Galilean principle of relativity

[roineust]

Galilean principle of relativity is for sure not absolutely true, isn't it?

Say one has a pool full of water within a spaceship, if the spaceship is accelerated and then acceleration stops, one can look at the ripples in the pool, analyze their form and then tell, up to a certain degree of preciseness, if there was acceleration, how long ago, what was the force accelerating? nop? and now say, the types of materials analyzable and measuring equipment become more and more available, then it can get to a point that some type of liquid-gas within the spaceship can be analyzed by some sort of newly discovered particles, and one can tell if the spaceship was accelerated up to 100 million years ago up to a 1000 years plus minus preciseness. Is there a basic physical law that denies that possibility?

Now, doesn't the special principle of relativity start at its very first sentences, by relying on the Galilean principle of relativity?

If there is any well informed math-physics guy here, who also thinks that this is not a die-hard joker question-view, then, can you please try to explain to me, how does this change the very mathematical basics of SR?

 

[PeterDonis]

The Galilean principle of relativity doesn't say anything about accelerated motion; it only says that inertial motion (i.e., free-fall, unaccelerated motion) is locally indistinguishable from rest. The principle of relativity in SR is the same; it says nothing about accelerated motion.

 

[WannabeNewton]

The Galilean transformations are limiting cases of the Lorentz transformations. The principle of relativity does not state that the transformations between inertial frames must necessarily be Galilean transformations. In SR, it leads to the Lorentz transformations after making an extra assumption. The principle of relativity is a statement about the non-privileged nature of inertial frames.

 

[roineust]

WanabeNewton and Peter:
1. Peter: In the scenario i presented, no measuring is done when spaceship is accelerating. Only when acceleration is over and even a million years after last and only acceleration took place .
2. Wanabe: In your comment, you are shooting over my laymen head, please speak very plainly and not these wizard incantation words such as transformation. I think that i described the scenario very clearly.

 

[PeterDonis]

In the scenario i presented, no measuring is done when spaceship is accelerating. Only when acceleration is over.

That doesn't mean that the Galilean principle of relativity requires that everything before acceleration look exactly the same as everything after acceleration. The principle doesn't say that every state of inertial motion has to look exactly the same; it only says that every state of inertial motion must obey the same laws of physics. Both of the inertial states in your scenario--the state before the acceleration, and the state after the acceleration--are valid solutions of the Newtonian laws of physics (which are the appropriate laws if we're talking about the Galilean principle of relativity); they are just different solutions.

 

[WannabeNewton]

Peter very clearly addressed your example in post #2. If you introduce acceleration for any period of time, you are clearly breaking the symmetry (implied by the principle of relativity) amongst inertial frames. All the POR says is that inertial frames by themselves are unprivileged. It doesn't state that states before and after acceleration must be identical.

 

[roineust]

Peter,
If i can know up to a very long ago period of time and up to a very high degree of preciseness, that an inertial state object was accelerated, then this piece of data should be considered as coming from an internal quality of matter itself, nop? - then nature does not act the same between these states - then laws of nature DO NOT act the same under different inertial states.

Of course the question is how long ago and how precise, should one be, to say this is an internal property of matter itself or is there some kind of physical principle or natural property ,that states that, no matter how precise and how long ago i will be, at measuring these ripples in the pool, still it is not an internal property of matter, because something else that has to do with SR or light or what not, always, always, always will be some degrees more precise than the hypothetical precision i am referring to.

But then, i am saying that at least that absoluteness aura of Galilean principle is not true. If i can get in this spaceship and have no windows in it (i mean outside ship radio measurement of any kind) and no active measurements made while accelerating and still i can tell where was my departure point, up to a certain degree of precision - can such a measurement ever be precise enough to conflict or change SR or would it alway 'lag' at the same precision error behind SR precision for some reason and never get the departure point better and better, as measuring equipment evolves?

What are the mathematical boundaries that make it an internal property of matter and how can this view be mathematically expressed in relation to SR, or without relation to SR, that is what i am trying to understand.

