Relativity

[MrFoolish]

Let's say I'm standing still in space (whatever that means). I observe a large clock with my telescope. The clock is moving at close to the speed of light. How do I see the clock evolving in the following two scenarios...?

1. It is moving away from me.

2. It is moving towards me.

I'm interested in the relative time of the moving clock compared to my own clock; and if it's appearing larger or smaller in the sky (as you'd expect with something being closer or further away).

A simple question, no doubt!

[ursaminortaur]

Let's say I'm standing still in space (whatever that means). I observe a large clock with my telescope. The clock is moving at close to the speed of light. How do I see the clock evolving in the following two scenarios...?

1. It is moving away from me.

2. It is moving towards me.

I'm interested in the relative time of the moving clock compared to my own clock; and if it's appearing larger or smaller in the sky (as you'd expect with something being closer or further away).

A simple question, no doubt!

The factor used in the lorentz transformation for calculating length contraction and time dilation is (1 - v^2/c^2)^-0.5. since it incorporates the square of the velocity the time dilation and length contraction are the same whether the clock was moving towards or away from you. It should also be noted that the length contraction only happens in the direction of motion and not in directions perpendicular to that motion. Hence a clock heading towards or away from you at close to the speed of light which is face on to you would appear to be ticking slower but its clock face would only appear to be smaller because of its distance rather than because of its speed.

One difference though which you would see between a clock coming towards you versus one moving away would be that the light by which you saw the clock face would be blue shifted if it was approaching and red shifted if it was moving away.

[MrFoolish]

Thanks. Apparently someone travelling on that moving clock also sees my clock as changing slower. They age at a slower rate. It's the twin paradox thing. But how do we really know who is moving? I thought all frames of reference were equally valid.

I've watched a few videos on this but I can't get my head round it. Maybe I should stop annoying myself and give up.

[MrFoolish]

Another thing confuses me. If the rest of the universe blinked out of existence, could we tell how fast we are travelling? On the one hand, I'd think not. But if we'd been previously accelerated to close to the speed of light, wouldn't it make a further increase in speed in that direction very difficult?

[Watis]

Glad I'm not the only one confused by this stuff.

What if the clock is travelling away from me at three quarters the speed of light - and I start to move in the opposite direction at three quarters the speed of light?

Surely, relative to me, the clock is now travelling at one and a half times the speed of light?

Yet we're told that's not possible.

Watis

[ursaminortaur]

Thanks. Apparently someone travelling on that moving clock also sees my clock as changing slower. They age at a slower rate. It's the twin paradox thing. But how do we really know who is moving? I thought all frames of reference were equally valid.

I've watched a few videos on this but I can't get my head round it. Maybe I should stop annoying myself and give up.

To explain it you need general relativity, which deals with accelerations, rather than special relativity. The normal case considered is of the two twins on Earth with synchronised clocks where one twin travels away at the speed of light and then returns. The situation with the two twins isn't equivalent because the traveling twin first accelerates up to near light speed and then slows down again before turning around and again accelerating upto near light speed until when approaching Earth slowing down again. I've never looked at the situation of an already existing clock approaching Earth at close to light speed and barrelling past Earth. However I think we can say two things about the situation without having to calculate anything with general relativity. Firstly, assuming we aren't just dealing with the twin paradox described above with just a tweaked ending where the clock barrels past, the clock has never been close enough to have been synchronised with a clock on Earth and secondly at some point since the big bang the atoms making up the clock were accelerated to a velocity close to that of light compared to Earth (since the clock is approaching Earth at such a high velocity).

[ursaminortaur]

Another thing confuses me. If the rest of the universe blinked out of existence, could we tell how fast we are travelling? On the one hand, I'd think not. But if we'd been previously accelerated to close to the speed of light, wouldn't it make a further increase in speed in that direction very difficult?

Since there are no observers in other inertial frames outside the ship you are travelling in (or indeed objects outside the ship which you can see are travelling at anything other than light speed and on which you could posit a theoretical observer existed ) the only valid inertial frame at any point in time is your own. And in your own inertial frame your velocity is zero relative to that frame. You could accelerate in which case you should* feel forces similar to gravity but after the acceleration you would be in another inertial frame but since you are in that frame you would still perceive your velocity to be zero. Since there are also no outside objects, ie no distant stars, you also can't even calculate a theoretical speed by measuring the distance to that object and how long it takes you to reach it.

