Co-Accelerating Ships: Explaining the Problem

[AnssiH]

I'll describe the problem in my own words.

The co-accelerating ships problem:

-There are two identical spaceships which are initially at rest in "lab-frame".

-These two ships perform IDENTICAL acceleration procedure.

-The ships are launched simultaneously in the lab-frame.

http://www.saunalahti.fi/~anshyy/PhysicsForums/Simultaneity03.jpg"
Red ones are the space ships. Right one is the "front ship". Blue line is an observer who stays at rest, added in there just for convenience. The acceleration events are instantaneous here, but you can imagine any sort of real-world acceleration instead)

Now, since the accelerations are identical in lab-frame, it should hold true that the distance between the ships does NOT change during the acceleration; As measured by the lab-frame, the distance between ships before and after the acceleration is exactly the same.

Obviously in the mechanics of SR, the acceleration procedures are NOT identical from the point of view of the ships. The distance between the ships should stretch in their own POV:

From the "POV" of FRONT SHIP:
Immediately after acceleration, the front ship exists in such an inertial frame that the rear ship must not have been launched yet. If you assert it has, then the front ship will receive information about the launch of the other ship at speeds slower than C

From the "POV" of the REAR SHIP:
Vice versa happens. Immediately after the acceleration, the rear ship exists in such an inertial frame, that the front ship must have been launched much earlier than the rear ship. If you assert it wasn't launched earlier, then the rear ship will receive information about the launch of the front ship at speeds faster than C.

POV is used here to refer to how things "are" in the inertial coordination system of an observer, according to Lorentz-transformation. POV is NEVER used in the meaning of what the observer can SEE; This talk concerns Lorentz-contraction.

In other words, the front ship will accelerate away from the other ship while it is still sitting on the launch pad. Here's what it all looks like from the inertial coordination system that the ships will end up to after acceleration.

http://www.saunalahti.fi/anshyy/PhysicsForums/Simultaneity04.jpg"
Black lines are planes of simultaneity

Even though the ships did go through the same acceleration procedure, after the fact these procedures exist in different moments in time.

We should arrive at the same conclusion even if there is a steel rod between the ships.

And that's not all. Since the ships are performing an identical acceleration, they should stay in the same inertial coordination system at all times. In other words, their notion of simultaneity should be identical at all times. In other words the ships (& the rod) should keep their length from their own perspective, and contract from the perspective of the blue observer.

So it seems that SR very concretely requires that from the POV of the front ship, the rear ship must still be on launch pad after the launch, AND it must be in the same inertial coordination system at all times (i.e. NOT on the launch pad).

There is odd asymmetry in Lorentz-contraction. It occurs to external objects when you switch inertial frames. But at the same time, it doesn't seem to occur if it is the external objects that are switching frames. And if the observer has any volume, he should stretch by the same mechanic that causes contraction (At least if he is being accelerated from the front and from the rear simultaneously).
---

When I first asked about this, it was noted that there is no standard way to construct a coordinate system where non-inertial observer is at rest.

However, if we place the launch pads at far enough distances from each others, and/or use rapid enough acceleration, it is trivial to show that AFTER the acceleration the front ship can exist in such an inertial frame, that the rear ship must not have been launched yet, IF it is true that light approaches the front ship in this new inertial coordination system at speed C.

I was also informed of a FAQ-page regarding this problem. I didn't understand the explanation, if any was even offered:

http://math.ucr.edu/home/baez/physics/Relativity/SR/spaceship_puzzle.html"

They first give instructions to draw similar spacetime diagrams as I have offered above, but with non-instantaneous acceleration. Then they note:

This first picture interprets "two ships with the equal constant accelerations" to mean "constant for the co-moving observers, and equal in the lab-frame". Note that the lab-frame says that the accelerations are not constant, and the co-moving observers say the accelerations are not equal!

It doesn't make any difference who thinks the accelerations are constant and who doesn't. All that matters is that the acceleration procedures themselves are identical. Surely one acceleration procedure looks the same when performed in any location of the lab-frame.

Then they say:

pick the same left-hand curve as before, but pick the right-hand curve to be:
x = sqrt(K^2 + t^2), K>1
Here it turns out that the distance between the ships is constant according to co-moving observers. The lab-frame people measure a Lorentz-contracted distance. The co-moving observers again say that the ships maintain constant acceleration. Both lab-frame people and co-moving observers find that the pursuer accelerates at a greater rate than the pursued.

What does this mean? Just pick the curve to be something else? Just decide that of the two identical accelerations, the other one is not identical?

What is the actual explanation?

 

[pervect]

I'll describe the problem in my own words.

The co-accelerating ships problem:From the "POV" of FRONT SHIP:
Immediately after acceleration, the front ship exists in such an inertial frame that the rear ship must not have been launched yet. If you assert it has, then the front ship will receive information about the launch of the other ship at speeds slower than C

It depends on what you mean by "immediately". There will not, in fact, be any sudden jump in simultaneity, but there will be a gradual shift in simultaneity as the ship accelerates.

The "point of view" of an accelerating observer needs to be defined, like any other coordinate system. A good choice is to use the "point of view" of an instantaneously co-moving observer.

This choice of POV is covered in textbooks (specifically MTW's Gravitation). The resulting expression is that the "POV" coordinates (which act fine locally and become non-unique too far away from the spaceship) are translated into inertial coordinates by the following expressions.

As I mentioned in another post
$$t = (1/g + \chi) \mathrm{sinh}(g \tau)$$
$$x = (1/g + \chi) \mathrm{cosh}(g \tau)$$

(t,x) are the inertial coordinates
$(\tau,\chi)$ are the "POV" coordinates.

Plot the lines of simultaneity ($\tau = constant$)

Let the acceleration, g, be 1 for simplicity.

Then at $\tau=0$, the lines of simultaneity are given by the expressions

$t = (1+\chi)$
$x = 0$

Plot this parametrically - you'll see a horizontal line, x=0, as you'd expect.

Now let's evaluate the expression at $\tau=.1$

You get approximately

$t = (1+\chi)*1.005$
$x = (1 + \chi)*.1$

Plot these parametrically - you'll see a slightly tilted horizontal line. This line starts at the location of the spaceship at t=.1, and has a slope of .1

Eventually these coordinate lines cross (the lines for tau=0 and tau=.1), this happens at x=0. (But the ship is at x=1).

See the attached plot. The single curved line is the plot of the ships position (it starts at x=1, t=0). The various straight lines are lines of simultaneity at tau = .1, .2, .5, and 1

I've talked at length about the significance of the coordinate lines intersecting previously - basically, multiple coordinates get assigned to the same point. This is rather ill-behaved, but perhaps not fatal. I usually don't use coordinates in this region, just because they act strangely, so I may not be aware of all the pitfalls of such usage. You are the person who wants to assign the ontological status of "reality" to coordinates, whereas I regard coordinates as being observer dependent, and thus in a sense not really "real". You are also the person who wants to use the coordinates beyond the point where they overlap - I'm the person who is leery of such usage. So when you complain about how weird they act, I tend to think "Then don't do it!"

 

[pervect]

When I first asked about this, it was noted that there is no standard way to construct a coordinate system where non-inertial observer is at rest.

