How Is The Relativity Of Simultaneity Consistent With Physics And Relativity

[hprog]

Hi.
The concept of relativity is that the laws of physics are the same in all inertial frames of reference.
As a result of relativity we have the relativity of simultaneity, which says that two events that are simultaneous in one inertial frame are not simultaneous in other frames.

Now consider we have a piece of wood and we put on a fire in exactly its middle, then according to the laws of physics (if the conditions are equal on both sides of the piece of wood) then the fire will arrive at the ends of the piece of wood simultaneously.
Or consider if we stand in the middle of a train and we trow two balls to the two ends of the train car with the same force, then according to physics the balls will arrive at the ends of the train simultaneously.

This is a result of the laws of physics and therefore according to relativity should be true regardless of the frame the situation is being observed.
However the relativity of simultaneity says that simultaneous events in one frame are not to be simultaneous according to another frame, so how is the situation to be explained?

(Note that every frame will agree on the middle point of objects since both halves are equaly contracted on frames that the object is in motion)

 

[bcrowell]

Hi, hprog,

In the two-balls version, there is nothing in the laws of physics that says that the balls have to have equal velocities. They just happen to have equal velocities in one frame.

In the fire version, there is nothing in the laws of physics that says that fire has to spread at equal speeds in both directions along a piece of wood that is moving with a certain velocity. The symmetry of the laws of physics only implies that the fire has to spread at equal speeds in both directions in a frame where nothing else breaks the symmetry, i.e., in a frame where the wood is at rest.

-Ben

 

[DaveC426913]

However the relativity of simultaneity says that simultaneous events in one frame are not to be simultaneous according to another frame, so how is the situation to be explained?

Wait wait.

Relatviity does not say that cannot be the same; it simply says they may not be the same.

Nothing in your scenarios would cause any frame to see those events as asimultanoeus, so both frames might see them the same (excepting some things you might do to change them).

What exactly is the problem?

 

[Naty1]

However the relativity of simultaneity says that simultaneous events in one frame are not to be simultaneous according to another frame, so how is the situation to be explained?

What situation??

oops, I just realized DaveC asked that...

So let me ask it this way: Are you asking if something would be non simultaneous from another inertial frame? from an accelerating frame?? Are your objects in an inertial frame or accelerating frame...say even rotating?

 

[Fredrik]

Nothing in your scenarios would cause any frame to see those events as asimultanoeus,

Did you perhaps mean "every" when you wrote "any"? The two events "fire reaches the left end of the piece" and "fire reaches the right end of the piece" aren't simultaneous to an observer with a non-zero (relative to the piece of wood) velocity component in the left-to-right direction.

What exactly is the problem?

The fire reaches both ends simultaneously in one frame, but not in another. So he has found something that's different in two frames, and is asking "hey wait a minute, wasn't everything supposed to be the same in both frames?"

A part of the answer is that the idea isn't that everything is the same. That wouldn't make much sense actually, because it would mean that if you get up from your chair and start walking towards the door, your speed relative to the chair would still be 0.

So what is the same? First of all, we need to understand that "the principle of relativity" is a rather loosely stated idea, so we shouldn't expect a complete answer to follow from it. The complete answer is contained in the theory that these ideas helped us find (i.e. special relativity). There are however lots of little details in the theory that could be interpreted as aspects of the principle of the relativity. For example, if A and B are two clocks, and the rate of change of B's clock in the frame comoving with A is slow by a factor of 25%, then the rate of change of A's clock in the frame comoving with B must also be slow by a factor of 25%. So I don't think it's possible to write down a complete answer.

One of the most important things that can be described as an aspect of the principle of relativity (the main thing really) is that equations that describe how properties of particles and fields change with time, can be stated in a coordinate-independent way. There's a slightly different version of each such equation associated with each inertial frame, but they will look more or less the same. (If a term that appears in the equation associated with one frame doesn't appear in the equation associated with another, it's just because its value is non-zero in the first frame and zero in the other). The coordinate-independent equations have coordinate-independent solutions, but there's a coordinate-dependent solution associated with each inertial frame. Example: The coordinate-dependent versions of Maxwell's equation associated with different inertial frames look the same, but the coordinate-dependent values of the E and B fields may be different in different frames.

