Understanding Relativity: A Blind Man's Perspective on Time and Physics

[newTonn]

Dear all,
I have a simple question.
Consider a long railway station. Say 2 km’s long. Station master put two synchronized clocks at each end of the platform. These clocks are showing as well shouting the time. Synchronization of time was done by seeing the clock but not hearing the clock.
A similar third clock was fixed inside the last compartment of the train. This was also synchronized by the station master by the same way (say yesterday when the train halted at the station).
Now consider a blind man is sitting inside the last compartment. Train is crossing the station almost with a uniform speed(say,80% speed of sound).Blind man can only hear the time. When the last compartment crosses the first clock, he can hear that clock and the clock inside the train is telling same time, but the clock at the other end of the platform is telling a time in the past.
As he approaches the other clock, he can hear that clock is moving fast(telling the time faster ) and finally when he reaches the other clock, he can hear the clock inside the train and the far end clock are telling same time, but the rear clock become slower and is telling a time in the past.
As a mathematician or physics expert, what you will do?
You will make appropriate corrections to the normal formula, incorporating the speed of train, speed of sound and the position of blind man at that instance.
But what the blind man will think if he doesn't know this explanation.He will of course deduce that the law's of physics are violated and the clocks will move faster when you approaches it and will move slower when you receedes from it.
If we establish the position of the observer at the instance,and incorporate the data to result,you can see that No fundamental laws are violated even in the case of of an accelerated frame.
Somebody please tell me with a simple example,how the fundamental laws are violated in an accelerated frame

 

[Ich]

Somebody please tell me with a simple example,how the fundamental laws are violated in an accelerated frame

Nobody claims that they are violated, so it could be hard to find an example.

 

[belliott4488]

newTonn - perhaps you are confusing the statement that "The Laws of Physics must be stated differently in an accelerating frame" to mean that there are fundamental laws being violated. This is not the case.

All that statement means is that if you were to place a billiards table on a carousel (merry-go-round in the US), or on an accelerating train car, both of which are accelerating frames, then you could not shoot pool the way you do in an inertial frame. This doesn't mean it can't be done, you just have to take the acceleration into account when you take your shot. This would mean taking into account the centrifugal and coriolis forces in the rotating frame, as well as the apparent force to the rear on the train (all inertial reaction forces).

The result of all of this is that accelerating frames are fundamentally different from inertial frames. We can always distinguish between them because of the behavior of the Physics that takes place in them. Contrast this with inertial frames, which cannot be distinguished one from another - in particular ones in motion from ones at rest - because Physics behaves the same way in all of them.

 

[RandallB]

clocks are showing as well shouting the time. Synchronization of time was done by seeing the clock but not hearing the clock.
A similar third clock was fixed inside the last compartment of the train. This was also synchronized by the station master by the same way (say yesterday when the train halted at the station). This

Allowing the Station Master to synchronize a train clock is not acceptable in a Relativity problem. However since this is not a relativity problem the speed of light signals from a stationmaster can be considered “instantaneous” when working with such slow speeds and accelerations. This is just Doppler effects of signals in a medium (sound in air). No reason a blind man can nor understands or even discover the simple issues involved in such a classical problem.
Not at all the same as relativistic issues raised by something that moves unencumbered by a medium (light).

Relativistic Linear Accelerations and GR Curves can leave you unable to define distances that can be agreed upon by all observers. A problem of defining a dependent background that has not been resolved. Rather complex issue and there is not agreement that GR can even have a dependent background.
For info look for Lee Smolin - Perimeter Institute for Theoretical Physics ; not an easy read.

 

[Dale]

Somebody please tell me with a simple example,how the fundamental laws are violated in an accelerated frame

I don't know how this question relates to your blind man on the train example (I thought you were going to go somewhere else with the blind man).

Anyway, to answer your question: Newton's laws are clearly violated in an accelerated frame. Take an example of a rocket in deep space away from any gravitational field, which is as simple of an example as I can come up with.

With the engines off, if the pilot gently releases a ball in the cockpit it will float as per Newton's 1st law. If the pilot pokes the ball the pilot will feel a reaction force as per Newton's 3rd law and the ball will accelerate as per Newton's 2nd.

With the engine on, if the pilot releases the ball it will accelerate to the floor, violating Newton's 1st and 2nd laws. So you can postulate a ficticious force which attracts things in the cockpit to the floor in order to satisfy the 1st and 2nd laws, but then that leaves the 3rd law violated.

 

[YellowTaxi]

With the engine on, if the pilot releases the ball it will accelerate to the floor, violating Newton's 1st and 2nd laws. So you can postulate a ficticious force which attracts things in the cockpit to the floor in order to satisfy the 1st and 2nd laws, but then that leaves the 3rd law violated.

what?

 

[Dale]

Can you be more specific?

 

[YellowTaxi]

Right, sorry.
It just seemed a very odd thing to say that Newton's laws don't apply just because you interpreted the spacecraft acceleration as the creation of a fictitous force, and in your opinion this automatically violates the laws of motion.

I was just hoping you could explain what you were saying explicitly that's all.
ie I was just asking you to be more specific ;-0

 

[YellowTaxi]

Surely he knows the engines engaged. i.e. That rocket fuel is being shot out the rear at high velocities in order to push the body of the spacecraft (of much greater mass) in the opposite direction. This is in fact is a perfect example of Newton's 3rd law. Also known as the conservation of linear momentum.

