Crisp, Thed, James R, and Q, and anyone else who cares, What are your answers to this problem: Example 1: A person is sitting on Earth and he is really sick of the Milky Way galaxy. He packs his bags and gets into his spaceship. He leaves one clock on Earth and takes another clock with him on his ship. He blasts off from earth and proceeds to leave the Milky Way galaxy at a speed of .90c. Question 1: While he is travelling away from his galaxy at .90 c, for every second that passes on his onboard clock, how much time passes on the clock he left on Earth?? Feel free to use any time dilation formulas you deem appropriate. Example 2: The person from example 1 is observing the other galaxies and comes to the conclusion that he is not moving away from the Milky Way at .90 c. He realises that he is stationairy and the Milky Way is moving away from him at .90c. Question 2: Based on example 2, for every second that passes on his onboard clock, how many seconds pass on the clock he left on Earth?? Tom
Tom, <i>Question 1: While he is travelling away from his galaxy at .90 c, for every second that passes on his onboard clock, how much time passes on the clock he left on Earth??</i> According to whom? That makes all the difference. According to him: 0.44 seconds. According to an Earth observer: 2.29 seconds. Both calculated using the "standard" time dilation formula. <i>Question 2: Based on example 2, for every second that passes on his onboard clock, how many seconds pass on the clock he left on Earth??</i> Answers are the same. There's no way to tell who's "really" moving, since there is no absolute frame of reference.
*Sniffles* Nobody ever mentions me. Everybody hates me. (Alright, stop that, Xev) Using the formula: Δ t = Δ t1/√ 1 -v^2/c^2 A: .436sec his time, and we can arbitrarily set earth time as 1sec=1sec. So, 1 earth second per .436 his second. Hell, it really does not matter. We could set earth time at any arbitrary number, no? You seem to be postulating a absolute frame of reference for this thought experiment. According to my understanding of relativity, there can be no absolute reference frames. Thus the problem is more or less meaningless. B: How can he be stationary? We could just as well say that the Milky Way is stationary and HE is moving. Edit to add: In other words, what JamesR said.
Another way of seeing it Hi all, Tom, I'll repeat exactly what has been told twice already, but I'll use the Lorentztransformations here to illustrate how these work. You'll find out that this approach takes a bit more work: the Lorentztransformations map events from one observer to another, while the time dilatation (and length contraction, but we'll not use that here) take time intervals as an input. The formula's are (for an observer O' moving along the x-axis of observer O) t' = <font face="symbol">g</font>(t - vx/c<sup>2</sup>) x' = <font face ="symbol">g</font>(x - vt) y' = y z' = z Situation 1: An earthling looks at the clock left behind on earth. Let's denote the observer in the spaceship as observer O and the earth observer as O'. Our man in the spaceship studies two events: first he looks at the clock he helds in his hand, and he marks the time as zero. The first event is E1 = (0,0,0,0) with the interpretation that (t,x,y,z) = (0,0,0,0). The second event E2 is when he looks again at the clock in his hand, seeing that one second has passed for him: E2 = (1,0,0,0). Using the Lorentztransformations for v = -0.9c (the earth observer is moving away from the spaceship's point of view) one obtains for the transformed events: E1' = (0,0,0,0) E2' = (<font face ="symbol">g</font>,0,0,0) Hence the time that has passed for the earth observer is <font face ="symbol">g</font> = 2.29s. Situation 2: Our man in the spaceship looks at the earth clock There are again two events, but this time marked by the earth clock: let's denote them E1' = (0,0,0,0) and E2' = (t',0,0,0) where t' is the time passed on the earth clock. We have to look for a value of t' such that for the spaceship, t = 1s i.e. that our man sees one second passing on his own clock. Once again using the Lorentztransforms, but this time from the earth clock to the spaceship clock, we get: E1 = (0,0,0,0) E2 = (<font face ="symbol">g</font>t',0,0,0) which must result in E2 = (1,0,0,0) Using <font face ="symbol">g</font> = 2.29, one obtains t' = 0.44s. The original events where hence: E1' = (0,0,0,0) E2' = (0.44 , 0,0,0) Hence our man in the spaceship will agree that 0.44s have to tick on the earth clock for him to measure one second. And now let's hope there are not too many flaws here Please Register or Log in to view the hidden image! Bye! Crisp
