Can mass go faster than the speed of light?

[MeJennifer]

OK, so imagine a clock that starts at Earth at the moment the light is emitted, accelerates to some high fraction of lightspeed, then later turns around and makes it back to Earth in time for the light's return. Here we have used a single clock to measure both departure and return too, so isn't this a "roundtrip" time? If you restrict roundtrip time to inertial clocks, what physical justification do you have for saying roundtrip time measured by inertial clocks is somehow more "real" than roundtrip time measured by non-inertial clocks?

You are missing the point, the traveling clock will not measure the roundtrip time of light at all it will simply desynchronize from the Earth's clock due to its speed differential when it traveled and hence all it will "measure" is the time difference between the Earth's clock when it will come back to Earth.

It is not about the clock but about the time it takes light to go from A to B. For instance if Earth or Sirius B were to accelerate the roundtrip time of light, due to special relativity, would obviously change. But obviously the time it takes light to go from A to B does not depend on Jimmy going on a trip with a clock that is going to be desynchronized with a clock on Earth.

Edited to add:

We actually do not have to restrict ourselves to intertial clocks. Suppose both Earth and Sirius B are accelerating then we still can record a roundtrip time and determine how long it takes light to go from Earth to Sirius B and back, however we would have to realize that the roundtrip time may not remain constant over time if the accelerations are variable, a situation a bit like distances in non-stationary spacetimes in GR.

 

[JesseM]

You are missing the point, the traveling clock will not measure the roundtrip time of light at all

Do you call it "traveling" in contrast to the Earth clock? But of course there are countless frames where the Earth clock is traveling too. There is no physical sense in which the time between two events as measured by an inertial clock that has the two events on its worldline is any more "real" than the time between the same two events as measured by a non-inertial clock that has the events on its worldline; they are just two different proper times for two different clocks.

It is not about the clock but about the time it takes light to go from A to B.

The only physical notion of time in relativity is proper time. Again, one clock's proper time isn't any more "real" than any other clock's proper time. So although you can talk about the proper time for light to go from Earth to Sirius B and back as measured by a clock on Earth, there's no reason to think of this as "the" time for light to go from Earth to Sirius B and back.

 

[Count Iblis]

It is interesting to consider tunneling. Suppose a clock on the North Pole tunnels to the South Pole. What will be the proper time that will have elapsed?

 

[peter0302]

The universe will have imploded before that was likely to occur, so I wouldn't worry about it. :)

 

[DaveC426913]

The universe will have imploded before that was likely to occur, so I wouldn't worry about it. :)

Funny thing about probabilities is that it is exactly as likely to happen tomorrow as on the last day of the universe.

 

[Count Iblis]

The universe will have imploded before that was likely to occur, so I wouldn't worry about it. :)

Let me reformulate the question to make it better defined. Suppose a scientists at the North Pole accidentally drops his watch. But to his amazement he can't find it on the ground. Then a scientist on the South pole sees a watch appear on the ground, apperently out of thin air. The watch has tunneled through the earth. What will be the time difference between the events of the watch being dropped and the watch reappering as indicated by the watch itself?

 

[MeJennifer]

The only physical notion of time in relativity is proper time. Again, one clock's proper time isn't any more "real" than any other clock's proper time.

A strawman argument as I am not disagreeing with that at all.

So although you can talk about the proper time for light to go from Earth to Sirius B and back as measured by a clock on Earth, there's no reason to think of this as "the" time for light to go from Earth to Sirius B and back.

There is only one proper time between any sequence of events or in this case 3 events, the emission, relfection and absorbtion of light. All observers must agree on the elapsed proper time between those events. That such an amount of elapsed proper time does not agree with their clocks is either due to relative motion or spacetime curvature.

 

[JesseM]

A strawman argument as I am not disagreeing with that at all.

Really? Then why did you place so much emphasis on this statement:

And however they accelerate, the fact remains that light takes 8.6 years to go from Earth to Sirus B, hence Sirus B is 8.6 light years away from Earth!

If you agree that light only takes 2*8.6 years round trip according to one arbitrary clock, and that the time would be different according to other equally valid clocks, then why do you think Sirius B "is" 8.6 light years from Earth? Do you agree that there is absolutely nothing physically special about the measurements that give the round-trip time as 2*8.6 years as opposed to some other number?

There is only one proper time between any sequence of events

There is only one proper time on a given worldline that contains those events, but there are multiple possible worldlines that contain the events, and they measure different proper times between the events. Do you disagree?

or in this case 3 events, the emission, relfection and absorbtion of light. All observers must agree on the elapsed proper time between those events.

Do you disagree that in relativity the term "proper time" is only used in the context of particular worldlines, that there is no unique "proper time" between distinct events which can have multiple worldlines that pass through both? If you do disagree, then you are using the term "proper time" incorrectly.

That such an amount of elapsed proper time does not agree with their clocks is either due to relative motion or spacetime curvature.

"Relative motion" relative to what exactly? You certainly can't talk about motion relative to the events themselves, since events are instantaneous...