The fact that the ball is not subject to any forces is trivially obvious.

 

[belliott4488]

I don't know how this question relates to your blind man on the train example (I thought you were going to go somewhere else with the blind man).

Anyway, to answer your question: Newton's laws are clearly violated in an accelerated frame. Take an example of a rocket in deep space away from any gravitational field, which is as simple of an example as I can come up with.

With the engines off, if the pilot gently releases a ball in the cockpit it will float as per Newton's 1st law. If the pilot pokes the ball the pilot will feel a reaction force as per Newton's 3rd law and the ball will accelerate as per Newton's 2nd.

With the engine on, if the pilot releases the ball it will accelerate to the floor, violating Newton's 1st and 2nd laws. So you can postulate a ficticious force which attracts things in the cockpit to the floor in order to satisfy the 1st and 2nd laws, but then that leaves the 3rd law violated.

I disagree pretty strongly with this characterization. Certainly Newton's Laws are not incorrect - that would be an alarming claim to make (QM not withstanding). Of course we can describe the dynamics on board the spaceship with no trouble if we refer to the inertial coordinates outside the spaceship - so Newton's Laws are still working. What does not work is simply to apply Newton's Laws using the coordinate frame of the spaceship as if it were an inertial frame. Instead, the Laws on board the spaceship would have to be modified to take into account the effects of the acceleration. In this case, Physics wouldn't even look so unusual, since a constant uniform acceleration could simply be accounted for as we do the approximately constant gravitational acceleration at the Earth's surface. A rotating frame is trickier, but it can be done as well.

What breaks down is the form of the laws and the forces at work. I would not conclude from this that Newton's Laws have been violated.

 

[Dale]

It just seemed a very odd thing to say that Newton's laws don't apply just because you interpreted the spacecraft acceleration as the creation of a fictitous force, and in your opinion this automatically violates the laws of motion.

Surely he knows the engines engaged. i.e. That rocket fuel is being shot out the rear at high velocities in order to push the body of the spacecraft (of much greater mass) in the opposite direction. This is in fact is a perfect example of Newton's 3rd law. Also known as the conservation of linear momentum.

The fact that the ball is not subject to any forces is trivially obvious.

Yes, it is obvious if you are in an accelerated reference frame in general, even when you cannot see things like the engines and the rocket fuel. The OP's question was simply about how fundamental laws of physics were violated in accelerated frames, not about whether or not it was obvious.

The equation of motion for a free object in the cockpit's rest frame (engine on) follows a parabola. So it is accelerating without a force acting on it, which is in violation of Newton's first and second law. Since you know that a parabola is the result of a constant force you can postulate the existence of a ficticious force to explain the motion, but this ficticious force has no source, which is in violation of Newton's third law. So in the cockpit's frame you cannot simultaneously satisfy all of Newton's laws.

 

[YellowTaxi]

OK thanks for the response Dale. I always appreciate your answers, simply because you seem to actually understand what you're talking about.

In all honesty I only looked at this thread because I was wondering if there were any startling similarities between how things might 'look' for a blind man, and how they look to people who have eyes to perceive the transmission of light. Actually I'm rather disappointed that the subject being discussed hasn''t really addressed that question, and has veered off into a different direction altogether to what I expected. But maybe I misunderstood what the OP was getting at. I didn't follow all that he said.

ps I think it's spelt fictitious, not 'ficticious'

 

[newTonn]

Yes, it is obvious if you are in an accelerated reference frame in general, even when you cannot see things like the engines and the rocket fuel. The OP's question was simply about how fundamental laws of physics were violated in accelerated frames, not about whether or not it was obvious.

The equation of motion for a free object in the cockpit's rest frame (engine on) follows a parabola. So it is accelerating without a force acting on it, which is in violation of Newton's first and second law. Since you know that a parabola is the result of a constant force you can postulate the existence of a ficticious force to explain the motion, but this ficticious force has no source, which is in violation of Newton's third law. So in the cockpit's frame you cannot simultaneously satisfy all of Newton's laws.

Sorry,the equation of motion for free object will be a straight line in the absence of gravity.
If you define an absolute(fixed) space,you can see that the ball is either at rest(if the rocket shoots from zero) or ball is having a momentum equal to that of the rockets initial velocity x mass of the ball-the velocity at the instance when the ball was dropped (balls position after 't' seconds will depend on this momentum and rockets position will depend on the acceleration it produced).No Laws are violated here.

 

[Dale]

Sorry,the equation of motion for free object will be a straight line in the absence of gravity.

Not in an accelerated frame, that is the whole point.

 

[Dale]

In all honesty I only looked at this thread because I was wondering if there were any startling similarities between how things might 'look' for a blind man, and how they look to people who have eyes to perceive the transmission of light. Actually I'm rather disappointed that the subject being discussed hasn''t really addressed that question, and has veered off into a different direction altogether to what I expected.

Me too. I actually had a fundamental misunderstanding of SR for about 5 years due to my own musings about blind men, so I looked to see if the OP was making the same logical mistake I was.

 

[Dale]

What does not work is simply to apply Newton's Laws using the coordinate frame of the spaceship as if it were an inertial frame. Instead, the Laws on board the spaceship would have to be modified to take into account the effects of the acceleration.

You say "modified" I say "violated". It is only a semantic difference, we are both referring to the same changes that you must make in your computations in order to get the right prediction for a physics experiment performed in the accelerated frame.

