Einstein's first Law

[geordief]

If I have this right it says that ,whatever the inertial frame any physical experiment gives the same result.

 

What might be the simplest such experiment that one could devise to show this to be the case ?

 

By simplest I mean perhaps  involving the smallest amount of energy and ideally involving just a system  being measured in one of two possible states.

 

If such an experiment exists  I would like to set up a scenario where two observers are in motion wrt each other  (so we have a v and a -v) and take measurements of an experiment like the one I have wondered about above  .

 

The site  of  the experiment  should be moving at v/2 and -v/2  wrt to the two observers. (so at an equal rate of motion to either)

 

Is there any mileage in my set up ?

 

I got the idea from this  document which I am attempting to understand 

 

https://arxiv.org/pdf/physics/0302045.pdf

 

Any comments on that document would also be welcome (eg is it  well worked)

 

There is also  this related document which I have not  looked at yet 

 

https://pdfs.semanticscholar.org/9d55/944b5c5bd8698ab2e9576ad8e69836e43601.pdf

[swansont]

2 hours ago, geordief said:

If I have this right it says that ,whatever the inertial frame any physical experiment gives the same result.

It says the same laws of physics apply. There is no experiment that shows that one frame must be at rest, while another must be in motion.

 

2 hours ago, geordief said:

What might be the simplest such experiment that one could devise to show this to be the case ?

 

By simplest I mean perhaps  involving the smallest amount of energy and ideally involving just a system  being measured in one of two possible states.

Energy is a relative value so in general different frames will measure a different energy.

 

 

[geordief]

1 minute ago, swansont said:

 

 

Energy is a relative value so in general different frames will measure a different energy.

 

 

I was thinking of the FOR  the physical experiment was carried out in.(if that helps)

[Bufofrog]

8 hours ago, geordief said:

If I have this right it says that ,whatever the inertial frame any physical experiment gives the same result.

 

What might be the simplest such experiment that one could devise to show this to be the case ?

Drop identical balls from the same height and measure the time it takes to fall that distance.  One frame can be on the ground and other frame can be a jet flying at 500 mph.

[geordief]

18 minutes ago, Bufofrog said:

Drop identical balls from the same height and measure the time it takes to fall that distance.  One frame can be on the ground and other frame can be a jet flying at 500 mph.

Those two frames don't agree though ,do they?

If they are moving wrt each other they will surely measure a different time interval of the same ball dropping.

The scenario I was attempting to set up in the OP  had 3 FOR's  ,one directly in the middle of 2 other FOR's moving away from each other at the rate of  v.

I think those two FOR's will agree on the timing of a simple physical event in the third FOR  because both are moving wrt it at the same speed (v/2)

[swansont]

1 hour ago, Bufofrog said:

Drop identical balls from the same height and measure the time it takes to fall that distance.  One frame can be on the ground and other frame can be a jet flying at 500 mph.

As geordief points out, the time is relative.

If you toss a ball in the air, and comes down again, you can solve for the up-down motion using simple kinematics. An observer in relative inertial-frame motion to you can also solve the problem with the same stable of equations (i.e. the same physics) but the solution will be a parabola. Further, you would not be able to say who is moving. If you’re on a train, or on the ground, you toss the ball straight up in your frame in order to catch it. In the other frame, the path is a parabola. All you can say is that there is relative motion.

That’s what the postulate means.

 

[md65536]

On 8/23/2019 at 5:30 PM, geordief said:

Those two frames don't agree though ,do they?

If they are moving wrt each other they will surely measure a different time interval of the same ball dropping.

The scenario I was attempting to set up in the OP  had 3 FOR's  ,one directly in the middle of 2 other FOR's moving away from each other at the rate of  v.

