How does Einstein define simultaneity in his 1905 paper?

This conversation is about Einstein's famous 1905 paper "On the Electrodynamics of Moving Bodies," in which he presents his key concepts of relativity. The paper discusses the role of clocks and how they are used to measure time. Einstein defines time as the measurement of events in relation to a clock, and explains how clocks must be synchronized in order to establish a common time for different locations. He also assumes the speed of light in empty space is a universal constant. While the paper has been refined and expanded upon in the following decades, the treatment of clocks remains consistent. However, the concept of "immediate neighborhood" is important to consider when discussing clock synchronizations and the
  • #36
JulianM said:
Where this becomes important is in Einstein's next step in choosing the position of his observers. His choice of placing an observer in the middle of a train is a special and unique choice, and is the only position that supports his train thought experiment.
Not really. It's just that this case is symmetric in one of the reference frames so is easy to analyse. You can use any other place on the train and come to the same conclusion, but the situation is more complex to describe and analyse.
 
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  • #37
JulianM said:
The implication of this is that in making any observation of time then the observer must know the distance to the other clock and must calculate backwards in order to know what the time is in that part of, even, stationary space.
Yes, this is correct

JulianM said:
His choice of placing an observer in the middle of a train is a special and unique choice, and is the only position that supports his train thought experiment
This is not correct. This unique choice simplifies the analysis, but is not necessary. The rest of your post, particularly the conclusion, does not follow.
 
  • #38
JulianM said:
The "shortening" of a moving rod is easily shown to be an illusion when we take into account the difference in time of each end when observed by a stationary observer.
Length contraction and time dilation are what's left over after you have properly corrected for light travel time, so they cannot be just an illusion of observation. Bell's Spaceship Paradox, in which length contraction generates stresses that cause a string to break, is a good example of the way in which the contraction of a moving rod is not an illusion (it is frame-dependent, in the sense that other frames will have different explanations of the breaking string, but it is not an illusion).

It is reasonable to consider relativity of simultaneity as the "real" explanation for observations of both length contraction and time dilation, but that doesn't make either phenomenon an illusion.
 
  • #39
JulianM said:
Einstein has simplified the situation which leads to his conclusions on length shortening etc. The "shortening" of a moving rod is easily shown to be an illusion when we take into account the difference in time of each end when observed by a stationary observer.
The idea that the length of an object is observer dependent causes a lot of people a lot of discomfort. It's easier to accept time dilation because you can fly a clock around the world, sit them next to each other and see that they show different elapsed time. But you can't do that with length contraction, can you?

Actually, yes you can: If you travel to Alpha Centurai at just under the speed of light, it might seem to you to take just 1 year. Since you can't exceed the speed of light (and indeed didn't measure yourself to be exceeding it), that means you must accept that you only traveled a touch under 1 light-year during your trip, not the 4.5 light years your friends on Earth saw.

The difference between length contraction and time dilation that people tend to miss is that it isn't elapsed time that dilates, it is the rate of time passage that dilates. That goes away when objects are brought together, just like length contraction does. So in both cases, only by measuring the accumulated/elapsed time/distance do you see the restults.

Time dilation and length contraction really are opposite sides of the same coin and each exactly as "real" as the other.
 
  • #40
Ibix said:
Not really. It's just that this case is symmetric in one of the reference frames so is easy to analyse. You can use any other place on the train and come to the same conclusion, but the situation is more complex to describe and analyse.

In fact I presented another position on the train where the same conclusion is not reached. A passenger sitting behind the center who arrives at the position of the stationary observer at the same time as the flashes does see them as simultaneous. Therefore you cannot "use any or all other places".
 
  • #41
JulianM said:
In fact I presented another position on the train where the same conclusion is not reached. A passenger sitting behind the center who arrives at the position of the stationary observer at the same time as the flashes does see them as simultaneous. Therefore you cannot "use any or all other places".
Your analysis is incorrect. He receives the flashes simultaneously, but he's not equidistant from the ends of the train so he does not conclude that they were emitted simultaneously. Whereas the platform observer is equidistant from the emission points and receives the flashes simultaneously so concludes that they were emitted simultaneously.
 
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  • #42
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.
 
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  • #43
Aufbauwerk 2045 said:
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.
Taylor and Wheeler, Spacetime Physics. Some chapters are online for free if you want to try before you buy.
 