In this case, Physics wouldn't even look so unusual, since a constant uniform acceleration could simply be accounted for as we do the approximately constant gravitational acceleration at the Earth's surface. ... I would not conclude from this that Newton's Laws have been violated.

Except that there is no massive object exerting the "gravitational acceleration" on which to place the equal and opposite reaction force required by the 3rd law. I don't know of a formulation that simultaneously satisfies both the 2nd and 3rd laws in an accelerated frame. I don't object to "modified", but I also think "violated" is a reasonable description since you cannot simultaneously satisfy all 3 laws.

 

[newTonn]

Not in an accelerated frame, that is the whole point.

No.In the absence of gravity,the onlycase it become parabola is (that also in the rockets frame only),if the rocket rotates with respect to the ball(i agree that is an acceleration).If we fix an absolute space you can see the ball is either at rest or in straight line and the rocket is rotating.

 

[Ich]

I don't know of a formulation that simultaneously satisfies both the 2nd and 3rd laws in an accelerated frame.

That formulation was done by http://en.wikipedia.org/wiki/D%27Alembert%27s_principle" .
newTonn: What is your point?

 

[newTonn]

You say "modified" I say "violated". It is only a semantic difference, we are both referring to the same changes that you must make in your computations in order to get the right prediction for a physics experiment performed in the accelerated frame.

Except that there is no massive object exerting the "gravitational acceleration" on which to place the equal and opposite reaction force required by the 3rd law. I don't know of a formulation that simultaneously satisfies both the 2nd and 3rd laws in an accelerated frame. I don't object to "modified", but I also think "violated" is a reasonable description since you cannot simultaneously satisfy all 3 laws.

Laws are modified only,not violated.For example,A bus is accelerating towards a man who is standing on the road.From the drivers reference frame,the man is accelerating towards him.
Can we introduce a fixious force which is bringing the man towards the driver,and hence solve the dynamics?.and can we assume that the 1st and 2nd laws are violated in this case?.

 

[neopolitan]

Laws are modified only,not violated.For example,A bus is accelerating towards a man who is standing on the road.From the drivers reference frame,the man is accelerating towards him.
Can we introduce a fixious force which is bringing the man towards the driver,and hence solve the dynamics?.and can we assume that the 3rd law is violated in this case?.

As far as Newtonian physics goes, won't the bus driver happily say he himself is accelerating and the man is standing still?

This fixation on claiming oneself to be at rest is more of an Einsteinian thing, isn't it? (By the way, you don't have to nominate yourself to be at rest, you just nominate a rest frame and do your calculations from there. I think.)

cheers,

neopolitan

 

[Dale]

Laws are modified only,not violated.

Again, this is only semantics, we are talking about the same alterations to the equations. By the way, it was you who introduced the word "violated" in your OP, not me. If you now prefer the word "modified" I am fine with that word too, as already discussed with belliott.

For example,A bus is accelerating towards a man who is standing on the road.From the drivers reference frame,the man is accelerating towards him.
Can we introduce a fixious force which is bringing the man towards the driver,and hence solve the dynamics?.and can we assume that the 1st and 2nd laws are violated in this case?.

You must introduce a fictitious force on the man in order to satisfy the 2nd law. This is simply a more confusing version of my rocket example.

 

[Dale]

As far as Newtonian physics goes, won't the bus driver happily say he himself is accelerating and the man is standing still?

This fixation on claiming oneself to be at rest is more of an Einsteinian thing, isn't it? (By the way, you don't have to nominate yourself to be at rest, you just nominate a rest frame and do your calculations from there. I think.)

You are exactly correct. The same thing applies in relativity, you don't need to use a reference frame where anything is at rest. The results will all come out correct whatever inertial frame you choose. Sometimes choosing a specific frame will make the computations come out easier, that is all.

 

[Dale]

That formulation was done by http://en.wikipedia.org/wiki/D%27Alembert%27s_principle" in particular.

 

[Dale]

No.In the absence of gravity,the onlycase it become parabola is (that also in the rockets frame only),if the rocket rotates with respect to the ball(i agree that is an acceleration).If we fix an absolute space you can see the ball is either at rest or in straight line and the rocket is rotating.

Work out the math, it is a parabola in a uniformly accelerating reference frame, it is not a parabola in a rotating reference frame.

You really need to do some basic homework on coordinate transformations here. Why don't you start by deriving the transformation equation for a reference frame undergoing uniform acceleration along the x axis. Start in the standard configuration where all of the axes are parallel to each other, and where the origins coincide at t=t'=0. Also, make the further simplifications that the relative velocity of the two frames is 0 at t=t'=0 and neglect any relativistic effects.

 

[Ich]

The inertial forces in the D'Alembert approach also violate Newton's 3rd law. See this post in particular.

I can't follow you. Why should the inertial forces violate the third law?

 

[RandallB]

Except that there is no massive object exerting the "gravitational acceleration" on which to place the equal and opposite reaction force required by the 3rd law.
I don't know of a formulation that simultaneously satisfies both the 2nd and 3rd laws in an accelerated frame. I don't object to "modified", but I also think "violated" is a reasonable description since you cannot simultaneously satisfy all 3 laws.

