The speed of light. What's the story, really?

[Drakkith]

But what if two objects move apart from the third observer at rest, and each experience the same amount of acceleration, and the same gravitational field strengths,

but one just happens to have gone further before turning around. So even though it experienced the exact same amount of acceleration, it was moving at .5 C relative to the third observer for a longer period of time.

When they all meet eventually, will their clocks all read the same?

No, their clocks will not read the same. If A moves away from C at 0.5c for 1 hour before returning, and B moves away from C at 0.5c for 2 hours before returning, and both accelerate the same amount, then B will have had less time pass than A.

 

[ghwellsjr]

No, their clocks will not read the same. If A moves away from C at 0.5c for 1 hour before returning, and B moves away from C at 0.5c for 2 hours before returning, and both accelerate the same amount, then B will have had less time pass than A.

And both A and B will have less time pass than C.

(Don't get confused--in this scenario, C is the stationary one. In jreelawg's scenario, A is the one that remains at rest.)

 

[pawprint]

I came to this thread late in it's evolution. Everything seems well sewn up except the subjective experience of the intrepid pilot.

His on-board clocks continue to show subjective elapsed time. He calculates his speed from his known rate of acceleration. After 3 years at at just under 1 g he calculates a velocity of c. Subjectively he is correct. He is one and a half a light years from his departure point.

Meanwhile observers at the pilot's departure point (they have his flight plan) calculate after (their) three years that his vessel is traveling at about .8 c. (That's from memory, I may be wrong as to the exact figure.) He is only 1.2 light years distant.

It looks like a free ride to the pilot. If he keeps accelerating at that rate he'll have traveled 4.5 light years after 6 subjective years, and after 9 he'll have AVERAGED 1 light year per subjective year. But things are not all beer and skittles for him. Unless he has extraordinary shielding he'll soon die from radiation sickness as photons originating from ahead have (subjectively) blue shifted radically. What he thought would be visible light is now hard xrays. Xrays have become gamma rays etc. etc..

So the universe does not impose speed limits on travellers unless they choose to catch up with friends. Our captain now reverses thrust but he'll have been away for 36 years subjective before he returns home. I leave it to the mathematicians to say how long 'home' thinks he's been away.

 

[lmoh]

C is a very special number. C is the speed of all massless particles in a vacuum, so anything with 0 mass travels at C.

Anything with mass does not and cannot travel at C. As anything with mass accelerates towards C it takes more and more energy to get closer to C, to actually reach the speed of light would take more energy than is in the entire universe.

General Relativity forbids anything reaching C as it is mathematically impossible for mass to go at that speed.

That is a simplified explanation but holds true.

I'm sorry if this makes no sense, but do massless particles have energy then? If so, would there be any difference in the speed of some massless particle that has more energy than another? I have a minimal understanding of SR but I just wanted to ask.

 

[ghwellsjr]

I came to this thread late in it's evolution. Everything seems well sewn up except the subjective experience of the intrepid pilot.

His on-board clocks continue to show subjective elapsed time. He calculates his speed from his known rate of acceleration. After 3 years at at just under 1 g he calculates a velocity of c. Subjectively he is correct. He is one and a half a light years from his departure point.

Meanwhile observers at the pilot's departure point (they have his flight plan) calculate after (their) three years that his vessel is traveling at about .8 c. (That's from memory, I may be wrong as to the exact figure.) He is only 1.2 light years distant.

It looks like a free ride to the pilot. If he keeps accelerating at that rate he'll have traveled 4.5 light years after 6 subjective years, and after 9 he'll have AVERAGED 1 light year per subjective year. But things are not all beer and skittles for him. Unless he has extraordinary shielding he'll soon die from radiation sickness as photons originating from ahead have (subjectively) blue shifted radically. What he thought would be visible light is now hard xrays. Xrays have become gamma rays etc. etc..

So the universe does not impose speed limits on travellers unless they choose to catch up with friends. Our captain now reverses thrust but he'll have been away for 36 years subjective before he returns home. I leave it to the mathematicians to say how long 'home' thinks he's been away.

Why do you keep saying subjective?

