On the idea of time in physics-relativity

[Syne]

In the modified animation it shows just what I said would happen. So why you say this can not happen is a bit strange.

These examples have to violate the requirement of the thought experiment that the flashes occur when both observers are equidistant from both. This is physically possible, but artificially maintains simultaneity. This is a special case where the timing of the flashes has to be very precisely offset from one of the observers being equidistant.

Now I understand your next animation with multiple light cones. Why would he not observe them come form the ends of the train?
You say "...as the platform observer would not observe them to originate from the ends of the train." without any sensible logic.

Actually, I think I messed that one up. I missed that the first one was a special case.

 

[Robittybob1]

These examples have to violate the requirement of the thought experiment that the flashes occur when both observers are equidistant from both. This is physically possible, but artificially maintains simultaneity. This is a special case where the timing of the flashes has to be very precisely offset from one of the observers being equidistant.

That is what I was thinking, in the discussion parts/conditions of the original thought experiment had been dropped.
Suppose:
Lightning strikes the two ends of the railway carriage. Were they simultaneous or not?
There might be a place and time and a velocity of an observer that no matter where the lightning strikes each end individually it is possible to say they were simultaneous.
Like, if in our frame it appears that the lightning strike was 1 year apart. Where does the other person have to be in order for him/her to say they were simultaneous?

You might say this is impossible but it isn't. If the train is 1 light year long, a flash of lightning will take a year for it to reach the other end, and as the light from that reaches the end another flash occurs just at the very moment, and this was with the train stationary.

 

[Pete]

There exists a reference frame such that the two events are observed to occur at the same time, but there is no reference frame in which the two events can occur in the same spatial location. -http://en.wikipedia.org/wiki/Spacetime#Space-like_interval​

That's defining a spacelike interval and proper length, not a proper frame for an event or pair of events.

The co-moving, or proper, frame is defined as that in which the time is minimal and the space maximal.

That's applies to an interval, not a pair of events. A pair of events is not the same thing as the interval between them.

No, a time-like interval is one where a signal of light from the first event has time to reach the second, and thus allow for a causative relationship between them. Simultaneous and spatially separated events do not allow for any causation between events.

There exists a reference frame such that the two events are observed to occur in the same spatial location, but there is no reference frame in which the two events can occur at the same time. -http://en.wikipedia.org/wiki/Spacetime#Time-like_interval​

As you can see, this does not apply to spatially separated, simultaneous events, nor proper time (as proper time exists in every frame, including the frame of events separated by a space-like interval as well).

Yes, that's what I said. And since the interval in question is not timelike, it doesn't have a proepr time.

The measure of a time-like spacetime interval is described by the proper time, $$\Delta \tau$$:
$$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \Delta \tau = \sqrt{\Delta t^2 - \Delta r^2 / c^2}$$
-http://en.wikipedia.org/wiki/Spacetime#Time-like_interval​

Yes, a proper frame is just one in which the proper time (minimal) and length (maximal) between events occur.

As in both of my quotes above, about space-like and time-like spacetime intervals, it should be clear that there is a natural frame, one defined by the properties of a rest frame, in which to view the events.

OK, we don't have any great disagreement, and we're down to semantics.
- I agree that the proper frame of an interval is the one in which the time is minimal and distance is maximal.
- I do not agree that you can call this the proper frame of the events, and certainly not the "source" of those events.
- I think that you need to distinguish more clearly the events from the interval between them.
- I think that "proper time" applies only to timelike intervals
- I think that "proper length" applies only to spacelike intervals

 

[Syne]

That's applies to an interval, not a pair of events. A pair of events is not the same thing as the interval between them.

So two events observed to occur at the same time is not the same minimal time between events used to define a rest frame? How so?

Yes, that's what I said. And since the interval in question is not timelike, it doesn't have a proepr time.

The measure of a time-like spacetime interval is described by the proper time, $$\Delta \tau$$:
$$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \Delta \tau = \sqrt{\Delta t^2 - \Delta r^2 / c^2}$$
-http://en.wikipedia.org/wiki/Spacetime#Time-like_interval​

I am not relying solely on wikipedia for my definition of proper time.

