1st highlight ... Yes, the coordinate time of a remotely located moving clock was the focus of my question there. 

Wrt 2nd highlight ... One can envision virtual clocks everywhere and anywhere in spacetime.  Any virtual clock should be substitutable by a real clock.  I would imagine this true no matter if 1-way = 2-way or not.  You said above that for 1-way <> 2-way, coordinate time calculations for remotely located clocks would differ from SR solns (using 1-way = 2-way), except where 2 clocks intersect.  However no matter the convention, we can still envision virtual clocks everywhere and anywhere in spacetime, including virtual clocks intersecting at any and all points in spacetime. Virtual clocks should always be substitutable by real clocks. So it seems that even for intersecting clocks, if 1-way <> 2-way then the spacetime solns should differ from SR's solns.  No?  

 

9 hours ago, Markus Hanke said:

Apologies if it came across wrongly, the intention was not to make you aware of anything “wrong” you might have said. It wasn’t even directed at you as such, it was more of a general comment.
My intent was simply to point out that looking at the situation in terms of geometry of world lines is the easiest and most straightforward way to do it, since that geometry is a quantity that all observers agree on. This is as opposed to reference frames, observers, clocks etc, which makes the situation unnecessarily confusing. But maybe that is just me

I see, that's fine Markus.  Thanx.   

I realize that everyone agrees on the twins solns, and why it happens.  My discussion with md65536 was focused strictly on whether one can say "acceleration does not cause the twin's relative aging differential".  Md65536 associates "felt force" with proper acceleration.  If twin B has thrusters on opposite sides of himself, and they fired equally, he feels his compression but goes nowhere.  Also, that the huge inertia felt by B at his own (virtually) instant turnabout can play (virtually) no role in the relative aging outcome, because (virtually) no proper time is accrued during that period. However, it's not really about the force felt during B's proper acceleration, it's about "the transitioning of inertial frames of reference", which requires a proper acceleration by B in this twins scenario.  This is just to say that twin B's proper accelerations are required to attain the worldline geometry that produces the result of twin B aging 8y to twin A aging 10y. 

I think this famous debate is the result of the scope in which one considers the question ...

... (1) Highest level consideration ... use the geometry of the A & B worldlines.

... (2) Easiest restricted consideration ... use the accrual of proper time alone, for both A & B.

... (3) Hardest restricted consideration ... use the accrual of proper time for A (or B), and the accrual of coordinate time for the other observer B (or A).

All 3 work in so far as calculating the round trip relative-aging.  And of coures, for otherwise SR would be an incomplete theory.

Regarding (2) vs (3), using (3) requires the consideration of the twin B transitioning of frames, from his own POV.  It is there that the role of frame-transitioning is revealed, because one must then consider the more difficult aspect of a dynamic change in twin B's sense-of-simultaneity at turnabout per himself.  My point is that while proper time is all you need, it's the frame transitioning that attains the required geometry of worldlines to produce 8y-B to 10y-A.  That said, while all 3 work, (1) presents everything in a nutshell.  A picture paints a 1000 words.

I'll have to address md65526's anaolgy wrt boiling water next, see where it all goes.

Best regards

Celeritas

Edited February 5, 2020 by Celeritas

[Celeritas]

On 2/5/2020 at 12:22 AM, md65536 said:

Also, I don't argue that acceleration plays no role in the twin paradox; B's path involves a turnaround that involves acceleration. I argue it plays no role in OP's experiment.

That sounds good to me.  The OP had no acceleration by definition.

On 2/5/2020 at 12:22 AM, md65536 said:

But if you can agree that in the water boiling analogy (two twin cups of water A and B, B is poured into a kettle that's on the stove and it boils)... if you agree that "pouring the water causes it to boil" then I'll agree that "B accelerating causes the difference in ageing", because then I'll understand the intended interpretation of the statement. Please, can we just agree??? Otherwise, I think that the role of acceleration in the twin paradox is the same as the role of pouring the water; something that establishes the necessary conditions for the outcome of the particular experiment.

