can't_think_of_a_name Posted July 23, 2020 Posted July 23, 2020 Let's say I am in Alice's frame.Alice is located on earth. A planet called planet 2 is located 20.3 Light years away. Bob is on a ship that starts on earth and is travelling at a constant velocity .99c. Ignore the acceleration of the ship to get .99c Alice and Bob's ship's clock reads 0 when they reach earth. Bob travels to the planet 2. Alice observers the time it takes for Bob to reach planet 2 using Alice's clock. What is this elapsed time? Is the Lorentz transform only used during switching frames? Let me define switching frames. I may have a mistake in my definition. Please correct me if I am wrong. In this example I have 2 frames Alice and Bob. Alice is stationary Bob is moving. I can calculate Bob's velocity in Alice's frame. I simply do t= d /v. 20.3 / .99c = 20.5 years. This gives me the elapsed time. If I wanted to know the time in Alice's frame. Here is where I get confused. I have a stationary frame. A moving frame I can switch between frames. When do I switch the stationary frame to become the moving frame, and the stationary frame becomes the moving frame? When do I stay in the same frame but use the moving frame or the stationary frame? What is the difference between the two previous questions? Thanks.
joigus Posted July 23, 2020 Posted July 23, 2020 On 7/23/2020 at 6:12 PM, can't_think_of_a_name said: I have a stationary frame. A moving frame I can switch between frames. When do I switch the stationary frame to become the moving frame, and the stationary frame becomes the moving frame? Expand I'm having difficulty understanding what you mean. Do you understand how you assign coordinates to events in SR? I don't know what you mean when you say "switching" frames. Jumping from one to another? That's not how you measure time intervals and distances in SR. It's by sending light rays and receiving them back, and then kind of "triangulating", but taking into account that the signal speed is c no matter what inertial frame you're in. Let me ask you a question: How do you picture in your mind that Alice knows Bob has already arrived in planet 2?
studiot Posted July 23, 2020 Posted July 23, 2020 On 7/23/2020 at 8:08 PM, joigus said: Let me ask you a question: How do you picture in your mind that Alice knows Bob has already arrived in planet 2? Expand Surely Alice just reads it off her clock ? On 7/23/2020 at 6:12 PM, can't_think_of_a_name said: I can calculate Bob's velocity journey time in Alice's frame. I simply do t= d /v. 20.3 / .99c = 20.5 years. This gives me the elapsed time. If I wanted to know the time in Alice's frame. Here is where I get confused. Expand 1
swansont Posted July 23, 2020 Posted July 23, 2020 On 7/23/2020 at 6:12 PM, can't_think_of_a_name said: Let's say I am in Alice's frame.Alice is located on earth. A planet called planet 2 is located 20.3 Light years away. Bob is on a ship that starts on earth and is travelling at a constant velocity .99c. Ignore the acceleration of the ship to get .99c Alice and Bob's ship's clock reads 0 when they reach earth. Bob travels to the planet 2. Alice observers the time it takes for Bob to reach planet 2 using Alice's clock. What is this elapsed time? Is the Lorentz transform only used during switching frames? Let me define switching frames. I may have a mistake in my definition. Please correct me if I am wrong. In this example I have 2 frames Alice and Bob. Alice is stationary Bob is moving. I can calculate Bob's velocity in Alice's frame. I simply do t= d /v. 20.3 / .99c = 20.5 years. This gives me the elapsed time. If I wanted to know the time in Alice's frame. Here is where I get confused. I have a stationary frame. A moving frame I can switch between frames. When do I switch the stationary frame to become the moving frame, and the stationary frame becomes the moving frame? When do I stay in the same frame but use the moving frame or the stationary frame? What is the difference between the two previous questions? Thanks. Expand All calculations of distance and time have to be done in the same frame. You use the transforms to get the values in the other frame. You have done the calculations in Alice’s frame. If you want the distance and/or time in Bob’s frame, you do the transform. 1
