Help Understanding special relativity

[sqljunkey]

I'm trying to understand something about relativity that doesn't seem to add up.

I will extend Einstein's carriage example to incorporate 4 clocks. At the beginning all these clocks are running at the same time when they are together.

I put two of the clocks far away from each other (100 km apart). I stand in the middle with one clock and a person B is riding in the carriage with one clock.

Now lightning hits both of the two far apart clocks at the same time, stopping both of them at exactly 1:00:00 PM. I see the lightning strikes at the same time as I'm standing in the middle. On my clock it happens at 1:00:01 PM. (because the light took 1 second to get to me)

Now the person in the carriage that's moving towards one lightning strike sees one hitting the clock at around 1:00:00.500 PM and the other at around 1:00:01.250 PM.

Now me and the observer can argue about the time, I can say they two lightning strikes happened at the same time and she can say they happened one after the other. However the two clocks at the spot show that they were hit at the same time, because they both stopped at 1:00:00 PM. We compare clocks/timers after the experiment.

I don't understand why people say in another frame of reference there things move slower. The light source may take t time to get to your eyes but that doesn't mean something out there happened at a different time.

From this experiment people derive the twins paradox. Stating that moving back and forth at speeds close to the light speed will make one twin brother age less. In my example above there was no physical effect caused by relativity. Even though the observers saw the clocks getting hit by lightning at different times, the clocks showed they happened simultaneously.

I don't think it really matters in which frame of reference an event takes place, the "true time/global time" will be the same everywhere for physical phenomena.

Can anyone help me understand this?

 

[jbriggs444]

Now me and the observer can argue about the time, I can say they two lightning strikes happened at the same time and she can say they happened one after the other. However the two clocks at the spot show that they were hit at the same time, because they both stopped at 1:00:00 PM. We compare clocks/timers after the experiment.

Clocks at rest to you and synchronized according to you are not necessarily synchronized according to someone who is moving relative to you. Clocks that stop when they each read 1:00:00 pm prove nothing when they were (according to the carriage observer) not synchronized correctly to start with.

 

[Mister T]

Now me and the observer can argue about the time, I can say they two lightning strikes happened at the same time and she can say they happened one after the other. However the two clocks at the spot show that they were hit at the same time, because they both stopped at 1:00:00 PM. We compare clocks/timers after the experiment.

Right. But you could explain the process you used to synchronize the clocks and she will point out to you where and how you made your errors. She will not agree that you properly synchronized your clocks, so she will tell you that just because they both stopped at 1:00 on the dot does not prove that they stopped at the same time.

I don't understand why people say in another frame of reference there things move slower.

This sounds like time dilation, which is an effect separate from the simultaneity issue discussed above.

The light source may take t time to get to your eyes but that doesn't mean something out there happened at a different time.

You are correct. The relativistic effects (time dilation and relativity of simultaneity) are present after allowing for light travel time. This is what is meant by "observing" something as opposed to simply seeing something. When we see something it's always what it looked like in the past, when the light we're using to look at it left.

I don't think it really matters in which frame of reference an event takes place, the "true time/global time" will be the same everywhere for physical phenomena.

No. As it turns out, Einstein got it right. There is no "true global time". The effects of relativity are correctly accounted for by scientists and engineers working at a variety of tasks all across the globe every minute of every day.

 

[sqljunkey]

So even if we sat down before the experiment and synchronized all the four clocks to run at the same time, she would still argue that both the clocks weren't running in sync. (assuming she knows the speed of light and the distance between the two clocks and the velocity she is moving with)

Let’s use the same Einstein carriage-embankment example, but this time let's make the two observers blind but not deaf. Let us say they can hear the thunder but not see the lightning, and that everywhere the thunder has the same decibel. This way the two observers cannot distinguish between a thunder strike that came from far away or one that came from close by.

So the observer standing on the embankment hears the two thunder strikes simultaneously, while the one accelerating in the carriage hears the thunders separately (several seconds apart). We can say that to these two observers time is different.

But we the invisible observers saw the two lightning strikes happen at more or less simultaneous times we also know the speed of sound.
So inside the aether that light travels there is or can be a "global time" or "true time" or "absolute time" like lorentz said.

(light isn't equal to sound waves. one travels at a much higher speed than the other, they have different frequencies too, so idk)

I fail to understand what time and the light speed have to do with each other.

