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

A.T.

21. Dec 3, 2016

Staff: Mentor

If you are interested in generalities and not specific numbers then ask the question in terms of generalities instead of specific numbers. All you have to say is "relativistic speed". Everything you add beyond that is a distraction.

Your first post could/should have been something like: "I am travelling inertially at relativistic speed on a path parallel to the plane of the ecliptic. What is the earth's orbit like in my frame?" That's all.

22. Dec 4, 2016

Battlemage!

If the bold is your main question, I think someone pointed out that an orbit can be considered a clock, and if you're at rest in the spaceship then it appears to me that the earth's orbit would constitute a "moving clock" according to your reference frame. Yes, no? Maybe so?

23. Dec 5, 2016

Chris Miller

Again, very helpful, thanks so much. Been trying to get my head around all weekend. Googled "relativity of simultaneity" which seemed, in the example (Alpha Centauri attacking us) paradox to do with direction. Is there any time in my near-c frame prior to earth's 100 revolutions around the sun? Seems not possible. If I extrapolate by continuing at this gamma factor of >1050 velocity for a second/hour/year, will the universe have "already" (at my t'<0) expanded into flat, dark, cold and be waiting for me? In other words, is an event's occurrence at my t'<0 tantamount to its never having happened in my my frame of reference?

I'm also having trouble resolving the seeming asymmetry of earth's and my perspectives. E.g., to me earth appears very close, but to earthlings, although my clock is running similarly slow (virtually stopped), I'm 100 light years away. Why no reciprocal foreshortening?

24. Dec 5, 2016

Dragon27

It's really hard to understand what you're trying to say. I think it would be better if you took it slow and easy, one basic concept and aspect at a time.
What do you mean by "event at $t'<0$ never happened"? It happened at the time $t'<0$.
An inertial frame of reference exists, so to speak, "forever". There were events in the past (relative to the moment $t'=0$ in it), there will be events in the future. If something happens in the future relative to some event in one frame of reference, it may have happened in the past relative to the same event in some other frame of reference, but only if this "something" happens far enough from the event - far enough to become unreachable.