[General] [NEW] SRT twin Paradox
Albrecht Giese
phys at a-giese.de
Fri Sep 1 01:17:25 PDT 2017
Wolf,
just a short answer to this mail.
Einstein's example is a simplified situation. It is simplified in so far
that the moving clock comes back to the clock at rest. So in the
equation which I have given:
t' = (t-xv/c^2 )* (1-c^2 /v^2 )^-1/2
the distance x becomes 0 (zero). Then your equation can be used. But if
two moving clocks are compared in a state where they are at different
positions then the full equation (above) has to be used.
The short version is also applicable for the twin experiment because at
the end both twins meet again at the same position.
In which respect is there a paradox?
Best
Albrecht
Am 30.08.2017 um 07:54 schrieb Wolfgang Baer:
>
> I've now looked up the reference from "on the Electrodynamics of
> moving Bodies" by Albert Einstein translated from Annalen der Physik
> 17,1905 in The Principle of Relativity by H.A. Lorentz, A Einstein,
> H. , wit notes by A Sommerfeld p 49 in Section #4
>
> " If we assume that the result proved for a polygonal line is also
> valid for a continuously curved line, we arrive at this result: If one
> of two synchronous clocks at A is moved in a closed curve with
> constant velocity until it returns to A, the journey lasting t
> seconds, then by the the clock remained at rest the traveled clock on
> its arrival at A will be 1/2 t v^2 /c^2 seconds slow."
>
> Am I wrong in interpreting these words as implying a twin paradox.?
> I'm not claiming that there is a twin paradox.
>
> Only that the straight forward interpretation of Einstein's words
> suggest there is a paradox
>
> best
>
> Wolf
>
>
> Dr. Wolfgang Baer
> Research Director
> Nascent Systems Inc.
> tel/fax 831-659-3120/0432
> E-mailwolf at NascentInc.com
> On 8/29/2017 3:41 AM, Dr Grahame Blackwell wrote:
>> Hi Albrecht,
>> Regrettably, you appear to have misread my text. If you read it
>> again more carefully, you will see that at NO point do I propose, or
>> even suggest, that acceleration gives rise to time dilation. I am
>> well aware that, as you say, "gravity and acceleration are different
>> regarding [time] dilation" - so your attempts to persuade me of this
>> are quite unnecessary.
>> The whole point of my text was, as I said at the outset, to resolve
>> the 'twins going opposite directions around a circle' paradox, with
>> reference to classical SR (and GR, as it happens - bear with me on
>> this). For SR to be self-consistent (which I believe it is - that's
>> not the same as it being correct!) there has to be an explanation
>> that fits the terms of Relativity which explains how it can be that
>> both A and B would expect their clocks to coincide on re-meeting - as
>> they clearly would from the perspective of a third observer, static
>> with respect to the circle centre, and so they must of course
>> coincide from everyone's perspective. If it can be shown that they'd
>> expect their clocks to be different then Relativity is dead - but it
>> is most definitely not that simple! [That's why it's survived for
>> over a century; it's not just that thousands of other physicists over
>> that century have been incapable of such analysis!]
>> Relativity states that any scenario can validly be assessed from the
>> perspective of any individual, who may consider themself to be static
>> - and that their assessment of that scenario is equally 'correct' to
>> any OTHER assessment from any other frame of reference. SR restricts
>> such assessment to inertial frames, GR extends it to non-inertial
>> frames - but this same principle holds true.
>> We can add to this the fact that if such an observer experiences what
>> we might refer to as a 'G-force' acting on them then they will know
>> that they must be in a non-inertial frame. The term 'G-force' is
>> convenient for our purposes as it is used to apply both to forces due
>> to gravitation and to accelerating forces; it is implicit in GR
>> (through the Equivalence Principle) that the observer will not know
>> which of these two applies (Einstein's 'man in a box' thought
>> experiment), but that if (as he fully validly may, under Relativity)
>> he considers himself to be at rest then he must necessarily attribute
>> such forces to gravitational effects (without having to ascertain
>> where those effects arise from - that could be tricky in our example
>> scenario!)