joigus Posted July 23, 2020 Posted July 23, 2020 On 7/23/2020 at 9:01 PM, studiot said: Surely Alice just reads it off her clock ? Expand Exactly! I want the OP to think: How do I measure separation of distant things? By measuring times. Observers cannot read space directly. How can distant "news reporters" at rest with respect to us liaise with us? It takes some time to realise that this is necessary. I hope this sketch clarifies the meaning of coordinates in SR: t=\frac{1}{2}\left(t_{1}+t_{2}\right) x=\frac{c}{2}\left(t_{2}-t_{1}\right) So everything, spacial coordinates included, is based on observation times. I'm not sure if that's what confusing you, @can't_think_of_a_name. It looks to me like that may be it. Once it's clear that you've got all of space-time mapped with these x's and t's, you do what Swansont is telling you and apply Lorentz transformations. But you don't get information back from distant events by sending someone back that "switches" inertial frames. It's a matter of sending light rays back and forth what gives meaning to the coordinates, not people on a spaceship with the news. I hope that helped and had to do with the source of your confusion. On 7/23/2020 at 9:01 PM, studiot said: On 7/23/2020 at 6:12 PM, can't_think_of_a_name said: I can calculate Bob's velocity journey time in Alice's frame. I simply do t= d /v. 20.3 / .99c = 20.5 years. This gives me the elapsed time. If I wanted to know the time in Alice's frame. Here is where I get confused. Expand Expand +1. Thank you. That got me confused too.
studiot Posted July 23, 2020 Posted July 23, 2020 On 7/23/2020 at 10:32 PM, joigus said: Exactly! I want the OP to think: How do I measure separation of distant things? By measuring times. Expand This is not how I understand the original situation. I understand it to mean that The distance from Earth to planet 2 has already been measured (and will not change in the lifetime of Alice) by othe astronomical means. Similarly the spaceship has a 'cruise control so its velocity is predetermined at a fixed rate of 0.99c. No one measures this. Bob starts out from Earth when both his clock and Alice's clock read zero. So by Alice will know that when her clock reads 20.5 years Bob is just arriving at planet 2 with his clock. Bob's clock will be reading a value given by the Lorenz transform of this time. 2
joigus Posted July 23, 2020 Posted July 23, 2020 On 7/23/2020 at 11:07 PM, studiot said: This is not how I understand the original situation. I understand it to mean that [...] Expand I see. And what about the switching frames? Did you understand that part?
swansont Posted July 24, 2020 Posted July 24, 2020 On 7/23/2020 at 11:07 PM, studiot said: Similarly the spaceship has a 'cruise control so its velocity is predetermined at a fixed rate of 0.99c. No one measures this. Expand Or it doesn’t matter, since it’s a relative speed, and both Alice and Bob will agree on it. 1
can't_think_of_a_name Posted July 24, 2020 Author Posted July 24, 2020 (edited) Let me clarify because my first situation was not explained well. Please refer to the picture from imgur. Find the time of Alice's clock when B reaches planet 2? Find the time of Bob's clock when B reaches planet 2? First question I think I understand . I just use d= vt t = d/v Second question. Shouldn't the time of B = A? But I know this is wrong because moving clocks tick slow. Why do I have to perform the Lorentz transform when from my picture it shows it as the same time but I know the Lorentz transform must be performed because Alice is moving. I think the answer is because I can only measure things in stationary frames and the Lorentz transform does this transform but also twists the graph . Since the graph is twisted during a Lorentz transform even if it is on the T_B axis T_B = 0 isn't 0. Is this correct? https://imgur.com/a/eWjTaT4 Should be X_A not X_B in Alice's frame. Edited July 24, 2020 by can't_think_of_a_name