The time will always be shortest as measured in its rest frame. The time measured in the frame in which the clock is at rest is called the "proper time". -http://hyperphysics.phy-astr.gsu.edu/‌hbase/relativ/tdil.html#c2​

Every frame has a proper time, including the one that can naturally be considered to be at rest relative to both events. Just because "the measurement of a time-like spacetime interval is described by the proper time" does not mean the time-like interval is equivalent to proper time. A time-like spacetime interval can still include some separation in space. It is not wholly a separation in time, as it is only defined as a larger separation in time than in space.

OK, we don't have any great disagreement, and we're down to semantics.
- I agree that the proper frame of an interval is the one in which the time is minimal and distance is maximal.
- I do not agree that you can call this the proper frame of the events, and certainly not the "source" of those events.
- I think that you need to distinguish more clearly the events from the interval between them.

The origins of the flashes in this TE are defined as being at rest relative to one another, so there is nothing untoward about defining the frame in which they are so.

The whole TE is about how those two events relate, which cannot be done without accounting for the spacetime interval between them and how it is observed from different frames.

- I think that "proper time" applies only to timelike intervals
- I think that "proper length" applies only to spacelike intervals

Both are wrong. You should already know this, as you have already agreed that the proper time is simply the minimal time. Even if there is a greater separation in space than time (space-like spacetime interval) between events, there is still a minimal time between them. Proper length and time are properties of all valid reference frames.

 

[Neddy Bate]

Syne,

Try replacing the lightning strikes with light bulbs mounted to the front and rear of the train. These bulbs would certainly not be at rest in the platform's reference frame. Yet, if the bulbs flash simultaneously according to the platform frame, then they do not flash simultaneously accordng to the train frame. In other words, the result is the same as the lighting strikes. So the thought experiment does not depend on the events being "at rest" in either frame. Indeed, as Pete says, events don't really even need to be considered to be at rest in any frame.

Of course this is a very minor point compared with P.Layman incorrectly claiming the events would be simultaneous in both frames.

 

[Syne]

Syne,

Try replacing the lightning strikes with light bulbs mounted to the front and rear of the train. These bulbs would certainly not be at rest in the platform's reference frame. Yet, if the bulbs flash simultaneously according to the platform frame, then they do not flash simultaneously accordng to the train frame. In other words, the result is the same as the lighting strikes. So the thought experiment does not depend on the events being "at rest" in either frame. Indeed, as Pete says, events don't really even need to be considered to be at rest in any frame.

Of course this is a very minor point compared with P.Layman incorrectly claiming the events would be simultaneous in both frames.

I guess you did not notice that I already did just that. I have made no claim that the TE depends on which frame the events are simultaneous in, only that the frame that observes them to be simultaneous is the one where the time between events is minimal and thus, by definition, at rest relative to.

Yes, this distinction is superfluous to the TE, but it is by no means incorrect. But where you seem to be agreeing that this is not necessary to the TE, Pete seems to be saying it is wrong, while erroneously equating proper time solely to a time-like spacetime interval.

 

[Pete]

So two events observed to occur at the same time is not the same minimal time between events used to define a rest frame? How so?

That's not what I said.

I am not relying solely on wikipedia for my definition of proper time.

The time will always be shortest as measured in its rest frame. The time measured in the frame in which the clock is at rest is called the "proper time". -http://hyperphysics.phy-astr.gsu.edu/‌hbase/relativ/tdil.html#c2​

That source also uses proper time only to describe timelike intervals. The time measured by a single clock is obviously a timelike interval.

Every frame has a proper time, including the one that can naturally be considered to be at rest relative to both events. Just because "the measurement of a time-like spacetime interval is described by the proper time" does not mean the time-like interval is equivalent to proper time. A time-like spacetime interval can still include some separation in space. It is not wholly a separation in time, as it is only defined as a larger separation in time than in space.

