Exploring the Paradox of Light's Mass & Speed

[Dave9600]

SR says that as an object reaches the speed of light its mass approaches infinity. How can light reach the speed of light without having an infinite mass?

 

[CompuChip]

Simple, it doesn't reach it :)
Light doesn't accelerate from a velocity below the speed of light. From the moment a photon gets created until the moment it is destroyed, it travels at the speed of light (in the medium it is in, of course).

Something which travels slower than c must have mass and cannot reach the speed of light. Something which travels at the speed of light must be massless and cannot reach speeds below c.

 

[Dave9600]

Simple, it doesn't reach it :)
Light doesn't accelerate from a velocity below the speed of light. From the moment a photon gets created until the moment it is destroyed, it travels at the speed of light (in the medium it is in, of course).

Something which travels slower than c must have mass and cannot reach the speed of light. Something which travels at the speed of light must be massless and cannot reach speeds below c.

Okay...

I guess I don't understand how something can be created / destroyed without acceleration / deceleration. Are you saying that photons are moving at C the instant they are created, and instantly decelerate to C=0 when destroyed?

 

[kavindra]

@CompuChip

Why are photons affected by gravity of black holes if they have no mass? F=GMm/r²... So, if photons are massless, then they shouldn't be affected but on the contrary, they are sucked in.

 

[Dave9600]

Why are photons affected by gravity of black holes if they have no mass? F=GMm/r²... So, if photons are massless, then they shouldn't be affected but on the contrary, they are sucked in.

No mass... nothing to suck in.

That's a good point.

 

[JesseM]

I guess I don't understand how something can be created / destroyed without acceleration / deceleration. Are you saying that photons are moving at C the instant they are created, and instantly decelerate to C=0 when destroyed?

Yes, they are moving at c from the moment they're created, and they don't decelerate when destroyed, they just get absorbed by some other particle.

 

[JesseM]

Why are photons affected by gravity of black holes if they have no mass? F=GMm/r²... So, if photons are massless, then they shouldn't be affected but on the contrary, they are sucked in.

Even in Newtonian gravity the rate at which an object accelerates in a gravitational field is totally independent of its own mass (remember F = ma, so ma=GMm/r^2 which implies a=GM/r^2). In general relativity gravity is not really a force but curvature of spacetime, and photons always follow geodesics which are the closest things to "straight lines" in curved spacetime, but which may look like curved paths from a purely spatial point of view.

 

[Dave9600]

Yes, they are moving at c from the moment they're created, and they don't decelerate when destroyed, they just get absorbed by some other particle.

Has this been measured, or is this an assumption based on SR?

 

[kavindra]

@Dave9600

c- the speed of all EM radiations is the speed of all particles having zero rest mass and yes, photon travels with c from the moment it is created to the moment it is annihilated. There is no acceleration or deceleration. One of the many nonsensical [to me] things of relativity.

 

[kavindra]

@Dave9600

No No No... I didn't mean that. I said if photons have zero mass, then they cann't be affected by gravitation. Actually photons have zero REST mass. But in motion, they too have mass.

 

[Dave9600]

No No No... I didn't mean that. I said if photons have zero mass, then they cann't be affected by gravitation. Actually photons have zero REST mass. But in motion, they too have mass.

Sorry. = )

How can photons have a rest mass if they are moving at the speed of light the instant they are created?

 

[fedaykin]

"I said if photons have zero mass, then they cann't be affected by gravitation."

This is not correct. Gravity is not viewed as a force, but as the curvature of space-time. Photons will follow geodesics (the shortest path on a curved space) in spacetime.
Since gravity is the warping of spacetime, it will affect the paths of photons.

Gravity affecting photons is not related to the photons' momentum.

"How can photons have a rest mass if they are moving at the speed of light the instant they are created? "

Photons have 0 rest mass. Rest mass is a misnomer, I think. I prefer the term invariant mass. If something moves at the speed of light, it has 0 invariant mass.

 

[Dave9600]

"I said if photons have zero mass, then they cann't be affected by gravitation."

This is not correct. Gravity is not viewed as a force, but as the curvature of space-time. Photons will follow geodesics (the shortest path on a curved space) in spacetime.
Since gravity is the warping of spacetime, it will affect the paths of photons.

The shortest path to what?

 

[HallsofIvy]

The shortest path between two nearby points- in the same sense that a straight line is, in Euclidean geometry, the shortest path between two points.

 

[Dave9600]

The shortest path between two nearby points- in the same sense that a straight line is, in Euclidean geometry, the shortest path between two points.

But what is the other point?

 

[kavindra]

I know very little about relativity. Please suggest some book.

 

[kavindra]

@HallsofIvy

Thanks. That was very informative.

please give ur suggestions about best science books here.
https://www.physicsforums.com/showthread.php?p=1847764#post1847764

 

[fedaykin]

For where the points are on the geodesic, think of it as trying to go the shortest distance on the curve as possible, your starting point is wherever you want on the photons path.

