Simple SR

[swansont]

No, this is wrong.

 

You'll excuse me if I don't take your word for it.

 

 

2) The co-location is a common point in time

 

There is no such thing. Time is relative, as is length — it depends on the observer. There is no art of relativity that permits you to make this statement. Assuming that time isn't relative leads to a contradiction, which proves it to be false.

 

Co-location does not remove length contraction, nor does it remove time dilation. You were able to show co-location with the LT. Can you show that t=t' ? NO. In your very first post you stated that t = r/c and t'= r/(γc). You have contradicted yourself.

[vuquta]

You'll excuse me if I don't take your word for it.

 

 

 

There is no such thing. Time is relative, as is length — it depends on the observer. There is no art of relativity that permits you to make this statement. Assuming that time isn't relative leads to a contradiction, which proves it to be false.

 

Co-location does not remove length contraction, nor does it remove time dilation. You were able to show co-location with the LT. Can you show that t=t' ? NO. In your very first post you stated that t = r/c and t'= r/(γc). You have contradicted yourself.

 

I posted the following.

 

I can ignore time. The co-location is at a point in time and not an interval. Are you now arguing O and O'1 are not co-located? Well, they are and I showed that. This strategy allows me to calculate everything based on the co-location of the two. Then, based on the relativity postulate, i.e. the rules of physics are the same from both frames, I calculate everything at that common instant, which is different times on the two clocks, using the rules of SR. Since SR must apply at all times in any frame, I am on solid footing.

 

As you can see, I agree the time on the clocks will be different.

 

I am not nor have I said the time on their clocks are the same. I am only showing they have a common endpoint and this you cannot refute.

 

If I chose to do so, I could have arranged an observer at (vxγ/(1+γ),0,0) in the stationary frame and one at (-vxγ/(1+γ),0,0) in the moving frame.

 

Then, and I am sure you can do the math, t'=t=r/c.

 

But, the same conclusions follow. One observer in the O frame will be located at r/c.

 

The other observer will be located at (vr/c + r/c)γ when transformed with LT.

 

Let me know if you need help with the math.

[swansont]

The observers agree they are co-located, but disagree on the time and the location in their coordinate systems (i.e. how far they have traveled). The observers agree light hits O'2, but disagree when that happens, and where O'2 is when that occurs.

 

You say common instant, but different times. You can't have it both ways. That's a contradiction. SR applies at all times, that's true. But that's actual SR, not your straw man version of it.

[vuquta]

The observers agree they are co-located, but disagree on the time and the location in their coordinate systems (i.e. how far they have traveled). The observers agree light hits O'2, but disagree when that happens, and where O'2 is when that occurs.

 

You say common instant, but different times. You can't have it both ways. That's a contradiction. SR applies at all times, that's true. But that's actual SR, not your straw man version of it.

 

As I have said, the readings on the clocks do not change the fact they are co-located. In addition, they disagree on their locations. I never disagreed. But, this is a straw man since none of this affects the outcome.

 

The observers agree light hits O'2, but disagree when that happens, and where O'2 is when that occurs.

This is where you go wrong. You use LT to map back and forth between the frames. You are attempting to isolate the frames as if there is no type of

transformation between them. So, your argument works very well only if LT is false. Is that your contention now that LT is false? So, since everything has been translated into the system of O, how do you explain that light is located at (r,0,0) and at (r (1+v/c),0,0) in O when O and O'2 are co-located?

 

You also failed to mention, when O'1 and O are at the same place, they disagree on the location of light in the stationary system of coords. Since there was a common light emission, they would be measuring different light speeds when the stationary measurements are used. Now, you mentioned length contraction. Well that coorresponds to time dilation as well. Hence, (r/γ) / (t/γ) = c. So, light should travel a length contracted distance but at a time dilated interval still making it c. But, that does not explain the distance differential.

 

When I said common instant or whatever, I meant, one can at that common place calculate all the truths of SR. That is what I did. Further, since I have show time dilation, I would not expect the clocks to read the same. For example, Einstein said for any interval in the stationary frame of t, that cooresponds to an interval t/γ. Therefore, when t elapses in O and t/γ in O', these translate to the same instant. See how that works under SR? You can have the same instant but different clock readings. This is what Einstein said, Is he wrong?

 

Here I will lay out the argument quoting which part of SR I use.

 

Light is a distance r in the O frame after light emission.

 

SR Conclusions

1) O and O'1 are co-located when light strikes them. (LT)

2) Since O is struck by the light, then light is located at (r,0,0) in the O coordinates. (Light Postulate)

3) Since O'1 is struck by the light, then light is located at (r/γ,0,0)/O'2 in the coordinates of O'. (Light and Relativity Postulate)

4) Since light is located at (r/γ,0,0) in the O' frame, then light is located at (r (1+v/c),0,0) in the stationary frame. (LT)

 

Therefore, when O and O'1 are co-located, light is located at (r,0,0) and at (r (1+v/c),0,0) in the stationary system of coordinates. (All of SR)

 

Please feel free to indicate which part of SR you are refuting.