 

[MeJennifer]

There is only one proper time on a given worldline that contains those events, but there are multiple possible worldlines that contain the events, and they measure different proper times between the events. Do you disagree?

Do you realize that there is only one possible worldline (or multiple in certain curved spacetimes) between events that are lightlike separated?

 

[JesseM]

Not at all, and hopefully you can see that light always travels on a particular worldline!

Sure, but the proper time along a null geodesic is always 0 (or maybe physicists don't even talk about 'proper time' for null geodesics, but in the limit as timelike geodesics get closer and closer to null geodesics the proper time should approach 0).

 

[spiffomatic64]

"Moving at 0.9c" doesn't mean anything unless you specify what it's relative to. If you're moving at 0.9c relative to Earth and you fire a photon, it will move at 1c relative to you, and also at 1c relative to the Earth, because of the way relativistic velocity addition works.

another quick question about this

If this were true, wouldn't that mean that the Earth observer sees the traveler going just .1 less than the speed as the light?

to the earth, the light would look like it was going .1c from the traveler right?

That would make it seem as though time were slowing down (from Earth's pov) for the traveler. when in fact its the opposite right? From Earth's pov, the traveler should look like he is speeding up, right?

sorry to de-rail the tangental arguments we have going :) but they are way over my head

 

[JesseM]

Do you realize that there is only one possible worldline (or multiple in certain curved spacetimes) between events that are lightlike separated?

Yes, but as I said in response to the earlier comment you edited, if it makes sense to talk about proper time on this worldline at all, the proper time would be zero. So this still doesn't help make sense of your comment that the time between light leaving Earth and arriving at Sirius B "is" 8.6 years.

 

[JesseM]

another quick question about this

If this were true, wouldn't that mean that the Earth observer sees the traveler going just .1 less than the speed as the light?

to the earth, the light would look like it was going .1c from the traveler right?

Yes, in the Earth frame the distance between the traveler and the photon is only increasing at a rate of 0.1 light-seconds per second.

That would make it seem as though time were slowing down (from Earth's pov) for the traveler. when in fact its the opposite right? From Earth's pov, the traveler should look like he is speeding up, right?

No, the Earth will measure the traveler's clocks to be slowed down rather than speeded up (and will also measure the traveler's rulers to be shrunk in the direction of motion). In relativity, any observer moving inertially (constant velocity) will measure clocks that are moving relative to themselves to be running slow.

 

[MeJennifer]

Sure, but the proper time along a null geodesic is always 0 (or maybe physicists don't even talk about 'proper time' for null geodesics, but in the limit as timelike geodesics get closer and closer to null geodesics the proper time should approach 0).

That is the proper time of the photon but alternatively we can use several affine parameters for a null geodesic.

 

[JesseM]

That is the proper time of the photon but alternatively we can use several affine parameters for a null geodesic.

But the affine parameters aren't really "time". Anyway, are you claiming that when you said the time "is" 8.6 years and the distance "is" 8.6 light-years, you were thinking in terms of affine parameters on the photon's worldline? If not, how is this relevant to what we were talking about before?

 

[MeJennifer]

Not true, one could for instance use "travel time" as an affine parameter.

 

[JesseM]

Not true, one could for instance use "travel time" as an affine parameter.

And couldn't you come up with different affine parameters for the same photon worldline based on travel time in different frames? There wouldn't be a unique choice of parameter forced on you by physics like there is with proper time on timelike worldlines.

 

[BWV]

In the recent book of essays entitled Year Million Catherine Asero speculates about superluminal speeds by using complex numbers in the relativity equations. Now she states that it is purely a mathematical exercise and has all sorts of weird implications such as an imaginary component to mass

 

[MeJennifer]

And couldn't you come up with different affine parameters for the same photon worldline based on travel time in different frames?

What you say does not make any sense to me. Affine parameters operate on spacetime curves while frames are 3D hypersurfaces of spacetime.

 

[JesseM]

What you say does not make any sense to me. Affine parameters operate on spacetime curves while frames are 3D hypersurfaces of spacetime.

You can parametrize a spacetime curve in terms of the time-coordinate assigned to each event on that curve by a particular frame, no? Of course I don't know if this parameter would qualify as an "affine" parameter since I'm not too familiar with GR. But what did you mean when you said "one could for instance use 'travel time' as an affine parameter"? Travel time according to what coordinate system or clock?

 

[matheinste]

Hello all

To clarify a point for myself I have paraphrased the original question in an attempt to remove the necessity of some of the additional and interesting material in the answers.

Given two separate points in space, if a massive object and a photon start from the first point at the same time as each other, is there any condition under which the massive object could arrive at the second point before the photon arrives. I am of course assuming that they can follow the same path. If the same path is not possible in GR then can we restrict the answer to SR in which I believe the same path can be followed.

Matheinste.

 

[MeJennifer]

Hello all

To clarify a point for myself I have paraphrased the original question in an attempt to remove the necessity of some of the additional and interesting material in the answers.

Given two separate points in space, if a massive object and a photon start from the first point at the same time as each other, is there any condition under which the massive object could arrive at the second point before the photon arrives. I am of course assuming that they can follow the same path. If the same path is not possible in GR then can we restrict the answer to SR in which I believe the same path can be followed.

