Conundrum Regarding the Lack of an Absolute Frame of Reference

[loseyourname]

This just popped into my head earlier tonight, for whatever reason. Imagine a photon, a lone photon, that was the only thing in existence. According to relativity theory, am I correct to say that without any other object by which it may be said to be in motion relative to, we cannot say that the photon is in motion? However, due to relativity, the photon would experience no passage of time, a phenomenon that is attributed to its velocity of c. It seems paradoxical to say that an object that is not in motion has a velocity, yet this seems to be what is happening here. Can anyone clarify exactly what is going on here for me?

 

[Janitor]

A very interesting question, that. Special relativity physics is in some sense embedded in a taken-for-granted background of spacetime that itself may only make sense if the universe has a whole bunch of stuff in it. Are there any threads on Mach's principle in the Physics Forum? I myself used to wonder what a universe consisting of one material particle would be like, but I never thought of asking what if a universe just had one massless particle in it and nothing else.

 

[OneEye]

I posted a similar contemplation a little while ago in which an empty universe was populated only by a spacecraft with an emission-free propulsion system (a kind of theoretical "impulse drive" I saw on the web some time ago which works thorough a revolving coil which is briefly energized at exactly the same point of each rotation - thus producing a pseudo-mass which accelerates the apparatus in a particular direction).

Given that such an engine could actually work, the question I asked was, "How can an object experience acceleration, but no change in velocity?" Acceleration is experienced directly, while velocity is only experienced relatively.

Several people picked my thought-experiment apart on practical grounds, but I can't remember anyone trying to answer the basic riddle.

 

[jdavel]

loseyourname,

How can there be a photon without any particles? You can't expect physics to explain a universe that physics says can't exist.

 

[loseyourname]

Whether or not it's possible for a photon to exist in isolation isn't the point. I'm just concerned that, without introducing any exotic elements, this seems to reveal an inconsistency in special relativity. The theory states that all velocity is relative, does it not? Yet it is at least possible to envision a scenario in which there could be velocity without relation. I'm just trying to think of a way to reconcile this. I've considered self-reference, but while that seems possible with temporal movement, it doesn't seem like it can explain spatial movement, at least not at a constant velocity. I'm far from being an expert on this subject. The puzzle just popped into my head a couple nights ago and I assumed that I'm just overlooking something, given that I really have very little knowledge of the details of relativity theory. I hoped someone here could fill in the gaps.

It seems a pointless besides to ask if this universe could actually be. Physics has yet to explain the existence of our own universe, and it probably never will. If you don't like the idea of a single photon because it is associated with a change in the energy state of another particle, just substitute it with any other massless particle.

 

[Hurkyl]

TMK, The problem of measurement is a very sticky one in modern physics. Measurement is extraordinarily difficult in General Relativity; for a time it was thought that it predicted measurement was impossible! In Quantum Mechanics the problem is real, and I don't mean the uncertainty principle; as I recall, there is a theorem that any clock has a nonzero probability of occasionally running backwards!

 

[loseyourname]

Sure. There's even a non-zero probability that the entropy of a closed system could decrease. Is no law sacred anymore?

 

[jdavel]

loseyourname said, "Whether or not it's possible for a photon to exist in isolation isn't the point."

You're mistaken; it's exactly the point. SR says that when the speed of light is MEASURED it will be c with respect to whoever measures it. It says absolutely nothing about what light does or doesn't do when a measurement isn't being made. It may seem like an irrelevant point, but the fact that instruments used to measure light speed are made out of particles with mass is absolutely essential to the theory. If there were a way to measure light speed without using any mass, SR would colapse!

 

[loseyourname]

You obviously ignored my point about how the velocity was determined. The fact that the photon experiences no passage of time is a relativistic effect meaning that it must be traveling at c. Obviously, unless the photon was conscious, there wouldn't be anyone in this universe to realize this, but it would still be happening. Nothing about SR says that an event must be observed in order for it to happen.