What are you talking about? Newton’s laws are perfectly capable of taking care of all these examples.
At least for your example you have shown no violation or even a modification. Changing speeds and forces and interactions all based on those 3 laws resolve all the issues quite fine with no problem including defining where and when everything is relative to a stationary buoy in open space where your experiment is being conducted and how much mass is ejected from the spaceship at what speeds to create an apparent force against any loose objects inside the ship.

You don’t run into a problem until you discover the need for SR. Now all of a sudden; changes in position relative to the buoy are inconstant due to different opinions on fundamental measurements for time and distance depend upon what frame you happen to measure them from.

And that can almost (but not quite) be solved by establishing a preferred reference frame, as they do in astrophysics. And that does not violate any requirement that physics work the same everywhere, it only means that when measurements in one inertial frame are compared with some other inertial frame that the experimenters must consider data from other reference frame sources to define a preferred frame (the one where time passes fastest). Only then can correct conversions be made one frame to another. Being able properly relate different frames via a preferred frame is the only way Astrophysics can define distances across space. They use CMBR to establish the most popular preferred frame.

But preferred frame, Newton and SR still could not resolve large scale details that required the using GR (not the same as space-time which Einstein did like much ). But some detail is sacrificed in using GR as well – you do not retain a dependent background.

So to answer the OP ?
“Somebody please tell me with a simple example, how the fundamental laws are violated in an accelerated frame”

If you have two observers set out on preplanned paths known to both of them as they set out in different directions on routes intended to return to a common starting buoy. High speeds, accelerations, and passing by a couple high mass gravitational objects in route requires the use of GR to resolves on paper exactly where the buoy and the other traveler will be at the end of the trip. The problem is GR does not give a good nor constant prediction of where all three objects will be relative to each other at the end of the trips.

Now I can “tell” this in this “simple example”; But explaining it requires understanding the difference between a “dependent” vs. “independent” background. As I said before that is not so easy to get – you have a bit of research to do on that one.

 

[YellowTaxi]

You are exactly correct. The same thing applies in relativity, you don't need to use a reference frame where anything is at rest. The results will all come out correct whatever inertial frame you choose. Sometimes choosing a specific frame will make the computations come out easier, that is all.

So would that also work if the acceleration isn't a constant ?
Can't visualise it simplifying things, but I just wondered. Maybe it can.

 

[belliott4488]

DaleSpam:

I echo the question that some others asked: why is the invocation of a fictitious force automatically a violation of any of Newton's 3 laws? I agree it's a violation of his law of gravity, but that's not one of the three laws. We could stick a charged particle in an electric field, and Newton's laws say nothing about the source of the force, but they are more than capable of describing any resulting motion.

I would say that the same is true in the rocket frame. The spaceman observes some constant force acting on him and his collection of tennis balls, and uses Newton's law to predict - correctly - how they move when he tosses them.

IOW, Newton's laws seem to me to be independent of the nature or source of the forces; they simply say how massive bodies react in their presence.

 

[Dale]

So would that also work if the acceleration isn't a constant ?
Can't visualise it simplifying things, but I just wondered. Maybe it can.

I cannot imagine a situation where it would simplify things either, but if you did it correctly you would get the right answer.

 

[YellowTaxi]

I cannot imagine a situation where it would simplify things either, but if you did it correctly you would get the right answer.

Isn't it connected with what Einstein had to do when he wanted to transform away the acceleration of gravity when the field was varying with position in space ?

 

[JesseM]

As far as Newtonian physics goes, won't the bus driver happily say he himself is accelerating and the man is standing still?

This fixation on claiming oneself to be at rest is more of an Einsteinian thing, isn't it? (By the way, you don't have to nominate yourself to be at rest, you just nominate a rest frame and do your calculations from there. I think.)

I've told you many times before that this is a misconception of yours--when solving problems in relativity you don't pick one frame to be "the rest frame", the phrase rest frame is only used in connection with particular objects, like "the rest frame of the rocket". You are free to do calculations in multiple frames, including ones where none of the objects you are analyzing are at rest; there is no "fixation" on claiming oneself to be at rest, although it is traditional in both Newtonian physics and relativity to use "my frame" as shorthand for "the frame where I am at rest".

 

[YellowTaxi]

I've told you many times before that this is a misconception of yours--when solving problems in relativity you don't pick one frame to be "the rest frame", the phrase rest frame is only used in connection with particular objects, like "the rest frame of the rocket". You are free to do calculations in multiple frames, including ones where none of the objects you are analyzing are at rest; there is no "fixation" on claiming oneself to be at rest, although it is traditional in both Newtonian physics and relativity to use "my frame" as shorthand for "the frame where I am at rest".

Well, I thought Einstein was interested in looking at things from the point of view of objects in free-fall. i.e. from a 'place' where the gravity field was undetectable and thus one which could easily be considered in effect a genuine inertial frame [a pure rest frame].
ie A specific frame in which the (possibly varying) acceleration through space is 'invisible' so long as you don't look out the window.

 

[Dale]

I can't follow you. Why should the inertial forces violate the third law?

What are you talking about? Newton’s laws are perfectly capable of taking care of all these examples.
At least for your example you have shown no violation or even a modification.

I echo the question that some others asked: why is the invocation of a fictitious force automatically a violation of any of Newton's 3 laws?

I would say that the same is true in the rocket frame. The spaceman observes some constant force acting on him and his collection of tennis balls, and uses Newton's law to predict - correctly - how they move when he tosses them.

