Spin Time Questions

[Zinjanthropos]

Would you be happy with more detail on just the dot at the centre and one at the edge?

Sure why not. It’s a science forum, not English Lit…

[Secular Sanity]

May seem simple but….

If I were to place a dot on the edge of centre hole and one on outside edge of lp as if they were lined up like a spoke on a wheel and start spinning the record on turntable then obviously the dot on outside edge is moving faster. Because it’s moving faster does outside dot age slower than inside edge dot?

Proportionally sized disc with humans at both rims….. When directly facing towards each other would the light beam from one person to another be ever so slightly bent and only provide an illusion of a straight line?

From my reference point outside disc they both rotate with the same time or do they?

Two people glued to different locations on a rotating disk would experience a difference in tangential velocity. The one at the edge would be covering a greater linear distance per unit of time, but an increase in tangential speed does not cause time dilation. Stryder is correct in saying that time dilation would only come into play in GR with large masses or at a significant fraction of light speed in SR, but even neutron stars can’t rotate fast enough for this to occur.

And yes, the Coriolis effect would be responsible for the apparent curvature.

In addition, you might find this video interesting. 

https://www.youtube-nocookie.com/embed/3oM7hX3UUEU

[confused2]

^^ in the light of..

Because it’s moving faster does outside dot age slower than inside edge dot?

A thought experiment is usually intended to go for the basics with as few distractions as possible - in this case a rotating frame with no mass - incidentally no neutron stars and no rotating balls.

Probably off topic but.. I've known the basic equations of special relativity for 50 years now. What has always interested me isn't the equations but the why?. With the arrival of the internet I could ask 'why?' and among the people I could reach it seems to be a non-question and you can't get an answer to something that isn't a question. One person was close but couldn't do the geometry (of a light clock) but I could see he was close ... the first real answer I got came from a report of a school project describing a vertical light clock .. looked good but not good enough.. then the MMA guy on Physorg did the same but with a horizontal light clock - finally a 'reason' (the constant speed of light). With one reason it's much easier to see another .. so next thanks go to rpenner for pointing out the way clocks actually work (they don't know where they are they just go tick-tock). I am fairly sure that just banging clocks against walls is sufficient to get the why of SR which for some people (me!) is the IT factor even though it doesn't directly generate any equations.

So a spinning disc with two dots on it or spinning balls and no, it isn't a neutron star?

[confused2]

GPS satellites are 'dots going round in a circle'..

HOW RELATIVISTIC TIME DILATION AND GPS ARE RELATED

from
https://www.scienceofgadgets.com/post/ho...re-related

..the clock in the fast-moving satellite falls behind 0,000007 seconds (7 microseconds) per day, compared to the clock on the ground.

The GPS receiver clock, located on the ground at the distance r from the Earth's center of gravity, experiences gravitational time dilation of 0.00006 seconds per day

The GPS satellite orbits about 20 000 kilometers above the Earth's surface .. experiences a time dilation of 0.000015 seconds per day

So, we get a time difference of 45 microseconds (0.00006 - 0.000015 = 0.000045) per day between the time measured on Earth and the time measured on the satellite. From the first equation, we found that the clock on the fast-moving satellite lags behind the receiver's clock by 7 microseconds per day. Subtracting time dilation of 7 microseconds from 45 microseconds, we find that the receiver clock runs 38 microseconds slower per day than the clock onboard of GPS satellite (0.000045 - 0.000007 = 0.000038 sec = 38 us).

[Secular Sanity]

Yes, but the OP’s question was about tangential speed, which depends on the radius.

https://www.texasgateway.org/resource/61...r-velocity

Gravity makes you age more slowly. If you were just floating in space, you would age faster than those on earth, but if you were zipping around earth, you’d age more slowly because velocity time dilation has a bigger effect than gravitational time dilation.

Side note: In regards to the OP, in group settings, people might ask questions to contribute to the conversation or maintain social cohesion, rather than to gain new information. In these situations, they may not focus on the answers as much as on the act of participation.

