# Thread: From who's perspective do we measure Lorentz Contraction?

1. Suppose we have 2 planets, planet #1 and planet #2, 5 light years apart, and in the same inertial frame of motion. A space ship near planet #1 accelerates instantaneously to .99C headed toward planet #2. What do three observers, located on the two planets and the space ship, respectively, see?

Planet #1:

Time: Flows normally at Planets #1, and #2, but any clocks aboard the space ship appear to move slowly.
Distance: The distance between planet #1 and #2 stays the same. The newly accelerated space ship appears to be very close by (or it should, right?)
Simultaneity: The space ship is observed to begin leaving immediately, but will not be observed to arrive at planet #2 until 10 years have passed.

The simultaneity question is the weird one. Doesn't a 10 year travel time imply the space ship is really being observed to travel at .5C? Is an apparent travel speed of .99C even possible?

Planet #2:

Time: Flows normally at Planets #1, and #2, but any clocks aboard the space ship appear to move slowly.
Distance: The distance between planet #1 and #2 stays the same. The newly accelerated space ship appears to be very close by (or it should, right?)
Simultaneity: The acceleration is being observed 5 years after it happened. By the time the acceleration is observed, the space ship would have almost arrived, so that could be a good explanation for the Lorentz contraction.

So, what observers on planet #2 see is that the space ship is sitting there stationary, then suddenly jumps most of the distance (arriving just behind the light signal that shows it having accelerated). However, that would imply that the space ship is being observed to move much, much faster than light for a moment there, so I must have something wrong about this.

The Space Ship:

Time: Flows normally aboard the ship, but appears to flow very slowly on both planets #1 and #2.
Distance: The distance between planets #1 and #2 appears to be very short, meaning the trip as a whole appears to be very short.
Simultaneity: ?? The trip appears to be so short it might not matter ??

2.

3. Originally Posted by kojax
Suppose we have 2 planets, planet #1 and planet #2, 5 light years apart, and in the same inertial frame of motion. A space ship near planet #1 accelerates instantaneously to .99C headed toward planet #2. What do three observers, located on the two planets and the space ship, respectively, see?

Planet #1:

Time: Flows normally at Planets #1, and #2, but any clocks aboard the space ship appear to move slowly.
Distance: The distance between planet #1 and #2 stays the same. The newly accelerated space ship appears to be very close by (or it should, right?)
Simultaneity: The space ship is observed to begin leaving immediately, but will not be observed to arrive at planet #2 until 10 years have passed.

The simultaneity question is the weird one. Doesn't a 10 year travel time imply the space ship is really being observed to travel at .5C? Is an apparent travel speed of .99C even possible?
This isn't a simultaneity issue, just a propagation delay issue. It is more related to the Doppler effect than it is to Relativity. Relativistic effects are those that are left after you remove the propagation delay. For instance, in this example, Planet #1 would see the clock run at 1/14 speed, but after accounting for light signal delay would determine the it actually runs at 1/7 speed. The planet #1 observer see the rocket arrive in ~10 years, but also knows that it took 5 years for this light to reach him from planet #2, and that it actually took the rocket ~5 yrs to travel the distance. Look at it this way: Assume that the the clocks on planets #1 and #2 are synchronized, according to the planets. Planet #1 looking at Planet #2's clock will see it reading 5 yrs behind his own, however he knows that it actually reads the same time because this information is 5 years out of date. 10 years later he sees the rocket arrive and planet #2's clock reads 10 yrs later, or 5 years later than Planet #1's clock read when the rocket left. He saw the rocket clock run at 1/14 speed so it reads ~8.6 months, which is 1/7 of the five years that actually passed on Planet #2's clock from during the trip.

Planet #2:

Time: Flows normally at Planets #1, and #2, but any clocks aboard the space ship appear to move slowly.
Distance: The distance between planet #1 and #2 stays the same. The newly accelerated space ship appears to be very close by (or it should, right?)
Simultaneity: The acceleration is being observed 5 years after it happened. By the time the acceleration is observed, the space ship would have almost arrived, so that could be a good explanation for the Lorentz contraction.

So, what observers on planet #2 see is that the space ship is sitting there stationary, then suddenly jumps most of the distance (arriving just behind the light signal that shows it having accelerated). However, that would imply that the space ship is being observed to move much, much faster than light for a moment there, so I must have something wrong about this.
No, what they would see is the rocket starting at planet #1 and then taking ~ 4.25 months to travel the distance (there would be no "jump". But again, since they know that the rocket was already almost upon them when they first see it leave planet#1, they can account for this in determining how fast the rocket actually traveled relative to themselves. Again, Relativity is what is left over after you take the light delay into account. It doesn't matter that you see the rocket travel towards you at greater than c speeds, only that its actual relative velocity is less than c. Again, consider the clock of Planet #1. They see the Rocket leave Planet#1 when its clock reads zero, and the Rocket arrives when their own clock reads ~5 years. Since the clock on Planet #1 is synchronized to their own this means that the rocket left planet #1 when their own clock read 0 and arrived when it read ~5 years. Thus the rocket took ~5 yrs to make the trip and traveled at 0.99c

The Space Ship:

Time: Flows normally aboard the ship, but appears to flow very slowly on both planets #1 and #2.
Careful here, he would conclude that time flows more slowly on the planets by a factor of 7, but he would see time running more slowly by a factor of 14 on planet #1 and fast by a factor of 14 on plant #2.
Thus he would start by seeing Planet #1's clock reading 0, he would take ~8.6 months to travel the length contracted distance between the planets, during which time he will see planet #1 clock tick off ~18 days. He would also start by seeing Planet #2's clock reading -5 years and then accumulate` 14 *~8.6 mo = ~10 years and read 5 years upon arrival.

