Can mass go faster than the speed of light?

[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).