Special theory of relativity question

[lovetruth]

A “light clock” consists of a mirror, a light source and a light detector. The light source and detector are very close to each other and both are at a distance ‘L’ from the mirror (or the mirror’s plane). In an inertial frame at rest, a light pulse is emitted from the light source perpendicularly towards the mirror; the light pulse is then reflected back from the mirror to the light detector. Thus, the time between a pulse of light to be emitted and detected is ‘2L/c’.
If the same “light clock” is moving with velocity ‘v’, the direction of the light pulse is shown inclined with respect to the light source in the diagrams.

http://users.powernet.co.uk/bearsoft/PictureGif/Ltclk.gif
http://galileo.phys.virginia.edu/classes/252/srelwhat_files/image017.gif

So my question is: why the direction of the light pulse or beam is inclined with respect to the source. Shouldn’t the light pulse just move perpendicularly to the mirror and not at some angle? Relativity theory tells that the speed of light is constant in any inertial frame but does not say that the direction of light should change with respect to the source. Thanks for any help in advance.

 

[PAllen]

Welcom to physics forums. An observer moving with the clock would see the light moving simply perpendicular to the mirror, with no displacement between source and detection. However, if the clock is moving relative to an observer, they see the light emitted at one position and dected at another position. There is no sense in which one is 'right' and the other is 'wrong'.

Does this answer your question?

 

[harrylin]

A “light clock” consists of a mirror, a light source and a light detector. The light source and detector are very close to each other and both are at a distance ‘L’ from the mirror (or the mirror’s plane). In an inertial frame at rest, a light pulse is emitted from the light source perpendicularly towards the mirror; the light pulse is then reflected back from the mirror to the light detector. Thus, the time between a pulse of light to be emitted and detected is ‘2L/c’.
If the same “light clock” is moving with velocity ‘v’, the direction of the light pulse is shown inclined with respect to the light source in the diagrams.

http://users.powernet.co.uk/bearsoft/PictureGif/Ltclk.gif
http://galileo.phys.virginia.edu/classes/252/srelwhat_files/image017.gif

So my question is: why the direction of the light pulse or beam is inclined with respect to the source. Shouldn’t the light pulse just move perpendicularly to the mirror and not at some angle? Relativity theory tells that the speed of light is constant in any inertial frame but does not say that the direction of light should change with respect to the source. Thanks for any help in advance.

I remember when I had the same question.

Perhaps the simplest explanation is to imagine that your light source is a laser.
With the laser in rest, the light will propagate like this inside the laser (laser vertical):

|
|
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But if the laser is moving laterally, the light must already inside the laser propagate like this (if it went straight up then it would go through the side of the laser!):

../
./
/

Thus, concerning direction it is similar as with a bullet from a gun.

 

[lovetruth]

Welcom to physics forums. An observer moving with the clock would see the light moving simply perpendicular to the mirror, with no displacement between source and detection. However, if the clock is moving relative to an observer, they see the light emitted at one position and dected at another position. There is no sense in which one is 'right' and the other is 'wrong'.

Does this answer your question?

My question was why should the light's direction change with respect to the light source when the light source is moving with some velocity 'v not equal to zero'. This is not implied by the relativity theory even though it is shown in the diagrams. I don't know what you mean by " no sense in which one is 'right' and the other is 'wrong'.". The only thing which exists should be the right one.

 

[lovetruth]

I remember when I had the same question.

Perhaps the simplest explanation is to imagine that your light source is a laser.
With the laser in rest, the light will propagate like this inside the laser (laser vertical):

|
|
|

But if the laser is moving laterally, the light must already inside the laser propagate like this (as it will not go through the side of the laser!):

../
./
/

I think that since the speed of light isn't affected by the light source in any way, so must be the direction of the light. Think if instead of the laser, i have a point light source. Also, bullet and the gun analogy can't be applied here bcoz bullet is matter and light is light. Both behave differently otherwise, we won't need theory of relativity in the first place. Otherwise, Galilean relativity should suffice then.
Thx for your valuable time thou

 

[PAllen]

My question was why should the light's direction change with respect to the light source when the light source is moving with some velocity 'v not equal to zero'. This is not implied by the relativity theory even though it is shown in the diagrams. I don't what you mean by " no sense in which one is 'right' and the other is 'wrong'.". The only thing which exists should be the right one.