Crisp, James R, and Xev, Crisp and James R claim that for every second for the observer, .44 seconds passes on the Earth's clock. While Xev claims for every .44 seconds for the observer, 1 second passes on Earth's clock. Which one is it, and why??? And James R and Crisp: Why do you assume that the observer is the one that's moving and not the Milky Way?? Xev: What would your answer be if the observer was the one moving, and not the galaxy??? Xev, The observer in example 2 knows that he is stationairy because he looks at the motions of all the galaxies and realizes that they are all expanding from a single point(Big Bang Theory). When he compares his motion to this point, he realizes that he is at rest and that the Milky Way is moving away from him at .90c. Tom
Prosoothus: I do not think it is either. It all depends on your frame of reference. The exact reverse, .44 for the galaxy and 2.26 (Relying on James R's calculations). Because it really is only dependent on your frame of reference. It's all, relative, you know? Hmmm...I do not think that would work. If memory serves, Hubble found that galaxies were receding from each other, not from a fixed point. I still do not see how such an observation could be made. Even if so, the answer would be the same as for A. *Xev wonders if she is making any sense with all this and stumbles away for more coffee*
Xev, You came to the same conclusion that I did. In both examples I have provided, the frame of reference is the same. In both cases the observer believes that he is moving away from the galaxy. Only in the second example does the observer know that the galaxy is moving away from him, and not the other way around. In the first example, the observer's clock slows down in relation to the clock on Earth because he is travelling at .90 c and time slows down as the observer moves faster. In the second example, the observer's clock speeds up in relation to the clock on Earth because his speed is actually decreasing compared to the moving galaxy. According to Einstein's theory of relativity, both examples should give the same result, but both of us have concluded that they don't. Your conclusion would also imply that there is an absolute frame of reference. After all, how do you determine what is moving, the observer or the galaxy, if you don't compare it to the absolute frame of reference??? Note: I just used the Big Bang Theory as an example of how the observer might determine the center of the universe. Maybe one day in the distant future, scientist will pinpoint the true center of the universe using techniques that we currently aren't familiar with. Tom
Okay, I will stipulate that we know that he is not moving. But how? It would require an absolute frame of reference which, according to relativity, is impossible. But he is stationary...okay, yes, his speed is indeed decreasing compared to the moving galaxy. But we have two reference frames now. Adding the clock on earth makes a third, and I am not exactly sure how they all relate. To compare his clock to the clock on earth would seem to require that we compare his speed to earth's speed, or earth's speed to the galaxy's speed. Am I correct? You're right. My bad, you cannot determine who is moving. In conclusion, I am confused. I think the whole example is flawed in that it really needs an absolute frame of reference to work. No offense, and I am probably wrong.
Xev, I completely agree with you. I've come to the conclusion that unless you use an absolute frame of reference, the relative time dilation results from the various frames of reference contradict each other. Therefore, since I have to choose between logic and relativity, I'll stick with logic. Right about now, James R, Thed, Crisp, Q, and the other super-relativists on this forum are probably blowing there tops while reading our posts. Expect to here from all of them very soon so they can explain to us why logic is wrong and Einstein is right.Please Register or Log in to view the hidden image! Tom
Prosoothus: Most excellent, then we only have the following to disagree on. Yes, that is true. Because time is not absolute. I'm afraid I must ask: A: Why is this illogical? B: Is not relativity well verified? I am all aquiver. Please Register or Log in to view the hidden image!
