My Problems With Relativity

[naita]

Originally Posted by tomh4040

1. Using the formulae on Wikipedia pointed to by "these are my own pants", the time passage on the rocket accelerating at 1G is 0.9999999989802 of the clock which is well away from any gravitational effect and ticks at 1 second per second.
The time passage on Earth is 0.9999999993045 of this same clock. Therefore the 2 clocks stay in sync to within 2 milliseconds per year.

Is no one going to point out that what I've bolded above is pretty much the definition of not staying in sync? If you've typed them in correctly the difference between the two is 50% of the total gravitational time dilation for the potential at Earth's surface, in other words, relatively speaking completely different.

[Asympotically fat]

Originally Posted by naita

Is no one going to point out that what I've bolded above is pretty much the definition of not staying in sync? If you've typed them in correctly the difference between the two is 50% of the total gravitational time dilation for the potential at Earth's surface, in other words, relatively speaking completely different.

Yep, if tomh were correct about the observed clock rate he would actually be proving the falsity of what he set out to prove. The problem is that when comapring inertial clocks the relationship between observed times is linear so Δt' = γΔt where γ is a constant for a constant relative velocity.

The problem is though that when the original frame is inertial and the primed frame is non-inertial γ becomes a non-constant function of t, i.e. Δt' = γ(t)Δt. Therefore γ can not be given as a single number as, say for example, a constant proper acceleration as it's a function of t.

Of course, this still proves that he is incorrect in his original idea. Why is he incorrect? Becuase the relationship between a uniformly accelerated observer and inertial observer and the relationship between an observer held stationary in a static graviational field and an inertial observer at spatial conformal infinity is not the same. What differinates them is that in the latter case the spacetime between the two observers is curved. A better comparison for the former case would be the relationship between an observer being held stationary in a static gravitational field and an free-falling observer passing close by them.

[tomh4040]

Originally Posted by These are my own pants

It's not linear, so your "seconds per second" depend on which particular second we're talking about which is why the figure you've quoted makes no sense. Infact as t goes to infinity the "seconds per seconds" go to zero when comapring the proper time of a uniformaly accelerated observer and the coorindate time of an inertial observer. Try it for yourself (thoguh I noticed I quoted it incorrectly in my last post), i.e. try inserting large values for t into the formula and notice how tau/t goes to zero.
Where in the equations representing the Lorentz transformation do you see a term for mass? Actually deriving so-called 'mass increase' from the Lorentz transformation is actually quite complicated. Also note that when you define mass in this manner you actually get two types of mass: transverse and longitudinal.

The particular second we are talking about is by the reference clock described in Wikipedia "...tf is the coordinate time between events A and B for a fast-ticking observer at an arbitrarily large distance from the massive object (this assumes the fast-ticking observer is using Schwarzschild coordinates, a coordinate system where a clock at infinite distance from the massive sphere would tick at one second per second of coordinate time, while closer clocks would tick at less than that rate)..."
You are trying to muddy the waters in talking about "...t going to infinity...", as that is not the scenario being discussed here. The formulae prove my original statement that clocks at 1G, whether accelerated or gravitational, run at the same rate to a high degree of precision.

The term for mass is :- m = m0 / sqrt( 1-(v/c)^2), and references can be found in chapter XV of Einstein's book which I have already mentioned, and chapter 8 of Asimov, "The Stars In Their Courses" (and of course a myriad of others).

[Asympotically fat]

Originally Posted by tomh4040

The particular second we are talking about is by the reference clock described in Wikipedia "...tf is the coordinate time between events A and B for a fast-ticking observer at an arbitrarily large distance from the massive object (this assumes the fast-ticking observer is using Schwarzschild coordinates, a coordinate system where a clock at infinite distance from the massive sphere would tick at one second per second of coordinate time, while closer clocks would tick at less than that rate)..."
You are trying to muddy the waters in talking about "...t going to infinity...", as that is not the scenario being discussed here. The formulae prove my original statement that clocks at 1G, whether accelerated or gravitational, run at the same rate to a high degree of precision

You're still not understanding, I'm talking about the accelerated observer in Minkowski space (i.e. flat spacetime). The time dilation factor increases as t increases which means you cannot express it as a single number for acceleration = 1g as it is a function of time.

In comparision the proper time of a stationary observer in a static gravational field as compared to Schwarzchild coordinate time is constant with time and hence can be expressed as a single numebr (for a given r).

Is it that difficult to understand?

The term for mass is :- m = m0 / sqrt( 1-(v/c)^2), and references can be found in chapter XV of Einstein's book which I have already mentioned, and chapter 8 of Asimov, "The Stars In Their Courses" (and of course a myriad of others).

Look up "Lorentz transformation" on google. Do you see that equation as one of the equations that describes the Lorentz transformation? The answer is no. It's a simple matter of fact/catergorization.

That's not to say that the equation isn't true when you define mass in a certain way of course, however as I've explained we don't define mass in this way any more

Try reading this paper: http://www.stat.physik.uni-potsdam.d...r/einstein.pdf

It explores Eisntein's understanding of the concept of mass (as well as some of the problems associated with the now defunct concept of relativstic mass)

[Leo Bloom]

::raises hand timidly from back of room::
Can gravity potential be likened, metaphorically, to potential (ie non kinetic) energy?

[tomh4040]

Originally Posted by These are my own pants

It's not linear, so your "seconds per second" depend on which particular second we're talking about which is why the figure you've quoted makes no sense. Infact as t goes to infinity the "seconds per seconds" go to zero when comapring the proper time of a uniformaly accelerated observer and the coorindate time of an inertial observer. Try it for yourself (thoguh I noticed I quoted it incorrectly in my last post), i.e. try inserting large values for t into the formula and notice how tau/t goes to zero.

I am not comparing IFRs with non IFRs, I am concerned only with accelerated/gravitational FRs, and their relationship to the "standard" clock. The formula for gravitational time delay was known to me; what was new was the different formula for accelerated time dilation. I had assumed, correctly as it turns out (try running the figures yourself through the 2 formulae, and work to 8 decimal places), that under 1G, whether caused by gravity or acceleration, the clocks run at (to a high degree of precision) the same rate.

[quote]You're still not understanding, I'm talking about the accelerated observer in Minkowski space (i.e. flat spacetime). The time dilation factor increases as t increases which means you cannot express it as a single number for acceleration = 1g as it is a function of time.
In comparision the proper time of a stationary observer in a static gravational field as compared to Schwarzchild coordinate time is constant with time and hence can be expressed as a single numebr (for a given r).[quote]

If Einstein's equivalence principle is correct, you are wrong, if your quote above is correct, Einstein is wrong and there is no equivalence.

