Twin Paradox (thorough explanation needed)

[JesseM]

The ambiguities are resolved by the principle of interval invariance - whether it be the orbits of satellites in motion, or the one way trip a pion makes in the lab - the problem can always be reduced to a thought experiment where no acceleration is needed - for example, it is not necessary that the twins be reunited in order to determine that the traveler has accumulated less time. Acceleration is simply a circumstance involved with getting the twin back home - the difference in time is the result of spacetime unity ... when one frame is selected to be at rest - the problem degenerates to a spacetime mensuration - and the twin taken to be at rest will necessarily have accumulated the most time because he has not accumulated a space distance - the traveler must always experience the same spacetime interval - so his interval comprises both a spatial and temporal component, ergo his temporal component must be less

But the fact of interval invariance means there is no need to consider either twins at rest, you could choose a frame where both twins have nonzero velocity from beginning to end and this frame would still get the same value for proper time along both paths through spacetime.

 

[DTThom]

You seemed willing enough to discuss it before when you said
"Replace the clock ticks with odometers, if you care to."

And I knew as I typed that, that it would come back to me again, and
in a manner that doesn't fit with what I mean by the "rate"
of clock ticking. A careless remark on my part.

I'll quote your earlier comment, then offer my most
concise explanation of what I mean by a clock's rate:

I don't see why you can't accept that there similarly may be no
"actual" truth about the rate a clock's reading is increasing
relative to the t-coordinate at a particular point on its worldline,

When you speak of the "rate" of a clock you are speaking of
the number of seconds the clock marks per second.

I do not mean to compare a clock's ticks with its own
time coordinate of its world line.

As a clock changes the speed of its translatory motion, the clock
ticks a different number of times per tick cycle
of a clock at rest relative to the universe.

For instance, a clock with a translatory speed of .6c, will tick
[.8 cycles] per [cycle of the "at rest" clock].

So its rate is .8 per cycle of the at rest clock.

That is all I mean by "rate". You see, I regard the "at rest"
clock to be the "truth of the matter". Thus I say a clock's
rate varies in actuality.

You need to be simple minded to see what I'm trying to say.
You also need to be simple minded to see that this all about
seeing relativity from a god's eye view whereby the process
of measuring can be diagrammed in an absolute manner, with
the inherent delay involving the finite speed of light included.

===========

[IMO, the Einstein convention doesn't nullify a master frame
(assuming it really exists). Because, if a master frame exists,
then Einstein's convention would have to be wrong.

Einstein's convention of course is not wrong. By "nullify",
I don't mean that we need to choose one or the other. By
"nullify", I simply mean that his clock synchronization gives
us a convenient way to ignore it for all predictive purposes.

As you note:

[I suppose DTThom's statement means only this ... Einstein's
convention makes any aether frame superfluous, because no frame
(including an aether frame if it exists) is preferred

But the following is not what I have done:

[However, DTThom suggests to assume a master frame "does exist",
and then draft Einstein's simultaneity convention on a spacetime diagram.

I have diagrammed Einstein's clock synchronization along
a single spatial coordinate. Along that coordinate, the
clock readings of two clocks are noted at various points,
as is the reading of a clock at rest with the the universe.

My approach (which I of course don't assume you'd want to invest
any time in):

An understanding of clock functioning follows immediately
from postulating the actual constant speed of light.

Length contraction can be deduced by considering the constant
speed of light in conjunction with the postulated need
for stability (specifically synchronization) at the base
of our structures (meaning atomic).

Mass increase can be deduced by considering the preceding
postulates in conjunction with the need to conserve
momentum experience across inertial frames.

I've derived the symmetrically mutual measuring results
across inertial frames using those considerations.

e=mc^2 follows from those considerations as well, as
I also derived.

Through it all, it's about the nature of light.

I've never used a spacetime diagram to make any conclusions
about what measures are obtained across inertial frames,
rather simple spatial line analyses in conjunction with
"assumed" vs. "actual" lengths of measuring rods. In this
manner, I discover how parties necessarily make their
calculations. It is easiest to do this on a large
scale, but the same method applies to the nature of
any measuring tool.

(Ticks are events and every frame ( inertial or not) will
agree on the number of ticks.

Of course that is right. My noting that all
inertial frames are in agreement was irrelevant,
as I had intended to point out this morning.

Tell me, what exactly do you think is different from the
LET aether frame and your cosmos frame? It is certainly not obvious.

My previous post:

Of course people are going to think I embrace LET. But I do not believe
in the aether. It's not rational for multiple reasons.

I believe in an evolving structure of the universe and an interconnectedness
between all elements. The communication which establishes the connectedness
can proceed only at light speed.

I don't have a G.U.T. to specify how it is that photons (or virtual
photon events) "know" how to behave in matters of dictating an object's
inertial properties (such as length contraction), though I have
a natural overview of the process.

A quote from Lee Smolin roughly summarizes my point of view about
the structure of space and the context for an object's inertial
properties:

“The properties of space and time evolve dynamically, in interaction
with everything they contain. Furthermore, the essence of space and
time now is just a set of relationships between events that take place in
the history of the world. ... There is no fixed framework, (rather) an
evolving network of relationships, making up the history of space, time,
and matter.” (Discovery magazine Sept 97)

And "no fixed" framework does not
mean "no overall" (as in summed) rest state. In other words,
the framework is simply not aether-like. Communication of inertial
properties occurs at light speed, just as all phenomena is
constrained by light speed.

Nor do I wish to imply that Smolin shares my point of view
concerning special relativity.

In my words:

An object's inertial properties, such as clock speed and length, are a
result of its current state of motion. Its relationship to the structure is an
expression of its net motion history. They are one and the same thing.


The problem with an aether is that it somehow manages to retain its autonomony
in spite of its interactions with the objects it contains, i.e., it somehow
manages to have a one-way relationship with the objects it contains.

