Maximum and minimum speed

1. Oct 20, 2014

Whitefire

If there is maximum speed in the universe and we call it c, and it is not relative, is there also some ultimate rest state, an unrelativistic "0" speed?

I sort-of know that there is none, because it would mean that there exists a non-relativistic frame of reference. But I can't quite grasp what is wrong with the following reasoning.

Let's start with the twin paradox. One of them has been accelerated and it makes the difference, non-inertial frame of reference was involved.

So far so good.

If the accelerated twin moved, say, with near-light speed, and he looked back at a clock on his twin's wrist, it would be ticking really fast, right?

So. Can I draw the conclusion that the faster the clock goes, the less accelerated that object had been? Why/why not?

Using this observation, can we determine that some hypothetical object has never been accelerated? That it has a minimum speed, as opposed to the maximum speed of light?

2. Oct 20, 2014

ghwellsjr

First off, the maximum speed c is relative to any Inertial Reference Frame (IRF) you want to pick. You can say that the value of c is absolute (not relative), if that is what you meant, but once you understand that the speed of light is relative to every IRF then I don't think your conclusion that there is some ultimate rest state makes any sense, do you?

No, a non-inertial frame of reference does not need to be involved, it only complicate things. You can figure out the twin paradox using any IRF. If you want to resort to a non-inertial frame of reference, then you have to define exactly what you meant because there is no commonly accepted way of doing that.

No, it would not be ticking really fast. Where did you get that idea?

Your conclusions are based on incorrect assumptions. You need to learn the basics of Special Relativity.

3. Oct 20, 2014

Staff: Mentor

We cannot. At most, we may be able to deduce that it has accelerated less than we have (or vice versa) since we last looked, but all that does is establish a speed relative to us.

If you're not familiar with relativistic velocity addition (google will find some good sources) read up on that as well - it will go a long ways towards explaining how we can have an upper speed limit without implying an absolute rest frame.

Last edited: Oct 20, 2014
4. Oct 20, 2014

Whitefire

I was drinking coffee and just clicked something on youtube. This, I think:

Minute 2:40

Well, my bad, I know that most of youtube is crap, really
The guy published some book though, so he looked sort of legitimate...

5. Oct 20, 2014

Whitefire

Last edited by a moderator: May 7, 2017
6. Oct 20, 2014

Staff: Mentor

Last edited by a moderator: May 7, 2017
7. Oct 20, 2014

phinds

Your "sort-of know" is correct. All speeds except c are relative. This means that there is no such thing as "absolute rest". Relativistic speeds do not "add" in the normal sense and nothing can go faster than c which is, as you note, the universal speed limit.

No, slow, not fast.

Check out the full explanation in this link: http://www.phys.vt.edu/~jhs/faq/twins.html

EDIT: OOPS ... I got sidetracked and didn't post this right away, so it's outdated by the previous responses.

8. Oct 20, 2014

ghwellsjr

9. Oct 20, 2014

PAllen

Yeah, anyone who starts by saying "I'm going to explain the relationship between time, existence, and energy", close it right away. It's a crock.

10. Oct 20, 2014

PAllen

It's not just bad pop sci, his statement at circa 2:50, about seeing fast running clock, is totally wrong. He would flunk any physics course. The reality is the opposite: each would see the other's clock running very slow.

11. Oct 21, 2014

Whitefire

Well, I am definitely not a person to defend the guy in the video. But he can't be totally wrong. There must exist at least some period of time, from "traveller's" point of view, when the other twin ages faster than him. This:
http://www.phys.vt.edu/~jhs/faq/twins.html
This http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_gap.html is somewhat to vague for me.

To simplify my point, let me use a childish example. Lets forget about twins, prime/unprime etc. We have two clocks. Red and Blue. Perfectly synchronized, standing next to each other. And they have eyes! They can see.

The Red one goes on a near-light speed trip through some point in space and immediately returns. They observe each other continuously. They do not take their eyes off each other. Upon arrival, the Red one shows 50 minutes. The Blue one shows that 1 minute has passed.

And we are only interested in what the Red one sees. The one that does the travelling. And even further, I am not interested in what space distortions the Red one sees (compared to Blue). Only what is on the Blue's face, from Red's perspective.

And he can't be seeing Blue clock being slowed all the time, and then "oops, 50 minutes". He must be seeing some "speed-up".

When, from his point of view/frame reference, this happens? During all accelerations? During the way back? During the accelerations toward the Blue?