OK md65536, wrt your pouring water into heated kettle analogy ...

The act of pouring the water, is akin to the act of the twin B starship being transported to the earth launchpad. Applying a flame to the kettle to raise the water temperature, is akin to burning the rocket thrusters (proper acceleration) to raise the starship velocity (frame transitioning).  Stabilizing at 212 deg F (boiling), is ~akin to coasting at speed inertially (no thruster burn, no acceleration).  The water boils because the water temperature reached 212F.  It reached 212F because the flame was applied.  OK, so let us imagine a kettle of cold water sitting on an un-lit burner.  Next, the professor says ... please boil the water.  Do we just wish the 212F into existence, or do we apply the required flame?  Bottom line, if twin B does not undergo proper accelerations, he can never age less than twin A (per the stated scenario).

I agree with the highlight above. (EDIT addition: Twin B is colocated and comoving wrt twin A at the getgo. For twin B to age less than A, in an absolute manner where all in the cosmos agree, he simply must change his worldline orientation to do so.  That is, he must make TURNs in 4d spacetime, ie transition fames of reference.  In flat spacetime, that requires twin B to undergo proper accelerations.  B must later re-unite with A.  B's proper saccelerations produce all the velocities that create the required geometry of worldlines, and their length which is the accrued proper time).

Anyways, I fully agree that the relative aging between the twins is determinable from the accrual of proper time alone.  And since by definition no time expires during periods of proper acceleration, the relative aging is determined strictly by the inertial phases of flight. This is nothing new.  All inertial scenarios possess relative time, and so relative aging is inherent there as well, although its relative per POV.  The OP has all that, as it's an all inertial scenario.  It's always the accrual of proper time that produces the worldline length, and/or vice versa.  What the OP does, which sums the proper time of 2 different POVs, is to show that the relative aging is the result of the worldline geometry.

One more ... I should say, I do like your posts md65536.  Very informative, always very well stated, and enjoyable.

Best regards,

Celeritas

Edited February 6, 2020 by Celeritas

[Celeritas]

Just FYI, the spacetime diagram, and geometry of worldlines ... 

Best regards,

Celeritas

Edited February 6, 2020 by Celeritas
Cosmetic cleanup

[md65536]

21 hours ago, Celeritas said:

One can envision virtual clocks everywhere and anywhere in spacetime.  Any virtual clock should be substitutable by a real clock.  I would imagine this true no matter if 1-way = 2-way or not.  You said above that for 1-way <> 2-way, coordinate time calculations for remotely located clocks would differ from SR solns (using 1-way = 2-way), except where 2 clocks intersect.  However no matter the convention, we can still envision virtual clocks everywhere and anywhere in spacetime, including virtual clocks intersecting at any and all points in spacetime. Virtual clocks should always be substitutable by real clocks. So it seems that even for intersecting clocks, if 1-way <> 2-way then the spacetime solns should differ from SR's solns.  No? 

Right. Where the clocks intersect, its only events at the other clock (which are now local events) whose coordinate time is independent of how you define remote simultaneity.

The solutions to the twin paradox remain the same. You can set all those other clocks everywhere else however you want to (eg. invent some alternative clock sync definition), but that won't affect the time measured by the two twins clocks.
 

[Celeritas]

md65536,

OK, so correct me if I'm wrong, but wrt your understanding of time sync conventions ...

Given a remotely located moving clock at an event, if the 1-way and 2-way speed-of-light is not equal, then coordinate time solns will differ from SR.  Also, the relative rate of a moving clock would not differ from SR (it's the same), given the same worldlines geometry.  Is that the way you see it?   I was wondering whether the relative rate of moving clocks would differ (wrt SR) with 1-way <> 2-way, or not.

Thanx,

Celeritas

Edited February 7, 2020 by Celeritas

[md65536]

10 hours ago, Celeritas said:

Given a remotely located moving clock at an event, if the 1-way and 2-way speed-of-light is not equal, then coordinate time solns will differ from SR.  Also, the relative rate of a moving clock would not differ from SR (it's the same), given the same worldlines geometry.  Is that the way you see it?   I was wondering whether the relative rate of moving clocks would differ (wrt SR) with 1-way <> 2-way, or not.