Not sure what your point is here.
Yes, time-like intervals can include spatial separation.
I don't know what you mean by timelike interval being not equivalent to proper time.

The origins of the flashes in this TE are defined as being at rest relative to one another, so there is nothing untoward about defining the frame in which they are so.

Do you mean the originating event, or an originating object, as a light source?
I think you mean event, but an event does not have the property of motion. It doesn't have a rest frame.
Two events can't be at rest relative to one another, that makes no sense.
For the TE, it's enough to say that the events are simultaneous in a given reference frame.

The whole TE is about how those two events relate, which cannot be done without accounting for the spacetime interval between them and how it is observed from different frames.

Agreed

Both are wrong.

Please provide a reference that refers to the proper time of a spacelike interval, or the proper length of a timelike interval.

You should already know this, as you have already agreed that the proper time is simply the minimal time.

No, I did not.
I agreed that the proper frame of an interval is that in which time is minimal and length is maximal.
I maintain that proper time is the minimal time of a timelike interval or a world line.

Even if there is a greater separation in space than time (space-like spacetime interval) between events, there is still a minimal time between them. Proper length and time are properties of all valid reference frames.

They're not properties of reference frames at all, they are properties of spacetime intervals (or curves).

 

[Neddy Bate]

I guess you did not notice that I already did just that. I have made no claim that the TE depends on which frame the events are simultaneous in, only that the frame that observes them to be simultaneous is the one where the time between events is minimal and thus, by definition, at rest relative to.

Well, if the events are simultaneous, then the time between the events is zero. Of course, that is as minimal as the timing can get. The definition of something being "at rest" in a frame is simply that its velocity relative to that frame is zero. I don't see how you take that definition, remove the part about velocity, replace it with simultaneity, and then apply it to pairs of events.

Yes, this distinction is superfluous to the TE, but it is by no means incorrect. But where you seem to be agreeing that this is not necessary to the TE, Pete seems to be saying it is wrong, while erroneously equating proper time solely to a time-like spacetime interval.

I don't know if its wrong or not, because I have never heard of the idea of pairs of events being considered to be at rest in any frame. I suppose you would agree that any one single event is not at rest in any particular frame? So, why treat pairs of events differently?

 

[Syne]

Well, if the events are simultaneous, then the time between the events is zero. Of course, that is as minimal as the timing can get. The definition of something being "at rest" in a frame is simply that its velocity relative to that frame is zero. I don't see how you take that definition, remove the part about velocity, replace it with simultaneity, and then apply it to pairs of events.

I don't know if its wrong or not, because I have never heard of the idea of pairs of events being considered to be at rest in any frame. I suppose you would agree that any one single event is not at rest in any particular frame? So, why treat pairs of events differently?

If these events had any duration in time it would be obvious which frame they were at rest relative to. The fact that the duration of these events is reduced to zero (instantaneous) does not change that relationship.

For example, the explosion of a firecracker may be considered to be an "event". We can completely specify an event by its four space-time coordinates: The time of occurrence and its 3-dimensional spatial location define a reference point. Let's call this reference frame S. -http://en.wikipedia.org/wiki/Specia...2C_coordinates_and_the_Lorentz_transformation​

A reference frame defines the specific coordinates of an event. You cannot meaningfully talk about any event, or its relationship to other events or frames, without defining a frame for that event. While it is true that events are independent of frames, we cannot do anything meaningful with events without some relation to frames.

 

[Write4U]

Forgive me, but I need to keep this simple. There seem to be too many variables to come to any definitive agreement on the different interpretations.

Is it not possible to illustrate the original parameters of the experiment which calls for a simultaneous flash at the front and the rear of the train the "moment" when the observer on the train passes the observer on station at right angle. Let us assume the train is destroyed by the flashes and disappears. The observer from the train now is just hurtling through the air along the tracks without the train.

questions:

a) Does the observer from the train observe the simultaneity of the flashes, while hurtling through space?

b) Does the stationary observer at the station observe the simultaneity of the flashes, while standing still?

c) Do both observers see the simultaneous flashes at the same time? If not, who sees the flashes first?

