Is Proper Time=0 Equivalent to Saying Proper Time Doesn't Apply?

[Nick666]

So apparently the concept of proper time doesn't apply to a photon . But I've seen in some places explained that the proper time=0 for a photon because this and because that.

So I'm a bit confused now, is proper time=0 equivalent or not to saying proper time doesn't apply ?

 

[Mentz114]

The proper time is given by the formula $t^2-x^2$. Because the distance traveled by light is the same as the time taken the value is 0.

 

[Nugatory]

So apparently the concept of proper time doesn't apply to a photon . But I've seen in some places explained that the proper time=0 for a photon because this and because that.

So I'm a bit confused now, is proper time=0 equivalent or not to saying proper time doesn't apply ?

Some people use the term "proper time" only for spacetime intervals whose squared length is greater than zero. If you use this convention, then proper time doesn't apply to the path that light like takes because the spacetime interval along that path is zero. Other people use the term "proper time" to apply to any space-time distance, or at least to ones whose squared length is equal to zero, not just the ones whose squared length is greater than zero. If you use this convention, then you will say that light does have a proper time, and it's always zero.

They're both OK ways of thinking about it. The important thing is that they both agree that the spacetime interval along the path that light takes is always zero; it's really not terribly important what they call these zero-length intervals.

 

[ghwellsjr]

So apparently the concept of proper time doesn't apply to a photon . But I've seen in some places explained that the proper time=0 for a photon because this and because that.

So I'm a bit confused now, is proper time=0 equivalent or not to saying proper time doesn't apply ?

Since time according to the precepts of Special Relativity is defined as what a clock measures, time cannot apply to a photon because no clock can travel at the speed of light. If you use the space time interval between two events that start out as time like and you continually move one of the events so that the interval gets smaller and smaller until it reaches zero, you might be tempted to think of this as a zero Proper Time but you can also start with two events that are space like and move one of them so that the interval gets smaller and smaller until it reach zero and you might be tempted to think of this as a zero Proper Length but the two are in fact identical, neither time like or space like but rather null, meaning it's not anything. Time like intervals can be measured with a clock and space like intervals can be measure with a ruler but there is no way to measure a null interval, neither with a clock nor a ruler.

So for these reasons, associating Proper Time or Proper Length to a photon misses a very important concept in Special Relativity and should be avoided.

 

[Finn]

Along the same lines as the OP, I've wondered if some sources object to the application of proper time to a photon because of these definitions:

a photon follows a light like path,

proper time is the time of an inertial clock along the path of an object,

"In relativity, proper time is the elapsed time between two events as measured by a clock that passes through both events... [Wikipedia] [In fact I thought the clock had to travel the path of the object.]

and these definitions conflict?

That is, you can't have a massive clock travel at light speed.

Or is there a way around the apparent conflict?

 

[rede96]

Since time according to the precepts of Special Relativity is defined as what a clock measures, time cannot apply to a photon because no clock can travel at the speed of light.

I don't disagree that a clock can't travel through space-time at the speed of light but I was wondering if a clock can travel at the speed of light or even faster than speed of light relative to another frame due to cosmological expansion. I know this may sound completely absurd but I don't know of any law of physics that prevents me from attaching a clock to an extremely long piece of wire, attaching the other end to a planet far away and then waiting for expansion to make the planet start to move away from me faster than speed of light. When the clock starts to move, it will be traveling at some point, past some objects, at the speed of light or greater.

 

[bcrowell]

I don't disagree that a clock can't travel through space-time at the speed of light but I was wondering if a clock can travel at the speed of light or even faster than speed of light relative to another frame due to cosmological expansion.

GR doesn't have any definite way of defining the velocity of one object relative to some other cosmologically distant object. For example, you might be able to say that galaxy A and galaxy B are both at rest, but the space between them is expanding, or you might equally well be able to say that B is receding from A at a velocity greater than c.

None of this has anything to do with special-relativistic time dilation. SR only applies locally.

 

[rede96]

GR doesn't have any definite way of defining the velocity of one object relative to some other cosmologically distant object. For example, you might be able to say that galaxy A and galaxy B are both at rest, but the space between them is expanding, or you might equally well be able to say that B is receding from A at a velocity greater than c.

But isn't correct to say that in either case, the distance between A and B is increasing and that this distance could be increasing at speeds greater than c?

None of this has anything to do with special-relativistic time dilation. SR only applies locally.

I know my thought experiment is ridicules as the wire would have to be thousands of light years long. But there must be something in the laws of physics that prevent a wire to be this long or it is theoretically possible that the clock, which is connected to some receding galaxy, could be moving locally through a system at speeds greater than c

EDIT: Which would mean it would be possible to measure the change in time of the clock between two points.

 

[bcrowell]

But isn't correct to say that in either case, the distance between A and B is increasing and that this distance could be increasing at speeds greater than c?

No. There is no preferred way of defining the distance between A and B, because that depends on fixing a definition of simultaneity, which is arbitrary.

