I How does Einstein define simultaneity in his 1905 paper?

[nitsuj]

You need two clock-readings.

same question

 

[Herman Trivilino]

same question

The first clock-reading is $t_1$. The second clock-reading is $t_2$. The elapsed time between them is $\Delta t=t_2-t_1$. You need two clock-readings to establish an elapsed time $\Delta t$.

 

[nitsuj]

The first clock-reading is $t_1$. The second clock-reading is $t_2$. The elapsed time between them is $\Delta t=t_2-t_1$. You need two clock-readings to establish an elapsed time $\Delta t$.

Its the half the time of the round trip, by definition. That's a main part of the paper..allowing this second clock be synchronized.

 

[Herman Trivilino]

Its the half the time of the round trip, by definition. That's a main part of the paper..allowing this second clock be synchronized.

There's no second clock involved in the point I was making. One clock, two readings taken on that clock. Their difference is an elapsed time, and that's something that requires a standard to be able to measure.

On the other hand, synchronizing two spatially separated clocks requires nothing of the kind, just a convention.

 

[JAYJACOBUS]

Don't all clocks exist at the same absolute time, but move at different relational speeds?

 

[PeterDonis]

Don't all clocks exist at the same absolute time, but move at different relational speeds?

No.

 

[Ibix]

Don't all clocks exist at the same absolute time

There is no absolute time in relativity.

but move at different relational speeds?

I've no idea what a "relational" speed is. Do you mean a relative speed? If so, then speed relative to what?

 

[pervect]

Don't all clocks exist at the same absolute time, but move at different relational speeds?

No. All clocks exist, but the concept of "at the same time" is not an absolute. The question verges on the philosophical (as we can tell by the fact that it talks about existence, which is a philosphical concept), but that's the short answer. We can say that "all clocks exist", but because of "EInstein's train" (a thought experiment about the issue at hand), we can't say that they all exist at the same absolute time.

For a fuller discussion, see any discussion about "Einstein's Train", or read Einstein's original discussion about it in his book on Relativity. See for instance http://www.bartleby.com/173/9.html.

 

[nitsuj]

There's no second clock involved in the point I was making. One clock, two readings taken on that clock. Their difference is an elapsed time, and that's something that requires a standard to be able to measure.

On the other hand, synchronizing two spatially separated clocks requires nothing of the kind, just a convention.

it can synchronize the first clock too...

 

[GrayGhost]

I changed my mind about reading the old stuff. It's old. Give it to me short and sweet in language I can understand. This is the 21st century and I don't have all day. Thank you.

Learning the Special theory (SR) from Einstein's 1905 paper (OEMB) is totally fine. There's nothing wrong with it. I consider it an excellent way to learn it. However afterwards, it is extremely beneficial to learn the geometric approach of Minkowski spacetime diagrams. The geometric approach brings about a complete understanding more quickly, in most cases. His OEMB scenario setup and assumptions were very carefully (and well) defined. His paper did not show all the derivation of the stated interim equations, but they are not difficult to determine. You only need algebra to derive the Lorentz transformations (Section 3), however Einstein used both algebra and calculus in his OEMB derivation. The reason it may be done using algebra alone, is because the relation between spacetime systems of relative motion "is assumed linear", because of the observed homogeneity of space and time.

The whole discussion about "perfect clocks" is a moot point IMO. He used "clocks with hands" because that's all they had in his day. In 1905, they had the usual spring & gear clocks, so of course, that's what he'd use in his description. And it makes no sense to define a theory of space and time by assuming the clocks (used) in one's thought experiments are poor time keepers. So as any anyone else would, he assumed good and accurate clocks for all his intents and purposes. And besides, he was modeling space and time, not the accuracy of clocks. His work at the Swiss Patent office certainly gave him much experience in clock synchronization techniques. Being an easy job for Einstein, it also gave him a great deal of time to focus on his own work.

Have at it, you can do it!

Best Regards,
GrayGhost

 

[GrayGhost]

Aufbauwerk 2045,

Also, in OEMB Section 1 when Einstein talks about an observer "in the neighborhood" of the clock, or the clock "in the neighborhood" of the event, he's only minimizing the light travel time (delay) from event to clock, and/or clock to observer('s eyes). An observer (A) at a train station with clock in hand, knows the train arrived at 7pm ... little hand at 7 and train at station. If an observer (B) 20 light seconds away (say also at rest with the train station) awaits light signals from that distant event, the received light image shows the clock arrived at the station at 7, by the clock on the wrist of he at the station. However, this distant observer's own clock then reads 7:00:20, not 7 ... because light takes 20 sec to traverse a 20 light-sec separation. If that observer (B) used his own clock to define the event, he'd say the train arrived at 20 sec after 7. So this is what Einstein is pointing out in Section 1, when he talks about "in the neighborhood of". As stated in the thread already, he's defining the situation whereby the light's flight time from event to clock, or clock to eyes, is "negligible enough for all intents and purposes". As such, your own clock's time readout that you see "is essentially" the time the event occurred (train at station). The observer, his clock, and the event, are essentially in-the-same-place-at-the-same-time.

Best Regards,
GrayGhost

 

[GrayGhost]

Sorry, I have a type-O correction in my prior ...

I wrote ... ", the received light image shows the clock arrived at the station at 7, by the clock on the wrist of he at the station."

I should have written ... ", the received light image shows the train arrived at the station at 7, by the clock on the wrist of he at the station."

The paper reference being ... http://www.fourmilab.ch/etexts/einstein/specrel/www/

Best Regards,
GrayGhost

 

[mabool]

EDoMb Section 1 is called Definition of Simultaneity.

It does not define simultaneity of separated clocks. It defines synchrony of separated clocks.

EDoMB Section 2, in connection with "discovered length" makes reference to "definite time." Definite time is simultaneity at separate locations, the endpoints of a rigid body.

Section 2 ultimately uses synchrony and not simultaneity for discovered length, synchrony having been plausibly defined in Section 1.

Einstein's article in The 14th Encyclopedia Britannica ( title: Space-Time ) roughly 1930, says "there is no such thing as absolute simultaneity."

Algebraically, simultaneity at separate locations A and B is: tA = tB. No such equation appears in EDoMB and is very hard to find anywhere on the web. It is not in the EB article.