  • #45
Aufbauwerk 2045 said:
P.S. one of my reasons for the previous post is that I think it's important to make sure the basic ideas are clear, before venturing into questions about the actual relativity theory. I wonder if the way Einstein uses his so-called "clocks" in defining time is helpful or confusing.
I agree with the interpretation, its exactly as he said. However I'd argue his use of clocks is significant. The ruler and photon became a perfect measure of time. "Ticks" of said clock being ab in length. Photon moves 299.7k.km in one second..the dang thing is great for measurements of Spacetime.
 
  • #46
Aufbauwerk 2045 said:
I wonder if the way Einstein uses his so-called "clocks" in defining time is helpful or confusing.

nitsuj said:
I agree with the interpretation, its exactly as he said. However I'd argue his use of clocks is significant. The ruler and photon became a perfect measure of time. "Ticks" of said clock being ab in length. Photon moves 299.7k.km in one second..the dang thing is great for measurements of Spacetime.

I don't think it's true that Einstein used any so-called "clocks" to define time. Time is simply the thing we measure with clocks. Metrologists tell us how to measure time, but there is no way that I know of to define time.

And I don't think it's true that photons are used to measure time. First of all there is no such thing as a perfect measure of anything. (The most precise measurements of distance, as far as I know, use digital interferometry; that technique makes use of waves of light as far as I know and has nothing to do with photons.) Photons are a part of quantum theory; it's true that quantum mechanics has provided us with very precise ways to measure things, and metrologists use those measurements to create better standards. They are even going so far as to set exact values for fundamental constants to establish standards rather than relying on artifacts to do so. They did that with the speed of light and they will likely do that with Avogadro's Number and other fundamental constants next year. But using that technique to establish standards does not mean we are making exact measurements. For example, when making measurements of the distance a light beam travels from ##a## to ##b## and the time it takes to make that trip, we are not measuring the speed of light but are instead calibrating the devices we're using to measure length.
 
  • #47
Mister T said:
I don't think it's true that Einstein used any so-called "clocks" to define time. Time is simply the thing we measure with clocks. Metrologists tell us how to measure time, but there is no way that I know of to define time.

And I don't think it's true that photons are used to measure time. First of all there is no such thing as a perfect measure of anything. (The most precise measurements of distance, as far as I know, use digital interferometry; that technique makes use of waves of light as far as I know and has nothing to do with photons.) Photons are a part of quantum theory; it's true that quantum mechanics has provided us with very precise ways to measure things, and metrologists use those measurements to create better standards. They are even going so far as to set exact values for fundamental constants to establish standards rather than relying on artifacts to do so. They did that with the speed of light and they will likely do that with Avogadro's Number and other fundamental constants next year. But using that technique to establish standards does not mean we are making exact measurements. For example, when making measurements of the distance a light beam travels from ##a## to ##b## and the time it takes to make that trip, we are not measuring the speed of light but are instead calibrating the devices we're using to measure length.

I meant to say "However I'd argue his use of clocks is NOT significant." I may have not made my point clear...I find he essentially said "I'll use this well known and easily measured length, to equate to the time it takes light to make a round trip. I define that half the distance traveled is half the time of the round trip." He referred to this as defining a "common time". Imo that is making a "clock" out of a "ruler and photon". a perfect and idealized clock.

For the underlined part of your post...YES. Same idea, leaning on the constant for making measurements of spacetime. in the case Einstein made the easily measured length IS known and the time (one half the full trip) is defined.
 
  • #48
nitsuj said:
He referred to this as defining a "common time". Imo that is making a "clock" out of a "ruler and photon". a perfect and idealized clock.

I think that's just a simultaneity convention. In that context "common time" means "common clock-reading". You need two clock-readings to measure the passage of time. In our everyday language we use the word "time" to refer to both ##t## and ##\Delta t##. When we speak of defining time we are referring to the establishment of a standard for measuring ##\Delta t##, but when we synchronize clocks we are referring to a way of establishing a common clock-reading ##t##, and that does not require a standard. The former is a matter of metrology requiring the most precise devices we can invent. The latter is instead a mere convention (unless the clocks are co-located in which case it's trivial).
 
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  • #49
Mister T said:
I think that's just a simultaneity convention. In that context "common time" means "common clock-reading". You need two clock-readings to measure the passage of time. In our everyday language we use the word "time" to refer to both ##t## and ##\Delta t##. When we speak of defining time we are referring to the establishment of a standard for measuring ##\Delta t##, but when we synchronize clocks we are referring to a way of establishing a common clock-reading ##t##, and that does not require a standard. The former is a matter of metrology requiring the most precise devices we can invent. The latter is instead a mere convention (unless the clocks are co-located in which case it's trivial).
I agree, it is a simultaneity convention.