Hi Tom, I don' t have the time to go into detail here, but judging from which I just read (in a glimpse) I'd say that there is an error in your statement a few posts back: "In the first example, the observer's clock slows down in relation to the clock on Earth because he is travelling at .90 c and time slows down as the observer moves faster. In the second example, the observer's clock speeds up in relation to the clock on Earth because his speed is actually decreasing compared to the moving galaxy." The first part is correct if you read it in the appropriate way: the observer's clock slows down in relation to the earth clock for an observer on the earth. The earthling will say that 2.29s have passed for the spaceship while the person onboard the spaceship will say only one second has passed. The 0.44s number exactly the opposite reasoning. The second example has no clock speedup, the results are the same: it makes no difference if the spaceship is considered travelling away from earth at 0.9c or if you say the earth travels away at 0.9c in the opposite direction: the relative motion of the earth and the spaceship is the same. I'll get deeper into this as soon as my exams are over (1st july), perhaps James, Thed, Q, Xev, ... or anybody else can supplement or correct me Please Register or Log in to view the hidden image! Bye! Crisp
Xev, If you use relativistic formulas and principles on the example I have provided above, you get at least two different answers. Since logic dictates that there can only be one answer(in this case does time speed up or slow down in relation to the clock on Earth), a theory that provides two or more results is illogical. About your second question, relativity is just a model like any other model. For a model to be correct it has to overlap reality 100 percent. Although, there is much overlapping between reality and relativity, nobody can claim that it's 100 percent. For example let's say that you drop a rock on the ground. You can devise a model that claims that the Earth is moving up to meet the rock instead of the rock moving down to hit the Earth. Even though your model is wrong, your model may give you correct results in many situations. Only after you step back and look at the whole picture, do you realize that your model is wrong and that the rock is moving to meet the Earth and not the other way around. Relativity is the same way, up close it looks great. But when you step back, you begin to see it's flaws. Tom
Only after you step back and look at the whole picture, do you realize that your model is wrong and that the rock is moving to meet the Earth and not the other way around. From the point of view of the Earth, yes, the rock is moving towards the Earth. But from the point of view (FOR) of the rock, the Earth is moving towards the rock. It all depends on which frame of reference you use as the rest frame, the Earth or the rock. If I'm a tiny speck sitting on the rock, I can't tell if I'm moving or not. Can you tell whether you are moving with the Earth ? Same difference. So for me, the tiny speck on the rock, it would appear the Earth is hurtling towards me. If the Earth somehow broke orbit and began to plunge towards the Sun, you would not know if the Earth was moving towards the Sun or if the Sun were moving towards the Earth. It's all relative. Please Register or Log in to view the hidden image!
Exactimundo, Crisp. Prosoothus: Okay, let's play a game. We play "Pretend Xev is blonde and you have to explain this to her veeeery slowly" Now, why does logic dictate only one answer? It seems to me that common sense would dictate only one answer, but then again, common sense does not really apply to relativistic physics, right? Why not? I think you are erring in assuming that reality is the same at speeds close to c as it is at speeds prevalent on earth. I don't see why it has to be the same. Please Register or Log in to view the hidden image!
Woah! Confusion reigns again. Let's see if we can clear this up. First, let me say that my answer is correct. I have been very careful to point out which observer I am talking about when giving my answers. Failing to do that is one of the things which causes the most problems for people learning relativity - as is evidenced by the amount of confusion here. <i>Crisp and James R claim that for every second for the observer, .44 seconds passes on the Earth's clock. While Xev claims for every .44 seconds for the observer, 1 second passes on Earth's clock.</i> Both are right, depending on which observer is looking at the two clocks. An Earth observer sees his own clocks as running at the normal rate, and the moving clock running slow. The "moving" observer sees his own clocks as running at the normal rate and the Earth clocks as running slow. Relativity is symmetrical. <i>And James R and Crisp: Why do you assume that the observer is the one that's moving and not the Milky Way??</i> I make no such assumption. <i>In the first example, the observer's clock slows down in relation to the clock on Earth because he is travelling at .90 c and time slows down as the observer moves faster.