# Understanding simultaneity

• fireball3004
In summary, Einstein argues that simultaneity depends on the observer. Two events that are simultaneous according to the train observer are not simultaneous according to the platform observer. This is because the train observer is moving relative to the platform observer. However, this does not require faith. It can be tested by experiment.f

#### fireball3004

I've picked up relativity, again after getting frustrated. I'm new but I need help understanding simultaneity. I tried to read further but it seems to be very important to all of Einstein’s other arguments. So here it goes.
In relativity, the special and general theory, P 30 about halfway through to the end of the page, Einstein talks about light how 2 beams of light will reach the midpoint from where they started given that they travel at the same speed. This I understand. Then he talks about how if you are on a train moving toward one of the beams of light from the midpoint that you reach one of the beams of light before the other, and there for it will not appear simultaneous. This to I understand and agree with. But then he says that this means that the two events occur at different times if you are on the train rather than the embankment. I don't understand this leap of understanding from it appears to be to it is. I keep thinking that this is true because you change the distance between two points and therefore are no longer at the midpoint. I would really appreciate someone explaining this.

Given that the speed of light appears to be constant to all observers (which appears to be true from all experiments that have been done), one must conclude from the result of the thought experiment that the notion of simultaneous events depends on the observer. Two events that are simultaneous according to the train observer are not simultaneous according to the platform observer.

I'm not sure how much this helps, but you'll have to accept that simultaneity is relative if you want to get very far with relativity. The only missing step from your description is the constancy of the speed of light - hopefully you can see how that prevents your notion from working.

But I was wondering... isn't this a characteristic of changing your location away from the midpoint... isn't this the case because you are closer to one beam as compared to the other? Because Einstein said that the definition of simultaneous was when two photons would reach the midpoint between their starting locations at the exact same time not a point that once was at the midpoint. Sorry for being a pain but I can’t except things on faith, it’s not in my nature.

But I was wondering... isn't this a characteristic of changing your location away from the midpoint... isn't this the case because you are closer to one beam as compared to the other? Because Einstein said that the definition of simultaneous was when two photons would reach the midpoint between their starting locations at the exact same time not a point that once was at the midpoint. Sorry for being a pain but I can’t except things on faith, it’s not in my nature.

Einstein actually chose this method of clock synchronization (via light signals) in order to preserve isotropy. He mentioned this in his 1905 paper, but only very briefly.

An isotropic clock synchronization is a fair clock synchronization.

In order to measure velocities, one needs two clocks, and a means of synchronizing them. One lays out a course of known length, and puts one clock on the "starting line" and another clock on the "finish line".

one then takes the difference between the time at which one crossed the starting line (measured on the clock at the start line) and the time at which one crosses the finish line (measured on the clock at the finish line) as the elapsed time for the trip, and one computes the velocity as the length of the course (measured with a ruler) divided by this time.

Only when the clocks are synchronized "fairly" will one correctly measure the trip times (and hence the velocity) to be the same going in one direction over the course (say east-west) as in the other direction (west-east).

The point that Einstein makes is that the clock synchronization that fairly measures the velocities of material objects is the same clock synchronization that makes the speed of light constant.

This doesn't actually require "faith", it can be tested by experiment.

For instance, one might say that for an object of a known mass, the clocks are synchronized properly when an east-west moving object of mass m has an equal and opposite momentum to a west-east moving object of mass m, such that they have a net velocity of zero when they collide.

There are other methods of defining "fair" clock synchronization, including a comparison of "rapidity" measurements using only one clock to "velocity" measurements.

A rapidity measurement requires a clock on the moving object. (this is possible for a physical moving object, but it's not possible to put a clock on a light beam, for instance). A fair clock synchronization scheme requires that a clock that transverses a course in a certain fixed amount of time E-W and the same fixed amount of time W-E as measured by an "onboard" clock also have equal trip times E-W and W-E using the "two clock" method.

Because of relativistic time dilation, the times measured by the one-clock method (rapidity) and the two clock methods won't be the same. What is important is that the relation between the one-clock and two-clock methods is independent of the direction chosen, i.e. that the relationship is isotropic.

As a consequence of this, and the constancy of the speed of light (also experimentally confirmed), the conclusion that a "fair" clock synchronization depends on the frame of reference can't be avoided.