[confused2]

Yes, but the OP’s question was about tangential speed, which depends on the radius.

https://www.texasgateway.org/resource/61...r-velocity

Gravity makes you age more slowly. If you were just floating in space, you would age faster than those on earth, but if you were zipping around earth, you’d age more slowly because velocity time dilation has a bigger effect than gravitational time dilation.

Side note: In regards to the OP, in group settings, people might ask questions to contribute to the conversation or maintain social cohesion, rather than to gain new information. In these situations, they may not focus on the answers as much as on the act of participation.

Going back to the original spot on a disc..

I (incorrectly) assumed circular motion and acceleration as known quantities..

https://www.savemyexams.com/a-level/phys...ar-motion/

Circular Motion:

Velocity and acceleration are both vector quantities
An object in uniform circular motion has a constant linear speed
However, it is continuously changing direction. Since velocity is the speed in a given direction, it, therefore, has a constantly changing velocity
The object therefore must be accelerating
This is because acceleration is defined as the rate of change of velocity
This acceleration is called the centripetal acceleration and is perpendicular to the direction of the linear speed
Centripetal means it acts towards the centre of the circular path

I then invoked Einstein's equivalence principle having (again) incorrectly assumed it as 'known'..
https://en.wikipedia.org/wiki/Equivalence_principle

In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference.

I then (wildly assuming things without justification) borrowed gravitational time dilation theory but with the acceleration away from the centre (opposite to the way the Earth goes) and concluded that with effects adding we could say the centre dot ages faster than outer (rotating) dot.

In the post before SS's (about GPS satellites) the writer showed that the gravitational effect was both opposite and greater than velocity effect so the satellite ages faster despite having considerable velocity.

Side note: I did make a 'divisive' post to help me decide whether or not anyone would be interested if I spent some (considerable) time diving deeper into SR - clearly not. Please accept my apologies - it wasn't intended to be 'socially' divisive.

[Secular Sanity]

Side note: I did make a 'divisive' post to help me decide whether or not anyone would be interested if I spent some (considerable) time diving deeper into SR - clearly not. Please accept my apologies - it wasn't intended to be 'socially' divisive.

Someone at sea level would age slower than someone on a mountain top. So, you’d expect the astronauts on the ISS to age faster because time passes more slowly in stronger gravitational fields, but the dominant effect is the time dilation due to their high relative velocity compared to Earth's surface. Well, that's what "they" say anyway.

No apologies are necessary because that was directed towards the OP.

[confused2]

Someone at sea level would age slower than someone on a mountain top. So, you’d expect the astronauts on the ISS to age faster because time passes more slowly in stronger gravitational fields, but the dominant effect is the time dilation due to their high relative velocity compared to Earth's surface. Well, that's what "they" say anyway.

The word on the street is that satellites (and any astronauts in them) age slower up to about 1.5 Earth radius (ie SR wins) and above that they age faster on account of the gravitational effect. GPS satellites are above the 1.5 Earth radius level so their clocks run faster than Earth clocks .. as shown by the calculations I linked to in my post on the topic. So what you suggest is correct for the ISS in low Earth orbit but not for GPS satellites which are much higher up. I have to admit I haven't checked the calculations beyond 'looks like he's doing the right things here' but I don't think we'd be any further forward even if I did. I think you will find you are correct within the scope of your claim and I am correct within the scope of mine.

Edit.. I think you will find the faster clock rate is generally accepted as 'true'.
From https://www.e-education.psu.edu/geog862/node/1714

Relativistic Effects on the [GPS] Satellite Clock
Albert Einstein’s special and general theories of relativity apply to the clocks involved here. At 3.874 kilometers per second, the clocks in the GPS satellites are traveling at great speed, and that makes the clocks on the satellites appear to run slower than the clocks on earth by about 7 microseconds a day. However, this apparent slowing of the clocks in orbit is counteracted by the weaker gravity around them. The weakness of gravity makes the clocks in the satellites appear to run faster than the clocks on earth by about 45 microseconds a day. Therefore, on balance, the clocks in the GPS satellites in space appear to run faster by about 38 microseconds a day than the clocks in GPS receivers on earth.

