On the idea of time in physics-relativity

[Syne]

A variable speed of light is not the only way that the flashes could be observed to be simultaneous. They did away with the aether theory, that says that there is a background where light travels at the same speed from a single frame. This was then replaced by Einsteins notion of spacetime, where spacetime dilation and contraction corrects for the speed of light in both frames.

You are right. The flashes could be observed as simultaneous in both frames if, and only if, both frames were not comparing the same flashes. This is trivially so. And your arm-waving about what most in this thread have already demonstrated they know does nothing to help your woefully ignorant case.

The only type of diagram that I think could serve as an accurate depiction of the speed of light would be Minkowski Diagrams . Like in my derivation in post #266, it assumes that distance is c t. It is also said that Minkowski Diagrams are accurate when dealing with these kind of problems. So most of the confusion here is just caused by the use of inaccurate diagrams. It is like you have all taken a laymans descriptions, in a book targeting layman, and then have posted it up as being actually science. If you wanted to know what the real science says about this problem would would want to use Minkowski Diagrams .

Now you are just transparently aping a point someone else made in refute of your nonsense.

It is really like you guys are saying that there is an aether. Having a difference of relative motion relative to photons is what aether theory says. So then everytime you say that there is a difference in relative motion relative to the photon you are just saying that there is really an aether. I think mazula would love to hear about this and these types of alternative theories, you should all rederict them to the thread Luminiferous-Aether-Exists! in the alternative theories section.

You are just too stubbornly dense to see that RoS is a necessary consequence of there not being "a difference in relative motion relative to the photon" (if I am even reading that word salad correctly).

 

[origin]

I think I actually got it from reading about quantum mechanics not relativity.

Please supply the source then.

Since you have implied you did not misspeak except that it was quantum mechanics application to simultaniety and not special relativity we are again down to you are either a liar or a fool.

So which is it?

I guess the third choice is to withdraw you claim if you can not find a source.

 

[Neddy Bate]

The only type of diagram that I think could serve as an accurate depiction of the speed of light would be Minkowski Diagrams .

There is an online applet that let's you make Minkowski diagrams:

http://www.trell.org/div/minkowski.html

1. Under "relative velocity," put in something like .5c.

2. There are two events, event A and event B. Event A is always located at x=x'=0 at time t=t'=0.

3. You get to choose the location and time of event B. For a train that is 5 units long in the platform frame, you put in x=5. To make event B simultaneous with event A in the platform frame, you put in t=0.

4. Hit the "calculate" button at the bottom. It tells you the time and location of event B in the train frame is t'=-2.88 and the location is d'=5.77.

5. You can even "play" the t worldline at the bottom and see the two events pop up simultaneously on the worldline. Next, when you "play" the t' worldline, you will see the two events pop up at different times on the worldline.

 

[Syne]

There is an online applet that let's you make Minkowski diagrams:

http://www.trell.org/div/minkowski.html

Nice applet. Good find.

 

[arfa brane]

What does setting the speed of light to 1 really mean? What does it "do"?

If c/c = 1 then setting the speed to 1 means everywhere c appears, divide it by itself. Does that make c 'dimensionless', or do we want c = 1 to retain its "metres per second" physical meaning?
Suppose that first you multiply t by c so physically you have a distance, then "setting c to 1" after this means you have t/c which is square seconds per metre.

Maybe you just set it to 1 and keep the physical units and don't consider that mathematically it's c/c? In other words you scale c's value but not 'direction'?

 

[Prof.Layman]

What does setting the speed of light to 1 really mean? What does it "do"?

If c/c = 1 then setting the speed to 1 means everywhere c appears, divide it by itself. Does that make c 'dimensionless', or do we want c = 1 to retain its "metres per second" physical meaning?
Suppose that first you multiply t by c so physically you have a distance, then "setting c to 1" after this means you have t/c which is square seconds per metre.

Maybe you just set it to 1 and keep the physical units and don't consider that mathematically it's c/c? In other words you scale c's value but not 'direction'?

I got c = 1 the other day, but it was because I didn't make a c^2 a c^4 when moving into the square root when trying to find a reltion between time and distance. I then got this equation where distance was replaced with time in the proper time equation, and then solved for c to get 1. I couldn't believe it so I went back to check it, since I couldn't beleive I always have this one popping up. So I think somewhere you have made d = t.

I don't think the one really has any meaning, other than putting it in creates one less c variable in the equation. Velocity over another velocity is unitless. You can often say v is a percent of the speed of light, so then it just acts like a difference of a ratio of that percentage.

I think it is actually $$ \frac {a^{2} - b^{2}}{a^2} $$ but actually in a different form. I have read that no one really knows what this 1 is, and didn't just want to assume that is what it is, but from my proof in post #266, I think that is what it really is if you had everything under the square root.

 

[Pete]

The origin of the flashes is necessarily either co-moving with the train or the platform. Here, I made them co-moving with the train. This is what is meant by them originating from one frame.