Distance: The distance between planets #1 and #2 appears to be very short, meaning the trip as a whole appears to be very short.
Simultaneity: ?? The trip appears to be so short it might not matter ??

4. I'm glad I asked this question, and must say I very much appreciate your answer (and willingness to keep it simple for me). It's really helping a lot to understand what's happening. My goal is to eventually be able to understand GR, but for now it's apparent to me that my understanding of SR is in need of a lot of work before I can even attempt to move onto the bigger theory.

So, the act of the space ship suddenly accelerating to .99C

1) - Cause the clock on planet #2 to immediately advance 4 years and 10 month ahead, compared with where it had been prior the acceleration.
2) - Left planet #1's clock where it had been
3) - Caused the distance between the space ship and planet #2 to shorten considerably.

If the space ship then suddenly decelerates back into the rest from of the two planets then,

1) - Planet #1's clock will immediately advance ~5 years
2) - Planet #2's clock will stay where it is now (at the ~5 year mark, matching planet #1's clock)
3) - The distance between the planets will return to its previous length.

4) - The occupants of the space ship will only appear to have aged ~8.6 months while everyone on the two planets aged ~5 years.

Now, let's suppose we do this thought experiment in reverse. Suppose, instead of a space ship accelerating to .99C in order to travel between planet #1 and planet #2, the space ship stays put, and the two planets accelerate to .99C so planet #1 starts out right next to the space ship, but begins moving away from the space ship at .99C, and planet #2 starts out 5 light years away from the space ship, but begins moving toward the space ship at .99C.

From the perspective of those people on planet#1 at the moment after the acceleration occurs:

1) - The clock on the space ship stays where it was initially, but then begins to advance at a slow rate.
2) - The clock on planet #2 also stays where it was initially, and then continues to advance at the normal rate.
3) - The space ship is already right next to it, but length contraction brings the space ship still closer initially, after which it begins moving away toward planet #2.
4) - The apparent distance between planet #1 and planet #2 remains the same as it was before because they're still in the same inertial frame.

From the perspective of those people on planet #2:

1) - The clock on the space ship immediately moves ahead by 4 years 10 months, and then begins to advance slowly from there.
2) - The clock on planet #1 stays where it was initially, and then continues to advance at the normal rate.
3) - The distance between planet #2 and the space ship contracts a great deal, ...... even though the distance between planet #2 and planet #1 stays the same. Does this mean the two planets disagree as to the space ship's present location?
4) - The apparent distance between planet #1 and planet #2 remains the same as it was before because they're still in the same inertial frame.

From the perspective of the occupants of the space ship:

1) - The clock on planet #1 remains where it was before accelerating initially, and then begins to advance slowly from there.
2) - The clock on planet #2 moves ahead by 4 years 10 months, and then begins to advance slowly from there.
3) - The distance between the space ship and planet #1 becomes insanely close (since it was already very close), and then begins to grow as planet #1 moves away
4) - The distance between the space ship and planet #2 contracts a lot, and then begins to shrink as planet #2 approaches.

Mostly, I'm just trying to be clear that it doesn't matter who accelerates, the result will be the same, but it also helps to go over the details and make sure I'm adding the effects up correctly. At first glance, it looks like there may be some problems, but also the situation is also getting more complex, so there is also a higher chance that there may be some basic logical errors in what I just posted.

I'm curious to try and understand how GR might resolve these issues, if I have even managed to describe the problem correctly. If I have misdescribed it, then maybe GR doesn't need to resolve anything, and my problems rest in failing to properly understand SR.

5. I'm just wondering what the point in this is.
If you suggest an instantaneous acceleration ( no proper time for this ), then there really is no way to calculate what the effects on the clocks or measurements are, because such an acceleration isn't allowed under the rules of SR. This is simply not defined because it would require an infinite amount of energy.
Even if the acceleration was smooth, you still cannot use SR because the frame of reference of the spaceship is not inertial.
The only scenario which admits a simple calculation and visualization of what happens is when the ships moves at constant speed between the planets.

6. Originally Posted by kojax
Mostly, I'm just trying to be clear that it doesn't matter who accelerates, the result will be the same
Surely it does matter who accelerates; and the results won't be the same.

You can detect if you are accelerating. But you can't tell if it is you moving or someone else moving (or both of you). Velocity is relative, acceleration isn't.

7. Originally Posted by Markus Hanke
I'm just wondering what the point in this is.
If you suggest an instantaneous acceleration ( no proper time for this ), then there really is no way to calculate what the effects on the clocks or measurements are, because such an acceleration isn't allowed under the rules of SR. This is simply not defined because it would require an infinite amount of energy.
Even if the acceleration was smooth, you still cannot use SR because the frame of reference of the spaceship is not inertial.
The only scenario which admits a simple calculation and visualization of what happens is when the ships moves at constant speed between the planets.
Usually a continuous change can be approximated as a series of small steps. Going from 0 to .99C is certainly not a small step, but I figure if I pose the question then it might give me an idea for how the smaller changes are going to look.

