[JSS]

Having a special reference frame would however allow you to [do stuff]

That is absolutely not how frames of reference work. You cannot create a FoR in which the laws of physics are miraculously broken. A FoR is just a frame from which you observe a [hypothetical] scenario. It does not change the scenario.

Agreed, let me clarify.

It's not that a special reference frame lets you do stuff, it solves one of many problems preventing it.  Without a special or preferred frame, any kind of FTL travel no matter how you do it will allow time travel paradoxes. Among other advantages, a preferred frame solves the time travel problem by providing a single reference point to order events by and eliminating the possibility of sending information backwards in time.

How you perform your FTL travel is another subject entirely, and it still may not be possible (which is either very bad or very good for our future as a species), but at least with a preferred frame you eliminate one of the major issues with it.

[pricelesspearl]

Well, no, it doesn't. It says that "In infinitesimal small durations there is always one inertial frame, which momentarily has the same velocity as the accelerated body, and in which the Lorentz transformation holds."

Saying that velocity is momentarily the same is not the same thing as saying that the rate of acceleration is momentarily the same.  Two cars can both be going 20mph at any given moment when one is accelerating at 10mph and the other at 5mph.

What’s more …an inertial observer always has a proper acceleration of zero.  Are you suggesting that there is some infinitesimal small duration of time, in some inertial frame where Earth’s acceleration is zero?

You claim that it is velocity that's decreasing as it approaches c.

You’re right, I should have been more precise and said that its velocity is decreasing relative the rate of acceleration.

It sounds to me like you've made a lot of assumptions about what's being proposed.

I’m just reading the wiki text and the way I read it says that the earth can have a proper acceleration of 1g forever and not reach c because from an inertial frame of reference the proper acceleration will appear to decrease at increasing rates and therefore an inertial observer will never see earth’s velocity reach the speed of light.

Is that a correct interpretation?  If it is, that explanation is wrong.  The reason an inertial observer never sees earth’s velocity reach the speed of light is because it never reaches the speed of light in the accelerating frame, even though it continues to accelerate at the same rate.  How and why that can be true is clearly explained, even simplistically, in the sources I cited. Because the formula for adding velocities must take time dilation into account, an object can accelerate ad infinitum without the total velocity ever exceeding c.  IOW, accelerating 100,000 mph will add less than 100,000 mph to the total velocity. Check the formula for yourself and see how it works out if you doubt it.

If that’s the correct interpretation, it also means that even though the proper acceleration will appear to decrease from an initial observer, it doesn’t decrease within the earth’s frame of reference, as measured by an accelerometer, and within its own frame, Earth would reach c.

[Pete Svarrior]

Saying that velocity is momentarily the same is not the same thing as saying that the rate of acceleration is momentarily the same.

Indeed. I take it you've realised your error, then?

[pricelesspearl]

Indeed. I take it you've realised your error, then?

This as is as simple as I can make it…if you don’t understand this, there is not any more I can say.

An accelerometer is a device that measures proper acceleration. If the earth always, at every single moment, for every infinitesimal duration, has a proper acceleration of 9.81 m/s2, an accelerometer will read 9.81 m/s2 at every single moment for every infinitesimal duration.

An inertial frame always has a proper acceleration of zero at every single moment, for every infinitesimal duration, so an accelerometer will always read zero at every single moment, for every infinitesimal duration.

Therefore the “relative” proper acceleration between the earth and an inertial observer will always be 9.81 m/s2 at every single moment, for every infinitesimal duration and an inertial observer will observe it accelerating at 9.81 m/s2  for every single, moment, for every infinitesimal duration.

The Earth’s proper acceleration is absolute, it doesn’t change as perceived from an inertial frame. Earth’s acceleration is objective.  It can be determined from within its own frame of reference, all you need to do is look at an accelerometer.

Earth is always in accelerating frame of reference, according to FET. 

[Pete Svarrior]

This as is as simple as I can make it…if you don’t understand this, there is not any more I can say.