Actually, the essence of relativity is that about many things there is no right or wrong. Many things ordinary common sense says must be one way or the other (e.g. A happened before B), relativity says NO, one observer sees A before B, another B before A, and there is no way to say one is more correct than the other.

If an observer moving with a clock sees the light leave the source and hit the 'attached' detector, then another observer for which the clock is moving sees the detector move betwen emission and receptions. They both agree that the detector detected light. The only way to resolve this is that for the observer for whom the detector moved, the light must be angled so it can hit the moved detector.

 

[rede96]

Actually, the essence of relativity is that about many things there is no right or wrong. Many things ordinary common sense says must be one way or the other (e.g. A happened before B), relativity says NO, one observer sees A before B, another B before A, and there is no way to say one is more correct than the other.

Is that strictly true? I connect a wire to a battery (A) and a light comes on (B). Although another observer may see the light and then the wire connecting to the battery, wouldn't the laws of physics prevail and the observer know that A had to happen before B?

 

[lovetruth]

Actually, the essence of relativity is that about many things there is no right or wrong. Many things ordinary common sense says must be one way or the other (e.g. A happened before B), relativity says NO, one observer sees A before B, another B before A, and there is no way to say one is more correct than the other.

If an observer moving with a clock sees the light leave the source and hit the 'attached' detector, then another observer for which the clock is moving sees the detector move betwen emission and receptions. They both agree that the detector detected light. The only way to resolve this is that for the observer for whom the detector moved, the light must be angled so it can hit the moved detector.

Thank you for your valuable suggestion.
I know that the common sense is not followed like the relativity of simultaneity you just said. So what we think as wrong like time dilation and length contraction are actually true because we have never experienced near light velocity situations. But I am questioning the internal consistency of the theory of reality. How can we deduce that the light will move at some angle with respect to the source, only by using the 2 hypothesis of the special theory of relativity. I hope you understand my question now.

 

[PAllen]

Is that strictly true? I connect a wire to a battery (A) and a light comes on (B). Although another observer may see the light and then the wire connecting to the battery, wouldn't the laws of physics prevail and the observer know that A had to happen before B?

If the relation between A and B is timelike, all observers agree on the order of events (that includes your example). If the relation is spacelike, different observers will see different orders. For example, suppose two lights are timed to go off at great distance from each other. One observer midway between them sees A go off before B. Another observer, moving relative to the first, sees B go off before A, even if they take light delays into account. Basically, causally connected events have an invariant ordering; causally disconnected events have observer dependent ordering.

 

[PAllen]

Thank you for your valuable suggestion.
I know that the common sense is not followed like the relativity of simultaneity you just said. So what we think as wrong like time dilation and length contraction are actually true because we have never experienced near light velocity situations. But I am questioning the internal consistency of the theory of reality. How can we deduce that the light will move at some angle with respect to the source, only by using the 2 hypothesis of the special theory of relativity. I hope you understand my question now.

No I don't understand your question. I thought I have answered it twice and harrylin has answered it once. Obviously, you are not satisfied. You need to explain as carefully as you can what is not clear about my explanation or Harrylin's.

 

[lovetruth]

No I don't understand your question. I thought I have answered it twice and harrylin has answered it once. Obviously, you are not satisfied. You need to explain as carefully as you can what is not clear about my explanation or Harrylin's.

Ok i will re-explain my question. Why should the light move at an angle cos^-1(v/c) with respect to the light source which is moving with velocity v. This is not deducible from the two hypothesis of special relativity:
1) all laws of physics are valid in all inertial frame
2)Speed of light is same in all inertial frame

If the direction of light is straight when the light source is at rest then, by using first hypothesis ( i.e. all laws of physics are valid in all inertial frame), the light direction should be same (i.e. straight with respect to light source). But this is not shown in the books.