Mostly I'm trying to find a way to follow the logical process that lead from SR to GR. I figure if I understand that process, the tensors and such will be easier to decipher. Is it possible that I am off to a bad start already?

Originally Posted by Strange
Originally Posted by kojax
Mostly, I'm just trying to be clear that it doesn't matter who accelerates, the result will be the same
Surely it does matter who accelerates; and the results won't be the same.

You can detect if you are accelerating. But you can't tell if it is you moving or someone else moving (or both of you). Velocity is relative, acceleration isn't.
Oh that makes sense. I forgot. There is a way to bounce light around locally in order to determine that, isn't there?

So GR isn't quite as relative as SR. It's good to be able to establish that.

8. Originally Posted by kojax
Originally Posted by Strange
Originally Posted by kojax
Mostly, I'm just trying to be clear that it doesn't matter who accelerates, the result will be the same
Surely it does matter who accelerates; and the results won't be the same.

You can detect if you are accelerating. But you can't tell if it is you moving or someone else moving (or both of you). Velocity is relative, acceleration isn't.
Oh that makes sense. I forgot. There is a way to bounce light around locally in order to determine that, isn't there?
Easier than that, you can feel it! An important aspect of GR is that you can't tell the difference between accelerating and gravity.

9. Originally Posted by kojax
Mostly I'm trying to find a way to follow the logical process that lead from SR to GR. I figure if I understand that process, the tensors and such will be easier to decipher. Is it possible that I am off to a bad start already?
The logical process that leads from SR to GR involves, amongst other things, the realisation of the equivalence between gravity and acceleration. So, "instantaneous" accelerations may not help you there.

Originally Posted by kojax
Originally Posted by Strange
Originally Posted by kojax
Mostly, I'm just trying to be clear that it doesn't matter who accelerates, the result will be the same
Surely it does matter who accelerates; and the results won't be the same.

You can detect if you are accelerating. But you can't tell if it is you moving or someone else moving (or both of you). Velocity is relative, acceleration isn't.
Oh that makes sense. I forgot. There is a way to bounce light around locally in order to determine that, isn't there?
Forget bouncing light around - you can feel if you are accelerating.

EDIT: Heh, trust Strange to get in there before me!

10. Originally Posted by Markus Hanke
.... acceleration isn't allowed under the rules of SR..........
Even if the acceleration was smooth, you still cannot use SR because the frame of reference of the spaceship is not inertial.
No one corrected you on this so I thought I would. Accelerating reference frames are part of SR. You just can't use the Lorentz Transformation. You have to use a different transformation. Please note the following references:

From the book “Special Relativity” by A. P. French
Copyright 1966 Massachusetts Institute of Technology
Chapter 5, Relativistic Kinematics, page 153

“Because Einstein developed a whole new theory (his general theory of relativity, published in 1916) based upon dynamical equivalence of an accelerated laboratory and a laboratory in a gravitational field, it is sometimes stated or implied that special relativity is not competent to deal with accelerated motions. This is a misconception. We can meaningfully discuss a displacement and all its time derivatives within the context of the Lorentz transformations.”

From the book “Basic Relativity” by Richard A Mould
Chapter 8, Uniform Acceleration, page 221

“Until the relationship between mater and metric is explicitly stated, we cannot be said to have left the domain of special relativity, even when working with non-inertial frames of reference.”
That’s a fancy way of saying that unless you have to take gravity into account, you are still doing Special Relativity even if you have acceleration.

11. The remaining posts of this thread has been moved to here:
http://www.thescienceforum.com/new-h...ny-worlds.html
as they are about one poster's non-mainstream personal ideas concerning Relativity.

12. I'm confused about how a person would feel them self accelerate in free fall. I wouldn't think that you would feel anything.

On Earth if you jump in a car and accelerate, what you're really feeling is the N forces transmitting the force from the seat behind you to the front of your body. That's just because it's an inherently non-uniform type of acceleration. If you start falling out of an airplane, you feel the absence of the N force that has usually been present most of your life whenever you stand on your feet in the Earth's gravitational field... .again because your feet are usually transferring an N force to your upper body to cancel gravity.

However, I have to admit that I've never experienced a uniform acceleration in the absence of these N forces, so I can't say for sure that I wouldn't feel something odd about it if I did.

Originally Posted by mikelizzi
“Because Einstein developed a whole new theory (his general theory of relativity, published in 1916) based upon dynamical equivalence of an accelerated laboratory and a laboratory in a gravitational field, it is sometimes stated or implied that special relativity is not competent to deal with accelerated motions. This is a misconception. We can meaningfully discuss a displacement and all its time derivatives within the context of the Lorentz transformations.”
This is one thing I'm really wondering about. Is it possible to take a derivative or integral of the lorentz transformations from one speed to the next as you accelerate, and use that to understand GR better?

It seems practical. In most situations that's how you move from speed to acceleration. Is relativity different in this respect?

13. Sortly because you move it ( if you cunt haf side exseleration you aciv halfe c ) the solotion sood came from time travel - its not good to be in the same plasce twiss or to be in difren plasce difrnt from the same , agine its time travel prablem but it exsist

14. You REALLY need to work on your English...

15. I'm confused about how a person would feel them self accelerate in free fall. I wouldn't think that you would feel anything.
You wouldn't ? Ever jumped off a dive tower at your local public pool ? Try it...

16. Originally Posted by kojax

This is one thing I'm really wondering about. Is it possible to take a derivative or integral of the lorentz transformations from one speed to the next as you accelerate, and use that to understand GR better?

