Sagnac Limit

[2inquisitive]

Tom2,

You just said in point (1) that in the pitcher's rest frame the ball moves at 80mph, and now you say that it is 100mph. Did you perhaps mean the batter's rest frame? If so, then you are mistaken. Using Galilean relativity the batter sees the ball approach his head at 80mph. Using SR, the value is slightly smaller.

No, what I meant is in the batter's rest frame, the pitcher's frame of reference would be stationary until after the ball was in flight. The problem is that if the pitcher begins moving backward after he releases the ball, it has no effect on the velocity of the ball relative to the batter.

my post,

“ You end up with two different distance measurements according to which 'rest frame' you are measuring from. That is also where 'relativity of simultaneity' comes from, which is what you were alluding to with your disagreements of starting and finishing points. ”

Tom2,

Yes, precisely. This is exactly what SR predicts. You can't simultaneously hold the speed of light invariant and still take spatial and temporal intervals to be invariant. Everyone knows this.

Why do you think this is a mistake?

The mistake results from the way distance is calculated in the two different frames of reference. Go back to just the spaceship/Earth example to make it less confusing. The speed of light is a constant in both the Earth frame and the spaceship frame, as is known to be a fact. When we measure the distance the photon has travelled after being emitted from the spaceship
in the Earth's rest frame, we measure 10 light years for the path-length of the photon. The motions of the spaceship, or its distance from the Earth after the photon was emitted has no bearing on the path-length the photon travels. The spaceship can change velocity, turn or whatever after it emitts the photon and we will still measure 10 light years as the path-length from Earth's FOR. Now consider what happens when we use the rest frame of the spaceship. In the spaceship's rest frame, the Earth is the frame in motion. Using Galilean relativity, assume that the photon is emitted when the spaceship is 10 light years from the Earth. The Earth will continue to recede farther from the spaceship while the photon is in flight until the photon impacts the Earth, according to Galilean relativity. The path-length of the photon would measure a greater distance than 10 light years. Special Relativity assumes that the distance is contracted in the spaceship's frame of reference, thus giving an equal distance of 10 light years in both frames and a constant 'c'. What SR is actually doing is correcting for a mistake made if using the Galilean frames. You see, the Earth was never actually receding from the point the photon was emitted in the spaceship's rest frame. The photon actually had the same 10 light year path distance to travel before impacting the Earth. It was an illusion that the Earth kept receding while the photon was in flight, caused by assuming it makes no difference which frame is used as the rest frame. It does make a difference in the assumed path length of a photon travelling between the two frames. SR simply corrects for this mistake by 'contracting' the distance in the moving object's frame of reference with the Lorentz transforms. I know you won't like this, but I believe light travels at 'c' relative to the rest frame local vacuum it is in, not relative to the emitter or the receiver of the photon. Motions of the emitter or receiver will affect the Doppler shift of the light, but not the value of 'c' relative to the rest frame of the local vacuum. The rest frame of the local vacuum can be determined by measuring the dipole anisotropy of the CMB.

 

[Neddy Bate]

... I know you won't like this, but I believe light travels at 'c' relative to the rest frame local vacuum it is in, not relative to the emitter or the receiver of the photon ...

If this is true, then, how can we determine if some thing is moving relative to the 'local vacuum'?

 

[2inquisitive]

If this is true, then, how can we determine if some thing is moving relative to the 'local vacuum'?

By measuring the Doppler shift of the CMB, of course. The local frame at rest relative to the CMB is called a 'privileged frame' and also a co-moving frame. It is the same thing as the old 'preferred frame' of aether theory, in this case the local rest frame of the CMB. We on Earth do not reside in the privileged frame. For instance, our local group of galaxies is moving at a peculiar velocity of 627 kms, and in a specific direction. The sun's velocity relative to the local group is 306 kms. The sun's peculiar velocity is 369 kms, which is measured against the rest frame of the CMB. By mapping these reference points, we can calculate the peculiar velocity and direction of any object's motion in our local vacuum.

 

[Neddy Bate]

By measuring the Doppler shift of the CMB, of course. The local frame at rest relative to the CMB is called a 'privileged frame' and also a co-moving frame. It is the same thing as the old 'preferred frame' of aether theory, in this case the local rest frame of the CMB. We on Earth do not reside in the privileged frame. For instance, our local group of galaxies is moving at a peculiar velocity of 627 kms, and in a specific direction. The sun's velocity relative to the local group is 306 kms. The sun's peculiar velocity is 369 kms, which is measured against the rest frame of the CMB. By mapping these reference points, we can calculate the peculiar velocity and direction of any object's motion in our local vacuum.

I like the idea of a preferred frame. So, what happens if we take it to the next step: Can we hypothesise that proper clocks which are in motion relative to the CMB are time-dilated according to their 'absolute' speed?

And therefore, should we consider the idea that there is no 'reciprocal time dilation'? (Relativity Theory's 'apparent' paradox ?)

(For now, neglecting gravitational effects...)

 

[MacM]

I like the idea of a preferred frame. So, what happens if we take it to the next step: Can we hypothesise that proper clocks which are in motion relative to the CMB are time-dilated according to their 'absolute' speed?

And therefore, should we consider the idea that there is no 'reciprocal time dilation'? (Relativity Theory's 'apparent' paradox ?)

(For now, neglecting gravitational effects...)

That certainly would be in the right direction. It remains to be seen where that might lead. Glad to see 2Q embrace the CMB background concept. I raised this issue a couple years ago and mister know it all Root phoo-phooed it.

But the CMB does reveal ansitrophy. It may not be an "absolute" rest frame but it certainly is a common reference frame.

 

[CANGAS]

I propose that the Sagnac effect should specifically apply to accelerated reference frames. I would think that purely "Sagnac" devices should only register positive results if the the frame is accelerating.

Yet there are rotating orbital frames where forces are essentially null (no F=ma at all), for example the International Space Station. Why would there be a difference in the time it takes for light to traverse "clockwise" around the globe, compared to anti-clockwise (counter clockwise) from the reference frame of an object in uniform orbit? It does not detect any forces, even as it moves through the gravity field of the central mass. Strange...

I I beg your pardon: the Sagnac effect originated in an emperical observation of circumstances in inertial ( non-accelerating ) reference frames.

And Sagnac devices are alive and well ( and very commercially successful ) in use where there is no acceleration between one observer and another.