Why are the effects of Time Dilation permanent but Length Contraction is Not?

ghwellsjr

The spaceship can measure the speed that the person standing on earth is traveling away from him by observing the Relativistic Doppler of a signal coming from earth and calculating the speed. It will be the same Doppler and therefor the same speed that the earth observer will measure of the spaceship.

dfaullin

Okay, imagine this scenario.

An observer on Earth is going to measure the distance to Alpha Centauri in two ways. First, he will send a photon and calculate the distance as 1/2 ct.

Then, he will send an odometer to Alpha Centauri traveling near the speed of light (say .9c) and have it return and will take 1/2 of the odometer reading.

Which distance will be shorter?

~Dylan

PAllen

Well, there really is no such thing as an odometer to measure travel through empty space. This is why, in my initial answer, what I posed for each twin to measure is the travel distance of the other, as they measure it. So let's say the twin A remains on earth and measures B traveling 4 lightyears away (to some star) and back - total distance 8 ly. Assume B has traveled there at .9c. B measures A traveling away and back to B. The distance B measures for A's trip will be approx 3.5 light years (assuming 'instant turnaround'). However, as soon as B stops at earth again and measures the distance to the star, they get 4 light years. So they say 'whoa, this relativity can be really strange'. Yes, it can.

As to how B can measure A (and the sun) distance as A travel's away and back (per B), any valid method will do (in our situation of constant speed). For example, they could use parallax with the aid of companion traveling along with them at some distance away. This modest distance (to the companion) could also be measured any convenient way (rulers, light travel time, it doesn't matter).

dfaullin

Mind blown!

Elroch

To an observer on the spaceship, the rest of the Universe appears to be squashed in the direction of flight. For example, when a spaceship slows down, in the (non-inertial) decelerating frame, things in front of it can appear to be receding (and things behind it can appear to be receding as well). Of course, it is also true that, to someone observing a spaceship, it appears to be squashed along the direction of (relative) motion.

Elroch

True. There can be no such thing since there is no aether. But measuring position and speed relative to the midpoint of source and destination seems a natural choice for this problem.

PAllen

In a generic twin problem, there is not necessarily a well defined destination, certainly not necessarily an obvious mid point (if you consider arbitrary trajectories). The thing that seems natural and completely general for me - best stand in for an odometer - is for each twin to measure the apparent travel distance of the other twin; as I have suggested in post #3 and again in #20.

Qzit

WOW, this is a fun thread. What would be the difference between your brain synapsis firing at 16 frames/second, 16 frames / day or 16 frames/year? If everything is relative in your FoR absolutely nothing. Your synapsis is your internal clock for judging time. So the traveling twin’s synapsis is slowed compared to the twin on Earth. Well I suspect so are your relative metabolism and the relative cycles of all the electrons in your body. In fact they can be so slowed that if you had a magic telescope to watch your twin on Earth he would seem to move so fast you would think of him as the comic book hero the Flash. Is the distance contracted? No. Your sense of time is contracted. If you were traveling at 0.9C and a photon closing the distance towards you would be 1.9C. A photon traveling parallel with your ship would have a relative departing speed of 0.1C. Now what is physically happening and what you observe to be happening are two different things because of the speed of your synapsis and the cycling electrons in your FoR.

ghwellsjr

Assuming that Alpha Centauri is 4 light years away from Earth, the observer on Earth will measure 8 years for a signal to get there and back and so will calculate its distance to be 4 light years.

He can send an odometer there and back at .9c and measure the distance that way. He can make an odometer by observing the spectrum of light coming from Alpha Centauri and from the Sun prior to sending away the odometer. Then, as the odometer is traveling, it continuously measures the Relativistic Doppler coming from both stars. One will be the reciprocal of the other. (Only one is required for the measurement but I'm showing that either one or both can be used.) Assuming that one of these ratios is R, the speed of the odometer is:

β = |(1-R²)/(1+R²)

Integrating the speed over time yields distance traveled as a function of time. To make the calculation easier, we will assume that the speed is constant throughout the entire roundtrip which means that we only have to multiply the speed by the total time to get the total distance.

Now let's work out the details for our example:

At .9c, the values of R will be √[(1-β)/(1+β)] and its reciprocal. So R for Earth will be 0.2294 and for Alpha Centari will be 4.359 during the outbound portion of the trip. For the inbound portion of the trip, these numbers are exchanged.

The odometer will use the equation above to determine that β is indeed 0.9c.

