How Is The Relativity Of Simultaneity Consistent With Physics And Relativity

[rede96]

There is a causal relatinship between setting the fire and the fire reaching the right end. There is also a causal relationship between setting the fire and the fire reaching the left end. There is no causal relationship between the fire reaching the left end and the fire reaching the right end.

Not quite sure I understand that. Isn't fair to say that depending on where the fire is first set on the piece of wood will determine how the fire will spread?

So when the fire reaches the left and right side is determined by the initial ignition, hence why they are causally related.

 

[Dale]

Not quite sure I understand that. Isn't fair to say that depending on where the fire is first set on the piece of wood will determine how the fire will spread?

So when the fire reaches the left and right side is determined by the initial ignition, hence why they are causally related.

They are both causally related to the initial ignition, not to each other. I.e. The fire reaching the left does NOT cause the fire to reach the right, and vice versa.

 

[atyy]

OK, here is an attempt to do it with forces. The question is most easily addressed by the Lorentz tranformations for each of the two events, or by the addition of velocities. However, the OP asked, what, in detail, happens with a force that is symmetric in both frames? Let's set up everything in the frame on the ground, and never switch frames.

At t=0 the front and back walls of the train are at x=±L. They move to the right with constant velocity U, so x=±L+Ut (Eq 1a,b). Each wall has constant charge density, and the walls are oppositely charged, generating a constant E field between them.

At t=0, two charges q of opposite sign and rest mass m are released from x=0. They experience constant forces in opposite directions f=±qE.

Starting with Newton's second law f=dp/dt, gives p=p_u±ft.

Substituting p=m_vV, where m_v is the relativistic mass, gives m_vV=m_uU±ft

Solving for V, and http://integrals.wolfram.com/index.jsp" over time to get displacement gives x(t)=±{sqrt[(m_uU)±ft)^2+m^2]∓sqrt[(m_uU))^2+m^2]}/f (Eq 2a,b).

Choosing specific values for all constants (U<1 since c=1; m_u=m/sqrt(1-U^2)), and http://fooplot.com/" Eq 1 and 2 to obtain the t values where they intersect, seems to indicate that the backward charge intersects the back wall before the forward charge intersects the front wall, consistent with answers obtained by changing frames. Corrections for conceptual^* and algebraic errors are of course welcome

*I neglected the self force

 

[rede96]

They are both causally related to the initial ignition, not to each other. I.e. The fire reaching the left does NOT cause the fire to reach the right, and vice versa.

Ah, ok. I see. Thanks

 

[rede96]

They are both causally related to the initial ignition, not to each other. I.e. The fire reaching the left does NOT cause the fire to reach the right, and vice versa.

After thinking about this for a while, I was wondering, there is some dependency between the fire spreading to the left and the fire spreading to the right.

Using a different example:

I get into my car, turn my engine on, put it in gear and put my foot down on the accelerator. There is causal relationship between the front of my car moving off and the accelerator being depressed and there is a causal relationship between the back of my car moving off and the accelerator being depressed.

Making this analogous to the wood and fire, you would say that the front of my car moving off does not cause the back of the car to move off.

However, I would say that that the physics of the car means that it is not possible for the front to move without the back moving. So they are dependent events. (If that is the right terminology)

In my frame the front and back of the car move simultaneously. As they are dependent, this is the proper sequence that all other observers must agree, even though certain frames may measure the front and back movements differently.

I see this being the same as the fire burning on the wood. The physics of the wood and where the fire was lit will determine how the fire will spread. So the movement of the flame is ‘predetermined’ (without going into quantum physics!)

Therefore, if it just so happens that the fire reaches the ends of the wood simultaneously, this must the sequence agreed by all observers. Even though some might measure a different result.


Anyway, the point being that in the case of the wood on fire or my car moving off, there is absolute simultaneity. E.g. both ends of my car must move off together and flame must spread to each end equally.

Any observations that show a different result do not accurately describe the events.

 

[harrylin]

OK thanks all of you for your effort, but I do not understand your answers.
Forget a moment about the relativity of simultaneity, if fire spreads out in two directions with every thing being equal is there any reason for the fire going in one side faster than the other, or the ball flying in one direction faster than the other? this is physics and we need to have an answer and rule why this should happen.
Here is another such experiment, suppose we have a pool and we pure water directly in the middle of the pool and the water is spreading out to both sides, is there a reason why the water should arrive to one end of the pool before the other? farther more if the pool is an exact rectangle the water will arrive to the left and right sides (perpendicular to the direction of motion) simultaneously so why is this not happening in the direction of motion (and the same can be said for the ball and fire in which going sideways will yield simultaneous results).