[Andy L]

[quote=tomh4040;14429193]I am not comparing IFRs with non IFRs, I am concerned only with accelerated/gravitational FRs, and their relationship to the "standard" clock. The formula for gravitational time delay was known to me; what was new was the different formula for accelerated time dilation. I had assumed, correctly as it turns out (try running the figures yourself through the 2 formulae, and work to 8 decimal places), that under 1G, whether caused by gravity or acceleration, the clocks run at (to a high degree of precision) the same rate.

[quote]You're still not understanding, I'm talking about the accelerated observer in Minkowski space (i.e. flat spacetime). The time dilation factor increases as t increases which means you cannot express it as a single number for acceleration = 1g as it is a function of time.
In comparision the proper time of a stationary observer in a static gravational field as compared to Schwarzchild coordinate time is constant with time and hence can be expressed as a single numebr (for a given r).

If Einstein's equivalence principle is correct, you are wrong, if your quote above is correct, Einstein is wrong and there is no equivalence.

The paper I cited above has experimental results showing that (as Einstein predicted) two clocks experiencing the (almost precisely*) same gravity but at different potentials will have different dilations.

* the (per mass) gravity force are very slightly different - by a factor of 1 meter divided by the radius of the Earth cubed, but the difference in dilation is proportional to the difference in potential (proportional to g*dh)

[ZenBeam]

Originally Posted by These are my own pants

I think you're going to be a little bit more specific about what you want cites and equations for.

Exactly what I asked for three times before (Yes three. Count them.), "an actual cite that gravitational time dilation depends on force".

I don't disagree with the 3 cites you've cited, but two wikipedia articles (and may I point out the aerticle on gravaitional time dilation actually makes at least one very contentious statement on the equivalnce principle) and an amateur paper don't in my mind consitute authortative cites.

They are more authoritative than anything you've provided. It's easy to sit back and say "Oh, they're not authoritative enough", without actually saying anything substantive about them, or providing any kind of cite yourself.

Part of the problem with providing cites is that gravaitional time dilation isn't that big an issue in general relativity. I've got a 500 page text book on general relatvity next to me that doesn't mention it once.

Perhaps you need a better text book on general relativity. I have Weinberg's Gravitation and Cosmology. It has sections on time dilation for both special and general relativity. As we've seen, papers are written on the subject. Cites on time dilation in GR are available. It's only cites that time dilation depends on force that don't exist.

Basically speaking gravaitional time dialtion is a cooridnate artifact and so somewhat arbitary.

No, it's not "arbitrary". This is just bizarre.

The reason I think force shouldn't be ruled out is that four force 'rotates' four vectors and curvature rotates parallel transports of four vectors and its this rotation of four velocity and it's parallel transports that can be seen as both due to 'force' and as responsible for the effect of graviational time dilation.

I will try one last time. Here's the time dilation for arbitrary motion in an arbitrary gravitational field from Weinberg:

dt/delta t = (-g_uv dx^u/dt dx^v/dt)^-1 (Eq. (3.5.1))

No explicit force terms in sight. No second derivatives (the metric tensor is first derivatives), so no acceleration terms, so no force terms in hiding, expressed as acceleration. Thus, force does not contribute to gravitational time dilation.

QED.

[Asympotically fat]

Originally Posted by ZenBeam

Exactly what I asked for three times before (Yes three. Count them.), "an actual cite that gravitational time dilation depends on force".

They are more authoritative than anything you've provided. It's easy to sit back and say "Oh, they're not authoritative enough", without actually saying anything substantive about them, or providing any kind of cite yourself.

I'm actually trying to argue its more complciated than that and that the very prescriptive statement you've made is not necessarily true. Note none of your cites actually support the prescritpive nature of your statement. Rather ask for cites for a psotion that I do not necessarily agree with (typing gravitional tiem dialtion and force in to Google will get you the cites you've asked for, but as I think these are equally if not more simplistic, there's no point in me psoting them).

Rather than asking for cites, tackle my objections to the prescriptiveness of your statement directly. Posting cites that don't actually disagree with what I've said doesn't acheive this.

Perhaps you need a better text book on general relativity. I have Weinberg's Gravitation and Cosmology. It has sections on time dilation for both special and general relativity. As we've seen, papers are written on the subject. Cites on time dilation in GR are available. It's only cites that time dilation depends on force that don't exist.

When dealing with the more theoretical side of the subject graviational time dialtion just isn't that importnat,mainly for the reasons I describe below

No, it's not "arbitrary". This is just bizarre.

I will try one last time. Here's the time dilation for arbitrary motion in an arbitrary gravitational field from Weinberg:

dt/delta t = (-g_uv dx^u/dt dx^v/dt)^-1 (Eq. (3.5.1))

Can you honestly not see what is wrong with what you've written?

Firstly, the fact that the equation uses the ordinary derivative should alert you as to its coordinate dependent nature.

Seocndly if what you'd said was actually true and there was a totally valid general method for non-arbitarily defining gravitational time dilation in an arbitary gravitational field, then the relationship between gravaitonal time dialtion and gravaitional potnetial must be very weak. This is as the gravaitional potnetial cannot be defined (satisfactorily) for an arbitary gravitational field.

The arbitariness in Weinberg's equation lies in the fact that choices of the cooridinate basisare arbitary. If we had an exact prescription for deciding the components of the metric at an event then it wouldn't be arbitary, but we don't, so they are. Even if we limit the possible cooridnate bases by imposing restricitions so as to make them 'physically sensible' we can still end up with being able to define multiple different coorindate bases or even worst none at all! E.g. Schwarzchild cooridnates are only a cooridnate patch in Schwarzchild spacetime as opposed to a global coorinate system as they fail to cover the region of spacetime bounded by the event horizon. So you cannot use Schwarzchild compoents to define the time dilation factor of an object inside the event horizon (this may seem sensible, but on the other hand using a cooridnate system thta does cover the inside of the event horizon you could).


Consequently different chocies of the cooridnate bases in the above equation will result in different time dilation factors.

Of course gravaitonal time dialtion is also an empirical phenemona, but this comes from being able to compare a particular spacetime or region of spacetime with a flat sapcetime either because it is asymptoically flat or a region of it can be viewed as a peturbation of the flat metric.

No explicit force terms in sight. No second derivatives (the metric tensor is first derivatives), so no acceleration terms, so no force terms in hiding, expressed as acceleration. Thus, force does not contribute to gravitational time dilation.

QED.

If we're assuming that we've defined the coordinate basis fields using physical prescriptions the 'force' (representing both gravaitional and four force) will appear in the connection of that coorinidate system and will help decide what the coordinate basis is.

