# Real life examples of simultaneity

Can you give me some "real life" examples of simultaneity?

For instance I know the one about the train and the lighting strikes but I was under the impression that this only holds up if the train is moving close to the speed of light.

Thanks.

Can you give me some "real life" examples of simultaneity?

For instance I know the one about the train and the lighting strikes but I was under the impression that this only holds up if the train is moving close to the speed of light.

Thanks.

A muon in a particle accelerator and an inertial observer would disagree on the timing of events, such as it's half life.

Predicting mercury's orbit is more accurately calculated with GR I think,

GPS is an example of both types, and shows that even tiny variations can have "real life" effects (sufficient accuracy).

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BruceW
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In special relativity, if two events are simultaneous according to one frame, then the difference in the time at which they happened according to some other frame is:
$$\frac{\beta}{\sqrt{1- \beta^2}} \Delta x$$
Where $\Delta x$ is the distance between the two events according to the first frame and $\beta$ is the relative speed of the two reference frames (as a fraction of the speed of light) (and assuming the relative movement of the two frames happens in the same dimension as the distance between the two events - i.e. the x direction).

So this means that for the principle of relativity of simultaneity to become apparent, we need both a spatial separation of the two events and we must be considering two reference frames with relative speed which is a significant fraction of the speed of light.

So I take it that simultaneity is not really observed on day to day life?

Could this be an example? If I was on a large field inside a house and my friend was on the same field but standing 100 miles away he would should disagree about the time I turned a light on in my house.

I should see the light turn on in my house slightly before he sees it. Considering he is only 100 miles away it seems that this wouldn't make much of a difference I suppose.

But let's say this was a really big field and he was standing 186,000 miles away. Would that mean he sees the light turn on 1 second after I do?

HallsofIvy
Homework Helper
Be careful of your words! "Simultaneity" is witnessed all the time. "Dependence of simultaneity on frame speed" could only be witnessed by two observers moving at near light speed relative to one another.

So this means that for the principle of relativity of simultaneity to become apparent, we need both a spatial separation of the two events and we must be considering two reference frames with relative speed which is a significant fraction of the speed of light.

I think all that is required for the principle of relativity of simultaneity to become apparent is two observers that measure time, measure it differently. The rest is implicit no?

Is this example correct though?

Person A and B are on an extremely large imaginary field. Person A is inside a house with a light switch and Person B is on the other side of the field 186,000 miles away.

When Person A turns on the light switch he should see it right away but Person B should see it one second later.

----

I'm not really sure if I understand this stuff correctly.

So I take it that simultaneity is not really observed on day to day life?

Could this be an example? If I was on a large field inside a house and my friend was on the same field but standing 100 miles away he would should disagree about the time I turned a light on in my house.

I should see the light turn on in my house slightly before he sees it. Considering he is only 100 miles away it seems that this wouldn't make much of a difference I suppose.

But let's say this was a really big field and he was standing 186,000 miles away. Would that mean he sees the light turn on 1 second after I do?

Thats not an example of the principle of relativity of simultaneity or what ever its called.

Time dilation / length contraction cause issues with what observers agree happened simultaneously.

The relative speeds / gravitational potential dont have to be significant fractions of c to become apparent, your measurements have to be more accurate.

However I do think it is kinda related to distance, because c is invariant.

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BruceW
Homework Helper
The example is not correct. According to both person A and person B, the light is switched on at the same time, since the people have no relative motion.

You only need to worry about the relativity of simultaneity when objects are moving at a significant fraction of the speed of light. Two good examples are particles and satellites.

So you are right in thinking relativity of simultaneity doesn't matter in 'every day life'. If we consider only the reference frames of people, then simultaneity is approximately absolute, because all people have very small relative speeds (as a fraction of c). So if two events on earth are simultaneous according to me, then they are approximately simultaneous according to everyone else on earth.

Nitsuj is right that simultaneity is always relative, its just that we don't notice it in every day life because the effects are tiny compared to the precision our measuring equipment.

Edit: of course, robphy's link seems to show some measuring equipment that is precise enough. So it takes very precise equipment to show that absolute relativity is only an approximation.

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The example is not correct. According to both person A and person B, the light is switched on at the same time, since the people have no relative motion.

You only need to worry about the relativity of simultaneity when objects are moving at a significant fraction of the speed of light. Two good examples are particles and satellites.

So you are right in thinking relativity of simultaneity doesn't matter in 'every day life'. If we consider only the reference frames of people, then simultaneity is approximately absolute, because all people have very small relative speeds (as a fraction of c). So if two events on earth are simultaneous according to me, then they are approximately simultaneous according to everyone else on earth.

Nitsuj is right that simultaneity is always relative, its just that we don't notice it in every day life because the effects are tiny compared to the precision our measuring equipment.

Edit: of course, robphy's link seems to show some measuring equipment that is precise enough. So it takes very precise equipment to show that absolute relativity is only an approximation.

But I thought that if someone is 186,000 miles away they would see the Light come to them one second later because light travels at 186,000 miles/second. I don't think this would really depend on motion.

BruceW
Homework Helper
Relativity of simultaneity refers to 2 events. What are the events in your example? I'm guessing one event is the first person seeing the light at the house and the other event is the other person seeing the light? These two events happen in different places and at different times.

So the example isn't really an example of relativity of simultaneity.

What if person A and person B were talking on the phone?

Would they still agree?

BruceW
Homework Helper
It looks like you're trying to make sense of 'relativity of simultaneity' by making a line of reasoning using the fact that light propagates at c according to all observers.