IOW, Newton's laws seem to me to be independent of the nature or source of the forces; they simply say how massive bodies react in their presence.

OK, I see that I am going to have to justify my statements a little better. I apologize for thinking my points were obvious. I was obviously not writing as clearly as I thought I was.

The question I am addressing is: "How are Newton's laws violated/modified in an accelerated reference frame?" I will address only v<<c so that we don't need to worry about relativistic effects and we will stick with the rocket in deep-space scenario so that we don't need to worry about gravity, friction, air resistance or any other confounding factors.

First, let's start in the inertial frame where the rocket is initially at rest at the origin with the engines off. This will be the unprimed frame and all unprimed coordinates will reference this frame.

At time t=0 the rocket turns on generating a steady 2000 N of thrust in the x direction. The rocket masses 1000 kg. The thrust is the only force acting on the rocket so, by Newton's 2nd law, the acceleration is 2 m/s². In SI units, the equations of motion for the rocket are therefore:
r(t)=(t²,0,0)
vr(t)=(2t,0,0)
ar(t)=(2,0,0)
for t>0.

At t=1 a ball is released in the cockpit. After release there is no force acting on the ball, so by Newton's 1st law, the acceleration is 0. In SI units, the equations of motion for the ball are therefore:
b(t)=(2t+1,0,0)
vb(t)=(2,0,0)
ab(t)=(0,0,0)
for t>1.

So far we have considered Newton's 2nd and 1st law, but not the 3rd law. The only force considered thus far is the thrust. There is a thrust force which is acting on the rocket exhaust which is equal-and-opposite to the thrust force acting on the rocket. This force accelerates the exhaust and satisfies Newton's 3rd law.

Now we will consider the situation in the primed reference frame in which the rocket is at rest at the origin for t>0, i.e. this frame is accelerating at a rate of 2 m/s² in the positive x direction wrt the inertial frame. The transformation equations are:
t'=t
x'=x-t²
y'=y
z'=z

By transforming we obtain the equations of motion for the rocket in the primed frame:
r'(t')=(0,0,0)
vr'(t')=(0,0,0)
ar'(t')=(0,0,0)
t'>0.
Since there is a non-zero net force acting on the rocket and since the acceleration is zero f≠ma, a clear violation of Newton's 1st and 2nd laws.

Similarly, by transforming we obtain the equations of motion for the ball in the primed frame are:
b'(t')=(-t²+2t+1,0,0)
vb'(t')=(-2t+2,0,0)
ab'(t')=(-2,0,0)
t'>1.
Since there is no force acting on the ball and since the acceleration is non-zero f≠ma, a clear violation of Newton's 1st and 2nd laws.

However, we can easily "fix" the first and second laws simply by introducing an inertial force (-2M,0,0) where M is the mass of the body on which the force is acting. So, for the rocket, this inertial force exactly balances the thrust such that the net force is zero which explains the acceleration of zero. For the ball, this inertial force is the only force acting on it so there is a non-zero net force which explains the non-zero acceleration. Thus, with this modification Newton's 1st and 2nd laws are now satisfied.

Now, let's consider Newton's 3rd law in the accelerated reference frame. Again, the thrust force on the rocket is equal and opposite to the thrust force on the exhaust, forming a 3rd law pair. That leaves only the inertial forces. However, all of the inertial forces act in the same direction, so they do not form 3rd law pairs. The inertial forces violate the 3rd law because there are no equal and opposite inertial forces.

I hope this clearly explains my above statements, because I really would have a hard time being more explicit or concrete.

 

[JesseM]

I've told you many times before that this is a misconception of yours--when solving problems in relativity you don't pick one frame to be "the rest frame", the phrase rest frame is only used in connection with particular objects, like "the rest frame of the rocket". You are free to do calculations in multiple frames, including ones where none of the objects you are analyzing are at rest; there is no "fixation" on claiming oneself to be at rest, although it is traditional in both Newtonian physics and relativity to use "my frame" as shorthand for "the frame where I am at rest".

Well, I thought Einstein was interested in looking at things from the point of view of objects in free-fall. i.e. from a 'place' where the gravity field was undetectable and thus one which could easily be considered in effect a genuine inertial frame [a pure rest frame].
ie A specific frame in which the (possibly varying) acceleration through space is 'invisible' so long as you don't look out the window.

I was talking more about special relativity in the above comments, where one can analyze a situation from any inertial frame using the same equations for the laws of physics, and there is no convention that one of these inertial frames is selected as "the" rest frame as neopolitan seems to imagine. In general relativity it's true that an observer in free-fall will "locally" observe the laws of physics to work just like they do in an inertial frame from special relativity, where locally means that the observer can only look at the results of experiments in a very small region of space for a very small window of time, small enough so the effects of spacetime curvature are negligible. In GR you wouldn't say that this observer is "accelerating" in a local sense, in fact if a freefalling observer falls past an observer at a constant height above the ground--sitting on a platform, say--then in a local sense it is the observer on the platform who is accelerating, not the frefalling observer.