The time it takes for light to go from points P1->P2 is the same as P2->P1 in a stationary system, by definition. The LT has a mathematical definition, it's not based on measured constants. It has c in it as a constant, which also is a defined (not measured) value. The metre is defined based on c. Which of those are you changing to get a 1-way speed not equal to 2-way speed? Depending on what you change, you'll change the LT. I don't know if it's possible to change multiple things to make a modified LT give the same results as the LT, while having different 1-way speeds of light in the x direction.

The relative rates of a moving clock would typically change, the lengths of world lines between events would not.

Here's an example. Suppose someone Q decided their own reference frame was privileged, and invented a system based on SR but where all relative measurements used their reference frame. Suppose they're moving relative to twins A and B (and clock C too), such that in their frame, the standard LT says that the time at A when B turns around (or passes C) is 6 years after A and B depart, as measured by A's clock. Then, on the outbound trip, B's clock measures 4 years while A's measures 6, so B's clock ticks at a rate of 2/3. On the inbound, B (and C) measure 4 years while A measures 4. As always, in this experiment A ages 10 years while B ages 8 in the end. These measurements are different than what the LT says for A and B (but it agrees with what the LT says for Q, so you know it isn't predicting something inconsistent with reality).

Normally A and B measure things using their own reference frames, but if they adopted this alternative, they'd use a definition where the time between P1->P2 is the same as P2->P1 (because it is in Q's), which is weird for them, because P1 and P2 are not stationary in A's or B's frames, so using normal SR measurements they'd measure those two times to be different.

So there's an alternative. It's bad, but it works. It doesn't match reality for A and B in the fact that their systems are not measurably distinguishable as less privileged than Q's, but they're defined to be, and things are measured differently in different frames to match what Q' measures. But they have still have consistent definitions for all the measurements they need wrt. things like the twin paradox, and can confirm them experimentally.

 

I hope I'm not just making things more confusing. The only reason I'd mention alternatives is to figure out what exactly SR says and doesn't say. The twin's ages when they meet, are invariants. The values that are relative can be consistent with various different systems of measurement that give different values.

 

I feel like I'm straying farther and farther off topic trying to clarify what I said earlier, but I'm failing in that because you keep thinking I'm saying something else.

 

PS. If you really get what I'm saying, I think I accidentally described a screwed-up system where the 2-way speed of light is still the same as the 1-way, according to the definitions, even though if you have two points p1 and p2 that are stationary in A's reference frame, A measures the time from p1->p2 as different than p2->p1, because it's using Q's measurements and they're not stationary to Q. Sorry, it's excessively complicated now, but if you get that then you probably understand the way I see this. All these measurements aren't "common sense" descriptions of what we understand as time and distance and speed, they have precise definitions that don't care what common sense says.

Edited February 7, 2020 by md65536

[Celeritas]

md65536,

Thanx for the response. 

I understand what you're saying there.  There are various ways of considering theories different from Einstein's. 

There's Lorentz's version, which uses a master frame while using the Einstein/Poincare convention for simultaneity.  The transformation solns are the same as Einstein's because obervers moving thru the preferred ether frame use length-contracted rulers to measure equally contracted-lengths, and similary for using time-retarded clocks and while measuring dilated durations.  Also, while all observers of a single frame use the Poinare/Einstein clock sync procedure, those co-moving thru the ether believe they are synchronised while in reality they are not (but don't know, and cannot tell).  Here, while simultaneity differs wrt SR, the LT solns are all the very same. I'm wondering whether Lorentz could even have developed his theory, had light been used as the definition for the metre in 1905? I suppose it could, since all observers measure its speed the same anyway.

Your example uses the sort of preferred-frame theory that differs from Lorentz's, using slightly different assumptions, principles, and/or postulates. Such as, light speed is invariant in only the preferred frame, but is measured variantly by observers moving wrt the preferred frame (different from Lorentz's).  I see your point, in that the transformations of space & time (of course) depend on the apriori assumptions, principles, and postulates used.

