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 ?