Relativity

[skepticalbip]

Is vsub2 c?
Is vsub1 c-1MPH?

When dealing with matter:
V1 is any velocity less than c.
V2 is any velocity less than c.

 

[Kharakov]

What about neutrinos?

 

[bilby]

Is vsub2 c?
Is vsub1 c-1MPH?

v₁ and v₂ are whatever velocities you are adding.

For the example of two photons approaching each other head on, v₁ and v₂ are both c, and the closing velocity of one photon, as observed by the other works out as:

\(v = \frac{v_1+v_2}{1+(\frac{v_1.v_2}{c^2})} \)


\( v = \frac{c+c}{1+(\frac{c.c}{c^2})} \)


\( v= \frac{c+c}{1+(\frac{c^2}{c^2})} \)


\( v = \frac{2c}{1+1} \)


\( v = \frac{2c}{2} \)


\( v= c \)

so lightspeed + lightspeed = lightspeed.

 

[fast]

So, if I'm traveling at 1/4c and you're next to me in a parallel vector traveling at 1/2c and we both cut our lights on at mile marker 1, our lights will pass mile marker 2 at precisely the same time and position or no? I'm speculating that the unintuitiveness of the answer can be explained away by illuminating the length contraction issue and time dilation issue with independent squeezing or stretching of two horizontal 2d parallel grids. It's like the distances on my x axis will not mesh on yours.

I've severely not articulated that right, and it needs fixing, but I gotta run at the moment.

 

[bilby]

So, if I'm traveling at 1/4c and you're next to me in a parallel vector traveling at 1/2c and we both cut our lights on at mile marker 1, our lights will pass mile marker 2 at precisely the same time and position or no? I'm speculating that the unintuitiveness of the answer can be explained away by illuminating the length contraction issue and time dilation issue with independent squeezing or stretching of two horizontal 2d parallel grids. It's like the distances on my x axis will not mesh on yours.

I've severely not articulated that right, and it needs fixing, but I gotta run at the moment.

Yes - but only from the perspective of an observer in the reference frame of (that is, moving at the same velocity as) the mile markers.

The light travels at c as measured by any observer. The speed of the emitter changes nothing - for an observer in the same reference frame as the markers, the light reaches the distant marker at the same time, if it originated the same distance from the marker, regardless of how the emitter is moving.

The observers on the two spaceships will have different opinions on the distances involved, and on the timing of events, but they will all agree that the light travels at c. Time and distance are not absolute; There is no such thing as 'the same time' or 'the same position' for observers who are in different reference frames.

This is a good resource that explains the effects of relative velocities on time and distance measurements in more detail: http://newt.phys.unsw.edu.au/einsteinlight/jw/module4_time_dilation.htm

Unfortunately, the 1962 Holden used in the experiment is no longer in production, so we are not able to repeat the experiment today.

 

[fast]

I'm still dumbfounded as to where in the cycle of logic that things are breaking down.

If I'm traveling at .5c and cut on a light, I know that the speed of light is c despite my speed. I'm thinking that the light emitted will travel at exactly c regardless of my speed. In this instance, I would measure the speed of light as being precisely twice my speed.

If I slow my ship down to .25c and cut on a light, the speed of light will still be c, but in this instance, the light emitted is traveling 4x my speed, so the speed of light is a constant regardless of how fast I'm traveling, not relative to how fast I'm traveling.

Good so far?

Now, if I'm traveling on a train moving at 30MPH, I'm both a) not moving relative to the train and b) moving 30MPH relative to the ground. If I throw a ball at 10MPH towards the front of the train, the ball is both traveling at 10MPH relative to the train and 40MPH relative to the ground (30 + 10). Notice that I added.

If I repeat the experiment with a brick, I'll still add, but if I'm traveling 30MPH on the train relative to the ground and repeat the experiment for a third time and use a flashlight instead, I should not add, for with light, an exception should be made. Light travel has a maximum speed regardless of everything else. In fact, the speed of light will have the same speed no matter what, as its a universal constant.

So, if I'm traveling at 30MPH and shine the light, then c is what it is, whether relative to the train or relative to the ground. C is c, period. If the Earth is static, then on the train, I'm moving at c-c+30. On the ground, I'm moving at c-c+0. If the earth isn't static, then we are already traveling at some % of C. If we decrease our speed so that we're at 0% of c, then we're absolutely not moving, even if we're moving relative to other objects.

 

[skepticalbip]

I'm still dumbfounded as to where in the cycle of logic that things are breaking down.
.

