Speed of Light and Energy...?

[dj357]

OK, a different tack, then.

Think about a Newtonian situation. The example of the cars as used in the earlier post will suffice. Imagine one of the cars moving toward you at 100 mph, while you are moving in front of it at 100 mph. The car is clearly never going to catch up with you, because you're moving away from it as fast as it's closing. Ask yourself what set of circumstances it would take for the car to catch up with you without you slowing down and without the car speeding up (this is moving from a Newtonian frame to a Relativistic frame). Does this question help you to understand, or to provide an answer to col's question?

Edit: Just to add a little clarity, think about what speed actually is, namely distance over time.

I can't see it ever catching up...

[oddmanout]

Here's an analogy I remember reading in an old book about GR; "the light watch", I think it was called. Imagine that you have two mirrors, and one photon bouncing between the them. Imagine that one "tick" on this clock is equal to the photon making it one way and then back again. Now, I'm not absolutely sure how this works, but the basic idea is to show how motion is connected with relativety (my mspaint illustration below). So when the clock is put in motion, the relative distance the photon travels is longer.

[hackenslash]

OK, a different tack, then.

Think about a Newtonian situation. The example of the cars as used in the earlier post will suffice. Imagine one of the cars moving toward you at 100 mph, while you are moving in front of it at 100 mph. The car is clearly never going to catch up with you, because you're moving away from it as fast as it's closing. Ask yourself what set of circumstances it would take for the car to catch up with you without you slowing down and without the car speeding up (this is moving from a Newtonian frame to a Relativistic frame). Does this question help you to understand, or to provide an answer to col's question?

Edit: Just to add a little clarity, think about what speed actually is, namely distance over time.

I can't see it ever catching up...

That doesn't deal with the question, and it demonstrates middle-world thinking. In a relativistic setting, it can indeed catch up (although in this specific example it couldn't unless it were massless and therefore travelling at light speed). There is a set of circumstances in which this can occur and does occur, although not with cars travelling at 100 mph. When you grasp the set of circumstances under which this can occur, you will understand relativity. This is the whole shebang, and once you get it, you've got it.

[hackenslash]

Here's an analogy I remember reading in an old book about GR; "the light watch", I think it was called. Imagine that you have two mirrors, and one photon bouncing between the them. Imagine that one "tick" on this clock is equal to the photon making it one way and then back again. Now, I'm not absolutely sure how this works, but the basic idea is to show how motion is connected with relativety (my mspaint illustration below). So when the clock is put in motion, the relative distance the photon travels is longer.

Brian Greene deals with this specific example at length in The Elegant UNiverse. It's very closely related to the example with the racing cars cited earlier in the thread, although it deals with it from a different perspective. The racing car example is an explanation of how it works, while the light clock is an illustration of the principle in action.

[oddmanout]

Brian Greene deals with this specific example at length in The Elegant UNiverse. It's very closely related to the example with the racing cars cited earlier in the thread, although it deals with it from a different perspective. The racing car example is an explanation of how it works, while the light clock is an illustration of the principle in action.

Yeah.. about that book; I actually had a copy (in Swedish), but I forgot it in a youth hostel in NZ And now it's impossible to find a copy of it in Swedish, and I just can't go back to all that "calabi-yau" stuff in English. Hey.. wait a minute; it was you that recommended "Road to reality" by Roger Penrose to me at the RD.net forum, wasn't it? I think it was. Damn, that book was impossible to read without absolute focus on the subject. I must read it though, some day.

Anyways, yes, it's is definitely the same principle as with the racing cars.

Would you mind giving your thoughts on my post on the previous page?

What about this:

1) Time dilation: one clock is accelerated, put into orbit and is then compared to a clock here on earth.

There is a measurable difference in time, even after the experiment.

2) Length contraction: a train moving near the speed of light is observed to be compressed. But when the train is decelerated, the train is returned to it's normal length.

The length contraction doesn't last after the experiment, due to the deceleration.


I know 1) is true, but what about 2)? Assuming that it is true, how come time can be changed into a new static state while length contraction cannot?


Also; how is it that time, by default, is moving with the speed of light (minus the relative movement and acceleration)? Why is it that the time-dimension, which we perceive as just another dimension in GR, "behaves" differently than other dimensions? Or do we, by default, move through all dimensions of space with lightspeed?

