Special Relativity

[The Gregorian]

Yes, this will get into the creation/evolution debate, so this is an on topic thread... but we're gonna start on a tangent, then work back to the topic.


I was wandering around youtube and found this:
http://www.youtube.com/watch?v=AZ6N85lNgHY

Pay special attention to the train example.

If lightning strikes two poles at the same time, someone standing motionless between the poles will observe the poles being hit at the same time... therefore he's moving at "normal time"... or through it at a normal rate.

the moving observer will see lightning hit one pole sooner than the other because while the light is traveling toward him, he's also moving... the distance becomes longer for the pole he's moving away from, therefore it takes longer for the light to reach his eye, therefore HE observes the two poles as not being struck simultaneously.

This is used to suggest that his motion caused time itself to slow... because he observes it happening at different times, therefore it DID happen at different times for him.

While, I understand the illustration, I don't draw the same conclusion. Yes, he'll observe the lightning hit the poles at different times due to an optical illusion. Optical illusions don't bend the fabric of time to remain real... he simply was moving, therefore saw one flash too soon and one too late and was mistaken. That doesn't prove time changed...

What about this illustration... something readily observable: Stand a good hundred yards away from someone dribbling a basketball. Watch as you see the ball contact the earth... but hear it later.

Yet, your motion hasn't changed. Should we assume that we are experiencing time flowing at TWO rates simultaneously because we see something happen before we hear it happen? We saw the ball hit, then LATER heard the ball hit... did time stand still? Did we go back in time? Or is it more likely to see different relative speeds tricking our perceptions than to assume the fabric of time has been altered based upon what we're looking at.

 

[The Gregorian]

So the question... does anyone else see this illustration as flawed, or would someone like to clarify how optical illusions dictate reality?

 

[Frumious Bandersnatch]

So the question... does anyone else see this illustration as flawed, or would someone like to clarify how optical illusions dictate reality?

We have been over this ground before. The example is not flawed. It is not an "optical illusion". Time passes differently for moving observers. GPS systems would not work without taking Special Relativity into account as I am sure you know by now.

Reality is indifferent to your inability to comprehend special relativity.

 

[ChordatesLegacy]

Time dilation has been tested many times including placing super accurate atomic clocks on planes (jumbos) and flying them around the world for a while.

These clocks are then compared to atomic clocks that remained stationary on the earth’s surface, and they had indeed increased in speed by a measurable amount.

So no matter what you thing of the illustration, it is correct, just a shame you cannot grasp it.

 

[Chalnoth]

If lightning strikes two poles at the same time, someone standing motionless between the poles will observe the poles being hit at the same time... therefore he's moving at "normal time"... or through it at a normal rate.

I think this is your problem. There is no such thing as "normal time". The observer on the train's time is as "normal" as the time of the observer on the ground. In fact, all observers see time as "normal" to themselves. No observer is preferred over any other.

What special relativity does is it allows us to understand how to look at what one observer sees, and translate that into what another observer sees (provided the two are moving at constant velocity). So, if we take the train example again, and take a train moving very, very fast, then we will see a clock held by a person on the train moving slower than our clock. We will also see the train as being shorter than the person on the train sees it.

If, by contrast, we consider what the observer on the train sees, he sees his own clock going at "normal" speed, and our clock moving more slowly. He also sees the track that the train is moving on as being much shorter than we on the ground would measure it.

In effect, what different observers moving at different velocities see is a kind of rotation being performed between length and time.

While, I understand the illustration, I don't draw the same conclusion. Yes, he'll observe the lightning hit the poles at different times due to an optical illusion. Optical illusions don't bend the fabric of time to remain real... he simply was moving, therefore saw one flash too soon and one too late and was mistaken. That doesn't prove time changed...

Let's take a different situation, then: cosmic ray muons. Cosmic ray muons are created high in the upper atmosphere as cosmic rays collide with nuclei, causing a massive shower of subatomic particles. These particles decay pretty much instantaneously into muons, which have a lifetime of 2.2 microseconds. Now, here's the apparent problem: the muons start their life at around 15km. These cosmic ray muons are moving at very close to the speed of light, which is around 300,000km/s, and thus it takes them approximately 50 microseconds to reach the ground.