 

[YellowTaxi]

I was talking more about special relativity in the above comments, where one can analyze a situation from any inertial frame using the same equations for the laws of physics, and there is no convention that one of these inertial frames is selected as "the" rest frame as neopolitan seems to imagine. In general relativity it's true that an observer in free-fall will "locally" observe the laws of physics to work just like they do in an inertial frame from special relativity, where locally means that the observer can only look at the results of experiments in a very small region of space for a very small window of time, small enough so the effects of spacetime curvature are negligible. In GR you wouldn't say that this observer is "accelerating" in a local sense, in fact if a freefalling observer falls past an observer at a constant height above the ground--sitting on a platform, say--then in a local sense it is the observer on the platform who is accelerating, not the frefalling observer.

yep that's obvious.
but the guy that's actually falling will get hurt the most when the ground hits him

on a more serious note
But I didn't understand why you said 'only for a small region of time' for the falling guy.
because: If the g field varies (over time - or whatever), actually it doesn't matter to the falling guy. For him g is always 'invisible' whatever its actual value my seem to the guy on the platform.

 

[harryjoon]

What everyone seems to forget is that relativistic effects can only be observed across two reference frames. Lorentz transform equations relate measurements of two observers with a non-zero relative velocity. In order to maintain the universal validity of the laws of physics we need Lorentz transform between two inertial frames, and generally covariant transformation laws for non-inertial frames. This is indeed the very essence of the Special and the General relativity theories.

 

[belliott4488]

DaleSpam:

Thanks for taking the time to type all that up.

I'm afraid I still don't get it though. Why is it any more difficult to identify the "equal and opposite pairs" in this case than it is in the simple case of constant gravity = m*9.8 m/s^2 that we all worked with when we first learn Newton's laws? We were told that if a rock rests on a table, its weight exerts a force = mg on the table, and the table (thanks to molecular deformation, we later learned) exerts the same magnitude force upward. The same would happen in the rocket ship, right? The hardest one to grasp when we were kids was the equal and opposite force when we allowed that rock to fall toward Earth - but we accepted that the Earth moves upward ever so slightly - even though we certainly never saw any evidence to that effect.

[EDIT: I originally typed "as long as the spaceman holds the rocket" in the next paragraph ... oops. sorry if I confused anyone.]

Is it any harder to believe that the spaceship moves "up" (or "forward") when the rock is released in it? After all, as long as the spaceman holds the rock, the thrusters are accelerating the total mass of spaceship + spaceman + rock. When he releases the rock, the thrusters suddenly are accelerating only spaceship + spaceman (until the rock strikes the floor), so the spaceship will accelerate slightly faster forward.

Isn't this all the same thing? Mustn't it be, if we are to take the Equivalence Principle seriously? Newton derived his laws in the (approximately) constant gravitational field of the Earth before he ever put together the concept of gravity as the force the holds the planets in place as well as pull rocks to Earth. Can't our spaceman do exactly the same thing?

 

[JesseM]

But I didn't understand why you said 'only for a small region of time' for the falling guy.
because: If the g field varies (over time - or whatever), actually it doesn't matter to the falling guy. For him g is always 'invisible' whatever its actual value my seem to the guy on the platform.

I asked the same question on this thread a while ago, see dicerandom's answer in post #9--even in a very small room, if you had two test particles on opposite sides of the room they would begin to drift together over an extended period of time due to tidal forces, just like what happens if you have a large room and you observe what happens to test particles on opposite sides for a brief period of time--see the bottom illustration in this article.

 

[harryjoon]

There are a number of points that need clarifying within the above arguments. Einstein said in non-inertial frames Newton's law do not hold good - this is not the same as the statement "Newtons' laws are violated." They don't hold good because we cannot adhere to the classical definition of space-time in which we can measure a unit of length and time regardless of our position. In non-inertial frame this is no longer valid, different position in space-time may have different metrics, which cause a straight line to appear as a curved line etc. The Euclidean geometry does not hold and must be replaced with a non-Euclidean geometry. The notion of straight line which is used to define Newton's laws no longer has the same meaning.
As to your question, if I understand it correctly, no it is not any different. In fact it is the very point that Einstein used to explain his equivalence principle. That a man in an elevator or a rocket will be unable to distinguish his system from a gravitational system since he will observe an object at rest (in another frame) to be falling with an acceleration which is independent of the mass of the object. Since this peculiar behavior belongs to gravitational systems, hence he concluded that a gravitational system is no different to an accelerated system. A fact further supported by experiments of Eotvos who verified the equivalence of the gravitational mass with the inertial mass.

 

[belliott4488]

Thanks, harryjoon. One question in response: the point about Newton's laws not holding in a non-inertial frame is due to relativistic effects, is it not? In the limit of small velocities (and small accelerations or small gravitational fields), are Newton's laws not as good an approximation as they are in inertial frames?

 

[JesseM]

DaleSpam:

Thanks for taking the time to type all that up.

I'm afraid I still don't get it though. Why is it any more difficult to identify the "equal and opposite pairs" in this case than it is in the simple constant gravity = m*9.8 m/s^2 that we all worked with when we first learn Newton's laws? We were told that if a rock rests on a table, its weight exerts a force = mg on the table, and the table (thanks to molecular deformation, we later learned) exerts the same magnitude force upward. The same would happen in the rocket ship, right? The hardest one to grasp when we were kids was the equal and opposite force when we allowed that rock to fall toward Earth - but we accepted that the Earth moves upward ever so slightly - even though we certainly never saw any evidence to that effect.

Is it any harder to believe that the spaceship moves "up" (or "forward") when the rock is released in it? After all, as long as the spaceman holds the rocket, the thrusters are accelerating the total mass of spaceship + spaceman + rock. When he releases the rock, the thrusters suddenly are accelerating only spaceship + spaceman (until the rock strikes the floor), so the spaceship will accelerate slightly faster forward.