[hackenslash]

Brian Greene deals with this specific example at length in The Elegant UNiverse. It's very closely related to the example with the racing cars cited earlier in the thread, although it deals with it from a different perspective. The racing car example is an explanation of how it works, while the light clock is an illustration of the principle in action.

Yeah.. about that book; I actually had a copy (in Swedish), but I forgot it in a youth hostel in NZ And now it's impossible to find a copy of it in Swedish, and I just can't go back to all that "calabi-yau" stuff in English. Hey.. wait a minute; it was you that recommended "Road to reality" by Roger Penrose to me at the RD.net forum, wasn't it? I think it was. Damn, that book was impossible to read without absolute focus on the subject. I must read it though, some day.

Yes, it was probably me. I've managed to get all the way through it twice now. Each time I read it through, I pick up a little more that I didn't understand last time. It's not something I would recommend to someone who didn't already have some grasp of the principles of some of it, or it will simply come across as gibberish.

What about this:

1) Time dilation: one clock is accelerated, put into orbit and is then compared to a clock here on earth.

There is a measurable difference in time, even after the experiment.

It's a little more complicated than that. The acceleration certainly does have an effect, not least because acceleration is equivalent to being immersed oin a gravitational field, but there's more to it than that. Even if you sync the clocks once the first is in orbit, they will still drift. Not by a huge amount, but you will find that after about 20 days they have drifted to a measurable amount, which is why we have relativistic corretion in GPS satellites. [ETA] There are several factors in play. The first is that time runs slightly faster in orbit because of the reduction of the gravitational field. The second is that it runs slightly slower due to the motion of the satellite. So the relativistic correction is two-fold to take these factors into account.

2) Length contraction: a train moving near the speed of light is observed to be compressed. But when the train is decelerated, the train is returned to it's normal length.

The length contraction doesn't last after the experiment, due to the deceleration.

Well, it isn't due to deceleration (which should actually be acceleration, because acceleration is defined as a change in direction, which includes speeding up and slowing down), but is actually due to the entities being brought into the same inertial frame.

I know 1) is true, but what about 2)? Assuming that it is true, how come time can be changed into a new static state while length contraction cannot?

Again, it really is all about the inertial frame of the observer. I'm trying not to answer your question too directly, because it goes some way toward answering the above question for dj537, and it's important that he deals with that question in order to grasp relativity.

Also; how is it that time, by default, is moving with the speed of light (minus the relative movement and acceleration)? Why is it that the time-dimension, which we perceive as just another dimension in GR, "behaves" differently than other dimensions? Or do we, by default, move through all dimensions of space with lightspeed?

That's exactly it. We move at a fixed rate through any combination of dimensions (with the usual caveat concerning relativistic effects on time when immersed in a gravitational field). This means that we may be travelling through time at light speed when not in motion, but when in motion some of that travel is transferred to spatial dimensions, which slows our travel through the time dimension. In other words, we are always travelling at the speed of light, regardless of how many dimensions we are actually moving through.

[dj357]

That's exactly it. We move at a fixed rate through any combination of dimensions (with the usual caveat concerning relativistic effects on time when immersed in a gravitational field). This means that we may be travelling through time at light speed when not in motion, but when in motion some of that travel is transferred to spatial dimensions, which slows our travel through the time dimension. In other words, we are always travelling at the speed of light, regardless of how many dimensions we are actually moving through.

my first reaction to this was "BOLLOX! NO WAY!" but now that I think on it more, it makes a perverse kind of sense... but then how can light (e.g. a photon) travel through space, at the speed of light...? is it due to it's being massless...?

but it brings me to the realisation that time travel is by definition impossible since we can only travel at a fraction of the speed of light through any dimension and never faster, which would imply the inability to travel into the future, or to travel backwards in time. Either would result in travelling faster than the speed of light, or travelling with a negative speed... am I on the right track here...?

[hackenslash]

That's exactly it. We move at a fixed rate through any combination of dimensions (with the usual caveat concerning relativistic effects on time when immersed in a gravitational field). This means that we may be travelling through time at light speed when not in motion, but when in motion some of that travel is transferred to spatial dimensions, which slows our travel through the time dimension. In other words, we are always travelling at the speed of light, regardless of how many dimensions we are actually moving through.

my first reaction to this was "BOLLOX! NO WAY!" but now that I think on it more, it makes a perverse kind of sense... but then how can light (e.g. a photon) travel through space, at the speed of light...? is it due to it's being massless...?