 

[Pete]

If these events had any duration in time it would be obvious which frame they were at rest relative to. The fact that the duration of these events is reduced to zero (instantaneous) does not change that relationship.

An event doesn't have any duration, by definition.

For example, the explosion of a firecracker may be considered to be an "event". We can completely specify an event by its four space-time coordinates: The time of occurrence and its 3-dimensional spatial location define a reference point. Let's call this reference frame S. -http://en.wikipedia.org/wiki/Specia...2C_coordinates_and_the_Lorentz_transformation​

A reference frame defines the specific coordinates of an event. You cannot meaningfully talk about any event, or its relationship to other events or frames, without defining a frame for that event.

Perhaps you meant "...without defining a frame for the event coordinates."
Coordinates are meaningless without a defined reference frame.
Events are not.
"The lightning struck" is an event. It occurs in any number of reference frames. No reference frame has any special claim to it.

You can describe some relationship between events without defining a reference frame. For example, whether their separation timelike or spacelike, and what it is the magnitude of their separation.
You can describe an event's relationship with any reference frame by simply identifying the event coordinates in that reference frame.

While it is true that events are independent of frames, we cannot do anything meaningful with events without some relation to frames.

This is true.

 

[Pete]

Forgive me, but I need to keep this simple. There seem to be too many variables to come to any definitive agreement on the different interpretations.

Is it not possible to illustrate the original parameters of the experiment which calls for a simultaneous flash at the front and the rear of the train the "moment" when the observer on the train passes the observer on station at right angle.

The original parameters of the experiment don't call for any simultaneous flashes.
Simultaneity is a conclusion drawn by an observer, not an experimental parameter.

The parameters of the experiment are:
- One flash occurs at the time and place that the front of the train passes one end (call it the back end) of the platform.
- One flash occurs at the time and place that the back of the train passes the other end (the front end) of the platform.
- The platform observer is standing in the middle of the platform, and receives both flashes at the same time.

The platform observer can then conclude that the two flashes occurred at the instant that two observers passed each other.

Let us assume the train is destroyed by the flashes and disappears. The observer from the train now is just hurtling through the air along the tracks without the train.

questions:

a) Does the observer from the train observe the simultaneity of the flashes, while hurtling through space?

No, they see the flash from the front end first.

b) Does the stationary observer at the station observe the simultaneity of the flashes, while standing still?

Yes, as before

c) Do both observers see the simultaneous flashes at the same time? If not, who sees the flashes first?

First, the train observer sees the flash from the front end of the train.
Then the platform observer sees both flashes at once.
Then, the train observer sees the flash from the back end of the train.

 

[Pete]

That is what I was thinking, in the discussion parts/conditions of the original thought experiment had been dropped.
Suppose:
Lightning strikes the two ends of the railway carriage. Were they simultaneous or not?
There might be a place and time and a velocity of an observer that no matter where the lightning strikes each end individually it is possible to say they were simultaneous.
Like, if in our frame it appears that the lightning strike was 1 year apart. Where does the other person have to be in order for him/her to say they were simultaneous?

You might say this is impossible but it isn't. If the train is 1 light year long, a flash of lightning will take a year for it to reach the other end, and as the light from that reaches the end another flash occurs just at the very moment, and this was with the train stationary.

Be aware that receiving the flashes simultaneously isn't the same as concluding that the originating events were simultaneous.
In Einstein's thought experiment, the platform observer measures the distance from where they received the flashes to where the flashes occurred (lightning burn marks on the platform) before concluding the strikes were simultaneous.

The train observer likewise measures the distance from where they received the flashes to where the flashes occurred (burn marks on the train) before concluding the strikes were not simultaneous.

Note that each lightning strike hit both the train and the platform.