If various theories can produce self-consistent space & time solns, based upon each their own (reasonable) apriori assumptions, principles, and postulates, then how to say the theory is wrong even if it produces space & time solns that differ from SR?  All the tests of relativity to date support Einstein's version, and Lorentz's.  Einstein's is preferred for various reasons, eg no ad hoc explanations are required, it's mathematically self consistent from 1st prinicples, it allowed for the general theory of gravity, and Occam's Razor supports it.  I'm supposing that all the (non-Lorentz) preferred frame theories of the prior para here, have been proven false by all the tests fo Relativity to date. Yes?

So out of interest, I re-derived the LTs (as per OEMB's) using a non-midpoint reflection event, whereby I defined the reflection event as a variable (e) whereby 0 > e < 1.  Einstein's convention would use ½, so only e = 0.5.  It turned out that no matter what "e" I select, the spreadsheet produces the very same LT results as SR, but that's only because I hadn't yet completed it ... whereby the outbound 1-way light speed must differ from the inbound 1-way light speed, given the reflection event does not occur at half the roundtrip durarion. Of course, the 2-way speed of light remains at c. So, that's next.  However, I was not assuming a preferred frame, but rather whereby all observers use the very same convention and assumed equally correct (which I'm not sure even makes sense yet?).  So, I'm not really sure yet if it's even worth the persuit.  And, how to define the meter's length, if light speed outbound differ's from light speed inbound?  It seems you could not use light's wavelength for defining the duration of the second or the length of a meter.  Yes?

Best regards

Celeritas

Edited February 8, 2020 by Celeritas

[md65536]

1 hour ago, Celeritas said:

Your example uses the sort of preferred-frame theory that differs from Lorentz's, using slightly different assumptions, principles, and/or postulates. Such as, light speed is invariant in only the preferred frame, but is measured variantly by observers moving wrt the preferred frame (different from Lorentz's).

No, I don't think so. How is the measure of speed defined? If other observers measure time AND distance the same as it is measured in the preferred frame, all observers measure the speed of light the same.

That's the point I keep trying and failing to make. These values have definitions, you have to go by how they're defined. You can't just use a common-sense definition of speed, or mix-and-match definitions, altering one quantity but not another that is based on it.

1 hour ago, Celeritas said:

If various theories can produce self-consistent space & time solns, based upon each their own (reasonable) apriori assumptions, principles, and postulates, then how to say the theory is wrong even if it produces space & time solns that differ from SR?  All the tests of relativity to date support Einstein's version, and Lorentz's.  Einstein's is preferred for various reasons, eg no ad hoc explanations are required, it's mathematically self consistent from 1st prinicples, it allowed for the general theory of gravity, and Occam's Razor supports it.  I'm supposing that all the (non-Lorentz) preferred frame theories of the prior para here, have been proven false by all the tests fo Relativity to date. Yes?

No. Multiple alternatives that give different values for RELATIVE quantities can be "right". There's no evidence of an ether frame, but lack of evidence isn't proof of non-existence. They haven't been proven false, just proven so-far useless. Everything still works if you decide a frame is preferred.

This is a waste of time...

... but for another example, suppose you have an event, and observer A uses coordinates with the origin in one place, and B has the origin in another place, and they get different results for the coordinates of the event. Which observer is right? They both are. Suppose A uses Cartesian coords and B uses spherical, and they get different results. Which coordinate system is wrong? Neither.

The LT gives you COORDINATES within a defined system, it doesn't claim that those coordinates are "real". Comparing different ageing at a meeting point is comparing values that are real. You can't come up with working alternative coordinates that make someone older or younger than they actually are at a given local event. You *can* come up with working alternative coordinates that make someone older or younger than the LT says they are relative to some distant event.