The logic breaks down because you are assuming a universe where there is a preferred universal inertial reference frame and a universally agreed to clock for time. This isn't reality even though it was assumed to be so before Einstein's understanding resolved all the "paradoxes" these assumptions created. These are the "paradoxes" that you seem to be trying to deal with.

 

[beero1000]

I'm still dumbfounded as to where in the cycle of logic that things are breaking down.

If I'm traveling at .5c and cut on a light, I know that the speed of light is c despite my speed. I'm thinking that the light emitted will travel at exactly c regardless of my speed. In this instance, I would measure the speed of light as being precisely twice my speed.

If I slow my ship down to .25c and cut on a light, the speed of light will still be c, but in this instance, the light emitted is traveling 4x my speed, so the speed of light is a constant regardless of how fast I'm traveling, not relative to how fast I'm traveling.

Good so far?

Now, if I'm traveling on a train moving at 30MPH, I'm both a) not moving relative to the train and b) moving 30MPH relative to the ground. If I throw a ball at 10MPH towards the front of the train, the ball is both traveling at 10MPH relative to the train and 40MPH relative to the ground (30 + 10). Notice that I added.

If I repeat the experiment with a brick, I'll still add, but if I'm traveling 30MPH on the train relative to the ground and repeat the experiment for a third time and use a flashlight instead, I should not add, for with light, an exception should be made. Light travel has a maximum speed regardless of everything else. In fact, the speed of light will have the same speed no matter what, as its a universal constant.

So, if I'm traveling at 30MPH and shine the light, then c is what it is, whether relative to the train or relative to the ground. C is c, period. If the Earth is static, then on the train, I'm moving at c-c+30. On the ground, I'm moving at c-c+0. If the earth isn't static, then we are already traveling at some % of C. If we decrease our speed so that we're at 0% of c, then we're absolutely not moving, even if we're moving relative to other objects.

If you are on a train moving at 30mph relative to the ground and you throw a ball forward at 10mph relative to the train, the observer on the ground does not see the ball moving at 40mph - they see it moving at 39.99999999999997mph.

The faster the train/ball are moving, the more the discrepancy between Gallilean relativity and general relativity. If the train is moving at 30MPH and the light is moving at c, the observer on the ground sees the light moving at c.

 

[fast]

I'm still dumbfounded as to where in the cycle of logic that things are breaking down.

If I'm traveling at .5c and cut on a light, I know that the speed of light is c despite my speed. I'm thinking that the light emitted will travel at exactly c regardless of my speed. In this instance, I would measure the speed of light as being precisely twice my speed.

If I slow my ship down to .25c and cut on a light, the speed of light will still be c, but in this instance, the light emitted is traveling 4x my speed, so the speed of light is a constant regardless of how fast I'm traveling, not relative to how fast I'm traveling.

Good so far?

Now, if I'm traveling on a train moving at 30MPH, I'm both a) not moving relative to the train and b) moving 30MPH relative to the ground. If I throw a ball at 10MPH towards the front of the train, the ball is both traveling at 10MPH relative to the train and 40MPH relative to the ground (30 + 10). Notice that I added.

If I repeat the experiment with a brick, I'll still add, but if I'm traveling 30MPH on the train relative to the ground and repeat the experiment for a third time and use a flashlight instead, I should not add, for with light, an exception should be made. Light travel has a maximum speed regardless of everything else. In fact, the speed of light will have the same speed no matter what, as its a universal constant.

So, if I'm traveling at 30MPH and shine the light, then c is what it is, whether relative to the train or relative to the ground. C is c, period. If the Earth is static, then on the train, I'm moving at c-c+30. On the ground, I'm moving at c-c+0. If the earth isn't static, then we are already traveling at some % of C. If we decrease our speed so that we're at 0% of c, then we're absolutely not moving, even if we're moving relative to other objects.

If you are on a train moving at 30mph relative to the ground and you throw a ball forward at 10mph relative to the train, the observer on the ground does not see the ball moving at 40mph - they see it moving at 39.99999999999997mph.

The faster the train/ball are moving, the more the discrepancy between Gallilean relativity and general relativity. If the train is moving at 30MPH and the light is moving at c, the observer on the ground sees the light moving at c.

Okay, but the observer on the train sees the light moving at c as well.

 

[Treedbear]

I'm still dumbfounded as to where in the cycle of logic that things are breaking down.

If I'm traveling at .5c and cut on a light, I know that the speed of light is c despite my speed. I'm thinking that the light emitted will travel at exactly c regardless of my speed. In this instance, I would measure the speed of light as being precisely twice my speed.

Yes. Your speed relative to the ground. (But you can also say the ground's speed relative to you.)