studiot Posted July 24, 2020 Posted July 24, 2020 On 7/23/2020 at 11:39 PM, joigus said: I see. And what about the switching frames? Did you understand that part? Expand Yes, but I didn't want to introduce the second part of the development before the first was digested. This comment also applies to swansont's more complete and comprehensive statements. On 7/23/2020 at 9:59 PM, swansont said: All calculations of distance and time have to be done in the same frame. You use the transforms to get the values in the other frame. You have done the calculations in Alice’s frame. If you want the distance and/or time in Bob’s frame, you do the transform. Expand On 7/24/2020 at 12:18 AM, swansont said: Or it doesn’t matter, since it’s a relative speed, and both Alice and Bob will agree on it. Expand Yes the next part of my offering would be for Bob to calculate his version of the journey and apply Lorenz to find his measurement of the distance travelled and thus find the same relative velocity as Alice observed. Then one could enquire about how the spaceship achieves constant velocity. On 7/24/2020 at 3:21 AM, can't_think_of_a_name said: Let me clarify because my first situation was not explained well. Please refer to the picture from imgur. Find the time of Alice's clock when B reaches planet 2? Find the time of Bob's clock when B reaches planet 2? First question I think I understand . I just use d= vt t = d/v Second question. Shouldn't the time of B = A? But I know this is wrong because moving clocks tick slow. Why do I have to perform the Lorentz transform when from my picture it shows it as the same time but I know the Lorentz transform must be performed because Alice is moving. I think the answer is because I can only measure things in stationary frames and the Lorentz transform does this transform but also twists the graph . Since the graph is twisted during a Lorentz transform even if it is on the T_B axis T_B = 0 isn't 0. Is this correct? https://imgur.com/a/eWjTaT4 Should be X_A not X_B in Alice's frame. Expand Thank you for addition. Did you follow the first steps of my explanation, which give the correct sequence to consider things ? Quote Find the time of Alice's clock when B reaches planet 2? First question I think I understand . I just use d= vt t = d/v Expand We have all said this is correct. Quote Find the time of Bob's clock when B reaches planet 2? Second question. Shouldn't the time of B = A? Expand No this is not correct and is the subject of the second part of my explanation that I have not yet provided. You need to fully understand why you have got the first part right before moving on to the second. Hopefully you will also take the opportunity to learn some correct terminology as you do this. 'Twist' is the wrong word. You should use 'Rotate'. If you swing a weight on a rope in a circle, the rope is straight not twisted. But it is rotating about an axis that is not along the axis of the rope. A twist would be about the axis of the rope.
joigus Posted July 24, 2020 Posted July 24, 2020 (edited) On 7/23/2020 at 10:32 PM, joigus said: t=\frac{1}{2}\left(t_{1}+t_{2}\right) x=\frac{c}{2}\left(t_{2}-t_{1}\right) So everything, spacial coordinates included, is based on observation times. Expand On further reflection, after reading Studiot's comments (+1) carefully, and to correct myself: This definition, while it's very widely used theoretically and very solid, is not universal; and in particular is not useful to assign space coordinates to distant planets. Also, it had nothing to do with the OP's confusion. Sorry, it was late, my reasoning was obfuscated by the phrasing of the question, and consequently I wasn't very helpful. Edited July 24, 2020 by joigus minor correction (semantics)
swansont Posted July 24, 2020 Posted July 24, 2020 On 7/24/2020 at 3:21 AM, can't_think_of_a_name said: First question I think I understand . I just use d= vt t = d/v Second question. Shouldn't the time of B = A? But I know this is wrong because moving clocks tick slow. Why do I have to perform the Lorentz transform when from my picture it shows it as the same time but I know the Lorentz transform must be performed because Alice is moving. I think the answer is because I can only measure things in stationary frames and the Lorentz transform does this transform but also twists the graph . Since the graph is twisted during a Lorentz transform even if it is on the T_B axis T_B = 0 isn't 0. Is this correct? https://imgur.com/a/eWjTaT4 Should be X_A not X_B in Alice's frame. Expand If you want Bob’s numbers, you either analyze the experiment in his frame, or transform from Alice’s frame. One thing we know is the answers will be different in each frame. In Bob’s frame, the trip will be about 3LY and consequently take about 3 years.