</i> Your statement that "time slows down as the observer moves faster" is incomplete. For completeness, it <b>must</b> say "time slows down for a moving object <b>from the point of view of a stationary frame of reference</b>". <i>In the second example, the observer's clock speeds up in relation to the clock on Earth because his speed is actually decreasing compared to the moving galaxy.</i> Again, you have failed to specify who is looking at the observer's clock, so your statement is useless. From an Earth observer's point of view, the moving observer's clock is running slow. From the moving observer's point of view, the Earth clock is running slow. <i>According to Einstein's theory of relativity, both examples should give the same result, but both of us have concluded that they don't.</i> And I have concluded they do. See my previous post. <i>Your conclusion would also imply that there is an absolute frame of reference. After all, how do you determine what is moving, the observer or the galaxy, if you don't compare it to the absolute frame of reference?</i> You can't determine who is moving and who isn't. How many times do I have to say it? <b>There is no absolute reference frame!</b> <i>Note: I just used the Big Bang Theory as an example of how the observer might determine the center of the universe.</i> That just shows that not only do you not understand relativity, but you don't understand the big bang theory either. <b>The universe has no centre.</b> <i>I've come to the conclusion that unless you use an absolute frame of reference, the relative time dilation results from the various frames of reference contradict each other.</i> Your conclusion is based on a misunderstanding and is incorrect. <i>Therefore, since I have to choose between logic and relativity, I'll stick with logic.</i> You'd better improve your logic if you're going to rely on it. At this stage, I wouldn't bet my life on your logic. <i>If you use relativistic formulas and principles on the example I have provided above, you get at least two different answers.</i> Yes. It depends on which observer you use. It depends on the <b>frame of reference</b>, which is what relativity is all about. <i>Since logic dictates that there can only be one answer(in this case does time speed up or slow down in relation to the clock on Earth), a theory that provides two or more results is illogical.</i> Wrong, wrong, wrong. Logic dictates that different observers get different answers. <i>About your second question, relativity is just a model like any other model. For a model to be correct it has to overlap reality 100 percent. Although, there is much overlapping between reality and relativity, nobody can claim that it's 100 percent.</i> Then show me why it isn't 100%. I say you can't. <i>For example let's say that you drop a rock on the ground. You can devise a model that claims that the Earth is moving up to meet the rock instead of the rock moving down to hit the Earth. Even though your model is wrong, your model may give you correct results in many situations.</i> Then show me why that model is wrong. I say you can't. <i>Only after you step back and look at the whole picture, do you realize that your model is wrong and that the rock is moving to meet the Earth and not the other way around.</i> Then explain the "whole picture" for me. <i>Relativity is the same way, up close it looks great. But when you step back, you begin to see it's flaws.</i> You haven't stepped up close enough yet. You think you know what you're talking about, but clearly that is not true. Before you can effectively refute an idea, you must understand it. I applaud your perseverence in trying to understand relativity. It is a difficult subject. But at the same time, I'm telling you you have a fair way to go before you get a grip on it.
Xev, It is clear that your understand of relativity could use a little work, too. But at least you admit it. <i> I think the whole example is flawed in that it really needs an absolute frame of reference to work. No offense, and I am probably wrong.</i> The example is perfectly ok, provided we keep track of whose point of view we are looking at things from at all times. It requires no absolute reference frame; such a thing does not exist.
JamesR: Firstoff, I have not studied relativity formally. So, as I asked Prosoothus, pretend Xev is blonde. I should clarify. I know that there are no absolute reference frames, I have stated so several times. *Xev grins* I am not that stupid! What I meant was that Prosoothus' interpretation seemed to require a absolute reference frame. The example is indeed perfectly okay, the interpretation is flawed, IMAO.
Xev, Rereading my previouspost, I think I probably came across as a little too critical. I didn't intend that. Sorry.
James, Stop complicating things. There are no observers in my example. I'm comparing the readings of the clock in the spaceship to the clock on Earth. Since you don't understand, I'll give you an even simpler problem in the thread "Unrelative Relativity Part 2" which I will post shortly. Tom
Xev, Common sense is the lowest form of logic, and logic applies to everything. If someone tells you that his/her theory goes against logic or common sense, the his/her theory is wrong. I will be posting a thread called "Unrelative Relativity Part 2" shortly. This thread will use a simpler example to explain the flaws of relativity. Feel free to join the discussion in the new thread. Tom
