Occasionally it's stated that "proper time is invariant",
as if a profundity.

I don't get this. Bob is in Los Angeles, looks at his
watch, it reads 9 AM. He boards a train, two hours
later he arrives in San Diego, his watch reads 11 AM.

A space traveler zooms his telescope into Bob,
observes that Bob is in LA, and Bob's watch reads
9 AM. Later, he sees Bob in San Diego, and sure
enough, Bob's watch reads 11 AM.

So everybody agrees on Bob's proper time interval.
This is profound? It's trivial, with practically no
physics content. Am I missing something?

Mark

On Friday, May 5, 2023 at 12:33:21 PM UTC-5, Mark-T wrote:
> Occasionally it's stated that "proper time is invariant",
> as if a profundity.
>
> I don't get this. Bob is in Los Angeles, looks at his
> watch, it reads 9 AM. He boards a train, two hours
> later he arrives in San Diego, his watch reads 11 AM.
>
> A space traveler zooms his telescope into Bob,
> observes that Bob is in LA, and Bob's watch reads
> 9 AM. Later, he sees Bob in San Diego, and sure
> enough, Bob's watch reads 11 AM.
>
> So everybody agrees on Bob's proper time interval.
> This is profound? It's trivial, with practically no
> physics content. Am I missing something?
>
> Mark

When people, especially relativists, say "proper time is invariant" it doesn't mean that proper time is invariant. In fact, it means that the change of proper time is uniform and independent of any physical environment. This concept of proper time is actually Newton's absolute time. They need to pretend to reject it, so they invented the concept of "proper time".

Re : Chapter six of https://drive.google.com/file/d/1VfhOL63jvB2Dmn4JCRmOx6S8Dh9nRbdC/view

On 5/5/23 12:33 PM, Mark-T wrote:
> Occasionally it's stated that "proper time is invariant", as if a
> profundity.

It's not really very profound.

> I don't get this. Bob is in Los Angeles, looks at his watch, it
> reads 9 AM. He boards a train, two hours later he arrives in San
> Diego, his watch reads 11 AM.
>
> A space traveler zooms his telescope into Bob, observes that Bob is
> in LA, and Bob's watch reads 9 AM. Later, he sees Bob in San Diego,
> and sure enough, Bob's watch reads 11 AM.
>
> So everybody agrees on Bob's proper time interval. This is profound?
> It's trivial, with practically no physics content. Am I missing
> something?

It's not really profound, and you're not missing anything major. But it
is important to know, as opposed to the coordinate time of a given
coordinate system, which is not invariant [#].

[#] Even it if it implemented with an array of clocks,
each of whose proper time is invariant. The difference
is that proper time exists along each 1-D path of each
clock, while coordinate time exists over the 3-D
region of the coordinate system.

Tom Roberts

On 5/5/23 12:50 PM, Jack Liu wrote:
> When people, especially relativists, say "proper time is invariant"
> it doesn't mean that proper time is invariant.

Nonsense.

> In fact, it means that the change of proper time is uniform and
> independent of any physical environment.

Well yes, that is part of it, but proper time implies considerably more
than just that.

> This concept of proper time is actually Newton's absolute time.

Complete nonsense. Those are VERY different concepts.

Newton's "absolute time" is exactly the same for every observer and
clock, everywhere and everywhen.

Proper time, however, is specific to the path through spacetime of a
single observer or clock; paths moving differently or in different
regions can have completely different proper times.

> They need to pretend to reject it, so they invented the concept of
> "proper time".

More nonsense. You REALLY need to learn basic physics before attempting
to write about it.

Tom Roberts

On Saturday, May 6, 2023 at 8:23:44 AM UTC-7, Tom Roberts wrote:
> On 5/5/23 12:50 PM, Jack Liu wrote:
> > When people, especially relativists, say "proper time is invariant"
> > it doesn't mean that proper time is invariant.
> Nonsense.
> > In fact, it means that the change of proper time is uniform and
> > independent of any physical environment.
> Well yes, that is part of it, but proper time implies considerably more
> than just that.
> > This concept of proper time is actually Newton's absolute time.
> Complete nonsense. Those are VERY different concepts.
>
> Newton's "absolute time" is exactly the same for every observer and
> clock, everywhere and everywhen.
>
> Proper time, however, is specific to the path through spacetime of a
> single observer or clock; paths moving differently or in different
> regions can have completely different proper times.
> > They need to pretend to reject it, so they invented the concept of
> > "proper time".
> More nonsense. You REALLY need to learn basic physics before attempting
> to write about it.
>
> Tom Roberts

"SR is local."

Einstein's relativity theory assigns a little space to each point in space-time.

The Riemann tensor and its metric vis-a-vis the absolute space-time and
its metric, illustrates that Einstein's inertial systems, are involved, and,
he has bridges everywhere, from absolute space time, about, relative velocity.

In this sense Dirac's positronic sea, is also Dirac-Einstein's positronic/white-hole sea.