However, if we place the launch pads at far enough distances from each others, and/or use rapid enough acceleration, it is trivial to show that AFTER the acceleration the front ship can exist in such an inertial frame, that the rear ship must not have been launched yet, IF it is true that light approaches the front ship in this new inertial coordination system at speed C.

The coordinate system of an accelerated observer is not an inertial coordinate system. Only when the coordinates of the same inertial observer are used consistently is the coordinate system inertial. The coordinate system of an accelerated observer is decidely non-inertial.

It is true that coordinates assigned to a forward-runing clock can run backwards when the clock is beyond the "Rindler horizon". This is just the region where I don't use the coordinates anymore because a single point has a multiple coordinates, thus the mapping of points to coordinates is not 1:1, but into (or was it onto? - never can keep that straight, but it's not 1:1 which must be both).

THis is the region where the coordinate lines cross in my previous post, at x=0.

This region (x=0) is also an event horizon - light signals emitted from behind the rindler horiozon (i.e. x<0) will never reach the spaceship!

If you look at the equation for accelrated motion I gave, you can see why. The signal of a lightbeam is given by x=t. The accelerated spaceship with an acceleration of unity has coordinates x=cosh(tau), t=sinh(tau). This means that x is always greater than t, because
$$\mathrm{cosh} \tau = (e^{\tau}+e^{-\tau})/2 \,\, \mathrm{sinh} \tau = (e^{\tau} - e^{-\tau})/2$$

and thus cosh(tau) > sinh(tau).

Therfore there is no solution for x=t, i.e. for cosh(tau) = sinh(tau), i.e. for the light beam reaching the spaceship.

I was also informed of a FAQ-page regarding this problem. I didn't understand the explanation, if any was even offered:

The Faq is trying to tell you that while the accelerations of the two spaceship appear to be the same in the lab frame, the accelerations of the two spaceships do not appear to be the same in the non-inertial coordinate system of the spaceships themselves.

The "upper" spaceship will appear to have clocks that tick faster than the lower spaceship, due to "gravitational time dilation". Gravitational time dilation occurs only in non-inertial frames, but the accelrating spaceships coordinate systems are just such frames.

Both spaceships will agree about this, in the accelerated frame higher objects have clocks that tick faster than lower objects. Because of this clock rate difference, coordinate accelerations will not be the same between the two spaceships.

In the problem as specified, the front spaceship will always have a greater coordinate accleration than the rear spaceship.

This means that any string connected betweent the two spaceships will break as the spaceships pull apart.

 

[Zanket]

What is the actual explanation?

I gave this one some thought before. I found the Usenet Physics FAQ explanation to be overly complex for my tastes. At the bottom of this thread is a layman's explanation.

Also consider The Pinwheel Paradox, which resolves to Bell's Spaceship Paradox for any two adjacent floors of the pinwheel. (You'll have to wade through the conversation but it's not long.) The symmetry of the pinwheel helps intuit both Bell's paradox and the concept of excess radius in general relativity.

 

[pervect]

Sorry for the large number of responses, but there is one more fact I forgot to mention.

The set of coordinates ($\tau,\chi$) which I will from now on call "accelerated coordinates" does not cover all of space-time.

If you refer to the equations I posted earlier which convert accelerated coordinates to the corresponding non-accelerated coordinates, no value of ($\tau,\chi$) maps to (t=0,x=10), as

t^2 - x^2 = (1+$\chi$)^2

Thus t^2 - x^2 must always be positive. Thus "accelerated coordinates" may not exist for a given point (t,x) specified in unaccelerated coordinates.

(I already mentioned that when they do exist, accelerated coordinates are not necessarily unique, but I'll mention it again).

This is yet another reason to view and treat accelerated coordinates cautiously.

 

[AnssiH]

Immediately after acceleration
/quote]
It depends on what you mean by "immediately". There will not, in fact, be any sudden jump in simultaneity, but there will be a gradual shift in simultaneity as the ship accelerates.

I just meant after the acceleration procedure.

The "upper" spaceship will appear to have clocks that tick faster than the lower spaceship, due to "gravitational time dilation". Gravitational time dilation occurs only in non-inertial frames, but the accelrating spaceships coordinate systems are just such frames.

Ah, that's right! That explains it all!

So no matter how you look at it, the distance between the spaceships will stay the same in the lab-frame, and grow in their own perspective because the front ship is accelerating more strongly.

And if you were to connect the ships with rod, in fact the front ship will physically pull the ship at the back, and then their distance will stay the same from their perspective, and they will Lorentz-contract in the lab-frame, like any solid object.

Why didn't they say so in the FAQ ;)

Anyway, thanks, I'll post a thread about those wheels soon.

You are the person who wants to assign the ontological status of "reality" to coordinates, whereas I regard coordinates as being observer dependent, and thus in a sense not really "real". You are also the person who wants to use the coordinates beyond the point where they overlap - I'm the person who is leery of such usage. So when you complain about how weird they act, I tend to think "Then don't do it!"

Heh, well, I certainly wish to think there are actually these observer-dependent 3D-slices - definite "moments" - surrounding us at all times. But in the world where these 3D-slices are extracted from a 4D-construct, I don't even see any reason to think of it as ill-behaviour when these moments "overlap". Why couldn't they? What indication do we have that makes such a thing impossible? It is purely semantical here what one calls "reality".

Anyway, the real reason why I'm putting so much pressure on the ontological consideration of reality is that I think any idea that can only be expressed through math, has not been developed to its real core. There is something to be found here. To idea that we cannot actually understand how universe works at low-level mechanics, is just false. The matter of the fact is, that there is always a wide number of "backwards" mechanisms to come up with the correct predictions of a behaviour of a complex system, and often it is these backward mechanisms that you figure out first, before realizing they are actually the same thing as some plain and easy to understand low-level mechanism.

Examples of such things come to my mind all the time. For example, here's what I thought about yesterday (off-topic);

Consider a clock A sitting on Earth's surface, in a gravitational field. Now during the time the clock will advance 100 seconds, it is suffering a time dilation. We can add a clock B, which we will synchronize with clock A in the beginning of the test, and then raise up in the air, and lower back down during the 100 seconds of measurement of clock A. According to GR, the clock B has advanced more than 100 seconds.

But we cannot raise clock B too high, because then just the raising and lowering at great speeds will cause it to time dilate more than the clock on the surface.

Working out what the optimal trajectory for maximum proper time for the clock B (i.e. direct path from 4D-coordinate of clock A to the same coordinate + 100 seconds), may be rather tricky mathemathically since the gravity field is not uniform. But if you work it out, it will be the same trajectory that the clock would take if it was simply thrown straight up in the air so that it would fall down at the exact moment that the clock A shows 100 seconds. (well ok, one probably doesn't even need math to figure that out)

->
Then, consider a world that works completely topsy turvy from GR. A world where time is absolute, and simultaneity is absolute. A world where any object is held together by information that propagates at speed C relative to any fundamental element of the object that is doing the propagation (i.e. letting other elements know its position).

Obviously all the physical processes that the object goes through, are subject to the speed with which this information is actually propagating inside the object. If by some sort of magic, the speed of information were to cut in half inside one object, we would observe all the physical phenomena of the object would progress at half the speed (be it a clock, or anything at all).

