Struggling with the Special Relativity and simultaneity

[Ut-Napishtim]

Here is the Einstein's thought experiment in his own words from his book cited above. In my version I ONLY have replaced mirrors with beer dispensers and made the results more obvious by sending tweets.

"Lightning has struck the rails on our railway embankment at two places A and B far distant from each other. I make the additional assertion that these two lightning flashes occurred simultaneously. We require a definition of simultaneity such that this definition supplies us with the method by means of which he [the observer Ut.] can decide by experiment whether or not both the lightning strokes occurred simultaneously.

The connecting line AB should be measured up and an observer placed at the midpoint M of the distance AB. This observer should be supplied with an arrangement (e.g. two mirrors inclined at 90o). If the observer perceives the two flashes of lightning at the same time, then they are simultaneous. There is only one [italic by Einstein Ut.]demand to be made of the definition of simultaneity, namely, that in every real case it must supply us with an empirical decision as to whether or not the conception that has to be defined is fulfilled. That my definition satisfies this demand is indisputable.

Suppose a very long train traveling along the rails with the constant velocity. People traveling in this train will use the train as a rigid reference-body (coordinate system); they regard all events in reference to the train. Then every event which takes place along the line [railway Ut.] also takes place at a particular point of the train. Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment.

Events A and B also correspond to positions A and B on the train. Let M' be the mid-point of the distance A---B on the traveling train. Just when the flashes of lightning occur, this point M' naturally coincides with the point M."

 

[Ut-Napishtim]

If they are setup to do so only if the events are simultaneous in the respective rest frames, then only one bottle willbe dispensed

WHICH observer will be lucky to get my beer (if the events are simultaneous in the respective rest frames, and only one bottle will be dispensed, as you state)?

As I understand, Einstein said (see the quotation from his book above) that simultaneity is an experimental fact and NOTHING else. He gave a method to determine YES/NO experimentally and described a feasible experiment where my change mirrors into dispensers and using tweets is also feasible to imagine. He also said, and that is IMPORTANT, that there is NO privileged frame of reference. It is possible that in this feasible experiment only one bottle and not two will be dropped, but please clarify once more why another observer will be discriminated of my drink.

 

[Nugatory]

As I understand, Einstein said (see the quotation from his book above) that simultaneity is an experimental fact and NOTHING else. He gave a method to determine YES/NO experimentally and described a feasible experiment where my change mirrors into dispensers and using tweets is also feasible to imagine. He also said, and that is IMPORTANT, that there is NO privileged frame of reference. It is possible that in this feasible experiment only one bottle and not two will be dropped, but please clarify once more why another observer will be discriminated of my drink.

If the two dispensers are both designed so that they dispense a drink if they are hit by two light flashes at the same time, and we arrange things so that they are both lined up at the exact same point when the two light flashes reach that point... Then they will both dispense. The fact that the two light flashes and the two dispensers all came together at one event is something that everyone will agree about, regardless of their state of motion. In this case, the train and the platform observers will disagree about whether the two light flashes were emitted at the same time; the emission events can only be simultaneous for one of the two observers.

 

[Mister T]

WHICH observer will be lucky to get my beer (if the events are simultaneous in the respective rest frames, and only one bottle will be dispensed, as you state)?

Never does he state that they are simultaneous in both frames. They are simultaneous in the frame of the observer on the embankment. They are not simultaneous in the frame of the observer on the train.

He also said, and that is IMPORTANT, that there is NO privileged frame of reference. It is possible that in this feasible experiment only one bottle and not two will be dropped, but please clarify once more why another observer will be discriminated of my drink.

No privileged frame means all frames are equivalent in the sense that the laws of physics are the same in all frames. Just because you get a bottle of beer in one frame and not the other doesn't mean that the laws of physics are different in those two frames. It means that if you set the experiment up so the events were simultaneous in the train's frame, the train observer would get the beer. But then the embankment observer would not.

 

[flyingace]

I don't understand the confusion between actual events and the perception of those events. Simultaneous events by definition happen at the same point in time. Just because an observer on a train perceives the lightning strikes at different times, that doesn't mean the events occurred at different times. If a huge solar flare occurs at 12:00 noon on the sun, does that mean the flare really didn't happen until 12:07 when the light from it hits? No, it happened at 12:00 noon.