It seems practical. In most situations that's how you move from speed to acceleration. Is relativity different in this respect?
I'm afraid you can't. Lorentz transformations can only be used between inertial frames, i.e. frames that are not subject to acceleration.

17. Originally Posted by Water Nosfim
Sortly because you move it ( if you cunt haf side exseleration you aciv halfe c ) the solotion sood came from time travel - its not good to be in the same plasce twiss or to be in difren plasce difrnt from the same , agine its time travel prablem but it exsist
I wouldn't normally suggest this, but please consider using something like Google Translate instead of trying to write in English. At least the words will be spelled correctly: Google Translate

Sortly כי אתה מעביר את זה (אם את כוסית פולטים exseleration צד אתה aciv halfe ג) solotion סוד הגיע מסע בזמן - לא שלה טוב להיות ב twiss plasce אותם או להיות difrnt plasce difren מ זאת, agine מסע בזמן שלו prablem אבל exsist.

18. Translationalsofunnyhere,with respect,Iwill try to postonlythings that interest me,toas little as possibleto scare

19. Originally Posted by kojax
........
This is one thing I'm really wondering about. Is it possible to take a derivative or integral of the lorentz transformations from one speed to the next as you accelerate, and use that to understand GR better?

It seems practical. In most situations that's how you move from speed to acceleration. Is relativity different in this respect?
I have not seen an author take that approach.

The book by French only develops an acceleration transformation (relating the acceleration in reference frame S’ when you know the acceleration in S). That is done by taking the time derivative of what he calls the parallel and perpendicular velocity transformations (I know them as the velocity addition formulas).

The book by Mould derives a new (t, x) transformation between an inertial and a “uniformly accelerating” reference frame. Mould starts from the SR relationship between change in momentum and force and ultimately, acceleration. The hard part is coming up with a definition for a uniformly accelerating reference frame. Mould’s goal was to define an accelerating reference frame such that everybody in it remains at rest with respect to everybody else. That way their positions are time independent (to each other but not to an observer in an inertial reference frame). To do that everybody in the accelerating reference frame has to have a different acceleration. The nominal value for the reference frame (the value you plug into the equation) is the acceleration of the origin. Mould prefers to call it an “accelerating system of coordinates”. I posted a summary of his results on my webs site at

http://www.relativitysimulation.com/...formation.html

It took me months to figure out what he was talking about and while I am comfortable working some simple acceleration problems I don’t feel proficient enough to explain any further to someone else.

20. I have a probably naive question. Is the gravity on any planet such as Earth entirely explainable in terms of acceleration according to relativity? I though gravity was not understood fully and we are searching for the mechanism such as a graviton? Sort of like a doctor can describe the symptoms of an illness but sometimes don't know the underlying etiology?

21. Originally Posted by ballyhoo
I have a probably naive question. Is the gravity on any planet such as Earth entirely explainable in terms of acceleration according to relativity? I though gravity was not understood fully and we are searching for the mechanism such as a graviton? Sort of like a doctor can describe the symptoms of an illness but sometimes don't know the underlying etiology?
It's not naive, don't worry, but let me set you straight on a few things before I proceed to answer your question. You seem to be approaching this from the wrong angle. You need to specify which subset of acceleration you're talking about. Is it consciousness acceleration, sentience acceleration or hyper acceleration?

Assuming it's the former, it is only explainable in terms of reality rather than relativity. If a hyperbeing is moving towards an undefined mass of metasentience then the conscious acceleration grows dramatically by a factor of ten every hypersecond (of Nor; Rift RIFT). When a being approaches the more dangerous speeds they become superconsciouss and move into trans(RIFT) state. This is all under the base K constant. Understood, repeat. Undirection RIFT RIFT.

I hope this helps you you you.

22. Originally Posted by ballyhoo
I have a probably naive question. Is the gravity on any planet such as Earth entirely explainable in terms of acceleration according to relativity? I though gravity was not understood fully and we are searching for the mechanism such as a graviton? Sort of like a doctor can describe the symptoms of an illness but sometimes don't know the underlying etiology?
Not a naive question, rather a subtle one. And one so subtle that I don't really understand the question even though I think I know the answer!

Yes, GR fully explains everything we know about gravity on the earth and elsewhere. However, we do know that is probably not the "final" theory. For example we don't know how to reconcile it with quantum theory (which is why the graviton is purely hypothetical - or even speculative). But any future theory of gravity will have to include everything that GR does but also work in some extreme cases wher GR appears to break down (in the same way that GR "include" Newtonian gravity as an approximation).

The bit I don't understand is the question about "mechanism". Under Newton, the "mechanism" was a force (like the electromagnetic forces). Under Einstein the "mechanism" is the geometry of space-time. A future theory might either modify that or replace it with a completely different "mechanism".

What these theories provide is a working description that is able to produce usable and useful results (e.g. accurate GPS).

And now the bit of your question I don't understand...

I suspect you are using "mechanism" to mean something like "how does it really work". I don't think that is a physics (or even scientific) question. It is philosophy and gets into all the tricky aspects like what does "reality" mean, etc. Whatver mechanism we might come up with, it will always be possible to ask, "but how does that work?".

As I say, GR is almost certainly not our final theory of gravity. But I doubt we will ever have such a final theory. Just better approximations.