Also, when such an object is at rest, its physical processes will advance faster than when similar object is accelerating (since the information inside the object is actually propagating in space between the fundamental elements, and not accelerating during its journey as if the object was a medium for the information. Objects mostly consist of space). Its not hard to imagine such information propagation between fundamental particles/elements in head, and why there will undoubtedly be slowdown to all physical processes.

In GR, the bending of spacetime near masses is fundamental. If we instead consider the bending of light/information towards masses to be fundamental, then the equivalence principle holds exactly. The clock A sitting on Earth's surface is accelerating, as far as its low-level physical processes are concerned. It does suffer the exact same slowdown to its physical processes as a clock being accelerated in spaceship with same strength. Likewise a clock in gravitational freefall is running equally fast as a clock in a "coasting" spaceship.

(If you just plot the necessary information propagation of the "fundamental forces" bonding the object, taking into account that this information is "bending" towards Earth all the time and is causing the object to change direction relative to Earth in the first place, you will see that the information propagates exactly at same speeds as in an object at rest in a coasting spaceship. In fact mass itself needs not be fundamental in such a world, but that is perhaps another story)

Well, you can probably see where this is going... In this world also, the maximum possible "proper time" (if that it may be called) in our experiment will obviously be measured by the clock B that is thrown up in the air, and falls back down when exactly 100 seconds has been measured on Earth's surface. Clock B will not experience any inertial acceleration during any moment of the experiment, and its physical processes will simply advance at maximum possible speed at all moments.

Co-incidence? Not a chance. I could be just thinking about the same system from two opposite angles. GR is a top-down macrolevel explanation. Emitter-theory is a bottom-up microlevel explanation. Predictions are mostly the same. There is a link in here somewhere... Where is it?

I can't hope to find any links until I understand the inner life of theory of relativity well enough.

However, if we place the launch pads at far enough distances from each others, and/or use rapid enough acceleration, it is trivial to show that AFTER the acceleration the front ship can exist in such an inertial frame

The coordinate system of an accelerated observer is not an inertial coordinate system. Only when the coordinates of the same inertial observer are used consistently is the coordinate system inertial. The coordinate system of an accelerated observer is decidely non-inertial.

Can we call such a system inertial in the sense that there could be an observer who has been on that system throughout the whole experiment? I.e. if you think there exists definite 3D-slices of reality as "decided" by an inertial coordinate systems, then regardless of the history of the worldline of the different observers, the slice around them both is the same as long as they exist in the same inertial coordinate system?

 

[AnssiH]

I gave this one some thought before. I found the Usenet Physics FAQ explanation to be overly complex for my tastes. At the bottom of this thread is a layman's explanation.

Also consider The Pinwheel Paradox, which resolves to Bell's Spaceship Paradox for any two adjacent floors of the pinwheel. (You'll have to wade through the conversation but it's not long.) The symmetry of the pinwheel helps intuit both Bell's paradox and the concept of excess radius in general relativity.

Seems like you've been thinking about the exact same problems that I have :)
I was thinking about the pinwheel paradox at some point too, but I figured it out when I realized that I was doing actually the same mistake what you were doing in the beginning of that thread; considering that from your perspective the next dude is aged more, and from HIS perspective the next one is aged more, etc...

I figured it out when I realized that this is in fact the same thing as considering two observers who are simply approaching each others without any acceleration. Let's say you both started moving from "lab frame" at the same instant. When your own clock is showing, say 100 seconds, the clock of the other is showing like 200 seconds (from your inertial frame). You cannot now just hop into the perspective of the other observer, whose clock is showing 200 seconds, and assert that at the same moment your clock must show 400 seconds.

And after you've passed each others the same thing happens. The clock of the other observer is always showing less than your clock, but you can't just jump immediately from the perspective of one observer to another, otherwise you end up zig-zagging back in time.

So with the pinwheel problem too is simply about the plain old failure of simultaneity.

Hmmm, in fact, let's hope they never invent immediate quantum teleportation, because if you had to teleport from spaceship to earthly McDonald's for lunch break, then when you teleported back to ship, it could be again the beginning of your lunch break, and you'd be in an infinite lunch-break loop, and get really fat. ;)

Have you by any chance also solved the problem regarding two spinning wheels? If you have two wheels spinning on the same axis to separate directions, they both should regard themselves as larger than the other wheel. This is not the same as two trains shrinking and both regarding themselves longer than the other because of failure of simultaneity, since the shrinking of the wheels occurs at direction other than the motion. I can't see how this is solved at all.

 

[pervect]

As far as the rotating disks go, I favor the explanation by Tartaglia

http://arxiv.org/abs/gr-qc/9805089

which is very interesting, but somewhat heavy reading.

In a nutshell, if you put a chalk mark around the disk and walk around the cirumference, you may wind up at the same location as the chalkmark, and thus you think you've traveled around the circumference. But when you look at the situation more closely, you realize that no matter how slowly you walk, your time will not agree with the time of a clock left on the chalkmark. The sign of the discrpenancy will depend on whether you walked around the disk in the same direction as the rotation, or in the opposite direction.

If you have three observers, one stationary at the chalkmark, one who walks around in the same direction as the rotation, and one who walks around in the direction opposite to the rotation, when they all get back together, all of their watches will read different times.

While you may tend to want to ignore this and say that you are concrened with length and not time, it bites you in the end, because time and space "mix together" in relativity. One man's time is another man's space. One ultimately gets hopelessly muddled when one thinks of a circle around a rotating disk as a closed geometric object. The explanation is that it's not really closed, and it turns out that the defintion of circumference is ambiguous.

 

[Ich]

Have you by any chance also solved the problem regarding two spinning wheels? If you have two wheels spinning on the same axis to separate directions, they both should regard themselves as larger than the other wheel. This is not the same as two trains shrinking and both regarding themselves longer than the other because of failure of simultaneity, since the shrinking of the wheels occurs at direction other than the motion. I can't see how this is solved at all.

Maybe it´s important to point out again that the shrinking occurs only in the direction of the motion: The circumference shrinks, the radius stays constant -> circumference/diameter != PI -> Spacetime is not flat -> better use GR.
And for your model of acceleration slowing processes down: The dilation is then proportional to the gravitational field, not to the gravitational potential as observed and described by GR. This model leads to wrong predictions and you better not use to get a better understanding of reality.

 

[AnssiH]

Maybe it´s important to point out again that the shrinking occurs only in the direction of the motion: The circumference shrinks, the radius stays constant -> circumference/diameter != PI -> Spacetime is not flat -> better use GR.

Yeah, it was probably important to point it out, although I don't quite grasp it yet how the circumference can shrink without the whole wheel shrinking. I have kind of thought of it as if the radius becomes curved in the 3D-space, which would also mean that the object has in fact shrunk. But I'll try to think about it and start another thread if I get hopelessly lost :)

Thank you pervect for your points as well.

And for your model of acceleration slowing processes down: The dilation is then proportional to the gravitational field, not to the gravitational potential as observed and described by GR. This model leads to wrong predictions and you better not use to get a better understanding of reality.

