[General] [NEW] SRT twin Paradox
Albrecht Giese
phys at a-giese.de
Fri Sep 1 02:49:42 PDT 2017
Hi Grahame,
you are right that you did not attribute dilation to acceleration. Sorry
if I was not reading carefully. But on the other hand you understand
that the twins A and B will attribute their acceleration to gravity and
so explain why they observe dilation in the system of the other one as
it is. But also this cannot explain any dilation as observed by the
twins, as the influence of gravity to be assumed here, is too small to
explain what has to be explained by the twins observing each other.
Your example of the twins moving on half-circles towards a common point
is a quite interesting one. But it is not a simple example as both, A
and B, are permanently accelerated. This is not covered by Standard-SRT
to say it this way.
To find an explanation by only using SRT I would like to describe first
another, also symmetric, experiment.
This is a twin experiment which is symmetric in contrast to the usual
one (not yours). (I have discussed this earlier with Wolf). Here both
twins will move from a position at rest into opposite directions with a
constant speed v(1). Then, after a fixed time, t(1), they will both turn
quickly and return to each other. How does dilation behave here? - Both
twins will see themselves at rest and see the other one moving off with
the speed v(1+1) (i.e. adding the speeds relativistically). Now let's
look at the view of A. A assumes in the beginning to be at rest. And for
A the other one, B, moves off with speed v(1+1). After the time t(1) A
will now start to move towards B. A will measure his acceleration and
accelerate until he reaches v(1+1) with respect to his previous state. B
has turned in the same moment, and in the view of A he will have a speed
of 0 with respect to the previous state of A. Now the summary as seen
from A: A moved in the first period with speed 0 as this was his frame
at rest. For the second period he has moved with v(1+1). B has in the
view of A moved in the first period with a speed v(1+1) off, in the
second period with speed 0 with respect to the original frame of A. (B
will see this whole process mirrored.) So now, with respect to dilation,
they have both undergone a symmetric history as seen from the original
position of each one. And when they meet again, they will not be
surprised to have the same clock indications.
Now a little modification. Assume that in this experiment both twins do
not move at constant speed but at a variable speed, but in a way that at
same times both move at the same speed, only in different directions.
Also this experiment would have the same result. This can be understood
if we decompose the variable speed into infinitesimal pieces of constant
speed, determine the dilation for these parts, and integrate the parts
for the whole process.
The only way in my view to solve your (circular) example in the scope of
SRT is to decompose the motion process into infinitesimal linear pieces
and to treat these pieces by SRT. Now, in the view of A, it moves for an
infinitesimal distance straight. And at the same time also B moves at
the same time in infinitesimal distance. Then, after treating and then
integrating all infinitesimal pieces we get the results of both paths
until the meeting point.But first, we have to treat as an example a
typical infinitesimal piece for both twins. For this, we can decompose
the slant direction of each infinitesimal piece into a component so that
the one component (for both twins) points straight away from each other,
parallel but in opposite directions. And the other component now is
perpendicular to this one and points roughly into the direction of the
final point. And now, let's treat both pairs of components separately.
The components towards the destination (but parallel to each other) are
similar for A and B. So from the view of A of B the other one has the
same speed vector and there is no reason for dilation in the view of both.
And now the other component. That is a situation discussed in my example
above. In that other dimension both twins move away from each other and
then return to each other in a symmetric way. And as visible in my
example above the will understand to have similar clock indications at
the end.
So, this is an explanation for your experiment of circular motion which
is here treated only using SRT (no need for gravity). It it shows that
nothing happens which appears to the twins as a paradox.
A further little remark to your mail text below: It is true that in the
view of Einstein an observer cannot distinguish between the effect of
gravity and of acceleration ("Einstein's 'man in a box' thought
experiment"). But that is falsified meanwhile. Because if the observer
has a charged object with him, this will radiate at acceleration but not
at rest in a gravitational field.
I hope that my explanations were understandable as I did not present a
drawing. - Or should I present one?
Best regards
Albrecht
Am 29.08.2017 um 12:41 schrieb Dr Grahame Blackwell:
> 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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