 

[rede96]

No. There is no preferred way of defining the distance between A and B, because that depends on fixing a definition of simultaneity, which is arbitrary.

Ah, ok. But we know at least galaxies are moving apart and we can measure this rate by red shifting.

 

[bcrowell]

Ah, ok. But we know at least galaxies are moving apart and we can measure this rate by red shifting.

If you like, you can say they're not moving at all, and attribute the redshift to the stretching of the electromagnetic waves due to cosmological expansion of the space through which they're moving.

 

[rede96]

If you like, you can say they're not moving at all, and attribute the redshift to the stretching of the electromagnetic waves due to cosmological expansion of the space through which they're moving.

Yes sure, they may not be moving through space time, but as far as I understand it, the distance between them and the rate that distance changes, increases with time, hence expansion. Which means at some point in the future the light from these distant galaxies will fail to reach us as they will be receding faster than c.

So I use this increasing speed of separation in my thought experiment as if I could attached an almost infinitely long wire to local galaxy and then hang around for a few million years until it starts to move away from me at greater and greater speeds, then as my wire unravelled in my local frame, it would eventually be moving at speeds >c

 

[bcrowell]

Yes sure, they may not be moving through space time, but as far as I understand it, the distance between them and the rate that distance changes, increases with time, hence expansion. Which means at some point in the future the light from these distant galaxies will fail to reach us as they will be receding faster than c.

No, this is a common misconception. A nice discussion of this is Davis and Lineweaver, "Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe," http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf .

 

[rede96]

No, this is a common misconception. A nice discussion of this is Davis and Lineweaver, "Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe," http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf .

Thanks for link, that was an interesting read. Although I probably need to digest some of it properly when I get time.
But in general it is pretty much how I understood and and thus still supports my thought experiement. E.g. below is quote from the article.

A good analogy is to imagine that you are an ant living on the surface of an inflating balloon. Your world is two-dimensional; the only directions you know are left, right, forward and backward. You have no idea what “up” and “down” mean. One day you realize that your walk to milk your aphids is taking longer than it used to: five minutes one day, six minutes the next day, seven minutes the next. The time it takes to walk to other familiar places is also increasing. You are sure that you are not walking more slowly and that the aphids are milling around randomly in groups, not systematically crawling away from you.

The point being that the distance between some galaxies is getting larger and they are moving apart faster. So although the galaxies itself is not traveling greater than c locally, any wire that was attached to a receding galaxy, that was long enough, could theoritically be moving faster than c in a local frame. Not because the galaxy it is attached to is moving at c, but the exansion of space is 'pushing' the galaxy away at speeds greater than c.

 

[A.T.]

Which means at some point in the future the light from these distant galaxies will fail to reach us as they will be receding faster than c.

Receding faster than c doesn't prevent their light from reaching us:

https://en.wikipedia.org/wiki/Ant_on_a_rubber_rope



Which light can reach us depends on the acceleration of the expansion.

 

[rede96]

Receding faster than c doesn't prevent their light from reaching us:

Which light can reach is depends on the acceleration of the expansion.

Yes, that's the bit I need to digest further, but understand it in principle thanks. But does that effect my thought experiement in any way?

 

[Nick666]

I believe the wire would stretch, simillar to length contraction in relativity but the other way around, length dilation. Maybe someone can correct me on this.

 

[rede96]

I believe the wire would stretch, simillar to length contraction in relativity but the other way around, length dilation. Maybe someone can correct me on this.

I am not 100% sure, but I would imagine that if it were possible to have a wire this long and you were to observe it moving past you then normal relativity would apply. So it would be the wire's speed relative to you. In which case you would see the wire length contracted not stretched.

 

[rede96]

I believe the wire would stretch, simillar to length contraction in relativity but the other way around, length dilation. Maybe someone can correct me on this.

Unless you meant you saw the wire moving past you at a speed relative to you greater than the speed of light, in which case I am really not sure! But first thoughts are that yes it would seem longer as it would be the oppisite effect of length contraction. But it is just theoretical so who knows.

 

[Ibix]

I think this is a variant on the old chestnut of spinning a long rod such that the tip exceeds the speed of light. Since matter is held together by electromagnetic forces which propagate at the speed of light there's no way, even in principle, for a body to hold together when some chain of reasoning suggests some part of it "ought to" exceed the speed of light. In other words your wire will snap, no matter what it's made out of.

There may also be issues related to your wire (which is long on cosmological scales) being spaghettified by the expansion of space, rather than towed along by one end. I'm not confident of that, however, so take with a pinch of salt.

 

[rede96]

I think this is a variant on the old chestnut of spinning a long rod such that the tip exceeds the speed of light. Since matter is held together by electromagnetic forces which propagate at the speed of light there's no way, even in principle, for a body to hold together when some chain of reasoning suggests some part of it "ought to" exceed the speed of light. In other words your wire will snap, no matter what it's made out of.