 

[nitsuj]

My question was why should the light's direction change with respect to the light source when the light source is moving with some velocity 'v not equal to zero'. This is not implied by the relativity theory even though it is shown in the diagrams. I don't know what you mean by " no sense in which one is 'right' and the other is 'wrong'.". The only thing which exists should be the right one.

It isn't actually moving at an angle to the mirrors.

It is actually moving at an angle to your eyes.

the two observations are independent (neither is "right" or "wrong").

EDIT: It isn't moving at an angle from the light source (and to the mirrors), the light source is in the same frame.

Using some of your terminology: All components of the clock that is in motion are in fact at REST RELATIVE TO EACH OTHER. The light emitted from the light source, leaves the light source, just as it would when at rest relative to you (not moving relative the light source).
That is the "all laws of physics are valid in all inertial frame" or something like that.

 

[PAllen]

Ok i will re-explain my question. Why should the light move at an angle cos^-1(v/c) with respect to the light source which is moving with velocity v. This is not deducible from the two hypothesis of special relativity:
1) all laws of physics are valid in all inertial frame
2)Speed of light is same in all inertial frame

If the direction of light is straight when the light source is at rest then, by using first hypothesis ( i.e. all laws of physics are valid in all inertial frame), the light direction should be same (i.e. straight with respect to light source). But this is not shown in the books.

The laws of physics are the same. The speed of light is the same in both frames. There isn't a law that says angles are the same in all frames. Consider Galilean relativity (pre-relativity mechanics):

1) The laws of physics are the same in all frames.

(No statement about light; the idea of an ether frame came with Maxwell, so pretend pre-Maxwell physics).

Doe this mean that all observers see a bullet move the same direction? No. Does this violate (1) ? No. This was Harrylin's explanation, and it is a good one.

 

[ZikZak]

How can we deduce that the light will move at some angle with respect to the source, only by using the 2 hypothesis of the special theory of relativity. I hope you understand my question now.

You can't. You appeal to the Postulate of Realism that is fundamental to all science--- that an external universe exists to be studied. In other words, that while observers may disagree on when and where events occur, if there is a real external reality, then they cannot legitimately disagree that the event occurred somewhere at some time.

The observer at rest with the clock observes that, at some point in time and space, the laser strikes the top plate of the clock. This event has a causal relationship to other events: in this case, it initiates the downwards track of the laser ray. But it could just as easily have set off a bomb that was programmed to explode when a laser ray hit it.

Therefore, all other observers must also agree that the ray hits the top plate. Either it struck the plate or it didn't. Either the bomb went off or it didn't. All must agree on this, otherwise reality itself depends on the observer, we're in the Matrix, and nothing can be said about nature at all.

Since all observers agree that the ray hits the top plate, in particular an observer who observes the clock in motion must agree. The only way for that to have happened was if the light ray took a diagonal course to get there.

 

[rede96]

If the relation between A and B is timelike, all observers agree on the order of events (that includes your example). If the relation is spacelike, different observers will see different orders. For example, suppose two lights are timed to go off at great distance from each other. One observer midway between them sees A go off before B. Another observer, moving relative to the first, sees B go off before A, even if they take light delays into account. Basically, causally connected events have an invariant ordering; causally disconnected events have observer dependent ordering.

Thanks for that. I don’t want to hijack this thread but I did have another question.

I am probably stretching a point too far, but suppose there were two unconnected random events separated by some distance. For the sake of this hypothetical, let's just say that these events were random flashes of light on two planets, A and B.

As they are disconnected they are observer dependent ordering.

I seek out the source of the flashes of light and put a device next to each that will imitate the flashes A and B. I'll call these devices C and D. I control these devices, thus making them connected.

I then randomly flash my lights in the order C then D. I'd have to be pretty lucky to get my flashes to coincide with random flashes on the planets A and B, but maybe I get lucky!