Exactly right. In fact, ALL massless particles necessarily travel at light speed. Moreover, the implication is that photons (and by association any particles with no rest mass) don't experience the passage of time.

but it brings me to the realisation that time travel is by definition impossible since we can only travel at a fraction of the speed of light through any dimension and never faster, which would imply the inability to travel into the future, or to travel backwards in time. Either would result in travelling faster than the speed of light, or travelling with a negative speed... am I on the right track here...?

You're definitely on the right track, although it should be mentioned that we don't fully understand the topology of the dimensional manifold as yet (even assuming that there are extra dimensions), and that until we do, time travel can't be ruled out. There are other mechanisms that may provide a route to time travel as well, but they are beyind the scope of this topic in reality, and will only serve to distract you from getting a good grasp of relativity. Certainly, until Kip Thorne, though, nobody took seriously the idea that time travel was possible, and this was a direct result of relativity, employing exactly the same principles to come to that conclusion as you have just done.

[oddmanout]

Yes, it was probably me. I've managed to get all the way through it twice now. Each time I read it through, I pick up a little more that I didn't understand last time. It's not something I would recommend to someone who didn't already have some grasp of the principles of some of it, or it will simply come across as gibberish.

Yeah, I did have some grasp of GR and the universe in general, but the math in that book.. THE MATH! Though I must admit, his enthusiasm for math (especially the imaginary plane) did rub off.

2) Length contraction: a train moving near the speed of light is observed to be compressed. But when the train is decelerated, the train is returned to it's normal length.

The length contraction doesn't last after the experiment, due to the deceleration.

Well, it isn't due to deceleration (which should actually be acceleration, because acceleration is defined as a change in direction, which includes speeding up and slowing down),

Ah, of course

but is actually due to the entities being brought into the same inertial frame.

I know 1) is true, but what about 2)? Assuming that it is true, how come time can be changed into a new static state while length contraction cannot?

Again, it really is all about the inertial frame of the observer. I'm trying not to answer your question too directly, because it goes some way toward answering the above question for dj537, and it's important that he deals with that question in order to grasp relativity.

Hm. From the perspective of the train, they experience us just as much contracted as we experience the train contracted, right? So if "they" (the people on the train) accelerate ("brake") to our speed, then they've "descended" into our inertial frame? And vice versa, if we (hypothetically, for the sake of the argument. Ok, the rail is frictionless) accelerated the earths spin to match that of the train (which is moving exactly in the same direction as the earth spins), we would've "ascended" to their inertial frame, yes?

Also; how is it that time, by default, is moving with the speed of light (minus the relative movement and acceleration)? Why is it that the time-dimension, which we perceive as just another dimension in GR, "behaves" differently than other dimensions? Or do we, by default, move through all dimensions of space with lightspeed?

That's exactly it. We move at a fixed rate through any combination of dimensions (with the usual caveat concerning relativistic effects on time when immersed in a gravitational field). This means that we may be travelling through time at light speed when not in motion, but when in motion some of that travel is transferred to spatial dimensions, which slows our travel through the time dimension. In other words, we are always travelling at the speed of light, regardless of how many dimensions we are actually moving through.

Now this is interesting! So, in a way; velocity in "spatial dimensions" + "time-dimension" = c. I.e. if we move with the speed of light through the spatial dimensions, then we do not move through time ("c+0=c"), and if we do not move through the spatial dimension we move through time with the speed of light ("0+c=c"). So everyday situations for us particles with mass is a combination of sorts, which adds up to a constant; c?

[colubridae]

Guys guys for christ sake this is all way over his head.

It’s much simpler…

Let him work it out for himself


When he gets the correct answer, yes, he will be mega-pissed.
He’ll say ‘fuck this’ ‘fuck that’ ‘fuck you colubridae you’re a total wanker etc etc…’

he will call me every thing under the sun.
he will probably despise me for the rest of his life.

Guess what? it won’t bother me one jot of buffalo spunk.

No matter how annoyed and angry he gets, he will calm down.


But it’s a lesson he will remember, also, for the rest of his life.
And it’s definitely not a philosophical point…
He nearly got it there.

When he’s learned this lesson he can build on it. But only after he types the answer himself.

[hackenslash]

Yeah, I did have some grasp of GR and the universe in general, but the math in that book.. THE MATH! Though I must admit, his enthusiasm for math (especially the imaginary plane) did rub off.

Tell me about it. Math is probably my weakest area, but I can understand the underlying principles behind the math, and I have a good feel for the implications.

