Frame of reference of light

[questionposter]

I don't know if this has been done already because I don't know what to search for in the find, but, why wouldn't a photon appear to be traveling at 1.5 times the speed of light if you were moving in the exact opposite direction at exactly half the speed of light? Doesn't that defy a principal of relativity?

[DrRocket]

I don't know if this has been done already because I don't know what to search for in the find, but, why wouldn't a photon appear to be traveling at 1.5 times the speed of light if you were moving in the exact opposite direction at exactly half the speed of light? Doesn't that defy a principal of relativity?

 

Because velocities do not add linearly in special relativity.

 

 

http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html

[questionposter]

Because velocities do not add linearly in special relativity.

 

 

http://math.ucr.edu/...R/velocity.html

 

I can see it mathematically, but I can't see how it occurs in reality. Plus, what about things that "could" travel past the speed of light by accelerating the fabric of space rather than particles using kinetic energy?

 

Light is the limit of classical speed, but why is it the limit of what we can "see"? Is it because no matter what a photon couldn't actually ever give us information that it looks to be traveling faster than light because the limit is light? And if so, I don't completely understand that.

Edited August 12, 2011 by questionposter

[ajb]

I don't know if this has been done already because I don't know what to search for in the find, but, why wouldn't a photon appear to be traveling at 1.5 times the speed of light if you were moving in the exact opposite direction at exactly half the speed of light? Doesn't that defy a principal of relativity?

 

Appear yes, it is perfectly fine what you said, one can add speeds in that way. This is the "separation speed" as defined in the frame at which you are moving at speed 0.5c. There is no violation of special relativity here.

 

However this will not be a velocity as measured in any comoving inertial frame of reference, which is what you are really after. To do this you follow DrRockets' link and use the velocity addition formula.

[questionposter]

Appear yes, it is perfectly fine what you said, one can add speeds in that way. This is the "separation speed" as defined in the frame at which you are moving at speed 0.5c. There is no violation of special relativity here.

 

However this will not be a velocity as measured in any comoving inertial frame of reference, which is what you are really after. To do this you follow DrRockets' link and use the velocity addition formula.

 

So your saying that if I stood in one place and watched both of them move away from each other, I wouldn't measure the velocity to be greater than C, but what if I was one of the objects moving away form the other object? Would I not measure the photon to be traveling at faster than C if I knew my speed and knew the speed of light? Or is that what your saying by separation speed, as in if I was one of the objects observing this phenomena, I would observe the velocity to appear greater than C?

 

 

 

[J.C.MacSwell]

So your saying that if I stood in one place and watched both of them move away from each other, I wouldn't measure the velocity to be greater than C, but what if I was one of the objects moving away form the other object? Would I not measure the photon to be traveling at faster than C if I knew my speed and knew the speed of light? Or is that what your saying by separation speed, as in if I was one of the objects observing this phenomena, I would observe the velocity to appear greater than C?

 

From an inertial frame you cannot measure anything to be travelling at greater than c, or two things separating faster than 2c.

[questionposter]

From an inertial frame you cannot measure anything to be travelling at greater than c, or two things separating faster than 2c.

 

 

Well why was ajb saying that it can appear that way? How would it appear that way? I don't get what he was referring to when he said that you could actually measure the separation speed at greater than C, making it appear an object appear to be going faster than C to the other object?

 

 

[ajb]

Well why was ajb saying that it can appear that way? How would it appear that way? I don't get what he was referring to when he said that you could actually measure the separation speed at greater than C, making it appear an object appear to be going faster than C to the other object?

 

 

Say you set off two rockets one to the right of you and one to the left of you. Both travel at the same speed, lets say 0.6c relative to you. Then you could say that they are separating at a speed of 1.2c. But this is not the speed you measure either one of the rockets travelling nor is it the speed that one of the rockets will measure the other one travelling at.

 

Maybe I have just confused things...