 

[jdavel]

loseyourname,

SR says:

1) All massless particles travel at c with respect to particles that have mass.

2) All particles that have mass travel at speeds less than c with respect to other particles that have mass.

In a universe with only one particle (of either kind) both those statements are meaningless. So in a universe with only one particle (of either kind), SR would be meaningless. SR would have nothing to say about that universe. It wouldn't apply to that universe.

But the job of physics is to explain OUR universe. Now sometimes physicists will imagine an idealized version of the universe in order to learn something about the real universe. But there are rules in physics about idealizations that can be used and ones that can't. And one absolute rule is that you can't disprove a theory by imagining a situation where it would be disproven.

 

[russ_watters]

Nothing about SR says that an event must be observed in order for it to happen.

Right, all it says is that the event must be observed for Relativity to be relevant.

 

[loseyourname]

I hope you guys don't think I'm one of those people trying to disprove relativity. It is well beyond my capacities to even think of such a thing. I would need to fully understand the theory first and besides, it makes perfect sense to me and as far as I know, it's been confirmed in every experiment capable of confirming it.

Addressing what Russ brought up, I was under the impression that relativity is relevant regardless. For instance, take the synchronization of clocks on the satellites we have in orbit. They use relativistic equations to remain in synch, do they not, and this is all automated, is it not? If all of the conscious lifeforms on this planet died off and this could no longer be observed, it would continue to take place and the equations would continue to work.

I suppose in the truest sense, nothing is relevant unless it is given relevance by a conscious observer, but that isn't to say that relativity doesn't apply unless the events it is describing are observed. Am I incorrect?

 

[jcsd]

Oneye re acceleration:

Think about it this way in SR spacetime can be thought of as 'absolute' (that is all observers agree on certain things that are happening in spacetime), objects all 'travel' with the same magnitude of 4-velocity in spacetime, but the 'direction' of this 4-velocity is depednent on both the magnitude and direction of their 3-velcoity (in some reference frame). Therefore we can recognize when an object is accelerating as it 'rotates' in spacetime and everyone agrees thta it rotates.

Looseyourname: It doesn't make much sense to talk about things from a photons point of view in relativity.

Hurkyl re the clock going backwards: that sounds like decoherence to me.

 

[hellfire]

I think the formulation of the postulates of special relativity given by jdavel is misleading. According to SR, speeds are defined to be relative to reference frames (the term "observer" is usually used to mean "reference frame"). If there is spacetime (a background globally flat spacetime), then there exist reference frames (infinite ones) and thus it exists the posibility to define motion. Whether only one physical body, or more than one exist on spacetime seams to be an irrelevant point to me.

Regards.

 

[billy_boy_999]

it seems to me like only jcsd has actually tried to address the fundamental answer to this particular riddle...

you are taking away all frames of reference and leaving just a photon and asking if it is in motion in the absence of reference frames...whether or not this is physically a valid idea, the essence of the riddle is whether motion is independent of frames of reference, is it not?

in relativity, isn't continuous motion only motion relative to other reference frames? and isn't only accelerated motion measured against absolute spacetime?...so the question is maybe whether light waves count as accelerated motion...they definitely can change direction - but not without other particles to warp space-time!

 

[russ_watters]

I suppose in the truest sense, nothing is relevant unless it is given relevance by a conscious observer, but that isn't to say that relativity doesn't apply unless the events it is describing are observed. Am I incorrect?

I don't recall anyone ever saying you need a human observer. A computer checking different clocks in different frames satisfies the observer requirement because it includes different clocks in different frames.

The importance of the observer isn't its/his/her nature, its its/his/her existence, takin a measurement that complies with the theory.

A photon with nothing to measure it fits some of the critereon for applicability of SR (its a photon, so it should be traveling at C), but not all the criterion for applicability of SR (without any reference points [the "observer"], it can't be said to have any velocity, not even C).