It would also seem to require that a continued force would need be
applied to keep a light wave moving through it. That relates to
the autonomy issue I just mentioned.

Furthermore, how did such a fixed framework ever become fixed?
I have a prejudice for evolving structures.

-------------

Wheeler's whole argument for the Principle of Relativity
resting on emptiness is that a distant observer cannot possibly
affect the mechanism of a clock.

Of course not. It is not a rational argument.

It is the totality of the universe (machian concept) that
provides the structure (the context) for the inertial properties
of all objects.



=================

Wheeler forces an inbound astronaut to
utilize Einstein's clock synchronization, a synchronization
which is not required to derive all the effects of relativity.
So the misperception to which Wheeler subjected her is a
strictly optional misperception.

Wheeler's astronaut: "As I turned around, a whole bunch
of Earth clock ticks went from my future to my past. This
accounts for the larger number of total clicks on the
earth clock."

Wheeler: "The astronaut renounces her profession and becomes
a stand-up comedian."

Okay.

================


Imagine a string of three spaceships moving in the same direction
at different speeds. Ship A is overtaking ship B as ship C whizzes past
ship A and past ship B. It is clear that there
is a hierarchy of speed.

A hierarchy of speed implies a lowest limit
of zero and perhaps some upper limit (which we know to be
light speed).

Sounds like there is a rational concept of "truth of the matter"
here.

But you are all very practical minded.

A "philosophy of physics" thread would be better suited to me.


=================

Attaching LET to my point of view seems to be an attempt
to discredrit my point of view.

It seems that you acknowledge the universe exists except when you are
discussing relativity, at which point it magically does not exist. (chuckle)

I know we "need not" consider it when all we wish to do is make
"predictions" about measures.


================================

For the record I doubt French's statement their
represents a majority view, but he seems to be referring to Mach's principle,
a philosophical idea that Einstein was inspired by in creating general
relativity even though he ultimately decided the finished theory didn't
really obey it. Julian Barbour has some ideas on how one might create a
theory of gravity similar to GR but more truly "Machian", though, he
discusses this on the website above and also in his book The End of Time.

Speaking of Barbour, the first (x number of pages -- I don't
remember how many) were extremely gratifying. I remember
excitingly telling a friend how gratifying it was to finally
encounter the writings of someone who has thought as I had
thought for the past three decades. Alot of it had to do
with our mutual epiphanies about how time arises from change.

But he then largely folds. Curiously, he bemoans, in his book,
the lack of a definition of a clock.
I found this flabbergasting, seeing as to how I've always regarded
clock functioning to be driven by the nature of light.

I then realized he doesn't use the word "light" in his
book even once that I can recall finding. How can anyone
think about or discuss time or relativity without thinking
about the nature of light?

I also did not think much of his contest-winning essay about
time a year or two back. Naturally, if I had entered the
contest, I would have won (ha). My essay would have been devoted
to showing the impossibilities of knowing what time is,
then a shift of focus to the nature of light and clock functioning.

But I didn't know about the contest until he emailed me
telling me he'd won.

 

[JDoolin]

I don't know if this has already been brought up, but the classical "twin paradox" can and ought to be described not only in terms of time, but distance.

In the traveling twin's perspective, the time spent moving away from earth, and moving toward the Earth are equal.

However, a simple calculation of apparent speeds yields that on the way out, Earth will appear* to be receding slower than it actually is. On the way in, however, Earth will be appear to be approaching faster than it actually is.

When you have the same amount of time, but different apparent speeds, that means different apparent distances!

In order to have a different distance immediately before and immediately after the acceleration, the Earth must appear to lurch away as he accelerates toward it.

*I'm carefully using the word "apparent" but when we talk about where we "see" things, that's pretty much where they are, as far as we are concerned. That should be contrasted with subjects like length contraction, which describes where things actually "are" and not necessarily how they are actually "seen."

 

[ghwellsjr]

A "philosophy of physics" thread would be better suited to me.

A different forum, not just a different thread. Try this one:

https://www.physicsforums.com/forumdisplay.php?f=112

You'll get yourself banned if you keep this up here.

 

[Dale]

Of course people are going to think I embrace LET. But I do not believe
in the aether. It's not rational for multiple reasons.

I believe in an evolving structure of the universe and an interconnectedness
between all elements. The communication which establishes the connectedness
can proceed only at light speed.

Relativity does that just fine without requiring any superfluous and undetectable "cosmos" reference frame. You are certainly free to believe in some metaphysical "absolute" reference frame (call it whatever you like), but if your theory uses the Lorentz transforms then such a frame is purely a philosophical crutch with no physical meaning whatsoever.

 

[Dale]

For instance, a clock with a translatory speed of .6c, will tick
[.8 cycles] per [cycle of the "at rest" clock].

So its rate is .8 per cycle of the at rest clock.

That is all I mean by "rate". You see, I regard the "at rest"
clock to be the "truth of the matter". Thus I say a clock's
rate varies in actuality.

In the "at rest" clock's rest frame this is all correct. In any other frame it is not correct.

 

[JesseM]

I don't have a G.U.T. to specify how it is that photons (or virtual
photon events) "know" how to behave in matters of dictating an object's
inertial properties (such as length contraction), though I have
a natural overview of the process.

A quote from Lee Smolin roughly summarizes my point of view about
the structure of space and the context for an object's inertial
properties:

“The properties of space and time evolve dynamically, in interaction
with everything they contain. Furthermore, the essence of space and
time now is just a set of relationships between events that take place in
the history of the world. ... There is no fixed framework, (rather) an
evolving network of relationships, making up the history of space, time,
and matter.” (Discovery magazine Sept 97)

And "no fixed" framework does not
mean "no overall" (as in summed) rest state. In other words,
the framework is simply not aether-like. Communication of inertial
properties occurs at light speed, just as all phenomena is
constrained by light speed.