[questionposter]

Say you set off two rockets one to the right of you and one to the left of you. Both travel at the same speed, lets say 0.6c relative to you. Then you could say that they are separating at a speed of 1.2c. But this is not the speed you measure either one of the rockets travelling nor is it the speed that one of the rockets will measure the other one travelling at.

 

Maybe I have just confused things...

 

Oh I get what your saying now, but I still don't see why you can add speeds same for everything except speeds that would add to be greater than C in reality. In reality, why wouldn't I measure the speed to be greater than C if I could measure speed the same way to get a speed that was less than C for other situations. If two rockets go left and right at 1mph, doesn't one of them measure the other to be going at 2mph? But why isn't this true for speeds greater than C?

Edited August 13, 2011 by questionposter

[ajb]

You should use the velocity addition formula for all velocities. However, for velocities much less than c the result is almost just the usual sum of velocities. So for Newtonian mechanics, upon the assumption of speeds no where near c, you can safely take the standard sum.

[questionposter]

You should use the velocity addition formula for all velocities. However, for velocities much less than c the result is almost just the usual sum of velocities. So for Newtonian mechanics, upon the assumption of speeds no where near c, you can safely take the standard sum.

 

Yeh, ok, but what I'm actually asking about is how it works visually, or in reality. What's going on in reality that makes those mathematicaly statements true? What are physicists observing that makes velocity behave that way? So in reality, why do I never measure a speed going at greater than the speed of light even if I am something else going away from something else in the opposite direction while both of us are moving at .6 the speed of light? The separation speed would be 1.2C, but why wouldn't I measure the velocity to be that as well even though for numbers that add up to way below C, the addition equations work just how you'd expect?

Edited August 13, 2011 by questionposter

[ajb]

So you want to know about the experimental verification of special relativity. A quick review can be found here.

[questionposter]

So you want to know about the experimental verification of special relativity. A quick review can be found here.

 

What's the thing I'm talking about called on that website?

[md65536]

From an inertial frame you cannot measure anything to be travelling at greater than c, or two things separating faster than 2c.

Out of curiosity, is it possible to define some type of abstract curved space where two things can separate faster than 2c?

It would require that while each thing travels away from you at < c, the distance between the 2 increases at a greater rate than the sum of the change in distance relative to you.

If possible, would it require that the 2 things are not traveling on the same geodesic which intersects you?

 

Or would it simply require inhomogeneous spacetime curvature?

 

OR is it true that the distance between any 2 points A and C is <= the distance from A to B + distance from B to C, for all possible points B? Is this true for any metric space? Or for any conceivable spacetime curvature?

 

 

 

What's the thing I'm talking about called on that website?

Probably "separation velocity" but after a quick glance at the website I didn't see anything specific. I think you may be giving a specific example of a situation that is handled by more general SR math that can be used to figure out that example as well as many more examples.

 

To see what I mean, try flipping the problem over, and instead of imagining an inertial observer in between 2 relatively separating objects, imagine it instead from the perspective of one of the separating objects. For example, if one object C is moving away from another A at 0.9 c, and then you imagine a third object B in the middle that's moving away at half the speed -- from A's perspective nothing is moving relative to anything else at > c -- and then calculate the velocities relative to the middle object B you should find that A and C are each moving away from each other with a separation velocity greater than c...

 

 

[questionposter]

Out of curiosity, is it possible to define some type of abstract curved space where two things can separate faster than 2c?

It would require that while each thing travels away from you at < c, the distance between the 2 increases at a greater rate than the sum of the change in distance relative to you.

If possible, would it require that the 2 things are not traveling on the same geodesic which intersects you?

 

Or would it simply require inhomogeneous spacetime curvature?

 

OR is it true that the distance between any 2 points A and C is <= the distance from A to B + distance from B to C, for all possible points B? Is this true for any metric space? Or for any conceivable spacetime curvature?

 

 

 

 

Probably "separation velocity" but after a quick glance at the website I didn't see anything specific. I think you may be giving a specific example of a situation that is handled by more general SR math that can be used to figure out that example as well as many more examples.