What is speed? Distance divided by time. For a photon with no observer, what is the distance and what is the time?

 

[yogi]

I would agree with hellfire - photons exist in largely empty space and they travel very nicely from place to place (whether or not there are masses or measuring fames) in accordance with Maxwell's equations. The fact that the photon is always measured to have the same velocity relative to an isotropic light frame, does not impact the physics that are responsible for the photon's trajectory.

 

[Janitor]

Does it do violence to modern-day physics ideas to imagine a universe with no real particles in it at all, just virtual particles? Is there any sense in which such a universe could be said, for instance, to be four-dimensional, or if you prefer, eleven-dimensional or whatever it is supposed to be in string theory?

 

[hellfire]

you are taking away all frames of reference and leaving just a photon and asking if it is in motion in the absence of reference frames...whether or not this is physically a valid idea, the essence of the riddle is whether motion is independent of frames of reference, is it not?

Yes, may be you are right and I might not have fully understood the problem.

In my previous comment I was addressing the question of internal consistency of special relativity. It seams to me that the existence of a globally flat background spacetime is a sufficient condition to define the motion of a single paticle.

But I agree that one could also, in principle, remove the background spacetime. I don’t know how to proceed then...

Regards.

 

[OneEye]

The thing that I find interesting, in my little Gedanken, is that one can accelerate without a change in velocity. This may be the natural consequence of GR (wherein such acceleration is regarded as a gravity field, if I am not mistaken), but then this means that it is theoretically possible in GR to have a sourceless gravity field!

I understand that such thought experiments must be restrained to sensible grounds. But I also feel that this particular contemplation implies an important conclusion:

Relativity - SR,at least, - is really only about observation using light - the natural consequence of using a non-inertial finite-velocity measuring tool. The math works, and it squares with observation, but SR can really only comment on what we can observe. The limits of v<c would then (as illustrated by my thought experiment) talk about what can be observed by someone who did not share my reference frame, not about what actually happens to me - precisely because we are using light as our yardstick.

 

[loseyourname]

A photon with nothing to measure it fits some of the critereon for applicability of SR (its a photon, so it should be traveling at C), but not all the criterion for applicability of SR (without any reference points [the "observer"], it can't be said to have any velocity, not even C).

I suppose you are right to say that it can't be "said" to have a velocity, given that there would exist nothing and no one to "say" anything. Still, nothing that I know of in SR says that an event must be measured or observed in some way in order to actually occur. It's almost like you're denying the objective existence of unobserved events. The central assumption of all science, including relativity physics, is that the laws are the same everywhere. According to the laws, all photons move at c in a vacuum, regardless of anything.

Another thing I was wondering about is the behavior of a photon in a black hole. Given that c is less than the escape velocity, would not the photon cease all motion and hence violate the constancy of the velocity of light? Is this avoided by postulating the non-existence of time in a black hole and thus giving an indeterminate answer (0/0) when a measurement is attempted? Wouldn't this mean then that the velocity of light is always either c or indeterminate rather than always c?

 

[russ_watters]

I suppose you are right to say that it can't be "said" to have a velocity, given that there would exist nothing and no one to "say" anything. Still, nothing that I know of in SR says that an event must be measured or observed in some way in order to actually occur. It's almost like you're denying the objective existence of unobserved events. The central assumption of all science, including relativity physics, is that the laws are the same everywhere. According to the laws, all photons move at c in a vacuum, regardless of anything.

Yes, the laws are the same anywhere - which means you can't just discard one on a whim. There are two issues here (a theory and a definition):

-According to SR, a photon must have a speed of C.
-Speed is defined as distance over time.

Does a photon in an empty universe have a speed of C? Does a photon in an empty universe have any definable speed at all?

SR is a theory that builds on other laws of physics and math. I don't consider it reasonable to throw out other parts of physics and math in order to create an artificial paradox in SR. Its all or nothing.