Hmmm, I seem to have missed your point. The higher the gravitational field, the lower the gravitational potential, the higher the time dilation?

In simple words, the stronger the acceleration effect is being felt by an observer (be it gravitational or inertial), the stronger the time dilation he suffers as observed by a non-accelerating observer. Yes?

 

[Ich]

No. You may float perfectly weightless at the center of the earth, but your clock would tick slower than a reference clock eg at the north pole. That´s contrary to an effect proportional to the gravitational field strength. It´s the difference in gravitational potential that matters, not field strength.

 

[RandallB]

I don’t understand why so may smart people can make something simple so complex they get it wrong.

Why would you think:

""The "upper" spaceship will appear to have clocks that tick faster than the lower spaceship, due to "gravitational time dilation". Gravitational time dilation occurs only in non-inertial frames, but the accelerating spaceships coordinate systems are just such frames.""

Ah, that's right! That explains it all!

So no matter how you look at it, the distance between the spaceships will stay the same in the lab-frame, and grow in their own perspective because the front ship is accelerating more strongly.

Is it because you bought the false argument:

In the problem as specified, the front spaceship will always have a greater coordinate acceleration than the rear spaceship.

This means that any string connected between the two spaceships will break as the spaceships pull apart.

But that is NOT what was given in your OP.
You gave at t = 0 both frames for ship 1 and ship 2 start accelerating together, that can only mean there respective frames are equivalent! Also known as, the SAME FRAME, until one of them changes acceleration – what could be simpler.
Let’s just make your set up a little clearer:

Use 3 very large ROCKETS 1, 2, & 3 with ladders on their sides facing each other in a triangle. Rocket 1 has red spaceship #1 on step 3. Rocket 2 has red spaceship #2 on step 5 and Rocket 3 has a Blue observer on step 1.
(Note: your diagram clearly shows these three to be at fixed different altitudes at t = 0 and all times prior so they cannot be “launched” from a common altitude launch pad.)
Rockets provide all the power needed to keep the ships observer and frames (ladders) all accelerating the same. They may as well be attached to each other.

Now the group of three have a non-powered ladder gaining on them though the center of the triangle moving at speed V. On this ladder is passengers 1 & 2 on steps 3 & 5 respectively and anther blue observer on step 1.

Now at time = 0 the three rockets reach speed V just as the powered ladder at fixed speed V is level with the three ladders on the rockets. Passengers 1 and 2 step across into ships 1 & 2 as Rocket 3 runs out of fuel and stops accelerating. The two blue observer continue together at the same speed. Strings tied between various steps between ladders 1, 2, & 3, all strings between ladder 3 connecting to 1 or 2 break at t = 0.

Now we can build the equivalent without the expensive rockets. Three ladders on Earth surface with #3 supported over a very deep hole. At t=0 the support holding ladder #3 is removed – – etc. etc.

The two red lines in your OP graph are the passengers, the blue line is the observer on the ladder of fixed speed V. Every thing else is relative.

No matter how long ladders 1 & 2 continue to accelerate, OR sit there under on the surface near a deep hole, the strings tied between them will never break I don’t care from who’s reference they are observed. The length of the strings and distances between the steps may well change based on the view of different observers, but those distance and length changes will be identical.

Complex explanations & math that ‘prove’ differently, just means to me that an error was made, not some profound explanation or paradox.

 

[AnssiH]

No. You may float perfectly weightless at the center of the earth, but your clock would tick slower than a reference clock eg at the north pole. That´s contrary to an effect proportional to the gravitational field strength. It´s the difference in gravitational potential that matters, not field strength.

Oh I see.
I presume there is such experimental data?

 

[AnssiH]

No matter how long ladders 1 & 2 continue to accelerate, OR sit there under on the surface near a deep hole, the strings tied between them will never break I don’t care from who’s reference they are observed. The length of the strings and distances between the steps may well change based on the view of different observers, but those distance and length changes will be identical.

Very interesting assertion.

In fact, in order for the hole scenario to be completely equivalent to your initial description of ladders in space, the 3rd ladder should not be initially supported above the well, but rather thrown up from the hole so that at the topmost point of its trajectory it would just meet the other ladders, and the passengers would step on the ladders resting on Earth (that way the 3rd ladder is non-accelerating at all times).

The reason I bought pervect's argument is that I remember hearing that clocks placed "higher up" in the direction of acceleration will run faster, but I must say I haven't quite grasped this idea, and now that I'm thinking about it, it does seem a bit cumbersome idea.

Like, let's say we have a completely uniform gravitational field in some room, and then we have a little rocket toy that is blasting at such strength that it will levitate absolutely stationary in this gravitational field.

Now it would seem that we can place this toy in any place of the uniform field, and it will stay stationary in relative to the room.

But GR claims that if we have two toys, the upper toy will tick faster than the lower toy, and so it will also accelerate more strongly.

I would find it hard to believe, that if I have one toy levitating in the field, then just by placing another toy somewhere below it, the upper toy would suddenly start to gain distance on the lower toy.

The description of all this in Feynman's "Six not-so-easy pieces" is quite superficial;
---
"Suppose we put a clock "A" at the "front" end of a ship, and we put another identical clock "B" at the "tail". If we compare these two clocks when the ship is accelerating, the clock at the head seems to run faster relative to the one at the tail. To see that, imagine that the front clock emits a flash of light each second, and that you are sitting at the tail comparing the arrival of the light flashes with the ticks of clock B.

The first flash travels the distance L1, and the second flash travels the shorter distance L2. It is a shorter distance because the ship is accelerating and has a higher speed at the time of the second flash.
---

Higher speed compared to what? Definitely not compared to you, since you are traveling inside the ship. While a non-accelerating observer would see it like he describes, what does this have to do with people inside the ship exactly?

He continues;
---
The same thing will also happen for all the later flashes. So if you were sitting in the tail you would conclude that clock A was running faster than clock B.
---
Another odd thing, how does the way you see the clock A running correlate with the way it IS running? He doesn't mention a failure of simultaneity anywhere (which I suspect must play a part here), so it would seem like he is just describing how each signal is arriving "faster" than the previous one, but all these signals would still have begun their journey one second apart, and so the clocks would in actuality tick at the same rate, as observed inside the ship.

So, some help here, anyone? If you want to explain it with math, please include common sense explanation too.

Can you Randall offer any alternative explanation to the original problem?

Complex explanations & math that ‘prove’ differently, just means to me that an error was made, not some profound explanation or paradox.

Yeah, it must be said that I also find complex math explanations to be dangerously deceptive. And I am now looking for the internal structure of GR rather than fundamental nature of nature. The more I learn about the theory of relativity, the less I consider it to describe anything fundamental. I think accepting its macro-level descriptions as the fundamental level of nature is just insult to intellect.

It's like the assertion that an electron is a particle and a wave. Please. No such thing as "a particle and a wave" can be fundamental. I don't know why such a thing is even being implied by smart people. Particles and waves are semantical concepts, neither of which fits to describe an electron. That doesn't mean electron is a particle and a wave any more than a swimming cat is a mammal and a fish.

Obviously what we understand as an electron and its behaviour is a manifestation of some fundamental mechanism that we don't know of yet. Look at the behaviour, look at the data, and figure out what could cause such a thing to exist. Don't stop at the notion that it simply is "a particle and a wave".

