Deriving Equations for Light Sphere in Collinear Motion - O and O' Observers

[cfrogue]

cfrogue

Note that events that are simultaneous in one frame cannot be simultaneous in a frame moving relative to it.

The times at which the light to reaches points on the surface of the sphere (circlular cross section of cone) in one frame are only equal when measured in that frame. The observer in that frame considers the times at which the light reaches the points on the "other" sphere (tilted, non circular, cross section of cone) to be not simultaneous.

The same reasoning applies if the observers are interchanged.

Matheinste.

I am guessing I said the above around 4 times in this thread already.

So, I have that part figured out.

But, we still have not resolved the light sphere origin problem.

Any ideas?

 

[matheinste]

I am guessing I said the above around 4 times in this thread already.

So, I have that part figured out.

But, we still have not resolved the light sphere origin problem.

Any ideas?

You need to realize that although in a purely spatial representation the origins, are represented by different POINTS moving apart, in four dimensional spacetime the coincidence of the origins and the emission are, and remain,the same EVENT. Events have no spatial or temporal extension and so do not move.

Matheinste.

 

[cfrogue]

Let's see.

By the light postulate, we need a light sphere expanding at the origin of O and we need a light sphere expanding at the origin of O' since O' emitted the light.

Yet, at any time t in the coordinates of O, O' is located at vt.

That would mean the light sphere is origined at 0 and at vt at the same time in O.

 

[Dale]

The t' is required to be simultaneous in O' according to the light postulate. The light was emitted from O'.

No, this is not what the second postulate requires at all. The second postulate requires that the speed of light be the same in O' as in O:

Using event A' we determine that the speed of light in O' is |x'/t'| = |2.5/2.5| = 1
Or, using event B' we determine that the speed of light in O' is |x'/t'| = |-10/10| = 1

So the speed of light in O' is 1 which is equal to the speed of light in O. The requirement of the second postulate is met.

 

[cfrogue]

You need to realize that although in a purely spatial representation the origins, are represented by different POINTS moving apart, in four dimensional spacetime the coincidence of the origins and the emission are, and remain,the same EVENT. Events have no spatial or temporal extension and so do not move.

Matheinste.

So, let's see the equations you have.

I would like you to note, the origin of O' is always located at vt from the coords of O.

See the t in the equation?

http://www.youtube.com/watch?v=V3Kd7IGPyeg&feature=related"

 

[matheinste]

So, let's see the equations you have.

I would like you to note, the origin of O' is always located at vt from the coords of O.

See the t in the equation?

No equations needed. You are again thinking purely spatially. The emission and the coincidence of the origins are one SPACETIME EVENT. Nothing that happens after the event altrers its coordinates.

Matheinste.

 

[cfrogue]

No equations needed. You are again thinking purely spatially. The emission and the coincidence of the origins are one SPACETIME EVENT. Nothing that happens after the event altrers its coordinates.

Matheinste.

So where have you included that O' moves to vt?

You have not resolved anything with this.

Are you claiming that the light postulate is false?

It requires that the light sphere expands in O' at the origin.

 

[cfrogue]

No, this is not what the second postulate requires at all. The second postulate requires that the speed of light be the same in O' as in O:

Using event A' we determine that the speed of light in O' is |x'/t'| = |2.5/2.5| = 1
Or, using event B' we determine that the speed of light in O' is |x'/t'| = |-10/10| = 1

So the speed of light in O' is 1 which is equal to the speed of light in O. The requirement of the second postulate is met.

Sorry, I did not see this post.

The light postulate requires in any frame from the light emission point, light proceeds spherically in all directions at c regardless of the motion of the light source.

So, yes, this is what the light postulate demands.

 

[matheinste]

cfrogue,

You must at some stage realize that you are dealing with four dimensional spacetime and not three dimensional space. The expanding sphere in space does not fully represent what is going on in spacetme where the real world's events are played out.

The coincidence of the origins and point of emission do remain the same event in spacetime and do obey all the relevant equations and the light postulate. The origins may appear to move apart in the geometric spatial representations, but in spacetime this is not the case.

Matheinste.

