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

by digi99
Tags: arguments, dilation, duration, time
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 Quote by digi99 Thanks Ghwellsjr. A little bit confused about length contraction, maybe it is as I think.
I think a major part of your confusion is that you keep trying to deal with two frames at the same time. I keep telling you to pick one frame and describe everything in that one frame. I told you in post #7 that a clock moving in a frame will be time dilated. I told you in post #16 that a car moving in a frame will be length contracted.
 Quote by digi99 So in frame A is the unit 1 meter and is the rest frame A for a person measuring the car when it was standing still. Suppose the car was 2 meter long. Now the car has a speed in rest frame A, with speed v = x / t (x = distance in t seconds). There is no time dilation for the car in frame A but a length contraction 1/γ.
When the car is at rest in Frame A, its length is 2 meters, that is, it is twice as long as the meter stick which is also at rest in Frame A. When the car accelerates to speed v in Frame A, both the meter stick and the car contract along the direction of motion and time dilates for them. Why do you say there is no time dilation for the car in Frame A when I just told you in post #7 that there was? Don't you read the posts that people respond to you?

OK, now you want to switch to Frame B:
 Quote by digi99 In the rest frame B where the car is standing still (same car driving in the measuring persons rest frame A), there is time dilation 1/γ . t, suppose a ruler in the car, 1 meter is now 1/γ meter and the car is 2/γ meter long.
In Frame B, you said the car is at rest, therefore, there is no time dilation and no length contraction for the car or the meter stick.
 Quote by digi99 Or is the car length contracted in A and has same new length in B ? What is the lenght from the car in frame B ?
In Frame A, since the car is moving, it is length contracted and time dilated. In Frame B, since the car is not moving, it is not length contracted and not time dilated. Its length is 2 meters.
 Quote by digi99 What is the new unit in frame B for as well time as length expressed in units from frame A ?
They are the same. A stationary meter stick in Frame A is the same length as a stationary meter stick in Frame B. A one-second tick in Frame A is the same duration as a one-second tick in Frame B.
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 Quote by digi99 Thanks for the answer JDoolin. Also relating to the previous answer, this is a topic for many, as a usefull collection to convince somebody (not only for me). I have a little question for you (if you want to answer), if a car is driving in frame A where somebody standing still (its rest frame A) is measuring its speed, than you have length contraction in the cars rest frame B. Is the car already smaller in frame A while measuring its speed because going smaller is something really physical or is this not real ?
If you look at a coin from an angle, it looks oval. Is it really an oval, or does it just "appear" to be oval. Is the oval appearance of the coin really physical? Or is it not real?

If you are driving a car in the snow, the snowflakes look like they are coming toward you, rather than falling toward the ground. Is the appearance of motion toward you really physical? Or is it not real?

If you see a meter-stick going by at near the speed of light, viewed from the right angle, it will appear length contracted. Is its appearance of length contraction really physical, or is it not real?

What's missing here is another category. Yes it's really physical. Yes, it is real. But it is not real in the sense that it affects the snow, or affects the coin, or affects the meter-stick. However, it does really affect the observer's real physical measurements of the snow, the coin, the meter-stick. What you have here is observer dependent changes. That is, they do not model any real change in the properties (shape, size, direction of motion) of the snow, coin, or meter-stick, but instead, they model a real change in the properties of the observer (position, facing, direction of motion).
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 Quote by ghwellsjr In Frame B, you said the car is at rest, therefore, there is no time dilation and no length contraction for the car or the meter stick.
Yes I understand, the car is already length contracted and time dilated compared to A but nobody knows that in this frame, we know that in frame A as the observer.

 Quote by ghwellsjr In Frame A, since the car is moving, it is length contracted and time dilated. In Frame B, since the car is not moving, it is not length contracted and not time dilated. Its length is 2 meters
Now a ? for me, a ruler in the car is length contracted in frame A as you said. A meter is still a meter in frame B, but when a person in frame B measure his car (floor also moving with the car), that person measure indeed 2 meter, but we know when he communicates with a walki-talki to us for his/her 2 meter, that he measured 1/γ meter expressed in the meter (unit) from frame A. So also his time (but we see the same time dilated time on the moving clock in frame A fixed to his car). Right (otherwise confused) ?

