What are your best arguments for time dilation, so duration is different ?

[ghwellsjr]

A person in the stadium is not concerned with a reference frame and it doesn't matter what reference frame we use to analyze what he sees. All reference frames will agree on what he sees, even the muon's frame. If you pick the muon's frame, you will just see a bunch of weird coordinates that you will then have to reinterpret to determine what someone in the stadium actually sees.

Your statement above: " If you pick the muon's frame, you will just see a bunch of weird coordinates that you will then have to reinterpret to determine what someone in the stadium actually sees." is confusing, though.

Sorry, I didn't mean to be confusing. Let me see if I can explain it better:

My first point was that a person who watches a football game is not cognizant of any reference frame. The purpose of a reference frame is to give coordinates to events that are distant from the origin or from any observers that we are considering. When an observer in the stands sees the football hitting the ground somewhere, he doesn't think, "Well, since the distance to that event is defined in my rest frame to be 200 feet, it must have occurred 200 microseconds before I saw it happen". And when he sees a player jump the line of scrimmage and the ref calls a penalty, he doesn't analyze it to see if in his frame of reference the penalty was really deserved.

My second point is if you want to use a frame of reference to analyze what a person in the stadium actually sees, you will have to describe the action on the playing field in terms of events and then calculate how long the image of those events takes to reach the person's eyes at the speed of light and at what angle they enter his eyes so that you can then determine what he actually sees. Now if you use the stadium's rest frame to describe the action and you want to use a muon's rest frame to analyze what the person in the stadium will see, you will have to transform all the events into the rest frame of the muon and do the calculations of how the events appear to the person in the stadium, so both the action on the field and the person watching the game will be traveling at a very high speed making the calculations very difficult. And for all that work, you will conclude that he sees exactly the same thing as when you analyze everything using the stadium's rest frame.

Does that clarify what I meant?

 

[JDoolin]

Thanks for your answer (I am happy to hear this, because it became more and more misty for me, I have to learn this all from remarks in this forum), you gave me in fact an answer on a problem I had, read next:

"I still find 1 thing difficult to see. The much known triangle how Lorentz can be derived in a more simple way (see wiki). If a light source is moving horizontally which let bounce 1 vibrating photon (pulse, direction vibration is horizontally) vertically between 2 mirrors (with speed of light C), we as standing still see that passing photon as two legs of a triangle (compare with a passing translucent train where somebody let's bounce a ball and we look to it from a station). Ok the direction of the photon is to understand for me (like the ball), but the vibration direction of the photon changes too (perpendicular to the legs of the triangle) for which the vibrated photon again may be seen as a beam (pulse) by us (and so again the speed of light is C)."

So both observers looks to the same pulse at the same moment from different frames, both see the same "photon" (pulse) but another vibration direction.

Time dilation is derived in a simple way, yes. However, once you make that derivation, you have to account for the symmetry of the situation. If I see YOUR clock going slower than mine, and you see MY clock going slower than yours, we cannot have a shared simultaneity.

Much like forward, backward, left, right, up, and down, which are observer-dependent directions, future, past, and simultaneity are observer dependent. Now when I say "observer dependent" I DO NOT mean ambiguous, unclear, inexact, open to interpretation.

The observer dependency of future, past, and simultaneity are explicit, fully defined, leaving no room for confusion or doubt.

When you look at a coin from an oblique angle, you see what you see. If you didn't see what you see, then you wouldn't know where the coin was. You wouldn't have any idea where to reach to pick it up. You can decide to "interpret" what you see, saying that coin is "round" and there's no reason to "prefer" describing the coin as an oval, over describing it as "round" but in order to literally see the round shape, you have to line the coin up in a certain way with your eye.

Is there an explanation (theory) we see different things (e.g. like many dimensions), or just to accept because this is nature (probably all must fit at any moment in physics laws in all frames for all observers, could be a logic reason) ?

Is there a theory that explains why I see the back of the coin, while you see the front of the coin, but we both agree that it is the same coin? I would recommend a reading of Bertrand Russell's "The Problems of Philosophy" You might benefit from a comparison of Empiricism, Idealism, and Rationalism. (I don't know if any of this develops a "theory" but it certainly does emphasize the question.)