Isn't this all the same thing? Mustn't it be, if we are to take the Equivalence Principle seriously? Newton derived his laws in the (approximately) constant gravitational field of the Earth before he ever put together the concept of gravity as the force the holds the planets in place as well as pull rocks to Earth. Can't our spaceman do exactly the same thing?

Even if you can make correct predictions in a Newtonian accelerating frame by introducing "fictitious forces", doesn't the very fact that you have to include forces not present in inertial frames mean that the laws of physics have a different form in this frame? For example, in an inertial frame the forces on a test particle depend only on its distance from other objects which exert gravitational forces on it, but this is no longer true in a non-inertial frame with 'fictitious forces'. If you wrote down the equations of motion for a given system of particles, the equations couldn't have the same form in non-inertial frames as they do in inertial ones.

 

[Dale]

The hardest one to grasp when we were kids was the equal and opposite force when we allowed that rock to fall toward Earth - but we accepted that the Earth moves upward ever so slightly - even though we certainly never saw any evidence to that effect.

Is it any harder to believe that the spaceship moves "up" (or "forward") when the rock is released in it? After all, as long as the spaceman holds the rocket, the thrusters are accelerating the total mass of spaceship + spaceman + rock. When he releases the rock, the thrusters suddenly are accelerating only spaceship + spaceman (until the rock strikes the floor), so the spaceship will accelerate slightly faster forward.

Isn't this all the same thing? Mustn't it be, if we are to take the Equivalence Principle seriously? Newton derived his laws in the (approximately) constant gravitational field of the Earth before he ever put together the concept of gravity as the force the holds the planets in place as well as pull rocks to Earth. Can't our spaceman do exactly the same thing?

You are thinking about effects that are many orders of magnitude smaller than what we are talking about here. The inertial forces are relatively large forces (2000 N on the rocket and .2 N on a .1 kg ball), the gravitational force between them would be about 6.7E-9 N or even less because of the geometry. However, the important point is that all of the inertial forces point in the same direction! Because they are all in the same direction they cannot possibly form equal-and-opposite pairs that satisfy the 3rd law.

I really don't know what more I can do here. I have given a very clear and concrete example fully worked out. I have shown my reasoning step-by-step and backed up my claims with explicit demonstrations. Please do the math yourself. Work a few of these problems and see that the inertial forces do not follow Newton's 3rd law. If you cannot see that from what I have already presented then I am sure that further write-ups on my part will not be helpful. There is really no substitute for getting down into the details and going through the work yourself.

PS Please don't take this wrong. There is nothing wrong with needing to work a few examples to understand a concept, particularly in this case. Most people go through all of their college physics courses without ever working a problem in a non-inertial reference frame.

 

[belliott4488]

Even if you can make correct predictions in a Newtonian accelerating frame by introducing "fictitious forces", doesn't the very fact that you have to include forces not present in inertial frames mean that the laws of physics have a different form in this frame? For example, in an inertial frame the forces on a test particle depend only on its distance from other objects which exert gravitational forces on it, but this is no longer true in a non-inertial frame with 'fictitious forces'. If you wrote down the equations of motion for a given system of particles, the equations couldn't have the same form in non-inertial frames as they do in inertial ones.

Right, but that means Newton's laws are also "violated" on the surface of the Earth when we make the approximation that g is a constant, independent of height. I know that's only an approximation, but I wouldn't have called that a "violation" of Newton's laws; I would have said that it's an application of those laws that is as correct as the initial assumption, i.e. of a constant force.

My main point was really that I don't see how Newton's laws of motion say anything about the source or the nature of the forces. They simply say, "you give me a force, and I'll tell you how object will react to it." As far as that goes, they work equally well on the Earth's surface (which really is non-inertial, after all, not that anyone claims Newton's laws don't apply there) and in the accelerating rocketship/elevator.

 

[JesseM]

Right, but that means Newton's laws are also "violated" on the surface of the Earth when we make the approximation that g is a constant, independent of height. I know that's only an approximation, but I wouldn't have called that a "violation" of Newton's laws; I would have said that it's an application of those laws that is as correct as the initial assumption, i.e. of a constant force.

My main point was really that I don't see how Newton's laws of motion say anything about the source or the nature of the forces. They simply say, "you give me a force, and I'll tell you how object will react to it." As far as that goes, they work equally well on the Earth's surface (which really is non-inertial, after all, not that anyone claims Newton's laws don't apply there) and in the accelerating rocketship/elevator.

But Newton's laws of motion aren't the whole of what is meant by Newtonian physics--the three laws of motion are insufficient in themselves to calculate the dynamical behavior of objects given their initial conditions. You also need some set of force laws, such as the equation of Newtonian gravitation. For Galilei-invariant force laws like Newtonian gravity, the law will obey the same equations in every inertial frame, but the same equations will not give correct predictions in a non-inertial frame.

 

[belliott4488]

But Newton's laws of motion aren't the whole of what is meant by Newtonian physics--the three laws of motion are insufficient in themselves to calculate the dynamical behavior of objects given their initial conditions. You also need some set of force laws, such as the equation of Newtonian gravitation. For Galilei-invariant force laws like Newtonian gravity, the law will obey the same equations in every inertial frame, but the same equations will not give correct predictions in a non-inertial frame.