 Quote by ghwellsjr They are the same. A stationary meter stick in Frame A is the same length as a stationary meter stick in Frame B. A one-second tick in Frame A is the same duration as a one-second tick in Frame B.
Same problem from me, than I understood something not right the last months. I thought a stationary meter stick is 1 meter in frame A, but lying in the car 1/γ meter, and so in frame B compared to frame A, but for somebody in frame B it is still 2 meter, but recalculated for frame A (like for GPS etc.) 2/γ. Right ?

Next time I go to reformulate the other topic about length contraction and time dilation for my example of my car, I come closer to understanding, so I don't need to stop, never give up :) ..
 P: 140 I feel that some of the problem is in the language used and that what one person says the other person reads him saying something totally different. Lets avoid the use of "rest frame". Lets say you have two frames of reference, frame A and frame B. Frame A is a car and in this frame the car is 1 meters. Frame B is a person standing on a road. and in this frame he has meter stick which in this frame is 1 meter. In frame B the car is moving at velocity V. In frame A the person is moving at velocity V. In frame B(person's frame of reference) the car and everything in the car is time dilated and length contracted. Such that in frame B the car is shorter than 1 meter and it's clocks are running slower than the clocks in frame B. In frame A(car's frame of reference) the person and everything in the person is time dilated and length contracted. Such that in frame A the meter stick the person standing on the road is holding is less than 1 meter, and that person is aging slower and his clocks are running slower than the clocks in frame A. Edit: and if you add another frame lets say C all you have to do is check it's velocity vs each frame to see how much that will be length contracted and time dilated compared to that frame.
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 Quote by darkhorror I feel that some of the problem is in the language used and that what one person says the other person reads him saying something totally different. Lets avoid the use of "rest frame". Lets say you have two frames of reference, frame A and frame B. Frame A is a car and in this frame the car is 1 meters. Frame B is a person standing on a road. and in this frame he has meter stick which in this frame is 1 meter. In frame B the car is moving at velocity V. In frame A the person is moving at velocity V. In frame B(person's frame of reference) the car and everything in the car is time dilated and length contracted. Such that in frame B the car is shorter than 1 meter and it's clocks are running slower than the clocks in frame B. In frame A(car's frame of reference) the person and everything in the person is time dilated and length contracted. Such that in frame A the meter stick the person standing on the road is holding is less than 1 meter, and that person is aging slower and his clocks are running slower than the clocks in frame A. Edit: and if you add another frame lets say C all you have to do is check it's velocity vs each frame to see how much that will be length contracted and time dilated compared to that frame.
What happens when the car starts out at rest with respect to the person standing on the road and then accelerates to a final speed, like digi99 asked about in post #18? What frame is the car's frame?
P: 183
BELOW YOU CAN SEE I COMPLETELY UNDERSTAND RELATIVITY NOW (NEVER GIVE UP :))

I thought I understood you, but the difference is you studied this area very well and this all is very known for you. I am trying and trying to see the differences, I have studied mathematics and was strong in geometry, so this can not be that difficult.

You talk about rest frames as seperated worlds without a connection, that confusing me every time after time. Like the sentence in both frames are the sticks equal 1 meter. Maybe I feel this is the symmetry where you are talking about.

Ok, so in your frame you see the other length contracted and time dilated, and the other in his frame sees your time dilated and length contracted. Maybe that's what you want to say to me. In understand this, so I have to condider my example just in one frame A (like the short derivation of Lorentz in Wiki).