[Asympotically fat]

Originally Posted by tomh4040

I am not comparing IFRs with non IFRs, I am concerned only with accelerated/gravitational FRs, and their relationship to the "standard" clock. The formula for gravitational time delay was known to me; what was new was the different formula for accelerated time dilation. I had assumed, correctly as it turns out (try running the figures yourself through the 2 formulae, and work to 8 decimal places), that under 1G, whether caused by gravity or acceleration, the clocks run at (to a high degree of precision) the same rate.

As I've explained the don't. Afetr a time you'd find the uniformly accelerated clock will appear to keep slowing down the more (inertial cooridnate) time passes, the clock in the graviational field will appear to run at slower, but constant rate.

If Einstein's equivalence principle is correct, you are wrong, if your quote above is correct, Einstein is wrong and there is no equivalence.

Nope because Eisnetin's equivalence principle only directly applies when comapring a free falling observer passing close by to the observer stationary in a gravtional field and only indriectly applies in the situation you describe.

[Asympotically fat]

Originally Posted by Andy L

The paper I cited above has experimental results showing that (as Einstein predicted) two clocks experiencing the (almost precisely*) same gravity but at different potentials will have different dilations.

* the (per mass) gravity force are very slightly different - by a factor of 1 meter divided by the radius of the Earth cubed, but the difference in dilation is proportional to the difference in potential (proportional to g*dh)

Which is not what I disagree with, however if it were to truly be due to gravitational potential at the msot basic level, you'd have a hard time explaining why gravaitonal potnetial was only a relatively non-trivial concept only applicable in certain sitautions in the context of the theory of general relativity.

[Half Man Half Wit]

Originally Posted by tomh4040

As to mass increase. The Lorentz equations are all linked, and derive time dilation, length contraction, and mass increase. If you don't agree with the mass increase formula, then you have to throw the lot out, you cannot cherry pick. Either Einstein is correct, or he is not correct - which is it?

Originally Posted by tomh4040

The term for mass is :- m = m0 / sqrt( 1-(v/c)^2), and references can be found in chapter XV of Einstein's book which I have already mentioned, and chapter 8 of Asimov, "The Stars In Their Courses" (and of course a myriad of others).

Einstein was certainly quite correct when he wrote:

Originally Posted by Einstein to Lincoln Barnet, June 1948

It is not good to introduce the concept of the mass M = m/sqrt{1 - v^2/c^2} of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the ’rest mass’ m. Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion.

[ZenBeam]

Originally Posted by These are my own pants

Can you honestly not see what is wrong with what you've written?

Firstly, the fact that the equation uses the ordinary derivative should alert you as to its coordinate dependent nature.

It is a fully general result, derived from the Equivalence Principal. It applies to any coordinates. For any arbitrary coordinate system you like, there are no force terms. There's the answer.

You can make all the hand-waving arguments you want, they don't prove anything.

[tomh4040]

Originally Posted by These are my own pants

"If Einstein's equivalence principle is correct, you are wrong, if your quote above is correct, Einstein is wrong and there is no equivalence."

[Nope because Eisnetin's equivalence principle only directly applies when comapring a free falling observer passing close by to the observer stationary in a gravtional field and only indriectly applies in the situation you describe.

Smoke and mirrors. You are making incorrect assumptions, and extrapolating from those assumptions. "... a free falling observer passing close by to the observer in a gravitational field..." is pure fiction. It is not what Einstein said (WRT the man on Earth and the man in the chest). His observers and my observers are not in free fall, they are all experiencing 1G, and he made no mention of them being close.

More smoke and mirrors. You asked "Where in the equations representing the Lorentz transformation do you see a term for mass? Actually deriving so-called 'mass increase' from the Lorentz transformation is actually quite complicated. Also note that when you define mass in this manner you actually get two types of mass: transverse and longitudinal."
You said that that their masses did not alter. L mass and T mass are old expressions which became relativistic mass, which definitely does alter with velocity when viewed from a different FR.

More smoke and mirrors. You said there was no Lorentz equation for mass increase, and yet in the next sentence said that deriving so-called mass increase fom the Lorentz equations is quite complicated. If there is no term for mass how can you derive it - complicated or not. Quote from Albert Einstein "It is not good to introduce the concept of the mass M = m/sqrt( 1-(v/c)^2)) of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the ’rest mass’ m."

Quote from Wikepedia (which I assume that we all trust as we all quote it). "So, according to Lorentz's theory no body can reach the speed of light because the mass becomes infinitely large at this velocity."

[Half Man Half Wit]

Originally Posted by tomh4040

Smoke and mirrors. You are making incorrect assumptions, and extrapolating from those assumptions. "... a free falling observer passing close by to the observer in a gravitational field..." is pure fiction. It is not what Einstein said (WRT the man on Earth and the man in the chest). His observers and my observers are not in free fall, they are all experiencing 1G, and he made no mention of them being close.

Take the following two situations: 1) you are a stationary observer, while I am accelerating away from you at 1g; 2) you are an observer far away from the central mass in a Schwarzschild spacetime, while I stay put at a point where I experience a gravitational pull of 1g.

You seem to be saying that the equivalence principle implies that the time dilation between us in both cases is the same; but this isn't so, as can easily be seen (and as These are my own pants has tried to point out). Obviously, in the second case, the dilation is constant, equal to t_m = t_y*sqrt(1 - 2*g*r/c²) = t_y*sqrt(1 - 2*G*M/r*c²), where t_m is my time, and t_y is yours -- you observe my clock ticking slower by a fixed factor.

But in the first case, things are different -- at any moment in time, my clock appears to you slowed by the factor sqrt(1 - v²/c²). However, I am accelerating, and thus, my speed is not constant -- it increases. Thus, the factor by which you observe my clock ticking slower is not constant, either -- it increases, as well.

The two situations thus are quite different, even though in both cases, I experience an acceleration of 1g; thus, it doesn't suffice to state the acceleration to work out the time dilation.

Nevertheless, this situation is quite consistent with the equivalence principle. The reason is that it is only valid locally -- I either in my spaceship or hovering in the Schwarzschild spacetime can't tell the difference.

Quote from Wikepedia (which I assume that we all trust as we all quote it). "So, according to Lorentz's theory no body can reach the speed of light because the mass becomes infinitely large at this velocity."

While it's an intuitive concept, this is a bad explanation -- it would, for instance, imply that a massless body can move at any speed, since its 'mass' doesn't increase. As has been pointed out, the modern understanding of special relativity typically eschews the concept of relativistic mass; unlike invariant mass, it's a concept that has no general validity, since you can make it have arbitrary values just by jumping to reference frames with different relative speeds, while invariant mass is the same in all frames of reference.