 

[DaveC426913]

Did you perhaps mean "every" when you wrote "any"? The two events "fire reaches the left end of the piece" and "fire reaches the right end of the piece" aren't simultaneous to an observer with a non-zero (relative to the piece of wood) velocity component in the left-to-right direction.


The fire reaches both ends simultaneously in one frame, but not in another.

Ok. Sure.

So he has found something that's different in two frames, and is asking "hey wait a minute, wasn't everything supposed to be the same in both frames?"

And here I thought he was asking: "hey wait a minute, wasn't everythning supposed to be different in each frame?"

See here:

simultaneous events in one frame are not to be simultaneous according to another frame

 

[Fredrik]

He's arguing that the principle of relativity seems to say that everything is the same, and that relativity of simultaneity seems to contradict this by saying that this one thing isn't the same.

 

[DaveC426913]

He's arguing that the principle of relativity seems to say that everything is the same, and that relativity of simultaneity seems to contradict this by saying that this one thing isn't the same.

Hm. OK.

To which my response would be:

Relativity does not say "everything is the same", it says "everyone follows the same rules , even though that might (and often does) lead them to completely different results. And everyone who does observe the rules has an equally valid viewpoint."

 

[hprog]

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).

 

[russ_watters]

The fire can be moving at different speeds with respect to different observers and be different distances from different observers. This doesn't even have anything to do with Einstein - Newton and Galileo would be fine with this as well.

 

[Fredrik]

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,

There are many different ways to obtain this result. You could e.g. get it from the relativistic formula for addition of velocities. I think the best way to see it is by drawing a spacetime diagram, but you would have to work on understanding relativity of simultaneity first.

The fire can be moving at different speeds with respect to different observers and be different distances from different observers. This doesn't even have anything to do with Einstein - Newton and Galileo would be fine with this as well.

But in Galilean spacetime, a boost to a different inertial frame would change the velocities of the two "fronts" of the fire by the same amount, [strike]so that the two speeds would be the same in the new frame too[/strike] so that the two speeds in the new frame would differ from their values in the old frame by the same amount.

Edit: I corrected the last part after russ watters pointed out that I messed it up.

 

[hprog]

There are many different ways to obtain this result. You could e.g. get it from the relativistic formula for addition of velocities. I think the best way to see it is by drawing a spacetime diagram, but you would have to work on understanding relativity of simultaneity first.

You are using the velocity addition formula which is based on the relativity of simultaneity, so it can not be considered a solution rather it is part of the problem itself.
Again my question every thing being equal why should things on one side be different than the other, and why should it be (1) only for different frames, (2) and only in the direction of motion.

 

[hprog]

The fire can be moving at different speeds with respect to different observers and be different distances from different observers. This doesn't even have anything to do with Einstein - Newton and Galileo would be fine with this as well.

No, in physics if every thing is being equal than we should get equal results.
In fact you have not disagreed that in the same frame every thing will be equal and that even in different frames it will be equal for the perpendicular direction, although the relativity of simultaneity does not require it...
This is clearly because of equal things will yield equal results, and the relativity of simultaneity cannot change this without breaking general physics, unless you come up with a better answer.

 

[Fredrik]

I'm not going to spend a lot of time on finding a solution that doesn't require you to understand relativity of simultaneity first. Maybe there is one, maybe there isn't. What's important here is what SR says about this situation. The Lorentz transformation is a part of the definition of SR, and the addition of velocities formula follow easily from that, so "what SR says" is precisely what you get from that formula.

 

[russ_watters]

But in Galilean spacetime, a boost to a different inertial frame would change the velocities of the two "fronts" of the fire by the same amount, so that the two speeds would be the same in the new frame too.

No, one might go up while the other goes down, say, if you're in a frame traveling with one flame front that one is motionless while the other is moving at twice the speed it moves wrt to the object that's burning.

 

[russ_watters]

No, in physics if every thing is being equal than we should get equal results.

No, that's not what relativity means at all. Relativity says they obey the same laws of nature, not that you get the same results when measuring the same phenomena from different reference frames.