 

To see what I mean, try flipping the problem over, and instead of imagining an inertial observer in between 2 relatively separating objects, imagine it instead from the perspective of one of the separating objects. For example, if one object C is moving away from another A at 0.9 c, and then you imagine a third object B in the middle that's moving away at half the speed -- from A's perspective nothing is moving relative to anything else at > c -- and then calculate the velocities relative to the middle object B you should find that A and C are each moving away from each other with a separation velocity greater than c...

 

 

 

So in other words, you wouldn't measure anything greater than C because physics teach you an equation that considers that the speed of light is the limit and that's the only equation you use for velocity? I'm not saying objects actually "are" moving past the speed of light, I'm saying "appear" to be, and in that, I don't see why I need to imagine an observer in the middle when I can just observe the object moving away from me.

[md65536]

So in other words, you wouldn't measure anything greater than C because physics teach you an equation that considers that the speed of light is the limit and that's the only equation you use for velocity? I'm not saying objects actually "are" moving past the speed of light, I'm saying "appear" to be, and in that, I don't see why I need to imagine an observer in the middle when I can just observe the object moving away from me.

No, the equations are based on mathematical and logical consequences of observations of the speed of light. Physicists determine the equations based on what is observed, not the other way around.

 

Nothing will ever appear to be moving at greater than c, relative to any observer. If you can imagine objects moving relative to you at near c, then you'll also have to imagine length contraction and time dilation. If you do this (guided by the equations to figure out precisely what will happen), you'll see that time will dilate and space will contract and make it impossible for anything to actually move or appear to move faster than c relative to you.

 

If you follow derivations of the Lorentz transformations you'll probably come to understand why--or at least that--this must be so.

 

 

[questionposter]

No, the equations are based on mathematical and logical consequences of observations of the speed of light. Physicists determine the equations based on what is observed, not the other way around.

 

Nothing will ever appear to be moving at greater than c, relative to any observer. If you can imagine objects moving relative to you at near c, then you'll also have to imagine length contraction and time dilation. If you do this (guided by the equations to figure out precisely what will happen), you'll see that time will dilate and space will contract and make it impossible for anything to actually move or appear to move faster than c relative to you.

 

If you follow derivations of the Lorentz transformations you'll probably come to understand why--or at least that--this must be so.

 

 

 

Ok, well time dilation is the visual explanation for this, so thanks.

[ajb]

Nothing will ever appear to be moving at greater than c, relative to any observer.

 

That is the point. The speed of one of my rockets relative to the other is <c. The speed of either rocket as measured by me is <c. The speed of either rocket, or indeed me relative to any other comoving observer is <c.

 

You can also have angular effects that give the illusion of faster than light motion. But again no individual particle is moving faster than c as measured by any inertial observer.

 

What's the thing I'm talking about called on that website?

 

I don't think there are any real direct tests of the velocity addition formula. (I beg to be corrected!) The closest is the limiting speed of light. This has been tested, see here for references.

 

Most modern approaches to the validity of special relativity phrase it on terms of Lorentz invariance. If Lorentz invariance holds, that is the system does not change when changing inertial frames of reference, then we must have all the kinematic laws of special relativity.

 

So, all the direct and indirect tests of special relativity support the relativistic velocity addition formula.

Edited August 14, 2011 by ajb

[questionposter]

That is the point. The speed of one of my rockets relative to the other is <c. The speed of either rocket as measured by me is <c. The speed of either rocket, or indeed me relative to any other comoving observer is <c.

 

You can also have angular effects that give the illusion of faster than light motion. But again no individual particle is moving faster than c as measured by any inertial observer.

 

 

 

I don't think there are any real direct tests of the velocity addition formula. (I beg to be corrected!) The closest is the limiting speed of light. This has been tested, see here for references.

