A thought experiment: Making astronomical measurements from different floors of a skyscraper

[Mikael17]

Bob lives on floor 500 in a 1000 meter high skyscraper.
Bob has measured the time it has taken a star to orbit 1 round in the Milky Way relative to Earth.

He started by measuring at the time when a single photon from the star was received exactly at the center of his telescope, and ended the measurement 500,000 years later when he again received a new photon from the exact same direction / star.
Both photons that started and ended the measurements were reflected further down to Alice on the first floor 1000 meters deeper in the Earth's gravity field.

Alice's clock ticks slower than Tom's clock, let's say it has a loss of 100 seconds relative to Bob's clock, - (from the start of the measurement to the end)

It only took 2 negligible split sesonds (2 x 1/300000 s) to send the 2 photons to Alice. - and lets say 20 seconds to travel from the star and to reeach Tom and Alice.

The photons have followed the same path to Bob and Alice.

According to d = v * t - (distance = velocity * time) Tom and Alice should measure the same orbit circumference distance of the star.
How is it possible that Tom and Alice disagree about d = v * t .
What is wrong to d = v * t ?

 

[PeroK]

What are ##d, v## and ##t## exactly?

 

[Mikael17]

distance = velocity * time

 

[PeroK]

distance = velocity * time

Which distance, velocity and time?

 

[Mikael17]

You almost decide that yourself
t is different for Tom and Alice hence d or v cannot both be the same for Tom and Alice (this is the point)

 

[PeroK]

You almost decide that yourself

It's your thought experiment! You have to say what you are calculating.

 

[Mikael17]

It's your thought experiment! You have to say what you are calculating.

After all, that is the point. -
If both Bob and Alice must agree that the speed of the star is 300 km/s
Then Alice will say that she calculated the circumference to be 30,000 km less than what Bob can calculate. Why ?

 

[PeroK]

After all, that is the point. -
If both Bob and Alice must agree that the speed of the star is 300 km/s
Then Alice will say that she calculated the circumference to be 30,000 km less than what Bob can calculate. Why ?

They are using different reference frames to measure distance, time and velocity. Velocity is and always has been dependent on your reference frame. We usually assign a velocity relative to the surface of the Earth. But, that's not an absolute velocity.

 

[PeroK]

Note that in your scenario, Alice and Bob have different velocities relative to someone at the North Pole, say.

 

[Mikael17]

Note that in your scenario, Alice and Bob have different velocities relative to someone at the North Pole, say.

Let's pretend the earth isn't rotating anymore

 

[Mikael17]

They are using different reference frames to measure distance, time and velocity. Velocity is and always has been dependent on your reference frame. We usually assign a velocity relative to the surface of the Earth. But, that's not an absolute velocity.

So what will change if we could compare the different reference frames for Bob and Alice ?
t is allready a relatevistic variable.
Do you mean that one more parameter also is a relatevistic variable ?
and if, do you mean d or m (the meter) or what ?
I mean distance d the star is travelling is not changing, - so left is only m, right ?

 

[PeroK]

Or orbiting the Sun? And the Sun isn't orbiting the galactic centre?

Even without relativity, the distance travelled by a star around the galactic centre would be a significant calculation based on raw observations from Earth. It might be interesting to think how a distance a star travels around the galactic centre might be calculated.

All relativity does in this case is add another layer of complexity to the calculations - assuming we take gravitational time dilation into account.

 

[Mikael17]

Or orbiting the Sun? And the Sun isn't orbiting the galactic centre?

Let's pretend Alice and Bob are at rest relative to the milky way, just to simplify as mush as possible

 

[berkeman]

Bob lives on floor 500 in a 1000 meter high skyscraper.

Just to clarify, a 1000m high skyscraper would typically have 235 storeys...

https://theskydeck.com/how-tall-is-a-storey-in-feet/

 

[Mikael17]

Just to clarify, a 1000m high skyscraper would typically have 235 storeys...

https://theskydeck.com/how-tall-is-a-storey-in-feet/

It is specially built for dwarves

 

[PeroK]

PS in fact, try to figure out how you would measure the distance to the Sun. How is that calculated?

 

[Mikael17]

Even without relativity, the distance travelled by a star around the galactic centre would be a significant calculation based on raw observations from Earth. It might be interesting to think how a distance a star travels around the galactic centre might be calculated.

All relativity does in this case is add another layer of complexity to the calculations - assuming we take gravitational time dilation into account.

Yes but at the end of the day Bob and Alice have to agree which parameters are compared variable, otherwise d = v * t doesn't make (universal comparable) sense right?

 

[Mikael17]

PS in fact, try to figure out how you would measure the distance to the Sun. How is that calculated?

When the speed of light must be the same for Bob and Alice and they measure different t , then it is probably the same challenge. Which parameters are comparable relative variables? If a photon from the sun is recieved by Bob and refelcted to Alice, we have the same situation, - Bob will not agree about m (or d) - But d is not changing just because of Bob is wacthing, what about m then ?

