# The Relativity of Simultaneity

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Einstein says:

"Just when the flashes 1 of lightning occur, this point M' naturally coincides with the point M, but it moves towards the right in the diagram with the velocity v of the train."

"Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A."

I contend there is no relativity of simultaneity, that the strikes occurred simultaneously, and that the observer on the embankment and the observer on the train will agree on when the strikes occurred.

There is however a distinction between the simultaneity of the strikes, and when the light from the strikes impacts the observers. I realize the light will hit the train observer at different times, as the train is in motion. Therefore, the observer on the train will be hit by the light from the front of the train before the light from the back of the train reaches him. That is a result of the light from the rear of the train having to travel a greater distance until it impacts the train observer.

The light from points A and B hits the embankment observer simultaneously, as the strikes occurred at both points when the train and embankment points coincided, and he was at the midpoint. The light from each strike traveled the same speed and the same distance to reach the observer. The conclusion from that is that the embankment observer could not have had a velocity, he was at a true zero velocity.

The perceived "relativity of simultaneity" in this example is due to the train observer's failure to acknowledge his own velocity, as is clearly shown with the directional arrow in the example. That incorrect assumption leads him to his false claim that the strikes must have occurred at different times.

edit: The board will not allow me to post the URL to Einstein's example. The example can be found in chapter 9 of Einstein's- Relativity
The Special and General Theory.

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The whole point of relativity is that the laws of physics still work if we consider the train to be stationary and the ground to be moving past. Bouncing a ball on the moving train feels exactly the same as bouncing a ball on the ground.

Galileo figured this out 400 years ago, and why he got in trouble with the Church - he said that the Earth could be spinning, and moving around the Sun, and you wouldn't feel it. The Pope didn't like that idea, and made him shut up about it.

Now, for Einstein's relativity things get trickier.
We add in the surprising truth that a particular speed of light is one of the laws of physics that are the same regardless of what you consider to be stationary. This very surprising fact has been carefully tested and found to be true.

So. If the person on the embankment measures the speed of the light from the lightning flashes as they goes past, they will measure 300,000km/s.
And if the person on the train measures the speed of the same flashes of light, they will also measure 300,000km/s.

So, the person on the train measures the flashes to have come from the same distance at the same speed, and concludes that they must have taken the same time in transit. So, since they arrived at different times, they must also have been emitted at different times.

Try this video:

The whole point of relativity is that the laws of physics still work if we consider the train to be stationary and the ground to be moving past. Bouncing a ball on the moving train feels exactly the same as bouncing a ball on the ground.

The embankment could not have had a velocity, as the strikes occurred when the train's and the embankment's points coincided, and the embankment observer was at the midpoint, and the light reached him at exactly the same time. If the embankment would have been in motion, and the train considered stationary, the lights would have struck the embankment observer at different times, but they didn't.

Now, for Einstein's relativity things get trickier.
We add in the surprising truth that a particular speed of light is one of the laws of physics that are the same regardless of what you consider to be stationary. This very surprising fact has been carefully tested and found to be true.

Light travels independently of all frames, which is why the velocity of the light source is irrelevant. But, the velocity of the "receiver" of the light is VERY important, as a light traveling towards an object with a zero velocity has to travel a shorter distance than if the light were traveling towards an object with a velocity moving away from the light. The light has to travel a greater distance to reach the object.

So. If the person on the embankment measures the speed of the light from the lightning flashes as they goes past, they will measure 300,000km/s.
And if the person on the train measures the speed of the same flashes of light, they will also measure 300,000km/s.

That is because the speed of light is independent of frames.

So, the person on the train measures the flashes to have come from the same distance at the same speed, and concludes that they must have taken the same time in transit. So, since they arrived at different times, they must also have been emitted at different times.

But again, the person on the train fails to realize that the light traveled a greater distance to reach his midpoint, as he was "hastening to the right." The observer thinks that the light traveled the same distance to reach him, which is false.