 

[PeterDonis]

I don't understand the confusion between actual events and the perception of those events.

There isn't any; that's not what's going on here. See below.

Simultaneous events by definition happen at the same point in time.

With respect to a particular frame. Simultaneity is frame-dependent; it's not an absolute.

Just because an observer on a train perceives the lightning strikes at different times, that doesn't mean the events occurred at different times.

Not necessarily; but in the particular case under discussion, it does--relative to the train.

If a huge solar flare occurs at 12:00 noon on the sun, does that mean the flare really didn't happen until 12:07 when the light from it hits? No, it happened at 12:00 noon.

Yes, that's true--relative to us on the Earth--but the delay from an event to its observation due to the travel time of the light is not what we're talking about when we say that simultaneity is relative. When we say simultaneity is relative, we mean after all adjustments for the travel time of the light we observe have been made.

 

[Janus]

I don't understand the confusion between actual events and the perception of those events. Simultaneous events by definition happen at the same point in time. Just because an observer on a train perceives the lightning strikes at different times, that doesn't mean the events occurred at different times. If a huge solar flare occurs at 12:00 noon on the sun, does that mean the flare really didn't happen until 12:07 when the light from it hits? No, it happened at 12:00 noon.

The point is that the train observer is halfway between the where the lightning strikes hit the train. Since the light from these strikes take an equal time to get to him, the strikes are only simultaneous if he sees the light from the strikes at the same time.

If another light producing event where to occur 7 light min in the opposite direction from the Sun and you saw the light from it and the light of the solar flare at the same time at 12:07, then you you would say that both events occurred simultaneously at 12:00 (by your clock). however, if you see the light from the solar flare at 12:07 and the light from the other event at 12:08, you would say that the two did not occur at the same time by your clock.

 

[Nugatory]

If a huge solar flare occurs at 12:00 noon on the sun, does that mean the flare really didn't happen until 12:07 when the light from it hits? No, it happened at 12:00 noon.

Indeed it it did, and it's easy to calculate this because the distance from sun to Earth is seven light-minutes and the speed of light is one light-minute per minute. (Of course we can do the calculation with the distance measured in meters and the speed of light in meters per second, or any other units we please, and we'll get the same seven minutes). So we take the time the light hit our eyes, subtract the light travel time, and we know when it left the source.

The tricky thing, and the point of Einstein's train experiment is that observers in motion relative to one another will get different answers when they use this procedure. That's how one observer can say that a solar flare on the sun and on alpha centauri happened at the same time (naturally in this case, the light from the two flares hit his eyes at very different times because the light from the alpha centauri flare had much farther to travel) while another observer can say that they happened at different times.

 

[flyingace]

I remain unconvinced. Again, I'm seeing the receiving of light from an event confused with the event itself. I will be the first to admit I'm no physicist, but to me this is just common sense. It reminds me of Carlin's routine about the 'arrogance of mankind' to think that an event doesn't happen until WE see it.

Of course, I will change my mind given some kind of explanation I can understand.

 

[Orodruin]

I remain unconvinced. Again, I'm seeing the receiving of light from an event confused with the event itself. I will be the first to admit I'm no physicist, but to me this is just common sense. It reminds me of Carlin's routine about the 'arrogance of mankind' to think that an event doesn't happen until WE see it.

Of course, I will change my mind given some kind of explanation I can understand.

If two events are at the same distance from you (as is the case here) and the light from these events reach you at the same time, then the events must be simultaneous. This is only based on the events being equidistant from you and that the speed of light is the same in all directions. Nobody is confusing the arrival time with the time of the events occured.

 

[Janus]

I remain unconvinced. Again, I'm seeing the receiving of light from an event confused with the event itself. I will be the first to admit I'm no physicist, but to me this is just common sense. It reminds me of Carlin's routine about the 'arrogance of mankind' to think that an event doesn't happen until WE see it.

Of course, I will change my mind given some kind of explanation I can understand.

Let's consider a different version of the experiment. We still have the same two observers, but here the things are arranged so that the light arrives at the same time that the observers are side by side.
Thus, for the observer stationary to the tracks, this happens:

He is at the midpoint between the origins of the light flashes (shown as the expanding rings), and since both travel at the same speed, their reaching him together only happens because they left simultaneously ( we don't even have to know what the speed of light is, just that it some constant value.)

