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.

 

[confutatis]

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

The question makes sense to me too, but I believe the answer is far simpler than anything offered so far.

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?

If I understood it correctly, this is only partly right. The notion of movement is meaningless without another frame of reference. It's not correct to say the photon is moving, but neither is it correct to say the photon is not moving.

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.

I believe your perception of a paradox comes from the idea that you need an observer to experience motion, but you don't need an observer to experience the passage of time. Apparently the idea makes sense, but only apparently. While it's true that in a universe with only one photon it becomes impossible to define velocity, it also becomes impossible to define time. Just as it is meaningless to say the photon is moving, or not moving, it's also meaningless to say the photon is experiencing time, or not experiencing it. Just as it is for movement, it is impossible to define 'time' without invoking an external reference.

I would also like to note, as others have noted, that a universe with a single photon cannot possibly exist. While the issue has no bearing on the original question itself, it's always good to keep it in mind, because we don't always fully understand what we mean by 'photon'. In essence, a photon is a physical entity that carries information; in a universe with only one photon, the photon has no information to carry. A universe with only one photon is similar to a universe with sound but no sound sources - it may exist in our imagination, but not in reality, and when our imagination allows things forbidden by reality, it always means we have misconceptions.

 

[hellfire]

You may be right, confutatis, but if someone claims in this forum that an universe with a single photon is not possible, or, that although it may be possible no motion nor time are possible then, I would expect to see this proven within the framework of SR or GR. IMHO either SR and GR do not exclude such a scenario. Regards.

 

[loseyourname]

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.

In case you're interested, this question that I've become fixated on and the answers provided have already given me a better understanding of SR. If it is you that is not getting anything from the thread, you are free to not post in it.

You may be right, confutatis, but if someone claims in this forum that an universe with a single photon is not possible, or, that although it may be possible no motion nor time are possible then, I would expect to see this proven within the framework of SR or GR. IMHO either SR and GR do not exclude such a scenario. Regards.

You seem to the only person that agrees with me about that. I initially figured that the problem could be solved within the framework of the theory, but I simply didn't know the theory well enough to do it. I hoped someone here would.

 

[confutatis]

You may be right, confutatis, but if someone claims in this forum that an universe with a single photon is not possible, or, that although it may be possible no motion nor time are possible then, I would expect to see this proven within the framework of SR or GR. IMHO either SR and GR do not exclude such a scenario.

What exactly do you think SR or GR imply should be happening to your photon? Apparently you think it proper to say the photon should be experiencing the passage of time, since we can't say it is moving. But what exactly does "experience the passage of time" mean in a universe where the only thing that exists is a photon?

I do not see how relativity even addresses such a scenario, let alone address it in a contradictory way. I'm curious to know what you have in mind.

 

[hellfire]

I do not understand why can't we say it is moving. If there is a background spacetime, one can define a reference frame at any point in spacetime. Then the photon's coordinates will vary in this reference frame and thus the photon will move.

 

[confutatis]

I do not understand why can't we say it is moving. If there is a background spacetime, one can define a reference frame at any point in spacetime. Then the photon's coordinates will vary in this reference frame and thus the photon will move.

I used to think so myself, but relativity is full of subtleties. The thing I came to understand is that objects don't move relative to spacetime, they only move relative to each other. At least in SR, spacetime is just a geometrical construct used to model the movement of physical bodies - it doesn't exist in the absence of movement.

Even if you think spacetime may be defined in your single-photon universe, you have to ask yourself how it's possible for your photon to move relative to it. If your photon's coordinates are changing with time, that can also be interpreted to mean your coordinate system is moving, but it doesn't make sense to say a coordinate system is moving when that coordinate system is not attached to anything real. The only thing you can use to define a coordinate system in your universe is the photon itself, so you can't really say it is moving relative to its own coordinates.

Hope that helps.

 

[hellfire]

I used to think so myself, but relativity is full of subtleties. The thing I came to understand is that objects don't move relative to spacetime, they only move relative to each other. At least in SR, spacetime is just a geometrical construct used to model the movement of physical bodies - it doesn't exist in the absence of movement.