The embankment could not have had a velocity, as the strikes occurred when the train's and the embankment's points coincided, and the embankment observer was at the midpoint, and the light reached him at exactly the same time. If the embankment would have been in motion, and the train considered stationary, the lights would have struck the embankment observer at different times, but they didn't.
The strikes only occur when the train's and the embankment's points coincided if we consider the embankment stationary.
If we consider the train to be stationary (and Galileo says we can), then we find that the front strike occurred before the train and embankment coincided, and the rear strike occurred afterward. So, we can consider the train to be stationary, and still have the light flashes still meet the embankment observer at the same time.
So yes, the embankment could indeed have had a velocity.

That is because the speed of light is independent of frames.
Don't you see that if the strikes are simultaneous in the train frame, then the train observer must measure a higher speed for the light coming from the front?
According to the train observer, both flashes go the same distance - half the length of the train.
If the front flash travels that distance in a shorter time, then it must have been going faster.

You know, that book by Einstein really isn't the best way to learn this stuff. It's a hundred years old, the language is archaic, and there have been a thousand better explanations written since then. It's not surprising that people find it hard to follow.

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Wrong again, MD.
Remember, the strikes only occurred when the train's and the embankment's points coincided if we consider the embankment stationary.
If we consider the train to be stationary (and Galileo says we can), then we find that the front strike occurred before the train and embankment coincided, and the rear strike occurred afterward.
According to the train observer, the light flashes still meet the embankment observer at the same time. So yes, the embankment could indeed have had a velocity.

The strikes occurred as the points lined up, at that instantaneous point in time. Choosing to say that it was the embankment with a velocity and the train that was stationary doesn't change the fact the points were aligned when the strikes occurred.

You could synchronize 4 clocks, place them on the two points at the train and two point on the embankment. When the clocks are struck they stop, to show what time it was when they were struck. ALL the clocks will read the same, as they were all struck simultaneously. Agreed, the observer on the train will (falsely) conclude that the strikes must have occurred at different times, as the light struck him at different times, but that is when the light strikes him, not when the lightening strikes occurred, which the clocks show simultaneously.

Don't you see that if the strikes are simultaneous in the train frame, then the train observer must measure a higher speed for the light coming from the front?
According to the train observer, both flashes go the same distance - half the length of the train.
If the front flash travels that distance in a shorter time, then it must have been going faster.

You know, that book by Einstein really isn't the best way to learn this stuff. It's a hundred years old, the language is archaic, and there have been a thousand better explanations written since then. It's not surprising that people find it hard to follow.

The observer on the train needs to know how far the light traveled, and how much time it took to travel that distance. The observer on the train must understand that the light from the rear had to travel a greater distance to reach him than the light from the front did. The speed of light is the same for both, but the distance and time travel of the two lights were different.

The strikes occurred as the points lined up, at that instantaneous point in time. Choosing to say that it was the embankment with a velocity and the train that was stationary doesn't change the fact the points were aligned when the strikes occurred.
It seems that you're assuming that simultaneity can't be relative before we begin. Why? I thought that's what you were trying to prove?

How can you prove that the strikes were simultaneous by assuming that the strikes were simultaneous?

You could synchronize 4 clocks, place them on the two points at the train and two point on the embankment.
Can't be done if simultaneity is relative. You're simply assuming that simultaneity is absolute.

It seems that you're assuming that simultaneity can't be relative before we begin. Why? I thought that's what you were trying to prove?

I'm showing there is no "relativity of simultaneity."

How can you prove that the strikes were simultaneous by assuming that the strikes were simultaneous?

The example clearly says the points were lined up when the strikeS occurred. There was only one point in time when that could have happened, not two points in time.

Can't be done if simultaneity is relative. You're simply assuming that simultaneity is absolute.

Not assuming, showing why it is absolute.

The observer on the train needs to know how far the light traveled, and how much time it took to travel that distance. The observer on the train must understand that the light from the rear had to travel a greater distance to reach him than the light from the front did. The speed of light is the same for both, but the distance and time travel of the two lights were different.