Perhaps a better, if also flawed, intuitive explanation is that you move at the speed of light all the time (the magnitude of the four-velocity is c), just that the bulk of this movement is through time; thus, as you move through space faster and faster, you move through time slower and slower, and going arbitrarily close to c means basically not moving through time at all.

[Asympotically fat]

Originally Posted by ZenBeam

It is a fully general result, derived from the Equivalence Principal. It applies to any coordinates. For any arbitrary coordinate system you like, there are no force terms. There's the answer.

You can make all the hand-waving arguments you want, they don't prove anything.

I think your missing the point here. Coorindinate systems are generally speaking, arbitary and they don't necessarily represent anything physical. Quite often we'll start off with an observer and extend their local coorindate system outwards, but there's multiple ways of extending an observer's local coordinate system.

The actual force terms appear in the coordinate system itself, for example non-vanishing Christoffel symbols at an event will tell you at that point there's an equivalnce between the coordinate basis and an accelerated observer's local cooridnates.

As I pointed out earlier the equation that you posted results in a non-tensor quantity and so depends purely on the chocie of cooridnate systems and nothing else.

[ZenBeam]

Blah blah blah. I'm done here.

[Hero From Sector 7G]

...and with that departure, the tone of civility returns to polite.

[Andy L]

Originally Posted by These are my own pants

Which is not what I disagree with, however if it were to truly be due to gravitational potential at the msot basic level, you'd have a hard time explaining why gravaitonal potnetial was only a relatively non-trivial concept only applicable in certain sitautions in the context of the theory of general relativity.

I'm not familiar with situations where potential doesn't apply (I'm more familiar with analyzing physical situations by treating potential energy as fundamental and forgetting about forces, frankly), but I'd like to hear more.

It's been years since I studied general relativity, but I was introduced to the concept via examples that did not include forces, but did include potential (the elevator example for example), and while I find papers such as this one in Nature http://www.nature.com/nature/journal...ture08776.html (which states "One of the central predictions of metric theories of gravity, such as general relativity, is that a clock in a gravitational potential U will run more slowly by a factor of 1 + U/c2, where c is the velocity of light, as compared to a similar clock outside the potential") about the use of potential in gravitational time dilation calculations, I haven't found anything helpful about force. Please give me some more information. Thanks.

[Andy L]

Originally Posted by Andy L

I'm not familiar with situations where potential doesn't apply (I'm more familiar with analyzing physical situations by treating potential energy as fundamental and forgetting about forces, frankly), but I'd like to hear more.

It's been years since I studied general relativity, but I was introduced to the concept via examples that did not include forces, but did include potential (the elevator example for example), and while I find papers such as this one in Nature http://www.nature.com/nature/journal...ture08776.html (which states "One of the central predictions of metric theories of gravity, such as general relativity, is that a clock in a gravitational potential U will run more slowly by a factor of 1 + U/c2, where c is the velocity of light, as compared to a similar clock outside the potential") about the use of potential in gravitational time dilation calculations, I haven't found anything helpful about force. Please give me some more information. Thanks.

I should say that I do understand that there is a problem with the setting of a zero for potential energy in GR (unlike in Newtonian gravity where the zero can be set anywhere), but I don't think this problem doesn't affect calculations of differences in potential, which is the quantity that affects gravitational potential energy.

[Asympotically fat]

The problem is precisely that general relatvity is a metric theory of gravity.

Take the stress-energy tensor, this is a rank-2 tensor field which among other things describes the (non-gravitational) enegry of spacetime. In a vacuum this vanishes, which is precisely what we'd expect as a vacuum is a region that contains no non-gravitational energy.

So far no problems, but let's imagine what sort of object could describe the gravaitional potential energy. By the equivalance principle, you can always choose a local frame (descrbing an observer in free fall) so that spacetime appears locally flat. Now a flat spacetime is one without an sort of gravitational energy, so locally the gravitational energy must also vanish. I.e. in gravitational energy, should it exist in general relatvity cannot be a local property of spacetime as it can be made to vanish locally just like the stress-energy tensor vanishes when describing a region containing no energy.

Already we're at odds with the idea of gravitational potential energy, because the precise point of GPE is to give gravitational energy a local definition on par with other kinds of energy.

So you cannot derive a cocnept of gravitational potential energy purely from the general relativstic description of gravity, you need either explicitly or implicitly add something else such as a preferred frame of reference or a decompostion of the metric in to a gravitational part and a background part (this is driectly paraphrased from Wald's General Relativity).

There are what are known as pseudo-tensor fields which can be defined on spacetime to allow us to find some sort of expression the total energy/energy flux (including graviational energy) of some arbitary volume of space, but that's still not the same as GPE as they can be made to vanish locally (whereas in Newtonian gravity GPE does not vanish).

I believe the statement that time dialtion due to GPE is a central prediction of metric theories of gravity comes from MWT's Gravity where it is shown that in the limit relativistic theories of gravity must reduce to a certain metric described by the Newtonian potential, from which graviational time dialtion can easily be related to gravitational potnetial.

The reason I think it's too prescriptive to rule out the role of force is that in general relatvity terms force-like terns appear as Christoffel symbols related to some coordinate system and I think it's just as easy to see time dialtion as a result of the aggregate effect they have on the transport of vectors in spacetime.

[Andy L]

Originally Posted by These are my own pants

The problem is precisely that general relatvity is a metric theory of gravity.

Take the stress-energy tensor, this is a rank-2 tensor field which among other things describes the (non-gravitational) enegry of spacetime. In a vacuum this vanishes, which is precisely what we'd expect as a vacuum is a region that contains no non-gravitational energy.

So far no problems, but let's imagine what sort of object could describe the gravaitional potential energy. By the equivalance principle, you can always choose a local frame (descrbing an observer in free fall) so that spacetime appears locally flat. Now a flat spacetime is one without an sort of gravitational energy, so locally the gravitational energy must also vanish. I.e. in gravitational energy, should it exist in general relatvity cannot be a local property of spacetime as it can be made to vanish locally just like the stress-energy tensor vanishes when describing a region containing no energy.

That makes sense, but we're not really talking locally when we're talking about gravitational time dilation - we're talking about two different places in curved space-time. If we pick a frame that makes one of those places flat, then that frame makes the other one non-flat, and thus at a different potential, no?

Already we're at odds with the idea of gravitational potential energy, because the precise point of GPE is to give gravitational energy a local definition on par with other kinds of energy.

So you cannot derive a cocnept of gravitational potential energy purely from the general relativstic description of gravity, you need either explicitly or implicitly add something else such as a preferred frame of reference or a decompostion of the metric in to a gravitational part and a background part (this is driectly paraphrased from Wald's General Relativity).