Since a G.U.T. would be a new theory, not just a philosophical interpretation of an existing theory like LET (which again does not assume any physical aether), then presumably you believe that the idea that "communication of inertial properties occurs at light speed" would eventually have some testable consequences which differ from relativity, i.e. you think the laws of physics are not all completely Lorentz-invariant locally. If this is the case, then this is not the forum to discuss such ideas, please read the IMPORTANT! Read before posting thread.

 

[OnlyMe]

Attaching LET to my point of view seems to be an attempt
to discredrit my point of view.

This is pretty much the same assessment I had.

In SR every POV (observer in an inertial frame of reference) is equal, not because every POV is a true and accurate representation of the universe, but because none are. None can claim to be at absolute rest wrt the universe. None has can claim a preferred universal POV/FoR. None can claim to have a completely objective frame of reference for events which do not occur effectively at rest wrt the observer. Both position in 3D space and over time in 4D space-time can potentially affect measurements of length and time.

Though I cannot see how you could successfully model a world view as suggested by DTThom, it is not inconsistent with SR. It is just a POV or FoR, in which the proper lengths and distances, of all objects and coordinate systems serve as the basis for a universal POV or FoR. The LTs then provide a means to exchange coordinates from the universal POV to those of any FoR in relative motion. (DTThom, if I misinterpreted your intent, please feel free to correct.)

 

[JesseM]

Though I cannot see how you could successfully model a world view as suggested by DTThom, it is not inconsistent with SR. It is just a POV or FoR, in which the proper lengths and distances, of all objects and coordinate systems serve as the basis for a universal POV or FoR. The LTs then provide a means to exchange coordinates from the universal POV to those of any FoR in relative motion. (DTThom, if I misinterpreted your intent, please feel free to correct.)

But that's exactly what a "Lorentz ether theory" is! As I said before, the modern understanding of LET doesn't presuppose any form of physical ether, just an absolute (or "universal") frame.

 

[OnlyMe]

But that's exactly what a "Lorentz ether theory" is! As I said before, the modern understanding of LET doesn't presuppose any form of physical ether, just an absolute (or "universal") frame.

Like I said I don't know how you could actually model "it".

As for the "modern understanding of LET", I have never run across it. If you have a reference it would be appreciated.

If you strip away the rigidly fixed luminiferous aether for the LET, you are left with the LTs and Einstein's repurposing them as a basis for SR. SR does not deal with any absolute concept of space. That's why all inertial frames of reference are equal.

 

[JesseM]

Like I said I don't know how you could actually model "it".

What do you mean by "model"? You just imagine there is one frame that's the absolute frame, and say that the "true" value of frame-dependent quantities like length, time, and velocity are the values in this frame. It's just an "interpretation" rather than a new theory (like the various interpretations of quantum mechanics) so it doesn't lead to any different predictions about measurable frame-independent facts.

As for the "modern understanding of LET", I have never run across it. If you have a reference it would be appreciated.

See the later activity and current status section of wikipedia's LET article.

If you strip away the rigidly fixed luminiferous aether for the LET, you are left with the LTs and Einstein's repurposing them as a basis for SR. SR does not deal with any absolute concept of space. That's why all inertial frames of reference are equal.

As far as measurable observations that's true, but nothing stops you from having a metaphysical belief that one frame is the absolute one whose judgments are the only "true" ones.

 

[OnlyMe]

What do you mean by "model"? ...

As far as measurable observations that's true, but nothing stops you from having a metaphysical belief that one frame is the absolute one whose judgments are the only "true" ones.

I do that sort of thing quite often...

I should have said something like I cannot imagine a frame of reference from which the proper lengths of all objects can be observed directly.

In the abstract and hypothetical.., yes, but all our theories and mathematical models are of little real use if they cannot or are not in some way a description of the "real world".

On the Wiki' article, I often miss quite a bit that Wiki has to offer. I very often want to know who it is that is presenting the information. It may be there somewhere, but I have no idea who D.H. is.

 

[yogi]

But the fact of interval invariance means there is no need to consider either twins at rest, you could choose a frame where both twins have nonzero velocity from beginning to end and this frame would still get the same value for proper time along both paths through spacetime.

That is interesting - if I am following your point, are you saying, if I laid out a distance on Earth separating two clocks and then measured the flyby times for two objects using the two clocks ...that both traveled at a uniform speed each at a different velocity, then I would still have the Earth frame and its time and distance as an "at rest" platform with a proper distance and proper time ..but I would have two different time(s) for the objects as meassured by the Earth clocks and they would have different times for each other -

This doesn't seem to violate what a posted or am I misreading your comment?

 

[JDoolin]

You are free to believe there is an absolute frame as a question of metaphysics, and if you assume rulers shrink length-contract in absolute terms when in motion relative to this frame, and clocks have their time dilated in absolute terms, and light has an absolute velocity of c relative to this frame, and the equations of the laws of physics when expressed in the coordinates of this frame are all Lorentz-symmetric, then this leads to predictions which are indistinguishable from the usual version of relativity which doesn't assume any absolute frame (this is known as a Lorentz ether theory). But the very fact that this leads to no new predictions means there would be no experimental way of determining which frame was the absolute one even if such a frame existed, and so in a practical sense it would be irrelevant to how physicists design all their experiments (including how they define 'inertial frames' in practice).

You might be free to believe this, but it comes with caveats. If you are to believe in an absolute frame of reference, then that goes hand-in-hand with treating time as "just another distance." i.e. the math works out, if you just take for granted that x, y, z, and t are all just continuous variables, and nothing makes t special except that it tends to work with hyperbolic sines and cosines instead of with regular sines and cosines.

If you think of time as something that just passes, and we are all predestined to make decisions, that is compatible with an "absolute frame of reference." However, if you think that you are actually making a choice, and the future does not yet exist, then I don't think you can rationally adopt the idea of an absolute frame.