You can't say much in general. You continue to change your mind on things and contradict yourself. You know, things like "as the Earth's velocity increases, the Earth's velocity decreases. Also, those changes in velocity are not acceleration." All I'm asking for you to do is stop doing that in the upper, since I do not for a moment believe you're arguing sincerely.

In short: the problem is not that I don't understand what you're saying. I do. You just end up contradicting simple physics every time you open your mouth. This is why you get thoroughly mocked by RE'ers and FE'ers alike.

The Earth’s proper acceleration

A friendly reminder that no part of the Wiki refers to proper acceleration. Several people pointed this out to you at different points in time. Your fixation here is not useful.

Earth is always in accelerating frame of reference, according to FET.

This continues not to be the case. You can consider any situation from any FoR. There is no such thing as an objective FoR, and it is nonsensical to claim that something "is in" a FoR. Every time you use this phrasing, you remind us that you (are pretending to) have no idea what you're doing.

[pricelesspearl]

You can consider any situation from any FoR.

That’s true, but from whatever inertial frame of reference you perceive the earth, its relative acceleration will always be 9.81 m/s2  .  The earth’s acceleration will always be 9.81 m/s2, from its own FoR.  Acceleration in any inertial frame will always be zero from it’s own FoR.  From any inertial frame, earth will always be accelerating at 9.81 m/s2  .  And from earth, an inertial frame will always be accelerating at zero.

A friendly reminder that no part of the Wiki refers to proper acceleration.

If FET did not consider earth’s acceleration to be proper acceleration, there could not be any “gravity” caused by UA. Proper acceleration is the “physical acceleration (i.e., measurable acceleration as by an accelerometer) experienced by an object.”   If the earth wasn’t physically experiencing proper acceleration of 9.81 m/s2  , there  could not the physical effect of “gravity” caused by the acceleration. 

[Pete Svarrior]

That’s true, but from whatever inertial frame of reference you perceive the earth, its relative acceleration will always be 9.81 m/s2

This directly contradicts your prior statement, in which there is one inertial FoR in which that applies for a given moment. This is the usual problem with your claims - you keep disagreeing with yourself.

Also, "relative acceleration"? Relative to what?

If FET did not consider earth’s acceleration to be proper acceleration

You are once again (pretending to be) hopelessly confused. The Earth's acceleration cannot be "considered to be proper acceleration" or not. It can be expressed as one or the other.

Proper acceleration is acceleration expressed within a specific frame of reference (or, rather, a set of FoR's). It just so happens that it's more useful and intuitive to express it as three-acceleration for the purpose of this explanation. You could express the same problem in terms of four-acceleration and get an equivalent result, just one that's harder to digest. Same goes for proper acceleration, if you really want to make your life difficult (and, given your proficiency, I'd seriously advise against artificially making your analysis more difficult).

This is just a restatement of your confusion as to which FoR the Earth "is in".

[Groit]

That’s true, but from whatever inertial frame of reference you perceive the earth, its relative acceleration will always be 9.81 m/s2

This directly contradicts your prior statement, in which there is one inertial FoR in which that applies for a given moment. This is the usual problem with your claims - you keep disagreeing with yourself.

Also, "relative acceleration"? Relative to what?

Relative to an observer in free fall.
In FET, if i was to jump from a high rise building, the moment i step off the building my acceleration would be zero. And from my inertial FoR, the Earth will be accelerating at -9.81 m/s^2 (towards me) so the Earth is accelerating relative to all inertial frames.

[Pete Svarrior]

Relative to an observer in free fall.

How long has the observer been in free-fall for? This may seem trivial, but is the very core of PP's objection.

so the Earth is accelerating relative to all inertial frames.

This is entirely incorrect, for reasons even PP accepted. Let's not waste time repeating ourselves - you can catch up with the thread you're contributing to in your own time.