 

[pawprint]

I'm sorry if this makes no sense, but do massless particles have energy then? If so, would there be any difference in the speed of some massless particle that has more energy than another? I have a minimal understanding of SR but I just wanted to ask.

Although photons are massless they carry momentum acording to their SR energy. It is arguable whether a photon with zero momentum truly exists.

 

[Mark M]

I'm sorry if this makes no sense, but do massless particles have energy then? If so, would there be any difference in the speed of some massless particle that has more energy than another? I have a minimal understanding of SR but I just wanted to ask.

Yes, massless particles, known in relativity as luxons, do in fact have energy. In the case of photons, the massless particles that make up light, one can find it's energy by the equation

E = ħf

Where E is the energy of the photon, f is it's frequency, and ħ is Planck's constant.

 

[lmoh]

Although photons are massless they carry momentum acording to their SR energy. It is arguable whether a photon with zero momentum truly exists.

Ok, but is it possible to have photons (or other massless objects in general) with varying amounts of energy and would that difference in energy have any effect on its speed, especially in relation to other photons (or other massless objects) or will it always move at c?

 

[Mark M]

Ok, but is it possible to have photons (or other massless objects in general) with varying amounts of energy and would that difference in energy have any effect on its speed, especially in relation to other photons (or other massless objects) or will it always move at c?

Photons always move at c. Even if you are traveling at 500 million miles per hour, you will still measure them moving at the speed of light. All observers always agree on the speed of photons at c.

 

[ghwellsjr]

I'm sorry if this makes no sense, but do massless particles have energy then? If so, would there be any difference in the speed of some massless particle that has more energy than another? I have a minimal understanding of SR but I just wanted to ask.

All massless particles are defined to travel at c.

 

[pawprint]

Why do you keep saying subjective?

Because everything is relative. The pilot cannot truly say whether it it he accelerating forward, or the universe that is accelerating in the opposite direction. He subjectively believes the first viewpoint rather than the second. Another observer with a different frame of reference might subjectively believe the effect to be somewhere between the two viewpoints.

 

[alexg]

The pilot cannot truly say whether it it he accelerating forward, or the universe that is accelerating in the opposite direction

If the pilot is undergoing non-accelerated motion, then yes, from his frame of reference he can consider the universe as moving while he stays still.

But if he is undergoing acceleration, then he can definitely determine that he is udergoing acceleration, and not the universe.

 

[ghwellsjr]

Because everything is relative. The pilot cannot truly say whether it it he accelerating forward, or the universe that is accelerating in the opposite direction. He subjectively believes the first viewpoint rather than the second. Another observer with a different frame of reference might subjectively believe the effect to be somewhere between the two viewpoints.

Every Frame of Reference will agree on what you are calling the subjective time on the pilot's clock. It's called Proper Time. It might be subjective according to Lorentz Ether Theory but it's objective in Special Relativity.

 

[lmoh]

Photons always move at c. Even if you are traveling at 500 million miles per hour, you will still measure them moving at the speed of light. All observers always agree on the speed of photons at c.

Okay, I think I get the gist of it now. Thanks.

 

[pawprint]

Every Frame of Reference will agree on what you are calling the subjective time on the pilot's clock. It's called Proper Time. It might be subjective according to Lorentz Ether Theory but it's objective in Special Relativity.

Agreed. I was about to post this when I refreshed the screen and saw your post.

If all observers make observations of the cosmic microwave background radiation (CMB) then they can at least discover their velocity relative to the universe at large. An observer who sees the same temperature (or eqivalently frequency) in all directions can be said to be at rest relative to the universe. By this measure the Earth is 'travelling' at about 370 km/s relative to the universe.

 

[Drakkith]

Because everything is relative. The pilot cannot truly say whether it it he accelerating forward, or the universe that is accelerating in the opposite direction. He subjectively believes the first viewpoint rather than the second. Another observer with a different frame of reference might subjectively believe the effect to be somewhere between the two viewpoints.

I'm not sure this is correct. Acceleration is easily measurable. If a pilot in a ship is accelerating at 1g there's no way he could say the rest of the universe is accelerating instead of him. Once he is no longer accelerating then it becomes relative as to who is moving at what velocity.

Edit: Whoops, just saw that Alexg already said this above, sorry.