... But if we chose a different Cartesian coordinate system with its x-axis oriented differently the slope would be different and so would rate of odometer increase relative to x-coordinate, and I bet unlike when we talk about the rate a clock is ticking relative to coordinate time t, in this case you wouldn't insist there has to be any "absolute" truth about the value of odometer increase relative to x-coordinate. That's the beauty of the geometric analogy, it shows you have a double standard with regard to time vs. space.

Well, let's take this analogy to where you can go with special relativity, in one reference frame, A person is looking at his watch and figuring out that the temperature of the cosmic background radiation is 2.7 Kelvin. In another reference frame, a person is looking at his watch and figuring out that the cosmic background radiation is 2.7 Kelvin.

They are both looking at the primordial atoms that make up the other. To each of them, the other person does not yet exist, and will not exist for trillions of years.

So, is this a double standard with regard to time and space?

In space, I say to the left, and to the right. Above and below. In front and behind. All of these are interchangable. In time, I say before and after. There is no way to convert a before to an after using Special Relativity. But you can convert "has existed for billions of years" to "won't exist for billions of years," by a simple Lorentz Transformation.

The conundrum of SRT is the reality of the possibility that "from my perspective you don't exist yet" and "from your perspective I don't exist yet." Is one of these reference frames the "correct one?" Or is there some absolute frame that encompasses both? (Yes, all of the reference frames if extended from t=-infinity to t=+infinity include all the events.) So yes, you could say, ANY arbitrarily chosen reference frame will do as an absolute reference frame, so long as you include all of the events which will happen in the future, as well as all events in the past.

But once you realize that ANY arbitrarily chosen reference frame will do fine as an absolute frame, well... that is essentially the whole point of relativity. You might as well just say its all relative as to say that you have an absolute theory that is equivalent to relativity.

 

[GrayGhost]

So, is this a double standard with regard to time and space?

In space, I say to the left, and to the right. Above and below. In front and behind. All of these are interchangable. In time, I say before and after. There is no way to convert a before to an after using Special Relativity. But you can convert "has existed for billions of years" to "won't exist for billions of years," by a simple Lorentz Transformation.

The conundrum of SRT is the reality of the possibility that "from my perspective you don't exist yet" and "from your perspective I don't exist yet." Is one of these reference frames the "correct one?" Or is there some absolute frame that encompasses both?

The correct option is the one you left out JDoolin. They are both correct, even though they disagree.

I might add that ... if your own worldline exists in its totality before you are even born, and long after you turn back to star dust, this does not necessarily require predetermism. Your predetermined worldline may be considered the result of all your free-will-choices, made at any and all times. But, I suppose that's for the philosophical forum to decide, so :)

GrayGhost

 

[JesseM]

You might be free to believe this, but it comes with caveats. If you are to believe in an absolute frame of reference, then that goes hand-in-hand with treating time as "just another distance." i.e. the math works out, if you just take for granted that x, y, z, and t are all just continuous variables, and nothing makes t special except that it tends to work with hyperbolic sines and cosines instead of with regular sines and cosines.

If you think of time as something that just passes, and we are all predestined to make decisions, that is compatible with an "absolute frame of reference." However, if you think that you are actually making a choice, and the future does not yet exist, then I don't think you can rationally adopt the idea of an absolute frame.

I'd say it's exactly the opposite! If you want to believe that "the future" is undetermined while "the past" is fixed, then you are adopting a presentist view of time where there is some objective truth about which events lie in the past/present, which only makes sense if you believe in an objective truth about simultaneity. But because of the relativity of simultaneity, this requires either that relativity is wrong, or that some frame's definition of simultaneity is "preferred" in a purely metaphysical sense which can never be determined by any empirical experiment. If you want to adopt the idea that no frame is preferred in either a physical or a metaphysical sense, you have to adopt an eternalist philosophy of time (see also the B-theory of time) which says future events "exist" in the same sense as past ones. Personally I find this philosophy to be more elegant even aside from relativity, but if you reject it then I don't see how you can avoid believing in a preferred definition of simultaneity (whether physically preferred or metaphysically preferred).

 

[Mike_Fontenot]

I'd say it can't be said who aged less in any objective frame-independent way, as you could always take the perspective of an inertial observer who was at rest relative to B during B's travel, but did not accelerate when B did and just continued past X inertially [Fontenot addition: I dubbed that observer "observer C" in a previous post].
[...]

Any observer (whether sometimes-accelerated or perpetually-inertial) can always determine the "point-of-view" (POV) of any other observer. And, if they want, they can use that other POV to determine all sorts of quantities ... both frame-independent quantities and frame-dependent quantities. Sometimes, that option can be an especially easy way for the original observer (particularly for an observer who sometimes accelerates) to determine some frame-independent fact that the observer considers to be relevant and important to himself (such as the ages of the twins when they are re-united). On the other hand, frame-dependent quantites, according to someone else's POV, are usually more like curiosities to the original observer, with few if any consequences for his own life.

Each observer has his OWN personal POV, and that POV has a SPECIALNESS for him, because it has a direct meaningfulness TO HIM that no one else's POV has.

Suggesting that the POV of the outbound observer (observer C) is a perfectly good POV for the traveler (during his whole trip) is just a silly as suggesting that the POV of observer C is a perfectly good POV for the home-twin.

And, for those that think that there are several (and perhaps many) personal POV's for a non-perpetually-inertial observer, all perfectly good, I contend that belief is equivalent to saying that such an observer really doesn't HAVE a "point-of-view" at all.

Mike Fontenot

 

[JesseM]

Any observer (whether sometimes-accelerated or perpetually-inertial) can always determine the "point-of-view" (POV) of any other observer.

The "point of view" you mention is a matter of arbitrary human convention, it is not in any way forced on us by nature.