Not so.
In the train's reference frame, the light flashes both travel the same distance. They both start at one end of the train, and meet in the middle.

You said before that "the speed of light is independent of frames". Well, this is what a "frame" is. Using the train reference frame means using rulers at rest on the train to define distance, and clocks at rest on the train to define time.
For example: Place a ruler at rest on the train so that lightning strikes at one end of the ruler, and the observer is at the other end of the ruler. The length of the ruler is the distance travelled by the light flash in that reference frame.

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I'm showing there is no "relativity of simultaneity."

The example clearly says the points were lined up when the strikeS occurred. There was only one point in time when that could have happened, not two points in time.

Not assuming, showing why it is absolute.

You said:
The strikes occurred as the points lined up, at that instantaneous point in time. Choosing to say that it was the embankment with a velocity and the train that was stationary doesn't change the fact the points were aligned when the strikes occurred.

i.e. You're simple declaring that the strikes occurred at the same time, in all reference frames.
Declaring something to be true is not the same as showing it or proving it.

Are you also known as _Jack?

Not so.
In the train's reference frame, the light flashes both travel the same distance. They both start at one end of the train, and meet in the middle.

The strikes occurred when the points were lined up. The points lined up once, not twice. Both strikes occurred at that time, which means simultaneously. The light impacted the train observer at different times from the front and rear. Light always travels at the same speed, independently of the frame. If the train observer were to have had a true zero velocity to consider himself "stationary", the lights would have impacted him at the same times, but they didn't. That means the observer had a velocity, which is clearly noted in the diagram with the arrow, and Einstein's own words.

You said before that "the speed of light is independent of frames". Well, this is what a "frame" is. It is using rulers at rest on the train to define distance.
Place a ruler at rest on the train so that lightning strikes at one end of the ruler, and the observer is at the other end of the ruler. The length of the ruler is the distance traveled by the light flash in that reference frame.

It is independent of frames, ie, the distance light travels is independent of the distance between the points of a single frame. Just because the observer sits midpoint of a frame doesn't mean light traveled the same distance to reach him. If the frame has a velocity the light has to travel a DIFFERENT distance, not the distance the observer in that frame measures.

Sorry MD, perhaps we'll talk again one day.
In the meantime, think about why declaring a statement doesn't help you to prove it. And if you want to talk about reference frames, you should first learn what that means.
Have fun!

Sorry MD, perhaps we'll talk again one day.
In the meantime, think about why declaring a statement doesn't help you to prove it. And if you want to talk about reference frames, you should first learn what that means.
Have fun!

How could you be bored? This is exciting stuff.

Do you agree the light from each strike traveled different distances to reach him than what the train observer measured at his midpoint of his own frame?

How could you be bored?
Because you're not the first person to come on here and claim to have demonstrated relativity is flawed using algebra on the level expected in a beginners SR textbook. Your problems and arguments are not new and previously have been retorted and explained away by people here and in the relativity research community as a whole.

This is exciting stuff.
Depends your point of view. If you have only just come across relativity and all these weird experiments involving trains and flash lights and light cones then it might seem exciting and novel, even if you disagree with it. For those who have known relativity for years, if not decades, the said experiments and results are old news. More often than not a relativity nay-sayer is new to relativity and is still too entrenched in their Newtonian intuition and thinks that their comments and criticisms are novel or insightful or deep or advanced. Almost invariably they are none of those and the nay-sayer fails to realise just how little they have read and understood of relativity. If you aren't just a sock puppet of Jack_ then I suggest you look at threads he's started. He's the canonical example of what I've just said, someone with little or no knowledge, naive about his level of understanding (especially compared to professional researchers in relativity) and utterly unwilling to accept that perhaps he doesn't understand something he's only just read about.

