Contradiction in Relativistic Simultaneity in Taylor-Wheeler Spacetime Physics?

[JM]

Greg
Where is the scene of Menzel described?
The 'two lightning' scene is so poorly described, as in fig 3.1 that its hard to make any clear conclusion. A single flash seems much more straight forward and instructive.
For example, a sound pulse originating at the mid point of train and track reaches the ends of the track segment at the same time, but does not reach the ends of the train at the same time (through the open air). Thus the Relativity of Simultaneaty (ros) is not a new and unique feature of Relativity. Since light is a wave, as sound is, this feature, ros, could be expected to exist for light.
But Relativity says otherwise. A light pulse originating at the mid point also does reach the ends of the track at the same time, but now the light pulse also reaches the end of the train at the same time. These results occur because the light postulate specifies that the speed of light must be the same for all inertial observers. Thus the startling result is that sumultaneity is not relative! How can this be? The answer magically invented by Einstein is to adjust the zero point of time, by adding the second term in the time transfer equation ct=m(cT- vX/c).
To me, this simple, clear example shows the heart of Special Relativity with easily visualized physics and minimum math. Why even get involved with the convolutions of the two-flash picture?
JM

 

[ghwellsjr]

Greg
Where is the scene of Menzel described?

I described and explained Menzel's scene in post #18:

I believe the reason you are having so much problem with this is because you are thinking of the "scene proposed by Menzel" where a single flash of light, set off at the location of when two observers, one stationary and the other moving, produces an expanding sphere of light in which the stationary and the moving observers both observe themselves to be at the center, even though they continue to get farther apart. This is very true but they only tell you half of the story. What they don't tell you is how you observe yourself to be in the center of an expanding sphere of light.

Here's the rest of the story: You cannot see light as it travels away from you unless you reflect it off of something and some of that light comes back to you. You cannot even tell where the light is. So what you do is put up a bunch of mirrors some equal distance from you in all directions so that when the sphere of light hits them they will start their trip back to you and when they arrive at your location, you can see that all of the returned light reflections arrive simultaneously. Now the other observer is doing the same thing except he has a different set of mirrors. Both of you are in the center of your set of mirrors but the traveling one's mirrors are moving with him. Now if you think very carefully about how this experiment could work, you will discover that it is necessary for the moving observer to have his mirrors not really equal distant from him, they are closer to him along the direction of motion. This is the Lorentz contraction. And for him, the light does not arrive at all the mirrors simultaneously but in such a manner as to cause the reflections to arrive simultaneously from all the mirrors at his location. Also, the two sets of reflections, one for the stationary observer and one for the traveling observer do not collapse on their respective observers at the same time. The stationary observer sees the reflections first and then some time later the traveling observer sees his reflections. Once you understand how this works, you will see that in this "scene proposed by Menzel" the light is making a round trip, starting from the co-location of the two observers and ending up after being reflected off of two separate sets of mirrors, on the two observers at different times and at different locations.

In the train situation, there are two flashes of light coming from a single pair of sources that are stationary with one observer. It would be like if the Menzel scene had only one set of mirrors for the stationary observer. It wouldn't work the same. That is why the Menzel scene is not the same as the train scene.

I know this is kind of hard to follow without a visual but it's the direction you're going to have to take to understand what's going on and why the two situations are completely different.

The 'two lightning' scene is so poorly described, as in fig 3.1 that its hard to make any clear conclusion. A single flash seems much more straight forward and instructive.
For example, a sound pulse originating at the mid point of train and track reaches the ends of the track segment at the same time, but does not reach the ends of the train at the same time (through the open air). Thus the Relativity of Simultaneaty (ros) is not a new and unique feature of Relativity. Since light is a wave, as sound is, this feature, ros, could be expected to exist for light.
But Relativity says otherwise. A light pulse originating at the mid point also does reach the ends of the track at the same time, but now the light pulse also reaches the end of the train at the same time. These results occur because the light postulate specifies that the speed of light must be the same for all inertial observers. Thus the startling result is that sumultaneity is not relative! How can this be? The answer magically invented by Einstein is to adjust the zero point of time, by adding the second term in the time transfer equation ct=m(cT- vX/c).
To me, this simple, clear example shows the heart of Special Relativity with easily visualized physics and minimum math. Why even get involved with the convolutions of the two-flash picture?
JM

JM, you have a mixed up view of relativity. If you understand my description of Menzel's scene, then you can see why the light would not arrive simultaneously at equidistant points for both the stationary and traveling observers. No matter what frame of reference you use, light can never behave the way you describe.

