
#19
Dec2111, 01:41 PM

P: 11

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 



#20
Dec2111, 02:01 PM

Sci Advisor
PF Gold
P: 4,862

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). 



#21
Dec2111, 02:08 PM

P: 11

Mind blown!




#22
Dec2111, 05:46 PM

P: 78





#23
Dec2111, 05:54 PM

P: 78





#24
Dec2111, 06:04 PM

Sci Advisor
PF Gold
P: 4,862





#25
Dec2211, 10:13 PM

P: 25

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.




#26
Dec2311, 03:29 AM

PF Gold
P: 4,521

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 = (1R^{2})/(1+R^{2}) 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 √[(1β)/(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/√(1β^{2}), so 1/γ = √(1β^{2}) 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. 



#27
Dec2311, 03:38 AM

PF Gold
P: 4,521

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". 



#28
Dec2311, 03:50 AM

PF Gold
P: 4,521

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. 



#29
Dec2311, 04:02 AM

P: 3,178

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



#30
Dec2311, 09:19 AM

P: 25

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. 



#31
Dec2311, 09:38 AM

P: 1,098

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. 



#32
Dec2311, 09:46 AM

Mentor
P: 16,473





#33
Dec2311, 09:58 AM

P: 1,098

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. 



#34
Dec2311, 10:09 AM

Mentor
P: 16,473





#35
Dec2311, 10:28 AM

Mentor
P: 16,473

On the other hand, in SR every reference frame is equally valid. So both of our observations are equally valid observations of what is physically happening. The disagreements between our observations are not because one of us "distorted" and the other is not but rather simply because we are each observing the same physics from different but valid perspectives. In this view, your coordinate time is a correct measure of the proper time, and so forth. Both of the above interpertations are valid, and in principle I have no problem with the LET interpretation. However, most of the proponents of LET that I have encountered are crackpots and my interactions with them are usually fairly unpleasant. So I have a certain "guilt by association" distaste for LET. I was not calling Qzit a crackpot nor even implying it, merely expressing the source of my distaste for LET. 



#36
Dec2311, 10:44 AM

P: 1,098

Understood Dalespam.
I appreciate what you are saying. You've been patient with me in that past with such things & George too to a lesser extent. It's really really helped me in trying to grasp the concepts of SR intuitively. So it kinda burns me to see a post like I've been commenting on. Where a poster is on the cusp of being correct, but is instead "written off" as being not worthy (the interpretations) of a helpfull reply. 


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