joigus Posted July 24, 2020 Posted July 24, 2020 (edited) On 7/24/2020 at 12:18 AM, swansont said: Or it doesn’t matter, since it’s a relative speed, and both Alice and Bob will agree on it. Expand True. +1 Edited July 24, 2020 by joigus
can't_think_of_a_name Posted July 24, 2020 Author Posted July 24, 2020 On 7/24/2020 at 10:31 AM, swansont said: If you want Bob’s numbers, you either analyze the experiment in his frame, or transform from Alice’s frame. One thing we know is the answers will be different in each frame. In Bob’s frame, the trip will be about 3LY and consequently take about 3 years. Expand I think your comment and my comment state Bob always has to be stationary. Is this correct? Another member mentioned I should use rotate instead of twist. So since I rotate the graph XB = 0. X_B is different to 0 compared to the non rotated graph giving a value different then 0. Is this correct? Or are you stating something different?
studiot Posted July 24, 2020 Posted July 24, 2020 On 7/24/2020 at 9:20 PM, can't_think_of_a_name said: I think your comment and my comment state Bob always has to be stationary. Is this correct? Another member mentioned I should use rotate instead of twist. So since I rotate the graph XB = 0. X_B is different to 0 compared to the non rotated graph giving a value different then 0. Is this correct? Or are you stating something different? Expand Any observer, Bob included, is stationary in their own frame. On 7/24/2020 at 9:20 PM, can't_think_of_a_name said: Another member mentioned I should use rotate instead of twist. So since I rotate the graph XB = 0. X_B is different to 0 compared to the non rotated graph giving a value different then 0. Is this correct? Or are you stating something different? Expand Why should I answer your question since you could not be bothered to answer mine. ? I was trying to help you simply. On 7/24/2020 at 8:37 AM, studiot said: Did you follow the first steps of my explanation, which give the correct sequence to consider things ? Expand
swansont Posted July 24, 2020 Posted July 24, 2020 On 7/24/2020 at 9:20 PM, can't_think_of_a_name said: I think your comment and my comment state Bob always has to be stationary. Is this correct? Another member mentioned I should use rotate instead of twist. So since I rotate the graph XB = 0. X_B is different to 0 compared to the non rotated graph giving a value different then 0. Is this correct? Or are you stating something different? Expand Bob is stationary in his frame. You always need to realize what frame you are in when analyzing.
studiot Posted July 25, 2020 Posted July 25, 2020 On 7/24/2020 at 10:44 PM, joigus said: Not a very useful line of thinking for homework help. Expand I agree there is a great deal of off topic discussion which makes it difficult for someone studying relativity from the beginning and for those trying to help that person (the OP). +1 1
joigus Posted July 25, 2020 Posted July 25, 2020 On 7/25/2020 at 11:28 AM, studiot said: I agree there is a great deal of off topic discussion which makes it difficult for someone studying relativity from the beginning and for those trying to help that person (the OP). +1 Expand Thanks. And you're dead right. +1. I stepped back on this particular topic because Swansont and you were more focused and had this more under control and I wasn't helping. I was "waxing theoretical". I think that's the idea.
can't_think_of_a_name Posted July 25, 2020 Author Posted July 25, 2020 I think I get it now. I am just going to the do the math. t = d/v. t = 20.5 if memory is correct. Since Bob is moving I perform the Lorentz transform for time. T = gamma(T' - (v/c^2)(x) Gamma is = 7.14 if memory serves correct. 20.5 year = 7.14 (T' - .99c/c^2)(20.3) = T = 7.14 (T' - 20.1) = T = 7.14( -20.1T' ) I think I made a mistake T' = gamma(T - (v/c^2)(x). The mistake x = 0. T = 7.14 (20.5 years) - .(99c/c^2)(0) = T = gamma (T') = T' = T / gamma = T' = 20.5 / 7.14 = 2.87 Is this correct? Any further questions I will ask.
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