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

[Raymond Potvin]

It is the same kind of mind experiment as the light clock one, so if its assumptions are not self-consistent, then the light clock ones are not either. The main difference between the two mind experiments is that one clock depends on the motion of light, whereas the other depends on the motion of the earth: we can see the Earth moving from a distance, but we cannot see the light traveling between the mirrors. We know that the light coming from the Earth would be traveling directly to our eyes, whereas we have to assume that the light would be traveling sideways between the mirrors. The light clock mind experiment was presented to explain time dilation, but there is no way to explain time dilation with the Earth clock. Yet, there should be since the two mind experiments are equivalent, and moreover, SR says there is when motion between source and observer is direct.

 

[Janus]

You are using the conclusions of SR in a pre-SR mind experiment. With doppler effect, what you see is what you get. It happens the same way for light or for sound, it only depends on motion between source and observer.

But it doesn't happen the same way for light as it does for sound. With sound, the Doppler shift is dependent upon whether it is the source or the observer that is moving with respect to the medium carrying the sound. With light, it is only the relative motion between source and observer that counts. The two give quite different end results for an observer separating from and returning to a clock.

If we are moving away from the earth, we will measure more seconds per year than if we are moving towards it. With the light clock, we could assume that light took more time while traveling sideways to the motion, but not this time. This time, it is traveling directly between us and the earth, so it doesn't take more time wether we are traveling one way or another: when we will get at one light year from the earth, we will see a light that has traveled during a year. It will only be blueshifted or redshifted whether we are traveling towards the Earth or away from it at that moment.

Actually when you reach 1 ly from the Earth, you will be seeing light that left Earth less than 1 year ago by your clock. Let's assume that you have a relative motion of 0.5c with respect to the Earth. So by your clock it will take 2 years to get 1 light year from Earth. But the light you now see from Earth is not light that left it one year ago. If the Earth is 1 ly away now, and it takes some non-zero time for light to travel from Earth to you, then the light you are seeing at the moment you are 1 ly away left Earth when it was less than 1 ly away. (~0.6667 light years away.) thus you will be seeing light that left Earth just 0.6667 yrs ago by your clock.

Now let's assume, as you are that there is no time dilation between Earth and our traveler. That means that the the Earth clock would have reading 1.333 yrs ( the same as the Traveler's clock) when the light left.

Now let's look at this from the perspective of the Earth. the light carrying the information of the Earth clock reading 1.333 yrs leaves Earth when the traveler is 1.33 yrs*.05c = 0.667 light years away. It is chasing after the ship at c, and catches up to it in 1.333 yrs. But assuming no time dilation, the ship clock was already reading 1.333 years (the same as the Earth) when the light left Earth, and so according to the Earth the traveler will read 2.667 years on his clock when he sees the Earth clock read 1.333 yrs. This does not jive with the 2 years the traveler would say was on his clock when he sees the the Earth clock reading 1.333 yrs.

If however, we assume time dilation, the inconsistency goes away.
Now according to the traveler, the clock on Earth is ticking at 0.866 the rate his own is. The light he sees when he is 1 ly from the Earth still left when his clock read 1.333 yrs, but now the Earth clock only reads ~1.1544 years. So when he is 1 ly from the Earth, And his clock reads 2 yrs, he sees the Earth clock read 1.1544 years.
Looking at this from the Earth's frame, The light carrying the 1.1544 yr reading leaves Earth when the ship is 0.577189 ly rs away and takes 1.1544 yrs to reach catch up to the ship. But according to the Earth, the ship's clock is running slow by a factor of 0.886, so when the light leaves Earth, the ship clock only reads 1 year, And in an additional 1.1544 yrs will have advanced another 1 year and reads 2 yrs when the light carrying the 1.1544 yr Earth clock reading arrives. This is in agreement with what are traveler says happened.
Also, the 1.1544 years that the traveler sees the Earth clock advancing in two yeas of his own time is consistant with the Relativistic Doppler shift formula.
which gives a Doppler shift rate of ~0.557 for a light source receding at a relative speed of 0.5c . 0.577 x 2yrs = 1.154 years.