Now we need to consider these same events from the perspective of the observer on the train car.

The light from the flashes reach him together also. And, as required by the second postulate, the speed of light for those flashes, relative to himself, must be equal in all directions and expand outward as circles from a point of origin that remains stationary with respect to the train car. The flashes still originate at the same red dots on the tracks, it is just that the red dots move away from the emission point after emission. This means that the train car must be closer to one red dot when it emits its light than it is to the other red dot when it emits its light, and this in turns means that in order for the both lights to reach the observer at the same time, the flashes must originate at different times.

This is not a case of confusing the reception of the light with the events emitting the light, but using your knowledge of the relative positions of the emitting events, and the invariant speed of light to determine when the emission events occurred. In this particular case, for one of the observers, seeing the lights at the same time forces the conclusion that the lights originated at different times.

 

[Mister T]

I remain unconvinced. Again, I'm seeing the receiving of light from an event confused with the event itself. I will be the first to admit I'm no physicist, but to me this is just common sense. It reminds me of Carlin's routine about the 'arrogance of mankind' to think that an event doesn't happen until WE see it.

Of course, I will change my mind given some kind of explanation I can understand.

You happen to be looking at the sun (through a protective filter such as a welder might use) when you see a solar flare. You note that the time is 11:29. You conclude that the flare occurred at 11:21.

The observers in this thought experiment are making this very same kind of adjustment.

I know of no easier way to explain this.

 

[Mister T]

Nice sims, Janus. Note that if you included the Lorentz contraction the tick marks on the track in the lower sim would be closer together and the expanding light pulses would not be circular.

 

[Janus]

Nice sims, Janus. Note that if you included the Lorentz contraction the tick marks on the track in the lower sim would be closer together

I didn't include length contraction in this example as it was not important to the argument. If on the other hand, if I had used a long train rather than a single car, I would have included into show how each frame agreed as to what section of the train was next to a red dot when the light was emitted. For example, with the original version of the experiment the following animations take it into account

and the expanding light pulses would not be circular.

No, the light pulses expand as circles in both frames as is required by the invariant speed of light.

 

[15characters]

You happen to be looking at the sun (through a protective filter such as a welder might use) when you see a solar flare. You note that the time is 11:29. You conclude that the flare occurred at 11:21.

The observers in this thought experiment are making this very same kind of adjustment.

I know of no easier way to explain this.

That's exactly it.

A rocketship speeding past Earth towards the sun could see light from the same solar flare and say the flare occurred many billions of years ago, when the sun was many billions of light years distance away (if it was traveling fast enough)

If there are two events, everyone will agree the events happened but they will disagree on time and distance between them.

For example, we consider Earth events now to be simultaneous to Sun events now at a distance of 500 light seconds (8 light minutes). So if Earth time is 12.00 noon and a solar flare occurs then Earth expects to see the flare at 12.08. And, will calculate or deduce that it occurred simultaneously to 12 noon on Earth. But, there's no easy way to prove that.

Therefore... .Another observer can measure a different time and distance between the two events...

For a rocket traveling at 0.99999999999c the solar flare would have occurred 111.8 million seconds ago (4 years). So from the rocket's perspective, the solar flare on the sun and 12 noon on Earth were not simultaneous events, rather they were separated in time by a gap of 4 years!

To clarify, what we consider is happening now on the sun, would in the rockets perspective have already occurred 4 years ago. So we consider the distance photons travel to reach us from the Sun is 500 light seconds. For the rocket the distance is 4 light years.

BTW when the rocket converts this 4 years of its time to Earth time, it will apply a gamma factor so that our clocks only move 500 seconds (8 light minutes) so everything will reconcile nicely - for the rocket Earth and the Sun's clocks are so slow that only 500 seconds will pass in 4 years. This means that the "timestamps" will match so to speak.

By time stamp, I mean if we set up a test where someone on the Sun sent synchronised radio signals to Earth and we said to the passing rocket ship, "why does the signal, which you say is 4 years old, say it is from 500 seconds ago?" The rocket ship will say, "ah , this is because, in the 4 years since you sent it, your slow clocks have only moved 500 seconds".

 

[Ut-Napishtim]

they will both dispense.