In frame A (measuring things here means in the moving direction for length contraction):

- for a person standing still in frame A, the meter stick is 1 meter (just a definition)
- when the car was standing still, its size was 2 meter (his units)
- when the car has speed V (speed measured by person standing still), the car and the same meter stick (laying in the car) are time dilated and length contracted, so the meter stick is 1/γ smaller and its time on the car's clock 1/γ slower
- when that person in the car while driving, measure the car's length from inside (suppose it is a block model), it will be measured as 2 meters because the person don't know it is length contracted
- when he talks by walki-talki to the person standing still, and give all details what he is measuring, the person standing still knows that all seen by him is 1/γ smaller, because this is not an illusion but reality length contracted, the same for a clock, but the measuring length data are the same in numbers, but not the time on his clock, that are other numbers, because it runs slower
- so a km counter in the car is smaller too and measures probably the same distances (all in ration), so when the driver in the car says I am on X km distance by walki-talki, the person standing still knows this WAS the location (walki-talki takes time too) 1/γ . X in his system with his meter stick (that locations/moments are considered equal by definition in relativity)

BUT this all is also valid seen by the driver in the car in his/her rest frame B when the other communicate to him/her about locations and time.

I hope I have make it clear to you I understand it well and have learn now to better communicate about this (the observer in his/her frame sees the other time dilated and length contracted).

Right (rest is not important, next text below) ?

So my topic is about length contraction to explain time dilation in the moving direction, not the other directions (because it must be different explained).

YES, yes, yes, I start now to see relativity. Because both are seeing from both rest frames the other is going smaller, and that is indeed not possible if everything had an absolute size, than only one is smaller but you will see only the difference (greater or smaller). If one is really bigger than the other, the other can't see that one not being smaller.

OK, so indeed is all relative and your whole live takes place seen in your own rest frame. So seperate frames are in fact different worlds. Funny I said this before but in the context I understood it (if it is true), but I see it more clear now (I am not busy with this subject the whole day). You will measure something is going smaller when it moves, but you see that only in your own rest frame. Light is also bound to your rest frame.

But one thing I started in my first topic was to consider the same light wave in both rest frames, but if nothing is absolute it is just what you see, so nothing is real, there is no physic connection between rest frames (maybe we live all in a unreal world, the matrix :)).

OK mysteries exist, nice to think about, but can never be solved I guess ... but time dilation in the moving direction in one frame can still be explained by length contraction and in another frame too ... that both see things smaller, does not need to be an explanation that duration would be different between two rest frames ... so there is still something to think about even when I understand relativity now better ..

Recalculation of data is for data seen by different rest frames, we consider earth and a GPS satelite both in their own rest frames ?

Why is time t in rest frame A, 1/γ t in rest frame B on equal moments, how is simultaneity defined by Einstein ?
P: 183
 Quote by JDoolin What's missing here is another category. Yes it's really physical. Yes, it is real. But it is not real in the sense that it affects the snow, or affects the coin, or affects the meter-stick. However, it does really affect the observer's real physical measurements of the snow, the coin, the meter-stick. What you have here is observer dependent changes. That is, they do not model any real change in the properties (shape, size, direction of motion) of the snow, coin, or meter-stick, but instead, they model a real change in the properties of the observer (position, facing, direction of motion).
Thanks JDoolin, I understand exactly now what you said ... our live is the matrix :) ..