If the origin is an instantaneous event, like a lightning bolt, then it doesn't have a well defined rest frame at all.

Which frame the flashes are co-moving with or simultaneous in does not matter one wit in demonstrating relative simultaneity.

True, but it is potentially something where intuition can get in the way. I've had discussions where people think that it matters whether the light comes from a source on the train, or a source on the platform
It's also a sneaky way of sidestepping issues related to ballistic theories of light propagation.

The relative speed is corrected in the latest gifs I posted (excuse the earlier, hasty exaggeration). It is not necessary to take length contraction into account to depict the RoS, only relative speed and the constancy of the speed of light. The relativity of simultaneity is a consequence of the two postulates of SR, just like time dilation and length contraction.

This is true from one perspective.

But I think that at a deeper level, length contraction and relative simultaneity are two sides of the same coin. You can't have one without the other.

This is easy to see using Minkowski spacetime. Consider - what is a length (distance), in terms of spacetime intervals?
Length is the magnitude of a spacetime interval between simultaneous events.

 

[eram]

But I think that at a deeper level, length contraction and relative simultaneity are two sides of the same coin. You can't have one without the other.

This is easy to see using Minkowski spacetime. Consider - what is a length (distance), in terms of spacetime intervals?
Length is the magnitude of a spacetime interval between simultaneous events.

LC and TD go hand-in-hand, but they only come about when trying to make both frames mutually symmetrical (sort of)

RoS is always present.

 

[Syne]

The origin of the flashes is necessarily either co-moving with the train or the platform. Here, I made them co-moving with the train. This is what is meant by them originating from one frame.

If the origin is an instantaneous event, like a lightning bolt, then it doesn't have a well defined rest frame at all.

Actually, the frame in which the events are simultaneous is, by definition, necessarily co-moving with those events, whether instantaneous or not. The proper time of any two events is that of the frame in which the time between them is minimal, as any other frame will introduce time dilation (delay) between the events.

Which frame the flashes are co-moving with or simultaneous in does not matter one wit in demonstrating relative simultaneity.

True, but it is potentially something where intuition can get in the way. I've had discussions where people think that it matters whether the light comes from a source on the train, or a source on the platform
It's also a sneaky way of sidestepping issues related to ballistic theories of light propagation.

Yeah, the "source" (co-moving) frame is only the one in which the events are simultaneous. This frame can be determined even if one source is on the train and the other on the platform. It is just simpler to avoid introducing a possible third frame.

It is not necessary to take length contraction into account to depict the RoS, only relative speed and the constancy of the speed of light. The relativity of simultaneity is a consequence of the two postulates of SR, just like time dilation and length contraction.

This is true from one perspective.

But I think that at a deeper level, length contraction and relative simultaneity are two sides of the same coin. You can't have one without the other.

This is easy to see using Minkowski spacetime. Consider - what is a length (distance), in terms of spacetime intervals?
Length is the magnitude of a spacetime interval between simultaneous events.

Yes, it is a bit trivial that LC and RoS are two sides of the same coin, both being direct consequences of the two postulates of SR. That does not necessarily require accounting for one to demonstrate the other.

Length between events is necessarily maximal in the frame in which the time is minimal, i.e. the proper frame of the events. There is always a frame which can be considered the natural source of the events.

 

[Robittybob1]

Both frames could possibly see two light signals as simultaneous,...

...but physics dictates that these could not be the same signals,...

...as the platform observer would not observe them to originate from the ends of the train.

With the train traveling less than c, the platform observer cannot reach the intersection of the two light spheres before the front one catches him. If both agree on simultaneity then both would disagree on the origin of the signals, which necessarily means that they cannot be comparing the observations of the same signals.



Corrected above.



No, as shown above, spatially separated events that can be observed as simultaneous in one frame cannot be so in another. Any such mutually observation of simultaneity is necessarily of a different set of events.

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

 

[eram]

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

The second diagram with blue light is a combination of Galilean relativity and the speed of light being the same in both frames.

"Platform Joe" would not observe them coming from the ends of the train. As Syne said, "these could not be the same signals,..."


In SR, they are. But simultaneity is violated as a result.

 

[Robittybob1]

The second diagram with blue light is a combination of Galilean relativity and the speed of light being the same in both frames.

"Platform Joe" would not observe them coming from the ends of the train. As Syne said, "these could not be the same signals,..."


In SR, they are. But simultaneity is violated as a result.

Why do you say simultaneity is violated. Either you haven't understood it properly or it has been found violated.
What does Einstein actually say about this?

It seems Einstein looked at a combination of 3 events but above we are just looking at 2 events (that is the two lightning strikes).

 

[Robittybob1]

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 train-car 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 train-car at the same time.

http://en.wikipedia.org/wiki/Relativity_of_simultaneity

This article is worded wrongly too, for it is the two way speed of light that you have to take into account. The light doesn't just go from the middle to the front but from the middle to the front and back again to the person in the middle again. And for the back of the train the light goes from the middle to the back and back again to the person in the middle again. When this is measured it will seem that the light takes just as long one way or the other.
He can't see it unless the light returns to him. The 2 legs of the light path take different length of times but added together they equal.