As long as you adhere to the postulate of the invariant speed of light in a vacuum, it doesn't matter if you use the Light clock or Doppler shift, you get the same time dilation.

 

[PeterDonis]

It is the same kind of mind experiment as the light clock one

No, it isn't, because you explicitly said you were using classical Doppler, not relativistic Doppler. Classical Doppler is inconsistent with the rest of the assumptions in the light clock thought experiment, which assumes standard SR and therefore relativistic Doppler. As I said, you can't change just one thing.

 

[Mister T]

This thread made me imagine a mind experiment about time: using only classical doppler effect, would we count more or less Earth cycles around the sun than those who really happened on Earth (years), during a round trip at 100 light years away from Earth at any speed, including at close to the speed of light, accelerations and decelerations included?

Perhaps you're unaware of what the phrase "classical Doppler effect" means. Usually it's a phrase used to describe an analysis of the Doppler effect that assumes the Newtonian approximation, thus ignoring things like time dilation.

If we remove the word "classical" from your question it becomes the typical twin paradox. The traveling twin will indeed count the same number of Earth orbits around the sun as "really" happened. It's just that the time that elapses for each orbit will be less for the traveler than for someone who remained on Earth.

You are correct in that any clock will behave this way. But time dilation describes the way different observers will measure the time between ticks, not the number of ticks. The number of ticks is a relativistic invariant, all observers will agree on its value.

 

[Raymond Potvin]

It's just that the time that elapses for each orbit will be less for the traveler than for someone who remained on Earth.

It will increase with redshift when going away, and decrease with blueshift when going back, so at the end, one year will have elapsed for each Earth cycle. As I said, there is no way to use that mind experiment to show how time dilation works.

Classical Doppler is inconsistent with the rest of the assumptions in the light clock thought experiment, which assumes standard SR and therefore relativistic Doppler.

The light clock mind experiment shows how light would appear to travel when motion between the clock and the observer is crosswise: it only explains time dilation for transverse motion. SR was developed to explain the null result of the Michelon-Morley experiment, so it has to apply to any kind of constant motion, but there is no mind experiment to explain the direct one.

If the Earth is 1 ly away now, and it takes some non-zero time for light to travel from Earth to you, then the light you are seeing at the moment you are 1 ly away left Earth when it was less than 1 ly away. (~0.6667 light years away.)

The time light takes to travel one light year is one year, it does not depend on the time the observer takes to get there. The motion of light does not depend on the motion of bodies.

 

[PeterDonis]

The light clock mind experiment shows how light would appear to travel when motion between the clock and the observer is crosswise: it only explains time dilation for transverse motion.

Are you aware that there is also a light clock thought experiment for the case where the light clock's beam is parallel to the direction of motion? There is.

In fact, you can even combine them both into a single thought experiment. That makes it even easier to see why the parallel case must work the same as the transverse case.

SR was developed to explain the null result of the Michelon-Morley experiment

First, this is historically false: the null Michelson-Morley result was only one of a number of clues that Einstein used.

Second, it's irrelevant anyway, because the range of phenomena that SR covers is independent of how it was historically developed. SR certainly covers both transverse and parallel light clocks, since both are set in flat spacetime and SR covers all physics that can be modeled as taking place in flat spacetime.

 

[Raymond Potvin]

Are you aware that there is also a light clock thought experiment for the case where the light clock's beam is parallel to the direction of motion?

If the clock is also moving sideways to the observer, then to me, it can probably not explain the direct motion. Do you have a link to such a mind experiment?

First, this is historically false: the null Michelson-Morley result was only one of a number of clues that Einstein used.

M-M was more than a clue, it was a data on which he could rely. He probably used it to formulate that the speed of light was independent from the speed of bodies, one of his two postulates.

Second, it's irrelevant anyway, because the range of phenomena that SR covers is independent of how it was historically developed. SR certainly covers both transverse and parallel light clocks, since both are set in flat spacetime and SR covers all physics that can be modeled as taking place in flat spacetime.

I know SR covers all the possibilities, I was only looking for a mind experiment to explain direct motion.

 

[Janus]

The time light takes to travel one light year is one year, it does not depend on the time the observer takes to get there. The motion of light does not depend on the motion of bodies.