So from my frame, I see A and C flash together then B and D together. (No issue with simultaneity here as A & C are right next to each other in space, as are B & D) Therefore, all observers must agree on this sequence as they are now causally connected, even the original unconnected random flashes of A and B.

Without my devices, we couldn’t determine sequence. With the devices we can. So is there a proper sequence of events, like there is proper length and proper time?

 

[lovetruth]

The laws of physics are the same. The speed of light is the same in both frames. There isn't a law that says angles are the same in all frames. Consider Galilean relativity (pre-relativity mechanics):

1) The laws of physics are the same in all frames.

(No statement about light; the idea of an ether frame came with Maxwell, so pretend pre-Maxwell physics).

Doe this mean that all observers see a bullet move the same direction? No. Does this violate (1) ? No. This was Harrylin's explanation, and it is a good one.

Pretend Galilean relativity?? If galilean relativity was true then there would be no need for special relativity theory. Also, the bullet has both vertical and horizontal momentum so the observer will see it moving at an angle. But light is no bullet; light is not matter. If the light behaved like bullet then, the light will have a vertical velocity 'c' and horizontal velocity 'v' and the speed of light as seen by the observer will be (v^2+c^2)^(1/2). Yes it will then move at an angle but will also break the fundamental law: Constancy of speed of light. So, your analogy of bullet and light is flawed.

 

[nitsuj]

Actually, the essence of relativity is that about many things there is no right or wrong.

I think that's one of the coolest results of coming to understand relativity. It even has implications socially, now how cool is that? (Morales are totally different of course )

 

[nitsuj]

Yes it will then move at an angle but will also break the fundamental law: Constancy of speed of light. So, your analogy of bullet and light is flawed.

Could time maybe ensure the "constancy" (consistency?) of c?

And at what point could an analogy not be flawed?

Also, the light clock would have to be moving at near c speeds for the light clock cycles to slow (noticeably for you) from time dilation. All other speeds within your ability to perceive, the light will NOT appear to be at an angle, its just too fast (you will never ever ever see light leave a moving object at an angle compared to its rest frame).

I'd guess there is a correlation between the angle the light appears to move along for a "stationary" observer and the effect time dilation has on the light clock, all on the promise of the "constancy" of c.

 

[PAllen]

Pretend Galilean relativity?? If galilean relativity was true then there would be no need for special relativity theory. Also, the bullet has both vertical and horizontal momentum so the observer will see it moving at an angle. But light is no bullet; light is not matter. If the light behaved like bullet then, the light will have a vertical velocity 'c' and horizontal velocity 'v' and the speed of light as seen by the observer will be (v^2+c^2)^(1/2). Yes it will then move at an angle but will also break the fundamental law: Constancy of speed of light. So, your analogy of bullet and light is flawed.

No, both observers see the speed of light the same, angle different, distance traveled different. It is precisely the angle and greater distance traveled (as seen by the observer for whom the clock is moving) that accounts for the time dilation as perceived by this observer. They see the moving clock call these greater distance traversals, at standard light speed, called 'one second'. Thus they see the clock ticking slow compared to similar clock at rest relative to them.

There is nothing in the principles you quoted that says distance, times, and angles are invariant. They are NOT. It is the laws of physics and the *speed* of light that are the same for all inertial observers.

 

[PAllen]

Thanks for that. I don’t want to hijack this thread but I did have another question.

I am probably stretching a point too far, but suppose there were two unconnected random events separated by some distance. For the sake of this hypothetical, let's just say that these events were random flashes of light on two planets, A and B.

As they are disconnected they are observer dependent ordering.

I seek out the source of the flashes of light and put a device next to each that will imitate the flashes A and B. I'll call these devices C and D. I control these devices, thus making them connected.

I then randomly flash my lights in the order C then D. I'd have to be pretty lucky to get my flashes to coincide with random flashes on the planets A and B, but maybe I get lucky!

So from my frame, I see A and C flash together then B and D together. (No issue with simultaneity here as A & C are right next to each other in space, as are B & D) Therefore, all observers must agree on this sequence as they are now causally connected, even the original unconnected random flashes of A and B.