When you warp the space a photon is traveling in, you create a new shortest path for it.

 

[Dave9600]

For where the points are on the geodesic, think of it as trying to go the shortest distance on the curve as possible, your starting point is wherever you want on the photons path.

But the other point... what is the photon traveling towards and why?

 

[Fredrik]

Isn't about a third of all threads in the relativity forum about the mass of the photon? Another third seems to be about the twin paradox. Isn't it time that someone makes a couple of sticky threads about these two questions?

 

[Fredrik]

But the other point... what is the photon traveling towards and why?

That question is the reason I think it's better to use the other definition of a geodesic: It's the straightest path.

The definition of a geodesic as the shortest/longest path is appropriate when two points on the path are known. The definition as the straightest path is appropriate when one point and the tangent vector (i.e. the velocity) at that point is known.

 

[Dave9600]

That question is the reason I think it's better to use the other definition of a geodesic: It's the straightest path.

The definition of a geodesic as the shortest/longest path is appropriate when two points on the path are known. The definition as the straightest path is appropriate when one point and the tangent vector (i.e. the velocity) at that point is known.

But a straight path implies direction towards something. What is the photon traveling towards? Or, what is causing photons to move in a straight path?

 

[Dale]

what is causing photons to move in a straight path?

Conservation of momentum.

 

[epkid08]

But a straight path implies direction towards something.

A straight path implies direction towards something just as much as a curved path would.

What is the photon traveling towards?

I don't understand what you're asking here. The photon continues to travel until it runs into mass.

Or, what is causing photons to move in a straight path?

An analogy here could be an electric current, it always looks for the path of least resistance, be it a straight path or curved.

 

[JesseM]

For where the points are on the geodesic, think of it as trying to go the shortest distance on the curve as possible, your starting point is wherever you want on the photons path.

When you warp the space a photon is traveling in, you create a new shortest path for it.

One important thing to realize, though, is that a photon doesn't follow a geodesic path which is the shortest one in curved space, instead it follows a geodesic path in spacetime. For a slower-than-light-object the geodesic path actually maximizes the proper time (time as measured by a clock following that worldline), rather than minimizing the spatial distance. Not having studied GR I'm not actually sure how a geodesic in spacetime is defined for a photon (whose path always has zero proper time), but presumably it's still different than a geodesic in space would be.

 

[MeJennifer]

But a straight path implies direction towards something. What is the photon traveling towards? Or, what is causing photons to move in a straight path?

Saying that a photon travels on a geodesic means a geodesic of spacetime. Spacetime is four dimensional without any particular preferred 3D+T slicing, so you cannot simply translate this geodesic to particular spatial directions.

In 3D space, e.g. how an observer sees the world around him, the path light does not always appear to be a straight line. This is for instance the case when a light path comes near an object of mass. Gravity influences how we observe those paths. Similarly we can observer that a radar signal takes longer when the path between two objects is influenced by gravity. In extreme cases we never even get the return signal from the radar signal we sent.

 

[Fredrik]

what is causing photons to move in a straight path?

"Conservation of momentum" isn't a bad answer, but I prefer to think of it simply as one of the postulates of the theory. We assume that null geodesics can be used to represent the world lines of massless particles, and only experiments can tell us if the theory (which includes that assumption) agrees with reality.

If we take this to be a postulate, we can derive conservation of momentum. But we can probably drop this postulate and instead postulate something else that implies conservation of momentum, and then use that to derive that the world line of an object with constant momentum is a geodesic.

I'm not saying that DaleSpam's answer is wrong. It isn't. My point is just that something needs to be postulated, and we might as well take this to be the postulate.

 

[JesseM]

We assume that timelike geodesics can be used to represent the world lines of massless particles

Minor quibble: timelike geodesics represent the worldlines of massive particles, while lightlike geodesics represent the worldlines of photons and other massless particles. And I don't think this is actually a postulate of the theory, but is rather derived from the Einstein field equations.

 

[Fredrik]

Minor quibble: timelike geodesics represent the worldlines of massive particles, while lightlike geodesics represent the worldlines of photons.

Oops. Thanks for catching it so fast that I could edit it.

And I don't think this is actually a postulate of the theory, but is rather derived from the Einstein field equations.

Hm, I have to think about this, but right now I have to get some sleep. So for now I'll just say that even though Einstein's equation completely defines the mathematical model of spacetime that we use in GR, it doesn't completely define GR as a theory of physics. We also have to postulate what things in the model correspond to things in the real world. For example, we have to postulate that a clock measures the proper time (defined as the familiar integral) along the curve that represents its motion. The idea that the motion of a particle is described by a geodesic must also be postulated.

Of course we're already postulating something like this when we say that the stress-energy tensor represents matter. I believe that a full specification of what the stress-energy tensor represents must include the postulate I'm talking about, but I really have to get some sleep now, so I can't really think about all the details now.