 

[AnssiH]

Anyone?

The above message about the toy rockets blasting in an uniform gravitational field or in an accelerating room... What's going on?

 

[pervect]

I think you (ANssih) had the right idea before you let RandallB confuse you.

You intended spaceships A and B to stay a constant distance apart in the inertial frame, yes? This implies that they do not stay a constant distance apart in their own coordinate systems.

It's always possible that I misunderstood you, but I don't think that's the case here.

If I appear to be mostly ignoring RandallB, that's because I am mostly ignoring him. Life's too short for me to spend a lot of time talking to someone (RandallB) who doesn't listen.

For a numerical treatment of the problem, I will refer you to some previous posts:
(BTW, I highly recommend actually sitting down and doing the math, it will teach you things that endless discussions just can't.)

https://www.physicsforums.com/showpost.php?p=909767&postcount=2

is one example of a coordinate system that an accelerated observer can use.

http://groups.google.ca/group/sci.physics/msg/91d8704c115d8899?dmode=source&hl=en
https://www.physicsforums.com/showpost.php?p=911526&postcount=4
https://www.physicsforums.com/showpost.php?p=911526&postcount=6

discuss at length another coordinate system accelerted observers can use, based on 'radar coordinates'. The radar coordinates are a bit distorted because they assume that the speed of light is constant in the accelerated frame, when the speed of light actually depends on distance. But you may be able to "come to grips" with these coordinates numerically a bit easier than the other ones I gave, because a derivation is presented.

For a derivation of the first set of coordinates, I will refer you to MTW's textbook, "Gravitation". Unfortunately, parts of it may be a bit advanced.

 

[AnssiH]

I think you (ANssih) had the right idea before you let RandallB confuse you.

You intended spaceships A and B to stay a constant distance apart in the inertial frame, yes? This implies that they do not stay a constant distance apart in their own coordinate systems.

It's always possible that I misunderstood you, but I don't think that's the case here.

Well, that was the case with the original problem. I haven't plotted with the math you gave yet, partly because I'm being hit with a flu :) And partly because it seems pretty evident that the clocks towards which we are accelerating should advance faster in time if I'm just thinking about how the simultaneity planes are tilting (regardless of which direction the clocks are moving). So that just goes to show that the notion of simultaneity is not the same for two observers who are accelerating "uniformly" in a lab frame?

But then the question is, is it not possible to have a room with uniform acceleration (let's say, inside a spaceship), and then have a little rocket accelerating inside the room, blasting with such strength that it could sit completely stationary inside the room. And do so ANYWHERE inside the room?

 

[RandallB]

In fact, in order for the hole scenario to be completely equivalent to your initial description of ladders in space, the 3rd ladder should not be initially supported above the well, but rather thrown up from the hole so that at the topmost point of its trajectory it would just meet ...

No the thrown ladder your referring to is equally to the non-powered ladder at a fixed speed the catches up to the rockets just as they accelerate up to and past that fixed speed. Both cases feel like the same free fall in comparison to the rockets. And now kicking out the support on the third ladder will duplicate that third rocket running out of fuel, joining the “fixed speed” ladder in a common free fall, now in a gravity field.

But GR claims that if we have two toys, the upper toy will tick faster than the lower toy, and so it will also accelerate more strongly.

No, GR doesn’t say that. No flaw in GR equivalence, – no paradox here.
Common mistake, your thinking of earth’s gravity field, not the one you defined “a completely uniform gravitational field”.
We don’t have one of those here on earth’s spherical mass! To duplicate that, you need to use a wall of mass with a uniform density/area built as a disc, edges going to an effective infinity for your experiment. Then you do have the up and down uniform gravitational field that does not change vertically, so no gravitational red shift time dilation. Too many people incorrectly expect that Earth style difference in space too. There have just built their gravitational force source incorrectly to be “Equivalent” to the in space rocket experiment reality. (This is the source of the upper rocket somehow gaining a “higher speed” due to time dilation to break the string.)

Don’t forget the detail: The ships are accelerating at the same start time, but start at different altitudes. That’s why I put the toy ships on different positions of the ladders of large rockets. That way we can see the rockets using a common launch pad & time. Hence the altitude (distance) between them will always be the same from either ship’s (Or rocket carrying the ship) view. Even as they appear to change clock speed and lengths from other reference frame views. No string will be breaking here.

Little details like these are what can get you to an incorrect conclusion or seeing a paradox when there is none. When pervect makes a mistake he has a tendency to shoot the messenger or some excuse rather than admit it. A mistake yelled loader is still a mistake. You just need to give him a little extra space, while you work out the details yourself.

 

[pervect]

Well, that was the case with the original problem. I haven't plotted with the math you gave yet, partly because I'm being hit with a flu :)

If it's the one that comes with a very drippy nose, it's making it's way around the world. I am just getting over it here, everyone else in the house has had it too, and I was talking to someone in Czechlosovokia just the other day who had the same thing.

And partly because it seems pretty evident that the clocks towards which we are accelerating should advance faster in time if I'm just thinking about how the simultaneity planes are tilting (regardless of which direction the clocks are moving). So that just goes to show that the notion of simultaneity is not the same for two observers who are accelerating "uniformly" in a lab frame?

Yep, exactly.

But then the question is, is it not possible to have a room with uniform acceleration (let's say, inside a spaceship), and then have a little rocket accelerating inside the room, blasting with such strength that it could sit completely stationary inside the room. And do so ANYWHERE inside the room?

Sure. However, if you mount an accelerometer on the "stationary" rocket, the accelerometer reading on that "stationary" rocket will decrease as the altitude of the rocket increases. It will be constant for any given "stationary" rocket, because that rocket will maintain a constant altitude - however, different rockets will have different constant accelerations required to "hold station" which depends on where they are located.

We just got through a long derivation in another thread for a more complicated version of the problem you are talking about.

https://www.physicsforums.com/showthread.php?t=110742

In this thread it is derived that if the equations of motion for an accelerated obserer are

x = cosh(g*tau)/g
t = sinh(g*tau)/g

(note- this is correct, my post #3 has a typo that's too old for me to correct that interchanges x and t)

then the equations of motion for a "stationary" observer with respect to x and t can be most simply written as

x' = cosh(g' * tau) / g'
t' = sinh(g' * tau ) / g'

where g' is not equal to g. (There is an alternate form of the equations of motion derived in that thread, but later on it is pointed out that they only look different than the above, that they are mathematically equivalent).

The description of these curves is that they are all hyperoblae which share the same "hyperbolic point", which gives rise to the name "hyperbolic motion" for the motion of an accelerated observer.

Just in case you didn't know, cosh(x)= (e^x + e^-x)/2
while sinh(x) = (e^x - e^-x)/2, these are the hyperbolic trig functions.

What this means is that the "stationary" rocket will have a lower proper acceleration depending on its height, where the proper acceleration is the aaccleration read by an accelerometer mounted on the hovering rocket. Mathematically the proper acceleration is derived by taking the magnitude of the 4-acceleration, which is just the deriviative of the 4-velocity with respect to proper time.

(I don't know if you know much about 4-vectors. They are used througout the above thread, though, and are an essential tool of special relativity.)

