# Real life examples of simultaneity

1. Oct 26, 2011

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.

2. Oct 26, 2011

### nitsuj

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).

Last edited: Oct 26, 2011
3. Oct 26, 2011

### BruceW

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.

4. Oct 26, 2011

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?

5. Oct 26, 2011

### HallsofIvy

Staff Emeritus
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.

6. Oct 26, 2011

### nitsuj

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?

7. Oct 26, 2011

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.

8. Oct 26, 2011

### nitsuj

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.

Last edited: Oct 26, 2011
9. Oct 26, 2011

### robphy

10. Oct 26, 2011

### BruceW

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.

Last edited: Oct 26, 2011
11. Oct 26, 2011

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.

12. Oct 26, 2011

### BruceW

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.

13. Oct 26, 2011

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

Would they still agree?

14. Oct 26, 2011

### BruceW

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.

15. Oct 26, 2011

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?

16. Oct 26, 2011

### BruceW

An event is different to two events.

17. Oct 26, 2011

### BruceW

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

18. Oct 26, 2011

### BruceW

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

19. Oct 26, 2011

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.

20. Oct 26, 2011