 

[Ibix]

So even if we sat down before the experiment and synchronized all the four clocks to run at the same time, she would still argue that both the clocks weren't running in sync. (assuming she knows the speed of light and the distance between the two clocks and the velocity she is moving with)

In relativity you can't just "synchronise clocks". You need to explain how you synchronised them. And when you write out the details of that process and when you analyse them in a different frame you will see why it doesn't synchronise them.

For example, two clocks can establish that they are at relative rest and how far apart they are using radar. One emits a light pulse at t=0. When the other receives it, it knows that the time is d/c, if d is the distance between the clocks. A moving observer will not agree that the clocks were distance d apart, and because they were moving he will not agree that the distance traveled was equal to the distance between the clocks anyway. He will agree on the value of c, though, so he'll say that the clocks aren't correctly synced.

You can use different synchronisation methods, but they all give you the same result. The reason you need to worry about this is that there is no "global time" of the kind you talk about.

Let’s use the same Einstein carriage-embankment example, but this time let's make the two observers blind but not deaf. Let us say they can hear the thunder but not see the lightning, and that everywhere the thunder has the same decibel. This way the two observers cannot distinguish between a thunder strike that came from far away or one that came from close by.

So the observer standing on the embankment hears the two thunder strikes simultaneously, while the one accelerating in the carriage hears the thunders separately (several seconds apart). We can say that to these two observers time is different.

Not so simply, we can't. We do not expect the speed of sound to be the same in all inertial frames of reference, so we first need to establish the speed of sound in the two directions (it will not be the same) as measured in the moving frame. Incidentally, you want the train to be moving at constant speed, not accelerating. You can do special relativity in accelerating frames but the maths is much more complex.

But we the invisible observers saw the two lightning strikes happen at more or less simultaneous times we also know the speed of sound.
So inside the aether that light travels there is or can be a "global time" or "true time" or "absolute time" like lorentz said.

(light isn't equal to sound waves. one travels at a much higher speed than the other, they have different frequencies too, so idk)

There is no ether and no global time. Trying to assume there is will make it impossible to make sense of relativity.

I fail to understand what time and the light speed have to do with each other.

There are many possible answers to this. Probably the most honest is that there is a speed that acts as a unit transform between space-like distances and time-like distances. Light happens to travel at that speed.

Probably the most helpful is to say that light speed has nothing to do with time. None of Einstein's thought experiments depend on light. They are usually done with light signals because the speed of the signals is equal in all frames, which means the experiments can be analysed without knowing how velocities in general transform between frames. But if you know the velocity transform, you can repeat the experiments using sound waves or rifle bullets or whatever to transmit information. It's harder to analyse, and you have to get the velocity transforms from somewhere (experiment, possibly), but you can do it.

 

[Janus]

I'm trying to understand something about relativity that doesn't seem to add up.

I will extend Einstein's carriage example to incorporate 4 clocks. At the beginning all these clocks are running at the same time when they are together.

I put two of the clocks far away from each other (100 km apart). I stand in the middle with one clock and a person B is riding in the carriage with one clock.

Now lightning hits both of the two far apart clocks at the same time, stopping both of them at exactly 1:00:00 PM. I see the lightning strikes at the same time as I'm standing in the middle. On my clock it happens at 1:00:01 PM. (because the light took 1 second to get to me)

Now the person in the carriage that's moving towards one lightning strike sees one hitting the clock at around 1:00:00.500 PM and the other at around 1:00:01.250 PM.

Now me and the observer can argue about the time, I can say they two lightning strikes happened at the same time and she can say they happened one after the other. However the two clocks at the spot show that they were hit at the same time, because they both stopped at 1:00:00 PM. We compare clocks/timers after the experiment.

I don't understand why people say in another frame of reference there things move slower. The light source may take t time to get to your eyes but that doesn't mean something out there happened at a different time.

From this experiment people derive the twins paradox. Stating that moving back and forth at speeds close to the light speed will make one twin brother age less. In my example above there was no physical effect caused by relativity. Even though the observers saw the clocks getting hit by lightning at different times, the clocks showed they happened simultaneously.

I don't think it really matters in which frame of reference an event takes place, the "true time/global time" will be the same everywhere for physical phenomena.

Can anyone help me understand this?