23. Originally Posted by HyperSentience
I hope this helps you you you.
I very much doubt it helped anyone but you.

I just noticed: you actually joined the forum specifically to post that drivel?

24. But if gravity is related to the geometry of space time what does that mean for how a smaller mass stays on the larger mass of Earth? - and if acceleration is just another way to view gravity - isn't the earth accelerating in many directions at the same time? accelerating away from the sun, away from the galactic center, etc. One of Einsteins examples was being in an elevator moving through space - the acceleration was akin to gravity from the perspective of a person riding the elevator. But people on the Earth on the surface opposite the direction of acceleration would not experience such an acceleration. Hopelessly confused.....

25. Originally Posted by Strange
Originally Posted by HyperSentience
I hope this helps you you you.
I very much doubt it helped anyone but you.
I've been a member of this forum for eighteen omnirifts.

26. no you're a troll who feels too stupid to answer the question hypersentience - ban him

27. anyway, I am a bit surprised to read that you would consider the 'mechanism' to be philosophical and not scientific. Surely the interactions of quantum particles -even hypothesized ones- is mechanistic? There seem to be several theories concerning gravity as a phenomenon mediating by a particle interacting with other particles. https://en.wikipedia.org/wiki/Graviton

28. Originally Posted by ballyhoo
anyway, I am a bit surprised to read that you would consider the 'mechanism' to be philosophical and not scientific.
Well, I guess my problem with this sort of question comes from the fact that it frequently comes from people who want to replace relativity with their own personal theory. One of the objections they raise is that "GR doesn't explain gravity it is just a load of mathematics".

As far as I am concerned, the geometry described by GR is the explanation/mechanism (until we get a better one). Even though it is completely abstract; i.e. space-time isn't "stuff" that can be curved.

And "graviton" doesn't really answer it for many people; they already ask "but what is a photon 'really'?"

As for the graviton; that may turn out to be an artefact of trying to apply our current understanding of quantum physics to our current understanding of gravity. When (if) we have a unified theory then it may be seen as irrelevant; all the things we currently call "particles" and "curvature of space-time" should emerge from some underlying model (whether that is loop quantum gravity or string theory or ...).

I suppose, for some people, something like string theory might be mechanism enough because strings sound like real "things". But I'm sure some people will just say, "but what are they strings of?". And if something like LQG turns out the be the right road[1], then that just gives a different view of the geometry of space-time. But space-time isn't "stuff", so what is that geometry describing?

They are all just models that work to different degrees of accuracy within the appropriate domains. They don't necessarily represent reality.

[1] See what I did there?

29. Originally Posted by ballyhoo
But if gravity is related to the geometry of space time what does that mean for how a smaller mass stays on the larger mass of Earth? - and if acceleration is just another way to view gravity - isn't the earth accelerating in many directions at the same time? accelerating away from the sun, away from the galactic center, etc. One of Einsteins examples was being in an elevator moving through space - the acceleration was akin to gravity from the perspective of a person riding the elevator. But people on the Earth on the surface opposite the direction of acceleration would not experience such an acceleration. Hopelessly confused.....
Oh boy. Let me offer some very superficial statements about GR. First, in GR mass does not produce a gravitational field. No field, no force. No force, no acceleration. The person in Einstein’s free falling elevator doesn’t know he is under the influence of a uniform gravitational field. Everything inside the elevator behaves as it would if the occupant were just drifting weightless in far away space not under the influence of any forces. You’ve heard that before.

But an observer in a reference frame beyond the influence of gravity would conclude that the elevator is in an area of space-time that is curved. According to this observer, the elevator is following a non-accelerating path through that curved space time, which works a lot like an accelerating path through flat space-time.

It is often stated that in GR the acceleration produced by gravity has been substituted by a change in the geometry of space time itself. Is it just semantics? Not by a long shot. To me the free falling elevator is a paradox in Newtonian Physics. Acceleration is supposed to be absolute. A body that is being accelerated is supposed to know it is being accelerated. But the elevator occupant does not know. In GR the paradox goes away.

If you are comfortable with that, I can go over the example of an object at rest on the surface of the earth next.

30. Originally Posted by HyperSentience
Originally Posted by ballyhoo
I have a probably naive question. Is the gravity on any planet such as Earth entirely explainable in terms of acceleration according to relativity? I though gravity was not understood fully and we are searching for the mechanism such as a graviton? Sort of like a doctor can describe the symptoms of an illness but sometimes don't know the underlying etiology?
It's not naive, don't worry, but let me set you straight on a few things before I proceed to answer your question. You seem to be approaching this from the wrong angle. You need to specify which subset of acceleration you're talking about. Is it consciousness acceleration, sentience acceleration or hyper acceleration?

Assuming it's the former, it is only explainable in terms of reality rather than relativity. If a hyperbeing is moving towards an undefined mass of metasentience then the conscious acceleration grows dramatically by a factor of ten every hypersecond (of Nor; Rift RIFT). When a being approaches the more dangerous speeds they become superconsciouss and move into trans(RIFT) state. This is all under the base K constant. Understood, repeat. Undirection RIFT RIFT.

I hope this helps you you you.
this is pure pseudowordsalad that does not belong in the physics forum. Please ignore the post.