..., but it's not possible to put a clock on a light beam, for instance).
Note that a light beam already has a pretty good "clock" on board, namely the period of the wave of the photon. And the behaviour of this "clock" is completely consistent with relativity, it stands still between two events.

wave as a clock

Note that a light beam already has a pretty good "clock" on board, namely the period of the wave of the photon. And the behaviour of this "clock" is completely consistent with relativity, it stands still between two events.
Please let me know if you have seen that interesting idea mentioned or used somewhere. Thanks

Please let me know if you have seen that interesting idea mentioned or used somewhere. Thanks
Honestly I do not remember ever seeing this particular illustration.

In an Einstein synchronized frame of reference the photon is everywhere at the same time on the emission's line of simutaneity, i.e. the line following the direction of the photon. So then it follows that each observer on that line encountering the photon would have to measure the same phase of the wave.

But, I would not mind to be proven wrong.

Note that a light beam already has a pretty good "clock" on board, namely the period of the wave of the photon. And the behaviour of this "clock" is completely consistent with relativity, it stands still between two events.

The wavelength of a beam of light is more of a measure of length than time. You can certainly use a "light clock" to keep time, but one can convert the natural "length" measurement of the wavelength into a time only by dividing by the speed.

It turns out, of course, that the speed of light is constant, so there is a natural and constant conversion from wavelengths to times,

Since I was trying to explain a bit about how we measure speed, it would have been a bit premature to assume without proof that the speed of light is constant. This is what we are trying to demonstrate, and to do this I think we should take an approach to defining clock synchronization that doesn't involve light signals at all, but only physical arguments about the "fair" way to synchronize clocks to insure a "fair" (isotropic) measurement of speed.

I think I understand now... though not necessarily what you were saying... I think that what I was missing was the fact that Einstein just means that it appears to be at different times even though it really is simultaneous.

I think I understand now... though not necessarily what you were saying... I think that what I was missing was the fact that Einstein just means that it appears to be at different times even though it really is simultaneous.

Ummm - nope, the point you should be getting is that there isn't any universally valid way to synchronize clocks.

It's not just a matter of appearances.

Couldn't you figure out the distance between things using simple trig. or a second reference followed by a few simple calculations by dividing the distance between you and the two given clocks by the speed of light compared to the time lapse? and does that not imply that there is in fact a universal view?

clock synchronization

Ummm - nope, the point you should be getting is that there isn't any universally valid way to synchronize clocks.

It's not just a matter of appearances.
Is there special relativity without clock synchronization?
If observers located in an electromagnetic wave use the periodic e.m.
oscillations as clocks should clock synchronization be involved?
Consider the questions as rised by a humble physicist interested in teaching SR. Thanks

I think I get it now and you can forget the universal view thing I said before... I found aphysics proffessor to explain it to me, and I think I understand now.

Is there special relativity without clock synchronization?
Yes of course there is.

Only if we insist on a kinematic and dynamic model where particles move in space over time we have to suffer "headaches" about clock synchronizations, spatial contractions and time dilations etc.

However, if we view the relationships between particles from a space-time perspective, we don't need these.

without clock synchronization?

Yes of course there is.

Only if we insist on a kinematic and dynamic model where particles move in space over time we have to suffer "headaches" about clock synchronizations, spatial contractions and time dilations etc.

However, if we view the relationships between particles from a space-time perspective, we don't need these.
Please be more specific concerning your last sentence. Could you direct me to some literature? Thanks

Please be more specific concerning your last sentence. Could you direct me to some literature? Thanks
For instance when you insist on using 4-vectors and proper properties only you avoid relativistic confusion.

There are no things like length contraction or time dilation for a 4-vector. You can define (in flat space) things like a space-time interval, velocity, acceleration, force and energy-momentum as 4-vectors and the nice property is that they are Lorentz invariant.
Obviously you can do the same in curved space-time but then you need a bit more than 4-vectors.

4-vectors are discussed very widely in the literature. A textbook example, relevant to relativity, which I particularly like for its transparency and being well organized, is http://www.courses.fas.harvard.edu/~phys16/Textbook/ch12.pdf" by David Morin, not a professor (yet?) from Harvard.

He even includes a limerick:

God said to his cosmos directors,
One is the clause
Shall be written in terms of 4-vectors.”

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Is there special relativity without clock synchronization?

Yes of course there is.

Only if we insist on a kinematic and dynamic model where particles move in space over time we have to suffer "headaches" about clock synchronizations, spatial contractions and time dilations etc.