Length contraction is my best argument now for relativity, not yet for duration ..
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 Quote by digi99 BELOW YOU CAN SEE I COMPLETELY UNDERSTAND RELATIVITY NOW (NEVER GIVE UP :)) I thought I understood you, but the difference is you studied this area very well and this all is very known for you. I am trying and trying to see the differences, I have studied mathematics and was strong in geometry, so this can not be that difficult.
Yes, I did spend about a year reading threads on this forum before I ever signed up and made my first post. As I read through the posts, I tried to anticipate how the next person would answer. Most of the time I was wrong but gradually I began to improve my success until I could tell when someone else made an incorrect statement that I knew would be corrected by another person. Even when I thought I understood, I still had a lot to learn and I'm still learning now, but at least I understand the basics.
 Quote by digi99 You talk about rest frames as seperated worlds without a connection, that confusing me every time after time. Like the sentence in both frames are the sticks equal 1 meter. Maybe I feel this is the symmetry where you are talking about.
There's only one world but different ways of defining how we measure it. Each frame uses its own length standard and time standard to establish a set of coordinates to define locations and times and that is the reason different frames have different sets of coordinates but they are all interconnected through the Lorentz Transform. So once you establish a scenario in one frame, you can't just switch to another and start talking about what's going on there, you have to use the Lorentz Transform to see exactly what the coordinates are in the second frame.
 Quote by digi99 Ok, so in your frame you see the other length contracted and time dilated, and the other in his frame sees your time dilated and length contracted. Maybe that's what you want to say to me. In understand this, so I have to condider my example just in one frame A (like the short derivation of Lorentz in Wiki). In frame A (measuring things here means in the moving direction for length contraction): - for a person standing still in frame A, the meter stick is 1 meter (just a definition) - when the car was standing still, its size was 2 meter (his units) - when the car has speed V (speed measured by person standing still), the car and the same meter stick (laying in the car) are time dilated and length contracted, so the meter stick is 1/γ smaller and its time on the car's clock 1/γ slower - when that person in the car while driving, measure the car's length from inside (suppose it is a block model), it will be measured as 2 meters because the person don't know it is length contracted - when he talks by walki-talki to the person standing still, and give all details what he is measuring, the person standing still knows that all seen by him is 1/γ smaller, because this is not an illusion but reality length contracted, the same for a clock, but the measuring length data are the same in numbers, but not the time on his clock, that are other numbers, because it runs slower - so a km counter in the car is smaller too and measures probably the same distances (all in ration), so when the driver in the car says I am on X km distance by walki-talki, the person standing still knows this WAS the location (walki-talki takes time too) 1/γ . X in his system with his meter stick (that locations/moments are considered equal by definition in relativity) BUT this all is also valid seen by the driver in the car in his/her rest frame B when the other communicate to him/her about locations and time. I hope I have make it clear to you I understand it well and have learn now to better communicate about this (the observer in his/her frame sees the other time dilated and length contracted). Right (rest is not important, next text below) ?
That's the best I've seen you express it so far. I'm still having a little trouble understanding some of what you are saying but I think you've got it right.
 Quote by digi99 So my topic is about length contraction to explain time dilation in the moving direction, not the other directions (because it must be different explained). YES, yes, yes, I start now to see relativity. Because both are seeing from both rest frames the other is going smaller, and that is indeed not possible if everything had an absolute size, than only one is smaller but you will see only the difference (greater or smaller). If one is really bigger than the other, the other can't see that one not being smaller. OK, so indeed is all relative and your whole live takes place seen in your own rest frame. So seperate frames are in fact different worlds. Funny I said this before but in the context I understood it (if it is true), but I see it more clear now (I am not busy with this subject the whole day). You will measure something is going smaller when it moves, but you see that only in your own rest frame. Light is also bound to your rest frame.
I'm afraid you're reading too much into what a frame is. Different frames have absolutely no bearing on what anybody sees or observes or measures. The purpose of establishing a Frame of Reference in Special Relativity is so that we can talk meaningfully about what we can't see, observe, or measure. That's why we are free to select any frame we want and why no frame is preferred, not even our own rest frame.