There are what are known as pseudo-tensor fields which can be defined on spacetime to allow us to find some sort of expression the total energy/energy flux (including graviational energy) of some arbitary volume of space, but that's still not the same as GPE as they can be made to vanish locally (whereas in Newtonian gravity GPE does not vanish).

Even in Newtonian gravity, you can assign the point where GPE is zero arbitrarily - two common choices are zero at infinity (which is helpful when talking about escape from a gravity well), and zero at "ground level" which is useful when distances are small.

I believe the statement that time dialtion due to GPE is a central prediction of metric theories of gravity comes from MWT's Gravity where it is shown that in the limit relativistic theories of gravity must reduce to a certain metric described by the Newtonian potential, from which graviational time dialtion can easily be related to gravitational potnetial.

The reason I think it's too prescriptive to rule out the role of force is that in general relatvity terms force-like terns appear as Christoffel symbols related to some coordinate system and I think it's just as easy to see time dialtion as a result of the aggregate effect they have on the transport of vectors in spacetime.

Ok. That makes sense - I'm a firm believer that it's useful to learn to address physics problems using a variety of different approaches, because sooner or later, you'll run into problems that are easy with approach 'a' and difficult with approach 'b', and other problems that are easy with 'b' and hard with 'a.'

[Asympotically fat]

Originally Posted by Andy L

That makes sense, but we're not really talking locally when we're talking about gravitational time dilation - we're talking about two different places in curved space-time. If we pick a frame that makes one of those places flat, then that frame makes the other one non-flat, and thus at a different potential, no?

Yes, graviational time dilation is an effect that comes from essentially not local. However; no, picking a local frame will not fix the frame at some other point, that I guess would be equivalent to saying that defining a local basis defines a tetrad basis for the whole of spacetime, which is not true and I'm not sure that there's any sensible conditions you could impose on a tetrad bsis to make it true.

Even in Newtonian gravity, you can assign the point where GPE is zero arbitrarily - two common choices are zero at infinity (which is helpful when talking about escape from a gravity well), and zero at "ground level" which is useful when distances are small.

[/quote]

The issue you've brought up is gauge arbitariness and that's not really the issue here. I feel a bit over my head discussing gauge theory aspects of general relativity, but the problem is not fixing a gauge for GPE (i.e. in particualr fixing a zero point)

Perhaps the best way to understand it is to compare to an elctrostatic field in general relativity. In an electrovacuum (i.e. a 'vacuum' containing only an elctromagnetic field), the stress-energy tensor does not vanish, unlike a 'true vacuum' in general relativity (i.e. one not containing any gravitational sources, though it still may contain a gravitational field) where it does vanish identically. Your just never goign to get a definition of graviational potential energy in general relativity where there's a basic equivalnce it and for example electrical potential energy. Electromagentic energy exists locally in general relatvity, graviataional energy does not.

Ok. That makes sense - I'm a firm believer that it's useful to learn to address physics problems using a variety of different approaches, because sooner or later, you'll run into problems that are easy with approach 'a' and difficult with approach 'b', and other problems that are easy with 'b' and hard with 'a.'

I'm not saying my description from my last post is better (it is in fact very hand wave-y), btu key to recognise is that in this situation there's so much more going on in the general relativistic description of gravitational time dialtion-like effects than gravitational potential energy making clocks run slower.

[Andy L]

Originally Posted by These are my own pants

Yes, graviational time dilation is an effect that comes from essentially not local. However; no, picking a local frame will not fix the frame at some other point, that I guess would be equivalent to saying that defining a local basis defines a tetrad basis for the whole of spacetime, which is not true and I'm not sure that there's any sensible conditions you could impose on a tetrad bsis to make it true.




The issue you've brought up is gauge arbitariness and that's not really the issue here. I feel a bit over my head discussing gauge theory aspects of general relativity, but the problem is not fixing a gauge for GPE (i.e. in particualr fixing a zero point)

Perhaps the best way to understand it is to compare to an elctrostatic field in general relativity. In an electrovacuum (i.e. a 'vacuum' containing only an elctromagnetic field), the stress-energy tensor does not vanish, unlike a 'true vacuum' in general relativity (i.e. one not containing any gravitational sources, though it still may contain a gravitational field) where it does vanish identically. Your just never goign to get a definition of graviational potential energy in general relativity where there's a basic equivalnce it and for example electrical potential energy. Electromagentic energy exists locally in general relatvity, graviataional energy does not.




I'm not saying my description from my last post is better (it is in fact very hand wave-y), btu key to recognise is that in this situation there's so much more going on in the general relativistic description of gravitational time dialtion-like effects than gravitational potential energy making clocks run slower.

Thanks for all of the above. Sometime I have to get back to the books I have on GR...

[tomh4040]

Hi, sorry for my enforced absence, I'm joining in again.
I got so carried away with the ongoing arguments about 1G gravity versus 1G acceleration that I forgot my original mission. I was wrong in pursuing the argument about the 1G accelerated frame not going out of sync with the reference clock as I had the wrong parameters. Here are the correct parameters, and why I have been keen to establish the time connection between 1G gravity and 1G acceleration.

There is a closed chest resting on the surface of the Earth. Naturally the man inside experiences 1G. During the course of this experiment he is not allowed outside the chest.
There is a closed chest with a man inside in a rocket ship which is about to be accelerated at 1G. During the course of this experiment he is not allowed outside the chest.
The Earth and the rocket to be accelerated are both placed in intergalactic space, far away from any other bodies so there are no reference points except each other. They are aware of each other, and know they are eg 1 million Km apart.
Their clocks are synchronised and the rocket motor is fired up. The distance between the two then rapidly increases at 9.8m/s^2. The man in the rocket (he does not know he is in a rocket remember) experiences 1G, and time for him passes normally - ie he cannot detect any change in the passage of time. He can also conduct experiments which tell him he is experiencing 1G, and all experiments he conducts behave normally, just as they did when he performed them on Earth before this experiment began. The man in the chest on Earth experiences 1G and for him the passage of time is "normal" also. He can also conduct experiments which tell him he is experiencing 1G, and all experiments he conducts behave normally, just as they did previously on Earth before this experiment began.
After 2,191.5 hours by the clock on the rocket, the motor on the rocket is cut, the rocket is rotated round 180 degrees, and the motor restarted. The man in the chest on board does not know this, all he knows is that he was weightless for 60 seconds, then all was normal again. Unknown to the man in the rocket, 2,191.5 hours after that period of weightlessness, the rocket very briefly (almost instantaneously) stops (relative to Earth) and starts accelerating back. 4,383 hours after the first period of weightlessness, the procedure is repeated. All he knows is he was weightless again for 60 seconds. Another 2,191.5 hours passes, and the Earth and the rocket are adjacent to each other again. One year has passed on the rocket. The experiment has now ended, they are back again to the 1 million Km apart. The rocket cuts its motor and the clocks are compared. Note that the man in the chest on Earth did not undergo two 60 seconds periods of weightlessness, and this will cause a disparity between the clocks of 0.00008 seconds, a trifling amount.
With the above scenario, any GR effects are present in both FRs, and therefore cancel each other out. Are the clocks in sync to within a few seconds. If not, which clock is slow, and why?
We have here of course the twin paradox, as each man can justifiably say that he was the one who was stationary, and the other was moving. Their only reference was each other. They both experienced 1G for one year (except for one man who experienced 0G for 120 seconds, wich will not affect the outcome.
It can be arranged for the man in the chest on Earth to be weightless also for 2 periods of 60 seconds, by having him suspended and dropped, but the experiment is simpler as laid out here, and just as accurate.