It is possible to make a line of reasoning this way. One way to do it is by the mind-experiment of the train and the lightning strikes (as you already mentioned).

But the example you're developing doesn't make a similar line of reasoning. In your example, the reason the people experience the flashes of light at different times is simply because they are in different places.

On another note - my equation in post #3 is written in natural units.

I guess I am not clearly understanding the theory. I am fairly new to all of this.

I just thought people can't agree on when an event happened (the light bulb turning on) is because they are separated by a distance.

Are you sure it's only dependent on motion?

BruceW
Homework Helper
An event is different to two events.

BruceW
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People can't agree on when an event happened because they have relative speed.

BruceW
Homework Helper
And this is not an example of relativity of simultaneity because we are only talking about one event.

So would it become two events if they both shined a light?

Now if we add an observer at in the middle of them, he could see them both shine a light at the same time but the person at A would say he shined his light before the person at B.

And person B would also say he shined his light before the person at A but the person in at M would say he saw them at the same time.

Correct?

Here's a real life example: Bill and Ruth walk past each other on the street. Since they are in motion relative to each other, they are each living in a different instantaneous 3-dimensional world, each one being a different cross-section of the 4-dimensional universe. Thus, in Bill's world a meeting is taking place in the Andromeda Galaxy in which it is being decided whether or not to attack earth. However, at the instant Bill and Run are passing each other, Ruth is living in a different 3-dimensional world from Bill (an instantaneous cross-section of the same 4-dimensional universe) in which the Andromeda leaders have already made their decision and the Andromeda Space Fleet has already been launched and is heading toward earth.

This is of course the example posed by the renowned physicist, Roger Penrose ("The Emperor's New Mind"), known as the Andromeda Paradox.

Disclaimer: Bill and Ruth passing each other, living in two different 3-D cross-sections of the universe is a real everyday happening. But, the attack of the Andromeda fleet is made up (I hope).

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So I take it that simultaneity is not really observed on day to day life?

Could this be an example? If I was on a large field inside a house and my friend was on the same field but standing 100 miles away he would should disagree about the time I turned a light on in my house.

I should see the light turn on in my house slightly before he sees it. Considering he is only 100 miles away it seems that this wouldn't make much of a difference I suppose.

But let's say this was a really big field and he was standing 186,000 miles away. Would that mean he sees the light turn on 1 second after I do?

Yes that is correct.

I have just completed reading Einstein's original relativity paper from 1905. I'd recommend it. It is written quite clearly, and this particular question is his starting point.

If you want my probably-distorted version:

In your field there is no problem with simultaneity. Your friend can find out how far away he is from you, he knows the speed of light, and he can correct for all this. So simultaneity is easy and makes sense.

Now somebody moving at half the speed of light is watching you two guys. He sees you do your corrections to get simultaneity. But to him your procedure seems to be wrong! What is going on? Einstein figures out a transform to restore sense to this crazy situation.

BruceW
Homework Helper
And person B would also say he shined his light before the person at A but the person in at M would say he saw them at the same time.

Correct?
not correct. All three would agree that they shined their lights at the same time.

Let me rephrase this again.

There is a large field with Person A separated from Person B at 186,000 miles (which is the speed that light travels in one second). Person M is located in the middle of AB.

Now person M sees lighting bolts hit A and B at the same time.

Would person A still see the lightning bolts at the same time as the person at B? I would think each sees their lighting bolt and then one second later sees the other persons lightning bolt.

BruceW
Homework Helper
Yep. each person would see their own lightning bolt, then 1 second later see the other lightning bolt. Therefore the time at which the lightning bolts struck the ground was the same, according to both observers.

What about the guy in the middle?

Wouldn't he see both at the same time?

Let me rephrase this again.

There is a large field with Person A separated from Person B at 186,000 miles (which is the speed that light travels in one second). Person M is located in the middle of AB.

Now person M sees lighting bolts hit A and B at the same time.

Would person A still see the lightning bolts at the same time as the person at B? I would think each sees their lighting bolt and then one second later sees the other persons lightning bolt.

Its clear what you are saying. An other way to put it is the moon is over a light second distance away. Whatever could possibly happen on the moon, earth wouldn't know of it until 1 second later at the earliest. That is not the same as "relativity of simultaneity". In the above example the frame of reference of the moon measures 1 second the same as the Earth FoR.

Now that being said, gravity on the moon is less then Earth so I imagine time on the moon is slightly faster then on Earth. That slight difference in measuring time equates to differences in determining simultaneous events.

vela
Staff Emeritus
Homework Helper
What about the guy in the middle?

Wouldn't he see both at the same time?
When A, B, and M see the light from the lighting bolts striking is different than when the lightning bolts strike. Because they are all at rest relative to each other, they will all agree that the bolts hit at the same time after accounting for light travel time. For example, A does not see the light from B until t=1 s, but because A knows B is one light-second away, A concludes that the bolt hit B at t=0 s.

If there were another observer, C, moving relative to them, even after accounting for the time it took the light to travel, C would say that the bolts hit at different times.

But what about the person situated in the middle of AB?

Wouldn't he see the lightning bolts at the same time?

I guess I am not clearly understanding the theory. I am fairly new to all of this.

I just thought people can't agree on when an event happened (the light bulb turning on) is because they are separated by a distance.

Are you sure it's only dependent on motion?

They are only separated in spatial dimensions, their clocks tick at the same rate, so they measure distance (spatial dimensions) the same. They can measure & calculate simultaneous events and will agree .