However, if we view the relationships between particles from a space-time perspective, we don't need these.

Some relationship among clocks is necessary, but no particular relationship is inherently preferred. Synchronization of clocks at separate locations depends on establishing a convention for relating signals exchanged over distances with the readings of stationary clocks. The bottom line is that the proper interval will be invariant among all synchronization conventions.

clock synchronization compulsory

For instance when you insist on using 4-vectors and proper properties only you avoid relativistic confusion.

There are no things like length contraction or time dilation for a 4-vector. You can define (in flat space) things like a space-time interval, velocity, acceleration, force and energy-momentum as 4-vectors and the nice property is that they are Lorentz invariant.
Obviously you can do the same in curved space-time but then you need a bit more than 4-vectors.

4-vectors are discussed very widely in the literature. A textbook example, relevant to relativity, which I particularly like for its transparency and being well organized, is http://www.courses.fas.harvard.edu/~phys16/Textbook/ch12.pdf" by David Morin, not a professor (yet?) from Harvard.

He even includes a limerick:

God said to his cosmos directors,
One is the clause
Shall be written in terms of 4-vectors.”

Thanks. As far as I know the construction of a four vector involves time dilation which at its turn involves clock synchronization at least in one of the involved reference frames. Am I right?

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In the URL, change "ch12" to any chapter at which you want to look.

Some relationship among clocks is necessary, but no particular relationship is inherently preferred. Synchronization of clocks at separate locations depends on establishing a convention for relating signals exchanged over distances with the readings of stationary clocks. The bottom line is that the proper interval will be invariant among all synchronization conventions.
Why is it necessary?
Can you give me an example where you think we need it?

Apart from answering meaningless questions like "what time is it, right now, on Andromeda" I do not see any need whatsoever.

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clock indicating time (date) and measuring time intervals

Why is it necessary?
Can you give me an example where you think we need it?

Apart from answering meaningless questions like "what time is it, right now, on Andromeda" I do not see any need whatsoever.

I think that beside "what time is it" we are interested in measuring time intervals. As long I am interested in proper time intervals clock synchronization can be avoided. But what hapens when I measure coordinate time intervals and I want to relate it to a proper time interval?
Is my question childish?

I think that beside "what time is it" we are interested in measuring time intervals.
If you are interested in Lorentz variant time-intervals then of course you have to think about synchronizations and deal with the contractions, dilations and synchronization

But my point is that if you use only 4-vectors and Lorentz invariant properties you don't have to.

Is my question childish?
I think we are all children when it comes to relativity.

Special relativity is concerned with space and time as we measure it. The values we put in the components of the 4-vector are measured space and time intervals. Using 4-vectors makes the calculations covariant, but we still have to relate the calculated quantities to rods and clocks. You need to define spatial coordinates and time coordinates at each point in order to do relativity. To see this, ask yourself how you measure proper time between two events. You take the difference between the two space coordinates and the difference between the time coordinates and calculate the proper time.

I would be happy to hear of a way to measure proper time directly, without using space and time coordinates.

Special relativity is concerned with space and time as we measure it. The values we put in the components of the 4-vector are measured space and time intervals. Using 4-vectors makes the calculations covariant, but we still have to relate the calculated quantities to rods and clocks. You need to define spatial coordinates and time coordinates at each point in order to do relativity. To see this, ask yourself how you measure proper time between two events. You take the difference between the two space coordinates and the difference between the time coordinates and calculate the proper time.

I would be happy to hear of a way to measure proper time directly, without using space and time coordinates.

Do you mean by proper time the reading of a wrist watch or you mean proper time interval which is a difference between the readings of a wrist watch. In the first case clock synchronization is necessary in order to make the wrist watch operational. In the second case clock synchronization is not compulsory and it is not necessary to know the location of the wrist watch (dx=0) Am I right? Somebody on the Forum told me that when it is about special relativity we all are childish.:rofl:

Do you mean by proper time the reading of a wrist watch or you mean proper time interval which is a difference between the readings of a wrist watch. In the first case clock synchronization is necessary in order to make the wrist watch operational. In the second case clock synchronization is not compulsory and it is not necessary to know the location of the wrist watch (dx=0) Am I right? Somebody on the Forum told me that when it is about special relativity we all are childish.:rofl:

I mean the interval of proper time between the two events. If the watch is in an inertial frame in which the two events happen at the same location, and the watch is at the location of the events, then it is the interval of time between the events read on the watch. In any other frame, both the distance between the events and the time interval between clocks at the events are needed to calculate the proper time.