Each observer has his OWN personal POV, and that POV has a SPECIALNESS for him, because it has a direct meaningfulness TO HIM that no one else's POV has.

Not in any physical sense, no. The fact that you are continually unable to actually explain what this "SPECIALNESS" consists of just shows how hollow your position--all you can do is shout more loudly IN CAPS that your particular convention is the only right one, not provide any sort of reasoned argument for this.

And, for those that think that there are several (and perhaps many) personal POV's for a non-perpetually-inertial observer, all perfectly good, I contend that belief is equivalent to saying that such an observer really doesn't HAVE a "point-of-view" at all.

It just means that "point of view" in the sense of what coordinate system to use (as opposed to the sense of what is seen visually) is a matter of aesthetic preference, nature does not single out anyone correct mapping between observers and coordinate systems.

 

[JDoolin]

I'd say it's exactly the opposite! If you want to believe that "the future" is undetermined while "the past" is fixed, then you are adopting a presentist view of time where there is some objective truth about which events lie in the past/present, which only makes sense if you believe in an objective truth about simultaneity. But because of the relativity of simultaneity, this requires either that relativity is wrong, or that some frame's definition of simultaneity is "preferred" in a purely metaphysical sense which can never be determined by any empirical experiment. If you want to adopt the idea that no frame is preferred in either a physical or a metaphysical sense, you have to adopt an eternalist philosophy of time (see also the B-theory of time) which says future events "exist" in the same sense as past ones. Personally I find this philosophy to be more elegant even aside from relativity, but if you reject it then I don't see how you can avoid believing in a preferred definition of simultaneity (whether physically preferred or metaphysically preferred).

I'd like to clarify the difference between "objective/subjective" and "relative/absolute"

There is a objective truth about what things lie to my left, and which things lie to my right. But that is not an "absolute truth." You can only say what is to my left and to my right in a relative sense--relative to me. Same thing with time. I can say "2001" is in my past and "2020" is in my future, that is objectively true relative to me and the time that I said it.

I'm not entirely sure I fit entirely into the presentist camp, but the eternalist camp seems incompatible with my own experience. My own experience tells me there is fundamentally different about the past than the future. Or more specifically, there is something different about MY past and MY future. It's a relative thing, much like MY left and MY right, but more profound.

Presentism suggests that ONLY the present exists, which I would say is not right. The past certainly exists, and the present is where the energy unleashed during the past rattles around until it comes to rest (wave function collapse) and becomes the past.

I think the article on "presentism" gets it wrong when it says "any real observer would need to be the extended contents of an observation to exist" The trouble is a pervasive misconception of Quantum Mechanics called "Shrodinger's Cat" The idea that for an event to have occured, it must have been observed by a lab assistant with an IQ above that of a cat's is ridiculous. Events occur constantly in places where there is no lab assistant, and no cat, and not even something as bright as your common rock to observe them. For an event to be in the past, it merely has to have affected a particle; not a whole cat, and certainly not more than a whole cat.

Yes, it is on the "small" geometric point of the light-cone where the present is determined. Of course, if you draw that space-time diagram on any scale that a human can actually comfotably perceive, you can't actually see that the light-cone isn't a plane. Say your scale is upwards of 10 miles = 1 inch, and less than .01 seconds = 1 inch you might begin to see that the cone isn't quite flat.

On the scale of the human body and the time of human reaction speed, light travels fast enough that you wouldn't be able to notice the little speed of light delays between your neurons, or notice that in fact, your consciousness is operating at several different relative "present's"

 

[JDoolin]

The "point of view" you mention is a matter of arbitrary human convention, it is not in any way forced on us by nature.

Not in any physical sense, no. The fact that you are continually unable to actually explain what this "SPECIALNESS" consists of just shows how hollow your position--all you can do is shout more loudly IN CAPS that your particular convention is the only right one, not provide any sort of reasoned argument for this.

It just means that "point of view" in the sense of what coordinate system to use (as opposed to the sense of what is seen visually) is a matter of aesthetic preference, nature does not single out anyone correct mapping between observers and coordinate systems.

What if you and a friend decided to play a first-person-shooter video game, but you decided to trade TV sets, so you were watching your friend's point-of-view, and your friend was watching your point-of-view? Is this just a matter of aesthetic preference, or don't you think it matters somewhat.

I would say that nature does force upon us our own point-of-view. We do not in fact have the option (except in this contrived situtation, by trading TV's) to trade points-of-view with another "player" so-to-speak.

 

[DrGreg]

What if you and a friend decided to play a first-person-shooter video game, but you decided to trade TV sets, so you were watching your friend's point-of-view, and your friend was watching your point-of-view? Is this just a matter of aesthetic preference, or don't you think it matters somewhat.

I would say that nature does force upon us our own point-of-view. We do not in fact have the option (except in this contrived situtation, by trading TV's) to trade points-of-view with another "player" so-to-speak.

I think Jesse's point, which I agree with, is that what you observe directly with your eyes or measure with instruments is not the same thing as the "POV" being discussed, i.e. the assignment of coordinates to events, which requires some calculation from raw measurements, and some convention of how to do this. There's more than one convention to choose from.

 

[GrayGhost]

Mike_Fontenot,

I don't think it matters that one may elect any arbitrary POV for an observer or not. All that matters, is whether the correct spacetime transformations are attained, as calculated by each for the other. This may be accomplished after the twin's flight test is completed, all the data laid out on the table, all transformations run, and the solns obtained. Only those that precisely match the other's experience is any good.

There are 3 matters of importance here ...

(1) what method is used to correctly determine the moving fellow's relative location and velocity?
(2) what convention-of-simultaneity is elected for use?
(3) what spacetime transformations are used?​

The 3rd depends upon the 2nd. Each wannabe expert runs his own process that addresses each of the above 3 questions, and attains what each believe to be the correct result. The correct solns must abide by mother nature, in which case they will match the actual twin A experience. All those wannabe experts that do attain the actual twin A experience, are each using methods that are correct. Whichever method is simplest (of the bunch), is the one everyone will prefer to use.