* or possibly not, as if Mach's principle is correct then there would be no acceleration in an empty universe.

[MrFoolish]

Another thing confuses me. If the rest of the universe blinked out of existence, could we tell how fast we are travelling? On the one hand, I'd think not. But if we'd been previously accelerated to close to the speed of light, wouldn't it make a further increase in speed in that direction very difficult?

Since there are no observers in other inertial frames outside the ship you are travelling in (or indeed objects outside the ship which you can see are travelling at anything other than light speed and on which you could posit a theoretical observer existed ) the only valid inertial frame at any point in time is your own. And in your own inertial frame your velocity is zero relative to that frame. You could accelerate in which case you should* feel forces similar to gravity but after the acceleration you would be in another inertial frame but since you are in that frame you would still perceive your velocity to be zero. Since there are also no outside objects, ie no distant stars, you also can't even calculate a theoretical speed by measuring the distance to that object and how long it takes you to reach it.

* or possibly not, as if Mach's principle is correct then there would be no acceleration in an empty universe.

Thanks for your detailed answers.

But what if I suddenly notice an object that I hadn't spotted before? Given all my previous accelerations, could I now be zooming past it at a speed greater than c?

[ursaminortaur]

Glad I'm not the only one confused by this stuff.

What if the clock is travelling away from me at three quarters the speed of light - and I start to move in the opposite direction at three quarters the speed of light?

Surely, relative to me, the clock is now travelling at one and a half times the speed of light?

Yet we're told that's not possible.

Watis

In relativity speeds don't add in that nice simple way.

See

https://galileo.phys.virginia.edu/classes/252/adding_vels.html

instead the addition of two speeds u and v is given by

( u + v ) / ( 1 + uv/c^2 )

If u = 0.75c and v = 0.75c then adding them gives. 1.5c / 1.5625 = 0.96c

[ursaminortaur]

Since there are no observers in other inertial frames outside the ship you are travelling in (or indeed objects outside the ship which you can see are travelling at anything other than light speed and on which you could posit a theoretical observer existed ) the only valid inertial frame at any point in time is your own. And in your own inertial frame your velocity is zero relative to that frame. You could accelerate in which case you should* feel forces similar to gravity but after the acceleration you would be in another inertial frame but since you are in that frame you would still perceive your velocity to be zero. Since there are also no outside objects, ie no distant stars, you also can't even calculate a theoretical speed by measuring the distance to that object and how long it takes you to reach it.

* or possibly not, as if Mach's principle is correct then there would be no acceleration in an empty universe.

Thanks for your detailed answers.

But what if I suddenly notice an object that I hadn't spotted before? Given all my previous accelerations, could I now be zooming past it at a speed greater than c?

If it had always existed but you hadn't noticed it then the universe obeying relativity would always have existed and hence your accelerations would not have sped you up faster than light relative to that object.

[stevensfo]

Apart from a slight headache this discussion reminds me of a question somebody asked our teacher, many, many years ago.

If you throw a rubber ball against a mirror and it bounces back along the same trajectory, then for a split second when it hits the mirror, its velocity must be zero.

If you do the same thing with a laser, is its velocity also zero when it hits the mirror?

Can't remember what the teacher said. Probably, "Shut up and show me your homework!"


Steve

[mc2fool]

If you throw a rubber ball against a mirror and it bounces back along the same trajectory, then for a split second when it hits the mirror, its velocity must be zero.

If you do the same thing with a laser, is its velocity also zero when it hits the mirror?

When a rubber ball bounces off a mirror and returns along the same trajectory, its velocity does briefly reach zero at the point of impact. This is because, at the exact moment of collision, the ball comes to a momentary stop before reversing direction due to the change in momentum.

In the case of a laser beam, it's important to note that light does not behave in the same way as a macroscopic object like a rubber ball. Light, including laser light, consists of photons, which are massless particles that always travel at the speed of light in a vacuum (approximately 299,792,458 meters per second or about 186,282 miles per second).