[slowlearner]

at one time (haha) Einstein said that there were only half a dozen people who understood his theories. are there more than that now?

[Andy L]

Originally Posted by tomh4040

After 2,191.5 hours by the clock on the rocket, the motor on the rocket is cut, the rocket is rotated round 180 degrees, and the motor restarted. The man in the chest on board does not know this, all he knows is that he was weightless for 60 seconds, then all was normal again.

You mean all he knows is that he was weightless for an instant, then accelerated sideways for almost a minute, then decelerated suddenly (to stop the rotation), then weightless for another instant, and then under 1G again. I think he'd notice that. Even if he was at the center of the ship, he'd notice the ship rotating around him, during the weightless period.

[GiantRat]

Originally Posted by DaveTheJackal

[OK I have to go now as guests are arriving so this may need some editing still. Hopefully it kinda makes sense]

A few of my problems with relativity, both of which might expose my extreme leymanish understanding of relativistic issues! Both problems are about the relatativistic effects of velocity.

I think the length of the OP proves without a doubt the existence of relativity - to the OP, "now" means" after I write 15 paragraphs about something that I'm unsure of, which will make time move even more slowly outside of my mind because it is engaged and (pre?)occupied; to the guests, who by the end of the post have been ringing the doorbell for 30 minutes whilst freezing their asses off, those thirty minutes seemed like at least two hours.

[Exapno Mapcase]

Originally Posted by slowlearner

at one time (haha) Einstein said that there were only half a dozen people who understood his theories. are there more than that now?

Einstein didn't say that. It was written about him in a newspaper article. It wasn't true at the time or since.

[Andy L]

Originally Posted by Exapno Mapcase

Einstein didn't say that. It was written about him in a newspaper article. It wasn't true at the time or since.

Here's a link to the article by the way http://query.nytimes.com/mem/archive...D9415B898DF1D3

[Exapno Mapcase]

The article does make an unsourced claim that Einstein said it to his publishers, but there's no evidence for it. And he would certainly know it wasn't true.

Although he did have an odd sense of humor...

[naita]

Originally Posted by Andy L

You mean all he knows is that he was weightless for an instant, then accelerated sideways for almost a minute, then decelerated suddenly (to stop the rotation), then weightless for another instant, and then under 1G again. I think he'd notice that. Even if he was at the center of the ship, he'd notice the ship rotating around him, during the weightless period.

And whether he noticed or not doesn't matter. The fact the the direction of accelleration changed makes all the difference.

[Asympotically fat]

Originally Posted by naita

And whether he noticed or not doesn't matter. The fact the the direction of accelleration changed makes all the difference.

There's a lot wrong with Tom's assumptions, but the best way (IMO) to view it is as an unnecessarily overcomplicated version of the standard special relativstic twin parados, but with one (or both - it's not clear from Tom's post) being subject to a small peturbation due to general relativistic effects.

What's clear is that the time dilation 'suffered' by the rocket ship observer massively outweighs the tiny peturbation caused by general relativstic effects and the rocket ship observer will experince much less time between the start and the end of their journey than is measured on the Earth bound observer's clock.

[Half Man Half Wit]

Originally Posted by tomh4040

Unknown to the man in the rocket, 2,191.5 hours after that period of weightlessness, the rocket very briefly (almost instantaneously) stops (relative to Earth) and starts accelerating back.

The rocket is going at about 0.25c at that point, so if it 'almost instantaneously' stops, its passenger will notice... If only for a fraction of a second, after which he will have ceased noticing things for good.

But it's easy to see that of course, the travelling clock will show less time elapsed than the stationary clock on Earth. As I said, after 2191.5 hours at 1g acceleration, the rocket is going at roughly 0.25c, meaning a gamma factor of roughly 1.03 -- small, but noticeable. By contrast, the equivalent factor for the observer in the gravity well, giving the slowing down of his time relatively to a 'far away' observer, is roughly 1.0000000007, utterly negligible in comparison. As These are my own pants said, we can thus just think of this as the familiar twin problem, where of course less time passes for the moving observer.

[Lemur866]

Originally Posted by Half Man Half Wit

The rocket is going at about 0.25c at that point, so if it 'almost instantaneously' stops, its passenger will notice... If only for a fraction of a second, after which he will have ceased noticing things for good.

No, what he means is that the rocket starts at zero velocity relative to Earth, then the rocket accelerates at 1g for 90 days, achieving .25c relative to Earth, then flips and accelerates in the opposite direction at 1g for another 90 days, at which point it will have zero velocity relative to Earth. The rocket keeps accelerating at 1g for another 90 days until it is back to .25c relative to Earth, then flips accelerates in the opposite direction at 1g for another 90 days, at which point it will have zero velocity relative to Earth.

At no point does the rocket instantaneously go from .25c to 0. The instantaneous point where the rocket changes from moving away from Earth to moving towards Earth won't be felt at all in the rocket, because it is accelerating smoothly at 1g the whole time.

[naita]

Originally Posted by These are my own pants

There's a lot wrong with Tom's assumptions, but the best way (IMO) to view it is as an unnecessarily overcomplicated version of the standard special relativstic twin parados, but with one (or both - it's not clear from Tom's post) being subject to a small peturbation due to general relativistic effects.

What's clear is that the time dilation 'suffered' by the rocket ship observer massively outweighs the tiny peturbation caused by general relativstic effects and the rocket ship observer will experince much less time between the start and the end of their journey than is measured on the Earth bound observer's clock.

I think a part of Tom's intention is to prove there are no special relativistic effects because it's impossible for the two observers to know which is which, but that might just be my interpretation of his first post where he argues against FTL reversing the flow of time.

There's also the issue of him considering 0.000008 s to be a trifling amount when doing GR calculations for 1G.