[Cap'n Refsmmat]

SR Conclusions

1) O and O'1 are co-located when light strikes them. (LT)

2) Since O is struck by the light, then light is located at (r,0,0) in the O coordinates. (Light Postulate)

3) Since O'1 is struck by the light, then light is located at (r/γ,0,0)/O'2 in the coordinates of O'. (Light and Relativity Postulate)

4) Since light is located at (r/γ,0,0) in the O' frame, then light is located at (r (1+v/c),0,0) in the stationary frame. (LT)

 

Lorentz transforms work on both space and time. When you're doing step 4, don't you have to transform the time between frames as well as the spatial coordinates?

 

Also, in the stationary frame, isn't the v in (r (1+v/c),0,0) equal to 0, making that expression simply (r,0,0)? Which is equal to what you calculated in step 2? Or is v some other number? I'm not familiar with Lorentz transformations.

Edited June 21, 2010 by Cap'n Refsmmat

[vuquta]

Lorentz transforms work on both space and time. When you're doing step 4, don't you have to transform the time between frames as well as the spatial coordinates?

 

Also, in the stationary frame, isn't the v in (r (1+v/c),0,0) equal to 0, making that expression simply (r,0,0)? Which is equal to what you calculated in step 2? Or is v some other number? I'm not familiar with Lorentz transformations.

 

Lorentz transforms work on both space and time. When you're doing step 4, don't you have to transform the time between frames as well as the spatial coordinates?

 

Sure do. But, that presents a problem for SR. The time calculated by LT is r/c (1+v/c). So, when O'2 is hit, SR says the time in the O frame is (r/c (1+v/c),0,0). Yet, O'2 is hit when O and O'1 are co-located and that time in O is r/c.

 

So, LT is confused on how to correctly decide the time also.

 

 

Also, in the stationary frame, isn't the v in (r (1+v/c),0,0) equal to 0, making that expression simply (r,0,0)? Which is equal to what you calculated in step 2? Or is v some other number? I'm not familiar with Lorentz transformations.

 

If step 2 is (r,0, 0) for both frames that would imply absolute simultaneity.

 

x = ( x' + vt')γ.

 

x' = r/γ and t'=r/(cγ).

 

x = ( r/γ + v(r/(cγ)))γ. = ( r + rv/c) = r ( 1 + v/c ).

y=0

z=0

 

No, v is not zero since it is the relative motion between the frames.

[Cap'n Refsmmat]

Sure do. But, that presents a problem for SR. The time calculated by LT is r/c (1+v/c). So, when O'2 is hit, SR says the time in the O frame is (r/c (1+v/c),0,0). Yet, O'2 is hit when O and O'1 are co-located and that time in O is r/c.

 

So, LT is confused on how to correctly decide the time also.

You're mixing frames. One frame will see the event happening at a different time when it looks at the other. There's no absolute simultaneity between frames.

 

If step 2 is (r,0, 0) for both frames that would imply absolute simultaneity.

That's not what I said. I said step 2 is (r,0,0) for the O frame, and if v is 0 in step 4, you also get (r,0,0) for the O frame. No contradiction.

 

No, v is not zero since it is the relative motion between the frames.

I see. I wasn't sure how it worked.

 

Why must you bring in all sorts of extra constraints, like the light postulate and the relativity postulate, when the Lorentz transformation is the special relativity way to translate between frames? When you do a Lorentz transform, it already accounts for everything -- it takes an observation in one frame and translates it into another. No extra stuff required.

 

It sounds like you're trying to go from one frame to another, then back to the first, and get inconsistent results. If you simply do the Lorentz transformations, you'll get the right answer.

[vuquta]

You're mixing frames. One frame will see the event happening at a different time when it looks at the other. There's no absolute simultaneity between frames.

 

 

I applied LT. How is that mixing frames.

 

The light postulate in O' says light hits O'2 when O and O'1 are co-located and that time is r/c.

 

LT say that time should be at O'2 when t = r/c ( 1 + v/c ).

 

Could you explain how I violated LT or the postulates of SR specifically with math?

 

 

That's not what I said. I said step 2 is (r,0,0) for the O frame, and if v is 0 in step 4, you also get (r,0,0) for the O frame. No contradiction.

 

Well v is not 0, so why does this matter?

 

 

Why must you bring in all sorts of extra constraints, like the light postulate and the relativity postulate, when the Lorentz transformation is the special relativity way to translate between frames? When you do a Lorentz transform, it already accounts for everything -- it takes an observation in one frame and translates it into another. No extra stuff required.

 

It sounds like you're trying to go from one frame to another, then back to the first, and get inconsistent results. If you simply do the Lorentz transformations, you'll get the right answer.

 

Well, SR is an axiomatic theory. That means you must always apply the postulates when drawing conclusions or you are outside the theory.

 

Let me give you an example where you cannot use LT to decide a problem.

 

Assume an observer in a frame is at (-r,0,0) and light is flashed at (0,0,0).

 

When will light reach (-r,0,0)? When will it reach (r,0,0)?