 

[PeroK]

Yes but at the end of the day Bob and Alice have to agree which parameters are compared variable, otherwise d = v * t doesn't make (universal comparable) sense right?

It doesn't. Neither ##d## nor ##t## nor ##v## are universal quantities. They are all frame dependent.

What we mean by a cosmological distance is the distance as measured in some hypothetical reference frame. Like the rest frame of galaxy.

What Alice and Bob measure is data that needs to be processed to represent something in that hypothetical reference frame.

That's the case even without taking relativity into account.

 

[PeroK]

And, if you think about it, all Alice and Bob get is light from distance stars. Nothing else. All quantities must be calculated from that very limited data. Just light from distant stars. Human ingenuity is amazing.

 

[Mikael17]

What Alice and Bob measure is data that needs to be processed to represent something in that hypothetical reference frame.

That's the case even without taking relativity into account.

So we have to conclude that then the fact that bob and Alice live in 2 different gravitational reference frames, these are "only hypotecital" - Sorry I think the chain went of for me here.

 

[Mikael17]

And, if you think about it, all Alice and Bob get is light from distance stars. Nothing else. All quantities must be calculated from that very limited data. Just light from distant stars. Human ingenuity is amazing.

Still Bob and alice can never gree about the lenght of m (or d) anywhere in the universe, only at their own gravitaional level.

 

[Dale]

Bob lives on floor 500 in a 1000 meter high skyscraper.
Bob has measured the time it has taken a star to orbit 1 round in the Milky Way relative to Earth.

He started by measuring at the time when a single photon from the star was received exactly at the center of his telescope, and ended the measurement 500,000 years later when he again received a new photon from the exact same direction / star.
Both photons that started and ended the measurements were reflected further down to Alice on the first floor 1000 meters deeper in the Earth's gravity field.

Alice's clock ticks slower than Tom's clock, let's say it has a loss of 100 seconds relative to Bob's clock, - (from the start of the measurement to the end)

It only took 2 negligible split sesonds (2 x 1/300000 s) to send the 2 photons to Alice. - and lets say 20 seconds to travel from the star and to reeach Tom and Alice.

The photons have followed the same path to Bob and Alice.

According to d = v * t - (distance = velocity * time) Tom and Alice should measure the same orbit circumference distance of the star.
How is it possible that Tom and Alice disagree about d = v * t .
What is wrong to d = v * t ?

@Mikael17 this is a very unclear description. It is unclear what ##d## is the distance between and in what frame it is measured. It is unclear what ##v## is the velocity of and in what frame it is measured. It is unclear what ##t## is the time between and in what frame it is measured. It is unclear what spacetime curvature we are to consider and what we are to neglect (earth, sun, galaxy). It is unclear what simplifying assumptions are being made. It is unclear what disagreement you see and it is unclear what kind of solution you are looking for.

Also, when people ask for clarification please just clarify without the guessing games. We are physicists not psychics. Please make a substantial effort to improve the clarity of your communication.

 

[PeroK]

Still Bob and alice can never gree about the lenght of m (or d) anywhere in the universe, only at their own gravitaional level.

Yes. They can profoundly agree if they know the laws of physics and process their respective data accurately. If there are intelligent beings on a different planet, then their raw data will be different from Earth's, but they should come to the same conclusion about cosmological distances.

As an example, consider all the calculations that Kepler had to do to show that planetary orbits were ellipses - in the Sun's rest frame. Kepler actually measured the planets going in complicated loop the loop orbits. He spent years processing that raw data.

That Alice and Bob have different raw data doesn't mean they disagree about anything important. Each can calculate the orbits of the planets and the orbits of stars around the galactic centre.

 

[PeterDonis]

He started by measuring at the time when a single photon from the star was received exactly at the center of his telescope, and ended the measurement 500,000 years later when he again received a new photon from the exact same direction / star.

More like 250,000,000 years if the star is anywhere in the vicinity of the solar system.

lets say 20 seconds to travel from the star and to reeach Tom and Alice.

This would mean the star is only 20 light seconds away, i.e., not much further away than the Moon. I think you mean something more on the order of years (the nearest star to Earth is 4.3 light years away).

You really need to check your numbers if you want them to be realistic.

As for your scenario in general, the obvious conclusion is that Bob and Alice will both agree that the star has made exactly one orbit, but they will disagree about how much time elapsed on their clocks during the orbit. Since Alice is lower, her elapsed time will be slightly shorter than Bob's. For a 1000 meter height difference, if we assume Alice is at sea level, her elapsed time is about 1 part in ##10^{13}## shorter. Over 250,000,000 years, that works out to about 860 seconds shorter. I'm not sure if that's the question you're asking.

 

[berkeman]

Please see a new thread where the OP is trying to formulate his thought experiment better:

https://www.physicsforums.com/threads/a-well-defined-thought-experiment.1058074/

(This thread is tied off for now -- please respond in the new thread. Thanks)