I think those two FOR's will agree on the timing of a simple physical event in the third FOR  because both are moving wrt it at the same speed (v/2)

I think you might be misunderstanding the principle of relativity. It's not that measurements of a single experiment, observed from different frames of reference, will make the same measurements. It's that the experiment, performed in each of the different frames of reference, will have the same measurements within those frames. Obviously, many measurements will be "relative" to the observer. In Galilean relativity, things like relative speeds will be different depending on inertial frame. In special relativity, things like lengths and times will also be different.

In the example mentioned, you don't have a person drop a ball while standing on the ground, and measure it from the ground and from a moving airplane. You drop the ball on the ground and measure it from the ground,  and you drop the ball on the plane, and measure it on the plane. If both adequately approximate an inertial frame and have the same gravity, both experiments behave the same. A more general example, if you had two trains, each at rest in a different perfectly inertial frame, there would be no experiment that could be performed that could identify that one train is at rest and another is in motion except relative to a frame of reference, and so there is no concept of universal motion or rest.

Edited August 25, 2019 by md65536

[geordief]

5 hours ago, md65536 said:

I think you might be misunderstanding the principle of relativity. It's not that measurements of a single experiment, observed from different frames of reference, will make the same measurements( I agree that  they don't). It's that the experiment, performed in each of the different frames of reference, will have the same measurements within those frames. Obviously, many measurements will be "relative" to the observer. In Galilean relativity, things like relative speeds will be different depending on inertial frame. In special relativity, things like lengths and times will also be different.

In the example mentioned, you don't have a person drop a ball while standing on the ground, and measure it from the ground and from a moving airplane. You drop the ball on the ground and measure it from the ground,  and you drop the ball on the plane, and measure it on the plane. If both adequately approximate an inertial frame and have the same gravity, both experiments behave the same. A more general example, if you had two trains, each at rest in a different perfectly inertial frame, there would be no experiment that could be performed that could identify that one train is at rest and another is in motion except relative to a frame of reference, and so there is no concept of universal motion or rest.

Are you saying that the two measurements of the physical experiment in the third FOR  will be different ? (they are moving at the same speed wrt  the FOR of  experiment )

I am not using Bufofrog's scenario ,but the one in my OP.

 

Is my scenario of 3 FOR'a a valid one?

[geordief]

1 hour ago, geordief said:

Are you saying that the two measurements of the physical experiment in the third FOR  will be different ? (they are moving at the same speed wrt  the FOR of  experiment )

I am not using Bufofrog's scenario ,but the one in my OP.

 

Is my scenario of 3 FOR'a a valid one?

EDIT:On reflection I can see that v will be the separation speed of the 2 observers wrt to the FOR of the physical experiment and not the speed that either observer will observe the other as moving at.

Still that doesn't change my claim that both observers measure the physical experiment identically since  they are moving at the same speed wrt it.(just not v/2 )

Either that or ,if I say the 2 observers are moving at v wrt each other ,then they won't move at v/2 wrt the physical experiment

But the purpose of the scenario is to attempt to prove the velocity addition formula in the first place and so that may be of no consequence.

 

[studiot]

OK let's go at this Gently  (did you like the tv series?)

Also +1 for working hard at it..

Note I started this a while back, but never quite finished it.

On 8/23/2019 at 3:47 PM, geordief said:

If I have this right it says that ,whatever the inertial frame any physical experiment gives the same result.

 

Not quite.

Einstein's first Postulate is the Principle of Relativity which states, not that the result is the same but

The Laws of mechanics have the same form in all inertial frames. This is called 'form invariance'.

Note Einstein did not claim this postulate he knew it had been around since the time of Galileo and Newton.
It's what he did with it that was brilliant.

 

I think  it is a very good idea of yours to study some examples.

Now your links make it very complicated by looking at the most general cases in 3 or 4 dimensions.

I suggest starting with just one dimension in your frames - Your example can be put in this form.

But do you realise that you have specified 3 frames ?

The frame of each moving observer and " the site of the experiment".

On 8/23/2019 at 3:47 PM, geordief said:

If such an experiment exists  I would like to set up a scenario where two observers are in motion wrt each other  (so we have a v and a -v) and take measurements of an experiment like the one I have wondered about above  .

