On the idea of time in physics-relativity

Now it's really not practical to build a solid ring of mirrors but all we really need is four mirrors that are placed 90 degrees apart and all equidistant from the observer. In this animation, I have used four circular mirrors so that when the light strikes them, they each create a new expanding circle of light. Notice how the four reflections arrive simultaneously on the observer.

[video=youtube;ygvY4AjwPmE]http://www.youtube.com/watch?v=ygvY4AjwPmE[/video]

I represent the stationary observer in green and I call him Homer (think green, green grass of home). I represent the original expanding circle of light in blue as well as a blue dot to represent its source, the mirrors in yellow, the collapsing circles of light in green when they reflect off stationary mirrors.

Please note that just as in the previous post when the collapsing circle of light arrived simultaneously from all directions on the observer, the four reflections from the four mirrors all arrive simultaneously on the observer. Although this is not actually how the Michelson-Morley Experiment (MMX) was configured, it still represents conceptually exactly what the experiment was doing.

The MMX experimenters assumed that the previous animation would represent only what would happen if they were stationary with respect to the ether which they assumed they never were. They believed that they were constantly moving with respect to the ether and also constantly changing their velocity through the ether as the earth rotated on its axis and as it revolved around the sun. This constant acceleration was very small so for all practical purposes, they could assume that they were moving at a constant speed through the ether during the brief time interval of the experiment. This is how they thought the light would behave and note that now all four reflection do not reach the man at the same time:

[video=youtube;U625Pjm9M-I]http://www.youtube.com/watch?v=U625Pjm9M-I[/video]

I represent the moving observer in red and I call him Rover (think Red Rover). The light that reflects off the moving mirrors is shown in red and a red dot is placed at the origin of each expanding reflection.

Note that when the light from the four mirrors arrives at Rover, it is not simultaneous, it first arrives from the top and bottom mirrors and then later arrives from the left and right mirrors. This is what the MMX experimenters expected to measure but instead, they got the same result as if they were stationary in the ether, the same result that Homer would have gotten.

So now the question is how can this happen? Well, Lorentz and others came up with an explanation and we will go through a process that will arrive at the same explanation.

First, we want to learn how we know where to put the mirrors so that the expanding circle of light can create a reflection that results in a collapsing circle of light in just the right place at just the right time. For Homer, it's easy:

[video=youtube;Y0XWb6Il92A]http://www.youtube.com/watch?v=Y0XWb6Il92A[/video]

 

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Just note the intersection of the blue expanding circle and the green collapsing circle and in this animation, we draw a black dashed line to show where that intersection occurs:

[video=youtube;7VftpL1KL6o]http://www.youtube.com/watch?v=7VftpL1KL6o[/video]

Now for Rover, it's a little more complicated because his collapsing circle of light is not centered on the expanding circle of light but rather the location of where he will be later on, shown as a red dot. Try to visualize in this animation where the blue and red circles intersect:

[video=youtube;dHO6jtkDXM8]http://www.youtube.com/watch?v=dHO6jtkDXM8[/video]

And here we have the black dashed line to show the points of reflection:

[video=youtube;q9qJhCaHotI]http://www.youtube.com/watch?v=q9qJhCaHotI[/video]

 

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Now this black dashed line shows the points of relection relative to the ether but we really want them relative to Rover, so here we show both for comparison:

[video=youtube;sE0G1wcvrRI]http://www.youtube.com/watch?v=sE0G1wcvrRI[/video]

Also, note that Lorentz realizes that everything contracts in the direction of motion so we now show Rover as being length contracted as well as his arrangement of mirrors. In addition, the time it takes for the light to traverse from Rover to the mirrors and back to Rover is longer than it was for Homer which illustrates time dilation. We can also see the issue of Relativity of Simultaneity because the reflections for Rover do not all occur at the same time whereas they do for Homer.

[video=youtube;S7r5GeIfZas]http://www.youtube.com/watch?v=S7r5GeIfZas[/video]

This illustrates how Lorentz believed MMX produced the null result. He believed that the experiment was moving through the ether and experienced length contraction, time dilation and relativity of simultaneity.

He also believed that Rover would measure the speed of light to be the same as Homer because even though time was going slower and stretching out (time dilation), it is the actual length that the light has to travel relative to the ether that is used to calculate the speed (length divided by time), so we need to use the lengths defined by the black dashed line, not the moving brown line representing the length contracted mirror. This length is dilated to the same extent that time is dilated and so the two dilations cancel each other out and give the same calculation for the speed of light.

However, Einstein put a new spin on the interpretation. He said that we could assume that MMX was actually stationary in the ether and everything else that was moving with respect to MMX was experiencing length contraction, time dilation and relativity of simultaneity.

Now I want to show what would happen if instead of a solid ring of mirrors, we used individual mirrors with gaps between them. This will allow some of the light to be reflected and some to pass through. First we go back to Homer:

[video=youtube;VU_812f0JtI]http://www.youtube.com/watch?v=VU_812f0JtI[/video]

 

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Now we do the same thing for Rover:

[video=youtube;_edUM0wBLsY]http://www.youtube.com/watch?v=_edUM0wBLsY[/video]

And finally, we show combine the two of them:

[video=youtube;dEhvU31YaCw]http://www.youtube.com/watch?v=dEhvU31YaCw[/video]

This shows how two observers moving with respect to each other can both conclude that they are each in the center of the same expanding sphere of light that was emitted when they were colocated.