Another thing I was wondering about is the behavior of a photon in a black hole.

As far as science is concerned, the universe may well stop at the event horizon. What happens inside isn't necessarily required to follow our laws of physics.

 

[NateTG]

What happens when an immovable object meets an unstoppable force?

If you think about it for a bit, you might realize that it's an impossible situation. Similarly, you postulate that c - a velocity - is meaningful in a universe where there is neither position, nor time.

By the way, the essential notion of science is not that theories are universally applicable, but that experiments are repeatable. The 'laws' of physics are neither universally applicable nor universally correct, and, as such are really misnomers and should really be called descriptions.

 

[jcsd]

Actually Russ, (in the Scwarzcchild solution) the singularity that occurs at the event horizon can be removed and the solution extended into the region r => R_BH (though you get a singularity that you can't remove at r = 0), so the laws of physics don't breakdown until the singularity.

Remember SR is only particular case of GR so what always holds true in SR does not necessarily always hold true in GR. In SR observers always see light traveling at c, this is not always the case in GR. In GR the speed of light is always c to a local observer (that is an observer occupying the same point of space as the light), but it's not always true that observer who is not local will observer the 'speed' of light to be c.

A photon at the event horizon traveling radially out from the black hole will *appear* to have a speed of zero to a remote observer, but if you were falling into the black hole you would observe the speed of light at the event horizon to be c as you passed it, this is due to the curvature of spacetime.

 

[loseyourname]

Does a photon in an empty universe have a speed of C? Does a photon in an empty universe have any definable speed at all?

SR is a theory that builds on other laws of physics and math. I don't consider it reasonable to throw out other parts of physics and math in order to create an artificial paradox in SR. Its all or nothing.

What has been thrown out? There is still space and there is still time in this universe. There is simply no measuring device.

GR I would guess (though I don't know enough about the theory to say for sure) is not applicable in this universe, as there exists no mass and thus no gravity.

 

[jdavel]

loseyourname said, "GR I would guess (though I don't know enough about the theory to say for sure) is not applicable in this universe, as there exists no mass and thus no gravity."

The same goes for SR regarding a universe with no mass; it's not applicable. Without at least one particle with mass it's impossible to define a frame of reference in which to measure the speed of your photon.

 

[loseyourname]

If that is the case, are we not left with the inevitable conclusion that SR is not a fundamental description of reality, but rather is a description of the limitations in our ability to observe and measure it? Surely you can't be saying that because there is no frame of reference in which we can measure its speed, that my imaginary photon has no speed.

 

[jdavel]

loseyournaem asked, "If that is the case, are we not left with the inevitable conclusion that SR is not a fundamental description of reality, but rather is a description of the limitations in our ability to observe and measure it?"

No, SR works fine for "reality". But your universe and its lone photon isn't "reality".

In case you're interested, this question that you've become fixated on isn't going to lead you to any better understanding of SR. And you won't get any better answers to it than you've already gotten. In other words, you're wasting your time wondering about it.

 

[hellfire]

The same goes for SR regarding a universe with no mass; it's not applicable. Without at least one particle with mass it's impossible to define a frame of reference in which to measure the speed of your photon.

I do not understand this. Why is a particle with mass needed to define a reference frame? There are infinite reference frames in an empty universe: just take one point within spacetime and define a set of coordinates. Then the photon will have speed c wrt this reference frame according to SR.

It is also not true (AFAIK) that a globally flat spacetime does not make sense in GR: if you take Tuv = 0, you may obtain a globally flat spacetime. This solution of Einstein equations is as valid as any other, isn't it?

For me the original question in this thread makes sense and it seams to me that it is possible to answer it within SR.

Regards.

 

[selfAdjoint]

As an abstract thing, from whatever inertial frame you may define, the photon is moving at c. As a physical matter, you need matter to measure. The photon itself does not have a rest frame.