 

[PeterDonis]

If i can know up to a very long ago and up to a high degree of preciseness, that an object was accelerated, then this an internal quality of matter itself - then nature does not act the same between these states - then laws of nature DO NOT act the same under different inertial stats.

I think you are confusing properties of the laws with properties of particular solutions. The same laws of nature can have multiple particular solutions that have different properties. There is nothing in that that is inconsistent with the principle of relativity.

 

[PeterDonis]

What are the mathematical boundaries that make it an internal property of matter and how, mathematically this can happen, that is what i am trying to understand.

I'm not sure how I can address your issue mathematically since (a) you haven't written down any mathematical description of the issue, and (b) you are basically claiming that the math I would be using, which is based on the principle of relativity, is wrong. So I'm not sure what you're looking for here.

 

[Mentz114]

Peter,
If i can know up to a very long ago period of time and up to a very high degree of preciseness, that an inertial state object was accelerated, then this piece of data should be considered as coming from an internal quality of matter itself - then nature does not act the same between these states - then laws of nature DO NOT act the same under different inertial stats. Of course the question is how long ago and how precise, should one be, to say this is an internal property of matter itself. But then, i am saying that at least that absoluteness aura of Galilean principle is not true. What are the mathematical boundaries that make it an internal property of matter and how, mathematically, can this view be mathematically expressed in relation to SR or without relation to it, that is what i am trying to understand.

This idea has been floated many times by folk who want there to be absolute motion and an absolute state of rest. It is pointless and adds nothing to the understanding of the universe.

 

[roineust]

Mentz, yours is a philosophical statement, i think that what i am asking here, indeed with my very laymen words and understanding, are physical, experimental and mathematical questions. BTW, please refer me to a thread that its subject is exactly or as close as possible to this pool experiment i am asking about here. Thanks.

 

[Dale]

If i can know up to a very long ago period of time and up to a very high degree of preciseness, that an inertial state object was accelerated, then this piece of data should be considered as coming from an internal quality of matter itself, nop? - then nature does not act the same between these states - then laws of nature DO NOT act the same under different inertial states.

This is a non sequitor. You are saying if we can distinguish non inertial motion from inertial motion then the laws of physics are not the same in different inertial frames. That simply doesn't follow logically.

Take a law of physics, expressed in one inertial frame. Transform that law to a different inertial frame. If the expression in the new frame has the same form as in the old frame then that law is the same in all inertial frames.

 

[Mentz114]

Mentz, yours is a philosophical statement, i think that what i am asking here, indeed with my very laymen words and understanding, are physical, experimental and mathematical questions. BTW, please refer me to a thread that its subject is exactly or as close as possible to this pool experiment i am asking about here. Thanks.

What you are suggesting is that some matter could encode all the information in its worldline from some time in the past to the present, say, and that this information will alter the way the matter behaves. It is possible in principle to build a machine that can do the path recording for a spaceship* - but how would a brick or a bowl of hot soup achieve this ?

In what way could the presence or absence of the information affect the physics ?

* a smartphone equipped with GPS and some software can record a rough itinerary ( worldline ) as it is carried about.

 

[roineust]

If it is possible to know the local time at another inertial state, up to a certain degree, without communicating by radio waves with that other inertial state, then does it not conflict with any physical principle? Never has any relativity principle denied the possibility of knowing the time at other inertial states, without radio communication?

 

[Dale]

If it is possible to know the local time at another inertial state, up to a certain degree, without communicating by radio waves with that other inertial state, then does it not conflict with any physical principle?

No, why would it?

 

[Mentz114]

If it is possible to know the local time at another inertial state, up to a certain degree, without communicating by radio waves with that other inertial state, then does it not conflict with any physical principle?

If one could optically track the path of another body for an interval of time, then combined with knowledge of the local gravitational fields it is possible to calculate how much time would have elapsed on a clock on that path. I don't know if that counts as 'communicating' to you.

if also, the time is not the same as the other state, would that mean that nothing has changed here? Never has any relativity principle denied the possibility of knowing the time at other inertial states, without radio communication?