An important concept to learn through this series of animations is that even though we see that Homer is stationary in the ether and Rover is moving, they themselves cannot tell the difference. Whatever Rover does to measure the positions of his mirrors, he will conclude that they are in a perfect circle since his ruler will contract when he measures the shortened distances. And whatever clock he carries will be time dilated to the same extent as the time it takes for the reflection to return to him. And of course, he has no way of knowing that the light is not reflecting off his mirrors simultaneously.

When Einstein came along, he re-interpreted the ideas of Lorentz by saying that Rover could consider himself to be "stationary in the ether" so that his ruler was not length contracted, and his clock was not time dilated, and the light reflects off his mirrors simultaneously, and all those things happen to Homer instead. Thus he showed that the concept of an absolute ether rest state was useless as any inertial state is indistinguishable from it.

For those that are familiar with Special Relativity, view these animations from the stand point of a Frame of Reference.

 

I said exactly what you said.. Simultaneous events can be simultaneous in other frames and non-simultaneous too.. I proved that through the videos that eram corrected!!

 

Thank you eram!! Did you watch the videos?? How is it?

 

I think they will both conclude that they're in the same sphere of light regardless of length contraction.

 

Yes.that is the conclusion.. These videos should be watched by prof layman.

 

The last videos depict the situation more like how I was trying to describe it, and corrects for the errors I was saying that the light sphere in one frame then gains more or less than the speed of light in another frame. I think it is a more accurate way to show the situation.

 

A single pair of simultaneous events which are in different places along the axis of relative motion cannot also be simultaneous in the relatively moving frame. If you think you proved otherwise, please tell me the post number. For me, the easiest way to think of relativity of simultaneity is to think of length contraction. Just as you said earlier, if the length of the platform is not equal to the length of the train, then the front and rear endpoints cannot line up simultaneously in that frame.

 

The way I'm thinking about it is two events and their expanding light cones. Any point where the circles have the same diameter and the circles intersect, these points will register the events as being simultaneous. So any observer that is able to manoeuvre into these points of intersection will confirm by experience the events as simultaneous.
OK this might be a different definition of the word simultaneous than is being used by you.
For you are now saying "a single pair of simultaneous events which are in different places along the axis of relative motion".
Were the two lightning strikes that hit the train "a single pair of simultaneous events which are in different places along the axis of relative motion"?
I don't think of the events as moving at all. To me they are stationary.
All light circles in the last few pages of this thread have the central event as stationary. The observer may move. but the event is stationary. So is it necessary to have an axis of relative motion?
If two things are moving one on the y axis and the other on the x axis they still have a relative motion wrt each other, but what is their axis of relative motion?

 

These animations are rather brilliantly done. I don't know if the conclusion is quite correct other than to say that is what it seems like.

 

Yes, the two lightning strikes that hit the train were "a single pair of simultaneous events which are in different places along the axis of relative motion". The axis of relative motion between the train and the platform is in the direction of the train tracks, and the lightning strikes occurred at different places along the train tracks. Therefore the lightning strikes were in different places along the axis of relative motion. The lightning strikes were also defined to be simultaneous in the platform frame, and from there it was determined that they would not be simultaneous in the train frame.

You are right to think of events as stationary, rather than moving. When I speak of relative motion, I am talking about the relative motion between the two reference frames. In this case, the train and the platform are in relative motion.

It makes more sense to think in terms of two reference frames with relative motion along one axis, like the train and the platform. It doesn't matter if someone on the train is juggling balls, or if someone on the platform is shooting arrows straight up toward the sky. The two reference frames are moving along an axis which is in the direction of the train tracks.

 

OK sounds OK. But what would happen if it was not contrived, how would the observer on the platform know that the lightning flashes were simultaneous. Could you instantaneously know something was simultaneous? I am tending to think you can't for all you can experience at the time is that you experience the lightning flashes at the same time. It requires a type of confirmation as to where the origins were at a later time to be able to say they were simultaneous.

OK

ok

 

The animation was made by one of the PF contributors I think.

 

PF?? Physics Forums?? If that is what you mean then yes!!!
He is right in this case. He proved that Simultaneous events can be simultaneous in other frame and this explains and is similar to MME.

 

These animations are right. And you should not think always that Simultaneous events are always simultaneous in other frame!! This is an example in ether frame. Remember this. Ether does not exist cannot be proved. But Einstein showed that it is not needed of any ether frame as they can conduct experiment as if they were rest.

Remember,this is case in which Einstein's relativity was used in explaining MME. I wanted this experiment to show you by myself but i don't know how to create these sort of animation.But later i found that Someone already explained this in PF!!!

Always remember layman : Simultaneous events in one framemay be simultaneous in another frame.

 

These conclusions are right. Don't worry about it!!

 

How can you say that after seeing the animations.

 

Actually i want to understand why not??!!