>> Please not that I am NOT saying that these principles actually apply
>> in our physical reality - I am simply stating the mantra of
>> Relativity, both SR and GR, since that's the mathematical framework
>> in which I'm seeking to show self-consistency. Others in the group
>> are proposing that Relativity is disproved by this 'twins thought
>> experiment', I'm observing that it is not; the truth or falsehood of
>> Relativity as a model of true reality is not what I'm about here - in
>> fact I'm seeking to show that Relativity CANNOT be disproved by such
>> a simple setup, it needs rather more thought than that!
>> Albrecht, I think you misunderstand my purpose here. It's not my
>> intention EITHER to prove OR to disprove Relativity; my sole
>> intention is to show that this 'twins scenario' does NOT show an
>> inconsistency in Relativity - it is NOT a paradox. In this respect
>> the question of whether Relativity does or does not match true
>> objective reality is totally irrelevant; the only question is whether
>> or not Relativity agrees with itself.
>> The importance if this exercise shouldn't be underestimated: if we
>> are to challenge the fundamental premises of Relativity, it has to be
>> on FAR stronger ground than a proposed 'paradox' that has been
>> refuted time and time again over the past 100 years - we do
>> ourselves, and science, a serious disservice if we convince fans of
>> Relativity that our view that it's wrong is based on a simplistic
>> misunderstanding of its basics!
>> So, again: external observer sees A and B perform mirror images of
>> each others' manoeuvres - so of course clocks will match on
>> re-meeting. So A and B will also see clocks coinciding - and fully
>> expect that to be the case. How come, given that Relativity allows
>> each to see their position in the universe as static?
>> Simple: since the external observer sees A (for example) as
>> experiencing acceleration towards the centre of the circle, A
>> him/herself will inevitably experience a G-force acting outward from
>> the centre of that observer's circle. Considering him/herself static
>> in space, A will have no option but to regard that as a gravitational
>> effect from some unknown source (note that physicists have no trouble
>> envisaging gravitation acting from unknown sources - we're told that
>> such sources make up the vast majority of the mass-energy in our
>> universe!). Since A knows that gravitation causes time dilation (NOTE
>> THAT I AM *NOT* PROPOSING, HERE OR ANYWHERE, THAT ACCELERATION CAUSES
>> SUCH DILATION), he/she will inevitably expect their clock to have
>> been slowed, as well as knowing that B's motion will have also slowed
>> B's clock. So matching of clocks on re-meeting is to be totally
>> expected by A (and B) - no paradox.
>> This is all about perceptions from different perspectives, and the
>> assertion in Relativity that all such perceptions are equally valid/true.
>> With regard to assessing time and distance of B, as assessed by A:
>> whilst not relevant to this analysis, the question has arisen - so
>> let's look at it from A's perspective. A sends out a broadcast radio
>> signal in the general direction of B; on receiving that signal, B
>> sends a time-stamped response (broadcast in A's general direction);
>> From the time between sending and receipt, 'knowing' such signals to
>> travel both ways at c relative to him/herself (according to SR), A
>> can calculate the distance to B at the time B responded - which will
>> be halfway between send and received, from A's perspective; A will
>> also have a record of B's clock-time at that point halfway between
>> A's send and receive - and so an indication of how B's time is
>> progressing compared with A's [This is all according to SR 'rules',
>> I'm not proposing that A's assessments will in fact be correct in
>> absolute terms - though of course SR considers them to be equally
>> correct to any other view].
>> Having glanced briefly at Wolf's latest response, I'd just say that
>> mass-energy considerations can also be very misleading in a
>> Relativistic scenario, unless handled exceedingly carefully with full
>> regard for different perspectives. As a very simple illustration: A
>> single photon observed from one reference frame may be red- or
>> blue-shifted when observed from a different frame, and so carry
>> different energy. Extension of this to massive energetic particles,
>> and applying mass-energy equivalence, makes it clear that we can't
>> simply assess the mass-energy characteristics of an object or system
>> from one frame then simply carry those measures across to another
>> frame. I don't know whether this has a bearing on Wolf's comments, I
>> didn't get to see much of what you sent previously, Wolf, for some
>> reason.