 

[cfrogue]

cfrogue,

You must at some stage realize that you are dealing with four dimensional spacetime and not three dimensional space. The expanding sphere in space does not fully represent what is going on in spacetme where the real world's events are played out.

The coincidence of the origins and point of emission do remain the same event in spacetime and do obey all the relevant equations and the light postulate. The origins may appear to move apart in the geometric spatial representations, but in spacetime this is not the case.

Matheinste.

Yea, that is how I am able to realize that the origin of the light sphere is at 0 and ct in O.

Let me know when you understand this.

 

[atyy]

http://www.youtube.com/watch?v=V3Kd7IGPyeg&feature=related"

Wow, I never knew the name of that song.

I'll lay off replying to my your last comment on my post, since so many have addressed it - I think A.T. in particular has addressed your comments on my posts.

 

[cfrogue]

Wow, I never knew the name of that song.

I'll lay off replying to my your last comment on my post, since so many have addressed it - I think A.T. in particular has addressed your comments on my posts.

I am glad you liked the song.
Otherwise, you are wrong.

 

[cfrogue]

Have any of you torch carriers resolved the light sphere origin problem?

I have not seen this.

 

[matheinste]

Yea, that is how I am able to realize that the origin of the light sphere is at 0 and ct in O.

Let me know when you understand this.

I understand that you do not understand, but I do not understand why you do not understand. If you do not undersatand that's OK, probably quite normal. If you think what people have told you is just plain wrong then how can they possibly help.

Perhaps a break from posting and some time spent studying what has been said would help. That is not a cynical statement, you may find that rapid fire on several threads across the forum gives you no time to take stock of the explanations given.

Matheinste.

 

[atyy]

I am glad you liked the song.
Otherwise, you are wrong.

Yes, I would be wrong if I did not like the song!

 

[cfrogue]

I understand that you do not understand, but I do not understand why you do not understand. If you do not undersatand that's OK, probably quite normal. If you think what people have told you is just plain wrong then how can they possibly help.

Perhaps a break from posting and some time spent studying what has been said would help. That is not a cynical statement, you may find that rapid fire on several threads across the forum gives you no time to take stock of the explanations given.

Matheinste.

Yea, maybe you are right.

This might give you time to figure out how the origin of the light sphere moves with O'.

 

[DrGreg]

cfrogue, in one dimension of space, consider this.

At time t in the O frame, the light is at two places P and Q, x_P = ct and x_Q = −ct. The centre of the sphere, in the O frame, is halfway between these points at ½(x_P + x_Q) = 0.

Transform these two events to the O' frame and you get values for x'_P and x'_Q. But these events are not simultaneous in the O' frame, so they are not of equal distance from O'. The sphere is expanding so the earlier event is nearer to O' than the later event, and the point that is halfway in between them at ½(x'_P + x'_Q) is not at distance zero from O'. In fact, if you do the calculation you should find that the midpoint is at x' = −vt'.

But these two events aren't simultaneous in the O' frame, so that's not how you find the centre of the sphere in the O' frame. If you choose two events R and S that are simultaneous in the O' frame (i.e. with the same t' value) you will get x'_R = ct' and x'_S = −ct' with a midpoint of zero.

What this shows that if an object does not maintain a constant shape (in this case, an expanding sphere), two observers can disagree over where the centre of the object is. And it is relativity of simultaneity that is responsible for this disagreement.

 

[cfrogue]

cfrogue, in one dimension of space, consider this.

At time t in the O frame, the light is at two places P and Q, x_P = ct and x_Q = −ct. The centre of the sphere, in the O frame, is halfway between these points at ½(x_P + x_Q) = 0.

Transform these two events to the O' frame and you get values for x'_P and x'_Q. But these events are not simultaneous in the O' frame, so they are not of equal distance from O'. The sphere is expanding so the earlier event is nearer to O' than the later event, and the point that is halfway in between them at ½(x'_P + x'_Q) is not at distance zero from O'. In fact, if you do the calculation you should find that the midpoint is at x' = −vt'.

But these two events aren't simultaneous in the O' frame, so that's not how you find the centre of the sphere in the O' frame. If you choose two events R and S that are simultaneous in the O' frame (i.e. with the same t' value) you will get x'_R = ct' and x'_S = −ct' with a midpoint of zero.