 

[Robittybob1]

Be aware that receiving the flashes simultaneously isn't the same as concluding that the originating events were simultaneous.
In Einstein's thought experiment, the platform observer measures the distance from where they received the flashes to where the flashes occurred (lightning burn marks on the platform) before concluding the strikes were simultaneous.

The train observer likewise measures the distance from where they received the flashes to where the flashes occurred (burn marks on the train) before concluding the strikes were not simultaneous.

Note that each lightning strike hit both the train and the platform.

I would tend to argue that "that receiving the flashes simultaneously IS the same as concluding that the originating events were simultaneous".
OK simultaneous in one frame may not be simultaneous in another. Not all frames will agree on simultaneity. But that does not negate that the experience is real. If the light from two events arrives at the same time they occurred simultaneously in the view of that observer.

 

[Pete]

I would tend to argue that "that receiving the flashes simultaneously IS the same as concluding that the originating events were simultaneous".
OK simultaneous in one frame may not be simultaneous in another. Not all frames will agree on simultaneity. But that does not negate that the experience is real. If the light from two events arrives at the same time they occurred simultaneously in the view of that observer.

Be careful to distinguish between the flashes being received and the flashes being sent.

If two flashes are received at the same time, then yes, that is real, they were received simultaneously.
And if one flash took longer to get from origin to receiver than the other, then they were obviously not sent simultaneously.

 

[Write4U]

#1
ash64449
On the idea of time in physics-relativity
i am now reading Theory of relativity written by Albert Einstein. It described on the idea of time in physics by the use of simultaneity. Lightning struck on two extreme parts of the train. In order to test whether the two lightning is simultaneous, a person is made to sit in the middle and two mirrors to let him see two lightning at the same time if it does, it is simultaneous.. but why is the observer kept at the middle of the train?? Won't those events to him be simultaneous even if he was not sitting in the middle??

He is made to sit in the middle because in order to test simultaneity one must be equidistant from both flashpoints.
In order to test simultaneity all observers must be equidistant from the flashpoints.
If one is not equidistant from the flashpoints, one can still receive the flashes simultaneously, but that is not proof of simultaneity. That just clever manipulation of the inherent potentials.

 

[hansda]

It doesn't matter what the speed is, they can set their watches to whatever time they like, including the same time as each other.

That is true. "Simultaneity" does not depend on clock-timing.

But that's not relevant to relative simultaneity,...

It seems "relative simultaneity" is relativity between two clocks.

... which is about whether things that happen in different places happen at the same time or not.

Say, things that happen in different places happen at different time. If things can happen at different time, why they can not happen at same time?

 

[Robittybob1]

He is made to sit in the middle because in order to test simultaneity one must be equidistant from both flashpoints.
In order to test simultaneity all observers must be equidistant from the flashpoints.
If one is not equidistant from the flashpoints, one can still receive the flashes simultaneously, but that is not proof of simultaneity. That just clever manipulation of the inherent potentials.

I am struggling with this simultaneity thought experiments (especially as they are described in http://en.wikipedia.org/wiki/Relativity_of_simultaneity#The_train-and-platform_thought_experiment

If the light beams are reduced to single photons and having mirrors at the ends, you end up with the photons traveling in two directions at once. What I mean is that if the person in the middle of the train fires two photons from his photon gun, one to the front and one to the rear, do the photons reflect from the end walls at different times such that depending on where you are looking at the situation, in one situation the photon is still heading toward the reflector but in another it is already turned around and heading back?
I said something about this yesterday and it is the speed of light that is the physics in question. The speed of light is the same in all frames. So the only way you can measure the speed of light is to send light there and back, a two way speed of light.
So it isn't that the person in the train sees light hit both ends at the same time, but the light returning to him comes back at the same time. A two path. There is no way he can determine if the photons hit the end walls at the same time as it says in the article.

A flash of light is given off at the center of the traincar just as the two observers pass each other. The observer on board the train sees the front and back of the traincar at fixed distances from the source of light and as such, according to this observer, the light will reach the front and back of the traincar at the same time.