Mass and charge are quantities, and magnitudes, and so is time.

The space contraction is rather real, though inertial systems in the
rotational and inertial systems in the linear, are quite different.

SR is local, and, GR is first.

In "Out of My Later Years" Einstein's "laws of nature" or "Einstein's relativity:
final edition" has that he has a clock hypothesis (that time is universal).
Also, he separates clocks from time.

On May 6, 2023 at 8:16:39 AM UTC-7, Tom Roberts wrote:
>> Bob is in Los Angeles, looks at his watch, it
>> reads 9 AM. He boards a train, two hours later he arrives in San
>> Diego, his watch reads 11 AM.
>> A space traveler zooms his telescope into Bob, observes that Bob is
>> in LA, and Bob's watch reads 9 AM. Later, he sees Bob in San Diego,
>> and sure enough, Bob's watch reads 11 AM.
>> So everybody agrees on Bob's proper time interval. This is profound?
>> It's trivial, with practically no physics content. Am I missing
>> something?
>
> It's not really profound, and you're not missing anything major. But it
> is important to know, as opposed to the coordinate time of a given
> coordinate system, which is not invariant [#].
>
> [#] Even it if it implemented with an array of clocks,
> each of whose proper time is invariant. The difference
> is that proper time exists along each 1-D path of each
> clock, while coordinate time exists over the 3-D
> region of the coordinate system.

Can you elaborate on this? How does 1-D differ from 3-D, if
we're talking about time measurements?

Mark

On Saturday, May 6, 2023 at 5:21:54 PM UTC-7, Mark-T wrote:
> On May 6, 2023 at 8:16:39 AM UTC-7, Tom Roberts wrote:
> >> Bob is in Los Angeles, looks at his watch, it
> >> reads 9 AM. He boards a train, two hours later he arrives in San
> >> Diego, his watch reads 11 AM.
> >> A space traveler zooms his telescope into Bob, observes that Bob is
> >> in LA, and Bob's watch reads 9 AM. Later, he sees Bob in San Diego,
> >> and sure enough, Bob's watch reads 11 AM.
> >> So everybody agrees on Bob's proper time interval. This is profound?
> >> It's trivial, with practically no physics content. Am I missing
> >> something?
> >
> > It's not really profound, and you're not missing anything major. But it
> > is important to know, as opposed to the coordinate time of a given
> > coordinate system, which is not invariant [#].
> >
> > [#] Even it if it implemented with an array of clocks,
> > each of whose proper time is invariant. The difference
> > is that proper time exists along each 1-D path of each
> > clock, while coordinate time exists over the 3-D
> > region of the coordinate system.
> Can you elaborate on this? How does 1-D differ from 3-D, if
> we're talking about time measurements?
>
> Mark

Consider if it's "only linear" (zero d-o-f) or "functionally free" (1 d-o-f).

This is where space-contraction linearly and rotationally are different.

Of course any mistakes are my own and you're to verify the proper
derivations of the entirety of things according to a consistent logical
theory, and here for example not picking up "coffee table book"
popularizations which are not mathematically justified.

On Friday, May 5, 2023 at 10:33:21 AM UTC-7, Mark-T wrote:
> Occasionally it's stated that "proper time is invariant",
> as if a profundity. I don't get this. Bob is in Los Angeles,
> looks at his watch, it reads 9 AM. He boards a train, two
> hours later he arrives in San Diego, his watch reads 11 AM.

There are two different definitions of proper time, one formal and one physical. Formally, in terms of standard inertial coordinates x,y,z,t and choosing units so c=1, we can define the elapsed "proper time" along an arbitrary path as the integral of sqrt(dt^2 - dx^2 - dy^2 - dz^2). Now, if we change to a different standard system of inertial coordinates x',y',z',t', we find that the values of dx', dy', dz', dt' are different all along that path (compared with dx, etc.), and yet the integral of sqrt(dt'^2 - dx'^2 - dy'^2 - dz'^2) is identical to the previous integral. So this quantity is invariant under Lorentz transformations. Admittedly, this is a fairly obvious algebraic identity, but perhaps not entirely self-evident.

Now, from a physical standpoint, it is obvious that (for example) the elapsed time on someone's watch between two events is invariant, meaning it doesn't depend on the choice of coordinate system (unlike the quantities x,y,z,t), so it stands to reason that in our pohysical theory we would identify the characteristic temporal progression of physical phenomena (e.g., how long it takes to boil and egg, how long it takes on average for radium atom to decay, etc.) with the formally defined "proper time".

By the way, in your example you glossed over "two hours later", because you didn't specify if that is two hours of coordinate time (e.g., the time he would see on the clock at the bank), or two hours on his watch.

> This is profound? It's trivial, with practically no
> physics content. Am I missing something?