But the mean muon lifetime is only 2.2 microseconds! Without special relativity, we would predict to see only one cosmic ray muon out of ten billion that are produced: we should see almost none of them reach the ground. This isn't the case, though: we see tons of cosmic ray muons. And furthermore, when we compare the muon rates at sea level and on mountains, we find that the rate varies much more slowly than we would expect, without taking special relativity into account.

So how do we explain the large number of cosmic ray muons? Simply put, because they are moving at such high velocities, time is slower for them. For example, for a cosmic ray muon moving at 0.99c, the "gamma factor" is 7. This means that the half-life of such a cosmic ray muon as seen by a person on Earth, while the muon is moving at 0.99c relative to Earth, is 2.2*7 ~15.5 microseconds. If the muons are moving this fast, then, we expect many, many more to reach the Earth, specifically around one in 24 muons. These are vastly better numbers than one in 10 billion, and actually explain why we see so many on the ground.

More detailed measurements of the actual energies of these muons, as well as their relative abundances at high and low altitudes, are one of the stronger confirmations of special relativity at high velocities.

 

[Allegory]

It's easier to understand if you think about it like this: c is not the speed of light, c is the speed limit on how fast things can go in the universe. Light goes "the speed of light" simply because it can't go any faster, and in fact light itself frequently goes much slower than c. The reason light goes exactly c (in a vacuum) is because it has no mass, anything with mass needs to go slower than c because the time dilation becomes too severe and the mass becomes infinite and then you have a little black hole ripping around the universe at the speed of light, which is probably not good for anyone.

 

[The Nihilist]

I'll be honest, I don't understand the train thought experiment either. I've heard some pretty great explanations for how special relativity works, but the train one just doesn't make sense. I guess the reason is that I don't understand why this would be surprising for someone who held a more traditional understanding of time. Clearly I'm missing something, and I'd appreciate it if someone could fill me in.

 

[Allegory]

I'll be honest, I don't understand the train thought experiment either. I've heard some pretty great explanations for how special relativity works, but the train one just doesn't make sense. I guess the reason is that I don't understand why this would be surprising for someone who held a more traditional understanding of time. Clearly I'm missing something, and I'd appreciate it if someone could fill me in.

I did some googling around to see if they maybe explained it wrong, but no luck..it just seems like it's the worst possible way to try to explain relativity. I thought a better explanation came a little later when they were talking about why the speed of light is the same in all frames of reference.

I was thinking that maybe the explanation for the example was that the events don't need to be regarded as occurring simultaneously because there's a finite speed at which the information of the event can reach us. But then I was thinking, that's kind of silly because we don't regard seeing celestial events thousands of light years away as happening "right now", and it's essentially the same effect isn't it?

Maybe it's just intended to illustrate that things can appear to happen in a different way to people in different frames of reference, and we shouldn't put more thought into it than that.

 

[Chalnoth]

I did some googling around to see if they maybe explained it wrong, but no luck..it just seems like it's the worst possible way to try to explain relativity. I thought a better explanation came a little later when they were talking about why the speed of light is the same in all frames of reference.

I was thinking that maybe the explanation for the example was that the events don't need to be regarded as occurring simultaneously because there's a finite speed at which the information of the event can reach us. But then I was thinking, that's kind of silly because we don't regard seeing celestial events thousands of light years away as happening "right now", and it's essentially the same effect isn't it?

Maybe it's just intended to illustrate that things can appear to happen in a different way to people in different frames of reference, and we shouldn't put more thought into it than that.

Well, I don't think that the video explains it all that well. I'll see if I can't do a better job here.

Consider this situation:

The person on the train is passing by the person on the ground at the exact moment that the person on the ground sees the two lights go off simultaneously. Because the person in the train is crossing that exact same place at that exact same time, the light from both lamps must also hit his mirror at the exact same time. He must observe the lights simultaneously.

However, what would he infer about the simultaneity of the light sources? Well, since he's moving towards one light source and away from the other, he would infer that the light source he is moving away from went off first, and the one he is moving towards went off a little bit later. So, they both see the flashes at the same time, but the one moving in the train infers that they were not simultaneous flashes, while the one on the ground infers that they were.

Note that this means that if one observer might see two events as being simultaneous, then another observer might see event A happening before event B, while a third observer moving in the opposite direction might see event B happening before event A. This is a big reason why it's really important that nothing move faster than the speed of light: if anything did, some observers would see events happening before their causes!

 

[Loudmouth]

Well, I don't think that the video explains it all that well. I'll see if I can't do a better job here.