Without my devices, we couldn’t determine sequence. With the devices we can. So is there a proper sequence of events, like there is proper length and proper time?

Assuming you control them by signal, there is causal connection between your signal and C, and your signal and D. There is still no causal connection between C and D, so a different observe will see them in a different order (but will agree that you controlled both with a signal).

 

[lovetruth]

You can't. You appeal to the Postulate of Realism that is fundamental to all science--- that an external universe exists to be studied. In other words, that while observers may disagree on when and where events occur, if there is a real external reality, then they cannot legitimately disagree that the event occurred somewhere at some time.

The observer at rest with the clock observes that, at some point in time and space, the laser strikes the top plate of the clock. This event has a causal relationship to other events: in this case, it initiates the downwards track of the laser ray. But it could just as easily have set off a bomb that was programmed to explode when a laser ray hit it.

Therefore, all other observers must also agree that the ray hits the top plate. Either it struck the plate or it didn't. Either the bomb went off or it didn't. All must agree on this, otherwise reality itself depends on the observer, we're in the Matrix, and nothing can be said about nature at all.

Since all observers agree that the ray hits the top plate, in particular an observer who observes the clock in motion must agree. The only way for that to have happened was if the light ray took a diagonal course to get there.

Thanks for responding to my question. You say that the light should bend in order for reality to be same for all the observers in the universe whether in inertial frame or non-inertial frame. You are right if the light doesn't bend, the reality would not be same for all observer. The idea of having separate reality for every observer is strange but not impossible. When I first read theory of relativity my views about universe shattered, but I can not deny the experiments. I think reality is what laws of physics dictates however strange they are. Besides I think living in Matrix will be much cooler than livin in this boring world.
All in all, I ask does any theory (including the relativity) predicts the light will move at an angle with respect to the light source when the light source is moving.

 

[lovetruth]

No, both observers see the speed of light the same, angle different, distance traveled different. It is precisely the angle and greater distance traveled (as seen by the observer for whom the clock is moving) that accounts for the time dilation as perceived by this observer. They see the moving clock call these greater distance traversals, at standard light speed, called 'one second'. Thus they see the clock ticking slow compared to similar clock at rest relative to them.

There is nothing in the principles you quoted that says distance, times, and angles are invariant. They are NOT. It is the laws of physics and the *speed* of light that are the same for all inertial observers.

Ok then tell me the name of the law of physics that says the direction of light depends on the velocity of the observer. The whole point of relativity theory was to avoid any influence of the light source on the propagation of light
Consider another case: the light source is movin with velocity v and is emitting light in the direction of its movement. You will say the light moves straight with respect to light source. WHY does the angle does not change in this case even if the light source is movin.

 

[PAllen]

Ok then tell me the name of the law of physics that says the direction of light depends on the velocity of the observer.
Consider another case: the light source is movin with velocity v and is emitting light in the direction of its movement. You will say the light moves straight with respect to light source. WHY does the angle does not change in this case even if the light source is movin.

The name of the law that says direction of light depends on observer's motion is aberration. See, for example:

http://en.wikipedia.org/wiki/Aberration_of_light

If you read about the law of aberration, you note that it does not apply to a light source moving directly towards an observer. Note that aberration is one of those laws that must be the same for all inertial frames - the law that is, not the specific parameters.

 

[lovetruth]

Could time maybe ensure the "constancy" (consistency?) of c?

And at what point could an analogy not be flawed?

Also, the light clock would have to be moving at near c speeds for the light clock cycles to slow (noticeably for you) from time dilation. All other speeds within your ability to perceive, the light will NOT appear to be at an angle, its just too fast (you will never ever ever see light leave a moving object at an angle compared to its rest frame).

I'd guess there is a correlation between the angle the light appears to move along for a "stationary" observer and the effect time dilation has on the light clock, all on the promise of the "constancy" of c.

If an event is TOO fast to be perceived, it does not imply that the event does not exist. All effects of relativity are too small to be perceived but nonetheless proved to exist by experiments.