 

Most modern approaches to the validity of special relativity phrase it on terms of Lorentz invariance. If Lorentz invariance holds, that is the system does not change when changing inertial frames of reference, then we must have all the kinematic laws of special relativity.

 

So, all the direct and indirect tests of special relativity support the relativistic velocity addition formula.

 

How could there be a system that doesn't change with the frame of reference? Is that what I was saying light was? A Lorentz thing?

[ajb]

Lorentz invariance basically says that any experimental result will not depend on the orientation or the velocity of the laboratory through space.

[questionposter]

Lorentz invariance basically says that any experimental result will not depend on the orientation or the velocity of the laboratory through space.

 

Wait, that can't be right. Because what if the laboratory is moving is moving at 99.99% the speed of light away from a gamma-ray photon its trying to measure? Wouldn't the radio-wave stretch out?

[ajb]

Photons in vacua will always be measured to be moving at speed c in any inertial frame of reference. You are asking about a comoving observer and source. Yes, we have the Doppler effect. Not everything you can measure is Lorentz invariant, but those properties that really have some "deep meaning" are. For example energy is not Lorentz invariant. The square of the 4-momentum is Lorentz invariant.

 

Anyway, the physics is the same in any inertial frame of reference, which is what we are really saying.

[questionposter]

Photons in vacua will always be measured to be moving at speed c in any inertial frame of reference. You are asking about a comoving observer and source. Yes, we have the Doppler effect. Not everything you can measure is Lorentz invariant, but those properties that really have some "deep meaning" are. For example energy is not Lorentz invariant. The square of the 4-momentum is Lorentz invariant.

 

Anyway, the physics is the same in any inertial frame of reference, which is what we are really saying.

 

Why is the physics universal but not even things like time are?

[ajb]

Why is the physics universal but not even things like time are?

 

 

Taking time as an example, the difficulty is that Lorentz transformations mix space and time. You do not have a well defined universally accepted way of splitting space-time into space and time. This is why the space-time interval is invariant (well defined) but time and spacial interval are not.

 

A similar thing happens for energy and momentum. Neither is by itself Lorentz invariant, one has to think about the 4-momentum which is a "mix" of energy and momentum.

[csmyth3025]

Why is the physics universal but not even things like time are?

 

You need to consider ajb's statement as it was written:"...Anyway, the physics is the same in any inertial frame of reference, which is what we are really saying..."

 

In this statement "physics" refers to the laws of physics as we know them and an "inertial frame of reference" can be thought of as a spaceship laboratory moving at a uniform velocity (neither accelerating or decelerating) outside of any measurable gravitational field.

 

In this case, if an experimenter would, for instance, apply a force of one Newton (1 kg*m/s²) for one second to a stationary mass of one kilogram, it would impart a velocity of one meter per second to the mass (all of this is as measured in the spaceship lab).

 

This experiment will turn out the same for any experimenter on any spaceship that's in uniform motion (an inertial frame of reference). More generally, any experiment carried out in such a spaceship lab that's an inertial frame of reference will produce the same results as the same experiment carried out in any other spaceship lab that's likewise in uniform motion (an inertial frame of reference) no matter what direction they're going relative to each other or how fast they're going relative to each other. This principle of relativity (in inertial frames of reference) is one of the assumptions upon which Einstein based his special theory of relativity:

 

The Principle of Relativity The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems in uniform translatory motion relative to each other.

(ref. http://en.wikipedia....vity#Postulates )

 

As far as I know, there has been no experiment performed that contradicts this principle.

 

When you ask why time isn't "universal" you're asking about how an experimenter in one spaceship would "see" the time in another spaceship as it zoomed past him. This would vary, along with the mass of the one kilogram object and the length of one meter, depending on the relative velocities of the two spaceships. By applying special relativity (particularly the Lorentz transformations) to what he "sees" in the other spaceship, an experimenter can convert his measurements to the same measurements that the experimenter in the other spaceship is getting.

 

Chris

 

Edited to correct spelling errors

Edited August 20, 2011 by csmyth3025