Consider this situation:

The person on the train is passing by the person on the ground at the exact moment that the person on the ground sees the two lights go off simultaneously. Because the person in the train is crossing that exact same place at that exact same time, the light from both lamps must also hit his mirror at the exact same time. He must observe the lights simultaneously.

However, the man on the train will measure a difference in the wavelengths of the light. The light from the pole in the direction of his velocity will be blueshifted and the light from the pole that he is moving away from will be redshifted. Using our knowledge of physics, the luminosity of the lightning, and it's spectra the person on the train can independently calculate his velocity with respect to the two poles.

 

[Allegory]

However, the man on the train will measure a difference in the wavelengths of the light. The light from the pole in the direction of his velocity will be blueshifted and the light from the pole that he is moving away from will be redshifted. Using our knowledge of physics, the luminosity of the lightning, and it's spectra the person on the train can independently calculate his velocity with respect to the two poles.

Okay I think you've brought up a good point in this post. The idea behind the experiment is that the simultaneity of two events is relative to the observers. So you might say "Yes, of course the forward bolt would be seen before the rear bolt" because the frame of reference in which the lightning bolts occurred simultaneously is moving from forward to rear in your frame of reference. These events didn't necessarily actually occur at the same time, rather they can be observed as occurring simultaneously in one frame of reference and at different times in a different frame of reference.

Perhaps a different way of thinking about it would be to consider that if the lightning bolts strike at the same time in the moving frame of reference of the train, they do not occur at the same time in the "stationary" frame of reference of the observer of the ground.

 

[keith99]

I think it might be helpful to go back to the Physics before relativity. At that time it was thought there was thought any wave had to have a medium to travel through. The invisible ether. If it should exist then it should be detectable. Tests to do this failed and in fact showed it did not exist.

With no ether the question is raised just which frame of reference is stationary? Of course we can define things relative to some other object. But we know the Earth is not the center of the universe. So forget teh train examples, make it two spaceships in the middle of nowhere. They are moving relative to eachother. Which is right? Is there a way to tell? The answer is no.

Train examples are very misleading in terms of common sense (as opposed to math and testing internally) as we know which is moving relative to a common frame of reference, the Earth. But if you had trains on perfect tracks and they are moving at constant speed and you close the window you can not detect which direction you are moving or how fast.

 

[Loudmouth]

Personally, I like the glass room thought experiment better.

In this example there is a glass room with furniture and a lamp in the center of the room. Inside this room is Bob. The glass room is accelerated to relativistic speeds and passes by Tom from left to right. At that moment the lamp is turned on. What do Bob and Tom observe?

Bob, inside the room, would observe that the light hits the all of the walls at the same time. Tom would observe the light hitting the left wall before hitting the right wall (relative to Tom) while the light would hit the wall nearest to him at the same time that it hits the wall farthest from him.

 

[Bombila]

Better, Loudmouth. I think trains should be left out of illustrations of this nature altogether - just sends us mathophobes back to life shattering nightmares from Grade three: "if a train leaves Philadelphia travelling at 84kph..."

Aggghhhh!!!! (covers head with pillow and sucks thumb...)

And why is it always leaving Philadelphia, anyway?

 

[MasterOfKrikkit]

Better, Loudmouth. I think trains should be left out of illustrations of this nature altogether - just sends us mathophobes back to life shattering nightmares from Grade three: "if a train leaves Philadelphia travelling at 84kph..."

Aggghhhh!!!! (covers head with pillow and sucks thumb...)

And why is it always leaving Philadelphia, anyway?

Why would it want to stay in Philly? (But I always thought it was Chicago, anyway.)

With regards to time dilation (rather than simultaneity per se), the thought-experiment I like is that of two people with light clocks: a photon of light is trapped in a box with mirrors at the top and bottom, so time is measured by counting the bounces of the photon off the mirrors. The two people move relative to each other (one on the ground, the other on the train). From their own perspectives, each "sees" the photon bounce directly up and down, traveling a length given by the height of the clock. But they both "see" the other's photon travel a zig-zag path (because it bounces off the bottom mirror and, by the time it reaches the top mirror, it's moved sideways a bit, and similarly down again). Consequently, the photon is traveling further (in the other observer's frame) in each pass:

|---/
| /
| /
| /
/

The |'s are the photon's path seen by the person holding the clock; the /s are the path seen by the other person. The hypotenuse of a triangle (/) is longer than the other sides (|).