 

[bcrowell]

Knowing "what goes on" means having equations which accurately predict observed behavior, which is all that is needed to check for Lorentz-invariance and figure out what would the observable behavior would be. "Why" is a question that no theory of physics has ever addressed or could ever address, physics is just about making quantitative predictions using mathematical equations, not about "why" those particular equations are the correct ones. "Why" is a question for philosophy or theology that has nothing to do with science or predictions about the results of empirical experiments (like predictions about how an organism would age if taken on a journey at relativistic speed relative to the Earth).

An extreme position. I certainly don't agree.

 

[nismaratwork]

An extreme position. I certainly don't agree.

You believe that "why" is a question for philosophy, and "how" one for physics is an extreme view? I hold it, I'll freely admit, and among people from hobbyists to professionals, it seems to be the majority opinion. Physics neither attempts nor is it capable of saying WHY something happens... the concept of an ultimate 'why' already invokes something like a god.

 

[JM]

If you understand my description of Menzel's scene, then you can see why the light would not arrive simultaneously at equidistant points for both the stationary and traveling observers.

See Einsteins 1905 paper, Dover Ed., p.46: A spherical wave is described by the equation X^2+Y^2+Z^2=c^2T^2 relative to the stationary frame K(X,Y,Z,T). The light wave arrives at all points of the sphere at time T, i.e. simultaneously. Transforming this equation by the Lorentz transforms leads to the equation of the sphere relative to the moving frame k( x,y,z,t): x^2+y^2+z^2=c^2t^2. So the light wave arrives at all points of this sphere at time t, i.e. simultaneously. Thats what I said. So what's your question?
Jm

 

[ghwellsjr]

Thus the startling result is that sumultaneity is not relative!

This is not true. The reason you think it's true is because you are switching between frames for the two observers but in anyone frame, it cannot be true that the light arrives at the remote locations simultaneously for two observers with a speed difference between them.

So my question for you is: where did you learn that "sumultaneity is not relative"?

 

[bcrowell]

You believe that "why" is a question for philosophy, and "how" one for physics is an extreme view? I hold it, I'll freely admit, and among people from hobbyists to professionals, it seems to be the majority opinion. Physics neither attempts nor is it capable of saying WHY something happens... the concept of an ultimate 'why' already invokes something like a god.

I never said anything about an ultimate why. But for example, I think there is an answer to the question of why an object that accelerates from rest at 1 m/s2 covers 0.5 m in 1 s.

 

[nismaratwork]

I never said anything about an ultimate why. But for example, I think there is an answer to the question of why an object that accelerates from rest at 1 m/s2 covers 0.5 m in 1 s.

If you take the argument that would ensue to its logical conclusion you would have an 'ultimate why' question. At no point when being asked "why" in physics can you do anything but retreat to a more basic principle until you reach posits. I'm not saying that's a bad thing, but it's true, and it makes 'why' something for philosophy or theology.

Physics can often answer 'how', which is not reducible to some fundamental question about a phantom motive... physics doesn't deal in motives, but methods.

 

[bcrowell]

If you take the argument that would ensue to its logical conclusion you would have an 'ultimate why' question. At no point when being asked "why" in physics can you do anything but retreat to a more basic principle until you reach posits.

I agree with this...

I'm not saying that's a bad thing, but it's true, and it makes 'why' something for philosophy or theology.

...but not with this.

 

[nismaratwork]

I agree with this...


...but not with this.

I admit to being confused and in need of some explanation. How can you accept the first and reject the second?

 

[JM]

,it cannot be true that the light arrives at the remote locations simultaneously for two observers with a speed difference between them.

Have you read post 55 and the related section of Einsteins 1905 Paper? Do you disagree with something in Einsteins analysis?
JM

 

[ghwellsjr]

No, I don't disagree with anything Einstein said or anything you quoted him as saying. Note that he talked about two different frames, the "stationary frame" and the "moving frame".

But you misquoted me, here is what I said:

"The reason you think it's true is because you are switching between frames for the two observers but in anyone frame, it cannot be true that the light arrives at the remote locations simultaneously for two observers with a speed difference between them."

Can't you see that this is in agreement with what Einstein said?