What this shows that if an object does not maintain a constant shape (in this case, an expanding sphere), two observers can disagree over where the centre of the object is.

Yes, but that is not what our problem is.

We have one observer O with the origin at 0 and at vt for one light sphere.

That is the problem.

 

[DrGreg]

Yes, but that is not what our problem is.

We have one observer O with the origin at 0 and at vt for one light sphere.

That is the problem.

As I understand it, your problem is that the first observer says the centre of the sphere is fixed at x=0. The second observer says the centre of the sphere is fixed at x'=0, a location which the first observer would say is moving at x=vt. That apparent contradiction is exactly the point I am addressing.

If that's not your problem, then I don't understand what is.

 

[Dale]

The light postulate requires in any frame from the light emission point, light proceeds spherically in all directions at c regardless of the motion of the light source.

I agree. This is why the equation must be ct = ±x in O and ct' = ±x' in O'. See my second approach back in https://www.physicsforums.com/showpost.php?p=2462629&postcount=11".

 

[Dale]

Have any of you torch carriers resolved the light sphere origin problem?

Yes.

I have not seen this.

So I have noticed.

Have you understood and resolved the simultaneity issue in your mind yet? Do you now understand how the equations x = ct in O and x' = ct' in O' are perfectly compatible with the relativity of simultaneity? If so then I can begin addressing the "moving center" issue, but I prefer to resolve one issue at a time.

 

[A.T.]

I am sticking to SR.

Your own version of it unfortunately

SR says by the light postulate that the light must expand spherically in the frame of O' at its origin since that was the emission point in O'.

Yes and this applies to both frames, not only O':
The light must also expand spherically in the frame of O at its origin since that was the emission point in O.

At any time t, that emission point is located at vt in the coords of O.

Wrong. The emission point is just a coordiante (0,0) and doesn't change with time. The light source is located at vt in the coords of O. You confuse two points in the coords of O:

x=0 : emission point, the point where the light source was at emission time t=0, center of the light sphere at any time in O

x = vt : the point where the light source is after a time t : completely irrelevant to the light sphere in O

Yet, the light postulate also says the light must expand spherically in O from the emission point which is 0, whether it was emitted from a stationary or moving light source.

Yes. Here you get it right.

 

[cfrogue]

As I understand it, your problem is that the first observer says the centre of the sphere is fixed at x=0. The second observer says the centre of the sphere is fixed at x'=0, a location which the first observer would say is moving at x=vt. That apparent contradiction is exactly the point I am addressing.

If that's not your problem, then I don't understand what is.

You have nailed one of the problems.

There are two of them.

I am happy to explore how you resolve the moving origin.

 

[cfrogue]

I agree. This is why the equation must be ct = ±x in O and ct' = ±x' in O'. See my second approach back in https://www.physicsforums.com/showpost.php?p=2462629&postcount=11".

I agree it must be this.

But, you have left of R of S.

If we look at my post of using rods in each frame of length d and a light source at the center of the O' d, the problem with this logic becomes obvious.

More spercifically,

t_L' = d/(2* λ *(c+v))

t_R' = d/(2* λ *(c-v))

where t_L' is the time when the left point -x' is struck and t_R' is the time when the right point is struck x'.

This is a direct application of R of S.

Note, it is false that these time are simultaneous. In fact, just like with the train enbankment experiment, both observers O and O' agree the right endpoint of the rod is struck after the right endpoint in the moving O'. The moving observer will claim the light shot toward the front occurred after the light shot toward the back whereas O will conclude in its frame and rod d, that both points are struck at the same time.

This is a more concrete way of looking at -x', x', -x, x.

 

[cfrogue]

Yes.So I have noticed.

LOL, I like this stuff.

Have you understood and resolved the simultaneity issue in your mind yet? Do you now understand how the equations x = ct in O and x' = ct' in O' are perfectly compatible with the relativity of simultaneity? If so then I can begin addressing the "moving center" issue, but I prefer to resolve one issue at a time.

No, I posted just before this showing a concrete example regarding the simultaneity issue.