Strictly speaking, motion of a physical body does not need of another body, at least in principle, but of a reference frame. This is due to the definition of motion as the change of position or coordinates. Position is always defined wrt a reference frame.

The question is whether it is necessary to have another body to define a reference frame. I think it is not necessary. OTOH, as far as I know in SR the globally flat spacetime is preexisting to any motion of bodies; it is a construct derived from the relations between reference frames.

Even if you think spacetime may be defined in your single-photon universe, you have to ask yourself how it's possible for your photon to move relative to it. If your photon's coordinates are changing with time, that can also be interpreted to mean your coordinate system is moving,

This is not correct, since the second principle of SR states that the photon will always move at speed c wrt to my reference frame.

but it doesn't make sense to say a coordinate system is moving when that coordinate system is not attached to anything real.

Well, again, why not? There is a background spacetime in which I can define any reference frame.

Sorry if the whole sounded repetitive, but I still have the impression I am right.

Regards.

 

[billy_boy_999]

but in GR spacetime becomes more than a mathematical construct, it is absolute, you cannot say that objects move in relation to spacetime but you can say that they accelerate relative to absolute spacetime...

is the motion of a photon acceleration?

 

[russ_watters]

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

You're throwing out my second bullet point: the definition of speed.

What is the speed of a photon in a universe where speed doesn't exist?

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.

Thanks - I get a little thin on the deeper (pun intended) aspects of black holes.

 

[confutatis]

Sorry if the whole sounded repetitive, but I still have the impression I am right.

Actually, that has been my experience too. We see things from a certain perspective, and no matter what other people tell us, all they manage to achieve is to get us to go round and round until we're back where we started.

I think what you're trying to get at is something I myself happen to believe: the idea of absolute motion is not only valid, it is actually necessary to explain some discrepancies between physics and our observations of the everyday world. While it must be granted that relativity perfectly explains what goes on in distant galaxies, it still poses a very difficult problem for the man driving his car on a road. For, according to modern physics, as soon as that man takes his foot out of the accelerator pedal, he no longer has the right to claim he is moving while the universe stays in place.

So, until I have more time to get back to you on this subject, on which I believe we share some common ground, I'll just tell you I believe you are addressing a legitimate problem, only not in a legitimate way.

Regards --

 

[selfAdjoint]

Aristotle had the problem of seeing how things could keep moving without a force continually pushing them. He refused to believe in the idea of conservation of momentum, and the whole western world refused the several suggestions for that until Galileo finally made it stick.

Relativity reduces to ordinary physics for velocities very much leass than light; you don't need any additional principles to make that happen. Take v/c around a billionth, which is reasonable, and work out on your calculator what the factor \sqrt{1 - v^2/c^2} is.

 

[loseyourname]

You hardly need a calculator for that.

Russ: What exactly is your definition of speed? I guess I'm going off of the classical definition here of space/time. If a point of reference is needed to define the distances involved, then without such a point, you simply end up with indeterminate/indeterminate, which is what you were asserting on the last page. This is fine, but an indeterminate speed does not equate with no speed. The simple fact that you do not know or cannot in any way determine the parameters of a given event does not mean that that event has no parameters.

Take, for instance, the uncertainty relation D_{p}D_{q}\geq\frac{h}{4\pi}. Now let's say you measure q to perfect accuracy, so that D_{q}=0. You are then left with D_{p}\geq\frac{h}{D_{q}4\pi} => D_{p}\geq\frac{h}{0}, which is clearly undefined. You cannot then assert that the particle being observed has no location. Such a notion is absurd. If it had no location, you would not be able to measure its momentum. This simple logical induction is enough to demonstrate that the particle does have a location, even though it cannot be defined. I think you can use a similar process to demonstrate that the photon in my hypothetical universe has a speed, and even that the speed is c.

I'll try to construct a proof and then post it here.

 

[kawikdx225]

I do not understand why can't we say it is moving. If there is a background spacetime, one can define a reference frame at any point in spacetime. Then the photon's coordinates will vary in this reference frame and thus the photon will move.

hmm...your imaginary reference frame has no mass which implies it could itself be traveling at speed c. What speed would you then measure for the photon?