Now at 0.9c, the clock on the odometer will be running slow by a factor of 1/γ. We calculate γ as 1/√(1-β²), so 1/γ = √(1-β²) which equals 0.4359. Now we need to calculate how long the trip will take. We do this first in the Earth frame as distance divided by speed which is 8 light years (round trip) divided by 0.9c which equals 8.8889 years. Now we multiply this by 1/γ to figure out what the time will be in the odometer's frame. This will be 8.8889 years times 0.4359 or 3.8747 years. This means that the total distance traveled is 3.8747 times 0.9 c or 3.4872 light years for the round trip or 1.7436 light years for the distance between Earth and Alpha Centauri. As a sanity check, this should be the distance in the Earth frame divided by γ or multiplied by 1/γ which we calculated as 0.4359. Indeed, 4 times 0.4359 is 1.7436 light years.

So to answer your question, the distance measured by the odometer is shorter.

ghwellsjr

Well, I just showed how to make an odometer to measure travel through empty space.

And I don't understand why you base your conclusion on the idea that "there is no aether". I don't see the connection.

I also don't understand your comments about "the midpoint of the source and destination".

ghwellsjr

WOW, I think you're having too much fun. A lot of erroneous ideas here.

What do you mean that there is no difference between 16 frames per second, day or year? It is true that all processes, including biological will be slowed down for the traveling twin, as determined by the rest frame of the Earth, but the traveling twin will also determine that the Earth twin is the one that is experiencing time dilation according to his own rest frame. And you're also mixed up on the speed of a photon being 1.9c or 0.1c according to the traveling twin. I suggest that you do a lot of reading or asking questions instead of trying to answer them until you get yourself up on the learning curve.

harrylin

I also wondered about that... My 2 cts: There are no mechanical odometers; I suppose that what was meant, is that there is no material ether on which we could let an odometer roll. Note also that if we could, then any odometer would measure "absolute" lengths, for the wheel is at rest wrt the road at the point of contact!

And I think that the midpoint of source and destination depends on the reference system for two twins in arbitrary motion.

Qzit

ghwellsjr
I think you were reading with your mind and not your eyes. You would not perceive a difference in time out in space if your relative synapsis fired 16 times a second, a day or a year. My other question to you is what is the closing speed between two photons traveling on a collision course? This was not in reference to the traveling twin. Of course the traveling twin would see it differently with his clock slowed.

nitsuj

I can't see one in his/her post. Could you be more specific since your are being so bold.

The closing distance comment is fairly accurate (#'s aren't). The concept is definitly right (excluding the "distance" contraction / "time contraction" comment).

Of course the 16 seconds, days, year comment is refering to time dilation. Im pretty sure you understand that. It means there is no difference in the traveling observers perception of time passing (tick tock / proper time ect) to that of an observer who is at "rest".

I suggest that you do a lot of reading or asking questions instead of trying to answer them until you get yourself up on the learning curve.

Nice ain't it?

You've helped me improve my understanding of SR on a number of occasions ghwellsjr, it is a shame to see you post a reply like that. When I know you are capable of getting Qzit's interpretations on a more defined track / train of thought.

DaleSpam

I don't know which ones ghwellsjr noticed, but I saw a few that were either wrong or only conditionally right:

So far everything is fine.

This would be true on the return journey, but false on the outward journey.

False. Distance is contracted too.

True only in the earth frame.

This is a LET interpretation, not a SR interpretation. However, interpretations cannot be experimentally proven one way or the other, so I have no objection other than a kind of general distaste for LET as a pet theory of crackpots.

nitsuj

Yes Dalespam I understand your point and even ghwellsjr's point. This forum like's to be techincaly right, which is awsome and seperates a poor quality physics forum from a great one. Leaving out discussions about biology, conciousness and the sorts is important to point out because of the add difficulty of interpretation among other things.

But do you understand my point?

Qzit's interpretations are not flat out wrong, they are poorly defined. This is a big difference if someone is going to call those interpretations as erroneous. Said differently alot of Qzits interpretations are correct, ghwellsjr implied most were wrong. In a sense, possibly pushing Qzit further down the learning curve.

I wouldn't have an issue if ghwellsjr replied pointing out the technicalities, like you did.

And yes, as I noticed too (a layman of SR) the "distance" contraction isn't right. Big deal, point it out and say good for you in noticing the impact of closing distances. So one wrong comment.

Your last comment, if I understand right, yes if Qzit wants to stay "true" to SR (or physics in general), the "reality" is the observation (measurement +calculation). But it is merely a prefference, and not crackpottery.

DaleSpam

Yes, I understand your point. Only the one comment was flat out wrong, the rest could be either wrong or right depending on the "poorly defined" details.