The higher the "stationary" rocket, the lower the (constant) reading on its accelerometer. If the "stationary" rocket is below the reference rocket, it actually has to accelerate harder. This acceleration increases towards infinity as the stationary rocket nears the hyperbolic point located at the origin of the coordinate system, a distance c/g "below" the reference rocket. This point also marks the plane of the "Rindler horizon", which I think I've talked about before (?).

ps - Anssih, if you see some point made by RandallB that you want me to address, please quote it specifically and point it out to me - there's no guarantee that I've read it.

 

[RandallB]

But then the question is, is it not possible to have a room with uniform acceleration (let's say, inside a spaceship), and then have a little rocket accelerating inside the room, blasting with such strength that it could sit completely stationary inside the room. And do so ANYWHERE inside the room?

You framed the problem well by putting the room in a spaceship. Therefore the apparent gravity throughout the room is uniform and any solution that calls for a different acceleration to “hold station” between different heights in the room is obviously wrong. Obvious common sense will make that clear.

But what of that room on Earth you wish was equivalent. The shape of the gravity field your using on earth, is not equivalent as there is a difference from top to bottom.

To build an equivalent field see:http://www.mathpages.com/home/kmath530/kmath530.htm"

 

[AnssiH]

But then the question is, is it not possible to have a room with uniform acceleration (let's say, inside a spaceship), and then have a little rocket accelerating inside the room, blasting with such strength that it could sit completely stationary inside the room. And do so ANYWHERE inside the room?

Sure. However, if you mount an accelerometer on the "stationary" rocket, the accelerometer reading on that "stationary" rocket will decrease as the altitude of the rocket increases. It will be constant for any given "stationary" rocket, because that rocket will maintain a constant altitude - however, different rockets will have different constant accelerations required to "hold station" which depends on where they are located.

Hmmm, so, if I have a rocket that is just blasting at specific strength, will it be good for only one location inside the room? Placing that rocket at "incorrect" height will cause it to lose or gain height inside he room, unless I tune its strength?

And if I just place accelerometers onto the walls of the room, they will each measure a different acceleration depending on their height? (An accelerometer resting on a wall, right next to an accelerometer that is hanging on a spaceship, should both measure the same acceleration?)

In which case, which of the accelerometers is good for figuring out how much speed the room has gained since it begun its acceleration?

And also I should be able to measure different acceleration from a single toy rocket by placing one accelerometer on its top and another on its bottom?

ps - Anssih, if you see some point made by RandallB that you want me to address, please quote it specifically and point it out to me - there's no guarantee that I've read it.

Hmmm, well there wasn't anything from Randall, but if you could explain me what is Feynman going on about in the quotes I placed in https://www.physicsforums.com/showpost.php?p=912661&postcount=14"

Basically he describes how successive flashes of light are all moving a shorter and shorter length as seen inside the spaceship itself, because the ship is gaining speed. How does this distance get shorter along with gained speed exactly, for anyone inside the ship?

 

[AnssiH]

But GR claims that if we have two toys, the upper toy will tick faster than the lower toy, and so it will also accelerate more strongly.

No, GR doesn’t say that. No flaw in GR equivalence, – no paradox here.
Common mistake, your thinking of earth’s gravity field, not the one you defined “a completely uniform gravitational field”.

That's what I thought, but what is Feynman talking about? See post #14.

He claims it is completely expected and that "there is nothing mysterious about" clocks running at different speeds at a uniform acceleration (one in head and one in tail of a spaceship)

Then he goes to claim that the mysterious thing is that as the law of equivalence would predict it, we have observed redshift in Earth's gravitational field.

I don't understand how the former is NOT mysterious, and what makes the latter so mysterious.

 

[RandallB]

That's what I thought, but what is Feynman talking about?

As you thought and already said “a completely uniform gravitational field” comparing to Earth .etc. etc.….we covered that.

I haven’t looked at "Six not-so-easy pieces" yet, but what you describe is just a small error, similar to what I see in Bell’s comments on ‘how to teach relativity’. It’s just a mistake in comparison that supports a small mistake on simultaneity.
Don’t let a small error here throw you off on their other good works.

Take some time to really really get to understand simultaneity.
Example, you cannot simultaneously observe something your holding with something across the room. What you seeing from across the room is in the past in comparison with what you’re holding. In “paradox’s” like these that get's to be a problem often overlooked.

 

[AnssiH]

As you thought and already said “a completely uniform gravitational field” comparing to Earth .etc. etc.….we covered that.

I haven’t looked at "Six not-so-easy pieces" yet, but what you describe is just a small error, similar to what I see in Bell’s comments on ‘how to teach relativity’. It’s just a mistake in comparison that supports a small mistake on simultaneity.
Don’t let a small error here throw you off on their other good works.

Take some time to really really get to understand simultaneity.
Example, you cannot simultaneously observe something your holding with something across the room. What you seeing from across the room is in the past in comparison with what you’re holding. In “paradox’s” like these that get's to be a problem often overlooked.

What are you talking about? It's not some sort of "small mistake" on the part of Feynman. This is on his lecture notes and I come across the same argument over and over everywhere. I must say it does seem problematic, and Feynman's description seems non-sensical at best, but it is pretty damn colossal mistake if it is really a mistake.

And you take some time to understand relativity of simultaneity. It's not simply about the observation delay associated with the speed of light. It's the relativity of the actual moment that something occurred for observers A & B (moving to different directions), taking into account the delay of light propagation, and assuming that the speed of light was C relative to both. Einstein didn't claim speed of light was "C". He claimed it was "C" for you AND your friend.

EDIT: Einstein's own "common sense" description of this is very very very misleading, until you take a look at what Lorentz-transformation is doing. I talked about this in the opening post of this thread: https://www.physicsforums.com/showthread.php?t=108748

And it's not like the paradox is solved by asserting that the clocks inside one spaceship run at the same speed. That is not what caused the problem in the first place. The problem is that the relativity of simultaneity requires them to run at different speeds, which is a requirement of the assertion that all inertial coordination systems are symmetrical AND all light approaching each coordination system moves at speed C.

At Bell's spaceship paradox this should translate into different acceleration strengths for spaceships that accelerate uniformly. I would expect it to be tricky to accelerate at different strengths, yet uniformly at the same time.

As the scientific paradigm goes, if we cannot measure different acceleration strenght at the bottom and at the tip of a spaceship, the whole idea comes down like a house of cards. Yes? (Well okay, perhaps there are more practical ways to test it :)

Oh, and Ich, if you are still there, you mentioned we have observed this. Care to elaborate on that?

 

[RandallB]

What are you talking about? It's not some sort of "small mistake" on the part of Feynman. This is on his lecture notes and I come across the same argument over and over everywhere. I must say it does seem problematic, and Feynman's description seems non-sensical at best, but it is pretty damn colossal mistake if it is really a mistake.

Now you’re just getting into to semantics over “little” mistake vs. “colossal” mistake.
To it me it would be colossal if it masked a problem that was showing the principals supporting SR and/or GR were wrong. This “little problem” doesn’t do that.
Can little problems get magnified into colossal miss-conceptions, which can result in misleading explanations? Sure it can, but by itself it just doesn’t seem colossal to me that sometimes smart people make mistakes too. After all that why real scientist’s double check each others work, experiments need to be both repeatable and repeated. Maybe I don’t make a big a deal out of this as I should, but then how could I make a big deal out of it?

