I did not begin with the attitude. I give what I am given. And i will not ever veer from that. I would much prefer to simply discuss the science and my attempt to understand it. That being said if you would like to add your own explanation for why i'm wrong I would like to hear it.Baluncore said:There is no paradox. There is only the misunderstanding of the science, by a beginner.
This is an attitude problem. Show some respect to science. When things do not make sense, you should be able to identify your misunderstanding, by studying the subject to which you are being introduced.
The mach 2 was simply to point out what would be the conclusion in a case where you apply your reasoning to a case where the speed is larger than the signal speed. The jet is travelling back in time as much as the 2 Mly journey takes 10 minutes (ie, not at all).Somoth Ergai said:no, it isn't. i never at any point suggested that anything traveled backwards in time. and in your analogy the jet is traveling faster than sound. which means that yes, the jet arrives in time to hear it's own arrival. that's the problem. that's fine for sound. but for light it's a huge problem.
I believe he is using ”observed” as sees. The journey time is 2 million years, but it will not take 2 million years from when the light from the launch reaches the observer until arrival.PeroK said:Yes, the journey time (as measured on Earth) is 2 million years.
We are not. We are answering two different questions as your question is inherently ambiguous. This may be why you are confusing yourself.Somoth Ergai said:well, you and Orodruin seem to be at odds as he says i am wrong on both counts. so which is it?
no it doesn’t. Not if you properly account for light travel time. We agreed that there was no paradox in the jet fighter arriving to hear its own sound. The resolution here is similar.Somoth Ergai said:actually appears to only take ten minutes.
The problem is that you are not comprehending why you are simply incorrect. Part of it may be due to the inpreciseness of regular language and the misunderstandings it leads to. Realize that you are conversing with people who actually understand the theory on a level which id not just descriptive with words, but know the actual underlying math.Somoth Ergai said:if we watch the ship launch and from launch to arrival it travels at near c, it must necessarily take 2 million years for the trip to complete. what part of that are you not comprehending?
This is entirely accurate. I am not getting how i'm wrong. Even though I know I am. your saying that, from our perspective, as we watch this ship travel the distance from a planet 2 million light years away, all the way to earth, that it's apparent travel time will be 10 minutes. that necessarily means we would have to observe the ship traveling many times faster than light in order to cover that distance in that amount of time. You're absolutely correct that i'm not able to get my head around how that could be.Orodruin said:The problem is that you are not comprehending why you are simply incorrect.
Somoth Ergai said:i'm genuinely asking. how is that possible?
The experts tried to explain it. I read your last few posts, can I ask you a few questions?Somoth Ergai said:that would mean that the ship, from our perspective, would travel two million light years in a weak. far exceeding the speed of light. which, would mean we would have to see light traveling faster than itself. This does not resolve the situation.
As a scientist, why would you talk about other than the "actual" launch event??That would be foolish.Somoth Ergai said:I'm acknowledging that there is a very clear difference between the "actual" launch event of the ship and the time we "see" the event.
Because you are addressing scientists in a science forum. QED. finis.Somoth Ergai said:That being said if you would like to add your own explanation for why i'm wrong I would like to hear it.
Take into account the Doppler effect. Your source (ship) is approaching the Earth, so the signals you see (watches on the ship) you see much faster.Somoth Ergai said:This is entirely accurate. I am not getting how i'm wrong. Even though I know I am. your saying that, from our perspective, as we watch this ship travel the distance from a planet 2 million light years away, all the way to earth, that it's apparent travel time will be 10 minutes. that necessarily means we would have to observe the ship traveling many times faster than light in order to cover that distance in that amount of time. You're absolutely correct that i'm not able to get my head around how that could be.
i'm genuinely asking. how is that possible?
There are a lot of replies already, so someone else may have mentioned it. But this is not correct. You need to actually calculate it and not just make a claim about it.Somoth Ergai said:TL;DR Summary: Ship travels faster than light while traveling slower than light. The same light is in two different places at the same time.
from our perspective watching the ship leave their planet and journey here that trip is going to take 2 million years to complete
We see it two million years after it actually launched, yes.Somoth Ergai said:we observe the ship at launch yes?