I must say though, it seems to me that our existing LTs must be used during any of these competing methods. They are all we have to relate spacetime systems. Since the LTs use an invariant 1-way speed of light, then I do not see how any other convention-of-simultaneity can be good. One exception maybe ... I suppose LET could be applied, however the meaning of the transformation solutions are technically not the same.

GrayGhost

 

[LightNg]

Hello, everyone. This is my first post in this forum.

I have a question regarding time dilation and twin paradox. It is because of symmetry problem. Sorry, I didn't read all the posts in this thread, since it is quite long.
Ok I don't claim to be a physics expert. I don't know stuff like Doppler effect. And I don't know much about general relativity. But I suppose that is not needed to understand special relativity.

I did read the twin paradox explanation in the wikipedia though.

Now it said that the traveling twin is distinguished from the rest-at-earth twin because the spaceship of the traveling twin did a deacceleration and acceleration to go back earth.

But to me that does not break the symmetry, since from the point of traveling twin, you can just as view the Earth is traveling apart from the spaceship, do deacceleration, then turn around and accelerate, then traveling move toward the spaceship.

In the article of wikipedia there is a section like this

Viewpoint of the traveling twin

During the turnaround, the traveling twin is in an accelerated reference frame. According to the equivalence principle, the traveling twin may analyze the turnaround phase as if the stay-at-home twin were freely falling in a gravitational field and as if the traveling twin were stationary. A 1918 paper by Einstein presents a conceptual sketch of the idea.[A 5] From the viewpoint of the traveler, a calculation for each separate leg, ignoring the turnaround, leads to a result in which the Earth clocks age less than the traveler. For example, if the Earth clocks age 1 day less on each leg, the amount that the Earth clocks will lag behind amounts to 2 days. The physical description of what happens at turnaround has to produce a contrary effect of double that amount: 4 days' advancing of the Earth clocks. Then the traveler's clock will end up with a net 2-day delay on the Earth clocks, in agreement with calculations done in the frame of the stay-at-home twin.

The mechanism for the advancing of the stay-at-home twin's clock is gravitational time dilation. When an observer finds that inertially moving objects are being accelerated with respect to themselves, those objects are in a gravitational field insofar as relativity is concerned. For the traveling twin at turnaround, this gravitational field fills the universe. In a weak field approximation, clocks tick at a rate of t' = t(1 + Φ / c2) where Φ is the difference in gravitational potential. In this case, Φ = gh where g is the acceleration of the traveling observer during turnaround and h is the distance to the stay-at-home twin. The rocket is firing towards the stay-at-home twin, thereby placing that twin at a higher gravitational potential. Due to the large distance between the twins, the stay-at-home twin's clocks will appear to be sped up enough to account for the difference in proper times experienced by the twins. It is no accident that this speed-up is enough to account for the simultaneity shift described above. The general relativity solution for a static homogeneous gravitational field and the special relativity solution for finite acceleration produce identical results.

Ok Einstein presented a solution to explain it from the point of view of the traveling twin. But I can't see why the phenomena in the Bold part can't also be symmetry.

That is, from the point of view of rest-at-earth twin, the spaceship clock lags 1 day on each leg. And the turn around of the spaceship causes the spaceship experiences similar gravitational time dilation, that is, 4 days advance of the spaceship clock. So the net effect is that the spaceship clock is 2 days ahead of Earth clock when it is back to earth, which is inconsistent with the result of the bold part (what the traveler twin calculated).

Can someone explain to me why is this so?

And another simpler question. Consider there is 2 object A and B. And they exists right from the beginning of the universe (forget about Big Bang). And right from the beginning of the universe, from the point of view of object A, object B is, and always, traveling at the contant speed of 0.5C, never accelerate or deaccelerate. So which object experience time slower? A or B?

 

[LightNg]

Anyone?

 

[Dale]

But to me that does not break the symmetry, since from the point of traveling twin, you can just as view the Earth is traveling apart from the spaceship, do deacceleration, then turn around and accelerate, then traveling move toward the spaceship.

Hi LightNg, welcome to PF,

It does break the symmetry since an accelerometer aboard one ship will detect the acceleration and an accelerometer aboard the other ship will not. That is asymmetric. This highlights the difference between coordinate acceleration (which is symmetric) and proper acceleration (which is asymmetric).

 

[JesseM]

Hi LightNg, welcome to PF,

It does break the symmetry since an accelerometer aboard one ship will detect the acceleration and an accelerometer aboard the other ship will not. That is asymmetric. This highlights the difference between coordinate acceleration (which is symmetric) and proper acceleration (which is asymmetric).

Yeah, and more generally the time dilation equation relating clock rate to speed only works in inertial frames, and it can be taken as part of the definition of an inertial frame that any object with a constant position coordinate (one which is "at rest" in that frame) should show zero reading on an accelerometer (not experiencing any G-forces).

 

[LightNg]

Thanks for the replies! :)

Hi LightNg, welcome to PF,

It does break the symmetry since an accelerometer aboard one ship will detect the acceleration and an accelerometer aboard the other ship will not. That is asymmetric. This highlights the difference between coordinate acceleration (which is symmetric) and proper acceleration (which is asymmetric).

Yeah, and more generally the time dilation equation relating clock rate to speed only works in inertial frames, and it can be taken as part of the definition of an inertial frame that any object with a constant position coordinate (one which is "at rest" in that frame) should show zero reading on an accelerometer (not experiencing any G-forces).

Oh. So the present of G-force should be taken into consideration.

So how about this one hypothetical example:

The twins are now in somewhere in space(vacum) separated by 1 meter with each other. There is not any planet near by. They are not in any spaceship. They only wear spacesuits in space(vacum). They experience no g-force now. They both have an accelerometer than show reading of no g-force. They both also have a clock with each of them. And they have synchronized their clocks with each other.