I can't follow this, sorry.

 

[roineust]

DaleSpam,

Because of the famous example, titled, as much as i recall, 'Galilean principle or relativity', with a man waking up from deep sleep, sitting at the bottom of that windowless inertial state ship, unable to say if the ship has left harbor or not.

 

[roineust]

Mentz,

Doesn't the pool replace the need to optically or by radio wave, communicate with that other inertial state, up to a certain degree of precision? If it does, doesn't it conflict with any existing physical principle?

Please take into account that i am referring to a case, where the two states where 'together', 'one', at a certain point back in time, and that the other state, the 'base ship' not the 'ship', did not change its state, since then ,while the 'ship' did - and the 'ship' can still use the pool to tell the local time at the 'base ship', without radio communicating to it. In this scenario, it is a negligible gravity area of space.

Regarding the other part of what i wrote, that you said you don't follow, i have rephrased it.

 

[Mentz114]

Mentz,

Doesn't the pool replace the need to optically or by radio wave, communicate with that other inertial state, up to a certain degree of precision? If it does, doesn't it conflict with any existing physical principle?

The recording device (your 'pool') records its own path so I don't see how it can tell you about another worldline.

Please take into account that i am referring to a case, where the two states where 'together', 'one', at a certain point back in time, and that the other state, the 'base ship' not the 'ship', did not change its state, since then ,while the 'ship' did - and the 'ship' can still use the pool to tell the local time at the 'base ship', without radio communicating to it. In this scenario, it is a negligible gravity area of space.

The same remark applies. When the split happens, the pools are no linger recording the same worldline.

The only way to predict accurately the time elapsed on another worldline is to have knowledge of the worldline and details of the gravitational configuration ( which includes the possibility of no gravity).

 

[roineust]

OK, so the formulas stay the same, and the term 'unprivileged' implies nothing about two identical experimental environments (ships), that all types of possible measurements becoming more and more identical between them, as more and more time passed from last non-inertial state goes by (measurements that have nothing to do with these two ships outside, only with its inside parts and material), if the whole experiment equipment tools and environment are exactly identical, but both copies are at different inertial states - 'unprivileged' will not imply that these identical experimental environments, will tend to show exactly the same measurement results, as time passes by?

 

[Dale]

Because of the famous example, titled, as much as i recall, 'Galilean principle or relativity', with a man waking up from deep sleep, sitting at the bottom of that windowless inertial state ship, unable to say if the ship has left harbor or not.

That is just an easy to grasp example. The scientific embodiment of the principle is in the invariance of the laws under the appropriate transform.

 

[Dale]

'unprivileged' will not imply that these identical experimental environments, will tend to show exactly the same measurement results, as time passes by?

Correct, unprivileged does not imply that.

 

[yuiop]

Let us say we had two radioactive blocks of material that formed at the same time and for some reason one of the blocks was briefly accelerated to relativistic speeds shortly after forming. Thousands of years later tthese blocks are discovered and both are moving inertially. When these blocks are examined carefully we discover that one the blocks is not homogeneous and the radioactive material at one end of the block has decayed to greater degree than at the other end. We can assume that this was the block that was accelerated while the other remained inertial (if we assume that both blocks were initially homogeneous, although we have no proof of that). There is nothing about this scenario that contradicts relativity. There are numerous other ways to make accelerometers that record the acceleration history of an object without any reference to external objects.

 

[roineust]

OK - so i still have here two more replies, that i don't completely (feel that i) understand:

1.Ments: please explain - if i can be that sort of 'Oracle' and 'look' at the ripples in the pool on my ship, why can't i tell the local time at the 'Base ship' (if it did not accelerate since)? If i can tell from the ripples, that 'these' kind of ripples, of a specific case, mean that my ship was accelerated at, say, a 1000 Newtons, for 100 seconds, and 100,000 seconds ago? This is supposed to be enough information to tell me the local time, at the 'Base ship', nop? if you did not understand, that hypothetically, i think, so many variables can be extracted from the ripples, then yes, that is what i mean. So now, does it still not conflict with any 'papa' physical principle?