[pricelesspearl]

This directly contradicts your prior statement, in which there is one inertial FoR in which that applies for a given moment. This is the usual problem with your claims - you keep disagreeing with yourself.

No, it doesn’t contradict.  What I said that for any given moment, for any infinitesimal duration, the “relative” acceleration would be 9.81 m/s2.   That means it is always 9.81 m/s2.  Pick whatever moment you want in any inertial frame you want…its always going to be 9.81 m/s2.   One inertial frame may apply for that moment, but in the next moment, in the next inertial frame and in every moment and ever inertial frame after that it will 9.81 m/s2.

You are once again (pretending to be) hopelessly confused. The Earth's acceleration cannot be "considered to be proper acceleration" or not. It can be expressed as one or the other.

It isn’t an either/or proposition.  Proper acceleration can be expressed as relative…but doing that doesn’t change proper acceleration into relative acceleration or mean that proper acceleration no longer applies.

Proper acceleration by definition cannot be relative.  It is “the physical acceleration experienced by an object”.  Relative means “considered in relation or in proportion to something else”.  What is being physically experienced isn’t considered in relation to something else, whether its acceleration or pain. You don’t have to ask anybody else if you have a toothache. It doesn't matter if someone else doesn't believe your tooth is hurting. You know “objectively” if your tooth hurts or not.  There is nothing subjective about it.

If you are accelerating in a car at 100mph, you will experience physical effects from that.  You will feel it. Without ever looking outside,  you can “objectively” know you are accelerating. It doesn’t matter if your “relative” acceleration is 5mph to the guy on the sidewalk.  If you hit a brick wall you will still die. His perception of how fast you were going doesn’t mean squat.  Do you deny that is true? Do you not understand that what is physically perceived from one frame doesn't effect what is physically occurring in another?

You can’t have it both ways.  Either the earth is constantly, physically accelerating at 9.81 m/s2 or not.  For the sake of argument, imagine someone else in an inertial frame in a galaxy far far away perceives earth’s “relative” acceleration as 7.2 m/s2.  Does that mean “gravity” is weaker on earth? What if someone else in another inertial frame perceives it at 12 m/s2? Is" gravity" stronger?

If there is an infinite number of inertial frames and the earth’s proper acceleration can be perceived at an infinite number of different rates…how can FET say it is accelerating at any specific one if it can't be objectively determined?  For that matter, how can FET even say that it is accelerating at all, if you can’t determine it objectively?  Has any flat earther ever observed the earth from an external inertial frame?

[Pete Svarrior]

No, it doesn’t contradict.  What I said that for any given moment, for any infinitesimal duration, the “relative” acceleration would be 9.81 m/s2.

Oh, so you just disagree with the definition of proper acceleration. Amazing. Perhaps stop using that term and define your own, then?

Proper acceleration by definition cannot be relative.

This continues to be factually incorrect, and you were provided with an explanation as to why. You're gonna have to address it, instead of simply restating the same error over and over.

For the sake of argument, imagine someone else in an inertial frame in a galaxy far far away perceives earth’s “relative” acceleration as 7.2 m/s2.  Does that mean “gravity” is weaker on earth? What if someone else in another inertial frame perceives it at 12 m/s2? Is" gravity" stronger?

Keeping in mind what time dilation is (and that you failed to account for it) - yes, that is more or less correct. If you somehow managed to observe the Earth from one of the FoR's you described, your observation would be drastically different from that of a local observer on the Earth.

If you are accelerating in a car at 100mph, you will experience physical effects from that.  You will feel it.

Applying classical mechanics to a discussion on special relativity is a schoolboy error. Don't waste our time with that.

You can’t have it both ways.  Either the earth is constantly, physically accelerating at 9.81 m/s2 or not.

Welcome to the amazing world of relativity, where the things you consider obvious and intuitive are completely wrong. Enjoy your stay, and do some reading before you humiliate yourself again.