If you measure speed 0 for the photon you could make two conclusions:
1. the photon isn't moving thus it's speed is 0
2. your massless reference frame is moving at c thus the photon is moving at c

You still wouldn't know it's speed.

 

[russ_watters]

Russ: What exactly is your definition of speed? I guess I'm going off of the classical definition here of space/time. If a point of reference is needed to define the distances involved, then without such a point, you simply end up with indeterminate/indeterminate, which is what you were asserting on the last page. This is fine, but an indeterminate speed does not equate with no speed. The simple fact that you do not know or cannot in any way determine the parameters of a given event does not mean that that event has no parameters.

Really? Well, since speed is relative and depends on what you are measuring it with respect to, what if there is nothing to measure it with respect to? Can I just pick any distance and time I want and call that speed? How about if I'm the only thing in the universe. Can I just say I'm traveling at 2C?

What about for me - what if I'm the only object in the universe? Can I arbitrarily assign myself a speed? If indeterminate doesn't mean nonexistant, doesn't that mean I have an intrinsic speed?

Since speed is relative and depends on the frame you are measuring it with respect to, if there is nothing to measure it with respect to, it doesn't exist. It isn't just impossible to find.

 

[loseyourname]

What about for me - what if I'm the only object in the universe? Can I arbitrarily assign myself a speed? If indeterminate doesn't mean nonexistant, doesn't that mean I have an intrinsic speed?

To be fair, you aren't a massless object. Is it even possible for a massless object to be at rest? This is in line with what I had in mind as far as deducing motion even without being able to measure it. Notice in my first post that I attempt to demonstrate the motion of the hypothetical photon from the axiom that all photons have a null world-line, meaning that it has no rest frame. Momentum is still defined on a null vector (p=E), and it seems absurd to say that a given particle can have momentum without being in motion.

Furthermore, although I understand that had I tried to construct this universe from one particle with mass, it wouldn't work, because the motion of such a particle is only defined wrt a certain inertial frame. The speed of light, however, is the one thing that is constant in all frames. It only takes a small leap of inductive logic to say that it would still be constant in the absence of a frame. Anyway, that's what I was thinking when this popped into my head. Maybe I'm wrong. You guys are the experts, not me.

 

[hellfire]

hmm...your imaginary reference frame has no mass which implies it could itself be traveling at speed c.

As far as I know, due to the definition of the four-velocity one is usually not allowed to define reference frames moving at speed c in special relativity.

Is one allowed to define a reference frame at speed c in an universe without mass (i.e. containing only one photon)?

If you think this is possible, then please explain me why should it be a qualitative difference in the rules of special relativity being applied to an universe with or without massive particles.

Regards.

 

[russ_watters]

To be fair, you aren't a massless object. Is it even possible for a massless object to be at rest?

Of course! Its at rest if I say its at rest. Thats from the definition of motion.

It only takes a small leap of inductive logic to say that it would still be constant in the absence of a frame. Anyway, that's what I was thinking when this popped into my head. Maybe I'm wrong. You guys are the experts, not me.

No, I'm not a Relativity expert - but that is a leap of logic I'm not willing to take. I think we understand each other pretty well in any case.

 

[Hai Tran]

How do I get my position (lattitude and longitude) if I know exact date and time

 

[russ_watters]

How do I get my position (lattitude and longitude) if I know exact date and time

You can observe the positions of the stars. It gets kinda involved though...

 

[selfAdjoint]

You have to observe the altitudes of two stars. From the epherimedes you get the declination and right ascension of the stars, which you can project down on the Earth as a point (latitude and longitude) where the star is overhead at that moment. And from the altitudes you get the radii of two "circles of position" on the Earth about those two geographic centers. You are at one of the two intersections of those circles; which one should be obvious because if you chose the stars well, the intersections will be thousands of miles apart.

The devil of course is in the details, and there are various ways of working this out using spherical trig. The US Navy no longer trains its officers to do this, relying entirely on GPS.