You already received a number of replies, but perhaps the following qualitative explanation may help.

"every thing being equal" implies that you deem the forest or house that is burning to be in rest. For a forest in rest (homogeneous and without wind), we expect the fire to go at the same speed in both directions.

Now the new thing with SR is that for a forest (or water waves) in motion, this is not the case. For example, if you use a reference system in which the forest (or swimming pool) is going at almost the speed of light, the fire will not in one direction go faster than the speed of light; that would be against the laws of physics.

Thus we predict that as measured in such a reference system, the fire will propagate less fast in the same direction as the forest than in the opposite direction. The transformation equation with which you can calculate this has already been mentioned.

Harald

 

[Dale]

rede96, I applaud you for really directly addressing the most challenging topic of special relativity in this manner. This is hard to learn, and once you grasp it, everything else will be "relatively" easy.

After thinking about this for a while, I was wondering, there is some dependency between the fire spreading to the left and the fire spreading to the right.

No, there is not. The fire spreading to the left could be extinguished at any time after ignition and the fire spreading to the right would still reach the right end.

I get into my car, turn my engine on, put it in gear and put my foot down on the accelerator. There is causal relationship between the front of my car moving off and the accelerator being depressed and there is a causal relationship between the back of my car moving off and the accelerator being depressed.

Yes, this is correct.

Making this analogous to the wood and fire, you would say that the front of my car moving off does not cause the back of the car to move off.

No, this is not correct. In fact, there is a causal relationship between the front moving and the back moving. Assuming a standard front-wheel drive vehicle the chain of causality goes as follows: the accelerator is depressed which causes the front wheel to move which causes stresses in the car frame which cause the rear wheel to move.

However, I would say that that the physics of the car means that it is not possible for the front to move without the back moving. So they are dependent events. (If that is the right terminology)

It is possible for the front to move without the back moving. The front is the cause so it happens first. If the car is chopped in half at any time before the stresses are transmitted from the front to the back then the front can move without moving the back.

In my frame the front and back of the car move simultaneously. As they are dependent, this is the proper sequence that all other observers must agree, even though certain frames may measure the front and back movements differently.

Actually, the way the laws of physics work out ensures that if two events are causally related then all frames agree that the cause came before the effect and conversely if two events are simultaneous in any frame then the laws of physics ensure that they cannot be causally related.

 

[rede96]

rede96, I applaud you for really directly addressing the most challenging topic of special relativity in this manner. This is hard to learn, and once you grasp it, everything else will be "relatively" easy.

Thanks for that:0) I consider myself to be a reasonably intelligent person, masters degree and good job etc. but this relativity stuff really makes me feel completely stupid at times!

conversely if two events are simultaneous in any frame then the laws of physics ensure that they cannot be causally related.

Wow, I'd not understood that before. That'll take some thinking about.

You already received a number of replies, but perhaps the following qualitative explanation may help.

"every thing being equal" implies that you deem the forest or house that is burning to be in rest. For a forest in rest (homogeneous and without wind), we expect the fire to go at the same speed in both directions.

Now the new thing with SR is that for a forest (or water waves) in motion, this is not the case. For example, if you use a reference system in which the forest (or swimming pool) is going at almost the speed of light, the fire will not in one direction go faster than the speed of light; that would be against the laws of physics.

Thus we predict that as measured in such a reference system, the fire will propagate less fast in the same direction as the forest than in the opposite direction. The transformation equation with which you can calculate this has already been mentioned.

Harald

I assume you mean the forest is moving near the speed of light wrt to another frame. And that this second frame would observe the fire propagating less fast in the direction of travel. Is that right?

So, in essence SR doesn't just state that the laws of physics are the same in all frames but also implies that we must observe all other frames to obeying the laws of physics with reference to our frame? (e.g. hence why c is always constant.)

However, the point I think the OP and I were trying to make (Please correct me if I am wrong) is that the fire can not propagate at 'two' different speeds. So only one result must be correct. Right?

Unless there is some link between quantum entanglement and SR. In so much as the result depends on who is doing the measurement! (I know that is very tenuous but it was an interesting thought!)

 

[PAllen]

I don't know if it will help the OP, but I'll take a crack at expanding one of the OP examples to show what features are invariant versus not.

Imagine on a train you simultaneously (from your point of view) turn over sand timers at each end of wooden stick and light the middle of the stick. You observer that the fire reaches each end of the stick simultaneously, and also that each sand timer runs out just as the fire reaches it.

Every observer will agree that as the fire reaches each end, the corresponding sand timer has run out. This constitutes a local measurement which everyone agrees on (you could take a picture of the fire reaching the end and the last sand falling; no one would see different result on the picture).