>> Best regards,
>> Grahame
>> ----- Original Message -----
>>
>> *From:* Albrecht Giese <mailto:phys at a-giese.de>
>> *To:* general at lists..natureoflightandparticles.org
>> <mailto:general at lists.natureoflightandparticles.org>
>> *Sent:* Monday, August 28, 2017 4:21 PM
>> *Subject:* Re: [General] [NEW] SRT twin Paradox
>>
>> Hi Grahame,
>>
>> sorry, but I find a very fundamental error in your arguments: You
>> describe a pair of twins which observe each other in a situation
>> where they are permanently accelerated. And then you argue with
>> dilation caused by gravity. But that does not fit the physical
>> reality.
>>
>> Gravity and acceleration are different regarding dilation.
>> Gravity causes dilation, no question. But acceleration does not
>> cause dilation. How can one know? 1) You find this in every
>> textbook about special relativity; 2) it was experimentally
>> proven in the Muon storage ring at CERN. The extension of the
>> life time of the muons was only dependent on the actual speed of
>> the particles, not on the very strong acceleration in the ring.
>> If that would have been an effect according to an equivalent
>> gravitational field, their lifetime would have to be extended by
>> an additional factor of roughly 1000 compared to the results
>> observed.
>>
>>
>> Am 27.08.2017 um 22:18 schrieb Dr Grahame Blackwell:
>>> Hi Albrecht,
>>> I'm afraid I have to disagree with you on a couple of points.
>>> First, I agree completely that gravitation doesn't come under
>>> SR. However the concept of gravitation is essential to
>>> explanation of the 'twins going in opposite directions around a
>>> circle and meeting on the far side' (non-)paradox. [It may be
>>> that in your view this scenario cannot then be simply a
>>> playing-out of SR, it must be a GR issue?]
>>> Consider: Twin A and twin B each view themselves as being
>>> static, with the other twin tracing out a path that takes them
>>> away and then brings them back into proximity from a different
>>> direction, having formed a loop of some kind; however, from the
>>> point of view of an observer static with respect to the centre
>>> of a large circle, A and B have started together at some point
>>> on the perimeter of that circle and have each followed opposite
>>> halves of that circle to meet again on its other side. I.e.
>>> from the perspective of that observer the motions of A and B are
>>> symmetric, so their clocks (synchronised at the start) will
>>> still be synchronised when they meet again. [We're assuming here
>>> that this all takes place in deep space, far from any
>>> gravitational influences.]
>> None of the twins can view himself as being static, because they
>> are accelerated all the time and they will notice that. So the
>> laws of SR are not applicable for this process in a simple way.
>>> From A's point of view, A has remained static and B has
>>> performed a large loop in space, finally coming back alongside
>>> A. According to SR, therefore, A will observe a slowing-down of
>>> B's clock and so will expect B's clock to have lost time, in
>>> real terms as measured in A's frame (if it were an inertial frame).
>> No, it is not an inertial frame.
>>> [We can deal with the issue of A reading B's clock whilst B is
>>> on the move by B digitally emitting their clock-time at
>>> intervals, to be received by A who will assess those
>>> transmissions on the basis of their crossing space at speed c
>>> across the distance that A measures B to be from him at times of
>>> transmission - this could be done fairly easily by A keeping a
>>> record of B's distance at all times as measured on A's clock.]
>> Also this is not possible. A can receive signals from B, but he
>> does not know the distance. According to SR this distance is not
>> clearly defined because the assessment of any distance depends on
>> the motion state of the observer. Which speed will A assume for
>> himself? He cannot assume to be static as he notices to be
>> accelerated.
>>> B will have a corresponding mirror-image experience of A's
>>> motion, and so will expect A to have lost time in real (B-frame)
>>> terms. This appears to suggest that both A and B would each
>>> expect the other's clock to have fallen behind their own - a
>>> paradox.
>> Also regarding time a similar problem like for distance is
>> applicable. When are signals in different frames synchronised or
>> when is time is running faster or slower? For any observer in
>> different frames the result of this question may be different.
