Conundrum Regarding the Lack of an Absolute Frame of Reference

[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.