When a laser beam hits a mirror, the individual photons making up the beam do not "stop" like a physical object would. Instead, they are reflected off the mirror's surface following the law of reflection, where the angle of incidence equals the angle of reflection. So, the photons change direction but continue to travel at the speed of light. Therefore, from a photon's perspective, its velocity remains constant at the speed of light both before and after hitting the mirror.

In summary, while the velocity of a macroscopic object like a rubber ball briefly reaches zero upon collision with a mirror, the velocity of light, including that of a laser beam, remains constant at the speed of light during reflection.

How is that explained by the wave theory of light?

The behavior of light when it reflects off a mirror can be explained by the wave theory of light, specifically the principles of wave reflection.

According to the wave theory of light:

1. Wavefronts: Light propagates as an electromagnetic wave, and it can be described in terms of wavefronts. A wavefront is an imaginary surface that connects all points of a wave that are in phase, meaning they have the same phase of oscillation.

2. Law of Reflection: When a wavefront encounters a reflecting surface, such as a mirror, the wavefront obeys the law of reflection. This law states that the angle of incidence (the angle between the incident ray and the normal line perpendicular to the mirror's surface) is equal to the angle of reflection (the angle between the reflected ray and the same normal line).

3. Phase Continuity: In the wave theory, it's important to understand that the wavefronts continue to propagate continuously. When a wavefront reaches the mirror's surface, it does not abruptly stop or change phase; instead, it continues to propagate as if it entered a new medium with the same frequency.

4. Superposition Principle: The principle of superposition applies to waves. When multiple wavefronts overlap, their effects combine. In the case of reflection, the incident wavefront combines with the reflected wavefront.

So, when a laser beam (a coherent source of light) hits a mirror, the individual wavefronts in the beam do not stop. Instead, they continue to propagate, maintaining their phase and frequency. However, they change direction according to the law of reflection, resulting in the reflected beam.

In summary, the wave theory of light explains the reflection of light off a mirror by treating light as an electromagnetic wave. The incident wavefronts continue to propagate and maintain their characteristics, including frequency and phase, as they change direction upon reflection, following the law of reflection. This behavior allows light to be reflected off a mirror while maintaining its wave-like properties.

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[hiriskpaul]

Apart from a slight headache this discussion reminds me of a question somebody asked our teacher, many, many years ago.

If you throw a rubber ball against a mirror and it bounces back along the same trajectory, then for a split second when it hits the mirror, its velocity must be zero.

If you do the same thing with a laser, is its velocity also zero when it hits the mirror?

Can't remember what the teacher said. Probably, "Shut up and show me your homework!"


Steve

Interesting question, but one which falls into the trap of treating the interaction between light an electrons in macroscopic terms. A ball has a macroscopic size and distorts as it comes into contact with another object, comes to a halt, then the change in direction is brought about by the ball resuming its shape. In contrast photons and electrons are fundamental particles which have no size. Or at least the best model available (the Standard Model) that describes fundamental particles treats them as point objects, with no size. As such, fundamental particles cannot be distorted like a ball, so reflection happens in a different way to that of macroscopic objects.

The part of the Standard Model which describes the interaction between photons and electrons is quantum electrodynamics (QED). QED can model reflection of photons extremely accurately. It is a long time since I studied particle physics, but as far as I am aware QED is still unassailable, with no measurement contradicting the theory or even coming close.

It would need someone with far more expertise than me to answer the question, but from what I can remember QED tells you nothing about whether a photon comes to a halt at some point during reflection. Possibly a deeper theory, such as string theory might lead to an answer.

Relativity comes into play as well (QED incorporates relativity) in that it muddies the field with frames of reference. Because photons have no mass, they travel at the speed of light and so do not experience time. In which case, another philosophical question is how do photons experience reflection if they do not experience time?

Perhaps the most honest answer then is "Don't know and don't even know whether the question has an answer, or meaning in terms of the real knowledge we have about light and fundamental particles".

[stevensfo]

Apart from a slight headache this discussion reminds me of a question somebody asked our teacher, many, many years ago.