This seems to make sense, as I didn't think it would be possible. Be nice to undertand this in a bit more detail so will have a scout around.

There may also be issues related to your wire (which is long on cosmological scales) being spaghettified by the expansion of space, rather than towed along by one end. I'm not confident of that, however, so take with a pinch of salt.

I am not sure either but from the article I just read linked to above it would seem to suggest that expansion does not effect physical objects. So don't think that would be an issue. But your first point seems to solve it.

 

[Ibix]

I am not sure either but from the article I just read linked to above it would seem to suggest that expansion does not effect physical objects. So don't think that would be an issue. But your first point seems to solve it.

More precisely, the effect of the expansion of space is negligible for any existing physical object, even taking a loose definition of "physical object" that includes things like galaxies. However, you are talking about something that is gigantic compared to even a galactic cluster, and I don't think you can neglect the effect so casually then.

Not prepared to go beyond that, since I'm not good enough at GR yet.

 

[Jimster41]

Isn't this (interesting and confusing) question related to the "Bell Spaceship Paradox" where two rockets are connected by a string. Seems an interesting variation on the puzzle, focusing on the question of what "rest frame" means in an expanding universe, what it means for a "single physical object" to span or occupy curved (or expanding) space-time?

https://en.m.wikipedia.org/wiki/Bell's_spaceship_paradox

 

[Nugatory]

I think this is a variant on the old chestnut of spinning a long rod such that the tip exceeds the speed of light. Since matter is held together by electromagnetic forces which propagate at the speed of light there's no way, even in principle, for a body to hold together when some chain of reasoning suggests some part of it "ought to" exceed the speed of light. In other words your wire will snap, no matter what it's made out of.

Yes.

 

[Nugatory]

Isn't this (interesting and confusing) question related to the "Bell Spaceship Paradox" where two rockets are connected by a string. Seems an interesting variation on the puzzle, focusing on the question of what "rest frame" means in an expanding universe, what it means for a "single physical object" to span or occupy curved (or expanding) space-time?

https://en.m.wikipedia.org/wiki/Bell's_spaceship_paradox

It looks to be related, but there's only so far you can push the comparison. Bell's Spaceship paradox is at heart a relativity of simultaneity problem within a flat local region; this cosmological question is about comparisons of coordinates across non-locally curved regions.

 

[Jimster41]

It looks to be related, but there's only so far you can push the comparison. Bell's Spaceship paradox is at heart a relativity of simultaneity problem within a flat local region; this cosmological question is about comparisons of coordinates across non-locally curved regions.

Thanks. That caution makes sense to me (I'm glad).

Hope it's okay to clarify my understanding in context. Is it correct to say the curvature between coordinates in the cosmological question is described, accounted for, by the second term of the FLRW solution to the GR field equations, an equation taken as a model of the shape of the our 4d universe?

{ -c }^{ 2 }d{ \tau }^{ 2 }={ -c }^{ 2 }d{ t }^{ 2 }+a{ \left( t \right) }^{ 2 }d{ \Sigma }^{ 2 }

And is t in that FLRW equation the coordinate time of a frame co-moving (at rest) with respect to the CMB? Or rather, what is that t?

[Edit] Sorry, maybe that should be a separate thread. I just wouldn't have the question if I wasn't trying to follow this one.

 

[ghwellsjr]

Along the same lines as the OP, I've wondered if some sources object to the application of proper time to a photon because of these definitions:

a photon follows a light like path,

proper time is the time of an inertial clock along the path of an object,

"In relativity, proper time is the elapsed time between two events as measured by a clock that passes through both events... [Wikipedia] [In fact I thought the clock had to travel the path of the object.]

and these definitions conflict?

That is, you can't have a massive clock travel at light speed.

Or is there a way around the apparent conflict?

Wikipedia's article on Proper Time makes it clear that the clock has to follow the world line, that is, it has to travel the path of the object, so I don't know where you are seeing a possible conflict. Where did you get that quote?

 

[Nick666]

Just so I don't open another thread.

If the photon doesn't have a referential frame, and relativity says the laws of physics are the same in all referential frames, can't one say that the laws of physics are ...not...the same for the photon ?

 

[Mentz114]

Just so I don't open another thread.

If the photon doesn't have a referential frame, and relativity says the laws of physics are the same in all referential frames, can't one say that the laws of physics are ...not...the same for the photon ?

the photon doesn't have a referential frame is a law of physics.

 

[jbriggs444]

the photon doesn't have a referential frame is a law of physics.

That's pithy but does not ring true. Maybe it's just my mathematical background showing through.

The principle of relativity seems to be a kind of "second order" law of physics. First order laws are valid within a particular frame of reference and specify the behavior of objects and phenomenon referenced against such a frame. But the term "frame of reference" is not even part of the first order language of physics. It is a second order concept.

Asking that the principle of relativity apply to second order concepts brings in the possibility of self-reference which is probably better avoided.