 

[Fredrik]

No, one might go up while the other goes down, say, if you're in a frame traveling with one flame front that one is motionless while the other is moving at twice the speed it moves wrt to the object that's burning.

Yes, I messed up what I was trying to say.

 

[atyy]

Quick guess: It's not sufficient to apply equal force. Equal force must be applied for equal time. While the force is being applied, the balls will move apart, so they are not released from exactly the same point.

 

[atyy]

OK, I give up. It's a mess. And they don't even have to learn about relativistic forces at http://ocw.mit.edu/courses/physics/8-033-relativity-fall-2006/lecture-notes/lecture11_dyn2.pdf" I'll stick with relativity of simultaneity.

 

[Dale]

All three scenarios fire/balls/water are governed by the same thing: relativistic velocity addition. If you know the velocity in one frame you use relativistic velocity addition to get the velocity in another frame. This ensures that if they arrive simultaneously in one frame then they do not in any other frame.

 

[PhilDSP]

Relatviity does not say that cannot be the same; it simply says they may not be the same.

That's an excellent point! In thinking about the meaning and use of the Lorentz transformation recently I've been led to the conclusion that the clearest and most indisputably valid use of the LT is to consider that it first of all provides the initial conditions for an invariant form of the wave equation for EM propagation. Physically meaningful results seem to occur when you restrict the choice of transformed values to t = t', both for setting the initial conditions for the solution of the wave equation and thereafter in evaluating it for other values of t.

 

[PhilDSP]

I imagine that last post raised a few eyebrows so I'll try to explain. If I'm not mistaken, from the 2 Lorentz transformation equations we can eliminate the mutual variables to arrive at 8 total equations:

x = \gamma (x' + vt') \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ t = \gamma (t' + \frac{vx'}{c^2})
x' = \gamma (x - vt) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ t' = \gamma (t - \frac{vx}{c^2})
x = \frac{c^2}{v}(t - \frac{1}{\gamma} t') \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ t = \frac{1}{v}(x - \frac{1}{\gamma}x')
x' = \frac{c^2}{v}(\frac{1}{\gamma}t - t') \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ t' = \frac{1}{v}(\frac{1}{\gamma}x - x')

This provides the inverse transformation without having to specify the change of direction of the velocity. That gives the Lorentz transformation special status in that it contains its own inverse transformation. While that seems to give it a basis for covariance, one might wonder if it, at the same time, destroys its value as a transformation in some way. At any rate, exactly 2 values of the variables x, x', t and t' may be chosen and the other 2 follow from the transformation.

If we choose to set t = t' = 0 (because we know the value of the wave equation for some parameter at that time) then x and x' are forced to be equal to zero. We force the origin of the coordinate systems both to be co-located. But for all other values where t = t', x and x' diverge at a linear rate proportional to v.

 

[rede96]

No, that's not what relativity means at all. Relativity says they obey the same laws of nature, not that you get the same results when measuring the same phenomena from different reference frames.

ok, I can see how we can measure an outcome differently. However, there can only be one outcome.

If I set fire to a piece of wood, the file will spread depending on what ever laws of physics are in effect.

However, there can only be one outcome, the fire will only spread in one way, despite what we measure. There is a causal relationship in effect here.

So my understanding of SR in the case mentioned is that different observers can measure different outcomes, however there is only one proper outcome.

 

[Fredrik]

I imagine that last post raised a few eyebrows so I'll try to explain. If I'm not mistaken, from the 2 Lorentz transformation equations we can eliminate the mutual variables to arrive at 8 total equations:
...
This provides the inverse transformation without having to specify the change of direction of the velocity. That gives the Lorentz transformation special status in that it contains its own inverse transformation.

The inverse transformation isn't among the equations you posted. The inverse would express t and x as functions of t' and x'. These equations are much prettier in matrix notation by the way, especially when we use units such that c=1: \begin{pmatrix}t&#039;\\ x&#039;\end{pmatrix}=\gamma\begin{pmatrix}1 &amp; -v\\ -v &amp; 1\end{pmatrix}\begin{pmatrix}t\\ x\end{pmatrix},\qquad<br /> \begin{pmatrix}t\\ x\end{pmatrix}=\gamma\begin{pmatrix}1 &amp; v\\ v &amp; 1\end{pmatrix}\begin{pmatrix}t&#039;\\ x&#039;\end{pmatrix}I also wouldn't say that there's something "special" about "containing its own inverse". Every square matrix with non-zero determinant does that. And the word "special" often refers specifically to determinant =1.