If you throw a rubber ball against a mirror and it bounces back along the same trajectory, then for a split second when it hits the mirror, its velocity must be zero.

If you do the same thing with a laser, is its velocity also zero when it hits the mirror?

Can't remember what the teacher said. Probably, "Shut up and show me your homework!"


Steve

Interesting question, but one which falls into the trap of treating the interaction between light an electrons in macroscopic terms. A ball has a macroscopic size and distorts as it comes into contact with another object, comes to a halt, then the change in direction is brought about by the ball resuming its shape. In contrast photons and electrons are fundamental particles which have no size. Or at least the best model available (the Standard Model) that describes fundamental particles treats them as point objects, with no size. As such, fundamental particles cannot be distorted like a ball, so reflection happens in a different way to that of macroscopic objects.

The part of the Standard Model which describes the interaction between photons and electrons is quantum electrodynamics (QED). QED can model reflection of photons extremely accurately. It is a long time since I studied particle physics, but as far as I am aware QED is still unassailable, with no measurement contradicting the theory or even coming close.

It would need someone with far more expertise than me to answer the question, but from what I can remember QED tells you nothing about whether a photon comes to a halt at some point during reflection. Possibly a deeper theory, such as string theory might lead to an answer.

Relativity comes into play as well (QED incorporates relativity) in that it muddies the field with frames of reference. Because photons have no mass, they travel at the speed of light and so do not experience time. In which case, another philosophical question is how do photons experience reflection if they do not experience time?

Perhaps the most honest answer then is "Don't know and don't even know whether the question has an answer, or meaning in terms of the real knowledge we have about light and fundamental particles".

Relativity comes into play as well (QED incorporates relativity) in that it muddies the field with frames of reference. Because photons have no mass, they travel at the speed of light and so do not experience time.

Light not having mass has always puzzled me. So how do light sails work? i.e. the idea that probes can be propelled through space by light from the star. I know it's something to do with momentum, but how can you have momentum without mass? How is light bent by high gravity if it hasn't got mass?

Time for the 2nd aspirin!

Steve

[tjh290633]

Relativity comes into play as well (QED incorporates relativity) in that it muddies the field with frames of reference. Because photons have no mass, they travel at the speed of light and so do not experience time.

Light not having mass has always puzzled me. So how do light sails work? i.e. the idea that probes can be propelled through space by light from the star. I know it's something to do with momentum, but how can you have momentum without mass? How is light bent by high gravity if it hasn't got mass?

Time for the 2nd aspirin!

Steve

Don't forget that the speed of light varies with the medium. That's how you get the effects of prisms and lenses. Solar wind is caused by the fact that space is not a void.

TJH

[ursaminortaur]

Interesting question, but one which falls into the trap of treating the interaction between light an electrons in macroscopic terms. A ball has a macroscopic size and distorts as it comes into contact with another object, comes to a halt, then the change in direction is brought about by the ball resuming its shape. In contrast photons and electrons are fundamental particles which have no size. Or at least the best model available (the Standard Model) that describes fundamental particles treats them as point objects, with no size. As such, fundamental particles cannot be distorted like a ball, so reflection happens in a different way to that of macroscopic objects.

The part of the Standard Model which describes the interaction between photons and electrons is quantum electrodynamics (QED). QED can model reflection of photons extremely accurately. It is a long time since I studied particle physics, but as far as I am aware QED is still unassailable, with no measurement contradicting the theory or even coming close.

It would need someone with far more expertise than me to answer the question, but from what I can remember QED tells you nothing about whether a photon comes to a halt at some point during reflection. Possibly a deeper theory, such as string theory might lead to an answer.

Relativity comes into play as well (QED incorporates relativity) in that it muddies the field with frames of reference. Because photons have no mass, they travel at the speed of light and so do not experience time. In which case, another philosophical question is how do photons experience reflection if they do not experience time?

Perhaps the most honest answer then is "Don't know and don't even know whether the question has an answer, or meaning in terms of the real knowledge we have about light and fundamental particles".

Relativity comes into play as well (QED incorporates relativity) in that it muddies the field with frames of reference. Because photons have no mass, they travel at the speed of light and so do not experience time.