As mentioned already, the speed of light is invariant. What this means is that two observers will measure the speed of light relative to himself as being ~3e8 m/s, regardless of any motion between the two observers.( or to be more accurate, there is a speed that is equal to ~3e8 m/s that is invariant. We use light in these examples because it happens to move at that speed and is easy to measure)

So let's say that you have a light source (the blue dot in the following animation). It emits a flash of light(the expanding circle) from a point midway from A and B while A and B are moving to the right. The light expands outward from the point of emission. Since A is moving towards this point, and B is moving away, the flash will hit A before it hits B.

If we now consider this same light pulse as seen by someone moving with A and B, we get a different result. Due to the invariant nature of light speed, according to this observer, the light pulse still expands outward from the point of emission at the same speed in all directions. However, in his case, it is the light source that is moving to the left, while A and B don't. So in his frame of reference, the light pulse hits A and B at the same time.

So let's say you want to sync separated clocks with each other. We set off a pulse of light from a point halfway between them, which starts each clock when it hits it:

Each clock starts at the same time and remain synced from then on.

However, this same synchronization scheme works like this for someone for which the two clocks are moving

The light hits and starts the clocks running at different times and remain out of sync from then on.. So while for someone at rest with respect to the clocks will say that they are synced to each other, for someone with a relative motion with respect to the clocks says that they are not. They will run at the same speed with respect once they both are running, but they will be offset of each other.

Now let's look at a slightly different version of the Train experiment.
Here, we will have two light flashes emitted at two points of the tracks at equal distances from an observer standing on the embankment. The two flashes arrive at the same instant as an observer on a railway car passes him. Thus both observers see the flashes at the same time. The embankment observer will conclude that the flashes originated at the same time.

The railway car observer sees both flashes at the same time also. However, since he is moving with respect to the two points on the tracks where the light emitted, he was closer to one then he was to the other when they originated. And since the lights must expand outward at the same speed relative to him, then this must be the sequence of events that occur for him to see the flashes at the same time as he passes the embankment observer.

(one thing that I need to note: Up till now I've ignored length contraction and time dilation. And while you would need to include them to do an accurate analysis of the above scenarios, ignoring them does not effect the over-all conclusion of the frames disagreeing on simultaneity.)

If we include length contraction, we can look at the original train experiment.
We start in the embankment frame. As it is set up, the lightning strikes both the train and embankment at points an equal distance from both embankment and train observers, and according to the embankment, the following happens.

The lightning strikes both the ends of the trains and the red dots at the same time, the flashes expand outward at c and reach the embankment observer at the same time. The train observer is moving towards one flash and away from the other so the flashes reach him at different times.

Now the train is moving in this frame, so its length as measured in this frame is a length contracted one.(shorter than the length the train itself will measure.)
So when we move to how things appear for the train, we must restore the train to its proper length. In addition, the tracks/embankment are now moving, so they will be measured as length contracted. The result will be that the train will no longer fit between the red dots that mark where the lightning strikes hit the embankment. So when one end of the train reaches the red dot and is hit by lightning the other end is short of reaching its red dot. In order for each lightning strike to hit when the end of the train and red dot are aligned, the strikes must occur at different times.

Note that this still leads to the flashes arriving at the embankment observer at the same time, and that the relative position of the train observer with respect to the tracks when each flash hits him is the same in this animation as it was in the last one.

The upshot is that there is no "global" time. Time is something that is measured differently for different frames in relative motion with respect to each other.

 

[sqljunkey]

Okay so relativity is true because no matter or particle can travel faster than the speed of light.
So it will be always physically impossible to be at two distant points at the same time.
That is why the speed of light has so much to do with the passing of time.

Light behaves weird when look at it on a quantum level. But it behaves predictably in a relativistic sense.
So relativity is all true I guess.
Thanks.

 

[sqljunkey]

I was thinking though. I am standing on that embankment, in the middle of the two clocks and the lightning strikes and stops these clocks at the same time at 12 AM each relative to where I'm standing.

You saw them getting hit at different times, because you were riding the train at 3/5 of the light speed and while you are in the train you conclude that the clocks were stopped at different times of each other.

Then several meters away the train stops and you walk towards me.
I am sitting with those two clocks and they are in sync in my hands, both clocks show 12 AM. When you arrive from your long walk and you take a look at the clocks you see different times on each of them because you saw them getting hit at different times while you were in the train. lol

just kidding though, I will continue to study this. Thanks

 

[Ibix]

You saw them getting hit at different times, because you were riding the train at 3/5 of the light speed and while you are in the train you conclude that the clocks were stopped at different times of each other.