>>> However, our external observer will have seen A performing a
>>> circular course - so A will inevitably have experienced a
>>> 'G-force' of some kind (centripetal, from our observer's
>>> persective). Since A considers him/herself to be static, he/she
>>> MUST attribute this to some gravitational influence - indeed,
>>> from the SR/GR perspective there must indeed be a gravitational
>>> influence in A's frame, from the perspective of that frame; one
>>> just does not get G-force without either acceleration or
>>> gravitation. (Here, of course, Relativity begins to become
>>> unravelled, as A is far from any massive body that could give
>>> rise to a gravitational field - maybe they'll need to start
>>> inventing their own local 'dark matter'). Note that the
>>> scenario being considered - A and B traversing opposite sides of
>>> a circle - involves NO gravitational fields - BUT A and B would
>>> HAVE TO PRESUME the existence of such a field in their reference
>>> frame if they are to reconcile a force they're experiencing with
>>> their assumption that they are static (a totally valid
>>> assumption, in Relativity terms).
>> As said above, even if both, A and B, attribute the force of
>> acceleration to gravity, they are in error; and it does anyway
>> not help the situation. For your consideration they need a
>> gravitational field for dilation, but this does not exist, and
>> acceleration does not replace it.
>>> Resolution of this (apparent) paradox, as I said before, rests
>>> on A (and likewise B) considering themselves to have been
>>> subject to a gravitational field - and experiment shows us that
>>> gravitational fields slow time - so their own clock will have
>>> slowed as well as the others. So they will both expect their
>>> clocks to be synchronised on re-meeting.
>> That is anyway true also in the absence of dilation.
>>> As I say, this is where Relativity begins to become unravelled:
>>> A and B will either each have to acknowledge that they are NOT
>>> in fact static, or they will have to invent a convincing
>>> explanation for a gravitational effect in the absence of any
>>> 'ponderous mass' (to use Einstein's term). But given that,
>>> synchronisation of clocks is not an issue - as long as we allow
>>> A and B to each presume existence of a gravitational field in
>>> their frame (which, as you say, takes it into the sphere of GR).
>> Not applicable as mentioned above.
>>> Second point: in your case of the travelling-twin versus the
>>> stay-at-home twin, the traveller would again experience G-force,
>>> which they could if they wish regard as a gravitational effect
>>> (since under Relativity they are free to consider themselves as
>>> static). They would therefore expect their clock (including
>>> biological clock) to have slowed (Pound-Rebka again), and so
>>> know that they have actually been travelling more than one year
>>> in 'objective' terms - whatever that might mean in this context.
>> The twin travelling, B, cannot assume that he is static because
>> he has to notice his acceleration. And that is different from
>> gravity. And even if it could be identified with gravity this
>> would not solve the example which I have given.
>>> But of course the reality is that slowing of time is NOT
>>> symmetric, it's a consequence of motion with respect to the
>>> unique objectively-static universal reference frame. Only
>>> when serious scientists start asking WHY Relativity does (or
>>> appears to do) what it does will we make any progress on this issue.
>> Which progress to you expect? There is no symmetry in the case
>> where twin B returns and so you cannot conclude anything from
>> symmetry.
>>> I think we're agreed on the key issues. Perhaps it's time to
>>> stop discussing how a self-consistent mathematical system (which
>>> doesn't happen to match true reality) copes with paradoxes of
>>> its own making!
>>> Best regards,
>>> Grahame
>> As I have mentioned in the other mail: It is in conflict with
>> Einstein's relativity to compare clocks residing in different
>> frames. The result of any comparison depends on the motion state
>> of the observer. That is what Einstein says.
>>
>> But the other solution is to follow the Lorentzian relativity. In
>> that case the imagination becomes easy (in contrast to Einstein).
>>
>> Greetings back
>> Albrecht.
>>> ----- Original Message -----
>>>
>>> *From:* Albrecht Giese <mailto:phys at a-giese.de>
>>> *To:* general at lists..natureoflightandparticles.org
>>> <mailto:general at lists.natureoflightandparticles.org>
>>> *Sent:* Sunday, August 27, 2017 7:48 PM
>>> *Subject:* Re: [General] [NEW] SRT twin Paradox
>>>
>>> Hi Grahame,
>>>
>>> without going into details of this discussion I only want to
>>> point to the following fact:
>>>
>>> Whereas you are of course right that the twin situation is
>>> not a paradox but logically clean, what we all as I think
>>> have sufficiently discussed here, the following is not
>>> correct in my view:
>>>
>>> The twin situation has absolutely NOTHING TO DO with gravity.