If I slow my ship down to .25c and cut on a light, the speed of light will still be c, but in this instance, the light emitted is traveling 4x my speed, so the speed of light is a constant regardless of how fast I'm traveling, not relative to how fast I'm traveling.

Again, that's how fast you're traveling relative to the ground.

Good so far?

Now, if I'm traveling on a train moving at 30MPH, I'm both a) not moving relative to the train and b) moving 30MPH relative to the ground. If I throw a ball at 10MPH towards the front of the train, the ball is both traveling at 10MPH relative to the train and 40MPH relative to the ground (30 + 10). Notice that I added.

...

Yes, and from within your relativistic frame the light is traveling at c + 40 mph relative to the ground. The only way to see that is to assume that the ground is moving rather than you moving. But that only gets resolved when the train decelerates so that it's stationary relative to the ground. Then it becomes apparent that it was you who accelerated and it was you who was moving and so you have aged at a slower rate than a person on the ground. It's the acceleration that changes the relative rate at which time progresses. In actual fact, time was moving slower for you, so that even though light was moving at less than c it seemed to be moving at c because time was also moving more slowly. (And that's why we always and can only measure light to be moving at c.) But this is only true because you decelerated to your original reference frame.

 

[beero1000]

I'm still dumbfounded as to where in the cycle of logic that things are breaking down.

If I'm traveling at .5c and cut on a light, I know that the speed of light is c despite my speed. I'm thinking that the light emitted will travel at exactly c regardless of my speed. In this instance, I would measure the speed of light as being precisely twice my speed.

If I slow my ship down to .25c and cut on a light, the speed of light will still be c, but in this instance, the light emitted is traveling 4x my speed, so the speed of light is a constant regardless of how fast I'm traveling, not relative to how fast I'm traveling.

Good so far?

Now, if I'm traveling on a train moving at 30MPH, I'm both a) not moving relative to the train and b) moving 30MPH relative to the ground. If I throw a ball at 10MPH towards the front of the train, the ball is both traveling at 10MPH relative to the train and 40MPH relative to the ground (30 + 10). Notice that I added.

If I repeat the experiment with a brick, I'll still add, but if I'm traveling 30MPH on the train relative to the ground and repeat the experiment for a third time and use a flashlight instead, I should not add, for with light, an exception should be made. Light travel has a maximum speed regardless of everything else. In fact, the speed of light will have the same speed no matter what, as its a universal constant.

So, if I'm traveling at 30MPH and shine the light, then c is what it is, whether relative to the train or relative to the ground. C is c, period. If the Earth is static, then on the train, I'm moving at c-c+30. On the ground, I'm moving at c-c+0. If the earth isn't static, then we are already traveling at some % of C. If we decrease our speed so that we're at 0% of c, then we're absolutely not moving, even if we're moving relative to other objects.

If you are on a train moving at 30mph relative to the ground and you throw a ball forward at 10mph relative to the train, the observer on the ground does not see the ball moving at 40mph - they see it moving at 39.99999999999997mph.

The faster the train/ball are moving, the more the discrepancy between Gallilean relativity and general relativity. If the train is moving at 30MPH and the light is moving at c, the observer on the ground sees the light moving at c.

Okay, but the observer on the train sees the light moving at c as well.

Yes, so?

 

[steve_bank]

In relativity the thing to understand is that C is finite, light and all phenomena take time to propagate.

There are animations on the net involving light and observers.

It may have changed names, AE's popular science book on relativity was on the Gutenberg Project in PDF for free.

 

[Loren Pechtel]

Something to keep in mind that might help clear up some of the confusion:

Everyone measures c to be the same. However, people disagree about the yardsticks and watches of others that are traveling at different speeds.

 

[fast]

Okay, but the observer on the train sees the light moving at c as well.

Yes, so?

To be relative is to be compared to. The train is moving 30MPH relative to the ground, and the ball is moving 10MPH relative to the train yet moving 40MPH relative to the ground. The speed of the ball is what? 10MPH or 4OMPH? The answer depends doesn't it? Same thing with the brick. It depends on what it's compared to. The train or the ground.

Light is an exception. How fast is light traveling? It's traveling the same thing relative to the train as it is relative to the ground. The ball is moving 10MPH relative to the train but 40MPH relative to the ground. With light, the speed is c relative to the train, but unlike the ball and brick, when compared to the ground, the answer doesn't change.

ETA: Einstein postulates light speed as a universal constant. There's none of this relativity bullshit when it comes to light. That it's used as a genuine defacto constant in the postulate is what allows for the possibility for the unintuitive consequences. The other two variables become unfixed. Length and time. Length contraction and time dilation is a mathematical necessity.

 

[Wiploc]

This is twisted.