And you (on the cruise ship) will see TWO tweets. A tweet is a notice that the experimental method, suggested by Einstein, proved the simultaneity of the light strikes for the observer that had sent his tweet.

Please tell, what will YOU (on the ship) conclude - DID or NOT the strikes take place simultaneously for EACH of these two observers.

 

[Ut-Napishtim]

One. The other won't tweet because the flashes of light arrive at different times.

I see the change in your opinion, so please clarify WHICH observer WILL get my drink, and WHICH WILL NOT.

 

[Mister T]

WHICH observer WILL get my drink, and WHICH WILL NOT.

The one on the embankment. Your thought experiment is set up so that only he receives the two flashes at the same time.

 

[Mister T]

No, the light pulses expand as circles in both frames as is required by the invariant speed of light.

Yes, they do. But the thing that's a circle in one frame is not a circle in the other.

 

[Nugatory]

And you (on the cruise ship) will see TWO tweets. A tweet is a notice that the experimental method, suggested by Einstein, proved the simultaneity of the light strikes for the observer that had sent his tweet.

Here we're discussing the case in which both dispensers are at the same place at the exact moment that the two flashes of light arrive at that same place, so both dispensers dispense a beer and two tweets are sent. (Note that I am only able to say "the exact moment" because we're talking about a single point in space).

In this case only one of the two observers will satisfy the other requirement of Einstein's procedure, namely that both light flashes traveled the same distance from point of emission to point of detection so were in flight for the same amount of time. Therefore only one of the two observers will find the emission events to be simultaneous.

Please tell, what will YOU (on the ship) conclude - DID or NOT the strikes take place simultaneously for EACH of these two observers.

The strikes were simultaneous for whichever observer calculates that the both of flashes of light spent the same amount of time in flight. This will be the observer for whom the distance between the strike point and the position of his detector when the strike happens is the same for both strikes. Because the detectors are moving relative to one another, you cannot arrange things so that they are both in the same place when the two light flashes arrive and that they are both the same distance from the strike points when the strikes happen - you can make it that way for one of the observers but not both.

 

[flyingace]

OK. I think then that I'm satisfied. Simultaneous is simultaneous, and nobody is really saying otherwise. Thanks all.

 

[Mister T]

Please tell, what will YOU (on the ship) conclude - DID or NOT the strikes take place simultaneously for EACH of these two observers.

Are you talking about the lightning strikes or the flashes arriving at the dispenser? You can arrange things so that the flashes arrive at both dispensers at the same time, but then the lightning strikes can be simultaneous for only one observer. In that scenario both dispensers have the same location when the flashes arrive, and they both dispense a beer.

But that's not the way it's presented in the book by Einstein that you referred us to, and it's not the way you originally presented it to us in your beer dispenser scenario.

The way you presented it the flashes arrive at one dispenser simultaneously and it dispenses a beer. The strikes are simultaneous in that dispenser's frame. Later one flash arrives at the other dispenser, and then later the other flash arrives.

The central issue is this. The strikes occur at different locations. The dispenser occupies one location.

If events are separated in space and occur at the same time in one frame, such as two lightning strikes, they might not occur at the same time in another frame of reference.

If events are not separated in space and occur at the same time in one frame, such as the arrival of the flashes at a dispenser, they must occur at the same time in all frames.

 

[Ut-Napishtim]

The one on the embankment. Your thought experiment is set up so that only he receives the two flashes at the same time.

Once again MANY THANKS to ALL posters for the very informative, thoughtful and helpful discussion.A train was moving with a constant speed along the very straight tracks when two lightnings perforated it vertically in two different places, leaving unmistakable holes under the train in the ground between the railways.

Mik was cringing in a dunk Earth pit between the tracks somewhere in-between the holes made by the lightnings in the GROUND, the sensors of his dispenser sticking out. Mit1 was enjoying life in a first class train compartment somewhere in-between the holes made by lightning strikes in the TRAIN, his dispenser on a velvet carpet nearby.

Mik and Mit1 both knew that their dispensers will drop beer bottles if and only if two light rays, coming from opposite directions, both touch a dispenser at exactly the same time. They have read also that a panel of philanthropists on a cruise ship is watching our discussion and will give a free iPhone 6s Plus 128GB (Rose Gold) to who of them will tweet an undisputable proof that he had determined FROM HIS SURROUNDING (aka reference system – train or ground respectively) that the two thunderstorm lightnings in question took place simultaneously.