What do you mean you need two clocks to measure the passage of time? The second clock is to be sync'd to the first, due to the "perfect timing" (invariant speed) of this idealized light clock it can be done across a distance. One clock is used to do this, with a round trip for light. Do whatever with the results...in this case synchronize clocks..
 
  • #50
nitsuj said:
What do you mean you need two clocks to measure the passage of time?

You need two clock-readings.
 
  • #51
Mister T said:
You need two clock-readings.
same question
 
  • #52
nitsuj said:
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##.
 
  • #53
Mister T said:
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.
 
  • #54
nitsuj said:
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.
 
  • #55
Don't all clocks exist at the same absolute time, but move at different relational speeds?
 
  • #56
JAYJACOBUS said:
Don't all clocks exist at the same absolute time, but move at different relational speeds?

No.
 
  • #57
JAYJACOBUS said:
Don't all clocks exist at the same absolute time
There is no absolute time in relativity.
JAYJACOBUS said:
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?
 
  • #58
JAYJACOBUS said:
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.
 
  • #59
Mister T said:
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...
 
  • #60
Aufbauwerk 2045 said:
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
 
  • #61
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
 
  • #62
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
 
  • #63
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.
 
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<h2>1. What is Einstein's definition of time?</h2><p>Einstein's definition of time is that it is a relative concept, meaning that the measurement of time can vary depending on the observer's perspective and relative motion. This is in contrast to the classical definition of time as a constant and absolute quantity.</p><h2>2. How did Einstein's theory of relativity impact our understanding of time?</h2><p>Einstein's theory of relativity revolutionized our understanding of time by showing that it is not a fixed and universal concept, but rather is influenced by factors such as gravity and relative motion. This theory also introduced the concept of spacetime, which combines space and time into a single entity.</p><h2>3. Does Einstein's definition of time apply to both the macroscopic and microscopic world?</h2><p>Yes, Einstein's theory of relativity applies to both the macroscopic and microscopic world. It has been extensively tested and confirmed through experiments and observations in both realms.</p><h2>4. How does Einstein's definition of time relate to the concept of time dilation?</h2><p>Einstein's definition of time is closely related to the concept of time dilation, which is the slowing down of time for an object in motion relative to an observer. This is a consequence of the theory of relativity and has been observed in various experiments, such as the famous Hafele-Keating experiment.</p><h2>5. Can Einstein's definition of time be applied to everyday life?</h2><p>Yes, Einstein's definition of time can be applied to everyday life. While we may not notice it in our daily routines, the effects of time dilation and the relativity of time can be observed in GPS systems, which must account for the differences in time between satellites in orbit and on the ground. Additionally, our understanding of time and its relativity has led to advancements in technologies such as atomic clocks and GPS devices.</p>

1. What is Einstein's definition of time?

Einstein's definition of time is that it is a relative concept, meaning that the measurement of time can vary depending on the observer's perspective and relative motion. This is in contrast to the classical definition of time as a constant and absolute quantity.

2. How did Einstein's theory of relativity impact our understanding of time?

Einstein's theory of relativity revolutionized our understanding of time by showing that it is not a fixed and universal concept, but rather is influenced by factors such as gravity and relative motion. This theory also introduced the concept of spacetime, which combines space and time into a single entity.

3. Does Einstein's definition of time apply to both the macroscopic and microscopic world?

Yes, Einstein's theory of relativity applies to both the macroscopic and microscopic world. It has been extensively tested and confirmed through experiments and observations in both realms.

4. How does Einstein's definition of time relate to the concept of time dilation?

Einstein's definition of time is closely related to the concept of time dilation, which is the slowing down of time for an object in motion relative to an observer. This is a consequence of the theory of relativity and has been observed in various experiments, such as the famous Hafele-Keating experiment.

5. Can Einstein's definition of time be applied to everyday life?

Yes, Einstein's definition of time can be applied to everyday life. While we may not notice it in our daily routines, the effects of time dilation and the relativity of time can be observed in GPS systems, which must account for the differences in time between satellites in orbit and on the ground. Additionally, our understanding of time and its relativity has led to advancements in technologies such as atomic clocks and GPS devices.

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