31. Originally Posted by mikelizzi
Originally Posted by ballyhoo
But if gravity is related to the geometry of space time what does that mean for how a smaller mass stays on the larger mass of Earth? - and if acceleration is just another way to view gravity - isn't the earth accelerating in many directions at the same time? accelerating away from the sun, away from the galactic center, etc. One of Einsteins examples was being in an elevator moving through space - the acceleration was akin to gravity from the perspective of a person riding the elevator. But people on the Earth on the surface opposite the direction of acceleration would not experience such an acceleration. Hopelessly confused.....
Oh boy. Let me offer some very superficial statements about GR. First, in GR mass does not produce a gravitational field. No field, no force. No force, no acceleration. The person in Einstein’s free falling elevator doesn’t know he is under the influence of a uniform gravitational field. Everything inside the elevator behaves as it would if the occupant were just drifting weightless in far away space not under the influence of any forces. You’ve heard that before. But an observer in a reference frame beyond the influence of gravity would conclude that the elevator is in an area of space-time that is curved. According to this observer, the elevator is following a non-accelerating path through that curved space time, which works a lot like an accelerating path through flat space-time. It is often stated that in GR the acceleration produced by gravity has been substituted by a change in the geometry of space time itself. Is it just semantics? Not by a long shot. To me the free falling elevator is a paradox in Newtonian Physics. Acceleration is supposed to be absolute. A body that is being accelerated is supposed to know it is being accelerated. But the elevator occupant does not know. In GR the paradox goes away. If you are comfortable with that, I can go over the example of an object at rest on the surface of the earth next.
but I thought the analogy was that the more massive an object then the more curved spacetime was near it. Isn't this curvature the gravitational field?

32. Originally Posted by Markus Hanke
Originally Posted by kojax

This is one thing I'm really wondering about. Is it possible to take a derivative or integral of the lorentz transformations from one speed to the next as you accelerate, and use that to understand GR better?

It seems practical. In most situations that's how you move from speed to acceleration. Is relativity different in this respect?
I'm afraid you can't. Lorentz transformations can only be used between inertial frames, i.e. frames that are not subject to acceleration.
And yet, before you begin accelerating, and after you have finished accelerating, you are in an inertial frame. What happens in the time in between that makes us unable to compare the two situations?

Originally Posted by Markus Hanke
I'm confused about how a person would feel them self accelerate in free fall. I wouldn't think that you would feel anything.
You wouldn't ? Ever jumped off a dive tower at your local public pool ? Try it...
My thinking is that feeling wouldn't be different from the feeling of weightlessness you would experience if you were drifting in space. But I have to admit I haven't tried both things yet, so I can't be sure.

33. Originally Posted by kojax
And yet, before you begin accelerating, and after you have finished accelerating, you are in an inertial frame. What happens in the time in between that makes us unable to compare the two situations?
Yes, that is correct. For the acceleration itself, however, the frame is not inertial. In practical terms that means that the passenger on board your spaceship would experience a force acting on him. Mathematically speaking this translates to the spaceship's coordinate system to become curvilinear.

My thinking is that feeling wouldn't be different from the feeling of weightlessness you would experience if you were drifting in space. But I have to admit I haven't tried both things yet, so I can't be sure.
You are absolutely right, it is a similar feeling. In essence, when you fall off something high enough, you are weightless once terminal velocity has been reached during your fall. That's SR - a free falling observer in a gravitational field is equivalent to an observer that experiences no gravity at all.

34. First, in GR mass does not produce a gravitational field.
This is completely wrong. All forms of energy, including mass, are a source of the gravitational field, thus space-time curvature, under General Relativity.
Most of the post I quoted above is thus wrong and should be ignored.

35. Originally Posted by Markus Hanke
First, in GR mass does not produce a gravitational field.
This is completely wrong. All forms of energy, including mass, are a source of the gravitational field, thus space-time curvature, under General Relativity.
Most of the post I quoted above is thus wrong and should be ignored.
I'm not so sure about that - that post seems okay to me. I think what Mike was saying is that in GR mass does not produce a gravitational field in the Newtonian sense, where a field means a force. In GR, you only feel a force due to your own accelerations against gravity. You only feel a force if you do not follow your geodesic, in other words.

If you are following your geodesic you are weightless - you are in free fall. You can be in free-fall in a gravitational field and you will feel no force. However, if you can feel your weight then you are not following your geodesic - you must be resisting gravity in some way.

Thought experiment: Imagine you are sitting on a satellite in orbit around the Earth. You are in free-fall, weightless, following yours and the satellites geodesic. Below you, on the Earth, engineers have undertaken a massive project and have bored a hole through the centre of the Earth. On each side of the Earth, where the hole emerges, they have fitted a tube that extends up to the top of the atmosphere, and the tube has had all the air evacuated from it, so it is filled with vacuum.

You jump off the satellite with the exact acceleration to change your geodesic from following the satellite to dropping into the top of the tube. You feel the acceleration as you change your geodesic, but now you are falling into the tube, in free-fall once more.

You fall right down that tube, through the Earth and emerge on the other side, falling "upwards" and out of Earths atmosphere once more. You come out of the top of the tube and continue to "fall upwards" until your path takes you right up to the level of the satellite once more - and guess what, the satellite is just passing by as you get there! You can just reach out and brush the satellite with your hand (careful not to accelerate yourself!) as it passes! Then you start falling back again, enter the tube and fall back through the Earth. When you come out of the tube on the other side, and reach the top of your path, there is the satellite again!

It takes the same amount of time to fall through the Earth as it does to fall around it!