 

[JDoolin]

Sorry, I didn't mean to be confusing. Let me see if I can explain it better:

My first point was that a person who watches a football game is not cognizant of any reference frame. The purpose of a reference frame is to give coordinates to events that are distant from the origin or from any observers that we are considering. When an observer in the stands sees the football hitting the ground somewhere, he doesn't think, "Well, since the distance to that event is defined in my rest frame to be 200 feet, it must have occurred 200 microseconds before I saw it happen". And when he sees a player jump the line of scrimmage and the ref calls a penalty, he doesn't analyze it to see if in his frame of reference the penalty was really deserved.

My second point is if you want to use a frame of reference to analyze what a person in the stadium actually sees, you will have to describe the action on the playing field in terms of events and then calculate how long the image of those events takes to reach the person's eyes at the speed of light and at what angle they enter his eyes so that you can then determine what he actually sees. Now if you use the stadium's rest frame to describe the action and you want to use a muon's rest frame to analyze what the person in the stadium will see, you will have to transform all the events into the rest frame of the muon and do the calculations of how the events appear to the person in the stadium, so both the action on the field and the person watching the game will be traveling at a very high speed making the calculations very difficult. And for all that work, you will conclude that he sees exactly the same thing as when you analyze everything using the stadium's rest frame.

Does that clarify what I meant?

I think you're answering a different question than what I was expecting.

My question is "what does the hypothetical observer in the rest frame of the muon see?"

It seems like you are answering "What does the hypothetical observer in the rest frame of the muon calculate that the football player sees?"

The football player does not have to do any calculations to figure out what he sees. And the observer in the rest frame of the muon shouldn't have to do any calculations to figure out what it sees, either.

 

[ghwellsjr]

In post #30 you asked about what an observer in different reference frames would see when watching a football game. Since I wasn't sure what exactly you were asking, I gave three different answers in post #32. Then in post #34 you quoted from the first of those three answers and asked for clarification which I gave in post #36. Now you're asking about the other two of those answers and again, I don't know which one you mean.

But all along I'm trying to get you to quit thinking in terms of a frame of reference when asking what an observer sees because it has nothing to do with what a frame of reference is for. Here's how you should ask the question: "what does the hypothetical observer traveling for a long time at the speed of a muon see?" (my second answer) or "what does the hypothetical observer traveling with a muon see?" (my third answer). You then can use any frame of reference to analyze those situations, even the rest frame of the stadium, in fact, that is the one I prefer (your alternate definition of prefer).

 

[JDoolin]

In post #30 you asked about what an observer in different reference frames would see when watching a football game. Since I wasn't sure what exactly you were asking, I gave three different answers in post #32. Then in post #34 you quoted from the first of those three answers and asked for clarification which I gave in post #36. Now you're asking about the other two of those answers and again, I don't know which one you mean.

Okay, I'm sorry about that. I didn't realize you were answering three different questions. I was also not thinking about the fact that muons are actually only created in the upper atmosphere, and only last for a very short time.

Now if you meant watching a football game from the rest frame of a muon, then you will have to start eons ago and far away and continue to eons in the future and all you will see is a pinpoint of blue-shifted light that then eventually gets large and then you have to look backwards and watch the rest of the game as a pinpoint of red-shifted light.

This is a pretty good answer to the question I meant to ask. Although technically if you watch the football game from that frame you won't start eons ago. If you went past the game at half-time, you'd watch the first half of the game in fast-forward, (blue-shifted), and the last half the game in slow-motion for eons.

 

[ghwellsjr]

This is a pretty good answer to the question I meant to ask. Although technically if you watch the football game from that frame you won't start eons ago. If you went past the game at half-time, you'd watch the first half of the game in fast-forward, (blue-shifted), and the last half the game in slow-motion for eons.

I like that, except I kind of overstated the time factor. Muons travel at about 0.98c with a gamma of 5 so if we considered a two-hour football game (no commercials), the first half would start for the muon-observer about one-half hour after the beginning of the game at about a distance of one-half light-hour away. The muon-observer would then see the first half at ten-times fast motion for him and blue-shifted. This would take about six minutes for him (one-fifth of a half hour). Then he would face the other way as he whizzed past the stadium and watch the second half at one-tenth slow motion for him and red-shifted. This would take about ten hours for him and would last until about fifty hours after the end of the game at which point he would be located about fifty-one light-hours away.

Thanks for the added insight into this situation.