Last edited: Oct 21, 2014
12. Oct 21, 2014

A.T.

This is a crucial distinction: What the traveling twin sees optically vs. What happens in his non-inertial frame.

For the purely optical impression you have to consider light signal arrivals, which increase in frequency on his way back. So that's when the traveling twin sees the other one aging faster.

For the description from a non-inertial frame, you have to consider the gravitational time dilation during the acceleration. So that's when the traveling twin computes the the other one to age faster.

Last edited: Oct 21, 2014
13. Oct 21, 2014

PAllen

The problem is, watching from the beginning, his statement about a clock appearing to run fast (for one observer, while the other sees slow) is for inertial observers. This is just completely, totally, wrong.

14. Oct 21, 2014

Staff: Mentor

This is the situation covered by the Doppler Shift section of the FAQ.

15. Oct 21, 2014

Staff: Mentor

Here's a detailed description of the same situation, using calendars instead of clocks:

16. Oct 21, 2014

Whitefire

I admit I did not read about Doppler Shift in the FAQ you mention--I it was my impression that the Shift (on its own) cannot be responsible for lack of symmetry in the twin situation.

As AT said, it is crucial that I want to discuss only what the twins see optically, not what happens in their non-inertial frames.

Here Jtbell's example comes very handy. If I'm reading this correctly, the example you used, Jtbell, can be simplified so:

From earth:
my 1 year is traveller's 1/3 year (x9)
my 1 year is traveller's 4 year (x1)
(my 10 years, traveller's 6 years total)

From traveller:
my 1 year is Earth's 1/3 year (x3)
my 1 year is Earth's 3 years (x3)
(my 6 years total, Earth's 10 years total)

This means that
1) The travelling twin sees the clocks on Earth go faster than his on his way back (which answers my question, by the way).

2) The paradox is explained because the symmetry is broken: mainly in that, from Earth, you observe the traveller's clock go slower for 9 Earth's years; while the traveller observes Earth's clocks go slower for only 3 of his years.

Of course if we take into account that no observations are immediate, because of light speed limits, the summary would be very different (for both sides). But it's another story. Is this correct?

17. Oct 21, 2014

Staff: Mentor

That's already taken into account. In the non-relativistic Doppler effect, the change in frequency is caused by the fact that successive signals from the source take different amounts of time to reach the observer because the source-to-observer distance is changing. The relativistic Doppler effect also includes the time dilation of the source with respect to the observer.

18. Oct 21, 2014

Whitefire

Right. Thank you guys, and as far as I am concerned, this topic can be closed.

19. Oct 21, 2014

Janus

Staff Emeritus
You have to take the the light delay into account to explain why the the two twin's see each others clock as running slow and fast for different periods.

The traveling twin sees his brother's clock run slow for half the time and fast for half the time because he sees the shift occur the instant he turns around to head back to his brother. The Earth twin, however has to wait for the light to travel from the turn around point to reach him before he sees the shift from his Brother's clock running slow to fast.

Example:
Traveling twin takes off at 0.8c and travels for what he measures to be 1 year. During this time, he see's his brother's clock run 1/3 as fast as his and accumulate 1/3 year of time. He turns around and heads back toward Earth. He immediately sees his Brother's clock run 3 times faster, and in the one year it takes to return to Earth, sees Earth accumulate 3 years for a total of 1 1/3 years for his own 2 years.

Meanwhile, the Earth twin watches his brother travel away at 0.8c and sees his clock run at 1/3 as fast as his own and observes this until he sees his brother's clock read 1 year. This takes 3 years by his clock. When his brother turned around, he was 1 1/3 light years away as measured by the Earth twin. So by the Earth's twin's clock, the traveling twin turned around when the Earth twin's clock read 1 2/3 years, which means by the time he sees his brother turn around, he has already been on his way back to Earth for 1 1/3 years, and is now only 4/15 light years away, and will arrive in 1/3 year Earth twin time. During that 1/3 year he sees the Traveling twin clock run 3 times faster and gain 1 year.

So to recap:
The Earth twin see's the Traveling twin's clock run 1/3 as fast as his own for 3 years and 3 times as fast as his for 1/3 year and thus accumulating 2 years for his own 3 1/3 years.

The Traveling twin sees the Earth twin's clock runs 1/3 as fast as his own for 1 year and 3 times as fast as his for 1 year, thus accumulating 3 1/3 years for his own 2 years.