Relativity and Cosmology

Can you tie this in to the Lorentzian contraction? This is something that was once a major part of the physics, but one sees little or no refernece to it these days...

Hi cwarner7.

Lorentz contraction does not play a part here, since it is not something that puts stress on an accelerating object. IMO, Lorentz contraction is not 'real', but just a measurement problem caused by the difficulties of simultaneity at high relative speed. The accelerated rod itself never experiences Lorentz contraction.

The temporal stress are however real for an accelerating rod. After the acceleration stops, one can easily compare the clocks at the front and rear and observe that they show different times, while they showed the same time before the acceleration.

Jorrie

My understanding of the Lorentz contraction, which may or may not be correct, is that it is proportional to the clock difference at light speed, and to the forshortening of objects traveling at light speed. It has been a while since I have looked at this, but I remember playing around with this some time ago by adding it to Einstein´s famous equation, trying to get to a point where one can use a fixed rest-mass in the energy equation. I am an amateur at this, unlike you, so I may be off on a wild goose chase. Anyway, divide divide mc^2 by (1-u^2/c^2) and see what happens...

Hi Jorrie,

You said "you do not need a reference frame to know that you are being accelerated".

That I don't understand. If there's no reference frame available, HOW can I know that I'm being accelerated? Say I'm in an accelerating spacecraft, do I know I'm accelerating because I can feel it, or do I need a clock fore and aft clock to detect the change in temporal phase after I stop? I'm a little confused as usual.

Thanks,

-John

Hi John, you asked: "HOW can I know that I'm being accelerated?"

Any form of accelerometer will do nicely. If you do not need accurate info, the seat of your pants will also do - you will feel it.

The only thing an accelerometer (or the seat of your pants) can't tell you is whether you are sitting stationary in a gravity field or are being accelerated. To tell, you will have to look out of the window, or do some very fancy tests inside your spaceship.

Jorrie

Thanks Jorrie,

But why look out the window, since in this scenario a frame of reference is not required and thus not there?

If I see some object such as a planet, asteroid, etc. it would therefore be a frame of reference wouldn't it?

-John

Hi again John.

I guess if you, your spaceship and one solo black hole were the only occupants of the universe, looking 'out the window' would not help you distinguish between linear acceleration and sitting stationary in the black hole's gravity field. One can't see such a lonely black hole...

The darn equivalence principle makes it very hard to tell which is which, but it is measurable over a finite distance due to differences between tidal gravity of a point mass and differential accelerations in accelerated frames. But that's a long story...

Jorrie

Thanks!

It appears that Inertia may be explained by changing spacetime metrics during acceleration. You may find a paper on this at:

http://www.m-hikari.com/astp/astp2008/astp17-20-2008/masreliezASTP17-20-2008.pdf

Johan Masreliez

Hi Johan, welcome to CR4!

In your referenced paper you wrote: "However, according to relation (4.3) and the Voigt transformation, a clock in the MIF that moves so that it remains fixed in the SIF always agrees with a fixed clock in the SIF. Since this is the case both on the outward leg and on the inward leg of the travel, the twins always age at the same pace!"

Do I read you correctly in that you claim that the your theory "solves the clock paradox" by finding no difference in elapsed time between an inertial clock and a clock moving outwards and then back to the inertial clock? (I.e. that the "away twin" does not age less than the "home twin"?)

If so, do you realize that your theory is in conflict with experiment?

I agree that the Hafele-Keating experiment was not accurate enough to test this premise of SR, but the Vessot Rocket Clock experiment was. It tested both the gravitational and relative motion effects on time accurately and was in full agreement with SR and GR. This proved the SR premise that the "away twin" ages less than the "home twin".

-J

Hi Jorrie,

Yes, I agree that intervals we observe in a moving frame appear contracted, including time intervals. However, when clocks are compared side by side after having traveled apart their elapsed times may still agree.

This may be explained if moving frames belong to different GR manifolds with different relative metrics. In this situation intervals observed in the moving frame will be 'projections' from the moving frame to the stationary reference frame. In other words, as a stationary observer we cannot observe what the moving observer sees.

If you are interested I could send you another paper pending publication that discusses this.

Cheers,

Johanm

Hi Johan, yes I would like to look at your new paper.

You wrote, "This may be explained if moving frames belong to different GR manifolds with different relative metrics. In this situation intervals observed in the moving frame will be 'projections' from the moving frame to the stationary reference frame. In other words, as a stationary observer we cannot observe what the moving observer sees."

I agree for GR manifolds, but then one would expect the gravitational time dilation to differ between manifolds, causing the clock readings to differ when they are brought together again.

-J

Jorrie,

You posted an interesting question regarding time intervals measured out by clocks in gravitational fields; are they the same as for clocks in 'empty space'? Of course, we know that there is time dilation for signals transmitted out of gravitational fields, but that does not necessarily mean that clocks brought together after being separated in a gravitational field will show different elapsed times. In the context of the Twin Paradox it is generally believed that acceleration does not cause any contribution to the elapsed times, so one might wonder why it should do it in gravitational fields.