Hm. From the perspective of the train, they experience us just as much contracted as we experience the train contracted, right?

No. They would measure the same length for the train as they would at rest.

So if "they" (the people on the train) accelerate ("brake") to our speed, then they've "descended" into our inertial frame? And vice versa, if we (hypothetically, for the sake of the argument. Ok, the rail is frictionless) accelerated the earths spin to match that of the train (which is moving exactly in the same direction as the earth spins), we would've "ascended" to their inertial frame, yes?

These aren't two different actions, but the same action. When you travel on the surface of the Earth, it is equally true to say that the Earth moved South as to say that you moved North because, in relativity, every entity has an equal claim to being at rest.

Now this is interesting! So, in a way; velocity in "spatial dimensions" + "time-dimension" = c. I.e. if we move with the speed of light through the spatial dimensions, then we do not move through time ("c+0=c"), and if we do not move through the spatial dimension we move through time with the speed of light ("0+c=c"). So everyday situations for us particles with mass is a combination of sorts, which adds up to a constant; c?

Bingo!

[oddmanout]

So if "they" (the people on the train) accelerate ("brake") to our speed, then they've "descended" into our inertial frame? And vice versa, if we (hypothetically, for the sake of the argument. Ok, the rail is frictionless) accelerated the earths spin to match that of the train (which is moving exactly in the same direction as the earth spins), we would've "ascended" to their inertial frame, yes?

These aren't two different actions, but the same action. When you travel on the surface of the Earth, it is equally true to say that the Earth moved South as to say that you moved North because, in relativity, every entity has an equal claim to being at rest.

Ah, got it

Now this is interesting! So, in a way; velocity in "spatial dimensions" + "time-dimension" = c. I.e. if we move with the speed of light through the spatial dimensions, then we do not move through time ("c+0=c"), and if we do not move through the spatial dimension we move through time with the speed of light ("0+c=c"). So everyday situations for us particles with mass is a combination of sorts, which adds up to a constant; c?

Bingo!

[dj357]

colubridae, i point-blank refuse to play along with whatever the hell you've got going on. initially the thought of time as a dimension was bollox to me, but now it makes sense. whatever point you're trying to make, too bad.

[hackenslash]

So if "they" (the people on the train) accelerate ("brake") to our speed, then they've "descended" into our inertial frame? And vice versa, if we (hypothetically, for the sake of the argument. Ok, the rail is frictionless) accelerated the earths spin to match that of the train (which is moving exactly in the same direction as the earth spins), we would've "ascended" to their inertial frame, yes?

These aren't two different actions, but the same action. When you travel on the surface of the Earth, it is equally true to say that the Earth moved South as to say that you moved North because, in relativity, every entity has an equal claim to being at rest.

Ah, got it

I meant to add that, as a corollary to the above, it's also equally true to say that the Earth speeded up as it is to say the train braked, and vice versa. This is why 'acceleration' is defined as 'change in direction'.

[colubridae]

colubridae, i point-blank refuse to play along with whatever the hell you've got going on. initially the thought of time as a dimension was bollox to me, but now it makes sense. whatever point you're trying to make, too bad.

Ok kid. I know you think I am a complete twat etc… Don’t worry most people think that. Mrs Colubridae thinks I am the most evil person on the planet. Bless her.

But you learned an important lesson. So you owe me big time.

There were three main points/demonstrations to the exercise


1 You stopped that interminable whining about ‘I don’t like time as a dimension’. Nobody likes it. It's definitely not intuitive. Anyone who thinks it is intuitive is an idiot. Suck it up like the rest of us…

2 You never, never mix up observation with theory. That’s why your gedanken experiments were so fucking absurd.

3 All the theories used are dependent for their worth on the supporting evidence. And they are never, never proof.



As for ‘the question’

You might possibly have answered:-

“because the Maxwell equations reduce c to 1/ sqrt( (pertmittivity of free space) * (permeability of free space))

And ( (pertmittivity of free space) * (permeability of free space)) are measured and found to be so far constant.



Though this would be indirect (through another ‘theory’) it would have been an answer.

But I would have simply re-questioned with

“Why is the value of ((pertmittivity of free space) * (permeability of free space)) constant”
Leading you straight back to an observed phenomena.



Despite your intense irritation with me I have another game to play, if you’re up for it.
It’s called ‘Dark Matter’

Let me know of you are interested and I will start the game.