>>>
>>> Two arguments for this:
>>>
>>> o The so called twin paradox is purely Special Relativity.
>>> Gravity on the other hand, is General Relativity. This is
>>> the formal point.
>>>
>>> o From practical numbers it is visible that gravity cannot
>>> be an explanation. Take the usual example saying that one
>>> twin stays at home and the other one travels - as seen from
>>> the twin at home - for twenty years away and then twenty
>>> years back. From the view of the twin at home, at the other
>>> ones return 40 years have gone. For the travelling twin only
>>> one year has gone (This case is theoretically possible if
>>> the proper speed is taken, about 0.9997c)). Then the
>>> travelling twin would have saved 39 years of life time. Now
>>> look at the possible influence of gravity: Assume it takes
>>> the travelling twin a year to change his speed from almost
>>> c to almost - c , then, even if the speed of proper time
>>> would decrease to zero, he would have saved only one year.
>>> But, in this example, he has saved 39 years. How could this
>>> work? No one in physics assumes that proper time can run
>>> inversely. So this is no possible explanation.
>>>
>>> How is it explained? I do not want to repeat again and again
>>> the correct (but a bit lengthy) explanation, but I attempt
>>> to give a short version: In Einstein's relativity the run of
>>> time in different frames can logically not be continuously
>>> compared, it can only be compared at interaction points
>>> where two clocks (or whatever) are at the same position. And
>>> the determination of the situation at such common position
>>> has to be done by the Lorentz transformation. And this
>>> determination works, as many times said here, without
>>> logical conflicts.
>>>
>>> If you solve this problem using the Lorentzian SRT, then the
>>> result is the same but the argument is different, more
>>> physics-related, and also better for the imagination. If
>>> wanted, I can of course explain it.
>>>
>>> Albrecht
>>>
>>>
>>>
>>> Am 27.08.2017 um 01:13 schrieb Dr Grahame Blackwell:
>>>> I'm sorry Wolf, but it seems that you're still not getting it.
>>>> This situation can be explained fully logically WITHOUT
>>>> either twin making any assumptions about SR or GR - simply
>>>> from their own observations and from well-proven
>>>> experimental findings.
>>>> If we label the twins A and B, then their situations are
>>>> effectively symmetric* - so we'll consider the scenario
>>>> from the viewpoint of twin A.
>>>> A considers him/herself static, and all motion to be
>>>> attributable to twin B. So - and this agrees with
>>>> experimental observation of clocks at high speed (in planes
>>>> and in GPS satellites) - twin A will observe twin B's clock
>>>> running slow, if A's own clock is not upset by any effect.
>>>> HOWEVER, since A is actually travelling in circular motion,
>>>> (s)he will experience a centripetal force; assuming
>>>> him/herself to be static, this will necessarily be
>>>> attributed to gravitational effects - and it's well known
>>>> from experiment (Pound-Rebka and successors) that
>>>> gravitational fields cause time dilation - so A will expect
>>>> their own clock to be running more slowly also due to that
>>>> 'gravitational' effect (note that this is not any
>>>> assumption of SR or GR, simply inference from proven
>>>> experimental results) [and so also A's observation of B's
>>>> clock, measured against A's own clock, will not fit the
>>>> standard SR time-dilation model, for reasons that A will
>>>> fully comprehend]. For A, the cumulative time-dilation for
>>>> B's perceived relative speed and for A's own perceived
>>>> 'gravitational' effect exactly balance - so A will fully
>>>> expect both clocks to coincide when the twins meet again
>>>> (as B will also).
>>>> No paradox.
>>>> * It needs to be said that further study of causation of
>>>> 'relativistic time dilation' leads to the understanding
>>>> that this is an objective effect due to travelling at speed
>>>> relative to the unique objectively-static universal
>>>> reference frame. So if the centre of the circle traced out
>>>> by A and B is itself in motion relative to that reference
>>>> frame then it cannot be assumed that A's and B's motions
>>>> will be symmetric; in that case their clocks may well not
>>>> be precisely synchronised on their meeting again. This is
>>>> an observation relating to physical reality, which in no
>>>> way contradicts the self-consistency of SR (or GR) as a
>>>> mathematical system.
>>>> Best regards,
>>>> Grahame
>>>
>>>
>>>
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