The metrics of spacetime change in a gravitational field. I have proposed that this also might be the case for frames in relative motion; the metrics of a moving frame might contract by the factor [1-(v/c)²] in relation to an instantaneous inertial reference frame, which would explain Inertia, since all accelerating trajectories then will be geodesics of GR. This scale-contraction will also have consequences familiar from SR.

But, if the scale contracts during acceleration relative to a stationary reference frame, the coordinates in inertial frames, as given by the Lorentz transformation, will have different metrics and can no longer be compared to the stationary coordinates on an equal basis. If this also holds true in gravitational fields, time intervals in a gravitational field will have different metrics in a relative sense. So, clocks may go at the same pace as perceived by local observers, but might appear to go at different paces as judged from signals transmitted between these observers. We might say that spacetime curvature distorts what we receive from a source in a gravitational field as well as from a moving inertial source.

But, how does this agree with SR? It appears that Einstein might have made a mistake in assuming that a linear transformation that preserves the metrics exists between the coordinates of inertial frames. This would not be true if the metrics change during acceleration. Therefore, coordinates related by the Lorentz transformation may have different metrics, which unambiguously would resolve the Twin Paradox and also explain Inertia.

Furthermore, this proposition may be tested by flying atomic clocks on a space mission and comparing their elapsed time with clocks on Earth.

Cheers,

Johan

P. S. How can I send you the paper?

Hi Johan, you can upload the paper to any website and give me the link. Alternatively, mail it to me at burtjordaan@engineering.com.

About your position on gravitational time dilation, I'm getting a little worried about you theory... It is fairly sure today that Einstein did not make any mistake on that - hundreds of tests and not a single verifiable discrepancy. The most directly applicable was Gravity_Probe_A, as I mentioned last time. Another everyday example is the GPS system, which would not work as advertised if the orbiting clocks were not adjusted to compensate for both gravitational and velocity time dilation at their altitude.

Einstein's whole theory stands or falls on both gravitational and velocity time dilation, i.e., (**)

where g_tt = 1-2GM/(rc²), g_rr = 1/g_tt, v_r is the radial velocity and v_t the transverse velocity in Schwarzschild coordinates. The facor in brackets is velocity time dialtion and g_tt is gravitational time dilation. If this equation was not very, very close to the truth, the universe would not have operated in the way it does, plain and simple.

-J

(**) Equation from Relativity 4 Engineers, chapter 1, (down-loadable).

PS: I see you have mentioned Dr Kelly in your paper. Be careful, he's a fellow engineer, but alas, known for "cranky" ideas.

Jorrie,

I understand your skepticism. However, I do not claim that there is no gravitational time dilation, yet it seems to be a general consensus that acceleration does not create 'inertial' time dilation in the Twin Paradox. If my theory of Inertia is right, what we observe in a moving frame has different metrics than in the reference frame, which causes all the effects familiar from SR. In other words, the Lorentz transformation coordinates may have different metrics.

My question is this: Is it possible that this also is the case with gravitation so that all observations and influences between locations in a gravitational field are 'distorted' by the different metrics? If this is the case all relativistic effects are real and GR is right, including the Gravity Probe results, but it might still be possible that clocks locally run at the same pace regardless of location in the sense that elapsed time intervals are the same. This would make possible a universal temporal reference, which sorely is needed for quantum mechanics and cosmology.

Do you know of any experiment other than the Hafele/Keating that compares clocks side-by-side after being apart during motion or in a gravitational field?

Johan

P. S. I am sending you the paper by email.

Hi Johan, thanks, I received the paper and will read it soon.

You wrote: "However, I do not claim that there is no gravitational time dilation, yet it seems to be a general consensus that acceleration does not create 'inertial' time dilation in the Twin Paradox."

There have been a number of tests in centrifuges and in particle accelerators that proved that acceleration per se does not influence clock rates. In the "twin paradox" (which is no paradox to the initiated), it is different spacetime paths that cause elapsed time differences between accelerated and inertial observers, not the acceleration.

"Do you know of any experiment other than the Hafele/Keating that compares clocks side-by-side after being apart during motion or in a gravitational field?"

There were two other similar test with more accurate atomic clocks, mentioned by Tom Roberts in: http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html#Twin_paradox

One must remember that in GR all clocks essentially run at the same pace: one second per second, as measured locally. It is only when compared with distant clocks (at a different gravitational potential and/or spacetime path) that a difference in elapsed time can be observed, according to GR.

If the "twin paradox" yields no difference in elapsed time, then GR must be wrong, which would be very surprising, to say the least. Think about the Shapiro time delay of light, half of which comes from gravitational time dilation and half from space curvature...

-J

Hi Jorrie,

Thanks for the reference.

Yes, it appears that several experiments confirm that clock intervals do not depend on spatial acceleration. If this is the case, I wonder why they should depend on gravitational acceleration. (Einstein's elevator thought experiment.)