This doesn't mean what you are reading into it. The reading on a clock at the time it is stopped is frame invariant. So if both clocks stopped when they read 12:00:00 according to observers moving along with them, then all observers agree that they stopped when they read 12:00:00. But that doesn't mean that they agree that the clocks stopped simultaneously. If the clocks are synchronised in some frame and stopped simultaneously in that frame, then in another frame where they didn't stop simultaneously they were not synchronised in the first place. If you follow the maths through, you'll find that the difference in synchronisation is exactly the same as the difference in the times the clocks stopped at, so you always expect the clocks to read the same time when they've stopped.

It couldn't be any other way, or you would end up with the kind of logical contradiction to which you allude.

 

[Mister T]

So even if we sat down before the experiment and synchronized all the four clocks to run at the same time, she would still argue that both the clocks weren't running in sync. (assuming she knows the speed of light and the distance between the two clocks and the velocity she is moving with)

But you can't sit down and do that because you are in relative motion with each other. You can't possibly synchronize clocks separated along the line of relative motion in both frames. If you think you can, please describe the process you would use to do it.

So inside the aether that light travels there is or can be a "global time" or "true time" or "absolute time" like lorentz said.

Here's the thing. You can suppose there's an aether and that in the rest frame of that either the time that's kept is the true time. There are two problems with that approach. The first is that there's no evidence to support the existence of an aether. But setting that aside, there's another. And it goes like this. Anyone else who's moving relative to you can also claim that they're at rest in the aether and that their time is the one that's true and absolute.

The Principle of Relativity is the assertion that anyone inertial reference frame is as good as any other.

 

[David Lewis]

I don't understand why people say in another frame of reference there things move slower.

Would it be correct to say things don't slow down, but time slows down? If so, things are still moving at the same rate.

 

[Ibix]

Would it be correct to say things don't slow down, but time slows down? If so, things are still moving at the same rate.

I think it depends on how you interpret "things".

If you interpret it as meaning "physical objects", which is what I think you have done, then the statement is plain wrong. Objects don't, in general, slow down - consider what happens to an object at rest in some frame when viewed from another frame.

If you interpret "things" as the sequence of events (for a more human-scaled example consider the sentence "when I saw he had a gun I got really scared and things seemed to slow down") then there's no distinction between your two phrasings. "Things" is just being used in place of "time".

I'd agree it's not a precise statement. If you want a precise statement, stick with observables. For example: clocks at rest in frame S tick slower than clocks at rest in frame S' when viewed in frame S', and vice versa.

 

[Ebeb]

Now let's look at a slightly different version of the Train experiment.

...

If we include length contraction, we can look at the original train experiment.

Why do you look at a different version of Einstein's train experiment? You are not allowed to use length contraction to prove relativity of simultaneity.
Einstein's train experiment to show relativity of simultaneity doesn't need or use any thoughts about length contraction, for the simple reason that length contraction is a result of relativity of simultaneity.

 

[Janus]

Why do you look at a different version of Einstein's train experiment?

I introduced the alternate version because sometimes people get confused by the fact that the embankment observer and train observer seeing the flashes at different times. By using using a scenario where both observers see the flashes at the same time I can show that even if they see the flashes simultaneously, they will still disagree as to whether the flashes origanated simultaneously.

You are not allowed to use length contraction to prove relativity of simultaneity.

Up until the last animation I ignored length contraction, so I don't really know where this comment comes from

Einstein's train experiment to show relativity of simultaneity doesn't need or use any thoughts about length contraction, for the simple reason that length contraction is a result of relativity of simultaneity.

If you are going to use an animation, as I did, you are going to have to show length contraction in order to prevent apparent contradictions between the frames. I brought attention to this in my explanation for the benefit for those that might not be as familiar with the subject. While time dilation, length contraction and the relativity of simultaneity are inter-related, I don't know if one can say that one is caused by another.

 

[Dale]

So even if we sat down before the experiment and synchronized all the four clocks to run at the same time, she would still argue that both the clocks weren't running in sync.

That is correct. Slow clock transport is equivalent to Einstein synchronization.

(light isn't equal to sound waves. one travels at a much higher speed than the other, they have different frequencies too, so idk)

They are indeed not equal, but the important factor is that the speed of a light wave is invariant, but the speed of a sound wave is not.

 

[David Lewis]

...clocks at rest in frame S tick slower than clocks at rest in frame S' when viewed in frame S', and vice versa.