HOWEVER, for an observer relative to whom the train was moving fast, the sequence of events would be very different from the train observer. They see that one of the timers was turned first, then the center was lit, then the other timer was turned. They would see the stick burn faster toward the timer that was turned 'early', such that they would agree that the "stick end burn/timer run out" events were each simultaneous, even though the fire reached one end faster.

 

[harrylin]

[...] I assume you mean the forest is moving near the speed of light wrt to another frame. And that this second frame would observe the fire propagating less fast in the direction of travel. Is that right?

So, in essence SR doesn't just state that the laws of physics are the same in all frames but also implies that we must observe all other frames to obeying the laws of physics with reference to our frame? (e.g. hence why c is always constant.)

Not clear what that means; the laws of physics (incl. the speed of light) must be obeyed wrt all inertial reference systems. That implies a different concept of "relative speed" as with Newton.

So, you measure the speed of light to be c, that means wrt your reference system (for example your lab, which is sufficiently inertial for short measurements). That also means that you cannot measure it to be c wrt a rocket that is also moving wrt your system. But if in the rocket an approximate inertial reference system is set up, then with that system the speed of that same light ray is measured to be c wrt that rocket. And you can explain that by the way the rocket measures, claiming that their measurement is wrong and yours is right. But the rocket can say just the contrary.

However, the point I think the OP and I were trying to make (Please correct me if I am wrong) is that the fire can not propagate at 'two' different speeds. So only one result must be correct. Right?

See above.

]
Unless there is some link between quantum entanglement and SR. In so much as the result depends on who is doing the measurement! (I know that is very tenuous but it was an interesting thought!)

Those are very different things. In QM what matters, is if a measurement is done or not. In SR one has to define which measurement system is used.

Harald

 

[rede96]

Not clear what that means; the laws of physics (incl. the speed of light) must be obeyed wrt all inertial reference systems. That implies a different concept of "relative speed" as with Newton.Harald

What I was trying to say is that if you and I measure the same thing and get different results, we both can't be right. (However, we both could be wrong!)

2 + 2 will always equal 4, even if someone may measure it to be 3 due to the effects of relativity.

 

[Dale]

What I was trying to say is that if you and I measure the same thing and get different results, we both can't be right.

Sure, but what does it mean for you and I to measure the same thing? Some quantities are relative, meaning that they only have meaning relative to some frame of reference.

So, if you and I are driving opposite directions on a freeway and we each measure the speed of some car on my side of the freeway then we could correctly say "the car is moving at 0 kph relative to me", "the car is moving at 100 kph relative to the earth", and "the car is moving at 200 kph relative to you". All three statements are correct since they are all referring to different things, and either of us can make any of those three statements.

What neither of us can do is correctly say only "the car is moving at X kph". That statement has no meaning since speed is a relative quantity.

 

[rede96]

Sure, but what does it mean for you and I to measure the same thing? Some quantities are relative, meaning that they only have meaning relative to some frame of reference.

So, if you and I are driving opposite directions on a freeway and we each measure the speed of some car on my side of the freeway then we could correctly say "the car is moving at 0 kph relative to me", "the car is moving at 100 kph relative to the earth", and "the car is moving at 200 kph relative to you". All three statements are correct since they are all referring to different things, and either of us can make any of those three statements.

What neither of us can do is correctly say only "the car is moving at X kph". That statement has no meaning since speed is a relative quantity.

Yes of course. But that is not what I mean. We can measure the car moving at various speeds due to our frame wrt to the car. However, there is only one proper speed for the car.

For example, let’s say the car is going to attempt to jump a gorge. The driver knows in his frame that he must be traveling at exactly 100km/hour in order to jump it. Any slower and he will not make the gap, any quicker and he will overshoot the ramp on the other side.

So I watch the driver in his car jump the gorge successfully. Me being a bit of an idiot, decide to try it with a similar gorge that is in my frame.

So I measure his speed in order jump the gorge successfully myself. However, as I am moving wrt to driver I measure the speed at say 80km/hour. If I use that speed to jump a similar gorge in my frame, I will not make the jump. Not a good thing!

So I would have to allow for the fact that I was moving wrt to his frame when I took the measurement and recalculate my result in order to get 100km/hour.

All if which is a pretty bad example to say that all measurements are valid, however in order to use that measurement in any practical way in my frame, I would need to allow for the fact that I was moving wrt to the frame I took the measurement.

Therefore, there is only one proper result and that is as measured in the rest frame. (rest wrt to the event.)