For ten minutes, yes.Somoth Ergai said:we continue to watch the ship as it travels accross space.
The trip takes two million years; the light arrives at Earth in a ten minute interval, because light emitted later in the trip has less distance to travel so arrives with less delay. As I explained in the post you quoted, you will see light from the launch at some time, light from the half way point five minutes later, and light from the arrival five minutes after that. There's no paradox and we see nothing out of sequence.Somoth Ergai said:if we watch the ship launch and from launch to arrival it travels at near c, it must necessarily take 2 million years for the trip to complete.
Your error has been explained several times by seven different people, if I count correctly. It is this: we calculate the speed by dividing the distance (two million light years) by the travel time (two million years and ten minutes). We do not divide by the period over which light arrives at us (ten minutes), because this would imply we believe the travel starts at the time the light reaches us, despite knowing that we're looking at something that happened two million years ago at the beginning of the observation and something that's happening right here and now at the end.Somoth Ergai said:I would much prefer to simply discuss the science and my attempt to understand it.
Thank you. This is the crux of my misunderstanding. The problem I was having is not understanding that the ship will appear to travel much faster than light speed as we watch it cover the distance. I acknowledge that this is the case according to the experts. what i'm still struggling with is understanding why. I understand that the light from the ship will take less and less time to reach us as the ship gets closer. but what i'm still failing to get is how that translates to the ship appearing to us to travel not just faster than light but orders of magnitude faster.Bandersnatch said:Three was a link supplied earlier, to the concept of 'superluminal motion' (in astronomy it means a very specific type of observables - rather than being a simple synonym for going faster than light). It's almost exactly the scenario at hand, and well worth working through.
It is concerned with looking at jets emitted from active galactic nuclei and resolving the issue of them appearing to travel over the speed limit. The main difference from the spaceship scenario is that we're looking at the sideways component of the motion (because that's what's actually measurable). The spaceship is in this sense a purer version, since we assume we can see it in all detail and measure its exact radial distance as it travels.
But to reiterate: this happens in nature; it's not just a matter of thought experiments that one may be worried to have not constructed properly.
The resolution is the same in both cases - and involves taking account of signals from an approaching source being received in shortened intervals. I.e. you will 'see' the spaceship cover the entirety of the distance in extremely short time, and you will observe processes on board speed up (unrelated to relativistic effects!), and if you were to take a stopwatch and try to ascertain its speed by dividing the distance you see it cover by the time on your stopwatch - you'd end up with superluminal velocities. But it would be a mistake of omission. Of ignoring the fact that the spaceship, or the jet, 'chases' its earlier signals (as seen from Earth), bunching them all up so that its entire history arrives to be observed almost at the same time.
No. My error was in failing to understand how the apparent trip will take an extremely short time to complete from an observational standpoint. not in misunderstanding the actual speed of the ship or it's actual travel time. If seven people all fail to adequately address the actual problem i'm having that's their problem. And should perhaps try a little harder to comprehend my issue than coming at with an unnecessary attitude.Ibix said:Your error has been explained several times by seven different people, if I count correctly. It is this: we calculate the speed by dividing the distance (two million light years) by the travel time (two million years and ten minutes). We do not divide by the period over which light arrives at us (ten minutes), because this would imply we believe the travel starts at the time the light reaches us, despite knowing that we're looking at something that happened two million years ago at the beginning of the observation and something that's happening right here and now at the end.
If you had read my initial post you would not need to ask me those questions. If you had understood my issue you would see that my error is in thinking our observation of the ship will take 2 million years to complete. this is the entire problem with my thought experiment that nearly everyone save for a few seems to be overlooking, and the reason why I was having a hard time seeing where i was going wrong.pinball1970 said:The experts tried to explain it. I read your last few posts, can I ask you a few questions?
When you are looking out into space do you realize you are effectively looking back in time? if you look at the moon you are seeing it was it was just over a second ago, the sun 8 minutes ago, Proxima Centauri 4,2 years ago?