I don't understand the rest of that post, but this part makes me think you are close to getting it.

But there can be truly stationary objects though.

Everything is truly stationary relative to itself. Everything is also truly stationary relative to things that are going the same speed.

That's the only kind of stationary that exists.

If an object is getting closer to another and there is a collision, we now know both are moving,

B could be stopped while A was moving. Or vice versa. Or both could be moving. It's all a question of viewpoint, and every viewpoint is as valid as every other. There is no underlying truth. There is no sense in which one or another was really moving.

I don't think you understand the magnitude of my mistake.

You think that Joe and Sara are agreeing when they both say light moves at c. In truth, Joe thinks it moves at c relative to him, and Sara thinks it moves at c relative to her. If they aren't stopped relative each other, that amounts to a disagreement.

But we don't style it as a disagreement because each can do the math to figure out what the other one is perceiving.

If you are standing still and I walk by you at 2MPH and we both cut a light on at precisely the same time shining towards a building, the beams should reach their destination simultaneously despite our difference in speed. If a third person came up in a very fast jet (3000MPH) and all three lights are cut on, then never mind all this observer jazz. Light can only travel so fast. It's universal. It's a universal constant.

Just use one light. That will reduce your confusion. It's not like one beam of light will get somewhere before another. Redshift--not speed--is the only thing changed by the speed of the source.

I always feel the observer element to be a distraction. What anyone observed from their respective frame of reference sidetracks the issue about the lights movement. If an instrument at the wall detects light as it arrives, it should be able to tell the order in which the lights beems arrived, irrespective of whatever varying accounts observers might report.

They get there at the same time. Always. They'll be different colors due to red shift, but they'll get there at the same time. That's why you should only use one light.

The bad news is that, even though they got there at the same time, the observers may not agree on what time that is. Bummer, I know.

If the train is traveling at the speed of light, the light on the caboose will not shine and light up the engine train,

Here's your error. Regardless of how fast the train is moving (relative to whatever) the speed of the light (as viewed by the conductor in the caboose) will always be the same. He is always stopped relative to himself, so he will always see the light behaving normally. The light will always light up the engine.

The train can't actually go the speed of light (perhaps because that would involve dividing by zero?) but you can look at this progression:

- When the train is stopped (relative to Sara) the flashlight works, and light reaches the cab in one unit of time.
- When the train is at .99c (relative to Sara) the flashlight works, and light reaches the cab in one unit of time.
- When the train is at .999c (relative to Sara) the flashlight works, and light reaches the cab in one unit of time.
- When the train is at .9999c (relative to Sara) the flashlight works, and light reaches the cab in one unit of time.
- When the train is at .99999c (relative to Sara) the flashlight works, and light reaches the cab in one unit of time.
- When the train is at .999999c (relative to Sara) the flashlight works, and light reaches the cab in one unit of time.
- When the train is at .9999999c (relative to Sara) the flashlight works, and light reaches the cab in one unit of time.

So you see, the faster the train goes, the more it doesn't make any difference. If there is a sense in which the train could get up to speed c (and my physicist friends would hate me for writing that much of this sentence) then the flashlight would still work normally.

for the speed of light would have to travel faster than the caboose, and light cannot do that because that would require the speed the light is traveling to exceed c.

Let's say the train is going at .5c (relative to Sara). Joe is on the train. If Joe and Sara had your Newtonian perspective, they might talk like this:

Joe: I'm stopped. You're moving south at .5c. The light is moving north at c. So the light is moving away from you at 1.5c.

Sara: No, I'm stopped. You're moving north at .5c. The light is moving north at c. So the light is moving away from you at .5c.

And then each would call the other a liar, because each can see that the light was moving at c relative to his or her own frame of reference.

And, yes, that is twisted.

 

[Wiploc]

To be relative is to be compared to. The train is moving 30MPH relative to the ground, and the ball is moving 10MPH relative to the train yet moving 40MPH relative to the ground. The speed of the ball is what? 10MPH or 4OMPH? The answer depends doesn't it? Same thing with the brick. It depends on what it's compared to. The train or the ground.

Light is an exception. How fast is light traveling? It's traveling the same thing relative to the train as it is relative to the ground.

There's your lexical peculiarity.

Let's bring back your magical horse to illustrate. The horse runs at 60mph always, relative to everything.

Sara is on the ground (stopped relative to Sara). Joe is in the train (moving north at 30mph relative to Sara). Joe throws the ball north at 10mph (relative to Joe).

The horse is running north too. (Remember, you don't need three different horses any more than you need three flashlights. If the horse is on the train, Sara thinks it's a red roan while Joe thinks it's a blue roan--but its speed is unaffected.)