[Half Man Half Wit]

Originally Posted by Lemur866

No, what he means is that the rocket starts at zero velocity relative to Earth, then the rocket accelerates at 1g for 90 days, achieving .25c relative to Earth, then flips and accelerates in the opposite direction at 1g for another 90 days, at which point it will have zero velocity relative to Earth. The rocket keeps accelerating at 1g for another 90 days until it is back to .25c relative to Earth, then flips accelerates in the opposite direction at 1g for another 90 days, at which point it will have zero velocity relative to Earth.

At no point does the rocket instantaneously go from .25c to 0. The instantaneous point where the rocket changes from moving away from Earth to moving towards Earth won't be felt at all in the rocket, because it is accelerating smoothly at 1g the whole time.

Ah OK, did not parse that. It's still just the twin thing twice, with some messy integration because of the acceleration, though.

[Asympotically fat]

Originally Posted by naita

I think a part of Tom's intention is to prove there are no special relativistic effects because it's impossible for the two observers to know which is which, but that might just be my interpretation of his first post where he argues against FTL reversing the flow of time.

There's also the issue of him considering 0.000008 s to be a trifling amount when doing GR calculations for 1G.

Yep, though of course as AndyL pointed out the two observers can distinguish each other due to the change in force. Not that that makes a huges difference in general relativity as it's perfectly possible to have two observers who cannot peform any local experiment to distinguish themselves from each other, but who measure different times between events at which they are both present.

One thing to note is that I didn't calculate the amount of time the rocket ship twin experinced,so when I said he will experince much less time that was a slight exaggeration (though to make iso its no exaggeration a all we need to do is to extend the time that the rocket accelerates) , however it is still painfully clear that the special relativstic twin effect dwarves the peturbation due to the Earth's gravity.

[tomh4040]

Originally Posted by These are my own pants

Yep, though of course as AndyL pointed out the two observers can distinguish each other due to the change in force. Not that that makes a huges difference in general relativity as it's perfectly possible to have two observers who cannot peform any local experiment to distinguish themselves from each other, but who measure different times between events at which they are both present.

One thing to note is that I didn't calculate the amount of time the rocket ship twin experinced,so when I said he will experince much less time that was a slight exaggeration (though to make iso its no exaggeration a all we need to do is to extend the time that the rocket accelerates) , however it is still painfully clear that the special relativstic twin effect dwarves the peturbation due to the Earth's gravity.

0.000008 secs is a trifling amount, when considering that the experiment lasts for one year. The main thrust of the argument seems to have been missed. These 2 observers have no reference other than each other, so which one "actually" moved? Each man can justifiably claim that he was the stationary one. I have used GRT in this twin paradox problem to remove one of the arguments which is often heard when "proving" which twin actually moves. As both are under the same 1G, except for 120 seconds for one man, their situations are identical. They have no reference to the what can be called the standard clock far away from any gravitational source. As stated in my last posting, it can be arranged for the man in the chest on Earth to be weightless also for 2 periods of 60 seconds, by having him suspended and dropped (starting at 34Km above the Earth, dropping for 60 seconds, which leaves him at 17Km, then again, which puts him on the surface. This neglects air resistance of course, and three calculations have to be done, not just one. This just leaves the SRT time dilation effect, and the question, wich one moved and which one was stationary? is still not answered.

[Asympotically fat]

Originally Posted by tomh4040

0.000008 secs is a trifling amount, when considering that the experiment lasts for one year. The main thrust of the argument seems to have been missed. These 2 observers have no reference other than each other, so which one "actually" moved?

Okay we can both agree the question of which one "moved" is totally subjective and metaphysical, however the question we want to ask is what interval of time does each one measure between events which, whilst in the scenario you've set up there is an elemtn of subjectivity (which we will ignore), is an objective physical question

Each man can justifiably claim that he was the stationary one. I have used GRT in this twin paradox problem to remove one of the arguments which is often heard when "proving" which twin actually moves. As both are under the same 1G, except for 120 seconds for one man, their situations are identical. They have no reference to the what can be called the standard clock far away from any gravitational source.

Okay, what your trying to do is to create some sort of symmetry between the observers, you haven't managed that, but see below.

As stated in my last posting, it can be arranged for the man in the chest on Earth to be weightless also for 2 periods of 60 seconds, by having him suspended and dropped (starting at 34Km above the Earth, dropping for 60 seconds, which leaves him at 17Km, then again, which puts him on the surface. This neglects air resistance of course, and three calculations have to be done, not just one. This just leaves the SRT time dilation effect, and the question, wich one moved and which one was stationary? is still not answered.

I think we can ignore air resistance without missing anything of qualitive importance.

As has been pointed out the rocket twin changes direction. In the special relativistic version, changing direction breaks the symmetry between the two twins and remember that special relativity is just a special case of GR.

However, try this scenario: after a period the twin on Earth drops through a hole which goes directly through the Earth's centre and where he comes out the other side and stops. This exactly simulates what the rocket bound twin feels when they stop and then turnaround and whilst it may have a significant effect on the GR correction, whatever effect it does have will still be much smaller than the time dilation effect from the standard twin paradox. We can alos adjust the set-up in other ways.

So now we do have two apparently symmetrical situations, however there will still be a time dilation like effect between the two twins. The reason is that there is a global asymmetry is in the spacetime which both twins occupy.

Compare to the cosmological twin paradox of GR. In this both twins start and finish at the same spot and neither twin is subject to acceleration and the spacetime they occupy is (or at least can be made) very symmetric, yet there is a significant time dilation effect due to the asymmetry introduced by something as esoteric as them having different winding numbers in spacetime.

[tomh4040]

Originally Posted by These are my own pants

Okay we can both agree the question of which one "moved" is totally subjective and metaphysical...
As has been pointed out the rocket twin changes direction. QUOTE]

You have made two contradictory statements here - the statements "which one "moved" is totally subjective and metaphysical" and "the rocket twin changes direction", are mutually exclusive. Also, Einstein did not believe the questions were subjective and metaphysical. He built a whole theory on relative movement, and went so far as to "prove" that time dilation, length contraction, and mass increase, were actual occurences in the moving FR.

[QUOTE. However, try this scenario: after a period the twin on Earth drops through a hole which goes directly through the Earth's centre and where he comes out the other side and stops. This exactly simulates what the rocket bound twin feels when they stop and then turnaround and whilst it may have a significant effect on the GR correction, whatever effect it does have will still be much smaller than the time dilation effect from the standard twin paradox. We can alos adjust the set-up in other ways. QUOTE]
This in no way equates to my scenario, when the rocket twin gradually comes to a halt and changes direction, he is totally unaware of the change and does not feel anything. He is experiencing 1G all the time. The man dropping through the Earth experiences 0G. Please do not set up your own version and ask your own question and then answer that one, answer mine.