I would be happy to hear of a way to measure proper time directly, without using space and time coordinates.

It is also possible to take proper time as measured by clocks as fundamental, and then to define time and space coordinates by the radar method.

It is also possible to take proper time as measured by clocks as fundamental, and then to define time and space coordinates by the radar method.
Correct, for instance consider in this context Bondi K-Calculus.

proper tme interval, coordinate time interval

I mean the interval of proper time between the two events. If the watch is in an inertial frame in which the two events happen at the same location, and the watch is at the location of the events, then it is the interval of time between the events read on the watch. In any other frame, both the distance between the events and the time interval between clocks at the events are needed to calculate the proper time.
Thanks. Now we understand the same thing. Because I am not familiar with the English names of physicsl quantities conider please the formula
dt=gdt(0).
Do you call dt coordinate time interval or other names are in use for it.

proper time approach

It is also possible to take proper time as measured by clocks as fundamental, and then to define time and space coordinates by the radar method.

I think that the photographic detection procedure does the same thing.

It is also possible to take proper time as measured by clocks as fundamental, and then to define time and space coordinates by the radar method.

Please explain how you measure proper time between events with clocks alone. It seems like that is possible only if the events happen at the same place. Are you referring to starting with an array of stationary clocks to define time at each point and then establishing the spatial grid with light signals? Does this definition of proper time (maybe I should say "invariant interval") apply to any two events?

Thanks. Now we understand the same thing. Because I am not familiar with the English names of physical quantities consider please the formula
dt=gdt(0).
Do you call dt coordinate time interval or other names are in use for it.

I am not quite sure what you mean here. I believe that dt is the time interval, or elapsed time, but I don't know what gdt(0) refers to. Please give more details.

Proper time intervals have nothing do with with clock synchronization.

Since proper time intervals are Lorentz invariant they could obviously not depend on a particular clock synchronization scheme.

Furthermore, the proper time interval between two space-time events depends solely on the particle's path in space-time. In case of a photon or any other massless particle this interval is always zero.

Note that in relativity it is not always possible to connect the path of a particle to two arbitrary events in space-time, not even the path of a photon!

Please explain how you measure proper time between events with clocks alone. It seems like that is possible only if the events happen at the same place. Are you referring to starting with an array of stationary clocks to define time at each point and then establishing the spatial grid with light signals? Does this definition of proper time (maybe I should say "invariant interval") apply to any two events?

I am not quite sure what you mean here. I believe that dt is the time interval, or elapsed time, but I don't know what gdt(0) refers to. Please give more details.
g stands for gamma and dt(0) for proper time

Proper time intervals have nothing do with with clock synchronization.

Since proper time intervals are Lorentz invariant they could obviously not depend on a particular clock synchronization scheme.

Furthermore, the proper time interval between two space-time events depends solely on the particle's path in space-time. In case of a photon or any other massless particle this interval is always zero.

Note that in relativity it is not always possible to connect the path of a particle to two arbitrary events in space-time, not even the path of a photon!

The metric of spacetime defines the clock synchronization and how rod lengths are related throughout the coordinate system. The invariant interval is then independent of sychronization and length conventions. Inside the light cone the invariant interval is the proper time. But, again, how do you measure the invariant interval without establishing some sychronization and length convention?

The metric of spacetime defines the clock synchronization and how rod lengths are related throughout the coordinate system. The invariant interval is then independent of sychronization and length conventions. Inside the light cone the invariant interval is the proper time. But, again, how do you measure the invariant interval without establishing some sychronization and length convention?

The interval along a given curve is a geometric object, one that is independent of any particular choice of coordinate or metric.

You do need a standard clock/ruler (generally but perhaps not always taken to be the SI definition) to define the length of the interval, however.

Thanks. Now we understand the same thing. Because I am not familiar with the English names of physicsl quantities conider please the formula
dt=gdt(0).
Do you call dt coordinate time interval or other names are in use for it.

g stands for gamma and dt(0) for proper time

As I understand it then, dt is the coordinate time and g is the reciprocal of the time component in the metric tensor. It might be better to write it dt(0)=gdt, in which case g is the metric component. In special relativity g=1.