Oh, absolutely ... and to describe electromagnetic forces fully, you should have Maxwell's equations, too. I think the post that I initially responded to referred only to the laws of motion, however. Of course I agree that Newton's Law of gravity won't do you much good in an accelerating rocketship far from any gravitational field.

I think this is all kind of tangential to the original post. It asked about why Newton's laws are said to be violated in accelerating frames. If that referred to the law of gravity, then fine - there's a simple enough answer. If it refers to the laws of motion, however, then I think it's misleading to say that these laws are "violated." Yes, additional conditions, in the form of inertial forces, must be added, but then the laws still work.

 

[Dale]

If it refers to the laws of motion, however, then I think it's misleading to say that these laws are "violated." Yes, additional conditions, in the form of inertial forces, must be added, but then the laws still work.

No they dont!

 

[belliott4488]

No they dont!

Again I ask you, why not? You said earlier that the 3rd law doesn't work, but I responded (https://www.physicsforums.com/showpost.php?p=1671401&postcount=37") by pointing out that in fact it does, much as it does for the case of a constant gravitational field, to which this case is equivalent.

Do you in fact believe that Newton's 3rd law is violated in the approximation of a constant gravitational field that is typically invoked for motion on the Earth's surface? If so, then at least you're consistent, although rather unconventional, since that approximation is often used in the presentation of Newton's Laws for the first time in introductory Physics.

[Edit: I'm adding more, while I wait to see a response ...]
One more thing: Suppose I'm riding in my rocket ship/space elevator, and I'm doing all kinds of Physics - I'm shooting pool, I'm tossing balls through the air (it's a big elevator), I'm playing with pendula, I'm spinning gyroscopes - at what point will I find myself unable to explain or predict what I'm seeing simply by applying Newton's laws and the assumption of a constant force field, which I'll call, for lack of a better term, "gravity"? If you tell me the laws of motion break down, then I'll be able to tell that I'm in an accelerating frame and not in a constant gravitational field, and the Principle of Equivalence just got shot to Hell.

 

[Dale]

Again I ask you, why not? You said earlier that the 3rd law doesn't work, but I responded (https://www.physicsforums.com/showpost.php?p=1671401&postcount=37") by pointing out that in fact it does, much as it does for the case of a constant gravitational field, to which this case is equivalent.

Show your work and justify your claim that it is equivalent.

Do you in fact believe that Newton's 3rd law is violated in the approximation of a constant gravitational field that is typically invoked for motion on the Earth's surface? If so, then at least you're consistent, although rather unconventional, since that approximation is often used in the presentation of Newton's Laws for the first time in introductory Physics.

In Newtonian physics gravity is a real force with two bodies interacting. It satisfies the 3rd law, and I have no problem with the approximation to a uniform field.

The fact that the uniform approximation has the same form as the inertial force is irrelevant here. The two situations are not equivalent wrt the 3rd law because the gravitational force is due to the interaction with another body and the inertial force is not.

 

[Dale]

One more thing: Suppose I'm riding in my rocket ship/space elevator, and I'm doing all kinds of Physics - I'm shooting pool, I'm tossing balls through the air (it's a big elevator), I'm playing with pendula, I'm spinning gyroscopes - at what point will I find myself unable to explain or predict what I'm seeing simply by applying Newton's laws and the assumption of a constant force field, which I'll call, for lack of a better term, "gravity"? If you tell me the laws of motion break down, then I'll be able to tell that I'm in an accelerating frame and not in a constant gravitational field, and the Principle of Equivalence just got shot to Hell.

What body is causing this "gravity"? Or in other words, where do you put your reaction force to "gravity"?

 

[belliott4488]

DaleSpam:

As I said in an earlier response to JesseM, I completely agree that Newton's Law of Gravity does not apply in the accelerating frame - this is trivially true. My point is that the Laws of Motion say nothing about the source or nature of the force. They simply say, "give me a force and I'll tell you how objects will react to it."

As for your request that I "show my work" to show that a constant gravitational field is equivalent to a frame undergoing constant acceleration ... um, hasn't that been done - a lot? I know you know the Principle of Equivalence, which I keep mentioning just as a short-hand because I assume we all know the argument. Otherwise, Google it - you'll find a better explanation than I'll come up with off the top of my head, which is fine since it's not my argument.

As far as I can tell, our only real disagreement has to do with the reaction forces, or the "equal and opposite pairs," as we've called them. Did you disagree with my examples? So long as the objects are accelerated along with the frame, something is applying a force, which is what the inertial "reaction force" is reacting to. To the observer in the accelerating frame, he detects this mysterious force (the nature of which is immaterial to him, since he only needs to call it "F" in his equations), and sees that an equal and opposite force is needed to support it so that it doesn't fall to the floor.

When he drops the object, he feels - with his very sensitive feet - that the "ground" is accelerating upwards toward the object, as it must, since as far as he's concerned it feels the equal and opposite force. We, in our inertial frame outside the spaceship, attribute this to the increase in acceleration due to the slight decrease in accelerated mass, but the result is all the same.

I hate to keep appealing to authority, but doesn't Einstein's Principle of Equivalence make this kind of a non-issue? His whole point is that an observer in an accelerating frame cannot distinguish between his accelerating frame and a frame at rest in a constant gravitational field. If he could detect a violation of Newton's laws, then he could make the distinction. All of GR depends on this principle, so I don't see how you think it could be so wrong.