Well, when people say proper time is invariant they are usually referring to the fact that the integral of sqrt(dt^2 - dx^2) is invariant under Lorentz transformation. They can also be referring to the impressive fact that there is a coherent proper time at all. It isn't self-evident that there would even be such a thing... various elements might have half-lives that do not transform in proportion to each other, so there would be no single "proper time" along a trajectory. But nature actually entails that simple structure... which is fairly profound and certainly hugely significant.

On Sunday, 7 May 2023 at 03:22:30 UTC+2, Trevor Lange wrote:
> On Friday, May 5, 2023 at 10:33:21 AM UTC-7, Mark-T wrote:
> > Occasionally it's stated that "proper time is invariant",
> > as if a profundity. I don't get this. Bob is in Los Angeles,
> > looks at his watch, it reads 9 AM. He boards a train, two
> > hours later he arrives in San Diego, his watch reads 11 AM.
> There are two different definitions of proper time, one formal and one physical.

And in the meantime in the real world,
improper clocks keep measuring impoper time.

On Saturday, May 6, 2023 at 11:01:08 PM UTC-7, Maciej Wozniak wrote:
> On Sunday, 7 May 2023 at 03:22:30 UTC+2, Trevor Lange wrote:
> > On Friday, May 5, 2023 at 10:33:21 AM UTC-7, Mark-T wrote:
> > > Occasionally it's stated that "proper time is invariant",
> > > as if a profundity. I don't get this. Bob is in Los Angeles,
> > > looks at his watch, it reads 9 AM. He boards a train, two
> > > hours later he arrives in San Diego, his watch reads 11 AM.
> > There are two different definitions of proper time, one formal and one physical.
> And in the meantime in the real world,
> improper clocks keep measuring impoper time.

Where was proper time before the event horizon ending another time?

On 5/6/23 7:21 PM, Mark-T wrote:
> On May 6, 2023 at 8:16:39 AM UTC-7, Tom Roberts wrote:
>> [proper time is invariant] as opposed to the coordinate time of a
>> given coordinate system, which is not invariant [#].
>>
>> [#] Even it if it implemented with an array of clocks, each of
>> whose proper time is invariant. The difference is that proper time
>> exists along each 1-D path of each clock, while coordinate time
>> exists over the 3-D region of the coordinate system.
>
> Can you elaborate on this? How does 1-D differ from 3-D, if we're
> talking about time measurements?

This is really about the geometry of Lorentzian manifolds (including the
Minkowski spacetime of SR). Let's consider inertial frames in Minkowski
spacetime.

A single clock has a 1-D path through spacetime, and for any given value
of its proper time everyone agrees on the spacetime point it designates.
This is actually deeper than invariance, it is coordinate independence.

On the other hand, each value of the time coordinate of an inertial
frame designates a 3-D spatial locus in which all points are
simultaneous in that coordinate system; the relativity of simultaneity
means that for relatively-moving inertial frames these loci are "skewed"
relative to each other. So no value of t in one frame designates the
same 3-D space as any value of t' in a differently-moving frame.

Tom Roberts

On Saturday, May 6, 2023 at 4:23:44 PM UTC+1, Tom Roberts wrote:
> On 5/5/23 12:50 PM, Jack Liu wrote:
> > When people, especially relativists, say "proper time is invariant"
> > it doesn't mean that proper time is invariant.
> Nonsense.
> > In fact, it means that the change of proper time is uniform and
> > independent of any physical environment.
> Well yes, that is part of it, but proper time implies considerably more
> than just that.
> > This concept of proper time is actually Newton's absolute time.
> Complete nonsense. Those are VERY different concepts.
>
> Newton's "absolute time" is exactly the same for every observer and
> clock, everywhere and everywhen.

> Tom Roberts

Sir Isaac tried to express the Equation of Time as absolute/relative time, however, the Equation of Time is a timekeeping facility which anchors the 24-hour cycle to the natural noon cycle.

"Absolute time, in astronomy, is distinguished from relative, by the equation of time. For the natural days are truly unequal, though they are commonly considered as equal and used for a measure of time; astronomers correct this inequality for their more accurate deducing of the celestial motions...The necessity of which equation, for determining the times of a phænomenon, is evinced as well from the experiments of the pendulum clock, as by eclipses of the satellites of Jupiter." Principia

He is basically mimicking Huygen's deficient expression of the same-

" Here take notice, that the Sun or the Earth passeth the 12. Signes,or makes an entire revolution in the Ecliptick in 365 days, 5 hours 49 min. or there about, and that those days, reckon'd from noon to noon,are of different lenghts; as is known to all that are vers'd in Astronomy" Huygens

https://adcs.home.xs4all.nl/Huygens/06/kort-E.html

Rather than dither around with Sir Isaac's silly notion, it is Huygen's deficient expression as the Equation of Time fits inside the calendar system and is not continuous as a 365/366 day set.

A total waste of time apart from the timekeeping correction and what it actually represents. There are contributors to this forum whose only purpose is to maintain the lifestyles, reputations and pensions of voodoo merchants and fair dues to them if they get away with it but they are enemies of humanity.