Different simultaneity conventions that still corresponded with reality as SR and Einstein's simultaneity definition do, would simply give you different time coordinates of distant events. Which is right? Maybe all. Which is useful? I've never seen any better than Einstein's. Which is "real"? There's no theoretical answer and the question is likely meaningless. Analogous to "what are the real coordinates of the event, A's or B's?"

Edited February 8, 2020 by md65536

[Celeritas]

md65536,

I realize that coordinate types are a choice, and that events in spacetime are what's true or real.  However, there's one particular point that I need to clear up.  I've asked before, and I may have misunderstood your response in regards to this. You've said that alternative theories can produce different coordinate values for remotely located moving clocks, yet still be right.  Consider these ...

Per SR, per our Time Handoff scenario, the A observer predicts the B clock to read 4y-B, and the C clock to read 4y-C, upon B/C flyby.  So ...

(1) In an alternate theory, A predicts the B clock to read 4y-B, and the C clock to read 6y-C, upon B/C flyby.   How can it be said that both theories are correct? 

Or ... 

(2) In an alternate theory, A predicts the B clock to read 6y-B, and the C clock to read 6y-C, upon B/C flyby.   How can it be said that both theories are correct?  

When 2 clocks execute a flyby event, they have a specific time readout when they do, and all in the cosmos must agree.  Only the theory that predicts the correct readouts, is a valid theory.  If 2 theories can disagree on coordinate time solns for remotely located moving clocks, how can those 2 theories agree on the coordinate time (current time-readout) of intersecting clocks at their flyby event?  

Said another way ... if the time readout of 2 distant intersecting clocks read 4y-B and 4y-C at their flyby event, those times being coordinate-times of B & C per A, how can a (assumed) valid theory "that produces differing coordinate times (wrt SR)" predict their flyby "at the same readouts of 4y-B and 4y-C"?

Thanx,

Celeritas

Edited February 9, 2020 by Celeritas

[md65536]

2 hours ago, Celeritas said:

You've said that alternative theories can produce different coordinate values for remotely located moving clocks

Not theories. I've only talked about the theory of SR in this thread. I think they'd be called different coordinate systems.

 

2 hours ago, Celeritas said:

(1) In an alternate theory, A predicts the B clock to read 4y-B, and the C clock to read 6y-C, upon B/C flyby.   How can it be said that both theories are correct? 

 

Or ... 

(2) In an alternate theory, A predicts the B clock to read 6y-B, and the C clock to read 6y-C, upon B/C flyby.   How can it be said that both theories are correct? 

So much wrong with this. B passing C is an event. OP has set it up so that B's clock shows 4 years at that event, and C's clock shows 4 years at that event. Those are invariants. No change in coordinates can change what B's clock shows at an event that it passes through.

It's the time at A, far away, not local!, when B and C pass, that depends on a coordinate system. You already know, that even using the standard coordinate systems of SR (I think we call them Minkowski coordinates?), A's time, when B and C pass, differs depending on which inertial frame you're describing it in. But it can also change if you use an alternative coordinate system.

2 hours ago, Celeritas said:

If 2 theories can disagree on coordinate time solns for remotely located moving clocks, how can those 2 theories agree on the coordinate time (current time-readout) of intersecting clocks at their flyby event?

Not theories. B and C disagree on the coordinate time at A, when they pass, yet all observers agree on the time at A when A and C pass. Do you understand how that's possible in SR?

2 hours ago, Celeritas said:

Said another way ... if the time readout of 2 distant intersecting clocks read 4y-B and 4y-C at their flyby event, those times being coordinate-times of B & C per A, how can a (assumed) valid theory "that produces differing coordinate times (wrt SR)" predict their flyby "at the same readouts of 4y-B and 4y-C"?

I don't know where you're getting this from. It's the coordinate time at A that is relative, when B and C pass. A is not intersecting any of the other given world lines when B and C pass.

It is only the time according to a clock that is some distance (not local) from the event, that is relative.

Edited February 9, 2020 by md65536

[Celeritas]

14 hours ago, md65536 said:

So much wrong with this. B passing C is an event. OP has set it up so that B's clock shows 4 years at that event, and C's clock shows 4 years at that event. Those are invariants. No change in coordinates can change what B's clock shows at an event that it passes through.