 

[pawprint]

I'm not sure this is correct. Acceleration is easily measurable. If a pilot in a ship is accelerating at 1g there's no way he could say the rest of the universe is accelerating instead of him. Once he is no longer accelerating then it becomes relative as to who is moving at what velocity.

There's no argument here. The post referred to was not intended to be 'the truth', but only to explain the use of the term 'subjectively' as requested.

 

[Drakkith]

There's no argument here. The post referred to was not intended to be 'the truth', but only to explain the use of the term 'subjectively' as requested.

I don't understand what you are trying to say. You can explain it "subjectively" but it still needs to be correct. Did I misunderstand you somehow?

 

[pawprint]

Why do you keep saying subjective?

I took this to be a question of semantics, not physics. I chose to express my answer in the way I did to answer that question.

 

[pawprint]

As I said in my above post, this is not true. The mass of an object does not change. If it did, then at a certain speed anything would be transformed into a black hole, which does not happen.

How do you know that Drakkith? If enough energy was pumped into a space vessel I think it might well become singularitised eventually. I think you've suggested a viable way to make lightweight black holes!

(Well- if spaghettification is an acceptable word why not singularitised?)

[Edit] I remember now- CERN is hoping it will happen. There was uninformed public outcry when they confirmed the rumour. Informed word was that any such BH formed at CERN would be so small and evaporate into Hawking Radiation so quickly as to pose no threat even to the detectors.

 

[jtbell]

If enough energy was pumped into a space vessel I think it might well become singularitised eventually.

We can produce a high relative velocity between you and the space vessel not only by accelerating the space vessel, but also by accelerating you. How can accelerating you turn the space vessel (which as far as its passengers know is just sitting there minding its own business) into a black hole?

 

[pawprint]

We can produce a high relative velocity between you and the space vessel not only by accelerating the space vessel, but also by accelerating you. How can accelerating you turn the space vessel (which as far as its passengers know is just sitting there minding its own business) into a black hole?

I took that position when I wanted to semantically enlighten ghwellsjr. I was criticised until I pointed out that that answer was about semantics, not physics.

Why do you keep saying subjective?

Extending your argument logically we find the Universe rotating at better than 0.9999997 c around Geneva. Not?

 

[ghwellsjr]

I took that position when I wanted to semantically enlighten ghwellsjr. I was criticised until I pointed out that that answer was about semantics, not physics.

I have not yet been enlightened. I pointed out to you that the time that the pilot experiences and sees on his clock is not merely in his mind (which is what subjective means), it is objective and it's called Proper Time. All reference frames agree on the time that the pilot reads on his clock. I have no idea why you refer to the pilot's experience as subjective so maybe you should try to enlighten me some more.

 

[pawprint]

I have not yet been enlightened. I pointed out to you that the time that the pilot experiences and sees on his clock is not merely in his mind (which is what subjective means), it is objective and it's called Proper Time. All reference frames agree on the time that the pilot reads on his clock. I have no idea why you refer to the pilot's experience as subjective so maybe you should try to enlighten me some more.

If you know this I don't understand your perplexity. I agree that any observer anywhere can, with the right equipment, agree on both Proper Time and, provided the observer also has data on another observer's relativity, both the second observer's Proper and Subjective Time, which are related but not identical.

The pilot is not experiencing Proper Time, nor are we. We can only infer it. I call that subjective.

 

[salvestrom]

We can produce a high relative velocity between you and the space vessel not only by accelerating the space vessel, but also by accelerating you. How can accelerating you turn the space vessel (which as far as its passengers know is just sitting there minding its own business) into a black hole?

In any situation with relative velocity there exists a reality that at some point, recent or distant, one of the two objects in question was accelerated to its velocity. That will always be the one that is actually moving, regardless of the symmetry and usefulness of treating that object as stationary in its own rest frame, or the ability of that observer to tell they are moving.

 

[pawprint]

In any situation with relative velocity there exists a reality that at some point, recent or distant, one of the two objects in question was accelerated to its velocity...