The light you can see from Andromeda was emitted from stars 2 million years ago, you are effectively looking at the past 2 million years ago, today.
If you see the ship launch, that event happened when there were no humans on the earth. The ship took off 2 million years ago and is landing around now, it has been flying through space that whole time.
With respect, your thread is titled "New Paradox Discovered, I think" not "Confused about Time Dilation" and you seem(ed) very resistant to contradiction and clarification. FYI.Somoth Ergai said:And should perhaps try a little harder to comprehend my issue than coming at with an unnecessary attitude.
No. This is not correct.Somoth Ergai said:the ship is already here. ahead of all those two million years worth of light from it's journey. meaning that the ship arrived on earth faster than it's own emitted light
If seven different people have explained it in seven different ways and you don’t get it … there is only one thing that is exactly the same across all of those explanation attempts …Somoth Ergai said:If seven people all fail to adequately address the actual problem i'm having that's their problem. And should perhaps try a little harder to comprehend my issue than coming at with an unnecessary attitude.
Have you stopped for two minutes to consider that if so many people who actually know relativity don’t understand your issue, perhaps you did not do such a good job at presenting it as you think you did?Somoth Ergai said:If you had read my initial post you would not need to ask me those questions. If you had understood my issue you would see that my error is in thinking our observation of the ship will take 2 million years to complete.
This! The thread title is confrontative by nature. If OP wanted to learn what was actually wrong, they should have said so rather than claiming to have discovered something fundamentally wrong with relativity (because that is the purpose of claiming a paradox).hutchphd said:With respect, your thread is titled "New Paradox Discovered, I think" not "Confused about Time Dilation" and you seem(ed) very resistant to contradiction and clarification. FYI.
Actually, it's about 4.47 years. Remember you have to take the square root in the relativistic Doppler formula. See my post #45.Ibix said:the light from the launch would arrive about a week before the ship
"Travel faster than light" is something of a misnomer. In post #45, I showed you the calculations that say that you see the ship leaving Andromeda 4.47 years before it arrives at Earth, and that the ship never outruns any of its light signals. That in itself should be enough to show that there is no "paradox".Somoth Ergai said:how that translates to the ship appearing to us to travel not just faster than light but orders of magnitude faster
That is the reason why.Somoth Ergai said:what i'm still struggling with is understanding why. I understand that the light from the ship will take less and less time to reach us as the ship gets closer.
This is called the relativistic Doppler shift, or in cases like this, relativistic blueshift.Somoth Ergai said:what i'm still failing to get is how that translates to the ship appearing to us to travel not just faster than light but orders of magnitude faster
No. if one person misunderstood then it would be reasonable to say “that was their problem”. When seven different experts all fail to address your problem then that is your problem. Your mistake in the analysis was correctly identified in post 3.Somoth Ergai said:If seven people all fail to adequately address the actual problem i'm having that's their problem.
Actually it was post #3 by @Ibix.Dale said:Your mistake in the analysis was correctly identified in post 4.
OK, I think I think I'm starting to understand. The issue i'm having is wrapping my head around how it could be that we could see an object which is in actual fact traveling slower than c appear to be traveling faster than c. I understand that you're telling me this is the case. I'm needing help understanding why though. conceptually I mean.PeterDonis said:No. This is not correct.
What is correct is that you will see the light from the entire journey of the ship, from launch to arrival, arrive at your location in a much, much shorter time interval than 2 million years. The light signals all still arrive in order--you see the launch, then the journey, then the arrival, all in their proper order. The ship arrives just after the last light signal emitted during its journey.