 

[nitsuj]

Pretend Galilean relativity?? If galilean relativity was true then there would be no need for special relativity theory.

Well duh, that's why he said pretend.

Your big words tricked me into thinking you were, well nvm...

 

[Mentz114]

All in all, I ask does any theory (including the relativity) predicts the light will move at an angle with respect to the light source when the light source is moving.

It is predicted by special realtivity. The Lorentz transformation that connects the two frames will convert a set of t-x-y axes into another. In the transformed frame the angle between the x and y axes is no longer 90^o. So the observer sees the light travel at an angle not equal to 90^o to the direction of travel.

 

[nitsuj]

Consider another case: the light source is movin with velocity v and is emitting light in the direction of its movement. You will say the light moves straight with respect to light source. WHY does the angle does not change in this case even if the light source is movin.

umm because it's leaving parallel to the direction of motion. There would still be time dilation.

In other words the light would still travel a longer distance and in more time, from your perspective of course.

 

[lovetruth]

The name of the law that says direction of light depends on observer's motion is aberration. See, for example:

http://en.wikipedia.org/wiki/Aberration_of_light

If you read about the law of aberration, you note that it does not apply to a light source moving directly towards an observer. Note that aberration is one of those laws that must be the same for all inertial frames - the law that is, not the specific parameters.

I have read Aberration of Light on wikipedia. It says it is an instrumental error and depends on the parameters of the telescope. Please read the links before you post them. And it considers only the motion of the observer and not of the light source

 

[PAllen]

I have read Aberration of Light on wikipedia. It says it is an instrumental error and depends on the parameters of the telescope. Please read the links before you post them. And it considers only the motion of the observer and not of the light source

Oh, and you think you can distinguish motion of observer relative to source versus motion of source relative to observer?! You will not get far in relativity until you can let go of such notions.

It is not an instrument error but a natural phenomenon. Aberration in special relativity was one whole section of Einstein's 1905 paper. Not only is it not inconsistent with his theory, but he used his theory to give a clearer understanding of this long observed phenomenon.

 

[lovetruth]

It is predicted by special realtivity. The Lorentz transformation that connects the two frames will convert a set of t-x-y axes into another. In the transformed frame the angle between the x and y axes is no longer 90^o. So the observer sees the light travel at an angle not equal to 90^o to the direction of travel.

Lorentz transform only affects the direction which is along the relative velocity v. Therefore, there is only length contraction and not height or width contraction. Therefore the system in consideration will have contraction in the horizontal direction. Since the light is moving in only vertical direction, it will not move at an angle by applyin lorentz transformation.

 

[nitsuj]

If an event is TOO fast to be perceived, it does not imply that the event does not exist. All effects of relativity are too small to be perceived but nonetheless proved to exist by experiments.

Yes I agree, why did you raise the point? it seems moot here.

 

[PAllen]

Lorentz transform only affects the direction which is along the relative velocity v. Therefore, there is only length contraction and not height or width contraction. Therefore the system in consideration will have contraction in the horizontal direction. Since the light is moving in only vertical direction, it will not move at an angle by applyin lorentz transformation.

This is just wrong. If you have a right triangle with base 1 and height 2, and you change the base from 1 to .5, how do you keep the hypotenuse at the same angle?

 

[lovetruth]

Well duh, that's why he said pretend.

Your big words tricked me into thinking you were, well nvm...

How can we use ancient theory to solve problems. I might well pretend that Earth is flat and Earth is the centre of the universe.

 

[nitsuj]

And it considers only the motion of the observer and not of the light source

well, thanks to the "Constancy" of c that is the same thing.

 

[PAllen]

How can we use ancient theory to solve problems. I might well pretend that Earth is flat and Earth is the centre of the universe.

The analogy had a precise purpose. Galilean relativity is extremely accurate for speeds slow compared to light. For such speeds, all laws are Galilean invariant. Yet even here, no SR effects, angles are not preserved across Galilean transforms. The point was that your belief that angles should be preserved is completely absurd.