How can something have both a constant speed and a precise location?

[Soumya_M]

How can something that moves at a constant speed for all reference frames have a specific location?

Suppose two observers Alice and Bob are in motion with respect to each other so that they do not have a common inertial frame. But when both of them measure the speed of a photon, they find it to move at a constant speed of 'c'. Now, suppose the motion between Alice and Bob comes to an end and they are now at rest with respect to each other and hence have a common frame of reference. However,when they measure the speed of the photon again, they still agree on its speed. Ofcourse, the stoppage of motion between Alice and Bob cannot have an impact on the motion of the photon. But it's speed remains constant even when the motion has stopped. Doesn't this imply that the photon does not have a specific spatial position?

 

[sophiecentaur]

Only Alice OR Bob can see any individual photon. It can only do its business once. So it is either at A or B, depending upon who sees it. The other observer will be seeing another photon.

 

[ko_kyi]

Doesn't this imply that the photon does not have a specific spatial position?

No, to measure speed you must measure time. Photons travel only at light speed, so the variable factor is time, not photon velocity. When they have a motion relative to one another, their time is not the same as when at rest with one another.

 

[sophiecentaur]

But isn't the message of QM that they have no defined position until actually measured / observed?
By that token, the question can't be asked.

 

[Soumya_M]

Photons travel only at light speed, so the variable factor is time, not photon velocity. When they have a motion relative to one another, their time is not the same as when at rest with one another.

It is true that time or passage of time must differ for Alice and Bob. But the question I am asking is about the "position". When Alice and Bob are in different frames of reference, to "agree" on the velocity of the photon, they must "disagree" on its position. This is because something traveling at the same (non-zero)velocity must be at different places in different points of time, because distance traveled varies with time. For example, when 5 secs have passed for Alice, 7 secs might have passed for Bob. Therefore, because they "see" the photon traveling at the same velocity, they will see it at different places. One will see it having traveled for 5 secs, while the other will see it to have traveled 7 secs.

Now, when Alice and Bob stop moving and are at rest with respect to each other, they still agree on the velocity. But surprisingly, they now "agree on its position as well"!

 

[Soumya_M]

But isn't the message of QM that they have no defined position until actually measured / observed?
By that token, the question can't be asked.

In QM surely the question about position is meaningless. But then, why do they say that QM and Relativity are incompatible?

Relativity shows that things traveling at the velocity of light must have the same velocity for all reference frames. QM suggests that they do not have a precise position. These two suggestion are not only compatible but are also complementary, because if particles had precise positions they couldn't have the same velocity for all reference frames. They manage to maintain the same velocity for all because they need not have precise positions. So, the theories should be considered not only compatible but also complementary. Why is it not so?

 

[ko_kyi]

Doesn't this imply that the photon does not have a specific spatial position?

I'm really not qualified to answer, but I think I understand the question. I would guess that the answer is that it does have a spatial position, but what the measurement of it is would depend upon where you measure it from, Alice, Bob, or a third observer, and each would be correct inside their frame.

 

[sophiecentaur]

They say that General Relativity and QM are not compatible.
But, as we are dealing with a single quantum of light, it can only be observed by one person. They cannot both detect it so they cannot disagree about its position, colour or the size of its shoes!
Once either one of them has seen the photon, it can't be anywhere else. Is this message still not getting through? Think of A and B as the two slits in 'that experiment'. Read all about it and see how what I am saying applies to Alice and Bob.

 

[ko_kyi]

I suspect what the "agreement" was in the question is "The path the photon ought to have taken" and my only point was that there wouldn't be agreement. There is no reason there should be, because the only way to agree would be to have Alice and Bob in the same inertial frame.

I seem to remember a thought experiment with a light beam bouncing between two mirrors, with the two mirrors traveling past a third observer. The path taken by the beam seems a straight back and forth to the people holding the mirror, yet to the observer the path looks like a diagonal zigzag. For all concerned, the beam travels at c but the length of the path is different. Which path is correct? It seems like they all are, with different values for the "position" of the beam if you are a mirror holder or the 3rd observer.

 

[Drakkith]

They say that General Relativity and QM are not compatible.
But, as we are dealing with a single quantum of light, it can only be observed by one person. They cannot both detect it so they cannot disagree about its position, colour or the size of its shoes!
Once either one of them has seen the photon, it can't be anywhere else. Is this message still not getting through? Think of A and B as the two slits in 'that experiment'. Read all about it and see how what I am saying applies to Alice and Bob.

I don't see how it applies to alice and bob. The slits in the experiment aren't observers, and they are very close together, unlike Alice and Bob which will be much further apart. The photon that Alice sees most definitely took the path to get to Alice's eye and not one to get to Bob's.

 

[rcgldr]

I seem to remember a thought experiment with a light beam bouncing between two mirrors, with the two mirrors traveling past a third observer. The path taken by the beam seems a straight back and forth to the people holding the mirror, yet to the observer the path looks like a diagonal zigzag. For all concerned, the beam travels at c but the length of the path is different. Which path is correct? It seems like they all are, with different values for the "position" of the beam if you are a mirror holder or the 3rd observer.

That's the issue, Alice and Bob would need to choose some common inertial (non-accelerating) frame of reference (call it Ted or Carol) with an origin and a grid (to demark distance from it's origin) in order to share some common reference system for "position". It's a though experiment trying to cheat by designating a frame of reference as an "absolute" in a "relative" universe.

About the only real world example I can think of is navigation used for spacecraft . Stars are treated as stationary frames of reference and used in star charts. One of the modes of navigation on the Apollo spacecraft was the equivalent of a sextant and scanning telescope to be used with the star charts. Obviously not relativistic speeds involved in this case, but distant stars could be used as a frame of reference in this thought experiment.

 

[sophiecentaur]

From your reply, you seem not to have read about the two slits in detail. It is the simplest example of how the quantum nature and the wave nature of EM can be discussed. As long as A or B don't actually observe the photon then it's final destination is statistical and can be predicted by wave theory; it 'goes past' both of them (equivalent to going through both slits). Once A or B looks at the photon the wave 'collapses' and it can't show up anywhere else. You really need to read further about this if you don't want to accept what I say.