The only acceleration occurred when you jumped off the satellite - once you are following your new geodesic you will remain in free-fall, and feel weightless, until you change your geodesic (either by accelerating yourself, or by hitting something!).

You are freely falling across curved space-time and feel no accelerations, although an observer either in a flatter space-time or assuming it will calculate you to be accelerating in relation to their flat space-time, you are not accelerating in relation to your curved space-time, you are following your geodesic!

You are not decelerating to a halt at the top of your arc and then accelerating back towards the Earth again, you are in free-fall all the way.

36. Originally Posted by SpeedFreek
Originally Posted by Markus Hanke
First, in GR mass does not produce a gravitational field.
This is completely wrong. All forms of energy, including mass, are a source of the gravitational field, thus space-time curvature, under General Relativity.
Most of the post I quoted above is thus wrong and should be ignored.
I'm not so sure about that - that post seems okay to me. I think what Mike was saying is that in GR mass does not produce a gravitational field in the Newtonian sense, where a field means a force.
If that is indeed the case, then you are of course right, and I might have been too hasty in my post.
It is just, whenever GR is mentioned, I never think of forces in the classical sense, but always of geometry - and in that sense, the presence of mass automatically leads to a curvature in spacetime.
Come to think of it, he did mention that for an observer the free-falling elevator will appear to be in a curved spacetime, which is correct in this picture, so I think you are right.
I offer my sincere apologies to Mike and hereby retract my previous comment - I didn't read the post properly. Entirely my mistake

37. Originally Posted by SpeedFreek
Originally Posted by Markus Hanke
First, in GR mass does not produce a gravitational field.
This is completely wrong. All forms of energy, including mass, are a source of the gravitational field, thus space-time curvature, under General Relativity.
Most of the post I quoted above is thus wrong and should be ignored.
I'm not so sure about that - that post seems okay to me. I think what Mike was saying is that in GR mass does not produce a gravitational field in the Newtonian sense, where a field means a force. In GR, you only feel a force due to your own accelerations against gravity. You only feel a force if you do not follow your geodesic, in other words.

If you are following your geodesic you are weightless - you are in free fall. You can be in free-fall in a gravitational field and you will feel no force. However, if you can feel your weight then you are not following your geodesic - you must be resisting gravity in some way.
So, is gravitational time dilation caused by attempting to resist your geodesic, or is it present either way, even if you conform to your geodesic?

38. Originally Posted by kojax
So, is gravitational time dilation caused by attempting to resist your geodesic, or is it present either way, even if you conform to your geodesic?
It is present either way, as it is due to the difference in gravitational potential between one observer and another, which is due to the difference in their respective local curvature. An observer freely falling in a gravitational field will be gravitationally time-dilated in relation to an observer further away from the gravitational source. If the free-faller then accelerates (in order to perhaps "hover" and keep themselves at rest in relation to the gravitational source) there will be more time-dilation in relation to the more distant observer, as that acceleration will increase the difference in gravitational potential between them.

It's worth a read, at any rate!

40. I like the practical approach the author uses. Does the fact we are accelerating ourselves against the Earth's gravity in order to oppose it reduce or increase the time dilation effect?

This part is interesting:

The Distance Dependence Objection finds it odd that Terence's turnaround ageing should depend on how far he is from Stella when it happens, and not just on Stella's measurement of the turnaround time. No mystery: uniform pseudo-gravitational time dilation depends on the "gravitational" potential difference, which depends on the distance.
So basically, when the space ship in the OP example starts moving and stops moving, we can consider real time to elapse at the target planet? Also more time is elapsing at the far planet than the near planet? (Because of the difference is pseudo-gravitational potential)

Also, does this imply there may be a cosmic acceleration limit just like how there's a cosmic speed limit?

41. Originally Posted by kojax
I like the practical approach the author uses. Does the fact we are accelerating ourselves against the Earth's gravity in order to oppose it reduce or increase the time dilation effect?
Err... reduce or increase the time-dilation effect, relative to whom? This question is not so straightforward to answer as it might seem.

An observer on the surface of Mars, which has less gravity than the Earth, would calculate everything on the surface of the Earth to be gravitationally redshifted in relation to them. An observer on "the surface of" Jupiter, which has more gravity than Earth, would calculate everything everything on the surface of the Earth to be gravitationally blueshifted in relation to them.

But I don't think that is quite what you are asking is it? You are asking how someone standing on the Earth and thus resisting Earths gravity would be time-dilated in relation to someone at the same distance from the gravitational source but who is not resisting Earths gravity?

Well that question requires comparing the clock of someone standing on the surface of the Earth with the clock of that free-faller falling through the Earth, at the moment they are instantaneously at the same distance from the gravitational source! The problem is, in order to compare clocks we need two measurements, and the free-faller will have a changing gravitational potential between those two measurements as their distance to the gravitational source is constantly decreasing.

But theoretically, the clock of an observer that is accelerating in order to keep themselves at rest in relation to a gravitational source will "run slower" than the clock of a free-faller at the same distance from that gravitational source, as the accelerating frame is sitting lower in its own pseudo-gravitational potential.

This means an observer on Mars would calculate the free-fallers clock to be running slower than their own, and the accelerated clock running slower still. The free-fallers clock is closer to their own measure of time on Mars. But an observer on Jupiter would calculate the free-fallers clock running faster than their own, with the accelerated clock running slower, so the accelerated clock would be closer to their own measure of time on Jupiter! So, the question as to whether the acceleration increases, or reduces the time-dilation is, err, relative in that sense.