2.yuiop: Is there no physically implied difference, between saying that i 'built' an accelerometer and that, intrinsically, every little bit of material in the universe, has a 'built in' accelerometer? Or maybe even every little bit of material in the universe, has a built in 'accelerometer', with a built-it 'memory buffer', for 'saving' a set of accelerations, it went through?

 

[Dale]

There is nothing about this scenario that contradicts relativity. There are numerous other ways to make accelerometers that record the acceleration history of an object without any reference to external objects.

Correct. Of course, you can always attach a clock and an accelerometer to a memory stick and simply record the data. The clock, accelerometer, and memory stick all work according to the laws of physics. So nothing that you can do with them represents a violation of the laws of physics.

 

[roineust]

OK,
DaleSpam - then why is it so important, for each and every junior relativity popular-science writer, already 80 or 100 years in a row now, to call time a '4th dimension' (not to mention the 1000 dimensions guys with the parallel universe hoohaa) - here you go - no added dimensions! only 3 of them! the rest of the data can, hypothetically, be extracted from matters 'inbuilt' accelerometer+memory stick.

 

[Dale]

It requires four coordinates to specify an event. Three coordinates represent space, one represents time. Therefore there are four dimensions.

It has nothing to do with where or how information about the event is stored.

 

[roineust]

Can't i replace, the, 'time', in 'one (coordinate) represents time' with 'one (coordinate) represents the state of the matter' - now the 'there are things that human senses cannot reach, such as higher dimensions' philosophical, irritating, lecture, becomes kind of diffused, nop?

 

[Dale]

I don't know what you are talking about. What is "nop", and what is the relationship between human senses and higher dimensions?

If you have a device where "the state of the matter" depends on time then you have a clock.

 

[roineust]

No, you have a device, where time depends on "the state of the matter" and not vice versa. Would that be just saying the same and replacing the order of words? if so, then i have no problem. 'Nop?' means 'Is that right or wrong and why?'

 

[Dale]

No, you have a device, where time depends on "the state of the matter" and not vice versa.

I don't see the distinction you are trying to make. If you have a function $y=f(x)$ then you can say y depends on x. You can also invert f and find that $x=f^{-1}(y)$ and say x depends on y. So they are equivalent assuming that f is invertible.

Now, if f is not invertible then you cannot do that, but you are, by construction, choosing scenarios where f is invertible. So the "not vice versa" doesn't make sense here. Furthermore, if you were to construct a scenario where f was not invertible then it would always be the state of matter that is a function of time, not the other way around.

'Nop?' means 'Is that right or wrong and why?'

Please stick with English. It doesn't help communication to invent nonsense words and assign them meanings which are opaque to your audience.

 

[roineust]

OK,
I will chose another word or phrase instead of 'Nop?'.

Can you explain or give an example of a non-invertible scenario, and then explain why in such a scenario it is the function of time and not the other way?

 

[Dale]

Sure, any periodic state is non-invertible. The matter is the same state at t and at t+T. So you can say that the state depends on time, but you cannot invert that to say that time depends on the state because you would have a multi-valued function, i.e. it would be multiple times at the same state.

 

[D H]

Can you explain or give an example of a non-invertible scenario, and then explain why in such a scenario it is the function of time and not the other way?

Suppose that while standing on a hard tile floor you are holding a ceramic coffee cup, full of coffee. The cup slips out of your fingers, drops to the floor, and shatters. The end result: A mess on the floor that you have to clean up. You will never see that mess magically reassemble itself into an intact coffee cup and then magically jumps from the floor up to your hand.

[Edit] That's two rather different answers to your question. Dale addressed the issue of invertibility in terms of a function that does not have an inverse. I addressed it in terms of the arrow of time. Which sense did you mean by non-invertible?

 

[roineust]

OK,
I guess that now you are already in the arena of rigorous mathematical definitions, so i will ask in short fashion question and maybe will be able to understand what you are saying: What is the problem with multiple time at the same state?