 

The site  of  the experiment  should be moving at v/2 and -v/2  wrt to the two observers. (so at an equal rate of motion to either)

Also I am not sure if you think the energy is a constant mass times velocity.

On 8/23/2019 at 3:47 PM, geordief said:

By simplest I mean perhaps  involving the smallest amount of energy and ideally involving just a system  being measured in one of two possible states.

 

If such an experiment exists  I would like to set up a scenario where two observers are in motion wrt each other  (so we have a v and a -v) and take measurements of an experiment like the one I have wondered about above  .

 

So perhaps you can clarify a few points to employ your example.

1) Restrict the frames to 1 dimension (the  x axis and time) plus time.

2) Confirm what 'a' is ?

3) To actually do some Physics, assign mass m1 and m2 to each observer.

Then we can explore this statement from

10 hours ago, md65536 said:

I think you might be misunderstanding the principle of relativity

To find out that some physical quantities are 'invariant' that is the same in all frames
and some vary with frame, when you calculate them according to the same equation in different frames.

 

[geordief]

18 minutes ago, studiot said:

1) Restrict the frames to 1 dimension (the  x axis and time) plus time.

2) Confirm what 'a' is ?

.3) To actually do some Physics, assign mass m1 and m2 to each observer.

 

Just "quickly"

 

1) I was only considering a line drawn between the two observers and the experiment (like 2  rockets leaving the Earth in directly  opposite directions at the same speed  and with the Earth as the site of the experiment) 

So one dimensional (plus time ) in my head

 

2) a v means just "a vee"  ,ie one quantity is "v" and  the other is "-v"

I didn't intend "a" to stand for anything mathematical (also my English was sloppy although it would have been understood as part of a spoken delivery)

 

3)Won't it the work in flat space? (the first  link I was looking at doesn't use mass does it?

 

Wrt your clarification re the First Postulate I am just  claiming  that both observers will measure the same physical experiment identically (maybe I was wrong** to even bring up the First Postulate as my main interest is to ask if this is a scenario with potential  for showing something along the lines of what is proved (apparently) in the first link I posted 

**and ,looking back  seemingly air headed 

 

ps :I have seen the IG series once or twice  but  not really enough form an opinion

 

 

[swansont]

On 8/23/2019 at 10:47 AM, geordief said:

If I have this right it says that ,whatever the inertial frame any physical experiment gives the same result.

 

What might be the simplest such experiment that one could devise to show this to be the case ?

 

The experiment you describe would be a bad example, since it has symmetry. You might expect identical behavior even if the first postulate did not hold in general

[studiot]

2 hours ago, swansont said:

The experiment you describe would be a bad example, since it has symmetry. You might expect identical behavior even if the first postulate did not hold in general

To move this thread forwards here is a simple variation to your example yet substantial enough to demonstrate the detail and the difference between invariant and relative variables.

 

Let the two bodies having masses m₁ and m₂ and located at x₁ and x₂ move only along the x axis, subject only to any force they exert on each other.

Establish the equation of motion of each body.

[geordief]

5 hours ago, studiot said:

To move this thread forwards here is a simple variation to your example yet substantial enough to demonstrate the detail and the difference between invariant and relative variables.

 

Let the two bodies having masses m₁ and m₂ and located at x₁ and x₂ move only along the x axis, subject only to any force they exert on each other.

Establish the equation of motion of each body.

That will be too hard for me ,but are you talking Newtonian  mechanics?

You place  the two bodies at negative x and positive x respectively? (observer at zero)

So the "negative"body moves according to  d(¦x₁¦ +¦x₂¦ )/dt =m_1/[m1+m_{2] all multiplied by} m_1*m_{2 over} ¦x₁¦ +¦x₂¦ squared

and the "positive" body is the same but replacing  the first m_{1 on the RHS  by} m₂

_{Anything like that???}

Edited August 26, 2019 by geordief