Originally Posted by kojax
This part is interesting:

The Distance Dependence Objection finds it odd that Terence's turnaround ageing should depend on how far he is from Stella when it happens, and not just on Stella's measurement of the turnaround time. No mystery: uniform pseudo-gravitational time dilation depends on the "gravitational" potential difference, which depends on the distance.
So basically, when the space ship in the OP example starts moving and stops moving, we can consider real time to elapse at the target planet? Also more time is elapsing at the far planet than the near planet? (Because of the difference is pseudo-gravitational potential)
That is what the occupants of the space ship think, yes. It is the same as you running up and down in your living room - every time you turn round, time in a distant galaxy in your direction of travel leaps either backwards or forwards by centuries, depending on whether you are accelerating towards or away from them!

Originally Posted by kojax
Also, does this imply there may be a cosmic acceleration limit just like how there's a cosmic speed limit?
Theoretically, only in as much as "instantaneous" acceleration leads to an instantaneous leap forwards/backwards in time. But reality, on the other hand, is a different matter!

42. As SpeedFreek has explained above, in GR, all notions such as acceleration, time, distance etc etc are relative to the chosen observer, and in the presence of gravitational fields or acceleration these observers will not necessarily agree on a measurement.

For me this is exemplified in the case of the astronaut falling into a black hole - for the in-falling astronaut, nothing special happens, he just falls and falls, through the event horizon and onwards, until tidal forces rip im apart. For an outside, far-away observer, however, the astronaut appears to slow down and become dimmer, fading away for an infinite time before ever reaching the event horizon. Which observer is right ? They both are, relative to their own frame of reference, which no longer agree.

43. If I'm not mistaken, then as you accelerate time appears to advance rapidly elsewhere. As Speedfreak was saying:

Originally Posted by SpeedFreek

Originally Posted by kojax
This part is interesting:

The Distance Dependence Objection finds it odd that Terence's turnaround ageing should depend on how far he is from Stella when it happens, and not just on Stella's measurement of the turnaround time. No mystery: uniform pseudo-gravitational time dilation depends on the "gravitational" potential difference, which depends on the distance.
So basically, when the space ship in the OP example starts moving and stops moving, we can consider real time to elapse at the target planet? Also more time is elapsing at the far planet than the near planet? (Because of the difference is pseudo-gravitational potential)
That is what the occupants of the space ship think, yes. It is the same as you running up and down in your living room - every time you turn round, time in a distant galaxy in your direction of travel leaps either backwards or forwards by centuries, depending on whether you are accelerating towards or away from them!
Presumably the same principle applies to rapid acceleration taking place at the event horizon of a black hole. The rate of acceleration is still not infinite, however, so I guess time couldn't appear to be advancing infinitely fast elsewhere.

Or well, I guess it might work out that way if clocks were getting set backwards at a rate equal to the rate at which they advance. This whole conflict between "coordinate" time and "proper" time is very confusing.

44. Originally Posted by kojax
Presumably the same principle applies to rapid acceleration taking place at the event horizon of a black hole. The rate of acceleration is still not infinite, however, so I guess time couldn't appear to be advancing infinitely fast elsewhere.
That is correct. There will be a time dilation effect, but it is finite.

Or well, I guess it might work out that way if clocks were getting set backwards at a rate equal to the rate at which they advance. This whole conflict between "coordinate" time and "proper" time is very confusing.[/
There is no conflict, because in GR there is no requirement for all observers to agree on how time is measured. We can all agree to disagree in this case
Actually it doesn't need to be confusing. Proper time ( in this case ) is what is measured by an observer subject to the gravitational field, coordinate time is the time of an asymptotically far away observer. So long as we understand that they don't always agree all is fine.

45. I guess the only requirement is for an observer's experience to match .... their own experience. So as long as objects at the event horizon aren't ever going to leave (and apparently they aren't), the outside observer never has to turn out to have been wrong about seeing time stop I guess?

Yet, the outside observer can observe a black hole itself to move, correct? He can even observe black holes moving relative to one another?

46. Originally Posted by kojax
I guess the only requirement is for an observer's experience to match .... their own experience. So as long as objects at the event horizon aren't ever going to leave (and apparently they aren't), the outside observer never has to turn out to have been wrong about seeing time stop I guess?
That's the idea, yes. As long as nobody observes a violation of causality, all is well in the universe.

But actually, there is a way out of this particular conundrum.

The in-faller is not seen to be "frozen in time" at the event horizon - that is an old and somewhat naive view of events. In more modern terms, they will be redshifted out of detectability as their redshift tends towards infinity at the event horizon - they will fade away...

Or, from another point of view, consider that for the in-faller they cross the event horizon and reach the gravitational singularity at r=0 in a finite time. This means the black hole gains their mass... which means the Schwarzschild radius increases ever so slightly, which means the event horizon moves outwards a little. Otherwise, how would a black hole gain any mass?

Originally Posted by kojax
Yet, the outside observer can observe a black hole itself to move, correct? He can even observe black holes moving relative to one another?
Well, yes, I suppose.

47. Originally Posted by kojax
Yet, the outside observer can observe a black hole itself to move, correct? He can even observe black holes moving relative to one another?
Yes, of course. The black hole as a body is something entirely different than an in-falling particle. The black hole has finite mass, and macroscopically behaves like any other body. The event horizon itself isn't even visible for an outside observer.

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