 

[Dale]

However, there is only one proper speed for the car. ...
Therefore, there is only one proper result and that is as measured in the rest frame. (rest wrt to the event.)

The word "proper" has a kind of reserved meaning in special relativity. It refers to something as measured in a given object's rest frame. E.g. "proper time" is the time measured by a clock carried by a specified object, and "proper length" is the length of an object in its own rest frame. So the "proper speed" of a car would usually be understood to be the speed of a car in its own rest frame, which would always be 0 by definition.

Btw, events do not have velocity, so it is impossible for something to be at rest wrt an event.

For example, let’s say the car is going to attempt to jump a gorge. The driver knows in his frame that he must be traveling at exactly 100km/hour in order to jump it.

That is unfortunate for the driver since in his frame he is always traveling at exactly 0, by definition. I think that what you want to say is that he must be traveling at exactly 100 kph relative to the gorge.

There are some laws of physics that determine that the driver must go at 100 kph relative to the gorge. In any other frame, you can apply those same laws of physics to determine what speed the driver must go in that frame. Each frame will get different speeds relative to that frame, but that does not imply any contradiction. In the end all frames will agree if he makes it or not.

 

[rede96]

The word "proper" has a kind of reserved meaning in special relativity. It refers to something as measured in a given object's rest frame. E.g. "proper time" is the time measured by a clock carried by a specified object, and "proper length" is the length of an object in its own rest frame. So the "proper speed" of a car would usually be understood to be the speed of a car in its own rest frame, which would always be 0 by definition.

Btw, events do not have velocity, so it is impossible for something to be at rest wrt an event.

That is unfortunate for the driver since in his frame he is always traveling at exactly 0, by definition. I think that what you want to say is that he must be traveling at exactly 100 kph relative to the gorge.

OK. Thanks for that. I know I need to learn the right terminology, but it is very fustrating at times!

There are some laws of physics that determine that the driver must go at 100 kph relative to the gorge. In any other frame, you can apply those same laws of physics to determine what speed the driver must go in that frame. Each frame will get different speeds relative to that frame, but that does not imply any contradiction. In the end all frames will agree if he makes it or not.

Again, I can see what you are saying but that does not address my point.

Each frame may get different speeds relative to the rest frame (the gorge) and I can see how that info can be used so to describe what they see.

However, that info is NOT transferable (in its observed form) into the other observer’s rest frames to use in order to repeat a similar situation.

For example: Assume that there were 3 other observers on three other planets. All moving wrt to my rest frame, where I am stood by the gorge.

As we have all visited each other's rest frame in the past, we know that we all have a gorge that is of identical width. We know we all have identical cars too. What we didn't do is swap info on how fast the car must travel wrt to the gorge in our own rest frames in order to jump the gorge correctly.

If the other 3 observers, who are moving wrt to my gorge, watch me jump it in my car, unless they adjust their result for their relative motion, they will all crash and burn!

So the point is that we can have many different results to describe the physics of a given situation, however there is only one correct result that will allow that situation to be repeated correctly in our respective rest frames.

The implications of this are that if we want to use any physics we observe in other frames not at rest wrt to us, we would need to re-calculate the results for our own rest frame.

So although I can't say I am at rest, I can say that all rest frames are equal. (Which is what SR was says anyway isn't it?)

 

[Dale]

However, that info is NOT transferable (in its observed form) into the other observer’s rest frames to use in order to repeat a similar situation.

The info is transferable. The process of transferring information from one frame to another is called "coordinate transformation".

The principle of relativity does not imply that you can skip coordinate transformations altogether, but rather that there is a class of coordinate systems in which the laws of physics have the same form. Those coordinate systems are called "inertial" and they are related to each other via the Lorentz transform.

 

[rede96]

The info is transferable. The process of transferring information from one frame to another is called "coordinate transformation".

The principle of relativity does not imply that you can skip coordinate transformations altogether, but rather that there is a class of coordinate systems in which the laws of physics have the same form. Those coordinate systems are called "inertial" and they are related to each other via the Lorentz transform.

Ah ok. Thanks for that DaleSpam.

So what I was saying is correct, just not using the right lingo. :~)

If I make an observation in a different frame than mine, I can use the Lorentz transform to make what I observed right for my frame.

This is now drawing me to make another conclusion. We can use the Lorentz to quite literally transform all observations into one common frame of reference, which is the 'rest' frame. This is where the laws of physics have the same form.

 

[Dale]

We can use the Lorentz to quite literally transform all observations into one common frame of reference, which is the 'rest' frame. This is where the laws of physics have the same form.

The laws of physics have the same form in any frame, but yes, you can use the Lorentz transform to transform all observations into any arbitrary inertial frame.