If you've made an honest attempt to learn some relativity and you're stuck on a few specific things then I'm sure people will be happy to help. If you're denouncing relativity because you haven't looked at it much and what you have looked at you've not bothered to think about then please don't let the door hit you on the way out.

One more fact to consider.

If the observer on the train were to have two synchronized clocks at his midpoint position, and then place one clock on each end of the train, and return to his midpoint position, when he looks at the clocks, they will not read the same thing. That is because the train has a velocity, and the light from the clocks has to travel different distances to reach him. Different distances take light a different amount of time to travel. The clocks remained synchronized, but the observer refuses to believe it, until he verifies it when he retrieves both clocks and they show they are synchronized. That phenomena is due to the fact that the observer has a velocity. If the embankment observer does the same experiment with two of his own clocks, that phenomena will not occur for him. The clocks appear to remain synchronized from his midpoint position, because the embankment observer has a true zero velocity, and the clocks prove it, as the light from each clock travels the same distance to reach the observer.

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One more fact to consider.

If the observer on the train were to have two synchronized clocks at his midpoint position, and then place one clock on each end of the train, and return to his midpoint position, when he looks at the clocks, they will not read the same thing. That is because the train has a velocity, and the light from the clocks has to travel different distances to reach him. Different distances take light a different amount of time to travel. The clocks remained synchronized, but the observer refuses to believe it, until he verifies it when he retrieves both clocks and they show they are synchronized. That phenomena is due to the fact that the observer has a velocity. If the embankment observer does the same experiment with two of his own clocks, that phenomena will not occur for him. The clocks appear to remain synchronized from his midpoint position, because the embankment observer has a true zero velocity, and the clocks prove it, as the light from each clock travels the same distance to reach the observer.

I think we've struck your problem here. One of the postulates of Special Relativity holds that the speed of light is the same for all observers, as measured relative to themselves, regardless of their relative motion.

Another way of putting it is that there is no test that the train observer can perform that will tell him whether or not it is the train or the embankment that is moving. He puts those clocks at the ends of the train and he will see them as reading the same time. They are an equal distance from him, and the light coming from both, traveling at the same speed relative to him, take the same amount of time to reach him.

And this is why the lightning strikes are not simultaneous for him. He is an equal distance from either end of the train, where the lightning strikes occurred. The light from the strikes travels at the same speed, meaning that the time between each strike occurring and when he sees the light from it is the same. However, he sees the light from each strike at different times, meaning the strikes occurred at different times for him.

Another way of putting it is that there is no test that the train observer can perform that will tell him whether or not it is the train or the embankment that is moving. He puts those clocks at the ends of the train and he will see them as reading the same time. They are an equal distance from him, and the light coming from both, traveling at the same speed relative to him, take the same amount of time to reach him.

There is no way the train observer will see the synchronized clocks as reading the same from his midpoint position, when the clocks are placed at each end of the train. The light from the clock on the front of the train will hit the observer first, making it appear that that clock is more advanced (in reality, less of a delay) than the rear clock, which is an illusion created because of the light travel time to impact the observer. Light speed is measured by how much distance the light travels, and how much time it takes to travel that distance.

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There is no way the train observer will see the synchronized clocks as reading the same from his midpoint position, when the clocks are placed at each end of the train. The light from the clock on the front of the train will hit the observer first, making it appear that that clock is more advanced (in reality, less of a delay) than the rear clock, which is an illusion created because of the light travel time to impact the observer. Light speed is measured by how much distance the light travels, and how much time it takes to travel that distance.

The ends of the train are equal distances from the train observer. they are not moving with respect to the observer, so the time it takes for light to travel from them to the observer as far as the observer is concerned is the same.

You seem to be laboring under the misconception that motion is absolute and that you can say which is moving, the train or embankment, in a way that everyone agrees to. This is not the case. All motion is relative, and anyone can make equal claim to being the one "at rest".

This is a cornerstone of Relativity and is the foundation for all of its (experimentally confirmed) predictions.

You can try to deny this, but you do so in the face of overwhelming evidence.