Regarding GR I have proposed in a number of papers that the 4D scale of spacetime may change during the cosmological expansion as well as during spatial acceleration. Although such a dynamic process cannot be modeled by GR because it changes the proper time interval ds, it would resolve several problems including what is causing the progression of time and Inertia. It would also make possible reconciliation between GR and quantum theory. I published a paper on this in Physics Scripta, which I also could send you.

Johanm

Johan, you wrote: "Yes, it appears that several experiments confirm that clock intervals do not depend on spatial acceleration. If this is the case, I wonder why they should depend on gravitational acceleration."

Clock intervals does not depend on gravitational acceleration, but rather on the gravitational potential (a scalar). Static gravitational acceleration (from rest) depends on the gradient of the potential only. You can have the same gravitational time dilation for a wide range of gravitational accelerations, as long as the potential is the same. This is clear from the GR equations for time dilation and acceleration respectively.

"I published a paper on this in Physics Scripta, which I also could send you."

Thanks. I will let you know when I have time to read more on your theory.

-J

Jorrie,

Yes, it is true that time dilation depends on the gravitational potential. However, under the right circumstances inertial acceleration and gravitational acceleration are indistinguishable, at least according to Einstein.

In my theory Inertia is caused by relative scale contraction by the scale-factor 1-(v/c)² for frames in motion. It causes all acceleration to take place on GR geodesics. Thus, the temporal inertial metric is 1-(v/c)². The corresponding inertial potential is v²/2. This may be compared to the gravitational temporal metric (1-r₀/r), which with r₀= 2GM/ c² gives the gravitational potential GM/r.

So, we might think of gravitation as being generated by an 'inertial field' with velocity v²=GM/r.

Now, if all inertial frames are equivalent, clocks in them must run at the same pace. Since this is true, and acceleration does not create time dilation, accelerating clocks must also run at the same pace. This means that the observed inertial time-dilation is a relative rather than absolute phenomenon. This may be explained if the scale contraction is relative in the sense that all inertial frames see the scales contracted in other, moving, frames.

The question then naturally arises whether this also might be the case in gravitational fields, suggesting that the pace of a clock in a gravitational field might always run at the same pace as in empty space. The observed time dilation could in this case also be a relative phenomenon caused by observing a frame in a different GR manifold, which cannot be converted to the observer's manifold by any continuous coordinate transformation of GR, which also would be the case if the 4D scale of the Minkowskian line-element of inertial frames is dynamic.

This is of course new stuff, but I think interesting, because it would explain Inertia. The inertial scale factor above also implies the relativistic energy-momentum from SR and Newton's second law of motion.

Johanm

Johan, you wrote: "Now, if all inertial frames are equivalent, clocks in them must run at the same pace. Since this is true, and acceleration does not create time dilation, accelerating clocks must also run at the same pace. This means that the observed inertial time-dilation is a relative rather than absolute phenomenon."

This is not quite true in Einstein's theory. Check Prof. John Mallinckrodt (Cal Poly Pomona): Simple, Interesting, and Unappreciated Facts about Relativistic Acceleration

It is about rigid rods accelerating lengthwise, but it illustrates Rindler coordinates (for linearly accelerating frames) very well. Linearly accelerating clocks run slower than inertial clocks, because they follow longer spacetime paths, meaning less elapsed time. It is nor the acceleration, neither the speed that causes the time dilation, but the change in spacetime path...

-J

Jorrie,

Thank you for this discussion. I do not claim to know all the answers and enjoy talking to someone who might help me understand.

As you know, the problem with SR in the context of the Twin Paradox (TP) is symmetry between frames. As has been pointed out repeatedly over the years since 1905 both twins cannot age slower. Everyone agrees that acceleration makes no difference, for example, we can consider symmetrical acceleration. Still SR is consistent and there is no TP if one solely uses either reference frame, but not both at the same time. In other words, the situation may be described consistently from either reference frame.

The reason seems to be that the Lorentz transformation not only translates coordinates between inertial frames but also changes the metrics, so that coordinate intervals no longer have the same meaning. The situation is conceptually similar to optical transmission though a lens, which may change the perceived dimensions viewed from either direction.

Einstein assumed that the LT coordinates have the same metrics, but this might not be the case. If we accept that the metrics might differ we can explain inertia as a curved spacetime phenomenon just like gravitation. And, as a bonus we get the relativistic expression for energy and momentum plus the law of conservation of energy-momentum even for a changing velocity. So, it seems well worth investigating this new angle.

There is more to it, because if acceleration curves spacetime it would according to GR induce spacetime energy density; the inertial potential would like the gravitational potential satisfy Poisson's equation with a corresponding equivalent new form of 'mass energy'. Under the right circumstances this new form of energy could become negative, which could have revolutionary technological consequences. If all this holds true we might say that SR has had the unintended consequence of preventing the development of this new technology.

Johanm

P. S. If you are interested in this, you may check: http://www.m-hikari.com/astp/astp2009/astp1-4-2009/masreliezASTP1-4-2009.pdf