If there is an infinite number of inertial frames and the earth’s proper acceleration can be perceived at an infinite number of different rates…how can FET say it is accelerating at any specific one if it can't be objectively determined?  For that matter, how can FET even say that it is accelerating at all, if you can’t determine it objectively?  Has any flat earther ever observed the earth from an external inertial frame?

The very core of relativity is that there is no objective frame of reference. It's not that FET can't determine these things objectively - it's that your idea of being "objective" doesn't exist in physics. The core point here is that a frame of reference in which the Earth exceeds the speed of light cannot be defined. We focus on two reasonably observable FoR's - a local observer, and an arbitrary external inertial observer. Those are the "important" ones to explain, and we've covered them both.

We can say that the Earth is accelerating relative to a local observer in free-fall (as we do), because we're local observers, and we can easily verify this. This remains true in FET and RET alike. You can jump off a chair (please do so more competently than most other things you do - be careful not to hurt yourself), and, taking your body as the frame of reference, you will observe the Earth accelerating towards you to meet you.

[Groit]

We can say that the Earth is accelerating relative to a local observer in free-fall (as we do), because we're local observers, and we can easily verify this. This remains true in FET and RET alike. You can jump off a chair (please do so more competently than most other things you do - be careful not to hurt yourself), and, taking your body as the frame of reference, you will observe the Earth accelerating towards you to meet you.

Pete, hypothetically, what if we have two local observers, one is standing on a chair with a height of 1 m and the other is standing on top of a skyscraper that stands 1000 km above sea level. According to FET both observers will be accelerating with the Earth (since they're both attached to the surface and in the same FoR). So, if both observers jumped at the same time they should both see the Earth accelerating towards them at 9.81 m/s^2. However, we know that this is not the case, the observer on the skyscraper would experience an acceleration of 7.3 m/s^2 and the one on the chair 9.81 m/s^2. How does UA account for this change in acceleration? 

[Pete Svarrior]

How does UA account for this change in acceleration?

It doesn't. UA is not the only component of gravity.

Please familiarise yourself with the basics, and please avoid derailing threads with unrelated questions.

[pricelesspearl]

The very core of relativity is that there is no objective frame of reference. It's not that FET can't determine these things objectively - it's that your idea of being "objective" doesn't exist in physics.

If you have a problem with the idea of being able to determine your state of motion objectively, you can take it up with Edwin Taylor and John Archibald Wheeler .  They are both on Wikipedia if you doubt credentials. 


Page 31 Spacetime Physics @ http://www.eftaylor.com/spacetimephysics/

A reference frame is said to an “inertial’ or “free-float” or “Lorentz” reference frame in a certain region of space and time when throughout that region of spacetime-and within some specified accuracy-every free test particle initially at rest with respect to that  frame remains at rest, and every free test particle initially in motion with respect to that frame continues it motion  without change in speed or direction.

Wonder of wonders! This test can be carried out entirely within the free-float frame.  The observer need not look out of the room or refer to any measurements made external to the room. A free-float- frame is “local” in the sense that it is limited in space and time-and also “local in the sense that its free-float character can be determined from within, locally.

Does the FET earth meet the definition in the first paragraph?

The core point here is that a frame of reference in which the Earth exceeds the speed of light cannot be defined

The core point is why it can't be defined. 

[Pete Svarrior]

If you have a problem with the idea of being able to determine your state of motion objectively, you can take it up with Edwin Taylor and John Archibald Wheeler .   

I can't help you with this. Taking your misconceptions and trying to shield yourself with big names who didn't say what you think they said is a common strategy or yours, but it just doesn't work.

Until you've understood the very basics of the subject you're trying to argue about, this thread is doomed to go the way of the magical spirit level.

Does the FET earth meet the definition in the first paragraph?

The Earth is not a frame of reference. It is a body.

[pricelesspearl]

I can't help you with this. Taking your misconceptions and trying to shield yourself with big names who didn't say what you think they said is a common strategy or yours, but it just doesn't work.