Now I know this may sound confusing to you, but I want to fall back on the issue of motion that I continually bring up as a way of illustrating what I mean. When two observers have a relative motion between them, they each perceive the other one to be moving, correct? But when we arbitrarily pick a Frame of Reference, we nail down which one is actually moving according to that FoR. And when we do that, even though they each measure and perceive the other one to be length contracted and time dilated, we nail down which one is actually length contracted and time dilated in that FoR. But even though we say in this selected Frame of Reference that only one is moving and experiencing length contraction and time dilation, we can still determine mathematically how each one sees the other one as being the one that is experiencing length contraction and time dilation.
 Quote by digi99 But one thing I started in my first topic was to consider the same light wave in both rest frames, but if nothing is absolute it is just what you see, so nothing is real, there is no physic connection between rest frames (maybe we live all in a unreal world, the matrix :)). OK mysteries exist, nice to think about, but can never be solved I guess ... but time dilation in the moving direction in one frame can still be explained by length contraction and in another frame too ... that both see things smaller, does not need to be an explanation that duration would be different between two rest frames ... so there is still something to think about even when I understand relativity now better ..
You cannot explain time dilation by length contraction. The two go hand in hand but it's like I said before, length contraction only exists along the direction of motion and time dilation exists independently of the direction of motion.
 Quote by digi99 Recalculation of data is for data seen by different rest frames, we consider earth and a GPS satelite both in their own rest frames ?
This question is outside the realm of Special Relativity which deals only with inertial Frames of Reference and not influences of gravity. I don't think you're ready for General Relativty.
 Quote by digi99 Why is time t in rest frame A, 1/γ t in rest frame B on equal moments, how is simultaneity defined by Einstein ?
Why don't you study his 1905 paper and see for yourself?
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 Quote by ghwellsjr I'm afraid you're reading too much into what a frame is. Different frames have absolutely no bearing on what anybody sees or observes or measures. The purpose of establishing a Frame of Reference in Special Relativity is so that we can talk meaningfully about what we can't see, observe, or measure. That's why we are free to select any frame we want and why no frame is preferred, not even our own rest frame. Now I know this may sound confusing to you,
Yes, that is very confusing. You can't come up with any situation where "our own rest frame" is preferred?
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 Quote by JDoolin Yes, that is very confusing. You can't come up with any situation where "our own rest frame" is preferred?
It's only preferred in the sense that calculations may be simpler or it's easier to discuss or visualize, but it offers no more validity than any other frame. And it doesn't provide any more insight into what we cannot see, measure or observe.
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 Quote by ghwellsjr It's only preferred in the sense that calculations may be simpler or it's easier to discuss or visualize, but it offers no more validity than any other frame. And it doesn't provide any more insight into what we cannot see, measure or observe.
I agree that all reference frames are equally valid. I was just confused by your statement that there's no reason to "prefer our own reference frame"

These are all great reasons to prefer our own reference frame:
• "calculations are simpler"
• "it's easier to discuss"
• "it's easier to visualize"

But preference isn't just a matter of logic. It's a matter of artistic, and aesthetic opinions and values.

Imagine trying to describe a football game in the rest frame of a muon traveling 99.99% of the speed of light. It would all be flat, and slow-motion, with things moving from the left-to-right really fast, and moving from right-to-left really slow.

For me, not being particularly fond of football, and quite interested in relativity, I probably prefer to see the game in the reference frame of the muon, just to see what it would look like.

But for someone who likes football, more than relativity, they would probably prefer to see it in the reference frame of the football stadium. Or better yet, from quickly changing, low-velocity reference frames as multiple cameras zoom in and follow the action.
P: 183
 Quote by ghwellsjr There's only one world but different ways of defining how we measure it. Each frame uses its own length standard and time standard to establish a set of coordinates to define locations and times and that is the reason different frames have different sets of coordinates but they are all interconnected through the Lorentz Transform. So once you establish a scenario in one frame, you can't just switch to another and start talking about what's going on there, you have to use the Lorentz Transform to see exactly what the coordinates are in the second frame.

1 day later (its like a circle) I understand I understood it well, but my communication must be more matched on physics communication, so I try from now on this doing better and not to quick mixing things by answering to fast. So more carefully in formulating.

I realise too just as you said length contraction and time dilation goes hand in hand.

Thats what I am thinking for a while in my blogs and my own website, its just the ration distance / time = C everywhere in the universe (discovered by light in space, so represented by light in space but not on earth, than it is just that ration). I am thinking in two scenarios all the time, if true and if not true.

So when something B is relative moving in a frame you choose, in relation to something A standing still, both see each other smaller (lets say the same size when both standing still), but I think its only an effect because of the general rule distance / time = C, so it is not necessary to find an explanation physically why its length contracted, its just because of the relation distance / time = C. So length and distance are time depended and vice versa. Thats expressed in Lorentz.