On the gravitational field vs. gravitational potential Ich was talking about, the best example I can think off is the “Lagrange point” (Google it) used by the SOHO satellite between the Earth and sun. Anywhere around the sun at that radius demands a Newtonian orbit speed much faster than the orbit of Earth, but the orbit of SOHO stays in sync with earth!
At this point the gravity field from Earth adds to the field from the Sun, but pointed away from the sun for a net reduction in gravitational potential. That’s an increased field but lower potential as compared to another satellite orbiting the sun at the same distance. So how does the clock on SOHO compare to the clock on the other satellite? Fast because of lower potential, or slow because of increased field? I’m sure Ich is right on this.

But remember in this example we’ve been working on we do not have any change in potential or field both are uniform.

 

[AnssiH]

Now you’re just getting into to semantics over “little” mistake vs. “colossal” mistake.
To it me it would be colossal if it masked a problem that was showing the principals supporting SR and/or GR were wrong. This “little problem” doesn’t do that.

Ok. Then how would you solve the original problem? If you have a solution let's go through it and see what it implies exactly.

And is this assertion, that Feynman and others were mistaken about the clocks running different speeds at different heights, a commonly known fact? Are there others here who know about this too? Has this been double checked?

At this point the gravity field from Earth adds to the field from the Sun, but pointed away from the sun for a net reduction in gravitational potential. That’s an increased field but lower potential as compared to another satellite orbiting the sun at the same distance. So how does the clock on SOHO compare to the clock on the other satellite? Fast because of lower potential, or slow because of increased field? I’m sure Ich is right on this.

Well, applying "Newtonian" mechanics to the information propagation inside the satellite, I would expect the satellite to work at a maximum possible speed at the lagrange point between sun and earth. Even if we could say that the gravitational field is conceptually increased, it is not so as far as the physical information between the atoms is concerned.

I.e. the information cannot accelerate to both directions at the same time. Equal tendency to accelerate to two opposite directions would cause the information to propagate as if there was no pull at all, and would cause the satellite to stay put at the lagrange point.

So emitter theory would imply its clock goes as fast or faster than other satellites.

So which way the observation is? Faster or slower?

 

[RandallB]

Ok. Then how would you solve the original problem?
... information propagation ...
So emitter theory would imply its clock goes as fast or faster than other satellites.

We already solved it. But if anyone wants to double check it, to show a way the length of a string shorting in the view of any frame while the distance between the attachment points used for it viewed from that same frame does not, I’d be OK with that.

I have no idea how “information propagation” applies here.

Your emitter concept matches a GR time dilation based on Gravitationalial potential, I disagree.
I agree with Ich that it will be slower based on a denser gravitational field.

You might check with NASA, but I doubt the reality of the example I gave is enough to provide a useful experiment. I’m not sure there are clocks sensitive enough to measure it in a place convent to observe the point Ich made. Maybe if we move Jupiter into Venus orbit to test at that “L1” (I think) of the five Lagrange points. Or a significantly deep mine into Earth's Magma (not just the light thin mantle). Or a mine shaft to the center of the moon. That’s all I can think of. If you find a verifying test that has been done let us know.

 

[pervect]

In which case, which of the accelerometers is good for figuring out how much speed the room has gained since it begun its acceleration?

All of them. The clocks tick at diferent rates (using the room's notion of simultaneity), and the accelerometers measure different accelerations.

The product of acceleration * time is constant, though (using room coordinates).

And also I should be able to measure different acceleration from a single toy rocket by placing one accelerometer on its top and another on its bottom?

I believe that is the case, yes. There will be an apparent tidal forces on the rocket "holding station", though there will be no tidal forces on an object that is free-falling.

Hmmm, well there wasn't anything from Randall, but if you could explain me what is Feynman going on about in the quotes I placed in https://www.physicsforums.com/showpost.php?p=912661&postcount=14"

Basically he describes how successive flashes of light are all moving a shorter and shorter length as seen inside the spaceship itself, because the ship is gaining speed. How does this distance get shorter along with gained speed exactly, for anyone inside the ship?

Try the explanation at

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/gratim.html

it might be clearer.

 

[AnssiH]

We already solved it. But if anyone wants to double check it, to show a way the length of a string shorting in the view of any frame while the distance between the attachment points used for it viewed from that same frame does not, I’d be OK with that.

Care to tell me too how you solved it?

How does the information from the launch of the other ship approach the other ship at speed C in the case of the original post? Or was the solution just that SR is wrong?

I have no idea how “information propagation” applies here.

Do you know what relativity of simultaneity means and how SR implies such a thing to exist? It's not the delay in observation of distant event, like I think you were implying couple posts back.

EDIT: If you were asking about what information propagation has to do with time dilation in emitter theory, then you probably forgot what I said about it in the post earlier in this thread, where I was describing this similarity between GR and emitter theory. I said;

Obviously all the physical processes that the object goes through, are subject to the speed with which this information is actually propagating inside the object. If by some sort of magic, the speed of information were to cut in half inside one object, we would observe all the physical phenomena of the object would progress at half the speed (be it a clock, or anything at all).

Also, when such an object is at rest, its physical processes will advance faster than when similar object is accelerating (since the information inside the object is actually propagating in space between the fundamental elements, and not accelerating during its journey as if the object was a medium for the information. Objects mostly consist of space). Its not hard to imagine such information propagation between fundamental particles/elements in head, and why there will undoubtedly be slowdown to all physical processes.

Your emitter concept matches a GR time dilation based on Gravitationalial potential, I disagree.

It doesn't match the GR time dilation, that's true. But are there experiments that it doesn't match? You cannot falsify a new idea by it being different from the old idea.

I agree with Ich that it will be slower based on a denser gravitational field.

Well that's cool, but what is your reasoning on that?

I was talking about how information propagates from one element to another inside an object, considering that the acceleration of the information towards matter is fundamental. In other words, if you have matter in all directions, there is no acceleration to the information.

And also clocks in satellites run faster than clocks on earth, while the notion of simultaneity is absolute for both. etc.

That's just a simple hypothesis with wild approximation as to what the structure of matter is. But if it implies somehow that "denser" gravitational field means always slower clocks, then please explain me how.

You might check with NASA, but I doubt the reality of the example I gave is enough to provide a useful experiment.

Well I was asking for useful experimental data. Why should we care about this experiment to indicate one way or another if the data is not good? Was your counter-argument simply that my idea must be false because GR predicts otherwise?

 

[AnssiH]

All of them. The clocks tick at diferent rates (using the room's notion of simultaneity), and the accelerometers measure different accelerations.

Oh yeah, that's right, every accelerometer needs to come with its own clock.

And so if you had two toy rockets that were good only for the "center height" of the room, you could attach them with a rope so that the midpoint would be at the center height, and the whole thing should remain stationary because of the upper rocket losing its extra acceleration to the lower rocket slacking the same amount. They would still register different acceleration rates due to time dilations. That should work.