It's the time at A, far away, not local!, when B and C pass, that depends on a coordinate system. You already know, that even using the standard coordinate systems of SR (I think we call them Minkowski coordinates?), A's time, when B and C pass, differs depending on which inertial frame you're describing it in. But it can also change if you use an alternative coordinate system.

Sorry md, but I'm not quite following your responses here.  For example, I'm talking about a deviation from SR whereby the 1-way <> 2-way speed of light (not Lorentz's theory tho), but you have responded with things like "there's no difference between polar coordinates and catesian coordinates.  Well, of course there ain't, but I don't see how that relates to what I've been asking about ... When it comes to 2 theories eg 1-way=2-way (SR) versus 1-way<>2-way (again, not talking Lorentz's theory), I just don't see how that relates to "choice of differing types of coordinate systems for a single theory (eg polar vs cartesian)?  I've been assuming the same coordinate system is used by alternate competing theories (eg Cartesian alone). If all you are saying is that "for differing theories, given they produce the same time readouts for any 2 intersecting clocks in space and time, then they are valid theories", then I'm in agreement with that.  Einstein's and Lorentz's theories are 2 such theories, although only one theory (eg as SR) may be preferred for various reasons.  And, of course ... the OP says 4y-B and 4y-C at their flyby event per scenario setup, per SR.  However ...

You say that the time readout (now) on the A-clock is a coordinate time per B & C at their flyby event, because A is remotely located wrt them.  I said that the time (now) on the B & C clocks at their flyby event is also a coordinate time per A, because B & C are remotely located wrt him.  If 2 competing theories produce different coordinate times, then how could both those theories allow A to predict the B & C clocks to read 4y-B and 4y-C per A at the B/C flyby event?  It just seems to me that if both theories predict the correct time readout on 2 clocks during their remote flyby event, which can be anywhere in space and time, then I don't see how they can disagree on the coordinate time of remotely located moving clocks.  SR, I understand.  Differing coordinate systems I understand, eg polar vs cartesian. I'm just trying to grasp the impact of deviations from SR, particularly in relation to time-sync-convention and the 1-way speed of light (<- not Lorentz's theory tho).  

Thanx for your time md.  I'll just try to complete my LT derivation of a variable reflection event, so t'₁ = e(t'₀+t'₂) , so not just the case (eg per SR) where e = ½ which requires the 1-way = 2-way.  All I was aiming to verify is whether such a theory would produce different coordinate times for remotely located clocks, and whether such a theory would differ from SR in the time readout of 2 clocks executing a remote flyby event ... eg the current time readout (per A) of the B & C clocks 3 ly downrange at their own flyby event.

Thanx,

Celeritas

Edited February 9, 2020 by Celeritas

[studiot]

16 hours ago, md65536 said:

Not theories. I've only talked about the theory of SR in this thread. I think they'd be called different coordinate systems.

Yes they would.

 

It is instructive to conside a slightly simpler situation (I think you two have been chewing over this) where there is no acceleration, both 'twins' are in constant relative motion at all times.

Clearly they can only meet once and then separate for ever.

But in doing so how does each consider their aging compared to the other one?

Since you have used four years in some examples, whose fourth birthday comes first?

[md65536]

38 minutes ago, studiot said:

It is instructive to conside a slightly simpler situation (I think you two have been chewing over this) where there is no acceleration, both 'twins' are in constant relative motion at all times.

Clearly they can only meet once and then separate for ever.

But in doing so how does each consider their aging compared to the other one?

Since you have used four years in some examples, whose fourth birthday comes first?

Good idea. In that case the twins are symmetrical. There are observers that can measure A and B symmetrically, the simplest being one for which the speeds of A and B are both 1/3 c (so the composition is .6 c). Which twin ages more, is relative.

[studiot]

10 minutes ago, md65536 said:

Good idea. In that case the twins are symmetrical. There are observers that can measure A and B symmetrically, the simplest being one for which the speeds of A and B are both 1/3 c (so the composition is .6 c). Which twin ages more, is relative.

