Tangible example of relativity of simultaneity

[Philip Dhingra]

I always liked the idea of starting relativity discussions with the idea that your father could travel at a substantial fraction of the speed of light and return back at roughly the same age as you. This makes time dilation seem interesting, and drives curiosity in students.

But I'm struggling to think of a parallel example for the relativity of simultaneity. One that I saw out there was that of car crashes in New York and London that seem to happen at the same time for one observer, but at different times for another observer.

I also thought of maybe suggesting that people could disagree about when you were actually born, sort of giving you the idea that you could have different birth days.

 

[Mentz114]

I always liked the idea of starting relativity discussions with the idea that your father could travel at a substantial fraction of the speed of light and return back at roughly the same age as you. This makes time dilation seem interesting, and drives curiosity in students.

But I'm struggling to think of a parallel example for the relativity of simultaneity. One that I saw out there was that of car crashes in New York and London that seem to happen at the same time for one observer, but at different times for another observer.

I also thought of maybe suggesting that people could disagree about when you were actually born, sort of giving you the idea that you could have different birth days.

Sounds like fun. Being born is one event so you'll need two separated births for that one.

The pole-and-barn 'paradox' is down to RoS but it would be difficult to arrange a demo. It does illustrate that the apparent contradiction follows from a bad assumption about simultaneity.

 

[Ibix]

I also thought of maybe suggesting that people could disagree about when you were actually born, sort of giving you the idea that you could have different birth days.

Well, an alien physicist born spacelike separated from Einstein's birth has the same birthday as Einstein! Or not.

Go far enough away and you could find entire civilisations that first figured out the secret was to bang the rocks together (RIP Douglas Adams) on the day of Einstein's birth according to some observers, and killed themselves in a nuclear war on the day of Einstein's birth according to others.

 

[Jorrie]

The pole-and-barn 'paradox' is down to RoS but it would be difficult to arrange a demo.

Two synchronized cameras, one at each end of the barn, taking well timed, simultaneous pictures of the pole should be easily doable.

 

[Mentz114]

Two synchronized cameras, one at each end of the barn, taking well timed, simultaneous pictures of the pole should be easily doable.

I think there could be a problem getting funding. You'll need a Large Pole Accelerator to get the pole to relativistic speeds.

 

[Ibix]

Two synchronized cameras, one at each end of the barn, taking well timed, simultaneous pictures of the pole should be easily doable.

The problem is a mix of accelerating the rod, camera reaction time, and camera resolution. I think I worked out that kilometre long rods (standing in for barn and pole) moving in opposite directions at orbital speeds would still not be length contracted to any plausible precision.

 

[Mentz114]

The problem is a mix of accelerating the rod, camera reaction time, and camera resolution. I think I worked out that kilometre long rods (standing in for barn and pole) moving in opposite directions at orbital speeds would still not be length contracted to any plausible precision.

The resolution required is $L_{garage}V_{pole}/c$ . From the national pole institute official handbook (remember to multiply by 2 for dipoles)

 

[Philip Dhingra]

All goo ideas!

Sounds like fun. Being born is one event so you'll need two separated births for that one.

Regarding that, though, I somehow thought that the two events in a single birth are the clock and the birth, so no two people could agree as to which hour, minute, and second the birth was synchronous with. Maybe I'm mistaken. If I am, someone let me know!

 

[vanhees71]

Well, but your age is without any ambiguity, namely your proper time, an invariant (scalar) quantity, which is thus independent of the reference frame. It's well known that "theory of relativity" is a bad name. It should be named "theory of invariants" (I forgot, which eminent physicist or mathematicians said this first).

 

[Nugatory]

It should be named "theory of invariants" (I forgot, which eminent physicist or mathematicians said this first).

It is widely attributed to Einstein himself. I haven't made a serious effort to find a citation direct from his writing so I don't know if this attribution is correct - but it is plausible.

 

[robphy]

It's well known that "theory of relativity" is a bad name. It should be named "theory of invariants" (I forgot, which eminent physicist or mathematicians said this first).

According to p.65 of How Einstein Created Relativity out of Physics and Astronomy By David Topper, it was Felix Klein.
[ https://books.google.com/books?id=2U6qvi5TlE4C&pg=PA65&dq="invariant+theory" ]

In 1911 a leading mathematician, Felix Klein, proposed the nomenclature " invariant-theory," which in some ways better expressed what the theory was about; that is, replacing old absolutes with new ones. But neither Einstein nor others adopted it.[27][27] Stachel [193], p. 192. As late as 1921 Einstein received a letter from an engineer who proposed
the term invariant-theory. Einstein Papers, Vol. 12, Doc. 250. Einstein replied: "Now to the name
relativity theory. I admit that it is unfortunate, and has given occasion to philosophical misunderstanding
. ... The description you proposed would perhaps be better; but I believe it would cause confusion
to change the generally accepted name after all this time." Quoted in Holton [101], p. 132.

 

[PAllen]

Traveling to a star at high speed relative to Earth and star, readily shows relativity of simulaneity. Consider the traveler passing Earth sees Earth clock reading noon on day1. They arrive one day later per their time and see the destination clock reading day 1200. It is claimed to them that the clocks always read the same at the same time per earth/star. Yet, factoring light delay, the traveler find both Earth and star clock to run slow compared to theirs. The only possible conclusion is that from the traveler’s notion of simultaneity, when the Earth clock read day 1, the star clock was already reading some time after day 1199. Thus, at starting point, Earth and traveler have radically different notions of which time on the distant clock is simultaneous with theirs. Note, it is best for this explanation to imagine that the traveler is moving uniformly forever, passing the Earth and the the distant star. Simultaneity for accelerating observers is a whole other can of worms.

 

[vanhees71]

According to p.65 of How Einstein Created Relativity out of Physics and Astronomy By David Topper, it was Felix Klein.
[ https://books.google.com/books?id=2U6qvi5TlE4C&pg=PA65&dq="invariant+theory" ]

Well, that's quite plausible since Klein was the expert in theory of invariants at his time. Emmy Noether did her PhD work on the subject under his advice, and for physicists Emmy Noether's most important an famous result is within the theory of invariants, namely the theorems precisely determining the relation between symmetries and conservation laws of 1918. Funnily Noether herself later called this work "bullshit", because it's too applied. I guess for mathematicians, indeed, her main contribution is the development of abstract algebra. For (theoretical) physicists however her work in the theory of invariants and the famous Noether theorems can not be underestimated in its importance for all of modern physics, particularly quantum physics, where we were completely lost in the sense of intuitions without the clear foundation in representation theory of the symmetry groups underlying the natural laws (space-time symmetries as well as more abstract symmetries as local gauge symmetries and topology).

 

[sweet springs]

One that I saw out there was that of car crashes in New York and London that seem to happen at the same time for one observer, but at different times for another observer.

The two crashes are space-like events, so sequence does not make difference on any physical consequences. The different sequences cause no physical different results. I am afraid there is not any tangible example as you expect.