# B How would the solar system appear if you approached at near c?

1. Dec 2, 2016

### Chris Miller

Approaching earth from 100 light years (by earth's measurement) at the fastest theoretically (not practically) possible velocity where from your relative near-c frame the distance is foreshortened to 1 Planck length and a century elapses in earth's time frame to 1 Planck time in yours, how would SR, from your ~c frame, generally describe the earth's solar orbit? It seems, because everything is flattened to almost 2D in your direction of travel, the earth would be oscillating back and forth across its orbit's 186 million mile diameter perpendicular to your approach at a very high frequency, which, I know can't be right, since this far exceeds c.

I use the word "present" vs. "see" because I have no clue how you'd observe any of this, but am more interested in how SR would expect earth's orbit around the sun to present if you, somehow, could.

2. Dec 2, 2016

### Ibix

An orbit is like the pendulum of a clock. How do clocks moving with respect to you look?

There is no "theoretical maximum speed". You can get arbitrarily close to c as measured in some frame, but you can always accelerate more.

3. Dec 2, 2016

### PeroK

We're back to "time dilation" in a given direction again, I see! Somehow, you need to get the idea out of your head that time dilation is directional.

Time dilation is time dilation. If the Earth clock is moving slow, it's moving slow and the Earth isn't going anywhere fast with respect to the sun. Not in any direction.

4. Dec 2, 2016

### Chris Miller

I'm getting contradictory responses to this question, which is why I'm trying to clarify. Most answer that 1 century passes on earth in the traveler's Planck time interval. It's not in my head that dime dilation is directional, only length foreshortening.

5. Dec 2, 2016

### Chris Miller

If I am approaching the pendulum, head on, then like a pendulum, unless my velocity brings SR into effect. The theoretical maximum speed is not c, but anything less, of course.

6. Dec 2, 2016

### PeroK

In the reference frame of a particle or spaceship traveling close to $c$
relative to the solar system, then the solar system is foreshortened in the direction of motion and its clocks (including the orbit of the planets, which is a fairly good clock of sorts) run slow.

If you imagine approaching from "above" the plane of the solar system, then it would be normal in size and shape (*), but very thin and travelling very fast towards you. The planets would hardly move as it passes you by.

(*) as I think you understand these are the measurements in your reference frame, not what you would see, which would be significantly affected by the finiteness of the speed of light.

That's just basic SR.

7. Dec 2, 2016

### Ibix

I have no idea what you are trying to say here. All I was pointing out was that you can use the Earth's orbital motion as a clock. Do clocks moving with respect to you tick fast or slow?

There is no theoretical maximum speed, as I just said. You can always accelerate.

8. Dec 2, 2016

### Staff: Mentor

Why do you insist on using annoying numbers in your examples? Why not 0.6 c?

If you are not going to do the calculations yourself then just be a little courteous of other people and don't make your question unnecessarily difficult to answer.

9. Dec 2, 2016

### Chris Miller

(Peter's response best clarifies my question maybe.) The above to excerpted responses would seem to suggest earth's clocks running faster, not slower?

10. Dec 2, 2016

### Chris Miller

Thanks, Dale, and sorry. I don't expect anyone to perform any calculations. I'm trying to clarify generalities by using extreme parameters.

11. Dec 2, 2016

### PeroK

That looks like an entirely different question. What a muddle!

12. Dec 2, 2016

### Chris Miller

Sorry, misunderstood: Slow.

13. Dec 2, 2016

### Chris Miller

Hm... clearly I don't speak your language yet. To me it's basically the same.

14. Dec 2, 2016

### PeroK

Here's what you can't do:

1) A spaceship is approaching the solar system at nearly $c$ - gamma factor of 50, say. In the Earth's reference frame, the ship's time is dilated (running 50 times slow). From passing Alpha Centauri, the ship takes 4.5 years (Earth time) to reach us. The ship time has advanced only 1 month (approx) in this time. This is all in the Earth's reference frame.