As it happened the Mik’s dispenser did drop a bottle and as soon as the train had passed Mik climbed out of the pit and hurried to measure (along the straight line connecting the holes), with HIS rigid measuring rod, the distances from HIS dispenser sensors to each of the holes made by the lightnings in the GROUND. Hurrah! he cried, as both these distances were exactly the same, and tweeted joyously:

My dispenser, positioned on the GROUND exactly in-between the lightning holes in the GROUND (as measured along the GROUND), dropped a bottle and therefore the two light signals that contacted my dispenser at the same time had traveled (from the lightnings to the dispenser) exactly the same time which means that these signals were generated by lightnings at the same time, which is the proof that AS DETERMINED ON THE GROUND the two lightnings DID happen SIMULTANEOUSLY.

Mit1 also determined (with HIS rigid measuring rod) INSIDE the MOVING TRAIN that the distances from the two MOVING holes (in the TRAIN) along the MOVING straight line towards the sensors of HIS dispenser (which was MOVING with the TRAIN’s velvet support) are exactly equal and tweeted cheerfully in almost the same words as Mik (instead of GROUND there were the words TRAIN) that he has HIS proof that AS DETERMINED FROM THE TRAIN the lightnings DID happen SIMULTANEOUSLY.

Both Mik and Mit1 looked forward in high spirits to a FedEx personal parcel with the Apple iPhone, but as it happened only Mik did actually receive it.

Philanthropists found Mit1’s description of the events on the train and his tweet, that he has proved FROM THE TRAIN that the lightnings struck the TRAIN simultaneously, implausible as being just a copycat of the Mik’s indubitable facts and proof, which were stolen from Mik by Chinese hackers.

To add insult to injury Mik for his part has tweeted that ONLY his proof of simultaneity is true and that he DISAGREES with the Mit1’s claim on the Apple as HE Mik had OBSERVED personally that the Mit1’s dispenser on the train was speeding TOWARD one and AWAY from another of the two places where HE Mik had found the lightning footprints in the GROUND, and that HE Mik CONSIDERS this observation as an unquestionable evidence that the Mit1’s dispenser SHOULD have stumbled into the light signal from the TRAIN’s front hole before the signal from the rear hole COULD have caught with this dispenser.

While Mik was enjoying the free Apple (for his successful proof of the lightnings’ simultaneity as determined on the Ground), Mit1 was beside himself and suspecting the role played by his gender, race, religion, skin color, sexual orientation, marital status, birth of place, citizenship, party affiliation, etc., Mit1 decided to fight for his constitutional rights to have the Apple also, and he tweeted again:

I will claim my free Apple in the Court with the following factual evidence:

A) This was an elite train that was MOVING so quiet, soft and UNIFORM that the passengers felt as if it was still staying put.

B) A written statement from Prof. Einstein: “People traveling in this train will with advantage use the train as a rigid reference body (co-ordinate system); they regard all events in reference to the train”

C) The bottle dropping testifies that the two light signals have reached the dispenser on the TRAIN at the same exact time. The dropping was witnessed by a high ranking traveler (on her election campaign trip), and in case she is suspected of lying the dropping is recorded in the dispenser’s hardware.

D) The distances ALONG THE TRAIN from the dispenser to the FRONT and the REAR places on the TRAIN where the lightnings struck the TRAIN were exactly equal.

According to Prof. Einstein’s statement it is LEGITIMATE TO MEASURE INSIDE AND ALONG THE MOVING TRAIN THE DISTANCES which the light rays, that have brought to the TRAIN dispenser the information about the lightnings piercing the TRAIN, had travelled. This statement gives a strong support to the validity and preeminence of my proof against the critique and considerations presented by Mit.

Because these DISTANCES were measured as EXACTLY THE SAME and these RAYS TOUCHED THE DISPENSER AT EXACTLY THE SAME MOMENT these information rays had TRAVELLED (along the MOVING TRAIN) EXACTLY THE SAME TIME and therefore ORIGINATED (at the points where the lightnigs struck the train) AT THE SAME TIME, and that therefore the lightnings DID happen and strike the train SIMUTANEOUSLY.