Now suppose twin A is on the left side, twin B on the right side.

And now suddenly there is a strong gravitational field appear to the left of 10km of twin A, and the gravitational field pulls twin A to accelerate to the left in coordinate acceleration to the speed of 0.3C in says, 10 seconds.

And also there is another gravitational field with the same strength appear to the right of 10km of twin B, and also pulls twin B to accelerate to the right in coordinate acceleration to the speed of 0.3C in 10 seconds.

The 2 gravitational forces cancel each other out in the middle points of the 2 twins. So the left gravitational force only pulls the twin A but not twin B, and the right gravitational force only pulls the twin B but not twin A.

And after the twin A and twin B accelerates to 0.3C in opposite directions, the 2 gravitational forces disappear. So now twin A and twin B travel in constant speed of 0.3C in opposite directions.

So after twin A and twin B travels for 1 light year in opposite directions, their distance is 2 light years.

So suppose now there is very strong gravitational field appears in the middle point of the twins. And it pulls twin A and twin B to deaccelerate, to halt, and accelerate to 0.3C back toward the middle graviational field. (all in coordinate acceleration)

After twin A and twin B accelerate to 0.3C back toward the middle point, the middle gravitational field also disappear. So now twin A and twin B travels in constant speed of 0.3C towards each other. Eventually they meet again at the middle point.

So now. In this example there is no g-force. Twin A and twin B appears to be symmetry. Their accelerometers show g-force at all. Now which one of them have the clock run slower?



And there is another example in my original post that is not answered yet.

And another simpler question. Consider there is 2 object A and B. And they exists right from the beginning of the universe (forget about Big Bang). And right from the beginning of the universe, from the point of view of object A, object B is, and always, traveling at the contant speed of 0.5C, never accelerate or deaccelerate. So which object experience time slower? A or B?

In this example object A and object B also appear to be symmetry. There is no acceleration or deacceleration at all.

I would like to see answer to this example as well.

 

[JesseM]

If there's a gravitational field, then in relativity you need the theory of general relativity which explains gravity in terms of curved spacetime, not special relativity which assumes non-curved spacetime. And no coordinate system covering a substantial region of curved spacetime qualifies as "inertial" so the SR time dilation equation won't apply (though in a very small region a freefalling observer can have a "locally inertial frame" according to the http://www.einstein-online.info/spotlights/equivalence_principle). As for your second question:

And another simpler question. Consider there is 2 object A and B. And they exists right from the beginning of the universe (forget about Big Bang). And right from the beginning of the universe, from the point of view of object A, object B is, and always, traveling at the contant speed of 0.5C, never accelerate or deaccelerate. So which object experience time slower? A or B?

In this case there is no objective frame-independent answer to who experiences time slower, in the rest frame of object A it is B's clock that's running slower, while in the rest frame of object B it is A's clock that is running slower. This is related to the relativity of simultaneity, which says different frames disagree about which events separated in space are "simultaneous". Suppose the two observers pass by each other at some point, and both their clocks read T=100 years at that moment. Then in the frame of object A, 50 years earlier when his clock read T=50, that event was simultaneous with the event of object B's clock reading 100 - 0.866*50 = 56.7 years, so according to object A, object B only aged 0.866 times as much as he did between the time his clock said T=50 and the time they met when his clock read T=100. But in object B's frame, the event of his clock reading 50 was simultaneous with A's clock reading 56.7, and the event of his clock reading 56.7 was simultaneous with A's clock reading 62.5, so in B's frame it is A who is only aging 0.866 times as much as B.

 

[LightNg]

Ok now i see the picture. In the rest frame of object A, when A's clock read T = 200 years (100 years in the future), B only experiences 86.6 years in the future.
And vice versa.

Thanks a lot.

By the way, relativity of simultaneity only apply in non curved spacetime?

 

[JesseM]

By the way, relativity of simultaneity only apply in non curved spacetime?

In curved spacetime you no longer have global inertial frames as I said, but there are an infinite variety of non-inertial coordinate systems you can choose where the laws of GR still work (see the comments here on "diffeomorphism invariance"), so simultaneity is still relative to your choice of coordinate system.

 

[Mike_Fontenot]

[...]

You are a fairly good approximation of a "perpetually inertial observer". So, according to your previous comments, you shouldn't have a strong preference for which inertial frame you personally (usually) choose for your own "point-of-view" (POV).

You could choose to use the ordinary wristwatches and measuring tapes that you can buy at numerous retail stores here on Earth (which provide the time and spatial coordinates which Einstein chose to use for any given one of his inertial frames, in his 1905 paper, OR you could choose to use the coordinates of some particular inertial frame that is moving at some given constant velocity very near the speed of light, relative to the (approximately) inertial frame of the Earth.

If you make the latter choice, you will need to acquire and wear a wristwatch that doesn't tick at the same rate that my Timex ticks at. And you will need a measuring tape that is different from those that I've bought at Lowe's hardware store. In fact, you will need to buy one tape for measuring distances along the direction of relative motion, and another tape for measuring distances perpendicular to that direction (and even additional tapes, if you want to measure distances along various other angles to the direction of relative motion).

Presumably, from your previous comments, you really don't have much preference for which of the above two alternative POV's you decide to choose ... they are both equally good.

So, which of those two types of wristwatch have you been using, during your life, so far? Which type of measuring tape?

Mike Fontenot

 

[ghwellsjr]

[...]

Mike's even worse off than I thought he was.

 

[JesseM]

You are a fairly good approximation of a "perpetually inertial observer". So, according to your previous comments, you shouldn't have a strong preference for which inertial frame you personally (usually) choose for your own "point-of-view" (POV).