You don't actually need velocities (numbers) to answer this.

I was however thinking of taking A or B as at rest and the other as uniformly moving away indefinitely, which is easier than flyby and requires no external observers, just the 'stay-at-home' twin and the travelling twin.

[md65536]

3 hours ago, Celeritas said:

I said that the time (now) on the B & C clocks at their flyby event is also a coordinate time per A, because B & C are remotely located wrt him.

Those are proper times, though. You're talking about the time of an event that is measured by a clock that passes through the event.

All observers agree that B's clock is at 4 years when it passes C. "The time at B" is a coordinate time for A for events at A. For example, if you have an event "half way through A's world line", which A's world line intersects at a proper time of 5 years, all observers will agree that A passes through that event at 5 years. What they don't agree on is the coordinate time at B or C relative to that event. For instance, A says that "half way through A's world line" is simultaneous with B and C's passing. Inertial B says that event happens before B and C's passing. C says it happens after.

3 hours ago, Celeritas said:

For example, I'm talking about a deviation from SR whereby the 1-way <> 2-way speed of light (not Lorentz's theory tho), but you have responded with things like "there's no difference between polar coordinates and catesian coordinates.

Sorry, I'm trying to look at this in too many ways. But alright, let's stick with 1-way <> 2-way speed. How are you defining that? You have the definition of simultaneity: "The time required for light to go from a to b is the same as the time required by light to go from b to a in a stationary system." Are you changing that, or leaving that alone? Are you leaving c as a constant, or will you replace it with a variable that depends on direction (and if so, how?). Finally are you leaving distance defined by c, or changing that? Will you have distance measured differently in different directions, or maybe change both c and the definition of distance so that distance is the same in different directions?

In SR, the 1-way speed of light is the same as the 2-way by definition. If you want to consider an alternative, you're going to have to change at least one of the definitions. If you want it to be consistent, and to agree with reality, I think you'll have to change multiple definitions. Which definitions are you changing?

I used the example of choosing a preferred inertial frame with which to define all the relative measurements. This is a bad alternative because it has no benefits for any other observers except the preferred frame. However, it is an easy way to make sure that all of the measurements are at least consistent, and can be physically verified (remembering that the one-way speed of light is a definition, not a measurement), and must give the same predictions (but with different coordinates) that SR does.

Edited February 10, 2020 by md65536

[Celeritas]

On 2/9/2020 at 3:53 PM, Celeritas said:

I said that the time (now) on the B & C clocks at their flyby event is also a coordinate time per A, because B & C are remotely located wrt him.

On 2/9/2020 at 6:54 PM, md65536 said:

Those are proper times, though. You're talking about the time of an event that is measured by a clock that passes through the event.

 

From A's POV at 5y-A, he runs the LTs to predict that the B & C clocks now read 4y-B and 4y-C at their flyby, way down yonder 3 ly distant.  Those are coordinate times as calculated by A using the LTs.  A is "not there", and the B/C flyby event does not occur on the A worldline.  On the other hand, if you ask B what his own clock reads at B/C flyby, he'll say 4y-B which is a proper time for he himself, because the flyby event occurs at B on the B worldline.  If you ask C what his clock reads at B/C flyby, he'll say 4y-C, which is a proper time for he himself, because the flyby event occurs at C on the C worldline.

I've brought up this point a ways back ... that a coordinate time of a remote moving clock (per one observer) is the proper time of that clock when it displays that time (per he who carries that clock).

So the point I've been making thus far, is this ... any alternate theory that produces coordinate times that differ from SR, should not be able to predict B & C to execute a flyby at 4y-B and 4y-C.  If it produces different coordinate times wrt SR, I'd expect such a theory to predict (for example, say) 5.2y-B and 5.2y-C at their flyby event.  The B & C clocks will verify they read some specific values at their flyby event, and only the theory that predicts that, wins.  Of course, we won't be running such a flyby test anytime soon. 

Best regards,

Celeritas