I will petition the Court to give preference (against the Mik’s rejection, by CONTEMPLATION) to My FACTS and MEASAUREMENTS based proof, so that I also get a free Apple for the lightnings SIMULTANEITY determined by me Mit1 FROM THE MOVING TRAIN as undeniable as their SIMULTANEITY was determined by Mik FROM THE GROUND.

 

[Mister T]

Mit1 also determined (with HIS rigid measuring rod) INSIDE the MOVING TRAIN that the distances from the two MOVING holes (in the TRAIN) along the MOVING straight line towards the sensors of HIS dispenser (which was MOVING with the TRAIN’s velvet support) are exactly equal and tweeted cheerfully in almost the same words as Mik (instead of GROUND there were the words TRAIN) that he has HIS proof that AS DETERMINED FROM THE TRAIN the lightnings DID happen SIMULTANEOUSLY.

Being equidistant from the two events is not proof that the events were simultaneous. Mit1's dispenser wouldn't have dispensed because a flash of light sent from one of the strikes would have arrived before the other. (The one in front would have reached him first because he was traveling towards it.) Since he was equidistant from the events he now has proof that the events were not simultaneous!

 

[Janus]

Once again MANY THANKS to ALL posters for the very informative, thoughtful and helpful discussion.A train was moving with a constant speed along the very straight tracks when two lightnings perforated it vertically in two different places, leaving unmistakable holes under the train in the ground between the railways.

Mik was cringing in a dunk Earth pit between the tracks somewhere in-between the holes made by the lightnings in the GROUND, the sensors of his dispenser sticking out. Mit1 was enjoying life in a first class train compartment somewhere in-between the holes made by lightning strikes in the TRAIN, his dispenser on a velvet carpet nearby.

Mik and Mit1 both knew that their dispensers will drop beer bottles if and only if two light rays, coming from opposite directions, both touch a dispenser at exactly the same time. They have read also that a panel of philanthropists on a cruise ship is watching our discussion and will give a free iPhone 6s Plus 128GB (Rose Gold) to who of them will tweet an undisputable proof that he had determined FROM HIS SURROUNDING (aka reference system – train or ground respectively) that the two thunderstorm lightnings in question took place simultaneously.

As it happened the Mik’s dispenser did drop a bottle and as soon as the train had passed Mik climbed out of the pit and hurried to measure (along the straight line connecting the holes), with HIS rigid measuring rod, the distances from HIS dispenser sensors to each of the holes made by the lightnings in the GROUND. Hurrah! he cried, as both these distances were exactly the same, and tweeted joyously:

My dispenser, positioned on the GROUND exactly in-between the lightning holes in the GROUND (as measured along the GROUND), dropped a bottle and therefore the two light signals that contacted my dispenser at the same time had traveled (from the lightnings to the dispenser) exactly the same time which means that these signals were generated by lightnings at the same time, which is the proof that AS DETERMINED ON THE GROUND the two lightnings DID happen SIMULTANEOUSLY.

Mit1 also determined (with HIS rigid measuring rod) INSIDE the MOVING TRAIN that the distances from the two MOVING holes (in the TRAIN) along the MOVING straight line towards the sensors of HIS dispenser (which was MOVING with the TRAIN’s velvet support) are exactly equal and tweeted cheerfully in almost the same words as Mik (instead of GROUND there were the words TRAIN) that he has HIS proof that AS DETERMINED FROM THE TRAIN the lightnings DID happen SIMULTANEOUSLY.

There is only one point on the train where the light flashes arrive simultaneously, and that is the point that is adjacent to To the point where the lights meet on the ground ( halfway between the holes in the ground). This point will not be halfway between the holes on the train. Everyone, no matter where they are or how they are moving will agree to this. Mik agrees to this, Mit1 agrees to this, you agrees to this, and everyone on the cruise ship agrees to this. Thus everyone agrees as to who's dispenser was triggered. The fact the Mit1 measures the distance to each hole in the train as being the same also means that he will say that the strikes took place at different times because he will not see the two flashes at the same time.

It is exactly because you cannot have a situation where one person says his dispenser gave him a bottle and the other didn't, while someone else says the opposite that leads one person to conclude that the lightning strikes occurred simultaneously and the other to conclude that they did not.

 

[PeterDonis]

The OP's question has been answered, multiple times. Thread closed.