But the light that the traveler sees when he is 1 light year from the Earth didn't leave the Earth when he and the Earth were 1 light year apart.

You and a friend are floating in space and moving apart at a rate of 1/2 a meter per second. When he is 6 2/3 meters from you he tosses a small object towards you so that it is coming at you at 1 meter per second. The object takes 6 2/3 sec to get to you, in which time your friend travels an additional 3 1/3 meters. So when you catch the object, he will be 10 meters from you. You do not use his distance at the moment you catch the object to determine how much time it took from the moment he tossed the object to your catching it, you have to use the distance he was from you when he tossed the object..

The same is true for our traveler and the Earth separating at 0.5c. The the light that the traveler sees when the Earth is one light year away left the Earth when the Earth and traveler were 0.667 light years apart and took 0.667 light years to reach the traveler, during that time, the Earth- traveler distance increased by an additional 0.333 light years and they are now 1 light year apart. How far the Earth is "now" when he sees the light does not determine how long it took the light to reach him, how far apart they were when the light left the Earth does.

 

[PeterDonis]

Do you have a link to such a mind experiment?

Rather than try to find a simple online presentation of the thought experiment, I'll just describe it directly.

We set up two light clocks, such that, in their common rest frame, the two beams go out in perpendicular directions, bounce off mirrors at equal distances from the origin, and arrive back at the origin at the same instant--i.e., at the same event (point) in spacetime. Obviously both of them tick at the same rate in this frame.

We now view the two clocks from a frame which is moving, relative to the clock rest frame, in such a way that one clock is parallel with the motion and one clock is transverse to it. We take it as established that the transverse clock will show time dilation. But, since the two clocks tick at the same rate in their common rest frame, they must tick at the same rate in any frame, since each meeting of the two light beams back at the origin, which is what establishes the tick rate of each clock, is a single event in spacetime. In other words, the worldlines of the two beams coincide each time they meet at the origin, and coincidence of worldlines is an invariant, the same in all frames. Therefore, if the transverse clock shows time dilation in the moving frame, the parallel clock must show time dilation in the moving frame as well.

He probably used it to formulate that the speed of light was independent from the speed of bodies, one of his two postulates.

Historically, it's pretty well established that Einstein based this postulate on Maxwell's Equations. In other words, he based it on the fact that the well-established equations for electromagnetism indicate that all electromagnetic waves must travel at an invariant speed. This is far more general than just the single null result of the M-M experiment.

However, as I said before, how SR was historically developed is irrelevant to what its domain of validity is. Its domain of validity is all phenomena that can be modeled as taking place in flat spacetime, i.e., all phenomena for which gravity is not significant.

 

[Raymond Potvin]

But the light that the traveler sees when he is 1 light year from the Earth didn't leave the Earth when he and the Earth were 1 light year apart.

The time the traveler takes does not change the way he counts the Earth cycles. If he knows about doppler effect, he knows that the years will look stretched when he will be going away from earth, and he knows that they will look contracted when he will be going towards to it, so he knows his clock will register the same total years on the roundtrip. The only way to change that is to add SR calculations to it, but then, we still have no mind experiment for direct motion.

 

[PeterDonis]

we still have no mind experiment for direct motion.

Yes, we do. Read my previous post.

Also, the SR calculations do not depend on any particular thought experiment. You can do the SR math and use it to make predictions independently of any of that. And those SR predictions have massive experimental confirmation, so taking the position that you aren't convinced they're valid until you've seen one particular thought experiment does not strike me as reasonable.

 

[Raymond Potvin]

Therefore, if the transverse clock shows time dilation in the moving frame, the parallel clock must show time dilation in the moving frame as well.

I see! As I thought, the observer is still looking at the clocks go by, so it is not really a new experiment, moreover, it only injects the result of a mind experiment into another one, which is far from deducing the same result out of two different experiments.

Historically, it's pretty well established that Einstein based this postulate on Maxwell's Equations. In other words, he based it on the fact that the well-established equations for electromagnetism indicate that all electromagnetic waves must travel at an invariant speed. This is far more general than just the single null result of the M-M experiment.