This is the part that is physically wrong

according to this observer, the light will reach the front and back of the traincar at the same time.

What is true is "according to this observer, the light from the front and back of the traincar will return and reach him at the same time."

Please comment.

 

[Neddy Bate]

I am struggling with this simultaneity thought experiments (especially as they are described in http://en.wikipedia.org/wiki/Relativity_of_simultaneity#The_train-and-platform_thought_experiment

If the light beams are reduced to single photons and having mirrors at the ends, you end up with the photons traveling in two directions at once. What I mean is that if the person in the middle of the train fires two photons from his photon gun, one to the front and one to the rear, do the photons reflect from the end walls at different times such that depending on where you are looking at the situation, in one situation the photon is still heading toward the reflector but in another it is already turned around and heading back?
I said something about this yesterday and it is the speed of light that is the physics in question. The speed of light is the same in all frames. So the only way you can measure the speed of light is to send light there and back, a two way speed of light.
So it isn't that the person in the train sees light hit both ends at the same time, but the light returning to him comes back at the same time. A two path. There is no way he can determine if the photons hit the end walls at the same time as it says in the article.

What is true is "according to this observer, the light from the front and back of the traincar will return and reach him at the same time."

Please comment.

In Einstein's original thought experiment, the lightning strikes originate at the far ends of the train, and then the light travels toward the middle of the train.
Einstein's observers are both located at the midpoint between the lighting strikes, so they are in the ideal location to determine whether the lightning strikes were simultaneous or not. All they have to do is compare whether the light from the lightning strikes reach them at the same time or not. In this case, the observer on the platform determines they were simultaneous, but the observer on the train determines they are not.

But in the wikipedia article, they change the problem around so that the photons are emitted from the middle of the train, and travel out to the far ends of the train.
In this case, there is slightly different reasoning involved. The observer on the train operates under the assumption that the "one-way" speed of light is the same in all directions in his inertial reference frame. Since he knows he sent the photons simultaneously from the midpoint of the train, he must conclude the photons will reach the end walls of the train simultaneously. He is not in the right location to verify this himself, but it follows from the assumption of "isotropy" of light, which is the assumption that the one-way speed is the same in all directions. Your question seems to be based on the idea that light might not be isotropic, which is a different problem altogether. These thought experiments are only designed to show how simultaneity of events depends on the frame of reference.

 

[Robittybob1]

In Einstein's original thought experiment, the lightning strikes originate at the far ends of the train, and then the light travels toward the middle of the train.
Einstein's observers are both located at the midpoint between the lighting strikes, so they are in the ideal location to determine whether the lightning strikes were simultaneous or not. All they have to do is compare whether the light from the lightning strikes reach them at the same time or not. In this case, the observer on the platform determines they were simultaneous, but the observer on the train determines they are not.

But in the wikipedia article, they change the problem around so that the photons are emitted from the middle of the train, and travel out to the far ends of the train.
In this case, there is slightly different reasoning involved. The observer on the train operates under the assumption that the "one-way" speed of light is the same in all directions in his inertial reference frame. Since he knows he sent the photons simultaneously from the midpoint of the train, he must conclude the photons will reach the end walls of the train simultaneously. He is not in the right location to verify this himself, but it follows from the assumption of "isotropy" of light, which is the assumption that the one-way speed is the same in all directions. Your question seems to be based on the idea that light might not be isotropic, which is a different problem altogether. These thought experiments are only designed to show how simultaneity of events depends on the frame of reference.

In the Einstein case the lightning strikes were simultaneous but not sensed as simultaneous by the person in the train because he was moving but he does NOT realize he is moving, so he assumes the lightning struck the front first. I have no problem with Einstein's reasoning.

Isotrophy of light - I don't have a problem with that either, but as they say inside an inertial moving frame of reference there is no experiment that can be done to show that the frame is in motion. If it was possible to measure the one way speed of light it would show photons released from the center of a moving carriage will take longer to reach the front than to reach the back. Yet return quicker from the front and take longer from the back, averages will still be the same.