 

Lt cannot give you this answer.

[swansont]

You also failed to mention, when O'1 and O are at the same place, they disagree on the location of light in the stationary system of coords.

 

The stationary system is O for the observer in O, and the stationary system for O'1 and O'2 is O'. What you have done is express the position in O. But there are still two observers, and they are in different frames of reference, i.e. they are moving with respect to each other. They make different observations.

 

SR Conclusions

1) O and O'1 are co-located when light strikes them. (LT)

2) Since O is struck by the light, then light is located at (r,0,0) in the O coordinates. (Light Postulate)

3) Since O'1 is struck by the light, then light is located at (r/γ,0,0)/O'2 in the coordinates of O'. (Light and Relativity Postulate)

4) Since light is located at (r/γ,0,0) in the O' frame, then light is located at (r (1+v/c),0,0) in the stationary frame. (LT)

 

Therefore, when O and O'1 are co-located, light is located at (r,0,0) and at (r (1+v/c),0,0) in the stationary system of coordinates. (All of SR)

 

Please feel free to indicate which part of SR you are refuting.

 

#4 is your problem. It's the O coordinates, but it's still the O' observer, and his clock is different. You have not accounted for time dilation effects (and by ignoring it, you have invoked absolute simultaneity). You should find that the two locations are not observed at the same time by the O observer.

 

Since the postulates of relativity are used to derive the LT, you should be able to do all of this only with the kinematic equation d = ct, and the LT. There is no reason to invoke the postulates at all, except to introduce errors by mixing frames.

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Sure do. But, that presents a problem for SR. The time calculated by LT is r/c (1+v/c). So, when O'2 is hit, SR says the time in the O frame is (r/c (1+v/c),0,0). Yet, O'2 is hit when O and O'1 are co-located and that time in O is r/c.

 

So, LT is confused on how to correctly decide the time also.

 

O'2 is hit when O and O'1 are co-located according to O'1. The "confusion" in the time is symmetric to the "confusion" in the distance. The two times will corresponds to the two distances — t1 for d1, and t2 for d2. These are the locations and times when the two observers see O'2 being hit. They see the distances as different due to length contraction, and the times as different due to time dilation. The two effect complement each other.

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Consecutive posts merged

Well, SR is an axiomatic theory. That means you must always apply the postulates when drawing conclusions or you are outside the theory.

 

Let me give you an example where you cannot use LT to decide a problem.

 

Assume an observer in a frame is at (-r,0,0) and light is flashed at (0,0,0).

 

When will light reach (-r,0,0)? When will it reach (r,0,0)?

 

Lt cannot give you this answer.

 

No, you only use the LT when moving from one frame to the other, and you only have one frame. You use d = ct to solve the problem. But you never have to apply the postulates, because they are incorporated in the transforms already. It's when you apply them incorrectly that you find the contradictions.

Edited June 22, 2010 by swansont
Consecutive posts merged.

[vuquta]

The stationary system is O for the observer in O, and the stationary system for O'1 and O'2 is O'. What you have done is express the position in O. But there are still two observers, and they are in different frames of reference, i.e. they are moving with respect to each other. They make different observations.

 

Agreed. However, when O and O'1 are co-located, light is at two different locatations under the calculations of SR.

 

That is the problem.

 

If you refute either calculation, then you refute SR.

 

 

 

 

 

#4 is your problem. It's the O coordinates, but it's still the O' observer, and his clock is different. You have not accounted for time dilation effects (and by ignoring it, you have invoked absolute simultaneity). You should find that the two locations are not observed at the same time by the O observer.

 

Agreed both frames disagree on the location of light when O and O'1 are co-located. So do you.

 

I am simply saying under SR, they are both right. If either are wrong, then SR is false.

 

If both are right, then SR is false.

 

 

Since the postulates of relativity are used to derive the LT, you should be able to do all of this only with the kinematic equation d = ct, and the LT. There is no reason to invoke the postulates at all, except to introduce errors by mixing frames.

Not true.

 

LT only maps frame to frame.

 

You need the light postulate in the frame to conclude light proceeds spherically fron the light emission point.

 

 

O'2 is hit when O and O'1 are co-located according to O'1. The "confusion" in the time is symmetric to the "confusion" in the distance. The two times will corresponds to the two distances — t1 for d1, and t2 for d2. These are the locations and times when the two observers see O'2 being hit. They see the distances as different due to length contraction, and the times as different due to time dilation. The two effect complement each other.

No, this does not work.

 

You can do this math yourself.

 

Lenght contraction and time dilation does not explain these differentials. If then did, then we would have absolute simultaneity with events but different times and distances.

 

 

No, you only use the LT when moving from one frame to the other, and you only have one frame. You use d = ct to solve the problem. But you never have to apply the postulates, because they are incorporated in the transforms already. It's when you apply them incorrectly that you find the contradictions.

 

Not true.

 

I have two frames by the co-location of O and O'1.

 

I must invoke LT to convert coords frame to frame.

 

Do you know another way under SR?