Sara sees the horse at 60mph relative to her, 30mph relative to Joe, and 20mph relative to the ball.
Joe sees the horse at 90mph relative to Sara, 60mph relative to himself, and 50mph relative to the ball.
The ball sees the horse at 100mph relative to Sara, 70mph relative to Joe, and 60mph relative to itself.

How to express that weirdness? We say that 60mph is the speed of horse, always, from every frame of reference.

Entertain the possibility that this has something to do with why the ball can never actually go the speed of horse. The ball only has one speed. The horse goes the same speed relative even to things going different speeds. The ball can't do that.

If you think this is twisted, you may be getting it.

 

[beero1000]

Okay, but the observer on the train sees the light moving at c as well.

Yes, so?

To be relative is to be compared to. The train is moving 30MPH relative to the ground, and the ball is moving 10MPH relative to the train yet moving 40MPH relative to the ground. The speed of the ball is what? 10MPH or 4OMPH? The answer depends doesn't it? Same thing with the brick. It depends on what it's compared to. The train or the ground.

No, it is not moving at 40mph relative to the ground. It is moving slightly slower due to relativistic effects. Speed is only defined relative to other objects or coordinates, so yes, it depends on what it is compared to. You are currently moving at around 67000mph relative to the sun, but about 490000mph relative to the center of the milky way. Unless you're traveling, you are also moving at 0mph relative to the surface of the earth. All of these are true at the same time, and you don't have an 'absolute speed' that isn't relative to something.

Light is an exception. How fast is light traveling? It's traveling the same thing relative to the train as it is relative to the ground. The ball is moving 10MPH relative to the train but 40MPH relative to the ground. With light, the speed is c relative to the train, but unlike the ball and brick, when compared to the ground, the answer doesn't change.

No, everything is shifted the same way. Light just happens to be moving so quickly that it gets shifted to the extreme of appearing to all observers to move at one fixed speed. Anything moving at c has this property. And again, it is not 40mph, it is less than 40mph. The faster the ball relative to the train, the less the effect of the 'addition' of the two speeds relative to the ground.

ETA: Einstein postulates light speed as a universal constant. There's none of this relativity bullshit when it comes to light. That it's used as a genuine defacto constant in the postulate is what allows for the possibility for the unintuitive consequences. The other two variables become unfixed. Length and time. Length contraction and time dilation is a mathematical necessity.

There's ONLY this relativity bullshit when it comes to light. The postulate that light propagates at c independent of the motion of the emitting body is one that comes directly from the results of major, repeatedly replicated experiments. The consequences that follow are a mathematical and logical necessity. Relativity predicts the actual, measured outcomes to a ludicrous amount of precision so it's up to you to reconcile that with your conclusions, not reality. Reality does not care if you don't like it, or if it doesn't make sense to you. It just is.

 

[Treedbear]

To be relative is to be compared to. The train is moving 30MPH relative to the ground, and the ball is moving 10MPH relative to the train yet moving 40MPH relative to the ground. The speed of the ball is what? 10MPH or 4OMPH? The answer depends doesn't it? Same thing with the brick. It depends on what it's compared to. The train or the ground.

No, it is not moving at 40mph relative to the ground. It is moving slightly slower due to relativistic effects. ...

Drat. You beat me to it.

...
Relativity predicts the actual, measured outcomes to a ludicrous amount of precision so it's up to you to reconcile that with your conclusions, not reality. Reality does not care if you don't like it, or if it doesn't make sense to you. It just is.

In defense of reason I seem to remember that Einstein's opinion on the matter was that if the experiments showed that reality behaved differently than his theory then it was God who was wrong (or something to that effect). Ah, here it is:

Einstein was convinced his theory was correct even before it was tested. A journalist asked him what he would do if the theory was wrong. His reply became famous: "Then I would feel sorry for the good Lord. The theory is correct."

 

[steve_bank]

In a collision of two objects whether they are both moving depends on reference frame, the point of relative motion.

A spaceship accelerates out to deep space. Using accelerometers it decorates to the starting velocity, is it at rest, and how do you know? In space all you can determine is a change in velocity from a starting point. A new spaceship leaves Earth orbit, it does not start at zero velocity relative to an absolute frame.

The 'all stop' order in Star Trek can not mean an absolute rest position.
Problems with relative motion existed well before AE.

A comment on the aether. Before Maxwell there were problems with action at a distance for electricity and magnetism Some thought there had to be a medium. Maxwell solved the problem with fields, and soon after particles as the power transfer mechanism.

 

[fast]

Could remaining relative to the point of the Big Bang be considered an ideal location for the makings of an imaginary grid from which to base absolute rest points?