 

[Fredrik]

So my understanding of SR in the case mentioned is that different observers can measure different outcomes, however there is only one proper outcome.

Yes, the results of measurements will be different, but this isn't exclusive to SR and GR. Even in pre-relativistic physics (Newtonian mechanics in Galilean spacetime), different observers will have different result. For example, if you measure the velocity of the chair you're sitting on right now, you will get the result 0. If you get up and start walking in your positive x direction, and then measure the velocity again, the result will be something like -1 m/s.

I wouldn't describe this as "different outcomes", because that sounds too much like "one observer finds that Mike crashed his spaceship into an asteroid and died at the age of 30, while another finds that he missed the asteroid and lived to be a hundred". (I understand that you didn't mean that).

 

[PhilDSP]

The inverse transformation isn't among the equations you posted. The inverse would express t and x as functions of t' and x'.

I think I see what you're saying. I believe the 8 equations above express the Lorentz transformation, with all its permutations, in the most general unrestricted form. You've chosen to retrieve solutions given the pre-existence of values for x and t as specified by your beautiful and useful matrix formulation. I've chosen to search for solutions given the pre-existence of values for t and t'. So the related matrix formulation would be the, not as pretty, but maybe not lacking in usefulness form here:

\begin{pmatrix}x\\ x&#039;\end{pmatrix}=\frac{1}{v\gamma}\begin{pmatrix} \gamma &amp; -1\\ 1 &amp; -\gamma\end{pmatrix}\begin{pmatrix}t\\ t&#039;\end{pmatrix},\qquad<br /> \begin{pmatrix}t\\ t&#039;\end{pmatrix}=\frac{1}{v\gamma}\begin{pmatrix} \gamma &amp; -1\\ 1 &amp; -\gamma\end{pmatrix}\begin{pmatrix}x\\ x&#039;\end{pmatrix}

Here the matrix is identical for both the forward and inverse cases.

I had in mind when using the term special, the more general concept of transforms which can't necessarily be expressed in matrix form, for instance, the Fourier, Laplace and Hilbert transforms. The Fourier transform is especially interesting since the transform and its inverse are the same except for a change in the sign from positive to negative. But that sign change lies within the exponent. Has anyone attempted to express the Fourier transform using a matrix formulation? That would be extremely useful.

 

[russ_watters]

Right fredrick: I would say there is one event that different observers can measure differently. I don't like the usage of the word "outcome" either: 'the fire reaches both sides simultaneously' is two events, not one.

 

[Fredrik]

The inverse transformation isn't among the equations you posted.

I said a little too much in this sentence. The second line of equations is of course the inverse transformation.

 

[rede96]

Right fredrick: I would say there is one event that different observers can measure differently. I don't like the usage of the word "outcome" either:

Yes, I can see what you are getting at. 'Outcome' may not be the best description but I was struggling to find the right terminology.

'the fire reaches both sides simultaneously' is two events, not one.

This is where I need some help with the terminology. I don't see this as two 'events'. The fire can reach both sides simultaneously in one frame and be measured to reach the left (or right) first in another. However only one 'event' could have occurred. (Or whatever the right word is.)

So if two observers were to get together after the fire to compare notes, they would both argue their respective observation were true. But there is only one correct result.

The question is how to tell which one?

I would suggest that they would have to take their relative speed and distance to the burning wood into account. If they did that, they would both come up with the same answer for when the fire reached the end of the piece of wood.

This is what I would call the 'proper' result.

 

[Dale]

However, there can only be one outcome, the fire will only spread in one way, despite what we measure. There is a causal relationship in effect here.

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.

 

[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 dependant events. (If that is the right terminology)

In my frame the front and back of the car move simultaneously. As they are dependant, 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 dependant 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 dependant, 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.