 

[Pete]

Actually, the frame in which the events are simultaneous is, by definition, necessarily co-moving with those events, whether instantaneous or not.

By what definition?
An event isn't doesn't have the property of motion, so it's meaningless to assign it a rest frame.
The frame in which two events are simultaneous is exactly that and nothing more.

The proper time of any two events is that of the frame in which the time between them is minimal, as any other frame will introduce time dilation (delay) between the events.

Hmm. If I understand correctly (not guaranteed), proper time is the magnitude of a timelike spacetime interval. This is the time between two events in the frame in which those events occur at the same location.

If two events are simultaneous in some frame, then the interval between those events is spacelike, and the magnitude of that interval is the proper length of an object that has one end at one event and one end at the other event.

Length between events is necessarily maximal in the frame in which the time is minimal

Yes

i.e. the proper frame of the events.

I haven't seen the phrase "proper frame of the events" used before. That might simply be my own ignorance, but I would have thought that "proper" refers to lengths and times, not frames.
Edit - According to Wikipedia and other online usage, "proper frame" means "rest frame".

There is always a frame which can be considered the natural source of the events.

I haven't seen that interpretation before, and I don't like it. Events are just events - they don't have a source, they don't have the property of motion, and they thus don't have a natural frame.

Is there a reference where you have seen this interpretation used that you can point me to?

 

[Write4U]

Those new gifs still do not show the actual time when the flash must be triggered.

The flash is triggered when both observers are equidistant from the front and back of the train. This is still lacking in the illustrations.

 

[Pete]

I see the person on the moving platform goes through the second light cone twice. If the animation and the speed of the platform were in the right proportion what difference would that make?
I see there is an intersection of the two light cones that crosses the path of the person on the moving platform so it looks like it would be possible to position the person at the right location that he intercepted this doubled portion and then both the person on the train and the platform would say the lightning struck simultaneously.
Can anyone else see this possibility (those simultaneous events would not be simultaneous themselves)?

The animation confuses things by offsetting the train sideways from the platform. It's simpler if things are kept one dimensional.

But, consider the case where the train observer high-fives the platform observer at the instant the flashes meet.
Both observers would then be at the intersection of the two light cones.
But, this doesn't mean they would both say they occurred simultaneously, because for the train observer one flash occurred further away than the other flash.

Don't be fooled by Syne's depiction of the flashes coming from the platform. According to the train observer, the platform moves away from where the flashes originate.

 

[hansda]

Let us consider this "thought experiment".

Suppose an observer is standing on a platform of a train-station. A passenger is travelling in the train. This train is moving past the observer/platform at a uniform speed. Consider both the observer and the passenger in the train are wearing/having same identical watch/clock.

If the train is moving at a slower, non-relativistic speed; when the passenger in the train reaches the observer's position in the platform, both their watch/clock will show same time signifying simultaneity.

Now, if the train travels at a relativistic speed; when the passenger in the train reaches the observer's position in the platform, will both their watch/clock show the same time?

 

[Pete]

If the train is moving at a slower, non-relativistic speed; when the passenger in the train reaches the observer's position in the platform, both their watch/clock will show same time signifying simultaneity.

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.
But that's not relevant to relative simultaneity, which is about whether things that happen in different places happen at the same time or not.

 

[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.
But that's not relevant to relative simultaneity, which is about whether things that happen in different places happen at the same time or not.

What is your answer for my last question in the previous post?

[Consider both their watch/clock show the same time in previous(non-relativistic) case.]

 

[Syne]

Actually, the frame in which the events are simultaneous is, by definition, necessarily co-moving with those events, whether instantaneous or not.

By what definition?
An event isn't doesn't have the property of motion, so it's meaningless to assign it a rest frame.
The frame in which two events are simultaneous is exactly that and nothing more.

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​

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

The proper time of any two events is that of the frame in which the time between them is minimal, as any other frame will introduce time dilation (delay) between the events.

Hmm. If I understand correctly (not guaranteed), proper time is the magnitude of a timelike spacetime interval. This is the time between two events in the frame in which those events occur at the same location.

If two events are simultaneous in some frame, then the interval between those events is spacelike, and the magnitude of that interval is the proper length of an object that has one end at one event and one end at the other event.

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).

Length between events is necessarily maximal in the frame in which the time is minimal

Yes

i.e. the proper frame of the events.

I haven't seen the phrase "proper frame of the events" used before. That might simply be my own ignorance, but I would have thought that "proper" refers to lengths and times, not frames.
Edit - According to Wikipedia and other online usage, "proper frame" means "rest frame".

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

There is always a frame which can be considered the natural source of the events.

I haven't seen that interpretation before, and I don't like it. Events are just events - they don't have a source, they don't have the property of motion, and they thus don't have a natural frame.

Is there a reference where you have seen this interpretation used that you can point me to?

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.