You could choose to use the ordinary wristwatches and measuring tapes that you can buy at numerous retail stores here on Earth (which provide the time and spatial coordinates which Einstein chose to use for any given one of his inertial frames, in his 1905 paper, OR you could choose to use the coordinates of some particular inertial frame that is moving at some given constant velocity very near the speed of light, relative to the (approximately) inertial frame of the Earth.

If you make the latter choice, you will need to acquire and wear a wristwatch that doesn't tick at the same rate that my Timex ticks at. And you will need a measuring tape that is different from those that I've bought at Lowe's hardware store. In fact, you will need to buy one tape for measuring distances along the direction of relative motion, and another tape for measuring distances perpendicular to that direction (and even additional tapes, if you want to measure distances along various other angles to the direction of relative motion).

Or I could just use the ruler and clock at rest relative to me, and do some simple calculations to figure how any given ruler/clock reading translates into the coordinates of a frame moving at high velocity relative to me. If you want to restrict me to using a coordinate system where I can't do any calculations of this sort, where the coordinates of a given event must be identical to the reading on some physical ruler and clock that were right next to the event when it happened, that would be a new "rule" you never mentioned before (which is itself just an arbitrary aesthetic choice), and applying the same criterion to your CADO system would show it would actually be quite complicated to construct a set of ruler/clocks whose readings matched that system, arguably more so than some other non-inertial systems where (as with CADO) you're at rest at the origin.

 

[LightNg]

If there's a gravitational field, then in relativity you need the theory of general relativity which explains gravity in terms of curved spacetime, not special relativity which assumes non-curved spacetime. And no coordinate system covering a substantial region of curved spacetime qualifies as "inertial" so the SR time dilation equation won't apply (though in a very small region a freefalling observer can have a "locally inertial frame" according to the equivalence principle). As for your second question:

Doesn't mean to interrupt the conversation, but I have another question.

Suppose the hypothetical example of the twin A and twin B given by me, doesn't involve gravitational field, but instead the gravitational field is replaced by electromagnetic force.

So say the twin A and twin B are actually just 2 magnets (that each has an accelerometer and a clock attached to it), they are not human.
So instead of being pulled by gravity, the magnets(A and B) are pulled by other strong big magnets (that appear and disappear), so the magnets (A and B)depart from each other, then reunite in the middle point again because of magnetic force.

So now, this is non curved space time, so time dilation equation applies. And still no g-force in effect. It appears that A and B is symmetry here. So now which clock run slower? A or B?

Or will both clock run slower? That is, relativity of simultaneity is in effect?
But if relativity of simultaneity is in effect, what the clocks of A and B show when they reunite? Note that the clocks have been synchronized in the beginning of the example, when A and B are 1 meter apart.

 

[JesseM]

Doesn't mean to interrupt the conversation, but I have another question.

Suppose the hypothetical example of the twin A and twin B given by me, doesn't involve gravitational field, but instead the gravitational field is replaced by electromagnetic force.

So say the twin A and twin B are actually just 2 magnets (that each has an accelerometer and a clock attached to it), they are not human.
So instead of being pulled by gravity, the magnets(A and B) are pulled by other strong big magnets (that appear and disappear), so the magnets (A and B)depart from each other, then reunite in the middle point again because of magnetic force.

So now, this is non curved space time, so time dilation equation applies. And still no g-force in effect.

In this case, the accelerometer would measure a nonzero g-force, the only way to not feel g-forces is if there aren't any non-gravitational forces acting on you (either inertial motion in flat spacetime, or freefall in a gravitational field)

 

[Dale]

So now. In this example there is no g-force. Twin A and twin B appears to be symmetry. Their accelerometers show g-force at all. Now which one of them have the clock run slower?

This example is completely symmetric, so their clocks will be equal when they meet again. However, as JesseM mentioned, actually calculating this would require GR and the simplified equations of SR would not apply.

So now, this is non curved space time, so time dilation equation applies. And still no g-force in effect. It appears that A and B is symmetry here. So now which clock run slower? A or B?

The accelerometers would read non-zero forces, but there is still symmetry so the clocks will be equal when they meet again.

 

[LightNg]

So, for mutual time dilation to occur without contradiction, I take that it is not possible for 2 objects (object A and object B in my example) to meet again after they depart, at least in the current framework of SR?

What if suddenly a magical portal appear in front of object B, and object B crosses the portal and meet with object A again?
Then what will their clocks read? Hahahaa

 

[Dale]

So, for mutual time dilation to occur without contradiction, I take that it is not possible for 2 objects (object A and object B in my example) to meet again after they depart, at least in the current framework of SR?

Correct, this is a simple geometrical fact. In a flat space two straight lines which are initially diverging can never intersect.

 

[LightNg]

Correct, this is a simple geometrical fact. In a flat space two straight lines which are initially diverging can never intersect.

I know bout this geometry, But is there any possibility, or is there any observed phenomena in the universe, that such line be not continuous in space?
Specifically, that the observed movement of an object is not continuous in space?

Ok this is not quite relevant to the topic of this thread, so someone may want to move this post to other thread/forum.

 

[JesseM]

So, for mutual time dilation to occur without contradiction, I take that it is not possible for 2 objects (object A and object B in my example) to meet again after they depart, at least in the current framework of SR?

What if suddenly a magical portal appear in front of object B, and object B crosses the portal and meet with object A again?
Then what will their clocks read? Hahahaa

Well, in this case the answer would depend on where in time the portal deposited object B! Because of the relativity of simultaneity, you can't just say that the portal transports B to A's "current" location, because there is no objective-frame independent fact about which event on A's worldline (which reading on its clock) is simultaneous with the event of B first reaching the position of the portal.

 

[Dale]

I know bout this geometry, But is there any possibility, or is there any observed phenomena in the universe, that such line be not continuous in space?
Specifically, that the observed movement of an object is not continuous in space?

Not yet. Even for quantum mechanical systems the wavefunction is continuous in space and time.