[QUOTE. Compare to the cosmological twin paradox of GR. In this both twins start and finish at the same spot and neither twin is subject to acceleration and the spacetime they occupy is (or at least can be made) very symmetric, yet there is a significant time dilation effect due to the asymmetry introduced by something as esoteric as them having different winding numbers in spacetime.

Here we have another argument often used to explain the twin paradox, the introduction of an assymetry, although the relatavist does not refer to it as such.

The questions, which one moved and which one was stationary? and what do the clocks show when compared? still have not been answered.

[Asympotically fat]

Originally Posted by tomh4040

Here we have another argument often used to explain the twin paradox, the introduction of an assymetry, although the relatavist does not refer to it as such.

it's not an argument, it's a fact. If the twins are truly symmetric their cannot be a time dilation effect between them as that would indicate an asymmetry. I'm pointing out where the asymmetry comes from in this situation

The questions, which one moved and which one was stationary? and what do the clocks show when compared? still have not been answered.

I've already said that your first question is totally subjective, you'd have to define, in technical terms, what you mean for that question to make any sense.

In answer to your second question: sorry, but if your going to create a reasonably complciated set-up like you have don't expect others to take the time (and it would be time-consuming especially if we were to include general relativistic effects) to solve it for you. I've already told you the qualitive answer which is easy to arrive at with some straight forward arguments.

[tomh4040]

[quote=These are my own pants;14466574]it's not an argument, it's a fact. If the twins are truly symmetric their cannot be a time dilation effect between them as that would indicate an asymmetry. I'm pointing out where the asymmetry comes from in this situation

And there we have the crux of the problem. In SRT, the twins are truly symmetrical as they carry on travelling for ever away from each other so the experiment is not falsifiable. They have to be brought together again for the clocks to be compared, and this is where the adherants say the assymmetry comes from, as acceleration was used to turn one around. By using FRs of 1G, there is symmetry.

[Andy L]

Originally Posted by tomh4040

And there we have the crux of the problem. In SRT, the twins are truly symmetrical as they carry on travelling for ever away from each other so the experiment is not falsifiable. They have to be brought together again for the clocks to be compared, and this is where the adherants say the assymmetry comes from, as acceleration was used to turn one around. By using FRs of 1G, there is symmetry.

But your thought experiment provided additional accelerations to one and only one of the participants (by rotating the ship)

[Andy L]

Originally Posted by naita

And whether he noticed or not doesn't matter. The fact the the direction of accelleration changed makes all the difference.

Yes - you're right.

[tomh4040]

Originally Posted by Andy L

But your thought experiment provided additional accelerations to one and only one of the participants (by rotating the ship)

The occupant of the ship is weightless for 2 periods of 60 seconds, and has been pointed out, this can be equalised by arranging for the man on Earth also to be weightless for 2 periods of 60 seconds. The additional accelerations you speak of are sideways forces, which are tiny, and can be equalised by having the chest on Earth also rotated while it is in freefall. Under these cicumstances, both men are undergoing the same accelerations. This objection is therefore null and void.
While I am answering objections, here is another
Quote:Originally Posted by naita (I think)
What's clear is that the time dilation 'suffered' by the rocket ship observer massively outweighs the tiny peturbation caused by general relativstic effects and the rocket ship observer will experince much less time between the start and the end of their journey than is measured on the Earth bound observer's clock.

The tiny pertubations caused by GR effects in fact add up to 8.72 hours over the year.
I asume this time dilation (suffered by the rocket ship observer) is caused by SRT, and that is what this posting is really about. Gravity and acceleration cause clocks to run slower when increased, and run faster when decreased. Actually that is not quite true, as a pendulum clock does exactly the opposite, but we'll leave that for now. It is SRT's prediction of time dilation and length contraction that I have an issue with. I shall now refer you to an address to the Prussian Acamedy of Sciences in 1921 given by A Einstein. In the paragraph starting "Sub specie aeterni" he recants. Recall that both Poincare and Lorentz believed in a "real" time.
It is to be found at :- http://www.relativitycalculator.com/...ience_1921.pdf

[Andy L]

Originally Posted by tomh4040

The occupant of the ship is weightless for 2 periods of 60 seconds, and has been pointed out, this can be equalised by arranging for the man on Earth also to be weightless for 2 periods of 60 seconds. The additional accelerations you speak of are sideways forces, which are tiny, and can be equalised by having the chest on Earth also rotated while it is in freefall. Under these cicumstances, both men are undergoing the same accelerations. This objection is therefore null and void.

I don't think the accelerations are tiny, but even if they are, you can't make them equal on earth and in space, because you need to rotate the person on earth by 360 degrees while he is in so-called free fall, and rotate the person in space by 180 degrees. And this brings up the real catch - the person on Earth is accelerating in a constant direction, while the person in space is accelerated in one direction for a while and then another direction.

[tomh4040]

Originally Posted by Andy L

But your thought experiment provided additional accelerations to one and only one of the participants (by rotating the ship)

I have already pointed out how the other FR can undergo the same accelerations.

[tomh4040]

Originally Posted by naita

The twin "paradox" only occurs when one twin changes direction and returns. If they carry on travelling for ever away from each other there is no paradox. This is falsifiable, as it's still possible to communicate.

Your thought experiment with 1G reference frames is not symmetric. One participant has one or more changes in accelleration. This means a change of reference frames, which means a break in symmetry. The direction of travel and the direction of accelleration matters.

What is more likely? a) The brightest physicists of the previous century overlooked basic results of their theories or the theories they were trying to falsify and every knowledgable doper here have been duped by a dogmatic education system, or b) You have misunderstood something basic about relativity?

Remember that the Ptolemaic system held sway for 1500 years, before it was replaced by the Corpernicus sytem, which as we all now know is correct.
The brightest physicists etc are all earning their wages on the back of relativity, they are hardly likely to renounce it. It takes a brave man like Professor Dingle to admit there is something wrong with the theory. None of the so called tests of SRT have actually proved it, they have merely failed to disprove it, which is entirely different. For instance, GPS satelites are time corrected by using relativity. Note that this is vague. The relativity used to correct these satelites is in fact not SRT but LET, which is Lorentian relativity, and all satelites are synchronised with the Earth clock. Tom Van Flandern was involved in the development of GPS, read what he has to say on the subject :- http://metaresearch.org/cosmology/gravity/gps-twins.asp

[Andy L]

Originally Posted by tomh4040

I have already pointed out how the other FR can undergo the same accelerations.

See post 147 for my discussion of why the other FR will not undergo the same acceleration.