Edit3..In reality what makes the difference to the times in GR isn't 'the gravity' but the gravitational potential so the site has copied the numbers from somewhere else without understanding the physics .

[Secular Sanity]

Someone at sea level would age slower than someone on a mountain top. So, you’d expect the astronauts on the ISS to age faster because time passes more slowly in stronger gravitational fields, but the dominant effect is the time dilation due to their high relative velocity compared to Earth's surface. Well, that's what "they" say anyway.

The word on the street is that satellites (and any astronauts in them) age slower up to about 1.5 Earth radius (ie SR wins) and above that they age faster on account of the gravitational effect. GPS satellites are above the 1.5 Earth radius level so their clocks run faster than Earth clocks .. as shown by the calculations I linked to in my post on the topic. So what you suggest is correct for the ISS in low Earth orbit but not for GPS satellites which are much higher up. I have to admit I haven't checked the calculations beyond 'looks like he's doing the right things here' but I don't think we'd be any further forward even if I did. I think you will find you are correct within the scope of your claim and I am correct within the scope of mine.

Edit.. I think you will find the faster clock rate is generally accepted as 'true'.
From https://www.e-education.psu.edu/geog862/node/1714

Relativistic Effects on the [GPS] Satellite Clock
Albert Einstein’s special and general theories of relativity apply to the clocks involved here. At 3.874 kilometers per second, the clocks in the GPS satellites are traveling at great speed, and that makes the clocks on the satellites appear to run slower than the clocks on earth by about 7 microseconds a day. However, this apparent slowing of the clocks in orbit is counteracted by the weaker gravity around them. The weakness of gravity makes the clocks in the satellites appear to run faster than the clocks on earth by about 45 microseconds a day. Therefore, on balance, the clocks in the GPS satellites in space appear to run faster by about 38 microseconds a day than the clocks in GPS receivers on earth.

Edit3..In reality what makes the difference to the times in GR isn't 'the gravity' but the gravitational potential so the site has copied the numbers from somewhere else without understanding the physics .

No, you’re right, both are true, but the rotational velocity of the GPS satellite is also much slower than the ISS.

If the ISS stayed in a fixed position like two dots on a disk, then you’d also be right. The dot closest to the center would see time passing more slowly if, and only if…there was gravity potential, which isn’t the case with an LP and two dots.

BTW, I was trying to point out the inattentive questioning behavior (not you).

Good day to you, C2!

[confused2]

Using Earth as a convenient spinning thing..

Atomic clocks all run at the same speed at sea level whether you are at the poles or the equator. If you google this and find it isn't true we'll have to have a google fight to sort out the true sites from the false sites. Any site that disagrees with me is a false site (by definition) except when I am wrong.

Two atomic clocks. Bob at the North pole and Colin at the equator.

Thing is that the Earth is fatter in the middle than at the top

equatorial radius is 6378 km, but its polar radius is 6357 km

see https://imagine.gsfc.nasa.gov/features/c..._info.html

If we had a clock at the pole at the same radius as one at the equator it would be 21 miles (6378-6357) higher than sea level, at a higher gravitational potential* , and would run faster than the one at the equator.

If we took away the Earth's gravitational field entirely (still forcing the equator clock to stay on the same circular path) the clock at the pole at the same radius as the one at the equator would still be at a higher gravitational potential. With the Earth gone we can drop the pole clock down to the centre of rotation and Bob is your clock running faster at the centre of a rotating disc.

*Higher is more a 'less low' than actually high. Clocks entirely away from any gravitational field run fastest of all which is what the pole clock would be without the Earth being there. The equator clock is in a pseudo field caused by the acceleration due to rotation and not being allowed to fly off in a straight line.