A Question About The Speed Of Light

[Drewish]

Ah, so velocity only appears addictive to us because we travel at speeds so far from the speed of light.

[JimC]

To add something a little more, if 2 objects travelling at close to the speed of light collide head on, then the impact velocity for each is still less than c. However, the kinetic energy of the collision would be as expected from a collision at a much higher impact velocity, because the mass of the objects (a contributor to their KE) is increased by that same Lorentz factor as their velocity increases...

This principle is at the heart of the ability of particles accelerators which cause collisions between sub-atomic particles travelling at relativistic speeds to release large amounts of energy when they collide...

[Xamonas Chegwé]

To add something a little more, if 2 objects travelling at close to the speed of light collide head on, then the impact velocity for each is still less than c. However, the kinetic energy of the collision would be as expected from a collision at a much higher impact velocity, because the mass of the objects (a contributor to their KE) is increased by that same Lorentz factor as their velocity increases...

This principle is at the heart of the ability of particles accelerators which cause collisions between sub-atomic particles travelling at relativistic speeds to release large amounts of energy when they collide...

When something moves, relative to you, its time slows down by the Lorentz factor, its mass increases by the Lorentz factor and its length (in the direction of motion) decreases by the Lorentz factor. However, from its POV, it is YOU that is moving - so it is YOU that undergoes all of these changes!

Of course, this is just taking into account special relativity. Once you start factoring the effects of gravity and acceleration (which are actually the same thing) things get... messier!

[mistermack]

To understand it, you have to understand that relativity is all about frames of reference.
Time is different, in every frame of reference. It's just hard to detect, until you deal with frames of reference that are getting near the speed of light, relative to you.

In any frame of reference you choose, nothing can travel faster than light.
In this example, in your observer's frame of reference, you see two photons, going in opposite directions, both at the speed of light, and think to yourself, ''so, from the point of view of one of those photons, the other is travelling at twice the speed of light''.

But what you have just done mentally, is jump from your original frame of reference to another, which is moving at the speed of light, without taking any account of how differently time is behaving in the second frame.

It's natural for us to imagine you can just add the two speeds, because we never notice time dilation in our day-to-day lives. It's too tiny, until you get up around c.
But in reality, from the point of view of either of the photons, time would be stopped completely.
No observer made of massive particles could ever experience that point of view anyway, because massive objects can never travel at c.

[Horwood Beer-Master]

...To all of the photons in that Cosmic Microwave Background, no time has passed since the big bang...

To all of the photons in the Cosmic Microwave Background, no time has passed since about 380,000 years after the big bang.

[mistermack]

...To all of the photons in that Cosmic Microwave Background, no time has passed since the big bang...

To all of the photons in the Cosmic Microwave Background, no time has passed since about 380,000 years after the big bang.

To all of the photons in the Cosmic Microwave Background, no time has passed.

[Horwood Beer-Master]

...To all of the photons in that Cosmic Microwave Background, no time has passed since the big bang...

To all of the photons in the Cosmic Microwave Background, no time has passed since about 380,000 years after the big bang.

To all of the photons in the Cosmic Microwave Background, no time has passed.

To all free photons no time has passed.

[JimC]

Free the photons!

[pErvinalia]

This stuff is a bit mind bending to get your head around. The one relativistic concept that has bothered me over the years is the "twins-paradox". In my naive view it seems to be granting special status to the Earth frame of reference. Why is it considered that the spaceship is moving away under relativistic effects, and hence returns with a younger twin than the one left on Earth? From the spaceship frame of reference the Earth is actually moving away relativistically and hence when the Earth returns to the spaceship the twin on Earth should be younger.

[Seth]

If c is absolute, and mass increases with velocity until at c it becomes infinite, and light travels at c, and photons have any mass at all (Photons inside superconductors do develop a nonzero effective rest mass; as a result, electromagnetic forces become short-range inside superconductors.[29] Source: Wikipedia), then photons may not be moving at all, the rest of the universe may be moving relative to a sea of static photons of infinite mass.

In layman's terms this is called the "IDHAFC theorem."

[Xamonas Chegwé]

This stuff is a bit mind bending to get your head around. The one relativistic concept that has bothered me over the years is the "twins-paradox". In my naive view it seems to be granting special status to the Earth frame of reference. Why is it considered that the spaceship is moving away under relativistic effects, and hence returns with a younger twin than the one left on Earth? From the spaceship frame of reference the Earth is actually moving away relativistically and hence when the Earth returns to the spaceship the twin on Earth should be younger.

There's no special frame of reference. But the spaceship undergoes acceleration and deceleration and thus changes inertial frames of reference during its journey. The Earth undergoes no such acceleration and remains in a constant frame of reference. The disparity in ages arises from this asymmetry.

[pErvinalia]

How do you tell which of the spacecraft or the earth is undergoing acceleration??

From the spacecraft's frame of reference, the Earth accelerated away from it.

[Hermit]

This stuff is a bit mind bending to get your head around. The one relativistic concept that has bothered me over the years is the "twins-paradox". In my naive view it seems to be granting special status to the Earth frame of reference. Why is it considered that the spaceship is moving away under relativistic effects, and hence returns with a younger twin than the one left on Earth? From the spaceship frame of reference the Earth is actually moving away relativistically and hence when the Earth returns to the spaceship the twin on Earth should be younger.

There's no special frame of reference. But the spaceship undergoes acceleration and deceleration and thus changes inertial frames of reference during its journey. The Earth undergoes no such acceleration and remains in a constant frame of reference. The disparity in ages arises from this asymmetry.

Having difficulties grasping the maths involved even for the special theory of relativity, this may be a stupid question borne of ignorance, but I'll ask anyway: Shouldn't the effects of acceleration and deceleration basically cancel each other out?

[pErvinalia]

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.

[Xamonas Chegwé]

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.