 

[cfrogue]

Your own version of it unfortunately


Yes and this applies to both frames, not only O':
The light must also expand spherically in the frame of O at its origin since that was the emission point in O.


Wrong. The emission point is just a coordiante (0,0) and doesn't change with time. The light source is located at vt in the coords of O. You confuse two points in the coords of O:


x=0 : emission point, the point where the light source was at emission time t=0, center of the light sphere at any time in O

x = vt : the point where the light source is after a time t : completely irrelevant to the light sphere in O

Oh, yes I agree with the half answer above. But, since the light source is in O' and O' is a frame, then light must expand spherically in O' from the emission point which after any time t is located at vt in the coords of O.

 

[A.T.]

the emission point which after any time t is located at vt in the coords of O.

No, the emission point is not located at vt in O. You confuse the emission point which is a constant coordinate in both frames, with the position of the light source which changes with time in O.

I have pointed your misconception as clearly as possible in my last post. The fact that you just ignore it, and repeat the same nonsense, shows that you just don't want to get it.

 

[Dale]

I agree it must be this.

But, you have left of R of S.

If we look at my post of using rods in each frame of length d and a light source at the center of the O' d, the problem with this logic becomes obvious.
...

OK, this may be new to you, but here is a spacetime diagram showing the situation under discussion. I apologize if you are familiar with such diagrams, but I am going to assume that you are not and walk you through in detail its construction and meaning.

This diagram is drawn from the perspective of O, and the coordinates of O are indicated by the black lines and black text. The vertical axis is time and the horizontal axis is distance, both as measured by a system of rods and synchronized clocks at rest in O, and the units are such that c=1.

O' is another system of rods and synchronized clocks all at rest wrt each other, but moving at v=0.6c wrt the rods and clocks in O. The O' coordinates are obtained by the Lorentz transform equations and are indicated on the diagram by the white lines and the white text.

Also indicated are two yellow lines given by the equation ct = ±x. This represents the flash of light emitted from the origin. Because we are using units where c=1 they proceed at a 45º angle.

OK, that should cover the explanation of the diagram. Do you have any questions about the diagram? Do you see how this represents the scenario we are discussing? If we use d=1 then we even have lines specifically for the endpoints of each rod as you describe (x=±1 and x'=±1). Is this diagram acceptable to you as a tool for discussing the scenario?

 

[cfrogue]

No, the emission point is not located at vt in O. You confuse the emission point which is a constant coordinate in both frames, with the position of the light source which changes with time in O.

I have pointed your misconception as clearly as possible in my last post. The fact that you just ignore it, and repeat the same nonsense, shows that you just don't want to get it.

Let me ask you this.
Since the light source is in O', does the light postulate hold for O'?

Let's only consider O' for the time being.

 

[cfrogue]

OK, this may be new to you, but here is a spacetime diagram showing the situation under discussion. I apologize if you are familiar with such diagrams, but I am going to assume that you are not and walk you through in detail its construction and meaning.

This diagram is drawn from the perspective of O, and the coordinates of O are indicated by the black lines and black text. The vertical axis is time and the horizontal axis is distance, both as measured by a system of rods and synchronized clocks at rest in O, and the units are such that c=1.

O' is another system of rods and synchronized clocks all at rest wrt each other, but moving at v=0.6c wrt the rods and clocks in O. The O' coordinates are obtained by the Lorentz transform equations and are indicated on the diagram by the white lines and the white text.

Also indicated are two yellow lines given by the equation ct = ±x. This represents the flash of light emitted from the origin. Because we are using units where c=1 they proceed at a 45º angle.

OK, that should cover the explanation of the diagram. Do you have any questions about the diagram? Do you see how this represents the scenario we are discussing? If we use d=1 then we even have lines specifically for the endpoints of each rod as you describe (x=±1 and x'=±1). Is this diagram acceptable to you as a tool for discussing the scenario?

No, the geometry of this is not able to look at the light sphere in O'. Further, it will only see R of S for O' which is fine by me.

But, the problem here is does the light postulate hold for O'. That is the question.

If the light postulate holds in O', as it should since the rules are all the same for each frame, then the light sphere must emerge from the emission point in the frame of O'.
Do you agree?