So are you suggesting that the quote does not say that you can determine your state of motion objectively? If so, what does it mean? What you call "shielding" myself, most others call providing support for your position.  Your objection is disingenuous considering your claim that my position does not "exist in physics".  When I provide support that it does...just responding "that's not what it means" is not very persuasive or intellectually honest.

The Earth is not a frame of reference. It is a body.

Fair enough...let me rephrase...does earth exist in a certain region of space and time when throughout that region of spacetime-and within some specified accuracy-every free test particle initially at rest with respect to that  frame remains at rest, and every free test particle initially in motion with respect to that frame continues it motion  without change in speed or direction?

[Clyde Frog]

You are currently traveling at 0 m/s relative to the couch you are sitting upon. And simultaneously, you are traveling at .996c relative to a really energetic cosmic ray flying in your direction. Both of those frames are equally valid. If you were on a rocket, hurtling directly toward that cosmic ray at, let's say for fun, .5c relative to your couch that you were on moments ago. What do you think your perception is regarding how fast that cosmic ray is now flying at you? And what do you think the cosmic ray, if it had eyes, would perceive your velocity to be? If your answer to both is less than c, I really don't know why you are still posting in this thread. And if your answer is greater than c, then I think you'll understand before you even reply that you need to read some things.

[Pete Svarrior]

So are you suggesting that the quote does not say that you can determine your state of motion objectively?

What I am suggesting is that you should learn to walk before you can run. Special relativity is complicated and unintuitive, and I'm doing my best to select sources you should be able to easily digest. You're going out of your way to find sources which disagree, but you don't understand the context or implications of what's being said in them, and I'm not a good enough educator to wade through it all for you (nor do I care for your strategy of quote-mining papers as a substitute for argumentation). I don't care if you find me persuasive or not - I won't be able to help you so long as you're unwilling to be helped.

Fair enough...let me rephrase...does earth exist in a certain region of space and time when throughout that region of spacetime-and within some specified accuracy-every free test particle initially at rest with respect to that  frame remains at rest, and every free test particle initially in motion with respect to that frame continues it motion  without change in speed or direction?

I answered that question a long time ago:

At any point in time, you can identify an inertial FoR with regard to which the acceleration will be 9.81ms^-2 for an infinitesimal length of time. That is to say, the Earth would not be immediately moving relative to that frame. A moment later, this would no longer hold.

Try reading TheRealDave's post. I think it might help you.

[Groit]

You are currently traveling at 0 m/s relative to the couch you are sitting upon. And simultaneously, you are traveling at .996c relative to a really energetic cosmic ray flying in your direction. Both of those frames are equally valid. If you were on a rocket, hurtling directly toward that cosmic ray at, let's say for fun, .5c relative to your couch that you were on moments ago. What do you think your perception is regarding how fast that cosmic ray is now flying at you? And what do you think the cosmic ray, if it had eyes, would perceive your velocity to be? If your answer to both is less than c, I really don't know why you are still posting in this thread. And if your answer is greater than c, then I think you'll understand before you even reply that you need to read some things.

Yes, the velocities will never exceed c.
According to UA the Earth doesn't have constant velocity, it has acceleration, and when a cosmic rays approach Earth with constant velocity it takes a certain amount of time to get from the upper atmoshpere (atmolayer) to the ground. During this time the Earth accelerates at 9.81 m/s^2 with respect to the cosmic ray. The Earth's change in velocity during this time is very small but it's still there, do you agree?   

[Clyde Frog]

During this time the Earth accelerates at 9.81 m/s^2 with respect to the cosmic ray.

It most certainly does not. Relativistic effects would make for pretty pronounced differences in the perception of the Earth's acceleration when observed from the cosmic ray's side of things versus the observation someone would make on the surface of the Earth. The cosmic ray would "see" the Earth accelerating at a much smaller rate. Smaller with each passing moment. Yet the observer on the Earth would observe no change in the Earth's acceleration at all.