Yes. I'll be more careful in the future. I wouldn't want my mass (relativistic or otherwise) to exceed a safe limit :{)

 

[jreelawg]

In any situation with relative velocity there exists a reality that at some point, recent or distant, one of the two objects in question was accelerated to its velocity. That will always be the one that is actually moving, regardless of the symmetry and usefulness of treating that object as stationary in its own rest frame, or the ability of that observer to tell they are moving.

Are you certain this is how relativity works? I thought that velocity was meaningless without a frame of reference.

Lets say you accelerate, in the opposite direction of your "unknown absolute velocity" or whatever you are referring to. You should now have reduced your velocity, and your clock should be effected.

So you should be able to tell which direction and how fast your moving in reference to some absolute frame in space time.

I thought that relativity says that there is no fixed space time that you can move in reference to? Am I wrong?

 

[pawprint]

...I thought that relativity says that there is no fixed space time that you can move in reference to? Am I wrong?

You aren't wrong. Relativity implies that. However we now have a great deal of high precision astronomical data from which we can infer certain things.

At least 25 years ago the 'Great Attractor' was hypothesised. It was thought to be a massive gravity sink in the direction of the constelation Leo. It was deduced from doppler observations, and suggested that the Milky Way and other galaxies were being attracted in that direction. A rough figure of 350 - 400 km/s was given. (Article published in Scientific American 1985 from memory.)

Since then we've had at least two high resolution looks at the globe of CMB radiation. Doppler observations and calculations agree with the 'Great Attractor' hypothesis. The figure is now generally quoted as 480 km/s.

Proper Time, as mentioned frequently in this thread, can be inferred from such observations. The Earth, being in orbit, is an accelerating body. (It is forever falling towards the Sun). However the acceleration is constant and velocity changes over a year are insignificant compared to the apparent relative velocity of our galaxy and others.

So although there is no 'Ether' as was believed until the 1880s, we can now answer the 'absolute velocity' question that Michelson and Morely's famous experiment was designed for.

The Wikipedia articles give lots of detail.

 

[ghwellsjr]

If you know this I don't understand your perplexity. I agree that any observer anywhere can, with the right equipment, agree on both Proper Time and, provided the observer also has data on another observer's relativity, both the second observer's Proper and Subjective Time, which are related but not identical.

How can you agree with me regarding any other observers when I said nothing about any other observers? And I still have no idea what you mean by Subjective Time. Is this your own personal definition or can I look up the subject somewhere?

The pilot is not experiencing Proper Time, nor are we. We can only infer it. I call that subjective.

Are you saying that the pilot's clock does keep Proper Time but he has a different experience of time? Are you saying that the pilot's clock might say that it only took him two years to make a long trip but when he got back he really aged a lot longer, in fact the same amount as those he left behind?

 

[salvestrom]

Are you certain this is how relativity works? I thought that velocity was meaningless without a frame of reference.

Lets say you accelerate, in the opposite direction of your "unknown absolute velocity" or whatever you are referring to. You should now have reduced your velocity, and your clock should be effected.

So you should be able to tell which direction and how fast your moving in reference to some absolute frame in space time.

I thought that relativity says that there is no fixed space time that you can move in reference to? Am I wrong?

Um. Let me be clear. My post is an opinion. However, in SR and GR accelerating frames are not considred symmetric.

I never mentioned an unknown absolute velocity...

You are correct that there is no "preferred" reference frame.

Nonetheless, the reality that nothing in the universe is stationary (everything has some amount of velocity and is going somewhere with it), shouldn't, in the opinion of this weekend physicist, be confused with actually suggesting that a spaceship traveling at 200000km/s past a local planet is stationary and it is the planet that is moving (at 200000km/s). No force has, in the past, acted upon this planet to accelerate it to such a speed. The crew of the spaceship, however, hopefully aren't incredulous enough to dismiss their recollection of blasting off from their homeworld and firing their engines to get their vessel upto 2/3c.

The maths is largely indifferent to anyone's point of view. Lorentz Transformations go both ways, each observer says the other is moving more slowly through time, and so on. The so-called Twin Paradox restores some sense of reality back to the whole ordeal by revealling that only one of them has actually experienced a slower rate of time (but been blissfully ignorant of it).

This - all of it - doesn't interfere with the maths and therefore the theory's usefulness. Why people have such a problem with it is beyond me. It's really just a question of philosophy. Or sanity.