Now, if light travels at the same speed in all frames, then it must take longer to travel the longer path, hence the other person counts a slower rate of bounces -- the other person's clock is running slower than their own.

To get back to the OP a bit: this is NOT just an optical illusion. It is reality, unless light does not travel at the same speed in all frames. However, experiments have confirmed that light does indeed do so, and that time dilation is real.


EDIT: I can't make the formatting work! Imagine the /s above form a nice diagonal line.

 

[keith99]

Why would it want to stay in Philly? (But I always thought it was Chicago, anyway.)

With regards to time dilation (rather than simultaneity per se), the thought-experiment I like is that of two people with light clocks: a photon of light is trapped in a box with mirrors at the top and bottom, so time is measured by counting the bounces of the photon off the mirrors. The two people move relative to each other (one on the ground, the other on the train). From their own perspectives, each "sees" the photon bounce directly up and down, traveling a length given by the height of the clock. But they both "see" the other's photon travel a zig-zag path (because it bounces off the bottom mirror and, by the time it reaches the top mirror, it's moved sideways a bit, and similarly down again). Consequently, the photon is traveling further (in the other observer's frame) in each pass:

|---/
| /
| /
| /
/

The |'s are the photon's path seen by the person holding the clock; the /s are the path seen by the other person. The hypotenuse of a triangle (/) is longer than the other sides (|).

Now, if light travels at the same speed in all frames, then it must take longer to travel the longer path, hence the other person counts a slower rate of bounces -- the other person's clock is running slower than their own.

To get back to the OP a bit: this is NOT just an optical illusion. It is reality, unless light does not travel at the same speed in all frames. However, experiments have confirmed that light does indeed do so, and that time dilation is real.


EDIT: I can't make the formatting work! Imagine the /s above form a nice diagonal line.

Bolding mine.

This is the point that those who have not been taught about special relativity often don't get. Simple veruion . There is a space ship going at 1/2 the speed of light relative to me. It passes me and I shine a flashlight jsut as it goes by. I see that light going at c relative to me. The guys in hte ship see it going at c relative to them and if there was a second ship going at 1/2 c towards the first ship it would aslo se the light coming toward it at c!

And this is exactly what has been observed. All the rest it trying to make sense out of this, which at first mmakes no sense.

 

[Loudmouth]

Bolding mine.

This is the point that those who have not been taught about special relativity often don't get. Simple veruion . There is a space ship going at 1/2 the speed of light relative to me. It passes me and I shine a flashlight jsut as it goes by. I see that light going at c relative to me. The guys in hte ship see it going at c relative to them and if there was a second ship going at 1/2 c towards the first ship it would aslo se the light coming toward it at c!

Not to belabor the point, while they measure the same speed they do not see the same color of light.

 

[keith99]

Not to belabor the point, while they measure the same speed they do not see the same color of light.

True. But so what? All it gives is the speed difference between two frames of reference. It does nothing to show one frame is the 'right' one. In fact going to the details it provides more evidence for no ether. For sound waves if you have an observer and a generator of sound there is a different frequency shift depending which is moving relative to the transmission medium. Not so for light. The shift only depends on the relative speed.

 

[Loudmouth]

True. But so what?

This is what links space and time.

For sound waves if you have an observer and a generator of sound there is a different frequency shift depending which is moving relative to the transmission medium. Not so for light. The shift only depends on the relative speed.

This is because sound propogates through a medium that has mass. Light does not.

 

[Dragar]

There's nothing to stop you in relativity (special or general) from claiming that there is some effect that influences our measurements (an 'optical illusion'), and that only in one, true, correct reference frame are we measuring 'real values'.

This isn't a very fruitful way of thinking about it, however, as every observer is just as justified in considering their reference frame the 'true' one. And one must come up with some very contrived rules for how measurements are being affected (e.g. when measuring muons moving at a particular velocity, our measurements of how many survive in a given tick of our clock is influenced in such and such a contrived fashion to reproduce precisely the predictions of special relativity), with no explanation for why this is taking place.

Reality is, after all, best defined in science as 'that which all honest and accurate observers agree upon'. Defining reality to be only what one arbitrary subset of accurate and honest observers can agree upon is a very poor definition. (This isn't the whole story, by any means, but ceratainly one shouldn't be picking and choosing which observer is accurate and which is not, based on a whim.)