How much shorter is the time interval in which you see all this? The relativistic Doppler formula tells us that For ##v = 0.99999999999## (in units where ##c = 1##), the formula gives for the Doppler factor ##f##:
$$
f = \sqrt{\frac{1 + v}{1 - v}} = \sqrt{\frac{1 + 0.99999999999}{1 - 0.99999999999}} = 447214
$$
The time interval ##\tau## during which you see the light signals all arrive is then the journey time ##T## divided by ##f##, i.e., for ##T## 2 million years, we have
$$
\tau = \frac{T}{f} = \frac{2000000}{447214} = 4.47
$$
So you will see the light from the launch at Andromeda 4.47 years before the spaceship arrives, and during that 4.47 years you will see all of the light signals emitted by the ship during its journey, in order.
Oops, yes it was.PeterDonis said:Actually it was post #3 by @Ibix.
”I don’t understand” or “wouldn’t this mean” or “can you show me how” would have all been more productiveSomoth Ergai said:we would have to see light traveling faster than itself. This does not resolve the situation
I think we're calculating different things. In the Earth frame the flight time of light is 2 million years; the flight time of the ship is approximately one part in ##10^{11}## longer. Thus the arrival time of the ship is one part in ##10^{11}## of 2 million years after the light - about ten minutes. The Doppler analysis invokes ticks of the shipboard clock, which I'm not doing.PeterDonis said:Actually, it's about 4.47 years. Remember you have to take the square root in the relativistic Doppler formula. See my post #45.
To illuminate the difference: The Doppler computation results in how much faster the clock on the ships looks to be running. The result of this includes the time dilation of the rocket. The Doppler factor tells us the ratio between the elapsed rocket clock time and the observation time - not the ratio between the 2 million year travel in the Earth rest frame and the observation time. The former ratio will be much smaller as time dilation at the quoted speed is significant.Ibix said:I think we're calculating different things. In the Earth frame the flight time of light is 2 million years; the flight time of the ship is approximately one part in ##10^{11}## longer. Thus the arrival time of the ship is one part in ##10^{11}## of 2 million years after the light - about ten minutes. The Doppler analysis invokes ticks of the shipboard clock, which I'm not doing.
Not necessarily. I'm telling you how it can be the case that you see light signals arriving from the ship in a much shorter time interval than they were emitted (where "time interval" here is in your frame, not the ship's frame). But, as I pointed out in post #48, interpreting that observation as the ship "appearing to be traveling much faster than light" is highly problematic.Somoth Ergai said:how it could be that we could see an object which is in actual fact traveling slower than c appear to be traveling faster than c. I understand that you're telling me this is the case.
No, we're not. We are both calculating the same invariant: the time interval registered by the observer's clock on Earth between seeing the light signal showing the ship departing Andromeda, and the ship arriving at Earth. I say that interval is 4.47 years. You say it's about a week. We can't both be right.Ibix said:I think we're calculating different things.
Oops, yes, I see where I went wrong. The Doppler factor has to be applied to the shipboard elapsed time, not the Earth elapsed time. Fortunately it's easy to fix that: for ##v = 0.99999999999## we have ##\gamma = 1 / \sqrt{1 - v^2} = 223607##. So the shipboard elapsed time is ##2000000 / \gamma = 8.94## years. And dividing that by the Doppler factor ##f = 447214## gives ##2 \times 10^{-5}## years.Ibix said:The Doppler analysis invokes ticks of the shipboard clock
Could you please explain how we could see all of the light from the ships journey in a short time frame. in chronological order. and it not have the appearance of traveling faster than light? I'm beginning to wrap my head around the mechanism of the doppler effect. but I don't see how that does not translate to the object appearing to move faster than it actually is moving.PeterDonis said:Not necessarily. I'm telling you how it can be the case that you see light signals arriving from the ship in a much shorter time interval than they were emitted (where "time interval" here is in your frame, not the ship's frame). But, as I pointed out in post #48, interpreting that observation as the ship "appearing to be traveling much faster than light" is highly problematic.
Somoth Ergai said:well that's nice and all but without an explanation of how or why i'm wrong that just sounds like "nuh uh"
Yes - as noted above, I initially used 2 billion light years and got a week, which turns out to be 10,080 minutes. 10.5 minutes is the correct figure.PeterDonis said:Note that this is not even a week; it's ##631## seconds, or about ##10.5## minutes.