Do you know what is the closest experimental verification of this sort of thing that anyone has done so far? There's still quite an extrapolation from gravitational redshift to registering different acceleration rates at different parts of one ship.

 

[RandallB]

Care to tell me too how you solved it?

Posts 12, 18, 20
If anyone has a good explanation with numbers how a length can Lorentz contract while the Distance between the ends of that length do not Lorentz contract it would certainly falsify my ‘assertion’. So I’d like to see it.

I can only thing of one way to do that, by using an “aether”. Which for me disqualifies it as being a “good” explanation, I understand the aether is still acceptable to a few.

On Gravitational Field vs. Gravitational Potential

Well that's cool, but what is your reasoning on that?
But if it implies somehow that "denser" gravitational field means always slower clocks, then please explain me how.
Was your counter-argument simply that my idea must be false because GR predicts otherwise?

Do you understand the difference between a Gravitational Potential and the same potential in a "denser" gravitational field?
What you’re arguing is that a clocks rate of time in deep space away from Earth will be the same for a clock also weightless but located at the center of the earth.
For “proof”? like I said I don’t now of a location that we can reach that will demonstrate the affect with hard data. Center of the Earth or Moon would do the trick I’m sure, but I don’t think we can reach it. Till someone comes up with a doable experiment that produces data otherwise I’m with Ich.

 

[AnssiH]

Posts 12, 18, 20
If anyone has a good explanation with numbers how a length can Lorentz contract while the Distance between the ends of that length do not Lorentz contract it would certainly falsify my ‘assertion’. So I’d like to see it.

The original problem was to explain how does length contraction NOT occur from the point of view of the accelerating object itself. Evidently it doesn't, but at the first look SR seems to imply it does for any object with volume.

If I interpetate Pervect correctly, the internal logics of relativity theory say that if you place an accelerometer w/ a clock at the bottom and at the top of accelerating ladder, you will get different time and acceleration readings from them.

But when you figure out how much distance has been covered from those readings, then both ends of the ladder have covered the same amount of distance. The bottom has accelerated more strongly for a shorter period of time, and the top vice versa.

And if you were to cut the ladder in half (and it had identical rocket on both ends), then the top wouldn't need to drag the bottom with it anymore and they would start moving apart. This is all basically because the notion of simultaneity for the parts are not the same even if they are in uniform acceleration in an inertial frame. Let's just put it this way; the "3D-slice" of the 4D-world that surrounds the bottom part, is tilting in such a manner that the top part is moving into the future faster than the bottom part itself, and vice versa.

I agree this is absolutely nuts, but it doesn't really matter how nuts I think it is as long as its internally consistent and there is some indication there that suggests it might even be true.

I can only thing of one way to do that, by using an “aether”. Which for me disqualifies it as being a “good” explanation, I understand the aether is still acceptable to a few.

Yeah, I don't think we should be completely discarding that thing just yet. It seems to be getting uncomfortably complex to explain all the experiments though, but I kind of think science is supposed to keep an open mind and merely say how much indication there is for idea A to be true versus idea B.

On Gravitational Field vs. Gravitational Potential
Do you understand the difference between a Gravitational Potential and the same potential in a "denser" gravitational field?

The same height has more potential in denser gravitational field? Or?

For “proof”? like I said I don’t now of a location that we can reach that will demonstrate the affect with hard data. Center of the Earth or Moon would do the trick I’m sure, but I don’t think we can reach it. Till someone comes up with a doable experiment that produces data otherwise I’m with Ich.

Yeah, I don't know of proof either, that's why I was asking, because Ichi said there is experimental proof but didn't say what it is.

Anyway, I'm not actually choosing sides here before I know of some proof. It's not like we are betting here :)

 

[pervect]

The original problem was to explain how does length contraction NOT occur from the point of view of the accelerating object itself. Evidently it doesn't, but at the first look SR seems to imply it does for any object with volume.

If I interpetate Pervect correctly, the internal logics of relativity theory say that if you place an accelerometer w/ a clock at the bottom and at the top of accelerating ladder, you will get different time and acceleration readings from them.

But when you figure out how much distance has been covered from those readings, then both ends of the ladder have covered the same amount of distance. The bottom has accelerated more strongly for a shorter period of time, and the top vice versa.

Yep, that's not the exact wording I would have used but you have the basic idea.

To really convince yourself takes some math, though. The first step is to convince yourself that constant proper acceleration leads to hyperbolic motion as described in the physics faq

http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html

The next step can be done several ways, one of the simplest is to show that the radar distance between two observers with different proper accelerations g1 and g2 but the same hyperbolic point remains constant. To take this approach, does have to argue that a constant radar distance implies a constant proper distance, but I think this is any easy argument to accept (YMMV). One is also free to do the analysis directly in terms of proper distance, the result will be the same.

 

[Ich]

I looked for a source for the dependence of time dilation from the gravitational potential. http://relativity.livingreviews.org/open?pubNo=lrr-2003-1&page=node5.html" covers the calculations that apply to the good old GPS.
In Eq. 35 you find two contributions to time dilation: The first is the velocity-dependent SR term, the second is the potential-dependent GR term.
Figure 2 shows the variation of these effects with height. The next paragraph talks about the experimental verification.

 

[AnssiH]

I looked for a source for the dependence of time dilation from the gravitational potential. http://relativity.livingreviews.org/open?pubNo=lrr-2003-1&page=node5.html" covers the calculations that apply to the good old GPS.
In Eq. 35 you find two contributions to time dilation: The first is the velocity-dependent SR term, the second is the potential-dependent GR term.
Figure 2 shows the variation of these effects with height. The next paragraph talks about the experimental verification.

I thank you for your trouble, but I was aware of the effects on GPS satellites. The thing is that emitter theory also predicts that the clocks would run faster on satellites in orbit. But even though the dilation is of same "direction", it is definitely true that the high accuracy of the GR prediction is indicative towards relativity.

That is why I was describing that there are some peculiar similarities between the mechanics of GR and emitter theory time dilation. But I am not able to carry out any actual calculations that would tell me if the emitter theory idea would actually predict the same amount of time dilation in the case of GPS clocks.

Perhaps someone much more competent than me could, but even then we are still always running the risk of merely choosing the fundamental structure of matter to be of such type that we can simply MAKE the predictions agree the experiments. That would be not much of a proof, unless we could prove the structure to actually be what we think it is due to GPS time dilation being of specific magnitude.

Anyway, interestingly you noted - quite correctly - that the GR mechanics actually predict maximum time dilation in the center of earth, without the object "feeling" any gravitational acceleration.

So it got me curious because such an experiment would yield completely opposite predictions from GR and emitter theory. If the clocks were indeed running slower in the center of the Earth (or in similar setup), that would be so much stronger indication towards GR than GPS clocks.

I've heard there has been some experiments with centrifuges, producing high acceleration rates on clocks, and that no time dilation has been observed. That is also good indication towards GR, but it is rather curious also because doesn't SR alone predict time dilation for such an experiment?

(btw, I don't know if there is any actual information about such emitter theory time dilation as I'm describing, or if anyone has actually tried to develop it further and seen that it doesn't lead anywhere. I haven't been able to find any information of this, unfortunately)

-Anssi