Light not having mass has always puzzled me. So how do light sails work? i.e. the idea that probes can be propelled through space by light from the star. I know it's something to do with momentum, but how can you have momentum without mass? How is light bent by high gravity if it hasn't got mass?

Time for the 2nd aspirin!

Steve

Photons have no mass but they do have momentum and energy.

https://www.wtamu.edu/~cbaird/sq/2014/04/01/light-has-no-mass-so-it-also-has-no-energy-according-to-einstein-but-how-can-sunlight-warm-the-earth-without-energy/

Light indeed carries energy and accomplishes this without having any mass. The Einstein equation that you are probably referring to is E = mc^2. This equation is actually a special case of the more general equation:

E^2 = p^2c^2 + m^2c^4

In the above equation, E is the total energy of the particle, p is the momentum of the particle (which is related to its motion), c is the speed of light, and m is the mass of the particle. This equation can be derived from the relativistic definitions of the energy and momentum of a particle. The above equation tells us that the total energy of a particle is a combination of its mass energy and its momentum energy (which is not necessarily related to its mass). When a particle is at rest (p = 0), this general equation reduces down to the familiar E = mc^2. In contrast, for a particle with no mass (m = 0), the general equation reduces down to E = pc. Since photons (particles of light) have no mass, they must obey E = pc and therefore get all of their energy from their momentum.
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How can an object have momentum without mass? It can do this if it is a wave. A wave transports momentum via its waving motion and not by physically transporting an object with mass. "Momentum" is the directional property of an object in motion that describes its ability to influence another object upon impact. An object with high momentum (such as a truck) can greatly influence the object it collides with (such as a barrel). If a giant water wave collides with a barrel, it can also influence the barrel to move. The water wave therefore carries momentum even though it has no mass. The water itself has mass, but the wave has no mass. A water wave is not a packet of water traveling along. In fact, the water that the wave is traveling through stays more or less in one place. Rather, the wave is a rippling domino-effect of motion. As another example, consider a long jump rope held taut at both ends by two girls. If one girl shakes her end of the rope violently enough to send a wave down the rope to the other girl, the wave can jerk the other girl. The rope has not transported any mass, but it still carries momentum through its waving motion. In this way, waves can have no mass but still carry momentum. In addition to being a particle, light is also a wave. This allows it to carry momentum, and therefore energy, without having mass.

https://www.astronomy.com/science/ask-astro-how-can-a-photon-be-massless/

Einstein’s famous mass-energy equivalence equation, or E = mc^2, is actually a special case of a slightly longer formula known as the energy-momentum relation, which is written out as E^2 = p^2c^2 + m^2c^4.

This equation relates energy (E) to rest mass (m), the speed of light (c), and momentum (p), which is the key to how photons can carry energy but have no mass. When a particle is at rest, it has no momentum and the equation simplifies to the more familiar E = mc^2. But if a particle has no mass, the equation becomes E = pc.
But wait, you might be asking, how can a particle have momentum without mass? That’s where light’s duality as both a wave and a particle comes into play. Unlike a particle, whose momentum is related to its mass, a wave’s momentum comes solely from its motion, meaning that it can carry momentum even without mass.

[ursaminortaur]

Relativity comes into play as well (QED incorporates relativity) in that it muddies the field with frames of reference. Because photons have no mass, they travel at the speed of light and so do not experience time.

Light not having mass has always puzzled me. So how do light sails work? i.e. the idea that probes can be propelled through space by light from the star. I know it's something to do with momentum, but how can you have momentum without mass? How is light bent by high gravity if it hasn't got mass?

Time for the 2nd aspirin!

Steve

Don't forget that the speed of light varies with the medium. That's how you get the effects of prisms and lenses. Solar wind is caused by the fact that space is not a void.

TJH

Here are three explanations depending on how you view light and its interaction with the material it is passing through

https://www.space.com/how-does-light-slow-down

[hiriskpaul]

Light not having mass has always puzzled me. So how do light sails work? i.e. the idea that probes can be propelled through space by light from the star. I know it's something to do with momentum, but how can you have momentum without mass? How is light bent by high gravity if it hasn't got mass?