Both clocks tick at the same rate. You can't use a clock in frame S' to measure time in frame S. The clocks will not stay in synch because they are measuring different amounts of time, not because they are ticking at different rates.

 

[Ibix]

Both clocks tick at the same rate. You can't use a clock in frame S' to measure time in frame S.

Of course I can. I can set up a single clock at rest in S, and a line of clocks that are synchronised and at rest in S'. As the S clock passes each S' clock, record the time each one shows.

The clocks will not stay in synch because they are measuring different amounts of time, not because they are ticking at different rates.

I don't see the difference between those two statements, assuming identical clocks and assuming my qualifier about which frame you are viewing the clocks in.

 

[David Lewis]

You can't use a clock in frame S' to measure time in frame S.

Of course I can. I can set up a single clock at rest in S, and a line of clocks that are synchronised and at rest in S'. As the S clock passes each S' clock, record the time each one shows.

But the view port through which you tell time is in frame S. The S' clocks don't even need to be clocks. The first "clock" can be a sign that says 12:00, the second sign can say 12:01, the third can say 12:02, and so on. Then space them one minute apart.

 

[Dale]

You can't use a clock in frame S' to measure time in frame S.

The GPS satellites do.

 

[David Lewis]

Please correct me, Dale, but to my knowledge a GPS clock only measures the time in its own frame.

 

[Dale]

Please correct me, Dale, but to my knowledge a GPS clock only measures the time in its own frame.

No, the GPS satellite clocks measure time in the Earth centered inertial frame. They are not at rest in this frame.

 

[PeterDonis]

the GPS satellite clocks measure time in the Earth centered inertial frame.

Actually, the GPS frame is an Earth Centered Earth Fixed (ECEF) frame (i.e., it's rotating with the Earth). GPS frame time is basically the "natural" clock rate of an observer at rest on the rotating Earth on the geoid. See here:

http://relativity.livingreviews.org/Articles/lrr-2003-1/fulltext.html

As the paper notes, often GPS calculations on receivers are actually done in an ECI frame; but that means the inputs from the satellites have to be transformed into an ECI frame (since they are defined relative to the GPS ECEF frame), and the final result has to be transformed back to the GPS ECEF frame.

Also, the reason the GPS satellite clocks "measure" GPS frame time is that they have a correction applied from their "natural" clock rate. This can be done because the difference between the "natural" clock rate and GPS frame time is known (because the satellite orbits are known) and constant in time to a good enough approximation (because the satellite orbits are circular to a good enough approximation).

 

[Dale]

Actually, the GPS frame is an Earth Centered Earth Fixed (ECEF) frame (i.e., it's rotating with the Earth).

Oops, but they are moving in that frame too.

Also, the reason the GPS satellite clocks "measure" GPS frame time is that they have a correction applied from their "natural" clock rate.

Yes, by design they do not correctly measure proper time. However, they demonstrate that it is possible to have a clock measure coordinate time in a frame in which it is moving. You just have to correct for the relativistic effects in that frame.

 

[David Lewis]

You would not have to correct for relativistic effects in order to find out how far you are from the satellites because you only need to know the difference in the time it takes each signal to reach you. The satellite clocks do not have to be ticking at the correct rate (i.e. they could run fast or slow) and they could be out of synch with clocks on Earth, and you would still be able to figure out where you are in relation to the satellites with a high degree of precision.

 

[PeterDonis]

The satellite clocks do not have to be ticking at the correct rate (i.e. they could run fast or slow) and they could be out of synch with clocks on Earth, and you would still be able to figure out where you are in relation to the satellites with a high degree of precision.

A more precise statement would be this: the satellites must all be using the same coordinates (time, including clock rate and simultaneity convention, and space) to define their own locations and motions; technically these coordinates do not have to be the same as the coordinates used by the Earth-bound segments of the system (receivers and master ground clocks)--but it's much, much, much more convenient for everyone if they are, which is why they are in actual fact.

Also, the above fact does not contradict what Dale said, because what is not possible is for each of the satellites to be using coordinates in which it is at rest--obviously that can't be, because the satellites are moving relative to each other and they must all use the same coordinates, so at most one of them can be at rest in whatever coordinates they are using. In practice, of course, it's much, much, much more convenient for the satellites to use coordinates in which the Earth is at rest and all of them are moving, which is why that is what is done in actual fact.