False conclusion: Earth time is faster than ship time.

2) In the ship's frame, the distance from Alpha Centauri is only 1 light month. The journey takes only 1 month for the ship and, in that time, 4.5 years pass on Earth. The ship measures the Earth orbit the sun 4.5 times in 1 month. (False conclusion)

The correct statement 2) is:

2) In the ship's frame, the distance from Alpha Centauri is only 1 light month and that's how long (approx) the journey takes. The Earth clocks are running slow, so only about 12 hours pass on Earth during the journey (as measured by the ship).

False conclusion: Earth time is slower than ship time.

By changing your question from one frame to the next (ask one question in Earth frame and one question in ship frame) you appear to get different answers about whose clock is "really" running slow. Then, you set the two answers up against each other and the waters just get muddier.

Your questions should be posed such as:

In the reference frame of a ship, it passes Alpha Centauri at $t=0$ and reaches Earth 1 month later ...

15. Dec 2, 2016

### Ibix

Correct.
I'm not correcting your semantics. I'm telling you that there's no maximum speed in relativity - three times now. Planck's length isn't anything special. It's not the "shortest possible length", if that's what you're thinking.

16. Dec 2, 2016

### Dragon27

The Earth would stand still. Like, almost not move at all. Why do you think it wouldn't? Because 100 years should pass while you approach the Earth from 100 light years at almost light speed? Well, it should, in the Earth's frame of reference, not in you near-c frame of reference. In that frame of reference the Earth has already done it's 100 hundred revolutions around the Sun, and now is waiting for you to come by (which would happen in a planck length over speed of light seconds) practically motionless. You should never forget about the relativity of simultaneity.

17. Dec 2, 2016

### Chris Miller

This is helpful. Thanks. I should probably learn about and understand "the relativity of simultaneity" before I never forget about it. I'm having trouble with the "already" in your explanation.

18. Dec 2, 2016

### Mister T

If a century passes on an Earth clock, that's the elapse of a proper time (measured with a single clock). If $10^{-44}\ \mathrm{s}$ passes on the traveler's clock, that's also the elapse of proper time (measured with a single clock).

There's no meaningful way to say the century elapses here while the $10^{-44}\ \mathrm{s}$ elapses there. It therefore appears to me that your question doesn't make sense.

For Earth and the traveler to each measure an elapsed amount of proper time between the same two events, they would each have to be present at each of those two events. The twin paradox is famous for measuring a difference in this way, but if your traveler and Earth are in inertial motion relative to each other, they can never both be present at two separate events.

I tried to straighten out your thinking on this in another thread. Until you realize that proper time is measured with one clock, and that at least two clocks (or their equivalent) are needed to measure dilated time, you'll never resolve the issue you're attempting to get at with your questions.

The only way to fulfill that expectation is to leave numbers out of your discussions.

They're so extreme that they do the opposite of clarify. With a speed negligibly close to the speed of light all you have to do is mention the value of $\gamma$. For example, $\gamma=100$. Then for every year of proper time that elapses between two events in either of the frames, 100 years of dilated time is measured between those same two events in the other.

19. Dec 3, 2016

### Dragon27

One need to understand exactly what the events look like in different frames of reference, of course. Here's what I meant by "already". We've got two frames of reference: the stationary one and the near-c one (these are just names). In the stationary frame of reference, at $t=0$, there's a space ship at the origin (which has near-c velocity in the direction of the Earth's orbit), and the Earth 100 light years away from the ship. The Earth has 0 revolution's around the Sun (years) on its clock (for convenience's sake). Now, in the near-c frame of reference, the ship is at the same origin (at $t'=0$), the Earth's orbit is (because of the length's contraction) 1 Planck's length away from the ship, and the Earth has 100 revolutions (and years) on its clock. When did they happen? In our near-c frame of reference, they happened in the past, $t'<0$, before the event $A$ (the ship is 100 light years away in the stationary frame or 1 Planck's length away in the near-c frame from the Earth).

20. Dec 3, 2016