Data is more important than assumptions though, and I think that Maxwell's Equations and Einstein's SR both assumed that the inertial frame principle applied to light. I have an objection against that assumption, but I'm afraid it is not reasonable, so I cannot discuss it here. :0)

 

[PeterDonis]

Maxwell's Equations and Einstein's SR both assumed that the inertial frame principle applied to light.

I'm not sure what you mean by "the inertial frame principle". If it just means invariance under Lorentz transformations, that's not an assumption for Maxwell's Equations, it is a proven theorem. If you mean SR, Lorentz invariance isn't an assumption either, it's deduced from the principle of relativity and the postulate that the speed of light is the same in all inertial frames.

 

[PeterDonis]

the observer is still looking at the clocks go by, so it is not really a new experiment

I don't understand what you mean by this.

it only injects the result of a mind experiment into another one, which is far from deducing the same result out of two different experiments.

I don't understand what you mean by this either. I suspect you have concocted some personal rules for "mind experiments" that don't correspond to how they are actually used in physics.

 

[anorlunda]

Responding to the thread title and the OP, APOD posted a wonderful video.

[/PLAIN]
Explanation: What would it look like to travel near the speed of light? Strange visual effects would appear as documented in the above relativistically-accurate animation. First of all, relativistic aberration would cause objects to appear to bunch up in front you. Next, the Doppler shiftwould cause the colors of forward objects to shift toward the blue, while things behind you would http://www.cbu.edu/~jvarrian/applets/doppler1/doppler.htm toward the red. Similarly, the world in front of you would seem to move unusually fast, while the world behind you http://casa.colorado.edu/~ajsh/sr/sr.shtml to slow down. Objects to the sides will appear rotated, possibly enabling surfaces normally hidden from you to become visible. Of course, since constant motion is relative, the same effects would occur were you to remain stationary and the entire world advanced toward you.

 

[Mister T]

It will increase with redshift when going away, and decrease with blueshift when going back, so at the end, one year will have elapsed for each Earth cycle.

It's true that there's a red shift going away and blue shift returning, It's not true that at the end one year will have elapsed on the traveling twin's clock for every trip Earth made around the sun.

 

[Mister T]

I see! As I thought, the observer is still looking at the clocks go by, so it is not really a new experiment, moreover, it only injects the result of a mind experiment into another one, which is far from deducing the same result out of two different experiments.

But you can do a complete and independent analysis of the parallel light clock with no reference to the perpendicular one. When you do the math two things stand out:

1. The results of the perpendicular light clock analysis match the results of the parallel light clock analysis.

2. The results of the perpendicular light clock analysis match what we observe real clocks doing.

Thousands of engineers, technicians, and scientists work with time dilation every minute of every day at hundreds of locations across the world. It's real.

 

[Dale]

Data is more important than assumptions though,

I agree completely:
http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

 

[Chris Miller]

It's just that the time that elapses for each orbit will be less for the traveler than for someone who remained on Earth.

So, if the traveler's velocity were close enough to c, she might "see" the Earth orbiting the sun millions of times per second?

 

[jbriggs444]

So, if the traveler's velocity were close enough to c, she might "see" the Earth orbiting the sun millions of times per second?

If by "see", you mean see with your eyes, using an appropriately powerful telescope then a traveler approaching the solar system could indeed see such a thing.

From the traveler's point of view, the explanation for this would be that the Earth is orbiting the sun quite slowly (time dilation), but that the solar system is approaching the traveler at such a high rate of speed that light from the "Earth last Christmas" has only moved ahead by 1000 feet or so by the time the light from "Earth this Christmas" is being emitted (Doppler effect for a moving emitter).

From the Earth's point of view, part of the explanation for this is that the traveler's clock is slowed down so much that the light from "Earth last Christmas" and "Earth this Christmas" arrive one microsecond tick apart according to the traveler's massively slowed clock (time dilation). The other part is the fact that the traveler is racing ahead to meet all the images of Christmases past so that the rate nearly doubles (Doppler effect for a moving receiver).

 

[PeterDonis]

you can get out anytime you want.

Done. Thread closed. Please read the PF rules on personal theories; further posts along the lines you have shown here will receive a warning.