So in my first topic and on my website explaining everything is going smaller, a lightwave too (and its amplitude), is just the effect of distance / time = C and no other physical explanation on atom level. That e.g. mass is depended on a possible Higgs field is different and has nothing to do with relativity.

But there is still no contradiction that there is a centre (an absolute world) were all is standing still and has its origanal size, and for what is moving Einstein is valid.

Ready for the General Relativity (?), no because this all takes time for me to accept but slower and slower I will accept it. The trigger for me is the length contraction, it must be time depended, but first I have to see for myself if there are no other explanations possible and if affects this all duration or not.

Why distance / time = C, is just a law to accept I guess, like someone said in a forum, if you don't like it you just have to go to another universe :).

Agreed ? (read distance / time = C, just as the lightspeed, so no new theory)

To be sure in understanding, would an exact device where width, height and length are important for working very well in a frame when standing still, still working for a higher speed lets say close to the lightspeed ?
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 Quote by JDoolin I agree that all reference frames are equally valid. I was just confused by your statement that there's no reason to "prefer our own reference frame" These are all great reasons to prefer our own reference frame: "calculations are simpler" "it's easier to discuss" "it's easier to visualize" But preference isn't just a matter of logic. It's a matter of artistic, and aesthetic opinions and values. Imagine trying to describe a football game in the rest frame of a muon traveling 99.99% of the speed of light. It would all be flat, and slow-motion, with things moving from the left-to-right really fast, and moving from right-to-left really slow. For me, not being particularly fond of football, and quite interested in relativity, I probably prefer to see the game in the reference frame of the muon, just to see what it would look like. But for someone who likes football, more than relativity, they would probably prefer to see it in the reference frame of the football stadium. Or better yet, from quickly changing, low-velocity reference frames as multiple cameras zoom in and follow the action.
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.

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. A frame doesn't let observers see things that "we" can see as a result of assigning coordinates to distant events from an observer in the frame.

But if you meant watching the game as a muon would see it, then there won't be much to see since the muon doesn't last very long.
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 Quote by digi99 Thanks JDoolin, I understand exactly now what you said ... our live is the matrix :) .. Length contraction is my best argument now for relativity, not yet for duration ..

No. That sounds like it may be a reference to the movie "The Matrix." It doesn't sound like you understand what I said at all.

What I'm saying is that Everything that you see is real. Everything I see is real. If we both look at the same object at the same time, we see different things. But my perspective is just as real as your perspective.

All perspectives/frames are equally valid, and just as real as any other.
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 Quote by 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. 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. A frame doesn't let observers see things that "we" can see as a result of assigning coordinates to distant events from an observer in the frame. But if you meant watching the game as a muon would see it, then there won't be much to see since the muon doesn't last very long.
I realize now, there are a couple different definitions to the word "preferred."

(1) to put before something or someone else in one's liking, opinion, etc.; like better
(2) to give preference or priority to

You are absolutely right by definition 2, there is no reason to prioritize one reference frame over another. Namely because all reference frames are equally valid.

However, I was thinking of the more "opinion" version of preferred (definition 2). As in, most people would prefer to watch a football game in the rest-frame of the football stadium, as opposed to the rest frame of some muon traveling past the stadium at near the speed of light.

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. That actually does sound like something out of "The Matrix." ;)

I don't know if you've seen this movie, but there are scenes in the movie, where mathematical symbols are more-or-less falling from the sky like rain, and there were parts of the movie where they really did "just see a bunch of weird coordinates."

I'm sure that's not what you meant, though.
P: 183
 Quote by JDoolin No. That sounds like it may be a reference to the movie "The Matrix." It doesn't sound like you understand what I said at all. What I'm saying is that Everything that you see is real. Everything I see is real. If we both look at the same object at the same time, we see different things. But my perspective is just as real as your perspective. All perspectives/frames are equally valid, and just as real as any other.
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 lets 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.

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 physic laws in all frames for all observers, could be a logic reason) ?
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Quote by JDoolin
 Quote by 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?

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