My understanding of relativity - is this correct?

[Urkelli]

Okay, I'm kind of new to the subject but I'm learning quite rapidly!
So I've been interested in Einstein's theories for some time now and been reading and watching movies about it and I need to know if I have understood it correctly.
This is my understanding of the relativity theory, it might be a little different, but probably just another side of the same coin.

Before I start, I need to talk about FPS, or Frames per Second. FPS is used mostly within movie and games so tell how many times the picture updates per second.
The most common number of FPS during a game is 60. That means the screen flashes pictures 60 times per second, creating an illusion that it is moving.

Just to make it easier to explain this, let's just assume life is in 100 FPS and the speed of light is 100 km/h (very much lower than the real number). Everything you see in real-life is pictures (let's assume this as well) flashing before our eyes, also creating the illusion that it is moving (like a TV-Screen)

Let's say I'm in space. 100 km to my left, there's a planet. 100 km to my right, there's another planet. These two planets are the exact same size. Since the speed of light is now 100 km/h, I will see 1 hour old stuff when looking at either of the planets because it take 1 hour for the light to reach me. If I travel towards the left planet at a speed of 100 km/h, I will "browse" the pictures at 200 km/h. This will make the time on the left planet go double as fast than it would if I would have been still.

But while moving towards the left planet at 100 km/h, I'm also moving away from the right planet at a 100 km/h. That means I am just as fast as the speed of light coming from the right planet. So if I would look at the right planet (while still heading towards the left one), I would see the same picture as long as I move at a the same speed (100 km/h). What would happen if I was moving at 150 km/h? The left planet would go 2.5 times faster than normal, and the right planet would go at a -0.5 times faster, it would go in rewind since I'm faster than the light.

So if the time on the both planets are 16:00. After traveling 1 hour to the left planet at 100 km/h, the time would be 18:00 when I'm at the left planet, since for me, the time goes at a double speed. When reaching the left planet, the right planet would still be at 16:00, since I was traveling at the speed of light, and my perception of the time has changed. If I would go back to my original position (100 km away from both planets), it would take me another hour. The time at the left planet would stop completely for 1 hour, and the right planet would go at double speed. When I'm at my destination, the time on both planets is 18:00.


Is this how it works?

 

[ghwellsjr]

No, you are describing non-relativistic Doppler shift which isn't the way the world works.

 

[Dale]

Let's say I'm in space. 100 km to my left, there's a planet. 100 km to my right, there's another planet. These two planets are the exact same size. Since the speed of light is now 100 km/h, I will see 1 hour old stuff when looking at either of the planets because it take 1 hour for the light to reach me. If I travel towards the left planet at a speed of 100 km/h, I will "browse" the pictures at 200 km/h. This will make the time on the left planet go double as fast than it would if I would have been still.

But while moving towards the left planet at 100 km/h, I'm also moving away from the right planet at a 100 km/h. That means I am just as fast as the speed of light coming from the right planet. So if I would look at the right planet (while still heading towards the left one), I would see the same picture as long as I move at a the same speed (100 km/h). What would happen if I was moving at 150 km/h? The left planet would go 2.5 times faster than normal, and the right planet would go at a -0.5 times faster, it would go in rewind since I'm faster than the light.

Hi Urkelli, welcome to PF!

First, if the speed of light is 100 kph then you cannot go 100 kph, let alone 150 kph. So, let's use a more realistic speed of 60 kph.

What you are describing is called the Doppler shift, and we would use units of Hz rather than fps, but it is the same idea. Classically, if you were traveling at v=60 kph into a f0=100 Hz signal transmitted on waves moving at c=100 kph then you would expect the frequency you received the signal to be:
$$f=\left(1+\frac{v}{c}\right) f_0 = \left(1+\frac{60 kph}{100 kph}\right) 100 Hz = 160 Hz$$

However, relativity predicts instead that the frequency of the received signal would be:
$$f= f_0 \sqrt{\frac{1+v/c}{1-v/c}} = 100 Hz \sqrt{\frac{1+60/100}{1-60/100}} = 200 Hz$$

Careful measurements confirm the relativistic prediction.

 

[Nugatory]

But while moving towards the left planet at 100 km/h, I'm also moving away from the right planet at a 100 km/h. That means I am just as fast as the speed of light coming from the right planet...
Is this how it works?

Nope - that's the key difference between how the world really works and our intuition about how it works. The intuition comes from a lifetime of experience dealing with speeds that are negligible compared with the speed of light, so doesn't prepare us for relativistic effects.

A key principle of special relativity is that all observers always see light moving at the same speed, regardless of the speed of the observers. So suppose you were moving towards the left-hand planet at 50km/h. (I chose 50km/h instead of your 100km/h, because 100km/h would be the speed of light in this imaginary world, and anything but light traveling at the the speed of light turns out to be impossible to sensibly describe).

The observer on the left-hand planet will measure the light from the right-hand planet approaching at 100km/s, will measure their own light leaving for you and the other planet at 100km/sec, and will see you approaching at 50km/sec.

The observer on the right-hand planet will measure the light from the left-hand planet approaching at 100km/s, will measure their own light leaving for you and the other planet at 100km/sec, and will see you moving away at 50km/sec.

But you see will the light from both both planets approaching you at 100km/sec. You will also see frames arriving from the left-hand planet at a rate greater than 100 fps, and from the right-hand planet at a rate less than 100 fps.

It would be that way even if you were moving at 99.99999999999 km/sec. You'd still measure the same 100km/s speed for the light approaching from both planets, and the rates of frame arrival between the two would be even more different.

 

[Urkelli]

Hi Urkelli, welcome to PF!

First, if the speed of light is 100 kph then you cannot go 100 kph, let alone 150 kph. So, let's use a more realistic speed of 60 kph.

What you are describing is called the Doppler shift, and we would use units of Hz rather than fps, but it is the same idea. Classically, if you were traveling at v=60 kph into a f0=100 Hz signal transmitted on waves moving at c=100 kph then you would expect the frequency you received the signal to be:
$$f=\left(1+\frac{v}{c}\right) f_0 = \left(1+\frac{60 kph}{100 kph}\right) 100 Hz = 160 Hz$$

However, relativity predicts instead that the frequency of the received signal would be:
$$f= f_0 \sqrt{\frac{1+v/c}{1-v/c}} = 100 Hz \sqrt{\frac{1+60/100}{1-60/100}} = 200 Hz$$

Careful measurements confirm the relativistic prediction.

So your first equation is for the Doppler Effect, and the second is for light?
If we use the real speeds, would V=13 M/S and C=300.000.000 m/s (approx)? What would f0 be and what does that mean?

Thank you all for answers, I really appreciate it and I'm learning loads! :D

 

[Dale]

So your first equation is for the Doppler Effect, and the second is for light?
If we use the real speeds, would V=13 M/S and C=300.000.000 m/s (approx)? What would f0 be and what does that mean?

Thank you all for answers, I really appreciate it and I'm learning loads! :D

Both equations are the Doppler effect. The first is the incorrect Newtonian formula. That is what you were using in your example. The second is the correct relativistic formula.

F0 is just the frequency of the source signal. It can be anything, depending on the nature of the signal. In your example it was 100 Hz.