In classical Newtonian physics, Momentum = mass * velocity. In quantum physics, momentum is a more fundamental concept than that. Massless particles have momentum and momentum is conserved. So if an electron emits a photon, the electron must recoil.

Although in Newtonian physics gravity only affects particles with mass, you can model light as having a vanishingly small mass and what the path might be as the mass goes to zero. If you do that you find that starlight visible in a solar eclipse might be bent as it passes the sun according to Newtonian gravity. General relativity predicts bending as well and by a pure fluke general relativity predicts twice* the amount of bending, so it was not so much the bending of light around the sun that Eddington observed which provided support for Einstein's theory, but the fact that light was bent more than could be accounted for under Newton.

General Relativity explains gravity in a completely different way to Newton. Under Newton, masses attract and the equation is really simple. Under General Relativity, spacetime is distorted by matter. Light travels in straight lines, but spacetime itself is curved. The mathematics of tensors is used to make accurate predictions with General Relativity and it very quickly gets hard. I covered it in a final year course at university and we barely scratched the surface. Several hours of maths and then say one lecture on the anomolous orbit of Mercury. Have not used tensors since and remember very little of it.

The maths used with fundamental particle physics is not only fiendishly difficult, but also conceptually hard. That is why it is really difficult to explain things like the interaction of particles, partial reflection, etc. Popular science ends up discussing models which are approximations (such as waves) to the solid theory as the solid theory is so damned hard. These approximate models then fail to explain certain observations, eg the wave model cannot explain the photoelectric effect, so we introduce wave-particle duality, etc.

* I think it is twice, but it is a few decades since I attended the lecture which covered this, and it might be half!

[ursaminortaur]

Light not having mass has always puzzled me. So how do light sails work? i.e. the idea that probes can be propelled through space by light from the star. I know it's something to do with momentum, but how can you have momentum without mass? How is light bent by high gravity if it hasn't got mass?

In classical Newtonian physics, Momentum = mass * velocity. In quantum physics, momentum is a more fundamental concept than that. Massless particles have momentum and momentum is conserved. So if an electron emits a photon, the electron must recoil.

Although in Newtonian physics gravity only affects particles with mass, you can model light as having a vanishingly small mass and what the path might be as the mass goes to zero. If you do that you find that starlight visible in a solar eclipse might be bent as it passes the sun according to Newtonian gravity. General relativity predicts bending as well and by a pure fluke general relativity predicts twice* the amount of bending, so it was not so much the bending of light around the sun that Eddington observed which provided support for Einstein's theory, but the fact that light was bent more than could be accounted for under Newton.

General Relativity explains gravity in a completely different way to Newton. Under Newton, masses attract and the equation is really simple. Under General Relativity, spacetime is distorted by matter. Light travels in straight lines, but spacetime itself is curved. The mathematics of tensors is used to make accurate predictions with General Relativity and it very quickly gets hard. I covered it in a final year course at university and we barely scratched the surface. Several hours of maths and then say one lecture on the anomolous orbit of Mercury. Have not used tensors since and remember very little of it.

The maths used with fundamental particle physics is not only fiendishly difficult, but also conceptually hard. That is why it is really difficult to explain things like the interaction of particles, partial reflection, etc. Popular science ends up discussing models which are approximations (such as waves) to the solid theory as the solid theory is so damned hard. These approximate models then fail to explain certain observations, eg the wave model cannot explain the photoelectric effect, so we introduce wave-particle duality, etc.

* I think it is twice, but it is a few decades since I attended the lecture which covered this, and it might be half!

https://imagine.gsfc.nasa.gov/educators/programs/cosmictimes/online_edition/1919/gravity.html

Dr. Einstein's theory, which is highly mathematical, predicts that the curvature of space caused by the Sun's mass should bend starlight twice as much as Newton's principles predict it should.

[hiriskpaul]

https://imagine.gsfc.nasa.gov/educators/programs/cosmictimes/online_edition/1919/gravity.html

Dr. Einstein's theory, which is highly mathematical, predicts that the curvature of space caused by the Sun's mass should bend starlight twice as much as Newton's principles predict it should.

Thanks, great link. Pleased to know my memory isn't failing me.