Matheinste.

The answer is no, think of a common point and the light traveling in the form of an expanding sphere then it is guaranteed that the massive object is always inside this sphere. If for the sake of argument that massive object were to be found outside the sphere then the spacetime causal structure would be violated under the constraints of GR.

 

[JesseM]

Hello all

To clarify a point for myself I have paraphrased the original question in an attempt to remove the necessity of some of the additional and interesting material in the answers.

Given two separate points in space, if a massive object and a photon start from the first point at the same time as each other, is there any condition under which the massive object could arrive at the second point before the photon arrives. I am of course assuming that they can follow the same path. If the same path is not possible in GR then can we restrict the answer to SR in which I believe the same path can be followed.

Matheinste.

The question is a little ambiguous. In GR it is possible that if a particular photon departs from a massive object, that particular photon will take longer than the massive object to reach some other destination (think of photon orbits around a black hole, and imagine the massive object and the photon departing in opposite directions, so that the object has a short distance to reach some nearby buoy that we label as the destination, while the photon has to go all the way around the black hole before it hits the buoy). Still, in this situation it should always be possible to imagine a different photon which departs from the same point in spacetime but in a different direction, and which reaches the destination before the massive object.

 

[matheinste]

Thanks for your reply JesseM

I know nothing of GR or black holes and so all that is lost one me.

What about specifically in SR flat spacetime.

Matheinste.

 

[JesseM]

Thanks for your reply JesseM

I know nothing of GR or black holes and so all that is lost one me.

All you really need to know is that at a certain distance from the event horizon, a photon released at the right angle will orbit in a circle around the black hole. And if you have a massive object and a photon going in opposite directions, and there's a buoy nearby in the direction that the massive object is going, the massive object could reach it before the photon, since the photon is making a longer trip all around the black hole.

What about specifically in SR flat spacetime.

As long as the photon is moving unimpeded (no mirrors to reflect it, for example), the photon will always reach a given destination before the massive object.

 

[yuiop]

Hello all

To clarify a point for myself I have paraphrased the original question in an attempt to remove the necessity of some of the additional and interesting material in the answers.

Given two separate points in space, if a massive object and a photon start from the first point at the same time as each other, is there any condition under which the massive object could arrive at the second point before the photon arrives. I am of course assuming that they can follow the same path. If the same path is not possible in GR then can we restrict the answer to SR in which I believe the same path can be followed.

Matheinste.

In GR a massive particle can not always follow the path taken by a photon. In the example of a photon orbiting a black hole as mentioned by JesseM it is not possible for a massive particle to follow the photon orbit path. What can be fairly safely stated is that if you find the fastest possible path for a photon between two given points then the minimum time for a massive particle to move between those two points by any path will always be longer. Stated in the logical reverse the minimum time for a massive particle to move from one point to another will always be longer than the minimum time taken by a photon when the massive particle and the photon taken the shortest route available to them. This is always true in a vacuum but an important exception is that in some mediums, photons can be slowed down sufficiently that they actually move slower than some massive massive particles in the same medium.

 

[George Jones]

It is interesting to consider tunneling. Suppose a clock on the North Pole tunnels to the South Pole. What will be the proper time that will have elapsed?

Here's a https://www.physicsforums.com/showpost.php?p=1543402&postcount=8" that compares a clock on the surface at the equator to a clock at the centre of the Earth. The rotation of the clock at the equator with the Earth and the differing gravitational potentials are both taken into account.

I also have done the calculation for the scenario you propose, as well as for one complete cycle, i.e., the clock falls from the north pole to the south pole, stops, turns around, and falls back to the north pole. I have compared the elapsed time on the falling clock to the elapsed time on a clock that stays at the north pole, and to elapse time on a clock at the centre between meetings. This requires some somewhat subtle numerical integration. I would have to dig to find these results, and I don't think I've posted any of the results.

 

[matheinste]

Thanks kev and JesseM you have fully answered my question. The SR question i was sure of but some of the other answers in this thread seemed to complicate matters. The GR case is along the lines i thought it would be because of a photon and a massive particle not being able to follow the same path in the presence of gravity.

Matheinste.

 

[JesseM]

In GR a massive particle can not always follow the path taken by a photon. In the example of a photon orbiting a black hole as mentioned by JesseM it is not possible for a massive particle to follow the photon orbit path.

By "path", I assume you mean the spatial path rather than the path through spacetime? In this case, a massive object moving on a freefall geodesic may not be able to follow the photon orbit path, but a rocket that's not in freefall could in principle (just as a rocket can maintain a constant radius from a black hole at any distance above the horizon).

What can be fairly safely stated is that if you find the fastest possible path for a photon between two given points then the minimum time for a massive particle to move between those two points by any path will always be longer.

Yeah, that's what I was saying, it's always possible to find a photon that reaches the destination faster than the massive object, even though there may be other examples of photon paths that take longer to get to the destination (like taking the long way around a black hole vs. taking the shortest path).