A Question About The Speed Of Light

[pErvinalia]

Ok. But back to my other question: How do we determine that it is the spacecraft accelerating and not the Earth? That implies that there must be a unique or privileged observational frame of reference to compare that acceleration to. What determines that it is the spacecraft accelerating away from the Earth, and not the other way around?

[JimC]

That's what I always wondered too, in addition to my other confusion with that 'paradox'. I assumed that in general relativity there must be some difference.

The Twins Paradox predates GR. It is specifically formulated and grounded in SR. Specifically, it uncovers an often-held misconception about SR - namely that all frames of reference are equivalent. Actually, only inertial frames of reference are equivalent - ie. those NOT undergoing acceleration. At some point during his journey, the twin on the spaceship has to change directions and head home - he moves from one inertial FOR (the outward one) to another (the homeward one) - during this change he is undergoing acceleration but the twin on Earth is not and, no matter how fast or slow the change-around happens, this will cause a disparity in the elapsed time experienced by the twins. The two periods of constant velocity travel indeed cancel out - but the necessary acceleration in-between cannot.

[pErvinalia]

[Xamonas Chegwé]

Ok. But back to my other question: How do we determine that it is the spacecraft accelerating and not the Earth? That implies that there must be a unique or privileged observational frame of reference to compare that acceleration to. What determines that it is the spacecraft accelerating away from the Earth, and not the other way around?

You cannot accelerate a body without inputting energy. F = ma (an approximation which needs adjustment by the Lorentz factor at close to light-speed - but the principle of energy being required holds.) Only one body (the spaceship) has energy input, ergo, only that body is accelerating. Contrast this with constant relative motion - no energy is required to continue at a constant speed, hence both bodies can be treated as equivalent. Acceleration is absolute due to the constant input of energy into one body only.

If the twins were both in spaceships and both accelerated away from each other at the same rate, turned around and came back to their starting point, their ages would be identical, as would the clocks on board. But input energy into one half of the system and not the other and symmetry breaks down.

[pErvinalia]

[Xamonas Chegwé]

Also, think of two cars - one stationary, the other accelerating. If either could be considered to be the accelerating vehicle, how come only one experiences g-force? This is equivalent to my explanation above, as the g-force is a result of the energy input into the system, but perhaps more intuitive.

[JimC]

Also, think of two cars - one stationary, the other accelerating. If either could be considered to be the accelerating vehicle, how come only one experiences g-force? This is equivalent to my explanation above, as the g-force is a result of the energy input into the system, but perhaps more intuitive.

Is it the car, or the contents, that experiences the "g-force"?

[pErvinalia]

Yeah, I figured it must be something like that. I was just not quite sure how the system differentiated between the at intertial rest vs the accelerating. I thought of g-force, but kind of considered that more of an observational measurement, not something that would be intrinsic to a dynamic system. But when you put in terms of energy, then yes, that makes sense.

[JimC]

A system that is accelerating rather than moving at some constant velocity requires very different mathematical treatment; the difference took Einstein many years to formulate, as the general theory of relativity. A key feature was the strong link between an accelerating framework of reference and gravitational fields.

[Xamonas Chegwé]

Also, think of two cars - one stationary, the other accelerating. If either could be considered to be the accelerating vehicle, how come only one experiences g-force? This is equivalent to my explanation above, as the g-force is a result of the energy input into the system, but perhaps more intuitive.

Is it the car, or the contents, that experiences the "g-force"?

Both. Technically "g-force" is not a force but a measurement of acceleration felt as weight. While the mass of an object is an invariant, scalar quantity (invariant to any observer in the same inertial frame of reference), its weight depends on both its mass and any acceleration (including that due to gravity) that it is undergoing, and is a vector quantity - ie. it has direction as well as magnitude. So you can have a weight component in the vertical downwards direction, due to gravity, and another component in a horizontal direction due to sitting in a moving vehicle - usually called "g-force". Since both the car and its contents are experiencing acceleration, they both feel the "g-force".



To elaborate on my earlier points.

The two key principles of special relativity are:

1. The Principle of Relativity: The rules of physics apply equally all observers irrespective of their relative constant motion with regard to each other.
2. The Principle of Invariant Light Speed: Light is emitted at c regardless of the relative motion of the emitting body

All of special relativity - including the famous E=mc2 mass-energy equivalence equation follow from these two postulates.

Another way of stating rule 1 is to say that there is no experiment that you can perform within an inertial frame of reference that will show whether or not it is moving. (Or, alternatively, there is NO absolute reference frame in the universe.)

So, imagine that two observers are both inside container crates that are moving in some uniform manner with respect to each other. Any experiments that the two carry out will give the same results +/- experimental error. If they both drop a ball from the same coordinates within their respective containers, they will observe it taking the same amount of time to hit the floor and the two balls will land at the same coordinates on the floor.

However, should one of the containers be accelerating, this is not the case. If the container is accelerating laterally, the ball's fall will be skewed away from the direction of acceleration. If the container is accelerating vertically, the time taken for the ball to fall will either increase or decrease, depending on the direction of acceleration. Hence accelerated frames of reference are NOT equivalent. As I stated above, this is because there is a variable input of energy to everything in such an F.O.R. which affects its behaviour.

[rainbow]

Velocity is not additive. The photons from each flashlight are traveling away from you at c but also from each other at c!

Here's a one:

Two photons are sent off at the same time in the same direction, say from a laser. Will one photon 'experience' the other as being stationary, or travelling away at C?

Why?

[Xamonas Chegwé]

Velocity is not additive. The photons from each flashlight are traveling away from you at c but also from each other at c!

Here's a one:

Two photons are sent off at the same time in the same direction, say from a laser. Will one photon 'experience' the other as being stationary, or travelling away at C?

Why?

To a photon, its existence is instantaneous. It is created in a 2-dimensional universe, infinitely compressed in the direction of its motion and in which time has stopped! Once it collides with another particle, it is destroyed - at exactly the same moment (from its perspective) as that in which it was born!

So your question has no real meaning.... to a photon.

[FBM]

Goddammit. Fuck this, I'm going to find some acid and read your posts again, XC.

[MiM]

Also, think of two cars - one stationary, the other accelerating. If either could be considered to be the accelerating vehicle, how come only one experiences g-force? This is equivalent to my explanation above, as the g-force is a result of the energy input into the system, but perhaps more intuitive.

Is it the car, or the contents, that experiences the "g-force"?

Neither the car nor you, but maybe your wife or daughter. Especially if the car is a rumbling V8.

[mistermack]

Two photons are sent off at the same time in the same direction, say from a laser. Will one photon 'experience' the other as being stationary, or travelling away at C?

Why?

It all becomes a bit illogical when you talk about photons 'experiencing' something.
The reason that it gets illogical is that infinity gets involved. As you approach the speed of light, the briefest portion of time imaginable stretches out to infinity.

So with this example, you could equally say that the one photon 'experiences' the other travelling away at the speed of light, but it would take infinite time to make any measurement.
Which you can regard as true and nonsense, at the same time, if you like. Infinity is like that.

So the real answer to the question is neither. The photon 'experiences' nothing in real time.
But if you're prepared to wait infinite time....